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  <metadata>
    <dcterms:identifier>ECHO:MXTKM8TF.xml</dcterms:identifier>
    <dcterms:creator identifier="GND:118880632">Clavius, Christoph</dcterms:creator>
    <dcterms:title xml:lang="it">Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur</dcterms:title>
    <dcterms:date xsi:type="dcterms:W3CDTF">1581</dcterms:date>
    <dcterms:language xsi:type="dcterms:ISO639-3">ita</dcterms:language>
    <dcterms:rights>CC-BY-SA</dcterms:rights>
    <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
    <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
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<div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/>
<pb file="0002" n="2"/>
<pb file="0003" n="3"/>
<pb file="0004" n="4"/>
<pb file="0005" n="5"/>
</div>
<div xml:id="echoid-div2" type="section" level="1" n="2">
<head xml:id="echoid-head1" xml:space="preserve">GNOMONICES</head>
<head xml:id="echoid-head2" xml:space="preserve">LIBRI OCTO,</head>
<head xml:id="echoid-head3" xml:space="preserve">IN QVIB VS</head>
<p>
  <s xml:id="echoid-s1" xml:space="preserve">Non ſolum horologiorum ſolariu, <lb/>ſed aliarum quo{q̀ue} rerum, <lb/>quæ ex gnomonis umbra <lb/>cognoſci poſsunt, descriptiones <lb/>Geometricè demonſtr antur.</s>
  <s xml:id="echoid-s2" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div3" type="section" level="1" n="3">
<head xml:id="echoid-head4" xml:space="preserve">AV CTORE <lb/>CHRIST OPHORO <lb/>CLAVIO BAMBERGENSI <lb/><emph style="sc">Societatis</emph> <emph style="sc">Ie sv</emph></head>
<p>
  <s xml:id="echoid-s3" xml:space="preserve">Maiovum permißu.</s>
  <s xml:id="echoid-s4" xml:space="preserve"/>
</p>
<pb file="0006" n="6"/>
<pb file="0007" n="7"/>
</div>
<div xml:id="echoid-div4" type="section" level="1" n="4">
<head xml:id="echoid-head5" xml:space="preserve">STEPHANO POLONIAE <lb/>REGI POTENTISSIMO, <lb/>MAGNOQ. LITHVANIAE DVCI, ETC.</head>
<head xml:id="echoid-head6" style="it" xml:space="preserve">CHRISTOPHORVS CLAVIVS SOCIET AT IS IESV <lb/>PERPETVAM FELICITATEM.</head>
  <figure>
    <image file="0007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0007-01"/>
  </figure>
<p>
  <s xml:id="echoid-s5" xml:space="preserve">QVOD meum hoc opus de Gnomonica tibi <lb/>potiſſimum dicare conſtituerim, Rex poten-<lb/>tiſſime, non dubito, quin aliqui minus pro-<lb/>bent. </s>
  <s xml:id="echoid-s6" xml:space="preserve">Neque enim, inquient, Regem publi-<lb/>cis rebus gerendis intentum, &amp; </s>
  <s xml:id="echoid-s7" xml:space="preserve">multo minus <lb/>hoc tempore grauiſſimi belli curis occupa-<lb/>tum hæc priuatorum hominum ſtudia dece-<lb/>re. </s>
  <s xml:id="echoid-s8" xml:space="preserve">Ego vero longealio, ac meliore, ni fal-<lb/>lor, iudicio, quàm illi, neque vlli magis hoc <lb/>munus, quàm Regi, neque Regum vlli potius, quàm tibi, neque vllo <lb/>commodius, quàm hoc tempore, conuenire ſtartui. </s>
  <s xml:id="echoid-s9" xml:space="preserve">Nam Regem qui-<lb/>dem, quemadmodum vtraque negocia, pacis ac belli, procurare, ita <lb/>quæ vtroque tempore vigent, amplecti ſtudia, ac promouere par eſt. <lb/></s>
  <s xml:id="echoid-s10" xml:space="preserve">Tibi vero, qui vtraque gloria ita flores, vt ad militarem peritiam, qua <lb/>excellis, hanc etiam laudem adiunxeris, quòd hominibus literatis ita <lb/>faues, vt foueas mirifice ſtudia ipſa literarum, ita diſciplinas omnes co-<lb/>lis, non modo vt ingenium, ſed ipſas etiam excolas, æquum eſt, vt <lb/>quemadmodum deuictarum vrbium atque arcium claues tuæ virtutis <lb/>argumenta deferuntur, ſic eriam deuinctorum hominum lucubratio-<lb/>nes ac labores offerantur, monumenta nonnulla doctrinæ tuæ. </s>
  <s xml:id="echoid-s11" xml:space="preserve">De-<lb/>nique hoc belli tempore nihilà tuis negotijs abhorrere videtur, ſi ha-<lb/>beas, vnde tibi detur occaſio recordandi, quanta ſit habenda ratio in <lb/>bello temporum &amp; </s>
  <s xml:id="echoid-s12" xml:space="preserve">horarum, quanti referat ſuo quidque tempore ac <lb/>loco exequi, ſuis quæq́; </s>
  <s xml:id="echoid-s13" xml:space="preserve">horis peragere: </s>
  <s xml:id="echoid-s14" xml:space="preserve">ſitq́; </s>
  <s xml:id="echoid-s15" xml:space="preserve">tibi frequenter ob oculos, <lb/>motum illum Solis, quo tempora metimur, atque diſtinguimus, nun-<lb/>quam intermitti, perpetuam eſſe temporis fugam, quod ſemel elapſum <lb/>eſt, redire nunquam, minimo momento magnas plerunque rerum in-<lb/>clinationes fieri. </s>
  <s xml:id="echoid-s16" xml:space="preserve">Ex quorum obſeruatione manauit, opinor, diuinum <lb/>illud Alexandri magni conſilium, μηδὲν ἀναβαλλόμενος, quo vno id con-<lb/>ſecutus eſſe dicitur diligentiſſimus Imperator, prope vt plures victorias <lb/>reportarit, quàm pugnas inierit, plura bella confecerit, quàm prælia <lb/>commiſerit, plures vrbes ceperit, quàm tentarit, plures hoſtes fuderit, <lb/>quàm nouerit, plura loca occuparit, quàm obierit. </s>
  <s xml:id="echoid-s17" xml:space="preserve">Quo te vti conſilio <lb/>&amp; </s>
  <s xml:id="echoid-s18" xml:space="preserve">felicitas haud multò minor, &amp; </s>
  <s xml:id="echoid-s19" xml:space="preserve">virtus certe maior, quàm illius, tua
<pb file="0008" n="8"/>
teſtatur. </s>
  <s xml:id="echoid-s20" xml:space="preserve">Sed præter has communes cauſas ſuntaliæ Societatis noſtræ <lb/>propriæ, &amp; </s>
  <s xml:id="echoid-s21" xml:space="preserve">ſane graues, quas hocloco commemorari neque facultatis <lb/>noſtræ eſt, neque verò modeſtiæ tuæ. </s>
  <s xml:id="echoid-s22" xml:space="preserve">Vnum tamen hoc dicam, ita no-<lb/>ſtræ Societatis homines à te cum ſemper antea, tum maxime poſt ſuſce-<lb/>ptam nobiliſſimi regni adminiſtrationem acceptos eſſe, vt merito du-<lb/>bitemus, vtrum pietatem magis tuam, an ſingularem munificentiam <lb/>admirari debeamus. </s>
  <s xml:id="echoid-s23" xml:space="preserve">Qui tuus erga nos animus eò nobis eſt charior, <lb/>quò clarius apparet, eum ab ardenti quodam Catholicæ religionis tuen <lb/>dæ, ac propagandæ ſtudio proficiſci. </s>
  <s xml:id="echoid-s24" xml:space="preserve">Accipe igitur noſtrum hoc ſiue <lb/>grati animi monumentum, ſiue fidei pignus, ſiue obſeruantiæ teſtimo-<lb/>nium. </s>
  <s xml:id="echoid-s25" xml:space="preserve">In quo, ſi quando tibi oblectare animum libuerit, pro tuo prę-<lb/>ſtanti ingenio, ac religioſa prudentia non obſcurum agnoſces recte ad-<lb/>miniſtrandi mortalis regni documentum. </s>
  <s xml:id="echoid-s26" xml:space="preserve">Vt enim librata illa gnomo-<lb/>nis conſtitutio, varij atque artificioſi linearum ductus, plurimi ſane la-<lb/>boris atque operę, prorſus inutiles redduntur, ſi nullum ipſis à Sole lu-<lb/>men affulgeat: </s>
  <s xml:id="echoid-s27" xml:space="preserve">ita etiam humana magnis ſæpelaboribus ſuſcepta conſi-<lb/>lia irrita ſunt, niſi cęleſtis, veræq́; </s>
  <s xml:id="echoid-s28" xml:space="preserve">ſapientię radijs illuſtrentur, &amp; </s>
  <s xml:id="echoid-s29" xml:space="preserve">ope <lb/>adiuta diuina ptomoueantur. </s>
  <s xml:id="echoid-s30" xml:space="preserve">Hoc ſi feceris, confido fore, vt neque <lb/>tu munuſculum hoc, etſi pro meritorum tuorum magnitudine per-<lb/>exiguum, pro noſtra tamen tenuitate non minimum, omnino con-<lb/>temnas: </s>
  <s xml:id="echoid-s31" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32" xml:space="preserve">ego ad alia eiuſdem generis, quæ ſatis multa inchoata mihi <lb/>ſunt, elaboranda fiam promptior: </s>
  <s xml:id="echoid-s33" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34" xml:space="preserve">intelligant cæteri, quanta in te <lb/>fuit bene de nobis merendi facultas, ſi non tantam, haud multò certe <lb/>minorem in nobis eſſe grati animi declarandi voluntatem: </s>
  <s xml:id="echoid-s35" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36" xml:space="preserve">quod ma-<lb/>ximè velim, tua cum in Societatem noſtram liberalitas, tum in Catho-<lb/>licam religionem fides, atque conſtantia, quæ ipſa per ſe notiſſima, &amp; </s>
  <s xml:id="echoid-s37" xml:space="preserve"><lb/>illuſtriſſima eſt, opera etiam aliqua noſtra teſtata maneat. </s>
  <s xml:id="echoid-s38" xml:space="preserve">Vale. <lb/></s>
  <s xml:id="echoid-s39" xml:space="preserve">Romę, Kalendis Aprilis. </s>
  <s xml:id="echoid-s40" xml:space="preserve">M D LXXXI.</s>
  <s xml:id="echoid-s41" xml:space="preserve"/>
</p>
  <figure>
    <image file="0008-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0008-01"/>
  </figure>
<pb file="0009" n="9"/>
</div>
<div xml:id="echoid-div5" type="section" level="1" n="5">
<head xml:id="echoid-head7" xml:space="preserve">IN GNOMONICEN <lb/>PR AE FATIO.</head>
  <figure>
    <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01"/>
  </figure>
<p style="it">
  <s xml:id="echoid-s42" xml:space="preserve">INTER artes ac diſciplinas omnes, quas rerum auctor Deus, tanquam in-<lb/>finitæ ſuæ ſapientiæ, potentiæ ac maieſtatis argumenta quædam hominum ge-<lb/>neri communicauit, non in poſtremis cenſendæ videntur eæ, quas veteres <lb/>Philoſophi Mathematicas appellarunt. </s>
  <s xml:id="echoid-s43" xml:space="preserve">Cum enim ipſæ ſint ita exploratæ, <lb/>vt nihil probabile admittant, ſed illuſtribus omnia argumentis, neceſſarĳs{q́ue} <lb/>demonſtrent, &amp; </s>
  <s xml:id="echoid-s44" xml:space="preserve">homines ipſos, id quod inter cæteros etiam Ptolemæus agno-<lb/>uit ac profeſſus eſt, ad Dei bonitatem indagandam diligendamq́, alliciunt, &amp; </s>
  <s xml:id="echoid-s45" xml:space="preserve"><lb/>noſtram omnium mentem à fluxarum caducarum{q́ue} rerum cupiditate auocan-<lb/>tes ſuadent, vt eam tantum in æterni, atque eiuſdem conſtantis boni amore <lb/>defigamus. </s>
  <s xml:id="echoid-s46" xml:space="preserve">Quod ipſum ſi commune eſt Mathematicis omnibus diſciplinis, quanto id erit magis Aſtro-<lb/>nomiæ proprium, quæ conſiderat cæleſtes illos orbes, quos Dei manus mir abili artificio ar chitectata eſt, <lb/>quorum tanta eſt in motu conſtantia, tanta etiam æqualitas, etiamſi nonnihil inter eos diſparile eſſe <lb/>videatur, vt fieri non poſſit, quin qui de his attente cogitet, eorum natura motuque perſpecto, ad ſum-<lb/>mum illorum motorem admir andum ſuſpiciendumque rapiatur. </s>
  <s xml:id="echoid-s47" xml:space="preserve">Et vero laudari Aſtronomia pro digni-<lb/>tate non poteſt, cum proponat videndam orbium cæleſtium magnitudinem, constantiſſimum Solis mo-<lb/>tum, varium eundemque certum Lunæ, ac reliquorum ſiderum curſum, eorum mutuum, &amp; </s>
  <s xml:id="echoid-s48" xml:space="preserve">cum Sole <lb/>congreſſum, ortum obitumque ſtellarum, earum collocationes, progreſſiones, inſtitiones, numerum, <lb/>amplitudinem, atque à terris diſtantiam. </s>
  <s xml:id="echoid-s49" xml:space="preserve">Mitto illud, (quod eſt multo maximum) vnam Aſtronomiam <lb/>eſſe, quæ Solis, Lunæque defectiones pronunciet, quamquam nullum certum ſit defectionis vnius ab al-<lb/>tera interuallum, id quod experientia ipſa demonſtrat. </s>
  <s xml:id="echoid-s50" xml:space="preserve">Aſtronomi autem etſi non varĳs modo litera-<lb/>rum monumentis tam admir abilem cælestium &amp; </s>
  <s xml:id="echoid-s51" xml:space="preserve">corporum, &amp; </s>
  <s xml:id="echoid-s52" xml:space="preserve">motuum doctrinam aliqua ex parte <lb/>hominibus tradere conati ſunt, verum etiam diuina propemodum ingenĳ abundantia multa instrumen-<lb/>ta inuenerunt, in quibus, tamquam in ſpeculo, cæleſtium motuum multitudinem ac varietatem <lb/>inſpicere liceret, nullum tamen ex eorum numero ſimplicius excuderunt, nullumque parabilius, <lb/>quam horologium id, quod Græci σ@ιοθηρικὸν, Latini, Solarium dicunt, in quo horæ in Sole inſpiciuntur; <lb/></s>
  <s xml:id="echoid-s53" xml:space="preserve">cuius ea natura eſt, vt in Sole poſitum, ex radĳ vnius, ſiue ſtyli vmbra, omnem motum poſitumque cæ-<lb/>li, quamuis varium, præcipue autem Solis, cernendũ præbeat. </s>
  <s xml:id="echoid-s54" xml:space="preserve">In hoc enim, ſi modo illuminetur à Sole, <lb/>quota ſit hora quolibet anni tempore apparet, quam ex duodecim ſigniferi or bis, qui græce ζοιακὸς dici-<lb/>tur, partibus Solipſe, quam cęli domum, quem Verticalem &amp; </s>
  <s xml:id="echoid-s55" xml:space="preserve">Horizontis parallelum obtineat, ecquod <lb/>ſupra Horizontem ſignum oriri, aut occidere incipiat, cuilibet horæ quota in cæteris terrę partibus re-<lb/>ſpondeat, cuius loci Meridianum Sol quauis hora poſſideat. </s>
  <s xml:id="echoid-s56" xml:space="preserve">Iam vero ſcientia, quæ in hac vnius inſtru-<lb/>menti ar chitectura verſatur, ὰπὸ τοῦ γνώμονος quem ſtylum, ſiue radium Latini dixerunt, γνομικὴ dicta <lb/>eſt, quam magnam afferre admirationem conſiderãtibus testatur Vitruuius, cũ doceat, in quodnam pun-<lb/>ctũ cuiusuis plani gnomonis vmbra qualibet hora incidat, qualẽ lineã totos dies, rectãne, an in orbẽ, aut <lb/>ſectionẽ aliquam conicã deſcribat, &amp; </s>
  <s xml:id="echoid-s57" xml:space="preserve">reliquaid genus. </s>
  <s xml:id="echoid-s58" xml:space="preserve">Porro hac de ſcientia ita admir abili, etſi complu <lb/>res tum ex veteribus, tũ etiã ex recẽtioribus, multa ſcripſerunt, eorũ tamen nemo, meo quidem iudicio, <lb/>(quod nemini obtrectandi cauſa dico) eam omni ex parte perſecut us videtur. </s>
  <s xml:id="echoid-s59" xml:space="preserve">Aut enim nudam praxim <lb/>tradunt, quaratione confici horologia poſſint, nullam ad ea præcepta demonſtr ationem adhibentes, vt <lb/>recentiores fere omnes; </s>
  <s xml:id="echoid-s60" xml:space="preserve">qua exre errores admittunt minime ferendos, vt ex Orontĳ Finæi de horologĳs <lb/>commentario conſtat: </s>
  <s xml:id="echoid-s61" xml:space="preserve">aut ſi qui conati ſunt ea præcepta demonſtrationum ponderibus examinare, id ita <lb/>breuiter, atque adeo obſcurè faciunt, vt vix vlla ex eorum lucubr ationibus vtilitas per cipi poſſit. </s>
  <s xml:id="echoid-s62" xml:space="preserve">Quod <lb/>cũ nõnulli magnis homines ingenĳs apud me quererentur, rogarentque, vt nõnihil operæ at q; </s>
  <s xml:id="echoid-s63" xml:space="preserve">induſtriæ in <lb/>ita eleganti, ſuaui, atque etiam ad tot res vtili Gnomonices ſcientia collocarem, multum studĳ ac tem <lb/>poris poſui, vt hoſce libros conſcriberem: </s>
  <s xml:id="echoid-s64" xml:space="preserve">in quibus illud laboro, vt non ſolum, quaratione cuiuſcunque <lb/>generis horæ in qualibet plana ſuperficie deſcribantur, verum etiam alia multa, quæ ad Solis cæli{q́ue} mo-<lb/>tum pertinent, quanta maxima fieri potuit perſpicuit ate demonſtrem. </s>
  <s xml:id="echoid-s65" xml:space="preserve">Opus ipſum octo libris totum con <lb/>cluſi. </s>
  <s xml:id="echoid-s66" xml:space="preserve">Primo demonſtrantur problemata varia ac theoremata, quæ pertinent ad Analemma, ad co-<lb/>nicas ſectiones, ad horarios circulos, ad communes linearum horariarum interſectiones, ad planorum <lb/>declinationes &amp; </s>
  <s xml:id="echoid-s67" xml:space="preserve">inclinationes, &amp; </s>
  <s xml:id="echoid-s68" xml:space="preserve">ad cætera huiuſmodi. </s>
  <s xml:id="echoid-s69" xml:space="preserve">Altero, quæ ſit Horizont alium, Vertica-<lb/>lium, Meridianorum, Polarium, &amp; </s>
  <s xml:id="echoid-s70" xml:space="preserve">Aequinoctialium horologiorum ratio deſcribendorum. </s>
  <s xml:id="echoid-s71" xml:space="preserve">Tertio, <lb/>quomodo pingi horologia poſſint, quæ vel à Verticali primario, aut ab Horizonte declinant, vel incli-<lb/>nantur ad Horizontem, vel ſimul &amp; </s>
  <s xml:id="echoid-s72" xml:space="preserve">declinant à Verticali, &amp; </s>
  <s xml:id="echoid-s73" xml:space="preserve">ad Horizontem inclinantur. </s>
  <s xml:id="echoid-s74" xml:space="preserve">Quartus <lb/>agit de horologĳs in ſphærarecta, &amp; </s>
  <s xml:id="echoid-s75" xml:space="preserve">obliquiſſima, quæ polum pro capitis vertice habet; </s>
  <s xml:id="echoid-s76" xml:space="preserve">illud etiam ex-<lb/>@licat, qua arte ſtylus in ſuo ipſius loco collocetur, quæ ſit ars intelligendi, ad quam poli altitudinẽ, aut
<pb file="0010" n="10"/>
declinationem, aut inclinationem quodlibet horologium conſtructum eſſe videatur, &amp; </s>
  <s xml:id="echoid-s77" xml:space="preserve">quæratio ſit cu-<lb/>iuslibet horologĳ, pro cuiusuis ſtyli magnitudine, aut amplificandi, aut etiam minuendi. </s>
  <s xml:id="echoid-s78" xml:space="preserve">Quintus do-<lb/>cet, qua via ac ratione tabulæ quædam compenantur, quibus poſtea facili negotio horologia deſcriban-<lb/>tur. </s>
  <s xml:id="echoid-s79" xml:space="preserve">Sextus Ptolemæi Analemma explicat, item{q́ue} Federici Commandini de horologiorum deſcriptin-<lb/>ne opus: </s>
  <s xml:id="echoid-s80" xml:space="preserve">ex quo conſtat, Analemmatis vſum (ni fallor) multo latius patere, quam ſit à Ptolemæo li-<lb/>terarum monumentis traditum. </s>
  <s xml:id="echoid-s81" xml:space="preserve">Addo etiam faciliorem viam in declinantibus, inclinatis{q́ue} horologĳs, <lb/>quam quæ à Commandino monſtrata eſt. </s>
  <s xml:id="echoid-s82" xml:space="preserve">Quid præterea tenendum ſit, vt ab Horizontali horologio al-<lb/>terum in pariete, cuius tamen nota ſit declinatio, ad quamcunque ſtyli magnitudinem deſcribatur. <lb/></s>
  <s xml:id="echoid-s83" xml:space="preserve">Septimo paucis repetuntur præcipuæ horarum deſcriptiones, de quibus ſecundo &amp; </s>
  <s xml:id="echoid-s84" xml:space="preserve">tertio libro eſt diſpu-<lb/>tatum; </s>
  <s xml:id="echoid-s85" xml:space="preserve">neque tamen demonſtrationes additæ ſunt, vt qui in Geometricis demonſtrationibus non ſunt <lb/>admodum verſati, quoduis horologium, ſine demonſtr ationum interiectione aut mora, formare non dif-<lb/>ficile poſſint. </s>
  <s xml:id="echoid-s86" xml:space="preserve">Octauus denique liber de vniuerſalibus quibuſdam horologĳs, quę ad omnes poli altitudi-<lb/>nes accommodantur, agit, &amp; </s>
  <s xml:id="echoid-s87" xml:space="preserve">de alĳs etiam nonnullis, quæ circumferri poſſint, &amp; </s>
  <s xml:id="echoid-s88" xml:space="preserve">in vna ſola poli altitu-<lb/>dine vſum habeant, vt quæque nobis magis ex vſu eſſe videbuntur. </s>
  <s xml:id="echoid-s89" xml:space="preserve">Atque ita, quicquid Gnomonices <lb/>eſt proprium, id omne complecti hiſce libris octo ita digeſtis, niſime valde fallit animus, videor. </s>
  <s xml:id="echoid-s90" xml:space="preserve">Quod <lb/>autem pleriſque propoſitionibus ſcholia adiecta ſunt, id eo conſilio factum eſt, vt vel in illis, quæ ad pla-<lb/>nius intelligendam propoſitionis demonſtrationem pertinent, explicarentur, vel alys vĳs eadem, quæ in <lb/>propoſitionibus demonſtrata ſunt, perueſtigarentur, vel denique noui aliquid, ab inſtituto non abhorrens, <lb/>proponeretur. </s>
  <s xml:id="echoid-s91" xml:space="preserve">Nam ſi omnia in propoſitiones conieciſſem, moleſtia lectorem ipſa longitudine affeciſ-<lb/>ſem. </s>
  <s xml:id="echoid-s92" xml:space="preserve">In demonſtrationibus ex Euclide, &amp; </s>
  <s xml:id="echoid-s93" xml:space="preserve">in eum ſcholĳs, ſecundum noſtram editionem, ex Apollonio <lb/>Pergæode conicis elementis ſecundum editionem Federici Commandini, &amp; </s>
  <s xml:id="echoid-s94" xml:space="preserve">ex Theodoſio de elementis <lb/>ſphæricis ſecundum etiam noſtram editionem, testimonia proferemus. </s>
  <s xml:id="echoid-s95" xml:space="preserve">Afferam etiam Ioannis de Regio-<lb/>monte libros de triangulis, aut Gebrum Hiſpalenſem Arabem de triangulis ſphæricis, aut noſtra triang@-<lb/>la ſphærica, quæ cum Theodoſio, &amp; </s>
  <s xml:id="echoid-s96" xml:space="preserve">cum tractatione ac tabula de ſinubus in volumen vnum vniuerſæ <lb/>Aſtronomiæ perneceſſarium coniecta breui prodibunt. </s>
  <s xml:id="echoid-s97" xml:space="preserve">Itaque qui rebus hiſce non diligenter oper am <lb/>dederit, non est cur in hac Gnomonica demonſtrationes noſtras ſe intelligere poſſe confidat: </s>
  <s xml:id="echoid-s98" xml:space="preserve">quanquam <lb/>etiam rerum omnium deſcriptionẽ ita doceo, vt quilibet etiam omnium demonſtrationum rudis, quid ta-<lb/>men in agendo obſeruare debeat, per ſeſe percipere valeat. </s>
  <s xml:id="echoid-s99" xml:space="preserve">Illud quoque lectorem admonitum velim, <lb/>omnia horologia in hac Gnomonica efficta eſſe ad almæ Vrbis Romæ latitudinem, etſi præcepta ipſa <lb/>ſunt cuiuis poli altitudini, aut latitudini loci communia. </s>
  <s xml:id="echoid-s100" xml:space="preserve">In ſecundi etiam &amp; </s>
  <s xml:id="echoid-s101" xml:space="preserve">tertĳ libri ſeholĳs, ac to-<lb/>to ſeptimo doceo, quo pacto ex cuiuſcunque dati ſtyli magnitudine, cuius etiam locus in horologĳ plano <lb/>aſſignetur, horologia deſcribantur, quod ante me nemo vnquàm (quod ego quidem ſciam) præſtitit, cum <lb/>plerique omnes horologia ante depingant, quàm ſtyli magnitudinem determinent. </s>
  <s xml:id="echoid-s102" xml:space="preserve">Vnus quidem certe <lb/>Federicus Commandinus idem facit, ſed &amp; </s>
  <s xml:id="echoid-s103" xml:space="preserve">Analemmatis via, neque ea ratione, quam plerique eorum, <lb/>quihorologia deſcribunt, communiter tenent. </s>
  <s xml:id="echoid-s104" xml:space="preserve">Neque verò illud dicere prętermittam, conatum me in-<lb/>uſitata quoque ratione, ex noua quadam cylindri via, horas deſcribere in quocunque plano, quæipſa via <lb/>(auſim dicere) inter omnes ſola eſt, per quam horæ omnes, &amp; </s>
  <s xml:id="echoid-s105" xml:space="preserve">horarum partes commode pingantur, vt li-<lb/>bro ſecundo &amp; </s>
  <s xml:id="echoid-s106" xml:space="preserve">tertio videbitur. </s>
  <s xml:id="echoid-s107" xml:space="preserve">Quamobrem ſi hoc in opere lumen aliquod ita nobilis, iucundæ ſcien <lb/>tiæ ſtudioſis attulero, bonorum omnium auctori Deo acceptum referri volo. </s>
  <s xml:id="echoid-s108" xml:space="preserve">Quod ſi magnis aliorum <lb/>ingenĳs minus cumulate ſatisfecero, quàm aut oportuiſſet, aut voluiſſem, cum ingenĳ mei tenuitati, tum <lb/>rei difficultati adſcribendum duco, quippe cum in pleriſque neminem habuerim ducem, quem ſequi aliqua <lb/>ratione poſſem, &amp; </s>
  <s xml:id="echoid-s109" xml:space="preserve">demonſtr ationes ferè omnes nuper à me excogitatę fuerint, vt facile exiſtimabit, quiſ-<lb/>quis noſtram hanc Gnomonicen cum aliorum horolograpĳs conferre voluerit. </s>
  <s xml:id="echoid-s110" xml:space="preserve">Arbitror tamen a me <lb/>ita viam hac inre patefactam eſſe, vt facile ſit vnicuique, etiamſi mediocriter in demonstrationibus <lb/>Geometricis intelligat, ſuapte ſponte progredi, &amp; </s>
  <s xml:id="echoid-s111" xml:space="preserve">extremam huic ſcientiæ manum, &amp; </s>
  <s xml:id="echoid-s112" xml:space="preserve">tanquam fasti-<lb/>gium operi inchoato imponere.</s>
  <s xml:id="echoid-s113" xml:space="preserve"/>
</p>
  <figure>
    <image file="0010-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0010-01"/>
  </figure>
<pb file="0011" n="11"/>
</div>
<div xml:id="echoid-div6" type="section" level="1" n="6">
<head xml:id="echoid-head8" xml:space="preserve">INDEX EORVM, QVAE TOTO <lb/>HOC OPERE CONTINENTVR.</head>
<note style="it" position="right" xml:space="preserve"> <lb/>A <lb/>ARgumentum libri primi. # pagina 1 <lb/>Argumentum libri ſecundi. # 142 <lb/>Argumentum libri tertĳ. # 293 <lb/>Argumentum libri quarti. # 414 <lb/>Argumentum libri quinti. # 447 <lb/>Argumentum libri ſexti. # 528 <lb/>Argumentum libri ſeptimi. # 575 <lb/>Argumentum libri octaui. # 634 <lb/>Antiqui cur diem quemcunque &amp; noctem in 12. horas diuiſerint. <lb/># pag. # 2. &amp; 6 <lb/>Aequinoctiale horologium tam Superius, quàm Inferius quod. # 4 <lb/>Antiquæ horæ quæ, &amp; cur ſic dictæ ſint. # 6 <lb/>Aequinoctialis hora, aut æqualis quid, &amp; cur ſic dicatur. # 6 <lb/>Aſtronomicæ horæ quæ. # 7 <lb/>Antiquum horologium quod. # 7 <lb/>Aſtronomicum horologium quod. # 7 <lb/>Anaximenes Mileſius Solarium horologiorum primus inuentor. # 7 <lb/>Analemma quid. # 8. &amp; 17 <lb/>Analemmatis ad quãcunque latitudinẽ cõſtructio ab. 11. vſq; ad # 17 <lb/>Analemmatis vtilitates variæ. # 17 <lb/>Amplitudo ortiua, vel occidua quomodo ex Analemmate cognoſca-<lb/># tur. # 18 <lb/>Aequinoctialis horologĳ planum ſecans conicam ſuperficiem, cuius <lb/># baſis Aequatori æquidiſtat, circulum facit. # 21 <lb/>Aequinoctialis linea, &amp; linea cuiuslibet horæ à mer. vel med. noc. <lb/># &amp; duæ lineæ horarum ab or. vel occ. diſtantium quadrante inte-<lb/># gro ab illa hora à mer. vel med noc. in maximo parallelorũ ſemper <lb/># apparentiũ, ſe mutuo interſecant in quouis horologio. # 53. &amp; 59 <lb/>Aequator, &amp; duo circuli horarum ab or. vel occ. tangentes maxi-<lb/># mum parallelorum ſemper apparẽtium in punctis oppoſitis, &amp; cir <lb/># culus horæ à mer. vel med. noc ſecans eundem parallelum in pun-<lb/># cto æqualiter, id eſt, ſex horis, à punctis contactuum diſtante, in-<lb/># terſecant ſe mutuo in vno eodemque puncto, habentque vnã &amp; ean <lb/># dem rectam lineam pro communi eorum ſectione. # 59 <lb/>Altitudo Solis quomodo per Analemma ex hora cognita, &amp; Solis <lb/># declinatione, vel ex longitudine vmbræ styli ad planum, quod Ho <lb/># riZonti æquidiſtet, recti, inueſtigetur. # 85 <lb/>Altitudo poli ſupra Horizontem quo pacto per Analemma inquira-<lb/># tur. # 98 <lb/>Altitudo poli ſupra quodcunque planum inclinatum ad Meridianũ, <lb/># vel ad Horizontem, qua ratione deprehendatur. # 99. &amp; 100 <lb/>Amplitudo ortiua, vel occidua qua arte per ſinus ſupputetur. # 115 <lb/>Altitudo Solis meridiana qua via ex declinatione Solis reperiatur. <lb/># pag. # 120 <lb/>Altitudo Solis ſupra Horizontem quo artificio ex hora cognita ſup-<lb/># putetur tam in ſphæra obliqua, quàm in recta. à 126. vſq; ad # 140 <lb/>Altitudo Solis in Verticali circulo proprie dicto qua ratione ſuppu-<lb/># tetur, etiamſi hora ignoretur. # 127. &amp; 134 <lb/>Altitudinis Solis inueniendæ ratio, quæ ſit omniũ expeditißima. # 131 <lb/>Altitudo Solis ex hora cognita quomodo exploretur, quando paral-<lb/># lelus borealis totus ſupra Horizontem extat. # 139 <lb/>Aſtronomici horologĳ in quouis plano deſcriptio, quæ omnium ſit <lb/># præſtantißima. # 142 <lb/>Analemmatis portio, ex qua horologia deſcribuntur, quid. # 143 <lb/>Astrononmici horologĳ horizontalis conſtructio ex portione Ana-<lb/># lemmatis. # 143 <lb/>Aſtronomici horologĳ horizontalis deſcriptio commodißima pro ho-<lb/># ris delineandis, quæ propinquæ ſunt horæ 6. à mer. vel med. noc. <lb/># &amp; vix lineam æquinoctialem ſecant. # 145 <lb/>Arcus circuli ex centro horology horizontalis deſcripti, inter lineã <lb/># meridianam, &amp; bin{as} hor{as} vtrinque a meridie æqualiter diſtan <lb/># tes interiecti ſunt æquales. # 145 <lb/>Astronomici horology: vſ{us} eſt, vt diſcamus, quot horæ à meridie, <lb/># vel med. noc. effluxerint, &amp; quot ſuperſint vſque ad ſequentem <lb/># meridiem, vel med noc. # 146 <lb/>Aſtronomici horologĳ horizontalis deſcriptio in plano ſtabili, quod <lb/># Horizonti æquidiſtet. # 148 <lb/>Aſtronomici horologĳ horizontalis deſcriptio ad datam ſtyli longi-<lb/># tudinem, cui{us} etiam locus dat{us} ſit. # 148. 575. &amp; 576 <lb/>Astronomici horologii horizõtalis deſcriptio noua, ac pulcherrima. <lb/># beneficio Ellipſis, ſine punctis in linea æquinoctiali inuentis, quæ <lb/># commodißima eſt pro horis, vel horarum partibus deſcribendis, quæ <lb/># vix æquinoctialem lineam, vel certe valde procul à linea meridia-<lb/># na interſecant. # à 149. vſque ad 153 <lb/>Aſtronomici horologĳ horizontalis deſcriptio, quando poli altitudo <lb/># vel perexigua eſt, vel nimis magna, etiamſi centrum horologĳ non <lb/># habeatur. # à 153. vſque ad 155 <lb/>Analemmatis portio, ex qua horologia deſcribuntur, inſtrumentum <lb/># eſt ad horologia cuiuſuis magnitudinis delineanda. # 159 <lb/>Aſcendentium ſignorum in horologio horizontali deſcriptio. <lb/># pag. # 178. 183. &amp; 187 <lb/>Aſcendentium ſignorum lineæ tangunt tropicos in quolibet horolo-<lb/># gio. # 180 <lb/>Aſcendentium ſignorum in horologio deſcriptorum vſus est, vt ſi-<lb/># tus toti{us} cæli quolibet momento temporis exploretur. # 187 <lb/>Aſcendentium ſignorum lineæ quo pacto in duab{us} figuris depingan <lb/># tur, vel in quatuor, in quouis horologio, vt mutuo ſe non interſe-<lb/># cent. # 189 <lb/>Aſcenſio recta cuiuſuis puncti Eclipticæ quomodo inquiratur. # 189 <lb/>Aſcenſionis rectæ, &amp; obliquæ cuiuſuis puncti Eclipticæ differentia, <lb/># qua via ad quamcunque latitudinem loci ſupputetur. # 191 <lb/>Aſcenſio obliqua cuiusuis puncti Eclipticæ quomodo ex differentia <lb/># aſcenſionali numeretur. # 191 <lb/>Aſcenſionales differentiæ punctorum quadrantis Eclipticæ ab Arie <lb/># te vſque ad Cancrum æq@@ales ſunt differentiis aſcenſionalibus <lb/># punctorum in alĳs tribus quadrantibus Eclipticæ. # 191 <lb/>Aſtronomici horologĳ, &amp; Italici, vel Babylonici ſimul vtilit{as} ad <lb/># eliciendam quantitatem diei ac noctis ex vmbra gnomonis; tempus <lb/># meridiei &amp; mediæ noctis, quoad hor{as} ab or. &amp; occ. temp{us} ort{us}<unsure/> <lb/># Solis, quoad hor{as} à med. noc. &amp; ab occ. temp{us} denique occaſ{us} <lb/># Solis, quoad hor{as} à mer. &amp; ab or. # 200 <lb/>Antiqui horologĳ horizontalis deſcriptio. # 201. 203. 584. &amp; 585 <lb/>Antiqui horologĳ vſus eſt, vt intelligam{us}, quanta pars diei ſit trã-<lb/># ſacta, &amp; quanta ſuperſit. # 203 <lb/>Astronomici horologii Verticalis conſtructio ex portione Analem-<lb/># matis. # 204 <lb/>Aſtronomici horologii Verticalis deſcriptio commodißima pro horis <lb/># delineãdis, quæ propinquæ ſunt lineæ horæ 6. à mer. vel med. noc. <lb/># &amp; vix æquinoctialem lineam ſecant. # 207 <lb/>Arcus circuli ex centro horologii Verticalis deſcripti inter lineam <lb/># meridianam, &amp; binas horas vtrinque à meridie æqualiter diſtan <lb/># tes, æquales ſunt. # 207 <lb/>Aſtronomici horologii Verticalis deſcriptio, cum altitudo poli ſupra<unsure/> <lb/># Horizontem tanta est, vt pol{us} parum à vertice capitis recedat, <lb/># vel perexigua eſt. # 208 <lb/>Auſtrale horologium ſecundum omnes ſui partes inuerſum, quo pa-<lb/># cto exhibeat horologium boreale. # 208. &amp; 209 <lb/>Aſtronomici horologĳ Verticalis deſcriptio in plano ſtabili, quod <lb/># Verticali circulo proprie dicto æquidiſtet. # 210 <lb/>Aſtronomici horologii Verticalis conſtructio ad datam ſtyli longitu <lb/># dinem, cuius etiam locus datus ſit. # 210. &amp; 585 <lb/>Aſtronomici horologii Verticalis deſcriptio noua ac pulcherrima, <lb/># beneficio Ellipſis, ſine punctis in linea æquinoctiali inuentis, quæ <lb/># commodiſsima eſt pro horis, @ vel horarum partibus, quæ vix æqui-<lb/># noctialem lineam, vel certe valde procul à linea meridiana ſe-<lb/># cant. # 211 <lb/>Aſtronomicum horologium horizontale ad quamcunque loci latitu <lb/># dinem conſtructum, Verticale eſt in regione, cuius latitudo comple-<lb/># mentum eſt prioris latitudinis. # 211 <lb/>Aſtronomicum horologium Verticale qua ratione ex figura radio-<lb/># rum Zodiaci deſcribatur. # 217 <lb/>Aſcendentium ſignorum in Verticali horologio deſcriptio. # 228 <lb/>Antiqui horologii Verticalis deſcriptio. # 236. &amp; 590 <lb/>Aſtronomici horologii Meridiani deſcriptio. # 237. 590. &amp; 591 <lb/>Aſtronomici horologii Meridiani deſcriptio in plano stabili, quod <lb/># Meridiano circulo æquidistet. # 240 <lb/>Aſcendentium ſignorum in Meridiano horologio deſcriptio. à # 249 <lb/># vſque ad # 252 <lb/>Antiqui horologii Meridiani deſcriptia. # 256. &amp; 594 <lb/>Antiquum horologium Meridianum Orientale im facie planihoro-<lb/># logii oppoſita deli ieatum, ita vt lineæ lineis reſpondeant, dat An-
<pb file="0012" n="12" rhead="INDEX."/>
# tiquum occidentale, &amp; contra. # 256. &amp; 594 <lb/>Aſtronomicum horologium Polare à Meridiano horologio quo modo <lb/># differat. # 257. &amp; 595 <lb/>Aſtronomici horologĳ Polaris conſtructio. # 257. &amp; 595 <lb/>Aſcendentium ſignorum in Polari horogio deſcriptio. à # 266. <lb/># vſq; ad 268 <lb/>Antiqui horologĳ Polaris conſtructio. # 272. &amp; 597 <lb/>Aequinoctialis horologĳ Astronomici conſtructio. # 273. &amp; 598 <lb/>Astronomici horologii Aequinoctialis constructio. # 273. &amp; 598 <lb/>Aequinoctiale horologium Aſtronomicũ quo pacto, ſi locus ſtyli de-<lb/># tur in plano stabili, quod Aequatori æquidistet, cõſtruatur. # 274 <lb/>Aſtronomicum horologium Aequinoctiale quo pacto, ſi locus ſtyli in <lb/># plano ſtabili detur, quod Aequatori æquidiſtet, conſtruatur. # 274 <lb/>Aequinoctialis linea in horologio æquinoctiali deſcribi nequit. # 275 <lb/>Aſcendentium ſignorum in horologio Aequinoctiali deſcriptio. <lb/># pag. # 284. &amp; 285 <lb/>Aequinoctialis horologii Italici conſtructio. # à 286. vſq; ad 290. <lb/># &amp; 599 <lb/>Aequinoctialis horologii Babylonici conſtructio. # 289. &amp; 599 <lb/>Aequinoctialis horologii Antiqui compoſitio. # 291. &amp; 600 <lb/>Antiqui horologii Aequinoctialis delineatio. # 291. &amp; 600 <lb/>Aequator, Meridianus, &amp; circul{us} horæ 6. à mer. vel med. noc. in <lb/># omni climate ſe mutuo ad angulos rectos ſecant. # 293 <lb/>Aſtronomici horologii à Verticali declinantis conſtructio. # à 294. <lb/># vſq; ad 301. &amp; à 601. vſq; ad 604 <lb/>Altitudo poli ſupra planũ à Verticali declinãs quo pacto deprehẽ-<lb/># datur ex conſtructione horologii declinantis à Verticali. # 295 <lb/>Astronomicum horologium declinans à Verticali quo modo in pla-<lb/># no ſtabili deſcribatur. # 303 <lb/>Aſtronomici horologĳ à Verticali circulo declinantis, ad datum <lb/># stylum, cuius etiam loc{us} datus ſit, deſcriptio. # 304. &amp; a 601 <lb/># vſque ad 603 <lb/>Astronomici horologii à Verticali declinantis deſcriptio, beneficio <lb/># Ellipſis, noua ac pulcherrima, ſine punctis in linea æquinoctiali in-<lb/># uentis, quæ commodißima eſt pro horis ducendis, quæ vix æquino-<lb/># ctialem lineam interſecant, vel certe valde procul à linea ſtyli. <lb/># pag. # 306 <lb/>Astronomicum horologium à Verticali declinans, quod parum à <lb/># Meridiano abeſt, quo pacto conſtruaiur, etiam ſi centrum horologii <lb/># non habeatur. # 307 <lb/>Aſtronomicum horologium declinans à borea in ortum conficitur, ſi <lb/># par s ſuperior horologii à meridie in ortum declinantis fiat infe-<lb/># rior: Item declinans à borea in occaſum fit, ſipars ſuperior horo-<lb/># logii à meridie in occaſum declinantis fiat inferior. # 311 <lb/>Aſcendentium ſignorum in horologio declinante à Verticali deſcri-<lb/># ptie. # a 326. vſque ad 328 <lb/>Antiqui horologii declinantis à Verticali conſtructio. # 332. 334. <lb/># 609. &amp; 610 <lb/>Aſtronomici horologii ab Horizonte declinantis deſcriptio. # à 334 <lb/># vſque ad 337. &amp; 511 <lb/>Altitudo poli ſupra Verticalem proprie dictum cuiuſcunq; regio-<lb/># nis æqualis est complemento altitudinis poli ſupra Horizontem <lb/># eiuſdem regionis. # 335. &amp; 489 <lb/>Aſtronomicum horologium ab Horizonte declinans constructum <lb/># erit, ſi deſcribatur declinans à Verticali pro ea latitudine loci, <lb/># quæ cum ea, ad quam horologium ab Horizonte declinans deſide-<lb/># ratur, gradus 90. conficit. # 335 <lb/>Altitudo poli ſupra planum ab Horizonte declinans quo pacto ex <lb/># conſtructione horologii ab Horizonte declinantis deprehendatur. <lb/># pag. # 335. &amp; 612 <lb/>Astronomicum horologium ab Horizonte declinans qua ratione in <lb/># plano ſtabili deſcribatur. # 338 <lb/>Aſtronomicum horologium ab Horizonte declinans, &amp; ad occaſum <lb/># ſpectans, qua ratione ſit permutandum, vt fiat aliud ſpectans ad or-<lb/># tum, &amp; contra. # 338. &amp; 613 <lb/>Aſtronomici horologii ab Horizonte declinantis conſtructio ad da-<lb/># tum ſtylum, cuius etiam loc{us} dat{us} ſit. # 339. &amp; 611 <lb/>Aſtronomici horologii ab Horizonte declinantis deſcriptio, benefi-<lb/># cio Ellipſis, noua ac pulcherrima, ſine punctis in linea æquinoctiali <lb/># inuentis, quæ commodißima eſt pro horis ducendis, quæ vix æquino-<lb/>ctialem lineam, vel certe valde procul à linea ſtyli ſecant. # 341 <lb/>Aſcendentium ſignorum in horologio declinante ab Horizonte de-<lb/># ſcriptio. # 349. &amp; 350 <lb/>Antiqui horologii ab Horizõte declinãtis deſcriptio. # 352. &amp; 613 <lb/>Altitudo poli ſupra planum inclinatum ad Horizontem quo pacto <lb/># reperiatur. # 353. 354. 615. &amp; 616 <lb/>Astronomici horologii ad Horizontem inclinati deſcriptio. # à 353 <lb/># vſque ad 356. &amp; 617 <lb/>As<unsure/>tronomicum horologium inclinatum ad Horizontem qua ratio-<lb/># ne ſit in plano ſtabili conſtruendum. # 357 <lb/>Astronomici horologii ad Horizontem inclinati pro dato ſtylo. <lb/># eiuſq; loco, deſcriptio. # 357 &amp; 617. <lb/>Aſtronomici horologii ad Horizontem inclinati deſcriptio noua ac <lb/># pulcherrima ex Ellipſi, quæ commodißima eſt pro horis ducendis. <lb/># quæ vix, aut valde procul à linea meridiana æquinoctialem line-<lb/># am ſecant. # 357 <lb/>Aſcendentium ſignorum in horologio ad Horizontem inclinato de-<lb/>ſcriptio. # 365. &amp; 366 <lb/>Antiqui horologii ad Horizontẽ inclinati deſcriptio. # 369. &amp; 6@9 <lb/>Aſtronomici horologii declinantis ſimul &amp; inclinati constructio. <lb/># pag. # a 371. vſq ad 387 <lb/>Altitudo poli ſupra planum declinans ſimul &amp; inclinatum quo mo-<lb/># do ex conſtructione horologii declinantis ſimul &amp; inclinati inueſti <lb/># getur. # 373 <lb/>Aequinoctialis linea, &amp; meridiana in quo horologio declinante ſi-<lb/># mul &amp; inclinato ſint parallelæ. # 383 <lb/>Astronomicum horologium declinans ſimul &amp; inclinatum quo pa-<lb/># cto in plano ſtabili deſcribatur. # 388 <lb/>Astronomici horologii declinantis ſimul &amp; inclinati pro dato ſtylo, <lb/># eiuſq́; loco deſcriptio. # 389. &amp; a 620. vſq; ad 624 <lb/>Aſtronomici horologii declinantis ſimul &amp; inclinati deſcriptio noua <lb/># ac pulcherrima ex Ellipſi, quæ commodiſsima est pro horis ducen-<lb/># dis, quæ vix, aut valde procul à linea ſtyli æquinoctialem lineam <lb/># ſecant. # 394 <lb/>Aſcendentium ſignorum in horologio declinante ſimul &amp; inclinato <lb/># delineatio # 409. &amp; 410 <lb/>Antiqui horologĳ declinantis ſimul &amp; inclinati constructio. <lb/># pag. # 413. &amp; 629 <lb/>Antiquum horologiũ in ſphæra recta à Babylonico non differt. # 415 <lb/>Amplitudines ortiuæ, &amp; occiduæ punctorum Eclipticæ in ſphæra <lb/># recta æquales ſunt eorundem punctorum declinationib{us}. # 416 <lb/>Aequinoctialia horologia cum omnib{us}, quæ in horologĳs ſphæræ <lb/># obliquæ deſcripta ſunt, quo modo depingantur in ſphæra recta. # 418 <lb/>Astronomici horologĳ à Verticali declinantis deſcriptio in ſphæra <lb/># recta ad datum ſtylum, cuius etiam loc{us} dat{us} ſit. # 420 <lb/>Aſtronomici horologĳ ab Horizonte declinantis deſcriptio in ſphæra<unsure/> <lb/># recta ad datũ ſtylum, cui{us} etiam loc{us} dat{us} ſit. # 422 <lb/>Astronomici horologĳ ad Horizontem inclinatis deſcriptio in ſphæra <lb/># recta ad datũ stylum, cuius etiam locus datus ſit. # 423 <lb/>Altitudo Solis ſupra quemcunq; circulum maximum ſphæra qua ar-<lb/># te pro data hora ſupputetur. # 449. 450. &amp; 451 <lb/>Altitudines Solis ſupra circulos maximos, qui per polos mundi du-<lb/># cuntur, iuuentæ in ſignis borealib{us}, æquales ſunt altitudinibus in <lb/># ſignis auſtralibus. Vnde ſatis eſt ſi inquirantur altitudines vel in-<lb/># ſignis borealibus tantum, vel in ſignis auſtralibus tantum. # 451 <lb/>Altitudo Solis ſupra Meridianum Horizontis pro qualibet hora <lb/># æqualis eſt altitudini Solis ſupra circulum horæ 6. a mer. vel <lb/># med. noc. pro alia hora, quæ tantum abeſt ab hoc circulo, quan-<lb/># tum illa à Meridiano abest. # 451 <lb/>Altitudo Solis ſupra Aequatorem æqualis ſemper eſt declinationi<unsure/> <lb/># eiuſdem. # 451 <lb/>Arctic{us}ne pol{us}, an antarctic{us} ſupra faciem cuiuſque circuli ma-<lb/># ximi propoſitam eleuetur, qua ratione cognoſcatur. # 452 <lb/>Altitudo Solis meridiana ſupra circulum maximum quemcunque <lb/># quo, pacto ſupputetur. # 452 <lb/>Angulus, quem planum inclinatum cum Aequatore facit, quo pact@ <lb/># cognoſcatur. # 457 <lb/>Arcus plani inclinati inter Aequatorem, &amp; parallelum quemcun-<lb/># que, qua ratione cognoſcatur. # 457 <lb/>Arcus Aequatoris inter planum inclinatum, &amp; circulum declina-<lb/># tionis paralleli Solis ductum per communem ſectionem plani incli-<lb/># nati, &amp; paralleli, qùa arte deprehendatur. # 457 <lb/>Altitudines Solis ſupra quẽcunque circulũ maximum pro horis cu-<lb/># iuſuis paralleli inuentæ æquales ſunt altitudinibus pro ĳſdẽ horis <lb/># numero paralleli oppoſiti, dũmodo quæ prius numer abantur à mer. <lb/># vel ab or. nunc à med. noc. vel ab occ. numerentur, &amp; contra: <lb/># Et quæ prius ſupra vnam faciem circuli dati cadebant, ſumantur <lb/># nunc ſupra faciem oppoſitam. # 459. &amp; 462 <lb/>Altitudo Solis quo pacto ex longitudine vmbræ ſiue rectæ, ſiue verſæ <lb/># inueſtigetur. # 475 <lb/>Aequinoctialiũ, &amp; Solſtitialium vmbrarũ longitudines qua ratione <lb/># ex vmbrarũ tabula ad quamcunque loci latitudinẽ eruantur. # 485
<pb file="0013" n="13" rhead="INDEX."/>
Arcus cuiuſuis circuli maximi interceptus inter eius Verticalẽ pro-<lb/># prie dictum, &amp; alium Verticalem, qui per eius polum, &amp; Solem <lb/># ducitur, qua via cognoſcatur. # 485. 486. &amp; 487 <lb/>Arcus cuiusuis circuli maximi per polos mundi non tranſeuntis <lb/># incluſus inter circulum maximum per polos mundi, cõmunes q; ſe-<lb/># ctiones Aequatoris ac dati circuli (inſtar circuli horæ 6. à mer. <lb/># vel med. noc. reſpectu dati circuli, tanquam Horizontis) ductum, <lb/># &amp; quemuis alium circulum horarium, qui per polos mundi, et So-<lb/># lem ducitur, qua arte ſupputetur. # 488 <lb/>Aequinoctialis linea, Meridiana, &amp; Gnomon quid ſecundum Pto-<lb/># lemæum. # 528 <lb/>Analemma quo pacto diuidatur in hor{as}, vt circunferentiæ ad con-<lb/># ſtructionem horologĳ horizontalis, Verticalis, ac Meridiani neceſ-<lb/># ſariæ inueſtigentur. # à 542. vſque ad 544 <lb/>Auſtrales horæ à borealibus qua ratione in Analemmate diſcer-<lb/># nantur. # 559 <lb/>Analemma qua ratione diuidatur in horas, vt circunferentiæ de-<lb/># ſcenſiuæ, horizontales que in Meridiano (circulo, tanquam Hori-<lb/># zonte, reperiantur. # 561 <lb/>Aequinoctiale horologium quo pacto ad modum horizontalis horo-<lb/># logii construatur ex circunferentĳs horizontalibus, &amp; deſcenſi-<lb/># uis inuentis in Aequatore, tanquam Horizonte. # 563 <lb/>Analemma quo modo in hor{as} diuidatur, vt circunferentiæ ad con-<lb/># ſtructionem horologiorum Declinantium, &amp; inclinatorum neceſſa-<lb/># riæ inueniantur. # à 563. vſque ad 567 <lb/>Aequinoctialis horologii vniuerſalis conſtructio. # 634. &amp; 635 <lb/>Altitudines Solis pro deſcriptione horarum in quadrante qua ra-<lb/># tione Geometrice, ſine tabulis altitudinum, inueniantur. <lb/># pag. # 649 <lb/>Altitudines Solis ex Analemmate pro ſingulis horis qua ratione in-<lb/># ueniantur. # 650 <lb/>B <lb/>BAbylonicæ horæ quæ. # 6 <lb/>Babylonicum horologium quod. # 7 <lb/>Babylonici horologii horizontalis deſcriptio. # 199. 200. &amp; à 581 <lb/># vſque ad 584. <lb/>Babylonici horologii vſus eſt, vt ſciamus, quotnam horæ à proximo <lb/># ortu Solis ſint elapſæ, &amp; quot ſuperſint ad alterum ortum. <lb/># pag. # 200 <lb/>Babylonici horologii, &amp; Italici, vel Aſtronomici ſimul vtilit{as} ad <lb/># eliciendam quantitatem diei ac noctis ex vmbra gnomonis; temp{us} <lb/># meridiei &amp; mediæ noctis, quoad hor{as} ab or. &amp; occ. temp{us} ortus <lb/># Solis, quoad hor{as} à med. noc. &amp; ab occ. temp{us} denique occaſ{us} <lb/># Solis, quoad hor{as} à mer. &amp; ab or. # 200 <lb/>Babylonicum horologium horizontale quomodo ab Italico differat, <lb/># &amp; qua ratione vnum ex altero componatur. # 201 <lb/>Boreale horologiũ quo pacto ex australi, cuius omnes partes inuer-<lb/># tantur, ortum habeat. # 208. &amp; 209 <lb/>Borealis horologĳ portio infra horizontalem lineam æqualis eſt <lb/># portioni auſtralis horologii ſupra lineam horizontalem. # 213 <lb/>Babylonici horologii Verticalis deſcriptio. # 234. 588. &amp; 589 <lb/>Babylonici horologii Meridiani conſtructio. # 255. 593. &amp; 594 <lb/>Babylonicum horologium Meridianum Orientale in facie oppoſita <lb/># plani horologii deſcriptum, ita vt lineæ lineis reſpondeant, qua ra-<lb/># tione det horologium Italicum occidentale: Et Babylonicum occi-<lb/># dentale det Italicum Orientale, &amp; contra. # 255. &amp; 594 <lb/>Babylonici horologĳ Polaris deſcriptio. # 272. &amp; 597 <lb/>Babylonicum horologium Polare quo modo ab Italico differat. <lb/># pag. # 272 <lb/>Babylonici horologii Aequinoctialis constructio. # 289. 290. &amp; 599 <lb/>Borealis facies planis declinantis cuiuſque an mane vel veſperi à So-<lb/># le illuminetur, quomodo cognoſcatur. # 317 <lb/>Babylonici horologii à Verticali declinantis deſcriptio. # 331. 608 <lb/># &amp; 609 <lb/>Babylonici horologii ab Horizonte declinantis conſtructio. # 352 <lb/># &amp; 613 <lb/>Babylonici horologii ad Horizontem inclinati compoſitio. # 369 <lb/># &amp; 619 <lb/>Babylonici horologii declinantis ſimul &amp; inclinati deſcriptio. <lb/># pag. # 413. 628. &amp; 629 <lb/>Babylonicum horologium, &amp; Italicum in ſphæra recta quo modo ab <lb/># Aſtronomico differat. # 415 <lb/>Babylonicum horologium in ſphæra recta ab Antiquo non differt. <lb/># pag. # 415 <lb/>Boreales horæ qua ratione in Analemmate ab auſtralibus diſcer-<lb/># @antur. # 559 <lb/>Babylonicum horologium in cylindro, &amp; quadrante quo modo ſit <lb/># etiam Italicum. # 649 <lb/>C <lb/>CLepſydræ quid ſint, &amp; vnde ſic dictæ. # 2 <lb/>Circulus quilibet qua via ſecandus ſit in du{as} portiones, qua-<lb/># rum vna arcui diurno, &amp; altera arcui nocturno cuiuſcunque pa-<lb/># ralleli ſimilis ſit. # 18. &amp; 195 <lb/>Circulus quando fiat in plano horologii conicam ſuperficiem, cuius <lb/># baſis Aequatori æquidistet, ſecante. # 21<unsure/> <lb/>Circulus maximus tangit illum parallelum, cuius declinatio æqua-<lb/># lis eſt complemento altitudinis poli ſupra illum circulum maximũ: <lb/># Vel cuius declinationis complementum æquale eſt altitudini poli <lb/># ſupra illum circulum maximum. # 23 <lb/>Circul{us} maxim{us} ſecat illum parallelum, cui{us} declinatio minor <lb/># eſt complemento altitudinis poli ſupra circulum illum maximum: <lb/># vel cuius declinationis complementum maius eſt altitudine poli ſu-<lb/># pra illum circulum maximum. # 24 <lb/>Circulus maximus parallelo illi neq; æquidistat, neq; eum tangit, <lb/># neq; ſecat, cuius declinatio maior eſt complemento altitudinis pol@ <lb/># ſupra illum circulum maximum: Vel cuius declinationis comple-<lb/># mentum min{us} eſt altitudine poli ſupra illum circulum maximum. <lb/># pag. # 26 <lb/>Conica ſectio, hoc est, Parabole, Hyperbole, vel Ellipſis, cuius in <lb/># dato cono diameter data ſit, quo pacto in plano deſcribatur. # a 26. <lb/># vſq; ad 28 <lb/>Circuli maximi ſecantes arcum diurnum Aequatoris, &amp; cuiuſuis <lb/># paralleli borealis in 12. partes æquales diuidunt quoq; arcum <lb/># diurnum paralleli auſtralis oppoſiti in 12. partes æquales. # 41 <lb/>Circuli tres maximi in ſphæra, quorum vnus quidem ſecet quem-<lb/># cunq; parallelum per polos, alĳ vero eundem tangant in punctis <lb/># æqualiter hinc inde remotis ab vtrouis punctorum, in quib{us} ab <lb/># altero maximo circulo ſecatur, habent vnam eandemq; ſectionem <lb/># communem. # 50 <lb/>Centrum horologĳ quid. # 77 <lb/>Circuls<unsure/> maximi, qui plani à Vertic ali declinantis inclinationem ad <lb/># Horizontem metitur, arcus inter Horizontem &amp; circulum horæ <lb/># 6. à mer. vel med. noc. poſitus quo pacto inueſtigetur. # 105 <lb/>Crepuſculi magnitudo quo modo inueſtigetur, Sole exiſtente inquo-<lb/># cunq; parallelo. # 118. 119. 122. &amp; 124 <lb/>Crepuſculum nullum fit, quando complementum altitudinis poli mi-<lb/># n{us} eſt declinatione borealis paralleli Solis. # 120 <lb/>Crepuſculum quantum ſit, dum parallelus auſtralis tot{us} ſub Hori-<lb/># zonte latet, &amp; quo modo inueniatur. # 121 <lb/>Crepuſculum quando nullum ſit, Sole exiſtente in auſtralib{us} ſignis, <lb/># &amp; quando continuum eſt, Sole exiſtente in æquinoctĳs. # 121 <lb/>Crepuſculum in ſphæra recta quo pacto inquiratur. # 123 <lb/>Crepuſcula duorum parallelorum oppoſitorum qua ratione vnico <lb/># labore inis<unsure/>eniantur. # 123 <lb/>Crepuſculum continuum in parallelo boreali quando. # 124 <lb/>Circulus quilibet maxim{us} per polos mundi ductus facit in horolo-<lb/># gio rectam lineam, cuius vna portio in centro horologii termina-<lb/># ta pertinet ad vnum ſemicirculum, &amp; altera ad alterum. # 147 <lb/>Cæli mediationes, cum initia ſignorum oriuntur, quo pacto inueſti-<lb/># gentur. # 181 <lb/>Circul{us} horæ 6. à mer. vel med. noc. Meridianus, atq; Aequator <lb/># ſe mutuo ſecant ad angulos rectos in omni climate. # 293 <lb/>Circuli maximi, quibus horologia irregularia æquidistant, quo mo-<lb/># do ſe habeant reſpectu Horizontis, Verticalis, ac Meridiani. # 293 <lb/>Circuli, quos præcipue in Analemmate Ptolemæ{us} cõſiderat, qui ſint, <lb/># &amp; quem illis motuum tribuat. # 528. &amp; 529 <lb/>Circunferentiæ ſex in ſex circulis, quos conſiderat Ptolæme{us} in <lb/># Analemmate, ſingulæ in ſingulis, obſeruandæ ſunt, &amp; earum prin <lb/># cipia vbi. # 529. &amp; 530 <lb/>Circunferentiarism in circulis, quos in Analemmate Ptolemæ{us} con <lb/># ſiderat, officia, # 530. &amp; 531 <lb/>Circunferentia horizontalis, deſcenſiua, Verticalis, horaria, meri-<lb/># diana, &amp; hectemoria quæ ſit. # 530 <lb/>Circunferentiæ pro conſtructione horologii horizontalis, Vertica-<lb/># lis, &amp; Meridiani, qua ratione ex Analemmate, Sole exiſtente in <lb/># Aequatore, vel quouis parallelo, tam in ſphæra recta, quàm obli-<lb/># qua, inueſtigetur. # à 532. vſque ad 541. &amp; 556 <lb/>Circunferentiæ eædem quo modo per ſinus, Solein quocunque paral <lb/># lelo exiſtente, ſupputentur tam in ſphæra obliqua, quàm recta. <lb/># à pag. # 545. vſque 548. &amp; 557. &amp; 558 <lb/>Circunferentiæ deſcenſiuæ, &amp; horizontales qua ratione in Ver-<lb/># ticali, Meridiano, circulo horæ ſextæ à mer. &amp; med. noc. &amp;
<pb file="0014" n="14" rhead="INDEX"/>
# Aequatore inueniãtur, tanquã in Horizõte. # à 560. vſq; ad 562 <lb/>Circunferentiæ horizontales in Aequatore, tanquam Horizonte, <lb/># pro horis inuent@æ ſecant Meridianum Analemmatis, Sole exiſten-<lb/># te in quouis parallelo, in partes æquales. # 562 <lb/>Circunferentiæ horizontales, deſcenſiuæque in planis declinanti-<lb/># bus, acſi eſſent Horizontes, quo pacto ex Analemmate, &amp; per ſi-<lb/># nus inuentantur. # 565. &amp; 567 <lb/>Circunferentiæ pro horis à mer. vel ab or. aut ab occ. in quolibet <lb/># parallelo inuentæ ſupra vnam faciem plani propoſiti ſunt etvam <lb/># eircunferentiæ pro horis à med. noc. vel ab occ. aut ab or. in oppo-<lb/># ſito parallelo ſupra alteram faciem plani oppoſitam. # 566 <lb/>Crucis, in qua horologium vniuerſale deſcribitur, cõſtructio. # 636 <lb/>Cylindrici horologii conuexi compoſitio. # 645 <lb/>Cylindrici horologii deſcriptio ex vmbra cadente in hor{as} horolo-<lb/># gii horizontalis, vel hemiſphærici concaui. # 647 <lb/>D <lb/>DIes ac nox cur ab Antiquis diuiſa ſit in 12. hor{as}. # 2. &amp; 6 <lb/>Declinans tam à meridie, quàm à borea in ortum vel occaſum <lb/># horologium quod. # 4 <lb/>Declinãs ab Horizõte horologiũ tã Superi{us}, quàm Inferi{us} quod. # 4 <lb/>Declinans ſimul &amp; inclinatũ horologium tam Superius, quàm Infe-<lb/># rius quod. # 4 <lb/>Diei varium initium apud vari{as} gentes. # 6. &amp; 7 <lb/>Declinationes par allelorum Solis per initia ſignorum, vel alia quæ-<lb/># uis puncta Eclipticæ ductorum, quo pacto in Analemmate Geome-<lb/># trice reperiantur. # ab 11. vſque ad 17 &amp; 652 <lb/>Declinationes omnium punctorum Eclipticæ quo pacto per ſin{us} ſup <lb/># putentur. # 15 <lb/>Diurn{us} arcus, nocturnusque; hora ortus atq; occaſ{us} Solis, ac tem <lb/># p{us} meridiet, qua ratione ex Analẽmate cognoſcantur. # 17. &amp; 18 <lb/>Declinatio cuiuſq; plani qua ratione per lineam meridianam, aut <lb/># per Analemma inquiratur, &amp; in quam partem planum declinet. <lb/># pag. # 79. &amp; 86 <lb/>Declinationis muri ad meridiem ſpectantis inuentio facilima in ipſo <lb/># meridie. # 88 <lb/>Declinatio paralleli, cui{us} arcus diurnus contineat propoſitum nu-<lb/># merum horarum, quo artificio per Analemma, aut per ſin{us} explo-<lb/># retur. # à 106. vſque ad 108 <lb/>Declinationes omnium arcuum diurnorum, qui contineant datum <lb/># horarum numerum, qua ratione ab Andrea Schonero inuenian-<lb/># tur. # 109. &amp; 553 <lb/>Diurnorum arcuum, qui datum horarum numerum contineant, de-<lb/># clinationes qua arte inquirantur. # à 106. vſq; ad 109. &amp; 653 <lb/>Depreſsio meridiana Solis quid, &amp; quo pacto reperiatur. # 121. <lb/># &amp; 122. <lb/>Depreſsio meridiana Selis in quouis parallelo æqualis eſt altitudini <lb/># meridianæ Solis in oppoſito parallelo. # 122 <lb/>Diurn{us} arc{us} quomodo ſe habeat, quando cõplementum altitudi-<lb/># nis poli mai{us} non fuerit declinatione propoſiti paralleli. # 123 <lb/>Diſtantia Solis à meridie, quoad grad{us}, quomodo ex data hora co-<lb/># gnoſcatur. # 125 <lb/>Dierum feſtorum in horologio deſcriptio. # 167. &amp; 580 <lb/>Diurni arc{us} in horologio horizontali quo pacto deſcribantur. <lb/># pag. # 169. &amp; 580 <lb/>Diurnorum arcuum in horologio deſcriptorum vſus eſt, vt cognoſca <lb/># mus, quot hor{as} dies quilibet complectatur. # 170 <lb/>Distantia Verticalis quid ſit, &amp; quo pacto ex Verticalib{us} circulis <lb/>in horologio deſcriptis cognoſcatur. # 171 <lb/>Domorum cæleſtium tam ſecundũ Ioan. Regiom. quàm ſecundũ Cam <lb/># panum in horologio horizontali deſcriptio. # 175. &amp; 176 <lb/>Domorum cælestium lineæ indicant initia domorum cæleſtiũ. # 177 <lb/>Domorum cæleſtium in horologio deſcriptarum vſ{us} eſt, vt diſcam{us}, <lb/># quanam in domo cælesti verſetur Sol. # 177 <lb/>Differentia aſcenſionis rectæ &amp; obliquæ cuiuſuis puncti Eclipticæ, <lb/># ad quamcunque latitudinem loci. # 191 <lb/>Differentiæ aſcenſionales quadrantis Eclipticæ ab Ariete vſque ad <lb/># Cancrum æquales ſunt differentĳs aſcenſionalibus punctorum in <lb/># alĳs trib{us} quadrantibus Eclipticæ. # 191 <lb/>Declinans horologium, autinclinatum in vna facie plani deſcriptũ <lb/># quo pacto exhibeat aliud in oppoſita facie delineandum. # 209 <lb/>Diurni arcus horologii auſtralis mutantur in boreali horologio in <lb/># arcus diurnos oppoſitos. # 214 <lb/>Diurnorum arcuum in Verticali horologio deſcriptio. # 222. &amp; 588 <lb/>Domorum cælestium deſcriptio in horologio Verticalitam ſecundũ <lb/># Ioan. Regiom. quàm ſecundum Campanum. # 226 <lb/>Diurnus aut nocturnus arcus horarum 24. qua in regione ſit in Ver <lb/># ticali horologio Ellipſis, Hyperbole, aut parabole. # 233 <lb/>Diurnorum arcuũ in Meridiano horologio deſcriptio. # 243. &amp; 593 <lb/>Domorum cæleſtium deſcriptio in Meridiano horologio tam ſecun-<lb/># dum Ioan. Regiom. quàm ſecundum Campanum. # 247. &amp; 248 <lb/>Diurnorum arcuum deſcriptio in horologio Polari. # 260. &amp; 596 <lb/>Domorum cæleſtium in Polari horologio tam ſecundum Ioan. Re-<lb/># giom. quàm ſecundum Campanum de ſcriptio. # 265. &amp; 266 <lb/>Diurnorũ arcuũ in Aequinoctiali horologio deſcriptio. # 277. &amp; 598 <lb/>Domorum cælestium in Aequinoctiali horologio deſcriptio tam ſe-<lb/># cundum Ioan. Region. quàm ſecundum Campanum. # 282. &amp; 283 <lb/>Declinantis à Verticali horologii Aſtronomici constructio. <lb/># pag. # à 294. vſque ad 301 <lb/>Declinans à Verticali horologium Aſtronomicum quo pacto in plano<unsure/> <lb/># ſtabili deſcribatur. # 303 <lb/>Declinantis à Verticali horologii deſcriptio commodiſsima pro ho-<lb/># ris, quæ vix, aut valde procul à linea ſtyli æquinoctialem lineam <lb/># ſecant. # 303 <lb/>Declinantis à Verticali horologii Aſtronomici ad datum stylum, <lb/># cuius etiam locus datus ſit, deſcriptio. # 304. &amp; a 601. vſq; ad 603 <lb/>Declinantis à Verticali horologii Aſtronomici deſcriptio noua ac <lb/># pulcherrima, beneficio Ellipſis ſine punctis in linea Aequinoctiali <lb/># inuentis, quæ commodißima eſt pro horis ducendis, quæ vix Aequ@ <lb/># noctialem lineam vel valde procul à linea styli interſecant. # 306 <lb/>Declinans à Verticali horologium Aſtronomicum, quod parum à <lb/># Meridiano abeſt, quo pacto deſcribatur, etiamſi centrum horologii <lb/># non habeatur. # 307 <lb/>Declinans à Borea in ortum horologium Astronomicum conficitur, <lb/># ſi pars ſuperior horologii à Meridie declinantis fiat inferior: De-<lb/># clinans item à Borea in occaſum fit ex Declinãte à meridie in occa <lb/># ſum, ſi pars ſuperior mutetur in inferiorem. # 311 <lb/>Declinans horologium tam Aſtronomicum, quàm Italicum &amp; Baby <lb/># lonicum à Borea in ortum vergens, &amp; à meridie in occaſum, &amp; à <lb/># Borea in occaſum, qua ratione ex horologio, quod à meridie decli-<lb/># nat in ortum, conficiatur. # 312. &amp; 331 <lb/>Declinans planum tam à meridie, quàm à borea quale longiore tem <lb/># pore illuminetur mane à Sole, quàm Veſperi, &amp; contra. # 317 <lb/>Diurnorum arcuum in horologio declinante à Verticali deſcriptio. <lb/># pag. # 320. &amp; 608 <lb/>Domorum cæleſtium in horologio declinante à Verticali deſcriptio <lb/># tam ſecundum Ioan. Regiom. quàm ſecundum Campanum. <lb/># pag. # 324. &amp; 325 <lb/>Declinantis à Verticali horologĳ Italici deſcriptio. # 329. 330. <lb/># 608. &amp; 609. <lb/>Declinantis à Verticali horologii Babylonici deſcriptio # 331. 608. <lb/># &amp; 609 <lb/>Declinantis à Verticali horologii Antiqui conſtructio. # 332. 334. <lb/># 609. &amp; 610 <lb/>Declinãtis ab Horizonte Horologii Aſtronomici deſcriptio. # à 334. <lb/># vſque ad 337 <lb/>Declinans ab Horizonte horologium Astronomicum conſtructum <lb/># erit, ſi deſcribatur declinans à Verticali pro ea latitudine loci, <lb/># quæ cum propoſita latitudine, pro qua horologium ab Horizonte <lb/># declinans conſtituitur, gradus 90. conficit. # 335 <lb/>Declinans ab Horizonte horologium Aſtronomicum qua ratione ſit <lb/># in plano ſtabili deſcribendum. # 338 <lb/>Declinans ab Horizonte horologium Aſtronomicum ad occaſum <lb/># ſpectans qua ratione ſit permutandum, vt fiat aliud ſpectans ad <lb/># ortum, &amp; contra. # 338. &amp; 613 <lb/>Declinantis ab Horizonte horologii deſcriptio commodißima pro ho <lb/># ris, quæ vix, aut valde procul à linea styli æquinoctialem lineam <lb/># ſecant. # 339 <lb/>Declinantis ab Horizonte horologĳ Aſtronomici ad datum ſtylum, <lb/># cuius etiam loc{us} dat{us} ſit, conſtructio. # 339. &amp; 611 <lb/>Declinantis ab Horizonte horologĳ Aſtronomici deſcriptio noua ac <lb/># pulcherrima, beneficio Ellipſis, ſine punctis in linea æquinoctiali in-<lb/># uentis, quæ commodiſsima eſt pro horis ducendis, quæ vix lineam <lb/># æquinoctialem, vel valde procul à linea ſtyli ſecant. # 341 <lb/>Diurnorum arcuum in horologio declinante ab Horizonte deſcri-<lb/># ptio. # 343. &amp; 612 <lb/>Domorum cæleſtium in horologio declinante ab Horizonte deſcri-<lb/># ptio tam ſecundum Ioan Regiom. quàm ſecunàum Campanũ. # 348 <lb/>Declinantis ab Horizonte horologii Italici deſcriptio. # 351. <lb/># 352. &amp; 613 <lb/>Declinantis ab Horizonte horologii Babylonici deſcriptio. <lb/># pag. # 352. &amp; 613 <lb/>Declinãtis ab Horizõte horologii Antiq{ui} deſcriptio. # 352. &amp; 614
<pb file="0015" n="15" rhead="INDEX."/>
Diurnorum arcuum in horologio ad Horizontem inclinato deſcri-<lb/># ptio. # 360. &amp; 617 <lb/>Domorũ cæleſtiũ in horologio ad Horizontẽ inclinato deſcriptio tam <lb/># ſecundum Ioan. Regiom. quàm ſecunaũ Campanum. # 363. &amp; 364 <lb/>Declinantis ſimul &amp; inclinati horologĳ Aſtronomici deſcriptio. <lb/># à pag. # 371. vſque ad 387 <lb/>Declinans ſimul &amp; inclinatum horologium Atronomicum qua ra-<lb/># tione in plano ſtabili deſcribatur. # 388 <lb/>Declinans ſimul &amp; inclinatum horologium Aſtronomicum quo pa-<lb/># cto ad datum ſtylum, cuius etiam locus datus ſit, deſcribaiur. # 388. <lb/># &amp; à 620. vſque ad 624 <lb/>Declinantis ſimul &amp; inclinati horologĳ deſcriptio commodiſsima <lb/># pro horis ducendis, quæ vix, aut valde procul lineam æquinoctia-<lb/># lem ſecant. # 389 <lb/>Declinantis ſimul &amp; inclinati horologĳ Aſtronomici deſcriptio no-<lb/># ua ac pulcherrima, beneficio Ellipſis, quæ commodiſsima est pro ho-<lb/># ris ducendis, quæ vix lineam æquinoctialem, aut valde procul à li-<lb/># nea ſtyli interſecant. # 394 <lb/>Diurnorum arcuum in horologio declinante ſimul &amp; inclinato de-<lb/># ſcriptio. # 399. &amp; 625 <lb/>Domorum cæleſtium in horologio declinante ſimul &amp; inclinato de-<lb/># ſcriptio tam ſecundum Ioan. Regiom. quam ſecundum Campa-<lb/># num. # 406 <lb/>Declinantis ſimul &amp; inclinati horologĳ Italici deſcriptio. # 411. 412 <lb/># 628. &amp; 629. <lb/>Declinantis ſimul &amp; inclinati horologĳ Babylonici constructio. # 413 <lb/># 628. &amp; 629 <lb/>Declinantis ſimul &amp; inclinati horologĳ Antiqui compoſitio. # 413. <lb/>&amp; 629 <lb/>Declinantia à Vertic ali horologia in ſphæra recta, cũ omnibus alĳs, <lb/># quæ in horologĳs ſphæræ obliquæ d@ſcripta ſunt, qua ratione de-<lb/># ſcribantur. # 419 <lb/>Declinans à Verticali horologium Aſtronomicũ in ſphæra recta quo <lb/># modo ad datum ſtylum, cuius etiã locus datus ſit, deſcribatur. # 420 <lb/>Declinantia ab Horizonte horologia in ſphæra recta cum omnibus <lb/># alĳs, quæ in horologĳs ſphæræ obliquæ deſcripta ſunt, qua ratione <lb/># delineentur. # 421 <lb/>Declinantis ab Horizonte horologĳ Aſtronomici in ſphæra recta ad <lb/># datum ſtylum, cuius etiam locus datus ſit, deſcriptio. # 422 <lb/>Declinantia ſimul &amp; inclinata horologia in ſphæra recta, cum om-<lb/># nibus alĳs, quæ in horologĳs ſphæræ obliquæ deſcripta ſunt, quo <lb/># pacto conſtruantur. # 424 <lb/>Diſtantia Solis à Meridiano proprio cuius que circuli maximi quo-<lb/># ad horas, qua arte exploretur. # 447. &amp; 462 <lb/>Deſcenſiuus circulus quid apud Ptolemæum. # 529 <lb/>Deſcenſiua circumferentia quæ. # 530 <lb/>Deſcenſiuæ circumferentiæ &amp; horizontales neceſſariæ ſunt ad con-<lb/># ſtructionem horologĳ horizontalis. # 531 <lb/>Deſcenſiuarum, &amp; horizontalium circunferentiarum inuentio in <lb/># Verticali, Meridiano, circulo horæ 6. à mer. vel med. noc. &amp; Ae-<lb/># quatore, tanquam in Horizonte. # à 560. vſq; ad 562 <lb/>Deſcenſiua circunferentia in Aequatore, tanquam Horizonte, vna <lb/># eademq; ſemper eſt pro ſingulis horis eiuſdem paralleli. # 562 <lb/>Declinans, au@ inclinatum horologium, qua ratione ex circumfe-<lb/># rentĳs horizontalibus, deſcenſiuisq́; proprĳs deſcribatur. # à 565 <lb/># vſque ad 568 <lb/>Dioptræ constructio, per quam ſine acu Magnete illita horologium <lb/># Aequinoctiale vniuerſale proprium ſitum habeat, &amp; hora indice-<lb/># tur ſine axe, ſeu ſtylo. # 635 <lb/>E <lb/>ELlipſis quibus in horologĳs, Sole quemcumq; parallelum poſsi-<lb/># dente, fiat. # 25. &amp; 26 <lb/>Ellipſis, cuius in dato cono diameter data ſit, quo pacto in plano <lb/># deſcribatur. # a 26. vſque ad 28 <lb/>Ellipſis, cuius diameter tranſuerſa in cono data ſit, latus rectũ quo <lb/># modo reperiatur. # 33 <lb/>Ellipſis, cuius axis tranſuerſus datus ſit, qua ratione in plano de-<lb/># ſcribatur. # 34 <lb/>Ellipſis qualiſcunq; quo pacto in plano deſcribatur, non habita ra-<lb/># tione coni, ex quo oritur. # 35 <lb/>Ellipſis qualiſcunq; per filum deſcriptio, etiam ſi eius longitudo, atq; <lb/># latitudo detur. # 35 <lb/>Ellipſis circa datum axem maiorem, &amp; per datum punctum deſcri-<lb/># ptio. # 36 <lb/>Eclipticæ quatuor arcus inter puncta æquinoctiorum, &amp; ſolstitio-<lb/># rum quadrantes ſunt. # 50 <lb/>Ellipſis fit à lineis perpendicularibus cadentibus à circunferentia <lb/># maximi circuli in ſphæra in planum alterius circuli maximi, ad <lb/># quem ille inclinatus eſt. # 89 <lb/>Ellipſis, quæ fit à lineis perpendicularibus cadentibus à circunf@-<lb/># rentia circuli inclinati in ſphæra ad alium circulum, minor dia-<lb/># meter quo modo inueniatur. # 91 <lb/>Ellipſis, cuius diametri datæ ſint, quo modo in plano deſcribatur. # 91. <lb/># &amp; 92. <lb/>Ellipſis fit à plano ſecante cylindrũ rectum, quod neq; per eius axẽ <lb/># ducitur, neq; axi æquidiſtat. # 153 <lb/>Eclipticæ puncta in circulo horæ 6 à mer. vel med. noc. vel in quo-<lb/># uis alio circulo horario, à mer. vel med. noc. collocata, cum ſignorũ <lb/># initia oriuntur, quo pacto reperiantur. # 182. &amp; 183 <lb/>Ellipſis quo pacto perficiatur tota ex altera eius medietate deſcri-<lb/># pta. # 281 <lb/>F <lb/>FIgura radiorum zodiaci, ex qua arcus ſignorum in horologio h@ <lb/># rizontali deſcribuntur, quid ſit, &amp; qua ratione conſtruatur. <lb/># pag. # 161. &amp; 577 <lb/>Festi dies quo pacto in horologio depingantur. # 167. &amp; 580 <lb/>Figuræ, inſtar inſtrumenti cuiuſdam, ex Andrea Schonero constru-<lb/># ctio, quam nos in duas partiti ſumus, vt inde ſigna aſcendentia in <lb/># horologĳs deſcribantur. # 186 <lb/>Figuræ radiorum zodiaci pro arcubus ſignorum in Verticali horolo-<lb/># gio deſcribendis conſtructio. # 215. 586. &amp; 587 <lb/>Figuræ radiorum amplitudinum ortiuarum, occiduarumue conſtru-<lb/># ctio. # 229 <lb/>Federici Commandini error in lineis horarum 10. &amp; 11. ducendis <lb/># in horologio boreali Italico. # 236 <lb/>Figuræ radiorum zodiaci pro arcubus ſignorum in horologio Meri-<lb/># diano, Polari, &amp; Aequinoctiali deline andis conſtructio. # 242. 259 <lb/># 274. &amp; 592 <lb/>Figuræ radiorum zodiaci pro arcubus ſignorum in horologio à Ver-<lb/># ticali declinante deſcribendis conſtructio. # 312. 313. 604. &amp; 605 <lb/>Figuræ radiorum zodiaci pro arcubus ſignorum in horologio decli-<lb/># nante ab Horizonte deſeribendis constructio. # 342 <lb/>Figuræ radiorũ zodiaci pro arcubus ſignorum in horologio ad Ho-<lb/># rizontem inclinato deſcribendis conſtructio. # 358 <lb/>Figuræ radiorum zodiaci pro arcubus ſignorum im horologio decli-<lb/># nante ſimul &amp; inclinato deſcribendis conſtructio. # 398. &amp; 627 <lb/>G <lb/>GNomonis vertex in quocunq; horologio centrum mundi eſſe in-<lb/># telligitur. # 19 <lb/>Gnomonis vmbra, &amp; radius Solis proĳcitur in communẽ ſectionem <lb/># plani horologĳ, &amp; circuli maximi, in quo Sol exiſtit. # 42 <lb/>Gnomonis vmbra in æquinoctĳs deſcribit lineam æquinoctialem re-<lb/># ctam in quocunq; horologio. # 43 <lb/>Gnomonis vmbra, &amp; radius Solis extra æquinoctia proĳcitur in ſe <lb/># ctionem conicam, quæ communis ſectio est plani horologĳ, &amp; coni-<lb/># cæ ſuperficiei, cuius baſis eſt parallelus parallelo Solis oppoſitus. # 44 <lb/>Gnomonis vmbra extra æquinoctia deſcribit conicam ſectionem in <lb/># horologio. # 44 <lb/>Gnomonica hæc quid in ſingulis horologĳs planis contineat. # 141 <lb/>Gnomonis locus in horologio quocunq; quando extra tropicos, &amp; <lb/># quando in tropicum præciſe, aut intra tropicos, aut in ipſam lineã <lb/># æquinoctialem cadat. # 429 <lb/>Gnomon cuiuſcunq; horologĳ qua ratione proprio in loco ad Hori-<lb/># zontem rectus collocetur, eiuſq; vertex in propriam ſedem, ſi quan <lb/># do ab ea deflexerit, reſtituatur. # 431 <lb/>Gnomon ad planum quodcunq; rectus, medio loco proportionalis eſt <lb/># inter vmbram rectam, &amp; verſam. # 475 <lb/>Gnomon, linea meridiana, &amp; æquinoctialis quid ſecundum Ptole-<lb/># mæum. # 528 <lb/>H <lb/>HOrologium quid. # 1 <lb/>Hora quid, &amp; vnde dictæ ſint horæ. # 2 <lb/>Horologiorum neceſsitas, eorumq́; varia genera. # 2 <lb/>Horologium Sciothericum quid, eiusq́; varia genera. # 3 <lb/>Horologiorum Sciothericorum, ſiue Solarium in plana ſuperficie de-<lb/># ſcriptorum ſeptemdecim genera, &amp; quæ. # 3. &amp; 4 <lb/>Horizontale horologium quod. # 3 <lb/>Horologia in plano deſcripta æquidi ſtant circulis maximis, à qui-<lb/># bus nomen accipiunt. # 5 <lb/>Horologiorũ Solariũ diuiſio ex tẽpore, quo horas monſtrant. # 5. &amp; 6 <lb/>Horarum quatuor genera. # 6 <lb/>Horæinæquales quæ, &amp; cur dictæ ſint inæquales. # 6
<pb file="0016" n="16" rhead="INDEX"/>
Horæ æqualis, aut æquinoctialis quid, &amp; cur ſic dicatur. # 6 <lb/>Horæ Babylonica quæ. # 6 <lb/>Horæ Italicæ quæ. # 6 <lb/>Horæ Aſtronomicæ quæ. # 6 <lb/>Horæ vulgares, ſiue cõmunes quomodo ab Aſtronomicis differant. # 7 <lb/>Horologiorũ Solariũ quatuor genera ex varietate horarũ orta. # 7 <lb/>Horologiorum variorum varĳ inuentores, &amp; ſcriptores. # 7. &amp; 8 <lb/>Horologium quodcunque tanto ſpatio à centre mnndi abeſt, quanta <lb/># eſt ſtyli longitudo. # 19 <lb/>Horologiũ quodcunq; nomen a@cipit à circulo maximo, cui æquidi@ <lb/># ſtat. # 19 <lb/>Hyperbolæ oppoſitæ &amp; æquales quib{us} in horologĳs, Sole in quocun@ <lb/># que parallelo exiſtente, fiant. # 23. &amp; 24 <lb/>Hyperbole, cuius in dato cono diameter data ſit, quo pacto in plano <lb/># deſcribatur. # a<unsure/> 26. vſque ad 28 <lb/>Hyperbolarum oppoſitarum, quarum diameter tranſuerſa in cono <lb/># data ſit, lat{us} rectum qua ratione reperiatur. # 31 <lb/>Hyperbolæ oppoſitæ, quarum latus rectum datum ſit, quo pacto in <lb/># plano deſcribantur. # 32 <lb/>Hyperbolæ oppoſitæ qualeſcunque quomodo in plano deſcribantur, <lb/># non habita ratione coni, ex quo oriuntur. # 35 <lb/>Horarĳ circuli a mer. velmed. noc. qui ſint. # 37 <lb/>Horarĳ circuli ab or. vel occ. qui ſint, &amp; vbi polos habeant. # 39 <lb/>Horarum inæqualium circuli qui ſint. # 41 <lb/>Horologĳ Solaris in plano deſcriptio quid ſit. # 43 <lb/>Horarii circuli a mer. vel med. noc. ſecant conic{as} ſuperficies, quarũ <lb/># baſes ſunt duo paralleli omnium ſemper apparentium ſemper laten <lb/># tium maximi, per lineas rect{as}, in quib{us} eaſdem tangunt circuli <lb/># horarum ab or. vel occ. # 44. &amp; 45 <lb/>Horariæ lineæ a mer. vel med. noc. ſecant ſectiones conicas, quæ cõ@ <lb/># munes ſectiones ſunt plani horologii, &amp; conicarum ſuperficierum, <lb/># quarũ baſes ſunt duo paralleli omniũ ſemper apparenti<unsure/>ũ, ſemperq; <lb/># latentium maximi, in punctis, in quibus eaſdem lineæ horarum ab <lb/># or. vel occ. tangunt. # 45 <lb/>Horariæ lineæ ab or. vel occ. quarum circuli tangunt parallelum <lb/># ſemper apparentiũ maximũ in eiſdem punctis, in quibus a circulo <lb/># alicuius horæ a mer. vel med. noc. qui<unsure/> horologio æquidiſtet, ſeca@ <lb/># tur, nõ conueniunt cũ ſectionibus conici<unsure/>s, quas in ſuperficiebus co@ <lb/># nicis baſes habẽtibus duos parallelos ſemper apparentiũ, ſemperq; <lb/># latentium maximos, facit planum horologĳ: ſemper tamen longius <lb/># productæ propinquiores fiunt conicis ſectionibus. # 46 <lb/>Horarum 12. &amp; 24. ab or. vel occ. lineæ no coeunt in horologio Me <lb/># ridiano cum ſectionibus conicis factis in conicis ſuperficiebus, qua@ <lb/># rum baſes ſunt paralleliſemper apparentium, ſemperq; latentium <lb/># maximi. # 49 <lb/>Horarum 6. &amp; 18. ab or. vel occ. lineæ non coeunt in horologio Po@ <lb/># lari cum ſectionibus conicis factis in conicis ſuperſiciebus, quarum <lb/># baſes ſunt paralleli ſemꝑ apparentiũ, ſemperq; latentiũ maximi. # 49 <lb/>Horizontis quatuor arcus inter Aequatorem, &amp; Meridianum <lb/># quadrantes ſunt. # 50 <lb/>Horariorum circulorum ab or. vel occ. arcus inter Aequatorem, <lb/># &amp; puncta, in quibus parallelos ſemper apparentium, ſemperque la <lb/># tentium maximos tangunt, quadrantes ſunt. # 50 <lb/>Horaria linea quæcunque à mer. vel med. noc. &amp; duæ lineæ horarũ <lb/># ab or. vel occ. ab illa æqualiter diſtantium in maximo parallelo@ <lb/># rum ſemper apparentium ſe mutuo interſecant in vno eodemque <lb/># puncto. # 55 &amp; 60 <lb/>Horarĳ duo circuli ab or. vel occ. tangẽtes maximũ parallelorũ ſem@ <lb/># per apparentiũ in duobus punctis quibuſcunque, &amp; circulus hora@ <lb/># rius a mer. vel med. noc. ſecans eundem parallelum in puncto æqua <lb/># liter à punctis contactuũ diſtante, ſe mutuo ſecant in vno eodemq; <lb/># pũcto, habentq; vnã eandemq; rectã lineã pro comuni ſectione. # 60 <lb/>Horariæ lineæ tam à mer. vel med. noc. quam ab ortu vel occ. quãdo <lb/># aut quib{us} in horologĳs ſe mutuo interſecent. # 77 <lb/>Horariæ lineæ tam a mer. vel med. noc. quam ab or. vel occ. quan-<unsure/> <lb/># do aut in quib{us} horogĳs ſint parallele. # 77. &amp; 78 <lb/>Hora quo pacto per Analemma, ſolis declinatione, &amp; eiuſdem alti-<lb/># tudine ſupra Horizontem cognita, inquir atur # 85 <lb/>Hora quo modo ex altitudine ſolis ſupra Horizontẽ cognita ſuppu <lb/># tetur tam in ſphæra obliqua, quam in recta. # à 127. vſq; ad 140 <lb/>Hora quota ſit, cum ſol in Verticali circulo exiſtit, qua ratione ex=<unsure/> <lb/># ploretu<unsure/>r<unsure/> # 128. &amp; 137 <lb/>Hora ex altitudine ſolis cognita quo modo exploretur, quãdo paral= <lb/># lel{us} borealis totus extat ſupra Horizontem. # 139 <lb/>Horologia plana, quæ in hoc libro deſcribũtur, quid cõtineant. # 141 <lb/>Horizontalis horologii Aſtronomici deſcriptio. # 143 <lb/>Horizontalis horologii Aſtronomici deſcriptio cõmodißima pro ho-<lb/># ris delineandis, quæ propinquæ ſunt horæ 6. a mer. vel med. noc. <lb/># &amp; vix æquinoctialem lineam ſecant. # 145 <lb/>Horariæ lineæ quæuis a mer. vltra centrum horologii producta, indi <lb/># cat eiuſdem numeri horam a med. noc. &amp; contra. # 147 <lb/>Horizontalis horologii Aſtronomici deſcriptio in plano ſtabili, quod <lb/># Horizonti æquidiſtet. # 148 <lb/>Horizontalis horologĳ Aſtronomici deſcriptio ad datum ſtylum, cu <lb/># ius etiam locus datus ſit. # 148. 575. &amp; 576 <lb/>Horizontalis horologii Aſtronomici deſcriptio noua ac pulcherri-<lb/># ma, beneficio Ellipſis, ſine punctis in linea æquinoctiali inuentis, <lb/># quæ commodiſsima eſt pro horis ducendis, quæ vix æquinoctialẽ <lb/># lineam, vel certe valde procul a linea meridiana interſecant. <lb/># a 149. vſque ad 153. <lb/>Horizontalis horologii Aſtronomici deſcriptio cur difficilior red-<lb/># datur, quando poli altitudo vel perexigua eſt, vel nimis magna, &amp; <lb/># quo pacto tunc deſcribatur, etiamſi centrum horologii non ha-<lb/># beatur. # 153 &amp; 154 <lb/>Hyperbolæ ſignorum auſtralium quomodo ex hyperbolis borealiũ ſi-<lb/># gnorum deſcribantur. # 163 <lb/>Hemiſphærii Superi quatuor quadrantes quiſint in horologio quo-<lb/># libet. # 171 <lb/>Horariæ lineæ terminos, ſeu fines horarum ſignificant. # 177 <lb/>Hora, qua quodlibet ſignum zodiaci ſupra Horizontem incipit a-<lb/># ſcendere, quo pacto inquiratur. # 177 <lb/>Horizontalis horologii Italici conſtructio. 192. 196. 197. &amp; a 581 <lb/># vſque ad 584 <lb/>Horæ 12. ab or. vel occ. linea quo pacto in horologio Horizontali <lb/># ducenda ſit. # 197 <lb/>Hora quælibet ab occ. producta vltra punctum, vbi arcum diurnũ, <lb/># nocturnum ve horarum 24. tangit, pertinet ad eandem numero ho-<lb/># ram ab or. &amp; contra. # 198 <lb/>Horizontalis horologii Babylonici deſcriptio. 199. 200. &amp; a 581 <lb/># vſque ad 584 <lb/>Horizontalis horologii Antiqui deſcriptio. # 201. 203. 584. &amp; 585 <lb/>Horæ inæquales, planetariæ dictæ, quarum nimirum ſingulæ quin-<lb/># denis gradibus Eclipticæ reſpõdent, quo pacto deprehendãtur. # 203 <lb/>Horizontale horologium Astronomicum ad quamcunque latitudi-<lb/># nem loci conſtructum Verticale eſt in regione, cuius latitudo com-<lb/># plementum eſt prioris latitudinis. # 211 <lb/>Horizontalis linea quid, &amp; quomodo in Verticali horologio duca-<lb/># tur, eiusque vſus. # 213. 214. 215. &amp; 587 <lb/>Horizontalis linea in omni horologio aufert portionem ſuperiorẽ, <lb/># quæ exhibet horologium in facie horologii oppoſita collocandum, ſi <lb/># prius ſuperior pars fiat inferior, &amp; quæ poſt hanc inuerſionem no-<lb/># bis ad horologium conuerſis dextra est, fiat ſiniſtra, &amp; contra. <lb/># pag. # 218. &amp; 537 <lb/>Horæ 12 ab or. vel occ. linea quo pacto in horologio Verticali de-<lb/># ſcribatur. # 233 <lb/>Horariarum linearum ab or. vel occ. vltra horizontalem lineam <lb/># productarum quæ ad horas ab or. &amp; quæ ad horas ab occ. perti-<lb/># neant, qua ratione cognoſcatur. # 235 <lb/>Horizontalis linea in horologio Meridiano quæ. # 237 <lb/>Horæ 12. ab or. vel occ. linea quo pacto in Meridiano horologio du-<lb/># catur. # 254 <lb/>Horizontalis lineæ in horologio Polari deſcriptio. # 259. &amp; 596 <lb/>Horæ 12. ab or. vel occ. linea qua ratione in horologio Polari de-<lb/># ſcribatur. # 271 <lb/>Horariæ lineæ ab or. vel occ. in latitudine minore, quàm grad. 66. <lb/># Min. 30. ſecant tropicos; in latitudine vero grad. 66. Min. 30. <lb/># tangunt tropicos; in maioredeniq; latitudine ad tropicos non per-<lb/># ueniunt, etiamſi in infinitũ producãtur, ſed tangunt alios paralle <lb/># los inter tropicos, &amp; æquinoctialem line am tam in horologio po-<lb/># lari, quàm in Meridiano. # 272. &amp; 429 <lb/>Horizontalis lineæ in horologio Aequînoct. deſcriptio. 276. et 598 <lb/>Horæ 12. abor. vel occ. in horologio Aequinoctiali delineatio. <lb/># pag. # 288. &amp; 289 <lb/>Horologia regularia, &amp; irregularia quæ, &amp; regularia quibus cæ-<lb/># li punctis opponantur. # 293 <lb/>Horizon, Verticalis, ac Meridianus in omni climate ſe mutuo ſecãt <lb/># ad angulos rectos. # 293. &amp; 528 <lb/>Horæ a mer. &amp; med. noc. quo pacto in horologio declinante à Verti-<lb/># cali deſcribantur beneficio horologii Horizontalis. # 299. &amp; 602 <lb/>Horizõtalis lineæ in horologio declinãte a Verticali deſcriptio. # 317 <lb/>Horæ amer. &amp; med. noc. qua rationein horologio declina@te ab Ho <lb/># rizonte ex horizontali horologio deſcribantur. # 336
<pb file="0017" n="17" rhead="INDEX"/>
Horizontalis lineæ deſcriptio in horologio declinante ab Horizon-<lb/># te. # 342. 343. &amp; 612 <lb/>Horizontalis lineæ deſcriptio in horologio ad Horizontem incli-<lb/># nato. # 359. 369. &amp; 617 <lb/>Horarum à mer. vel med. noc. in horologio declinante ſimul &amp; in-<lb/># clinato ex horologio hori zontali deſcriptio. # 381 <lb/>Horizontalis lineæ deſcriptio in horologio declinante ſimul &amp; incli <lb/># nato. # 398. &amp; 627 <lb/>Hora, qua Sol in Aequatore exiſtens ad quemcunque Verticalem <lb/># perueniat, quo pacto inueniatur. # 402 <lb/>Hora, qua Sol in Aequatore exiſtens ad propoſitum circulum domus <lb/># cælestis perueniat, qua via deprehendatur. # 408 <lb/>Horologia in ſphæra obliquißima, vbi polus arcticus ſupra Horizon <lb/># tem eleuatur grad, 90 qua ratione conficiantur. # 426. &amp; 427 <lb/>Horologia in ſphæra obliqua, vbi polus antarcticus ſupra Horizon-<lb/># tem atiollitur, qua ratione deſcribantur. # 427 <lb/>Horologia pro ſphæra obliqua boreali conſtructa, qua ratione ſphæ-<lb/># ræ obliquæ auſt@ali ſint accõmodanda. # 427 &amp; 428 <lb/>Horæ ab or. &amp; occ. quam diuerſitatem habeant in diuerſis latitu-<lb/># dinibus. # 429 <lb/>Horarum ab or. &amp; occ tangentiũ parallelum aliquem quænam ſeg-<lb/># menta ad hor{as} ab occ. &amp; quæ ad hor{as} ab or pertineant. # 429 <lb/>Horologium datum vnà cum ſtylo, eiusque loco, ad quam poli altitu <lb/># dinem fabricatum ſit, &amp; quam declinationem habeat à Verticali, <lb/># &amp; inclinationem ad Horizontem, ſi declinans eſt, aut inclinatum, <lb/># necnon quanta ſit altitudo poli ſupra ipſum planum declinans aut <lb/># inclinatum, quo pacto cognoſcatur: Et contra ſi detur horologiũ, <lb/># vna cum altitudine poli, ad quam conſtructum eſt, necnon inclina <lb/># tione eius ad Horizontem, ſi inclinatum eſt, qua ratione longitu-<lb/># do styli, eiuſq; loc{us} inquiratur, vna cum declinatione à Vertica-<lb/># li, ſi horologium declinans eſt, at que altitudo poli ſupra ipſum pla-<lb/># num declinans inclinatumve. # à 433. vſque ad 441 <lb/>Horologium propoſitum quo modo ad maiorem minoremve formam <lb/># pro data ſtyli longitudine redigatur. # à 442. vſque ad 446 <lb/>Hora propoſita, pro qua altitudo Solis inueſtigatur, an cadat in fa-<lb/># ciem plani dati propoſitã, an in alterã, quomodo cognoſcatur. # 449 <lb/>Horæ cadentes ſupra datam faciem maximi circuli propoſiti quo pa <lb/># cto cognoſcantur. # à 451. vſque ad 458. &amp; 564 <lb/>Hora, qua incipit aut deſinit à Sole illuminari facies propoſita maxi <lb/># mi circuli, quo pacto reperiatur. # 452. 453 &amp; 456 <lb/>Horarĳ arc{us} qui ſint, &amp; quo pacto in quolibet plano inueſtigen-<lb/># tur. # 488. &amp; 489 <lb/>Horarii arcus omnium Horizontum qua ratione ſint etiam arcus <lb/># horarii omnium Verticalium proprie dictorum. # 489 <lb/>Horologiorum omnium conſtructio ex tabulis latitudinum, longitu <lb/># dinumque vmbrarum, vel ex tabulis arcuum horariorum. # à 490 <lb/># vſque ad 529 <lb/>Horarum à mer. &amp; med. noc. per arcus horarios deſcriptio expedi-<lb/># tißima eſt. # 496 <lb/>Horizon mobilis quid apud Ptolemæum. # 529 <lb/>Hectemorion circulus quid apud Ptolemæum. # 529 <lb/>Horari{us} circulus quid apud Ptolemæum. # 529 <lb/>Horizontalis circunferentia quæ. # 530 <lb/>Horaria circunferentia quæ. # 530 <lb/>Hectemoria circunferentia quæ. # 530 <lb/>Horizontales circunferentiæ, ac deſcenſiuæ ad conſtructionem hori-<lb/># zontalis horologĳ neceſſariæ ſunt. # 531 <lb/>Horariæ circunferentiæ, &amp; Verticales neceſſariæ ſunt ad conſtru-<lb/># ctionem horologĳ Verticalis. # 531 <lb/>Hectemoriæ circunferentiæ, &amp; meridianæ neceſſariæ ſunt ad horo-<lb/># logĳ Meridiani conſtructionem. # 531 <lb/>Horizontalis horologĳ ex circunferentĳs horizontalib{us}, deſcenſi-<lb/># uis que compoſitio. # 559 <lb/>Horizontales, ac deſcenſiuæ circunferentiæ, qua ratione in Vertica <lb/># li, Meridiano, circulo horæ 6. à mer. vel med. noc. &amp; Aequatore <lb/># inueniantur, tanquàm in Horizonte. # à 560. vſq; ad 562 <lb/>Horologia ad Horizontem recta, qualia ſunt ea, quæ in muris pin-<lb/># guntur, qua ratione ex horizontali horologio, cum omnibus illis, <lb/># quæ in eo deſcripta ſunt ſecũdo lib. conficiãtur.à 568. vſq; ad 572 <lb/>Horologia ad Horizontem recta, nempe ea, quæ in muris pingi ſo-<lb/># lent, qua ratione ex circunferentiis horizontalibus, deſcenſiuisq; <lb/># in Horizonte inuentis componantur. # 572 <lb/>Horologia quo pacto in quouis plano per instrumentum ad hunc fi-<lb/># nem conſtructum deſcribantur. # à 630. vſque ad 632 <lb/>Horologia quo pacto in quouis plano ex vmbra cadente in horologiũ <lb/># borizontale, vel aliud quoduis facilime deſcribantur. # 632 <lb/># 633. &amp; 642 <lb/>Horæ à mer. &amp; med. noc. quo pacto ex horologio quodam vniuerſali <lb/># in ſuperficie plana deſcripto reducãtur ad horas ab or. &amp; occ. 639 <lb/>Hemiſphærici horologii concaui coſtructio, quoad hor{as} cuiuſcunq; <lb/># generis, &amp; alia omnia, quæ in horologiis lib. 2. &amp; 3. deſcripta <lb/># ſunt. # à 640 vſque ad 642 <lb/>Horologii plani, inſtar cylindri conuexi, conſtructio. # 645. &amp; 646 <lb/>Horarum cognitio facilima ex altitudine Solis instrumento aliquo <lb/># inuenta. # 646. &amp; 647 <lb/>I <lb/>IN clinatum ad Horizontem horologium quod. # 4 <lb/>Inæquales horæ quæ, &amp; cur ſic dictæ ſint. # 6 <lb/>Italicæ horæ quæ. # 6 <lb/>Italicum horologium quod. # 7 <lb/>Inuentor primus horologiorum Solarium Anaximenes Mileſius. # 7 <lb/>Inuentores varĳ variorum horologiorum, &amp; ſcriptores. # 7. &amp; 8 <lb/>Inſtrumentum pro deſcriptione Ellipſis per filum. # 36 <lb/>Inclinatio plani propoſiti ad Horizotem qua ratione inueſtigetur, <lb/># &amp; in quam partem cadat inclinatio. # 81. &amp; 82 <lb/>Inſtrumentum ad vmbram notandam pro lineæ meridianæ, &amp; de-<lb/># clinationis plani propoſiti inuentione. # 82 <lb/>Inclinatio plani propoſiti ad Meridianũ quo pacto deprehẽdatur. # 93 <lb/>Inclinati plani arc{us} inter eius Meridianum proprium, &amp; Meridia <lb/># num Horizontis, quo artificio deprehendatur. # 101 <lb/>Inclinationis, quam Meridianus proprius plani inclinati habet ad <lb/># Meridianum Horizontis, inuentio. # 102 <lb/>Inclinati plani arcus inter maximum circulum per eius polos, et per <lb/># polos Horizontis ductum, &amp; tam Meridianu ei{us} propriũ, quàm <lb/># Meridianũ Horizotis interiect{us}, qua via cognoſcatur # 103. et 104 <lb/>Ioan. Eaptiſta Benedictus nõ recte reprehendit deſcriptionem arcuũ <lb/># ſignorum ex figura radiorum zodiaci<unsure/>. # 161 <lb/>Italici horologii horizontalis conſtructio. 192. 196. 197. &amp; à 581 <lb/># vſque ad 584 <lb/>Italici horologii vſus eſt, vt cognoſcatur, quot ſint horæ elapſæ à pro-<lb/># ximo occaſu Solis, quotque ad alterum occaſum ſuperſint. # 198 <lb/>Italici horologii, &amp; Eabylonici, vel Aſtronomici ſim@l vtilitas ad <lb/># eliciendam quantitatem diei ac noctis ex vmbra gnomonis; temp{us} <lb/># meridiei &amp; mediæ noctis, quoad hor{as} ab or. &amp; occ. tempus ortus <lb/># Solis, quoad hor{as} a med. noc. &amp; ab occ. temp{us} denique occaſus <lb/># Solis, quoad hor{as} à mer. &amp; ab or. # 200 <lb/>Inclinatum horologium aut declinansin vna facie plani deſcriptum <lb/># quo pacto exhibeat aliud in oppoſita facie delineandum. # 209 <lb/>Italici horologii Verticalis cõpoſitio. # à 231. vſq; ad 234. &amp; 588 <lb/>Italici horologĳ Meridiani conſtructio. # à 252. vſq; ad 254. &amp; 593 <lb/>Italicũ horologiũ Meridianũ Orientale in facie oppoſita plani deſcri <lb/># ptũ, ita vt lineæ lineis reſpõdeant, qua ratione det Italicũ Occidẽ@ <lb/># tale: Et Italicũ occidentale det Babylonicũ oriẽtale, &amp; cõtra. # 255 <lb/>Italici horologii Polaris deſcriptio. # 269. 271. &amp; 597 <lb/>Italici horologĳ Aequinoctialis cõſtructio. # à 286. vſq; ad 290. et 599 <lb/>Ioan. Baptiſta Benedictus non recte reprehendit deſcriptionem hor@ <lb/># logii à Verticali declinantis. # 298 <lb/>Italici horologii à Verticali declinantis deſcriptio<unsure/>. # 329. 330 <lb/># 608. &amp; 609 <lb/>Inclinati ad Horizontem horologii Aſtronomici deſcriptio. # à 353 <lb/># vſque ad 356. &amp; 617 <lb/>Inclinatum ad Horizontem horologium Aſtronomicum, qua ratio <lb/># ne ſit in plano ſtabili conſtruendum. # 357 <lb/>Inclinati ad Horizontẽ horologii Aſtronomici pro dato ſtylo, eiusq; <lb/># loco deſcriptio. # 357. 615. &amp; 616 <lb/>Inclinati ad Horizontem horologĳ Aſtronomici deſcriptio noua, ae <lb/># pulcherrima beneficio Ellipſis, quæ commodißima eſt pro horis du-<lb/># cendis, quæ vix aut valde procul à linea meridiana æquinoctialẽ <lb/># lineam ſecant. # 357 <lb/>Inclinati ad Horizontẽ horologii Italici cõſtructio. # 367. 368. et 619 <lb/>Inclinati ad Horizontẽ horologĳ Babylonici deſcriptio. # 369. &amp; 619 <lb/>Inclinati ad Horizontẽ horologĳ Antiqui deſcriptio. # 369. &amp; 619 <lb/>Italici horologii declinantis ſimul &amp; inclinati deſcriptio. # 411. 412 <lb/># 628. 629 <lb/>Inclinata ad Horizontem horologia cum omnibus, quæ in aliis hor@ <lb/># logiis ſphæræ obliquæ deſcripta ſunt, qua ratione in ſphæra recta <lb/># delineentur. # 423 <lb/>Inclinati ad Horizontem horologĳ Aſtronomici in ſphæra recta de-<lb/># ſcriptio ad datum ſtylum, eiuſque locum. # 423 <lb/>Inclinatum aut declinans horologium, qua ratione ex circunferen-<lb/># tiis horizontalibus deſcenſiuisque propriis deſcribatur. # a 565 <lb/># vſque ad 568
<pb file="0018" n="18" rhead="INDEX"/>
<gap/>ſtrumentum pro horologiis in quocunque plano cõficiendis, eiuſq; <lb/># vſus. # à 630. vſque ad 632 <lb/>Italicum horologium in quadrante, &amp; cylindro quo modo ſit etiam <lb/># Babylonicum. # 649 <lb/>L <lb/>LAtitudo ortiua, vel occidua quo pacto ex Analemmate depre-<lb/># hendatur. # 18. &amp; 229 <lb/>Latitudo ortiua, occiduave qua via per ſtylum in muro ad rectos <lb/># angulos affixum exploretur. # 97 <lb/>Latitudo ortiua occiduave, qua ratione ex ſinubus inueſtigetur. <lb/># pag. # 115. &amp; 116 <lb/>Latitudines vmbrarum quid ſint, &amp; quo modo in quolibet plano <lb/># inueſtigentur. # à 485. vſque ad 487 <lb/>Latitudines vmbrarum pro horis ſupra vnam faciem circuli propo-<lb/># ſiti ſupputatæ eædem ſunt pro horis ſupra oppoſitam faciem eiuſdẽ <lb/># circuli ſi horæ à mer. &amp; or. mutentur in hor{as} à med. noc &amp; occ. <lb/># &amp; paralleli boreales in australes, &amp; contra. # 487 <lb/>Latitudinum regionum ſcala pro horologĳs vniuerſalibus quomodo <lb/># construatur. # 735 <lb/>M <lb/>MEridianũ horologiũ tam orientale, quam occidentale quod. # 3 <lb/>Meridianæ lineæ inuentio ex aſtrolabii deſcriptione, Analem-<lb/># mate, &amp; ſinubus. # 83. &amp; 84 <lb/>Meridiani ar cus inter Horizontem, &amp; planum inclinatum, qua ar <lb/># te ſit inueſtigandus. # 93. &amp; 94 <lb/>Meridiani arcus inter planuminclinatum, &amp; polum arcticum, aut <lb/># inter verticem capitis, quo pacto cognoſcatur. # 55 <lb/>Meridiana altitudo Solis quo pacto ex declinatione Solis reperia-<lb/># tur. # 120 <lb/>Meridiana depreßio Solis quid, &amp; quo pacto reperiatur. 121. et 122 <lb/>Meridiana altitudo Solis ſupra Horizontem duplex est, quando cõ-<lb/># plementum altitudim<unsure/>s poli minus eſt declinatione borealis paralle-<lb/># li Solis. # 120 <lb/>Meridianorum deſcriptio in horologio horizontali. # 172 <lb/>Meridianorum in horologio deſcriptorum vſus eſt, vt intelligam{us}, <lb/># quibusnam populis meridies fiat quolibet tempore, &amp; quota hora <lb/># ſit in quouis loco, cuius longitudo ſit nota. # 173 <lb/>Mediationes cæli, cum initia ſignorum oriuntur, quo pacto inueſti-<lb/># gentur. # 181 <lb/>Meridianorum deſcriptio in horologio Verticali. # 225 <lb/>Meridianì horologii Aſtronomici deſcriptio. # 237. 590. &amp; 591 <lb/>Meridiani horologii Aſtronomici deſcriptio in plano ſtabili, quod <lb/># Meridiano æquidiſtet. # 240 <lb/>Meridiani horologii Aſtronomici deſcriptio ad datam ſtyli longitu-<lb/># dinem, cuius etiã locus datus ſit. # 240. 590. &amp; 591 <lb/>Meridianorum in horologio Meridiano deſcriptio. # 246 <lb/>Meridiani horologii Italici conſtructio. # 252. 253. 254. 593. &amp; 594 <lb/>Meridiani horologĳ Babylonici conſtructio. # 255. 593. &amp; 594 <lb/>Meridiani horologii Antiqisi deſcriptio. # 256. &amp; 594 <lb/>Meridianum horologium Antiquum orientale in facie oppoſita deli-<lb/># neatum, ita vt lineæ lineis reſpondeant, dat Antiquum occidẽtale, <lb/># &amp; contra. # 256. &amp; 594 <lb/>Meridianum horologium Aſtronomicum à Polari horologio quomo-<lb/># do differat. # 257. &amp; 595 <lb/>Meridianorum deſcriptio in Polari horologio. # 264 <lb/>Meridianorum in horologio Aequinoctiali deſcriptio. # 281 <lb/>Meridianus, Horizon, &amp; Verticalis in omni climate ſe mutuo ſe-<lb/># cant ad angulos rectos. # 193. &amp; 528 <lb/>Meridianus, circulus horæ 6. à mer. vel med. noc. atque Aequator in <lb/># omni climate ſe mutuo ſecant ad angulos rectos # 293 <lb/>Meridianorum in horologio declinante à Verticali deſcriptio. # 323 <lb/>Meridianorum in horologio declinante ab Horizote deſcriptio. # 347 <lb/>Meridianorum in horologio ad Horizontẽ inclinato deſcriptio. # 362 <lb/>Meridiana linea, &amp; æqui<unsure/>noctialis in quo horologio declinante ſimul <lb/># &amp; inclinato ſint parallelæ. # 383 <lb/>Meridianorũ deſcriptio ĩ horologio declinãte ſimul et inclinato. # 405 <lb/>Meridiana horologia in ſphæra recta qua rõne delineentur, vna cum <lb/># omnibus, quæ in horologĳs ſphæræ obliquæ deſcripta ſunt. # 418 <lb/>Meridiana altitudo Solis ſupra circulum maximum quemcunque quo <lb/># pacto inquir atur. # 452 <lb/>Meridiani arc{us} inter planum inclinatum, &amp; Aequatorẽ ſupra Ho-<lb/># rizontem quantus ſit. # 456 <lb/>Meridiana linea, æquinoctialis, &amp; gnomon quid ſecundum Ptole-<lb/># mæum. # 528 <lb/>Meridianus mobilis quid apud Ptolemæum. # 529 <lb/>Meridiana circunferentia quæ # 530 <lb/>Meridianæ circunferentiæ &amp; hectemoriæ neceſſariæ ſunt ad conſtr@ <lb/># ctionem horologĳ Meridiani. # 531 <lb/>Meridiani horologĳ ex circunferentiis meridianis, atq@ hectemoriis <lb/># conſtructio. # 560 <lb/>Meridianum horologium quo pacto ad modum horizontalis horologĳ <lb/># conſtruatur ex circunferentĳs horizontalibus deſcenſiuisq; inuen-<lb/># tis in Meridiano, tanquam in Horizonte. # 560 <lb/>N <lb/>NOx &amp; dies cur ab Antiquis diuiſa ſit in 12. horas. # 2. &amp; 6 <lb/>Nocturni arc{us} ſunt arcuum diurnorum complement a vſq; ad <lb/># 24. # 215 <lb/>O <lb/>ORontĳ Finæi error in deſcriptione horologĳ horizontalis &amp; <lb/># Verticalis. # 155 <lb/>P <lb/>POlare horologium tam ſuperius, quàm inferius quod. # 3. &amp; 4 <lb/>Parabole quibus in horologĳs, Solein quocunque parallelo com-<lb/># morante, fiat. # 22 <lb/>Parabole, cuius in dato cono diameter data ſit, quo pacto in plan@ <lb/># deſcribatur. # à 26. vſque ad 28 <lb/>Paraboles, cuius diameter in cono data ſit, latus rectum quo pact@ <lb/># reperiatur. # 29 <lb/>Parabole, cuius latus rectum ſit datum, qua ratione in plano de-<lb/># ſcribatur. # 30 <lb/>Parabole qualiſcunque quo pacto in plano deſcribatur, non habit@@ <lb/># ratione coni, ex quo oritur. # 34 <lb/>Parallelorum maximus in ſphæra, &amp; duo circuli maximi tangentes <lb/># quemcunque parallelum in duobus punctis oppoſitis, habent vnam <lb/># eandemque ſectionem communem. # 50 <lb/>Planum ſecans quotcunque plana eandem cõmunem ſectionem haben <lb/># tia, cui planum illud æquidiſtet, facit communes ſectiones paralle-<lb/># las: ſi vero communem illam ſectionem ſecet, facit communes ſe-<lb/># ctiones coeuntes in illo puncto, in quo planum ſecans communem <lb/># illorum ſectionem diuidit. # 52 <lb/>Poli altitudo ſupra Horizontem quo artificio per Analemma re-<lb/># periatur. # 96 <lb/>Poli altitudo ſupra quodcunque planum inclinatum quo modo de-<lb/># prehendatur. # 99. &amp; 100 <lb/>Paralleli ſignorum in horologio horizontali quo pacto deſcriban-<lb/># tur. # 157. 159. &amp; 578 <lb/>Paralleli ſignorum in horologio horizontali an hyperbolæ ſint, a@ <lb/># parabolæ, an Ellipſes, quo pacto ex figura radiorum zodiaci co-<lb/># gnoſcatur. # 163. &amp; 578 <lb/>Parallelus cuiuſque ſigni quo pacto integer in horologio, vna cum <lb/># parallelo ſigni oppoſiti deſcribatur ex ſola portione paralleli vſq@ <lb/># ad lineam meridianam deſcripta. # 164 <lb/>Parallelus, in quo Sol existit quolibet die propoſito, qua ratione in <lb/># horologio deſcribatur. # 167. &amp; 580 <lb/>Paralleli ſignorum in horologio horizontali, quod centrum non ha-<lb/># bet, qua arte deſcribantur. # 167 <lb/>Parallelorum ſignorum in horologio deſcriptorum vſus est, vt diſcæ<unsure/> <lb/># mus, qua in partezodiaci Sol verſetur. # 169 <lb/># Paralleli Horizontis in horologio horizõtali quo modo deſcriban-<lb/># tur. # 171 <lb/>Parallelorum Horizontis in horologio deſcriptorum vſus est, vt co-<lb/># gnoſcamus altitudinem Solis ſupra Horizontem. # 172 <lb/>Parallelorum ciuitatum, hoc est, circulorum latitudinum in horolo <lb/># gio horizontali deſcriptio. # 174 <lb/>Parallelorũ ciuitatũ in horologio deſcript@rũ vſus eſt, vt diſcam{us}, <lb/># quinã populi Solẽ habeãt in vertice capitis tẽpore Meridiano. # 174 <lb/>Planetariæ horæ, quæ nimirũ inæquales ſunt, reſpondentq; ſingulæ <lb/># quindenis gradibus Eclipticæ, quo pacto deprehendantur. # 203 <lb/>Paralleli ſignorum qua ratione in horologio Verticali deſcriban-<lb/># tur. # 211. 215. &amp; 587 <lb/>Portio cuiuſcunq; horologĳ ſupra lineã horizontalẽ eſt horologium <lb/># in facie oppoſita collocandum, ſi omnes partes inuertantur. # 214 <lb/>Paralleli ſignorum in horologio Verticali an hyperbolæ ſint, an Pa-<lb/># rabolæ, an Ellipſes, quo modo cognoſcatur. # 217. &amp; 587 <lb/>Paralleli ſignorum quo modo deſcribantur in horologio Verticali, <lb/># vbi centrum non habetur. # 217 <lb/>Parallelorum Horizontis in horologio Verticalideſcriptio. # 223 <lb/>Parallelorum ciuitatum, hoc est, circulorum latitudinum deſcriptio<unsure/> <lb/># in Verticali horologio. # 226 <lb/>Paralleli ſignorum, qua ratione in horologio Meridiano deſcriban-<lb/># tur. # 240. 242. &amp; 592 <lb/>Parallelorum Horizontis in Meridiano<unsure/> horologio deſcriptio. # 244
<pb file="0019" n="19" rhead="INDEX"/>
Parallelorum ciuitatum, hoc est, circul@rum latitudinum deſcriptio <lb/># in horologio Meridiano. # 247 <lb/>Polare horologium Aſtronomicum à Meridiano horologio quo modo <lb/># differa t. # 257. &amp; 595 <lb/>Polaris horologĳ Astronomici deſcriptio. # 257. &amp; 595 <lb/>Polare horologium in plano ſtabili, quod circulo horæ 6. à mer. vel <lb/># med. noc. æquidistet, quo pacto deſcribatur. # 258 <lb/>Polare horologium ad datum stylum, cuius etiam locus datus ſit, <lb/># qua ratione construatur. # 258 <lb/>Paralleli ſignorum in polari horologio quo pacto deſcribantur. # 258 <lb/># &amp; 596 <lb/>Parallelorũ Horizontis in horologio polari deſcriptio. # 260. &amp; 261 <lb/>Parallelorum ciuitatum deſcriptio in polari horologio. # 265 <lb/>Polaris horologii Italici deſcriptio. # 269. 271. &amp; 597 <lb/>Polaris horologĳ Babylonici deſcriptio. # 272. &amp; 597 <lb/>Polaris horologĳ Antiqui deſcriptio. # 272. &amp; 597 <lb/>Paralleli ſignorum in horologio æquinoctiali, qua rati@ne deſcriban-<lb/># tur. # 274. 275. &amp; 598 <lb/>Parallelorum Horizontis in æquinoctiali horologio deſcriptio. <lb/># 279. &amp; 280 <lb/>Parallelorum ciuitatũ in æquinoctiali horologio deſcriptio. # 282 <lb/>Poli altitudo ſupra planum à Verticali declinans quo pacto ex con-<lb/># ſtructione horologĳ à Verticali declinantis deprehendatur. # 295 <lb/>Paralleli ſignorum in horologio declinante à Verticali quo modo de-<lb/># ſcribantur. # à @ 12. vſque ad 318. &amp; 606 <lb/>Paralleli ſignorum in horologio declinante à Verticali, quinam ſint <lb/># hyperbolæ, qui parabolæ, &amp; qui Ellipſes. # 315 <lb/>Paralleli ſignorum in horologio declinante à Verticali, cuius centrũ <lb/># non habetur, qua ratione deſcribantur. # 319 <lb/>Parallelorum Horizontis in horologio declinante à Verticali de-<lb/># ſcriptio. # 322 <lb/>Poli altitudo ſupra Verticalem proprie dictum cuiuſcunque regionis <lb/># æqualis eſt complemento altitudinis poli ſupra Horizontem eiuſ-<lb/># dem regionis. # 335. &amp; 489 <lb/>Poli altitudo ſupra planum declinans ab Horizonte quo pacto ex <lb/># ipſa conſtructione horologii ab Horizonte declinantis eliciatur. <lb/># pag. # 335. &amp; 612 <lb/>Paralleli ſignorum in horologio declin<unsure/>ante ab Horizonte, qua ra-<lb/># tione deſcribantur. # 341. 342. &amp; 612 <lb/>Parallelorum Horizontis in horologio declinante ab Horizonte <lb/># deſcriptio. # 346 <lb/>Paralleli Horizontis in horologio declinante ab Horizonte quinam <lb/># ſint hyperbolæ, qui parabolæ, &amp; qui Ellipſes. # 346 <lb/>Parallelorum ciuitatum deſcriptio in horologio declinante ab Hori <lb/># zonte. # 347 <lb/>Poli altitudo ſupra planum inclinatum ad Horizontem quo pacto <lb/># reperiatur. # 353. 354. 615. &amp; 616 <lb/>Paralleli ſignorum in horologio ad Horizoteminclinato, qua ratio-<lb/># ne deſcribantur. # 358. &amp; 617 <lb/>Parallelorum Horizontis in horologio ad Horizontem inclinato <lb/># deſcriptio # 361 <lb/>Parallelorum ciuitatum deſcriptio in horologio ad Horizontem in-<lb/># clinato. # 363 <lb/>Poli altitudo ſupra planum declinans ſimul &amp; inclinatum, qua ra-<lb/># tione ex conſtructione horologii declinantis ſimul &amp; inclinati eli-<lb/># ciatur. # 373 <lb/>Paralleli ſignorum in horologio declinante ſimul &amp; incliæ<unsure/>ato, qua <lb/># ratione deſcribantur. # 395. 396. 625. &amp; 626 <lb/>Paralleli ſignorum in horologio declinante ſimul &amp; inclinato, qui <lb/># ſint hyperbolæ qui parabolæ, &amp; qui ellipſes. # 399. &amp; 627 <lb/>Parallelorum Horizontis in horologio declinante ſimul &amp; inclina-<lb/># to delineatio. # 403 <lb/>Parallelorum ciuitatum in declinante ſimul &amp; inclinato horolo-<lb/># gio deſcriptio. # 406 <lb/>Polarium horologiorum in ſphæra recta, quoad omnia, quæ in horo-<lb/># logiis ſphæræ obliquæ deſcribuntur, conſtructio. # 428 <lb/>Polus mundi ſupra faciem cuiuſque circuli maximi propoſitam ele-<lb/># uatus arcticusne ſit, an antarctic{us}. # 452 <lb/>Parallelus Solis quilibet quot hor{as} contineat ſupra faciem datam <lb/># circuli maximi propoſit@. # à 452. vſque ad 458 <lb/>Paralleli Solis quinã a Verticali proprio cuiuſq; plani ſecẽtur. # 487 <lb/>Paralleli ſignorum quo pacto ex tabulis latitudinum, longitudi-<lb/># numque vmbrarum deſcribantur in horologĳs. # 493 <lb/>Paralleli ſignorum qua ratione in horologio Aſtronomico per arc{us} <lb/># horarios constructo deſcribi poſsint. # 527 <lb/>Pi<unsure/>olemæu<unsure/>s in Analemmate quos præcipue circulos conſideret, &amp; <lb/># quos illis mot{us} tribuat. # 529 <lb/>Polare horologium quo pacto ad modum horizontalis horologĳ con-<lb/># struatur ex circunferẽtiis horizontalibus, &amp; deſcenſiuis inuẽtis in <lb/># circulo horæ 6. à mer. vel med. noc. tanquàm in Horizonte. # 562 <lb/>Q <lb/>QVadrãtis mirificos vſus habẽtis in horologiorũ deſcriptionib{us}, <lb/># &amp; in alĳs rebus Aſtronomicis, cõſtructio, &amp; vſus. 8. 9. et 492 <lb/>Quadrantes quatuor hemiſphærĳ Superi qui ſint in horologio. # 171 <lb/>Quadrantis h@rarĳ conſtructio. # 647 <lb/>R <lb/>RAdĳ ſignorum, vel zodiaci qui. # 12 <lb/>Rectanguli ſub diametro tranſuerſa Hyperboles, &amp; latere re-<lb/># cto cõprehenſi quarta pars, qua ratione ad diametrũ tranſuerſam <lb/># ex vtraq; parte applicetur, ita vt excedat figura quadrata. # 31 <lb/>Rectanguli ſub diametro tranſuerſa Ellipſis, &amp; latere recto cõpre-<lb/># henſi quarta pars quo pacto ad trãſuerſam diametrum ex vtraq; <lb/># parte applicetur, ita vt deficiat figura quadrata. # 33 <lb/>Rectæ lineæ in horologio nomẽ accipiũt à circulis maximis, quie{as} in <lb/># horologio efficiunt; &amp; quorum circulorũ lineæ deſcribi nequeant <lb/># in horologio. # 43 <lb/>Radii arcuum diurnorum qui, &amp; quo modo ducantur. # 109. &amp; 580 <lb/>Radĳ amplitudinum ortiuarum, &amp; occiduarum qui. # 229 <lb/>S <lb/>SCiothericum, vel Solare horologium, quid, eiuſq; varia genera. # 3 <lb/>Sinus toti cum ſinubus tam rectis, quàm verſis arcuum ſimilium <lb/># proportionales ſunt: Et arcus, quorum ſinus tam recti, quàm verſi <lb/># cum ſinubus totis ſunt proportionales, ſimiles ſunt. # 14 <lb/>Styli vertexin quocunque horologio centrum mundi eſt. # 19 <lb/>Solin Aequatore exiſtens ſuo radio, velpunctum quodlibet cæli li-<lb/># nea recta per centrũ mundi tranſeunte deſcribit Aequinoctialẽ cir <lb/># culũ; extra vero Aequatorẽ du{as} conic{as} ſuperficies, quarũ vnius <lb/># baſis eſt parallel{us} à centro Solis, vel puncto cæli deſcript{us}, alte-<lb/># ri@s autem, parallel{us} huic oppoſit{us}. Harum vna dicitur ſuper-<lb/># ficies conica luminis, &amp; vmbræ altera. # 20 <lb/>Styli vmbra, &amp; radius Solis proiicitur in cõmunẽ ſectionẽ plani ho-<lb/># rologii, &amp; circuli maximi, in quo Sol existit: Et in æquinoctĳs li-<lb/># nea rectã æquinoctialem deſcribit in quouis horologio. # 42. &amp; 43 <lb/>Styli vmbra, &amp; radi{us} Solis extra æquinoctia proiicitur in ſectio-<lb/># nem conicam, quæ communis ſectio est plani horologii, &amp; conicæ<unsure/> <lb/># ſuperficiei, cuius baſis est parallel{us} parallelo Solis oppoſit{us}, deſcri <lb/># bitq́ eam ſectionem conicam in quouis horologio. # 44 <lb/>Semidiurnus arc{us} quo pacto ſupputetur. # 115. &amp; 123 <lb/>Solin ſignis borealib{us} exiſtens num Verticalem attigerit, necne, <lb/># quo pacto cognoſcatur. # 129 <lb/>Semidiurnt arcus in ſignorũ initiis, ad latitudinam gr. # 42. &amp; 180 <lb/>Styli locus in quolibet horologio quãdo c<unsure/>xtra tropicos, &amp; quando <lb/># in tropicum præciſe, aut @ntra tropicos, aut inipſam lineam æqui-<lb/># noctialem cadat. # 429 <lb/>Stylus cuiuſcunque horologii, qua ratione proprio in loco ad horo-<lb/># logĳ planum rectus collocetur, eiusq́ vertex in propriamſedem, ſi <lb/># quando ab ea deflexerit, reſtituatur. # 431 <lb/>Styl{us} medio loco proportionalis eſt inter vmbrã rectã, et versã. # 475 <lb/>Solſtitialium, &amp; æquinoctialiũ vmbrarũ longitudines qua ratione <lb/># ad quamcunque latitudinem ex tabula vmbrarũ cognoſcãtur. # 485 <lb/>Sol an in Verticali proprio cuiuſque plani, an citra, vel vltra eun-<lb/># dem exiſtat, quo pacto ex data hora cognoſcatur. # 487 <lb/>Scala latit<unsure/>udinum regionum pro horologiis vniuerſalibus quo mo-<lb/># do conſtruatur. # 635 <lb/>T <lb/>TAbula continens horas à mer. vel med. noc. &amp; ab or. vel occ. ſe <lb/># mutuo interſecãtes in linea æquinoctiali cuiuſque horologĳ in <lb/># vno eodemque puncto. # 54 <lb/>Tabulæ 36. continentes horas à mer. vel med. noc. &amp; ab or. vel occ. <lb/># ſe mutuo interſecantes in linea horizontali, ſeu horæ 24. ab or. <lb/># vel occ. Et in linea horæ 12. ab or. vel occ. Et in linea horæ 6. à <lb/># mer. vel med. noc. Et in linea meridiana, ſeu horæ 12. à mer. vel <lb/># med. noc. Et denique in aliis lineis horarũ tam ab or. vel occ. quàm <lb/># à mer. vel med. noc. # 56. 57. &amp; à 61. vſque ad 76 <lb/>Tabulæ arcuum diurnorũ, nocturnorumq; continentes hor{as} à mer. <lb/># vel med. noc. &amp; ab or. vel occ. nec non inæquales ſe mutuo in ipſis <lb/># arcubus diurnis, nocturnisq; interſecantes in vno eodemq; puncto, <lb/># in quocunque horologio. # à 111. vſque ad 114 <lb/>Tabulæ horarum, quibus initia ſignorum ſupra Horizontem aſcen-<lb/># dunt, ad latitudinem grad. 41. # 178 <lb/>Tabula mediationum cæli, &amp; angulorum terræ, vnà cum declinatio-<lb/># ni<unsure/>bus, cum ſignorum initia oriuntur, ad latitudinem gr. 42. # 181
<pb file="0020" n="20" rhead="INDEX."/>
Tabula punctorum Eclipticæ in circulo horæ 6. à mer. vel med. noc. <lb/># conſtitutorum, vna cum declinationibus, cum principia ſignorum <lb/># oriuntur, ad latitudinem grad. 42. # 182 <lb/>Tabulæ punctorũ Eclipticæ in circulis horarum 11. 1. 7. &amp; 5.à mer. <lb/># vel med. noc conſtitutorum, vna cum declinationibus, cum ſignorũ <lb/># principia oriuntur, ad latitudinem grad. 42. # 184 &amp; 185 <lb/>Tabula pũctorũ Eclipticæ in medio cæli, &amp; angulo terræ cõſtitutorũ, <lb/># vna cũ ſignis deſcẽdentibus, cũ principia ſignorũ oriuntur. # 188 <lb/>Tabula aſcenſionum rectarum quo pacto conſtruatur. # 190 <lb/>Tabula aſcenſionum obliquarum qua ratione ex differentĳs aſcen-<lb/># ſionalibus componatur. # 192 <lb/>Tabulæ horarum, quibus principia ſignorum ſupra Horizontẽ aſcen <lb/># dunt in ſphæra recta. # 416 <lb/>Tabulæ distantiarum Solis à Meridianis proprĳs variorum circulo-<lb/># rum maximorum ſphæræ. # 460. &amp; 461 <lb/>Tabulæ altitudinum Solis ſupra varios circulos in ſphæra maximos <lb/># tam pro horis à mer. vel med. noc. &amp; ab or. vel occ. quàm pro ho-<lb/># ris inæqualibus, ad latitudinem grad. 42. # à 462. vſq; ad 474 <lb/>Tabula longitudinum vmbrarum tam rectarũ, quàm verſarũ in par <lb/># tibus, qualium Gnomon eſt 12. ad ſingulos gradus, &amp; Minuta alti <lb/># tudinum Solis ſupputatarum. # à 476. vſque ad 484 <lb/>Tabulæ lati tudinum, longitudinumque vmbrarum, &amp; arcuum ho-<lb/># rariorum, pro varĳs horologiis planis deſcribendis, ad latitudinẽ <lb/># grad. 42. # à 490. vſque ad 525 <lb/>Tabula altitudinum Solis ſupra Horizontem inſignorũinitĳ<unsure/>s, pro <lb/># horis à mer. &amp; med. noc. ad latitudinem grad. 42. # 643 <lb/>Tabula altitudinũ Solis ſupra Horizontem, pro horis ab occ. in tro <lb/># picis, &amp; in parallelis, quorum arcus diurni cõplectuntur hor. 15. <lb/># 14. 13. 12. 11. 10. &amp; 9. vna cum declinationibus illorũ parallelo-<lb/># rum, ad latitudinem grad. 42. # 643. &amp; 644 <lb/>V <lb/>VErticale horologiũ tam ad auſtrũ vergẽs, quàm ad boreã, qđ. # 3 <lb/>Verticaliũ circulorũ in horologio horizontali deſcriptio. # 170 <lb/>Verticaliũ circulorũ in horologio deſcriptorum vſus est, vt cogno-<lb/># ſcamus, quonam in quadrante hemſphærĳ Superi Sol existat. # 171 <lb/>Verticalis horologĳ Aſtronomici compoſitio. # 204 <lb/>Verticalis horologĳ Aſtronomici deſcriptio percommoda pro horis du <lb/># cendis, quæ vix, aut valde procul à linea meridiana æquinoctia-<lb/># lem lineam ſecant. # 207 <lb/>Verticalis horologĳ Astronomici conſtructio, cum altitudo poliſu-<lb/># pra Horizontem tanta eſt, vt pol{us} parum à vertice capitis rece-<lb/># dat, vel perexigua est. # 208 <lb/>Verticalis horologĳ Aſtronomici deſcriptio in plano ſtabili, quod <lb/># Verticali circulo proprie dicto æquidiſtet. # 210 <lb/>Verticalis horologii Aſtronomici conſtructio ad datum ſtylum, cu-<lb/># ius etiam locus datus ſit. # 210. &amp; 585 <lb/>Verticalium circulorum in horologio Verticali deſcriptio. # 222 <lb/>Verticalis horologĳ Italici cõpoſitio. # à 231. vſq; ad 234 &amp; 588 <lb/>Verticalis horologĳ Babylonici conſtructio. # 234. &amp; 588 <lb/>Verticalis horologĳ Antiqui deſcriptio. # 236. &amp; 590 <lb/>Verticalium circulorum in horologio Meridiano delineatio. # 243 <lb/>Verticalium circulorum in Polari horologio deſcriptio. # 260 <lb/>Verticalium circulorum deſcriptio in Aequinoctiali horologio. # 277 <lb/>Verticalis, Horizon, ac Meridianus in omni climate ſe mutuo ad re-<lb/># ctos angulos ſecant. # 293. &amp; 528 <lb/>Verticali<unsure/>ũ circulorũ in horologio declinãte à Vertic. deſcriptio. # 321 <lb/>Verticali<unsure/>ũ circulorũ in horolog. declinãte ab Horiz. delineatio. # 344 <lb/>Verticaliũ circulorũ deſcriptio in horolog. ad Horizontẽinclin. # 350 <lb/>Verticali<unsure/>ũ circulorũ ĩ horol declinãte ſimul et inclinato deſ@ri. # 400 <lb/>Verticalium horologiorum delineatio in ſphæra recta, cum omnib{us}, <lb/># quæ in horologĳs ſphæræ obliquæ deſcripta ſunt. # 416 <lb/>Vmbra tam recta, quàm verſa à dato ſtylo proiecta quo pacto ex So<unsure/> <lb/># lis al@itudine data inueſtigetur. # 474. &amp; 475 <lb/>Vmbra recta cuiuſcunque altitudinis Solis ſupra Horizontem ea-<lb/># dem eſt, quæ vmbra verſa complementi eiuſdem altitudinis. # 475 <lb/>Verticalis mobilis quid apud Ptolemæum. # 529 <lb/>Verticalis circunferentia quæ. # 530 <lb/>Verticales circunferentiæ, horariæque ad conſtructionem horologii <lb/># Verticalis adhibendæ ſunt. # 531 <lb/>Verticalis horologĳ ex circunferentĳs Verticalib{us}@, atque horariis <lb/># conſtructio. # 559 <lb/>Verticale horologium quo pacto ad modum horologĳ horizontalis <lb/># conſtruatur ex circunferentĳs horizontalib{us}, deſcenſiuisq; inuen <lb/># tis in Verticali circulo, tanquàm in Horizonte. # 560 <lb/>Vniuerſalis horologĳ Aequinoctialis conſtructio. # 634. &amp; 635 <lb/>Vniuerſalis horologĳ in formam crucis conſtructio. # 636 <lb/>Vniuerſalis horologĳ in ſuperficie plana deſcriptio in formam pa-<lb/># rallelogrammi. # à 637. vſque ad 639 <lb/>Z <lb/>ZOdiaci puncta in circulo horæ 6. à mer. vel med. noc. conſtitu <lb/># ta, eorumq; declinationes, cum ſignorum initia @riuntur, que <lb/># pacto reperiantur. # 182. &amp; 183 <lb/></note>
</div>
<div xml:id="echoid-div7" type="section" level="1" n="7">
<head xml:id="echoid-head9" xml:space="preserve"><emph style="sc">FINIS</emph>.</head>
<note position="right" xml:space="preserve"> <lb/>#### ERRATORVM CORRECTIO. <lb/>Pag. # Linea. # Errata. # Correcta. <lb/>5. # 59. # indicat. # indicant. <lb/>22. # 15. # per propoſ. 6. # per pro@oſ. 5. <lb/>22. # 20. # ꝓpoſ. 1. eiuſdẽ. # ꝓpoſ. 1. lib. 2. eiuſdẽ. <lb/>23. # 19. # in centro E. # in centro A. <lb/>40. # 16. # Secentaut. # Secentautem. <lb/>42. # 8. # arcum l<unsure/> k. # arcum l<unsure/> L. <lb/>55. # 42. # circuli D E. # circuli D F. <lb/>60. # 32. 33. # D N K. # D N B. <lb/>60. # 33. # D A K. # D A B. <lb/>60. # 25. # E F H. # E F. <lb/>80. # 59. # præſcriptum. # præſcriptam. <lb/>90. # 17. # rectangulum \\C E, E A. # rectangulum ſub \\C E, E A. <lb/>101. # 21. # ſupra Hori<unsure/>zõtẽ. # ſupra ipſum planũ. <lb/>109. # 49. # diametrũ C D. # diametium B D. <lb/>113. ### In principic ſecundæ tabellæ pro I X. re- \\ pone X II. <lb/>115. # 26. ## arcui diurno I E. arcui diurno F K. <lb/>Pag. # Linea. # Errata. # Correcta. <lb/>118. # 59. # tranſeuntis. # tranſeunte. <lb/>119. # 48. # inuenieniemus. # inueniemus. <lb/>121. ### In margine prope finem, pro [crepuſculũ \\ quando nullum] lege [crepuſculũ quã- \\ do continuum.] <lb/>123. # 53. # arcui ſemino- \\ cturno. # arcui ſeminocturno \\ paralleli oppoſiti. <lb/>127. # 1. # inuenimus. # inueniemus. <lb/>162. # 28. # coniuntur. # coniungatur. <lb/>180. ### Præponatur titulo tabellæ hæc litera [V.] <lb/>292. # 45. # horam 18. # horarum 18. <lb/>360. ### In margine prope initium, pro [a@cuum ſi \\ gnorum.] ſcribe [arcuum diurnorũ.] <lb/>382. # 30. # ſtyli ea facie. # ſtyli in ea facie. <lb/>384. # 38. # proprii. # proprio. <lb/>390. # 53. 57. # H b. # H d. <lb/>390. # 55. # Hd, quę ad Hb. # H b, quæ ad H d. <lb/>390. # 56. # H d. # H b. <lb/>Pag. # Linea. # Errata. # Correcta. <lb/>411. # 39. # lineis rectis cõ \\ iuncta. # ſi lineis rectis con- \\ iungantur. <lb/>418. # 21. # obſeruentur. # obſeruetur. <lb/>447. # 60. # ſumpto hemi- \\ phęrio. # ſupero hemiſphæ- \\ rio. <lb/>462. # 43. ## deleatur in fine lineæ dictio [ſiue.] <lb/>467. ### In tabella 11. infra horã 7. lege 56. 51. &amp; ſub \\ hora 8 lege 66. &amp; ſub hora 10. lege 71. 7. <lb/>477. ### ſub G. 18. &amp; è regione M. 22. pro vmbra \\ 26. lege 36. <lb/>495. # 37. ## altitudinis. Solis. altitudinis Solis. <lb/>525. # ### In titulo tabulæ pro [ex parte inclinato.] \\ ſubſti@ue [ex parte auſtrali inclinato.] <lb/>#### In figura paginæ 60. inter puncta G, D, ponatur \\ ſupra arcum G D, litera I. <lb/>#### In tertia figura paginæ 355. loco hui<emph style="sub">9</emph> lituræ [@] \\ ſcribatur litera [N.] <lb/>#### In fig. pag. 157. clari<emph style="sub">9</emph> exprimãtur literę K, L, M, I, Q, eo ordine quo rectę D ♑, D ♐, D ♏, D ♎, D ♍, rectã R O, ſecãt. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>#### ERRATA, QVAE SEQVVNTVR, QVONIAM NON AD OMNIA VOLVMINA \\ pertinent, ſeorſum poſita ſunt, vt in ijs emendari poſſint, in quæ irr<unsure/>epſerint. <lb/>87. # 45. # Verticali. # Verticalis. <lb/>87. # 46. # à Verticalis. # à Verticali. <lb/>196. # 24. # arcu. # arcus. <lb/>511. # 46. ## Gak. Cak &amp; 581. figura inuerſa eſt. <lb/>476. ### ſub G. 8 &amp; è regione M. 37. pro vmbra \\ 79. 31. lege 79. 11. <lb/>#### 291. 41. deleatur ſyllaba [hoc] in principio lineæ, &amp; ſcribatur in fine eiuſdẽ. In linea aũt 60. pro [{3/2}] reponatur [{1/2}] <lb/></note>
</div>
<div xml:id="echoid-div8" type="section" level="1" n="8">
<head xml:id="echoid-head10" xml:space="preserve">AD LECTOREM.</head>
<p style="it">
  <s xml:id="echoid-s114" xml:space="preserve">VNum eſt, quod lectorẽ præmonitũ velim, duo eſſe, in quibus cum plurimũ labor aſſem, cõſequi tamẽ, quod contendebã, mature nõ potui: <lb/></s>
  <s xml:id="echoid-s115" xml:space="preserve">Alterũ eſt, vt conſtructionẽ Analẽmatis poſitã lib. </s>
  <s xml:id="echoid-s116" xml:space="preserve">1. </s>
  <s xml:id="echoid-s117" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s118" xml:space="preserve">1. </s>
  <s xml:id="echoid-s119" xml:space="preserve">clari{us} aliquãto, quàm Petr{us} Noni{us}, demonſtrarẽ: </s>
  <s xml:id="echoid-s120" xml:space="preserve">alterũ, vt praxim <lb/>illam inueſtigandæ arcuũ diurnorũ declinationis ab Andrea Schonero traditã, quæ habetur in ſcholio propoſ. </s>
  <s xml:id="echoid-s121" xml:space="preserve">33. </s>
  <s xml:id="echoid-s122" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s123" xml:space="preserve">1. </s>
  <s xml:id="echoid-s124" xml:space="preserve">demõſtrationis præ-<lb/>ſidio cõmunirem. </s>
  <s xml:id="echoid-s125" xml:space="preserve">Sed neſcio quo pacto accidit, vt quod tum negatum eſt, cumid agerem maxime, id deinde mihi noua rurſ{us} occaſione oblata <lb/>tentantib nit{as} diuina conceſſerit. </s>
  <s xml:id="echoid-s126" xml:space="preserve">Quamobrem vtrumque præstiti ſatis ex voto ad calcem octaui libri: </s>
  <s xml:id="echoid-s127" xml:space="preserve">quæ duo, cum ſuo vtrumque l@@@ <lb/>reponere tum integrum non eſſet, ce<unsure/>act{us} ſum in vnum eum locum conferre. </s>
  <s xml:id="echoid-s128" xml:space="preserve">qua de re monendum lectorem cenſui.</s>
  <s xml:id="echoid-s129" xml:space="preserve"/>
</p>
<pb file="0021" n="21"/>
</div>
<div xml:id="echoid-div9" type="section" level="1" n="9">
<head xml:id="echoid-head11" xml:space="preserve">GNOMONICES <lb/>LIBER PRIMVS.</head>
  <figure>
    <image file="0021-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0021-01"/>
  </figure>
</div>
<div xml:id="echoid-div10" type="section" level="1" n="10">
<head xml:id="echoid-head12" xml:space="preserve">AVCTORE <lb/>
CHRISTOPHORO CLAVIO BAMBERGENSI
SOCIETATISIESV.</head>
<p>
  <s xml:id="echoid-s130" xml:space="preserve">QVONIAM ea omnia, quæ per Gnomonis vmbrã, lu-<lb/>cente Sole, cognoſci poſſunt, exquiſitis rationibus in <lb/>hac noſtra Gnomonica, hoc eſt, demonſtrationibus <lb/>Geometricis firmiſſimis, ijsq́; </s>
  <s xml:id="echoid-s131" xml:space="preserve">quo ad eius fieri poterit <lb/>
<anchor type="note" xlink:label="note-0021-02a" xlink:href="note-0021-02"/>
clariſſimis, deſcribere (Deo Optimo Maximo bene iu-<lb/>uante) inſtituimus, quod pauci admodum ante nos fe <lb/>cerunt, cum alios omnes, vno aut altero excepto, nudã <lb/>earum rerum deſcriptionem, nulla adhibita demon-<lb/>ſtratione, tradidiſſe videamus; </s>
  <s xml:id="echoid-s132" xml:space="preserve">non ab re fore arbitra-<lb/>mur, ſi totum primũ hunc librum in variis problema-<lb/>tibus, theorematibusq́; </s>
  <s xml:id="echoid-s133" xml:space="preserve">cum Geometricis, tum Aſtro-<lb/>nomicis explicandis conſumamus, iis inquam, quæ <lb/>magnopere profutura, immo neceſſaria omnino eſſe iudicamus, vt breuius deinde <lb/>ſingula ad horologiorum deſcriptionem attinentia, apertiusq; </s>
  <s xml:id="echoid-s134" xml:space="preserve">demonſtrari poſſint. <lb/></s>
  <s xml:id="echoid-s135" xml:space="preserve">
<anchor type="note" xlink:label="note-0021-03a" xlink:href="note-0021-03"/>
Quæ autem demonſtranda nobis eſſe videntur, antequam horologium vllum de-<lb/>ſcribamus, præcipua hęc ferè ſunt. </s>
  <s xml:id="echoid-s136" xml:space="preserve">Qua ratione Analemma, ex quo ferè ſolo omnis <lb/>
<anchor type="note" xlink:label="note-0021-04a" xlink:href="note-0021-04"/>
deſcribendorum horologiorũ ratio petitur, conſtruendum ſit: </s>
  <s xml:id="echoid-s137" xml:space="preserve">Quod vertex gnomo-<lb/>nis in quolibet horologio centri totius mundi vicem in horologiis obtineat: </s>
  <s xml:id="echoid-s138" xml:space="preserve">Qua-<lb/>les ſectiones conicæ (quas nonnulli arcus ſignorum appellant) in quocunq; </s>
  <s xml:id="echoid-s139" xml:space="preserve">plano <lb/>propoſito ab extrema gnomonis vmbra deſcribantur, hoc eſt, num circuli, an para-<lb/>bolæ, hyperbolæve oppoſitæ, an verò Ellipſes: </s>
  <s xml:id="echoid-s140" xml:space="preserve">Qua deinde arte eiuſm<unsure/>odi ſectiones <lb/>in plano expoſito figurentur; </s>
  <s xml:id="echoid-s141" xml:space="preserve">ſemper enim aliquam harũ ſectionum percurrit vm-<lb/>bræ extremum, tempore æquinoctiorum excepto, quo lineam rectã (vt demonſtra-<lb/>bimus) extrema vmbra deſcribit: </s>
  <s xml:id="echoid-s142" xml:space="preserve">Quem ſitum circuli horarij habeant in cælo, vt <lb/>
<anchor type="note" xlink:label="note-0021-05a" xlink:href="note-0021-05"/>
poſtea lineas horarias, quæ nihil aliud ſunt, quã communes ſectiones eorum circu-<lb/>lorum, &amp; </s>
  <s xml:id="echoid-s143" xml:space="preserve">eius plani, in quo horologium depingitur, rectè ducamus: </s>
  <s xml:id="echoid-s144" xml:space="preserve">Quænam lineæ <lb/>horarum à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s145" xml:space="preserve">ab ortu, aut occaſu, in quolibet plano ſe mu-<lb/>tuò interſecent in vno eodemq́; </s>
  <s xml:id="echoid-s146" xml:space="preserve">puncto; </s>
  <s xml:id="echoid-s147" xml:space="preserve">magno enim hæc res vſui futura eſt horis <lb/>ab ortu, vel occaſu ſolis deſcribendis: </s>
  <s xml:id="echoid-s148" xml:space="preserve">Quibus in planis lineæ horarum a meridie vel <lb/>media nocte in vno puncto, veluti centro quopiam, coeant, &amp; </s>
  <s xml:id="echoid-s149" xml:space="preserve">in quibus parallelæ in <lb/>ter ſe ſint: </s>
  <s xml:id="echoid-s150" xml:space="preserve">Qua via cuiuſq; </s>
  <s xml:id="echoid-s151" xml:space="preserve">plani propoſiti declinatio à Verticali circulo, &amp; </s>
  <s xml:id="echoid-s152" xml:space="preserve">eiuſdem <lb/>tam ad Horizontem, quam ad Meridianum inclinatio deprehendatur: </s>
  <s xml:id="echoid-s153" xml:space="preserve">Quanta ſit <lb/>poli altitudo ſupra planum quodlibet declinans inclinatumve, &amp; </s>
  <s xml:id="echoid-s154" xml:space="preserve">alia id genus, quæ <lb/>ad huiuſmodi plana declinantia, inclinataq́; </s>
  <s xml:id="echoid-s155" xml:space="preserve">pertinere, &amp; </s>
  <s xml:id="echoid-s156" xml:space="preserve">ad rem factura eſſe vide-<lb/>
<anchor type="note" xlink:label="note-0021-06a" xlink:href="note-0021-06"/>
buntur: </s>
  <s xml:id="echoid-s157" xml:space="preserve">Quo artificio declinatio paralleli, cuius arcus diurnus notus ſit, inueſtigetur; <lb/></s>
  <s xml:id="echoid-s158" xml:space="preserve">Deniq; </s>
  <s xml:id="echoid-s159" xml:space="preserve">pleraq; </s>
  <s xml:id="echoid-s160" xml:space="preserve">alia, ſine quibus demonſtrationes, quas in horologiorum delineatio-<lb/>nibus adhibebimus, confici &amp; </s>
  <s xml:id="echoid-s161" xml:space="preserve">intelligi nullo modo poſſunt. </s>
  <s xml:id="echoid-s162" xml:space="preserve">His omnibus accedent <lb/>tria alia problemata, quibus arcus ſemidiurnus, crepuſculi magnitudo, altitudo ſo-<lb/>lis ex hora diei cognita, &amp; </s>
  <s xml:id="echoid-s163" xml:space="preserve">viciſſim hora ex altitudine ſolis, quouis anni tempore, &amp; </s>
  <s xml:id="echoid-s164" xml:space="preserve"><lb/>ad quamcunq; </s>
  <s xml:id="echoid-s165" xml:space="preserve">poli eleuationem, ſeu latitudinem loci, poſſit indagari. </s>
  <s xml:id="echoid-s166" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s167" xml:space="preserve">hæc de <lb/>argumento primi huius libri. </s>
  <s xml:id="echoid-s168" xml:space="preserve">Nunc antequam rem ipſam aggrediamur, pauca pri-<lb/>mum dicenda videntur de horologijs in vniuerſum, eorumq; </s>
  <s xml:id="echoid-s169" xml:space="preserve">neceſſitate, &amp; </s>
  <s xml:id="echoid-s170" xml:space="preserve">inuen-<lb/>tione. </s>
  <s xml:id="echoid-s171" xml:space="preserve">Deinde etiam de horologij<unsure/>s Sciothericis, quæ magis ad noſtram Gnomonicã <lb/>pertinent, eorumq́; </s>
  <s xml:id="echoid-s172" xml:space="preserve">varijs generibus, atq; </s>
  <s xml:id="echoid-s173" xml:space="preserve">inuentoribus, denique de horarum varie-<lb/>tate breuiter agendum erit.</s>
  <s xml:id="echoid-s174" xml:space="preserve"/>
</p>
<div xml:id="echoid-div10" type="float" level="2" n="1">
<note position="left" xlink:label="note-0021-02" xlink:href="note-0021-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0021-03" xlink:href="note-0021-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0021-04" xlink:href="note-0021-04a" xml:space="preserve">Argumentum <lb/>primi libri.</note>
<note position="left" xlink:label="note-0021-05" xlink:href="note-0021-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0021-06" xlink:href="note-0021-06a" xml:space="preserve">50</note>
</div>
<pb o="2" file="0022" n="22" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div12" type="section" level="1" n="11">
<head xml:id="echoid-head13" xml:space="preserve">DE HOROLOGIIS IN VNIVERSVM, <lb/>eorumque neceſſitate, atque inuentione.</head>
<p style="it">
  <s xml:id="echoid-s175" xml:space="preserve">HOROLOGIVM inſtrumentum eſſe, quo horæ deſignantur, deprehendun-<lb/>
<anchor type="note" xlink:label="note-0022-01a" xlink:href="note-0022-01"/>
turve<unsure/>, vocabulum ipſum indicat. </s>
  <s xml:id="echoid-s176" xml:space="preserve">Significat enim horologium, quaſi horarum ra <lb/>tionem, ita vt quicquid quodammodo horas indicat, horologium dici poſſit. </s>
  <s xml:id="echoid-s177" xml:space="preserve">Eſt <lb/>
<anchor type="note" xlink:label="note-0022-02a" xlink:href="note-0022-02"/>
autem hora vnum ex illis ſpatĳs æqualibus, in quæ dies quælibet diuidi conſue-<lb/>uit. </s>
  <s xml:id="echoid-s178" xml:space="preserve">Quamuis enim apud veteres quatuor anni tempora, Ver, Æstas, Autum-<lb/>
<anchor type="note" xlink:label="note-0022-03a" xlink:href="note-0022-03"/>
nus, &amp; </s>
  <s xml:id="echoid-s179" xml:space="preserve">Hyems, horæ dictæ ſint, {ἐπὸ} τοῦ ὁρίζ{ει}ν, vt Platoni placet in Cratylo, ꝙ <lb/>
<anchor type="note" xlink:label="note-0022-04a" xlink:href="note-0022-04"/>
illas anni partes terminẽt, atq; </s>
  <s xml:id="echoid-s180" xml:space="preserve">definiant; </s>
  <s xml:id="echoid-s181" xml:space="preserve">hodie tamen æqualia illa diei ſpatia ho <lb/>ras nũcupamus, eo ꝙ, vt Macrobio placet lib. </s>
  <s xml:id="echoid-s182" xml:space="preserve">1. </s>
  <s xml:id="echoid-s183" xml:space="preserve">Saturnaliorũ, e{as} ſol, qui apud <lb/>Aegyptios Horus (ita enim Apollinẽ, qui idem eſt, qui ſol, appellabãt.) </s>
  <s xml:id="echoid-s184" xml:space="preserve">vocaba-<lb/>tur, ſuo curſu, motu{q́ue} efficiat. </s>
  <s xml:id="echoid-s185" xml:space="preserve">Alĳ tamen malunt, horas dici à nomine græco @@os, quod terminum, ſeu finẽ <lb/>ſignificat, propterea quod ſpatiũ illud continuũ temporis horis tanquam finibus diſtinguimus, ac termina-<lb/>mus. </s>
  <s xml:id="echoid-s186" xml:space="preserve">Deniq; </s>
  <s xml:id="echoid-s187" xml:space="preserve">horarum not atione inueſtig anda etiã ad ſordes ventum eſt, Non enim deſunt, qui arbitrẽtur, <lb/>æquales illas diei particul{as} hor{as} eſſe appellat{as} à verbo græco @pos, quod vrinã ſignificat. </s>
  <s xml:id="echoid-s188" xml:space="preserve">Aiunt enim <lb/>Hermetẽ Triſmegiſtum hor{as} primum obſeruaſſe, hoc eſt, diei ſpatia æqualia, ex vrina ſacri cuiuſdam ani-<lb/>malis apud Aegyptios, quod Serapi, id eſt, ſolierat dicatũ. </s>
  <s xml:id="echoid-s189" xml:space="preserve">Nam cum animaduertiſſet illud animal (rem <lb/>ſanè ridiculã, &amp; </s>
  <s xml:id="echoid-s190" xml:space="preserve">AEgyptĳs magis, quàm Triſmegiſto dignam) duodecies in die, toties{q́ue} in nocte tum lon-<lb/>
<anchor type="note" xlink:label="note-0022-05a" xlink:href="note-0022-05"/>
ga, tum breui, vrinam emittere, æqualibus ſemper interuallis, conſent ancum eſſe rationi put auit, diem no-<lb/>ctem{q́ue} in totidem æqualia ſpatia diſtingui, quæ horæ ab vrina illi{us} animalis nuncuparentur. </s>
  <s xml:id="echoid-s191" xml:space="preserve">Hinc for-<lb/>taſſis factum eſt, vt tota ferme antiquit{as} duodecim horis diem quemcunque, noctem{q́ue} diuiſerit. </s>
  <s xml:id="echoid-s192" xml:space="preserve">Qua de <lb/>re paulo poſt plura dicem{us}.</s>
  <s xml:id="echoid-s193" xml:space="preserve"/>
</p>
<div xml:id="echoid-div12" type="float" level="2" n="1">
<note position="left" xlink:label="note-0022-01" xlink:href="note-0022-01a" xml:space="preserve">Horologium <lb/>quid.</note>
<note position="left" xlink:label="note-0022-02" xlink:href="note-0022-02a" xml:space="preserve">Hora quid.</note>
<note position="left" xlink:label="note-0022-03" xlink:href="note-0022-03a" xml:space="preserve">Vnde dict@ ſint <lb/>horæ.</note>
<note position="left" xlink:label="note-0022-04" xlink:href="note-0022-04a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0022-05" xlink:href="note-0022-05a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">Neceſſitas ho-<lb/>rologiorum.</note>
<p style="it">
  <s xml:id="echoid-s194" xml:space="preserve">DE neceſſitate vero horologiorum non eſt, quod multa verba faciam. </s>
  <s xml:id="echoid-s195" xml:space="preserve">Neminem ſiquidem latere arbi-<lb/>tror, quam miſerum, &amp; </s>
  <s xml:id="echoid-s196" xml:space="preserve">infelix foret genus humanum, ſi hor arum diſtinctionem nullam haberet. </s>
  <s xml:id="echoid-s197" xml:space="preserve">Videm{us} <lb/>enim plerunq; </s>
  <s xml:id="echoid-s198" xml:space="preserve">eos, (quod &amp; </s>
  <s xml:id="echoid-s199" xml:space="preserve">in ſeipſo quiuis experitur) qui quota ſit hora neſciunt, ſimiliter vt eos, qui <lb/>qua in regione verſentur, ignorant, quaſi ſtupore quodam animi affectos eſſe, &amp; </s>
  <s xml:id="echoid-s200" xml:space="preserve">meo quidem iudicio non <lb/>immerito. </s>
  <s xml:id="echoid-s201" xml:space="preserve">Nam horarum diſcrimine ſinguli ſuos labores, ſua{q́ue} otia metiuntur, &amp; </s>
  <s xml:id="echoid-s202" xml:space="preserve">certa ſibi tempora <lb/>in ſuis occupationibus omnibus præfiniunt. </s>
  <s xml:id="echoid-s203" xml:space="preserve">Immo vero cum vita hominum magna ex parte cõmertĳs con-<lb/>
<anchor type="note" xlink:label="note-0022-07a" xlink:href="note-0022-07"/>
ſumatur fere, at q; </s>
  <s xml:id="echoid-s204" xml:space="preserve">conuentibus, ægre profecto carere poſſemus vſu horologiorum, quandoquidem ipſorum <lb/>beneficio cert{as} nobis horas, certa{q́ue} temporum ſpatia præſtituim{us}, quibus ad res nostras per agend{as} <lb/>commodè, ſine vlla rei familiaris, aut aliarum rerum iactura, conuenire poſſimus. </s>
  <s xml:id="echoid-s205" xml:space="preserve">Teſtantur hoc ipſum om <lb/>nes propemodum benè inſtitutæ respublicæ, quæ in vrbib{us} at q; </s>
  <s xml:id="echoid-s206" xml:space="preserve">oppidis paſſim publicis, priuatis{q́ue} ſumpti <lb/>bus varia horologiorum genera tum ſolaria, tum alia fabricant, eorum{q́ue} cuſtodes ac moderatores annuis <lb/>ſtipendĳs alunt: </s>
  <s xml:id="echoid-s207" xml:space="preserve">quod nulla ſanè ratione facerent, niſi horum vſum ſummè ciuitatibus neceſſarium iudica-<lb/>rent. </s>
  <s xml:id="echoid-s208" xml:space="preserve">Teſtantur quoq; </s>
  <s xml:id="echoid-s209" xml:space="preserve">id ipſum omnes propemodum agricolæ, ac ſolitarĳ homines, qui cum horologia non <lb/>habeant, neq; </s>
  <s xml:id="echoid-s210" xml:space="preserve">vero eis ſine magno incommodo poſſint carere, annituntur, quacunque id ratione poſſint, <lb/>hoc incommodum ſubleuare. </s>
  <s xml:id="echoid-s211" xml:space="preserve">Hinc enim videmus eos plerunq; </s>
  <s xml:id="echoid-s212" xml:space="preserve">vmbram ſuorum corporum metiri, vel alia, <lb/>at q; </s>
  <s xml:id="echoid-s213" xml:space="preserve">alia radĳs ſolaribus ſignafigere, vel deniq; </s>
  <s xml:id="echoid-s214" xml:space="preserve">in ipſo cælo certa motus ſolis interdiu, noctu aliorum ſy-<lb/>
<anchor type="note" xlink:label="note-0022-08a" xlink:href="note-0022-08"/>
derum interualla notare, vt hiſce ſaltem obſeruationibus quoquo modo, licet non omni ex parte accuratè, <lb/>&amp; </s>
  <s xml:id="echoid-s215" xml:space="preserve">ad vnguem, hor arum diſcrimina, ſpatia{q́ue} deprehendere, ac dimetiri queant.</s>
  <s xml:id="echoid-s216" xml:space="preserve"/>
</p>
<div xml:id="echoid-div13" type="float" level="2" n="2">
<note position="left" xlink:label="note-0022-07" xlink:href="note-0022-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0022-08" xlink:href="note-0022-08a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s217" xml:space="preserve">CVM igitur horarum cognitio tam vtilis ſit, atq; </s>
  <s xml:id="echoid-s218" xml:space="preserve">adeo neceſſaria omnibus rebuspub. </s>
  <s xml:id="echoid-s219" xml:space="preserve">ſummo ſemper <lb/>studio maiores noſtri varia, &amp; </s>
  <s xml:id="echoid-s220" xml:space="preserve">ingenioſa inſtrumenta, (quæ horologia appellam{us}) quibus hor arum in-<lb/>terualla dignoſceremus, excogit arunt; </s>
  <s xml:id="echoid-s221" xml:space="preserve">quæ quidem omnia ad duo genera reuocari poſſunt. </s>
  <s xml:id="echoid-s222" xml:space="preserve">Quædam inter-<lb/>
<anchor type="note" xlink:label="note-0022-09a" xlink:href="note-0022-09"/>
diu ex ſola vmbra ſolis, noctu vel ex Lunæ vmbra, vel ex inſpectione aliorum ſyderum, hor{as} indicant, <lb/>de quibus infra plura ſcribemus. </s>
  <s xml:id="echoid-s223" xml:space="preserve">Quædam verò inſtrumento aliquo mechanico, &amp; </s>
  <s xml:id="echoid-s224" xml:space="preserve">varĳs motibus oſtendũt <lb/>hor{as}, quæ multiplicia ſunt. </s>
  <s xml:id="echoid-s225" xml:space="preserve">Cum enim priora illa horologia tempore nubilo null{as} prorſus monſtrarent <lb/>hor{as}, oportuit illos aliam viam, qua hor{as} not arent, inuenire. </s>
  <s xml:id="echoid-s226" xml:space="preserve">Hinc effectum eſt, vt quidam hydrauli-<lb/>cis horologĳs vſi ſint, in quibus beneficio motus aquæ horæ exquiruntur: </s>
  <s xml:id="echoid-s227" xml:space="preserve">qua in re mirum in modum lau-<lb/>
<anchor type="note" xlink:label="note-0022-10a" xlink:href="note-0022-10"/>
dat{us} fuit Cteſibius Alexandrin{us}. </s>
  <s xml:id="echoid-s228" xml:space="preserve">Hic enim, vt Vitruuius lib. </s>
  <s xml:id="echoid-s229" xml:space="preserve">9. </s>
  <s xml:id="echoid-s230" xml:space="preserve">refert, ingenio mir abili cõſtituit (Vtor <lb/>verbis Vitruuĳ) cauũ ex auro perfectum, aut ex gemma terebrata, ea enim nec teruntur percuſſu aquæ, <lb/>nec ſordes recipiunt, vt obturentur. </s>
  <s xml:id="echoid-s231" xml:space="preserve">Namq; </s>
  <s xml:id="echoid-s232" xml:space="preserve">æqualiter per id cauum influens aqua ſubleuabat ſcapbum <lb/>inuerſum, in quo collocata regula, verſatilia tympana denticulis æqualibus ſunt perfecta: </s>
  <s xml:id="echoid-s233" xml:space="preserve">qui denticuli <lb/>alius aliũ impellentes, verſationes modicas faciunt, &amp; </s>
  <s xml:id="echoid-s234" xml:space="preserve">motiones, &amp; </s>
  <s xml:id="echoid-s235" xml:space="preserve">cætera huiuſmodi, vnde diei partes, <lb/>id eſt, horæ cognoſci poterant, &amp; </s>
  <s xml:id="echoid-s236" xml:space="preserve">dĳudicari. </s>
  <s xml:id="echoid-s237" xml:space="preserve">Plinius vero ad finem lib. </s>
  <s xml:id="echoid-s238" xml:space="preserve">7. </s>
  <s xml:id="echoid-s239" xml:space="preserve">ſcribit, Scipionem Naſicam pri-<lb/>mum aqua diuiſiſſe hor{as} æquè noctium, ac dierum, anno Vrbis 595. </s>
  <s xml:id="echoid-s240" xml:space="preserve">Non nulli aut em ponebant vaſa quæ <lb/>dam ænea aquis plena, &amp; </s>
  <s xml:id="echoid-s241" xml:space="preserve">ſubtiliter perforata. </s>
  <s xml:id="echoid-s242" xml:space="preserve">quantum enim aquarum in aliud vas @ecidiſſet, cum ad <lb/>inſcripta inſpexiſſent ſigna, quid temporis elapſum eſſet, intelligebant. </s>
  <s xml:id="echoid-s243" xml:space="preserve">Talia horologia à perforati vaſis <lb/>ſimilitudine clepſydr{as} appellabant, quòd furarentur quodammodo aquam, &amp; </s>
  <s xml:id="echoid-s244" xml:space="preserve">guttat im infundendo per <lb/>anguſtum for amen de vaſe in v{as} emitterẽt. </s>
  <s xml:id="echoid-s245" xml:space="preserve">Vnde ſæpe legimus, oratoribus tres, aut quatuor clepſidras,
<pb o="3" file="0023" n="23" rhead="LIBER PRIMVS."/>
id eſt, horas olim ad dicendum fuiſſe conceſſas. </s>
  <s xml:id="echoid-s246" xml:space="preserve">Alĳ aſſerunt, ea vaſa fuiſſe vitrea ſubtiliter perforata, in <lb/>quibus horæ æqualib{us} dimenſionibus erant ſignatæ, &amp; </s>
  <s xml:id="echoid-s247" xml:space="preserve">ad quorum fundum foramen illud paruũ guttatim <lb/>aquam emittebat, ſic{q́ue} per aquæ diminutionem horæ elapſæ deprehendebantur. </s>
  <s xml:id="echoid-s248" xml:space="preserve">His hac noſtra tempeſtate <lb/>ſucceſſerunt horologia quædam è vitro fabrefacta, quæ arenam, pulueremve ſubtiliſſimum habent inclu-<lb/>ſum, qui per for amen admodum exiguum ſenſim ex parte ſuperiore in inferiorem delabitur, horas{q́ue} ela-<lb/>pſas hac ratione oſtendũ<unsure/>t. </s>
  <s xml:id="echoid-s249" xml:space="preserve">Scd procul dubio cuncta hactenus enumer at a horologia multis partibus anteit <lb/>horologium illud, quod hac noſtra f<unsure/>ere ætate, mir abili artificio, ingenio{q́ue} præctanti inuentum eſt, conſtat {q́ue} <lb/>rotulis quibuſdam denticulatis, libratis{q́ue} ponderibus ad hor{as}, horarum{q́ue} partes, &amp; </s>
  <s xml:id="echoid-s250" xml:space="preserve">ad motus cælestes <lb/>demonstrandos, &amp; </s>
  <s xml:id="echoid-s251" xml:space="preserve">alia buiuſmodi per commodum. </s>
  <s xml:id="echoid-s252" xml:space="preserve">Verum nos de hiſce horologĳs Mechanicis, quòd à no-<lb/>
<anchor type="note" xlink:label="note-0023-01a" xlink:href="note-0023-01"/>
ſtro inſtituto abborreant, in hoc opere nihil ſcripturi ſumus. </s>
  <s xml:id="echoid-s253" xml:space="preserve">Quare ad prior a horologia, quæ per vmbram <lb/>ſolis, vel radios aliorum aſtrorum hor{as} diximus indicare, reuertamur.</s>
  <s xml:id="echoid-s254" xml:space="preserve"/>
</p>
<div xml:id="echoid-div14" type="float" level="2" n="3">
<note position="left" xlink:label="note-0022-09" xlink:href="note-0022-09a" xml:space="preserve">Horologiorum <lb/>uaria genera.</note>
<note position="left" xlink:label="note-0022-10" xlink:href="note-0022-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0023-01" xlink:href="note-0023-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div16" type="section" level="1" n="12">
<head xml:id="echoid-head14" xml:space="preserve">DE HOROLOGIIS SCIOTHERICIS <lb/>eorum{q́ue} varĳs generibus.</head>
<p style="it">
  <s xml:id="echoid-s255" xml:space="preserve">HOROLOGIA omnia, quæ paulo ante ex ſola vmbra ſolis hor{as} monſtrare diximus, ſolaria à <lb/>ſcriptorib{us} appellari ſolent, ſeu ſciotherica, ab vmbra ſolis. </s>
  <s xml:id="echoid-s256" xml:space="preserve">σκιόθηρον enim locum ſignificat captan-<lb/>dæ vmbræ idoneum. </s>
  <s xml:id="echoid-s257" xml:space="preserve">Vnde σκιοθηρα inſtrumenta ſunt mathematica, quibus vmbrę excipi ſolent; </s>
  <s xml:id="echoid-s258" xml:space="preserve">vt horolo-<lb/>gium ſciothericum ſit inſtrumentum, in quo ex vmbra ſolis, ſiue aliorum aſtrorum radys, qui inſtar vmbræ <lb/>
<anchor type="note" xlink:label="note-0023-02a" xlink:href="note-0023-02"/>
ſunt, certa diei hora &amp; </s>
  <s xml:id="echoid-s259" xml:space="preserve">quantitas, ortus &amp; </s>
  <s xml:id="echoid-s260" xml:space="preserve">occaſus ſolis, ſigna zodiaci, in quib{us} ſol verſatur, atque ple-<lb/>
<anchor type="note" xlink:label="note-0023-03a" xlink:href="note-0023-03"/>
raq; </s>
  <s xml:id="echoid-s261" xml:space="preserve">alia ad res cœleſtes ſpectantia, artificioſè demõſtrantur. </s>
  <s xml:id="echoid-s262" xml:space="preserve">Multis autem modis diuidi poteſt horologiũ <lb/>ſciothericum. </s>
  <s xml:id="echoid-s263" xml:space="preserve">Primum enim quædam dicta ſunt penſilia, eo quod ex ipſis è manu liberè pendentib{us}, &amp; </s>
  <s xml:id="echoid-s264" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0023-04a" xlink:href="note-0023-04"/>
verſus ſolem, vel alia quæcũq; </s>
  <s xml:id="echoid-s265" xml:space="preserve">aſtra directis, horas cognoſcam{us}: </s>
  <s xml:id="echoid-s266" xml:space="preserve">qualia ſunt illa omnia, in quibus vtimur <lb/>aut pinnacidĳs, hoc eſt, tabellis quibuſdam quadratis perforatis, quales in dioptra Aſtrolabĳ affigi ſolẽt, <lb/>aut foramine aliquo per exiguo, aut deniq; </s>
  <s xml:id="echoid-s267" xml:space="preserve">filo cum perpendiculo, in quo nonnunquã nodulus quidam mobi-<lb/>lis apponitur, ad hor{as} diſcernend{as}; </s>
  <s xml:id="echoid-s268" xml:space="preserve">cuiuſmodi ſunt Aſtrolabia, Cylindri, quadrantes, annuli aſtronomi-<lb/>ci, horarĳve, &amp; </s>
  <s xml:id="echoid-s269" xml:space="preserve">id genus alia, de quib{us} in lib. </s>
  <s xml:id="echoid-s270" xml:space="preserve">@. </s>
  <s xml:id="echoid-s271" xml:space="preserve">agemus. </s>
  <s xml:id="echoid-s272" xml:space="preserve">Quædam verò ſtabilia ſunt, certumq́, ſitum in <lb/>aliquo plano requirunt, ita vt neceſſe non ſit ea pendere, quæ quidem per gnomonis, stylive vmbram ho-<lb/>r{as} oſtendunt, diſtribuuntur{q́ue} in duo genera. </s>
  <s xml:id="echoid-s273" xml:space="preserve">Alia enim in ſuperficie plana, quæ alicui circulo cœleſti ma-<lb/>
<anchor type="note" xlink:label="note-0023-05a" xlink:href="note-0023-05"/>
ximo æquidiſtet, delineantur: </s>
  <s xml:id="echoid-s274" xml:space="preserve">Alia vero in ſuperficie non plana, vt in hemiſphærio concauo aut conuexo, <lb/>vel in Cylindro conuexo, vel concauo, vel in quacunq; </s>
  <s xml:id="echoid-s275" xml:space="preserve">alia ſuperficie, quæ plana non eſt, depinguntur, de <lb/>quibus in octauo libro ſcribemus; </s>
  <s xml:id="echoid-s276" xml:space="preserve">nunc genera illorum, quæ in ſuperficiebus planis deſcribuntur, &amp; </s>
  <s xml:id="echoid-s277" xml:space="preserve">de qui-<lb/>bus potiſſimum in hoc opere diſſeremus, recenſeamus.</s>
  <s xml:id="echoid-s278" xml:space="preserve"/>
</p>
<div xml:id="echoid-div16" type="float" level="2" n="1">
<note position="right" xlink:label="note-0023-02" xlink:href="note-0023-02a" xml:space="preserve">Horologium <lb/>Sciochericum <lb/>quid.</note>
<note position="left" xlink:label="note-0023-03" xlink:href="note-0023-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0023-04" xlink:href="note-0023-04a" xml:space="preserve">Sciothericorũ <lb/>horologiorum <lb/>varia genera.</note>
<note position="left" xlink:label="note-0023-05" xlink:href="note-0023-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s279" xml:space="preserve">HOROLOGIORVM igitur ſolarium, quæ in plana aliqua ſuperficie deſcribuntur, plurima ſunt <lb/>
<anchor type="note" xlink:label="note-0023-06a" xlink:href="note-0023-06"/>
genera, pro multitudine cælestium circulorum maximorum, quibus ſuperficies planæ horologiorũ æquidi-<lb/>ſtant, &amp; </s>
  <s xml:id="echoid-s280" xml:space="preserve">à quibus horologia ipſa nomina inuenerunt, vt propoſ. </s>
  <s xml:id="echoid-s281" xml:space="preserve">2. </s>
  <s xml:id="echoid-s282" xml:space="preserve">huius libri docebimus. </s>
  <s xml:id="echoid-s283" xml:space="preserve">Sed quoniã præ-<lb/>cipuè nouem circuli maximi in cœlo conſider ari poſſunt ſitu, &amp; </s>
  <s xml:id="echoid-s284" xml:space="preserve">poſitione differentes, efficitur, vt totidem <lb/>ſint gener a horologiorum, quæ in ſuperficie aliqua plana deſcribuntur. </s>
  <s xml:id="echoid-s285" xml:space="preserve">Circuli autem maximi ſunt hi, Ho-<lb/>rizon; </s>
  <s xml:id="echoid-s286" xml:space="preserve">verticalis circulus proprie dictus, incedens per verticem capitis, &amp; </s>
  <s xml:id="echoid-s287" xml:space="preserve">communes ſectiones A E qua-<lb/>toris, at q; </s>
  <s xml:id="echoid-s288" xml:space="preserve">Horizontis; </s>
  <s xml:id="echoid-s289" xml:space="preserve">Meridianus; </s>
  <s xml:id="echoid-s290" xml:space="preserve">Circulus horæ 6. </s>
  <s xml:id="echoid-s291" xml:space="preserve">a meridie, vel media nocte, per polos mundi, &amp; </s>
  <s xml:id="echoid-s292" xml:space="preserve">eaſ-<lb/>
<anchor type="note" xlink:label="note-0023-07a" xlink:href="note-0023-07"/>
dem ſectiones communes A E quatoris, &amp; </s>
  <s xml:id="echoid-s293" xml:space="preserve">Horizontis ductus; </s>
  <s xml:id="echoid-s294" xml:space="preserve">A E quator; </s>
  <s xml:id="echoid-s295" xml:space="preserve">Verticalis cir culus quicunque <lb/>à proprie dicto Verticali deflectens, &amp; </s>
  <s xml:id="echoid-s296" xml:space="preserve">ad Horizontem rect{us}; </s>
  <s xml:id="echoid-s297" xml:space="preserve">Circul{us} maximus ab Horizonte declinãs <lb/>&amp; </s>
  <s xml:id="echoid-s298" xml:space="preserve">per communes ſectiones Meridiani, Horizontis{q́ue} tranſiens, at q; </s>
  <s xml:id="echoid-s299" xml:space="preserve">ad verticalem proprie dictum rect{us}; <lb/></s>
  <s xml:id="echoid-s300" xml:space="preserve">Circul{us} maxim{us} ad Horizontem inclinatus, qui per cõmunes ſectiones Aequatoris, Verticalis propriè <lb/>dicti, &amp; </s>
  <s xml:id="echoid-s301" xml:space="preserve">Horizontis deſcribitur, rect{us}{q́ue} eſt ad Meridianum; </s>
  <s xml:id="echoid-s302" xml:space="preserve">Circulus deniq; </s>
  <s xml:id="echoid-s303" xml:space="preserve">maximus &amp; </s>
  <s xml:id="echoid-s304" xml:space="preserve">ad Horizontẽ, <lb/>&amp; </s>
  <s xml:id="echoid-s305" xml:space="preserve">ad Meridianũ, &amp; </s>
  <s xml:id="echoid-s306" xml:space="preserve">ad Verticalem propriè dictum inclinatus. </s>
  <s xml:id="echoid-s307" xml:space="preserve">Quoniã vero quilibet horum circulorum <lb/>præter Horizõtem, du{as} habet facies, quæ interdiu à ſole illustrari poſſunt, vt Verticalis tam proprie di-<lb/>ct{us}, quàm ille, qui ab eo declinat, vnã habet, quæ ad meridiẽ vergit, &amp; </s>
  <s xml:id="echoid-s308" xml:space="preserve">alterã, quæ ſpectat ad boreã; </s>
  <s xml:id="echoid-s309" xml:space="preserve">Me-<lb/>ridian{us} autẽ unam, quæ ortum, &amp; </s>
  <s xml:id="echoid-s310" xml:space="preserve">alterã, quæ occaſum reſpicit; </s>
  <s xml:id="echoid-s311" xml:space="preserve">Cæteri deniq; </s>
  <s xml:id="echoid-s312" xml:space="preserve">Circuli ad Horizontem in-<lb/>clinati habent ſuperiorem vnam, quæ ad Zenith, ſeu verticem capitis, &amp; </s>
  <s xml:id="echoid-s313" xml:space="preserve">inferiorẽ alteram, quæ ad Nadir <lb/>
<anchor type="note" xlink:label="note-0023-08a" xlink:href="note-0023-08"/>
ſpectat; </s>
  <s xml:id="echoid-s314" xml:space="preserve">fit vt in vniuerſum ſint ſeptemdecim genera huiuſmodi horologiorum, quæ it a appellari poterunt.</s>
  <s xml:id="echoid-s315" xml:space="preserve"/>
</p>
<div xml:id="echoid-div17" type="float" level="2" n="2">
<note position="right" xlink:label="note-0023-06" xlink:href="note-0023-06a" xml:space="preserve">Horologia ſo@a <lb/>ria diuiduntur <lb/>ratione circulo <lb/>rum maximo-<lb/>rũ, quibus equi-<lb/>diſtant, &amp; à qui <lb/>bus nomen ac-<lb/>eipiunt.</note>
<note position="left" xlink:label="note-0023-07" xlink:href="note-0023-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0023-08" xlink:href="note-0023-08a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Quot ſint gene <lb/>ra horologiorũ <lb/>ſolariũ, quæin <lb/>ſuperficie plana <lb/>deſcribuntur.</note>
<p style="it">
  <s xml:id="echoid-s316" xml:space="preserve">1. </s>
  <s xml:id="echoid-s317" xml:space="preserve">HORIZONTALE, quod Horizonti æquidiſtat.</s>
  <s xml:id="echoid-s318" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s319" xml:space="preserve">2. </s>
  <s xml:id="echoid-s320" xml:space="preserve">VERTICALE ad meridiẽ ſpectãs, qđ<unsure/> circulo Verticali p<unsure/>priè dicto par allelũ eſt, meridiẽ{q́ue} reſpicit.</s>
  <s xml:id="echoid-s321" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s322" xml:space="preserve">3. </s>
  <s xml:id="echoid-s323" xml:space="preserve">VERTICALE ad Boream vergens, quod eidem Verticali Circulo æquidiſtat, ſpectat{q́ue} ad Se-<lb/>ptentrionem, ſeu Boream.</s>
  <s xml:id="echoid-s324" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s325" xml:space="preserve">4. </s>
  <s xml:id="echoid-s326" xml:space="preserve">MERIDIANVM Orientale, quod circulo Meridiano æquidiſtat, &amp; </s>
  <s xml:id="echoid-s327" xml:space="preserve">ad ortum ſolis vergit.</s>
  <s xml:id="echoid-s328" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s329" xml:space="preserve">5. </s>
  <s xml:id="echoid-s330" xml:space="preserve">MERIDIANVM Occidentale, quod eidem Meridiano circulo eſt par allelum, reſpicitque ad <lb/>Occidentem ſolem.</s>
  <s xml:id="echoid-s331" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s332" xml:space="preserve">6. </s>
  <s xml:id="echoid-s333" xml:space="preserve">POLARE ſuperius, quod æquidiſtat circulo illi maximo, qui per puncta veri, æquinoctialiſve <lb/>ortus, &amp; </s>
  <s xml:id="echoid-s334" xml:space="preserve">occaſus, (hoc eſt, per communes ſectiones A E quatoris, Horizontis, Verticaliſ{q́ue}) at q; </s>
  <s xml:id="echoid-s335" xml:space="preserve">per vtrũq; <lb/></s>
  <s xml:id="echoid-s336" xml:space="preserve">mundi polum tra@ſit, ſpectat{q́ue} ad Zenith.</s>
  <s xml:id="echoid-s337" xml:space="preserve"/>
</p>
<pb o="4" file="0024" n="24" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s338" xml:space="preserve">7. </s>
  <s xml:id="echoid-s339" xml:space="preserve">POLARE inferius, quod eidẽ maximo circulo per puncta veri, ſiue æquinoctialis ortus, occaſuſ{q́ue}, <lb/>ac per vtrumque polum mundi ducto æquidiſtat, &amp; </s>
  <s xml:id="echoid-s340" xml:space="preserve">ad Nadir ſpectat.</s>
  <s xml:id="echoid-s341" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s342" xml:space="preserve">8. </s>
  <s xml:id="echoid-s343" xml:space="preserve">AEQVINOCTIALE ſuperius, quod parallelum eſt A E quinoctiali circulo, reſpicit{q́ue} polũ <lb/>mundi ſupra Horizontem eleuatum.</s>
  <s xml:id="echoid-s344" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s345" xml:space="preserve">9. </s>
  <s xml:id="echoid-s346" xml:space="preserve">AEQVINOCTIALE inferius, quod eidem circulo æquinoctiali æquidistat, ſed ad eum mun-<lb/>dipolum ſpectat, qui ſub Horizonte latet.</s>
  <s xml:id="echoid-s347" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s348" xml:space="preserve">10. </s>
  <s xml:id="echoid-s349" xml:space="preserve">DECLINANS à meridie in ortum, occaſumve, quod æquidistat cuicunq; </s>
  <s xml:id="echoid-s350" xml:space="preserve">circulo Verticali, <lb/>qui à Verticali propriè dicto declinet, &amp; </s>
  <s xml:id="echoid-s351" xml:space="preserve">vergat ad meridiẽ, non tamen directo, rectumq́, eſt ad Horizon-<lb/>tem; </s>
  <s xml:id="echoid-s352" xml:space="preserve">quale depingi ſolet in muro cuiuſuis ædificĳ, qui ad meridiem reſpicit, ſed non directo, &amp; </s>
  <s xml:id="echoid-s353" xml:space="preserve">ad Hori-<lb/>zontem rectus eſt.</s>
  <s xml:id="echoid-s354" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s355" xml:space="preserve">11. </s>
  <s xml:id="echoid-s356" xml:space="preserve">DECLINANS à Borea, Septẽtrioneve in ortum, vel occaſum, quod cuilibet circulo Vertica-<lb/>li par allelum eſt, qui à primario Verticali deflectat, &amp; </s>
  <s xml:id="echoid-s357" xml:space="preserve">ad Boream, non tamen directo, ſpectet, rectum{q́ue} <lb/>eſt ad Horizontem; </s>
  <s xml:id="echoid-s358" xml:space="preserve">quale deſcribitur in muro cuiuslibet ædificĳ, qui ad Horizontem rectus eſt, &amp; </s>
  <s xml:id="echoid-s359" xml:space="preserve">non <lb/>directò ad boream ſpectat.</s>
  <s xml:id="echoid-s360" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s361" xml:space="preserve">12. </s>
  <s xml:id="echoid-s362" xml:space="preserve">DECLINANS ab Horizonte ſuperius, quod ad Zenith ſpectat, &amp; </s>
  <s xml:id="echoid-s363" xml:space="preserve">ad ortum, occaſumve di-<lb/>rectò vergit, æquidiſtat{q́ue} circulo maximo, qui ad Horizontẽ inclinatus eſt, &amp; </s>
  <s xml:id="echoid-s364" xml:space="preserve">ad Verticalem primarium <lb/>rectus, tranſit{q́ue} per communes ſectiones Meridiani, &amp; </s>
  <s xml:id="echoid-s365" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s366" xml:space="preserve">Huiuſmodi horologium depingeretur <lb/>in ſuperiori facie tecti alicuius, quod ad Verticalem cir culum propriè dictum rectum eſſet, hoc eſt, directo <lb/>in ortum, vel occaſum ſpectaret.</s>
  <s xml:id="echoid-s367" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s368" xml:space="preserve">13. </s>
  <s xml:id="echoid-s369" xml:space="preserve">DECLINANS ab Horizõte inferi{us}, quod ad Nadir ſpectat, &amp; </s>
  <s xml:id="echoid-s370" xml:space="preserve">directò ad ortum, occasũve <lb/>
<anchor type="note" xlink:label="note-0024-02a" xlink:href="note-0024-02"/>
vergit, æquidiſtat{q́ue} eidem circulo maximo, cui ſuperius parallelum eſſe diximus. </s>
  <s xml:id="echoid-s371" xml:space="preserve">Cuiuſmodi horologium <lb/>deſcriberetur in eodem tecto, in quo ſuperius, ſed in facie inferiori, quæ ad Nadir ſpectat, ſi facies tamen <lb/>hæc inferior àſole illuminaretur.</s>
  <s xml:id="echoid-s372" xml:space="preserve"/>
</p>
<div xml:id="echoid-div18" type="float" level="2" n="3">
<note position="left" xlink:label="note-0024-02" xlink:href="note-0024-02a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s373" xml:space="preserve">14. </s>
  <s xml:id="echoid-s374" xml:space="preserve">INCLINATVM ad Horizõtem ſuperius, quod ſpectat ad Zenith, &amp; </s>
  <s xml:id="echoid-s375" xml:space="preserve">ad meridiem, boreãve <lb/>directò vergit, æquidiſtat{q́ue} maximo circulo ad Horizontem inclinato, qui ad Meridianum rectus est, trã-<lb/>ſit{q́ue} per communes ſectiones A E quatoris, &amp; </s>
  <s xml:id="echoid-s376" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s377" xml:space="preserve">Quale eſſet horologium delineatum in facie ſu-<lb/>periori alicuius tecti, quod ad Meridianũ eſſet rectũ, id eſt, directò in meridiẽ, Septentrionẽve ſpectaret.</s>
  <s xml:id="echoid-s378" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s379" xml:space="preserve">15. </s>
  <s xml:id="echoid-s380" xml:space="preserve">INCLINATVM ad Horizontem inferius, quod ad Nadir ſpectat, &amp; </s>
  <s xml:id="echoid-s381" xml:space="preserve">directò in meridiem, <lb/>vel Boream vergit, æquidistat{q́ue} eidem maximo circulo, cui ſuperius diximus eſſe parallelum. </s>
  <s xml:id="echoid-s382" xml:space="preserve">Quale eſſet <lb/>horologium depictum in facie inferiori eiuſdem tecti, in cuius ſuperiori facie ſuperius diximus delincari.</s>
  <s xml:id="echoid-s383" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s384" xml:space="preserve">16. </s>
  <s xml:id="echoid-s385" xml:space="preserve">DECLINANS ſimul &amp; </s>
  <s xml:id="echoid-s386" xml:space="preserve">inclinatum ſuperius, quod ſpectat ad Zenith, ſed neq; </s>
  <s xml:id="echoid-s387" xml:space="preserve">directò in me-<lb/>ridiem, boreamve, vt inclinatum ad Horizontem, neq; </s>
  <s xml:id="echoid-s388" xml:space="preserve">in ortum, aut occaſum, vt declinãs ab Horizonte, <lb/>vergit; </s>
  <s xml:id="echoid-s389" xml:space="preserve">æquidistat tamen circulo maximo, qui nec ad Horizontem, nec ad Verticalem propriè dictum, nec <lb/>ad Meridianum rectus eſt, ſed ad omnes hoſce circulos inclinatus, ita vt per nullius polos, qui ſunt Zenith <lb/>&amp; </s>
  <s xml:id="echoid-s390" xml:space="preserve">Nadir, communes ſectiones Meridiani &amp; </s>
  <s xml:id="echoid-s391" xml:space="preserve">Horizontis, at q; </s>
  <s xml:id="echoid-s392" xml:space="preserve">ſectiones communes Horizontis &amp; </s>
  <s xml:id="echoid-s393" xml:space="preserve">Aequa <lb/>toris, tranſeat. </s>
  <s xml:id="echoid-s394" xml:space="preserve">Tale eſſet horologium deſcriptum in ſuperiori facie alicuius tecti, quod directò non ſpecta-<lb/>ret in ortum occaſumve, aut in meridiem Septentrionemve.</s>
  <s xml:id="echoid-s395" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s396" xml:space="preserve">17. </s>
  <s xml:id="echoid-s397" xml:space="preserve">DECLINANS ſimul &amp; </s>
  <s xml:id="echoid-s398" xml:space="preserve">inclinatum inferius, quod ad Nadir ſpectat, reliqua autem omnia <lb/>communia habet cum ſuperiori. </s>
  <s xml:id="echoid-s399" xml:space="preserve">Quale eſſet horologium delineatum in facie inferiori eiuſdẽ tecti, in cuius <lb/>ſuperiori facie ſuperius deſcribi diximus.</s>
  <s xml:id="echoid-s400" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s401" xml:space="preserve">HAEC omnia genera ante oculos ponemus in appoſita figura. </s>
  <s xml:id="echoid-s402" xml:space="preserve">Horologium enim in plano A B C D <lb/>
<anchor type="note" xlink:label="note-0024-05a" xlink:href="note-0024-05"/>
quod Horizonti æquidiſtet, depictum, appellabitur Horizontale. </s>
  <s xml:id="echoid-s403" xml:space="preserve">Si deinde ſupra ſingulas baſes octogonas, <lb/>hexagon{as}, tetragonas, &amp; </s>
  <s xml:id="echoid-s404" xml:space="preserve">trigonam intelligantur erecta ædificia, ſpectabunt muriſupra rectas E F, G H, <lb/>collocati directò ad A, punctum meridiei, &amp; </s>
  <s xml:id="echoid-s405" xml:space="preserve">ad C, punctum Septentrionis, at q; </s>
  <s xml:id="echoid-s406" xml:space="preserve">in eorum faciebus ad A, <lb/>vergentibus horologia Verticalia ad meridiem, auſtrumve ſpectantia deſcribentur. </s>
  <s xml:id="echoid-s407" xml:space="preserve">In faciebus autem eo-<lb/>rundem ſpectantibus ad C, delineabuntur horologia Verticalia ad Boream, ſeptentrionei<unsure/>nve ſpectantia. <lb/></s>
  <s xml:id="echoid-s408" xml:space="preserve">In muris porrò ſupra rectas I K, L M, erectis, qui verſus B, directò in ortum ſpectant, aut verſus D, in <lb/>occaſum, deſcribentur in eorum faciebus ad B, ſpectantibus, horologia Meridiana orientalia. </s>
  <s xml:id="echoid-s409" xml:space="preserve">At in facie-<lb/>bus punctum D, reſpicientibus, horologia Meridiana occidentalia.</s>
  <s xml:id="echoid-s410" xml:space="preserve"/>
</p>
<div xml:id="echoid-div19" type="float" level="2" n="4">
<note position="left" xlink:label="note-0024-05" xlink:href="note-0024-05a" xml:space="preserve">Exempla prædi <lb/>ctorum horolo-<lb/>giorum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s411" xml:space="preserve">RVRSVS ſi ſupra rectas E F, G H, intelligantur plana ad Horizontem inclinata verſus ſepten-<lb/>
<anchor type="note" xlink:label="note-0024-06a" xlink:href="note-0024-06"/>
trionem C, ſecundum altitudinem poli, dicentur horologia in ſuperioribus facieb{us} deſcripta, Polaria ſu-<lb/>periora, in inferioribus aut em inferiora. </s>
  <s xml:id="echoid-s412" xml:space="preserve">Si vero ſupra eaſdem rectas E F, G H, cogitentur plana incli-<lb/>nata ad Horizontem verſus meridiem A, ſecundum altitudinem Aequatoris, ſeu complementum alti-<lb/>tudinis poli, delineabuntur in faciebus ſuperioribus horologia Aequinoctialia ſuperiora. </s>
  <s xml:id="echoid-s413" xml:space="preserve">Inferiora autem <lb/>in inferioribus.</s>
  <s xml:id="echoid-s414" xml:space="preserve"/>
</p>
<div xml:id="echoid-div20" type="float" level="2" n="5">
<note position="left" xlink:label="note-0024-06" xlink:href="note-0024-06a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s415" xml:space="preserve">IAM verò quoniam muri ad Horizontem recti ſupra rectas E I, H M, collocati non directò ſpectãt <lb/>ad A, punctum meridiei, @@ut ad C, punctum ſeptentrionis, ſed ab vtroq; </s>
  <s xml:id="echoid-s416" xml:space="preserve">declinant verſ{us} B, punctum <lb/>ortus, aut verſus D, punctum occaſus, deſcribentur quidem in eorum faciebus puncta inter A, &amp; </s>
  <s xml:id="echoid-s417" xml:space="preserve">B, po-<lb/>ſita reſpicientibus, horologia declinantia à meridie, id eſt, à puncto meridiei A, in ortum, in oppoſitis autẽ <lb/>faciebus, quæ puncta inter C, &amp; </s>
  <s xml:id="echoid-s418" xml:space="preserve">D, locata reſpiciunt, horologia declinantia à ſeptentrione, hoc eſt, à pun <lb/>cto ſeptentrionis C, in occaſum. </s>
  <s xml:id="echoid-s419" xml:space="preserve">Contra verò, quia muri ſuprarectas F L, G K, extructi, &amp; </s>
  <s xml:id="echoid-s420" xml:space="preserve">ad Horizon-
<pb o="5" file="0025" n="25" rhead="LIBER PRIMVS."/>
<anchor type="figure" xlink:label="fig-0025-01a" xlink:href="fig-0025-01"/>
<anchor type="note" xlink:label="note-0025-01a" xlink:href="note-0025-01"/>
<anchor type="note" xlink:label="note-0025-02a" xlink:href="note-0025-02"/>
<anchor type="note" xlink:label="note-0025-03a" xlink:href="note-0025-03"/>
tem recti non vergunt directò ad A, punctum meridiei, aut ad C, punctum ſeptentrionis, ſed ab utroque <lb/>declinant verſus D, punctum occaſus, aut verſus B, punctum ortus, delineabuntur quidem in eorum fa-<lb/>cieb{us}, quæ ſpectant ad puncta inter A, &amp; </s>
  <s xml:id="echoid-s421" xml:space="preserve">D, locata, horologia declinantia à meridie, hoc eſt, à puncto <lb/>A, meridiei in occaſum, in faciebus verò oppoſitis ad puncta inter C, &amp; </s>
  <s xml:id="echoid-s422" xml:space="preserve">B, conuerſis, horologia à ſepten <lb/>trione, id eſt, à puncto C, ſeptentrionis in ortum declinantia.</s>
  <s xml:id="echoid-s423" xml:space="preserve"/>
</p>
<div xml:id="echoid-div21" type="float" level="2" n="6">
  <figure xlink:label="fig-0025-01" xlink:href="fig-0025-01a">
    <image file="0025-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0025-01"/>
  </figure>
<note position="left" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0025-02" xlink:href="note-0025-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0025-03" xlink:href="note-0025-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s424" xml:space="preserve">QVOD ſi ſupra rectas I K, L M, conſtruantur plana verſus ortum B, vel occaſum D, ad Horizon-<lb/>tem inclinata, deſcribentur in eorum faciebus ſuperioribus horologia ſuperiora declinantia ab Horizon-<lb/>te: </s>
  <s xml:id="echoid-s425" xml:space="preserve">Inferiora autem in inferioribus faciebus. </s>
  <s xml:id="echoid-s426" xml:space="preserve">Ita quoq; </s>
  <s xml:id="echoid-s427" xml:space="preserve">ſi ſupra rectas E F, G H, inclinata ſint ad Horizon <lb/>tem plana verſ{us} A, meridiem, vel verſus C, ſeptentrionem, appellabuntur horologia in eorum faciebus <lb/>ſuperiorib{us} delineata, ſuperior a ad Horizont em inclinata: </s>
  <s xml:id="echoid-s428" xml:space="preserve">Inferiora autem in inferioribus facieb{us} de-<lb/>ſcripta. </s>
  <s xml:id="echoid-s429" xml:space="preserve">Si deniq; </s>
  <s xml:id="echoid-s430" xml:space="preserve">ſupra rect{as} E I, H M, F L, G K, inclinata ſint plana ad Horizontem quomodocunq; <lb/></s>
  <s xml:id="echoid-s431" xml:space="preserve">deſcribentur in eorum facieb{us} ſuperiorib{us} horologia ſuperior a declinantia ſimul, &amp; </s>
  <s xml:id="echoid-s432" xml:space="preserve">inclinata. </s>
  <s xml:id="echoid-s433" xml:space="preserve">In infe-<lb/>riorib{us} autem facieb{us} inferiora. </s>
  <s xml:id="echoid-s434" xml:space="preserve">Ex quibus facile colligitur, infinita propemodum eſſe poſſe genera horo <lb/>logiorum declinantium à Verticali, declinantium ab Horizonte, inclinatorum ad Horizontem, at q; </s>
  <s xml:id="echoid-s435" xml:space="preserve">de-<lb/>clinantium ſimul &amp; </s>
  <s xml:id="echoid-s436" xml:space="preserve">inclinatorum, propterea quod vna ſuperficies plus, aut minus in infinitum deflectere <lb/>poteſt à Verticali, aut Horizonte, &amp; </s>
  <s xml:id="echoid-s437" xml:space="preserve">ad Horizontem inclinare. </s>
  <s xml:id="echoid-s438" xml:space="preserve">Hoc igitur modo Sciotherica horologia <lb/>
<anchor type="note" xlink:label="note-0025-05a" xlink:href="note-0025-05"/>
distribui ſolent, habita ratione ſitus planorum, in quibus depinguntur.</s>
  <s xml:id="echoid-s439" xml:space="preserve"/>
</p>
<div xml:id="echoid-div22" type="float" level="2" n="7">
<note position="left" xlink:label="note-0025-05" xlink:href="note-0025-05a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s440" xml:space="preserve">CAETERVM omnia hæc horologia, quæ recenſuimus, diximus æquidiſtare circulis illis maximis, <lb/>
<anchor type="note" xlink:label="note-0025-06a" xlink:href="note-0025-06"/>
à quibus nomina trahunt, quoniam vertex ſtyli ad horologĳ planum rectus collocari intelligitur in centro <lb/>mundi, at q; </s>
  <s xml:id="echoid-s441" xml:space="preserve">adeò in communi centro illorum omnium circulorum maximorum. </s>
  <s xml:id="echoid-s442" xml:space="preserve">Vnde fit, vt horologiorum <lb/>plana tantum ab ipſis circulis abſint, quanta eſt cuiuſq; </s>
  <s xml:id="echoid-s443" xml:space="preserve">styli longitudo. </s>
  <s xml:id="echoid-s444" xml:space="preserve">Quam ob rem decipiuntur illi, qui <lb/>docent horologia omnia deſcribi in ipſiſmet circulis maximis, à quibus nomina accipiunt. </s>
  <s xml:id="echoid-s445" xml:space="preserve">Sed hæc vberi{us} <lb/>explicabimus propoſ. </s>
  <s xml:id="echoid-s446" xml:space="preserve">2. </s>
  <s xml:id="echoid-s447" xml:space="preserve">huius libri.</s>
  <s xml:id="echoid-s448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div23" type="float" level="2" n="8">
<note position="right" xlink:label="note-0025-06" xlink:href="note-0025-06a" xml:space="preserve">Quare horo <lb/>logia plana di-<lb/>cantur æqui@i-<lb/>ſtare circulis<unsure/> <lb/>maximis, a qui-<lb/>bus nomen ſu-<lb/>munt.</note>
</div>
<note position="right" xml:space="preserve">Horologio-<lb/>rum ſolauum <lb/>diuiſio ſumpta <lb/>@x tẽpore, quo <lb/>horas mõ@trãt.</note>
<p style="it">
  <s xml:id="echoid-s449" xml:space="preserve">ALIO modo diuidi ſolent inſtrumenta, quæ hor{as} indicat, ex eo tempore, quo horas monſtr are ſolẽt. <lb/></s>
  <s xml:id="echoid-s450" xml:space="preserve">Quædam enim appellantur diurna, quòd ſolurn in die, ſplendente ſole, horas indicent: </s>
  <s xml:id="echoid-s451" xml:space="preserve">Quædam nocturna, <lb/>quæ vel ſplendente luna, vel alĳs aſtris, hor{as} noctu oſtendunt: </s>
  <s xml:id="echoid-s452" xml:space="preserve">Quædam deniq; </s>
  <s xml:id="echoid-s453" xml:space="preserve">diurna ſimul ac nocturna;</s>
  <s xml:id="echoid-s454" xml:space="preserve">
<pb o="6" file="0026" n="26" rhead="GNOMONICES"/>
quia tã interdiu, quàm noctu ex ipſis horas cognoſcim{us}; </s>
  <s xml:id="echoid-s455" xml:space="preserve">qualia ſunt Aſtrolabia, ſeu Planiſphæria, annuli <lb/>aſtronomici, &amp; </s>
  <s xml:id="echoid-s456" xml:space="preserve">c. </s>
  <s xml:id="echoid-s457" xml:space="preserve">Pariratione alia horas indicant per dimidĳ anni ſpatium, cuiuſmodi est horologium <lb/>Aequinoctiale ſuperi{us}, horas eo anni tempore indicãs, quo ſol à principio ♈, ad principiũ ♎ mouetur: <lb/></s>
  <s xml:id="echoid-s458" xml:space="preserve">Alia per reliquam partem anni, quale eſt A Equinoctiale inferius, quod horas monſirat, dum ſol à princi-<lb/>pio ♎, ad principium ♈, mouetur. </s>
  <s xml:id="echoid-s459" xml:space="preserve">Rurſus quædam indicant horas mane duntaxat &amp; </s>
  <s xml:id="echoid-s460" xml:space="preserve">veſperi, quale <lb/>eſt horologium verticale ad ſeptentrionem ſpectans, &amp; </s>
  <s xml:id="echoid-s461" xml:space="preserve">Polare inferius, &amp; </s>
  <s xml:id="echoid-s462" xml:space="preserve">nonnulla alia declinantia, &amp; </s>
  <s xml:id="echoid-s463" xml:space="preserve"><lb/>inclinata inferiora: </s>
  <s xml:id="echoid-s464" xml:space="preserve">quædam reliquas horas diei, quale eſt Verticale ad meridiem vergens, &amp; </s>
  <s xml:id="echoid-s465" xml:space="preserve">Polare ſupe-<lb/>rius, nec non aliqua declinantia, &amp; </s>
  <s xml:id="echoid-s466" xml:space="preserve">inclinata ſuperiora. </s>
  <s xml:id="echoid-s467" xml:space="preserve">Sic etiam horologiorum alia horas antemeridia-<lb/>nas ſolum indicant, cuiuſmodi cſt Meridianum Orientale; </s>
  <s xml:id="echoid-s468" xml:space="preserve">alia pomeridianas, quale cſt Meridianum occi-<lb/>dentale. </s>
  <s xml:id="echoid-s469" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s470" xml:space="preserve">hac ratione plura alia genera horologiorum excogitari poterunt.</s>
  <s xml:id="echoid-s471" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div25" type="section" level="1" n="13">
<head xml:id="echoid-head15" style="it" xml:space="preserve">DE QV ADRVPLICI HORARVM, <lb/>atque ex ipſis horologiorum varietate.</head>
<p style="it">
  <s xml:id="echoid-s472" xml:space="preserve">RETVLIMVS varia horologiorum genera ex uario duntaxat planorum, in quibus deſcribuntur, <lb/>ſitu, nunc de quatuor horarum generibus, ex quibus ſingulæ prædictæ horologiorum ſpecies quadrupli <lb/>cantur, dicam{us}. </s>
  <s xml:id="echoid-s473" xml:space="preserve">Principio autem horarum duo prima ſunt genera inter ſe diſtincta, vnæ quidem inæqua-<lb/>
<anchor type="note" xlink:label="note-0026-02a" xlink:href="note-0026-02"/>
les dicuntur, æquales alteræ. </s>
  <s xml:id="echoid-s474" xml:space="preserve">Hora inæqualis eſt pars duodecima tam diei, quàm noctis artificialis. </s>
  <s xml:id="echoid-s475" xml:space="preserve">Diuide-<lb/>
<anchor type="note" xlink:label="note-0026-03a" xlink:href="note-0026-03"/>
batur enim olim quæuis artificialis dies, &amp; </s>
  <s xml:id="echoid-s476" xml:space="preserve">quælibet nox in 12 particulas æquales inter ſe, quæ horæ inæ-<lb/>quales, &amp; </s>
  <s xml:id="echoid-s477" xml:space="preserve">antiquæ à ſcriptorib{us} dicuntur: </s>
  <s xml:id="echoid-s478" xml:space="preserve">Antiquæ quidem, quoniam apud omnes antiquos earum vſus <lb/>extitit. </s>
  <s xml:id="echoid-s479" xml:space="preserve">Inæquales autem, non quòd horæ vnius diei vel noctis inter ſe ſint inæquales; </s>
  <s xml:id="echoid-s480" xml:space="preserve">hoc enim falſum eſt, <lb/>
<anchor type="note" xlink:label="note-0026-04a" xlink:href="note-0026-04"/>
<anchor type="note" xlink:label="note-0026-05a" xlink:href="note-0026-05"/>
cum quamlibet diem, ac noctem in 12 partes æquales diſtribui aſſeruerimus; </s>
  <s xml:id="echoid-s481" xml:space="preserve">ſed quia cũ dies artificiales, <lb/>&amp; </s>
  <s xml:id="echoid-s482" xml:space="preserve">noctes ſint inæquales, horæ diei vel noctis longioris maiores ſunt horis diei, vel noctis breuioris. </s>
  <s xml:id="echoid-s483" xml:space="preserve">Quan-<lb/>do enim duæ magnitudines inæquales in partes numero æquales diuiduntur, efficiuntur ſingulæ partes ma-<lb/>ioris magnitudinis ſingulis partibus minoris inæquales, puta maiores. </s>
  <s xml:id="echoid-s484" xml:space="preserve">Rurſus dicuntur huiuſmodi partes <lb/>duodecimæ diei vel noctis, horæ inæquales, quoniam cum tam dies, quàm nox artificialis æqualib{us} duo-<lb/>decim horis conſtet, ſit autem in ſphæra obliqua perpetuo dies ſuæ nocti inæqualis, excepto tempore æqui-<lb/>noctiorum, ſole in principio ♈, vel ♎ exiſtente, neceſſario efficitur, hor{as} diurn{as} inæquales eſſe no-<lb/>cturnis horis. </s>
  <s xml:id="echoid-s485" xml:space="preserve">Deniq; </s>
  <s xml:id="echoid-s486" xml:space="preserve">nominatæ ſunt huiuſmodi horæ inæquales, quia nunquam, niſi in æquinoctĳs, conue-<lb/>niunt cum horis æquinoctialibus, quæ æquales dicuntur, vt mox docebim{us}, ſed ſemper aut minores ſunt, <lb/>vt diurnæ in hyeme, &amp; </s>
  <s xml:id="echoid-s487" xml:space="preserve">nocturnæ in æſtate, aut maiores, vt ſunt diurnæ in æſtate, &amp; </s>
  <s xml:id="echoid-s488" xml:space="preserve">nocturnæ in hyeme. <lb/></s>
  <s xml:id="echoid-s489" xml:space="preserve">
<anchor type="note" xlink:label="note-0026-06a" xlink:href="note-0026-06"/>
Cur autem duodecim hor{as} diurn{as}, totidem{q́ue} nocturnas conſtituerint veteres, partim ſupra cõmemora-<lb/>
<anchor type="note" xlink:label="note-0026-07a" xlink:href="note-0026-07"/>
uim{us}, cum de etymologia hui{us} nominis, hora, diſſereremus, partim etiam hoc loco aperiemus. </s>
  <s xml:id="echoid-s490" xml:space="preserve">@eteres <lb/>magnam ſemper rationem habuiſſe temporis, quo ſingulæ partes zodiaci ſupra Horizontem exoriuntur, <lb/>perſpicuè conſtat. </s>
  <s xml:id="echoid-s491" xml:space="preserve">Vnde non temerè hor{as} à partib{us} zodiaci inſtituiſſe videntur. </s>
  <s xml:id="echoid-s492" xml:space="preserve">Sed quoniã 12 partes <lb/>ſunt præcipuæ in zodiaco, nempe 12. </s>
  <s xml:id="echoid-s493" xml:space="preserve">ſigna cœleſtia, quorum ſex qualibet die, &amp; </s>
  <s xml:id="echoid-s494" xml:space="preserve">totidem quauis nocte oriũ-<lb/>tur, vt in ſphær a docuim{us}; </s>
  <s xml:id="echoid-s495" xml:space="preserve">ſi ſingulis ſignis horam tribuiſſent, ſex hor{as} duntaxat conſtituiſſent tam in <lb/>die, quàm in nocte qualibet, eaſ{q́ue} lõgiores, quàm par eſt, effeciſſent. </s>
  <s xml:id="echoid-s496" xml:space="preserve">Quocirca viſum eſt illis cuilibet medie <lb/>tati vnius ſigni ſupra Horizontem emergenti horam aſcribere. </s>
  <s xml:id="echoid-s497" xml:space="preserve">Vnde factum eſt, vt quemuis diem, &amp; </s>
  <s xml:id="echoid-s498" xml:space="preserve">no-<lb/>ctem in 12 hor{as} partitiſint. </s>
  <s xml:id="echoid-s499" xml:space="preserve">Hiſce horis inæqualib{us} olim Iudæi vtebantur, vt ex ſacris literis conſtat, <lb/>nec non Romani, &amp; </s>
  <s xml:id="echoid-s500" xml:space="preserve">tota ferme antiquit{as}, vt &amp; </s>
  <s xml:id="echoid-s501" xml:space="preserve">hyſtoriæ, &amp; </s>
  <s xml:id="echoid-s502" xml:space="preserve">libri veterum Mathematicorum teſtantur. <lb/></s>
  <s xml:id="echoid-s503" xml:space="preserve">
<anchor type="note" xlink:label="note-0026-08a" xlink:href="note-0026-08"/>
His enim noctem in quatuor vigili{as} diſtribuebant, ſingulis vigilĳs tern{as} tribuendo hor{as}. </s>
  <s xml:id="echoid-s504" xml:space="preserve">Immo &amp; </s>
  <s xml:id="echoid-s505" xml:space="preserve">Ec-<lb/>cleſia Romana laudes Deo Opt. </s>
  <s xml:id="echoid-s506" xml:space="preserve">Max. </s>
  <s xml:id="echoid-s507" xml:space="preserve">quæ ab horarum nomine quidem horæ canonicæ, numero autem Pri <lb/>ma, Tertia, Sexta, &amp; </s>
  <s xml:id="echoid-s508" xml:space="preserve">Nona vocatę ſunt, ſecundum hoc gen{us} hor arum inſtituit decantand{as}.</s>
  <s xml:id="echoid-s509" xml:space="preserve"/>
</p>
<div xml:id="echoid-div25" type="float" level="2" n="1">
<note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve">Horarum di <lb/>u<unsure/>iſio.</note>
<note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve">Hora inæ <lb/>qualis.</note>
<note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve">Cur dictæ ſint <lb/>horæ antiquæ@ <lb/>&amp; inæquales.</note>
<note position="left" xlink:label="note-0026-05" xlink:href="note-0026-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0026-06" xlink:href="note-0026-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0026-07" xlink:href="note-0026-07a" xml:space="preserve">Cur Antiqui <lb/>diem, &amp; noctẽ <lb/>quãlibet in 12. <lb/>horas ſecuerint.</note>
<note position="left" xlink:label="note-0026-08" xlink:href="note-0026-08a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s510" xml:space="preserve">HORA verò æqualis eſt viceſima quarta pars dieinaturalis, qui ex die, nocte{q́ue} conficitur. </s>
  <s xml:id="echoid-s511" xml:space="preserve">Quia verò <lb/>
<anchor type="note" xlink:label="note-0026-09a" xlink:href="note-0026-09"/>
circulus A Equinoctialis continens grad. </s>
  <s xml:id="echoid-s512" xml:space="preserve">360. </s>
  <s xml:id="echoid-s513" xml:space="preserve">ſemel in die cir cumagitur, ſupra{q́ue} Horizontem vbiuis gen-<lb/>tium totus aſcendit, (negligimus hic particulam illam, quæ portiunculæ illi zodiaci reſpondet, quam inte-<lb/>rim proprio motu ſol percurrit) neceſſe eſt ſingulis horis aſcendere grad. </s>
  <s xml:id="echoid-s514" xml:space="preserve">15. </s>
  <s xml:id="echoid-s515" xml:space="preserve">qua de cauſa hę horæ dictæ <lb/>ſunt æquinoctiales, quòd videlicet à cir cũuolutione æquinoctialis circuli efficiãtur. </s>
  <s xml:id="echoid-s516" xml:space="preserve">Dictæ quoq; </s>
  <s xml:id="echoid-s517" xml:space="preserve">ſunt æqua-<lb/>
<anchor type="note" xlink:label="note-0026-10a" xlink:href="note-0026-10"/>
les. </s>
  <s xml:id="echoid-s518" xml:space="preserve">Nam ſemper æquali temporis ſpatio emergunt grad. </s>
  <s xml:id="echoid-s519" xml:space="preserve">15. </s>
  <s xml:id="echoid-s520" xml:space="preserve">A Equatoris, qui cuiq; </s>
  <s xml:id="echoid-s521" xml:space="preserve">horæ tribuuntur, ſupra <lb/>Horizontem: </s>
  <s xml:id="echoid-s522" xml:space="preserve">Siquidem in omni regione vniformiter eleuatur, ac deprimitur infra Horizontem circulus <lb/>
<anchor type="note" xlink:label="note-0026-11a" xlink:href="note-0026-11"/>
æquinoctialis, vt alibi oſtendim{us}.</s>
  <s xml:id="echoid-s523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div26" type="float" level="2" n="2">
<note position="left" xlink:label="note-0026-09" xlink:href="note-0026-09a" xml:space="preserve">Hora æqua-<lb/>lis.</note>
<note position="left" xlink:label="note-0026-10" xlink:href="note-0026-10a" xml:space="preserve">Cur dictæ <lb/>ſint horæ æqui-<lb/>noctiales, atq; <lb/>æquales.</note>
<note position="left" xlink:label="note-0026-11" xlink:href="note-0026-11a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s524" xml:space="preserve">PORRO haſce hor{as} æquales olim non omnes nationes, ſicut ncc hodie, eodem modo numerabant; <lb/></s>
  <s xml:id="echoid-s525" xml:space="preserve">quoniam non idem initium diei natur alis apud omnes erat conſtitutum. </s>
  <s xml:id="echoid-s526" xml:space="preserve">Babylonĳ etenim, teſte Plinio lib. </s>
  <s xml:id="echoid-s527" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0026-12a" xlink:href="note-0026-12"/>
2. </s>
  <s xml:id="echoid-s528" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s529" xml:space="preserve">Macrobio lib. </s>
  <s xml:id="echoid-s530" xml:space="preserve">1. </s>
  <s xml:id="echoid-s531" xml:space="preserve">Saturnaliorum, diem appellabant motum ſolis ab vno ortu ad alterum ortum, quos <lb/>hac tempeſtate imitantur incolæ inſularum Balearium. </s>
  <s xml:id="echoid-s532" xml:space="preserve">Vnde hor{as} ab exortu ſolis ſupputabant, quæ Ba-<lb/>bylonicæ à pleriſ ſcriptoribus dicuntur, propterea quod apud Babylonios in vſu fuerunt. </s>
  <s xml:id="echoid-s533" xml:space="preserve">Athenienſes <lb/>
<anchor type="note" xlink:label="note-0026-13a" xlink:href="note-0026-13"/>
autem, quos nunc ſequitur tota Italia vna cum Bohemia, diem definiebant ab uno ſolis occaſu ad occaſum <lb/>alterũ, inde{q́ue} hor{as} æquales numer abant: </s>
  <s xml:id="echoid-s534" xml:space="preserve">quæ iã Italicæ nuncupãtur ab Italia, vbi maxime earũ vſus vi-<lb/>
<anchor type="note" xlink:label="note-0026-14a" xlink:href="note-0026-14"/>
get. </s>
  <s xml:id="echoid-s535" xml:space="preserve">Vmbri deinde (quem etiam morem Aſtronomi omnes obſeruant) totum temp{us} à meridie ad ſequen-<lb/>tem meridiem vo<unsure/>cabant diem, hor{as}{q́ue} æquales 24. </s>
  <s xml:id="echoid-s536" xml:space="preserve">computabant à meridie, quę quoniam in motibus cœlo-
<pb o="7" file="0027" n="27" rhead="LIBER PRIMVS."/>
rum ſupputandis ab Aſtronomis vſurpantur, Aſtronomicæ dici conſueuerunt. </s>
  <s xml:id="echoid-s537" xml:space="preserve">Aegyptĳ deniq;</s>
  <s xml:id="echoid-s538" xml:space="preserve">, &amp; </s>
  <s xml:id="echoid-s539" xml:space="preserve">teſte <lb/>
<anchor type="note" xlink:label="note-0027-01a" xlink:href="note-0027-01"/>
Macrobio lib. </s>
  <s xml:id="echoid-s540" xml:space="preserve">1. </s>
  <s xml:id="echoid-s541" xml:space="preserve">Saturnaliorum, popul{us} Roman{us}, diẽ numer abant à media nocte in proximè ſequentem <lb/>mediam noctem, atq; </s>
  <s xml:id="echoid-s542" xml:space="preserve">hinc horas elapſas obſeruabant. </s>
  <s xml:id="echoid-s543" xml:space="preserve">Id quod Eccleſia quoq; </s>
  <s xml:id="echoid-s544" xml:space="preserve">Romana obſeruat in celebra-<lb/>tione ſolennitatum &amp; </s>
  <s xml:id="echoid-s545" xml:space="preserve">ieiuniorum. </s>
  <s xml:id="echoid-s546" xml:space="preserve">Cæterum ab horis, quæ Vmbris, Aſtronomis, Aegyptĳs, atq; </s>
  <s xml:id="echoid-s547" xml:space="preserve">Romanis <lb/>
<anchor type="note" xlink:label="note-0027-02a" xlink:href="note-0027-02"/>
in vſu fuerunt, non multum diſcrepant horæ vulgares, ſiue communes, quibus Germania, Gallia, Hiſpa-<lb/>nia, &amp; </s>
  <s xml:id="echoid-s548" xml:space="preserve">tota fermè Europa hodie vtitur. </s>
  <s xml:id="echoid-s549" xml:space="preserve">Numer ant enim harum regionum populi hor{as} æquales 12 à me-<lb/>ridie vſq; </s>
  <s xml:id="echoid-s550" xml:space="preserve">ad noctem mediam, totidem{q́ue} hinc ad proximum meridiem. </s>
  <s xml:id="echoid-s551" xml:space="preserve">Quo fit, vt in numer atione hor arum <lb/>à meridie in mediam noctem nulla in re differant ab Vmbris, Aſtronomiſve; </s>
  <s xml:id="echoid-s552" xml:space="preserve">à media verò nocte in meri-<lb/>diẽ vſq; </s>
  <s xml:id="echoid-s553" xml:space="preserve">ab ĳſdẽ diſſentiant in numer atione duntaxat horarum. </s>
  <s xml:id="echoid-s554" xml:space="preserve">Nam quæ Vmbris, Aſtronomiſ{q́ue} dicitur <lb/>hora 13. </s>
  <s xml:id="echoid-s555" xml:space="preserve">à meridie, apud vulgus Europæum appellatur prima poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s556" xml:space="preserve">quæ apud illos eſt <lb/>14. </s>
  <s xml:id="echoid-s557" xml:space="preserve">à meridie, his dicitur ſecunda poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s558" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s559" xml:space="preserve">Pari ratione in numer atione ho-<lb/>
<anchor type="note" xlink:label="note-0027-03a" xlink:href="note-0027-03"/>
rarũ à media nocte in meridiẽ vſq; </s>
  <s xml:id="echoid-s560" xml:space="preserve">cum Aegyptĳs, &amp; </s>
  <s xml:id="echoid-s561" xml:space="preserve">Romanis conueniũt, at à meridie in mediã noctem <lb/>ab ĳſdem in ſola numer atione diſcrepant. </s>
  <s xml:id="echoid-s562" xml:space="preserve">Quæ enim hora apud Romanos, vel A Egyptios appellatur 13. <lb/></s>
  <s xml:id="echoid-s563" xml:space="preserve">poſt mediam noctem, hodie apud Europæos dicitur prima poſt meridiem, &amp; </s>
  <s xml:id="echoid-s564" xml:space="preserve">quam illi vocant 14. </s>
  <s xml:id="echoid-s565" xml:space="preserve">à media <lb/>nocte, dicitur Europęis ſecunda à meridie, &amp; </s>
  <s xml:id="echoid-s566" xml:space="preserve">c. </s>
  <s xml:id="echoid-s567" xml:space="preserve">Hinc efficitur, vnum idem{q́ue} horologium oſtẽdere &amp; </s>
  <s xml:id="echoid-s568" xml:space="preserve">horas <lb/>à meridie, &amp; </s>
  <s xml:id="echoid-s569" xml:space="preserve">hor{as} à media nocte numer atas, dummodo horarum numeros commutes, vt dictum est. </s>
  <s xml:id="echoid-s570" xml:space="preserve">So-<lb/>lent tamen in huiuſmodi horologĳs apponi numeri horarum iuxta numerationem vulgi, vt 12. </s>
  <s xml:id="echoid-s571" xml:space="preserve">à meridie <lb/>ad mediam noctem, &amp; </s>
  <s xml:id="echoid-s572" xml:space="preserve">totidem à media nocte in meridiem, vt ex ſequentibus erit manifeſtum. </s>
  <s xml:id="echoid-s573" xml:space="preserve">Itaque vt <lb/>
<anchor type="note" xlink:label="note-0027-04a" xlink:href="note-0027-04"/>
omnia paucis comprehendamus, quoniam duo ſunt horarum genera, inæqualium vnum, &amp; </s>
  <s xml:id="echoid-s574" xml:space="preserve">alterum æqua-<lb/>lium; </s>
  <s xml:id="echoid-s575" xml:space="preserve">æquales verò horæ initium habent vel ab ortu ſolis, vel ab occaſu, vel à meridie, ſeu media nocte, fit <lb/>vt in quouis horologio ſiue penſili, ſiue concauo, conuexove, ſiue plano, quatuor horarum genera deſcribi <lb/>
<anchor type="note" xlink:label="note-0027-05a" xlink:href="note-0027-05"/>
<anchor type="note" xlink:label="note-0027-06a" xlink:href="note-0027-06"/>
poſſint, puta horæ inæquales, ſiue antiquæ, horæ æquales ab ortu ſolis, horæ æquales à ſolis occaſu, &amp; </s>
  <s xml:id="echoid-s576" xml:space="preserve">horæ <lb/>æquales à meridie &amp; </s>
  <s xml:id="echoid-s577" xml:space="preserve">media nocte ſupputatæ: </s>
  <s xml:id="echoid-s578" xml:space="preserve">Quareratione horarum quodcunq; </s>
  <s xml:id="echoid-s579" xml:space="preserve">horologium quadruplex <lb/>erit, habebit{q́ue}, hæc nomina.</s>
  <s xml:id="echoid-s580" xml:space="preserve"/>
</p>
<div xml:id="echoid-div27" type="float" level="2" n="3">
<note position="left" xlink:label="note-0026-12" xlink:href="note-0026-12a" xml:space="preserve">Initium va-<lb/>rium diei apud <lb/>varias gentes.</note>
<note position="left" xlink:label="note-0026-13" xlink:href="note-0026-13a" xml:space="preserve">Horæ Baby-<lb/>lonicæ.</note>
<note position="left" xlink:label="note-0026-14" xlink:href="note-0026-14a" xml:space="preserve">Horę Italicę.</note>
<note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">Horæ Aſtro-<lb/>nomicæ.</note>
<note position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve">Horæ vulga-<lb/>res, ſiue commu <lb/>nes quo modo <lb/>diffe ant ab ho <lb/>ris Aſtronomi-<lb/>ci@.</note>
<note position="left" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0027-04" xlink:href="note-0027-04a" xml:space="preserve">In quolibe@ <lb/>horologio ſola-<lb/>ri quatuor hora <lb/>rum genera de-<lb/>ſcribi poſſunt.</note>
<note position="left" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0027-06" xlink:href="note-0027-06a" xml:space="preserve">Horologiot<unsure/>ũ <lb/>quatuor gene-<lb/>ra ex varietate <lb/>horarum orta.</note>
</div>
<note position="right" xml:space="preserve">Horologium <lb/>Antiquum.</note>
<p style="it">
  <s xml:id="echoid-s581" xml:space="preserve">ANTIQVVM, quod hor{as} inæquales, quibus antiqui vtebantur, continet.</s>
  <s xml:id="echoid-s582" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s583" xml:space="preserve">BABYLONICVM, quod indicat hor{as} ab ortu ſolis, quæ apud Babylonios in vſu fuerunt.</s>
  <s xml:id="echoid-s584" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horologium <lb/>Babylo@@cum.</note>
<p style="it">
  <s xml:id="echoid-s585" xml:space="preserve">ITALICVM, quod hor{as} complectitur à ſolis occaſu, quibus Itali vtuntur.</s>
  <s xml:id="echoid-s586" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horologium <lb/>Italicum.</note>
<p style="it">
  <s xml:id="echoid-s587" xml:space="preserve">ASTRONOMICVM, quod hor{as} notat à meridie in mediam noctem, &amp; </s>
  <s xml:id="echoid-s588" xml:space="preserve">à medianocte in me-<lb/>ridiem, quæ non ſolum Europæ ferè vniuerſæ, ſed omnibus Aſtronomis etiam communes ſunt.</s>
  <s xml:id="echoid-s589" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horologium <lb/>Aſtronomicũ.</note>
</div>
<div xml:id="echoid-div29" type="section" level="1" n="14">
<head xml:id="echoid-head16" style="it" xml:space="preserve">DE INVENTORIBVS SCIOTHERI-<lb/>
corum horologiorum, eorum{q́ue} ſcriptoribus.</head>
<p style="it">
  <s xml:id="echoid-s590" xml:space="preserve">SCIOTHERICORVM horologiorum primus inuentor perhibetur fuiſſe Anaximenes Mileſi{us}, <lb/>
<anchor type="note" xlink:label="note-0027-12a" xlink:href="note-0027-12"/>
de quo habentur hæc verba apud Plinium lib. </s>
  <s xml:id="echoid-s591" xml:space="preserve">2, cap. </s>
  <s xml:id="echoid-s592" xml:space="preserve">76. </s>
  <s xml:id="echoid-s593" xml:space="preserve">Vmbrarum rationem, &amp; </s>
  <s xml:id="echoid-s594" xml:space="preserve">quam vocant Gno-<lb/>monicen, inuenit Anaximenes Mileſius Anaximandri diſcipulus, primus{q́ue} horologium, quod appellant <lb/>Sciothericum Lacedæmone oſtendit. </s>
  <s xml:id="echoid-s595" xml:space="preserve">hæc Plini{us}. </s>
  <s xml:id="echoid-s596" xml:space="preserve">Verum horologiorũ vſum antiquiorem multo fuiſſe, ſa-<lb/>tis euidentib{us} argumentis compertum eſt. </s>
  <s xml:id="echoid-s597" xml:space="preserve">Legimus enim in ſacris literis, Achaz Regem habuiſſe ſolare <lb/>
<anchor type="note" xlink:label="note-0027-13a" xlink:href="note-0027-13"/>
horologium, qui multo antiquior Anaximene fuit. </s>
  <s xml:id="echoid-s598" xml:space="preserve">Regnauit enim Achaz circa olympiadem primam, hoc <lb/>eſt, anno 775. </s>
  <s xml:id="echoid-s599" xml:space="preserve">ante Chriſtum natum, vel minimum, vt alĳs placet, circa olympiadem ſeptimam, id eſt, anno <lb/>ante Chriſtum 751. </s>
  <s xml:id="echoid-s600" xml:space="preserve">Anaximenes autem floruit circa olympiadem quinquageſimã, id eſt, circa annũ 579. <lb/></s>
  <s xml:id="echoid-s601" xml:space="preserve">
<anchor type="note" xlink:label="note-0027-14a" xlink:href="note-0027-14"/>
ante Chriſtum; </s>
  <s xml:id="echoid-s602" xml:space="preserve">vt hic illo fuerit iunior annis fere 196. </s>
  <s xml:id="echoid-s603" xml:space="preserve">vel 172. </s>
  <s xml:id="echoid-s604" xml:space="preserve">Quare rationem hanc horologiorum à pri-<lb/>mis illis Patrib{us} (quod &amp; </s>
  <s xml:id="echoid-s605" xml:space="preserve">de alĳs ſcientĳs affirmat Ioſeph{us} in lib. </s>
  <s xml:id="echoid-s606" xml:space="preserve">de antiquitate.) </s>
  <s xml:id="echoid-s607" xml:space="preserve">originem traxiſſe <lb/>crediderim, eam{q́ue}, ſenſim ad A Egyptios, ab his ad Græcos, à Græcis deniq; </s>
  <s xml:id="echoid-s608" xml:space="preserve">ad Latinos perueniſſe. </s>
  <s xml:id="echoid-s609" xml:space="preserve">In-<lb/>uentores autem alĳ aliorum horologiorum Sciothericorum cõmemor antur à Vitruuio lib. </s>
  <s xml:id="echoid-s610" xml:space="preserve">9. </s>
  <s xml:id="echoid-s611" xml:space="preserve">Beroſ{us} enim <lb/>
<anchor type="note" xlink:label="note-0027-15a" xlink:href="note-0027-15"/>
Chaldæus inueniſſe fertur hemicyclium excauatum ex quadrato, in quo lineæ hor{as} indicantes deſcriptæ <lb/>erant. </s>
  <s xml:id="echoid-s612" xml:space="preserve">Ariſtarch{us} Sami{us} Scaphen, ſeu hemiſphærium, qualia fortaſſis nunc ſunt horologia hemiſphęrica <lb/>concaua. </s>
  <s xml:id="echoid-s613" xml:space="preserve">Idem excogitaſſe dicitur Diſcum, horologium videlicet parum excauatum in modum diſci, ſeu pa <lb/>tinæ, ita vt interior pars non fuerit perfecte ſphærica. </s>
  <s xml:id="echoid-s614" xml:space="preserve">Eudox{us} Aſtrologus fertur reperiſſe Arachnen, id <lb/>eſt, ar aneam, horologium videlicet in modum araneæ, quale nunc eſt horologium horizontale continens ho-<lb/>r{as} aſtronomic{as}, &amp; </s>
  <s xml:id="echoid-s615" xml:space="preserve">cir culos altitudinũ ſolis, quos Almucantarath Arabes dicunt. </s>
  <s xml:id="echoid-s616" xml:space="preserve">Vel etiam quodcũq; <lb/></s>
  <s xml:id="echoid-s617" xml:space="preserve">
<anchor type="note" xlink:label="note-0027-16a" xlink:href="note-0027-16"/>
horologium, in quo deſcriptæ ſint &amp; </s>
  <s xml:id="echoid-s618" xml:space="preserve">lineæ horariæ, &amp; </s>
  <s xml:id="echoid-s619" xml:space="preserve">arc{us} ſignorum zodiaci. </s>
  <s xml:id="echoid-s620" xml:space="preserve">Sunt qui huiuſce horologĳ <lb/>Apollonium faciant inuentorem. </s>
  <s xml:id="echoid-s621" xml:space="preserve">Scop{as} Syracuſius prædicatur inuentor Plinthi, ſiue lacunaris, inſtar <lb/>trabis cuiuſdam quadratę, in qua tam horologium Verticale auſtrale, boreale{q́ue}, quàm Meridianũ Orien-<lb/>tale, &amp; </s>
  <s xml:id="echoid-s622" xml:space="preserve">Occidentale, nec non in plano ſuperiori Horizontale deſcribi poterat, quale in circo Flaminio po-<lb/>ſitum erat. </s>
  <s xml:id="echoid-s623" xml:space="preserve">Parmenionem faciunt inuentorem horologiorum, quę vocabantur πρὸς τὰ ἱςοροὐμενα, quę qua-<lb/>lia fuerint, difficile iudicare poſſumus, niſi fortè dicam{us}, in illis contentas fuiſſe non ſolum line{as} hora-<lb/>ri{as}, verum etiam ſigna zodiaci, menſes, &amp; </s>
  <s xml:id="echoid-s624" xml:space="preserve">dies, quę omnia per indicem monſtr abantur, ita vt horologia <lb/>illa fuerint inſtar hyſtorię cuiuſdam. </s>
  <s xml:id="echoid-s625" xml:space="preserve">Theodoſium aſſerunt excogitaſſc horologium dictum πρὸς πᾶν κλῖμα <lb/>quia omnibus ſeruiebat climatib{us} mundi. </s>
  <s xml:id="echoid-s626" xml:space="preserve">Patrocles reperiſſe narratur πελέκινον, id est, horarium figurã <lb/>habens ſecuris, ſeu bipennis, qualem formam nũc pene gerit horologium Meridianum, in quo ſigna zodiaci
<pb o="8" file="0028" n="28" rhead="GNOMONICES"/>
deſcripta ſint. </s>
  <s xml:id="echoid-s627" xml:space="preserve">Dionyſiou<unsure/>or{us} inuentor fuit, vt aiunt, coni, ſeu horologĳ figurę conicę. </s>
  <s xml:id="echoid-s628" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s629" xml:space="preserve">ita alĳ alias <lb/>form{as} horologiorũ excogitaſſe memorantur à Vitruuio. </s>
  <s xml:id="echoid-s630" xml:space="preserve">Horologiorũ autem vſum ſerius Romę cœpiſſe, <lb/>auctor eſt Plinius lib. </s>
  <s xml:id="echoid-s631" xml:space="preserve">7. </s>
  <s xml:id="echoid-s632" xml:space="preserve">cap. </s>
  <s xml:id="echoid-s633" xml:space="preserve">60. </s>
  <s xml:id="echoid-s634" xml:space="preserve">Primum enim duodecim, inquit, tabulis ort{us} tantum, &amp; </s>
  <s xml:id="echoid-s635" xml:space="preserve">occaſus nomi-<lb/>nantur, poſt aliquot annos adiectus eſt &amp; </s>
  <s xml:id="echoid-s636" xml:space="preserve">Meridies, Accenſo conſulum id pronuntiante, vſq; </s>
  <s xml:id="echoid-s637" xml:space="preserve">ad primum <lb/>punicum bellum. </s>
  <s xml:id="echoid-s638" xml:space="preserve">Deinde ſolare horologium, imperfectum tamen, ſecundum rostra in columna poſitum eſſe <lb/>à M. </s>
  <s xml:id="echoid-s639" xml:space="preserve">Valerio Meſſala conſule, tradit M. </s>
  <s xml:id="echoid-s640" xml:space="preserve">Varro, Catina capta in Sicilia anno vrbis 477. </s>
  <s xml:id="echoid-s641" xml:space="preserve">quo quidem vſi <lb/>ſunt annis vndecentum, donec Q. </s>
  <s xml:id="echoid-s642" xml:space="preserve">Marti{us} Philipp{us}, qui cum L. </s>
  <s xml:id="echoid-s643" xml:space="preserve">Paulo fuit cenſor, diligenti{us} or dinatũ <lb/>iuxta poſuit, id{q́ue} mun{us} inter cenſoria opera gratiſſimè acceptum eſt. </s>
  <s xml:id="echoid-s644" xml:space="preserve">Scipio autem Naſica Collega Lęna-<lb/>tis prim{us} aqua diuiſit hor{as} ęquè noctium, ac dierum. </s>
  <s xml:id="echoid-s645" xml:space="preserve">Id{q́ue} horologium ſub tecto dicauit anno vrbis 595. <lb/></s>
  <s xml:id="echoid-s646" xml:space="preserve">hęc ferè Plinius.</s>
  <s xml:id="echoid-s647" xml:space="preserve"/>
</p>
<div xml:id="echoid-div29" type="float" level="2" n="1">
<note position="right" xlink:label="note-0027-12" xlink:href="note-0027-12a" xml:space="preserve">Anaximenes <lb/>Mileſius horo-<lb/>logiorum ſola-<lb/>rium primus<unsure/> <lb/>inuentor.</note>
<note position="right" xlink:label="note-0027-13" xlink:href="note-0027-13a" xml:space="preserve">4. Reg. cap. <lb/>20.</note>
<note position="left" xlink:label="note-0027-14" xlink:href="note-0027-14a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0027-15" xlink:href="note-0027-15a" xml:space="preserve">Inuentores <lb/>varij variorum <lb/>horologiorum.</note>
<note position="left" xlink:label="note-0027-16" xlink:href="note-0027-16a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s648" xml:space="preserve">SCRIPTOREM porrò qui de Gnomonica, ſeu horologiorum ratione egerit, non reperio antiquio-<lb/>
<anchor type="note" xlink:label="note-0028-01a" xlink:href="note-0028-01"/>
<anchor type="note" xlink:label="note-0028-02a" xlink:href="note-0028-02"/>
rem Vitruuio, qui libro 9. </s>
  <s xml:id="echoid-s649" xml:space="preserve">pauca quædam diſſerit de Analemmatis conſtructione, per quod qua ratione ho <lb/>rologia cõficiend<unsure/>a ſint, potius innuit, quàm docet. </s>
  <s xml:id="echoid-s650" xml:space="preserve">Ptolemęus autem libellum acutiſſimum edidit de Ana-<lb/>lemmate, in quem Federic{us} Commandinus doctiſſimos commentarios conſcripſit vna cum libro de horo-<lb/>logiorum deſcriptione, cuius omnes demonſtrationes ex Analemmate Ptolemęi petuntur, ex quo libro <lb/>Daniel Barbarus in commentarĳs in lib. </s>
  <s xml:id="echoid-s651" xml:space="preserve">9. </s>
  <s xml:id="echoid-s652" xml:space="preserve">Vitruuĳ omnia decerpſit, quę de horologiorum deſcriptione <lb/>tradit. </s>
  <s xml:id="echoid-s653" xml:space="preserve">Analemma autem Ptolemęi vna cum libro Federici Commandini de horologiorum deſcriptione <lb/>longè clari{us}, hreui{us}{q́ue} proponemus, Deo iuuante, lib. </s>
  <s xml:id="echoid-s654" xml:space="preserve">6. </s>
  <s xml:id="echoid-s655" xml:space="preserve">huius operis. </s>
  <s xml:id="echoid-s656" xml:space="preserve">Albategnius quoq; </s>
  <s xml:id="echoid-s657" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s658" xml:space="preserve">56. </s>
  <s xml:id="echoid-s659" xml:space="preserve">in li-<lb/>bro de ſcientia stellarum breuiſſimè docet, qua ratione horologium horarum inęqualium ad quamcunq; <lb/></s>
  <s xml:id="echoid-s660" xml:space="preserve">latitudinem poſſit conſtrui. </s>
  <s xml:id="echoid-s661" xml:space="preserve">Inter recentiores, qui hanc Matheſeos partem illustrarunt, numer ari poteſt <lb/>Petrus Noni{us} Luſitanus celebris Mathematicus, qui in libello de Erratis Orontĳ demonstrat, qua ra-<lb/>
<anchor type="note" xlink:label="note-0028-03a" xlink:href="note-0028-03"/>
tione horizontalia, &amp; </s>
  <s xml:id="echoid-s662" xml:space="preserve">Verticalia horologia tantum, alĳs omiſſis, deſcribantur; </s>
  <s xml:id="echoid-s663" xml:space="preserve">Federic{us} Commandin{us}, <lb/>qui, vt dixim{us}, commentarios in Analemma Ptolemęi, &amp; </s>
  <s xml:id="echoid-s664" xml:space="preserve">libellum de horologiorum deſcriptione in lu-<lb/>cem edidit; </s>
  <s xml:id="echoid-s665" xml:space="preserve">Oronti{us} Finę{us}; </s>
  <s xml:id="echoid-s666" xml:space="preserve">Ioannes Conrad{us} Vlmer{us} German{us}; </s>
  <s xml:id="echoid-s667" xml:space="preserve">Ioannes Baptiſta Vimercatus ordi-<lb/>nis Carthuſianorum lingua Italica; </s>
  <s xml:id="echoid-s668" xml:space="preserve">Andreas Schonerus Norimbergenſis; </s>
  <s xml:id="echoid-s669" xml:space="preserve">Ioãnes Paduanius Veronenſis; <lb/></s>
  <s xml:id="echoid-s670" xml:space="preserve">Petr{us} Roderic{us} Hiſpan{us} ſermone Hiſpanico; </s>
  <s xml:id="echoid-s671" xml:space="preserve">Franciſcus Maurolyc{us} Abb{as} Sicul{us}, qui tres ſubti-<lb/>liſſimos libros de lineis horarĳs conſcripſit; </s>
  <s xml:id="echoid-s672" xml:space="preserve">Ioannes Baptiſta Benedict{us}, qui nouiſſimè librum compoſuit <lb/>de Gnomonum, vmbrarum{q́ue} ſolarium vſu, in quo plurima continentur ſcitu digniſſima.</s>
  <s xml:id="echoid-s673" xml:space="preserve"/>
</p>
<div xml:id="echoid-div30" type="float" level="2" n="2">
<note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">Scriptores ho <lb/>rologiorum.</note>
<note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0028-03" xlink:href="note-0028-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s674" xml:space="preserve">IGITVR vt &amp; </s>
  <s xml:id="echoid-s675" xml:space="preserve">nos aliquam huic tam pręſtanti ſcientiæ Gnomonices lucem afferam{us}, exordiemur <lb/>à conſtructione Analemmatis, quod mirabile ſanè veterum inuentum eſt, &amp; </s>
  <s xml:id="echoid-s676" xml:space="preserve">baſis, ac fundamentum om-<lb/>nium ferè, quę demonſtr aturi ſum{us} in hoc opere. </s>
  <s xml:id="echoid-s677" xml:space="preserve">Eſt autẽ Analemma figura quædam circularis circa cen-<lb/>
<anchor type="note" xlink:label="note-0028-04a" xlink:href="note-0028-04"/>
<anchor type="note" xlink:label="note-0028-05a" xlink:href="note-0028-05"/>
trum Meridiani, vel cuiusuis alteri{us} circuli maximi per polos mundi tranſeuntis, &amp; </s>
  <s xml:id="echoid-s678" xml:space="preserve">in ei{us} plano deſcri <lb/>pta, communes ſectiones præcipuorum cir culorum ſphęrę (quales ſunt Aequator, eius{q́ue} paralleli, Eclipti <lb/>ca, Horizon, atq; </s>
  <s xml:id="echoid-s679" xml:space="preserve">Verticalis) ac Meridiani, vel illi{us} maximi circuli per mundi polos ducti, continens. </s>
  <s xml:id="echoid-s680" xml:space="preserve">Quę <lb/>quidem deſcriptio ex ſequenti prima propoſitione clariſſimè intelligetur. </s>
  <s xml:id="echoid-s681" xml:space="preserve">Dixerunt autem veteres huiuſ-<lb/>modi figuram Analemma, quaſi reſumptionem, quoniam antequam diametros aliorum cir culorum deſcri-<lb/>berent, deſignationes quaſdam vmbr arum ſu@ebant, &amp; </s>
  <s xml:id="echoid-s682" xml:space="preserve">reſumebant, vt in cir culo Analemmatis diame-<lb/>tros aliorum cir culorum in proprio ſitu collocarent, vt ex ĳs colligitur, quę Vitruui{us}, eiuſ{q́ue} interpres <lb/>Daniel Barbar{us} docent lib. </s>
  <s xml:id="echoid-s683" xml:space="preserve">9. </s>
  <s xml:id="echoid-s684" xml:space="preserve">Vnde factũ eſt, vt Vitruui{us} eo loco Analemma ita deſcriberet. </s>
  <s xml:id="echoid-s685" xml:space="preserve">Analem-<lb/>
<anchor type="note" xlink:label="note-0028-06a" xlink:href="note-0028-06"/>
ma eſt ratio conquiſita ſolis curſu, &amp; </s>
  <s xml:id="echoid-s686" xml:space="preserve">vmbrę creſcentis à Brumę obſeruatione inuenta, è qua per rationes <lb/>architectonic{as}, cir cini{q́ue} deſcriptiones eſt inuentus cęli effectus in mundo. </s>
  <s xml:id="echoid-s687" xml:space="preserve">Quia videlicet à ſolis, &amp; </s>
  <s xml:id="echoid-s688" xml:space="preserve">vm-<lb/>
<anchor type="note" xlink:label="note-0028-07a" xlink:href="note-0028-07"/>
brę à Gnomone proiectę curſu incipientes à bruma, hoc eſt, à ſolſtitio hyberno, antiqui, vt ex Vitruuio col <lb/>ligitur, in Analemmate not ahant diametros par allelorum ſolis ſecundum propri{as} diſtanti{as} inter ſeſe, <lb/>ex quo deinde Analemmate inuentus eſt effect{us} cœli in mundo, nemperatio ſolarium horologiorũ ad quã-<lb/>cunque poli altitudinem, quantitates dierum &amp; </s>
  <s xml:id="echoid-s689" xml:space="preserve">noctium, ort{us} &amp; </s>
  <s xml:id="echoid-s690" xml:space="preserve">occaſus ſolis, &amp; </s>
  <s xml:id="echoid-s691" xml:space="preserve">alia penè innumer abi-<lb/>lia, quę omnia recenſere non eſt huius loci. </s>
  <s xml:id="echoid-s692" xml:space="preserve">Sed noſtra deſcriptio magis accommodata eſt ad vſum, quem <lb/>Analemma nobis pręſtat, vt ex ĳs, quę ſequuntur, fiet perſpicuum. </s>
  <s xml:id="echoid-s693" xml:space="preserve">Quare ad Analemma deſcribendum <lb/>&amp; </s>
  <s xml:id="echoid-s694" xml:space="preserve">ad alia theoremata, problemata{q́ue} explicanda iam aggrediamur; </s>
  <s xml:id="echoid-s695" xml:space="preserve">Sitamen prius conſtructionem qua-<lb/>drantis cuiuſdam pręmittamus, qui mirificum vſum non ſolum in horologiorum deſcriptione, verum etiã <lb/>in aſtrolabĳ, aliorum{q́ue} inſtrumentorum tum ad Aſtronomiam, tum ad Geometriam ſpectantium, conſtru-<lb/>ctione nobis prębet, &amp; </s>
  <s xml:id="echoid-s696" xml:space="preserve">opus ipſum quodam modo facilius reddit, &amp; </s>
  <s xml:id="echoid-s697" xml:space="preserve">breui{us}. </s>
  <s xml:id="echoid-s698" xml:space="preserve">Id quod experientia ipſa <lb/>
<anchor type="note" xlink:label="note-0028-08a" xlink:href="note-0028-08"/>
quilibet vel facile diſcet.</s>
  <s xml:id="echoid-s699" xml:space="preserve"/>
</p>
<div xml:id="echoid-div31" type="float" level="2" n="3">
<note position="left" xlink:label="note-0028-04" xlink:href="note-0028-04a" xml:space="preserve">Analemma <lb/>quì<unsure/>d ſit.</note>
<note position="left" xlink:label="note-0028-05" xlink:href="note-0028-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0028-06" xlink:href="note-0028-06a" xml:space="preserve">Analemma <lb/>quo modo de-<lb/>ſcribatur à Vi-<lb/>truuio.</note>
<note position="left" xlink:label="note-0028-07" xlink:href="note-0028-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0028-08" xlink:href="note-0028-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s700" xml:space="preserve">CONTINEANT igitur duę rectę AB, AC, intabella quapiam ęnea, vel lignea ductę angulũ <lb/>
<anchor type="note" xlink:label="note-0028-09a" xlink:href="note-0028-09"/>
rectum in A, puncto, ex quo, vt centro, quadrans circuli deſcribatur BC, atque hic in gradus 90. </s>
  <s xml:id="echoid-s701" xml:space="preserve">diuida-<lb/>tur, initio facto à puncto B. </s>
  <s xml:id="echoid-s702" xml:space="preserve">Deinde ex centro A, ad ſingulos gradus rectę lineę emittantur, ac tandem <lb/>ex A, quotuis alĳ quadrantes minores deſcribantur inter rect{as} AB, AC, comprehenſi. </s>
  <s xml:id="echoid-s703" xml:space="preserve">Deſcriptus igi-<lb/>tur erit hac ratione quadrans, qui quant{as} in rebus mathematicis habeat vtilitates, vix dici poteſt. </s>
  <s xml:id="echoid-s704" xml:space="preserve">Nã <lb/>dicto citi{us} ea omnia nobis pręſtat, quæ per multas alioquin cir culorum diuiſiones non ſine magno labore, <lb/>atque molestia nobis eſſent inquirenda. </s>
  <s xml:id="echoid-s705" xml:space="preserve">Cui{us} rei vnum, aut alterum exemplum in medium hic adducam. <lb/></s>
  <s xml:id="echoid-s706" xml:space="preserve">Nam vberrimi ei{us} fructus ex ĳs, quę in toto hoc opere dicturi ſumus, paſſim colligentur. </s>
  <s xml:id="echoid-s707" xml:space="preserve">Sit exempligra <lb/>
<anchor type="note" xlink:label="note-0028-10a" xlink:href="note-0028-10"/>
tia in figura quapiam, in qua circulus H I, ex centro G, &amp; </s>
  <s xml:id="echoid-s708" xml:space="preserve">ad interuallum ſemidiametri G H, deſcript{us}
<pb o="9" file="0029" n="29" rhead="LIBER PRIMVS."/>
ſit, numeranda in cir cumferentia H I, à puncto H, verſus I, altitudo poli, nempe grad. </s>
  <s xml:id="echoid-s709" xml:space="preserve">42. </s>
  <s xml:id="echoid-s710" xml:space="preserve">quanta ferè <lb/>eſt Romæ. </s>
  <s xml:id="echoid-s711" xml:space="preserve">Hoc vt fiat, circino ſumemus ſemidiametrum G H, &amp; </s>
  <s xml:id="echoid-s712" xml:space="preserve">ei in quadr ante aliquam accipiemus <lb/>æqualem, ad cuius interuallũ aliquis ex quadrantibus ex A, deſcriptus ſit, (ſi tamen eiuſmodi ſemidia-<lb/>meter inueniri queat.) </s>
  <s xml:id="echoid-s713" xml:space="preserve">qualis in dato exemplo eſt ſemidiameter A E, ad cuius interuallum quadrans E F, <lb/>deſcriptus eſt. </s>
  <s xml:id="echoid-s714" xml:space="preserve">Deinde in hoc quadrante E F, accipiemus circino arcum inter rectam A B, &amp; </s>
  <s xml:id="echoid-s715" xml:space="preserve">rectam <lb/>A D, quæ per gradum 42. </s>
  <s xml:id="echoid-s716" xml:space="preserve">ducitur, poſitum, eum{q́ue}@ transferemus eodem circino ex H, in circumferen-<lb/>tiam H I, vſque ad I. </s>
  <s xml:id="echoid-s717" xml:space="preserve">Habebimus enim hac ratione altitudinem poli H I, quæſitam, nempe grad. </s>
  <s xml:id="echoid-s718" xml:space="preserve">42. <lb/></s>
  <s xml:id="echoid-s719" xml:space="preserve">licet circulum H I, non diuiſerimus in ſuos gradus. </s>
  <s xml:id="echoid-s720" xml:space="preserve">Rurſus ſit in eodem circulo H I, ſupputanda incli-<lb/>na@io plani alicuius ad Horizontem, quæ contineat grad. </s>
  <s xml:id="echoid-s721" xml:space="preserve">15. </s>
  <s xml:id="echoid-s722" xml:space="preserve">Itaque ſi ſumatur circino in eodem quadran-<lb/>te E F, arcus poſitus inter A B, &amp; </s>
  <s xml:id="echoid-s723" xml:space="preserve">rectam A O, quæ per grad. </s>
  <s xml:id="echoid-s724" xml:space="preserve">15. </s>
  <s xml:id="echoid-s725" xml:space="preserve">ducitur, transferatur{q́ue} in cir cumfe-<lb/>
<anchor type="note" xlink:label="note-0029-01a" xlink:href="note-0029-01"/>
ren iam H I, ex H, vſque ad P, continebit arcus H P, grad. </s>
  <s xml:id="echoid-s726" xml:space="preserve">15. </s>
  <s xml:id="echoid-s727" xml:space="preserve">Atque it a beneficio quadrantis E F, <lb/>accipiemus in cir culo H I, quotcunque quis voluerit gradus.</s>
  <s xml:id="echoid-s728" xml:space="preserve"/>
</p>
<div xml:id="echoid-div32" type="float" level="2" n="4">
<note position="left" xlink:label="note-0028-09" xlink:href="note-0028-09a" xml:space="preserve">Conſtructio <lb/>quadrantis plu-<lb/>rimas vtilitates <lb/>habentis in ho-<lb/>rologiorum de-<lb/>ſeriptionibus, <lb/>&amp; in alijs inſtru <lb/>mentis Mathe-<lb/>maticis conſtru <lb/>endis.</note>
<note position="left" xlink:label="note-0028-10" xlink:href="note-0028-10a" xml:space="preserve">Vſus deſcri-<lb/>pti quadrantis.</note>
<note position="left" xlink:label="note-0029-01" xlink:href="note-0029-01a" xml:space="preserve">10</note>
</div>
  <figure>
    <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-01"/>
  </figure>
<p style="it">
  <s xml:id="echoid-s729" xml:space="preserve">QVOD ſi fortè ſemidiametro G H, non inueniatur æqualis ſemidiameter in quadrante, vt ferè ſem <lb/>
<anchor type="note" xlink:label="note-0029-02a" xlink:href="note-0029-02"/>
per accidit, ſumemus quamcunque ſemidiametrum libuerit, vt A K, ad cuius interuallum quadrans K L, <lb/>deſcriptus eſt, &amp; </s>
  <s xml:id="echoid-s730" xml:space="preserve">ad interuallum ſumptæ ſemidiametri A K, arcum occultum deſcribemus M N, in <lb/>quem transferemus arcum M N, æqualem arcui quadr antis K L, qui inter A B, &amp; </s>
  <s xml:id="echoid-s731" xml:space="preserve">lineam A D, du-<lb/>ctam per grad. </s>
  <s xml:id="echoid-s732" xml:space="preserve">42. </s>
  <s xml:id="echoid-s733" xml:space="preserve">interĳcitur. </s>
  <s xml:id="echoid-s734" xml:space="preserve">Nam recta ducta G N, ſecabit circumferentiam H I, in I, continebit <lb/>arcus H I, grad. </s>
  <s xml:id="echoid-s735" xml:space="preserve">42. </s>
  <s xml:id="echoid-s736" xml:space="preserve">cum ex ĳs, quæ in commentarĳs in ſphæram ſcripſimus ad calcem ferè primi capi-<lb/>tis, arcus H I, M N, ſimiles ſint. </s>
  <s xml:id="echoid-s737" xml:space="preserve">Sic etiam ſi arcui eiuſdem quadrantis K L, poſito inter duas rectas, <lb/>quæ grad. </s>
  <s xml:id="echoid-s738" xml:space="preserve">15. </s>
  <s xml:id="echoid-s739" xml:space="preserve">comprehendunt, ſumamus æqualem M Q, auferet recta ducta G Q, ex circulo H I, arcum <lb/>H P, graduum 15. </s>
  <s xml:id="echoid-s740" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s741" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s742" xml:space="preserve"/>
</p>
<div xml:id="echoid-div33" type="float" level="2" n="5">
<note position="left" xlink:label="note-0029-02" xlink:href="note-0029-02a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s743" xml:space="preserve">PRAETEREA ſi verbigratia, ad rectam G H, in puncto G, conſtituendus ſit angulus altitudi-<lb/>nis poli grad. </s>
  <s xml:id="echoid-s744" xml:space="preserve">42. </s>
  <s xml:id="echoid-s745" xml:space="preserve">Item angulus inclinationis alicuius plani ad Horizontem grad. </s>
  <s xml:id="echoid-s746" xml:space="preserve">15. </s>
  <s xml:id="echoid-s747" xml:space="preserve">vel angulus quot-<lb/>cunque graduum, etſinullus ibi deſeriptus ſit circulus, (Id quod non raro vſu venire ſolet) accipiemus
<pb o="10" file="0030" n="30" rhead="GNOMONICES"/>
circino ſemidiametrum quamcunque, vt A E, vel A K, in quadrante, &amp; </s>
  <s xml:id="echoid-s748" xml:space="preserve">ad eius interuallum circunfe-<lb/>rentiam occultam deſcribemus H I, vel M N, in qua ſi ſumatur arcus H I, vel M N, æqualis @arcui qua-<lb/>drantis E F, vel K L, qui complectatur grad@ 42. </s>
  <s xml:id="echoid-s749" xml:space="preserve">Item arcus H P, vel M Q, æqualis arcui quadran-<lb/>tis E F, vel K L, qui grad. </s>
  <s xml:id="echoid-s750" xml:space="preserve">15. </s>
  <s xml:id="echoid-s751" xml:space="preserve">contineat, &amp; </s>
  <s xml:id="echoid-s752" xml:space="preserve">c. </s>
  <s xml:id="echoid-s753" xml:space="preserve">ducantur{q́ue} rectæ G N I, G Q P, erunt I G H, P G H, <lb/>anguli quæſiti, &amp; </s>
  <s xml:id="echoid-s754" xml:space="preserve">c.</s>
  <s xml:id="echoid-s755" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s756" xml:space="preserve">VIDES igitur, quanto labore nos leuet quadrans eo modo, quo diximus, conſtructus. </s>
  <s xml:id="echoid-s757" xml:space="preserve">Si enim eo <lb/>careamus, cogemur ſemper cir culum propoſitum diuidere in ſuos gradus, quod quàm laborioſum ſit, atq; <lb/></s>
  <s xml:id="echoid-s758" xml:space="preserve">moleſtum, nemo ignorat. </s>
  <s xml:id="echoid-s759" xml:space="preserve">Itaque vt paucis vniuer ſum vſum quadrantis huius complectamur, quotieſcun-<lb/>qu@ in hac Gnomonica numeranda eſt altitudo poli, vel declinatio alicuius plani à verticali, inclinatioue <lb/>ad Horizontem certo numero graduum comprebenſa, vel certè conſtituendus ad aliquam rectam in dato <lb/>
<anchor type="note" xlink:label="note-0030-01a" xlink:href="note-0030-01"/>
puncto angulus graduum 20. </s>
  <s xml:id="echoid-s760" xml:space="preserve">vel 35. </s>
  <s xml:id="echoid-s761" xml:space="preserve">vel quotcunque, recurrendum erit ad quadr antem hoc loco conſtru-<lb/>ctum, atque ex eo gradus propcſiti in datam figuram transferendi, vt in ſuperioribus exemplis factũ eſt, <lb/>ne cogamur cir culos in ſuos gradus partiri: </s>
  <s xml:id="echoid-s762" xml:space="preserve">quæ res plena eſſet laboris, atque moleſtiæ.</s>
  <s xml:id="echoid-s763" xml:space="preserve"/>
</p>
<div xml:id="echoid-div34" type="float" level="2" n="6">
<note position="left" xlink:label="note-0030-01" xlink:href="note-0030-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s764" xml:space="preserve">IAM verò ſi in centro A, figatur clauiculus aliquis acutus, &amp; </s>
  <s xml:id="echoid-s765" xml:space="preserve">perexiguus, &amp; </s>
  <s xml:id="echoid-s766" xml:space="preserve">omnes partes qua-<lb/>drantis extra lineas A B, A C, &amp; </s>
  <s xml:id="echoid-s767" xml:space="preserve">circunferentiam B C, reſecentur, relicta tamen portiuncula quadam <lb/>circa centrum A, quæ clauiculum includat, vt figura indicat; </s>
  <s xml:id="echoid-s768" xml:space="preserve">habebit noster hic quadr ans multo commo-<lb/>diorem vſum, &amp; </s>
  <s xml:id="echoid-s769" xml:space="preserve">expeditiorem. </s>
  <s xml:id="echoid-s770" xml:space="preserve">Nam ſi clauiculus ille in centro affixus ponatur in centro G, propoſitæ <lb/>figuræ, recta{q́ue}, A B, rectę G H, congruat, ſignabimus ſtatim ſtylo quopiam acuto prope grad. </s>
  <s xml:id="echoid-s771" xml:space="preserve">42. </s>
  <s xml:id="echoid-s772" xml:space="preserve">pun-<lb/>ctum S, &amp; </s>
  <s xml:id="echoid-s773" xml:space="preserve">prope gradum 15. </s>
  <s xml:id="echoid-s774" xml:space="preserve">punctum R. </s>
  <s xml:id="echoid-s775" xml:space="preserve">Rectæ enim ductæ G S, G R, auferent ex cir culo H I, arcum <lb/>H I, grad. </s>
  <s xml:id="echoid-s776" xml:space="preserve">42. </s>
  <s xml:id="echoid-s777" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s778" xml:space="preserve">arcum H P, grad. </s>
  <s xml:id="echoid-s779" xml:space="preserve">15. </s>
  <s xml:id="echoid-s780" xml:space="preserve">continebunt{q́ue} angulos S G H, R G H, grad. </s>
  <s xml:id="echoid-s781" xml:space="preserve">42. </s>
  <s xml:id="echoid-s782" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s783" xml:space="preserve">grad. <lb/></s>
  <s xml:id="echoid-s784" xml:space="preserve">
<anchor type="note" xlink:label="note-0030-02a" xlink:href="note-0030-02"/>
15. </s>
  <s xml:id="echoid-s785" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s786" xml:space="preserve">c. </s>
  <s xml:id="echoid-s787" xml:space="preserve">Cætera vſus quotidianus docebit.</s>
  <s xml:id="echoid-s788" xml:space="preserve"/>
</p>
<div xml:id="echoid-div35" type="float" level="2" n="7">
<note position="left" xlink:label="note-0030-02" xlink:href="note-0030-02a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s789" xml:space="preserve">EX altera parte quadrantis deſcribi poterunt radĳ Signorum Zodiaci, de quibus in propoſ. </s>
  <s xml:id="echoid-s790" xml:space="preserve">1. </s>
  <s xml:id="echoid-s791" xml:space="preserve">quæ <lb/>iamiam ſequitur, agemus, vt eos, quando opus erit, transferre poſſimus in aliam figuram, quæ pro deſcri-<lb/>bendis arcubus ſignorum in horologĳs conſtruenda eſt, vt ex ſequentibus patebit.</s>
  <s xml:id="echoid-s792" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s793" xml:space="preserve">LIBVIT hoc loco quadrantem hunc explicare, non quòd eius vſus ſit omnino neceſſarius, ſed <lb/>quòd per eum facilius &amp; </s>
  <s xml:id="echoid-s794" xml:space="preserve">expeditius horologia deſcribamus, cum in noſtra hac Gnomo-<lb/>nica frequentiſſimè numeranda ſit altitudo poli, vel Aequatoris, decli-<lb/>natio plani, inclinatio{q́ue}, &amp; </s>
  <s xml:id="echoid-s795" xml:space="preserve">denique accipiendus arcus quot-<lb/>cunque graduum, &amp; </s>
  <s xml:id="echoid-s796" xml:space="preserve">c. </s>
  <s xml:id="echoid-s797" xml:space="preserve">Quæ quidem omnia dicto ci-<lb/>tius per Quadrantem eo modo diui-<lb/>
<anchor type="note" xlink:label="note-0030-03a" xlink:href="note-0030-03"/>
ſum abſoluuntur, vt ex pro-<lb/>poſitis exemplis ma-<lb/>nifeſtum eſt.</s>
  <s xml:id="echoid-s798" xml:space="preserve"/>
</p>
<div xml:id="echoid-div36" type="float" level="2" n="8">
<note position="left" xlink:label="note-0030-03" xlink:href="note-0030-03a" xml:space="preserve">30</note>
</div>
  <figure>
    <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/>
  </figure>
<pb o="11" file="0031" n="31" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div38" type="section" level="1" n="15">
<head xml:id="echoid-head17" xml:space="preserve">PROBLEMA PRIMVM.</head>
<head xml:id="echoid-head18" xml:space="preserve">PROPOSITIO PRIMA.</head>
<p>
  <s xml:id="echoid-s799" xml:space="preserve">ANALEMMA ad quamcunque poli altitudinem deſcribere.</s>
  <s xml:id="echoid-s800" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s801" xml:space="preserve">SIT Meridianus, vel potius in Meridiani plano circulus A B C D, circa <lb/>
<anchor type="note" xlink:label="note-0031-01a" xlink:href="note-0031-01"/>
mundi centrum E, deſcriptus, cuius &amp; </s>
  <s xml:id="echoid-s802" xml:space="preserve">Horizontis ſectio communis in-<lb/>
<anchor type="note" xlink:label="note-0031-02a" xlink:href="note-0031-02"/>
telligatur recta B D; </s>
  <s xml:id="echoid-s803" xml:space="preserve">Supputata autem altitudine poli illius loci, pro quo <lb/>
<anchor type="note" xlink:label="note-0031-03a" xlink:href="note-0031-03"/>
Analemma conſtruimus, à punctis B, &amp; </s>
  <s xml:id="echoid-s804" xml:space="preserve">D, in diuerſas partes vſque ad <lb/>G, &amp; </s>
  <s xml:id="echoid-s805" xml:space="preserve">F, ducatur diameter F G, quæ axis mundi erit, vt facile intelligi po-<lb/>
<anchor type="note" xlink:label="note-0031-04a" xlink:href="note-0031-04"/>
teſt, ſi circulus A B C D, in plano Meridiani ſtatuatur, ita vt E, centrum <lb/>idẽ ſit, quod centrũ mundi, &amp; </s>
  <s xml:id="echoid-s806" xml:space="preserve">recta B D, in plano Horizontis iaceat, tan-<lb/>
<anchor type="note" xlink:label="note-0031-05a" xlink:href="note-0031-05"/>
quam cõmunis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s807" xml:space="preserve">Meridiani; </s>
  <s xml:id="echoid-s808" xml:space="preserve">hac tamen lege, vt pun-<lb/>ctum F, ad polum arcticum, &amp; </s>
  <s xml:id="echoid-s809" xml:space="preserve">G, ad antarcticum vergat. </s>
  <s xml:id="echoid-s810" xml:space="preserve">Hac enim ra-<lb/>
<anchor type="note" xlink:label="note-0031-06a" xlink:href="note-0031-06"/>
tione fiet, vt recta F G, producta in vtrunque polum cadat, ac proinde axi mundi cõgruat. </s>
  <s xml:id="echoid-s811" xml:space="preserve">quod <lb/>ita planum fiet. </s>
  <s xml:id="echoid-s812" xml:space="preserve">Axis mundi, &amp; </s>
  <s xml:id="echoid-s813" xml:space="preserve">li-<lb/>
<anchor type="figure" xlink:label="fig-0031-01a" xlink:href="fig-0031-01"/>
nea meridiana Horizõtis, hoc eſt, <lb/>communis ſectio Horizontis ac <lb/>
<anchor type="note" xlink:label="note-0031-07a" xlink:href="note-0031-07"/>
Meridiani, auferunt ex Meridiano <lb/>circulo, &amp; </s>
  <s xml:id="echoid-s814" xml:space="preserve">circulo A B C D, circa <lb/>idem cẽtrum cum ipſo deſcripto, <lb/>arcus ſimiles, vt in commenta-<lb/>rijs in ſpheram ad finem primi ca-<lb/>pitis oſtendimus. </s>
  <s xml:id="echoid-s815" xml:space="preserve">Cum ergo ex cõ <lb/>ſtructione, arcus D F, ſimilis ſit ar-<lb/>cui, qui in Meridiano inter po-<lb/>lum arcticum, &amp; </s>
  <s xml:id="echoid-s816" xml:space="preserve">Horizontem in-<lb/>@ercipitur, (propterea quod arcus <lb/>
<anchor type="note" xlink:label="note-0031-08a" xlink:href="note-0031-08"/>
D F, contineat gradus altitudinis <lb/>poli) &amp; </s>
  <s xml:id="echoid-s817" xml:space="preserve">recta E D, ponatur cõmu-<lb/>nis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s818" xml:space="preserve">Meridia-<lb/>ni, atque centrum E, in centro mũ-<lb/>di collocatum ſit, erit neceſſario <lb/>E F, axis mundi, quandoquidem <lb/>ex circulo A B C D, aufert arcum <lb/>D F, ſimilem arcui altitudinis po-<lb/>li in Meridiano, vt diximus. </s>
  <s xml:id="echoid-s819" xml:space="preserve">Dein-<lb/>de ducatur diameter A C, ad Ho-<lb/>
<anchor type="note" xlink:label="note-0031-09a" xlink:href="note-0031-09"/>
rizontẽ B D, perpendicularis, quæ <lb/>communis ſectio erit Meridiani &amp; </s>
  <s xml:id="echoid-s820" xml:space="preserve">Verticalis circuli propriè dicti. </s>
  <s xml:id="echoid-s821" xml:space="preserve">Cum enim Verticalis circulus <lb/>
<anchor type="note" xlink:label="note-0031-10a" xlink:href="note-0031-10"/>
quadrante circuli maximi à ſuis polis, qui in B, D, ſunt, abſit, vt ex coroll. </s>
  <s xml:id="echoid-s822" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s823" xml:space="preserve">16. </s>
  <s xml:id="echoid-s824" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s825" xml:space="preserve">1. </s>
  <s xml:id="echoid-s826" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s827" xml:space="preserve">ſecundum noſtram editionem, conſtat, ſintq́; </s>
  <s xml:id="echoid-s828" xml:space="preserve">arcus A B, A D, quadrantes, propter rectos angu-<lb/>los A E B, A E D, tranſibit omnino Verticalis circulus per punctũ A, in Meridiano circulo: </s>
  <s xml:id="echoid-s829" xml:space="preserve">Tran-<lb/>ſit autem &amp; </s>
  <s xml:id="echoid-s830" xml:space="preserve">per centtum mundi E. </s>
  <s xml:id="echoid-s831" xml:space="preserve">Igitur recta A C, quam per centrum E, ad B D, duximus per-<lb/>pendicularem, communis ſectio erit Meridiani &amp; </s>
  <s xml:id="echoid-s832" xml:space="preserve">Verticalis circuli propriè dicti. </s>
  <s xml:id="echoid-s833" xml:space="preserve">Rurſus duca-<lb/>tur diameter H I, ad axem F G, perpendicularis, quæ eadem prorſus ratione cõmunis ſectio erit <lb/>Meridiani &amp; </s>
  <s xml:id="echoid-s834" xml:space="preserve">Aequatoris, propterea quòd Aequator quoque quadrante circuli maximi à ſuis po-<lb/>
<anchor type="note" xlink:label="note-0031-11a" xlink:href="note-0031-11"/>
lis, qui ſunt F, G, remoueatur, vt ex eodem coroll. </s>
  <s xml:id="echoid-s835" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s836" xml:space="preserve">16. </s>
  <s xml:id="echoid-s837" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s838" xml:space="preserve">1. </s>
  <s xml:id="echoid-s839" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s840" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s841" xml:space="preserve">Quòd ſi <lb/>
<anchor type="note" xlink:label="note-0031-12a" xlink:href="note-0031-12"/>
<anchor type="note" xlink:label="note-0031-13a" xlink:href="note-0031-13"/>
ducamus per puncta D, B, ipſi H I, parallelas D K, B L, erunt hæ, communes ſectiones Meridia-<lb/>ni, &amp; </s>
  <s xml:id="echoid-s842" xml:space="preserve">parallelorum, qui ſunt omnium ſemper apparentium, ſemperq́; </s>
  <s xml:id="echoid-s843" xml:space="preserve">latentium maximi: </s>
  <s xml:id="echoid-s844" xml:space="preserve">quan-<lb/>doquidem Meridianus ſecans Aequatorem, &amp; </s>
  <s xml:id="echoid-s845" xml:space="preserve">dictos parallelos, ſectiones communes facit paral-<lb/>
<anchor type="note" xlink:label="note-0031-14a" xlink:href="note-0031-14"/>
lelas; </s>
  <s xml:id="echoid-s846" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s847" xml:space="preserve">parallelus quidem maximus ſemper apparentium Horizontem tangit in D, maximus ve-<lb/>ro ſemper occultorum in B.</s>
  <s xml:id="echoid-s848" xml:space="preserve"/>
</p>
<div xml:id="echoid-div38" type="float" level="2" n="1">
<note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">Meridianus.</note>
<note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">Horizon.</note>
<note position="left" xlink:label="note-0031-03" xlink:href="note-0031-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0031-04" xlink:href="note-0031-04a" xml:space="preserve">Axis mundi.</note>
<note position="right" xlink:label="note-0031-05" xlink:href="note-0031-05a" xml:space="preserve">Centrũ mũdi.</note>
<note position="right" xlink:label="note-0031-06" xlink:href="note-0031-06a" xml:space="preserve">Poli mundi.</note>
  <figure xlink:label="fig-0031-01" xlink:href="fig-0031-01a">
    <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0031-01"/>
  </figure>
<note position="left" xlink:label="note-0031-07" xlink:href="note-0031-07a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0031-08" xlink:href="note-0031-08a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0031-09" xlink:href="note-0031-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0031-10" xlink:href="note-0031-10a" xml:space="preserve">Verticalis.</note>
<note position="right" xlink:label="note-0031-11" xlink:href="note-0031-11a" xml:space="preserve">Aequinoctialis.</note>
<note position="left" xlink:label="note-0031-12" xlink:href="note-0031-12a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0031-13" xlink:href="note-0031-13a" xml:space="preserve">Paralleli ſemp <lb/>apparentiũ, ſem <lb/>perq́; latentium <lb/>maximi.</note>
<note position="right" xlink:label="note-0031-14" xlink:href="note-0031-14a" xml:space="preserve">16. vnde@.</note>
</div>
<p>
  <s xml:id="echoid-s849" xml:space="preserve">VT autem parallelos Aequatoris ducamus, qui per ſigna, vel gradus Eclipticæ trãſeunt, in qui-<lb/>bus quidem accurate deſcribendis tota induſtria, &amp; </s>
  <s xml:id="echoid-s850" xml:space="preserve">labor cõſtruendi Analemmatis ponitur, pro-<lb/>pter declinationes ipſorum parallelorum ab Aequatore, quæ uix ſine errore ſupputari poſſunt ab <lb/>
<anchor type="note" xlink:label="note-0031-15a" xlink:href="note-0031-15"/>
Aequatoris diametro H I, hinc inde, ob minuta, &amp; </s>
  <s xml:id="echoid-s851" xml:space="preserve">ſecunda, quæ gradibus declinationum adhæ-<lb/>rent, hac arte à veteribus tradita, vt apud Vitruuium lib. </s>
  <s xml:id="echoid-s852" xml:space="preserve">9. </s>
  <s xml:id="echoid-s853" xml:space="preserve">videre licet, vtemur. </s>
  <s xml:id="echoid-s854" xml:space="preserve">Sumantur in cir-<lb/>cunferentia A B C D, duo arcus H M, H N, quorum vterque maximę declinationi ſolis ſit æqua-
<pb o="12" file="0032" n="32" rhead="GNOMONICES"/>
lis, hoc eſt, contineat gradus 23. </s>
  <s xml:id="echoid-s855" xml:space="preserve">minuta 30. </s>
  <s xml:id="echoid-s856" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s857" xml:space="preserve">coniungatur recta M N, ſecans H I, in O. </s>
  <s xml:id="echoid-s858" xml:space="preserve">Quoniã <lb/>verò ductis rectis E M, E N, latera O E, E M, trianguli O E M, lateribus O E, E N, triãguli O E N, <lb/>ſunt æqualia, continentq́; </s>
  <s xml:id="echoid-s859" xml:space="preserve">angulos ad centrum E, æquales, propterea quòd arcubus æqualibus <lb/>
<anchor type="note" xlink:label="note-0032-01a" xlink:href="note-0032-01"/>
H M, H N, inſiſtant, erunt &amp; </s>
  <s xml:id="echoid-s860" xml:space="preserve">baſes O M, O N, æquales, &amp; </s>
  <s xml:id="echoid-s861" xml:space="preserve">anguli ad O, ac proinde recti. </s>
  <s xml:id="echoid-s862" xml:space="preserve">Si igitur <lb/>
<anchor type="figure" xlink:label="fig-0032-01a" xlink:href="fig-0032-01"/>
ex O, ad interuallũ O M, vel O N, <lb/>deſcribatur circulus M P N, ex-<lb/>tendaturq́; </s>
  <s xml:id="echoid-s863" xml:space="preserve">recta I H, ad Q, erunt <lb/>arcus M P, P N, N Q, Q M, qua-<lb/>drantes, propterea quòd, cum ip-<lb/>ſis inſiſtant æquales anguli ad cen <lb/>
<anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/>
trum O, nẽpe recti, æquales ſint. <lb/></s>
  <s xml:id="echoid-s864" xml:space="preserve">
<anchor type="note" xlink:label="note-0032-03a" xlink:href="note-0032-03"/>
Quod ſi ſinguli quadrãtes in ter-<lb/>nas partes æquales ſecentur (atq; <lb/></s>
  <s xml:id="echoid-s865" xml:space="preserve">adeò totus circulus in partes 12. </s>
  <s xml:id="echoid-s866" xml:space="preserve"><lb/>æquales, inſtar Zodiaci, qui in 12. </s>
  <s xml:id="echoid-s867" xml:space="preserve"><lb/>ſigna æqualia diſtribuitur) in pun <lb/>ctis R, S, &amp;</s>
  <s xml:id="echoid-s868" xml:space="preserve">c quorum bina à pun <lb/>ctis P, Q, æqualiter remota lineis <lb/>rectis iungantur (quæ quidem pa <lb/>rallelæ erunt &amp; </s>
  <s xml:id="echoid-s869" xml:space="preserve">ipſi H I, &amp; </s>
  <s xml:id="echoid-s870" xml:space="preserve">inter <lb/>
<anchor type="note" xlink:label="note-0032-04a" xlink:href="note-0032-04"/>
ſe, ex ijs, quæ in ſcholio propoſ. <lb/></s>
  <s xml:id="echoid-s871" xml:space="preserve">27. </s>
  <s xml:id="echoid-s872" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s873" xml:space="preserve">3. </s>
  <s xml:id="echoid-s874" xml:space="preserve">Euclidis demonſtrata <lb/>ſunt à nobis) ſecantibus arcus <lb/>H M, H N in punctis, β, γ, δ, @, <lb/>erunt arcus H β, H γ, H δ, H @, <lb/>declinationibus reliquorũ ſigno-<lb/>rum Zodiaci inter ♋, &amp; </s>
  <s xml:id="echoid-s875" xml:space="preserve">♑, <lb/>æquales, vt mox oſtendemus@</s>
</p>
<div xml:id="echoid-div39" type="float" level="2" n="2">
<note position="right" xlink:label="note-0031-15" xlink:href="note-0031-15a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ae-<lb/>quatoris per ini <lb/>tia ſignorũ Zo-<lb/>diaci ductor@.</note>
<note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">27. tertĳ. <lb/>4. primi.</note>
  <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a">
    <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0032-01"/>
  </figure>
<note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">26. tertĳ.</note>
<note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s876" xml:space="preserve">IAM verò ſi his arcubus æquales arcus abſcindantur I θ, I λ, I μ, I ξ, I π, I ρ, ducanturq́; </s>
  <s xml:id="echoid-s877" xml:space="preserve">rectæ <lb/>M θ, β λ, γ μ, δ ξ, ε π, N ρ, vel certè parallelæ X R, Y S, &amp;</s>
  <s xml:id="echoid-s878" xml:space="preserve">c. </s>
  <s xml:id="echoid-s879" xml:space="preserve">producantur, (Nam &amp; </s>
  <s xml:id="echoid-s880" xml:space="preserve">rectæ H I, <lb/>
<anchor type="note" xlink:label="note-0032-05a" xlink:href="note-0032-05"/>
γ μ, β λ, M θ, parallelę ſunt, ex demonſcratis à nobis in ſcholio propoſ. </s>
  <s xml:id="echoid-s881" xml:space="preserve">27. </s>
  <s xml:id="echoid-s882" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s883" xml:space="preserve">3. </s>
  <s xml:id="echoid-s884" xml:space="preserve">Euclidis, pro-<lb/>pter æqualitatem arcuum H γ, I μ, &amp; </s>
  <s xml:id="echoid-s885" xml:space="preserve">γ β, μ λ, &amp;</s>
  <s xml:id="echoid-s886" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s887" xml:space="preserve">erunt hæ, communes ſectiones parallelorũ <lb/>per initia ſignorum ductorum, ac Meridiani circuli. </s>
  <s xml:id="echoid-s888" xml:space="preserve">Sunt enim earum diſtantiæ à recta H I, com@ <lb/>muni ſectione Aequatoris &amp; </s>
  <s xml:id="echoid-s889" xml:space="preserve">Meridiani, proportionales diſtantijs ſectionum eorundem parallelo-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s890" xml:space="preserve">Meridiani, in ipſo Meridiano; </s>
  <s xml:id="echoid-s891" xml:space="preserve">cum rectæ ex centro E, per puncta M, β, γ, &amp;</s>
  <s xml:id="echoid-s892" xml:space="preserve">c. </s>
  <s xml:id="echoid-s893" xml:space="preserve">emiſſæ au-<lb/>ferant ex Meridiano circa idem centrum E, deſcripto arcus ſimiles arcubus H M, H β, H γ, &amp;</s>
  <s xml:id="echoid-s894" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s895" xml:space="preserve">ex ijs, quæ in commentarijs in Sphæram ſcripſimus ad finem primi capitis.</s>
  <s xml:id="echoid-s896" xml:space="preserve"/>
</p>
<div xml:id="echoid-div40" type="float" level="2" n="3">
<note position="left" xlink:label="note-0032-05" xlink:href="note-0032-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s897" xml:space="preserve">SVNT autem rectæ E M, E β, E γ, &amp;</s>
  <s xml:id="echoid-s898" xml:space="preserve">c. </s>
  <s xml:id="echoid-s899" xml:space="preserve">communes ſectiones Meridiani, atque Eclipticæ va-<lb/>
<anchor type="note" xlink:label="note-0032-06a" xlink:href="note-0032-06"/>
rias poſitiones obtinen tis in ipſo Meridiano. </s>
  <s xml:id="echoid-s900" xml:space="preserve">Nam EM, eſt eiuſmodi ſectio, cum principiũ ♋ <lb/>in Meridiano fuerit poſitum: </s>
  <s xml:id="echoid-s901" xml:space="preserve">At E β, cum fuerit principium ♊ aut ♌ in Meridiano poſitũ<unsure/>: <lb/></s>
  <s xml:id="echoid-s902" xml:space="preserve">
<anchor type="note" xlink:label="note-0032-07a" xlink:href="note-0032-07"/>
Et E γ, quando initium ♉, vel ♍ Meridianũ poſſederit, &amp;</s>
  <s xml:id="echoid-s903" xml:space="preserve">c. </s>
  <s xml:id="echoid-s904" xml:space="preserve">vt conſtat, ſi Analemma in plano <lb/>Meridiani proprium intelligatur habere ſitum. </s>
  <s xml:id="echoid-s905" xml:space="preserve">quæ res perfacilis eſt etiam ex Sphæra materiali.</s>
  <s xml:id="echoid-s906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div41" type="float" level="2" n="4">
<note position="left" xlink:label="note-0032-06" xlink:href="note-0032-06a" xml:space="preserve">Variæ poſitio-<lb/>nes Eclipticæ.</note>
<note position="left" xlink:label="note-0032-07" xlink:href="note-0032-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s907" xml:space="preserve">HAS quoque rectas, cum de Horologiorum deſcriptionibus agemus, appellabimus radios <lb/>
<anchor type="note" xlink:label="note-0032-08a" xlink:href="note-0032-08"/>
ſignorum, vel Zodiaci, quoniam Sole exiſtente in ſignorum initijs, referunt radios, quos in me-<lb/>ridie Sol per centrũ mundi E, proijcit. </s>
  <s xml:id="echoid-s908" xml:space="preserve">At verò rectæ M θ, β λ, γ μ, &amp;</s>
  <s xml:id="echoid-s909" xml:space="preserve">c. </s>
  <s xml:id="echoid-s910" xml:space="preserve">diametri ſunt parallelo-<lb/>
<anchor type="note" xlink:label="note-0032-09a" xlink:href="note-0032-09"/>
rum, qui per initia ſignorum Zodiaci incedunt, nempe H I, diameter Aequatoris; </s>
  <s xml:id="echoid-s911" xml:space="preserve">γ μ, diame-<lb/>ter paralleli ♉, &amp; </s>
  <s xml:id="echoid-s912" xml:space="preserve">♍, &amp;</s>
  <s xml:id="echoid-s913" xml:space="preserve">c. </s>
  <s xml:id="echoid-s914" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s915" xml:space="preserve">B D, diameter eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s916" xml:space="preserve">A D, Ver-<lb/>ticalis, &amp;</s>
  <s xml:id="echoid-s917" xml:space="preserve">c.</s>
  <s xml:id="echoid-s918" xml:space="preserve"/>
</p>
<div xml:id="echoid-div42" type="float" level="2" n="5">
<note position="left" xlink:label="note-0032-08" xlink:href="note-0032-08a" xml:space="preserve">Radij ſignerũ, <lb/>vel Zodiaci qui <lb/>ſint.</note>
<note position="left" xlink:label="note-0032-09" xlink:href="note-0032-09a" xml:space="preserve">Diametri paral <lb/>lelorũ per pun-<lb/>cta Zodiaci du-<lb/>ctorum.</note>
</div>
<p>
  <s xml:id="echoid-s919" xml:space="preserve">ALII has diametros M θ, β λ, &amp;</s>
  <s xml:id="echoid-s920" xml:space="preserve">c. </s>
  <s xml:id="echoid-s921" xml:space="preserve">hac ratione ducunt, &amp; </s>
  <s xml:id="echoid-s922" xml:space="preserve">rectè quidem, meo iudicio, quia vna <lb/>
<anchor type="note" xlink:label="note-0032-10a" xlink:href="note-0032-10"/>
opera, vnoq́ue labore &amp; </s>
  <s xml:id="echoid-s923" xml:space="preserve">declinationes parallelorum reperiunt, &amp; </s>
  <s xml:id="echoid-s924" xml:space="preserve">diametros eorundem rectę H I, <lb/>
<anchor type="note" xlink:label="note-0032-11a" xlink:href="note-0032-11"/>
æquidiſtantes ducunt. </s>
  <s xml:id="echoid-s925" xml:space="preserve">Sumptis arcubus H M, H N, I θ, I ρ, quorum quiſque maximæ Solis de-<lb/>clinationi æqualis ſit, coniungunt rectas M N, θ ρ, ſecantes rectam H I, in O, &amp; </s>
  <s xml:id="echoid-s926" xml:space="preserve">e. </s>
  <s xml:id="echoid-s927" xml:space="preserve">Deinde ex O, &amp; </s>
  <s xml:id="echoid-s928" xml:space="preserve"><lb/>e, deſcribunt circa diametros M N, θ ρ, ſe<unsure/>micirculos duntaxat M Q N, θ f ρ, quia vt ſupra de-<lb/>monſtratum eſt, recta M N, in O, atque adeo eadem ratione &amp; </s>
  <s xml:id="echoid-s929" xml:space="preserve">θ ρ in e, ſecatur bifariam, &amp; </s>
  <s xml:id="echoid-s930" xml:space="preserve">ad <lb/>angulos rectos. </s>
  <s xml:id="echoid-s931" xml:space="preserve">Diſtributis uerò his ſemicirculis in ſex partes æquales in punctis α, z, x, Y, <lb/>g, h, m, n, connectunt lineis rectis reſpondentia puncta, qualia ſunt M, θ Y, g; </s>
  <s xml:id="echoid-s932" xml:space="preserve">X, h, &amp;</s>
  <s xml:id="echoid-s933" xml:space="preserve">c. </s>
  <s xml:id="echoid-s934" xml:space="preserve">Hæ enim <lb/>dabunt parallelorum diametros, vt prius, quia inter ſe parallelæ erunt, vt rectę Y S, X R, &amp;</s>
  <s xml:id="echoid-s935" xml:space="preserve">c. </s>
  <s xml:id="echoid-s936" xml:space="preserve">cum <lb/>ſemicirculus θ f ρ<unsure/>, eundem ſitum habeat reſpectu ſemicirculi M Q N, quem ſemicirculus M P N, <lb/>
<anchor type="note" xlink:label="note-0032-12a" xlink:href="note-0032-12"/>
vt manifeſtum eſt.</s>
  <s xml:id="echoid-s937" xml:space="preserve"/>
</p>
<div xml:id="echoid-div43" type="float" level="2" n="6">
<note position="left" xlink:label="note-0032-10" xlink:href="note-0032-10a" xml:space="preserve">Alia deſcriptio <lb/>parallelorum <lb/>Aequatoris per <lb/>ſignorum ini-<lb/>tia tranſeun-<lb/>tium.</note>
<note position="left" xlink:label="note-0032-11" xlink:href="note-0032-11a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0032-12" xlink:href="note-0032-12a" xml:space="preserve">Deſcriptio pa-<lb/>rall@lorum Ae-<lb/>quatoris per ſin <lb/>gulos grad<emph style="sub">9</emph> Ecli <lb/>pticæ ductorũ.</note>
</div>
<p>
  <s xml:id="echoid-s938" xml:space="preserve">QVOD ſi ſinguli arcus Q X, X Y, &amp;</s>
  <s xml:id="echoid-s939" xml:space="preserve">c. </s>
  <s xml:id="echoid-s940" xml:space="preserve">bifariam ſecentur, &amp; </s>
  <s xml:id="echoid-s941" xml:space="preserve">eadem fiant, quæ prius, habebun-<lb/>tur communes ſectiones parallelorum, qui per dimidia ſignorum, id eſt, per quindenos gradus
<pb o="13" file="0033" n="33" rhead="LIBER PRIMVS."/>
ipſorum ducuntur: </s>
  <s xml:id="echoid-s942" xml:space="preserve">atque eodem modo paralleli ſingulorum graduum Eclipticæ inu ſtigari poſ-<lb/>ſunt; </s>
  <s xml:id="echoid-s943" xml:space="preserve">ſi nimirum circulus M P N Q, in ſingulos gra dus diſtribuatur, &amp; </s>
  <s xml:id="echoid-s944" xml:space="preserve">reliqua fiant, quæ prius. <lb/></s>
  <s xml:id="echoid-s945" xml:space="preserve">Nam in vniuerſu@ rectæ, quæ ipſi P Q, parallelæ ſunt, abſcindunt ex Meridiano arcus declinatio-<lb/>num eorum arcuum Eclipticæ, qui arcubus circuli M P N Q, ſi miles ſunt, ſicut &amp; </s>
  <s xml:id="echoid-s946" xml:space="preserve">duodecim ſi-<lb/>gna Zodiaci duodecim arcubus Q X, X Y, &amp;</s>
  <s xml:id="echoid-s947" xml:space="preserve">c. </s>
  <s xml:id="echoid-s948" xml:space="preserve">ſimilia ſunt. </s>
  <s xml:id="echoid-s949" xml:space="preserve">Quod quidem hac fere ratione cum <lb/>Petro Nonio lib. </s>
  <s xml:id="echoid-s950" xml:space="preserve">2. </s>
  <s xml:id="echoid-s951" xml:space="preserve">de arte nauigandi demonſtrabimus.</s>
  <s xml:id="echoid-s952" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s953" xml:space="preserve">INTELLIGATVR circa E M, deſcriptus ſemicirculus Eclipticæ A M B, &amp; </s>
  <s xml:id="echoid-s954" xml:space="preserve">circa E H, ſe-<lb/>
<anchor type="note" xlink:label="note-0033-01a" xlink:href="note-0033-01"/>
micirculus Aequatoris A H B, &amp; </s>
  <s xml:id="echoid-s955" xml:space="preserve">vtriuſque ſectio communis ſit recta A B; </s>
  <s xml:id="echoid-s956" xml:space="preserve">ſitq́; </s>
  <s xml:id="echoid-s957" xml:space="preserve">A, principium ♈, <lb/>&amp; </s>
  <s xml:id="echoid-s958" xml:space="preserve">B, principium ♎. </s>
  <s xml:id="echoid-s959" xml:space="preserve">Et quoniam M, eſt principium ♋, vel ♑, cum H M, portio Meridiani <lb/>circuli ſit maxima declinatio ſolis; </s>
  <s xml:id="echoid-s960" xml:space="preserve">diſtat autem vtrumque horũ ab æquinoctialibus punctis qua-<lb/>
<anchor type="note" xlink:label="note-0033-02a" xlink:href="note-0033-02"/>
drante integro; </s>
  <s xml:id="echoid-s961" xml:space="preserve">erunt arcus A M, B M, quadrantes, atque adeo anguli A E M, B E M, recti. </s>
  <s xml:id="echoid-s962" xml:space="preserve">Secet <lb/>iam recta X R, in plano Meridiani per arcum H M, &amp; </s>
  <s xml:id="echoid-s963" xml:space="preserve">rectas E H, E M, M O, ducto rectã M O, <lb/>in puncto φ, &amp; </s>
  <s xml:id="echoid-s964" xml:space="preserve">rectam E M, in puncto C. </s>
  <s xml:id="echoid-s965" xml:space="preserve">Intelligatur quoque per rectam X R, planũ duci Aequa-<lb/>tori A H B, parallelum occurrens rectæ E M in C, (quoniam enim circulus M P N Q, cum in <lb/>Analemmate iaceat in plano Meridiani, ad Aequatorem rectus eſt, eſtq́; </s>
  <s xml:id="echoid-s966" xml:space="preserve">Q H P E, communis ſe-<lb/>ctio Aequatoris &amp; </s>
  <s xml:id="echoid-s967" xml:space="preserve">eiuſdem pla <lb/>ni Meridiani, &amp; </s>
  <s xml:id="echoid-s968" xml:space="preserve">recta X R, di-<lb/>ctæ ſectioni Q H P E, parallela, <lb/>
<anchor type="figure" xlink:label="fig-0033-01a" xlink:href="fig-0033-01"/>
poterit per ipſam X R, duci <lb/>planũ Aequatori æquidiſtans.) <lb/></s>
  <s xml:id="echoid-s969" xml:space="preserve">
<anchor type="note" xlink:label="note-0033-03a" xlink:href="note-0033-03"/>
faciensq́; </s>
  <s xml:id="echoid-s970" xml:space="preserve">in Ecliptica quidem <lb/>cõmunem ſectionem D K, re-<lb/>ctam; </s>
  <s xml:id="echoid-s971" xml:space="preserve">In Sphæra autem circu-<lb/>
<anchor type="note" xlink:label="note-0033-04a" xlink:href="note-0033-04"/>
lum D γ k, ex propos. </s>
  <s xml:id="echoid-s972" xml:space="preserve">1. </s>
  <s xml:id="echoid-s973" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s974" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s975" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s976" xml:space="preserve">tranſeuntem per pun-<lb/>ctum γ, in quo recta X R, arcũ <lb/>Meridiani H M, ſecat. </s>
  <s xml:id="echoid-s977" xml:space="preserve">Quo-<lb/>niam igitur eſt, vt M C, ad C E, <lb/>
<anchor type="note" xlink:label="note-0033-05a" xlink:href="note-0033-05"/>
ita M φ, ad φ O, erit &amp; </s>
  <s xml:id="echoid-s978" xml:space="preserve">compo <lb/>nendo, vt M E, ad CE, ita M O, <lb/>
<anchor type="note" xlink:label="note-0033-06a" xlink:href="note-0033-06"/>
ad φ O; </s>
  <s xml:id="echoid-s979" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s980" xml:space="preserve">permutando, vt M E, ſemidiameter Eclipticæ ad M O, ſemidiametrũ circuli M P Q, <lb/>ita C E, ad φ O: </s>
  <s xml:id="echoid-s981" xml:space="preserve">Eſt autem C E, æqualis ſinui arcus D A, hoc eſt, rectæ D F, ex D, ad A B, ad rectos <lb/>
<anchor type="note" xlink:label="note-0033-07a" xlink:href="note-0033-07"/>
angulos ductæ (ſunt enim A B, D K, communes ſectiones planorum parallelorũ, nempe Aequa-<lb/>
<anchor type="note" xlink:label="note-0033-08a" xlink:href="note-0033-08"/>
toris A H B, &amp; </s>
  <s xml:id="echoid-s982" xml:space="preserve">circuli D γ K, factæ ab Eclipticæ plano A M B, parallelæ nec non &amp; </s>
  <s xml:id="echoid-s983" xml:space="preserve">C E, D F, pa-<lb/>
<anchor type="note" xlink:label="note-0033-09a" xlink:href="note-0033-09"/>
rallelæ) &amp; </s>
  <s xml:id="echoid-s984" xml:space="preserve">φ O, eadem ratione ęqualis ſinui arcus Q X, hoc eſt, rectæ X ω, quæ ad Q E, perpendi-<lb/>cularis eſt. </s>
  <s xml:id="echoid-s985" xml:space="preserve">Igitur ſemidiametri M E, M O, eandem habent proportionem, quam ſinus D F, X ω, <lb/>ac propterea arcus A D, Q X, ſimiles ſunt, vt mox lemmate ſequenti demonſtrabimus. </s>
  <s xml:id="echoid-s986" xml:space="preserve">Oſtenden <lb/>dum ergo eſt, arcum H γ, quem aufert parallela X R, ex Meridiano, æqualem eſſe arcui declina-<lb/>tionis, quam habet Eclipticæ arcus A D, quem arcui Q X, circuli M P Q, ſimilem iam demonſtra <lb/>uimus. </s>
  <s xml:id="echoid-s987" xml:space="preserve">quod quidem facile præſtabimus hoc modo. </s>
  <s xml:id="echoid-s988" xml:space="preserve">Deſcripto per polos mundi, hoc eſt, per po-<lb/>
<anchor type="note" xlink:label="note-0033-10a" xlink:href="note-0033-10"/>
los parallelorum A H B, D γ K, &amp; </s>
  <s xml:id="echoid-s989" xml:space="preserve">per D, punctum circulo maximo D G, erit arcus D G, arcus de-<lb/>clinationis puncti D, cum intercipiatur inter ipſum punctum, &amp; </s>
  <s xml:id="echoid-s990" xml:space="preserve">Aequatorem. </s>
  <s xml:id="echoid-s991" xml:space="preserve">Cum ergo arcus <lb/>circulorum maximorum, qui per polos parallelorum deſcribuntur, inter ipſos parallelos interce-<lb/>pti, ex propoſitione 15. </s>
  <s xml:id="echoid-s992" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s993" xml:space="preserve">2. </s>
  <s xml:id="echoid-s994" xml:space="preserve">Theodoſii, æquales ſint; </s>
  <s xml:id="echoid-s995" xml:space="preserve">Sint autem arcus H γ, D G, circulorum ma-<lb/>ximorum per polos parallelorum A H B, D γ K, deſcriptorum, intercipianturq́; </s>
  <s xml:id="echoid-s996" xml:space="preserve">inter ipſos paral-<lb/>lelos, æqualis erit arcus H γ, arcui D G. </s>
  <s xml:id="echoid-s997" xml:space="preserve">Aufert igitur in Analemmate parallela X R, arcum H γ, <lb/>æqualem arcui declinationis illius arcus Eclipticæ, qui arcui Q X, ſimilis eſt, qualis eſtarcus A D. <lb/></s>
  <s xml:id="echoid-s998" xml:space="preserve">Idemq́ue dicendum eſt de reliquis parallelis Y S, Z T, &amp; </s>
  <s xml:id="echoid-s999" xml:space="preserve">α V. </s>
  <s xml:id="echoid-s1000" xml:space="preserve">Conſtat ergo arcus H γ, H β, H δ, &amp; </s>
  <s xml:id="echoid-s1001" xml:space="preserve"><lb/>H ε. </s>
  <s xml:id="echoid-s1002" xml:space="preserve">æquales eſſe declinationibus reliquorum ſignorum Zodiaci inter ♋ &amp; </s>
  <s xml:id="echoid-s1003" xml:space="preserve">♑, quandoqui-<lb/>dem arcus ſignorũ in Ecliptica ſimiles ſunt arcubus Q X, X Y, &amp;</s>
  <s xml:id="echoid-s1004" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1005" xml:space="preserve">in circulo M P N Q. </s>
  <s xml:id="echoid-s1006" xml:space="preserve">tam enim <lb/>
<anchor type="note" xlink:label="note-0033-11a" xlink:href="note-0033-11"/>
hi, quàm illi, duodecimæ partes ſunt ſuorum circulorum. </s>
  <s xml:id="echoid-s1007" xml:space="preserve">Quoniam verò ſectiones parallelorũ <lb/>per ſignorum initia ductorum factæ à Meridiani plano parallelæ ſunt, liquido conſtat, parallelas <lb/>illas per puncta M, β, γ, H, &amp;</s>
  <s xml:id="echoid-s1008" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1009" xml:space="preserve">ductas, eſſe diametros parallelorum, cum auferant ex circulo A B <lb/>C D, arcus ſimiles illis, quos ex Meridiano ab@cindunt re uera diametri dictorum parallelorum, <lb/>vt ante dictum eſt. </s>
  <s xml:id="echoid-s1010" xml:space="preserve">Quòd ſi circulus A B C D, æqualis eſſet Meridiano in Sphæra, tranſirent om-<lb/>nino per illas parallelas paralleli per initia ſignorum ducti. </s>
  <s xml:id="echoid-s1011" xml:space="preserve">Idem prorſus demonſtrabimus, ſi pro <lb/>Meridiano circulus A B C D, intelligatur quicunque alius circulus maximus per polos mundi <lb/>ductus, qualis eſt Colurus ſolſtitiorum, vt ſupra in definitione Analemmatis diximus. </s>
  <s xml:id="echoid-s1012" xml:space="preserve">Analemma <lb/>ergo ad quamcunque poli altitudinem deſcripſimus. </s>
  <s xml:id="echoid-s1013" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s1014" xml:space="preserve"/>
</p>
<div xml:id="echoid-div44" type="float" level="2" n="7">
<note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve">Demon ſtrati@ <lb/>deſcriptionis <lb/>Analemmatis.<unsure/></note>
<note position="left" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0033-01" xlink:href="fig-0033-01a">
    <image file="0033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0033-01"/>
  </figure>
<note position="left" xlink:label="note-0033-03" xlink:href="note-0033-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0033-04" xlink:href="note-0033-04a" xml:space="preserve">3. vndec.</note>
<note position="right" xlink:label="note-0033-05" xlink:href="note-0033-05a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0033-06" xlink:href="note-0033-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0033-07" xlink:href="note-0033-07a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0033-08" xlink:href="note-0033-08a" xml:space="preserve">16. undec.</note>
<note position="right" xlink:label="note-0033-09" xlink:href="note-0033-09a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0033-10" xlink:href="note-0033-10a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0033-11" xlink:href="note-0033-11a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div46" type="section" level="1" n="16">
<head xml:id="echoid-head19" xml:space="preserve">LEMMA.</head>
<p>
  <s xml:id="echoid-s1015" xml:space="preserve">QVAM proportionem habent ſinus toti, hoc eſt, ſemidiametri quorumlibet
<pb o="14" file="0034" n="34" rhead="GNOMONICES"/>
circulorum, eandem habent ſinus tam recti, quàm verſi arcuum ſimilium. </s>
  <s xml:id="echoid-s1016" xml:space="preserve">Et co<unsure/>n-<lb/>
<anchor type="note" xlink:label="note-0034-01a" xlink:href="note-0034-01"/>
tra, arcus, quorum ſinus tam recti, quàm verſi eandem proportionem habent, quam <lb/>ſinus toti, ſimiles ſunt.</s>
  <s xml:id="echoid-s1017" xml:space="preserve"/>
</p>
<div xml:id="echoid-div46" type="float" level="2" n="1">
<note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">Sinus toti pro-<lb/>portionales sũt <lb/>ſinubus tam re-<lb/>ctis, quàm uer-<lb/>ſis arcuum ſi@i <lb/>lium, &amp; contra.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1018" xml:space="preserve">SINT arcus A B, C D, circulorum, quorum ſemidiametri A E, C F, ſimiles, &amp; </s>
  <s xml:id="echoid-s1019" xml:space="preserve"><lb/>eorum ſinus recti B G, D H, verſi autem A G, C H. </s>
  <s xml:id="echoid-s1020" xml:space="preserve">Dico eße, vt A E, ad C F, ita &amp; </s>
  <s xml:id="echoid-s1021" xml:space="preserve"><lb/>B G, ad D H, &amp; </s>
  <s xml:id="echoid-s1022" xml:space="preserve">A G, ad C H. </s>
  <s xml:id="echoid-s1023" xml:space="preserve">Ductis enim rurſum ſemidiametris B E, D F, erunt ob ſi-<lb/>militudinem arcuum A B, C D, anguli E, &amp; </s>
  <s xml:id="echoid-s1024" xml:space="preserve">F, æquales, ex ĳs, quæ ad propoſ. </s>
  <s xml:id="echoid-s1025" xml:space="preserve">33. </s>
  <s xml:id="echoid-s1026" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s1027" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0034-01a" xlink:href="fig-0034-01"/>
6. </s>
  <s xml:id="echoid-s1028" xml:space="preserve">Euclidis ostendimus; </s>
  <s xml:id="echoid-s1029" xml:space="preserve">at-<lb/>que adeò, cum &amp; </s>
  <s xml:id="echoid-s1030" xml:space="preserve">anguli ad <lb/>
<anchor type="note" xlink:label="note-0034-02a" xlink:href="note-0034-02"/>
G, H, æquales ſint, nempe <lb/>recti, æquiangula erunt triã-<lb/>
<anchor type="note" xlink:label="note-0034-03a" xlink:href="note-0034-03"/>
gula B E G, D F H. </s>
  <s xml:id="echoid-s1031" xml:space="preserve">Quare <lb/>erit, vt B E, ad B G, ita D F, <lb/>ad D H; </s>
  <s xml:id="echoid-s1032" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1033" xml:space="preserve">permutando, vt <lb/>B E, hoc eſt, A E, ad D F, <lb/>hoc eſt, ad C F, ita B G, <lb/>ad D H.</s>
  <s xml:id="echoid-s1034" xml:space="preserve"/>
</p>
<div xml:id="echoid-div47" type="float" level="2" n="2">
  <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a">
    <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0034-01"/>
  </figure>
<note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">32. primi. <lb/>4. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1035" xml:space="preserve">RVRSVS, quoniam propter ſimilitudinem arcuum A B, C D, triangula B E G, <lb/>
<anchor type="note" xlink:label="note-0034-04a" xlink:href="note-0034-04"/>
D F H, eodem modo ſimilia ſunt; </s>
  <s xml:id="echoid-s1036" xml:space="preserve">erit, vt B E, hoc eſt, A E, ad E G, ita D F, hoc eſt, C F, <lb/>
<anchor type="note" xlink:label="note-0034-05a" xlink:href="note-0034-05"/>
ad F H; </s>
  <s xml:id="echoid-s1037" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1038" xml:space="preserve">per conuerſionem rationis, vt A E, ad A G, ita C F, ad C H; </s>
  <s xml:id="echoid-s1039" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1040" xml:space="preserve">permutando, <lb/>vt A E, ad C F, ita A G ad C H. </s>
  <s xml:id="echoid-s1041" xml:space="preserve">quod eſt primum.</s>
  <s xml:id="echoid-s1042" xml:space="preserve"/>
</p>
<div xml:id="echoid-div48" type="float" level="2" n="3">
<note position="left" xlink:label="note-0034-04" xlink:href="note-0034-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0034-05" xlink:href="note-0034-05a" xml:space="preserve">4. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1043" xml:space="preserve">SED iam ſit, vt A E, ad C F, ita tam B G, ad D H, quàm A G, ad C H. </s>
  <s xml:id="echoid-s1044" xml:space="preserve">Dicoarcus <lb/>A B, C D, ſimiles eſſe. </s>
  <s xml:id="echoid-s1045" xml:space="preserve">Ductis enim rurſus rectis B E, D F; </s>
  <s xml:id="echoid-s1046" xml:space="preserve">quoniam eſt, vt A E, ad C F, <lb/>ita B G, ad D H; </s>
  <s xml:id="echoid-s1047" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1048" xml:space="preserve">permutando, vt A E, hoc est, B E, ad B G, ita C F, hoc eſt, D F, ad <lb/>D H; </s>
  <s xml:id="echoid-s1049" xml:space="preserve">ſunt{q́ue} anguli ad G, H, æquales, nemperecti, habebunt triangula B E G, D F H, an-<lb/>gulos G, H, æquales, &amp; </s>
  <s xml:id="echoid-s1050" xml:space="preserve">latera B E, BG, circa angulum B, lateribus D F, D H, circa an-<lb/>
<anchor type="note" xlink:label="note-0034-06a" xlink:href="note-0034-06"/>
gulum D, proportionalia. </s>
  <s xml:id="echoid-s1051" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s1052" xml:space="preserve">@trumque reliquorum angulorum E, F, minc<unsure/>rem <lb/>
<anchor type="note" xlink:label="note-0034-07a" xlink:href="note-0034-07"/>
habeant recto, quod anguli G, H, recti ſint, erunt ipſa triangula B E G, D F H, æquian-<lb/>gula, æquales{q́ue} habebunt angulos B, D, circum quos proportionalia ſunt latera, atq; </s>
  <s xml:id="echoid-s1053" xml:space="preserve">adeo <lb/>&amp; </s>
  <s xml:id="echoid-s1054" xml:space="preserve">reliquos E, F. </s>
  <s xml:id="echoid-s1055" xml:space="preserve">Quocirca, ex ĳs, quæ ad propoſ. </s>
  <s xml:id="echoid-s1056" xml:space="preserve">33. </s>
  <s xml:id="echoid-s1057" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1058" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1059" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1060" xml:space="preserve">oſtendimus, arcus A B, <lb/>C D, ſimiles erunt. </s>
  <s xml:id="echoid-s1061" xml:space="preserve">Quare conſtat, arcus, quorum ſinus recti proportionales ſunt ſinubus <lb/>totis, ſimiles eße.</s>
  <s xml:id="echoid-s1062" xml:space="preserve"/>
</p>
<div xml:id="echoid-div49" type="float" level="2" n="4">
<note position="left" xlink:label="note-0034-06" xlink:href="note-0034-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0034-07" xlink:href="note-0034-07a" xml:space="preserve">17. primi. <lb/>7. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1063" xml:space="preserve">DEINDE quia eſt, vt A E, ad C F, ita A G, ad C H; </s>
  <s xml:id="echoid-s1064" xml:space="preserve">erit permutando, vt A E, ad <lb/>A G, ita C F, ad C H; </s>
  <s xml:id="echoid-s1065" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1066" xml:space="preserve">per conuerſionem rationis, vt A E, hoc eſt, B E, ad E G, ta C F, <lb/>hoc est, D F, ad F H. </s>
  <s xml:id="echoid-s1067" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s1068" xml:space="preserve">anguli ad G, H, æquales ſint, nimirum recti, habebunt <lb/>
<anchor type="note" xlink:label="note-0034-08a" xlink:href="note-0034-08"/>
triangula B E G, D F H, angulos G, H, æquales, &amp; </s>
  <s xml:id="echoid-s1069" xml:space="preserve">latera B E, E G, circa angulum E, la-<lb/>teribus D F, F H, circa angulum F, proportionalia. </s>
  <s xml:id="echoid-s1070" xml:space="preserve">Habent autem &amp; </s>
  <s xml:id="echoid-s1071" xml:space="preserve">vtrumque reliquo<unsure/>-<lb/>rum angulorũ B, D, rect<unsure/>o minorem, quod anguli<unsure/> G, H, ſint recti. </s>
  <s xml:id="echoid-s1072" xml:space="preserve">Igitur æquiangula erunt <lb/>
<anchor type="note" xlink:label="note-0034-09a" xlink:href="note-0034-09"/>
triangula B E G, D F H, æquales{q́ue} habebunt angulos E, F, circum quos proportionalia <lb/>ſunt latera. </s>
  <s xml:id="echoid-s1073" xml:space="preserve">Quam ob rem, per ea, quæ ad propoſ. </s>
  <s xml:id="echoid-s1074" xml:space="preserve">33. </s>
  <s xml:id="echoid-s1075" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1076" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1077" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1078" xml:space="preserve">ſcripſimus, arcus A B, C D, <lb/>ſimiles erunt. </s>
  <s xml:id="echoid-s1079" xml:space="preserve">Ex quibus liquet, arcus, quorum ſinus verſi ſunt ſinubus totis proportiona-<lb/>les, ſimiles eſſe: </s>
  <s xml:id="echoid-s1080" xml:space="preserve">Sed &amp; </s>
  <s xml:id="echoid-s1081" xml:space="preserve">idem de ſinubus rectis proxime oſtenſum eſt. </s>
  <s xml:id="echoid-s1082" xml:space="preserve">@uam ergo proportio-<lb/>nem habent ſinus toti, &amp;</s>
  <s xml:id="echoid-s1083" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1084" xml:space="preserve">Quod demonſtrandum erat.</s>
  <s xml:id="echoid-s1085" xml:space="preserve"/>
</p>
<div xml:id="echoid-div50" type="float" level="2" n="5">
<note position="left" xlink:label="note-0034-08" xlink:href="note-0034-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0034-09" xlink:href="note-0034-09a" xml:space="preserve">17. Primi. <lb/>7. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1086" xml:space="preserve">CONSTAT igitur ex his, arcus A D, Q X, in figura præcedentis demonſtrationis <lb/>
<anchor type="note" xlink:label="note-0034-10a" xlink:href="note-0034-10"/>
ſimiles eſſe, vt in demonſtratione huius propoſ. </s>
  <s xml:id="echoid-s1087" xml:space="preserve">aſſumebatur; </s>
  <s xml:id="echoid-s1088" xml:space="preserve">quandoquidem eorum ſinus <lb/>recti eandem proportionem habent, quam ſemidiametri circulorum, quorum ſunt arcus. <lb/></s>
  <s xml:id="echoid-s1089" xml:space="preserve">Item ita eſſe ſinum totum Zodiaci ad M O, ſinum totum circuli M P N Q, vt eſt ſinus <lb/>arcus Zodiaci grad. </s>
  <s xml:id="echoid-s1090" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1091" xml:space="preserve">ad O φ, ſinum arcus Q X, continentis etiam 30. </s>
  <s xml:id="echoid-s1092" xml:space="preserve">gradus; </s>
  <s xml:id="echoid-s1093" xml:space="preserve">propterc<unsure/>a <lb/>quòd eiuſm<unsure/>odi arcus ſimiles ſint. </s>
  <s xml:id="echoid-s1094" xml:space="preserve">Id quod in ſequenti corollario vſui nobis futurum eſt.</s>
  <s xml:id="echoid-s1095" xml:space="preserve"/>
</p>
<div xml:id="echoid-div51" type="float" level="2" n="6">
<note position="left" xlink:label="note-0034-10" xlink:href="note-0034-10a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div53" type="section" level="1" n="17">
<head xml:id="echoid-head20" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s1096" xml:space="preserve">Ex demonſtratione huius propoſitionis manifeſtum eſt, vt eſt M E, ſinus totus ad M O, ſinum maxi-<lb/>
<anchor type="note" xlink:label="note-0034-11a" xlink:href="note-0034-11"/>
mæ declinationis Solis, i@a eſie C E, ſinum arcus Eclipticæ A D, ab æquinoctio A, computati ad φ O, ſi-
<pb o="15" file="0035" n="35" rhead="LIBER PRIMVS."/>
num declinationis, quam habet punctum D, eundem arcum A D, terminans. </s>
  <s xml:id="echoid-s1097" xml:space="preserve">Eſt enim recta C E, æqua-<lb/>
<anchor type="note" xlink:label="note-0035-01a" xlink:href="note-0035-01"/>
lis ſinui D F, arcus Eclipticę A D; </s>
  <s xml:id="echoid-s1098" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1099" xml:space="preserve">eadem quoque ratione recta φ O, æqualis ſinui γ I, arcus H γ, quẽ <lb/>æqualem eſſe demonſtrauimus arcui D G, qui declinationem puncti D, metitur. </s>
  <s xml:id="echoid-s1100" xml:space="preserve">Hinc facili negocio <lb/>ex tabula ſinuum ſupputari poſſunt declinationes omnium punctorum Eclipticę, vt à nobis in commenta-<lb/>rijs in Sphęram factum eſt. </s>
  <s xml:id="echoid-s1101" xml:space="preserve">Vt exempli gratia inuenienda ſit declinatio grad. </s>
  <s xml:id="echoid-s1102" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1103" xml:space="preserve">♈, vel 20. </s>
  <s xml:id="echoid-s1104" xml:space="preserve">♓, vel <lb/>10. </s>
  <s xml:id="echoid-s1105" xml:space="preserve">♎, vel 20. </s>
  <s xml:id="echoid-s1106" xml:space="preserve">♍, quatuor enim horum graduum priores duo æqualiter recedunt ab æquinoctio ver-<lb/>no hinc inde, poſteriores autem duo ab autumnali, vnde eandem omnes declinationem habebunt. </s>
  <s xml:id="echoid-s1107" xml:space="preserve">Fiat <lb/>vt ſinus totus 100000. </s>
  <s xml:id="echoid-s1108" xml:space="preserve">ad ſinũ <lb/>
<anchor type="figure" xlink:label="fig-0035-01a" xlink:href="fig-0035-01"/>
maximæ declinationis 39874. <lb/></s>
  <s xml:id="echoid-s1109" xml:space="preserve">
<anchor type="note" xlink:label="note-0035-02a" xlink:href="note-0035-02"/>
ita ſinu@ arcus grad. </s>
  <s xml:id="echoid-s1110" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1111" xml:space="preserve">in Ecli-<lb/>ptica ab alterutro ęquinoctio <lb/>
<anchor type="note" xlink:label="note-0035-03a" xlink:href="note-0035-03"/>
vtrinque computati 17364. </s>
  <s xml:id="echoid-s1112" xml:space="preserve">ad <lb/>aliud; </s>
  <s xml:id="echoid-s1113" xml:space="preserve">Inuenieturq́; </s>
  <s xml:id="echoid-s1114" xml:space="preserve">per regulam <lb/>proportionũ hic ferè<unsure/> ſinus 6923. <lb/></s>
  <s xml:id="echoid-s1115" xml:space="preserve">cui in tabula ſinuum reſpondet <lb/>arcus grad. </s>
  <s xml:id="echoid-s1116" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1117" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1118" xml:space="preserve">58. </s>
  <s xml:id="echoid-s1119" xml:space="preserve">fere. </s>
  <s xml:id="echoid-s1120" xml:space="preserve">tanta <lb/>ergo eſt declinatio cuiuslibet ꝓ-<lb/>poſitorum quatuor graduũ. </s>
  <s xml:id="echoid-s1121" xml:space="preserve">Ea-<lb/>demq́; </s>
  <s xml:id="echoid-s1122" xml:space="preserve">ratio eſt de omnib@ alijs. </s>
  <s xml:id="echoid-s1123" xml:space="preserve"><lb/>Cęterum eam eſſe proportionẽ <lb/>ſinus totius ad maximę declina-<lb/>tionis ſinum, quę eſt ſinus arcus <lb/>
<anchor type="note" xlink:label="note-0035-04a" xlink:href="note-0035-04"/>
Eclipticę ab alterutro ęquino-<lb/>ctio inchoati ad ſinum declina-<lb/>tionis puncti illius in Ecliptica, quod dictum arcum terminat, faciliori, &amp; </s>
  <s xml:id="echoid-s1124" xml:space="preserve">breuiori demonſtratione con-<lb/>firmatum eſt à Ioanne Regiom. </s>
  <s xml:id="echoid-s1125" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1126" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1127" xml:space="preserve">Epito. </s>
  <s xml:id="echoid-s1128" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s1129" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1130" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1131" xml:space="preserve">à Petro Nonio in lib. </s>
  <s xml:id="echoid-s1132" xml:space="preserve">de Crépuſculis, &amp; </s>
  <s xml:id="echoid-s1133" xml:space="preserve"><lb/>nos alibi etiam oſtendimus.</s>
  <s xml:id="echoid-s1134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div53" type="float" level="2" n="1">
<note position="left" xlink:label="note-0034-11" xlink:href="note-0034-11a" xml:space="preserve">Eadem eſt pro-<lb/>poruo ſinus to-<lb/>tius ad ſinũ ma</note>
<note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">ximæ declina-<lb/>tionis, quæ ſi-<lb/>nus arcus Ecli-<lb/>pticæ ab ęquino <lb/>ctio computati <lb/>ad ſinum decli <lb/>nationis punct@ <lb/>Eclip@@cæ dictũ <lb/>arcum terminã <lb/>tis.</note>
  <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a">
    <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-01"/>
  </figure>
<note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">Supputatio de-<lb/>clinationũ em-<lb/>nium punctorũ <lb/>Eclipticæ per <lb/>ſinus.</note>
<note position="left" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s1135" xml:space="preserve">PERSPICVVM quoque eſt, in Analemmate deſcripto diametros per centrum E, tranſeuntes, e@-<lb/>
<anchor type="note" xlink:label="note-0035-05a" xlink:href="note-0035-05"/>
ſe communes ſectiones Meridiani, &amp; </s>
  <s xml:id="echoid-s1136" xml:space="preserve">circulorum maximorum, cum omnes circuli maximi per centrum <lb/>Sphęrę, in quo poſuimus centrum E, ducantur, atque adeò ibidem ſe mutuo interſecent. </s>
  <s xml:id="echoid-s1137" xml:space="preserve">rectas uerò non <lb/>per centrum E, tranſeuntes non eſſe re ipſa ſectiones communes Meridiani, &amp; </s>
  <s xml:id="echoid-s1138" xml:space="preserve">circulorum non maximo-<lb/>rum, cum in Meridiano longè maiores diſtantias inter ſe habeant, quàm in circulo A B C D; </s>
  <s xml:id="echoid-s1139" xml:space="preserve">ſed auferre <lb/>ex circulo A B C D, arcus ſimiles illis, quos ex Meridiano reuera circuli non maximi, atque adeò eorum, <lb/>&amp; </s>
  <s xml:id="echoid-s1140" xml:space="preserve">Meridiani communes ſectiones, abſcindunt, ut demonſtrauimus. </s>
  <s xml:id="echoid-s1141" xml:space="preserve">Quod ſi Meridianus Spherę ęqualis <lb/>
<anchor type="note" xlink:label="note-0035-06a" xlink:href="note-0035-06"/>
eſſet circulo A B C D, tunc eſſent etiam illę rectę non per centrum ductę, communes ſectiones circulo-<lb/>rum non maximorum, &amp; </s>
  <s xml:id="echoid-s1142" xml:space="preserve">Meridiani; </s>
  <s xml:id="echoid-s1143" xml:space="preserve">quia arcus circuli A B C D, omnino ęquales eſſent arcubus Me-<lb/>ridiani circuli.</s>
  <s xml:id="echoid-s1144" xml:space="preserve"/>
</p>
<div xml:id="echoid-div54" type="float" level="2" n="2">
<note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">Quid ſint rectę <lb/>in Analemma-<lb/>te ductæ.</note>
<note position="left" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div56" type="section" level="1" n="18">
<head xml:id="echoid-head21" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s1145" xml:space="preserve">QVOD ſi pro uero, atque conceſſo ſumere uelimus, tanquàm alibi demonſtratum, ut eſt ſinus totus <lb/>ad ſinum maximæ declinationis, ita eſſe ſinum cuiuſuis arcus Zodiaci ab ♈, vel ♎, inchoati ad ſinũ <lb/>declinationis illius arcus: </s>
  <s xml:id="echoid-s1146" xml:space="preserve">Id quod <lb/>
<anchor type="figure" xlink:label="fig-0035-02a" xlink:href="fig-0035-02"/>
&amp; </s>
  <s xml:id="echoid-s1147" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s1148" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s1149" xml:space="preserve">in Epitom. </s>
  <s xml:id="echoid-s1150" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s1151" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1152" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1153" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1154" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1155" xml:space="preserve">Petrus Nonius in <lb/>
<anchor type="note" xlink:label="note-0035-07a" xlink:href="note-0035-07"/>
lib. </s>
  <s xml:id="echoid-s1156" xml:space="preserve">de crepuſculis demonſtrauit, &amp; </s>
  <s xml:id="echoid-s1157" xml:space="preserve"><lb/>à nobis etiam alibi demonſtratum <lb/>eſt; </s>
  <s xml:id="echoid-s1158" xml:space="preserve">oſtendemus breuius mult@, &amp; </s>
  <s xml:id="echoid-s1159" xml:space="preserve"><lb/>apertius, parallelas X R, Y S, Z T, <lb/>α V, in Analemmate auferre ex Me <lb/>ridiano arcus declinationum, hoc <lb/>modo. </s>
  <s xml:id="echoid-s1160" xml:space="preserve">Quoniam in Analemmate <lb/>
<anchor type="note" xlink:label="note-0035-08a" xlink:href="note-0035-08"/>
ſuperiori, vt ſinus totus in Zodia-<lb/>co ad M O, ſinum totum in circulo <lb/>M P N Q, hoc eſt, ad ſinum maxi-<lb/>
<anchor type="note" xlink:label="note-0035-09a" xlink:href="note-0035-09"/>
mæ declinationis, ita eſt, vt ex Lem <lb/>mate præcedenti perſpicuum eſt, ſi-<lb/>nus arcus Zodiaci grad. </s>
  <s xml:id="echoid-s1161" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1162" xml:space="preserve">ab ini-<lb/>tio ♈, vel ♎, computati ad <lb/>O φ, ſinum arcus Q X, circuli M P <lb/>N Q, qui continet quoque grad. <lb/></s>
  <s xml:id="echoid-s1163" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1164" xml:space="preserve">Eſt autem, vt ſinus totus Zo-<lb/>diaci ad ſinum maximæ declinatio-<lb/>nis, it a ſinus quoque@ arcus Eclipti-<lb/>cę grad. </s>
  <s xml:id="echoid-s1165" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1166" xml:space="preserve">à principio ♈, vel <lb/>♎, inchoati ad ſinũ declinationis
<pb o="16" file="0036" n="36" rhead="GNOMONICES"/>
eiuſdẽ arcus 30. </s>
  <s xml:id="echoid-s1167" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s1168" xml:space="preserve">ex demonſtratis à Ioanne Regiom. </s>
  <s xml:id="echoid-s1169" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1170" xml:space="preserve">Petro Nonio, vt dictum eſt, &amp; </s>
  <s xml:id="echoid-s1171" xml:space="preserve">nos pro ver@ <lb/>at que conceſſo ſumpſimus. </s>
  <s xml:id="echoid-s1172" xml:space="preserve">Igitur ſinus O φ, ęqualis eſt ſinui declinationis illius arcus Eclipticæ, qui 30. <lb/></s>
  <s xml:id="echoid-s1173" xml:space="preserve">gradus complectitur, eſt arcui QX, ſimilis. </s>
  <s xml:id="echoid-s1174" xml:space="preserve">Quare arcus H γ, æqualis eſt arcui declinationis illius ar-<lb/>cus Eclipticæ 30. </s>
  <s xml:id="echoid-s1175" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s1176" xml:space="preserve">qui ar cui QX, 30. </s>
  <s xml:id="echoid-s1177" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s1178" xml:space="preserve">eſt ſimilis. </s>
  <s xml:id="echoid-s1179" xml:space="preserve">Eademq́, de cæteris arcubus zodiaci est ratio, <lb/>quod erat demonſtr andum.</s>
  <s xml:id="echoid-s1180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div56" type="float" level="2" n="1">
  <figure xlink:label="fig-0035-02" xlink:href="fig-0035-02a">
    <image file="0035-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-02"/>
  </figure>
<note position="left" xlink:label="note-0035-07" xlink:href="note-0035-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0035-08" xlink:href="note-0035-08a" xml:space="preserve">Alia dem@ſtra <lb/>tio deſcriptio-<lb/>nis parallelorũ <lb/>Aequatoris per <lb/>puncta Eclipti-<lb/>cæ incedentiũ.</note>
<note position="left" xlink:label="note-0035-09" xlink:href="note-0035-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s1181" xml:space="preserve">INVENIRI quoque poſſunt declinationes omnium ſignorũ Eclipticæ hoc modo. </s>
  <s xml:id="echoid-s1182" xml:space="preserve">Circulus Ana-<lb/>
<anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/>
lemmatis A B C D, diuidatur in 12. </s>
  <s xml:id="echoid-s1183" xml:space="preserve">partes æquales, initio facto à puncto M, maximæ declinationis; </s>
  <s xml:id="echoid-s1184" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1185" xml:space="preserve"><lb/>quælibet duo puncta diuiſionum æqualiter à puncto M, remota, rectis lineis iungantur; </s>
  <s xml:id="echoid-s1186" xml:space="preserve">quales ſunt in <lb/>Analemmate lineæ punctis diſtinctæ, &amp; </s>
  <s xml:id="echoid-s1187" xml:space="preserve">in punctis l, p, E, q, u, rectam M ρ, ſecantes; </s>
  <s xml:id="echoid-s1188" xml:space="preserve">quæ omnes paral-<lb/>lelæ inter ſe erunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s1189" xml:space="preserve">27. </s>
  <s xml:id="echoid-s1190" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1191" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1192" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s1193" xml:space="preserve">Hæ lineæ vbi rectam M ρ, ſecabunt, per ea <lb/>
<anchor type="note" xlink:label="note-0036-02a" xlink:href="note-0036-02"/>
<anchor type="figure" xlink:label="fig-0036-01a" xlink:href="fig-0036-01"/>
puncta, qualia ſunt l, p, E, q, u, du-<lb/>cendæ erunt rectæ lineæ β λ, γ μ, <lb/>&amp; </s>
  <s xml:id="echoid-s1194" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1195" xml:space="preserve">æquinoctiali lineæ H I, paral-<lb/>lelæ pro diametris parallelorũ per <lb/>ſignorum initia deſcriptorum; </s>
  <s xml:id="echoid-s1196" xml:space="preserve">ita <lb/>vt rurſus arcus H β, H γ, &amp;</s>
  <s xml:id="echoid-s1197" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1198" xml:space="preserve">ſint <lb/>declinationes ſignorum Zodiaci. <lb/></s>
  <s xml:id="echoid-s1199" xml:space="preserve">Quod vt demonſtremus, intelligen-<lb/>dus est circulus A B C D, eſſe <lb/>Ecliptica, cuius ſignorũ initia ſunt <lb/>
<anchor type="note" xlink:label="note-0036-03a" xlink:href="note-0036-03"/>
in illis punctis diuiſionum 12. </s>
  <s xml:id="echoid-s1200" xml:space="preserve">ita <lb/>vt M, ρ, ſint principia ♋ &amp; </s>
  <s xml:id="echoid-s1201" xml:space="preserve"><lb/>♑. </s>
  <s xml:id="echoid-s1202" xml:space="preserve">Deindemanente hac Eclipti-<lb/>caimmobili, &amp; </s>
  <s xml:id="echoid-s1203" xml:space="preserve">in coſitu, quem in <lb/>Sphæra habet, poſito principio <lb/>♋ M, in Meridiano circulo ſu-<lb/>pra Horizontẽ, &amp; </s>
  <s xml:id="echoid-s1204" xml:space="preserve">principio ♑, <lb/>ρ, in eodem ſub Horizonte, intelli-<lb/>gendus eſt idem circulus inſtar Co-<lb/>luri ſolſtitiorum circa diametrum <lb/>
<anchor type="note" xlink:label="note-0036-04a" xlink:href="note-0036-04"/>
M ρ, conuerti, donec rectus ſit ad <lb/>Eclipticæ planum, &amp; </s>
  <s xml:id="echoid-s1205" xml:space="preserve">punctum F, <lb/>directo ad polum arcticum, &amp; </s>
  <s xml:id="echoid-s1206" xml:space="preserve">G, <lb/>ad antarcticum ſpectet, ita ut Ae-<lb/>quator ad hunc Colurum rectus per rectam H I, ductus, faciat in plano Eclipticæ communem ſectionem, <lb/>
<anchor type="note" xlink:label="note-0036-05a" xlink:href="note-0036-05"/>
rectam illam punctis not at am, quæ ipſam M ρ, ad angulos rectos ſecat in E, centro. </s>
  <s xml:id="echoid-s1207" xml:space="preserve">Cum enim tam pla-<lb/>num Eclipticæ, quàm Aequatoris ad Colurum ſit rectum, erit quoque communis illorum ſectio ad eundem <lb/>
<anchor type="note" xlink:label="note-0036-06a" xlink:href="note-0036-06"/>
recta, at que adeo &amp; </s>
  <s xml:id="echoid-s1208" xml:space="preserve">ad rectam M ρ, in eodem Coluro exiſtentem. </s>
  <s xml:id="echoid-s1209" xml:space="preserve">Si igitur per punctum p, verbi gratia, <lb/>concipiamus tranſire planum Aequatori par allelum, faciet id in plano Eclipticæ rectam punctis diſtin-<lb/>ctam, &amp; </s>
  <s xml:id="echoid-s1210" xml:space="preserve">per p, tranſeuntem, at que alteri rectæ per E, ductæ, punctis{q́ue} diſtinctæ par allelam; </s>
  <s xml:id="echoid-s1211" xml:space="preserve">propterea <lb/>
<anchor type="note" xlink:label="note-0036-07a" xlink:href="note-0036-07"/>
<anchor type="note" xlink:label="note-0036-08a" xlink:href="note-0036-08"/>
quòd hæ lineæ per E, &amp; </s>
  <s xml:id="echoid-s1212" xml:space="preserve">p, ductæ ſint ſectiones planorum parallelorum, nempe Aequatoris, &amp; </s>
  <s xml:id="echoid-s1213" xml:space="preserve">plani ipſi <lb/>paralleli, factæ à plano Eclipticæ. </s>
  <s xml:id="echoid-s1214" xml:space="preserve">In Sphera autem circulum efficiet ex propoſ. </s>
  <s xml:id="echoid-s1215" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1216" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1217" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1218" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s1219" xml:space="preserve">Aequa-<lb/>tori parallelum, cuius diameter per p, incedens parallela erit diametro Aequatoris H I; </s>
  <s xml:id="echoid-s1220" xml:space="preserve">propterea quòd <lb/>
<anchor type="note" xlink:label="note-0036-09a" xlink:href="note-0036-09"/>
H I, &amp; </s>
  <s xml:id="echoid-s1221" xml:space="preserve">diameter huius circuli ſint ſectiones planorum parallelorum, nimirum Aequatoris, &amp; </s>
  <s xml:id="echoid-s1222" xml:space="preserve">plani <lb/>ipſi æquidiſtantis, factæ à plano Coluri ſolſtitiorum. </s>
  <s xml:id="echoid-s1223" xml:space="preserve">Igitur recta γ ω, per p, ducta ipſi H I, parallela dia-<lb/>meter eſt illius paralleli, qui in Ecliptica per puncta terminantia rectam illam punctis not at am, &amp; </s>
  <s xml:id="echoid-s1224" xml:space="preserve">per <lb/>p, ductam, tranſit, nempe per arcus 30. </s>
  <s xml:id="echoid-s1225" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s1226" xml:space="preserve">ab æquinoctialibus punctis computatos; </s>
  <s xml:id="echoid-s1227" xml:space="preserve">quæ quidem pun-<lb/>cta æquinoctialia terminantur àrecta illa punctis notata, &amp; </s>
  <s xml:id="echoid-s1228" xml:space="preserve">per centrum E, ducta. </s>
  <s xml:id="echoid-s1229" xml:space="preserve">Quare cum arcus <lb/>Coluri ſolſtitiorum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s1230" xml:space="preserve">parallelum circulum quemcunque interceptus metiatur decli-<lb/>nationem illius paralleli ab Aequatore, erit arcus H γ, declinatio paralleli, cuius diameter γ μ, qui{q́ue} <lb/>
<anchor type="note" xlink:label="note-0036-10a" xlink:href="note-0036-10"/>
per ea puncta in Ecliptica incedit, quæ à recta punctis diſtincta, at que per punctum p, ducta terminan-<lb/>tur. </s>
  <s xml:id="echoid-s1231" xml:space="preserve">Eadem{q́ue} eſt ratio de cæteris. </s>
  <s xml:id="echoid-s1232" xml:space="preserve">Quòd ſi circulus A B C D, non ſolum in 12. </s>
  <s xml:id="echoid-s1233" xml:space="preserve">partes, ſed in ſingulos <lb/>etiam diſtribuatur gradus, eadem{q́ue} fiant, quæ prius, deſcribemus eodem artificio diametros parallelorum <lb/>per ſingulos gradus Eclipticæ incedentium.</s>
  <s xml:id="echoid-s1234" xml:space="preserve"/>
</p>
<div xml:id="echoid-div57" type="float" level="2" n="2">
<note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">Alia deſcriptio <lb/>pa@allelorã Ae-<lb/>quatoris per ſi-<lb/>gnorum prin-<lb/>cipia ductorum.</note>
<note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0036-01" xlink:href="fig-0036-01a">
    <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0036-01"/>
  </figure>
<note position="left" xlink:label="note-0036-03" xlink:href="note-0036-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0036-04" xlink:href="note-0036-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0036-05" xlink:href="note-0036-05a" xml:space="preserve">3. vndec.</note>
<note position="left" xlink:label="note-0036-06" xlink:href="note-0036-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0036-07" xlink:href="note-0036-07a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0036-08" xlink:href="note-0036-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0036-09" xlink:href="note-0036-09a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0036-10" xlink:href="note-0036-10a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s1235" xml:space="preserve">DENIQVE, ſi declinationes ſignorum, vel quorumlibet punctorum Eclipticæ, inuentæ per doctri-<lb/>
<anchor type="note" xlink:label="note-0036-11a" xlink:href="note-0036-11"/>
nam ſinuum, vt in coroll. </s>
  <s xml:id="echoid-s1236" xml:space="preserve">huius propoſ. </s>
  <s xml:id="echoid-s1237" xml:space="preserve">docuimus, ſupputentur ab Aequatoris diametro H I, ad vtram-<lb/>que partem in circulo Analemmatis, &amp; </s>
  <s xml:id="echoid-s1238" xml:space="preserve">per fines ſupputationum ipſi H I, parallelæ agantur, erunt hæ <lb/>rurſus diametri parallelorum per initia ſignorum, vel per data puncta Eclipticæ, tranſeuntium, vt prius; <lb/></s>
  <s xml:id="echoid-s1239" xml:space="preserve">quamuis vt in initio diximus, incerta eſt per hanc viam Analemmatis deſcriptio, propter declinationes, <lb/>quæ uix ſine errore in circulo A B C D, ſupputari poſſunt, cum in eo minuta, &amp; </s>
  <s xml:id="echoid-s1240" xml:space="preserve">ſecunda graduum de-<lb/>ſignari nequeant.</s>
  <s xml:id="echoid-s1241" xml:space="preserve"/>
</p>
<div xml:id="echoid-div58" type="float" level="2" n="3">
<note position="left" xlink:label="note-0036-11" xlink:href="note-0036-11a" xml:space="preserve">Alia adhue de-<lb/>ſcriptio paralle-<lb/>lorũ per puncta <lb/>Eclipticæ tran-<lb/>ſeuntium.</note>
</div>
<pb o="17" file="0037" n="37" rhead="LIBER PRIMVS."/>
<p style="it">
  <s xml:id="echoid-s1242" xml:space="preserve">CAETERVM quainduſtria poli eleuatio in quacunque regione inueſtigari debeat, quod quidem <lb/>
<anchor type="note" xlink:label="note-0037-01a" xlink:href="note-0037-01"/>
ad rectam Analemmatis conſtructionem requiritur, (neque enim axis F G, duci poterit, ſi quantus eſſe <lb/>debeat altitudinis poli arcus D F, ignoretur.) </s>
  <s xml:id="echoid-s1243" xml:space="preserve">oſtendimus &amp; </s>
  <s xml:id="echoid-s1244" xml:space="preserve">in vſu Aſtrolabĳ, &amp; </s>
  <s xml:id="echoid-s1245" xml:space="preserve">in Coſmographia, nec <lb/>non in commentarĳs in Sphæram, cum de Meridiani circuli officĳs verba faceremus. </s>
  <s xml:id="echoid-s1246" xml:space="preserve">Eandem tamen al-<lb/>titudinem poli alio modo per Analemma inueniemus in ſcholio 2. </s>
  <s xml:id="echoid-s1247" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s1248" xml:space="preserve">28. </s>
  <s xml:id="echoid-s1249" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s1250" xml:space="preserve"/>
</p>
<div xml:id="echoid-div59" type="float" level="2" n="4">
<note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">Cognitio altit <lb/>dinis poli ad <lb/>Analemmatisu <lb/>deſcriptionẽ no<unsure/> <lb/>ceſſalia eſt.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1251" xml:space="preserve">HAEC igitur ſigura, quam hactenus conſtruximus, continens dictorum circulorum ſectiones commu-<lb/>nes cum Meridiano circulo, apud veteres, &amp; </s>
  <s xml:id="echoid-s1252" xml:space="preserve">recẽtiores potiſſimum Analemma nuncupatur, quamuis ip-<lb/>ſum non vno modo deſinierint omnes, cum alius alium in eo definiendo ſcopum habuerit. </s>
  <s xml:id="echoid-s1253" xml:space="preserve">Placuit ta-<lb/>men nobis illud explicare per communes ſectiones, quas circuli præcipui ſphæræ in plano Meridia-<lb/>ni faciunt.</s>
  <s xml:id="echoid-s1254" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve">Alij etiam cir-<lb/>culi, præter di-<lb/>ctos in Analem <lb/>mate deſcribi <lb/>poſſunt.</note>
<p style="it">
  <s xml:id="echoid-s1255" xml:space="preserve">POSSVNT autem &amp; </s>
  <s xml:id="echoid-s1256" xml:space="preserve">aliorum circulorũ ſectiones cum eodem Meridiano (quales ſunt paralleli <lb/>Horizontis, paralleli Eclipticæ, &amp;</s>
  <s xml:id="echoid-s1257" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s1258" xml:space="preserve">deſcribi in eodem Meridiano, ut in deſcriptione Aftrolabĳ fit, &amp; </s>
  <s xml:id="echoid-s1259" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0037-04a" xlink:href="note-0037-04"/>
in ſequentibus etiam nonnunquam fiet. </s>
  <s xml:id="echoid-s1260" xml:space="preserve">Immo verò &amp; </s>
  <s xml:id="echoid-s1261" xml:space="preserve">figura circularis, cuius circulus referat alium <lb/>quempiam circulum maximum, præter Meridianum, continens ſectiones communes aliorum circulorum <lb/>cum illo circulo maximo, Analemma dici conſueuit, vt ſuo loco docebimus. </s>
  <s xml:id="echoid-s1262" xml:space="preserve">Cæterum Analemma hacte <lb/>
<anchor type="note" xlink:label="note-0037-05a" xlink:href="note-0037-05"/>
nus conſtructum, quod attinet ad parallelos per circulum M P N Q, inuentos, omnibus mundi climati-<lb/>bus inſeruit. </s>
  <s xml:id="echoid-s1263" xml:space="preserve">Hi enim paralleli nunquam mutantur, in quocunque Horizonte Analemma conſtituatur, <lb/>niſi prius maxima declinatio Solis mutata ſit, cum eorum deſcriptio ex hac ſola maxima declinatione <lb/>pendeat, vt conſtat. </s>
  <s xml:id="echoid-s1264" xml:space="preserve">Cæteræautem ſectiones, vel rectæ lineæ, variantur pro varia altitudine poli ſupra <lb/>Horizontem. </s>
  <s xml:id="echoid-s1265" xml:space="preserve">Nec enim vbique eadem poli altitudo ſupra Horizontem reperitur. </s>
  <s xml:id="echoid-s1266" xml:space="preserve">Vnde ſi prius in Ana-<lb/>
<anchor type="note" xlink:label="note-0037-06a" xlink:href="note-0037-06"/>
lemmate deſcribantur paralleli per ſigna Zodiaci ducti, tanquam immutabiles in quocunque climate, <lb/>
<anchor type="note" xlink:label="note-0037-07a" xlink:href="note-0037-07"/>
(ducendo nimirum primum pro diametro Aequatoris rectam H I, deinde maximas Solis declinationes <lb/>ſupputando H M, H N, &amp;</s>
  <s xml:id="echoid-s1267" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s1268" xml:space="preserve">abſoluemus reliquas eius partes pro data altitudine poli, hac ratione. <lb/></s>
  <s xml:id="echoid-s1269" xml:space="preserve">Per centrum E, ducatur ad diametrum Acquatoris H I, perpendicularis F G, pro axe mundi. </s>
  <s xml:id="echoid-s1270" xml:space="preserve">Deinde <lb/>à punctis F, G, in diuerſas partes numerata altitudine poli, vſque ad D, B, ducatur diameter B D, pro <lb/>Horizonte, &amp; </s>
  <s xml:id="echoid-s1271" xml:space="preserve">pro Verticali ducatur alia diameter A C, ſecans B D, ad angulos rectos. </s>
  <s xml:id="echoid-s1272" xml:space="preserve">Ex punctis <lb/>denique D, B, educantur Aequatoris diametro H I, parallelæ D K, B L, pro diametris parallelorum, <lb/>qui inter perpetuo apparentes, &amp; </s>
  <s xml:id="echoid-s1273" xml:space="preserve">deliteſcentes maximi ſunt.</s>
  <s xml:id="echoid-s1274" xml:space="preserve"/>
</p>
<div xml:id="echoid-div60" type="float" level="2" n="5">
<note position="right" xlink:label="note-0037-04" xlink:href="note-0037-04a" xml:space="preserve">Alia acceptio <lb/>Analemmatis.</note>
<note position="right" xlink:label="note-0037-05" xlink:href="note-0037-05a" xml:space="preserve">Quæ lineamen <lb/>ta Analemma-<lb/>tis eadem per-<lb/>maneantin om <lb/>ni climate, &amp; <lb/>quæ non.</note>
<note position="left" xlink:label="note-0037-06" xlink:href="note-0037-06a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0037-07" xlink:href="note-0037-07a" xml:space="preserve">Initium deſcri-<lb/>ptienis Analẽ-<lb/>matis à paralle <lb/>lis per ſigna Zo <lb/>diaci tranſeun-<lb/>tibus quomodo <lb/>fiat.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1275" xml:space="preserve">INCREDIBILE porrò eſt, quàm multiplicem, ac varium vſum in rebus Aſtronomicis habeat <lb/>
<anchor type="note" xlink:label="note-0037-08a" xlink:href="note-0037-08"/>
Analemma. </s>
  <s xml:id="echoid-s1276" xml:space="preserve">Ex eo enim non ſolum conſtructio Aſtrolabĳ, quod planiſphærium Ptolemæus appellat, Geo-<lb/>
<anchor type="note" xlink:label="note-0037-09a" xlink:href="note-0037-09"/>
metricis demonſtrationibus perficitur, verum etiã omnia ferè, quæ ad phænomcna primi mobilis demon-<lb/>stranda pertinent, ſine magno labore eruuntur: </s>
  <s xml:id="echoid-s1277" xml:space="preserve">quod non eſt huius loci explicare. </s>
  <s xml:id="echoid-s1278" xml:space="preserve">In hoc etiã opere noſtro <lb/>Gnomonico non obſcurè eius excellentia, inſignis{q́ue} vtilitas eluceſcet, cum propemodũ omnes demonſtra-<lb/>tiones, quæ in horologiorum deſcriptionibus vſurpantur, ex Analemmate eliciantur, vt ex ſequentibus <lb/>fiet perſpicuum, maximè cum de Analemmate Ptolemæi, ex quo miraiucundit ate horologia deſcribun-<lb/>tur, agemus. </s>
  <s xml:id="echoid-s1279" xml:space="preserve">Nunc contentus ero, ſi quàm facile ex Analemmate dierum magnitudines &amp; </s>
  <s xml:id="echoid-s1280" xml:space="preserve">noctium; <lb/></s>
  <s xml:id="echoid-s1281" xml:space="preserve">tempus ortus, &amp; </s>
  <s xml:id="echoid-s1282" xml:space="preserve">occaſus Solis, quoad horas Italicas, &amp; </s>
  <s xml:id="echoid-s1283" xml:space="preserve">Babylonicas, &amp; </s>
  <s xml:id="echoid-s1284" xml:space="preserve">tempus Meridiei; </s>
  <s xml:id="echoid-s1285" xml:space="preserve">tempus itẽ <lb/>ortus &amp; </s>
  <s xml:id="echoid-s1286" xml:space="preserve">occaſus ratione horarum aſtronomicarum, nec non latitudines ortiuæ, &amp; </s>
  <s xml:id="echoid-s1287" xml:space="preserve">occiduæ omnium pun-<lb/>ctorum Eclipticæ quolibet anni tempore, &amp; </s>
  <s xml:id="echoid-s1288" xml:space="preserve">ad quamcunque latitudinem loci cognoſcantur, breui-<lb/>
<anchor type="note" xlink:label="note-0037-10a" xlink:href="note-0037-10"/>
ter declarem.</s>
  <s xml:id="echoid-s1289" xml:space="preserve"/>
</p>
<div xml:id="echoid-div61" type="float" level="2" n="6">
<note position="right" xlink:label="note-0037-08" xlink:href="note-0037-08a" xml:space="preserve">Vtilitates Ana-<lb/>lẽmatis uariæ.</note>
<note position="left" xlink:label="note-0037-09" xlink:href="note-0037-09a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0037-10" xlink:href="note-0037-10a" xml:space="preserve">Inuentio arcus <lb/>diurni, noctur-<lb/>n@q́; ex Analẽ <lb/>mate, &amp; horæ <lb/>ortus occaſusq; <lb/>Solis.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s1290" xml:space="preserve">SIT ergo propoſitum hæc omnia perdiſcere, cum ſol parallelum ♋ vel ♑ percurrit motu pri-<lb/>mi mobilis. </s>
  <s xml:id="echoid-s1291" xml:space="preserve">Circa diametrum paralleli ♋, M θ, vel ♑, N ρ, ex centro b, (cum enim axis F G, <lb/>ſecet omnes parallelos ad angulos rectos, quòd &amp; </s>
  <s xml:id="echoid-s1292" xml:space="preserve">Aequatoris diametrum, cui æquidiſtant, ad angulos <lb/>
<anchor type="note" xlink:label="note-0037-12a" xlink:href="note-0037-12"/>
rectos ſecet, ac proinde &amp; </s>
  <s xml:id="echoid-s1293" xml:space="preserve">bifariam, erit b, centrum circuli circa M θ, deſcribendi) ſeorſum circulus de-<lb/>
<anchor type="note" xlink:label="note-0037-13a" xlink:href="note-0037-13"/>
ſcribatur M d θ e, ſumpta{q́ue} recta M a, ipſi M a, in Analemmate æquali, ducatur per a, ad M θ, perpen-<lb/>dicularis d e, quæ communis ſectio erit Horizontis, &amp; </s>
  <s xml:id="echoid-s1294" xml:space="preserve">propoſiti par alleli. </s>
  <s xml:id="echoid-s1295" xml:space="preserve">Quoniam enim tam Horizon, <lb/>quàm parallelus ♋ ad Meridianum rectus eſt, erit ad eundem communis eorum ſectio quoque recta, <lb/>
<anchor type="note" xlink:label="note-0037-14a" xlink:href="note-0037-14"/>
ac proinde ex defin. </s>
  <s xml:id="echoid-s1296" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1297" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1298" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1299" xml:space="preserve">Euclidis, ad rectam M θ, in Analemmatis Meridiano exiſtentem perpen-<lb/>dicularis in puncto a, vbi ſe mutuo ſecant in Meridiano Horizon, &amp; </s>
  <s xml:id="echoid-s1300" xml:space="preserve">parallelus. </s>
  <s xml:id="echoid-s1301" xml:space="preserve">Quare recta d e, quæ in <lb/>circulo M d θ e, per a, ad M θ, ducta eſt perpendicularis, communis ſectio erit Horizontis, &amp; </s>
  <s xml:id="echoid-s1302" xml:space="preserve">paralleli <lb/>
<anchor type="note" xlink:label="note-0037-15a" xlink:href="note-0037-15"/>
♋; </s>
  <s xml:id="echoid-s1303" xml:space="preserve">adeò vt, ſi intelligatur circulus M d θ e, circa diametrum M θ, in Analemmate circumuerti, do-<lb/>nec rectus ſit ad planum Meridiani, atque idcirco &amp; </s>
  <s xml:id="echoid-s1304" xml:space="preserve">recta d e, huius circuli ſeorſum deſcripti ad <lb/>idem perpendicularis, Horizon ad idem planum Meridiani exiſtens rectus tranſeat per puncta d, e, ac <lb/>proinde per rectam d e. </s>
  <s xml:id="echoid-s1305" xml:space="preserve">Hanc autem rationem repetemus in propoſ. </s>
  <s xml:id="echoid-s1306" xml:space="preserve">33. </s>
  <s xml:id="echoid-s1307" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s1308" xml:space="preserve">vbi fortaſſis planior <lb/>fiet, cum ibi parallelus Solis in ipſo Analemmate circa propriam diametrum deſcriptus ſit. </s>
  <s xml:id="echoid-s1309" xml:space="preserve">Itaque arcus <lb/>d M e, erit arcus diurnus ♋, nempe qui ſupra terram extat, &amp; </s>
  <s xml:id="echoid-s1310" xml:space="preserve">d θ c, nocturnus. </s>
  <s xml:id="echoid-s1311" xml:space="preserve">Vel ille erit arcus <lb/>nocturnus ♑, &amp; </s>
  <s xml:id="echoid-s1312" xml:space="preserve">hic diurnus. </s>
  <s xml:id="echoid-s1313" xml:space="preserve">Vnde ſi totus circulus M d θ e, ſecetur in horas 24. </s>
  <s xml:id="echoid-s1314" xml:space="preserve">æquales, initio facto <lb/>a puncto d, vele, (Nos ab e, incepimus, quod nunc refert punctum ortus in Horizonte pro horis Babylo-<lb/>nicis, nunc vero punctum occaſus pro horis Italicis) confeſtim apparebit, quot horas comprehendat tam <lb/>arcus d M e, quàm d θ e. </s>
  <s xml:id="echoid-s1315" xml:space="preserve">Ita vides arcum diurnum ♋ d M e, complecti horas quindecim, &amp; </s>
  <s xml:id="echoid-s1316" xml:space="preserve">paulo <lb/>amplius, arcum verò nocturnum d θ e, non omnino horas 9. </s>
  <s xml:id="echoid-s1317" xml:space="preserve">ſed paulo minus. </s>
  <s xml:id="echoid-s1318" xml:space="preserve">Sic etiam intelligis, Solem
<pb o="18" file="0038" n="38" rhead="GNOMONICES"/>
in priori arcu occidere, more hor arum ab ortu, paulo post horam decimamquintam, oriri verò paulo ante <lb/>horam nonam more hor arum ab occaſu, &amp;</s>
  <s xml:id="echoid-s1319" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1320" xml:space="preserve">Horæ externæ in arcu diurno ♋ d M e, &amp; </s>
  <s xml:id="echoid-s1321" xml:space="preserve">nocturno d θ e, <lb/>pertinent ad horas Italicas, &amp; </s>
  <s xml:id="echoid-s1322" xml:space="preserve">internæ ad Babylonicas. </s>
  <s xml:id="echoid-s1323" xml:space="preserve">Contra verò in arcu diurno ♑ d θ e, &amp; </s>
  <s xml:id="echoid-s1324" xml:space="preserve">no-<lb/>cturno d M e, externæ horæ ad horas Babylonicas, &amp; </s>
  <s xml:id="echoid-s1325" xml:space="preserve">internæ ad Italicas ſpectant. </s>
  <s xml:id="echoid-s1326" xml:space="preserve">Semper tamen pun-<lb/>ctume, ſumitur pro ortu Solis, ſi de horis ab ortu loquamur, &amp; </s>
  <s xml:id="echoid-s1327" xml:space="preserve">punctum d, pro occaſu. </s>
  <s xml:id="echoid-s1328" xml:space="preserve">E contrario au-<lb/>tem, ſi de horis ab occaſu ſermo habeatur, punctum e, ſumendum eſt pro occaſu Solis, &amp; </s>
  <s xml:id="echoid-s1329" xml:space="preserve">d, pro ortu, vt <lb/>numeri horarum demonſtrant.</s>
  <s xml:id="echoid-s1330" xml:space="preserve"/>
</p>
<div xml:id="echoid-div62" type="float" level="2" n="7">
<note position="right" xlink:label="note-0037-12" xlink:href="note-0037-12a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0037-13" xlink:href="note-0037-13a" xml:space="preserve">3. tertĳ.</note>
<note position="right" xlink:label="note-0037-14" xlink:href="note-0037-14a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0037-15" xlink:href="note-0037-15a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0038-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s1331" xml:space="preserve">IDEM videre licet in horis astronomicis, ſi circuli diuiſio incipiat à puncto M, Meridiei, ut manife-<lb/>ſtum est in alio circulo minori A B C D, circa centrum E, deſcripto, qui per rectam B D, diuiſus eſt ad <lb/>ſimilitudinem circuli M d θ e, ita vt ſit inſtar paralleli ♋, vel ♑, deſcripti ex minore aliquo Ana-<lb/>lemmate. </s>
  <s xml:id="echoid-s1332" xml:space="preserve">Itaque cernis etiam hic arcum diurnum ♋, B A D, complecti horas quindecim, &amp; </s>
  <s xml:id="echoid-s1333" xml:space="preserve">eo am-<lb/>plius, nocturnum verò B C D, paulo minus, quàm horas 9. </s>
  <s xml:id="echoid-s1334" xml:space="preserve">Item in priori Solem oriri in D, paulo ante <lb/>horam 4 {1/2} post mediam noctem, &amp; </s>
  <s xml:id="echoid-s1335" xml:space="preserve">occidere in B, paulo poſt horam 7 {1/2} poſt meridiem, &amp;</s>
  <s xml:id="echoid-s1336" xml:space="preserve">c.</s>
  <s xml:id="echoid-s1337" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s1338" xml:space="preserve">HAEC omnia experiri licebit in omnibus alĳs parallelis Solis, &amp; </s>
  <s xml:id="echoid-s1339" xml:space="preserve">in quocunque climate, ſi pro alti-<lb/>tudine poli in dato climate Analemma conſtituatur.</s>
  <s xml:id="echoid-s1340" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Quo modo da-<lb/>tus citculus di-<lb/>uidatur in duas <lb/>portiones, qua-<lb/>rum vna ſimi-<lb/>lis ſit arcui diur <lb/>no, &amp; nocturno <lb/>aliera, Sole in <lb/>qu@cunque gra <lb/>du Ecliptiçæ <lb/>exiſtente.</note>
<p>
  <s xml:id="echoid-s1341" xml:space="preserve">SED doceamus, quanam arte circulus ille minor A B C D, vel quiuis alius, etiam maior, beneficio <lb/>Analemmatis diuidendus ſit in duas portiones, quarum vna ſimilis ſit arcui diurno, &amp; </s>
  <s xml:id="echoid-s1342" xml:space="preserve">altera nocturno, <lb/>
<anchor type="note" xlink:label="note-0038-05a" xlink:href="note-0038-05"/>
Sole exiſtente in principio ♋ vel in quouis alio gradu Eclipticæ. </s>
  <s xml:id="echoid-s1343" xml:space="preserve">Egregium enim vſum hæc res habebit <lb/>in deſcribendis horis ab ortn, vel occaſu Solis, vt ex ĳs, quæ ſcquuntur, liquido conſtabit. </s>
  <s xml:id="echoid-s1344" xml:space="preserve">Sit ergo exem <lb/>pli gratia, circulus A B C D, diuidendus in ar cum diurnum, &amp; </s>
  <s xml:id="echoid-s1345" xml:space="preserve">nocturnum ♋ quemadmodum circu-<lb/>lus M d θ e, diuiſus eſt. </s>
  <s xml:id="echoid-s1346" xml:space="preserve">Ducta diametro vtcunque A C, ducatur ex A, recta A G, faciens cum A C, <lb/>quemeunque angulum, ex qua abſcindatur A G, æqualis diametro paralleli ♋ M θ, in Analemmate, <lb/>&amp; </s>
  <s xml:id="echoid-s1347" xml:space="preserve">rurſus recta A H, æqualis portioni M a, eiuſdem diametri. </s>
  <s xml:id="echoid-s1348" xml:space="preserve">Coniuncta deinde recta G C, agatur ei per <lb/>H, parallela H F, ſecans diametrum A C, in F, &amp; </s>
  <s xml:id="echoid-s1349" xml:space="preserve">per F, ad A C, excitetur perpendicularis B D. </s>
  <s xml:id="echoid-s1350" xml:space="preserve">Di-<lb/>co arcum B A D, ſimilem eſſe arcui diurno ♋ &amp; </s>
  <s xml:id="echoid-s1351" xml:space="preserve">arcum B C D nocturno, hoc eſt, arcum B A D, arcui <lb/>d M e, in maiori circulo, &amp; </s>
  <s xml:id="echoid-s1352" xml:space="preserve">arcum B C D, arcui d θ e, ſimilem eſſe. </s>
  <s xml:id="echoid-s1353" xml:space="preserve">Quoniam enim eſt, vt A H, ad H G, <lb/>hoc eſt M a, ad a θ, ita A F, ad F C, erit componendo, vt M θ, ad a θ, ita A C, ad F C, &amp; </s>
  <s xml:id="echoid-s1354" xml:space="preserve">permutan-<lb/>
<anchor type="note" xlink:label="note-0038-06a" xlink:href="note-0038-06"/>
<anchor type="note" xlink:label="note-0038-07a" xlink:href="note-0038-07"/>
do vt M θ, ad A C, ita a θ, ad F C. </s>
  <s xml:id="echoid-s1355" xml:space="preserve">Vt autem M θ, ad A C, diameter ad diametrum, ita eſt M b, ſemi-<lb/>
<anchor type="note" xlink:label="note-0038-08a" xlink:href="note-0038-08"/>
diameter ad ſemidiametrum A E. </s>
  <s xml:id="echoid-s1356" xml:space="preserve">Igitur erit quoque, vt M b, ſemidiameter ad ſemidiametrum A E, ita <lb/>a θ, ſinus verſus arcus nocturni ♋ d θ e, ad F C, ſinum verſum arcus B C D. </s>
  <s xml:id="echoid-s1357" xml:space="preserve">Per lemma ergo ſupe-<lb/>rius, arcus nocturnus ♋ d θ e, &amp; </s>
  <s xml:id="echoid-s1358" xml:space="preserve">B C D, ſimiles ſunt; </s>
  <s xml:id="echoid-s1359" xml:space="preserve">ac proinde arcus B C D, tot horas ſui circuli cõ-<lb/>prehendet, quot in arcu d θ e, continentur. </s>
  <s xml:id="echoid-s1360" xml:space="preserve">Quamobrem &amp; </s>
  <s xml:id="echoid-s1361" xml:space="preserve">reliquus B AD, reliquo arcui diurno d M e, <lb/>ſimilis erit. </s>
  <s xml:id="echoid-s1362" xml:space="preserve">quod eſt propoſitum.</s>
  <s xml:id="echoid-s1363" xml:space="preserve"/>
</p>
<div xml:id="echoid-div63" type="float" level="2" n="8">
<note position="left" xlink:label="note-0038-05" xlink:href="note-0038-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0038-06" xlink:href="note-0038-06a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0038-07" xlink:href="note-0038-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0038-08" xlink:href="note-0038-08a" xml:space="preserve">15. quinti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1364" xml:space="preserve">IAM verò latitudo ortiua, vel occidua ex Analemmate ita inuenietur. </s>
  <s xml:id="echoid-s1365" xml:space="preserve">Ex puncto a, vbi paralle-<lb/>
<anchor type="note" xlink:label="note-0038-09a" xlink:href="note-0038-09"/>
lus Horizontem ſecat, ducatur ad Horizontis diametrum B D, perpendicularis a d. </s>
  <s xml:id="echoid-s1366" xml:space="preserve">Dico arcum d A, <lb/>eſſe latitudinem ortiuam, vel occiduam. </s>
  <s xml:id="echoid-s1367" xml:space="preserve">Quoniam enim, vt paulo ante demonſtrauimus, communis ſe-<lb/>ctio paralleli, &amp; </s>
  <s xml:id="echoid-s1368" xml:space="preserve">Horizontis recta eſt ad planum Meridiani, at que adeo, ex definitione 3. </s>
  <s xml:id="echoid-s1369" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1370" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1371" xml:space="preserve">Eucli-<lb/>dis, perpendicularis ad rectam B D, in plano Meridiani exiſtentem; </s>
  <s xml:id="echoid-s1372" xml:space="preserve">fit vt ſi circulus Analemmatis
<pb o="19" file="0039" n="39" rhead="LIBER PRIMVS."/>
A B C D, pro Horizonte ſumatur, recta a d, in Horizonte communis ſectio ſit ipſius, &amp; </s>
  <s xml:id="echoid-s1373" xml:space="preserve">paralleli Solis; <lb/></s>
  <s xml:id="echoid-s1374" xml:space="preserve">adeo, vt ſol in d, oriatur, vel occidat, ſi Horizon propriam poſitionem habeat, it a vt B D, ſit linea Meri-<lb/>diana, hoc eſt, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s1375" xml:space="preserve">Meridiani; </s>
  <s xml:id="echoid-s1376" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1377" xml:space="preserve">A C, communis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s1378" xml:space="preserve">ver-<lb/>ticalis, at que adeò &amp; </s>
  <s xml:id="echoid-s1379" xml:space="preserve">Acquatoris; </s>
  <s xml:id="echoid-s1380" xml:space="preserve">ita vt Sol in Aequatore exiſtens oriatur, vel occidat in A. </s>
  <s xml:id="echoid-s1381" xml:space="preserve">Quare <lb/>arcus d A, Horizontis inter d, ortũ, occaſumve paralleli Solis, &amp; </s>
  <s xml:id="echoid-s1382" xml:space="preserve">A, ortum occaſumve Aequatoris, <lb/>latitudo ortiua erit, vel occidua, Sole parallelũ diametri M θ, deſcribente. </s>
  <s xml:id="echoid-s1383" xml:space="preserve">Eadem{q́ue} ratio de cæteris <lb/>habenda eſt. </s>
  <s xml:id="echoid-s1384" xml:space="preserve">Erit autem ſemper a d, in Analemmate æqualis rectæ a d, vel a e, in parallelo M d θ e, pro-<lb/>pterea quòd vtraque communis ſectio eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s1385" xml:space="preserve">paralleli, excurrens ex a, vſque ad ſuperficiem <lb/>Sphæræ, in qua ſibi mutuo congruunt, ſi &amp; </s>
  <s xml:id="echoid-s1386" xml:space="preserve">Horizon, &amp; </s>
  <s xml:id="echoid-s1387" xml:space="preserve">parallelus in propria poſitione concipiatur.</s>
  <s xml:id="echoid-s1388" xml:space="preserve"/>
</p>
<div xml:id="echoid-div64" type="float" level="2" n="9">
<note position="left" xlink:label="note-0038-09" xlink:href="note-0038-09a" xml:space="preserve">Inuentio latitu <lb/>dinis ortiuæ &amp; <lb/>occiduæ ex A-<lb/>nalemmate.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div66" type="section" level="1" n="19">
<head xml:id="echoid-head22" xml:space="preserve">THEOREMA PRIMVM. <lb/>PROPOSITIO SECVNDA.</head>
<p>
  <s xml:id="echoid-s1389" xml:space="preserve">IN quolibet horologio vertex ſtyli idem cenſeri debet, quod <lb/>
<anchor type="note" xlink:label="note-0039-02a" xlink:href="note-0039-02"/>
centrum mundi: </s>
  <s xml:id="echoid-s1390" xml:space="preserve">planum verò ipſius horologij tantum à <lb/>centro mundi abeſſe intelligendum eſt, quanta eſt ſtyli lon-<lb/>
<anchor type="note" xlink:label="note-0039-03a" xlink:href="note-0039-03"/>
gitudo, æquidiſtareq; </s>
  <s xml:id="echoid-s1391" xml:space="preserve">circulo maximo, ad cuius planum <lb/>ſtylus rectus eſt, &amp; </s>
  <s xml:id="echoid-s1392" xml:space="preserve">à quo nomen habet horologium.</s>
  <s xml:id="echoid-s1393" xml:space="preserve"/>
</p>
<div xml:id="echoid-div66" type="float" level="2" n="1">
<note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">Vert ex ſtyli cu <lb/>iusuis horologii <lb/>centrum mũdi <lb/>eſt, planum au-<lb/>tem horologij <lb/>extra centum <lb/>mundi exiſti@.</note>
<note position="left" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s1394" xml:space="preserve">SIT ſtylus horologij cuiuſpiam A B, inſiſtens ad angulos rectos plano horologij, quod per <lb/>rectam C D, duci intelligitur. </s>
  <s xml:id="echoid-s1395" xml:space="preserve">Quoniam igitur tota terra cum Sphæra Solis comparata eſt inſtar <lb/>puncti, ac centri, vt in commentarijs in Sphæram ex Ptolemæo, alijsq́ Aſtronomis oſtendimus, <lb/>nihil differet centrum mundi à puncto A, vertice <lb/>
<anchor type="figure" xlink:label="fig-0039-01a" xlink:href="fig-0039-01"/>
gnomonis, ſeu ſtyli, quandoquidem à vertice A, <lb/>ad centrum terræ, quod idem eſt, quod centrum <lb/>mundi, vt in iiſdem commentarijs docuimus, nõ <lb/>
<anchor type="note" xlink:label="note-0039-04a" xlink:href="note-0039-04"/>
eſt diſtantia notabilis, ſi ea conferatur cum diſtan-<lb/>tia, quam habet Sol ab eodem vertice; </s>
  <s xml:id="echoid-s1396" xml:space="preserve">atque adeo <lb/>circulus per verticem A, ductus, planoq́; </s>
  <s xml:id="echoid-s1397" xml:space="preserve">horolo-<lb/>gii per C D, ducto æquidiſtans pro circulo maxi-<lb/>mo ſumi non immerito poterit. </s>
  <s xml:id="echoid-s1398" xml:space="preserve">Quare iure op <lb/>timo ii, qui de horologiorum deſcriptione agunt, <lb/>vt rationem umbrarum, quas Sol quouis momen <lb/>to temporis efficit, demonſtrare poſſint, concipiũt <lb/>verticem ſtyli in centro mundi ſtatui, ad quod om <lb/>nes radii Solis incidentes proiiciunt per gnomo-<lb/>
<anchor type="note" xlink:label="note-0039-05a" xlink:href="note-0039-05"/>
nis verticem vmbram in planum horologii; </s>
  <s xml:id="echoid-s1399" xml:space="preserve">vt fi-<lb/>gura demonſtrat, in qua vmbra eſt B G, in horolo-<lb/>gii plano, Sole habente altitudinem E H, ſupra cir <lb/>culum maximum EF, cui planum C D, in quod vmbra cadit, æquidiſtat, Cum enim H A G, ra-<lb/>dius Solis in puncto H, exiſtentis perueniat ad punctum G, &amp; </s>
  <s xml:id="echoid-s1400" xml:space="preserve">ſtylus ſit opacus, erit totum trian-<lb/>gulum A B G, vmbroſum, quòd in eius aream radij Solis non cadant; </s>
  <s xml:id="echoid-s1401" xml:space="preserve">atque adeo B G, longitudo <lb/>erit vmbræ in plano horologij, reliquæ verò omnes partes, vt G D, &amp; </s>
  <s xml:id="echoid-s1402" xml:space="preserve">B C, à Sole illuſtrabuntur. <lb/></s>
  <s xml:id="echoid-s1403" xml:space="preserve">Eodem modo longitudinem vmbræ quolibet tempore inueſtigare poterimus, ſi altitudinem So-<lb/>lis ſupra circulum maximũ, qui plano horologij æquidiſtet, cognouerimus, vt ſuo loco dicemus. </s>
  <s xml:id="echoid-s1404" xml:space="preserve"><lb/>Ex his manifeſtum eſt, planum horologij per rectam C D, ductum tantum abeſſe à centro mun-<lb/>
<anchor type="note" xlink:label="note-0039-06a" xlink:href="note-0039-06"/>
di, quanta eſt longitudo gnomonis A B, quandoquidem vertex A, in cẽtro collocatur, vt diximus. <lb/></s>
  <s xml:id="echoid-s1405" xml:space="preserve">Quod ſi per rectam E A F, circulus maximus intelligatur duci, ad quem Gnomon A B, rectus ſit, <lb/>æquidiſtans erit planum horologij huic circulo; </s>
  <s xml:id="echoid-s1406" xml:space="preserve">cum gnomon A B, &amp; </s>
  <s xml:id="echoid-s1407" xml:space="preserve">ad planum circuli per re-<lb/>
<anchor type="note" xlink:label="note-0039-07a" xlink:href="note-0039-07"/>
ctam E F, &amp; </s>
  <s xml:id="echoid-s1408" xml:space="preserve">ad planum horologij per rectam C D, ductum rectus ponatur.</s>
  <s xml:id="echoid-s1409" xml:space="preserve"/>
</p>
<div xml:id="echoid-div67" type="float" level="2" n="2">
  <figure xlink:label="fig-0039-01" xlink:href="fig-0039-01a">
    <image file="0039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0039-01"/>
  </figure>
<note position="left" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0039-06" xlink:href="note-0039-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0039-07" xlink:href="note-0039-07a" xml:space="preserve">14. undec.</note>
</div>
<p>
  <s xml:id="echoid-s1410" xml:space="preserve">HABET autem horologium nomen à circulo diametri E F, cui æquidiſtat. </s>
  <s xml:id="echoid-s1411" xml:space="preserve">Nam ſi circu-<lb/>
<anchor type="note" xlink:label="note-0039-08a" xlink:href="note-0039-08"/>
lus ille fuerit Horizon, horologium dicitur Horizontale. </s>
  <s xml:id="echoid-s1412" xml:space="preserve">Si Verticalis, Verticale: </s>
  <s xml:id="echoid-s1413" xml:space="preserve">ſi Meridianus, <lb/>Meridianum: </s>
  <s xml:id="echoid-s1414" xml:space="preserve">Si Aequinoctialis, Aequinoctiale: </s>
  <s xml:id="echoid-s1415" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1416" xml:space="preserve">ſic de reliquis, vt ſupra diximus, cum varia ho-<lb/>rologiorũ genera explicaremus. </s>
  <s xml:id="echoid-s1417" xml:space="preserve">Tot enim horologia fieri poſſunt, quot circuli maximi in Sphæ-<lb/>ra per centrum mundi poſſunt duci, cũ ſingulis plana parallela poſſint duci ad interuallum lon-<lb/>gitudinis ſtyli, in quibus horologia deſcribantur, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s1418" xml:space="preserve">In quolibet ergo horologio <lb/>vertex ſtyli, &amp;</s>
  <s xml:id="echoid-s1419" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1420" xml:space="preserve">quod erat oſtendendum.</s>
  <s xml:id="echoid-s1421" xml:space="preserve"/>
</p>
<div xml:id="echoid-div68" type="float" level="2" n="3">
<note position="right" xlink:label="note-0039-08" xlink:href="note-0039-08a" xml:space="preserve">Horologium <lb/>quodcunq; no-<lb/>men accipit à <lb/>circulo maxi-<lb/>mo, cui ęquidi-<lb/>ſtat.</note>
</div>
<pb o="20" file="0040" n="40" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div70" type="section" level="1" n="20">
<head xml:id="echoid-head23" xml:space="preserve">THEOREMA 2. PROPOSITIO 3.</head>
<p>
  <s xml:id="echoid-s1422" xml:space="preserve">RADIVS Solis in Aequatore quidem exiſtentis, motu diurno cir-<lb/>
<anchor type="note" xlink:label="note-0040-01a" xlink:href="note-0040-01"/>
ca centrum mundi deſcribit circulum, nem pe ipſummet Aequatorem: <lb/></s>
  <s xml:id="echoid-s1423" xml:space="preserve">extra verò Aequatorem conſtituti, duas conicas ſuperficies ad centrum <lb/>mundi, tanquam ad communem verticem, coniunctas, quarum vnius <lb/>baſis eſt parallelus à centro Solis deſcriptus, alterius autem, parallelus pa-<lb/>
<anchor type="note" xlink:label="note-0040-02a" xlink:href="note-0040-02"/>
rallelo huic oppoſitus; </s>
  <s xml:id="echoid-s1424" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1425" xml:space="preserve">vtriuſque axis idem, qui mundi.</s>
  <s xml:id="echoid-s1426" xml:space="preserve"/>
</p>
<div xml:id="echoid-div70" type="float" level="2" n="1">
<note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">Sol in Aequa-<lb/>tore exiſtens de <lb/>ſcribit ſuo ra-<lb/>dio æquinoctia <lb/>lem circulum. <lb/>extra vero Ae-<lb/>quatorem duas <lb/>conicas ſuperfi-<lb/>cies.</note>
<note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s1427" xml:space="preserve">IN Analemmate A B C D, cuius centrum E, axis mundi ſit D B; </s>
  <s xml:id="echoid-s1428" xml:space="preserve">communis ſectio Aequatoris, <lb/>&amp; </s>
  <s xml:id="echoid-s1429" xml:space="preserve">Meridiani recta A C; </s>
  <s xml:id="echoid-s1430" xml:space="preserve">duorum parallelorum oppoſitorum, &amp; </s>
  <s xml:id="echoid-s1431" xml:space="preserve">eiuſdem Meridiani communes <lb/>ſectiones rectæ F G, H I, ſecantes axem in Q, R, punctis, quæ centra erunt ipſorum parallelorũ, <lb/>ex propoſ. </s>
  <s xml:id="echoid-s1432" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1433" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1434" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1435" xml:space="preserve">Theodoſii, quandoquidem axis per ipſorum polos ducitur, atque adeo ex di-<lb/>cta propoſ. </s>
  <s xml:id="echoid-s1436" xml:space="preserve">per centra eorundem tranſit. </s>
  <s xml:id="echoid-s1437" xml:space="preserve">In telligantur quoque circa diametros A C, F G, H I, de-<lb/>
<anchor type="figure" xlink:label="fig-0040-01a" xlink:href="fig-0040-01"/>
ſcripti circuli, nempe Aequator <lb/>A K C L, &amp; </s>
  <s xml:id="echoid-s1438" xml:space="preserve">duo paralleli F M <lb/>G N, H O I P, ad Meridianum <lb/>
<anchor type="note" xlink:label="note-0040-03a" xlink:href="note-0040-03"/>
recti. </s>
  <s xml:id="echoid-s1439" xml:space="preserve">In Sphæra enim Aequator, <lb/>&amp; </s>
  <s xml:id="echoid-s1440" xml:space="preserve">ei<emph style="sub">9</emph> paralleli ad Meridiani pla-<lb/>num, ex propoſ. </s>
  <s xml:id="echoid-s1441" xml:space="preserve">15. </s>
  <s xml:id="echoid-s1442" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1443" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1444" xml:space="preserve">Theo <lb/>doſii, recti ſunt, cum eos Meri-<lb/>dianus circulus per ipſorum po-<lb/>los ſecet. </s>
  <s xml:id="echoid-s1445" xml:space="preserve">Quoniam igitur, Sole <lb/>in Aequatore exiſtente, nimirũ <lb/>in puncto A, centrum eius à cir-<lb/>cunferẽtia Aequatoris A K C L, <lb/>&amp; </s>
  <s xml:id="echoid-s1446" xml:space="preserve">radius A E, ad centrum mun-<lb/>
<anchor type="note" xlink:label="note-0040-04a" xlink:href="note-0040-04"/>
di pertinens à plano eiuſdem <lb/>Aequatoris, quod per centrum <lb/>etiam mundi ducitur, non rece-<lb/>dit, ſed motu diurno in eo ſem-<lb/>per circunfertur, (Negligimus <lb/>enim nũc declinationem, quam <lb/>proprio motu Sol acqui@it.) </s>
  <s xml:id="echoid-s1447" xml:space="preserve">per-<lb/>ſpicuum eſt, ex definitione circu <lb/>li, à Solis radio circulum, nem-<lb/>pe ipſummet Aequa@orem A K-<lb/>
<anchor type="note" xlink:label="note-0040-05a" xlink:href="note-0040-05"/>
C L, deſcribi, cuius circunferen-<lb/>tiam centrum eiuſdẽ deſcribit.</s>
  <s xml:id="echoid-s1448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div71" type="float" level="2" n="2">
  <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a">
    <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0040-01"/>
  </figure>
<note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s1449" xml:space="preserve">AT vero Sole extra Aequatorem conſtituto, vt in puncto F, radius eius F E, ad mundi centrũ <lb/>pertinens, &amp; </s>
  <s xml:id="echoid-s1450" xml:space="preserve">in rectum, continuumq́; </s>
  <s xml:id="echoid-s1451" xml:space="preserve">productus, conuertitur (manente puncto E, ſixo) circa cir-<lb/>cunferentiam circuli F M G N, (cũ ad motum diurnum cẽtrum Solis ab ea non recedat) &amp; </s>
  <s xml:id="echoid-s1452" xml:space="preserve">altera <lb/>ex parte circa circunferentiam circuli H O I P, qui illi æqualis eſt, &amp; </s>
  <s xml:id="echoid-s1453" xml:space="preserve">oppoſitus. </s>
  <s xml:id="echoid-s1454" xml:space="preserve">Igitur radius So-<lb/>lis F E, productus ad I, deſcribit conicas ſuperficies E F G, E I H, ad centrum E, aptatas, quarum <lb/>baſes ſunt paralleli oppoſiti F M G N, H O I P; </s>
  <s xml:id="echoid-s1455" xml:space="preserve">vertex communis E, centrum mundi; </s>
  <s xml:id="echoid-s1456" xml:space="preserve">axis verò <lb/>vtriuſque E Q, E R, idem, qui axis mundi, quandoquidem, Q, R, centra ſunt, vt oſtendimus, cir-<lb/>culorum F M G N, H O I P. </s>
  <s xml:id="echoid-s1457" xml:space="preserve">Quæ omnia perſpicua ſunt ex definitionibus Apollonij Pergæi.</s>
  <s xml:id="echoid-s1458" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s1459" xml:space="preserve">EAEDEM ſuperficies conicæ deſcribentur, dum Sol in puncto I, oppoſito fuerit conſtitutus, <lb/>vt patet.</s>
  <s xml:id="echoid-s1460" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1461" xml:space="preserve">DENIQVE, ſi à quouis puncto cęli per centrum mundi recta linea ducatur, deſcribet <lb/>ipſa motu diurno circumlata duas ſuperficies conicas ad centrum mundi connexas, quarum baſes <lb/>deſcribuntur à puncto illo, eiusq́; </s>
  <s xml:id="echoid-s1462" xml:space="preserve">oppoſito, axesq́; </s>
  <s xml:id="echoid-s1463" xml:space="preserve">habent partes axis mundi. </s>
  <s xml:id="echoid-s1464" xml:space="preserve">Vt ſi a puncto S, <lb/>paralleli ſemper apparentium maximi recta S E, per centrum mundi extendatur, deſcribentur mo-<lb/>tu diurno conicæ ſuperficies E S V, E α Y, ad centrum E, tanquam verticem communem aptatas, <lb/>quarum baſes ſunt paralleli à puncto S, eiusq́; </s>
  <s xml:id="echoid-s1465" xml:space="preserve">oppoſito α, deſcripti, quorum S T V X, maximus <lb/>eſt eorum, qui ſemper apparent, at Y Z α β, maximus eorum, qui nunquam apparent ſupra Ho-<lb/>rizontem Y V. </s>
  <s xml:id="echoid-s1466" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s1467" xml:space="preserve">eſt ratio de cæteris celi punctis. </s>
  <s xml:id="echoid-s1468" xml:space="preserve">Radius ergo Solis in Aequatore quidem <lb/>exiſtentis, motu diurno, &amp;</s>
  <s xml:id="echoid-s1469" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1470" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s1471" xml:space="preserve"/>
</p>
<pb o="21" file="0041" n="41" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div73" type="section" level="1" n="21">
<head xml:id="echoid-head24" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s1472" xml:space="preserve">SOLET à nonnullis, &amp; </s>
  <s xml:id="echoid-s1473" xml:space="preserve">rectè, illa ſuperficies conica, cuius baſim deſcribit centrum Solis, appellari <lb/>
<anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/>
ſuperficies conica luminis, quòd à radio Solis deſcribatur; </s>
  <s xml:id="echoid-s1474" xml:space="preserve">altera verò, cuius baſim punctum centro So-<lb/>lis oppoſitum deſcribit, ſuperſicies conica vmbræ, quia ab vmbra, quam centrum mundi proĳcit, deſcri-<lb/>
<anchor type="note" xlink:label="note-0041-02a" xlink:href="note-0041-02"/>
bitur. </s>
  <s xml:id="echoid-s1475" xml:space="preserve">Vt Sole exiſtente in puncto F, ſuperficies luminis eſt E F G, quia tota à Sole illuminatur, ſuper-<lb/>ficies verò vmbræ E I H, quia ab vmbra centri E, ſecundum rectam E I, proiectam deſcripta eſt. </s>
  <s xml:id="echoid-s1476" xml:space="preserve">Contra <lb/>autem, Sole punctum I, poſſidente, ſuperficies luminis dicitur E I H, &amp; </s>
  <s xml:id="echoid-s1477" xml:space="preserve">vmbræ E F G. </s>
  <s xml:id="echoid-s1478" xml:space="preserve">Ponimus enim <lb/>nunc, centrum E, vim habere vmbram proĳciendi; </s>
  <s xml:id="echoid-s1479" xml:space="preserve">quia vt in propoſ. </s>
  <s xml:id="echoid-s1480" xml:space="preserve">præcedenti diximus, centrum mun <lb/>di intelligitur in quolibet borologio eſſe vertex ſtyli, qui vtique corpus opacum cum ſit, vmbram proĳ-<lb/>
<anchor type="note" xlink:label="note-0041-03a" xlink:href="note-0041-03"/>
cit, vt manifeſtum eſt.</s>
  <s xml:id="echoid-s1481" xml:space="preserve"/>
</p>
<div xml:id="echoid-div73" type="float" level="2" n="1">
<note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">Superficies co-<lb/>nica luminis <lb/>quæ.</note>
<note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">Superficies coni <lb/>ca vmbræ quæ.</note>
<note position="left" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div75" type="section" level="1" n="22">
<head xml:id="echoid-head25" xml:space="preserve">THEOREMA 3. PROPOSITIO 4.</head>
<note position="right" xml:space="preserve">Planum horo-<lb/>logij æquidiftãs <lb/>baſibus conica-<lb/>rum ſuperficie-<lb/>rum facit in al-<lb/>tera ſuperſicie-<lb/>rum circulum.</note>
<p>
  <s xml:id="echoid-s1482" xml:space="preserve">SECTIO communis ſuperficierum conicarum in centro mundi, <lb/>tanquam vertice communi iunctarum, quarum baſes duo ſunt paralle-<lb/>li Sphærę oppoſiti, &amp; </s>
  <s xml:id="echoid-s1483" xml:space="preserve">æquales, ad motum diurnum circa mundi polos <lb/>deſcripti, &amp; </s>
  <s xml:id="echoid-s1484" xml:space="preserve">plani horologij æquidiſtantis circulo maximo, qui baſibus <lb/>
<anchor type="note" xlink:label="note-0041-05a" xlink:href="note-0041-05"/>
conicarum ſuperficierum æquidiſtat, circulus eſt, centrum habens in <lb/>axe mundi.</s>
  <s xml:id="echoid-s1485" xml:space="preserve"/>
</p>
<div xml:id="echoid-div75" type="float" level="2" n="1">
<note position="left" xlink:label="note-0041-05" xlink:href="note-0041-05a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s1486" xml:space="preserve">IN Sphæra, cuius centrum A, ſint duæ ſuperſicies conicæ A D E, AFG, coniunctæ ad mundi <lb/>centrum A, tanquam ad verticem communem, quarum baſes paralleli ſint ad motum diurnum <lb/>deſcripti, oppoſiti &amp; </s>
  <s xml:id="echoid-s1487" xml:space="preserve">æquales D E, F G; </s>
  <s xml:id="echoid-s1488" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1489" xml:space="preserve">axis B C. </s>
  <s xml:id="echoid-s1490" xml:space="preserve">Sit quoque HI, circulus maximus in Sphæra <lb/>ęquidiſtans baſibus D E, F G, di-<lb/>
<anchor type="figure" xlink:label="fig-0041-01a" xlink:href="fig-0041-01"/>
ctarum ſuperficierum conicarũ: <lb/></s>
  <s xml:id="echoid-s1491" xml:space="preserve">Huic autem circulo æquidiſtet <lb/>horologij planum K L, faciens <lb/>
<anchor type="note" xlink:label="note-0041-06a" xlink:href="note-0041-06"/>
in conica ſuperficie A F G, ſe-<lb/>ctionem M N. </s>
  <s xml:id="echoid-s1492" xml:space="preserve">Dico M N, eſſe <lb/>circulum, qui cẽtrum habeat in <lb/>axe mundi. </s>
  <s xml:id="echoid-s1493" xml:space="preserve">Cum enim plana <lb/>F G, K L, plano H I, parallela <lb/>ponantur, &amp; </s>
  <s xml:id="echoid-s1494" xml:space="preserve">ipſa inter ſe paral-<lb/>lela erunt, per ea, quę ad propoſ. <lb/></s>
  <s xml:id="echoid-s1495" xml:space="preserve">16. </s>
  <s xml:id="echoid-s1496" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1497" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1498" xml:space="preserve">Euclidis demonſtra <lb/>uimus. </s>
  <s xml:id="echoid-s1499" xml:space="preserve">Quamobrem, cùm ſu-<lb/>perficies conica A F G, ſecetur <lb/>
<anchor type="note" xlink:label="note-0041-07a" xlink:href="note-0041-07"/>
plano K L, quod baſi F G, æqui-<lb/>diſtat, ſectio facta M N, per pro-<lb/>poſitionem 4. </s>
  <s xml:id="echoid-s1500" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1501" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1502" xml:space="preserve">Apollonii, <lb/>circulus erit centrum habens in <lb/>axe B C, vbi nimirum planum <lb/>horologii axi occurrit. </s>
  <s xml:id="echoid-s1503" xml:space="preserve">Eodem <lb/>modo, ſi planum circulo HI, <lb/>æquidiſtans ſecet conicam ſu-<lb/>perficiem A D E, ſectio circulus <lb/>erit. </s>
  <s xml:id="echoid-s1504" xml:space="preserve">Sectio igitur communis <lb/>
<anchor type="note" xlink:label="note-0041-08a" xlink:href="note-0041-08"/>
ſuperficierum conicarum, &amp;</s>
  <s xml:id="echoid-s1505" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1506" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s1507" xml:space="preserve"/>
</p>
<div xml:id="echoid-div76" type="float" level="2" n="2">
  <figure xlink:label="fig-0041-01" xlink:href="fig-0041-01a">
    <image file="0041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0041-01"/>
  </figure>
<note position="left" xlink:label="note-0041-06" xlink:href="note-0041-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0041-07" xlink:href="note-0041-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0041-08" xlink:href="note-0041-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div78" type="section" level="1" n="23">
<head xml:id="echoid-head26" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s1508" xml:space="preserve">HINC fit, communem ſectionem plani horologij Aequinoctialis, &amp; </s>
  <s xml:id="echoid-s1509" xml:space="preserve">ſuperficierum conicarum, qua-<lb/>
<anchor type="note" xlink:label="note-0041-09a" xlink:href="note-0041-09"/>
rum baſes ſunt quicunque paralleli à Sole deſcripti, oppoſiti, &amp; </s>
  <s xml:id="echoid-s1510" xml:space="preserve">æquales, vel alij quicunque his ęquidiſtan <lb/>tes, quales etiam ſunt maximi parallelorum ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s1511" xml:space="preserve">ſemper deliteſcentium, eſſe circu-<lb/>lum: </s>
  <s xml:id="echoid-s1512" xml:space="preserve">propterea quòd æquinoctialis circulus, cui planum horologii æquidiſtat, æquidiſtans eſt baſibus <lb/>ſuperficierum huiuſmodi conicarum.</s>
  <s xml:id="echoid-s1513" xml:space="preserve"/>
</p>
<div xml:id="echoid-div78" type="float" level="2" n="1">
<note position="right" xlink:label="note-0041-09" xlink:href="note-0041-09a" xml:space="preserve">Aequinoctiale <lb/>horologiũ ſecãs <lb/>ſuperficiem co-<lb/>nicam, cuius ba <lb/>ſis ſit parallelus <lb/>Aequatoris, fa-<lb/>cit circulum.</note>
</div>
<pb o="22" file="0042" n="42" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div80" type="section" level="1" n="24">
<head xml:id="echoid-head27" xml:space="preserve">THEQREMA 4. PROPOSITIQ 5.</head>
<p>
  <s xml:id="echoid-s1514" xml:space="preserve">SECTIO communis earundem ſuperficierum conicarum, &amp; </s>
  <s xml:id="echoid-s1515" xml:space="preserve">pla-<lb/>
<anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
ni horologij æquidiſtantis circulo maximo, qui baſes conicarum ſuper-<lb/>ficierum tangit, Parabole eſt.</s>
  <s xml:id="echoid-s1516" xml:space="preserve"/>
</p>
<div xml:id="echoid-div80" type="float" level="2" n="1">
<note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">Planum horo-<lb/>logij æquidiſtãs <lb/>maximo circu-<lb/>lo baſes conica <lb/>rum ſuperficie-<lb/>rum tãgenti fa-<lb/>cit in altera ſu-<lb/>per@cierum Pa <lb/>tabolen.</note>
</div>
<p>
  <s xml:id="echoid-s1517" xml:space="preserve">SINT in eadem Sphæra duæ conicæ ſuperficies, quæ prius; </s>
  <s xml:id="echoid-s1518" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1519" xml:space="preserve">E F, maximus circulus tangens <lb/>baſes oppoſitas in punctis E, &amp; </s>
  <s xml:id="echoid-s1520" xml:space="preserve">F. </s>
  <s xml:id="echoid-s1521" xml:space="preserve">Huic autem circulo æquidiſtet horologij planum H I, faciens <lb/>in conica ſuperficie A F G, ſectionem K L M. </s>
  <s xml:id="echoid-s1522" xml:space="preserve">Dico K L M, Parabolen eſſe. </s>
  <s xml:id="echoid-s1523" xml:space="preserve">Ducatur per paralle-<lb/>
<anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
<anchor type="figure" xlink:label="fig-0042-01a" xlink:href="fig-0042-01"/>
lorum polos B, C, &amp; </s>
  <s xml:id="echoid-s1524" xml:space="preserve">per conta-<lb/>ctum E, circulus maximus B D-<lb/>C G, per ꝓpoſ. </s>
  <s xml:id="echoid-s1525" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1526" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1527" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1528" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s1529" xml:space="preserve">qui neceſſario quoque per po-<lb/>los circuli F E, per propoſ. </s>
  <s xml:id="echoid-s1530" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1531" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1532" xml:space="preserve"><lb/>2. </s>
  <s xml:id="echoid-s1533" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s1534" xml:space="preserve">atque adeo per polos <lb/>circuli H I, quem in Sphæra ex <lb/>propoſ. </s>
  <s xml:id="echoid-s1535" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1536" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1537" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1538" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s1539" xml:space="preserve">efficit <lb/>planum horologij, (cũ ex pro-<lb/>poſ. </s>
  <s xml:id="echoid-s1540" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1541" xml:space="preserve">eiuſdem, eoſdem habeant <lb/>
<anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
polos paralleli F E, H I,) tranſi-<lb/>bit, ideoq́; </s>
  <s xml:id="echoid-s1542" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s1543" xml:space="preserve">15 lib. </s>
  <s xml:id="echoid-s1544" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s1545" xml:space="preserve">Theodoſ. </s>
  <s xml:id="echoid-s1546" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1547" xml:space="preserve">circulum F G, &amp; </s>
  <s xml:id="echoid-s1548" xml:space="preserve">cir <lb/>culum H I, per rectas F G, H I, <lb/>ſe mutuo in N, ſecantes, (ſeca-<lb/>bunt enim ſe ſe rectæ F G, H I, <lb/>mutuo, quòd in eodem plano <lb/>circuli B D C G, exiſtant) bifa-<lb/>riam &amp; </s>
  <s xml:id="echoid-s1549" xml:space="preserve">ad angulos rectos ſeca-<lb/>bit, facietq́; </s>
  <s xml:id="echoid-s1550" xml:space="preserve">communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0042-04a" xlink:href="note-0042-04"/>
nes planorum parallelorũ F E, <lb/>
<anchor type="note" xlink:label="note-0042-05a" xlink:href="note-0042-05"/>
H I, parallelas. </s>
  <s xml:id="echoid-s1551" xml:space="preserve">Faciat quoque <lb/>idem circulus B D C G, cũ per <lb/>axem B C, incedat, triangulum <lb/>per axem A F G, ſecans rectam <lb/>H I, &amp; </s>
  <s xml:id="echoid-s1552" xml:space="preserve">ſectionẽ conicã in k: </s>
  <s xml:id="echoid-s1553" xml:space="preserve">Secet etiã planũ H I, per rectam K N, tranſiens, circulum F G, per rectã <lb/>M N L, per punctum N, tranſeuntẽ. </s>
  <s xml:id="echoid-s1554" xml:space="preserve">Nam cum planum per K N, ductum per punctum N, quod <lb/>in plano G F, eſt, tranſeat, trãſibit quoque L M, communis ſectio planorum H I, F G, per punctum <lb/>N. </s>
  <s xml:id="echoid-s1555" xml:space="preserve">Quoniam igitur plana F G, H I, recta ſunt ad planum circuli B D C G; </s>
  <s xml:id="echoid-s1556" xml:space="preserve">erit quoq; </s>
  <s xml:id="echoid-s1557" xml:space="preserve">eorum com <lb/>munis ſectio L M, ad idem recta in puncto N, atque adeò &amp; </s>
  <s xml:id="echoid-s1558" xml:space="preserve">ad rectam F G, baſ@m trianguli per <lb/>
<anchor type="note" xlink:label="note-0042-06a" xlink:href="note-0042-06"/>
<anchor type="note" xlink:label="note-0042-07a" xlink:href="note-0042-07"/>
axem, perpendicularis erit, ex definitione 3. </s>
  <s xml:id="echoid-s1559" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1560" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1561" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1562" xml:space="preserve">Quare cum conus A F G, ſecetur plano <lb/>B D C G, per axem, ſecetur autem &amp; </s>
  <s xml:id="echoid-s1563" xml:space="preserve">altero plano H I, quod baſim coni ſecat per rectam lineam <lb/>L M, perpendicularem ad F G, baſim trianguli per axem, ſitq́; </s>
  <s xml:id="echoid-s1564" xml:space="preserve">K N, ſectionis diameter lateri A F, <lb/>trianguli per axem parallela; </s>
  <s xml:id="echoid-s1565" xml:space="preserve">erit, per propoſ. </s>
  <s xml:id="echoid-s1566" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1567" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1568" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1569" xml:space="preserve">Apollonij, ſectio K L M, parabole. </s>
  <s xml:id="echoid-s1570" xml:space="preserve">Sectio <lb/>
<anchor type="note" xlink:label="note-0042-08a" xlink:href="note-0042-08"/>
ergo communis earundem ſuperficierum, &amp;</s>
  <s xml:id="echoid-s1571" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1572" xml:space="preserve">Quod demonſtrandum erat.</s>
  <s xml:id="echoid-s1573" xml:space="preserve"/>
</p>
<div xml:id="echoid-div81" type="float" level="2" n="2">
<note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a">
    <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0042-01"/>
  </figure>
<note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0042-04" xlink:href="note-0042-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0042-05" xlink:href="note-0042-05a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0042-06" xlink:href="note-0042-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0042-07" xlink:href="note-0042-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0042-08" xlink:href="note-0042-08a" xml:space="preserve">Planum horo-<lb/>logii horizonta-<lb/>lis cuiuſque, &amp; <lb/>Verticalis ad la <lb/>titudinẽ gr. 45. <lb/>immo &amp; æqui-<lb/>diſtantis cuili-<lb/>bet circulo ho-<lb/>rarum ab ortu <lb/>vel occaſu, facit <lb/>in altera ſuper-<lb/>ficierum coni-<lb/>carum quarum <lb/>baſes ſunt pa-<lb/>rallelus ſemper <lb/>apparentiũ ma-<lb/>ximus &amp; maxi-<lb/>mus ſemper la-<lb/>tentium, Para-<lb/>bolam.</note>
</div>
</div>
<div xml:id="echoid-div83" type="section" level="1" n="25">
<head xml:id="echoid-head28" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s1574" xml:space="preserve">ITAQVE, cum Horizon quilibet obliquus tangat duos parallelos, quorum alter eſt maximus eo-<lb/>rum, qui ſemper apparent, alter uerò maximus eorum, qui ſemper ſub terra occultantur; </s>
  <s xml:id="echoid-s1575" xml:space="preserve">erit communis <lb/>
<anchor type="note" xlink:label="note-0042-09a" xlink:href="note-0042-09"/>
ſectio plani horologii Horizontalis, &amp; </s>
  <s xml:id="echoid-s1576" xml:space="preserve">coni, cuius baſis parallelus eſt maximus eorum, qui deliteſcunt, <lb/>(neque enim alter conus, cuius baſis ſemper apparet, ſecatur, cum totus extet ſupra Horizontem) Parabo-<lb/>le. </s>
  <s xml:id="echoid-s1577" xml:space="preserve">Idem continget in horologio Verticali ad latitudinem graduum 45. </s>
  <s xml:id="echoid-s1578" xml:space="preserve">Item in horologio, cuius planum <lb/>circulo horæ cuiuslibet ab ortu, vel occaſu æquidiſtat. </s>
  <s xml:id="echoid-s1579" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s1580" xml:space="preserve">Verticalis circulus latitudinis graduum <lb/>45. </s>
  <s xml:id="echoid-s1581" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1582" xml:space="preserve">circulus cuiuslibet horæ ab ortu, uel occaſu, in omni Horizonte tangit maximum parallelum eo-<lb/>rum, qui toti ſupra Horizontem extant, vt propoſ. </s>
  <s xml:id="echoid-s1583" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1584" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s1585" xml:space="preserve">demonſtrabitur.</s>
  <s xml:id="echoid-s1586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div83" type="float" level="2" n="1">
<note position="left" xlink:label="note-0042-09" xlink:href="note-0042-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s1587" xml:space="preserve">DENIQVE communis ſectio cuiuſcunque horologii, &amp; </s>
  <s xml:id="echoid-s1588" xml:space="preserve">coni, cuius baſis tantum ab Aequatore de-<lb/>clinat ad Auſtrum, quantum eſt complementum altitudinis poli arctici ſupra circulum maximum, cui pla <lb/>
<anchor type="note" xlink:label="note-0042-10a" xlink:href="note-0042-10"/>
num horologii æquidiſtat, Parabole erit. </s>
  <s xml:id="echoid-s1589" xml:space="preserve">Talis erit ſectio coni baſim habentis parallelum ♑, &amp; </s>
  <s xml:id="echoid-s1590" xml:space="preserve">horo-<lb/>logii horizontalis ad latitudinem ſeptentrionalem grad. </s>
  <s xml:id="echoid-s1591" xml:space="preserve">66. </s>
  <s xml:id="echoid-s1592" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1593" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1594" xml:space="preserve">Nam complementum huius lati-<lb/>tudinis continet grad. </s>
  <s xml:id="echoid-s1595" xml:space="preserve">23. </s>
  <s xml:id="echoid-s1596" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1597" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1598" xml:space="preserve">quanta nimirum eſt declinatio paralleli ♑. </s>
  <s xml:id="echoid-s1599" xml:space="preserve">Talis etiam erit ſectio <lb/>coni baſim habentis parallelum ♒ &amp; </s>
  <s xml:id="echoid-s1600" xml:space="preserve">♐, &amp; </s>
  <s xml:id="echoid-s1601" xml:space="preserve">horologii horizontalis ad latitudinem ſeptentrionalem <lb/>graduum 69. </s>
  <s xml:id="echoid-s1602" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1603" xml:space="preserve">48. </s>
  <s xml:id="echoid-s1604" xml:space="preserve">Complementum enim latitudinis iſtius, nempe grad. </s>
  <s xml:id="echoid-s1605" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1606" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1607" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1608" xml:space="preserve">ęquale eſt declina
<pb o="23" file="0043" n="43" rhead="LIBER PRIMVS."/>
tioni prædicti paralleli. </s>
  <s xml:id="echoid-s1609" xml:space="preserve">Sic quoque ſectio coni, cuius baſis parallelus eſt ♏, &amp; </s>
  <s xml:id="echoid-s1610" xml:space="preserve">♓, &amp; </s>
  <s xml:id="echoid-s1611" xml:space="preserve">horologii Hori-<lb/>zontalis ad latitudinem borealem grad. </s>
  <s xml:id="echoid-s1612" xml:space="preserve">78. </s>
  <s xml:id="echoid-s1613" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1614" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1615" xml:space="preserve">Parabole erit; </s>
  <s xml:id="echoid-s1616" xml:space="preserve">quippe cum huiuſce latitudinis com-<lb/>plementum, hoc eſt, grad. </s>
  <s xml:id="echoid-s1617" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1618" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1619" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1620" xml:space="preserve">æquale ſit declinationi paralleli ♏ &amp; </s>
  <s xml:id="echoid-s1621" xml:space="preserve">♓. </s>
  <s xml:id="echoid-s1622" xml:space="preserve">Idem dic de conis, <lb/>quorum baſes ſunt paralleli boreales prædictis oppoſiti, nempe parallelus ♋; </s>
  <s xml:id="echoid-s1623" xml:space="preserve">♊, &amp; </s>
  <s xml:id="echoid-s1624" xml:space="preserve">♌; </s>
  <s xml:id="echoid-s1625" xml:space="preserve">♉ υ, &amp; </s>
  <s xml:id="echoid-s1626" xml:space="preserve">♍, vbi <lb/>tamen polus antarcticus ſupra Horizontem eleuatur. </s>
  <s xml:id="echoid-s1627" xml:space="preserve">Ex his facile erit iudicare, quænam plana horolo-<lb/>giorum Parabolas faciant, Sole quemcunque parallelum poſſidente. </s>
  <s xml:id="echoid-s1628" xml:space="preserve">Si enim Sol exiſtat in parallelo ſe-<lb/>ptentrionali, quem circulus maximus plano horologii æquidiſtãs tangit, erit communis ſectio horologij, <lb/>&amp; </s>
  <s xml:id="echoid-s1629" xml:space="preserve">coni vmbræ baſim habentis parallelum auſtralem oppoſitum, Parabole; </s>
  <s xml:id="echoid-s1630" xml:space="preserve">vbi videlicet polus arcticus ſu-<lb/>pra horologii planum extollitur. </s>
  <s xml:id="echoid-s1631" xml:space="preserve">At vero ſi antarcticus polus ſupra planum horologii conſpiciatur, &amp; </s>
  <s xml:id="echoid-s1632" xml:space="preserve">Sol <lb/>obtineat parallelum auſtralem, quem circulus maximus horologii plano æquidiftans contingit, fiet Pa-<lb/>rabole in cono vmbræ, cuius baſis eſt parallelus ſeptentrionalis oppoſitus, vt ex dictis patet. </s>
  <s xml:id="echoid-s1633" xml:space="preserve">Nam in figu-<lb/>
<anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/>
ra ſuperiore, ſi B, ponatur polus arcticus, &amp; </s>
  <s xml:id="echoid-s1634" xml:space="preserve">Sol exiſtat in parallelo ſeptentrionali D E, deſcribet quidem <lb/>radius Solis conos A D E, A F G, ſed horologii planum H I, in cono vmbræ A F G, cuius baſis F G, paral-<lb/>lelo Solis D E, opponitur, faciet parabolen K L M. </s>
  <s xml:id="echoid-s1635" xml:space="preserve">Si uerò B, ponatur polus antarcticus, &amp; </s>
  <s xml:id="echoid-s1636" xml:space="preserve">Sol percur-<lb/>rat parallelum auſtralem D E, faciet eodem modo planum horologii parabolen in cono vmbræ ſepten-<lb/>trionali A F G, &amp;</s>
  <s xml:id="echoid-s1637" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1638" xml:space="preserve">In eadem quoque figura vides polum arcticum B, tantum eleuari ſupra planum F E, <lb/>tangens parallelum D E, Borealem, quantum eſt cõplementum declinationis paralleli oppoſiti auſtralis <lb/>F G, &amp;</s>
  <s xml:id="echoid-s1639" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1640" xml:space="preserve">cum altitudo poli ſit arcus B E, complementum uero declinationis arcus C F, qui illi æqualis <lb/>
<anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/>
eſt, propter æquales angulos ad verticem in centro E, quibus inſiſtunt. </s>
  <s xml:id="echoid-s1641" xml:space="preserve">In vniuerſum enim circulus qui-<lb/>libet maximus tangit illum parallelum, cuius declinatio æqualis eſt complemento altitudinis poli ſupra <lb/>illum circulum maximum, vel quod idem eſt, cuius declinationis complementum æquale eſt altitudi-<lb/>ni poli ſupra circulum maximum. </s>
  <s xml:id="echoid-s1642" xml:space="preserve">id quod figura ſatis indicat.</s>
  <s xml:id="echoid-s1643" xml:space="preserve"/>
</p>
<div xml:id="echoid-div84" type="float" level="2" n="2">
<note position="left" xlink:label="note-0042-10" xlink:href="note-0042-10a" xml:space="preserve">Quæ horologia <lb/>faciant in coni-<lb/>eis ſuperfic@eb<emph style="sub">9</emph>, <lb/>quarum baſes <lb/>ſunt quicũque <lb/>paralleli Solis, <lb/>Parabolas.</note>
<note position="left" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">26. tertĳ.</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div86" type="section" level="1" n="26">
<head xml:id="echoid-head29" xml:space="preserve">THEOREMA 5. PROPOSITIO 6.</head>
<p>
  <s xml:id="echoid-s1644" xml:space="preserve">SECTIONES communes earundem ſuperficierum conicarum, <lb/>
<anchor type="note" xlink:label="note-0043-04a" xlink:href="note-0043-04"/>
&amp; </s>
  <s xml:id="echoid-s1645" xml:space="preserve">plani horologij æquidiſtantis circulo maximo, qui baſes conicarum <lb/>ſuperficierum ſecat, Hyperbolę ſunt oppoſitæ, &amp; </s>
  <s xml:id="echoid-s1646" xml:space="preserve">ęquales.</s>
  <s xml:id="echoid-s1647" xml:space="preserve"/>
</p>
<div xml:id="echoid-div86" type="float" level="2" n="1">
<note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">Planum horolo <lb/>gii æquidiſtans <lb/>maximo circu-<lb/>lo baſes conica <lb/>rum ſuperficie-<lb/>rum ſecanti fa-<lb/>@it duas hyper-<lb/>bolas oppoſitas <lb/>&amp; æquales.</note>
</div>
  <figure>
    <image file="0043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0043-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s1648" xml:space="preserve">SINT in eadem Sphæra duæ ſuperficies conicæ, quæ prius; </s>
  <s xml:id="echoid-s1649" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1650" xml:space="preserve">H I, circulus maximus ſecans <lb/>vtramque baſim: </s>
  <s xml:id="echoid-s1651" xml:space="preserve">Cui circulo æquidiſtet planum horologii K L, faciens in ſuperficiebus conicis <lb/>ſectiones M N O, P Q R. </s>
  <s xml:id="echoid-s1652" xml:space="preserve">Dico ſectiones M N O, P Q R, Hyperbolas eſſe oppoſitas, &amp; </s>
  <s xml:id="echoid-s1653" xml:space="preserve">æquales. <lb/></s>
  <s xml:id="echoid-s1654" xml:space="preserve">Cum enim ſuperficies conicæ A D E, A F G, ad verticem A, coniunctæ, ſecentur plano K L, non <lb/>per verticem; </s>
  <s xml:id="echoid-s1655" xml:space="preserve">erit in vtraque ſuperficierum, per propoſ. </s>
  <s xml:id="echoid-s1656" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1657" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1658" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1659" xml:space="preserve">Apollonij, ſectio, quæ appella-<lb/>tur Hyperbole, &amp; </s>
  <s xml:id="echoid-s1660" xml:space="preserve">duarum ſectionum eadem erit diameter K L, &amp;</s>
  <s xml:id="echoid-s1661" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1662" xml:space="preserve">Hyperbolæ igitur ſunt MNO, <lb/>P Q R, oppoſitæ, &amp; </s>
  <s xml:id="echoid-s1663" xml:space="preserve">æquales quoque, vt ex dicta propoſ. </s>
  <s xml:id="echoid-s1664" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1665" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1666" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1667" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s1668" xml:space="preserve">elicitur. </s>
  <s xml:id="echoid-s1669" xml:space="preserve">Sectiones ergo <lb/>communes earundem ſuperficierum conicarum, &amp;</s>
  <s xml:id="echoid-s1670" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1671" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s1672" xml:space="preserve"/>
</p>
<pb o="24" file="0044" n="44" rhead="GNOMONICES"/>
  <figure>
    <image file="0044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0044-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div88" type="section" level="1" n="27">
<head xml:id="echoid-head30" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s1673" xml:space="preserve">QVOD ſi quando planum K L, cir culo maximo H I, æquidiſtans tantum à centro A, abſit, vt in fi-<lb/>gura B D C E, non ſecet vtramque ſuperficiem conicam, ſed vnam tantum, vel neutram, augenda erit <lb/>vtraque ſuperficies, donec à plano K L, ſecetur, vt in duabus appoſitis figuris vides.</s>
  <s xml:id="echoid-s1674" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Planũ horolo-<lb/>gii Meridiani, <lb/>atque æquidi-<lb/>ſtantis cuilibet <lb/>circulo horarũ <lb/>à meridie uel <lb/>media noctc, im <lb/>mo &amp; Vertica-<lb/>lis ad maiorẽ la <lb/>citudinẽ quàm <lb/>gr. 45 facit in co <lb/>nicis ſuperficie-<lb/>bus, quarũ ba-<lb/>ſes ſunt paralle <lb/>lus ſemper ap-<lb/>parentium ma-<lb/>ximus, &amp; maxi-<lb/>mus ſemper la-<lb/>tentium, duas <lb/>hyperbolas op-<lb/>poſitas, &amp; æqua <lb/>les.</note>
</div>
<div xml:id="echoid-div89" type="section" level="1" n="28">
<head xml:id="echoid-head31" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s1675" xml:space="preserve">CVM ergo &amp; </s>
  <s xml:id="echoid-s1676" xml:space="preserve">Meridianus, &amp; </s>
  <s xml:id="echoid-s1677" xml:space="preserve">circulus cuiuslibet horæ à meridie, vel media nocte, vt propoſ. </s>
  <s xml:id="echoid-s1678" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1679" xml:space="preserve">dice-<lb/>mus, ſiue Horizon rectus, immo &amp; </s>
  <s xml:id="echoid-s1680" xml:space="preserve">Verticalis circulus maioris latitudinis, quàm grad. </s>
  <s xml:id="echoid-s1681" xml:space="preserve">45. </s>
  <s xml:id="echoid-s1682" xml:space="preserve">ſecet vtrum que <lb/>parallelum, quorum alter maximus eſt eorum, qui ſemper apparent, alter maximus eorum, qui ſemper oc-<lb/>cultantur; </s>
  <s xml:id="echoid-s1683" xml:space="preserve">erunt communes ſectiones ſuperficierum conicarum baſes habentium dictos parallelos, quas <lb/>
<anchor type="note" xlink:label="note-0044-04a" xlink:href="note-0044-04"/>
faciunt plana horologiorum dictis circulis maximis æquidiſtantia, hyperbolæ oppoſitæ, &amp; </s>
  <s xml:id="echoid-s1684" xml:space="preserve">æquales.</s>
  <s xml:id="echoid-s1685" xml:space="preserve"/>
</p>
<div xml:id="echoid-div89" type="float" level="2" n="1">
<note position="left" xlink:label="note-0044-04" xlink:href="note-0044-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s1686" xml:space="preserve">ITA quoque communes ſectiones cuiuſque horologij, &amp; </s>
  <s xml:id="echoid-s1687" xml:space="preserve">conorum, quorum baſes paralleli ſunt Solis <lb/>minorem declinationem habentes, quàm quantum eſt cõplementum altitudinis poli ſupra circulum ma-<lb/>ximum, cui planum horologii æquidiſtat, hyperbolæ erunt oppoſitæ, &amp; </s>
  <s xml:id="echoid-s1688" xml:space="preserve">æquales. </s>
  <s xml:id="echoid-s1689" xml:space="preserve">Tales erunt ſectiones <lb/>conorum, quorum baſes ſunt paralleli ♋ &amp; </s>
  <s xml:id="echoid-s1690" xml:space="preserve">♑, ac proinde omnium aliorum inter hos, (cum alii om <lb/>nes minorem habeant declinationem, quàm illi) &amp; </s>
  <s xml:id="echoid-s1691" xml:space="preserve">horologii Horizontalis ad latitudinem minorẽ quàm <lb/>grad. </s>
  <s xml:id="echoid-s1692" xml:space="preserve">66. </s>
  <s xml:id="echoid-s1693" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1694" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1695" xml:space="preserve">quia hac ratione complementum altitudinis poli maius erit, quàm grad. </s>
  <s xml:id="echoid-s1696" xml:space="preserve">23. </s>
  <s xml:id="echoid-s1697" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1698" xml:space="preserve">30. <lb/></s>
  <s xml:id="echoid-s1699" xml:space="preserve">quæ eſt declinatio ♋, &amp; </s>
  <s xml:id="echoid-s1700" xml:space="preserve">♑. </s>
  <s xml:id="echoid-s1701" xml:space="preserve">Idem dic de ſectionibus eorundem conorum, &amp; </s>
  <s xml:id="echoid-s1702" xml:space="preserve">horologii cuiusuis ęqui-<lb/>diſtantis circulo maximo, ſupra quem polus mundi extollitur paucioribus gradibus, quam 66. </s>
  <s xml:id="echoid-s1703" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1704" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1705" xml:space="preserve"><lb/>Ex quibus facile cognoſces, quænam plana horologiorum hyperbolas faciant, Sole quemcunque paralle-<lb/>
<anchor type="note" xlink:label="note-0044-05a" xlink:href="note-0044-05"/>
lum percurrente. </s>
  <s xml:id="echoid-s1706" xml:space="preserve">Si enim Sol exiſtat in parallelo, quem circulus maximus plano horologii ęquidiſtans, <lb/>
<anchor type="note" xlink:label="note-0044-06a" xlink:href="note-0044-06"/>
atque adeo &amp; </s>
  <s xml:id="echoid-s1707" xml:space="preserve">eius oppoſitum ſecat, erunt communes ſectiones horologii, &amp; </s>
  <s xml:id="echoid-s1708" xml:space="preserve">conorum baſes habentium <lb/>parallelum illum, eiusq́; </s>
  <s xml:id="echoid-s1709" xml:space="preserve">oppoſitum, Hyperbolæ. </s>
  <s xml:id="echoid-s1710" xml:space="preserve">Quæ quidem omnia ex figura ſuperiore facile intelligi <lb/>poſſunt. </s>
  <s xml:id="echoid-s1711" xml:space="preserve">In vniuerſum autem circulus quilibet maximus illum parallelum ſecat, cuius declinatio minor <lb/>eſt complemento altitudinis poli ſupra circulum illum maximum, vel cuius declinationis complementũ <lb/>maius eſt altitudine poli ſupra circulum maximum, vt figura indicat.</s>
  <s xml:id="echoid-s1712" xml:space="preserve"/>
</p>
<div xml:id="echoid-div90" type="float" level="2" n="2">
<note position="left" xlink:label="note-0044-05" xlink:href="note-0044-05a" xml:space="preserve">Quæ horologia <lb/>in ſuperficiebus <lb/>eonicis, quarũ <lb/>baſes sũt cũq; <lb/>paralleli Aequa <lb/>toris, facianthy <lb/>perbolas oppoſi <lb/>tas &amp; æquales.</note>
<note position="left" xlink:label="note-0044-06" xlink:href="note-0044-06a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div92" type="section" level="1" n="29">
<head xml:id="echoid-head32" xml:space="preserve">THEOREMA 6. PROPOSITIO 7.</head>
<p>
  <s xml:id="echoid-s1713" xml:space="preserve">SECTIO communis ſuperficierum earundem conicarum, &amp; </s>
  <s xml:id="echoid-s1714" xml:space="preserve">pla-<lb/>
<anchor type="note" xlink:label="note-0044-07a" xlink:href="note-0044-07"/>
ni horologii æquidiſtantis circulo maximo, qui neque baſibus conica-<lb/>
<anchor type="note" xlink:label="note-0044-08a" xlink:href="note-0044-08"/>
rum ſuperficierum ęquidiſtat, neque eas tangit, neque ſecat, Ellipſis eſt.</s>
  <s xml:id="echoid-s1715" xml:space="preserve"/>
</p>
<div xml:id="echoid-div92" type="float" level="2" n="1">
<note position="left" xlink:label="note-0044-07" xlink:href="note-0044-07a" xml:space="preserve">Planum horo-<lb/>logii æquidiſtãs <lb/>circulo maxi-<lb/>mo baſibus co-<lb/>nicarum ſuper-<lb/>ficierum neque <lb/>æquidiſtanti, <lb/>neque eas tan-<lb/>genti, aut ſecan <lb/>ti, facit in altera <lb/>ſuperficierum <lb/>Ellipſim.</note>
<note position="left" xlink:label="note-0044-08" xlink:href="note-0044-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s1716" xml:space="preserve">SINT in eadem Sphæra duæ conicæ ſuperficies, quæ prius; </s>
  <s xml:id="echoid-s1717" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1718" xml:space="preserve">circulus maximus H I, neque <lb/>æquidiſtet baſibus D E, F G, neque eas tangat, neque ſecet, etiamſi in infinitum augeantur ipſæ <lb/>ſuperficies: </s>
  <s xml:id="echoid-s1719" xml:space="preserve">Cui circulo æquidiſtet planum horologii K L, faciens in conica ſuperficie A F G, <lb/>fectionem M N O. </s>
  <s xml:id="echoid-s1720" xml:space="preserve">Dico M N O, Ellipſim eſſe. </s>
  <s xml:id="echoid-s1721" xml:space="preserve">Ducatur enim per polos circulorum F G, H I, at-<lb/>que adeo &amp; </s>
  <s xml:id="echoid-s1722" xml:space="preserve">per polos circuli K L, quem planum horologii in Sphæra efficit, ex propoſ. </s>
  <s xml:id="echoid-s1723" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1724" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1725" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s1726" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s1727" xml:space="preserve">(cum huius poli ſint iidem, qui circuli H I, per propoſ. </s>
  <s xml:id="echoid-s1728" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1729" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1730" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1731" xml:space="preserve">Theod.) </s>
  <s xml:id="echoid-s1732" xml:space="preserve">circulus ma-<lb/>ximus B D C E, qui ſecabit, per propoſ. </s>
  <s xml:id="echoid-s1733" xml:space="preserve">15. </s>
  <s xml:id="echoid-s1734" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1735" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1736" xml:space="preserve">Theodoſii, circulos F G, K L, bifariam, &amp; </s>
  <s xml:id="echoid-s1737" xml:space="preserve">ad angu <lb/>los rectos per rectas F G, K L, quæ ſe mutuo interſecabunt, nempe in puncto P, propterea quòd
<pb o="25" file="0045" n="45" rhead="LIBER PRIMVS."/>
non æquidiſtent inter ſe; </s>
  <s xml:id="echoid-s1738" xml:space="preserve">facietq́ue <lb/>
<anchor type="figure" xlink:label="fig-0045-01a" xlink:href="fig-0045-01"/>
communes ſectiones H I, K L, pla-<lb/>norum parallelorum H I, K L, pa-<lb/>
<anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/>
rallelas. </s>
  <s xml:id="echoid-s1739" xml:space="preserve">Faciat quoque idem circu-<lb/>lus B D C E, triangulum per axem <lb/>A F G, ſecans rectam K L, &amp; </s>
  <s xml:id="echoid-s1740" xml:space="preserve">ſectio-<lb/>nem conicam in M. </s>
  <s xml:id="echoid-s1741" xml:space="preserve">Secet etiã pla-<lb/>num K L, per rectam L M, tranſiens <lb/>planum circuli F G, (ſecabunt au-<lb/>tem neceſſario ſe mutuo plana F G, <lb/>
<anchor type="note" xlink:label="note-0045-02a" xlink:href="note-0045-02"/>
K L, cum non ponantur parallela.) <lb/></s>
  <s xml:id="echoid-s1742" xml:space="preserve">vel certè eius planum productum, <lb/>per rectam N P O, quæ per punctũ <lb/>P, ducitur. </s>
  <s xml:id="echoid-s1743" xml:space="preserve">Cum enim recta K L, <lb/>rectam F G, ſecet in P, tranſibit pla <lb/>num per K L, ductum etiam per P; </s>
  <s xml:id="echoid-s1744" xml:space="preserve"><lb/>ac proinde communis ſectio pla-<lb/>norum F G, K L, per punctum P, <lb/>tranſibit. </s>
  <s xml:id="echoid-s1745" xml:space="preserve">Quoniam igitur plana <lb/>F G, k L, recta ſuntad planum cir-<lb/>
<anchor type="note" xlink:label="note-0045-03a" xlink:href="note-0045-03"/>
culi B D C E, propterea quòd hic <lb/>circulus illa plana ad rectos angu-<lb/>los ſecat, vt paulo ante oſtendimus; <lb/></s>
  <s xml:id="echoid-s1746" xml:space="preserve">
<anchor type="note" xlink:label="note-0045-04a" xlink:href="note-0045-04"/>
erit quoque eorum communis ſe-<lb/>ctio N O, ad idẽ recta, atque adeo <lb/>per defin. </s>
  <s xml:id="echoid-s1747" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1748" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1749" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1750" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1751" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1752" xml:space="preserve">ad rectã <lb/>F G, baſim trianguli per axim, per-<lb/>pendicularis erit. </s>
  <s xml:id="echoid-s1753" xml:space="preserve">Et quia rectæ <lb/>H I, k L, oſtenſæ ſunt parallelæ, <lb/>
<anchor type="note" xlink:label="note-0045-05a" xlink:href="note-0045-05"/>
erunt anguli H A M, k M A, duo-<lb/>
<anchor type="note" xlink:label="note-0045-06a" xlink:href="note-0045-06"/>
bus rectis æquales; </s>
  <s xml:id="echoid-s1754" xml:space="preserve">atque adeo an-<lb/>guli F A M, k M A, duobus rectis <lb/>minores. </s>
  <s xml:id="echoid-s1755" xml:space="preserve">Conuenient ergo, per <lb/>pronunciatum 11. </s>
  <s xml:id="echoid-s1756" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1757" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1758" xml:space="preserve">Euclidis, <lb/>rectæ A F, k L, productæ ad partes <lb/>F, k, ac proinde planum horologii <lb/>per k L, ductum latus A F, ſecabit <lb/>ad eaſdem partes F, k. </s>
  <s xml:id="echoid-s1759" xml:space="preserve">Quam ob <lb/>rem, cum conus A F G, ſecetur pla-<lb/>no B D C E, per axem, ſecetur autẽ <lb/>
<anchor type="note" xlink:label="note-0045-07a" xlink:href="note-0045-07"/>
&amp; </s>
  <s xml:id="echoid-s1760" xml:space="preserve">altero plano k L, conueniente <lb/>cum utroque latere A F, A G, trian-<lb/>guli per axem A F G, quod quidem <lb/>planum k L, neque æquidiſtat baſi <lb/>F G, neque triangulum ad verticẽ <lb/>A, aufert ſimile &amp; </s>
  <s xml:id="echoid-s1761" xml:space="preserve">ſubcontrarie po-<lb/>ſitum triangulo per axem, propte-<lb/>rea quòd angulus A M P, maior ſit <lb/>
<anchor type="note" xlink:label="note-0045-08a" xlink:href="note-0045-08"/>
angulo A G F, externus interno, <lb/>hoc eſt, angulo A F G, cum hic æqualis ſit angulo A G F; </s>
  <s xml:id="echoid-s1762" xml:space="preserve">eſtq́; </s>
  <s xml:id="echoid-s1763" xml:space="preserve">N O, communis ſectio plani ſecan-<lb/>
<anchor type="note" xlink:label="note-0045-09a" xlink:href="note-0045-09"/>
<anchor type="note" xlink:label="note-0045-10a" xlink:href="note-0045-10"/>
tis k L, &amp; </s>
  <s xml:id="echoid-s1764" xml:space="preserve">baſis coni F G, perpendicularis ad F G, baſim trianguli per axem, vel certè ad eam, quæ <lb/>in directum ipſi conſtituitur; </s>
  <s xml:id="echoid-s1765" xml:space="preserve">erit communis ſectio M N O, per propoſ. </s>
  <s xml:id="echoid-s1766" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1767" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1768" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1769" xml:space="preserve">Apollonij, El-<lb/>
<anchor type="note" xlink:label="note-0045-11a" xlink:href="note-0045-11"/>
lipſis. </s>
  <s xml:id="echoid-s1770" xml:space="preserve">Sectio ergo communis ſuperficierum earundem, &amp;</s>
  <s xml:id="echoid-s1771" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1772" xml:space="preserve">quod oſtendendum erat.</s>
  <s xml:id="echoid-s1773" xml:space="preserve"/>
</p>
<div xml:id="echoid-div93" type="float" level="2" n="2">
  <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a">
    <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0045-01"/>
  </figure>
<note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">16. undec.</note>
<note position="left" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0045-05" xlink:href="note-0045-05a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0045-06" xlink:href="note-0045-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0045-07" xlink:href="note-0045-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0045-08" xlink:href="note-0045-08a" xml:space="preserve">16. primi.</note>
<note position="left" xlink:label="note-0045-09" xlink:href="note-0045-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0045-10" xlink:href="note-0045-10a" xml:space="preserve">5. primi.</note>
<note position="right" xlink:label="note-0045-11" xlink:href="note-0045-11a" xml:space="preserve">Planũ horolo-<lb/>gij Verticalis ad <lb/>minorẽ latitu-<lb/>dinẽ, quàm gr. <lb/>45 facit in alte <lb/>ra ſuperficierũ <lb/>conicarũ, quarũ <lb/>baſes ſunt pa-<lb/>rallelus ſemper <lb/>apparentiũ ma-<lb/>ximus, &amp; maxi-<lb/>mus ſemper oc-<lb/>cultorum, Elli-<lb/>pſim.</note>
</div>
</div>
<div xml:id="echoid-div95" type="section" level="1" n="30">
<head xml:id="echoid-head33" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s1774" xml:space="preserve">IGITVR, quia Verticalis circulus minoris latitudinis, quàm grad. </s>
  <s xml:id="echoid-s1775" xml:space="preserve">45. </s>
  <s xml:id="echoid-s1776" xml:space="preserve">neque æquidiſtat parallelis, <lb/>quorum vnus maximus eſt eorum, qui ſemper apparent, alter verò maximus eorum, qui perpetuo ſub Ho-<lb/>rizonte latent, neque ipſos tangit, neque ſecat; </s>
  <s xml:id="echoid-s1777" xml:space="preserve">erit communis ſectio plani horologii Verticalis, cuius la-<lb/>titudo minor eſt, quàm grad. </s>
  <s xml:id="echoid-s1778" xml:space="preserve">45. </s>
  <s xml:id="echoid-s1779" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1780" xml:space="preserve">coni, cuius baſis parallelus eſt maximus eorum, qui ſemper occultantur <lb/>ſub terra, ſi planum horologii ſit ad partes poli occulti, reſpiciatq́; </s>
  <s xml:id="echoid-s1781" xml:space="preserve">polum conſpicuum, vel maximus eorũ, <lb/>qui perpetuo apparent, ſi horologii planum ad partes poli conſpicui recedat, reſpiciatq́; </s>
  <s xml:id="echoid-s1782" xml:space="preserve">partes poli oc-<lb/>@ulti, Ellipſis.</s>
  <s xml:id="echoid-s1783" xml:space="preserve"/>
</p>
<pb o="26" file="0046" n="46" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s1784" xml:space="preserve">EODEM modo communis ſectio cuiuslibet horologii, &amp; </s>
  <s xml:id="echoid-s1785" xml:space="preserve">coni, cuius baſis maiorem habet declina-<lb/>
<anchor type="note" xlink:label="note-0046-01a" xlink:href="note-0046-01"/>
tionem auſtralẽ quàm quantum eſt complementum altitudinis poli arctici ſupra circulum maximum, cui <lb/>planum horologii æquidiſtat, Ellipſis erit. </s>
  <s xml:id="echoid-s1786" xml:space="preserve">Talis erit ſectio coni baſim habentis parallelum ♑, &amp; </s>
  <s xml:id="echoid-s1787" xml:space="preserve">horolo-<lb/>gij horizontalis ad latitudinem ſeptentrionalem, quæ excedit grad. </s>
  <s xml:id="echoid-s1788" xml:space="preserve">66. </s>
  <s xml:id="echoid-s1789" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1790" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1791" xml:space="preserve">quia hac ratione declinatio <lb/>♑, nempe grad. </s>
  <s xml:id="echoid-s1792" xml:space="preserve">23. </s>
  <s xml:id="echoid-s1793" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1794" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1795" xml:space="preserve">maior erit complemento altitudinis poli. </s>
  <s xml:id="echoid-s1796" xml:space="preserve">Huiuſmodi quoque erit ſectio <lb/>coni baſim habentis parallelum ♐, &amp; </s>
  <s xml:id="echoid-s1797" xml:space="preserve">♒, atque horologii horizontalis ad latitudinem Borealem, quę <lb/>excedit grad. </s>
  <s xml:id="echoid-s1798" xml:space="preserve">69. </s>
  <s xml:id="echoid-s1799" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1800" xml:space="preserve">48. </s>
  <s xml:id="echoid-s1801" xml:space="preserve">Nam huius paralleli declinatio continens grad. </s>
  <s xml:id="echoid-s1802" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1803" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1804" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1805" xml:space="preserve">maior eſt comple-<lb/>mento altitudinis poli. </s>
  <s xml:id="echoid-s1806" xml:space="preserve">Talis quoque erit ſectio coni baſim habentis parallelum ♏, &amp; </s>
  <s xml:id="echoid-s1807" xml:space="preserve">♓, atque horo-<lb/>logii horizontalis ad latitudinem ſeptentrionalem maiorem, quàm grad. </s>
  <s xml:id="echoid-s1808" xml:space="preserve">78. </s>
  <s xml:id="echoid-s1809" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1810" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1811" xml:space="preserve">cum paralleli huius <lb/>declinatio, nimirum grad. </s>
  <s xml:id="echoid-s1812" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1813" xml:space="preserve">min. </s>
  <s xml:id="echoid-s1814" xml:space="preserve">30. </s>
  <s xml:id="echoid-s1815" xml:space="preserve">excedat hoc modo complementum altitudinis poli. </s>
  <s xml:id="echoid-s1816" xml:space="preserve">Idem dic de <lb/>conis, quorum baſes ſunt paralleli Boreales prædictis oppoſiti, vt parallelus ♋; </s>
  <s xml:id="echoid-s1817" xml:space="preserve">♊, &amp; </s>
  <s xml:id="echoid-s1818" xml:space="preserve">♌; </s>
  <s xml:id="echoid-s1819" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s1820" xml:space="preserve">♍, <lb/>
<anchor type="note" xlink:label="note-0046-02a" xlink:href="note-0046-02"/>
vbi polus tamen antarcticus ſupra Horizontem extollitur.</s>
  <s xml:id="echoid-s1821" xml:space="preserve"/>
</p>
<div xml:id="echoid-div95" type="float" level="2" n="1">
<note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">Quæ horologia <lb/>in ſuperficiebus <lb/>conicis, quarum <lb/>bales ſunt qui-<lb/>cunque paralle-<lb/>li Aequatoris, <lb/>t<unsure/>aciant Ellip@es.</note>
<note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s1822" xml:space="preserve">HINC facile diſces, quęnam plana horologiorum Ellipſes faciant, Sole exiſtente in quouis paralle-<lb/>lo. </s>
  <s xml:id="echoid-s1823" xml:space="preserve">Etenim ſi Sol exiſtat in parallelo ſeptẽtrionali, cui circulus maximus plano horologii æquidiſtans ne-<lb/>que æquidiſtat, neque eum tangit, neque ſecat, erit communis ſectio horologii, &amp; </s>
  <s xml:id="echoid-s1824" xml:space="preserve">coni vmbrę baſim ha-<lb/>bentis parallelum auſtralem oppoſitum, Ellipſis; </s>
  <s xml:id="echoid-s1825" xml:space="preserve">vbi nimirum polus arcticus ſupra horologii planum ele <lb/>uatur. </s>
  <s xml:id="echoid-s1826" xml:space="preserve">At uerò ſi antarcticus polus ſupra planum horologii extollatur, &amp; </s>
  <s xml:id="echoid-s1827" xml:space="preserve">Sol ſit in parallelo auſtrali, cui <lb/>maximus circulus plano horologii æquidiſtans neque ęquidiſtat, neque eum tangit, neq; </s>
  <s xml:id="echoid-s1828" xml:space="preserve">ſecat, fiet Ellipſis <lb/>in cono vmbræ, cuius baſis parallelus eſt borealis oppoſitus, vt ex dictis perſpicuum eſt. </s>
  <s xml:id="echoid-s1829" xml:space="preserve">Tunc autem cir-<lb/>culus maximus parallelo cuiuis neque ęquidiſtat, neque eum tangit, neque ſecat, quando declinatio pa-<lb/>ralleli maior eſt complemento altitudinis poli ſupra circulum maximum: </s>
  <s xml:id="echoid-s1830" xml:space="preserve">Vel quando cõplementum de-<lb/>clinationis paralleli minus eſt altitudine poli ſupra maximum circulum, vt ex figura manifeſtum eſt.</s>
  <s xml:id="echoid-s1831" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div97" type="section" level="1" n="31">
<head xml:id="echoid-head34" xml:space="preserve">PROBLEMA 2. PROPOSITIO 8.</head>
<p>
  <s xml:id="echoid-s1832" xml:space="preserve">DATO cono, &amp; </s>
  <s xml:id="echoid-s1833" xml:space="preserve">diametro conicæ ſectionis, ipſam conicam ſe-<lb/>ctionem in plano deſcribere.</s>
  <s xml:id="echoid-s1834" xml:space="preserve"/>
</p>
  <figure>
    <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
  <figure>
    <image file="0046-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-02"/>
  </figure>
<note position="left" xml:space="preserve">40</note>
  <figure>
    <image file="0046-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-03"/>
  </figure>
<note position="left" xml:space="preserve">50</note>
  <figure>
    <image file="0046-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-04"/>
  </figure>
<p>
  <s xml:id="echoid-s1835" xml:space="preserve">SIT datus conus A B C, qui ſecetur plano per axem faciente, per propoſ. </s>
  <s xml:id="echoid-s1836" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1837" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1838" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1839" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s1840" xml:space="preserve">trian-<lb/>
<anchor type="note" xlink:label="note-0046-07a" xlink:href="note-0046-07"/>
gulum per axem A B C; </s>
  <s xml:id="echoid-s1841" xml:space="preserve">ſecetur autem &amp; </s>
  <s xml:id="echoid-s1842" xml:space="preserve">alio plano faciente vel Parabolen, vel Hyperbolen, vel <lb/>Ellipſim, cuius diameter D E, æquidiſtans quidem trianguli lateri A C, in Parabola, ſecans verò <lb/>idem latus A C, productum ſupra verticem A, in Hyperbola, vel intra conum, ſiue hoc fiat ſupra
<pb o="27" file="0047" n="47" rhead="LIBER PRIMVS."/>
baſim B C, ſiue infra in Ellipſi, vt ex tribus propoſitionibus proximè dictis conſtat. </s>
  <s xml:id="echoid-s1843" xml:space="preserve">Sumantur <lb/>in diametro E D, quotcunque partes ſiue æquales, ſiue inæquales E k, k L, &amp; </s>
  <s xml:id="echoid-s1844" xml:space="preserve">per puncta k, L, agan-<lb/>tur baſi B C, parallelæ F H, G I; </s>
  <s xml:id="echoid-s1845" xml:space="preserve">eruntq́ue tam partes C H, H I, quàm E k, k L, (ſumendo in Elli-<lb/>
<anchor type="note" xlink:label="note-0047-01a" xlink:href="note-0047-01"/>
pſi punctum E, in B C, baſi trianguli) partibus B F, F G, proportionales: </s>
  <s xml:id="echoid-s1846" xml:space="preserve">Immo in parabola æqua-<lb/>les ſunt partes C H, H I, partibus E k, k L, propter parallelogramma C k, k I.</s>
  <s xml:id="echoid-s1847" xml:space="preserve"/>
</p>
<div xml:id="echoid-div97" type="float" level="2" n="1">
<note position="left" xlink:label="note-0046-07" xlink:href="note-0046-07a" xml:space="preserve">Qua ratione co <lb/>nica ſectio, cu-<lb/>ius diameter in <lb/>cono data ſit, <lb/>deſcribatur in <lb/>plano.</note>
<note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">2. ſexti.</note>
</div>
<note position="right" xml:space="preserve">34. primi.</note>
<p>
  <s xml:id="echoid-s1848" xml:space="preserve">QVOD ſi conus rectus fuerit, vt ſunt omnes illi, quibus in deſcriptionibus horologiorum <lb/>vtimur, (omnes enim hi recti ſunt, cum eorum axes ſint partes axis mundi, qui ad parallelos pri-<lb/>mi motus, nempead baſes conorum, per propoſ. </s>
  <s xml:id="echoid-s1849" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1850" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1851" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1852" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s1853" xml:space="preserve">rectus eſt) commodiſſime ita <lb/>agemus. </s>
  <s xml:id="echoid-s1854" xml:space="preserve">Sumantur in recta B D, quotcunque partes ſiue æquales, ſiue inæquales B F, F G, &amp; </s>
  <s xml:id="echoid-s1855" xml:space="preserve">his <lb/>æquales in alio latere C H, H I, ſingulæ ſingulis, iunganturq́; </s>
  <s xml:id="echoid-s1856" xml:space="preserve">rectæ F H, G I, ſecantes diametrum <lb/>
<anchor type="note" xlink:label="note-0047-03a" xlink:href="note-0047-03"/>
D E, in K, L. </s>
  <s xml:id="echoid-s1857" xml:space="preserve">Nam hę lineę, cum ſecent latera A B, A C, proportionaliter, parallelæ erunt, propor <lb/>
<anchor type="note" xlink:label="note-0047-04a" xlink:href="note-0047-04"/>
tionalesq́; </s>
  <s xml:id="echoid-s1858" xml:space="preserve">propterea erunt partes E K, K L, partibus B F, F G. </s>
  <s xml:id="echoid-s1859" xml:space="preserve">Exponatur deinde ſeorſum baſis <lb/>B E C, trianguli A B C, &amp; </s>
  <s xml:id="echoid-s1860" xml:space="preserve">ex puncto E, quod inſtar ſit omnium punctorum E, K, L, perpendicula-<lb/>ris educatur E M, atque in rectam B C, ex puncto E, in vtramque partem transferantur partes <lb/>K F, K H, &amp; </s>
  <s xml:id="echoid-s1861" xml:space="preserve">L G, L I; </s>
  <s xml:id="echoid-s1862" xml:space="preserve">ita vt EF, E G, partibus K F, L G, &amp; </s>
  <s xml:id="echoid-s1863" xml:space="preserve">E H, E I, partibus K H, L I, ſint equales: <lb/></s>
  <s xml:id="echoid-s1864" xml:space="preserve">quæ quidem ex parte C, in parabola omnes in punctum C, cadent, propterea quòd E C, K H, L I, <lb/>
<anchor type="note" xlink:label="note-0047-05a" xlink:href="note-0047-05"/>
ęquales ſint. </s>
  <s xml:id="echoid-s1865" xml:space="preserve">In Hyperbola autem ſemper minores fient, quàm E C, &amp; </s>
  <s xml:id="echoid-s1866" xml:space="preserve">in Ellipſi maiores, vt patet. <lb/></s>
  <s xml:id="echoid-s1867" xml:space="preserve">In omnibus tamen erunt partes B F, FG, in primis figuris, (voco primas figuras, ipſos conos, ſecun-<lb/>das autem, eas, in quibus ſeorſum expoſuimus baſim B E C.) </s>
  <s xml:id="echoid-s1868" xml:space="preserve">partibus B F, F G, in ſecundis, nec <lb/>non &amp; </s>
  <s xml:id="echoid-s1869" xml:space="preserve">C H, H I, in primis, partibus C H, H I, in ſecundis proportionales. </s>
  <s xml:id="echoid-s1870" xml:space="preserve">Ducta enim G N, in <lb/>
<anchor type="note" xlink:label="note-0047-06a" xlink:href="note-0047-06"/>
primis figuris, parallela ipſi D E, erit vt G B, ad B N, ita G F, ad F O; </s>
  <s xml:id="echoid-s1871" xml:space="preserve">(cum triangula G B N, GFO, <lb/>
<anchor type="note" xlink:label="note-0047-07a" xlink:href="note-0047-07"/>
ſimilia ſint, ex corolla. </s>
  <s xml:id="echoid-s1872" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s1873" xml:space="preserve">4 lib. </s>
  <s xml:id="echoid-s1874" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1875" xml:space="preserve">Euclidis) &amp; </s>
  <s xml:id="echoid-s1876" xml:space="preserve">permutando, vt G B, ad G F, ita B N, ad F O. <lb/></s>
  <s xml:id="echoid-s1877" xml:space="preserve">Cum ergo B N, in primis figuris, equalis ſit ipſi B G, in ſecundis; </s>
  <s xml:id="echoid-s1878" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1879" xml:space="preserve">F O, in primis, ipſi F G, in ſe-<lb/>cundis; </s>
  <s xml:id="echoid-s1880" xml:space="preserve">(propterea quòd N E, ipſi G L, in primis, hoc eſt, ipſi G E, in ſecundis, ſit æqualis; </s>
  <s xml:id="echoid-s1881" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1882" xml:space="preserve">B N, <lb/>idcirco ipſi B G, &amp; </s>
  <s xml:id="echoid-s1883" xml:space="preserve">F O, ipſi F G. </s>
  <s xml:id="echoid-s1884" xml:space="preserve">Poſitæ enim ſunt E B, E F, E G, in ſecundis figuris ipſis E B, K F, <lb/>L G, in primis, æquales.) </s>
  <s xml:id="echoid-s1885" xml:space="preserve">erit quoque vt G B, ad G F, in primis, ita B G, ad F G, in ſecundis; </s>
  <s xml:id="echoid-s1886" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1887" xml:space="preserve">di-<lb/>uidendo, vt F B, ad G F, in primis, ita B F, ad F G, in ſecundis. </s>
  <s xml:id="echoid-s1888" xml:space="preserve">Idemq́; </s>
  <s xml:id="echoid-s1889" xml:space="preserve">oſtendemus de C H, H I, <lb/>ſi ex I, ducatur in primis figuris ipſi D E, parallela. </s>
  <s xml:id="echoid-s1890" xml:space="preserve">Vnde ſi B F, F G, ęquales fuerint in primis fi-<lb/>guris, erunt &amp; </s>
  <s xml:id="echoid-s1891" xml:space="preserve">E K, K L, in primis, nec non &amp; </s>
  <s xml:id="echoid-s1892" xml:space="preserve">B F, F G, &amp; </s>
  <s xml:id="echoid-s1893" xml:space="preserve">C H, H I, in ſecundis, æquales, vt ex fi-<lb/>guris apparet. </s>
  <s xml:id="echoid-s1894" xml:space="preserve">Sumpſimus enim facilitatis gratia partes B F, F G, in primis figuris æquales.</s>
  <s xml:id="echoid-s1895" xml:space="preserve"/>
</p>
<div xml:id="echoid-div98" type="float" level="2" n="2">
<note position="left" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0047-04" xlink:href="note-0047-04a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0047-05" xlink:href="note-0047-05a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0047-06" xlink:href="note-0047-06a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0047-07" xlink:href="note-0047-07a" xml:space="preserve">4. ſexti.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s1896" xml:space="preserve">POST Hæc circa diametros B C, F H, G I, ſemicirculi deſcribantur ſecantes rectam E M, in <lb/>punctis M, P, Q. </s>
  <s xml:id="echoid-s1897" xml:space="preserve">Habebuntur autem ſemidiametri, ſi axis coni in primis figuris ducatur ſecans ba-<lb/>ſim trianguli bifariam. </s>
  <s xml:id="echoid-s1898" xml:space="preserve">Hic enim diuidet etiam omnes diametros F H, G I, &amp; </s>
  <s xml:id="echoid-s1899" xml:space="preserve">reliquas, bifariam, <lb/>vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s1900" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1901" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1902" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1903" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1904" xml:space="preserve">oſtẽdimus. </s>
  <s xml:id="echoid-s1905" xml:space="preserve">Quare ſi in primis figuris accipiamus diſtantias in-<lb/>ter axem coni, &amp; </s>
  <s xml:id="echoid-s1906" xml:space="preserve">puncta E, K, L, easq́; </s>
  <s xml:id="echoid-s1907" xml:space="preserve">transferamus in ſecundas figuras à puncto E, in lineã<unsure/> B E C, <lb/>vel ad partes B, vel ad partes C, prout primæ figuræ indicant, habebimus centra, &amp;</s>
  <s xml:id="echoid-s1908" xml:space="preserve">c.</s>
  <s xml:id="echoid-s1909" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1910" xml:space="preserve">POSTREMO diameter ſectionis conicæ D E, ſeorſum diuidatur, vt in cono, hoc eſt, E K, <lb/>K L, ęquales ſint partibus E K, KL, in cono, ſingulę ſingulis: </s>
  <s xml:id="echoid-s1911" xml:space="preserve">Et per E, K, L, ad D E, perpendicula-<lb/>res educantur; </s>
  <s xml:id="echoid-s1912" xml:space="preserve">quod quidem facile fiet, &amp; </s>
  <s xml:id="echoid-s1913" xml:space="preserve">breuiſſimè, (præſertim quando plurima puncta fuerint <lb/>ſumpta in diametro D E,) ſi per E, perpendicularem eduxeris, à cuius duobus punctis ipſi D E, pa-<lb/>
<anchor type="note" xlink:label="note-0047-09a" xlink:href="note-0047-09"/>
rallelæ erigantur, diuidanturq́ue, vt D E. </s>
  <s xml:id="echoid-s1914" xml:space="preserve">Nam rectæ puncta diuiſionum coniungẽtes erunt ad DE, <lb/>perpendiculares in punctis K, L, propterea quòd hac ratione ad rectas E K, E L, parallelogramma <lb/>
<anchor type="note" xlink:label="note-0047-10a" xlink:href="note-0047-10"/>
ſint conſtituta, quæ rectangula ſunt, obangulum rectum ad E, conſtitutum, vt manifeſtum eſt. <lb/></s>
  <s xml:id="echoid-s1915" xml:space="preserve">Quod ſi ordinatim applicatæ ad D E, diametrum ſectionis non ſint ad ipſam perpendiculares, (vt <lb/>fit in conis ſcalenis, cum triangulum per axem non eſt rectum ad baſim coni, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s1916" xml:space="preserve"><lb/>7. </s>
  <s xml:id="echoid-s1917" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1918" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1919" xml:space="preserve">Apollonii) ducendę erunt per puncta E, K, L, in tertiis figuris, lineę parallelę facientes an-<lb/>gulos ad diametrum D E, ęquales illis, quos ordinatim applicatę in primis figuris faciunt.</s>
  <s xml:id="echoid-s1920" xml:space="preserve"/>
</p>
<div xml:id="echoid-div99" type="float" level="2" n="3">
<note position="left" xlink:label="note-0047-09" xlink:href="note-0047-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0047-10" xlink:href="note-0047-10a" xml:space="preserve">29. primi.</note>
</div>
<p>
  <s xml:id="echoid-s1921" xml:space="preserve">POST hęc ex perpendicularibus, parallelisve per puncta E, K, L, ductis, in tertiis figuris, ad <lb/>vtramque partem punctorum E, K, L, abſcindantur rectę E M, k P, L Q, rectis E M, E P, E Q, in <lb/>ſecundis figuris, ęquales, nimirum k P, ęqualis illi, quę inter diametrum F H, &amp; </s>
  <s xml:id="echoid-s1922" xml:space="preserve">eius ſemicirculũ <lb/>
<anchor type="note" xlink:label="note-0047-11a" xlink:href="note-0047-11"/>
intercipitur, qualis eſt E P, in ſecundis figuris; </s>
  <s xml:id="echoid-s1923" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1924" xml:space="preserve">L Q, equalis ipſi E Q, inter diametrum G I, <lb/>eiusq́ ſemicirculum poſitam, &amp; </s>
  <s xml:id="echoid-s1925" xml:space="preserve">ſic de cęteris, obſeruando diligenter, quę puncta diametri D E, <lb/>quibus diametris ſemicirculorum reſpondeant. </s>
  <s xml:id="echoid-s1926" xml:space="preserve">Iam ſi puncta D, Q, P, &amp;</s>
  <s xml:id="echoid-s1927" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1928" xml:space="preserve">appoſitè linea qua-<lb/>dam flexa coniunxeris, deſcripta erit ſectio conica propoſita, nempe Parabole, Hyperbole, vel El-<lb/>lipſis, vt mox demonſtrabimus. </s>
  <s xml:id="echoid-s1929" xml:space="preserve">Ex his manifeſtum eſt, quò crebriora fuerint puncta in diame-<lb/>tro D E, eò aptius ſectionem conicam deſcribi, vt vides factum eſſe in Hyperbola, &amp; </s>
  <s xml:id="echoid-s1930" xml:space="preserve">Ellipſi vtra-<lb/>que; </s>
  <s xml:id="echoid-s1931" xml:space="preserve">ſumptum enim eſt in his ſectionibus aliud punctum præter K, L. </s>
  <s xml:id="echoid-s1932" xml:space="preserve">Quod ſi augere inſtituas <lb/>Parabolẽ, &amp; </s>
  <s xml:id="echoid-s1933" xml:space="preserve">Hyperbolem, augendi erunt coni, &amp; </s>
  <s xml:id="echoid-s1934" xml:space="preserve">puncta infra baſim B C, ſumenda ad ęqualitatẽ<unsure/> <lb/>punctorum F, G, &amp;</s>
  <s xml:id="echoid-s1935" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1936" xml:space="preserve">vt figurę indicant. </s>
  <s xml:id="echoid-s1937" xml:space="preserve">Quod idem dicendum eſt de Ellipſi, cuius diameter ſecet <lb/>alterum latus trianguli per axem infra baſim, vt in ſecunda Ellipſi; </s>
  <s xml:id="echoid-s1938" xml:space="preserve">alias enim pars tantum Ellipſis <lb/>deſcriberetur M P Q D Q P M. </s>
  <s xml:id="echoid-s1939" xml:space="preserve">In priori porrò Ellipſi, cuius diameter baſim trianguli non ſecat,
<pb o="28" file="0048" n="48" rhead="GNOMONICES"/>
non deſcribitur ſemicirculus circa diametrum B C, quia non ſecaret rectã E M. </s>
  <s xml:id="echoid-s1940" xml:space="preserve">Aliquando etiam <lb/>ſemicirculi ſe interſecant in recta E M, in deſcriptione Ellipſis, vt@emicirculi F P H, R V S, in <lb/>priori Ellipſi, v@i rectę E P, E V, æquales ſunt, atque perpendiculares k P, T V, ſumptę <lb/>i<unsure/>pſis ęquales in tertijs figuris.</s>
  <s xml:id="echoid-s1941" xml:space="preserve"/>
</p>
<div xml:id="echoid-div100" type="float" level="2" n="4">
<note position="left" xlink:label="note-0047-11" xlink:href="note-0047-11a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">In poſteriori <lb/>harũ media -<lb/>runi figurar@ <lb/>vbi eſt P, po-<lb/>ne M, &amp; loco <lb/>M, repone P.</note>
<note position="left" xml:space="preserve">20</note>
  <figure>
    <image file="0048-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-02"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
  <figure>
    <image file="0048-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-03"/>
  </figure>
<p>
  <s xml:id="echoid-s1942" xml:space="preserve">SED iam demonſtremus, ſectionem conicam tranſire in plano per puncta Q, P, &amp;</s>
  <s xml:id="echoid-s1943" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1944" xml:space="preserve">circa <lb/>
<anchor type="note" xlink:label="note-0048-05a" xlink:href="note-0048-05"/>
diametrum D E, atque adeo lineam per ipſa puncta in plano aptè deſcriptam, eſſe conicam ſectio-<lb/>nem, vt diximus. </s>
  <s xml:id="echoid-s1945" xml:space="preserve">Ducto in primis figuris per rectam F H, plano, quod baſi coni æquidiſtet, erit <lb/>
<anchor type="note" xlink:label="note-0048-06a" xlink:href="note-0048-06"/>
ſectio facta F X H, circulus, per propoſ. </s>
  <s xml:id="echoid-s1946" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1947" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1948" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1949" xml:space="preserve">Apollonii, cuius quidem &amp; </s>
  <s xml:id="echoid-s1950" xml:space="preserve">ſectionis communis ſe-<lb/>ctio ſit recta X Y, quæ per K, tranſibit, vbi ſe ſecant rectæ D E, F H, &amp; </s>
  <s xml:id="echoid-s1951" xml:space="preserve">vbi circulus F X H, per rectã <lb/>F H, ductus ſectioni conicæ occurrit. </s>
  <s xml:id="echoid-s1952" xml:space="preserve">Et quoniam plana B C, F H, parallela ſecantur plano D E, fa-<lb/>ciente conicam ſectionem, erunt communes ſectiones Z α X Y, parallelæ: </s>
  <s xml:id="echoid-s1953" xml:space="preserve">Eſt autem Z α, ad re-<lb/>
<anchor type="note" xlink:label="note-0048-07a" xlink:href="note-0048-07"/>
ctam B C, perpendicularis, (vt enim fiat ſectio aliqua conica, neceſſe eſt, vt ſectio communis pla-<lb/>ni ſecantis, &amp; </s>
  <s xml:id="echoid-s1954" xml:space="preserve">baſis coni, qualis eſt recta Z α, perpendicularis ſit ad baſim trianguli per axem, vt <lb/>conſtat<unsure/> ex propoſ. </s>
  <s xml:id="echoid-s1955" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1956" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1957" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s1958" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1959" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1960" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1961" xml:space="preserve">Apollonii) &amp; </s>
  <s xml:id="echoid-s1962" xml:space="preserve">anguli B E Z, F K X, æquales ſunt, propte-<lb/>
<anchor type="note" xlink:label="note-0048-08a" xlink:href="note-0048-08"/>
rea quòd rectæ B E, E Z, rectis F K, k X, ſunt parallelæ. </s>
  <s xml:id="echoid-s1963" xml:space="preserve">Igitur erit &amp; </s>
  <s xml:id="echoid-s1964" xml:space="preserve">angulus F K X, rectus, at-<lb/>que adeo X K, ad F H, perpendicularis, ac proinde X K, in ſemicirculo F X H, media erit propor-<lb/>tionalis inter F K, K H, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s1965" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1966" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s1967" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1968" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s1969" xml:space="preserve">Atqui &amp; </s>
  <s xml:id="echoid-s1970" xml:space="preserve">in ſecundis figuris E P, eadem <lb/>
<anchor type="note" xlink:label="note-0048-09a" xlink:href="note-0048-09"/>
ratione media eſt proportionalis inter F E, E H, hoc eſt, inter eaſdẽ F k, K H, in primis figuris, at-<lb/>que adeo ipſi X K, in primis figuris æqualis: </s>
  <s xml:id="echoid-s1971" xml:space="preserve">(ſumptæ enim ſunt E F, E H, in ſecundis figuris, ip-<lb/>ſis K.</s>
  <s xml:id="echoid-s1972" xml:space="preserve">F, K H, in primis æquales) Eſt autem eadem E P, in ſecundis figuris, ipſi k P, in tertiis æqua-<lb/>lis. </s>
  <s xml:id="echoid-s1973" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s1974" xml:space="preserve">k P, in tertiis figuris, ipſi K X, in primis, ęqualis eſt. </s>
  <s xml:id="echoid-s1975" xml:space="preserve">Quare cum in primis figuris <lb/>per X, in conica ſuperficie tranſeat ſectio conica, tranſibit eadem in plano per punctum P; </s>
  <s xml:id="echoid-s1976" xml:space="preserve">quo-<lb/>niam hac ratione, poſito puncto K, tertiarum figurarum in puncto k, primarum, ita vt diameter <lb/>k D, tertiarum congruat diametro k D, primarum, congruet perpendicularis k P, in tertiis figu-<lb/>ris, perpendiculari k X, in primis; </s>
  <s xml:id="echoid-s1977" xml:space="preserve">atque adeo punctum P, in punctum X, cader, (ob æqualitatem <lb/>rectarũ k P, k X,) &amp; </s>
  <s xml:id="echoid-s1978" xml:space="preserve">ſectio conica per punctum P, quod à puncto X, non differt, tranſibit. </s>
  <s xml:id="echoid-s1979" xml:space="preserve">Ea-<lb/>demq́ue ratione oſtendemus, ſectionem eandem tranſire per punctum Q, &amp; </s>
  <s xml:id="echoid-s1980" xml:space="preserve">per reliqua, ſi qua <lb/>ſunt. </s>
  <s xml:id="echoid-s1981" xml:space="preserve">Dato ergo cono, &amp; </s>
  <s xml:id="echoid-s1982" xml:space="preserve">diametro conicæ ſectionis, &amp;</s>
  <s xml:id="echoid-s1983" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1984" xml:space="preserve">quod faciendum erat.</s>
  <s xml:id="echoid-s1985" xml:space="preserve"/>
</p>
<div xml:id="echoid-div101" type="float" level="2" n="5">
<note position="left" xlink:label="note-0048-05" xlink:href="note-0048-05a" xml:space="preserve">Demonſtratio <lb/>ſuperioris de-<lb/>ſcriptionis.</note>
<note position="left" xlink:label="note-0048-06" xlink:href="note-0048-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0048-07" xlink:href="note-0048-07a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0048-08" xlink:href="note-0048-08a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0048-09" xlink:href="note-0048-09a" xml:space="preserve">50</note>
</div>
<pb o="29" file="0049" n="49" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div103" type="section" level="1" n="32">
<head xml:id="echoid-head35" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s1986" xml:space="preserve">HAEC ratio deſcribendæ conicæ ſectionis, vna cum demonſtratione, non differt ab ea, quam Fede-<lb/>ricus Commandinus adducit in libro de horologiorum deſcriptione, niſi quòd ipſe de cono recto ſolum lo-<lb/>quitur, nos autem problema omni cono tam recto, quàm ſcaleno accommodauimus, &amp; </s>
  <s xml:id="echoid-s1987" xml:space="preserve">praxes, quæ ad <lb/>deſcriptionem ſectionum conorum rectorum requiruntur, ſimul complexi ſumus. </s>
  <s xml:id="echoid-s1988" xml:space="preserve">Præcipit enim ipſe, vt <lb/>ſumantur in primis figuris, in diametro D E, quotcunque puncta K, L, atque per ipſa baſi B C, paralle-<lb/>læ agantur. </s>
  <s xml:id="echoid-s1989" xml:space="preserve">Sed facilius eſt in cono recto, beneficio circini in vtroque latere A B, A C, puncta ſumere F, <lb/>G, H, I. </s>
  <s xml:id="echoid-s1990" xml:space="preserve">Rectæ enim hæc puncta connectentes parallelæ ſunt, vt oſtendimus. </s>
  <s xml:id="echoid-s1991" xml:space="preserve">Deinde iubet in primis figu-<lb/>ris, inter K F, k H, &amp; </s>
  <s xml:id="echoid-s1992" xml:space="preserve">L G, L I, inuenire medias proportionales: </s>
  <s xml:id="echoid-s1993" xml:space="preserve">quod quidem nos præstitimus ſemi-<lb/>
<anchor type="note" xlink:label="note-0049-01a" xlink:href="note-0049-01"/>
circulis deſcriptis in ſecundis figuris. </s>
  <s xml:id="echoid-s1994" xml:space="preserve">Poſtremo, diuiſa diametro D E, in plano ſeorſum, nimirum in <lb/>tertijs figuris, vt diuiſa eſt in cono primarum figurarum, iubet ex punctis diuiſionum in tertĳs figuris <lb/>perpendiculares vtrinque educere ad diametrum: </s>
  <s xml:id="echoid-s1995" xml:space="preserve">quod &amp; </s>
  <s xml:id="echoid-s1996" xml:space="preserve">nos in tertĳs figuris fecimus praxi perfacili <lb/>&amp; </s>
  <s xml:id="echoid-s1997" xml:space="preserve">breui, præſertim vbi multa eſſent puncta. </s>
  <s xml:id="echoid-s1998" xml:space="preserve">In has perpendiculares transfert medias proportionales <lb/>inuentas, vt nos, &amp; </s>
  <s xml:id="echoid-s1999" xml:space="preserve">per extrema puncta mediarum proportionalium translatarum ducit ſectionem coni-<lb/>cam, quemadmodum &amp; </s>
  <s xml:id="echoid-s2000" xml:space="preserve">à nobis factum eſt.</s>
  <s xml:id="echoid-s2001" xml:space="preserve"/>
</p>
<div xml:id="echoid-div103" type="float" level="2" n="1">
<note position="left" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s2002" xml:space="preserve">FRANCISCVS Maurolycus abbas libro tertio de lineis horarĳs vtitur alĳs deſcriptionibus <lb/>particularibus trium conicarum ſectionum: </s>
  <s xml:id="echoid-s2003" xml:space="preserve">ſed ratio deſcriptionis à nobis tradita ſimplicior est, &amp; </s>
  <s xml:id="echoid-s2004" xml:space="preserve">fa-<lb/>cilior, conuenit{q́ue} in omnes ſectiones, vt conſtat. </s>
  <s xml:id="echoid-s2005" xml:space="preserve">Nihil autem diximus de conica illa ſectione deſcriben-<lb/>da, quæ circulus eſt, quia perfacilis eſt eius deſcriptio, cognita diametro.</s>
  <s xml:id="echoid-s2006" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s2007" xml:space="preserve">PLACET autem hoc loco tradere aliam rationem non iniucundam, &amp; </s>
  <s xml:id="echoid-s2008" xml:space="preserve">fortaſſis ea, quam expli-<lb/>cauimus, faciliorem, deſcribendi parabolam, duas hyperbolas oppoſitas, &amp; </s>
  <s xml:id="echoid-s2009" xml:space="preserve">Ellipſim, quarum axes dati <lb/>ſint, quæ quidem ratio (quod vehementer miror) à nemine hactenus, quod ſciam, obſeruata eſt. </s>
  <s xml:id="echoid-s2010" xml:space="preserve">Hanc au-<lb/>tem conis rectis duntaxat accommodabimus, propterea quòd ĳs ſolum in horologiorum deſcriptionibus <lb/>vſuri ſumus. </s>
  <s xml:id="echoid-s2011" xml:space="preserve">Pro Parabola igitur præmittendum eſt huiuſmodi lemma conueniens tam cono recto <lb/>quàm Scaleno.</s>
  <s xml:id="echoid-s2012" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div105" type="section" level="1" n="33">
<head xml:id="echoid-head36" xml:space="preserve">LEMMA.</head>
<p>
  <s xml:id="echoid-s2013" xml:space="preserve">DATO cono &amp; </s>
  <s xml:id="echoid-s2014" xml:space="preserve">diametro parabolæ, inuenire latus rectum parabolæ.</s>
  <s xml:id="echoid-s2015" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve">Inuentio late-<lb/>ris recti Parabo <lb/>les, cuius diam@ <lb/>ter in cono da-<lb/>ta ſit.</note>
  <figure>
    <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01"/>
  </figure>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s2016" xml:space="preserve">SIT datus conus A B C, in quo triangulum per axem A B C: </s>
  <s xml:id="echoid-s2017" xml:space="preserve">ſecetur autem conus <lb/>plano faciente parabolam E F G, iuxta ea, quæ ab Apollonio demonstrata ſunt propoſ. </s>
  <s xml:id="echoid-s2018" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s2019" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2020" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2021" xml:space="preserve">ita vt eius axis E H, æquidiſtans ſit lateri A C, trianguli per axem. </s>
  <s xml:id="echoid-s2022" xml:space="preserve">Huius igitur <lb/>paraboles rectum latus inueniemus hoc modo. </s>
  <s xml:id="echoid-s2023" xml:space="preserve">Fiat vt alterum latus trianguli per axem, <lb/>
<anchor type="note" xlink:label="note-0049-06a" xlink:href="note-0049-06"/>
nempe A B, ad baſim B C, ita B C, ad A I. </s>
  <s xml:id="echoid-s2024" xml:space="preserve">Deinde vt alterum latus A C, ad A I, inuen-<lb/>
<anchor type="note" xlink:label="note-0049-07a" xlink:href="note-0049-07"/>
tam, ita A E, ad E K. </s>
  <s xml:id="echoid-s2025" xml:space="preserve">Dico E K, eſſe rectum latus paraboles E F G, hoc eſt, illam eſſere-<lb/>
<anchor type="note" xlink:label="note-0049-08a" xlink:href="note-0049-08"/>
ctam, iuxta quam poſſunt or dinatim applicatæ ad diametrum E H. </s>
  <s xml:id="echoid-s2026" xml:space="preserve">Sit enim rectangulũ <lb/>C B, contentum ſub lateribus trianguli per axem A B, A C; </s>
  <s xml:id="echoid-s2027" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2028" xml:space="preserve">ad A B, applicetur rectan-<lb/>gulum B I, contentum ſub A B, A I, quod æquale erit quadrato baſis B C, propterea quòd <lb/>
<anchor type="note" xlink:label="note-0049-09a" xlink:href="note-0049-09"/>
tres rectæ A B, B C, A I, continuè proportionales ſunt, ex conſt<unsure/>ructione; </s>
  <s xml:id="echoid-s2029" xml:space="preserve">erit{q́ue} C A I, <lb/>vna linea recta, quòd duo anguli ad A, recti ſint. </s>
  <s xml:id="echoid-s2030" xml:space="preserve">Quoniam igitur eſt, vt C A, ad A I, <lb/>
<anchor type="note" xlink:label="note-0049-10a" xlink:href="note-0049-10"/>
ita A E, ad E K, per conſtructionem; </s>
  <s xml:id="echoid-s2031" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2032" xml:space="preserve">conuertendo, vt A I, ad A C, ita E K, ad A E; <lb/></s>
  <s xml:id="echoid-s2033" xml:space="preserve">Vt autem A I, ad A C, ita eſt rectangulum B I, hoc eſt, quadr atum baſis B C, ad rectan-<lb/>
<anchor type="note" xlink:label="note-0049-11a" xlink:href="note-0049-11"/>
<pb o="30" file="0050" n="50" rhead="GNOMONICES"/>
gulum B C, ſub lateribus trianguli per axem comprehenſum; </s>
  <s xml:id="echoid-s2034" xml:space="preserve">erit, vt quadratum baſis BC, <lb/>ad rectangulum ſub lateribus A B, A C, contentum, ita E K, ad A E. </s>
  <s xml:id="echoid-s2035" xml:space="preserve">Quare ex propoſ. <lb/></s>
  <s xml:id="echoid-s2036" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2037" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2038" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2039" xml:space="preserve">Apollonĳ, E K, latus rectum eſt paraboles E F G, hoc eſt, Recta, iuxta quam poſ-<lb/>ſunt ordinatim applicatæ, &amp; </s>
  <s xml:id="echoid-s2040" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2041" xml:space="preserve"/>
</p>
<div xml:id="echoid-div105" type="float" level="2" n="1">
<note position="left" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0049-07" xlink:href="note-0049-07a" xml:space="preserve">11. ſexti.</note>
<note position="right" xlink:label="note-0049-08" xlink:href="note-0049-08a" xml:space="preserve">12. ſexti.</note>
<note position="right" xlink:label="note-0049-09" xlink:href="note-0049-09a" xml:space="preserve">17. ſexti.</note>
<note position="right" xlink:label="note-0049-10" xlink:href="note-0049-10a" xml:space="preserve">14. primi.</note>
<note position="right" xlink:label="note-0049-11" xlink:href="note-0049-11a" xml:space="preserve">1. ſexti.</note>
</div>
  <figure>
    <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
  <figure>
    <image file="0050-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-02"/>
  </figure>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s2042" xml:space="preserve">INVENTO igitur latere recto, ſumatur in plano aliquo axis parabolæ quicunque E H. </s>
  <s xml:id="echoid-s2043" xml:space="preserve">(De <lb/>
<anchor type="note" xlink:label="note-0050-03a" xlink:href="note-0050-03"/>
illa enim Parabola hic agimus, cuius diameter etiam axis eſt, ſecans omnes ordinatim applicatas bifa-<lb/>riam, &amp; </s>
  <s xml:id="echoid-s2044" xml:space="preserve">ad rectos angulos) in quo ſumantur quot cunque partes inter ſe æquales, (quò autem minores hæ <lb/>partes fuerint, eò accuratius parabola deſcribetur) ita vt E A, ſit 1; </s>
  <s xml:id="echoid-s2045" xml:space="preserve">A B, 3; </s>
  <s xml:id="echoid-s2046" xml:space="preserve">B C, 5; </s>
  <s xml:id="echoid-s2047" xml:space="preserve">C H, 7, &amp; </s>
  <s xml:id="echoid-s2048" xml:space="preserve">ſic <lb/>deinceps, ſecundum numerorum imparium ſeriem: </s>
  <s xml:id="echoid-s2049" xml:space="preserve">atque per puncta A, B, C, H, &amp;</s>
  <s xml:id="echoid-s2050" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2051" xml:space="preserve">ad E H, perpen-<lb/>diculares vtrinque ducantur eo modo, quo ſupra docuimus. </s>
  <s xml:id="echoid-s2052" xml:space="preserve">Deinde inter latus rectum E k, &amp; </s>
  <s xml:id="echoid-s2053" xml:space="preserve">rectam <lb/>E A, inuenta media proportionali, abſcindatur ei vtrinq; </s>
  <s xml:id="echoid-s2054" xml:space="preserve">æqualis A D; </s>
  <s xml:id="echoid-s2055" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2056" xml:space="preserve">ex B, vtrinq; </s>
  <s xml:id="echoid-s2057" xml:space="preserve">abſcindatur <lb/>B F, dupla ipſius A D; </s>
  <s xml:id="echoid-s2058" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2059" xml:space="preserve">ex C, vtrinque C G, tripla eiuſdem A D, &amp; </s>
  <s xml:id="echoid-s2060" xml:space="preserve">ex H, ipſa H I, quadrupla, &amp; </s>
  <s xml:id="echoid-s2061" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0050-04a" xlink:href="note-0050-04"/>
ſic deinceps ſecundum naturalem ſeriem numerorum. </s>
  <s xml:id="echoid-s2062" xml:space="preserve">Nam per puncta D, F, G, I, deſcribenda erit para-<lb/>bola. </s>
  <s xml:id="echoid-s2063" xml:space="preserve">Quod enim per punctum D, tranſeat, ex eo probatur, quod quadratum ex A D, recta, quæ media <lb/>proportionalis est inter E K, E A, æquale eſt rectangulo ſub E K, E A, atque adeò A D, ordinatim <lb/>
<anchor type="note" xlink:label="note-0050-05a" xlink:href="note-0050-05"/>
applicata eſt in parabola, cuius latus rectum E K, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s2064" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2065" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2066" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2067" xml:space="preserve">Apollonĳ. </s>
  <s xml:id="echoid-s2068" xml:space="preserve">Quare pa-<lb/>rabola per punctum D, tranſibit. </s>
  <s xml:id="echoid-s2069" xml:space="preserve">Si enim per aliud punctum, vt per P, tranſiret, eſſet quadratum quc<unsure/>-<lb/>que ex A P, rectangulo ſub E K, E A, æquale, ex propoſ. </s>
  <s xml:id="echoid-s2070" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2071" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2072" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2073" xml:space="preserve">Apollonĳ, quòd A P, ordinatim ap-<lb/>plicata eſſet ad diametrum. </s>
  <s xml:id="echoid-s2074" xml:space="preserve">Quare quadrata ex A D, A P, æqualia, &amp; </s>
  <s xml:id="echoid-s2075" xml:space="preserve">ipſæ rectæ æquales eſſent, pars <lb/>&amp; </s>
  <s xml:id="echoid-s2076" xml:space="preserve">totum, quod eſt abſurdum. </s>
  <s xml:id="echoid-s2077" xml:space="preserve">Tranſit ergo parabola, cuius latus rectum E K, per D, punctum. </s>
  <s xml:id="echoid-s2078" xml:space="preserve">Quod <lb/>autem tranſeat quoque per puncta F, G, I, ita oſtendemus. </s>
  <s xml:id="echoid-s2079" xml:space="preserve">Quoniam recta B F, dupla eſt rectæ A D, <lb/>habebit quadr at um illius ad huius quadr at um proportionem quadruplam; </s>
  <s xml:id="echoid-s2080" xml:space="preserve">(quòd quadrata habeant du-<lb/>
<anchor type="note" xlink:label="note-0050-06a" xlink:href="note-0050-06"/>
<anchor type="note" xlink:label="note-0050-07a" xlink:href="note-0050-07"/>
plicatam proportionem laterum) quemadmodum &amp; </s>
  <s xml:id="echoid-s2081" xml:space="preserve">recta E B, rectæ E A, quadrupla eſt. </s>
  <s xml:id="echoid-s2082" xml:space="preserve">Rurſus quia <lb/>
<anchor type="note" xlink:label="note-0050-08a" xlink:href="note-0050-08"/>
recta C G, rectæ A D, tripla est, erit quadratum illius noncuplum quadrati huius, ſicut &amp; </s>
  <s xml:id="echoid-s2083" xml:space="preserve">recta E C, <lb/>noncupla eſt rectæ E A. </s>
  <s xml:id="echoid-s2084" xml:space="preserve">Eodem modo habebit quadratum ex H I, ad quadratum ex A D, eandem pro-<lb/>portionem, quam recta E H, ad E A, nempe ſedecuplam, &amp; </s>
  <s xml:id="echoid-s2085" xml:space="preserve">ſic deinceps. </s>
  <s xml:id="echoid-s2086" xml:space="preserve">Quare vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s2087" xml:space="preserve">20. <lb/></s>
  <s xml:id="echoid-s2088" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2089" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2090" xml:space="preserve">Apollonĳ, parabola per puncta F, G, I, tranſibit. </s>
  <s xml:id="echoid-s2091" xml:space="preserve">Nam ſi per aliud punctum, vt per Q, tranſi-<lb/>re dicatur, erit ex dicta propoſ. </s>
  <s xml:id="echoid-s2092" xml:space="preserve">20. </s>
  <s xml:id="echoid-s2093" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2094" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2095" xml:space="preserve">Apollonĳ, quadratum ex B Q, ad quadratum ex A D, vt recta <lb/>E B, ad rectam E A, hoc eſt, vtquadratum ex B F, ad quadratum ex A D. </s>
  <s xml:id="echoid-s2096" xml:space="preserve">ſunt ergo æqualia quadrata <lb/>B Q, &amp; </s>
  <s xml:id="echoid-s2097" xml:space="preserve">B F, &amp; </s>
  <s xml:id="echoid-s2098" xml:space="preserve">ipſæ rectæ æquales, pars &amp; </s>
  <s xml:id="echoid-s2099" xml:space="preserve">totum, quod est abſurdum. </s>
  <s xml:id="echoid-s2100" xml:space="preserve">Nonigitur parabola per Q, <lb/>ſed per F, deſcribenda erit, &amp; </s>
  <s xml:id="echoid-s2101" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s2102" xml:space="preserve"/>
</p>
<div xml:id="echoid-div106" type="float" level="2" n="2">
<note position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">Alia deſ@riptio <lb/>Paraboles in <lb/>plano.</note>
<note position="left" xlink:label="note-0050-04" xlink:href="note-0050-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0050-05" xlink:href="note-0050-05a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0050-06" xlink:href="note-0050-06a" xml:space="preserve">20. ſexti.</note>
<note position="left" xlink:label="note-0050-07" xlink:href="note-0050-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0050-08" xlink:href="note-0050-08a" xml:space="preserve">20. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2103" xml:space="preserve">QVOD ſi quando puncta nimium inter ſe diſtare videantur, qualia ſunt G, &amp; </s>
  <s xml:id="echoid-s2104" xml:space="preserve">I, accipiemus in dia-<lb/>
<anchor type="note" xlink:label="note-0050-09a" xlink:href="note-0050-09"/>
metro E H, inter C, H, puncta, punctum aliquod, quod terminet particulas diametri, quas quaterna-<lb/>rius numeret, vt 8, vel 12. </s>
  <s xml:id="echoid-s2105" xml:space="preserve">vel 16. </s>
  <s xml:id="echoid-s2106" xml:space="preserve">vel 20. </s>
  <s xml:id="echoid-s2107" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s2108" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2109" xml:space="preserve">cuiuſmodiest punctum M, terminans duodecim parti-<lb/>culas. </s>
  <s xml:id="echoid-s2110" xml:space="preserve">Deinde lineæ E M, ſumemus quartam partem, vt in dato exemplo rectam E L, continentem <lb/>tres particulas, &amp; </s>
  <s xml:id="echoid-s2111" xml:space="preserve">ex L, perpendicularem ducemus ad E H, nempe L N, quæ parabolam ſecet in N, pun <lb/>cto. </s>
  <s xml:id="echoid-s2112" xml:space="preserve">Si enim per M, ducamus aliam perpendicularem ad E H, ex qua abſcindamus M O, duplam ipſius <lb/>L N, tranſibit parabola per punctum O; </s>
  <s xml:id="echoid-s2113" xml:space="preserve">propterca quod L M, ipſius E L, tripla eſt, &amp; </s>
  <s xml:id="echoid-s2114" xml:space="preserve">M O, ipſius <lb/>L N, dupla, quemadmodum &amp; </s>
  <s xml:id="echoid-s2115" xml:space="preserve">A B, ipſius E A, tripla, &amp; </s>
  <s xml:id="echoid-s2116" xml:space="preserve">B F, ipſius A D, dupla exiſtit.</s>
  <s xml:id="echoid-s2117" xml:space="preserve"/>
</p>
<div xml:id="echoid-div107" type="float" level="2" n="3">
<note position="left" xlink:label="note-0050-09" xlink:href="note-0050-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s2118" xml:space="preserve">HAEC eadem ratio accommodari poteſt Parabolæ, in qua ordinatim applicatæ non ſunt perpendi-<lb/>culares ad diametrum E H, vt in conis ſcalenis contingit, cum triangulum per axem ad baſim conirectũ <lb/>non eſt, vt ex propoſ. </s>
  <s xml:id="echoid-s2119" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2120" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2121" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2122" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s2123" xml:space="preserve">liquet: </s>
  <s xml:id="echoid-s2124" xml:space="preserve">Sed tunc E H, non erit axis Parabolæ, ſed diameter. </s>
  <s xml:id="echoid-s2125" xml:space="preserve">Vn-<lb/>de per puncta A, B, C, H, ducendæ erunt lineæ inter ſe parallelæ, facientes cum diametro E H, angu-
<pb o="31" file="0051" n="51" rhead="LIBER PRIMVS."/>
los æquales illis, quos ordinatim applicatæ cum diametro Paraboles conſtituunt. </s>
  <s xml:id="echoid-s2126" xml:space="preserve">Multo magis conue-<lb/>niet hæc ratio conis Scalcnis, cum triangulum per axem ad coni baſim rectum eſt, quia tunc, ex propoſ. </s>
  <s xml:id="echoid-s2127" xml:space="preserve">7. <lb/></s>
  <s xml:id="echoid-s2128" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2129" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2130" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s2131" xml:space="preserve">ordinatim applicatæ ſunt ad diametrum Paraboles perpendiculares, quemadmodum in <lb/>cono recto, ita vt E H, ſit quoque axis Parabolæ.</s>
  <s xml:id="echoid-s2132" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2133" xml:space="preserve">PRO hyperbolis verò oppoſitis demonſtranda ſunt duo alia lemmata, quæ omni cono tam recto, <lb/>quàm ſcaleno conucniunt; </s>
  <s xml:id="echoid-s2134" xml:space="preserve">quorum primum hoc eſt.</s>
  <s xml:id="echoid-s2135" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div109" type="section" level="1" n="34">
<head xml:id="echoid-head37" xml:space="preserve">LEMMA PRIMVM.</head>
<p>
  <s xml:id="echoid-s2136" xml:space="preserve">DATO cono, &amp; </s>
  <s xml:id="echoid-s2137" xml:space="preserve">diametro tranſuerſa Hyperbolarum oppoſitarum, inuenire <lb/>
<anchor type="note" xlink:label="note-0051-01a" xlink:href="note-0051-01"/>
<anchor type="note" xlink:label="note-0051-02a" xlink:href="note-0051-02"/>
latus rectum Hyperboles.</s>
  <s xml:id="echoid-s2138" xml:space="preserve"/>
</p>
<div xml:id="echoid-div109" type="float" level="2" n="1">
<note position="left" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">Inuentio late-<lb/>ris recti hyper-<lb/>bolarũ oppoſi-<lb/>tarum, quatũ <lb/>diameter tranſ-<lb/>uerſa in cono <lb/>data ſit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2139" xml:space="preserve">SIT datus conus A B C, in quo triangulum per axem A B C, producatur {q́ue} conus vnà <lb/>cum triangulo per axem ad verticem A, vt fiant duo coni A B C, A D E, ad verticem <lb/>A, coniuncti. </s>
  <s xml:id="echoid-s2140" xml:space="preserve">Secetur quoque vtraque ſuperficies conica plano non per verticem facien <lb/>te ſectiones F G H, I K L, quæ hyperbolæ ſunt oppoſitæ, ex propoſ. </s>
  <s xml:id="echoid-s2141" xml:space="preserve">14. </s>
  <s xml:id="echoid-s2142" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2143" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2144" xml:space="preserve">Apallonĳ, <lb/>quarum diameter tranſuerſa communis F I, &amp; </s>
  <s xml:id="echoid-s2145" xml:space="preserve">la-<lb/>
<anchor type="figure" xlink:label="fig-0051-01a" xlink:href="fig-0051-01"/>
tera recta æqualia. </s>
  <s xml:id="echoid-s2146" xml:space="preserve">Vtriuſque ergo lat{us} rectum <lb/>ita inueniem{us}. </s>
  <s xml:id="echoid-s2147" xml:space="preserve">Per A, ducatur A M, ipſi F I, <lb/>parallela ſecans B C, in M; </s>
  <s xml:id="echoid-s2148" xml:space="preserve">fiat{q́ue} vt C M, altera <lb/>
<anchor type="note" xlink:label="note-0051-03a" xlink:href="note-0051-03"/>
parsbaſis, ad A M, ita A M, ad M N. </s>
  <s xml:id="echoid-s2149" xml:space="preserve">Rurſ{us} <lb/>fiat, vt M N, ad B M, alteram baſis partem, ita <lb/>
<anchor type="note" xlink:label="note-0051-04a" xlink:href="note-0051-04"/>
<anchor type="note" xlink:label="note-0051-05a" xlink:href="note-0051-05"/>
F I, tranſuerſa diameter ad F O. </s>
  <s xml:id="echoid-s2150" xml:space="preserve">Dico F O, eſſe la-<lb/>tusrectum vtriuſque Hyperboles; </s>
  <s xml:id="echoid-s2151" xml:space="preserve">hoc eſt, eſſe re-<lb/>ctam, iuxta quam poſſunt ordinatim applicatæ ad <lb/>diametrum vtriuſque hyperboles. </s>
  <s xml:id="echoid-s2152" xml:space="preserve">Sit enim re-<lb/>ctangulum B C, contentum ſub baſis partibus B M, <lb/>M C; </s>
  <s xml:id="echoid-s2153" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2154" xml:space="preserve">ad M C, applicetur rectangulum C N, ſub <lb/>
<anchor type="note" xlink:label="note-0051-06a" xlink:href="note-0051-06"/>
<anchor type="note" xlink:label="note-0051-07a" xlink:href="note-0051-07"/>
M C, M N, contentum, quod æquale erit quadrato <lb/>rectæ A M, propterea quòdtres rectæ M C, A M, <lb/>M N, continuè proportionales ſunt ex conſtructio-<lb/>ne: </s>
  <s xml:id="echoid-s2155" xml:space="preserve">erit{q́ue} B M N, vna linearecta, quòd duo an-<lb/>
<anchor type="note" xlink:label="note-0051-08a" xlink:href="note-0051-08"/>
guli ad M, recti ſint. </s>
  <s xml:id="echoid-s2156" xml:space="preserve">Quoniam igitur eſt, vt <lb/>M N, ad B M, ita F I, ad F O; </s>
  <s xml:id="echoid-s2157" xml:space="preserve">Vt autem M N, ad B M, ita eſt rectangulum C N, hoc est, <lb/>
<anchor type="note" xlink:label="note-0051-09a" xlink:href="note-0051-09"/>
quadratum ex A M, ad rectangulum B C, ſub baſis partibus B M, M C, contentum; </s>
  <s xml:id="echoid-s2158" xml:space="preserve">erit <lb/>quoque vt quadratum ex A M, adrectangulum ſub B M, M C, ita tranſuerſa diameter <lb/>F I, ad rectam F O. </s>
  <s xml:id="echoid-s2159" xml:space="preserve">Eſt igitur F O, latus rectum hyperboles, ex propoſ. </s>
  <s xml:id="echoid-s2160" xml:space="preserve">12. </s>
  <s xml:id="echoid-s2161" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2162" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2163" xml:space="preserve">Apollo-<lb/>
<anchor type="note" xlink:label="note-0051-10a" xlink:href="note-0051-10"/>
nĳ, hoc eſt, Recta, iuxta quam poſſunt or dinatim applicatæ, &amp;</s>
  <s xml:id="echoid-s2164" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2165" xml:space="preserve"/>
</p>
<div xml:id="echoid-div110" type="float" level="2" n="2">
  <figure xlink:label="fig-0051-01" xlink:href="fig-0051-01a">
    <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0051-01"/>
  </figure>
<note position="left" xlink:label="note-0051-03" xlink:href="note-0051-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0051-04" xlink:href="note-0051-04a" xml:space="preserve">11. ſexti.</note>
<note position="right" xlink:label="note-0051-05" xlink:href="note-0051-05a" xml:space="preserve">12. ſexti.</note>
<note position="left" xlink:label="note-0051-06" xlink:href="note-0051-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0051-07" xlink:href="note-0051-07a" xml:space="preserve">17. ſexti.</note>
<note position="right" xlink:label="note-0051-08" xlink:href="note-0051-08a" xml:space="preserve">14. primi.</note>
<note position="right" xlink:label="note-0051-09" xlink:href="note-0051-09a" xml:space="preserve">1. ſexti.</note>
<note position="left" xlink:label="note-0051-10" xlink:href="note-0051-10a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Quomodo <lb/>quarta pats ſub <lb/>diametro trãſ-<lb/>uerſa hyperbo-<lb/>les, &amp; latere re-<lb/>cto cõprehenſi <lb/>applicetur ad <lb/>diametrũ trã<unsure/>ſ-<lb/>uerſam ex vtra-<lb/>que parte, ita vt <lb/>excedat figura <lb/>quadraata.</note>
</div>
<div xml:id="echoid-div112" type="section" level="1" n="35">
<head xml:id="echoid-head38" xml:space="preserve">LEMMA II.</head>
<p>
  <s xml:id="echoid-s2166" xml:space="preserve">QVARTAM partem rectanguli ſub diametro tranſuerſa Hyperboles, &amp; </s>
  <s xml:id="echoid-s2167" xml:space="preserve">late-<lb/>re recto comprehenſi ad tranſuerſam diametrum ex vtraque parte applicare, ita vt <lb/>excedatfigura quadrata.</s>
  <s xml:id="echoid-s2168" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2169" xml:space="preserve">POSITA eadem figura, reperiatur inter tranſuer ſam diametrum F I, &amp; </s>
  <s xml:id="echoid-s2170" xml:space="preserve">latus re-<lb/>ctum F O, media proportionalis A B, quæ bifariam ſecetur in C. </s>
  <s xml:id="echoid-s2171" xml:space="preserve">Erit igitur quadratum <lb/>
<anchor type="note" xlink:label="note-0051-12a" xlink:href="note-0051-12"/>
<anchor type="note" xlink:label="note-0051-13a" xlink:href="note-0051-13"/>
ex A B, æquale rectangulo ſub F I, F O; </s>
  <s xml:id="echoid-s2172" xml:space="preserve">at que adeo quadratum ex A C, quod ex ſcholio <lb/>
<anchor type="note" xlink:label="note-0051-14a" xlink:href="note-0051-14"/>
propoſ. </s>
  <s xml:id="echoid-s2173" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2174" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2175" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2176" xml:space="preserve">Euclidis, quarta pars eſt quadrati ex A B, quartæ parti rectanguli ſub F I, <lb/>F O, æquale erit. </s>
  <s xml:id="echoid-s2177" xml:space="preserve">Huic igitur quadrato ex A C, applicabim{us} ad diametrum tranſuer ſam <lb/>F I, ex vtraque parte, æquale rectangulum excedens figura quadrata, hoc modo. </s>
  <s xml:id="echoid-s2178" xml:space="preserve">Diuiſa <lb/>recta F I, bifariam in D, fiat angulus rectus H K L, &amp; </s>
  <s xml:id="echoid-s2179" xml:space="preserve">recta H K, rectæ A C, &amp; </s>
  <s xml:id="echoid-s2180" xml:space="preserve">recta <lb/>K L, rectæ D I, æqualis, connectatur{q́ue} recta H L, quæ maior erit, quàm recta K L, hoc <lb/>
<anchor type="note" xlink:label="note-0051-15a" xlink:href="note-0051-15"/>
eſt, quàm D I, propterea quòd H L, maiori angulo opponatur, quàm K L. </s>
  <s xml:id="echoid-s2181" xml:space="preserve">Producta recta <lb/>F I, in vtramque partem, abſcindantur vtrinque ex D, rectæ D Q, D R, ipſi H L, æqua-<lb/>les. </s>
  <s xml:id="echoid-s2182" xml:space="preserve">Dico tam rectangulum ſub F Q, Q I, applicatum ad F I, excedens{q́ue} quadrato ex
<pb o="32" file="0052" n="52" rhead="GNOMONICES"/>
QI, quàm rectangulum ſub I R, R F, ad candem I F, applicatum, cxcedens{q́ue} quadrato<unsure/> <lb/>ex R F, æquale eſſe quadrato ex A C, hoceſt, quartæ partirectanguli ſub F I, F O. </s>
  <s xml:id="echoid-s2183" xml:space="preserve">De-<lb/>ſcripto enim ex D I, quadrato D E, ducatur per Q, ipſi I E, parallela P N, occurrensrectæ <lb/>G E, productæ in P, &amp; </s>
  <s xml:id="echoid-s2184" xml:space="preserve">diametro G I, productæ in N, perficiatur{q́ue} figura, vt vides. </s>
  <s xml:id="echoid-s2185" xml:space="preserve">Quo-<lb/>niam igitur pallelogramma D E, M P, N I, circa eandem diametrum exiſtentia ſimilia <lb/>
<anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/>
ſunt, eſt{q́ue} D E, quadratum; </s>
  <s xml:id="echoid-s2186" xml:space="preserve">erunt quo-<lb/>
<anchor type="note" xlink:label="note-0052-02a" xlink:href="note-0052-02"/>
<anchor type="figure" xlink:label="fig-0052-01a" xlink:href="fig-0052-01"/>
que M P, N I, quadrata. </s>
  <s xml:id="echoid-s2187" xml:space="preserve">Et quoniam <lb/>quadratum ex H L, æquale eſt quadratis <lb/>ex H K, K L; </s>
  <s xml:id="echoid-s2188" xml:space="preserve">eſt autem recta H L, rectæ <lb/>
<anchor type="note" xlink:label="note-0052-03a" xlink:href="note-0052-03"/>
D Q, ſeu M N, &amp; </s>
  <s xml:id="echoid-s2189" xml:space="preserve">recta H K, rectæ AC, <lb/>&amp; </s>
  <s xml:id="echoid-s2190" xml:space="preserve">recta K L, rectæ D I, æqualis, ex con-<lb/>ſtructione; </s>
  <s xml:id="echoid-s2191" xml:space="preserve">Erit quoque quadratũ M P, <lb/>ex D Q, ſeu M N, deſoriptum, æquale <lb/>quadrato D E, ex D I, deſcripto, vnà cũ <lb/>quadrato ex A C. </s>
  <s xml:id="echoid-s2192" xml:space="preserve">Quare ablato commu-<lb/>ni quadrato D E, erit@ reliqu{us} gnomon <lb/>D N E, æqualis reliquo quadrato ex AC. <lb/></s>
  <s xml:id="echoid-s2193" xml:space="preserve">
<anchor type="note" xlink:label="note-0052-04a" xlink:href="note-0052-04"/>
Cum ergo gnomon D N E, æqualis ſit re-<lb/>ctangulo F N, (Nam cum F M, ipſi M I, <lb/>
<anchor type="note" xlink:label="note-0052-05a" xlink:href="note-0052-05"/>
hoc eſt, ipſi I P, æquale ſit, addito communi M Q, æquale erit F N, gnomoni D N E,) eris<unsure/> <lb/>
<anchor type="note" xlink:label="note-0052-06a" xlink:href="note-0052-06"/>
quoque rectangulum F N, contcntum ſuh F Q, Q I, (quòdrecta Q I, rectæ Q N, æqua-<lb/>lis ſit, ob quadratum I N, %%%% æquale quadrato ex A C, hoc eſt, quartæ parti quadrati ex AB, <lb/>hoc eſt, rectanguli ſub F I, F O, comprehenſi. </s>
  <s xml:id="echoid-s2194" xml:space="preserve">Applicatum eſt ergo ad F I, diametrũ tranſ-<lb/>uerſam rectangulum ſub F Q, Q I, æquale quartæ parti rectanguli ſub F I, F O, exce-<lb/>dens quadrato rectæ Q I. </s>
  <s xml:id="echoid-s2195" xml:space="preserve">Eodem modo demonſtr abitur rectangulum ſub I R, R F, ap-<lb/>plicatum ad F I, excedens{q́ue} quadrato ex R F, æquale eſſe quartæ parti rectanguli ſub F I, <lb/>
<anchor type="note" xlink:label="note-0052-07a" xlink:href="note-0052-07"/>
F O. </s>
  <s xml:id="echoid-s2196" xml:space="preserve">Quod est propoſitum.</s>
  <s xml:id="echoid-s2197" xml:space="preserve"/>
</p>
<div xml:id="echoid-div112" type="float" level="2" n="1">
<note position="right" xlink:label="note-0051-12" xlink:href="note-0051-12a" xml:space="preserve">13. ſexti.</note>
<note position="left" xlink:label="note-0051-13" xlink:href="note-0051-13a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0051-14" xlink:href="note-0051-14a" xml:space="preserve">17. ſexti.</note>
<note position="right" xlink:label="note-0051-15" xlink:href="note-0051-15a" xml:space="preserve">19. primi.</note>
<note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">24. ſexti.</note>
<note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">47. primi.</note>
  <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a">
    <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0052-01"/>
  </figure>
<note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0052-05" xlink:href="note-0052-05a" xml:space="preserve">36. primi.</note>
<note position="left" xlink:label="note-0052-06" xlink:href="note-0052-06a" xml:space="preserve">43. primi.</note>
<note position="left" xlink:label="note-0052-07" xlink:href="note-0052-07a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s2198" xml:space="preserve">HIS præmiſſis, ſit F I, axis tranſuerſus duarum hyperbolarum oppoſitarum F G H, I K L, vt in <lb/>
<anchor type="note" xlink:label="note-0052-08a" xlink:href="note-0052-08"/>
figur a primi lemmatis, &amp; </s>
  <s xml:id="echoid-s2199" xml:space="preserve">latus rectum F O, datum ex eodem primo lemmate, applicetur per ſecun-<lb/>dum lemma ad F I, ex vtraque parte rectangulum ſub F Q, Q I, &amp; </s>
  <s xml:id="echoid-s2200" xml:space="preserve">I R, R F, quartæ parti rectanguli <lb/>ſub F I, F O, æquale, excedens{q́ue} quadrato ex I Q, &amp; </s>
  <s xml:id="echoid-s2201" xml:space="preserve">F R, &amp; </s>
  <s xml:id="echoid-s2202" xml:space="preserve">infra R, ſumantur vtcunque puncta <lb/>quotlibet A, B, C, D. </s>
  <s xml:id="echoid-s2203" xml:space="preserve">Deinde ad interuallum I A, deſcribantur ex punctis Q, &amp; </s>
  <s xml:id="echoid-s2204" xml:space="preserve">R, quatuor arcus, <lb/>quos inpuncto E, ſecent alĳ quatuor arcus ex eiſdem punctis Q, &amp; </s>
  <s xml:id="echoid-s2205" xml:space="preserve">R, ad interuallum F A, deſcripti. <lb/></s>
  <s xml:id="echoid-s2206" xml:space="preserve">Item ex eiſdem punctis Q, &amp; </s>
  <s xml:id="echoid-s2207" xml:space="preserve">R, ad interuallum I B, quatuor arcus deſcribantur, quos in puncto G, in-<lb/>terſecent alĳ quatuor ex eiſdem punctis Q, &amp; </s>
  <s xml:id="echoid-s2208" xml:space="preserve">R, deſcripti ad interuallum F B. </s>
  <s xml:id="echoid-s2209" xml:space="preserve">Eodem modo ad inter-<lb/>
<anchor type="note" xlink:label="note-0052-09a" xlink:href="note-0052-09"/>
ualla I C, F C, ex punctis Q, &amp; </s>
  <s xml:id="echoid-s2210" xml:space="preserve">R, arcus deſcripti ſe mutuo ſecent in H, &amp; </s>
  <s xml:id="echoid-s2211" xml:space="preserve">ſic de cæte<unsure/>ris punctis, ſi <lb/>quaſint; </s>
  <s xml:id="echoid-s2212" xml:space="preserve">obſeruando ſemper, vt bini maiores arcus ex ſingulis quatuor, qui ex Q, &amp; </s>
  <s xml:id="echoid-s2213" xml:space="preserve">R, deſcribendi <lb/>ſunt, deſcribantur ex Q, vltra punctum F, &amp; </s>
  <s xml:id="echoid-s2214" xml:space="preserve">bini ex R, vltra punctum I, bini autem minores ex Q, <lb/>citra punctum I, &amp; </s>
  <s xml:id="echoid-s2215" xml:space="preserve">bini ex R, citra punctum F. </s>
  <s xml:id="echoid-s2216" xml:space="preserve">Nam per puncta F, E, G, H, &amp; </s>
  <s xml:id="echoid-s2217" xml:space="preserve">I, E, G, H, oppoſitæ <lb/>hyperbolæ deſcribendæ erunt. </s>
  <s xml:id="echoid-s2218" xml:space="preserve">Quoniam enim recta Q E, hoc est, I A, ſuperat rectam E R, hoc eſt, <lb/>F A, diametro tranſuerſa F I; </s>
  <s xml:id="echoid-s2219" xml:space="preserve">Item recta Q G, rectam G R, eadem diametro ſuperat, &amp; </s>
  <s xml:id="echoid-s2220" xml:space="preserve">ſic de cæ-<lb/>teris, tranſibunt hyperbolæ oppoſitæ, quarum axis F I, &amp; </s>
  <s xml:id="echoid-s2221" xml:space="preserve">vertices F, I, per puncta E, G, H, quan-<lb/>doquidem, vt vult propoſitio 51. </s>
  <s xml:id="echoid-s2222" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2223" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2224" xml:space="preserve">Apollonĳ, ſi lineæ rectæ ex punctis Q, R, ad vnum idem{q́ue} pun-<lb/>ctum Hyperboles inclinentur, maior minorcm ſuperat ipſo axe F I. </s>
  <s xml:id="echoid-s2225" xml:space="preserve">Si enim hyperbole, cuius axis F I, <lb/>&amp; </s>
  <s xml:id="echoid-s2226" xml:space="preserve">vertex F, non tranſit per punctum E, tranſeat, ſi fieri pote<unsure/>ſt, per K, ſecans rectam Q E, in K, ſiue in-<lb/>
<anchor type="note" xlink:label="note-0052-10a" xlink:href="note-0052-10"/>
fra E, ſiue ſupra; </s>
  <s xml:id="echoid-s2227" xml:space="preserve">coniungstur{q́ue} recta R K. </s>
  <s xml:id="echoid-s2228" xml:space="preserve">Quoniam igitur Hyperbole tranſit per K, ſuperabit recta <lb/>Q K, rectam K R, axe F I, per propoſ. </s>
  <s xml:id="echoid-s2229" xml:space="preserve">51. </s>
  <s xml:id="echoid-s2230" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2231" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2232" xml:space="preserve">Apollonĳ: </s>
  <s xml:id="echoid-s2233" xml:space="preserve">Sed eodem axe F I, ſuperat ex conſtructio-<lb/>ne recta Q E, rectam E R. </s>
  <s xml:id="echoid-s2234" xml:space="preserve">Idem ergo eſt exceſſus inter rectas Q K, K R, qui inter rectas Q E, E R. <lb/></s>
  <s xml:id="echoid-s2235" xml:space="preserve">Quare permutando, ex lemmate propoſ. </s>
  <s xml:id="echoid-s2236" xml:space="preserve">79. </s>
  <s xml:id="echoid-s2237" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2238" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2239" xml:space="preserve">Euclidis, idem exccſſus erit inter rectas Q K, Q E, <lb/>qui inter rectas K R, E R. </s>
  <s xml:id="echoid-s2240" xml:space="preserve">Cum ergo exceſſus inter Q K, &amp; </s>
  <s xml:id="echoid-s2241" xml:space="preserve">Q E:</s>
  <s xml:id="echoid-s2242" xml:space="preserve">, ſit recta E K, erit quoque eadem re-<lb/>cta E K, exceſſus inter K R, &amp; </s>
  <s xml:id="echoid-s2243" xml:space="preserve">E R. </s>
  <s xml:id="echoid-s2244" xml:space="preserve">Quare recta E K, addita minori@earum, fiet aggregatum exhis <lb/>duabus reliquæ æquale, ac proinde duo later a trianguli E K R, reliquo lateri æqualia erunt, ſed &amp; </s>
  <s xml:id="echoid-s2245" xml:space="preserve">maio-<lb/>
<anchor type="note" xlink:label="note-0052-11a" xlink:href="note-0052-11"/>
ra ſunt. </s>
  <s xml:id="echoid-s2246" xml:space="preserve">Quod eſt abſurdum. </s>
  <s xml:id="echoid-s2247" xml:space="preserve">Non ergo dicta Hyperbole per punctum K, ſed per E, tranſibit. </s>
  <s xml:id="echoid-s2248" xml:space="preserve">Eodem{q́ue} <lb/>pacto oſtendemus eandem pe<unsure/>r reliqua puncta G, H, &amp;</s>
  <s xml:id="echoid-s2249" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2250" xml:space="preserve">tranſire, quod est propoſitum.</s>
  <s xml:id="echoid-s2251" xml:space="preserve"/>
</p>
<div xml:id="echoid-div113" type="float" level="2" n="2">
<note position="left" xlink:label="note-0052-08" xlink:href="note-0052-08a" xml:space="preserve">Alia deſcriptio <lb/>hyperbolarum <lb/>oppoſitarum@in <lb/>plano.</note>
<note position="left" xlink:label="note-0052-09" xlink:href="note-0052-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0052-10" xlink:href="note-0052-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0052-11" xlink:href="note-0052-11a" xml:space="preserve">20. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2252" xml:space="preserve">MANIFESTVM autem eſt, deſcriptione<unsure/>m hanc ſolum conuenire conis rectis, vel etiam Sca-<lb/>lenis, in quibus triangula per axem ad baſes conorum recta ſunt; </s>
  <s xml:id="echoid-s2253" xml:space="preserve">quia in his dunt axat diamc<unsure/>ter tranſuer-
<pb o="33" file="0053" n="53" rhead="LIBER PRIMVS."/>
ſa axis eſt Hyperbolarum, cum ſecet ordinatim applicatas ad angulos rectos, vt ex propoſ. </s>
  <s xml:id="echoid-s2254" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2255" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2256" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s2257" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s2258" xml:space="preserve">liquet.</s>
  <s xml:id="echoid-s2259" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2260" xml:space="preserve">PRO Ellipſi denique duo rurſus lemmata præmittenda ſunt, quæ ſequuntur, quadrant{q́ue} in om-<lb/>nem conum tam rectum, quàm ſcalenum.</s>
  <s xml:id="echoid-s2261" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div115" type="section" level="1" n="36">
<head xml:id="echoid-head39" xml:space="preserve">LEMMA PRIMVM.</head>
<p>
  <s xml:id="echoid-s2262" xml:space="preserve">DATO cono, &amp; </s>
  <s xml:id="echoid-s2263" xml:space="preserve">diametro tranſuerſa Ellipſis, inuenirelatus rectum Ellipſis.</s>
  <s xml:id="echoid-s2264" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Inuentio late-<lb/>ris recti Ellipſis, <lb/>cuius tranſuer-<lb/>ſa diameter in <lb/>cono data ſit.</note>
<note position="left" xml:space="preserve">10</note>
  <figure>
    <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01"/>
  </figure>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s2265" xml:space="preserve">SIT datus conus A B C, in quo triangulum per axem A B C; </s>
  <s xml:id="echoid-s2266" xml:space="preserve">ſecetur autem conus <lb/>pla@@ faciente Ellipſim E F, iuxta propoſ. </s>
  <s xml:id="echoid-s2267" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2268" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2269" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2270" xml:space="preserve">Apollonĳ, ita vtrecta E F, ſit diame-<lb/>ter tra@ſuerſa Ellipſis. </s>
  <s xml:id="echoid-s2271" xml:space="preserve">Huius igitur latus rectum ita inueniemus. </s>
  <s xml:id="echoid-s2272" xml:space="preserve">Per A, ducatur <lb/>A G, ipſi E F, parallela ſecans B C, productam in G; </s>
  <s xml:id="echoid-s2273" xml:space="preserve">fiat{q́ue} vt C G, recta inter punctum <lb/>G, &amp; </s>
  <s xml:id="echoid-s2274" xml:space="preserve">alterum latus trianguli per axem, ad A G, ita A G, ad G H. </s>
  <s xml:id="echoid-s2275" xml:space="preserve">Rurſ{us} fiat, vt G H, <lb/>
<anchor type="note" xlink:label="note-0053-04a" xlink:href="note-0053-04"/>
ad G B, rectam inter idem punctum G, &amp; </s>
  <s xml:id="echoid-s2276" xml:space="preserve">alterum latus trianguli per axem, ita E F, dia-<lb/>
<anchor type="note" xlink:label="note-0053-05a" xlink:href="note-0053-05"/>
meter tranſuerſa ad E I. </s>
  <s xml:id="echoid-s2277" xml:space="preserve">Dico E I, eſſe latus rectum Ellipſis, id eſt, eſſe rectam, iuxta quã <lb/>
<anchor type="note" xlink:label="note-0053-06a" xlink:href="note-0053-06"/>
poſſunt ordinatim applicatæ ad diametrum. </s>
  <s xml:id="echoid-s2278" xml:space="preserve">Sit enim rectangulum B C, contentum ſub <lb/>B G, G C, rec<unsure/>tis inter punctum G, &amp; </s>
  <s xml:id="echoid-s2279" xml:space="preserve">later a trianguli per axem interiectis: </s>
  <s xml:id="echoid-s2280" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2281" xml:space="preserve">ad G C, ap-<lb/>plicetur rectangulum C H, ſub G C, G H, contentum; </s>
  <s xml:id="echoid-s2282" xml:space="preserve">quod æquale crit quadrato ex A G; <lb/></s>
  <s xml:id="echoid-s2283" xml:space="preserve">
<anchor type="note" xlink:label="note-0053-07a" xlink:href="note-0053-07"/>
quòd tresrectæ C G, A G, G H, ſint continuè proportionales ex conſtructione; </s>
  <s xml:id="echoid-s2284" xml:space="preserve">erit{q́ue} <lb/>B G H, vna linea recta, propter duos angulos rectos ad G. </s>
  <s xml:id="echoid-s2285" xml:space="preserve">Quoniam igitur eſt, vt H G, <lb/>
<anchor type="note" xlink:label="note-0053-08a" xlink:href="note-0053-08"/>
ad G B, ita E F, ad E I; </s>
  <s xml:id="echoid-s2286" xml:space="preserve">vt autem H G, ad G B, ita eſt H C, rectangulum ad rectangulũ <lb/>
<anchor type="note" xlink:label="note-0053-09a" xlink:href="note-0053-09"/>
C B, hoc eſt, quadratum ex A G, ad rectangulum ſub B G, G C, contentum. </s>
  <s xml:id="echoid-s2287" xml:space="preserve">Igitur E I, <lb/>latus rectum eſt Ellipſis E F, ex propoſ. </s>
  <s xml:id="echoid-s2288" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2289" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2290" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2291" xml:space="preserve">Apollonĳ, id eſt, Recta, iuxta quam poſ-<lb/>
<anchor type="note" xlink:label="note-0053-10a" xlink:href="note-0053-10"/>
<anchor type="note" xlink:label="note-0053-11a" xlink:href="note-0053-11"/>
ſunt or dinatim applicatæ &amp;</s>
  <s xml:id="echoid-s2292" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2293" xml:space="preserve"/>
</p>
<div xml:id="echoid-div115" type="float" level="2" n="1">
<note position="right" xlink:label="note-0053-04" xlink:href="note-0053-04a" xml:space="preserve">11. ſexti.</note>
<note position="right" xlink:label="note-0053-05" xlink:href="note-0053-05a" xml:space="preserve">12. ſexti.</note>
<note position="left" xlink:label="note-0053-06" xlink:href="note-0053-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0053-07" xlink:href="note-0053-07a" xml:space="preserve">17. ſexti.</note>
<note position="right" xlink:label="note-0053-08" xlink:href="note-0053-08a" xml:space="preserve">14. primi.</note>
<note position="right" xlink:label="note-0053-09" xlink:href="note-0053-09a" xml:space="preserve">1. ſexti.</note>
<note position="left" xlink:label="note-0053-10" xlink:href="note-0053-10a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0053-11" xlink:href="note-0053-11a" xml:space="preserve">Quomodoquar <lb/>t<unsure/>a pars rectan-<lb/>guli ſub diame-<lb/>tro tianſuerſa <lb/>Ellipſis, &amp; latere <lb/>recto compre-<lb/>henſi applicetur <lb/>ad tranſuerſam <lb/>diametrum ex <lb/>vtraque parte, <lb/>ita vt deficiat fi <lb/>gura quadrata.</note>
</div>
</div>
<div xml:id="echoid-div117" type="section" level="1" n="37">
<head xml:id="echoid-head40" xml:space="preserve">LEMMA II.</head>
<p>
  <s xml:id="echoid-s2294" xml:space="preserve">QVARTAM partem rectanguli ſub diametro tranſuerſa Ellipſis, &amp; </s>
  <s xml:id="echoid-s2295" xml:space="preserve">latere re-<lb/>cto comprehenſi, ad tranſuerſam diametrum ex,<unsure/> vtraque parte applicare, ita vt de-<lb/>ficiat figura quadrata.</s>
  <s xml:id="echoid-s2296" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2297" xml:space="preserve">POSITA eadem figura, reperiatur inter E F, diametrum tranſuerſam, &amp; </s>
  <s xml:id="echoid-s2298" xml:space="preserve">latus re-<lb/>ctum E I, media proportionalis A B, quæ bifariam ſecetur in C. </s>
  <s xml:id="echoid-s2299" xml:space="preserve">Erit igitur quadratum ex <lb/>
<anchor type="note" xlink:label="note-0053-12a" xlink:href="note-0053-12"/>
A B, rectangulo ſub E F, E I, æquale, atque adeò quadratum ex A C, quod ex ſc<unsure/>holio pro-<lb/>
<anchor type="note" xlink:label="note-0053-13a" xlink:href="note-0053-13"/>
poſ. </s>
  <s xml:id="echoid-s2300" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2301" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2302" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2303" xml:space="preserve">Euclidis, quarta pars eſt quadrati ex <lb/>
<anchor type="note" xlink:label="note-0053-14a" xlink:href="note-0053-14"/>
<anchor type="figure" xlink:label="fig-0053-02a" xlink:href="fig-0053-02"/>
A B, quartæ parti rectanguli ſub E F, E I, æquale <lb/>crit. </s>
  <s xml:id="echoid-s2304" xml:space="preserve">Huic igitur quadrato ex A C, applicabimus <lb/>ad diametrum tranſuerſam E F, ex vtraque par-<lb/>te æquale rectangulum, deficiens figura quadrata, <lb/>hac arte. </s>
  <s xml:id="echoid-s2305" xml:space="preserve">Diuiſa recta E F, bifariam in D; </s>
  <s xml:id="echoid-s2306" xml:space="preserve">quo-<lb/>niam per ea, quæ ad definitiones ſecundas lib. </s>
  <s xml:id="echoid-s2307" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s2308" xml:space="preserve">Apollonĳ ab Eutocio ſunt demonſtrata, latus re-<lb/>ctum E I, minus est diametro tranſuerſa E F, hoc <lb/>est, diametro maiore Ellipſis, erit quoque A B, media proportionalis inter E F, E I, mi-
<pb o="34" file="0054" n="54" rhead="GNOMONICES"/>
nor quàm E F. </s>
  <s xml:id="echoid-s2309" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s2310" xml:space="preserve">A C, dimidia ipſius A B, minor erit quàm D F, dimidia ipſius <lb/>E F. </s>
  <s xml:id="echoid-s2311" xml:space="preserve">Deſcripto igitur circa D F, ſemicirculo, accommodetur in eorecta F I, æqualis re-<lb/>
<anchor type="note" xlink:label="note-0054-01a" xlink:href="note-0054-01"/>
ctæ A C, quæ minor eſt ostenſa, quàm D F, ſubtendatur{q́ue} recta D I, quæ minor quoque <lb/>
<anchor type="note" xlink:label="note-0054-02a" xlink:href="note-0054-02"/>
erit, quàm D F. </s>
  <s xml:id="echoid-s2312" xml:space="preserve">Abſcindantur vtrinque ex D, rectæ D N, D O, ipſi D I, æquales. </s>
  <s xml:id="echoid-s2313" xml:space="preserve">Dico <lb/>t<unsure/>am rectangulum ſub E N, N F, ad rectam E F, applicatum, deficiens{q́ue} quadrato ex N F, <lb/>quàm rectangulum ſub F O, O E, ad eandem rectam E F, applicatum, deficiens{q́ue} qua-<lb/>drato ex O E, æquale eße quadrato ex A C, hoc eſt, quartæ parti rectanguli ſub E F, E I. <lb/></s>
  <s xml:id="echoid-s2314" xml:space="preserve">Deſcripto enim ex D F, quadrato D H, perficia-<lb/>
<anchor type="note" xlink:label="note-0054-03a" xlink:href="note-0054-03"/>
<anchor type="figure" xlink:label="fig-0054-01a" xlink:href="fig-0054-01"/>
tur figura, vt vides. </s>
  <s xml:id="echoid-s2315" xml:space="preserve">Quoniam igitur parallelo-<lb/>
<anchor type="note" xlink:label="note-0054-04a" xlink:href="note-0054-04"/>
gramma D H, G L, L F, circa eandem diame-<lb/>trum exiſtentia, ſimilia ſunt, eſt{q́ue} D H, quadra-<lb/>tum, erunt quoque G L, L F, quadrata. </s>
  <s xml:id="echoid-s2316" xml:space="preserve">Et quia <lb/>quadratum D H, æquale est quadratis ex F I, <lb/>
<anchor type="note" xlink:label="note-0054-05a" xlink:href="note-0054-05"/>
D I, hoc eſt, quadrato ex A C, vna cum quadra-<lb/>to G L; </s>
  <s xml:id="echoid-s2317" xml:space="preserve">(Eſt enim angul{us} D I F, rect{us}, &amp; </s>
  <s xml:id="echoid-s2318" xml:space="preserve">rectæ <lb/>
<anchor type="note" xlink:label="note-0054-06a" xlink:href="note-0054-06"/>
F I, D I, æquales fuerunt rectis A C, D N, vel <lb/>K L.) </s>
  <s xml:id="echoid-s2319" xml:space="preserve">erit gnomon K N H, quadrato ex A C, æqualis. </s>
  <s xml:id="echoid-s2320" xml:space="preserve">Cum ergo gnomon K N H, æqua-<lb/>
<anchor type="note" xlink:label="note-0054-07a" xlink:href="note-0054-07"/>
lis quoque ſit rectangulo E L, (Nam cum E K, ipſi K F, hoc eſt, ipſi N H, æquale ſit; </s>
  <s xml:id="echoid-s2321" xml:space="preserve">addi-<lb/>
<anchor type="note" xlink:label="note-0054-08a" xlink:href="note-0054-08"/>
to communi D L, fit totum E L, toti gnomoni K N H, æquale) erit quoque rectangulum <lb/>E L, contentum ſub E N, N F; </s>
  <s xml:id="echoid-s2322" xml:space="preserve">(quòd recta N F, rectæ N L, æqualis ſit, ob quadratum <lb/>L F.) </s>
  <s xml:id="echoid-s2323" xml:space="preserve">æquale quadrato ex A C. </s>
  <s xml:id="echoid-s2324" xml:space="preserve">Applicatum eſt ergo ad E F, diametrum tranſuerſam <lb/>rectangulum ſub E N, N F, æquale quartæ parti rectanguli ſub E F, E I, deficiens{q́ue} qua-<lb/>drato rectæ N F. </s>
  <s xml:id="echoid-s2325" xml:space="preserve">Eodem modo demonſtrabitur rectangulum ſub F O, O E, applicatum ad <lb/>E F, deficiens{q́ue} quadrato ex E O, æquale eße quartæ parti rectanguli ſub E F, E I. </s>
  <s xml:id="echoid-s2326" xml:space="preserve">Quod <lb/>eſt propoſitum.</s>
  <s xml:id="echoid-s2327" xml:space="preserve"/>
</p>
<div xml:id="echoid-div117" type="float" level="2" n="1">
<note position="right" xlink:label="note-0053-12" xlink:href="note-0053-12a" xml:space="preserve">13. ſexti.</note>
<note position="right" xlink:label="note-0053-13" xlink:href="note-0053-13a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0053-14" xlink:href="note-0053-14a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0053-02" xlink:href="fig-0053-02a">
    <image file="0053-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-02"/>
  </figure>
<note position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve">1. quarti.</note>
<note position="left" xlink:label="note-0054-02" xlink:href="note-0054-02a" xml:space="preserve">15. tertĳ.</note>
<note position="left" xlink:label="note-0054-03" xlink:href="note-0054-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a">
    <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0054-01"/>
  </figure>
<note position="left" xlink:label="note-0054-04" xlink:href="note-0054-04a" xml:space="preserve">34. ſexti.</note>
<note position="left" xlink:label="note-0054-05" xlink:href="note-0054-05a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0054-06" xlink:href="note-0054-06a" xml:space="preserve">31. tertĳ.</note>
<note position="left" xlink:label="note-0054-07" xlink:href="note-0054-07a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0054-08" xlink:href="note-0054-08a" xml:space="preserve">36. primi.</note>
</div>
<note position="left" xml:space="preserve">Alia deſcriptio <lb/>Ellipſis in pla-<lb/>no.</note>
<p style="it">
  <s xml:id="echoid-s2328" xml:space="preserve">HIS præmiſſis ſit E F, axis tranſuerſus Ellipſis E F, &amp; </s>
  <s xml:id="echoid-s2329" xml:space="preserve">lat{us} rectum E I, datum ex lemmate 1. <lb/></s>
  <s xml:id="echoid-s2330" xml:space="preserve">
<anchor type="note" xlink:label="note-0054-10a" xlink:href="note-0054-10"/>
Applicetur per 2. </s>
  <s xml:id="echoid-s2331" xml:space="preserve">lemma, ad E F, ex vtraque parte rectangulum tam ſub F O, O E, quàm ſub E N, <lb/>N F, quartæ parti rectanguli ſub E F, E I, æquale, quorum illud quidem deficiat quadrato ex E O, hoc <lb/>vero, quadrato ex F N. </s>
  <s xml:id="echoid-s2332" xml:space="preserve">Et diuiſa N O, bifariam in A, ſumantur inter A, &amp; </s>
  <s xml:id="echoid-s2333" xml:space="preserve">N, quotlibet puncta vt-<lb/>cunque B, C, D. </s>
  <s xml:id="echoid-s2334" xml:space="preserve">Deinde ad interuallum E A, vel F A, ex punctis O, &amp; </s>
  <s xml:id="echoid-s2335" xml:space="preserve">N, deſcribantur quatuor ar-<lb/>cus ſemutuo ſecantes hinc inde in G. </s>
  <s xml:id="echoid-s2336" xml:space="preserve">Item ex eiſdem punctis O, &amp; </s>
  <s xml:id="echoid-s2337" xml:space="preserve">N, ad interuallum E B, quatuor ar-<lb/>cus deſcribantur, quos in puncto H, ſecent alĳ quatuor arcus ex eiſdem punctis ad interuallum F B, de-<lb/>ſcripti. </s>
  <s xml:id="echoid-s2338" xml:space="preserve">Eodem modo ad interualla E C, F C, ex eiſdem punctis O, &amp; </s>
  <s xml:id="echoid-s2339" xml:space="preserve">N, arcus deſcripti ſemutuo ſecent <lb/>in I; </s>
  <s xml:id="echoid-s2340" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2341" xml:space="preserve">ſic de cæteris punctis, ſi qua ſint; </s>
  <s xml:id="echoid-s2342" xml:space="preserve">obſeruando ſemper, vt bini maiorcs arcus ex ſingulis quatuor, <lb/>qui ex O, &amp; </s>
  <s xml:id="echoid-s2343" xml:space="preserve">N, deſcribendi ſunt, deſcribantur ex O, vltra punctum A, &amp; </s>
  <s xml:id="echoid-s2344" xml:space="preserve">bini ex N, vltra idem pun-<lb/>ctum A; </s>
  <s xml:id="echoid-s2345" xml:space="preserve">bini autem minores ex O, citra punctum A, &amp; </s>
  <s xml:id="echoid-s2346" xml:space="preserve">bini ex N, citra idem punctum A. </s>
  <s xml:id="echoid-s2347" xml:space="preserve">Nam per <lb/>
<anchor type="note" xlink:label="note-0054-11a" xlink:href="note-0054-11"/>
puncta E, G, H, I, F, Ellipſis erit deſcribenda. </s>
  <s xml:id="echoid-s2348" xml:space="preserve">Quoniam enimtam rectæ N G, O G, hoc eſt, E A, F A, <lb/>quàm rectæ N H, O H, id est, E B, F B, &amp;</s>
  <s xml:id="echoid-s2349" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2350" xml:space="preserve">axi E F, æquales ſunt, tranſibit Ellipſis, cuius axis E F, <lb/>per puncta E, G, H, I, F; </s>
  <s xml:id="echoid-s2351" xml:space="preserve">quandoquidem, vt vult propoſitio 52. </s>
  <s xml:id="echoid-s2352" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2353" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2354" xml:space="preserve">Apollonĳ, lineæ rectæ ex punctis <lb/>N, O, ad vnum idem{q́ue} Ellipſis punctum inclinatæ æquales ſunt axi E F. </s>
  <s xml:id="echoid-s2355" xml:space="preserve">Sinamque dicta Ellipſis non <lb/>tranſit per punctum I, tranſeat, ſifieri poteſt, per K, ſecans rectam N I, in K, vel vltra, vel citra I, <lb/>iungatur{q́ue}, recta O K. </s>
  <s xml:id="echoid-s2356" xml:space="preserve">Quoniam igitur Ellipſis prædicta tranſit per K, erunt rectæ N K, O K, ſimul æqua-<lb/>les axi E F, ex propoſ. </s>
  <s xml:id="echoid-s2357" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2358" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2359" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2360" xml:space="preserve">Apollonĳ: </s>
  <s xml:id="echoid-s2361" xml:space="preserve">Sed per conſtructionem &amp; </s>
  <s xml:id="echoid-s2362" xml:space="preserve">rectæ N I, O I, eidem axi E F, <lb/>æquales ſunt. </s>
  <s xml:id="echoid-s2363" xml:space="preserve">Igitur N K, O K, rectis N I, O I, æquales erunt: </s>
  <s xml:id="echoid-s2364" xml:space="preserve">Sed &amp; </s>
  <s xml:id="echoid-s2365" xml:space="preserve">inæquales ſunt; </s>
  <s xml:id="echoid-s2366" xml:space="preserve">(Nam cadente pun-<lb/>cto K, vltra I, erunt rectæ I K, K O, maiores recta I O; </s>
  <s xml:id="echoid-s2367" xml:space="preserve">addita ergo communi I N, erunt N K, O K, <lb/>
<anchor type="note" xlink:label="note-0054-12a" xlink:href="note-0054-12"/>
maiores, quàm N I, O I: </s>
  <s xml:id="echoid-s2368" xml:space="preserve">Cadente verò puncto K, citra I, erunt I K, I O, maiores, quàm K O. </s>
  <s xml:id="echoid-s2369" xml:space="preserve">addi-<lb/>
<anchor type="note" xlink:label="note-0054-13a" xlink:href="note-0054-13"/>
<anchor type="note" xlink:label="note-0054-14a" xlink:href="note-0054-14"/>
ta ergo communi K N, erunt N I, O I, maiores, quàm N k, O K) Quod est abſurdum. </s>
  <s xml:id="echoid-s2370" xml:space="preserve">Non ergo dicta <lb/>Ellipſis per aliud punctum, quàm per I, tranſibit. </s>
  <s xml:id="echoid-s2371" xml:space="preserve">Eodc<unsure/>m{q́ue} modo demonſtrabimus eandem per reliqua <lb/>puncta H, G, &amp;</s>
  <s xml:id="echoid-s2372" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2373" xml:space="preserve">tranſire, quod eſt propoſitum.</s>
  <s xml:id="echoid-s2374" xml:space="preserve"/>
</p>
<div xml:id="echoid-div118" type="float" level="2" n="2">
<note position="left" xlink:label="note-0054-10" xlink:href="note-0054-10a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0054-11" xlink:href="note-0054-11a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0054-12" xlink:href="note-0054-12a" xml:space="preserve">20. primi.</note>
<note position="left" xlink:label="note-0054-13" xlink:href="note-0054-13a" xml:space="preserve">20. primi.</note>
<note position="left" xlink:label="note-0054-14" xlink:href="note-0054-14a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s2375" xml:space="preserve">PERSPICVVM etiam eſt, hanc deſcriptionem non conuenire conis ſcalenis, niſi cum triangula <lb/>
<anchor type="note" xlink:label="note-0054-15a" xlink:href="note-0054-15"/>
per axem ad baſes conorum recta ſunt. </s>
  <s xml:id="echoid-s2376" xml:space="preserve">Tunc enim ſolum diameter ellipſis ad angulos rectos ſecat ordi-<lb/>natim applicatas, vt ex propoſ. </s>
  <s xml:id="echoid-s2377" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2378" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2379" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2380" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s2381" xml:space="preserve">conſtat, atque adeo axis eſt.</s>
  <s xml:id="echoid-s2382" xml:space="preserve"/>
</p>
<div xml:id="echoid-div119" type="float" level="2" n="3">
<note position="left" xlink:label="note-0054-15" xlink:href="note-0054-15a" xml:space="preserve">Qua ratione <lb/>Parabola qua-<lb/>liſ<unsure/>unque in <lb/>plano deſcriba-<lb/>tur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2383" xml:space="preserve">QVOD ſi vt cunque Parabolã aliquam, Hyperbolã, vel etiã duas oppoſitas, aut Ellipſim deſcribere<unsure/> <lb/>velimus, nulla habita ratione conorũ, à quibus oriuntur, accipiemus pro parabola axem cuiuſcunque ma-<lb/>gnitudinis E H, vt in ſuperiori parabola, &amp; </s>
  <s xml:id="echoid-s2384" xml:space="preserve">in eo quotcunque partes æquales vt libet, et per puncta termi <lb/>nantia primam partem, &amp; </s>
  <s xml:id="echoid-s2385" xml:space="preserve">ſequẽtes tres, &amp; </s>
  <s xml:id="echoid-s2386" xml:space="preserve">ſequentes quinque, &amp; </s>
  <s xml:id="echoid-s2387" xml:space="preserve">ſeque<unsure/>ntes ſeptem, &amp;</s>
  <s xml:id="echoid-s2388" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2389" xml:space="preserve">ducemus lineas <lb/>inter ſe parallelas; </s>
  <s xml:id="echoid-s2390" xml:space="preserve">ſumpta autem ex prima, quantacunque linea vtrinque A D, accipiemus eius duplam
<pb o="35" file="0055" n="55" rhead="LIBER PRIMVS."/>
in ſecunda, triplam intertia, &amp; </s>
  <s xml:id="echoid-s2391" xml:space="preserve">quadruplam in quarta, &amp;</s>
  <s xml:id="echoid-s2392" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2393" xml:space="preserve">Per extremitates enim harum linearum <lb/>parabole deſcribenda erit.</s>
  <s xml:id="echoid-s2394" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2395" xml:space="preserve">PRO Hyperbolis verò ſumemus axem quemcunque F I, vt in antecedentibus hyperbolis, cui ex <lb/>
<anchor type="note" xlink:label="note-0055-01a" xlink:href="note-0055-01"/>
vtraque parte addemus rectas vtcunque F R, I Q, inter ſe æquales, &amp; </s>
  <s xml:id="echoid-s2396" xml:space="preserve">intelligemus ad axem F I, ap-<lb/>plicatum eſſe rectangulum ſub F Q, Q I, æquale quartæ parti rectanguli ſub axe F I, &amp; </s>
  <s xml:id="echoid-s2397" xml:space="preserve">recto latere <lb/>comprehenſi, excedens{q́ue}, quadrato ex Q I, &amp;</s>
  <s xml:id="echoid-s2398" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2399" xml:space="preserve"/>
</p>
<div xml:id="echoid-div120" type="float" level="2" n="4">
<note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">Qua ratione <lb/>duæ hyperbolæ <lb/>oppoſitæ qua-<lb/>leſcunque de-<lb/>ſcribantur in <lb/>plano.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2400" xml:space="preserve">PRO Ellipſi denique accipiemus axem E F, ad libitum, vt in proxima ellipſi, ex quo abſcindemus <lb/>
<anchor type="note" xlink:label="note-0055-02a" xlink:href="note-0055-02"/>
æquales hinc inde vtcunque E O, F N, intelligem{us}{q́ue} ad axem E F, applicatum eſſe rectangulum ſub <lb/>F O, O E, æquale quartæ parti rectanguli ſub axe E F, &amp; </s>
  <s xml:id="echoid-s2401" xml:space="preserve">latere recto contenti, deficiens{q́ue} quadrato ex <lb/>E O; </s>
  <s xml:id="echoid-s2402" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s2403" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2404" xml:space="preserve">Reliqua autem perficiemus vt prius.</s>
  <s xml:id="echoid-s2405" xml:space="preserve"/>
</p>
<div xml:id="echoid-div121" type="float" level="2" n="5">
<note position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">Qua ratione El <lb/>lipſis qualiſcun <lb/>que in plano de <lb/>ſcribatur.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s2406" xml:space="preserve">IMMO verò ſi in recta aliqua quantumuis protracta E F, nempe in eodem axe ellipſis, in duobus <lb/>
<anchor type="note" xlink:label="note-0055-04a" xlink:href="note-0055-04"/>
punctis, vt in N, &amp; </s>
  <s xml:id="echoid-s2407" xml:space="preserve">O, duo clauiculi infigantur, quibus filum circumponatur, ita vt duplicatum exce-<lb/>dat rectam N O, &amp; </s>
  <s xml:id="echoid-s2408" xml:space="preserve">liberè poſſit circumuolui, deſcribetur Ellipſis facilè, &amp; </s>
  <s xml:id="echoid-s2409" xml:space="preserve">expedite, ſi ſtylum aliquem <lb/>huic filo imponamus, eum{q́ue} circunducamus vnà cumfilo, extendentes ſemper filum, quantum fieri poteſt. <lb/></s>
  <s xml:id="echoid-s2410" xml:space="preserve">Vt ſi filum circa clauiculos N, O, extendatur vſque ad I, quantum poteſt, ſi ſtylus aliquis ferreus in I, <lb/>ponatur, &amp; </s>
  <s xml:id="echoid-s2411" xml:space="preserve">manentefilo ſemper ita extenſo circunducatur, donec eo reuertatur, vnde moueri incepit, de-<lb/>ſc<unsure/>ripta erit Ellipſis E G F; </s>
  <s xml:id="echoid-s2412" xml:space="preserve">Nam hac ratione erunt ſemper duæ rectæ ex N, &amp; </s>
  <s xml:id="echoid-s2413" xml:space="preserve">O, vſque ad ſtylum cir-<lb/>cumductum ęquales axi E F, quem idem ſtylus circumductus ſecat in E, &amp; </s>
  <s xml:id="echoid-s2414" xml:space="preserve">F. </s>
  <s xml:id="echoid-s2415" xml:space="preserve">Id quod longè facilius re <lb/>ipſa, &amp; </s>
  <s xml:id="echoid-s2416" xml:space="preserve">vſu percipi poteſt, quàm multis verbis doceri.</s>
  <s xml:id="echoid-s2417" xml:space="preserve"/>
</p>
<div xml:id="echoid-div122" type="float" level="2" n="6">
<note position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">Quo pacto El-<lb/>lipſis qualiſcun <lb/>que filo aliquo <lb/>deſctibatur in <lb/>plano.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2418" xml:space="preserve">SED quoniam deſcriptio hæc Ellipſis per filum circa clauiculos accommodatum &amp; </s>
  <s xml:id="echoid-s2419" xml:space="preserve">per ſe ipſa iucun-<lb/>
<anchor type="note" xlink:label="note-0055-05a" xlink:href="note-0055-05"/>
daeſt, &amp; </s>
  <s xml:id="echoid-s2420" xml:space="preserve">ad multa vtilis, li-<lb/>
<anchor type="figure" xlink:label="fig-0055-01a" xlink:href="fig-0055-01"/>
bet paulo vberius eam hoc <lb/>
<anchor type="note" xlink:label="note-0055-06a" xlink:href="note-0055-06"/>
loco explicare. </s>
  <s xml:id="echoid-s2421" xml:space="preserve">Primum igi-<lb/>tur, ſi datus ſit vterque axis <lb/>Ellipſis, nempe A B, maior, <lb/>et C D, minor, ita vt Ellipſis <lb/>deſcribenda longitudinẽ ha-<lb/>beat A B, latitudinem ve-<lb/>rò C D, inueniemus puncta <lb/>in maiore axe, in quibus fi-<lb/>
<anchor type="note" xlink:label="note-0055-07a" xlink:href="note-0055-07"/>
gendi ſunt clauiculi, &amp; </s>
  <s xml:id="echoid-s2422" xml:space="preserve">lon <lb/>gitudinem fili circa clauicu-<lb/>los circumducendi, hac ra-<lb/>tione. </s>
  <s xml:id="echoid-s2423" xml:space="preserve">Diuiſo maiore axe <lb/>A B, bifariam in E, duca-<lb/>tur per E, ad A B, perpen-<lb/>dicularis C D, ſit{q́ue} tam E C, <lb/>quàm E D, dimidio minoris <lb/>axis æqualis, ita vt C D, to-<lb/>ti axi minori ſit æqualis. <lb/></s>
  <s xml:id="echoid-s2424" xml:space="preserve">
<anchor type="note" xlink:label="note-0055-08a" xlink:href="note-0055-08"/>
Deinde centro C, vel D, &amp; </s>
  <s xml:id="echoid-s2425" xml:space="preserve"><lb/>interuallo E A, vel E B, duo <lb/>arcus circuli deſcribantur <lb/>ſecantes rectam A B, in F, <lb/>&amp; </s>
  <s xml:id="echoid-s2426" xml:space="preserve">G, punctis, quæomnino <lb/>
<anchor type="note" xlink:label="note-0055-09a" xlink:href="note-0055-09"/>
citra puncta A, &amp; </s>
  <s xml:id="echoid-s2427" xml:space="preserve">B, erunt. <lb/></s>
  <s xml:id="echoid-s2428" xml:space="preserve">Quoniam enim recta C A, <lb/>
<anchor type="note" xlink:label="note-0055-10a" xlink:href="note-0055-10"/>
maior eſt, quàm A E, ob <lb/>angulum rectum A E C, fit, vt arcus ex C, ad interuallum A E, deſcriptus ſecet ipſam C A, atque adeò <lb/>
<anchor type="note" xlink:label="note-0055-11a" xlink:href="note-0055-11"/>
&amp; </s>
  <s xml:id="echoid-s2429" xml:space="preserve">ipſam A E, citra punctum A, &amp;</s>
  <s xml:id="echoid-s2430" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2431" xml:space="preserve">Dico in punctis F, G, clauiculos eſſe figendos, vt propoſita Elli-<lb/>pſis deſcribatur, filum autem circa F, G, poſitum duplicandũ eſſe, ita vt extenſum pertingat præcisè ad <lb/>punctũ A, vel ad punctũ D, aut B, totum{q́ue} filum ſit D F G D, hac lege clauiculis in F, &amp; </s>
  <s xml:id="echoid-s2432" xml:space="preserve">G, affixis cir-<lb/>cũpoſitum, vt liberè circa ipſos poſſit circũduci vnà cum ſtylo, adeò vt neque à clauiculis, neque à filo ſty-<lb/>lus impediatur, quo minus circumduci queat, vt integram ellipſim deſcribat. </s>
  <s xml:id="echoid-s2433" xml:space="preserve">Cum enim portiones G A, <lb/>F A, fili duplicati (relicta portione F G, inter clauiculos poſita) æquales ſint maiori axi A B, quòd A F, <lb/>ipſi B G, æqualis ſit, atq; </s>
  <s xml:id="echoid-s2434" xml:space="preserve">eodẽ modo reliquæ portiones, circũducto filo circa pũcta F, G, eidẽ aximaiori ſint <lb/>æquales, propterea quòd filum neq; </s>
  <s xml:id="echoid-s2435" xml:space="preserve">augetur, neque diminuitur in illa circũductione, manet{q́ue} eadẽ ſemper <lb/>portio communis F G, (Ita enim vides, exempli gratia, cum extremũ duplicati fili in D, collocatũ fuerit, <lb/>portiones D F, D G, toti axi A B, æquales eſſe, propterea quod ipſis A E, B E, ſumptæ ſunt æquales, &amp;</s>
  <s xml:id="echoid-s2436" xml:space="preserve">c.) <lb/></s>
  <s xml:id="echoid-s2437" xml:space="preserve">perſpicuum eſt, ex propoſ. </s>
  <s xml:id="echoid-s2438" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2439" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2440" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2441" xml:space="preserve">Apollonĳ, beneficio illius fili deſcribi Ellipſim, cuius maior axis <lb/>A B, &amp; </s>
  <s xml:id="echoid-s2442" xml:space="preserve">minor C D: </s>
  <s xml:id="echoid-s2443" xml:space="preserve">quandoquidem lineæ rectæ ex punctis F, &amp; </s>
  <s xml:id="echoid-s2444" xml:space="preserve">G, inclinatæ ad quodcunque punctum
<pb o="36" file="0056" n="56" rhead="GNOMONICES"/>
lineæ curuæ per puncta A, C, D, B, deſcriptæ æquales ſunt maiori axi AB, vt vult illa ꝓpoſitio Apollonĳ.</s>
  <s xml:id="echoid-s2445" xml:space="preserve"/>
</p>
<div xml:id="echoid-div123" type="float" level="2" n="7">
<note position="left" xlink:label="note-0055-05" xlink:href="note-0055-05a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a">
    <image file="0055-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0055-01"/>
  </figure>
<note position="right" xlink:label="note-0055-06" xlink:href="note-0055-06a" xml:space="preserve">Qua ratione <lb/>Ellipſis deſcri-<lb/>batur per filũ, <lb/>ſecundum lon-<lb/>gitudinem &amp; la <lb/>titudinem da-<lb/>tam.</note>
<note position="left" xlink:label="note-0055-07" xlink:href="note-0055-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0055-08" xlink:href="note-0055-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0055-09" xlink:href="note-0055-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0055-10" xlink:href="note-0055-10a" xml:space="preserve">19. primi.</note>
<note position="right" xlink:label="note-0055-11" xlink:href="note-0055-11a" xml:space="preserve">Loca clauiculo-<lb/>rum, &amp; longitu <lb/>do fili pro Elli-<lb/>pſi deſctibẽda.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2446" xml:space="preserve">INVENIEMVS quoque puncta F, G, pro clauiculorum locis hac ratione, &amp; </s>
  <s xml:id="echoid-s2447" xml:space="preserve">fortaſſe certius, <lb/>
<anchor type="note" xlink:label="note-0056-01a" xlink:href="note-0056-01"/>
propterea quod, cum minor axis fermè æqualis eſt maiori, arcus cir culorum ex C, vel D, deſcripti ualdè <lb/>
<anchor type="figure" xlink:label="fig-0056-01a" xlink:href="fig-0056-01"/>
obliquè ſecant rectam A B. <lb/></s>
  <s xml:id="echoid-s2448" xml:space="preserve">Diuiſa recta B E, quæ dimi-<lb/>dium eſt axis maioris, bifa-<lb/>riã in H, deſcribatur ex H, <lb/>ad interuallũ H B, vel H E, <lb/>ſemicir culus B I E, &amp; </s>
  <s xml:id="echoid-s2449" xml:space="preserve">in eo <lb/>accõmodetur recta B I, dimi-<lb/>
<anchor type="note" xlink:label="note-0056-02a" xlink:href="note-0056-02"/>
<anchor type="note" xlink:label="note-0056-03a" xlink:href="note-0056-03"/>
dio minoris axis D E, æqua-<lb/>lis, ducatur{q́ue} recta E I. </s>
  <s xml:id="echoid-s2450" xml:space="preserve">Dico <lb/>rectã E I, æqualem eſſe tam <lb/>rectæ E F, quàm rectæ E G, <lb/>atque adeò, ſi abſcindantur <lb/>rectæ E F, E G, ipſi E I, <lb/>æquales, inuenta eſſe eadem <lb/>puncta F, G, pro locis claui-<lb/>culorum. </s>
  <s xml:id="echoid-s2451" xml:space="preserve">Quoniã enim qua-<lb/>
<anchor type="note" xlink:label="note-0056-04a" xlink:href="note-0056-04"/>
dratum ex B E, æquale eſt <lb/>
<anchor type="note" xlink:label="note-0056-05a" xlink:href="note-0056-05"/>
quadratis ex E I, I B; </s>
  <s xml:id="echoid-s2452" xml:space="preserve">Et tã <lb/>quadratum ex D G, quadra-<lb/>tis ex D E, E G, quàm qua-<lb/>dratum ex D F, quadratis ex <lb/>D E, E F, æquale: </s>
  <s xml:id="echoid-s2453" xml:space="preserve">Eſt aũt qua-<lb/>dratũ ex BE, tã quadrato ex <lb/>D G, quàm quadrato ex D F, <lb/>æquale, quod hæ lineæ æqua-<lb/>les ſint ex conſtructione; </s>
  <s xml:id="echoid-s2454" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2455" xml:space="preserve"><lb/>quadratũ ex B I, æquale qua-<lb/>
<anchor type="note" xlink:label="note-0056-06a" xlink:href="note-0056-06"/>
drato ex D E, quòd per con-<lb/>ſtructionẽ æquales quoque ſint poſitæ rectæ B I, D E; </s>
  <s xml:id="echoid-s2456" xml:space="preserve">crit reliquũ quadratũ ex E I, reliquo quadrato tam ex <lb/>E G, quàm ex E F, deſcripto æquale, ac proinde recta E I, rectis E G, E F, æqualis erit, quod eſt propoſitũ.</s>
  <s xml:id="echoid-s2457" xml:space="preserve"/>
</p>
<div xml:id="echoid-div124" type="float" level="2" n="8">
<note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">Loca claniculo-<lb/>rũ ad Ellipſim <lb/>deſcribendam <lb/>alia ratione in-<lb/>ueniuntur.</note>
  <figure xlink:label="fig-0056-01" xlink:href="fig-0056-01a">
    <image file="0056-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0056-01"/>
  </figure>
<note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">1. quarti.</note>
<note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s2458" xml:space="preserve">DEINDE ſi datus ſit maior duntaxat axis Ellipſis A B, &amp; </s>
  <s xml:id="echoid-s2459" xml:space="preserve">aliquod punctum K, per quod tranſi-<lb/>
<anchor type="note" xlink:label="note-0056-07a" xlink:href="note-0056-07"/>
re debeat Ellipſis circa axem A B, deſcripta, reperiemus minorem axem, hoc eſt, latitudinem Ellipſis, <lb/>&amp; </s>
  <s xml:id="echoid-s2460" xml:space="preserve">puncta F, G, in quibus affigendi ſunt clauiculi, hac ratione. </s>
  <s xml:id="echoid-s2461" xml:space="preserve">Diuiſa A B, bifariam in E, ducatur per <lb/>E, ad A B, perpendicularis C D, &amp; </s>
  <s xml:id="echoid-s2462" xml:space="preserve">ex dato puncto K, ad eandem A B, alia perpendicularis K L, vel ip-<lb/>ſi C D, parallela. </s>
  <s xml:id="echoid-s2463" xml:space="preserve">Deinde per ea, quæ in problemate tertio ſcholĳ propoſ. </s>
  <s xml:id="echoid-s2464" xml:space="preserve">vltimæ lib. </s>
  <s xml:id="echoid-s2465" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2466" xml:space="preserve">Euclidis demon-<lb/>ſtr ata ſunt à nobis, fiat, vt rectangulum ſub A L, L B, contentum ad rectangulum contentum ſub A E, <lb/>E B, hoc eſt, ad quadratum ex A E, vel E B, (Hoc enim rectangulum quadratum eſt, ob æqualitatem re-<lb/>
<anchor type="note" xlink:label="note-0056-08a" xlink:href="note-0056-08"/>
ctarum A E, E B) ita quadratum ex K L, ad aliud quadratũ, cuius latus ſit E D, vel E C. </s>
  <s xml:id="echoid-s2467" xml:space="preserve">Erit{q́ue} ex de-<lb/>monſtratis ab Apollonio propoſ. </s>
  <s xml:id="echoid-s2468" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2469" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2470" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2471" xml:space="preserve">E D, vel E C, dimidium axis minoris; </s>
  <s xml:id="echoid-s2472" xml:space="preserve">per quam, vt paulo an-<lb/>te docuimus, inueniemus puncta F, &amp; </s>
  <s xml:id="echoid-s2473" xml:space="preserve">G, quorum beneficio Ellipſim deſcribemus.</s>
  <s xml:id="echoid-s2474" xml:space="preserve"/>
</p>
<div xml:id="echoid-div125" type="float" level="2" n="9">
<note position="left" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve">Quomodo El-<lb/>lipſis circa datũ <lb/>axem maiorem, <lb/>&amp; per datũ pun <lb/>ctum deſcriba-<lb/>tur.</note>
<note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s2475" xml:space="preserve">ITA autem expedite quadratum lateris E D, vel E C, quæſiti comperiemus. </s>
  <s xml:id="echoid-s2476" xml:space="preserve">Ex E, ad interuallum <lb/>E A, vel E B, ſemicir culus deſcribatur A M B, quem recta L K, producta ſecet in M; </s>
  <s xml:id="echoid-s2477" xml:space="preserve">Eritq́, ex ſcholio <lb/>propoſ. </s>
  <s xml:id="echoid-s2478" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2479" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2480" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2481" xml:space="preserve">Euclidis, recta L M, media proportionalis inter A L, L B, atq; </s>
  <s xml:id="echoid-s2482" xml:space="preserve">adeo eius quadratũ re-<lb/>
<anchor type="note" xlink:label="note-0056-09a" xlink:href="note-0056-09"/>
ctangulo ſub A L, L B, cõtento æquale. </s>
  <s xml:id="echoid-s2483" xml:space="preserve">Vnde facili negotio reperiemus quadratũ, ad quod eandẽ propor-<lb/>tionẽ habeat quadratũ ex L K, quã habet quadratũ ex L M, hoc eſt, rectangulũ ſub A L, L B, comprehen-<lb/>ſum, ad quadratum ex E A, vel E B, hoc eſt, ad rectangulum ſub A E, E B, contentum, ſi tribus rectis <lb/>
<anchor type="note" xlink:label="note-0056-10a" xlink:href="note-0056-10"/>
L M, E A, L K, quartam proportionalem inueniamus E D; </s>
  <s xml:id="echoid-s2484" xml:space="preserve">propterea quod eandem proportionẽ habent <lb/>
<anchor type="note" xlink:label="note-0056-11a" xlink:href="note-0056-11"/>
quadrata ſupra rectas L M, E A, L K, E D, deſcripta, quam ipſęmet rectæ. </s>
  <s xml:id="echoid-s2485" xml:space="preserve">Hoc autem artificio dictam <lb/>
<anchor type="note" xlink:label="note-0056-12a" xlink:href="note-0056-12"/>
quartam proportionalem E D, reperiemus. </s>
  <s xml:id="echoid-s2486" xml:space="preserve">Ductis rectis duabus N O, N P, facientibus angulum in N, <lb/>quemcunque, ſumatur N Q, ipſi L M, &amp; </s>
  <s xml:id="echoid-s2487" xml:space="preserve">Q O, ipſi E A, &amp; </s>
  <s xml:id="echoid-s2488" xml:space="preserve">N R, ipſi L K, æqualis. </s>
  <s xml:id="echoid-s2489" xml:space="preserve">Deinde ducta Q R, <lb/>agatur per O, ipſi Q R, parallela O P. </s>
  <s xml:id="echoid-s2490" xml:space="preserve">Erit R P, dicta quarta proportionalis; </s>
  <s xml:id="echoid-s2491" xml:space="preserve">cum ſit, vt N Q, hoc eſt, <lb/>
<anchor type="note" xlink:label="note-0056-13a" xlink:href="note-0056-13"/>
L M, ad Q O, hoc eſt, ad E A, ita N R, hoc eſt, L K, ad R P. </s>
  <s xml:id="echoid-s2492" xml:space="preserve">Quare ſi ſumamus E D, ipſi R P, æqualem, <lb/>habebimus minoris axis dimidium E D, &amp; </s>
  <s xml:id="echoid-s2493" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2494" xml:space="preserve"/>
</p>
<div xml:id="echoid-div126" type="float" level="2" n="10">
<note position="left" xlink:label="note-0056-09" xlink:href="note-0056-09a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0056-10" xlink:href="note-0056-10a" xml:space="preserve">12. ſexti.</note>
<note position="left" xlink:label="note-0056-11" xlink:href="note-0056-11a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0056-12" xlink:href="note-0056-12a" xml:space="preserve">22. ſexti.</note>
<note position="left" xlink:label="note-0056-13" xlink:href="note-0056-13a" xml:space="preserve">2. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2495" xml:space="preserve">CAETERVM loco clauiculorum vti poterimus inſtrumento quodam ad ſimilitudinẽ circini fabri-<lb/>
<anchor type="note" xlink:label="note-0056-14a" xlink:href="note-0056-14"/>
cato, cuius crura in extremitatibus ſint reſecta, &amp; </s>
  <s xml:id="echoid-s2496" xml:space="preserve">frusta abſciſſa ita adaptata, vt hinc inde poſſint di-<lb/>moueri, &amp; </s>
  <s xml:id="echoid-s2497" xml:space="preserve">cochleolis aſtringi, vt quãtumuis dilatentur circini crura, ſemper fruſta illa cochleolis aſtricta <lb/>recta ſint ad planũ, in quo Ellipſis deſcribenda eſt. </s>
  <s xml:id="echoid-s2498" xml:space="preserve">Hæc autẽ fruſta habeant etiã in extremis partibus ca-<lb/>naliculos quoſdam per circuitum inciſos, ita vt filum in ĳs circumuolutum neque ſurſum aſcendat, neque
<pb o="37" file="0057" n="57" rhead="LIBER PRIMVS."/>
deſcendat deorſum. </s>
  <s xml:id="echoid-s2499" xml:space="preserve">Hoc enim inſtrumento facile Ellipſim deſcribemus, ſi eius cruribus dilatatis, frusta <lb/>illa ſtatuantur in punctis inuentis F, &amp; </s>
  <s xml:id="echoid-s2500" xml:space="preserve">G, ita vt recta ſint ad planũ, filum{q́ue} cir cũponamus, vt ſupra dixi-<lb/>mus. </s>
  <s xml:id="echoid-s2501" xml:space="preserve">Sed quoniã filũ intenditur ſemper &amp; </s>
  <s xml:id="echoid-s2502" xml:space="preserve">remittitur aliquantulũ, multo accuratius Ellipſis deſcribetur, <lb/>licet non tam facile, inſtrumento, quod Guidus V baldus è Marchionibus Montis, vir hac ętate non minus <lb/>ingenĳ, at que doctrinæ præstantia, quàm generis nobilitate clariſſimus, in Theorica planiſphęriorum vni-<lb/>uerſalium, quæ nuper ab eo edita est, inuenit, &amp; </s>
  <s xml:id="echoid-s2503" xml:space="preserve">acutiſſimè demonſtrauit.</s>
  <s xml:id="echoid-s2504" xml:space="preserve"/>
</p>
<div xml:id="echoid-div127" type="float" level="2" n="11">
<note position="left" xlink:label="note-0056-14" xlink:href="note-0056-14a" xml:space="preserve">Inſtrumentum <lb/>pro Ellipſi per <lb/>filum deſcriben <lb/>da.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2505" xml:space="preserve">INSTRVMENTV Minſtar circini in proxima figura eſt S T V, cuius crura reſecta ſunt in T, <lb/>&amp; </s>
  <s xml:id="echoid-s2506" xml:space="preserve">V, fruſta autẽ abſciſſa T a, V b, ita aptata in T, &amp; </s>
  <s xml:id="echoid-s2507" xml:space="preserve">V, vt liberè hinc inde moueri poſſint, &amp; </s>
  <s xml:id="echoid-s2508" xml:space="preserve">cochleo-<lb/>lis astringi. </s>
  <s xml:id="echoid-s2509" xml:space="preserve">Canaliculi autem ſunt in X, &amp; </s>
  <s xml:id="echoid-s2510" xml:space="preserve">Y, in quibus filũ X Y f, cir cumuoluitur. </s>
  <s xml:id="echoid-s2511" xml:space="preserve">ſtylus denique eſt d e, <lb/>canaliculũ etiã habens in f, vt circa filum extentum commodè poſſit cir cumagi, ita vt filũ ſemper triangu-<lb/>
<anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/>
lum conſtituat angulos habens in canaliculis circini, &amp; </s>
  <s xml:id="echoid-s2512" xml:space="preserve">ſtyli, cuiuſmodi in figura est triangulũ X Y f. </s>
  <s xml:id="echoid-s2513" xml:space="preserve">Solũ <lb/>ſtylo poſito in A, vel B, triangulũ non conſtituitur, ſed linea recta. </s>
  <s xml:id="echoid-s2514" xml:space="preserve">Porrò ſegmenta e f, a X, d Y, æqualia <lb/>eſſe debent, &amp; </s>
  <s xml:id="echoid-s2515" xml:space="preserve">minimæ altitudinis. </s>
  <s xml:id="echoid-s2516" xml:space="preserve">Sed vſus ipſe inſtrumẽti plani{us} docebit, qua ratione conſtruendũ ſit.</s>
  <s xml:id="echoid-s2517" xml:space="preserve"/>
</p>
<div xml:id="echoid-div128" type="float" level="2" n="12">
<note position="left" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div130" type="section" level="1" n="38">
<head xml:id="echoid-head41" xml:space="preserve">THEOREMA 7. PROPOSITIO 9.</head>
<p>
  <s xml:id="echoid-s2518" xml:space="preserve">CIRCVLI maximi in ſphęra, quorum vnus ſit Meridianus, per po-<lb/>
<anchor type="note" xlink:label="note-0057-02a" xlink:href="note-0057-02"/>
los Aequatoris incedentes, ſecantesq́; </s>
  <s xml:id="echoid-s2519" xml:space="preserve">parallelum, qui Horizontẽ tangit, <lb/>eſtq́; </s>
  <s xml:id="echoid-s2520" xml:space="preserve">parallelorum ſemper apparentium maximus, in partes 24. </s>
  <s xml:id="echoid-s2521" xml:space="preserve">æquales, <lb/>
<anchor type="note" xlink:label="note-0057-03a" xlink:href="note-0057-03"/>
indicant horas æquales à meridie, vel media nocte initium habentes.</s>
  <s xml:id="echoid-s2522" xml:space="preserve"/>
</p>
<div xml:id="echoid-div130" type="float" level="2" n="1">
<note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">Circuli horarũ <lb/>a meridie vel <lb/>media nocte <lb/>qui ſint.</note>
<note position="left" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">20</note>
</div>
  <figure>
    <image file="0057-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0057-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s2523" xml:space="preserve">SECENT parallelum A B C D, cuius centrum E, omnium ſemper apparentiũ maximum, <lb/>quiq́; </s>
  <s xml:id="echoid-s2524" xml:space="preserve">tangit Horizontem F G, (tangit inquam in puncto, in quo recta H I, communis ſectio plani <lb/>Horizontis, &amp; </s>
  <s xml:id="echoid-s2525" xml:space="preserve">plani circuli A B C D, tangit quoque, per definitionem lib. </s>
  <s xml:id="echoid-s2526" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2527" xml:space="preserve">Theodoſii, &amp; </s>
  <s xml:id="echoid-s2528" xml:space="preserve">Hori-<lb/>zontem F G, &amp; </s>
  <s xml:id="echoid-s2529" xml:space="preserve">circulum A B C D,) circuli maximi, quorũ vnus ſit Meridianus, per polos Aequa-<lb/>toris, ac proinde &amp; </s>
  <s xml:id="echoid-s2530" xml:space="preserve">circuli A B C D, (cum, per propoſ. </s>
  <s xml:id="echoid-s2531" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2532" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2533" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2534" xml:space="preserve">Theodoſii, Aequator, &amp; </s>
  <s xml:id="echoid-s2535" xml:space="preserve">parallelus
<pb o="38" file="0058" n="58" rhead="GNOMONICES"/>
A B C D, eoſdem habeant polos) incedentes, atque per centrum E, (quòd omnes circuli maximi <lb/>per polos paralleli A B C D, tranſeuntes ipſum diuidant bifariam, hoc eſt, per centrum, &amp; </s>
  <s xml:id="echoid-s2536" xml:space="preserve">ad an-<lb/>gulos rectos, per propoſ. </s>
  <s xml:id="echoid-s2537" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2538" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2539" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2540" xml:space="preserve">Theodoſii) in partes 24. </s>
  <s xml:id="echoid-s2541" xml:space="preserve">æquales, ita vt Meridianus tranſeat per <lb/>
<anchor type="figure" xlink:label="fig-0058-01a" xlink:href="fig-0058-01"/>
<anchor type="note" xlink:label="note-0058-01a" xlink:href="note-0058-01"/>
<anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
<anchor type="note" xlink:label="note-0058-03a" xlink:href="note-0058-03"/>
rectam A C. </s>
  <s xml:id="echoid-s2542" xml:space="preserve">Dico hos circulos maximos indicare horas æquales à meridie, vel media nocte nu-<lb/>
<anchor type="note" xlink:label="note-0058-04a" xlink:href="note-0058-04"/>
meratas. </s>
  <s xml:id="echoid-s2543" xml:space="preserve">Cum enim tranſeant per polos Aequatoris, &amp; </s>
  <s xml:id="echoid-s2544" xml:space="preserve">parallelorũ omniũ, ſecabunt omnes paral-<lb/>lelos, per propoſ. </s>
  <s xml:id="echoid-s2545" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2546" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2547" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2548" xml:space="preserve">Theodoſii, in partes ſimiles: </s>
  <s xml:id="echoid-s2549" xml:space="preserve">Ac propterea cùm partes paralleli A B C D, <lb/>ponantur æquales, erunt &amp; </s>
  <s xml:id="echoid-s2550" xml:space="preserve">partes cuiuslibet paralleli inter ſe æquales. </s>
  <s xml:id="echoid-s2551" xml:space="preserve">Quare illas Sol motu diur-<lb/>no æqualibus 24. </s>
  <s xml:id="echoid-s2552" xml:space="preserve">temporibus percurret, initio facto à meridie, vel media nocte: </s>
  <s xml:id="echoid-s2553" xml:space="preserve">Sed 24. </s>
  <s xml:id="echoid-s2554" xml:space="preserve">hæc tem <lb/>pora æqualia, horæ ſunt æquales 24. </s>
  <s xml:id="echoid-s2555" xml:space="preserve">à meridie, vel media nocte inchoatæ. </s>
  <s xml:id="echoid-s2556" xml:space="preserve">Igitur circuli illi ma-<lb/>ximi, horas æquales 24. </s>
  <s xml:id="echoid-s2557" xml:space="preserve">à meridie, vel media nocte numeratas indicant. </s>
  <s xml:id="echoid-s2558" xml:space="preserve">Ac propterea circuli ma-<lb/>ximi in ſphæra, quorum vnus ſit Meridianus, &amp;</s>
  <s xml:id="echoid-s2559" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2560" xml:space="preserve">quod erat demonſtrandum.</s>
  <s xml:id="echoid-s2561" xml:space="preserve"/>
</p>
<div xml:id="echoid-div131" type="float" level="2" n="2">
  <figure xlink:label="fig-0058-01" xlink:href="fig-0058-01a">
    <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0058-01"/>
  </figure>
<note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0058-04" xlink:href="note-0058-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">Circuli dimi-<lb/>diatas partes, <lb/>quartas, octa-<lb/>uas, &amp;c. horarũ <lb/>à mer, uel med. <lb/>noc. indicantes.</note>
</div>
<div xml:id="echoid-div133" type="section" level="1" n="39">
<head xml:id="echoid-head42" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s2562" xml:space="preserve">QVOD ſi ſingula ſpatia æqualia paralleli A B C D, bifariam ſecentur, &amp; </s>
  <s xml:id="echoid-s2563" xml:space="preserve">hæc dimidia rurſum bi-<lb/>
<anchor type="note" xlink:label="note-0058-06a" xlink:href="note-0058-06"/>
fariam, &amp; </s>
  <s xml:id="echoid-s2564" xml:space="preserve">ſic deinceps, ducantur autem per diuiſiones, &amp; </s>
  <s xml:id="echoid-s2565" xml:space="preserve">polos paralleli A B C D, circuli maximi, indi-<lb/>cabunt hi horas dimidias, quartas partes horarum, octauas, &amp; </s>
  <s xml:id="echoid-s2566" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2567" xml:space="preserve">à meridie, vel media nocte. </s>
  <s xml:id="echoid-s2568" xml:space="preserve">Eadẽ enim <lb/>
<anchor type="note" xlink:label="note-0058-07a" xlink:href="note-0058-07"/>
eſt demonſtratio partium, at que horarum integrarum. </s>
  <s xml:id="echoid-s2569" xml:space="preserve">Hi autem circuli maximi recte Horarĳ à meri-<lb/>die, vel media nocte appellari poſſunt.</s>
  <s xml:id="echoid-s2570" xml:space="preserve"/>
</p>
<div xml:id="echoid-div133" type="float" level="2" n="1">
<note position="left" xlink:label="note-0058-06" xlink:href="note-0058-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0058-07" xlink:href="note-0058-07a" xml:space="preserve">Horatii circuli <lb/>à mer. vel med. <lb/>noc.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2571" xml:space="preserve">CAETERVM horum circulorum ſemicir culi inter duos polos mundi collocati, quos quidem om-<lb/>
<anchor type="note" xlink:label="note-0058-08a" xlink:href="note-0058-08"/>
nes axis mundi dirimit, procedendo à Meridiani ſemicir culo ſupra Horizontem extante per occidentem <lb/>vſque ad ſemicirculum Meridiani infra Horizontem, indicant horas à meridie, reliqui verò ſemicirculi <lb/>eaſdem horas à media nocte, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s2572" xml:space="preserve">Vnde non difficile erit cognoſcere, quænam puncta ma-<lb/>ximi parallelorum ſemper apparentium conueniant horis à meridie, &amp; </s>
  <s xml:id="echoid-s2573" xml:space="preserve">quænam horis à media nocte de-<lb/>beantur. </s>
  <s xml:id="echoid-s2574" xml:space="preserve">Nam puncta in ſemicirculo A D C, ſi parallelus intelligatur Horizontẽ tangere in infimo pun-<lb/>cto verſus C, ita vt D, ad occaſum, &amp; </s>
  <s xml:id="echoid-s2575" xml:space="preserve">B, ad ortum vergat, indicant horas à meridie, cum in illis punctis
<pb o="39" file="0059" n="59" rhead="LIBER PRIMVS."/>
horarĳ ſemicirculi inter duos polos à Meridiani ſemicirculo ſupra Horizontem extante per occidentem <lb/>procedendo vſq; </s>
  <s xml:id="echoid-s2576" xml:space="preserve">ad ſemicir culum Meridiani inſra Horizontẽ, parallelum ſecent, vt perſpicuũ es@: </s>
  <s xml:id="echoid-s2577" xml:space="preserve">puncta <lb/>verò in reliquo ſemicir culo C B A, ostendunt horas à media nocte; </s>
  <s xml:id="echoid-s2578" xml:space="preserve">quia in illis parallelus ſecatur à reliquis <lb/>ſemicir culis horarĳs. </s>
  <s xml:id="echoid-s2579" xml:space="preserve">Pari ratione in parallelo ſemper occultorum maximo puncta ſemicirculi verſus <lb/>occidentem poſiti incipiendo ab eo puncto, vbi Horizontem tangit, dabunt horas à meridie, punct a verò <lb/>alterius ſemicir culi verſus Orientem horas à media nocte indicabunt, propter eandem rationem. </s>
  <s xml:id="echoid-s2580" xml:space="preserve">Id quod <lb/>facile intelligi poteſt, ſi duo illi paralleli, &amp; </s>
  <s xml:id="echoid-s2581" xml:space="preserve">circuli horarĳ in propria poſitione cogitentur eſſe poſiti.</s>
  <s xml:id="echoid-s2582" xml:space="preserve"/>
</p>
<div xml:id="echoid-div134" type="float" level="2" n="2">
<note position="left" xlink:label="note-0058-08" xlink:href="note-0058-08a" xml:space="preserve">Qui ſemicircu-<lb/>li ad horas. à <lb/>meridie, &amp; qui <lb/>ad horas à med. <lb/>noc. pertineant.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2583" xml:space="preserve">MALVIMVS autem proponere, circulos horarios ſecare parallelum omnium, qui ſemper appa-<lb/>rent, maximum in vigintiquatuor partes æquales, quàm Aequatorem, (quamuis &amp; </s>
  <s xml:id="echoid-s2584" xml:space="preserve">hoc verum ſit, vt <lb/>ex demonſtratione constat) quoniam &amp; </s>
  <s xml:id="echoid-s2585" xml:space="preserve">cognitio circulorum horariorum, qui horas ab ortu &amp; </s>
  <s xml:id="echoid-s2586" xml:space="preserve">occaſu <lb/>
<anchor type="note" xlink:label="note-0059-01a" xlink:href="note-0059-01"/>
monſtrant, &amp; </s>
  <s xml:id="echoid-s2587" xml:space="preserve">plcraque alia ad horas tam à mer. </s>
  <s xml:id="echoid-s2588" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s2589" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s2590" xml:space="preserve">quàm ab Or. </s>
  <s xml:id="echoid-s2591" xml:space="preserve">vel Occ. </s>
  <s xml:id="echoid-s2592" xml:space="preserve">attinentia, ex pun-<lb/>ctis horarĳs dicti paralleli pendent, vt ex ſequentibus fiet perſpicuum.</s>
  <s xml:id="echoid-s2593" xml:space="preserve"/>
</p>
<div xml:id="echoid-div135" type="float" level="2" n="3">
<note position="left" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div137" type="section" level="1" n="40">
<head xml:id="echoid-head43" xml:space="preserve">THEOREMA 8. PROPOSITIQ 10.</head>
<note position="right" xml:space="preserve">Circuli horatũ <lb/>ab @r@u vel oc-<lb/>caſu qui ſint.</note>
<p>
  <s xml:id="echoid-s2594" xml:space="preserve">CIRCVLI maximi in Sphæra, quorum vnus ſit Horizon, tangen-<lb/>tes eundem parallelum omnium ſemper apparentium maximum in 24. <lb/></s>
  <s xml:id="echoid-s2595" xml:space="preserve">punctis, quibus diuiditur à circulis horarum à meridie, vel media nocte, <lb/>
<anchor type="note" xlink:label="note-0059-03a" xlink:href="note-0059-03"/>
monſtrant horas æquales ab ortu, vel occaſu Solis inchoatas: </s>
  <s xml:id="echoid-s2596" xml:space="preserve">Eorum au-<lb/>tem poli ſunt puncta paralleli per verticem loci, ſeu polum Horizontis <lb/>deſcripti, quibus à circulis horarum à meridie, vel media nocte ſecatur.</s>
  <s xml:id="echoid-s2597" xml:space="preserve"/>
</p>
<div xml:id="echoid-div137" type="float" level="2" n="1">
<note position="left" xlink:label="note-0059-03" xlink:href="note-0059-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s2598" xml:space="preserve">TANGANT eundem parallelum A B C D, in 24. </s>
  <s xml:id="echoid-s2599" xml:space="preserve">punctis horarum à meridie, vel media <lb/>nocte circuli maximi, quorum vnus ſit Horizon. </s>
  <s xml:id="echoid-s2600" xml:space="preserve">Dico hos circulos maximos monſtrare horas <lb/>æquales ab ortu, vel occaſu Solis inchoatas, &amp;</s>
  <s xml:id="echoid-s2601" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2602" xml:space="preserve">Cum enim tangant parallelum A B C D, &amp; </s>
  <s xml:id="echoid-s2603" xml:space="preserve">pro-<lb/>pterea, per propoſitionem 6. </s>
  <s xml:id="echoid-s2604" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2605" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2606" xml:space="preserve">Theodoſii, parallelum quoque ei æqualem, nempe omnium, <lb/>
<anchor type="note" xlink:label="note-0059-04a" xlink:href="note-0059-04"/>
qui ſemper ſub terra occultantur, maximum; </s>
  <s xml:id="echoid-s2607" xml:space="preserve">ſecabunt omnes parallelos intermedios, per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s2608" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2609" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2610" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2611" xml:space="preserve">Theodoſii, in partes (quæ ſcilicet intercipiuntur inter quoſuis duos proximos ſe-<lb/>micirculos non concurrentes) ſimiles partibus paralleli A B C D: </s>
  <s xml:id="echoid-s2612" xml:space="preserve">Ac propterea, cum partes paral-<lb/>leli A B C D, ponantur æquales, erunt &amp; </s>
  <s xml:id="echoid-s2613" xml:space="preserve">partes paralleli cuiuslibet intermedij inter ſeæquales. <lb/></s>
  <s xml:id="echoid-s2614" xml:space="preserve">Quare illas ſol motu diurno æqualibus 24. </s>
  <s xml:id="echoid-s2615" xml:space="preserve">temporibus percurret, initio facto ab Horizonte, hoc <lb/>eſt, ab ortu, vel occaſu Solis: </s>
  <s xml:id="echoid-s2616" xml:space="preserve">Sed hæc 24. </s>
  <s xml:id="echoid-s2617" xml:space="preserve">tempora æqualia, horæ ſunt 24. </s>
  <s xml:id="echoid-s2618" xml:space="preserve">æquales ab ortu, vel <lb/>occaſu inchoatæ. </s>
  <s xml:id="echoid-s2619" xml:space="preserve">Circuli igitur illi maximi monſtrant horas 24. </s>
  <s xml:id="echoid-s2620" xml:space="preserve">æquales ab ortu, vel occaſu in-<lb/>choatas. </s>
  <s xml:id="echoid-s2621" xml:space="preserve">quod eſt primum.</s>
  <s xml:id="echoid-s2622" xml:space="preserve"/>
</p>
<div xml:id="echoid-div138" type="float" level="2" n="2">
<note position="left" xlink:label="note-0059-04" xlink:href="note-0059-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s2623" xml:space="preserve">NEQVE vero vlli alij circuli, præter dictos, in cælo excogitari poſſunt, qui horas ab ortu, vel <lb/>occaſu indicent. </s>
  <s xml:id="echoid-s2624" xml:space="preserve">Cum enim huiuſmodi horæ ab Horizonte incipiant, diuidantq́; </s>
  <s xml:id="echoid-s2625" xml:space="preserve">ſingulos paralle-<lb/>los, quos ſecant, in partes 24. </s>
  <s xml:id="echoid-s2626" xml:space="preserve">æquales, ſequitur ex propoſ. </s>
  <s xml:id="echoid-s2627" xml:space="preserve">16. </s>
  <s xml:id="echoid-s2628" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2629" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2630" xml:space="preserve">Theodoſii, circulos maximos <lb/>
<anchor type="note" xlink:label="note-0059-05a" xlink:href="note-0059-05"/>
ea ratione parallelos diuidentes vel tranſire per parallelorum polos, vel eundem vnũ parallelum <lb/>tangere. </s>
  <s xml:id="echoid-s2631" xml:space="preserve">Cum ergo per polos non tranſeant, quòd Horizon, qui vnus eſt ex illis, per polos mini-<lb/>mè tranſeat, niſi in ſphæra recta, tangent neceſſario eundem unum parallelum. </s>
  <s xml:id="echoid-s2632" xml:space="preserve">Quare cum Ho-<lb/>rizon tangat parallelum ſemper apparentium maximum, tangent &amp; </s>
  <s xml:id="echoid-s2633" xml:space="preserve">reliqui eundem. </s>
  <s xml:id="echoid-s2634" xml:space="preserve">Omnino igi-<lb/>tur circuli maximi horas ab ortu, vel occaſu monſtrantes tangunt parallelum ſemper apparen-<lb/>tium maximum.</s>
  <s xml:id="echoid-s2635" xml:space="preserve"/>
</p>
<div xml:id="echoid-div139" type="float" level="2" n="3">
<note position="left" xlink:label="note-0059-05" xlink:href="note-0059-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s2636" xml:space="preserve">QVONIAM verò circuli hi omnes eundem parallelum, qui ſemper apparentium maximus <lb/>eſt, tangunt, fit, vt æqualiter inclinati ſint ad Aequatorem, ex Theorem. </s>
  <s xml:id="echoid-s2637" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2638" xml:space="preserve">ſcholij propoſ. </s>
  <s xml:id="echoid-s2639" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2640" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2641" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s2642" xml:space="preserve">Theodoſii, quod quidem eſt, ſecundum traditionem Franciſci Maurolyci, propoſitio 26. </s>
  <s xml:id="echoid-s2643" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2644" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2645" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0059-06a" xlink:href="note-0059-06"/>
Theodoſii. </s>
  <s xml:id="echoid-s2646" xml:space="preserve">Quare ex Theoremate 2. </s>
  <s xml:id="echoid-s2647" xml:space="preserve">eiuſdem ſcholij, quod eſt propoſitio 27. </s>
  <s xml:id="echoid-s2648" xml:space="preserve">ſecundum Mauro-<lb/>lycum, polos habent in circunferentia eiuſdem paralleli. </s>
  <s xml:id="echoid-s2649" xml:space="preserve">Cum ergo polus Horizontis, qui vnus eſt <lb/>
<anchor type="note" xlink:label="note-0059-07a" xlink:href="note-0059-07"/>
ex illis circulis horarijs, ſit in parallelo per polum Horizontis, ſeu verticem loci deſcripto, neceſſa-<lb/>rio &amp; </s>
  <s xml:id="echoid-s2650" xml:space="preserve">poli aliorum circulorum in eodem parallelo exiſtent. </s>
  <s xml:id="echoid-s2651" xml:space="preserve">Et quia circuli horarum à meridie, <lb/>vel media nocte tranſeuntes per puncta contactuum, &amp; </s>
  <s xml:id="echoid-s2652" xml:space="preserve">per polos paralleli ſemper apparentium <lb/>maximi, tranſeunt quoque ex propoſ. </s>
  <s xml:id="echoid-s2653" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2654" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2655" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2656" xml:space="preserve">Theodoſii, per polos circulorum monſtrantium ho-<lb/>ras ab ortu, vel occaſu, qui nimirum illum parallelum tangunt, erunt omnino poli horum circu-<lb/>lorum puncta paralleli per verticem loci, ſeu Horizontis polum deſcripti, per quæ circuli horarũ <lb/>à meridie, vel media nocte tranſeunt, quandoquidem in hoc parallelo omnes poli exiſtunt, vt de-<lb/>monſtratum eſt. </s>
  <s xml:id="echoid-s2657" xml:space="preserve">Conſtat ergo etiam ſecundum. </s>
  <s xml:id="echoid-s2658" xml:space="preserve">Quamobrem circuli maximi in ſphæra, quorum <lb/>vnus ſit Horizon, &amp;</s>
  <s xml:id="echoid-s2659" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2660" xml:space="preserve">Quod erat oſtendendum.</s>
  <s xml:id="echoid-s2661" xml:space="preserve"/>
</p>
<div xml:id="echoid-div140" type="float" level="2" n="4">
<note position="left" xlink:label="note-0059-06" xlink:href="note-0059-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0059-07" xlink:href="note-0059-07a" xml:space="preserve">Poli circuloru <lb/>hoias ab or. uel <lb/>occ. indicantiũ <lb/>ſunt in paralle-<lb/>lo per verticem <lb/>loci deſcripto.</note>
</div>
<pb o="40" file="0060" n="60" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div142" type="section" level="1" n="41">
<head xml:id="echoid-head44" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s2662" xml:space="preserve">EX his ſequitur, polos circulorum horas ab ortu, vel occaſu monſtrantium diuidere parallelum per <lb/>
<anchor type="note" xlink:label="note-0060-01a" xlink:href="note-0060-01"/>
verticem loci, ſiue polum Horizontis deſcriptum in partes 24. </s>
  <s xml:id="echoid-s2663" xml:space="preserve">æquales, initio facto à Meridia no circulo: <lb/></s>
  <s xml:id="echoid-s2664" xml:space="preserve">quia &amp; </s>
  <s xml:id="echoid-s2665" xml:space="preserve">puncta, vbi dictus parallelus à circulis horarum à meridie, vel media nocte ſecatur, quæ quidem <lb/>poli ſunt circulorum horas ab ortu, vel occaſu monſtrantium, vt oſtendimus, eundem parallelum in par-<lb/>tes 24. </s>
  <s xml:id="echoid-s2666" xml:space="preserve">æquales ſecant, initio facto à Meridiano circulo, vt conſtat ex propos. </s>
  <s xml:id="echoid-s2667" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2668" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2669" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2670" xml:space="preserve">Theodoſii.</s>
  <s xml:id="echoid-s2671" xml:space="preserve"/>
</p>
<div xml:id="echoid-div142" type="float" level="2" n="1">
<note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">Poli circulorũ <lb/>horas ab or uel <lb/>otc. indicantiũ <lb/>partiuntur pa-<lb/>rallelũ per ver-<lb/>ticem loci de-<lb/>ſeriptum in 24. <lb/>partes æquales.</note>
</div>
</div>
<div xml:id="echoid-div144" type="section" level="1" n="42">
<head xml:id="echoid-head45" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s2672" xml:space="preserve">VT autem videas, quonam modo partes illæ parallelorum intercipiantur inter duos ſemicirculos <lb/>
<anchor type="note" xlink:label="note-0060-03a" xlink:href="note-0060-03"/>
proximos non concurrentes; </s>
  <s xml:id="echoid-s2673" xml:space="preserve">Sint paralleli quotcunque; </s>
  <s xml:id="echoid-s2674" xml:space="preserve">A B C, ſemper apparentium maximus; </s>
  <s xml:id="echoid-s2675" xml:space="preserve">D E F, <lb/>parallelus ♋; </s>
  <s xml:id="echoid-s2676" xml:space="preserve">G H I, Aequator; </s>
  <s xml:id="echoid-s2677" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2678" xml:space="preserve">K L M, parallelus ♑. </s>
  <s xml:id="echoid-s2679" xml:space="preserve">Sumantur in A B C, ſpatia horarum æqua-<lb/>lia C N, N O, &amp; </s>
  <s xml:id="echoid-s2680" xml:space="preserve">in punctis C, N, O, parallelum A B C, tangant maximi circuli C P H Q, N R S T, <lb/>O V X Γ, quorum C P H Q, ſit <lb/>
<anchor type="figure" xlink:label="fig-0060-01a" xlink:href="fig-0060-01"/>
Horizon. </s>
  <s xml:id="echoid-s2681" xml:space="preserve">Secent aut ſe mutuo <lb/>C P H Q, N R S T, in Z, &amp; </s>
  <s xml:id="echoid-s2682" xml:space="preserve">α; <lb/></s>
  <s xml:id="echoid-s2683" xml:space="preserve">erunt{q́ue} per propoſ. </s>
  <s xml:id="echoid-s2684" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2685" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2686" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2687" xml:space="preserve"><lb/>Theodoſii, Z Q α, Z T α, ſemi-<lb/>circuli, &amp; </s>
  <s xml:id="echoid-s2688" xml:space="preserve">idcirco P Q α, ſemi-<lb/>
<anchor type="note" xlink:label="note-0060-04a" xlink:href="note-0060-04"/>
circulo minor. </s>
  <s xml:id="echoid-s2689" xml:space="preserve">Sumatur arcus <lb/>α β, arcui P Z, &amp; </s>
  <s xml:id="echoid-s2690" xml:space="preserve">arcus α γ, <lb/>arcui Z δ, æqualis; </s>
  <s xml:id="echoid-s2691" xml:space="preserve">eruntq́, P Q <lb/>α β, δ Z T γ, ſemicirculi non <lb/>concurrentes, cum mutuo ſe non <lb/>interſecent. </s>
  <s xml:id="echoid-s2692" xml:space="preserve">Eadem ratione, ſi <lb/>circuli N R S T, O V X Y, ſe <lb/>mutuo ſecent in @, &amp; </s>
  <s xml:id="echoid-s2693" xml:space="preserve">θ, ſuma-<lb/>tur{q́ue} arcus θλ, arcui V ε, æqua-<lb/>lis, erunt δ Z T γ, V Y θ λ, <lb/>
<anchor type="note" xlink:label="note-0060-05a" xlink:href="note-0060-05"/>
ſemicirculi nõ coeuntes, vt con-<lb/>ſtat. </s>
  <s xml:id="echoid-s2694" xml:space="preserve">Eodemq́, modo in circu-<lb/>lis reliquis maximis parallelum <lb/>A B C, tangentibus in reliquis <lb/>ſpatĳs horarĳs æqualibus inue-<lb/>niemus ſemicirculos non concur-<lb/>rentes. </s>
  <s xml:id="echoid-s2695" xml:space="preserve">Spatia igitur P R, R V, <lb/>H S, S X, Q T, T Y, &amp; </s>
  <s xml:id="echoid-s2696" xml:space="preserve">reli-<lb/>qua huiuſmodi diximus ſpatĳs <lb/>horarĳs C N, N O, &amp; </s>
  <s xml:id="echoid-s2697" xml:space="preserve">alĳs eſſe <lb/>
<anchor type="note" xlink:label="note-0060-06a" xlink:href="note-0060-06"/>
ſimilia, &amp; </s>
  <s xml:id="echoid-s2698" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2699" xml:space="preserve">at que adeo ſpatia <lb/>cuiuslibet paralleli æqualia in-<lb/>
<anchor type="note" xlink:label="note-0060-07a" xlink:href="note-0060-07"/>
ter ſe eſſe, quemadmodum &amp; </s>
  <s xml:id="echoid-s2700" xml:space="preserve">C N, N O, &amp; </s>
  <s xml:id="echoid-s2701" xml:space="preserve">reliqua ſpatia paralleli A B C, æqualia ſunt inter ſe.</s>
  <s xml:id="echoid-s2702" xml:space="preserve"/>
</p>
<div xml:id="echoid-div144" type="float" level="2" n="1">
<note position="left" xlink:label="note-0060-03" xlink:href="note-0060-03a" xml:space="preserve">Quomodo in <lb/>circulis horatũ <lb/>ab or. uel occ. <lb/>ſumantur ſemi <lb/>circuli noa con <lb/>currentes.</note>
  <figure xlink:label="fig-0060-01" xlink:href="fig-0060-01a">
    <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0060-01"/>
  </figure>
<note position="left" xlink:label="note-0060-04" xlink:href="note-0060-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0060-05" xlink:href="note-0060-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0060-06" xlink:href="note-0060-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0060-07" xlink:href="note-0060-07a" xml:space="preserve">Circuli dimi-<lb/>diatas partes, <lb/>quartas, octa-<lb/>uas, &amp;c. horarũ <lb/>ab or. vel occ. <lb/>monſtrantes.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2703" xml:space="preserve">QVOD ſi alĳ circuli maximi tangant eundem parallelum in punctis alĳs, quibus diuiditur à circu-<lb/>lis horarĳs à meridie, vel media nocte dimidias horas, quartas partes horarum, octauas, &amp; </s>
  <s xml:id="echoid-s2704" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2705" xml:space="preserve">indicanti-<lb/>bus, indicabunt hi horas dimidias, quartas horarum partes, octauas, &amp; </s>
  <s xml:id="echoid-s2706" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2707" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s2708" xml:space="preserve">Eadem <lb/>enim eſt demonſtratio partium, at que horarum integrarum. </s>
  <s xml:id="echoid-s2709" xml:space="preserve">Hi autem circuli non ineptè Horarĳ ab ortu, <lb/>
<anchor type="note" xlink:label="note-0060-08a" xlink:href="note-0060-08"/>
vel occaſu poſſunt appellari.</s>
  <s xml:id="echoid-s2710" xml:space="preserve"/>
</p>
<div xml:id="echoid-div145" type="float" level="2" n="2">
<note position="left" xlink:label="note-0060-08" xlink:href="note-0060-08a" xml:space="preserve">Horarii circuli <lb/>ab or. uel occ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2711" xml:space="preserve">HORVM porrò circulorum ſemicir culi inter bina puncta contactuum poſiti, quorum vnum ſemper <lb/>eſt horæ alicuius à meridie, &amp; </s>
  <s xml:id="echoid-s2712" xml:space="preserve">alterum horæ eiuſdem à media nocte, vt patet exĳs, quæ in ſcholio præce-<lb/>
<anchor type="note" xlink:label="note-0060-09a" xlink:href="note-0060-09"/>
<anchor type="note" xlink:label="note-0060-10a" xlink:href="note-0060-10"/>
dentis propoſ. </s>
  <s xml:id="echoid-s2713" xml:space="preserve">ſcripſimus, procedendo per puncta horaria æquinoctialis circuli infra Horizontem, initio <lb/>facto à ſemicirculo Horizontis occidentali, procedendo{q́ue} ab ortu in occaſum, ſeu contra ſucceſſionem <lb/>ſignorum, pertinent ad horas ab occaſu inchoatas, ita vt ſemicirculus Horizontis occidentalis indicet <lb/>horam 24. </s>
  <s xml:id="echoid-s2714" xml:space="preserve">ab occaſu, ſemicirculus autem proximus occidentalis infra Horizontem dct horam primam <lb/>ab occaſu, &amp; </s>
  <s xml:id="echoid-s2715" xml:space="preserve">ſequens ad partes occidentales horam ſecundã, &amp; </s>
  <s xml:id="echoid-s2716" xml:space="preserve">ita deinceps, procedendo ſemper verſus <lb/>occidentales partes, ſeu contra ſucceſſionem ſignorum, donec iterum ad ſemicirculum Horizontis occi-<lb/>dentalem reuertamur. </s>
  <s xml:id="echoid-s2717" xml:space="preserve">Reliqui autem ſemicirculi, qui incedunt per puncta horaria æquinoctialis circuli <lb/>ſupra Horizontem, initio facto à ſemicirculo Horizontis orient ali, procedendoq́, ab ortu in occaſum, hoc <lb/>eſt, contra ſucceſſionem ſignorum, ad horas ab ortu Solis ſpectant, ita vt ſemicirculus Horizontis orier-<lb/>talis monſtret horam 24. </s>
  <s xml:id="echoid-s2718" xml:space="preserve">ab ortu, proximus autem ſemicirculus orient alis ſupra Horizontem exhibeat <lb/>@oram primam ab ortu, &amp; </s>
  <s xml:id="echoid-s2719" xml:space="preserve">ſequens contra ſucceſſionem ſignorum horam ſecundam, &amp; </s>
  <s xml:id="echoid-s2720" xml:space="preserve">ita deinceps, pro-
<pb o="41" file="0061" n="61" rhead="LIBER PRIMVS."/>
grediendo ſemper ab ortu in occaſum, ſiue contra ſucceſſionem ſignorum, donec rurſus ad ſemicirculum <lb/>Horizontis orient alem perueniamus.</s>
  <s xml:id="echoid-s2721" xml:space="preserve"/>
</p>
<div xml:id="echoid-div146" type="float" level="2" n="3">
<note position="left" xlink:label="note-0060-09" xlink:href="note-0060-09a" xml:space="preserve">Qui ſemicirculi <lb/>ad horas ab or-<lb/>tu, &amp; qui ad ho-<lb/>ras ab occaſu <lb/>pertineant.</note>
<note position="left" xlink:label="note-0060-10" xlink:href="note-0060-10a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s2722" xml:space="preserve">FORTASSE planius, &amp; </s>
  <s xml:id="echoid-s2723" xml:space="preserve">apertius intelligemus, quinam ſemicir culi ad horas ab occaſu, vel ortu <lb/>Solis pertineant, hoc modo. </s>
  <s xml:id="echoid-s2724" xml:space="preserve">Cogitemus nos extra cælum poſitos prope parallelum ſemper apparentium <lb/>maximum, ita vt pedes habeamus in hora 12. </s>
  <s xml:id="echoid-s2725" xml:space="preserve">mediæ noctis, vel 24. </s>
  <s xml:id="echoid-s2726" xml:space="preserve">ab ortu, vel occaſu, caput autem <lb/>uerſus polum arcticum. </s>
  <s xml:id="echoid-s2727" xml:space="preserve">Hoc poſito, ſemicir culus Horizontis, ſeu horæ 24. </s>
  <s xml:id="echoid-s2728" xml:space="preserve">qui nobis eſt ad dexteram, in-<lb/>dicabit horam 24. </s>
  <s xml:id="echoid-s2729" xml:space="preserve">ab occaſu; </s>
  <s xml:id="echoid-s2730" xml:space="preserve">alter verò ad ſiniſtram, horam 24. </s>
  <s xml:id="echoid-s2731" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s2732" xml:space="preserve">Similiter ſi pedes ſtatuamus in <lb/>alĳs horis dicti paralleli, &amp; </s>
  <s xml:id="echoid-s2733" xml:space="preserve">caput verſus polum, pertinebunt ſemicir culi horarum ab ortu, vel occaſu, <lb/>qui nobis ad dexteram ponuntur, ad horas ab occaſu; </s>
  <s xml:id="echoid-s2734" xml:space="preserve">qui verò ſunt ad ſiniſtram, ad horas ab ortu Solis. <lb/></s>
  <s xml:id="echoid-s2735" xml:space="preserve">Quæ omnia perſpicua erunt ei, qui diligenter percipiat parallelum ſemper apparentium maximum, quem <lb/>
<anchor type="note" xlink:label="note-0061-01a" xlink:href="note-0061-01"/>
circulus in propoſ. </s>
  <s xml:id="echoid-s2736" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2737" xml:space="preserve">nobis reſert, &amp; </s>
  <s xml:id="echoid-s2738" xml:space="preserve">circulos horarum ab ortu, vel occaſu dictũ parallelum tangentes in <lb/>proprio ſitu poſitos.</s>
  <s xml:id="echoid-s2739" xml:space="preserve"/>
</p>
<div xml:id="echoid-div147" type="float" level="2" n="4">
<note position="left" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s2740" xml:space="preserve">QVOD verò attinet ad circulos horarum inæqualium, manifestum est, illos tranſire debere per duo-<lb/>
<anchor type="note" xlink:label="note-0061-02a" xlink:href="note-0061-02"/>
decimas partes omnium arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s2741" xml:space="preserve">nocturnorum, cum huiuſmodi partes duodecimæ appellen-<lb/>tur horæ inæquales. </s>
  <s xml:id="echoid-s2742" xml:space="preserve">Quod autem circuli maximi per horas inæquales Aequatoris, (quæ quidem eædem <lb/>
<anchor type="note" xlink:label="note-0061-03a" xlink:href="note-0061-03"/>
ſunt, quæ æquales) &amp; </s>
  <s xml:id="echoid-s2743" xml:space="preserve">arcuum diurnorum Borealium deſcripti tranſeant quoque per eaſdem horas arcuũ <lb/>diurnorum Auſtralium, hac ratione cum Federico Commandino demonſtr abimus. </s>
  <s xml:id="echoid-s2744" xml:space="preserve">Quoniam in Horizon-<lb/>te quolibet obliquo, duobus parallelis æqualiter diſtantibus ab Aequatore, arcus diurnus vnius æqualis <lb/>eſt arcui nocturno alterius, &amp; </s>
  <s xml:id="echoid-s2745" xml:space="preserve">cõtra, vt manifeſtè apparet ex 19. </s>
  <s xml:id="echoid-s2746" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s2747" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2748" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2749" xml:space="preserve">Theodoſii; </s>
  <s xml:id="echoid-s2750" xml:space="preserve">Et ideo, quãto <lb/>dies augentur, Sole ab æquinoctio verno ad ♋, tendente, tanto minuuntur, eodem ab æquinoctio autum-<lb/>
<anchor type="note" xlink:label="note-0061-04a" xlink:href="note-0061-04"/>
nali ad ♑, tendente: </s>
  <s xml:id="echoid-s2751" xml:space="preserve">ſequitur vt dies ♋, tanto maior ſit æquinoctĳ die, quanto dies ♑, minor eſt eodẽ <lb/>die æquinoctĳ. </s>
  <s xml:id="echoid-s2752" xml:space="preserve">Cum igitur arcus diurnus cuiuslibet paralleli in 12. </s>
  <s xml:id="echoid-s2753" xml:space="preserve">partes æquales diuidatur, eadem{q́ue} ſit <lb/>proportio partis ad partem, quæ totius ad totum; </s>
  <s xml:id="echoid-s2754" xml:space="preserve">fit, vt arcus quoque vnius horæ ♋, eadem quantitate <lb/>
<anchor type="note" xlink:label="note-0061-05a" xlink:href="note-0061-05"/>
ſuperet arcum vnius horæ æquinoctialis, qua arcus vnius horæ ♑, ab eodem ſuperatur. </s>
  <s xml:id="echoid-s2755" xml:space="preserve">Quod etiam hinc <lb/>patere potest; </s>
  <s xml:id="echoid-s2756" xml:space="preserve">quia hoc modo omnes illi 12. </s>
  <s xml:id="echoid-s2757" xml:space="preserve">exceſſus duodecim horarum ♋, ſimul ſumpti æquales erunt <lb/>duodecim his defectibus duodecim horarum ♑, ſimul ſumptis. </s>
  <s xml:id="echoid-s2758" xml:space="preserve">Quod non contingeret, ſi vna hora ♋, nõ <lb/>ſuperaret vnam horam æquinoctialem eadem quantitate, qua vna hora ♑, ab hora æquinoctiali ſupera-<lb/>tur. </s>
  <s xml:id="echoid-s2759" xml:space="preserve">Eademq́, eſt ratio arcuum durarum horarum, trium, vel quatuor, &amp; </s>
  <s xml:id="echoid-s2760" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2761" xml:space="preserve">Et ita in alĳs parallelis, qui <lb/>ab Aequatore pari diſtant interuallo, vt in parallelis ♊, &amp; </s>
  <s xml:id="echoid-s2762" xml:space="preserve">♐. </s>
  <s xml:id="echoid-s2763" xml:space="preserve">Item in parallelis ♉, &amp; </s>
  <s xml:id="echoid-s2764" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s2765" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2766" xml:space="preserve"/>
</p>
<div xml:id="echoid-div148" type="float" level="2" n="5">
<note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">Circuli horarũ <lb/>inæqualiũ qui <lb/>ſint.</note>
<note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">Circuli maximi <lb/>ſecantes arcus <lb/>diurnos Ae-<lb/>quatoris, &amp; pa-<lb/>rallclorum bo-<lb/>realium in 12. <lb/>partes æquales, <lb/>diuidunt quo-<lb/>que arcus diur-<lb/>nos auſtralium <lb/>parallelorũ ĩ 12. <lb/>partes æquales.</note>
<note position="left" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0061-05" xlink:href="note-0061-05a" xml:space="preserve">15. quinti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2767" xml:space="preserve">SIT iam in ſphæra parallelus ♋, <lb/>
<anchor type="note" xlink:label="note-0061-06a" xlink:href="note-0061-06"/>
<anchor type="figure" xlink:label="fig-0061-01a" xlink:href="fig-0061-01"/>
A B C D; </s>
  <s xml:id="echoid-s2768" xml:space="preserve">Aequator E F G H; </s>
  <s xml:id="echoid-s2769" xml:space="preserve">paral-<lb/>lelus ♑, I K L M; </s>
  <s xml:id="echoid-s2770" xml:space="preserve">circulus parallelo-<lb/>rum ſemper apparentiũ maximus N O-<lb/>P Q, &amp; </s>
  <s xml:id="echoid-s2771" xml:space="preserve">horum omnium polus R; </s>
  <s xml:id="echoid-s2772" xml:space="preserve">Hori <lb/>zon obliquus I E A N D H M, tangens <lb/>parallelum N O P Q, in N. </s>
  <s xml:id="echoid-s2773" xml:space="preserve">Deinde <lb/>arcus Aequatoris, &amp; </s>
  <s xml:id="echoid-s2774" xml:space="preserve">paralleli ♋, qui <lb/>ſunt ſupra Horizontem, diuidantur in <lb/>duodecim partes æquales, vt ſit pri-<lb/>mahora paralleli ♋, punctum B, ſe-<lb/>
<anchor type="note" xlink:label="note-0061-07a" xlink:href="note-0061-07"/>
cunda hora eiuſdem paralleli punctum <lb/>C: </s>
  <s xml:id="echoid-s2775" xml:space="preserve">Aequatoris autem prima hora F, <lb/>ſecunda G. </s>
  <s xml:id="echoid-s2776" xml:space="preserve">Et per puncta B, F; </s>
  <s xml:id="echoid-s2777" xml:space="preserve">Item <lb/>per puncta C, G, deſcribantur per 20. <lb/></s>
  <s xml:id="echoid-s2778" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s2779" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2780" xml:space="preserve">primi Theodoſii, duo circuli <lb/>maximi ſecantes parallelum ♑, in pun-<lb/>ctis K, L. </s>
  <s xml:id="echoid-s2781" xml:space="preserve">Dico circulum B F K, etiam <lb/>per primam horam ♑, tranſire, &amp; </s>
  <s xml:id="echoid-s2782" xml:space="preserve"><lb/>C G L, per ſecundam, hoc eſt, I K, <lb/>eſſe primam horam ♑, &amp; </s>
  <s xml:id="echoid-s2783" xml:space="preserve">K L, ſecun-<lb/>
<anchor type="note" xlink:label="note-0061-08a" xlink:href="note-0061-08"/>
dam. </s>
  <s xml:id="echoid-s2784" xml:space="preserve">Deſcribantur enim per propoſ. <lb/></s>
  <s xml:id="echoid-s2785" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2786" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2787" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2788" xml:space="preserve">Theodoſii, per puncta F, &amp; </s>
  <s xml:id="echoid-s2789" xml:space="preserve"><lb/>G, alĳ duo circuli maximi tangentes parallelum N O P Q, ſecantes{q́ue}, parallelos ♋, &amp; </s>
  <s xml:id="echoid-s2790" xml:space="preserve">♑, in S, T, V, <lb/>X. </s>
  <s xml:id="echoid-s2791" xml:space="preserve">Erunt igitur, per propoſ. </s>
  <s xml:id="echoid-s2792" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2793" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2794" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2795" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s2796" xml:space="preserve">arcus A S, S T, I V, V X, arcubus E F, F G, ſimiles, <lb/>cum omnes hi arcus intercipiantur inter ſemicir culos non concurrentes, vt ex præcedenti ſcholio conſtat: </s>
  <s xml:id="echoid-s2797" xml:space="preserve"><lb/>Sunt autem E F, F G, arcus horarum æquinoctialium æquales. </s>
  <s xml:id="echoid-s2798" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s2799" xml:space="preserve">A S, S T, &amp; </s>
  <s xml:id="echoid-s2800" xml:space="preserve">I V, V X, arcus <lb/>ſunt horarum æquinoctialiũ, &amp; </s>
  <s xml:id="echoid-s2801" xml:space="preserve">æquales; </s>
  <s xml:id="echoid-s2802" xml:space="preserve">atque adeo, cum paralleli A C D, I X M, æquales ſint, æquales <lb/>erunt quatuor arcus A S, S T, I V, V X. </s>
  <s xml:id="echoid-s2803" xml:space="preserve">Et quoniam paralleli A C D, I X M, æquales ſunt, erunt &amp; </s>
  <s xml:id="echoid-s2804" xml:space="preserve"><lb/>arcus S F, F V, &amp; </s>
  <s xml:id="echoid-s2805" xml:space="preserve">B F, F K, circulorũ maximorum à parallelis abſciſſi, æquales, ex propoſ. </s>
  <s xml:id="echoid-s2806" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2807" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2808" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2809" xml:space="preserve"><lb/>Theod. </s>
  <s xml:id="echoid-s2810" xml:space="preserve">Igitur ex propoſ. </s>
  <s xml:id="echoid-s2811" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2812" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2813" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2814" xml:space="preserve">Theodoſii, recta linea coniungens puncta B, S, æqualis erit rectæ con-<lb/>nectenti puncta K, V; </s>
  <s xml:id="echoid-s2815" xml:space="preserve">atque adeo &amp; </s>
  <s xml:id="echoid-s2816" xml:space="preserve">arcus B S, arcui k V, æqualis erit. </s>
  <s xml:id="echoid-s2817" xml:space="preserve">Eodem{q́ue}, modo &amp; </s>
  <s xml:id="echoid-s2818" xml:space="preserve">arcus T G, <lb/>
<anchor type="note" xlink:label="note-0061-09a" xlink:href="note-0061-09"/>
<pb o="42" file="0062" n="62" rhead="GNOMONICES"/>
G X, &amp; </s>
  <s xml:id="echoid-s2819" xml:space="preserve">C G, G L, &amp; </s>
  <s xml:id="echoid-s2820" xml:space="preserve">rectæ C T, L X, arcus{q́ue} C T, L X, æquales erunt. </s>
  <s xml:id="echoid-s2821" xml:space="preserve">Itaque quoniam arcus A S, <lb/>arcui I V, æqualis est, &amp; </s>
  <s xml:id="echoid-s2822" xml:space="preserve">arcus B<unsure/> S, arcui K V, ſuperabit A B, arcus primæ horæ ♋, eadem quantita-<lb/>te arcum A S, horæ æquinoctialis, qua I K, arcus ab arcu I V, horæ æquinoctialis ſuperatur. </s>
  <s xml:id="echoid-s2823" xml:space="preserve">Ergo per <lb/>ea, quæ dictaſunt, erit I K, arcus primæ horæ ♑; </s>
  <s xml:id="echoid-s2824" xml:space="preserve">at que adeò circulus maximus B F K, per primam ho-<lb/>ram ♋, &amp; </s>
  <s xml:id="echoid-s2825" xml:space="preserve">Acquatoris ductus, tran-<lb/>
<anchor type="figure" xlink:label="fig-0062-01a" xlink:href="fig-0062-01"/>
ſit quoque per primam horam ♑. </s>
  <s xml:id="echoid-s2826" xml:space="preserve">Eo-<lb/>dem prorſus pacto demonſtr abimus ar-<lb/>cum I K, eſſe duarum horarum ♑, <lb/>quemadmodum &amp; </s>
  <s xml:id="echoid-s2827" xml:space="preserve">arcus A C, duas ho-<lb/>ras ♋, complectitur, &amp; </s>
  <s xml:id="echoid-s2828" xml:space="preserve">E G, arcus <lb/>
<anchor type="note" xlink:label="note-0062-01a" xlink:href="note-0062-01"/>
duas horas Aequatoris; </s>
  <s xml:id="echoid-s2829" xml:space="preserve">quoniam vide-<lb/>licet arcus T C, quo A C, arcus dua-<lb/>rum horarum ♋, ſuperat arcum A T, <lb/>duarum horarum æquinoctialium, ęqua-<lb/>lis eſt arcui L X, quo I L, arcus ab ar-<lb/>cu I X, duarum horarum æquinoctia-<lb/>lium ſuperatur. </s>
  <s xml:id="echoid-s2830" xml:space="preserve">Cum igitur I K, oſten-<lb/>ſus ſit arcus primæ horæ ♑, erit K L, <lb/>arcus ſecundæ horæ. </s>
  <s xml:id="echoid-s2831" xml:space="preserve">Eadem{q́ue}, demon-<lb/>ſtratio erit in reliquis horis inæquali-<lb/>
<anchor type="note" xlink:label="note-0062-02a" xlink:href="note-0062-02"/>
bus ♑, &amp; </s>
  <s xml:id="echoid-s2832" xml:space="preserve">aliorum ſignorum, ſi loco <lb/>parallelorum ♋, &amp; </s>
  <s xml:id="echoid-s2833" xml:space="preserve">♑, aſſumantur <lb/>alĳ duo oppoſiti, &amp; </s>
  <s xml:id="echoid-s2834" xml:space="preserve">æquales. </s>
  <s xml:id="echoid-s2835" xml:space="preserve">Quod est <lb/>propoſitum.</s>
  <s xml:id="echoid-s2836" xml:space="preserve"/>
</p>
<div xml:id="echoid-div149" type="float" level="2" n="6">
<note position="left" xlink:label="note-0061-06" xlink:href="note-0061-06a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0061-01" xlink:href="fig-0061-01a">
    <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01"/>
  </figure>
<note position="left" xlink:label="note-0061-07" xlink:href="note-0061-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0061-08" xlink:href="note-0061-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0061-09" xlink:href="note-0061-09a" xml:space="preserve">28. tert@.</note>
  <figure xlink:label="fig-0062-01" xlink:href="fig-0062-01a">
    <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-01"/>
  </figure>
<note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s2837" xml:space="preserve">OMNIA autem, quæ proximis <lb/>
<anchor type="note" xlink:label="note-0062-03a" xlink:href="note-0062-03"/>
duabus propoſ. </s>
  <s xml:id="echoid-s2838" xml:space="preserve">demonſtr auimus, intel-<lb/>ligenda ſunt in ſphæra obliqua tantum. <lb/></s>
  <s xml:id="echoid-s2839" xml:space="preserve">Nam in recta non eſt vllus parallelus perpetuo apparens, cum omnes paralleli ab Horizonte per il-<lb/>lorum polos ducto bifariam ſecentur, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s2840" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2841" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2842" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2843" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s2844" xml:space="preserve">Vnde in ſphæra recta <lb/>maximi circuli, inter quos eſt &amp; </s>
  <s xml:id="echoid-s2845" xml:space="preserve">Meridianus &amp; </s>
  <s xml:id="echoid-s2846" xml:space="preserve">Horizon, incedentes per polos mundi, ſecantes{q́ue} <lb/>
<anchor type="note" xlink:label="note-0062-04a" xlink:href="note-0062-04"/>
Aequatorem, ac proinde, per propoſ. </s>
  <s xml:id="echoid-s2847" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2848" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2849" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2850" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s2851" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2852" xml:space="preserve">reliquos omnes parallelos in 24. <lb/></s>
  <s xml:id="echoid-s2853" xml:space="preserve">partes æquales, indicabunt &amp; </s>
  <s xml:id="echoid-s2854" xml:space="preserve">horas à meridie vel media nocte, &amp; </s>
  <s xml:id="echoid-s2855" xml:space="preserve">ab ortu vel occaſu Solis. </s>
  <s xml:id="echoid-s2856" xml:space="preserve">Ho-<lb/>ræ autem inæquales ibi nuliæ ſunt, cum perpetuum ſit æquinoctium, ac proinde horæ æquinoctiales ſint <lb/>partes duodecimæ cuiuslibet diei, quemadmodum &amp; </s>
  <s xml:id="echoid-s2857" xml:space="preserve">horæ inæquales in ſphæra obliqua partes ſunt duo-<lb/>decimæ cuiuſque diei.</s>
  <s xml:id="echoid-s2858" xml:space="preserve"/>
</p>
<div xml:id="echoid-div150" type="float" level="2" n="7">
<note position="left" xlink:label="note-0062-03" xlink:href="note-0062-03a" xml:space="preserve">In ſphęra recta <lb/>iidẽ circuli indi <lb/>cãt horas à mer. <lb/>vel med. noc &amp; <lb/>ab or. vel occ <lb/>Nullæ autẽ ibi <lb/>ſunt horę in-<lb/>æquales.</note>
<note position="left" xlink:label="note-0062-04" xlink:href="note-0062-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div152" type="section" level="1" n="43">
<head xml:id="echoid-head46" xml:space="preserve">THEOREMA 9. PROPOSITIO 11.</head>
<note position="left" xml:space="preserve">Vmbra ſtyli, &amp; <lb/>radius Solis ꝓ-<lb/>iicitur in cõem <lb/>ſectionem plani <lb/>horologij, &amp; cir <lb/>culi maximi, in <lb/>quo Sol exiſtit.</note>
<p>
  <s xml:id="echoid-s2859" xml:space="preserve">SOLE in quocunque circulo horario, vel alio maximo exiſtente, <lb/>
<anchor type="note" xlink:label="note-0062-06a" xlink:href="note-0062-06"/>
radius Solaris, atque adeò vmbra verticis ſtyli proijcitur in rectam li-<lb/>neam, quæ communis ſectio eſt ipſius circuli horarij vel maximi, &amp;</s>
  <s xml:id="echoid-s2860" xml:space="preserve"><unsure/> <lb/>plani horologij.</s>
  <s xml:id="echoid-s2861" xml:space="preserve"/>
</p>
<div xml:id="echoid-div152" type="float" level="2" n="1">
<note position="left" xlink:label="note-0062-06" xlink:href="note-0062-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s2862" xml:space="preserve">SIT circulus horarius, vel quicunque alius maximus A B C D, ſecans planum horologii <lb/>E F G H, per rectam E G, ſitq́ ſtylus I K, cuius vertex I, in centro I, collocetur, per propoſ. </s>
  <s xml:id="echoid-s2863" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2864" xml:space="preserve">Di-<lb/>co Sole in quocunque puncto L, exiſtente in circulo A B C D, radium eius, &amp; </s>
  <s xml:id="echoid-s2865" xml:space="preserve">vmbram verticis <lb/>
<anchor type="note" xlink:label="note-0062-07a" xlink:href="note-0062-07"/>
ſtyli I, proijci in rectam E G. </s>
  <s xml:id="echoid-s2866" xml:space="preserve">Nam radius L I, pertinens ad centrum I, per quod &amp; </s>
  <s xml:id="echoid-s2867" xml:space="preserve">planum cir-<lb/>culi A B C D, ducitur, à plano circuli A B C D, non recedet, Sole exiſtente in circunferentia <lb/>ipſius circuli, ſed productus ſecabit circunferentiam eiuſdem circuli in puncto M, quod puncto <lb/>L, opponitur, ita vt ipſe radius ſit circuli diameter. </s>
  <s xml:id="echoid-s2868" xml:space="preserve">Cum ergo recta E G, in plano eiuſdem <lb/>circuli exiſtat, ſecabit radius L I M, rectam E G, in N, puncto; </s>
  <s xml:id="echoid-s2869" xml:space="preserve">atque adeo radius Solis L M, &amp; </s>
  <s xml:id="echoid-s2870" xml:space="preserve"><lb/>vmbra verticis ſtyli I, proiicietur in rectam E G, communem ſectionem circuli horarii A B-<lb/>C D, &amp; </s>
  <s xml:id="echoid-s2871" xml:space="preserve">plani horologij E F G H. </s>
  <s xml:id="echoid-s2872" xml:space="preserve">Eodem modo, ſi alius quidam circulus horarius, vel alius <lb/>maximus A F C H, idem planum horologij E F G H, ſecet per rectam F H, &amp; </s>
  <s xml:id="echoid-s2873" xml:space="preserve">Sol exiſtat in pun-<lb/>cto O, circuli horarij, vel maximi, demonſtrabimus radium O I, &amp; </s>
  <s xml:id="echoid-s2874" xml:space="preserve">vmbram eiuſdem verticis <lb/>ſtyli I, proiici in rectam F H, propterea quod radius productus ad punctum oppoſitum P, re-<lb/>ctam FH, in eodem plano circuli A F C H, exiſtentem ſecet in Q, puncto. </s>
  <s xml:id="echoid-s2875" xml:space="preserve">Eademq́ eſt ratio de
<pb o="43" file="0063" n="63" rhead="LIBER PRIMVS."/>
cæteris. </s>
  <s xml:id="echoid-s2876" xml:space="preserve">Sole igitur in quocunque cir <lb/>
<anchor type="figure" xlink:label="fig-0063-01a" xlink:href="fig-0063-01"/>
culo horario, vel alio maximo, exi-<lb/>ſtente, radius Solaris, atque adeò <lb/>vmbra verticis ſtyli proijcitur in re-<lb/>ctam lineam, quæ communis ſectio <lb/>eſt ipſius circuli horarij vel maximi, <lb/>&amp; </s>
  <s xml:id="echoid-s2877" xml:space="preserve">plani horologij.</s>
  <s xml:id="echoid-s2878" xml:space="preserve"/>
</p>
<div xml:id="echoid-div153" type="float" level="2" n="2">
<note position="left" xlink:label="note-0062-07" xlink:href="note-0062-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0063-01" xlink:href="fig-0063-01a">
    <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-01"/>
  </figure>
</div>
</div>
<div xml:id="echoid-div155" type="section" level="1" n="44">
<head xml:id="echoid-head47" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s2879" xml:space="preserve">QVEM ADMODVM autem <lb/>circuli illi maximi, qui horas tam à me-<lb/>ridie vel media nocte, quàm ab ortu vel <lb/>occaſu indicant, Horarĳ appellantur, <lb/>vt propoſ. </s>
  <s xml:id="echoid-s2880" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2881" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2882" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2883" xml:space="preserve">diximus: </s>
  <s xml:id="echoid-s2884" xml:space="preserve">ita quo-<lb/>que communes ſectiones ipſorum, &amp; </s>
  <s xml:id="echoid-s2885" xml:space="preserve"><lb/>plani horologĳ, in quas vmbram ſtyli <lb/>proĳci hac propoſ. </s>
  <s xml:id="echoid-s2886" xml:space="preserve">demonſtr auimus, li-<lb/>neę horarię nuncupantur; </s>
  <s xml:id="echoid-s2887" xml:space="preserve">quia extre-<lb/>
<anchor type="note" xlink:label="note-0063-02a" xlink:href="note-0063-02"/>
mitas vmbræ in illas incidens, quota <lb/>
<anchor type="note" xlink:label="note-0063-03a" xlink:href="note-0063-03"/>
ſit hora, hoc eſt, quemnam circulum <lb/>horariũ tunc occupet Sol, demonſtrat.</s>
  <s xml:id="echoid-s2888" xml:space="preserve"/>
</p>
<div xml:id="echoid-div155" type="float" level="2" n="1">
<note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">Horariæ lineæ <lb/>quæ ſint.</note>
<note position="left" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s2889" xml:space="preserve">EADEM ratione communes ſectiones aliorum cir culorum maximorum, &amp; </s>
  <s xml:id="echoid-s2890" xml:space="preserve">plani horologĳ, nomen <lb/>
<anchor type="note" xlink:label="note-0063-04a" xlink:href="note-0063-04"/>
accipiunt à circulis illis maximis, qui eas in horologio efficiunt: </s>
  <s xml:id="echoid-s2891" xml:space="preserve">Vt communis ſectio Aequinoctialis circu <lb/>li, &amp; </s>
  <s xml:id="echoid-s2892" xml:space="preserve">plani horologĳ, dicitur linea Aequinoctialis: </s>
  <s xml:id="echoid-s2893" xml:space="preserve">Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s2894" xml:space="preserve">plani horologĳ ſectio communis <lb/>linea Verticalis: </s>
  <s xml:id="echoid-s2895" xml:space="preserve">Meridiani, &amp; </s>
  <s xml:id="echoid-s2896" xml:space="preserve">eiuſdem plani horologĳ communis ſectio, linea Meridiana, &amp; </s>
  <s xml:id="echoid-s2897" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2898" xml:space="preserve"/>
</p>
<div xml:id="echoid-div156" type="float" level="2" n="2">
<note position="right" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve">Omnes lineæ <lb/>rectæ in horolo <lb/>gio nomen acci <lb/>piunt à circulis<unsure/> <lb/>maximis, qui <lb/>eas efficiunt in <lb/>horologio.</note>
</div>
<p style="it">
  <s xml:id="echoid-s2899" xml:space="preserve">QVOD ſi circulus maximus plano Horologĳ æquidiſtet, euaneſcet linea illa à circulo maximo denc-<lb/>minata, hoc eſt, in horologio deſcribi non poteſt. </s>
  <s xml:id="echoid-s2900" xml:space="preserve">Cum enim circulus ille non ſecet planum horologĳ, ſed ei <lb/>æquidiſtet, non habebunt communem ſectionem circulus ille, &amp; </s>
  <s xml:id="echoid-s2901" xml:space="preserve">horologĳ planum, neq; </s>
  <s xml:id="echoid-s2902" xml:space="preserve">radius ſolis in eo <lb/>circulo exiſtentis in planum horologĳ proĳcietur, ſed infinitam faciet propemodum umbram, æquidiſtan-<lb/>
<anchor type="note" xlink:label="note-0063-05a" xlink:href="note-0063-05"/>
<anchor type="note" xlink:label="note-0063-06a" xlink:href="note-0063-06"/>
tem{q́ue} plano horologĳ. </s>
  <s xml:id="echoid-s2903" xml:space="preserve">Vnde neque in horologio Horizontali linea horizontalis, ſeu horæ 24. </s>
  <s xml:id="echoid-s2904" xml:space="preserve">ab ortu, uel <lb/>occaſu; </s>
  <s xml:id="echoid-s2905" xml:space="preserve">neque in horologio uerticali linea uerticalis; </s>
  <s xml:id="echoid-s2906" xml:space="preserve">neque in Polari linea horæ ſextæ à meridie uel me-<lb/>dia nocte; </s>
  <s xml:id="echoid-s2907" xml:space="preserve">neque in Meridiano linea horæ 12. </s>
  <s xml:id="echoid-s2908" xml:space="preserve">à meridie uel media nocte; </s>
  <s xml:id="echoid-s2909" xml:space="preserve">neque in Verticaligrad. </s>
  <s xml:id="echoid-s2910" xml:space="preserve">45. </s>
  <s xml:id="echoid-s2911" xml:space="preserve">linea <lb/>horæ 12. </s>
  <s xml:id="echoid-s2912" xml:space="preserve">ab ortu uel occaſu; </s>
  <s xml:id="echoid-s2913" xml:space="preserve">neque in Aequinoctiali linea Aequinoctialis deſcribi pot eſt, ſed prorſus eua-<lb/>neſcit. </s>
  <s xml:id="echoid-s2914" xml:space="preserve">Id quod ex figura ſuperiori facile intelligi poteſt. </s>
  <s xml:id="echoid-s2915" xml:space="preserve">Sole enim exiſtente in puncto B, circuli B D, <lb/>erit radius B I, &amp; </s>
  <s xml:id="echoid-s2916" xml:space="preserve">umbra I D, plano horologĳ E G, æquidiſtans, ſicut &amp; </s>
  <s xml:id="echoid-s2917" xml:space="preserve">circulus ipſe ipſe eidem plano <lb/>æquidiſtat, &amp; </s>
  <s xml:id="echoid-s2918" xml:space="preserve">c.</s>
  <s xml:id="echoid-s2919" xml:space="preserve"/>
</p>
<div xml:id="echoid-div157" type="float" level="2" n="3">
<note position="left" xlink:label="note-0063-05" xlink:href="note-0063-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0063-06" xlink:href="note-0063-06a" xml:space="preserve">Quorum circu-<lb/>lo@um maximo <lb/>rum lineæ in <lb/>horologio de-<lb/>ſcribi nequeãt.</note>
</div>
</div>
<div xml:id="echoid-div159" type="section" level="1" n="45">
<head xml:id="echoid-head48" xml:space="preserve">COROLLARIVM PRIMVM.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve">Horologiũ pla-<lb/>nũ Solare quid <lb/>ſit.</note>
<p>
  <s xml:id="echoid-s2920" xml:space="preserve">HINC ſequitur, Horologium planum Solare nihil eſſe aliud, quàm figuram planam continentem <lb/>communes ſectiones (quæ quidem omnes rectæ ſunt lineæ) omnium circulorum horariorum ſiue à me-<lb/>
<anchor type="note" xlink:label="note-0063-09a" xlink:href="note-0063-09"/>
ridie vel media nocte, ſiue ab ortu uel occaſu, &amp; </s>
  <s xml:id="echoid-s2921" xml:space="preserve">plani ipſius horologij: </s>
  <s xml:id="echoid-s2922" xml:space="preserve">Propterea quòd, vt in hac pro-<lb/>poſ. </s>
  <s xml:id="echoid-s2923" xml:space="preserve">demonſtrauimus, Sole exiſtente, verbi gratia, in circulo horæ 12. </s>
  <s xml:id="echoid-s2924" xml:space="preserve">vmbra ſtyli proijcitur in rectam <lb/>quæ communis eſt ſectio dicti circuli, &amp; </s>
  <s xml:id="echoid-s2925" xml:space="preserve">plani horologij, atque adeo horam indicat duodecimam, cuius <lb/>circulum tunc ſol occupat, atque ita de reliquis horis.</s>
  <s xml:id="echoid-s2926" xml:space="preserve"/>
</p>
<div xml:id="echoid-div159" type="float" level="2" n="1">
<note position="right" xlink:label="note-0063-09" xlink:href="note-0063-09a" xml:space="preserve">3. vndec.</note>
</div>
</div>
<div xml:id="echoid-div161" type="section" level="1" n="46">
<head xml:id="echoid-head49" xml:space="preserve">COROLLARIVM II.</head>
<note position="right" xml:space="preserve">Vmbra ſtyli in <lb/>æquinoctijs de-<lb/>ſcribit bne@m <lb/>æquin@ctialem <lb/>r<unsure/>ectam in horo <lb/>legio.</note>
<p>
  <s xml:id="echoid-s2927" xml:space="preserve">PERSPICVVM quoque eſt ex his, Sole exiſtente in æquinoctiali circulo, vt in principio ♈, uel <lb/>♎, radium ſolarem, &amp; </s>
  <s xml:id="echoid-s2928" xml:space="preserve">extremitatem vmbrę ſtyli deſcribere motu diurno lineam rectam, communem <lb/>
<anchor type="note" xlink:label="note-0063-11a" xlink:href="note-0063-11"/>
videlicet ſectionem Aequatoris, &amp; </s>
  <s xml:id="echoid-s2929" xml:space="preserve">plani horologij: </s>
  <s xml:id="echoid-s2930" xml:space="preserve">quia eo tempore radius Solis per mundi centrũ tran-<lb/>ſiens, atque adeò vmbræ extremitas à plano Aequatoris non recedit, (negligimus enim hic modicam il-<lb/>lam declinationem, quam proprio motu Sol acquirit.) </s>
  <s xml:id="echoid-s2931" xml:space="preserve">ſed ſemper in communem ſectionem Aequato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s2932" xml:space="preserve">plani horologij, id eſt, in lineam Aequinoctialem proijcitur, vt oſtenſum eſt. </s>
  <s xml:id="echoid-s2933" xml:space="preserve">Quare ad motum diur <lb/>num ipſam deſcribet.</s>
  <s xml:id="echoid-s2934" xml:space="preserve"/>
</p>
<div xml:id="echoid-div161" type="float" level="2" n="1">
<note position="left" xlink:label="note-0063-11" xlink:href="note-0063-11a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div163" type="section" level="1" n="47">
<head xml:id="echoid-head50" xml:space="preserve">THEOREMA 10. PROPOSITIO 12.</head>
<p>
  <s xml:id="echoid-s2935" xml:space="preserve">SOLE in quocunque puncto extra Aequatorem exiſtente, radius <lb/>Solaris, atq; </s>
  <s xml:id="echoid-s2936" xml:space="preserve">adeo vmbra verticis ſtyli, proijcitur in lineam curuam, quę
<pb o="44" file="0064" n="64" rhead="GNOMONICES"/>
<anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/>
communis ſectio eſt plani horologij, &amp; </s>
  <s xml:id="echoid-s2937" xml:space="preserve">conicæ ſuperficiei, cuius baſis <lb/>eſt parallelus parallelo Solis oppoſitus.</s>
  <s xml:id="echoid-s2938" xml:space="preserve"/>
</p>
<div xml:id="echoid-div163" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">Vmbra ſtyli, &amp; <lb/>radiu Solari@ <lb/>extra æꝗnoctia <lb/>proiicitur in ſe <lb/>ctionem conicã, <lb/>quæ commun@s <lb/>ſectio eſt plani <lb/>horologu, &amp; co-<lb/>nicę ſuperficiei, <lb/>cuius baſis eſt <lb/>parallelus paral <lb/>lelo Solis oppo-<lb/>ſitus.</note>
</div>
<p>
  <s xml:id="echoid-s2939" xml:space="preserve">SOL extra Aequatorem A B, exiſtat in puncto C, quod motu diurno parallelum D C E, &amp; </s>
  <s xml:id="echoid-s2940" xml:space="preserve"><lb/>eius punctum oppoſitum F, parallelũ <lb/>
<anchor type="figure" xlink:label="fig-0064-01a" xlink:href="fig-0064-01"/>
G F H, radius verò C F, per centrum <lb/>mundi I, extenſus conicas ſuperficies <lb/>I D E, I G H, deſcribat. </s>
  <s xml:id="echoid-s2941" xml:space="preserve">Sit quoque <lb/>planum horologij K L M N, circulo <lb/>maximo O P, æquidiſtans, faciensq́ue <lb/>
<anchor type="note" xlink:label="note-0064-02a" xlink:href="note-0064-02"/>
in conica ſuperficie vmbræ I G H, cõ-<lb/>munem ſectionem curuam lineam <lb/>Q L N, quæ vel circulus erit, vel Para-<lb/>bole, vel Hyperbole, vel Ellipſis, vt pa <lb/>tet ex propoſ. </s>
  <s xml:id="echoid-s2942" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2943" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2944" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2945" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s2946" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2947" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s2948" xml:space="preserve">Dico radium Solarem C F, atque id-<lb/>circo vmbram I F, proiici in curuam <lb/>lineam Q L N. </s>
  <s xml:id="echoid-s2949" xml:space="preserve">Nam radius C F, cum <lb/>deſcribat motu diurno vtramque ſu-<lb/>perficiem conicam, non recedet ab <lb/>
<anchor type="note" xlink:label="note-0064-03a" xlink:href="note-0064-03"/>
vtraque earum, Sole exiſtente in C, <lb/>(Negligimus enim etiam hic modi-<lb/>cam illam declinationem, quam Sol <lb/>motu proprio acquirit.) </s>
  <s xml:id="echoid-s2950" xml:space="preserve">ſed produ-<lb/>ctus ſecabit parallelum oppoſitum in <lb/>puncto F, quod puncto C, opponitur, <lb/>ita vt, per propoſ. </s>
  <s xml:id="echoid-s2951" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2952" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2953" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2954" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s2955" xml:space="preserve">iaceat in ſuperficie vtraque conica. </s>
  <s xml:id="echoid-s2956" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s2957" xml:space="preserve">curua linea <lb/>Q L N, in ſuperficie conica vmbræ I G H, exiſtat, ſecabit radius C F, curuam lineam Q L N, in <lb/>puncto R; </s>
  <s xml:id="echoid-s2958" xml:space="preserve">ac propterea radius Solis C I F, &amp; </s>
  <s xml:id="echoid-s2959" xml:space="preserve">vmbra verticis ſtyli I, proijcietur in lineam curuam <lb/>Q L N, cõmunem ſectionem conicæ ſuperficiei vmbræ I G H, &amp; </s>
  <s xml:id="echoid-s2960" xml:space="preserve">plani horologij K L M N. </s>
  <s xml:id="echoid-s2961" xml:space="preserve">Idemq́ <lb/>
<anchor type="note" xlink:label="note-0064-04a" xlink:href="note-0064-04"/>
oſtendemus contingere, in quocunque puncto cæli Sol ponatur extra Aequatorem. </s>
  <s xml:id="echoid-s2962" xml:space="preserve">Sole igitur <lb/>in quocunque puncto extra Aequatorem exiſtente, &amp;</s>
  <s xml:id="echoid-s2963" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2964" xml:space="preserve">Quod oſtendendum erat.</s>
  <s xml:id="echoid-s2965" xml:space="preserve"/>
</p>
<div xml:id="echoid-div164" type="float" level="2" n="2">
  <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a">
    <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0064-01"/>
  </figure>
<note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div166" type="section" level="1" n="48">
<head xml:id="echoid-head51" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s2966" xml:space="preserve">EX his conſtat, Sole exiſtente extra æquinoctialem circulum, vt in quocunque puncto Zodiaci, præ-<lb/>
<anchor type="note" xlink:label="note-0064-05a" xlink:href="note-0064-05"/>
terquam in principio ♈, &amp; </s>
  <s xml:id="echoid-s2967" xml:space="preserve">♎, radium ſolarem, &amp; </s>
  <s xml:id="echoid-s2968" xml:space="preserve">extremitatem vmbræ ſtyli deſcribere motu diurno <lb/>lineam curuam, communem nimirum ſectionem conicæ ſuperficiei, quam vmbra deſcribit, &amp; </s>
  <s xml:id="echoid-s2969" xml:space="preserve">plani ho-<lb/>rologij: </s>
  <s xml:id="echoid-s2970" xml:space="preserve">quia eo tempore radius Solis per centrum mundi incedens, atque adeò vmbræ extremitas, à ſu-<lb/>perficie conica vmbræ non recedit, ſed ſemper proijcitur in communem ſectionem ſuperficiei vmbræ, &amp; </s>
  <s xml:id="echoid-s2971" xml:space="preserve"><lb/>plani horologij, id eſt, in curuam lineam, nempe circulum, vel Parabolen, vel Hyperbolen, vel Ellipſim, <lb/>
<anchor type="note" xlink:label="note-0064-06a" xlink:href="note-0064-06"/>
vt demonſtratum eſt. </s>
  <s xml:id="echoid-s2972" xml:space="preserve">Quare ipſam deſcribet ad motum diurnum.</s>
  <s xml:id="echoid-s2973" xml:space="preserve"/>
</p>
<div xml:id="echoid-div166" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-05" xlink:href="note-0064-05a" xml:space="preserve">Vmbra ſtyli <lb/>extra æꝗnoctia <lb/>deſcribit coni-<lb/>cam ſectionem <lb/>in horologio.</note>
<note position="left" xlink:label="note-0064-06" xlink:href="note-0064-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s2974" xml:space="preserve">DENOMINATVR tamen eiuſmodi ſectio conica à parallelo, in quo Sol moratur. </s>
  <s xml:id="echoid-s2975" xml:space="preserve">Vt Sole exi-<lb/>ſtente in principio ♋, appellatur ſectio conica, quam vmbra percurrit, circulus, vel Parabole, vel Hyper-<lb/>bole, vel Ellipſis cancri, &amp; </s>
  <s xml:id="echoid-s2976" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s2977" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div168" type="section" level="1" n="49">
<head xml:id="echoid-head52" xml:space="preserve">THEOREMA 11. PROPOSITIO 13.</head>
<p>
  <s xml:id="echoid-s2978" xml:space="preserve">CIRCVLI horarum à meridie, vel media nocte, ſecant ſuperficies <lb/>
<anchor type="note" xlink:label="note-0064-07a" xlink:href="note-0064-07"/>
duas conicas, quarum vertex eſt centrum mundi, baſes autem duo pa-<lb/>
<anchor type="note" xlink:label="note-0064-08a" xlink:href="note-0064-08"/>
ralleli tangentes Hoiizontem, quorum vnus eſt maximus ſemper appa-<lb/>rentium, alter verò maximus ſemper deliteſcentium, lineis rectis ſe mu-<lb/>tuo ſecantibus in centro mundi: </s>
  <s xml:id="echoid-s2979" xml:space="preserve">In ijſdem autem lineis circuli horarũ <lb/>ab ortu, vel occaſu, eaſdem ſuperficies conicas tangunt.</s>
  <s xml:id="echoid-s2980" xml:space="preserve"/>
</p>
<div xml:id="echoid-div168" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-07" xlink:href="note-0064-07a" xml:space="preserve">Circuli horarũ <lb/>à mer. vel med. <lb/>noc. ſecant ſu-<lb/>perficies coni-<lb/>cis, quarum ba-<lb/>ſes ſunt maxi-<lb/>mus parallelo-<lb/>rum ſemper ap <lb/>parentium, &amp; <lb/>maximus ſem-<lb/>per occultorũ, <lb/>p lineas rectas, <lb/>in quibus eaſdẽ <lb/>tangunt circuli <lb/>horarum ab or. <lb/>vel occaſu.</note>
<note position="left" xlink:label="note-0064-08" xlink:href="note-0064-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s2981" xml:space="preserve">IN Sphæra ABCD, cuius centrum E, &amp; </s>
  <s xml:id="echoid-s2982" xml:space="preserve">axis A C, ſint duæ conicæ ſuperficies E F G, E H I, <lb/>quarum vertex communis E, centrum mundi, &amp; </s>
  <s xml:id="echoid-s2983" xml:space="preserve">baſes paraileli F G, H I, maximi eorum, qui ſem <lb/>per apparent, &amp; </s>
  <s xml:id="echoid-s2984" xml:space="preserve">ſub terra occultantur, axis quoque communis recta A C. </s>
  <s xml:id="echoid-s2985" xml:space="preserve">Sit quoque circulus <lb/>horarius à meridie, vel media nocte quicunque A N C k, qui per polos mundi A, C, tranſibit, per <lb/>propoſ. </s>
  <s xml:id="echoid-s2986" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2987" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s2988" xml:space="preserve">ſecans parallelos rectis K L, M N; </s>
  <s xml:id="echoid-s2989" xml:space="preserve">conicas autem ſuperficies lineis k N, L M.</s>
  <s xml:id="echoid-s2990" xml:space="preserve">
<pb o="45" file="0065" n="65" rhead="LIBER PRIMVS."/>
Dico has lineas k N, L M, rectas eſſe, ſeq́ mutuo ſecare in centro E. </s>
  <s xml:id="echoid-s2991" xml:space="preserve">Cum enim circulus maximus <lb/>A N C k, per centrum E, tranſeat, per propoſ. </s>
  <s xml:id="echoid-s2992" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2993" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s2994" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2995" xml:space="preserve">Theodoſii, ſecabit vtique conicas ſuperfi-<lb/>cies E F G, E H I, per verticem E, atque adeo per axem A C, quòd idem circulus A N C K, per po-<lb/>los mundi A, C, tranſeat. </s>
  <s xml:id="echoid-s2996" xml:space="preserve">Quare communes ſectiones circuli, &amp; </s>
  <s xml:id="echoid-s2997" xml:space="preserve">conorum, nempe E k L, E M N, <lb/>triangula erunt, per propoſ. </s>
  <s xml:id="echoid-s2998" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2999" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3000" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3001" xml:space="preserve">Apoll. </s>
  <s xml:id="echoid-s3002" xml:space="preserve">ac propterea E k, E L, E M, E N, communes ſectiones <lb/>ciuídem circuli, &amp; </s>
  <s xml:id="echoid-s3003" xml:space="preserve">conicarum ſuperficierum, rectæ lineæ erunt. </s>
  <s xml:id="echoid-s3004" xml:space="preserve">Dico adhuc rectas E K, E N, &amp; </s>
  <s xml:id="echoid-s3005" xml:space="preserve">EL, <lb/>E M, in directum eſſe conſtitutas. <lb/></s>
  <s xml:id="echoid-s3006" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0065-01a" xlink:href="fig-0065-01"/>
Cum enim duo latera E C, E L, trian-<lb/>guli E C L, (coniunctis prius rectis <lb/>A M, C L) ęqualia ſint duobus lateri-<lb/>
<anchor type="note" xlink:label="note-0065-01a" xlink:href="note-0065-01"/>
bus E A, E M, trianguli E A M, quòd <lb/>omnia ducantur è centro ſphæræ ad <lb/>eius ſuperficiem: </s>
  <s xml:id="echoid-s3007" xml:space="preserve">ſint autem &amp; </s>
  <s xml:id="echoid-s3008" xml:space="preserve">baſes <lb/>C L, A M, æquales, ex theorem. </s>
  <s xml:id="echoid-s3009" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s3010" xml:space="preserve">ſcholij propoſ. </s>
  <s xml:id="echoid-s3011" xml:space="preserve">21. </s>
  <s xml:id="echoid-s3012" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3013" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3014" xml:space="preserve">Theodoſii, <lb/>propterea quòd circuli F G, HI, ſunt <lb/>æquales; </s>
  <s xml:id="echoid-s3015" xml:space="preserve">erunt anguli C E L, A E M, <lb/>æquales: </s>
  <s xml:id="echoid-s3016" xml:space="preserve">Ac proinde cum A C, ſit re-<lb/>
<anchor type="note" xlink:label="note-0065-02a" xlink:href="note-0065-02"/>
cta linea, nempeaxis, conſtituent quo-<lb/>que rectæ E L, E M, per ea, quæ ad pro-<lb/>
<anchor type="note" xlink:label="note-0065-03a" xlink:href="note-0065-03"/>
poſ. </s>
  <s xml:id="echoid-s3017" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3018" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3019" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3020" xml:space="preserve">Euclidis ex Proclo oſten-<lb/>dimus, vnam lineam rectam L M. </s>
  <s xml:id="echoid-s3021" xml:space="preserve">Eſt <lb/>igitur linea L M, communis nimirum <lb/>ſectio conicarum ſuperficierum, &amp; </s>
  <s xml:id="echoid-s3022" xml:space="preserve">cir <lb/>culi A N C K, recta. </s>
  <s xml:id="echoid-s3023" xml:space="preserve">Eademq́ ratione <lb/>&amp; </s>
  <s xml:id="echoid-s3024" xml:space="preserve">k N, recta erit linea, nec non &amp; </s>
  <s xml:id="echoid-s3025" xml:space="preserve">com <lb/>munes ſectiones reliquorum circulo-<lb/>rum horariorum, &amp; </s>
  <s xml:id="echoid-s3026" xml:space="preserve">dictarum ſuper-<lb/>ficierum conicarum, ſecantes ſeſe mutuo in centro E, per quod tranſeunt. </s>
  <s xml:id="echoid-s3027" xml:space="preserve">Quod primo loco <lb/>erat oſtendendum.</s>
  <s xml:id="echoid-s3028" xml:space="preserve"/>
</p>
<div xml:id="echoid-div169" type="float" level="2" n="2">
  <figure xlink:label="fig-0065-01" xlink:href="fig-0065-01a">
    <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/>
  </figure>
<note position="left" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">8. primi.</note>
<note position="left" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s3029" xml:space="preserve">SINT rurſus circuli horarum ab ortu, vel occaſu K R N Q, L P M O, tangentes parallelos <lb/>F G, H I, in punctis K, L, M, N, in quibus eoſdem ſecat circulus horarius à meridie, vel media no-<lb/>cte A N C K, vt propoſ. </s>
  <s xml:id="echoid-s3030" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3031" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3032" xml:space="preserve">eſt demonſtratum. </s>
  <s xml:id="echoid-s3033" xml:space="preserve">Dico eos conicas ſuperficies tangere in <lb/>lineis rectis K N, L M, in quibus eaſdem ſuperficies ſecari demonſtrauimus à circulo A N C k. <lb/></s>
  <s xml:id="echoid-s3034" xml:space="preserve">Sit enim recta S T, communis ſectio planorum, in quibus circuli F G, L M, quæ per definitionem <lb/>lib. </s>
  <s xml:id="echoid-s3035" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3036" xml:space="preserve">Theodoſii, vtrumque circulum tanget. </s>
  <s xml:id="echoid-s3037" xml:space="preserve">Et quia circulus L P M O, maximus, per propoſ. </s>
  <s xml:id="echoid-s3038" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3039" xml:space="preserve"><lb/>lib. </s>
  <s xml:id="echoid-s3040" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3041" xml:space="preserve">Theodoſii, tranſit per centrum ſphæræ E, manifeſtum eſt, ipſum tranſire per rectam L M, <lb/>quæ ex L, in M, per centrum E, extenditur: </s>
  <s xml:id="echoid-s3042" xml:space="preserve">alioqui, ducta in circulo L P M O, recta ex L, in M, <lb/>clauderent duæ rectæ lineæ, nempe ea, quæ modo ducta eſt, &amp; </s>
  <s xml:id="echoid-s3043" xml:space="preserve">L M, ſuperficiem, quod eſt abſur-<lb/>dum. </s>
  <s xml:id="echoid-s3044" xml:space="preserve">Dico iam, circulum L P M O, conicas ſuperficies tangere in recta L M, nullo autem modo <lb/>
<anchor type="note" xlink:label="note-0065-05a" xlink:href="note-0065-05"/>
ſecare. </s>
  <s xml:id="echoid-s3045" xml:space="preserve">Si namque eas ſecaret, fierent communes ſectiones, triangula, per propoſ. </s>
  <s xml:id="echoid-s3046" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3047" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3048" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3049" xml:space="preserve">Apollo-<lb/>nij, quorum baſes in parallelis F G, H I, exiſterent, quandoquidem circulus L P M O, per verticẽ <lb/>E, conicarum ſuperficierum tranſit. </s>
  <s xml:id="echoid-s3050" xml:space="preserve">Igitur communis ſectio planorum, in quibus circuli F G, <lb/>L M, ſunt, circulum F G, ſecaret, faciens nimirum baſim trianguli in circulo F G, quod eſt abſur-<lb/>dum. </s>
  <s xml:id="echoid-s3051" xml:space="preserve">Tangit enim ipſum, vt dictum eſt, ex definitione lib. </s>
  <s xml:id="echoid-s3052" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3053" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s3054" xml:space="preserve">Tangit ergo circulus <lb/>L P M O, conicas ſuperficies E F G, E H I, in recta L M, eademq́; </s>
  <s xml:id="echoid-s3055" xml:space="preserve">eſt ratio in cæteris, quod ſecun-<lb/>do loco propoſitum erat. </s>
  <s xml:id="echoid-s3056" xml:space="preserve">Circuli igitur horarũ à meridie, vel media nocte, ſecant ſuperficies, &amp;</s>
  <s xml:id="echoid-s3057" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s3058" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s3059" xml:space="preserve"/>
</p>
<div xml:id="echoid-div170" type="float" level="2" n="3">
<note position="left" xlink:label="note-0065-05" xlink:href="note-0065-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div172" type="section" level="1" n="50">
<head xml:id="echoid-head53" xml:space="preserve">THEOREMA 12. PROPOSITIO 14.</head>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Lineæ horarum <lb/>à mer. uel med. <lb/>noc. ſecant ſe-<lb/>ct@ones coni-<lb/>cas, quas pla-<lb/>num horologii <lb/>in conis, quorú <lb/>baſes ſunt pa-<lb/>rall elus ſemper <lb/>apparentiũ ma-<lb/>ximus, &amp; maxi-<lb/>mus ſemper la-<lb/>tentium efficit, <lb/>in punctis, in <lb/>quibus eaſdem <lb/>tangunt linez<unsure/> <lb/>horarum ab or. <lb/>uel occ.</note>
<p>
  <s xml:id="echoid-s3060" xml:space="preserve">LINEAE horarum à meridie, vel media nocte ſecant communes <lb/>ſectiones plani horologij cuiuſcunque, &amp; </s>
  <s xml:id="echoid-s3061" xml:space="preserve">ſuperficierum conicarum, <lb/>quarum vertex eſt centrum mundi, baſes autem duo paralleli tangentes <lb/>Horizontem, quorum vnus eſt maximus ſemper apparentiũ, alter vero <lb/>maximus ſemper latentium: </s>
  <s xml:id="echoid-s3062" xml:space="preserve">In punctis autem ſectionum eaſdem com-<lb/>munes ſectiones tangunt lineæ horarum ab ortu, vel occaſu.</s>
  <s xml:id="echoid-s3063" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3064" xml:space="preserve">QVONIAM circuli horarum à meridie, vel media nocte ſecant ſuperficies has conicas li-
<pb o="46" file="0066" n="66" rhead="GNOMONICES"/>
neis rectis in centro mundi ſe ſecantibus, per præcedentem propoſ. </s>
  <s xml:id="echoid-s3065" xml:space="preserve">ſit vt communes eorum, &amp; </s>
  <s xml:id="echoid-s3066" xml:space="preserve"><lb/>plani horologij ſectiones, id eſt, lineæ eorum horariæ, ſecent communes ſectiones illarum ſuper-<lb/>ficierum conicarum, &amp; </s>
  <s xml:id="echoid-s3067" xml:space="preserve">plani horologii, in illis punctis, in quibus lineæ illæ rectæ, quibus circuli <lb/>horarij ſuperficies conicas ſecant, plano horologij, &amp; </s>
  <s xml:id="echoid-s3068" xml:space="preserve">conicis ſectionibus occurrunt; </s>
  <s xml:id="echoid-s3069" xml:space="preserve">quandoqui-<lb/>dem lineæ huiuſmodi horariæ, communes ſcilicet ſectiones circulorum horariorum, &amp; </s>
  <s xml:id="echoid-s3070" xml:space="preserve">plani ho-<lb/>rologij, exiſtunt in planis horariorum circulorum, qui ſuperficies conicas, atque adeo &amp; </s>
  <s xml:id="echoid-s3071" xml:space="preserve">ſectiones <lb/>conicas in plano horologij exiſtentes ibidem ſecant. </s>
  <s xml:id="echoid-s3072" xml:space="preserve">Hinc enim fit, vt cum planum horologij, &amp; </s>
  <s xml:id="echoid-s3073" xml:space="preserve"><lb/>plana circulorum horariorum in illis punctis ſe interſecent, &amp; </s>
  <s xml:id="echoid-s3074" xml:space="preserve">tam illud quàm hæc plana intra <lb/>conum, atque adeo &amp; </s>
  <s xml:id="echoid-s3075" xml:space="preserve">intra conicas ſectiones tendant, earum communes ſectiones, nempe lineæ <lb/>horariæ, cadant quoque ab illis punctis intra conum, ac proinde &amp; </s>
  <s xml:id="echoid-s3076" xml:space="preserve">intra ſectiones conicas, cum <lb/>
<anchor type="note" xlink:label="note-0066-01a" xlink:href="note-0066-01"/>
poſt illa puncta neque à plano horologij, neque à planis dictorum circulorum recedant, ſed in <lb/>vtriſque perpetuo exiſtant. </s>
  <s xml:id="echoid-s3077" xml:space="preserve">Conſtat ergo id, quod primo loco propoſitum eſt.</s>
  <s xml:id="echoid-s3078" xml:space="preserve"/>
</p>
<div xml:id="echoid-div172" type="float" level="2" n="1">
<note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s3079" xml:space="preserve">Q V I A vero circuli horarum ab ortu, vel occaſu tangunt eaſdem ſuperficies conicas, per <lb/>candem propoſ. </s>
  <s xml:id="echoid-s3080" xml:space="preserve">antecedentem, in lineis illis, quibus eas ſecant circuli horarum à meridie, vel me-<lb/>dia nocte; </s>
  <s xml:id="echoid-s3081" xml:space="preserve">efficitur, vt communes illorum, &amp; </s>
  <s xml:id="echoid-s3082" xml:space="preserve">plani horologij ſectiones, hoc eſt, lineæ eorum ho-<lb/>rariæ, tangant ſectiones conicas, quas facit horologij planum, in illis punctis, in quibus lineæ il-<lb/>lę rectæ, quibus circuli horarii ſuperficies conicas tangunt, plano horologij, &amp; </s>
  <s xml:id="echoid-s3083" xml:space="preserve">conicis ſectionibus <lb/>occurrunt, in ijs nimirum, in quibus lineæ horarum à meridie, vel media nocte, ſectiones coni-<lb/>cas ſecant; </s>
  <s xml:id="echoid-s3084" xml:space="preserve">quandoquidem lineæ horariæ ab ortu, vel occaſu, communes videlicet ſectiones cir-<lb/>culorum horariorum, &amp; </s>
  <s xml:id="echoid-s3085" xml:space="preserve">plani horologij, exiſtunt in planis circulorum horariorum, qui ibidem <lb/>
<anchor type="note" xlink:label="note-0066-02a" xlink:href="note-0066-02"/>
ſuperficies conicas, atque adeò &amp; </s>
  <s xml:id="echoid-s3086" xml:space="preserve">conicas ſectiones in plano horologij exiſtentes tangunt. </s>
  <s xml:id="echoid-s3087" xml:space="preserve">Hinc <lb/>enim efficitur, vt cum planum horologij, &amp; </s>
  <s xml:id="echoid-s3088" xml:space="preserve">plana circulorum horariorum in illis punctis ſe in-<lb/>terſecent, &amp; </s>
  <s xml:id="echoid-s3089" xml:space="preserve">illud quidem intra conum, atque adeo intra conicas ſectiones extendatur, hæc ve-<lb/>ro plana extra conum, &amp; </s>
  <s xml:id="echoid-s3090" xml:space="preserve">ideo extra ſectiones conicas protendantur, earum communes ſectiones, <lb/>hoc eſt, horariæ lineæ, cadant ab illis punctis totæ extra conum, ac proinde &amp; </s>
  <s xml:id="echoid-s3091" xml:space="preserve">extra ſectiones coni-<lb/>cas; </s>
  <s xml:id="echoid-s3092" xml:space="preserve">cum poſt illa puncta neque à plan o horologij, nec à planis dictorum circulorum recedant, <lb/>ſed in vtriſque perpetuo exiſtant, quorum hæc tota extra conum, &amp; </s>
  <s xml:id="echoid-s3093" xml:space="preserve">conicas ſectiones reperiuntur. <lb/></s>
  <s xml:id="echoid-s3094" xml:space="preserve">Patet igitur &amp; </s>
  <s xml:id="echoid-s3095" xml:space="preserve">id, quod ſecundo loco fuit propoſitum. </s>
  <s xml:id="echoid-s3096" xml:space="preserve">Lineæ ergo horarum à meridie, vel media <lb/>nocte ſecant, &amp;</s>
  <s xml:id="echoid-s3097" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3098" xml:space="preserve">Quod oſten dendum erat.</s>
  <s xml:id="echoid-s3099" xml:space="preserve"/>
</p>
<div xml:id="echoid-div173" type="float" level="2" n="2">
<note position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div175" type="section" level="1" n="51">
<head xml:id="echoid-head54" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s3100" xml:space="preserve">QVOD ſi planum horologĳ æquidiſtet alicui circulo horæ à meridie, vel media nocte, non ſecabit <lb/>hic cir culus conicam ſectionem à plano horologĳ factam, cum nec ipſum planum horologĳ ſecet, vt con-<lb/>ſtat. </s>
  <s xml:id="echoid-s3101" xml:space="preserve">Vnde neque linea horaria illius eandem conicam ſectionem ſecabit, at que adeo lineæ horariæ ab or-<lb/>tu, vel occaſu, quarum circuli tangunt conicas ſuperficie<unsure/>s in lineis, in quibus à circulo illo horario à meri-<lb/>die, vel media nocte ſccatur, non tangent conicas ſectiones, vt propoſ. </s>
  <s xml:id="echoid-s3102" xml:space="preserve">ſequenti demonſlrabitur.</s>
  <s xml:id="echoid-s3103" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div176" type="section" level="1" n="52">
<head xml:id="echoid-head55" xml:space="preserve">THEOREMA 13. PROPOSITIO 15.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s3104" xml:space="preserve">SI circulus cuiuſuis horæ à meridie, vel media nocte plano horolo-<lb/>
<anchor type="note" xlink:label="note-0066-05a" xlink:href="note-0066-05"/>
gij æquidiſtet, tangant autem maximum parallelorum ſemper apparen-<lb/>tium duo circuli horarum ab ortu, vel occaſu in eiſdem punctis, in qui-<lb/>bus à circulo illo horæ à meridie, vel media nocte ſecatur; </s>
  <s xml:id="echoid-s3105" xml:space="preserve">erunt duæ <lb/>illæ lineæ horarum ab ortu, vel occaſu ἀσύμπτοτοι, hoc eſt, non conue-<lb/>nientes cum conicis ſectionibus, quas planum horologij facitin ſu-<lb/>perficiebus conicis, quarum baſes ſunt maximi parallelorum ſemper ap-<lb/>
<anchor type="note" xlink:label="note-0066-06a" xlink:href="note-0066-06"/>
parentium, &amp; </s>
  <s xml:id="echoid-s3106" xml:space="preserve">deliteſcentium, ſemperq́; </s>
  <s xml:id="echoid-s3107" xml:space="preserve">longius productæ fient coni-<lb/>cis ſectionibus propinquiores.</s>
  <s xml:id="echoid-s3108" xml:space="preserve"/>
</p>
<div xml:id="echoid-div176" type="float" level="2" n="1">
<note position="left" xlink:label="note-0066-05" xlink:href="note-0066-05a" xml:space="preserve">Lineæ horarum <lb/>ab or. vel occ. <lb/>quarum circuli <lb/>tangunt paralle <lb/>lum ſemper ap-<lb/>parentium ma-<lb/>ximum in eiſ-<lb/>dem punctis, in <lb/>quibus a circu-<lb/>lo alicuius horę <lb/>à mer. uel med. <lb/>noc qui horolo <lb/>gio æquidiſter, <lb/>ſecatur, non cõ-<lb/>ueniunt cum ſe <lb/>ctionibus coni-<lb/>cis, quas in ſu-<lb/>perficiebus coni <lb/>cis, quarum ba-<lb/>ſes ſunt maxi-<lb/>mi parallelorũ <lb/>ſemper apparé-<lb/>tium &amp; laten-<lb/>tium, facit horo <lb/>logit planum: <lb/>ſemper tamen <lb/>longius produ-<lb/>ctæ propinquio <lb/>res fiunt coni-<lb/>cis ſectionibus.</note>
<note position="left" xlink:label="note-0066-06" xlink:href="note-0066-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s3109" xml:space="preserve">SECET ſuperficies conicas A B C, A D E, ad centrum A, coniunctas, quarum baſes ſint pa-<lb/>rallelus D E, ſemper apparentium maximus, &amp; </s>
  <s xml:id="echoid-s3110" xml:space="preserve">B C, parallelus maximus ſemper latentium ſub <lb/>Horizonte, circulus aliquis horarius à meridie, vel media nocte F G, per axem F G, rectis H I, <lb/>K L, faciensq́, diametros parallelorum H K, L I, (cum eos, per propoſ. </s>
  <s xml:id="echoid-s3111" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3112" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3113" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3114" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s3115" xml:space="preserve">ſecet <lb/>bifariam, atque adeo per eorum diametros) &amp; </s>
  <s xml:id="echoid-s3116" xml:space="preserve">æquidiſtans plano horologij M N, quod per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s3117" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3118" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3119" xml:space="preserve">faciet duas hyperbolas oppoſitas, &amp; </s>
  <s xml:id="echoid-s3120" xml:space="preserve">æquales O P Q, R S T. </s>
  <s xml:id="echoid-s3121" xml:space="preserve">Et quoniam plana <lb/>F G, M N, parallela ponuntur, erunt eorum communes ſectiones factæ à parallelo D E, nęmpe
<pb o="47" file="0067" n="67" rhead="LIBER PRIMVS."/>
rectæ L I, S T, parallelæ. </s>
  <s xml:id="echoid-s3122" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s3123" xml:space="preserve">ratione H k, P Q, parallelæ erunt, cum ſint communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0067-01a" xlink:href="note-0067-01"/>
nes planorum parallelorum F G, M N, factæ à parallelo B C. </s>
  <s xml:id="echoid-s3124" xml:space="preserve">Tangat quoque circulus aliquis <lb/>horarius ab ortu, vel occaſu parallelos B C, D E, in H, I, punctis, atque adeo &amp; </s>
  <s xml:id="echoid-s3125" xml:space="preserve">conicas ſuperficies <lb/>
<anchor type="figure" xlink:label="fig-0067-01a" xlink:href="fig-0067-01"/>
<anchor type="note" xlink:label="note-0067-02a" xlink:href="note-0067-02"/>
<anchor type="note" xlink:label="note-0067-03a" xlink:href="note-0067-03"/>
<anchor type="note" xlink:label="note-0067-04a" xlink:href="note-0067-04"/>
in recta H I, per propoſ. </s>
  <s xml:id="echoid-s3126" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3127" xml:space="preserve">huius lib, faciens in plano horologii lineam horariam V X. </s>
  <s xml:id="echoid-s3128" xml:space="preserve">Dico re-<lb/>ctam V X, eſſe ἀσύμπτοτον, id eſt, non conuenire vnquam cum hyperbolis O P Q, R S T, fieri ta-<lb/>men ipſis ſemper propinquiorem, ſi tam recta, quàm hyperbolæ producantur. </s>
  <s xml:id="echoid-s3129" xml:space="preserve">Cum enim cir-<lb/>culus H I V X, conicas ſuperficies tangat in recta H I, tantum, ita vt omnia alia puncta circuli <lb/>
<anchor type="note" xlink:label="note-0067-05a" xlink:href="note-0067-05"/>
H I V X, exiſtentia extra rectam H I, ſint extra conicas ſuperficies, erit horaria linea V X, tota ex-<lb/>tra conicas ſuperficies, propterea quod non coire poteſt cum recta H I, quandoquidem plana F G, <lb/>M N, parallela ponuntur, ac propterea rectæ H I, V X, ipſorum communes ſectiones factæ à pla-<lb/>no H I V X, parallelæ ſunt. </s>
  <s xml:id="echoid-s3130" xml:space="preserve">Non igitur conueniet recta V X, cum hyperbolis O P Q, R S T, etiã <lb/>
<anchor type="note" xlink:label="note-0067-06a" xlink:href="note-0067-06"/>
ſi recta V X, &amp; </s>
  <s xml:id="echoid-s3131" xml:space="preserve">hyperbolæ in eodem ſint plano horologii. </s>
  <s xml:id="echoid-s3132" xml:space="preserve">Eodem modo erit V X, extra conicas <lb/>ſuperficies, etiamſi producantur in infinitum. </s>
  <s xml:id="echoid-s3133" xml:space="preserve">Idemq́ dices de linea horaria, cuius circulus tan-<lb/>git ſuperficies conicas in recta K L.</s>
  <s xml:id="echoid-s3134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div177" type="float" level="2" n="2">
<note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">16. vndec.</note>
  <figure xlink:label="fig-0067-01" xlink:href="fig-0067-01a">
    <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/>
  </figure>
<note position="left" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0067-06" xlink:href="note-0067-06a" xml:space="preserve">16. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s3135" xml:space="preserve">DICO iam rectam V X, productam in vtramque partem fieri ſemper hyperbolis pro pinquio <lb/>rem. </s>
  <s xml:id="echoid-s3136" xml:space="preserve">Augeatur enim conica ſuperficies A B C, &amp; </s>
  <s xml:id="echoid-s3137" xml:space="preserve">auctæ baſis ſit Y Z; </s>
  <s xml:id="echoid-s3138" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3139" xml:space="preserve">protrahantur rectæ I H, <lb/>F G, M N, V X, ad puncta α, β, γ, δ, vnà cum planis F G, M N, H I V X; </s>
  <s xml:id="echoid-s3140" xml:space="preserve">augeaturq́ue hyper-<lb/>
<anchor type="note" xlink:label="note-0067-07a" xlink:href="note-0067-07"/>
bole O P Q, vt fiat O ε θ. </s>
  <s xml:id="echoid-s3141" xml:space="preserve">Secentur quoque conicæ ſuperficies plano, in quo circulus maximus <lb/>D B C E, per diametros D E, B C, quæ ad diametros L I, H K, atque ob id &amp; </s>
  <s xml:id="echoid-s3142" xml:space="preserve">ad rectas S T, P Q, <lb/>illis æquidiſtantes, perpendiculares ſint. </s>
  <s xml:id="echoid-s3143" xml:space="preserve">Poſtremo ſint H λ, α δ, communes ſectiones planorum <lb/>B C, Y Z, &amp; </s>
  <s xml:id="echoid-s3144" xml:space="preserve">plani, in quo circulus H I V X, quæ tangent circulos B C, Y Z, in punctis H, α, per <lb/>definitionem lib. </s>
  <s xml:id="echoid-s3145" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3146" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s3147" xml:space="preserve">ſecabuntq́ue ſe mutuo tres rectæ V X, Q P, H λ, extra ſuperficies co-<lb/>nicas in puncto λ. </s>
  <s xml:id="echoid-s3148" xml:space="preserve">Quælibet enim duæ ſe mutuo ſecant. </s>
  <s xml:id="echoid-s3149" xml:space="preserve">Nam cum H I, V X, parallelæ ſint oſten <lb/>ſæ, ſitq́ue H λ, in eodem cum ipſis plano, nempe in plano circuli H I V X; </s>
  <s xml:id="echoid-s3150" xml:space="preserve">ſecet autem H λ, ip-<lb/>ſam H I, in H, ſecabit quoque eadem H λ, rectam V X, vt ad 28, propoſ. </s>
  <s xml:id="echoid-s3151" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3152" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3153" xml:space="preserve">Euclidis demon-<lb/>ſtrauimus. </s>
  <s xml:id="echoid-s3154" xml:space="preserve">Secant ergo ſe mutuo rectæ H λ, V X. </s>
  <s xml:id="echoid-s3155" xml:space="preserve">Rurſus eadem H λ, ipſam P Q, ſecabit. </s>
  <s xml:id="echoid-s3156" xml:space="preserve">Nam <lb/>cum H K, P Q, parallelæ ſint, vt ſupra oſtenſum eſt, ſecet autem H λ, ipſam H K, ſecabit quo-<lb/>que ipſam P Q, ex iis, quæ ad propoſ. </s>
  <s xml:id="echoid-s3157" xml:space="preserve">28. </s>
  <s xml:id="echoid-s3158" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3159" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3160" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s3161" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s3162" xml:space="preserve">Quòd autem &amp; </s>
  <s xml:id="echoid-s3163" xml:space="preserve">P Q, V X, ſe
<pb o="48" file="0068" n="68" rhead="GNOMONICES"/>
mutuo ſecent, ita palam fiet. </s>
  <s xml:id="echoid-s3164" xml:space="preserve">Si enim non ſe interſecent, cum ſint in eodem plano horologii, pa-<lb/>rallelæ erunt. </s>
  <s xml:id="echoid-s3165" xml:space="preserve">Cum igitur vtraque H I, P Q, ipſi V X, parallela ſit, &amp; </s>
  <s xml:id="echoid-s3166" xml:space="preserve">inter ſe parallelæ erunt H I, <lb/>
<anchor type="note" xlink:label="note-0068-01a" xlink:href="note-0068-01"/>
P Q. </s>
  <s xml:id="echoid-s3167" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s3168" xml:space="preserve">H K, ipſi P Q, parallela, vt ſupra demonſtrauimus. </s>
  <s xml:id="echoid-s3169" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s3170" xml:space="preserve">H I, H k, inter <lb/>
<anchor type="figure" xlink:label="fig-0068-01a" xlink:href="fig-0068-01"/>
<anchor type="note" xlink:label="note-0068-02a" xlink:href="note-0068-02"/>
<anchor type="note" xlink:label="note-0068-03a" xlink:href="note-0068-03"/>
<anchor type="note" xlink:label="note-0068-04a" xlink:href="note-0068-04"/>
<anchor type="note" xlink:label="note-0068-05a" xlink:href="note-0068-05"/>
ſe parallelæ erunt. </s>
  <s xml:id="echoid-s3171" xml:space="preserve">Quod eſt abſurdũ, cùm conueniant in H Secant ergo ſe mutuo P Q, V X. </s>
  <s xml:id="echoid-s3172" xml:space="preserve">Qua-<lb/>re V X, vtramque H λ, P Q, ſecans, per punctum λ, vbi ſe mutuo ſecant H λ, Q P, tranſibit. </s>
  <s xml:id="echoid-s3173" xml:space="preserve">Nam <lb/>ſi verbi gratia, V X, ſecet rectam H λ, citra punctum λ, vel vltra, ſi producatur vlterius, ſtatim ſe-<lb/>cabit planum circuli B C, in eodem puncto, in quo rectam H λ, ſecat, ac proinde ſecare non po-<lb/>terit amplius rectam Q P, in eodem plano circuli B C, exiſtentem. </s>
  <s xml:id="echoid-s3174" xml:space="preserve">Pari ratione, ſi V X, ſecet P Q, <lb/>
<anchor type="note" xlink:label="note-0068-06a" xlink:href="note-0068-06"/>
citra, vel vltra punctum λ, ſecabit quoque producta ſtatim planum circuli B C, in eodem puncto, <lb/>in quo rectam P Q, ſecat, ac propterea ſecare non poterit rectam H λ, in eodem ſemper plano <lb/>circuli B C, exiſtentem. </s>
  <s xml:id="echoid-s3175" xml:space="preserve">Quare V X, niſi per punctum λ, tranſeat, vtramque H λ, Q P, non ſeca-<lb/>bit, Quod eſt abſurdum. </s>
  <s xml:id="echoid-s3176" xml:space="preserve">oſtenſum eſt enim eam ſecare vtramque. </s>
  <s xml:id="echoid-s3177" xml:space="preserve">Eodem modo in δ, ſe mutuo <lb/>
<anchor type="note" xlink:label="note-0068-07a" xlink:href="note-0068-07"/>
ſecabunt tres rectæ α δ, θ ε, V X. </s>
  <s xml:id="echoid-s3178" xml:space="preserve">Quoniam igitur rectæ μ β, ξ γ, parallelæ ſunt, vtpote commu-<lb/>nes ſectiones planorum parallelorum F G, M N, factæ à plano circuli D B C E, nec non &amp; </s>
  <s xml:id="echoid-s3179" xml:space="preserve">rectæ <lb/>μ ξ, β γ, nempe communes ſectiones planorum parallelorum B C, Y Z, factæ à plano eodem <lb/>
<anchor type="note" xlink:label="note-0068-08a" xlink:href="note-0068-08"/>
circuli D B C E; </s>
  <s xml:id="echoid-s3180" xml:space="preserve">æquales erunt μ ξ, β γ. </s>
  <s xml:id="echoid-s3181" xml:space="preserve">Et quia H λ, μ ξ, necnon &amp; </s>
  <s xml:id="echoid-s3182" xml:space="preserve">α δ, β γ, parallelæ etiam ſunt, <lb/>
<anchor type="note" xlink:label="note-0068-09a" xlink:href="note-0068-09"/>
propterea quòd anguli ω H λ, β α δ, ad puncta contactuum H, α, recti ſunt, (ſunt enim H μ, α β, <lb/>diametri circulorum B C, Y Z, nempe communes ſectiones ipſorum, &amp; </s>
  <s xml:id="echoid-s3183" xml:space="preserve">plani F G, quod eos per <lb/>
<anchor type="note" xlink:label="note-0068-10a" xlink:href="note-0068-10"/>
<anchor type="note" xlink:label="note-0068-11a" xlink:href="note-0068-11"/>
polos bifariam ſecat, ex propo@. </s>
  <s xml:id="echoid-s3184" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3185" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3186" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3187" xml:space="preserve">Theod.) </s>
  <s xml:id="echoid-s3188" xml:space="preserve">necnon &amp; </s>
  <s xml:id="echoid-s3189" xml:space="preserve">anguli H μ ξ, α β γ, ad centra μ, β. <lb/></s>
  <s xml:id="echoid-s3190" xml:space="preserve">Cum enim per conſtructionem, recta B C, rectam H k, ad angulos rectos ſecet, rectus erit angu-<lb/>lus H μ ξ. </s>
  <s xml:id="echoid-s3191" xml:space="preserve">Cum igitur rectis H μ, μ ξ, parallelæ ſint α β, β γ, erit &amp; </s>
  <s xml:id="echoid-s3192" xml:space="preserve">angulus α β γ, ipſi H μ ξ, æqualis, <lb/>
<anchor type="note" xlink:label="note-0068-12a" xlink:href="note-0068-12"/>
rectus: </s>
  <s xml:id="echoid-s3193" xml:space="preserve">ſunt autem &amp; </s>
  <s xml:id="echoid-s3194" xml:space="preserve">rectæ H μ, λ ξ, nec non α β, δ γ, parallelæ, nimirum ſectiones communes <lb/>
<anchor type="note" xlink:label="note-0068-13a" xlink:href="note-0068-13"/>
planorum parallelorum F G, M N, factæ à plano circuli B C, ſi de prioribus, &amp; </s>
  <s xml:id="echoid-s3195" xml:space="preserve">à plano circuli <lb/>
<anchor type="note" xlink:label="note-0068-14a" xlink:href="note-0068-14"/>
Y Z, ſi de poſterioribus loquamur; </s>
  <s xml:id="echoid-s3196" xml:space="preserve">fit vt recta δ ε, minor ſit, quàm recta λ P, vt mox demonſtra-<lb/>bimus ſequenti lemmate. </s>
  <s xml:id="echoid-s3197" xml:space="preserve">Quare propinquior eſt recta V X, producta hyperbolæ O ε θ, in pun-<lb/>cto δ, quàm in puncto P; </s>
  <s xml:id="echoid-s3198" xml:space="preserve">atque ita deinceps, ſi longius producantur linea horaria, &amp; </s>
  <s xml:id="echoid-s3199" xml:space="preserve">hyperbo-<lb/>le. </s>
  <s xml:id="echoid-s3200" xml:space="preserve">Idemq́ue oſtendemus in hyperbola R S T. </s>
  <s xml:id="echoid-s3201" xml:space="preserve">Item de linea horaria, quam facit circulus tan-<lb/>gens conicas ſuperficies in recta K L. </s>
  <s xml:id="echoid-s3202" xml:space="preserve">Quamobrem ſi circulus cuiuſuis horæ à meridie, vel media <lb/>nocte plano horologii æquidiſtet, &amp;</s>
  <s xml:id="echoid-s3203" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3204" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s3205" xml:space="preserve"/>
</p>
<div xml:id="echoid-div178" type="float" level="2" n="3">
<note position="left" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">9. vndec.</note>
  <figure xlink:label="fig-0068-01" xlink:href="fig-0068-01a">
    <image file="0068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0068-01"/>
  </figure>
<note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0068-04" xlink:href="note-0068-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0068-05" xlink:href="note-0068-05a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0068-06" xlink:href="note-0068-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0068-07" xlink:href="note-0068-07a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0068-08" xlink:href="note-0068-08a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0068-09" xlink:href="note-0068-09a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0068-10" xlink:href="note-0068-10a" xml:space="preserve">18. tertĳ.</note>
<note position="left" xlink:label="note-0068-11" xlink:href="note-0068-11a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0068-12" xlink:href="note-0068-12a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0068-13" xlink:href="note-0068-13a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0068-14" xlink:href="note-0068-14a" xml:space="preserve">16. vndec.</note>
</div>
<pb o="49" file="0069" n="69" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div180" type="section" level="1" n="53">
<head xml:id="echoid-head56" xml:space="preserve">LEMMA.</head>
<p>
  <s xml:id="echoid-s3206" xml:space="preserve">SI duos circulos inæquales tangant duæ lineæ rectæ diametris æquidiſtantes, <lb/>coniunganturq́; </s>
  <s xml:id="echoid-s3207" xml:space="preserve">puncta contactuum, &amp; </s>
  <s xml:id="echoid-s3208" xml:space="preserve">centra duabus rectis lineis, quibus per duo <lb/>puncta ſemidiametrorum æqualiter à centris remota parallelæ agantur ſecantes <lb/>circulorum peripherias; </s>
  <s xml:id="echoid-s3209" xml:space="preserve">erunt rectę inter lineas tangentes, &amp; </s>
  <s xml:id="echoid-s3210" xml:space="preserve">peripherias interce-<lb/>ptæ, inæquales, minorq́; </s>
  <s xml:id="echoid-s3211" xml:space="preserve">ea, quæ extra maioreni circulum exiſtit.</s>
  <s xml:id="echoid-s3212" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3213" xml:space="preserve">SIT circulus a Y Z, maior circulo H B C, &amp; </s>
  <s xml:id="echoid-s3214" xml:space="preserve">vtrumque<unsure/> tangant rectæ α δ, H λ, <lb/>æquidiſtantes diametris Y Z, B C, connectantur {q́ue} puncta contactuum α, H, &amp; </s>
  <s xml:id="echoid-s3215" xml:space="preserve">centra <lb/>
<anchor type="note" xlink:label="note-0069-01a" xlink:href="note-0069-01"/>
β, μ, rectis α β, H μ; </s>
  <s xml:id="echoid-s3216" xml:space="preserve">ſumptis autem rectis β γ, μ ξ, æqualibus ex ſemidiametris β Z, μ C, <lb/>agantur per γ, ξ, rectis α β, H μ, parallelæ γ δ, ξ λ, ſecantes peripherias in ε, P. </s>
  <s xml:id="echoid-s3217" xml:space="preserve">Dico <lb/>rectam δ ε, minorem eſſe, quàm <lb/>
<anchor type="figure" xlink:label="fig-0069-01a" xlink:href="fig-0069-01"/>
λ P. </s>
  <s xml:id="echoid-s3218" xml:space="preserve">Cum enim circulus α Y Z, <lb/>maior ſit circulo H B C, erit &amp; </s>
  <s xml:id="echoid-s3219" xml:space="preserve"><lb/>ſemidiameter α β, ſemidiame-<lb/>tro H μ, maior. </s>
  <s xml:id="echoid-s3220" xml:space="preserve">Abſciſſa ergo <lb/>recta α A, quæ ipſi H μ, ſit æqua-<lb/>lis, deſcribatur ad interuallum <lb/>
<anchor type="note" xlink:label="note-0069-02a" xlink:href="note-0069-02"/>
A α, ex A, circulus α E, qui æ-<lb/>qualis erit circulo H B C, propter <lb/>æqualitatem ſemidiametrorum <lb/>α A, H μ, tanget {q́ue} circulũ α Y Z, <lb/>in α. </s>
  <s xml:id="echoid-s3221" xml:space="preserve">Et quoniam ducta ex A, <lb/>ad γ δ, perpendicularis A D, <lb/>ipſi β γ, parallela eſt, parallelogrammum erit A γ; </s>
  <s xml:id="echoid-s3222" xml:space="preserve">ac propterea recta A D, rectæ β γ, hoc <lb/>
<anchor type="note" xlink:label="note-0069-03a" xlink:href="note-0069-03"/>
eſt, rectæ μ ξ, æqualis erit. </s>
  <s xml:id="echoid-s3223" xml:space="preserve">Cum ergo μ ξ, minor ſit ſemidiametro μ C, vel H μ, hoc eſt, <lb/>
<anchor type="note" xlink:label="note-0069-04a" xlink:href="note-0069-04"/>
<anchor type="note" xlink:label="note-0069-05a" xlink:href="note-0069-05"/>
quàm α A, quæ æqualis eſt ipſi H μ, erit quoque A D, minor, quàm α A, ac idcirco <lb/>punctum D, intra circulum α E, exiſtet. </s>
  <s xml:id="echoid-s3224" xml:space="preserve">Quare circunferentia α E, rectam D δ, ſeca-<lb/>bit infra punctum ε, nempe in E. </s>
  <s xml:id="echoid-s3225" xml:space="preserve">Quia ver ò ductis rectis A E, μ P, quadratum ex A E, <lb/>quadratis ex A D, D E, &amp; </s>
  <s xml:id="echoid-s3226" xml:space="preserve">quadratum ex μ P, quadratis ex μ ξ, ξ P, æquale eſt; </s>
  <s xml:id="echoid-s3227" xml:space="preserve">ſunt {q́ue} <lb/>
<anchor type="note" xlink:label="note-0069-06a" xlink:href="note-0069-06"/>
quadrata ex A E, μ P, inter ſe æqualia; </s>
  <s xml:id="echoid-s3228" xml:space="preserve">erunt quadrata ex A D, D E, quadratis ex μ ξ, <lb/>ξ P, æqualia. </s>
  <s xml:id="echoid-s3229" xml:space="preserve">Ablatis ergo æqualibus quadratis rectarum A D, μ ξ, reliqua quadrata ex <lb/>D E, ξ P, æqualia erunt, ac propterea &amp; </s>
  <s xml:id="echoid-s3230" xml:space="preserve">rectæ ipſæ æquales. </s>
  <s xml:id="echoid-s3231" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s3232" xml:space="preserve">totæ D δ, ξ λ, <lb/>æquales ſint, quòd D δ, ipſi A α, &amp; </s>
  <s xml:id="echoid-s3233" xml:space="preserve">ξ λ, ipſi μH, æqualis ſit; </s>
  <s xml:id="echoid-s3234" xml:space="preserve">erunt quoque reliquæ δ E, <lb/>
<anchor type="note" xlink:label="note-0069-07a" xlink:href="note-0069-07"/>
λ P, æquales. </s>
  <s xml:id="echoid-s3235" xml:space="preserve">Eſt autem δ ε, minor quàm δ E. </s>
  <s xml:id="echoid-s3236" xml:space="preserve">Igitur δ ε, minor quoque erit, quàm λ P, <lb/>
<anchor type="note" xlink:label="note-0069-08a" xlink:href="note-0069-08"/>
quod erat demonſtrandum.</s>
  <s xml:id="echoid-s3237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div180" type="float" level="2" n="1">
<note position="left" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a">
    <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0069-01"/>
  </figure>
<note position="left" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">47. primi.</note>
<note position="right" xlink:label="note-0069-07" xlink:href="note-0069-07a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0069-08" xlink:href="note-0069-08a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s3238" xml:space="preserve">EX his manifeſtum eſt, in figura ſuperiori rectam δ ε, minorem eſſe recta λ P, vt <lb/>
<anchor type="note" xlink:label="note-0069-09a" xlink:href="note-0069-09"/>
in demonſtratione aſſumebatur; </s>
  <s xml:id="echoid-s3239" xml:space="preserve">propterea quòd circulus Y Z, maior eſt circulo B C, &amp; </s>
  <s xml:id="echoid-s3240" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s3241" xml:space="preserve">vt lemma proponit.</s>
  <s xml:id="echoid-s3242" xml:space="preserve"/>
</p>
<div xml:id="echoid-div181" type="float" level="2" n="2">
<note position="right" xlink:label="note-0069-09" xlink:href="note-0069-09a" xml:space="preserve">Lin@æ horarũ <lb/>12. &amp; 24. ab or. <lb/>vel occ. non co-<lb/>cunt in horolo <lb/>gio Meridiano <lb/>cũ ſectionibus <lb/>conicis factis in <lb/>conicis ſuperfi-<lb/>ciebus, quarum <lb/>baſes ſunt pa-<lb/>ralleli ſemper <lb/>apparentium, <lb/>ſemperq́; laten-<lb/>tium maximi.</note>
</div>
</div>
<div xml:id="echoid-div183" type="section" level="1" n="54">
<head xml:id="echoid-head57" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s3243" xml:space="preserve">SEQVITVR ex ha@ propoſ. </s>
  <s xml:id="echoid-s3244" xml:space="preserve">lineas horarum 12. </s>
  <s xml:id="echoid-s3245" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3246" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3247" xml:space="preserve">ab ortu, vel occaſu in horologio Meridia-<lb/>no non conuenire cum Hyperbolis, quas planum horologii facit, per propoſ. </s>
  <s xml:id="echoid-s3248" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3249" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3250" xml:space="preserve">in conicis ſu-<lb/>perficiebus, quarum baſes ſunt parallelus eorum, qui ſemper apparent, maximus, &amp; </s>
  <s xml:id="echoid-s3251" xml:space="preserve">maximus eorum, qui <lb/>
<anchor type="note" xlink:label="note-0069-10a" xlink:href="note-0069-10"/>
ſub terra occultantur: </s>
  <s xml:id="echoid-s3252" xml:space="preserve">quia Meridianus, hoc eſt, circulus horæ 12. </s>
  <s xml:id="echoid-s3253" xml:space="preserve">à meridie, vel media nocte, ęquidi-<lb/>ſtat plano horologii, ſecatq́; </s>
  <s xml:id="echoid-s3254" xml:space="preserve">maximum parallelorum ſemper apparentium in punctis, in quibus eundem <lb/>tangit &amp; </s>
  <s xml:id="echoid-s3255" xml:space="preserve">circulus horæ 12. </s>
  <s xml:id="echoid-s3256" xml:space="preserve">ab ortu vel occaſu, &amp; </s>
  <s xml:id="echoid-s3257" xml:space="preserve">circulus horę 24. </s>
  <s xml:id="echoid-s3258" xml:space="preserve">ſiue Horizon, vt conſtat ex figura <lb/>propoſ. </s>
  <s xml:id="echoid-s3259" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3260" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s3261" xml:space="preserve"/>
</p>
<div xml:id="echoid-div183" type="float" level="2" n="1">
<note position="left" xlink:label="note-0069-10" xlink:href="note-0069-10a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Lineæ horarum <lb/>6. &amp; 18. ab or. <lb/>vel occ. non <lb/>coeunt in horo <lb/>logio Polari cũ <lb/>ſectionibus co-<lb/>nicis factis in <lb/>conicis ſuperfi-<lb/>ciebus, quarum <lb/>baſes ſunt pa-<lb/>ralleli ſemper <lb/>apparentium, <lb/>ſemperq́; laten <lb/>tium maximi.</note>
<p>
  <s xml:id="echoid-s3262" xml:space="preserve">EODEM modo lineæ horarum 6. </s>
  <s xml:id="echoid-s3263" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3264" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3265" xml:space="preserve">ab ortu, vel occaſu non coibunt cum eiſdem hyperbolis <lb/>in horologio polari. </s>
  <s xml:id="echoid-s3266" xml:space="preserve">Aequidiſtat enim horologium polare circulo horæ 6. </s>
  <s xml:id="echoid-s3267" xml:space="preserve">à meridie, vel media nocte, <lb/>qui quidem ſecat parallelum dictum in punctis, in quibus eundem tangunt circuli horarum 6. </s>
  <s xml:id="echoid-s3268" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3269" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3270" xml:space="preserve">ab <lb/>ortu vel occaſu, ut ex eadem figura propoſ. </s>
  <s xml:id="echoid-s3271" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3272" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3273" xml:space="preserve">patet.</s>
  <s xml:id="echoid-s3274" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div185" type="section" level="1" n="55">
<head xml:id="echoid-head58" xml:space="preserve">THEOREMA 14. PROPOSITIO 16.</head>
<p>
  <s xml:id="echoid-s3275" xml:space="preserve">SI in Sphæra duo circuli maximi tangant vnum, eundemque pa-
<pb o="50" file="0070" n="70" rhead="GNOMONICES"/>
rallelum in punctis oppoſitis: </s>
  <s xml:id="echoid-s3276" xml:space="preserve">erit eorum, &amp; </s>
  <s xml:id="echoid-s3277" xml:space="preserve">maximi parallelorum ea-<lb/>
<anchor type="note" xlink:label="note-0070-01a" xlink:href="note-0070-01"/>
dem communis ſectio.</s>
  <s xml:id="echoid-s3278" xml:space="preserve"/>
</p>
<div xml:id="echoid-div185" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">Maximus pa-<lb/>rallelorum, &amp; <lb/>duo circuli ma <lb/>ximi tangentes <lb/>quemcunque <lb/>patallelum in <lb/>duobus punctis <lb/>oppoſitis habẽt <lb/>vnã eand@mq́; <lb/>ſectionem com <lb/>munem.</note>
</div>
<p>
  <s xml:id="echoid-s3279" xml:space="preserve">IN Sphæra A B C D, tangant duo circuli maximi A C, B D, parallelum B C, in punctis op-<lb/>poſitis B, C, quorum communis ſectio ſit recta E F. </s>
  <s xml:id="echoid-s3280" xml:space="preserve">Dico maximum parallelorum G H, ſecare <lb/>vtrumque per rectam E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, ſit communis ſectio <lb/>trium circulorum maximorum A C, B D, G H. </s>
  <s xml:id="echoid-s3281" xml:space="preserve">Per polum enim I, parallelorum B C, G H, &amp; </s>
  <s xml:id="echoid-s3282" xml:space="preserve"><lb/>per contactum B, deſcribatur circulus maximus A B C D, qui cum per propoſ. </s>
  <s xml:id="echoid-s3283" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3284" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3285" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3286" xml:space="preserve">Theo-<lb/>
<anchor type="figure" xlink:label="fig-0070-01a" xlink:href="fig-0070-01"/>
doſii, ſecet parallelum B C, bifariam, tranſibit <lb/>quoque per contactum oppoſitum C. </s>
  <s xml:id="echoid-s3287" xml:space="preserve">Quia er-<lb/>
<anchor type="note" xlink:label="note-0070-02a" xlink:href="note-0070-02"/>
go circulus maximus A B C D, deſcriptus per <lb/>polum paralleli B C, &amp; </s>
  <s xml:id="echoid-s3288" xml:space="preserve">per contactus B, C, <lb/>tranſit quoque per polos circulorum A C, B D, <lb/>per propoſ. </s>
  <s xml:id="echoid-s3289" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3290" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3291" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3292" xml:space="preserve">Theodoſii, ſecabit neceſ-<lb/>ſario, per propoſ. </s>
  <s xml:id="echoid-s3293" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3294" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3295" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3296" xml:space="preserve">eiuſdem, eorum ſeg-<lb/>menta A E F, B E F, C E F, D E F, bifariam in <lb/>punctis A, B, C, D. </s>
  <s xml:id="echoid-s3297" xml:space="preserve">Cum ergo hæc ſegmenta ſe-<lb/>micirculi ſint, (quod maximi circuli cum ſint, <lb/>ſe mutuo bifariam ſecent in punctis E, F, per <lb/>propoſ. </s>
  <s xml:id="echoid-s3298" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3299" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3300" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3301" xml:space="preserve">Theodoſii) quadrantes erunt <lb/>
<anchor type="note" xlink:label="note-0070-03a" xlink:href="note-0070-03"/>
ſegmenta A E, A F, B E, B F, C E, C F, D E, <lb/>D F, vtpote ſemicirculorum dimidia. </s>
  <s xml:id="echoid-s3302" xml:space="preserve">Rurſus <lb/>quia circulus maximus A B C D, cum per po-<lb/>los circulorum G H, B D, incedat, ſecat ſegmen <lb/>ta circulorum G H, B D, quæ quidem per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s3303" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3304" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3305" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3306" xml:space="preserve">Theodoſii, ſemicirculi ſunt, bifa-<lb/>riam, ex propoſ. </s>
  <s xml:id="echoid-s3307" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3308" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3309" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3310" xml:space="preserve">Theodoſii, in punctis G, B; </s>
  <s xml:id="echoid-s3311" xml:space="preserve">erunt arcus circuli B D, inter punctum B, &amp; </s>
  <s xml:id="echoid-s3312" xml:space="preserve"><lb/>circulum G H, poſiti, quadrantes: </s>
  <s xml:id="echoid-s3313" xml:space="preserve">ac propterea cum B E, B F, oſtenſi ſint quadrantes, tranſibit <lb/>neceſſario circulus G H, per puncta E, F, atque adeò vtrumque circulum A C, B D, per rectam <lb/>E F, ſecabit. </s>
  <s xml:id="echoid-s3314" xml:space="preserve">Quare recta E F, communis ſectio eſt trium circulorum maximorum A C, B D, G H; <lb/></s>
  <s xml:id="echoid-s3315" xml:space="preserve">
<anchor type="note" xlink:label="note-0070-04a" xlink:href="note-0070-04"/>
Ac proinde, ſi in ſphęra duo circuli maximi tangant vnum, &amp;</s>
  <s xml:id="echoid-s3316" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3317" xml:space="preserve">Quod demonſtrandum erat,</s>
</p>
<div xml:id="echoid-div186" type="float" level="2" n="2">
  <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a">
    <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0070-01"/>
  </figure>
<note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div188" type="section" level="1" n="56">
<head xml:id="echoid-head59" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s3318" xml:space="preserve">QVONIAM oſtenſum eſt, arcus B E, B F, inter contactum B, &amp; </s>
  <s xml:id="echoid-s3319" xml:space="preserve">maximum parallelorum G H, <lb/>
<anchor type="note" xlink:label="note-0070-05a" xlink:href="note-0070-05"/>
poſitos, eſſe quadrantes, efficitur, arcus cuiuslibet circuli maximi tangentis aliquem parallelorum poſi-<lb/>tos inter contactum, &amp; </s>
  <s xml:id="echoid-s3320" xml:space="preserve">maximum parallelorum eſſe quadrantes. </s>
  <s xml:id="echoid-s3321" xml:space="preserve">Eadem enim in omnibus eſt demon-<lb/>ſtratio, cum ſemper circuli maximi per polos parallelorum, &amp; </s>
  <s xml:id="echoid-s3322" xml:space="preserve">contactus deſcripti, tranſeant, per propoſ. <lb/></s>
  <s xml:id="echoid-s3323" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3324" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3325" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3326" xml:space="preserve">Theodoſii, per polos etiam circulorum tangentium; </s>
  <s xml:id="echoid-s3327" xml:space="preserve">atque adeò ſingulorum ſegmenta inter con-<lb/>tactus, &amp; </s>
  <s xml:id="echoid-s3328" xml:space="preserve">maximum parallelorum poſita, quæ quidem per propoſ. </s>
  <s xml:id="echoid-s3329" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3330" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3331" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3332" xml:space="preserve">Theodoſii, ſemicirculi ſunt, <lb/>bifariam ſecent, per propoſ. </s>
  <s xml:id="echoid-s3333" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3334" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3335" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3336" xml:space="preserve">Theodoſii, hoc eſt, in quadrantes diuidant. </s>
  <s xml:id="echoid-s3337" xml:space="preserve">Huiuſmodi ſunt quatuor <lb/>
<anchor type="note" xlink:label="note-0070-06a" xlink:href="note-0070-06"/>
arcus Zodiaci inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s3338" xml:space="preserve">puncta ſolſtitiorum, in quibus Zodiacus tropicos Aequatori paralle-<lb/>los tangit, intercepti. </s>
  <s xml:id="echoid-s3339" xml:space="preserve">Item quatuor arcus Horizontis inter Aequatorem &amp; </s>
  <s xml:id="echoid-s3340" xml:space="preserve">puncta, in quibus Horizon tan <lb/>git maximum parallelorum ſem per apparentium, &amp; </s>
  <s xml:id="echoid-s3341" xml:space="preserve">maximum ſemper deliteſcentium, ſecaturq; </s>
  <s xml:id="echoid-s3342" xml:space="preserve">à Meri-<lb/>diano, poſiti. </s>
  <s xml:id="echoid-s3343" xml:space="preserve">Omnes denique arcus circulorum horas ab ortu, vel occaſu indicantium inter Aequatorem, <lb/>&amp; </s>
  <s xml:id="echoid-s3344" xml:space="preserve">puncta, in quibus maximum parallelorum ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s3345" xml:space="preserve">maximum ſemper latentium, tan-<lb/>gunt, interpoſiti. </s>
  <s xml:id="echoid-s3346" xml:space="preserve">Nam omnes hi arcus quadrantes ſunt, vt demonſtratum eſt.</s>
  <s xml:id="echoid-s3347" xml:space="preserve"/>
</p>
<div xml:id="echoid-div188" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">Quatuor arcus <lb/>Eclipticæ inter <lb/>puncta ſolſtitio <lb/>rum, &amp; æquino <lb/>ctiorum; Item <lb/>Horizontis in-<lb/>ter Aequatorẽ, <lb/>ac Meridianũ; <lb/>omnium deni-<lb/>que circulorum <lb/>horarum ab or. <lb/>vel occ. inter <lb/>Aequatorem, &amp; <lb/>puncta, in qui-<lb/>bus maximum <lb/>parallelorũ ſem <lb/>per apparentiũ, <lb/>&amp; maximũ ſem <lb/>per latentium, <lb/>tangunt, inter-<lb/>poſiti ſunt qua-<lb/>drantes.</note>
<note position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div190" type="section" level="1" n="57">
<head xml:id="echoid-head60" xml:space="preserve">THEOREMA 15. PROPOSITIO 17.</head>
<p>
  <s xml:id="echoid-s3348" xml:space="preserve">SI in Sphæra duo circuli maximi tangant vnum, eundemq́; </s>
  <s xml:id="echoid-s3349" xml:space="preserve">paralle-<lb/>
<anchor type="note" xlink:label="note-0070-07a" xlink:href="note-0070-07"/>
<anchor type="note" xlink:label="note-0070-08a" xlink:href="note-0070-08"/>
lum; </s>
  <s xml:id="echoid-s3350" xml:space="preserve">ſecet autem alius circulus maximus eundem parallelum per polos <lb/>parallelorum, æqualiterque diſtet à punctis contactuum: </s>
  <s xml:id="echoid-s3351" xml:space="preserve">erit circulo-<lb/>rum tangentium, &amp; </s>
  <s xml:id="echoid-s3352" xml:space="preserve">ſecantis eadem ſectio communis.</s>
  <s xml:id="echoid-s3353" xml:space="preserve"/>
</p>
<div xml:id="echoid-div190" type="float" level="2" n="1">
<note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">Tres circuli ma <lb/>ximi, quorum <lb/>vnus quidem ſe <lb/>cer quemcun-<lb/>que parallelum <lb/>per polos, alii <lb/>vero eundem <lb/>tangant in pun <lb/>ctis æqualiter <lb/>hinc inde remo <lb/>tis ab vtrouis <lb/>punctorum, in <lb/>quibus ab alte-<lb/>ro circulo ma-<lb/>ximo ſecatur, <lb/>habent unam <lb/>eandemq́; ſe-<lb/>ctionem com <lb/>munem.</note>
<note position="left" xlink:label="note-0070-08" xlink:href="note-0070-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s3354" xml:space="preserve">IN Sphæra A B C D, tangant primum duo circuli maximi A C, B D, parallelum B C, in pun-<lb/>ctis oppoſitis B, C, ita vt BIC, B k C, ſemicirculi ſint, ſitq́ue eorum communis ſectio recta E F: <lb/></s>
  <s xml:id="echoid-s3355" xml:space="preserve">Secet autem eundem parallelum B C, alius circulus maximus G H, per paralleli polos G, H, in-<lb/>cedens in punctis I, K, ęqualiter diſtantibus à punctis B, C, ita vt arcus I B, I C, &amp; </s>
  <s xml:id="echoid-s3356" xml:space="preserve">K B, k C, qua-<lb/>drantes ſint. </s>
  <s xml:id="echoid-s3357" xml:space="preserve">Dico circulum G H, ſecare vtrumque circulum maximum A C, B D, per rectam <lb/>E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, communis ſectio ſit trium maximorum cir-
<pb o="51" file="0071" n="71" rhead="LIBER PRIMVS."/>
culorum A C, B D, G H. </s>
  <s xml:id="echoid-s3358" xml:space="preserve">Deſcribatur enim maximus parallelorum L M, qui per puncta E, F, tran <lb/>ſibit, cum per præcedentem propoſ. </s>
  <s xml:id="echoid-s3359" xml:space="preserve">E F, ſit communis ſectio trium circulorum A C, B D, L M, <lb/>propterea quòd A C, BD, tangunt parallelum B C, <lb/>
<anchor type="figure" xlink:label="fig-0071-01a" xlink:href="fig-0071-01"/>
in punctis oppoſitis, &amp; </s>
  <s xml:id="echoid-s3360" xml:space="preserve">L M, eſt parallelorum ma-<lb/>ximus. </s>
  <s xml:id="echoid-s3361" xml:space="preserve">Deſcripto autem per polos parallelorum, <lb/>&amp; </s>
  <s xml:id="echoid-s3362" xml:space="preserve">per contactum B, circulo maximo G L H M, <lb/>tranſibit hic idem per polos quoque circuli B D, <lb/>per propoſ. </s>
  <s xml:id="echoid-s3363" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3364" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3365" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3366" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s3367" xml:space="preserve">Quare ſecabit <lb/>ſegmenta B E F, L E F, per propoſ. </s>
  <s xml:id="echoid-s3368" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3369" xml:space="preserve">eiuſdem, <lb/>bifariam. </s>
  <s xml:id="echoid-s3370" xml:space="preserve">Cum ergo L E F, ſemicirculus ſit, quòd <lb/>
<anchor type="note" xlink:label="note-0071-01a" xlink:href="note-0071-01"/>
maximi circuli ſe bifariam ſecent, per propoſ. </s>
  <s xml:id="echoid-s3371" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s3372" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3373" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3374" xml:space="preserve">Theodoſii, erunt arcus L E, L F, quadran-<lb/>res. </s>
  <s xml:id="echoid-s3375" xml:space="preserve">Quoniam verò circuli maximi G L H M, <lb/>G E H F, per G, H, polos parallelorum B C, <lb/>L M, deſcripti ſunt, erunt per propoſ. </s>
  <s xml:id="echoid-s3376" xml:space="preserve">10. </s>
  <s xml:id="echoid-s3377" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3378" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3379" xml:space="preserve"><lb/>Theodoſii, arcus inter ipſos intercepti ſimiles: </s>
  <s xml:id="echoid-s3380" xml:space="preserve">ſunt <lb/>autem arcus B I, B k, paralleli B C, inter ipſos inter-<lb/>cepti, ex hypotheſi, quadrantes. </s>
  <s xml:id="echoid-s3381" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s3382" xml:space="preserve">arcus pa-<lb/>ralleli L M, intercepti inter eoſdem, quadrantes e-<lb/>runt: </s>
  <s xml:id="echoid-s3383" xml:space="preserve">ac proinde, cum L E, L F, oſtenſi ſint quadrantes, tranſibit circulus G H, per puncta E, F, <lb/>
<anchor type="note" xlink:label="note-0071-02a" xlink:href="note-0071-02"/>
atque adeo vtrunque circulum A C, B D, per rectam E F, ſecabit. </s>
  <s xml:id="echoid-s3384" xml:space="preserve">Quare recta E F, communis <lb/>eſt ſectio trium circulorum A C, B D, G H. </s>
  <s xml:id="echoid-s3385" xml:space="preserve">Quod oſtendendum erat.</s>
  <s xml:id="echoid-s3386" xml:space="preserve"/>
</p>
<div xml:id="echoid-div191" type="float" level="2" n="2">
  <figure xlink:label="fig-0071-01" xlink:href="fig-0071-01a">
    <image file="0071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071-01"/>
  </figure>
<note position="left" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s3387" xml:space="preserve">TANGANT deinde in eadem Sphæra A B C D, eundem parallelum B C, in punctis non <lb/>oppoſitis E, F, duo circuli maximi E G, F H, quorum communis ſectio ſit recta I K, quæ diameter <lb/>erit ipſorum, cum per propoſ. </s>
  <s xml:id="echoid-s3388" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3389" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3390" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3391" xml:space="preserve">Theod, ſe <lb/>
<anchor type="figure" xlink:label="fig-0071-02a" xlink:href="fig-0071-02"/>
mutuo bifariam ſecent: </s>
  <s xml:id="echoid-s3392" xml:space="preserve">Secet autem eundem pa-<lb/>rallelum B C, alius circulus maximus L M, per pa-<lb/>ralleli polos L, M, &amp; </s>
  <s xml:id="echoid-s3393" xml:space="preserve">per axem L M, incedens, in <lb/>punctis O, P, æqualiter diſtantibus à punctis E, F, <lb/>ita vt arcus O E, O F, &amp; </s>
  <s xml:id="echoid-s3394" xml:space="preserve">P B E, P C F, æquales ſint. <lb/></s>
  <s xml:id="echoid-s3395" xml:space="preserve">
<anchor type="note" xlink:label="note-0071-03a" xlink:href="note-0071-03"/>
Dico circulum L M, ſecare vtrumque maximum <lb/>E G, F H, per rectam I k, hoc eſt, tranſire per <lb/>puncta I, K, ita vt recta I K, ſit communis ſectio <lb/>trium circulorum maximorum E G, F H, L M. <lb/></s>
  <s xml:id="echoid-s3396" xml:space="preserve">Cum enim circulus L M, ſecet parallelum B C, <lb/>per polos, ſecabit ipſum, per propoſ. </s>
  <s xml:id="echoid-s3397" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3398" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3399" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3400" xml:space="preserve"><lb/>Theodoſii, bifariam. </s>
  <s xml:id="echoid-s3401" xml:space="preserve">Sectio igitur communis O P, <lb/>diameter erit paralleli B C, tranſiens per centrum <lb/>Q, in quod axis L M, cadit, per propoſ. </s>
  <s xml:id="echoid-s3402" xml:space="preserve">10. </s>
  <s xml:id="echoid-s3403" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3404" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3405" xml:space="preserve"><lb/>Theodoſii. </s>
  <s xml:id="echoid-s3406" xml:space="preserve">Sit quoque R, centrum ſphęrę, per quod <lb/>
<anchor type="note" xlink:label="note-0071-04a" xlink:href="note-0071-04"/>
&amp; </s>
  <s xml:id="echoid-s3407" xml:space="preserve">axis L M, &amp; </s>
  <s xml:id="echoid-s3408" xml:space="preserve">I K, diameter circulorum maximorũ <lb/>tranſit. </s>
  <s xml:id="echoid-s3409" xml:space="preserve">Et quia circuli in Sphęra ſe mutuo tangere dicuntur, cum communis ſectio planorum, in <lb/>quibus circuli exiſtunt, vtrum que circulum tangit, ex defin. </s>
  <s xml:id="echoid-s3410" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3411" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3412" xml:space="preserve">Theodofii: </s>
  <s xml:id="echoid-s3413" xml:space="preserve">Sint communes ſe-<lb/>ctiones circulorum E G, B C, &amp; </s>
  <s xml:id="echoid-s3414" xml:space="preserve">F H, B C, rectę E S, F S, tangentes ipſos circulos. </s>
  <s xml:id="echoid-s3415" xml:space="preserve">Ductis ergo è <lb/>centro Q, ſemidiametris Q E, Q F, erunt anguli S E Q, S F Q, recti, &amp; </s>
  <s xml:id="echoid-s3416" xml:space="preserve">idcirco, ducta recta E F, <lb/>
<anchor type="note" xlink:label="note-0071-05a" xlink:href="note-0071-05"/>
anguli S E F, S F E, rectis minores. </s>
  <s xml:id="echoid-s3417" xml:space="preserve">Quare rectæ E S, F S, in eodem plano paralleli B C, quem tan <lb/>gunt, exiſtentes conuenient in aliquo puncto, vtpote in S, per 11. </s>
  <s xml:id="echoid-s3418" xml:space="preserve">pronunciatum lib. </s>
  <s xml:id="echoid-s3419" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3420" xml:space="preserve">Euclidis. <lb/></s>
  <s xml:id="echoid-s3421" xml:space="preserve">Et quoniam K I, communis ſectio circulorum E G, F H, conuenit quoque cum vtraque E S, F S, <lb/>vt mox oſtendemus lemmate ſequenti; </s>
  <s xml:id="echoid-s3422" xml:space="preserve">fit vt KI, producta vtrique occurrat in S. </s>
  <s xml:id="echoid-s3423" xml:space="preserve">Nam ſi alteram ip <lb/>ſarũ ſecaret infra, aut ſupra S, non coiret cũ reliqua, vt patet. </s>
  <s xml:id="echoid-s3424" xml:space="preserve">Si enim K I, occurrat, verbi gratia, re-<lb/>
<anchor type="note" xlink:label="note-0071-06a" xlink:href="note-0071-06"/>
ctæ E S, alibi, quàm in puncto S, ſecabit ea producta ſtatim planũ circuli B C, in eo puncto, in quo <lb/>rectam E S, ſecat, ac proinde nullo modo ſecabit rectam F S, in plano eodem circuli BC, exiſtentẽ. <lb/></s>
  <s xml:id="echoid-s3425" xml:space="preserve">Et ſi K I, occurrat rectæ F S, alibi quàm in puncto S, oſtendemus eodẽ modo, ipſam ſecare nõ poſ-<lb/>ſe rectam E S. </s>
  <s xml:id="echoid-s3426" xml:space="preserve">Quamobrem recta K I, niſi per punctum S, tranſeat, non ſecabit vtramque E S, F S, <lb/>Quod eſt abſurdum. </s>
  <s xml:id="echoid-s3427" xml:space="preserve">Vtramque enim ſecat, vt in lemmate ſequenti oſtendemus. </s>
  <s xml:id="echoid-s3428" xml:space="preserve">Ducantur iam <lb/>rectæ E O, F O, O S, in plano circuli B C. </s>
  <s xml:id="echoid-s3429" xml:space="preserve">Quia igitur arcus E O, F O, ponuntur æquales, æqua-<lb/>les erunt &amp; </s>
  <s xml:id="echoid-s3430" xml:space="preserve">rectæ E O, F O: </s>
  <s xml:id="echoid-s3431" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s3432" xml:space="preserve">tangentes S E, S F, per 2. </s>
  <s xml:id="echoid-s3433" xml:space="preserve">coroll. </s>
  <s xml:id="echoid-s3434" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s3435" xml:space="preserve">36. </s>
  <s xml:id="echoid-s3436" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3437" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3438" xml:space="preserve">Eu-<lb/>
<anchor type="note" xlink:label="note-0071-07a" xlink:href="note-0071-07"/>
clidis, æquales. </s>
  <s xml:id="echoid-s3439" xml:space="preserve">Igitur erunt duo latera E O, O S, trianguli E O S, duobus lateribus F O, O S, trian <lb/>guli F O S, æqualia, &amp; </s>
  <s xml:id="echoid-s3440" xml:space="preserve">baſis E S, baſi F S; </s>
  <s xml:id="echoid-s3441" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s3442" xml:space="preserve">anguli E O S, F O S, æquales erunt. </s>
  <s xml:id="echoid-s3443" xml:space="preserve">Non <lb/>
<anchor type="note" xlink:label="note-0071-08a" xlink:href="note-0071-08"/>
aliter oſtendemus angulos E O Q, F O Q, æquales eſſe; </s>
  <s xml:id="echoid-s3444" xml:space="preserve">propterea quòd latera E O, O Q, trian-<lb/>guli E O Q, lateribus F O, O Q, trianguli F O Q, æqualia ſunt, &amp; </s>
  <s xml:id="echoid-s3445" xml:space="preserve">baſis E Q, baſi F Q. </s>
  <s xml:id="echoid-s3446" xml:space="preserve">Sunt
<pb o="52" file="0072" n="72" rhead="GNOMONICES"/>
ergo duo anguli E O S, E O Q, duobus angulis F O S, F O Q, ęquales, ac proinde tam hi, quàm <lb/>illi, dimidium conſtituent quatuor angulorum ad punctum O, exiſtentium in plano circuli B C: <lb/></s>
  <s xml:id="echoid-s3447" xml:space="preserve">Sed hi quatuor, per 2. </s>
  <s xml:id="echoid-s3448" xml:space="preserve">corollarium propoſ. </s>
  <s xml:id="echoid-s3449" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3450" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3451" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3452" xml:space="preserve">Euclidis, quatuor rectis ſunt æquales. </s>
  <s xml:id="echoid-s3453" xml:space="preserve">Igi-<lb/>tur tam E O S, E O Q, quàm F O S, F O Q, duobus rectis æquales erunt, ac propterea in dire-<lb/>
<anchor type="note" xlink:label="note-0072-01a" xlink:href="note-0072-01"/>
<anchor type="note" xlink:label="note-0072-02a" xlink:href="note-0072-02"/>
ctum erunt rectæ S O, O Q, Triangulum ergo eſt Q R S, atque adeo in vno plano erit, in eo ſci-<lb/>licet, quod per S Q, Q R, ducitur. </s>
  <s xml:id="echoid-s3454" xml:space="preserve">Ducitur autem planum circuli L M, per has rectas S Q, Q R, <lb/>vt patet. </s>
  <s xml:id="echoid-s3455" xml:space="preserve">In eodem ergo plano cireuli L M, erit recta R S; </s>
  <s xml:id="echoid-s3456" xml:space="preserve">ac proinde circulus L M, per rectam <lb/>I k, tranſibit, ita vt per eandem ſecet duos circulos tangentes E G, F H. </s>
  <s xml:id="echoid-s3457" xml:space="preserve">Quare I k, communis ſe-<lb/>ctio eſt trium circulorum E G, F H, L M. </s>
  <s xml:id="echoid-s3458" xml:space="preserve">Quapropter ſi in Sphæra duo circuli maximi, &amp;</s>
  <s xml:id="echoid-s3459" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s3460" xml:space="preserve">Quod demonſtrandum erat. </s>
  <s xml:id="echoid-s3461" xml:space="preserve"><lb/></s>
</p>
</div>
<div xml:id="echoid-div193" type="section" level="1" n="58">
<head xml:id="echoid-head61" xml:space="preserve">LEMMA.</head>
<p style="it">
  <s xml:id="echoid-s3462" xml:space="preserve">QVOD autem K I, coeat cum vtra-<lb/>
<anchor type="figure" xlink:label="fig-0072-01a" xlink:href="fig-0072-01"/>
que E S, F S, hac ratione demonſtrabimus. <lb/></s>
  <s xml:id="echoid-s3463" xml:space="preserve">Si enim K I, E S, non conueniunt, erunt vti-<lb/>que parallelæ, per definitionem 34. </s>
  <s xml:id="echoid-s3464" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3465" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3466" xml:space="preserve"><lb/>Euclidis, cum ſint in eodem plano circuli E G. </s>
  <s xml:id="echoid-s3467" xml:space="preserve"><lb/>Nam E S, tangens circulum E G, in eodem eſt <lb/>
<anchor type="note" xlink:label="note-0072-04a" xlink:href="note-0072-04"/>
circuli plano, in quo videlicet ctiam eſt K I. <lb/></s>
  <s xml:id="echoid-s3468" xml:space="preserve">Quare ſi ducatur &amp; </s>
  <s xml:id="echoid-s3469" xml:space="preserve">R T, ipſi S F, paral-<lb/>lela, erit planum per K R, R T, ductum pla-<lb/>
<anchor type="note" xlink:label="note-0072-05a" xlink:href="note-0072-05"/>
no per S E, S F, ducto parallelum, atque adeò <lb/>rectæ K I, F S, in illis planis parallelis exiſten-<lb/>tes nunquam conuenient, cum nec ipſa plana <lb/>coeant vnquam. </s>
  <s xml:id="echoid-s3470" xml:space="preserve">I gitur K I, F S, non conue-<lb/>nientes, &amp; </s>
  <s xml:id="echoid-s3471" xml:space="preserve">in codem plano circuli F H, exi-<lb/>ſtentes (Nam F S, tangens circulum F H, in <lb/>
<anchor type="note" xlink:label="note-0072-06a" xlink:href="note-0072-06"/>
eodem eſt circuli plano, in quo ni mirum eſt quoque K I.) </s>
  <s xml:id="echoid-s3472" xml:space="preserve">parallelæ ſunt, per definitionem <lb/>34. </s>
  <s xml:id="echoid-s3473" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3474" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3475" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s3476" xml:space="preserve">Ac proi nde &amp; </s>
  <s xml:id="echoid-s3477" xml:space="preserve">E S, F S, inter ſe parallelæ erunt, cum vtraque ipſi <lb/>
<anchor type="note" xlink:label="note-0072-07a" xlink:href="note-0072-07"/>
I K, parallela ſit, quod eſt abſurdum. </s>
  <s xml:id="echoid-s3478" xml:space="preserve">Oſtenſum eſt enim, rectas E S, F S, in puncto S, coi-<lb/>re. </s>
  <s xml:id="echoid-s3479" xml:space="preserve">Conuenient ergo rectæ K I, E S, cum non ſint parallelæ, in eodemq́ existant plano, vt <lb/>demonſtratum est. </s>
  <s xml:id="echoid-s3480" xml:space="preserve">Eademq́ ratione oſtendemus K I, F S, conuenire.</s>
  <s xml:id="echoid-s3481" xml:space="preserve"/>
</p>
<div xml:id="echoid-div193" type="float" level="2" n="1">
  <figure xlink:label="fig-0071-02" xlink:href="fig-0071-02a">
    <image file="0071-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071-02"/>
  </figure>
<note position="left" xlink:label="note-0071-03" xlink:href="note-0071-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0071-04" xlink:href="note-0071-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0071-05" xlink:href="note-0071-05a" xml:space="preserve">18. tertĳ.</note>
<note position="left" xlink:label="note-0071-06" xlink:href="note-0071-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0071-07" xlink:href="note-0071-07a" xml:space="preserve">28. tertĳ.</note>
<note position="right" xlink:label="note-0071-08" xlink:href="note-0071-08a" xml:space="preserve">8. primi.</note>
<note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">14. primi.</note>
<note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">2. vndec.</note>
  <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a">
    <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-01"/>
  </figure>
<note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">15. vndec.</note>
<note position="left" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">9. vndec.</note>
</div>
</div>
<div xml:id="echoid-div195" type="section" level="1" n="59">
<head xml:id="echoid-head62" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s3482" xml:space="preserve">QVAE in hac, &amp; </s>
  <s xml:id="echoid-s3483" xml:space="preserve">præcedenti propoſ. </s>
  <s xml:id="echoid-s3484" xml:space="preserve">oſtendimus, demonſtrabimus alio modo, &amp; </s>
  <s xml:id="echoid-s3485" xml:space="preserve">fortaſſis facilio-<lb/>
<anchor type="note" xlink:label="note-0072-08a" xlink:href="note-0072-08"/>
vi, in ſcholio propoſ. </s>
  <s xml:id="echoid-s3486" xml:space="preserve">20. </s>
  <s xml:id="echoid-s3487" xml:space="preserve">hui{us} lib.</s>
  <s xml:id="echoid-s3488" xml:space="preserve"/>
</p>
<div xml:id="echoid-div195" type="float" level="2" n="1">
<note position="left" xlink:label="note-0072-08" xlink:href="note-0072-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div197" type="section" level="1" n="60">
<head xml:id="echoid-head63" xml:space="preserve">THEOREMA 16. PROPOSITIO 18.</head>
<note position="left" xml:space="preserve">Planum ſecans <lb/>quotcunque pla <lb/>na eandem cõ-<lb/>munem ſectio-<lb/>nẽ habentia, cui <lb/>planũ illud æ-<lb/>quidiſtet, facit <lb/>communes ſe-<lb/>ctiones paralle-<lb/>las: ſi vero com-<lb/>munẽ illam ſe-<lb/>ctionẽ: ſecet, fa-<lb/>git communes <lb/>ſectiones coeun <lb/>tes in illo pun-<lb/>cto, in quo pla-<lb/>nũ ſecans com-<lb/>munẽ illorum <lb/>ſectionem diui-<lb/>dit.</note>
<p>
  <s xml:id="echoid-s3489" xml:space="preserve">SI PLANA quotcunq; </s>
  <s xml:id="echoid-s3490" xml:space="preserve">vnam eandemq́; </s>
  <s xml:id="echoid-s3491" xml:space="preserve">habentia ſectionem com-<lb/>munem ſecentur plano quopiam alio, quod vni corum, vel communi <lb/>illorum ſectioni æquidiſtet, erunt omnium illorũ planorum, &amp; </s>
  <s xml:id="echoid-s3492" xml:space="preserve">plani <lb/>ſecantis communes ſectiones, lineæ parallelæ: </s>
  <s xml:id="echoid-s3493" xml:space="preserve">Si verò eadem plana ſe-<lb/>
<anchor type="note" xlink:label="note-0072-10a" xlink:href="note-0072-10"/>
centur plano, quod non æquidiſtet communi illorum ſectioni, coi-<lb/>bunt communes omnium illorum, &amp; </s>
  <s xml:id="echoid-s3494" xml:space="preserve">plani ſecantis ſectiones in illo <lb/>puncto ſectionis communis, in quo planum ſecans ipſam interſecat.</s>
  <s xml:id="echoid-s3495" xml:space="preserve"/>
</p>
<div xml:id="echoid-div197" type="float" level="2" n="1">
<note position="left" xlink:label="note-0072-10" xlink:href="note-0072-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s3496" xml:space="preserve">PLANA quotcunque A B, C D, E F, R S, habentia eandem communem ſectionem G H, <lb/>ſecentur plano I K, quod æquidiſter primum, vt in priori figura, plano R S, vel communi ſectio-<lb/>ni G H, (Voco autem planum rectæ cuipiam æquidiſtans, quod infinitè productum nunquam <lb/>conuenlt cum linea illa recta infinitè quoque producta: </s>
  <s xml:id="echoid-s3497" xml:space="preserve">vel cui per rectam illam lineam planum <lb/>aliquod æquidiſtans duci poteſt.) </s>
  <s xml:id="echoid-s3498" xml:space="preserve">ſintq́ue communes ſectiones planorum A B, C D, E F, &amp; </s>
  <s xml:id="echoid-s3499" xml:space="preserve">plani <lb/>ſecantis I k, rectæ L M, N O, P Q. </s>
  <s xml:id="echoid-s3500" xml:space="preserve">Dico has communes ſectiones parallelas eſſe. </s>
  <s xml:id="echoid-s3501" xml:space="preserve">Ducto enim
<pb o="53" file="0073" n="73" rhead="LIBER PRIMVS."/>
per rectam G H, plano R S, (ſi forte planum I k, ſoli rectę G H, æquidiſtare ponatur, &amp; </s>
  <s xml:id="echoid-s3502" xml:space="preserve">non ali-<lb/>cui plano.) </s>
  <s xml:id="echoid-s3503" xml:space="preserve">quod plano I K, æquidiſtet, ſecabitur planum A B, planis parallelis I K, R S. </s>
  <s xml:id="echoid-s3504" xml:space="preserve">Igitur <lb/>communes ſectiones L M, G H, parallelæ ſunt. </s>
  <s xml:id="echoid-s3505" xml:space="preserve">Eadem ratione parallelæ erunt N O, G H, &amp; </s>
  <s xml:id="echoid-s3506" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/>
P Q, G H. </s>
  <s xml:id="echoid-s3507" xml:space="preserve">Quare rectæ L M, N O, <lb/>
<anchor type="figure" xlink:label="fig-0073-01a" xlink:href="fig-0073-01"/>
P Q, cum parallelæ ſint ipſi G H, <lb/>inter ſe quoque parallelæ erunt. <lb/></s>
  <s xml:id="echoid-s3508" xml:space="preserve">Quod erat oſtendendum. </s>
  <s xml:id="echoid-s3509" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/>
</s>
</p>
<div xml:id="echoid-div198" type="float" level="2" n="2">
<note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">16. vndec.</note>
  <figure xlink:label="fig-0073-01" xlink:href="fig-0073-01a">
    <image file="0073-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0073-01"/>
  </figure>
<note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">9. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s3510" xml:space="preserve">SED iam planum ſecans I k, <lb/>non æquidiſtet communi ſectioni <lb/>G H, ſed illi productæ ad partes H, <lb/>
<anchor type="note" xlink:label="note-0073-03a" xlink:href="note-0073-03"/>
occurrat in puncto R, vt in figura <lb/>poſteriori. </s>
  <s xml:id="echoid-s3511" xml:space="preserve">Dico L M, N O, P Q, <lb/>communes ſectiones planorum A B, <lb/>C D, E F, &amp; </s>
  <s xml:id="echoid-s3512" xml:space="preserve">plani ſecantis I k, coire <lb/>in eodem puncto R, in quo planum <lb/>ſecans I K, communem ſectionem <lb/>G H, productam interſecat. </s>
  <s xml:id="echoid-s3513" xml:space="preserve">Nam <lb/>planum A B, per rectam G H, pro-<lb/>ductam ad partes H, extenſum ſeca-<lb/>bit planum I K, in R, puncto, cum <lb/>
<anchor type="note" xlink:label="note-0073-04a" xlink:href="note-0073-04"/>
ſemper producatur per rectam G R. <lb/></s>
  <s xml:id="echoid-s3514" xml:space="preserve">Cum ergo idem planum A B, ſecet <lb/>idem planum I k, in punctis L, M; </s>
  <s xml:id="echoid-s3515" xml:space="preserve"><lb/>Communis autem ſectio planorum <lb/>ſit linea recta; </s>
  <s xml:id="echoid-s3516" xml:space="preserve">collocabuntur tria <lb/>
<anchor type="note" xlink:label="note-0073-05a" xlink:href="note-0073-05"/>
puncta L, M, R, in linea recta, nempe in communi ſectione planorum A B, I k, Quare recta L M, <lb/>(communis, ſcilicet, ſectio planorum A B, I K.) </s>
  <s xml:id="echoid-s3517" xml:space="preserve">producta ad partes M, coibit cum G H, producta <lb/>in R. </s>
  <s xml:id="echoid-s3518" xml:space="preserve">Eodem argumento oſtendemus, rectas N O, P Q, conuenire in eodem puncto R, cum G H. <lb/></s>
  <s xml:id="echoid-s3519" xml:space="preserve">Communes igitur ſectiones L M, N O, P Q, productæ coeunt cum ſectione G H, producta in <lb/>puncto R, in quo planũ ſecans I K, eidem ſectioni G H, occurrit. </s>
  <s xml:id="echoid-s3520" xml:space="preserve">Quod eſt propoſitũ. </s>
  <s xml:id="echoid-s3521" xml:space="preserve">Si plana igi-<lb/>
<anchor type="note" xlink:label="note-0073-06a" xlink:href="note-0073-06"/>
tur quotcunque vnam, eandemq́; </s>
  <s xml:id="echoid-s3522" xml:space="preserve">habentia ſectionem communem, &amp;</s>
  <s xml:id="echoid-s3523" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3524" xml:space="preserve">Quod erat demonſtrandũ.</s>
  <s xml:id="echoid-s3525" xml:space="preserve"/>
</p>
<div xml:id="echoid-div199" type="float" level="2" n="3">
<note position="left" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve">3. vndec.</note>
<note position="left" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div201" type="section" level="1" n="61">
<head xml:id="echoid-head64" xml:space="preserve">THEOREMA 17. PROPOSITIO 19.</head>
<p>
  <s xml:id="echoid-s3526" xml:space="preserve">IN quo puncto linea quæuis horaria à meridie, vel media nocte li-<lb/>
<anchor type="note" xlink:label="note-0073-07a" xlink:href="note-0073-07"/>
neam Aequinoctialem horologii cuiuslibet ſecat, in eodem duæ lineæ <lb/>horariæ ab ortu, vel occaſu, quarum circuli à circulo lineæ horariæ à me-<lb/>ridie, vel media nocte abſunt quadrante integro, id eſt, ſex horis, in ma-<lb/>
<anchor type="note" xlink:label="note-0073-08a" xlink:href="note-0073-08"/>
ximo parallelorum ſemper apparentium, eandem æquinoctialem li-<lb/>neam interſecabunt.</s>
  <s xml:id="echoid-s3527" xml:space="preserve"/>
</p>
<div xml:id="echoid-div201" type="float" level="2" n="1">
<note position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve">Linea euiuſcun <lb/>que herę à mer. <lb/>uel med. noc. &amp; <lb/>duæ lineę hora-<lb/>rum ab or. vel <lb/>occ, diſtantium <lb/>ab illa in maxi <lb/>mo parallelorũ <lb/>ſemper appa-<lb/>rentium qua-<lb/>drante integro, <lb/>ſe mutuo inter <lb/>ſecant in un@ <lb/>eodemq́; pun-<lb/>cto lineæ æqui-<lb/>noctialis in ho-<lb/>rologio quosu@ <lb/>que.</note>
<note position="left" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s3528" xml:space="preserve">SIT parallelorum ſemper apparentium maximus A B C D, quem circulus quiuis horarius <lb/>à meridie, vel media nocte A C, ſecet in punctis A, C, per rectam A C, quæ diameter erit circuli <lb/>A B C D, propterea quòd circulus horarius ſecans, ex propoſ. </s>
  <s xml:id="echoid-s3529" xml:space="preserve">9. <lb/></s>
  <s xml:id="echoid-s3530" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0073-02a" xlink:href="fig-0073-02"/>
huius lib. </s>
  <s xml:id="echoid-s3531" xml:space="preserve">circulum A B C D, per polos, bifariam eum ſecat, <lb/>per propoſ. </s>
  <s xml:id="echoid-s3532" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3533" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3534" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3535" xml:space="preserve">Theodoſii, Sumantur autem ab A, duo <lb/>quadrantes A B, A D, ita vt quilibet arcus A B, A D, C B, C D, <lb/>ſex integras complectatur horas: </s>
  <s xml:id="echoid-s3536" xml:space="preserve">Etin B, D, tangant parallelũ <lb/>
<anchor type="note" xlink:label="note-0073-09a" xlink:href="note-0073-09"/>
A B C D, duo circuli horarii ab ortu, vel occaſu B E, D F, per <lb/>propoſ. </s>
  <s xml:id="echoid-s3537" xml:space="preserve">10. </s>
  <s xml:id="echoid-s3538" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3539" xml:space="preserve">Dico in quocunque puncto linea hora-<lb/>ria circuli A C, ſecet lineam æquinoctialem in quouis horolo-<lb/>gio, in eodem puncto duas lineas horarias circulorum B E, D F, <lb/>ſecare eandem lineam æquinoctialem. </s>
  <s xml:id="echoid-s3540" xml:space="preserve">Nam cum circuli ho-<lb/>rarii B E, D F, parallelum A B C D, in B, D, tangentes, &amp; </s>
  <s xml:id="echoid-s3541" xml:space="preserve">hora-<lb/>rius A C, eundem ſecans per rectam A C, habeant, per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s3542" xml:space="preserve">17. </s>
  <s xml:id="echoid-s3543" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3544" xml:space="preserve">vnam, eandemq́ue communem ſectionem: <lb/></s>
  <s xml:id="echoid-s3545" xml:space="preserve">Habeant autem iidem tangentes circuli, &amp; </s>
  <s xml:id="echoid-s3546" xml:space="preserve">Aequator vnam eandemq́ue ſectionem quoque com-<lb/>munem, per propoſ. </s>
  <s xml:id="echoid-s3547" xml:space="preserve">16. </s>
  <s xml:id="echoid-s3548" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3549" xml:space="preserve">Habebunt quatuor hi circuli, Aequator, duo tangentes B E, <lb/>D F, &amp; </s>
  <s xml:id="echoid-s3550" xml:space="preserve">ſecans A C, vnam eandemq́ue ſectionem communem. </s>
  <s xml:id="echoid-s3551" xml:space="preserve">Igitur ſi planum horologii com-
<pb o="54" file="0074" n="74" rhead="GNOMONICES"/>
muni huic ſectioni non æquidiſtet, ſed ipſam in terſecet in aliquo puncto, ſeeabunt eandem com-<lb/>munes ſectiones dictorum circulorum, &amp; </s>
  <s xml:id="echoid-s3552" xml:space="preserve">plani horologii, hoc eſt, linea ęquinoctialis, lineę duę <lb/>horarię ab ortn, vel occaſu circulorum B E, D F, &amp; </s>
  <s xml:id="echoid-s3553" xml:space="preserve">linea horaria à meridie, vel media nocte circu-<lb/>li A C, in eodem puncto, per propoſ. </s>
  <s xml:id="echoid-s3554" xml:space="preserve">pręcedentem. </s>
  <s xml:id="echoid-s3555" xml:space="preserve">Ac propterea, in quo puncto linea horaria à <lb/>meridie, vel media nocte circuli A C, ſecat lineam ęquinoctialem in aliquo horologio, in illo pun <lb/>cto occurret plano horologii communis ſectio dictorum circulorum, ac proinde in eodem ſeca-<lb/>bunt eandem lineam æquinoctialem duæ lineæ horarie ab ortu, vel occaſu circulorum B E, D F. <lb/></s>
  <s xml:id="echoid-s3556" xml:space="preserve">Eademq́ue eſt ratio de ceteris. </s>
  <s xml:id="echoid-s3557" xml:space="preserve">In quocunque ergo puncto linea quæuis horaria à meridie, &amp;</s>
  <s xml:id="echoid-s3558" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3559" xml:space="preserve"><lb/>Quod erat oſtendendum.</s>
  <s xml:id="echoid-s3560" xml:space="preserve"/>
</p>
<div xml:id="echoid-div202" type="float" level="2" n="2">
  <figure xlink:label="fig-0073-02" xlink:href="fig-0073-02a">
    <image file="0073-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0073-02"/>
  </figure>
<note position="left" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div204" type="section" level="1" n="62">
<head xml:id="echoid-head65" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s3561" xml:space="preserve">EX hac propoſitione conſtruximus ſequentem tabulam, cuius titulus eſt, AE QVINOCTI A. <lb/></s>
  <s xml:id="echoid-s3562" xml:space="preserve">
<anchor type="note" xlink:label="note-0074-02a" xlink:href="note-0074-02"/>
LIS LINE A. </s>
  <s xml:id="echoid-s3563" xml:space="preserve">Indicat enim, quænam lineæ horariæ ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3564" xml:space="preserve">à meridie, vel media <lb/>nocte æquinoctialem lineam cuiuſcunque horologĳ in vno eodemq́; </s>
  <s xml:id="echoid-s3565" xml:space="preserve">puncto interſecent, vt facile colligi po-<lb/>teſt ex hac propoſitione. </s>
  <s xml:id="echoid-s3566" xml:space="preserve">Vt ſi ſumatur in tabula ſequenti quæcunque hora, vel pars, partesve horæ à <lb/>meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s3567" xml:space="preserve">duæ horę, vel partes horarum ab ortu, vel occaſu illi collaterales; </s>
  <s xml:id="echoid-s3568" xml:space="preserve">ſecabunt <lb/>lineę illarum trium hor arum, vel etiam partium horarum, lineam ęquinoctialem in uno eodemq, puncto. <lb/></s>
  <s xml:id="echoid-s3569" xml:space="preserve">Exempli gratia, linea horæ ſeptimæ à meridie, vel media nocte, linea horæ 1. </s>
  <s xml:id="echoid-s3570" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3571" xml:space="preserve">linea horæ 13. </s>
  <s xml:id="echoid-s3572" xml:space="preserve">ab ortu, <lb/>vel occaſu, in vno eodem{q́ue} puncto lineam æquinoctialem interſecant. </s>
  <s xml:id="echoid-s3573" xml:space="preserve">Eodem modo linea horę 7 {1/4}. </s>
  <s xml:id="echoid-s3574" xml:space="preserve">à <lb/>meridie, vel media nocte, linea horæ 1 {1/4}. </s>
  <s xml:id="echoid-s3575" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3576" xml:space="preserve">linea horæ 13 {1/4}. </s>
  <s xml:id="echoid-s3577" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s3578" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s3579" xml:space="preserve">in vno eodemq́, puncto li-<lb/>
<anchor type="note" xlink:label="note-0074-03a" xlink:href="note-0074-03"/>
neam æquinoctialem ſecant, &amp; </s>
  <s xml:id="echoid-s3580" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s3581" xml:space="preserve">Si enim rectè conſideretur hæc tabula, &amp; </s>
  <s xml:id="echoid-s3582" xml:space="preserve">figura propoſ. </s>
  <s xml:id="echoid-s3583" xml:space="preserve">9. <lb/></s>
  <s xml:id="echoid-s3584" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3585" xml:space="preserve">reperientur quælibet huiuſmodi duæ horæ ab ortu, vel occaſu, ab intermedia hora à meridie, <lb/>vel media nocte diſtare quadrante integro, ſeu ſex horis. </s>
  <s xml:id="echoid-s3586" xml:space="preserve">Quare lineæ ipſarum in eodem puncto lineam <lb/>æquinoctialem interſecant, in quo linea horæ à meridie, vel media nocte eandem lineam æquinoctialem <lb/>ſecat, vt in hac propoſ. </s>
  <s xml:id="echoid-s3587" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s3588" xml:space="preserve">Itaque ſinotum fuerit punctum in æquinoctialiv linea cuiuſcun-<lb/>que horologĳ, per quod tranſit vna ex tribus horis, ſciemus per idem illud punctum tranſire debere reli-<lb/>quas duas horas. </s>
  <s xml:id="echoid-s3589" xml:space="preserve">Pariratione, ſi perſpectum fuerit punctum, in quo duæ ex tribus horis quæcumque ſe <lb/>mutuo ſecent, cognoſcemus etiam, per illud idem punctum duci debere lineam æquinoctialem, &amp;</s>
  <s xml:id="echoid-s3590" xml:space="preserve">c.</s>
  <s xml:id="echoid-s3591" xml:space="preserve"/>
</p>
<div xml:id="echoid-div204" type="float" level="2" n="1">
<note position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve">Compoſitio ta-<lb/>bulæ, in qua cõ <lb/>tineantur horę <lb/>à mer. vel med. <lb/>noc. &amp; ab or. uel <lb/>occ. ſe mutuo <lb/>interſecantes in <lb/>uno eodemq́ue <lb/>puncto lineæ <lb/>æquinoctialis <lb/>cuiuſuis horolo <lb/>gii.</note>
<note position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve">20</note>
</div>
<note position="right" xml:space="preserve"> <lb/>########### AE QVINOCTIALIS LINEA. <lb/>Horæ ab ortu \\ vel occaſu. # Horæ à meridic \\ vel media noct. # Horæ ab ortu \\ vel occaſu. # # Horæ ab ortu \\ vel occaſu. # Horę à meridic \\ vel media noct. # Horę ab ortu \\ vel occaſu. # # Horę ab ortu \\ vel occaſu. # Horę à meridic \\ vel media noct. # Horę ab ortu \\ vel occaſu. <lb/>
{1/4} # 6 {1/4} # 12 {1/4} # # 4 {1/4} # 10 {1/4} # 16 {1/4} # # 8 {1/4} # 2 {1/4} # 20 {1/4}
{1/2} # 6 {1/2} # 12 {1/2} # # 4 {1/2} # 10 {1/2} # 16 {1/2} # # 8 {1/2} # 2 {1/2} # 20 {1/2}
{3/4} # 6 {3/4} # 12 {3/4} # # 4 {3/4} # 10 {3/4} # 16 {3/4} # # 8 {3/4} # 2 {3/4} # 20 {3/4}
1 # VII # 13 # # 5 # XI # 17 # # 9 # III # 21
1 {1/4} # 7 {1/4} # 13 {1/4} # # 5 {1/4} # 11 {1/4} # 17 {1/4} # # 9 {1/4} # 3 {1/4} # 21 {1/4}
1 {1/2} # 7 {1/2} # 13 {1/2} # # 5 {1/2} # 11 {1/2} # 17 {1/2} # # 9 {1/2} # 3 {1/2} # 21 {1/2}
1 {3/4} # 7 {3/4} # 13 {3/4} # # 5 {3/4} # 11 {3/4} # 17 {3/4} # # 9 {3/4} # 3 {3/4} # 21 {3/4}
2 # VIII # 14 # # 6 # XII # 18 # # 10 # IIII # 22
2 {1/4} # 8 {1/4} # 14 {1/4} # # 6 {1/4} # {1/4} # 18 {1/4} # # 10 {1/4} # 4 {1/4} # 22 {1/4}
2 {1/2} # 8 {1/2} # 14 {1/2} # # 6 {1/2} # {1/2} # 18 {1/2} # # 10 {1/2} # 4 {1/2} # 22 {1/2}
2 {3/4} # 8 {3/4} # 14 {3/4} # # 6 {3/4} # {3/4} # 18 {3/4} # # 10 {3/4} # 4 {3/4} # 22 {3/4}
3 # IX # 15 # # 7 # I # 19 # # 11 # V # 23
3 {1/4} # 9 {1/4} # 15 {1/4} # # 7 {1/4} # 1 {1/4} # 19 {1/4} # # 11 {1/4} # 5 {1/4} # 23 {1/4}
3 {1/2} # 9 {1/2} # 15 {1/2} # # 7 {1/2} # 1 {1/2} # 19 {1/2} # # 11 {1/2} # 5 {1/2} # 23 {1/2}
3 {3/4} # 9 {3/4} # 15 {3/4} # # 7 {3/4} # 1 {3/4} # 19 {3/4} # # 11 {3/4} # 5 {3/4} # 23 {3/4}
4 # X # 16 # # 8 # II # 20 # # 12 # VI # 24
</note>
<p style="it">
  <s xml:id="echoid-s3592" xml:space="preserve">In horologio Aequinoctiali lineę quarumlibet trium horarum huius tabulę parallelę ſunt (vt ex ſcho <lb/>lio propoſ. </s>
  <s xml:id="echoid-s3593" xml:space="preserve">22. </s>
  <s xml:id="echoid-s3594" xml:space="preserve">huius libri perſpicuum eſt) Similiter &amp; </s>
  <s xml:id="echoid-s3595" xml:space="preserve">in quibuſdam alĳs horologiis parallelę ſunt li-<lb/>neę iſtarum horarum, nimirum 12. </s>
  <s xml:id="echoid-s3596" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3597" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3598" xml:space="preserve">ab ortu vel occaſu, &amp; </s>
  <s xml:id="echoid-s3599" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3600" xml:space="preserve">à meridie vel media nocte, vt in e<unsure/>o-<lb/>dem ſcholio docetur.</s>
  <s xml:id="echoid-s3601" xml:space="preserve"/>
</p>
<pb o="55" file="0075" n="75" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div206" type="section" level="1" n="63">
<head xml:id="echoid-head66" xml:space="preserve">THEOREMA 18. PROPOSITIO 20.</head>
<p>
  <s xml:id="echoid-s3602" xml:space="preserve">SI ſumantur quæcunque duæ lineæ horariæ ab ortu, vel occaſu, qua-<lb/>
<anchor type="note" xlink:label="note-0075-01a" xlink:href="note-0075-01"/>
rum circuli ęqualiter diſtent à circulo horæ cuiuſpiam à meridie, vel me-<lb/>dia nocte in maximo parallelorum ſemper apparentium, interſecabunt <lb/>ſe ſe mutuo tam duæ illę lineæ horariæ ab ortu, vel occaſu in linea ho-<lb/>raria illius circuli à meridie, vel media nocte, in vno eodemque puncto, <lb/>
<anchor type="note" xlink:label="note-0075-02a" xlink:href="note-0075-02"/>
quàm altera illarum ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3603" xml:space="preserve">linea illa à meridie, vel media <lb/>nocte, in linea reliqua ab ortu, vel occaſu, in vno quoque &amp; </s>
  <s xml:id="echoid-s3604" xml:space="preserve">eodem <lb/>puncto.</s>
  <s xml:id="echoid-s3605" xml:space="preserve"/>
</p>
<div xml:id="echoid-div206" type="float" level="2" n="1">
<note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">Linea cuiuſcun <lb/>que horę à mer. <lb/>vel med. noc. &amp;c <lb/>duæ lineæ hora <lb/>rum ab or. vel <lb/>occ. æqualiter <lb/>diſtantiũ hinc <lb/>inde ab illa in <lb/>maximo paral-<lb/>lelorũ ſemper <lb/>apparentium, ſe <lb/>mutuo interſe-<lb/>cant in uno eo-<lb/>dcmq́; puncto <lb/>cui u@que horo-<lb/>logii.</note>
<note position="left" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s3606" xml:space="preserve">SIT parallelorum ſemper apparentium maximus A B C D, quem circulus quiuis horarius <lb/>à meridie, vel media nocte A C, ſecet in punctis A, C, per rectam A C, quæ diameter erit circuli <lb/>A B C D, vt in demonſtratione præcedentis propoſ oſtenſum eſt. </s>
  <s xml:id="echoid-s3607" xml:space="preserve">Sumantur autem duo puncta <lb/>B, D, æqualiter remota ab alterutro punctorum <lb/>A, C, ita vt tot horas complectatur arcus A B, quot <lb/>
<anchor type="note" xlink:label="note-0075-03a" xlink:href="note-0075-03"/>
<anchor type="figure" xlink:label="fig-0075-01a" xlink:href="fig-0075-01"/>
arcus A D. </s>
  <s xml:id="echoid-s3608" xml:space="preserve">Item tot horas contineat arcus C B, <lb/>quot arcus C D: </s>
  <s xml:id="echoid-s3609" xml:space="preserve">Et in B, D, tangant parallelum <lb/>propoſitum A B C D, duo circuli horarii ab ortu, <lb/>vel occaſu B E, D F, per propoſ. </s>
  <s xml:id="echoid-s3610" xml:space="preserve">10. </s>
  <s xml:id="echoid-s3611" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3612" xml:space="preserve">Di-<lb/>co lineas horarias ab ortu, vel occaſu circulorum <lb/>B E, D F, in vno eodemq́ue puncto ſe interſecare in <lb/>linea horaria à meridie, vel media nocte circuli <lb/>A C. </s>
  <s xml:id="echoid-s3613" xml:space="preserve">Cum enim circuli horarii B E, D F, parallelũ <lb/>A B C D, in B, D, tangentes, &amp; </s>
  <s xml:id="echoid-s3614" xml:space="preserve">horarius A C, eun-<lb/>dem ſecans per rectam A C, habeant per propoſ. <lb/></s>
  <s xml:id="echoid-s3615" xml:space="preserve">
<anchor type="note" xlink:label="note-0075-04a" xlink:href="note-0075-04"/>
17. </s>
  <s xml:id="echoid-s3616" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3617" xml:space="preserve">vnam, &amp; </s>
  <s xml:id="echoid-s3618" xml:space="preserve">eandem ſectionem commu <lb/>nem; </s>
  <s xml:id="echoid-s3619" xml:space="preserve">fit vt ſi planum horologij communi huic ſe-<lb/>ctioni non æquidiſter, ſed ipſam in aliquo puncto <lb/>ſecet, in eodem puncto coeant tres horariæ lineæ <lb/>dictæ, nempe communes ſectiones plani horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s3620" xml:space="preserve">circulorum A C, B E, D F, per propoſ. </s>
  <s xml:id="echoid-s3621" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s3622" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3623" xml:space="preserve">Quare in quocunque puncto vna illarum alteram reliquarum ſecet, in eodem &amp; </s>
  <s xml:id="echoid-s3624" xml:space="preserve">reliqua <lb/>eandem ſecabit. </s>
  <s xml:id="echoid-s3625" xml:space="preserve">Hoc eſt, ſi linea horaria ab ortu, vel occaſu circuli B E, horariam lineam à me-<lb/>tidie, vel media nocte circuli A C, ſecuerit in aliquo puncto, ſecabit in eodem &amp; </s>
  <s xml:id="echoid-s3626" xml:space="preserve">horaria linea ab <lb/>ortu, vel occaſu circuli D F, eandem horariam lineam à meridie, vel media nocte circuli A C. </s>
  <s xml:id="echoid-s3627" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0075-05a" xlink:href="note-0075-05"/>
Item ſi linea circuli B E, lineam circuli D F, in aliquo puncto ſecuerit, ſecabit in eodem &amp; </s>
  <s xml:id="echoid-s3628" xml:space="preserve">linea <lb/>circuli A C, eandem lineam circuli D E. </s>
  <s xml:id="echoid-s3629" xml:space="preserve">Et ſi linea circuli A C, ſecuerit lineam circuli B E, in <lb/>aliquo puncto, ſecabit in eodem, &amp; </s>
  <s xml:id="echoid-s3630" xml:space="preserve">linea circuli D F, eandem lineam circuli B E, &amp;</s>
  <s xml:id="echoid-s3631" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3632" xml:space="preserve">Quocir-<lb/>ca, ſi ſumantur quęcunque duæ lineę horarię ab ortu, vel occaſu in linea horaria illius circuli à me <lb/>ridie, vel media nocte, in vno eodemq́ue puncto, quàm altera illarum ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3633" xml:space="preserve">linea <lb/>illa à meridie, vel media nocte, in linea reliqua ab ortu, vel occaſu, in vno quoque &amp; </s>
  <s xml:id="echoid-s3634" xml:space="preserve">eodem pun-<lb/>cto. </s>
  <s xml:id="echoid-s3635" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s3636" xml:space="preserve"/>
</p>
<div xml:id="echoid-div207" type="float" level="2" n="2">
<note position="left" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0075-01" xlink:href="fig-0075-01a">
    <image file="0075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0075-01"/>
  </figure>
<note position="left" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div209" type="section" level="1" n="64">
<head xml:id="echoid-head67" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Cõpoſitio qua-<lb/>tuor tabularũ, <lb/>in qua cõtineã-<lb/>tur horæ à mer. <lb/>vel med. noc. &amp; <lb/>ab or. uel occ. ſe <lb/>mutuo ſecantes <lb/>in uno eodem-<lb/>q́ue puncto li-<lb/>neæ horę 24. ab <lb/>or. vel occ. &amp; li-<lb/>neæ horæ 12. ab <lb/>or uel occ Item <lb/>lineæ horę 6. à <lb/>mer. vel med. <lb/>noc &amp; lineæ ho <lb/>ræ 12. à mer. vel <lb/>med. noc. cuiuſ <lb/>cunque horolo-<lb/>gii.</note>
<p style="it">
  <s xml:id="echoid-s3637" xml:space="preserve">EX hac propoſitione confectæ ſunt ſequentes quatuor tabulę, quarum tituli ſunt.</s>
  <s xml:id="echoid-s3638" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3639" xml:space="preserve">LINEA HORAE XXIIII, AB ORTV, VEL OCCASV.</s>
  <s xml:id="echoid-s3640" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3641" xml:space="preserve">LINEA HORAE XII. </s>
  <s xml:id="echoid-s3642" xml:space="preserve">AB ORTV, VEL OCCASV.</s>
  <s xml:id="echoid-s3643" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3644" xml:space="preserve">LINEA HORAE VI. </s>
  <s xml:id="echoid-s3645" xml:space="preserve">AMERIDIE, VEL MEDIA NOCTE.</s>
  <s xml:id="echoid-s3646" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3647" xml:space="preserve">LINEA HORAE XII. </s>
  <s xml:id="echoid-s3648" xml:space="preserve">AMERIDIE, VEL MEDIA NOCTE.</s>
  <s xml:id="echoid-s3649" xml:space="preserve"/>
</p>
<pb o="56" file="0076" n="76" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div210" type="section" level="1" n="65">
<head xml:id="echoid-head68" xml:space="preserve">Linea horæ 24. ab ortu vel occaſu. Vel horizontalis linea.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media noct@ # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # {1/8} # 4 {1/4} # 2 {1/8} # 8 {1/4} # 4 {1/8} # 12 {1/4} # 6 {1/8} # 16 {1/4} # 8 {1/8} # 20 {1/4} # 10 {1/8}
{1/2} # {1/4} # 4 {1/2} # 2 {1/4} # 8 {1/2} # 4 {1/4} # 12 {1/2} # 6 {1/4} # 16 {1/2} # 8 {1/4} # 20 {1/2} # 10 {1/4}
{3/4} # {3/8} # 4 {3/4} # 2 {3/8} # 8 {3/4} # 4 {3/8} # 12 {3/4} # 6 {3/8} # 16 {3/4} # 8 {3/8} # 20 {3/4} # 10 {3/8}
1 # {1/2} # 5 # 2 {1/2} # 9 # 4 {1/2} # 13 # 6 {1/2} # 17 # 8 {1/2} # 21 # 10 {1/2}
1 {1/4} # {5/8} # 5 {1/4} # 2 {5/8} # 9 {1/4} # 4 {5/8} # 13 {1/4} # 6 {5/8} # 17 {1/4} # 8 {5/8} # 21 {1/4} # 10 {5/8}
1 {1/2} # {3/4} # 5 {1/2} # 2 {3/4} # 9 {1/2} # 4 {3/4} # 13 {1/2} # 6 {3/4} # 17 {1/2} # 8 {3/4} # 21 {1/2} # 10 {3/4}
1 {3/4} # {7/8} # 5 {3/4} # 2 {7/8} # 9 {3/4} # 4 {7/8} # 13 {3/4} # 6 {7/8} # 17 {3/4} # 8 {7/8} # 21 {3/4} # 10 {7/8}
2 # I # 6 # III # 10 # V # 14 # VII # 18 # IX # 22 # XI
2 {1/4} # 1 {1/8} # 6 {1/4} # 3 {1/8} # 10 {1/4} # 5 {1/8} # 14 {1/4} # 7 {1/8} # 18 {1/4} # 9 {1/8} # 22 {1/4} # 11 {1/8}
2 {1/2} # 1 {1/4} # 6 {1/2} # 3 {1/4} # 10 {1/2} # 5 {1/4} # 14 {1/2} # 7 {1/4} # 18 {1/2} # 9 {1/4} # 22 {1/2} # 11 {1/4}
2 {3/4} # 1 {3/8} # 6 {3/4} # 3 {3/8} # 10 {3/4} # 5 {3/8} # 14 {3/4} # 7 {3/8} # 18 {3/4} # 9 {3/8} # 22 {3/4} # 11 {3/8}
3 # 1 {1/2} # 7 # 3 {1/2} # 11 # 5 {1/2} # 15 # 7 {1/2} # 19 # 9 {1/2} # 23 # 11 {1/2}
3 {1/4} # 1 {5/8} # 7 {1/4} # 3 {5/8} # 11 {1/4} # 5 {5/8} # 15 {1/4} # 7 {5/8} # 19 {1/4} # 9 {5/8} # 23 {1/4} # 11 {5/8}
3 {1/2} # 1 {3/4} # 7 {1/2} # 3 {3/4} # 11 {1/2} # 5 {3/4} # 15 {1/2} # 7 {3/4} # 19 {1/2} # 9 {3/4} # 23 {1/2} # 11 {3/4}
3 {3/4} # 1 {7/8} # 7 {3/4} # 3 {7/8} # 11 {3/4} # 5 {7/8} # 15 {3/4} # 7 {7/8} # 19 {3/4} # 9 {7/8} # 23 {3/4} # 11 {7/8}
4 # II # 8 # IIII # 12 # VI # 16 # VIII # 20 # X # 24 # XII
</note>
<p style="it">
  <s xml:id="echoid-s3650" xml:space="preserve">In horologio horizõtali lineæ quarũlibet duarũ horarũ huius tabulę ſunt par@llelę, vt cõſtat ex ſcholio propoſ. </s>
  <s xml:id="echoid-s3651" xml:space="preserve">22. <lb/></s>
  <s xml:id="echoid-s3652" xml:space="preserve">Similiter in quibuſdã alĳs horologĳs parallelæ ſunt lineæ iſtarũ horarũ, nimirũ 12. </s>
  <s xml:id="echoid-s3653" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s3654" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s3655" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3656" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3657" xml:space="preserve">à meridie vel <lb/>
<anchor type="note" xlink:label="note-0076-04a" xlink:href="note-0076-04"/>
nedia nocte. </s>
  <s xml:id="echoid-s3658" xml:space="preserve">Item 24. </s>
  <s xml:id="echoid-s3659" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s3660" xml:space="preserve">uel occ. </s>
  <s xml:id="echoid-s3661" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3662" xml:space="preserve">12. </s>
  <s xml:id="echoid-s3663" xml:space="preserve">à meridie vel media nocte, vt patet ex eodem ſcholio propoſ. </s>
  <s xml:id="echoid-s3664" xml:space="preserve">22.</s>
  <s xml:id="echoid-s3665" xml:space="preserve"/>
</p>
<div xml:id="echoid-div210" type="float" level="2" n="1">
<note position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div212" type="section" level="1" n="66">
<head xml:id="echoid-head69" xml:space="preserve">Linea horæ 12. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 6 {1/8} # 4 {1/4} # 8 {1/8} # 8 {1/4} # 10 {1/8} # 12 {1/4} # {1/8} # 16 {1/4} # 2 {1/8} # 20 {1/4} # 4 {1/8}
{1/2} # 6 {1/4} # 4 {1/2} # 8 {1/4} # 8 {1/2} # 10 {1/4} # 12 {1/2} # {1/4} # 16 {1/2} # 2 {1/4} # 20 {1/2} # 4 {1/4}
{3/4} # 6 {3/8} # 4 {3/4} # 8 {3/8} # 8 {3/4} # 10 {3/8} # 12 {3/4} # {3/8} # 16 {3/4} # 2 {3/8} # 20 {3/4} # 4 {3/8}
1 # 6 {1/2} # 5 # 8 {1/2} # 9 # 10 {1/2} # 13 # {1/2} # 17 # 2 {1/2} # 21 # 4 {1/2}
1 {1/4} # 6 {5/8} # 5 {1/4} # 8 {5/8} # 9 {1/4} # 10 {5/8} # 13 {1/4} # {5/8} # 17 {1/4} # 2 {3/8} # 21 {1/4} # 4 {5/8}
1 {1/2} # 6 {3/4} # 5 {1/2} # 8 {3/4} # 9 {1/2} # 10 {3/4} # 13 {1/2} # {3/4} # 17 {1/2} # 2 {3/4} # 21 {1/2} # 4 {3/4}
1 {3/4} # 6 {7/8} # 5 {3/4} # 8 {7/8} # 9 {3/4} # 10 {7/8} # 13 {3/4} # {7/8} # 17 {3/4} # 2 {7/8} # 21 {3/4} # 4 {7/8}
2 # VII # 6 # IX # 10 # XI # 14 # I # 18 # III # 22 # V
2 {1/4} # 7 {1/8} # 6 {1/4} # 9 {1/8} # 10 {1/4} # 11 {1/8} # 14 {1/4} # 1 {1/8} # 18 {1/4} # 3 {1/8} # 22 {1/4} # 5 {1/8}
2 {1/2} # 7 {1/4} # 6 {1/2} # 9 {1/4} # 10 {1/2} # 11 {1/4} # 14 {1/2} # 1 {1/4} # 18 {1/2} # 3 {1/4} # 22 {1/2} # 5 {1/4}
2 {3/4} # 7 {3/8} # 6 {3/4} # 9 {3/8} # 10 {3/4} # 11 {3/8} # 14 {3/4} # 1 {3/8} # 18 {3/4} # 3 {3/8} # 22 {3/4} # 5 {3/8}
3 # 7 {1/2} # 7 # 9 {1/2} # 11 # 11 {1/2} # 15 # 1 {1/2} # 19 # 3 {1/2} # 23 # 5 {1/2}
3 {1/4} # 7 {5/8} # 7 {1/4} # 9 {5/8} # 11 {1/4} # 11 {5/8} # 15 {1/4} # 1 {5/8} # 19 {1/4} # 3 {5/8} # 23 {1/4} # 5 {5/8}
3 {1/2} # 7 {3/4} # 7 {1/2} # 9 {3/4} # 11 {1/2} # 11 {3/4} # 15 {1/2} # 1 {3/4} # 19 {1/2} # 3 {3/4} # 23 {1/2} # 5 {3/4}
3 {3/4} # 7 {7/8} # 7 {3/4} # 9 {7/8} # 11 {3/4} # 11 {7/8} # 15 {3/4} # 1 {7/8} # 19 {3/4} # 3 {7/8} # 23 {3/4} # 5 {7/8}
4 # VIII # 8 # X # 12 # XII # 16 # II # 20 # IIII # 24 # VI
</note>
<p style="it">
  <s xml:id="echoid-s3666" xml:space="preserve">In horologio V erticali ad latitudinẽ<unsure/>gr. </s>
  <s xml:id="echoid-s3667" xml:space="preserve">45. </s>
  <s xml:id="echoid-s3668" xml:space="preserve">vel in horologio, qd'<unsure/> circulo horę 12. </s>
  <s xml:id="echoid-s3669" xml:space="preserve">ab ortu vel occaſu ęquidiſtat, lineę <lb/>quarũlibet duarũ horarũ huius tabulæ ſunt parallelæ. </s>
  <s xml:id="echoid-s3670" xml:space="preserve">Pari rõne in quibuſdã alĳs horologĳs parallelę ſunt lineæ iſta-<lb/>rum horarũ. </s>
  <s xml:id="echoid-s3671" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3672" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3673" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3674" xml:space="preserve">à meridie, vel medianocte, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s3675" xml:space="preserve">22. </s>
  <s xml:id="echoid-s3676" xml:space="preserve">manifeſtum eſt.</s>
  <s xml:id="echoid-s3677" xml:space="preserve"/>
</p>
<pb o="57" file="0077" n="77" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div213" type="section" level="1" n="67">
<head xml:id="echoid-head70" xml:space="preserve">Linea horæ ſextæ à meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 11 {3/4} # 4 {1/4} # 7 {3/4} # 8 {1/4} # 3 {3/4} # 12 {1/4} # 23 {3/4} # 16 {1/4} # 19 {3/4} # 20 {1/4} # 15 {3/4}
{1/2} # 11 {1/2} # 4 {1/2} # 7 {1/2} # 8 {1/2} # 3 {1/2} # 12 {1/2<unsure/>} # 23 {1/2} # 16 {1/2} # 19 {1/2} # 20 {1/2} # 15 {1/2}
{3/4} # 11 {1/4} # 4 {3/4} # 7 {1/4} # 8 {3/4} # 3 {1/4} # 12 {3/4} # 23 {1/4} # 16 {3/4} # 19 {1/4} # 20 {3/4} # 15 {1/4}
1 # 11 # 5 # 7 # 9 # 3 # 13 # 23 # 17 # 19 # 21 # 15
1 {1/4} # 10 {3/4} # 5 {1/4} # 6 {3/4} # 9 {1/4} # 2 {3/4} # 13 {1/4} # 22 {3/4} # 17 {1/4} # 18 {3/4} # 21 {1/4} # 14 {3/4}
1 {1/2} # 10 {1/2} # 5 {1/2} # 6 {1/2} # 9 {1/2} # 2 {1/2} # 13 {1/2} # 22 {1/2} # 17 {1/2} # 18 {1/2} # 21 {1/2} # 14 {1/2}
1 {3/4} # 10 {1/4} # 5 {3/4} # 6 {1/4} # 9 {3/4} # 2 {1/4} # 13 {3/4} # 22 {1/4} # 17 {3/4} # 18 {1/4} # 21 {3/4} # 14 {1/4}
2 # 10 # 6 # 6 # 10 # 2 # 14 # 22 # 18 # 18 # 22 # 14
2 {1/4} # 9 {3/4} # 6 {1/4} # 5 {3/4} # 10 {1/4} # 1 {3/4} # 14 {1/4} # 21 {3/4} # 18 {1/4} # 17 {3/4} # 22 {1/4} # 13 {3/4}
2 {1/2} # 9 {1/2} # 6 {1/2} # 5 {1/2} # 10 {1/2} # 1 {1/2} # 14 {1/2} # 21 {1/2} # 18 {1/2} # 17 {1/2} # 22 {1/2} # 13 {1/2}
2 {3/4} # 9 {1/4} # 6 {3/4} # 5 {1/4} # 10 {3/4} # 1 {1/4} # 14 {3/4} # 21 {1/4} # 18 {3/4} # 17 {1/4} # 22 {3/4} # 13 {1/4}
3 # 9 # 7 # 5 # 11 # 1 # 15 # 21 # 19 # 17 # 23 # 13
3 {1/4} # 8 {3/4} # 7 {1/4} # 4 {3/4} # 11 {1/4} # {3/4} # 15 {1/4} # 20 {3/4} # 19 {1/4} # 16 {3/4} # 23 {1/4} # 12 {3/4}
3 {1/2} # 8 {1/2} # 7 {1/2} # 4 {1/2} # 11 {1/2} # {1/2} # 15 {1/2} # 20 {1/2} # 19 {1/2} # 16 {1/2} # 23 {1/2} # 12 {1/2}
3 {3/4} # 8 {1/4} # 7 {3/4} # 4 {1/4} # 11 {3/4} # {1/4} # 15 {3/4} # 20 {1/4} # 19 {3/4} # 16 {1/4} # 23 {3/4} # 12 {1/4}
4 # 8 # 8 # 4 # 12 # 24 # 16 # 20 # 20 # 16 # 24 # 12
</note>
<p style="it">
  <s xml:id="echoid-s3678" xml:space="preserve">In horologio Polari lineæ quarumlibet duarum horarum huius tabulę ſunt parallelę. </s>
  <s xml:id="echoid-s3679" xml:space="preserve">Similiter in quibuſdã alĳs <lb/>horologĳs parallelæ ſunt lineæ iſtarum horarum, nempe 12. </s>
  <s xml:id="echoid-s3680" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3681" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3682" xml:space="preserve">ab ortu vel occaſu, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s3683" xml:space="preserve">22. <lb/></s>
  <s xml:id="echoid-s3684" xml:space="preserve">apparet.</s>
  <s xml:id="echoid-s3685" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div214" type="section" level="1" n="68">
<head xml:id="echoid-head71" xml:space="preserve">Linea horæ 12. à meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 23 {3/4} # 4 {1/4} # 19 {3/4} # 8 {1/4} # 15 {3/4} # 12 {1/4} # 11 {3/4} # 16 {1/4} # 7 {3/4} # 20 {1/4} # 3 {3/4}
{1/2} # 23 {1/2} # 4 {1/2} # 19 {1/2} # 8 {1/2} # 15 {1/2} # 12 {1/2} # 11 {1/2} # 16 {1/2} # 7 {1/2} # 20 {1/2} # 3 {1/2}
{3/4} # 23 {1/4} # 4 {3/4} # 19 {1/4} # 8 {3/4} # 15 {1/4} # 12 {3/4} # 11 {1/4} # 16 {3/4} # 7 {1/4} # 20 {3/4} # 3 {1/4}
1 # 23 # 5 # 19 # 9 # 15 # 13 # 11 # 17 # 7 # 21 # 3
1 {1/4} # 22 {3/4} # 5 {1/4} # 18 {3/4} # 9 {1/4} # 14 {3/4} # 13 {1/4} # 10 {3/4} # 17 {1/4} # 6 {3/4} # 21 {1/4} # 2 {3/4}
1 {1/2} # 22 {1/2} # 5 {1/2} # 18 {1/2} # 9 {1/2} # 14 {1/2} # 13 {1/2} # 10 {1/2} # 17 {1/2} # 6 {1/2} # 21 {1/2} # 2 {1/2}
1 {3/4} # 22 {1/4} # 5 {3/4} # 18 {1/4} # 9 {3/4} # 14 {1/4} # 13 {3/4} # 10 {1/4} # 17 {3/4} # 6 {1/4} # 21 {3/4} # 2 {1/4}
2 # 22 # 6 # 18 # 10 # 14 # 14 # 10 # 18 # 6 # 22 # 2
2 {1/4} # 21 {3/4} # 6 {1/4} # 17 {3/4} # 10 {1/4} # 13 {3/4} # 14 {1/4} # 9 {3/4} # 18 {1/4} # 5 {3/4} # 22 {1/4} # 1 {3/4}
2 {1/2} # 21 {1/2} # 6 {1/2} # 17 {1/2} # 10 {1/2} # 13 {1/2} # 14 {1/2} # 9 {1/2} # 18 {1/2} # 5 {1/2} # 22 {1/2} # 1 {1/2}
2 {3/4} # 21 {1/4} # 6 {3/4} # 17 {1/4} # 10 {3/4} # 13 {1/4} # 14 {3/4} # 9 {1/4} # 18 {3/4} # 5 {1/4} # 22 {3/4} # 1 {1/4}
3 # 21 # 7 # 17 # 11 # 13 # 15 # 9 # 19 # 5 # 23 # 1
3 {1/4} # 20 {3/4} # 7 {1/4} # 16 {3/4} # 11 {1/4} # 12 {3/4} # 15 {1/4} # 8 {3/4} # 19 {1/4} # 4 {3/4} # 23 {1/4} # {3/4}
3 {1/2} # 20 {1/2} # 7 {1/2} # 16 {1/2} # 11 {1/2} # 12 {1/2} # 15 {1/2} # 8 {1/2} # 19 {1/2} # 4 {1/2} # 23 {1/2} # {1/2}
3 {3/4} # 20 {1/4} # 7 {3/4} # 16 {1/4} # 11 {3/4} # 12 {1/4} # 15 {3/4} # 8 {1/4} # 19 {3/4} # 4 {1/4} # 23 {3/4} # {1/4}
4 # 20 # 8 # 16 # 12 # 12 # 16 # 8 # 20 # 4 # 24 # 24
</note>
<p style="it">
  <s xml:id="echoid-s3686" xml:space="preserve">In horologio Meridiano lineę quarumlibet duarum horarum huius tabulæ ſunt parallelæ. </s>
  <s xml:id="echoid-s3687" xml:space="preserve">Pari ratione in quibuſ-<lb/>dam alĳs horologĳs parallelę ſunt lineæ iſtarum horarum, ſcilicet 18. </s>
  <s xml:id="echoid-s3688" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3689" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3690" xml:space="preserve">ab ortu, vel occaſu, vt in ſcholio propo-<lb/>ſitionis 22. </s>
  <s xml:id="echoid-s3691" xml:space="preserve">demons {1/5}<unsure/>r abitur.</s>
  <s xml:id="echoid-s3692" xml:space="preserve"/>
</p>
<pb o="58" file="0078" n="78" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s3693" xml:space="preserve">PRIM Aindicat, quænam duæ lineę horarię, quarũ altera ſumitur ab ortu, vel occaſu, altera verò à <lb/>meridie, vel media nocte, ſecent in eodem puncto lineam horę 24. </s>
  <s xml:id="echoid-s3694" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s3695" xml:space="preserve">Secunda, quænam <lb/>duæ lineæ horariæ, quarum altera quoque ab ortu, uel occaſu, altera verò à meridie, vel media nocte <lb/>ſumitur, ſecent lineam horæ 12. </s>
  <s xml:id="echoid-s3696" xml:space="preserve">ab ortu, vel occaſu, in eodem puncto. </s>
  <s xml:id="echoid-s3697" xml:space="preserve">Tertia, quænam duæ lineæ hora-<lb/>riæ ab ortu, vel occaſu, ſecent in vno, eodemq́, puncto lineam horę 6. </s>
  <s xml:id="echoid-s3698" xml:space="preserve">à meridie, vel media nocte. </s>
  <s xml:id="echoid-s3699" xml:space="preserve">Quar-<lb/>ta denique, quænam duæ lineæ horarię ab ortu, vel occaſu lineam horæ 12. </s>
  <s xml:id="echoid-s3700" xml:space="preserve">à meridie, vel media nocte, in <lb/>vno eodem{q́ue} puncto interſecent. </s>
  <s xml:id="echoid-s3701" xml:space="preserve">Quæ omnia facile ex hac propoſitione colligi poſſunt. </s>
  <s xml:id="echoid-s3702" xml:space="preserve">Nam ſi rectè con-<lb/>ſiderentur hæ tabulæ, &amp; </s>
  <s xml:id="echoid-s3703" xml:space="preserve">figur a propoſ. </s>
  <s xml:id="echoid-s3704" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3705" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3706" xml:space="preserve">comperientur in prioribus duabus tabulis hora ab <lb/>ortu, vel occaſu in titulis poſita, &amp; </s>
  <s xml:id="echoid-s3707" xml:space="preserve">hora quælibet ab ortu, vel occaſu in ipſis tabulis deſcripta, æqualiter <lb/>diſtare ab hora collater ali à meridie, vel media nocte. </s>
  <s xml:id="echoid-s3708" xml:space="preserve">Quare illarum lineæ ſecabunt huius lineam in <lb/>
<anchor type="note" xlink:label="note-0078-01a" xlink:href="note-0078-01"/>
codem puncto, vt in hac propoſitione eſt oſtenſum; </s>
  <s xml:id="echoid-s3709" xml:space="preserve">atque adeò &amp; </s>
  <s xml:id="echoid-s3710" xml:space="preserve">lineæ quarumuis duarum horarum in <lb/>tabulis poſitarum, in vno eodem{q́ue} puncto lineam horæ in titulis poſitæ interſecabunt. </s>
  <s xml:id="echoid-s3711" xml:space="preserve">In poſterioribus <lb/>autem duabus tabulis deprehendentur quælibet duæ horæ ab ortu, vel occaſu in tabulis poſitæ ab hora <lb/>à meridie, vel media nocte, in titulis deſcripta distare æqualiter. </s>
  <s xml:id="echoid-s3712" xml:space="preserve">Quare per hanc eandem propeſitio-<lb/>nem lineæ illarum lineam huius in vno puncto interſecabunt. </s>
  <s xml:id="echoid-s3713" xml:space="preserve">Itaque ſi cognitum fuerit punctum, in quo <lb/>lineam horæ 24. </s>
  <s xml:id="echoid-s3714" xml:space="preserve">vel 12. </s>
  <s xml:id="echoid-s3715" xml:space="preserve">ab ortu, vel occaſu, vel horæ 6. </s>
  <s xml:id="echoid-s3716" xml:space="preserve">vel 12. </s>
  <s xml:id="echoid-s3717" xml:space="preserve">à meridie, vel media nocte ſecet altera <lb/>horarum in tabulis poſitarum, ſciemus, per idem illud punctum duci debere reliquam horam in tabulis <lb/>deſcriptam, &amp;</s>
  <s xml:id="echoid-s3718" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3719" xml:space="preserve">Vt in prima tabula, per quod punctum lineæ 24. </s>
  <s xml:id="echoid-s3720" xml:space="preserve">ab ortu, vel occaſu tranſierit linea <lb/>horæ {1/2} à meridie, vel media nocte, per idem ducenda erit linea horę primæ ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3721" xml:space="preserve">ſic <lb/>de cæteris.</s>
  <s xml:id="echoid-s3722" xml:space="preserve"/>
</p>
<div xml:id="echoid-div214" type="float" level="2" n="1">
<note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s3723" xml:space="preserve">EADEM via, ac ratione inueſtigabimus per hanc propoſitionem, quænam lineæ horarię ab ortu, <lb/>
<anchor type="note" xlink:label="note-0078-03a" xlink:href="note-0078-03"/>
vel occaſu, propoſitam aliam quamcunque lineam horariam à meridie, vel media nocte, in vno eodemq́, <lb/>puncto interſecent. </s>
  <s xml:id="echoid-s3724" xml:space="preserve">Item quamnam lineam horariam ab ortu, vel occaſu, duę quæcunque lineę hora-<lb/>rię, altera quidem ab ortu, vel occaſu, altera verò à meridie, vel media nocte, ſecent in vno, &amp; </s>
  <s xml:id="echoid-s3725" xml:space="preserve">eo-<lb/>dem puncto, &amp;</s>
  <s xml:id="echoid-s3726" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3727" xml:space="preserve">Nam ſi accipiantur in figura propoſ. </s>
  <s xml:id="echoid-s3728" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3729" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3730" xml:space="preserve">tres horæ, vna quidem à meridie, <lb/>vel media nocte quęcunque, reliquę verò ab ortu, vel occaſu quotæcunque, remotę tamen hinc inde ab <lb/>hora à meridie, vel media nocte ęqualiter, ſecabunt lineam cuiuslibet illarum trium lineæ reliquarum <lb/>duarum in vno, &amp; </s>
  <s xml:id="echoid-s3731" xml:space="preserve">eodem puncto: </s>
  <s xml:id="echoid-s3732" xml:space="preserve">Vt lineam horæ 23. </s>
  <s xml:id="echoid-s3733" xml:space="preserve">ab ortu, vel occaſu, in vno puncto interſecant <lb/>duę lineæ, quarum altera horam 13. </s>
  <s xml:id="echoid-s3734" xml:space="preserve">ab ortu, vel occaſu, altera vero horam ſextam à meridie, vel me-<lb/>dia nocte indicat: </s>
  <s xml:id="echoid-s3735" xml:space="preserve">quia in figura propoſ. </s>
  <s xml:id="echoid-s3736" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3737" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3738" xml:space="preserve">hora ſexta à merid. </s>
  <s xml:id="echoid-s3739" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s3740" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s3741" xml:space="preserve">æqualiter ab <lb/>
<anchor type="note" xlink:label="note-0078-04a" xlink:href="note-0078-04"/>
hora 23. </s>
  <s xml:id="echoid-s3742" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3743" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3744" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s3745" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s3746" xml:space="preserve">abeſt. </s>
  <s xml:id="echoid-s3747" xml:space="preserve">Eodem @odo lineam horæ ſextę à meridie, vel media nocte ſe-<lb/>cabunt in vno puncto lineæ horarum 23. </s>
  <s xml:id="echoid-s3748" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3749" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3750" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s3751" xml:space="preserve">Sic etiam lineam horę tertiæ à <lb/>meridie, vel media nocte, ſecabunt lineæ horarum 14. </s>
  <s xml:id="echoid-s3752" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3753" xml:space="preserve">16. </s>
  <s xml:id="echoid-s3754" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s3755" xml:space="preserve">Et ſic de reliquis.</s>
  <s xml:id="echoid-s3756" xml:space="preserve"/>
</p>
<div xml:id="echoid-div215" type="float" level="2" n="2">
<note position="left" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">Quænam lineæ <lb/>horarum ab or. <lb/>u@l occ. &amp; à <lb/>mer. uel med. <lb/>noc. ſe mutuo <lb/>in eodem pun-<lb/>cto interſecen@.</note>
<note position="left" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s3757" xml:space="preserve">EX his facili negotio alias tabulas præcedentibus ſimiles conficiemus, ſingulas nimirum pro ſingu-<lb/>
<anchor type="note" xlink:label="note-0078-05a" xlink:href="note-0078-05"/>
lis lineis horarĳs tam ab ortu, vel occaſu, quàm à meridie, vel media nocte; </s>
  <s xml:id="echoid-s3758" xml:space="preserve">quales ſunt ſequentes tri-<lb/>ginta duæ tabulæ. </s>
  <s xml:id="echoid-s3759" xml:space="preserve">Sed quia ad deſcribendas lineas horarias ab ortu, vel occaſu, in quocunque plano, de-<lb/>ſcriptis prius lineis horarĳs à meridie, vel media nocte, (In hunc etenim vſum prædictas tabulas con-<lb/>ſtruximus) ſufficiunt prædictę quinque tabulæ, vt ſuo loco oſtendemus, propterea eas ab alĳs triginta <lb/>duabus, quæ paulo infra ponentur, ſeiunximus, vt nimirum ſemper in promptu haberi poſſint, cum earum <lb/>vſus neceſſarius erit.</s>
  <s xml:id="echoid-s3760" xml:space="preserve"/>
</p>
<div xml:id="echoid-div216" type="float" level="2" n="3">
<note position="left" xlink:label="note-0078-05" xlink:href="note-0078-05a" xml:space="preserve">Compoſitio a-<lb/>liarum tabula-<lb/>rum præceden-<lb/>tibus ſimilium, <lb/>pro ſingulis li-<lb/>neis horarũ ab <lb/>or. vel occ &amp; à <lb/>mer. vel med. <lb/>noc@</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s3761" xml:space="preserve">PORRO Franciſcus Maurolycus Abbas Meſſanenſis primus est, quod ego ſciam, inuentor harum <lb/>interſectionum, quas inter ſe faciunt mutuo lineæ hor ariæ ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s3762" xml:space="preserve">à meridie, vel media <lb/>nocte. </s>
  <s xml:id="echoid-s3763" xml:space="preserve">Primum enim eas obſeruaui in ipſius libello de lineis borarĳs deſcribendis, quem ipſe Meſſana <lb/>propria manu conſcriptum Romam ad me miſit: </s>
  <s xml:id="echoid-s3764" xml:space="preserve">nondum enim in lucem eum ediderat. </s>
  <s xml:id="echoid-s3765" xml:space="preserve">Et quoniam <lb/>conſideratio hæc interſectionum &amp; </s>
  <s xml:id="echoid-s3766" xml:space="preserve">iucundiſſima eſt, &amp; </s>
  <s xml:id="echoid-s3767" xml:space="preserve">ad lineas horarias ab ortu, vel occaſu deſcriben-<lb/>das vtiliſſima, faciendum mihi omnino putaui, vt ad communem ftudioſorum vtilitatem demonſtratio-<lb/>nibus Geometricis (quod quidem in pręcedentibus propoſitionibus præſtitimus) eam confirmarem. </s>
  <s xml:id="echoid-s3768" xml:space="preserve">Nam <lb/>ſine demonſtrationibus huiuſmodi ſectiones linearum horariarum allatæ mibi fuerunt ex Sicilia, neque <lb/>earum demonſtrationem apud vllum potui comperire. </s>
  <s xml:id="echoid-s3769" xml:space="preserve">Vnde paſſi non ſumus, eam diutius deſiderari. <lb/></s>
  <s xml:id="echoid-s3770" xml:space="preserve">Solus Ioan. </s>
  <s xml:id="echoid-s3771" xml:space="preserve">Baptiſta Benedictus cap. </s>
  <s xml:id="echoid-s3772" xml:space="preserve">65. </s>
  <s xml:id="echoid-s3773" xml:space="preserve">ſuæ Gnomonices mutuam hanc interſectionem in linea ſola horæ <lb/>
<anchor type="note" xlink:label="note-0078-07a" xlink:href="note-0078-07"/>
12. </s>
  <s xml:id="echoid-s3774" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s3775" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s3776" xml:space="preserve">demonſtrare eſt aggreſſus.</s>
  <s xml:id="echoid-s3777" xml:space="preserve"/>
</p>
<div xml:id="echoid-div217" type="float" level="2" n="4">
<note position="left" xlink:label="note-0078-07" xlink:href="note-0078-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s3778" xml:space="preserve">VT autem clarior adbuc reddatur mutua hæc interſectio horariarum linearum, libet alio modo de-<lb/>monſtrare hoc loco, quaratione prædictę tabulæ ſint conſtruendæ. </s>
  <s xml:id="echoid-s3779" xml:space="preserve">Atque vt à tabula Aequinoctia-<lb/>lis lineę incipiamus, quam in ſcholio propoſ. </s>
  <s xml:id="echoid-s3780" xml:space="preserve">19. </s>
  <s xml:id="echoid-s3781" xml:space="preserve">huius libri deſcripſimus; </s>
  <s xml:id="echoid-s3782" xml:space="preserve">Sit Aequator A B, &amp; </s>
  <s xml:id="echoid-s3783" xml:space="preserve">paral-<lb/>lelus ſemper apparentium maximus C D, polusq́, parallelorum, ſiue mundi, E. </s>
  <s xml:id="echoid-s3784" xml:space="preserve">Tangant autem paralle-<lb/>lum C D, in punctis oppoſitis C, D, duo circuli horarum ab ortu, vel occaſu C F, D F, &amp; </s>
  <s xml:id="echoid-s3785" xml:space="preserve">eundem ſecet <lb/>per polum E, circulus alicuius horæ à meridie, vel media nocte in puncto G, quod ęqualibus ſpatĳs, nem-<lb/>pe ſex horis, abſit à punctis C, &amp; </s>
  <s xml:id="echoid-s3786" xml:space="preserve">D, ita vt C G, D G, quadrantes ſint. </s>
  <s xml:id="echoid-s3787" xml:space="preserve">Dicotres circulos C F, D F, E G, <lb/>ſe mutuo ſecare in Aequatore A B, vt in puncto F. </s>
  <s xml:id="echoid-s3788" xml:space="preserve">Deſcribatur enim per E, polum parallelorum, &amp; </s>
  <s xml:id="echoid-s3789" xml:space="preserve">per <lb/>C, punctum contactus, circulus maximus E C, ſecans Aequatorem in A, &amp; </s>
  <s xml:id="echoid-s3790" xml:space="preserve">B, qui quoniam per polos <lb/>paralleli C D, tranſiens eum ſecat, per propoſ. </s>
  <s xml:id="echoid-s3791" xml:space="preserve">15. </s>
  <s xml:id="echoid-s3792" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3793" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3794" xml:space="preserve">Theodoſii, bifariam, tranſibit quoque per D,
<pb o="59" file="0079" n="79" rhead="LIBER PRIMVS."/>
contactum oppoſitum, atque adeo per polos circulorum C F, D F, per propoſ. </s>
  <s xml:id="echoid-s3795" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3796" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3797" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3798" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s3799" xml:space="preserve">Quo-<lb/>
<anchor type="note" xlink:label="note-0079-01a" xlink:href="note-0079-01"/>
niam igitur duo circuli A B, C F, ſe mutuo ſecant, ſecabit maximus circulus E C, per eorum polos du-<lb/>ctus, ſegmenta ipſorum bifariam, per propoſ. </s>
  <s xml:id="echoid-s3800" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3801" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s3802" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0079-01a" xlink:href="fig-0079-01"/>
2. </s>
  <s xml:id="echoid-s3803" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s3804" xml:space="preserve">Quare cum ſegmenta ipſorum ſint ſe-<lb/>micirculi, quòd per propoſ. </s>
  <s xml:id="echoid-s3805" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3806" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3807" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3808" xml:space="preserve">Theodoſii, ma-<lb/>ximi<unsure/> circuli cum ſint, ſe mutuo bifariam ſecent, erit <lb/>tam arcus circuli C F, inter punctum C, &amp; </s>
  <s xml:id="echoid-s3809" xml:space="preserve">Aequa-<lb/>torem poſitus, quàm arcus Aequatoris inter circu-<lb/>lum E C, &amp; </s>
  <s xml:id="echoid-s3810" xml:space="preserve">circulum C F, poſitus quadrans, vtpote <lb/>dimidium ſemicirculi. </s>
  <s xml:id="echoid-s3811" xml:space="preserve">Eadem ratione erit tam arcus <lb/>
<anchor type="note" xlink:label="note-0079-02a" xlink:href="note-0079-02"/>
circuli D F, inter punctum D, &amp; </s>
  <s xml:id="echoid-s3812" xml:space="preserve">Aequatorem po-<lb/>ſitus, quàm arcus Aequatoris inter circulos E B, <lb/>D F, poſitus, quadrans. </s>
  <s xml:id="echoid-s3813" xml:space="preserve">Rurſus quia duo circuli C F, <lb/>D F, ſe mutuo ſecant, ſecabit maximus circulus C D, <lb/>per eorum polos ductus ſegmenta ipſorũ bifariam, per <lb/>propoſ. </s>
  <s xml:id="echoid-s3814" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3815" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3816" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3817" xml:space="preserve">Theodoſii. </s>
  <s xml:id="echoid-s3818" xml:space="preserve">Cum ergo ſegmenta ipſo-<lb/>rum ſint, per propoſ. </s>
  <s xml:id="echoid-s3819" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3820" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3821" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3822" xml:space="preserve">Theodoſii, ſemicirculi, <lb/>erunt arcus circulorum C F, D F, inter puncta C, <lb/>D, &amp; </s>
  <s xml:id="echoid-s3823" xml:space="preserve">punctum ſectionis poſiti, quadrantes: </s>
  <s xml:id="echoid-s3824" xml:space="preserve">atque adeò cum oſtenſum ſit, &amp; </s>
  <s xml:id="echoid-s3825" xml:space="preserve">arcus eorundem inter pun-<lb/>cta C, D, &amp; </s>
  <s xml:id="echoid-s3826" xml:space="preserve">Aequatorem poſitos eſſe quadrantes, mutuo ſe ſecabunt in Aequatore, vt in puncto F, ita <lb/>
<anchor type="note" xlink:label="note-0079-03a" xlink:href="note-0079-03"/>
vt arcus C F, D F, A F, B F, ſint quadrantes. </s>
  <s xml:id="echoid-s3827" xml:space="preserve">Rurſus quoniam ci@culi maximi E G, C D, per polos <lb/>parallelorum C D, A B, ducti, parallelos ſecant, per propoſ. </s>
  <s xml:id="echoid-s3828" xml:space="preserve">10. </s>
  <s xml:id="echoid-s3829" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3830" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3831" xml:space="preserve">Theodoſii, in arcus ſimiles; </s>
  <s xml:id="echoid-s3832" xml:space="preserve">Eſt <lb/>autem arcus C G, inter E C, E G, quadrans, ex hypotheſi, erit quoque arcus Aequatoris A B, inter eoſ-<lb/>dem circulos maximos E C, E G, poſitus, quadrans: </s>
  <s xml:id="echoid-s3833" xml:space="preserve">Ac proinde cum arcus A F, oſtenſus ſit quadrans, <lb/>tranſibit circulus maximus E G, per punctum F. </s>
  <s xml:id="echoid-s3834" xml:space="preserve">Quamobrem quatuor circuli maximi A B, C F, D F, <lb/>E F, vnam eandemq́, communem habent ſectionem, quod eſt propoſitum: </s>
  <s xml:id="echoid-s3835" xml:space="preserve">Atque idcirco, in quo puncto <lb/>planum horologĳ communi huic ſectioni occurrit, per idem communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s3836" xml:space="preserve"><lb/>plani horologĳ tranſibunt, per propoſ. </s>
  <s xml:id="echoid-s3837" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3838" xml:space="preserve">huius libri: </s>
  <s xml:id="echoid-s3839" xml:space="preserve">adeo vt in eodem puncto ſe interſecent in horolo-<lb/>gio communes illæ ſectiones, hoc eſt, linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s3840" xml:space="preserve">lineæ horariæ circulorum C F, D F, E F. <lb/></s>
  <s xml:id="echoid-s3841" xml:space="preserve">
<anchor type="note" xlink:label="note-0079-04a" xlink:href="note-0079-04"/>
Quocircain quo puncto horaria linea circuli E F, æquinoctialem lineam ſecat, per idem ducendæ erunt <lb/>
<anchor type="note" xlink:label="note-0079-05a" xlink:href="note-0079-05"/>
lineæ horariæ circulorum C F, D F. </s>
  <s xml:id="echoid-s3842" xml:space="preserve">Vt autem ſciamus, quarumnam hor arum ſint circuli C F, D F, E F, <lb/>contemplabimur diligenter figuram propoſ. </s>
  <s xml:id="echoid-s3843" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3844" xml:space="preserve">huius libri, quæ parallelum ſemper apparentium maximũ <lb/>refert, &amp; </s>
  <s xml:id="echoid-s3845" xml:space="preserve">in qua numeri exteriores ad horas ab ortu, vel occaſu, interiores verò ad horas à meridie, vel <lb/>media nocte pertinent. </s>
  <s xml:id="echoid-s3846" xml:space="preserve">Nam ſi C F, ponatur v. </s>
  <s xml:id="echoid-s3847" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3848" xml:space="preserve">eſſe circulus horæ 19. </s>
  <s xml:id="echoid-s3849" xml:space="preserve">ab ortu, vel occaſu, ac pro-<lb/>inde D F, circulus horæ ſeptimæ ab ortu, vel occaſu, quæ illi per diametrum opponitur, quemadmodum <lb/>&amp; </s>
  <s xml:id="echoid-s3850" xml:space="preserve">punctum D, puncto C; </s>
  <s xml:id="echoid-s3851" xml:space="preserve">erit E F, circulus horæ primæ à meridie, vel media nocte, quòd hęc quad ante <lb/>abſit ab vtraque illarum, quemadmodum &amp; </s>
  <s xml:id="echoid-s3852" xml:space="preserve">punctum G, quadr ante abeſt à puncto C, &amp; </s>
  <s xml:id="echoid-s3853" xml:space="preserve">à puncto D. <lb/></s>
  <s xml:id="echoid-s3854" xml:space="preserve">Sic etiam ſi C F, ponatur eſſe circulus horæ 21 {1/2} ab ortu, vel occaſu, atque adeò D F, circulus horæ <lb/>9 {1/2}. </s>
  <s xml:id="echoid-s3855" xml:space="preserve">ab ortu, vel occaſu, erit E F, circulus, horæ 3 {1/2}. </s>
  <s xml:id="echoid-s3856" xml:space="preserve">à meridie, vel media nocte, atque ita de cæteris, <lb/>vt ex figura propoſ. </s>
  <s xml:id="echoid-s3857" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3858" xml:space="preserve">huius libri perſpicuum eſt. </s>
  <s xml:id="echoid-s3859" xml:space="preserve">Item ſi E F, ponatur circulus cuiuſcunque horæ à me-<lb/>
<anchor type="note" xlink:label="note-0079-06a" xlink:href="note-0079-06"/>
ridie, vel media nocte, ſtatim cognoſcemus, ad quas horas ab ortu, vel occaſu pertineant circuli C F, D F. <lb/></s>
  <s xml:id="echoid-s3860" xml:space="preserve">Nam ſi E F, ponatur circulus horæ δ{1/4}. </s>
  <s xml:id="echoid-s3861" xml:space="preserve">à meridie, vel media nocte, erit alter reliquorum, nempe C F, <lb/>circulus horæ 14 {1/4}. </s>
  <s xml:id="echoid-s3862" xml:space="preserve">ab ortu, vel occaſu, alter verò D F, circulus horæ 2 {1/4}. </s>
  <s xml:id="echoid-s3863" xml:space="preserve">ab ortu, vel occaſu, cum <lb/>vtraque harum horarum ab illa abſit quadrante, hoc eſt, ſex horis, vt ex dicta figura conſtat, quemad-<lb/>modum &amp; </s>
  <s xml:id="echoid-s3864" xml:space="preserve">punctũ G, quadrante abeſt à punctis C, &amp; </s>
  <s xml:id="echoid-s3865" xml:space="preserve">D, &amp;</s>
  <s xml:id="echoid-s3866" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3867" xml:space="preserve">Ex his autem facile componemus tabulam <lb/>
<anchor type="note" xlink:label="note-0079-07a" xlink:href="note-0079-07"/>
æquinoctialis lineæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s3868" xml:space="preserve">19. </s>
  <s xml:id="echoid-s3869" xml:space="preserve">huius libri poſitam.</s>
  <s xml:id="echoid-s3870" xml:space="preserve"/>
</p>
<div xml:id="echoid-div218" type="float" level="2" n="5">
<note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">Aequinoctialis <lb/>circulus, &amp; <lb/>duo circuli ho-<lb/>rarum ab or. <lb/>vel occ. tangen-<lb/>tes maximum <lb/>parallelorũ ſem <lb/>per apparentiũ <lb/>in punctis op-<lb/>poſitis, &amp; circu-<lb/>lus horæ à mer. <lb/>vel med. noc. ſe <lb/>cans eundẽ pa-<lb/>rallelũ in pun-<lb/>cto æqualiter à <lb/>punctis conta-<lb/>ctuum diſtan-<lb/>te ſe mutuo <lb/>interſecant in <lb/>vno eodemq́ue <lb/>puncto.</note>
  <figure xlink:label="fig-0079-01" xlink:href="fig-0079-01a">
    <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-01"/>
  </figure>
<note position="left" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve">Quænam horæ <lb/>ab or. vel occ. <lb/>&amp; à mer. vel <lb/>med. noc. ſe mu <lb/>tuo ſecent in li-<lb/>nea ęquinoctia <lb/>li in vno pun-<lb/>cto.</note>
<note position="left" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">Conſtructio ta-<lb/>bulæ in propoſ. <lb/>19 deſcriptæ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s3871" xml:space="preserve">PRO conſtructione autem aliarum tabularum, <lb/>
<anchor type="figure" xlink:label="fig-0079-02a" xlink:href="fig-0079-02"/>
quæ lineis horarum tam ab ortu, vel occaſu, quàm à <lb/>meridie, vel media nocte ſunt dicatæ; </s>
  <s xml:id="echoid-s3872" xml:space="preserve">ſit rurſum Ae-<lb/>quator A B, &amp; </s>
  <s xml:id="echoid-s3873" xml:space="preserve">parallelus eorum, qui ſemper ap-<lb/>
<anchor type="note" xlink:label="note-0079-08a" xlink:href="note-0079-08"/>
parent, maximus C D, atque polus mundi, ſeu pa-<lb/>rallelorum, E. </s>
  <s xml:id="echoid-s3874" xml:space="preserve">Tangant autem parallelum C D, in <lb/>punctis C, &amp; </s>
  <s xml:id="echoid-s3875" xml:space="preserve">D, duo circuli horarum ab ortu, vel <lb/>occaſu C B, D A, ſe mutuo quidem in F, Aequato-<lb/>rem autem ſecãtes in punctis B, A, &amp; </s>
  <s xml:id="echoid-s3876" xml:space="preserve">circulus A D, <lb/>productus ſecet quoque Aequatorem in N. </s>
  <s xml:id="echoid-s3877" xml:space="preserve">Eundem <lb/>verò parallelum C D, ſecet per polum E, circulus ali-<lb/>cuius horæ à meridie, vel media nocte in puncto G, <lb/>quod æqualiter à punctis C, &amp; </s>
  <s xml:id="echoid-s3878" xml:space="preserve">D, distet, ita vt ar-<lb/>cus C G, D G, ſint æquales. </s>
  <s xml:id="echoid-s3879" xml:space="preserve">Dico hunc circulum E G, <lb/>productum tranſire per punctum F, ita vt tres circuli horarĳ C B, D A, E G, ſe mutuo ſecent in
<pb o="60" file="0080" n="80" rhead="GNOMONICES"/>
eodem puncto F. </s>
  <s xml:id="echoid-s3880" xml:space="preserve">Si enim puncta cont actuum C, D, per diametrum ſunt oppoſita, ita vt arcus C G, D G, <lb/>ſint quadrantes, perſpicuum eſt ex ĳs, quæ proximè demonſtrata ſunt, tres hos circulos ſe mutuo interſe-<lb/>care in Aequatore in vno eodemq́, puncto. </s>
  <s xml:id="echoid-s3881" xml:space="preserve">Si verò puncta contactuum C, D, non ſunt oppoſita, deſcri-<lb/>bantur per polum E, &amp; </s>
  <s xml:id="echoid-s3882" xml:space="preserve">per contactus C, D, circuli maximi E C, E D. </s>
  <s xml:id="echoid-s3883" xml:space="preserve">Item per puncta C, G, arcus <lb/>
<anchor type="figure" xlink:label="fig-0080-01a" xlink:href="fig-0080-01"/>
circuli maximi C H G, &amp; </s>
  <s xml:id="echoid-s3884" xml:space="preserve">per puncta G, D, arcus <lb/>maximi circuli G I D, deſcribatur, ducantur{q́ue} chor <lb/>dę C G, G D. </s>
  <s xml:id="echoid-s3885" xml:space="preserve">Quoniam igitur per defin. </s>
  <s xml:id="echoid-s3886" xml:space="preserve">poli à Theo-<lb/>doſio traditam, rectæ ex polo E, ad puncta C, D, <lb/>cadentes æquales ſunt, erũt &amp; </s>
  <s xml:id="echoid-s3887" xml:space="preserve">arcus E C, E D, æqua-<lb/>
<anchor type="note" xlink:label="note-0080-01a" xlink:href="note-0080-01"/>
les. </s>
  <s xml:id="echoid-s3888" xml:space="preserve">Rurſus, quia arcus C G, G D, paralleli C D, <lb/>
<anchor type="note" xlink:label="note-0080-02a" xlink:href="note-0080-02"/>
æquales ſunt, erunt &amp; </s>
  <s xml:id="echoid-s3889" xml:space="preserve">rectę C G, G D, æquales. </s>
  <s xml:id="echoid-s3890" xml:space="preserve">Igi-<lb/>
<anchor type="note" xlink:label="note-0080-03a" xlink:href="note-0080-03"/>
tur &amp; </s>
  <s xml:id="echoid-s3891" xml:space="preserve">arcus maximorum circulorum C H G, G I D, <lb/>
<anchor type="note" xlink:label="note-0080-04a" xlink:href="note-0080-04"/>
<anchor type="note" xlink:label="note-0080-05a" xlink:href="note-0080-05"/>
ęquales erunt. </s>
  <s xml:id="echoid-s3892" xml:space="preserve">Quare duo latera E C, E G, triangu-<lb/>li ſphærici C E G, duobus lateribus E D, E G, trian-<lb/>guli ſphęrici D E G, ęqualia erunt: </s>
  <s xml:id="echoid-s3893" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s3894" xml:space="preserve"><lb/>baſes C H G, D I G, æquales. </s>
  <s xml:id="echoid-s3895" xml:space="preserve">Igitur per propoſ. </s>
  <s xml:id="echoid-s3896" xml:space="preserve">35. <lb/></s>
  <s xml:id="echoid-s3897" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3898" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3899" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s3900" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s3901" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s3902" xml:space="preserve"><lb/>18. </s>
  <s xml:id="echoid-s3903" xml:space="preserve">nostrorum triangulorum ſphęricorum, anguli <lb/>C E G, D E G, ęquales erunt, ac proinde arcus E G, angulum C E D, diuidet bifariam. </s>
  <s xml:id="echoid-s3904" xml:space="preserve">Quoniam verò <lb/>circulus maximus per polum E, &amp; </s>
  <s xml:id="echoid-s3905" xml:space="preserve">punctum F, deſcriptus diuidit eundem angulum CED, bifariam, vt <lb/>
<anchor type="note" xlink:label="note-0080-06a" xlink:href="note-0080-06"/>
mox demonſtrabimus, perſpicuum eſt, circulum maximum E G, productum per punctum F, tranſire: <lb/></s>
  <s xml:id="echoid-s3906" xml:space="preserve">alias duo maximi circuli, nempe E G, &amp; </s>
  <s xml:id="echoid-s3907" xml:space="preserve">ille qui ex E, per F, ducitur, diuiderent eundem angulum <lb/>C E D, bifariam, quod est<unsure/> abſurdum. </s>
  <s xml:id="echoid-s3908" xml:space="preserve">Quòd autem circulus maximus per E, &amp; </s>
  <s xml:id="echoid-s3909" xml:space="preserve">F, deſcriptus di-<lb/>uidat bifariam angulum C E D, ita demonſtrabimus. </s>
  <s xml:id="echoid-s3910" xml:space="preserve">Intelligatur per polum E, &amp; </s>
  <s xml:id="echoid-s3911" xml:space="preserve">per F, deſcri-<lb/>ptus circulus maximus E F H. </s>
  <s xml:id="echoid-s3912" xml:space="preserve">Dico angulum C E F, æqualem eſſe angulo D E F. </s>
  <s xml:id="echoid-s3913" xml:space="preserve">Quoniam enim cir-<lb/>culi maximi E C, E D, tranſeunt, per propoſ. </s>
  <s xml:id="echoid-s3914" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3915" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3916" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3917" xml:space="preserve">Theodoſii, per polos circulorum C F, D F, quòd per <lb/>contactus C, D, &amp; </s>
  <s xml:id="echoid-s3918" xml:space="preserve">per polum E, circuli C D, ducti ſint; </s>
  <s xml:id="echoid-s3919" xml:space="preserve">Tranſeunt autem &amp; </s>
  <s xml:id="echoid-s3920" xml:space="preserve">per polum Aequatoris <lb/>A B; </s>
  <s xml:id="echoid-s3921" xml:space="preserve">fit vt per propoſ. </s>
  <s xml:id="echoid-s3922" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3923" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3924" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3925" xml:space="preserve">Theodoſii, circulus E C, ſecet ſegmenta circulorum C B, A B, ſe ſe in <lb/>B, ſe<unsure/>cantium, quæ quidem, per propoſ. </s>
  <s xml:id="echoid-s3926" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3927" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3928" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3929" xml:space="preserve">Theodoſii, ſemicirculi ſunt, bifariam: </s>
  <s xml:id="echoid-s3930" xml:space="preserve">Ac propterea ar-<lb/>cus C B, ſit quadrans. </s>
  <s xml:id="echoid-s3931" xml:space="preserve">Eadem{q́ue} ratione quadrans erit arcus D A. </s>
  <s xml:id="echoid-s3932" xml:space="preserve">Quia vero per Theorema 1. </s>
  <s xml:id="echoid-s3933" xml:space="preserve">ſcholĳ <lb/>
<anchor type="note" xlink:label="note-0080-07a" xlink:href="note-0080-07"/>
propoſ. </s>
  <s xml:id="echoid-s3934" xml:space="preserve">21. </s>
  <s xml:id="echoid-s3935" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3936" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3937" xml:space="preserve">Theodoſii, circuli maximi C B, D N, eundem parallelum C D, tangentes, æqualiter in-<lb/>clinantur ad A B, maximum parallelorum, æquales erunt anguli ſphærici C B A, D N K. </s>
  <s xml:id="echoid-s3938" xml:space="preserve">Cum ergo an-<lb/>gulo D N K, æqualis quoque ſit angulus D A K, per propoſ. </s>
  <s xml:id="echoid-s3939" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3940" xml:space="preserve">noſtrorum triangulorum ſphæricorum, <lb/>quòd A D N, ABN, per propoſ. </s>
  <s xml:id="echoid-s3941" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3942" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3943" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3944" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s3945" xml:space="preserve">ſemicirculi ſint; </s>
  <s xml:id="echoid-s3946" xml:space="preserve">æquales erunt anguli ſphærici F B A, <lb/>F A B; </s>
  <s xml:id="echoid-s3947" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s3948" xml:space="preserve">arcus B F, A F, æquales erunt, per propoſ. </s>
  <s xml:id="echoid-s3949" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3950" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3951" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3952" xml:space="preserve">Menelai, vel per propoſ. </s>
  <s xml:id="echoid-s3953" xml:space="preserve">40. <lb/></s>
  <s xml:id="echoid-s3954" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3955" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3956" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s3957" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s3958" xml:space="preserve">de triangulis, vel certè per propoſ. </s>
  <s xml:id="echoid-s3959" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3960" xml:space="preserve">noſtrorum triangulorũ ſphæricorum. </s>
  <s xml:id="echoid-s3961" xml:space="preserve">Cum ergo <lb/>&amp; </s>
  <s xml:id="echoid-s3962" xml:space="preserve">toti arcus B C, A D, æquales ſint, nempe quadrantes, vt oſtendimus; </s>
  <s xml:id="echoid-s3963" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s3964" xml:space="preserve">reliqui arcus F C, F D, <lb/>æquales. </s>
  <s xml:id="echoid-s3965" xml:space="preserve">Et quoniam ostenſi ſunt arcus E C, E D, æquales, erunt duo latera E C, E F, trianguli ſphærici <lb/>C E F, æqualia duobus lateribus E D, E F, trianguli ſphærici D E F. </s>
  <s xml:id="echoid-s3966" xml:space="preserve">Cum ergo habeant &amp; </s>
  <s xml:id="echoid-s3967" xml:space="preserve">baſes C F, <lb/>D F, æquales, vt oſtenſum eſt, erunt per propoſ. </s>
  <s xml:id="echoid-s3968" xml:space="preserve">35. </s>
  <s xml:id="echoid-s3969" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3970" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3971" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s3972" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s3973" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s3974" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0080-08a" xlink:href="note-0080-08"/>
18. </s>
  <s xml:id="echoid-s3975" xml:space="preserve">noſtrorum triangulorum ſphæricorum, anguli C E F, D E F, æquales. </s>
  <s xml:id="echoid-s3976" xml:space="preserve">Diuidit ergo arcus E F, cir-<lb/>culi maximi angulum C E D, bifariam; </s>
  <s xml:id="echoid-s3977" xml:space="preserve">Ac propterea cum eundem bifariam ſecet arcus E G, vt de-<lb/>monſtratum eſt, tranſibit omnino arcus E G, productus per F, adeo vt ab arcu E F, non differat, ne <lb/>duo arcus concedantur eundem angulum C E D, bifariam ſecare. </s>
  <s xml:id="echoid-s3978" xml:space="preserve">Quapropter tres circuli horarĳ C F, <lb/>D F, E F, vnam eandem{q́ue} ſectionem habent communem. </s>
  <s xml:id="echoid-s3979" xml:space="preserve">Quod eſt propoſitum: </s>
  <s xml:id="echoid-s3980" xml:space="preserve">Acproinde in quo pun-<lb/>
<anchor type="note" xlink:label="note-0080-09a" xlink:href="note-0080-09"/>
cto planum horologĳ communem hanc ſectionem ſecat, per idem communes ſectiones eorundem circulo-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s3981" xml:space="preserve">plani horologĳ tranſibunt, per propoſ. </s>
  <s xml:id="echoid-s3982" xml:space="preserve">18. </s>
  <s xml:id="echoid-s3983" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s3984" xml:space="preserve">adeo vt in eodem puncto horologĳ ſe inter-<lb/>ſecent lineæ horariæ illorum circulorum. </s>
  <s xml:id="echoid-s3985" xml:space="preserve">Quocirca in quo puncto horaria linea circuli C F, horariam li-<lb/>neam circuli E F, ſecat, per idem ducenda erit linea horaria circuli D F, &amp; </s>
  <s xml:id="echoid-s3986" xml:space="preserve">e contrario. </s>
  <s xml:id="echoid-s3987" xml:space="preserve">Quibus autem <lb/>horis deputentur circuli C F, D F, E F, docebit nos figura, quam in propoſ. </s>
  <s xml:id="echoid-s3988" xml:space="preserve">9. </s>
  <s xml:id="echoid-s3989" xml:space="preserve">huius libri poſuimus. </s>
  <s xml:id="echoid-s3990" xml:space="preserve">Si <lb/>
<anchor type="note" xlink:label="note-0080-10a" xlink:href="note-0080-10"/>
enim alter circulorum C F, D F, nempe C F, tribuatur, verbi gratia, horæ 12. </s>
  <s xml:id="echoid-s3991" xml:space="preserve">ab ortu, vel occaſu; </s>
  <s xml:id="echoid-s3992" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s3993" xml:space="preserve"><lb/>alter D F, exempli cauſa, horæ 20. </s>
  <s xml:id="echoid-s3994" xml:space="preserve">ab ortu, vel occaſu, erit E F, circulus horæ quartæ à meridie, vel me-<lb/>dia nocte, cum hæc hora in medio illarum ſit poſita in figura dicta propoſitionis 9. </s>
  <s xml:id="echoid-s3995" xml:space="preserve">huius libri, quemad-<lb/>modum &amp; </s>
  <s xml:id="echoid-s3996" xml:space="preserve">punctum G, in medio punctorum C, &amp; </s>
  <s xml:id="echoid-s3997" xml:space="preserve">D, poſitum eſt. </s>
  <s xml:id="echoid-s3998" xml:space="preserve">Sic etiam, ſi E F, ponatur eſſe <lb/>circulus horæ 1 {1/2}. </s>
  <s xml:id="echoid-s3999" xml:space="preserve">à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s4000" xml:space="preserve">E C, horæ tertiæ ab ortu, vel occa-<lb/>ſu; </s>
  <s xml:id="echoid-s4001" xml:space="preserve">erit E D, circulus horæ 24. </s>
  <s xml:id="echoid-s4002" xml:space="preserve">ab ortu, vel occaſu, quòd hæ duę horę ab <lb/>illa hinc inde ęqualiter abſint, ſicuti &amp; </s>
  <s xml:id="echoid-s4003" xml:space="preserve">puncta C, D, à puncto <lb/>G, ęqualibus interuallis diſiunguntur, &amp;</s>
  <s xml:id="echoid-s4004" xml:space="preserve">c. </s>
  <s xml:id="echoid-s4005" xml:space="preserve">Ex his <lb/>
<anchor type="note" xlink:label="note-0080-11a" xlink:href="note-0080-11"/>
autem nullo negotio conficiemus trigin-<lb/>ta ſex illas tabulas, quas in hoc <lb/>ſcholio conſcripſimus.</s>
  <s xml:id="echoid-s4006" xml:space="preserve"/>
</p>
<div xml:id="echoid-div219" type="float" level="2" n="6">
  <figure xlink:label="fig-0079-02" xlink:href="fig-0079-02a">
    <image file="0079-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-02"/>
  </figure>
<note position="left" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a">
    <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-01"/>
  </figure>
<note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">28. tertĳ.</note>
<note position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">29. tertĳ.</note>
<note position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">28. tertĳ.</note>
<note position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">Duo circuli ho <lb/>rarum ab or. <lb/>vel ò<unsure/>cc. tangen-<lb/>tes maximum <lb/>parallelorũ ſem <lb/>per apparentiũ <lb/>in duob<unsure/>us pun-<lb/>ctis quibuſcun-<lb/>que, &amp; circulus <lb/>horæ à mer. uel <lb/>med. noc. ſecans <lb/>eundem paral-<lb/>lela<unsure/>m in pun-<lb/>cto æqualiter à <lb/>punctis conta-<lb/>ctuum diſtante, <lb/>ſe mutuo ſecãt <lb/>in vno eodéq́ue <lb/>puncto.</note>
<note position="left" xlink:label="note-0080-06" xlink:href="note-0080-06a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0080-07" xlink:href="note-0080-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0080-08" xlink:href="note-0080-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0080-09" xlink:href="note-0080-09a" xml:space="preserve">Quænam horæ <lb/>ab or. vel occ. <lb/>&amp; à mer. vel <lb/>med. noc. ſe mu <lb/>tuo ſecẽt in eo-<lb/>dem puncto.</note>
<note position="left" xlink:label="note-0080-10" xlink:href="note-0080-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0080-11" xlink:href="note-0080-11a" xml:space="preserve">Compoſitio ſu-<lb/>periorum qua-<lb/>tuot, &amp; ſequen-<lb/>tium duarum <lb/>&amp; triginta ta-<lb/>bularum.</note>
</div>
<pb o="61" file="0081" n="81" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div221" type="section" level="1" n="69">
<head xml:id="echoid-head72" xml:space="preserve">Linea horæ 23. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 11 {5/8} # 4 {1/4} # 1 {5/8} # 8 {1/4} # 3 {5/8} # 12 {1/4} # 5 {5/8} # 16 {1/4} # 7 {5<unsure/>/8} # 20 {1/4} # 9 {5/8}
{1/2} # 11 {3/4} # 4 {1/2} # 1 {3/4} # 8 {1/2} # 3 {3/4} # 12 {1/2} # 5 {3/4} # 16 {1/2} # 7 {3/4} # 20 {1/2} # 9 {3/4}
{3/4} # 11 {7/8} # 4 {3/4} # 1 {7/8} # 8 {3/4} # 3 {7/8} # 12 {3/4} # 5 {7/8} # 16 {3/4} # 7 {7/8} # 20 {3/4} # 9 {7/8}
1 # XII # 5 # II # 9 # IIII # 13 # VI # 17 # VIII # 21 # X
1 {1/4} # {1/8} # 5 {1/4} # 2 {1/8} # 9 {1/4} # 4 {1/8} # 13 {1/4} # 6 {1/8} # 17 {1/4} # 8 {1/8} # 21 {1/4} # 10 {1/8}
1 {1/2} # {1/4} # 5 {1/2} # 2 {1/4} # 9 {1/2} # 4 {1/4} # 13 {1/2} # 6 {1/4} # 17 {1/2} # 8 {1/4} # 21 {1/2} # 10 {1/4}
1 {3/4} # {3/8} # 5 {3/4} # 2 {3/8} # 9 {3/4} # 4 {3/8} # 13 {3/4} # 6 {3/8} # 17 {3/4} # 8 {3/8} # 21 {3/4} # 10 {3/8}
2 # {1/2} # 6 # 2 {1/2} # 10 # 4 {1/2} # 14 # 6 {1/2} # 18 # 8 {1/2} # 22 # 10 {1/2}
2 {1/4} # {5/8} # 6 {1/4} # 2 {5/8} # 10 {1/4} # 4 {5/8} # 14 {1/4} # 6 {5/8} # 18 {1/4} # 8 {5/8} # 22 {1/4} # 10 {5/8}
2 {1/2} # {3/4} # @{1/2} # 2 {3/4} # 10 {1/2} # 4 {3/4} # 14 {1/2} # 6 {3/4} # 18 {1/2} # 8 {3/4} # 22 {1/2} # 10 {3/4}
2 {3/4} # {7/8} # 6 {3/4} # 2 {7/8} # 10 {3/4} # 4 {7/8} # 14 {3/4} # 6 {7/8} # 18 {3/4} # 8 {7/8} # 22 {3/4} # 10 {7/8}
3 # I # 7 # III # 11 # V # 15 # VII # 19 # IX # 23 # XI
3 {1/4} # 1 {1/8} # 7 {1/4} # 3 {1/8} # 11 {1/4} # 5 {1/8} # 15 {1/4} # 7 {1/8} # 19 {1/4} # 9 {1/8} # 23 {1/4} # 11 {1/8}
3 {1/2} # 1 {1/4} # 7 {1/2} # 3 {1/4} # 11 {1/2} # 5 {1/4} # 15 {1/2} # 7 {1/4} # 19 {1/2} # 9 {1/4} # 23 {1/2} # 11 {3/4}
3 {3/4} # 1 {3/8} # 7 {3/4} # 3 {3/8} # 11 {3/4} # 5 {3/8} # 15 {3/4} # 7 {3/8} # 19 {3<unsure/>/4} # 9 {3/8} # 23 {3/4} # 11 {3/8}
4 # 1 {1/2} # 8 # 3 {1/2} # 12 # 5 {1/2} # 16 # 7 {1/2} # 20 # 9 {1/2} # 24 # 11 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4007" xml:space="preserve">In horologio, quod circulo horæ 23. </s>
  <s xml:id="echoid-s4008" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumlibet duarum horarum huius ta-<lb/>hulæ parallclæ ſunt, vt perſpicuum eſt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4009" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4010" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div222" type="section" level="1" n="70">
<head xml:id="echoid-head73" xml:space="preserve">Linea horæ 22. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à mer@die \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 11 {1/8} # 4 {1/4} # 1 {1/8} # 8 {1/4} # 3 {1/8} # 12 {1/4} # 5 {1/8} # 16 {1/4} # 7 {1/8} # 20 {1/4} # 9 {1<unsure/>/8}
{1/2} # 11 {1/4} # 4 {1/2} # 1 {1/4} # 8 {1/2} # 3 {1/4} # 12 {1/2} # 5 {1/4} # 16 {1/2} # 7 {1/4} # 20 {1/2} # 9 {1/4}
{3/4} # 11 {3/8} # 4 {3/4} # 1 {3/8} # 8 {3/4} # 3 {3/8} # 12 {3/4} # 5 {3/8} # 16<unsure/> {3/4} # 7 {3/8} # 20 {3/4} # 9 {3/8}
1 # 11 {1/2} # 5 # 1 {1/2} # 9 # 3 {1/2} # 13 # 5 {1/2} # 17 # 7 {1/2} # 21 # 9 {1/2}
1 {1/4} # 11 {5/8} # 5 {1/4} # 1 {5/8} # 9 {1/4} # 3 {5/8} # 13 {1/4} # 5 {5/8} # 17 {1/4} # 7 {5/8} # 21 {1/4} # 9 {5/8}
1 {1/2} # 11 {3/4} # 5 {1/2} # 1 {3/4} # 9 {1/2} # 3 {3/4} # 13 {1/2} # 5 {3/4} # 17 {1/2} # 7 {3/4} # 21 {1/2} # 9 {3/4}
1 {3/4} # 11 {7/8} # 5 {3/4} # 1 {7/8} # 9 {3/4} # 3 {7/8} # 13 {3/4} # 5 {7/8} # 17 {3/4} # 7 {7/8} # 21 {3/4} # 9 {7/8}
2 # XII # 6 # II # 10 # IIII # 14 # VI # 18 # VIII # 22 # X
2 {1/4} # {1/8} # 6 {1/4} # 2 {1/8} # 10 {1/4} # 4 {1/8} # 14 {1/4} # 6 {1/8} # 18 {1/4} # 8 {1/8} # 22 {1/4} # 10 {1/8}
2 {1/2} # {1/4} # 6 {1/2} # 2 {1/4} # 10 {1/2} # 4 {1/4} # 14 {1/2} # 6 {1/4} # 18 {1/2} # 8 {1/4} # 22 {1/2} # 10 {1/4}
2 {3/4} # {3/8} # 6 {3/4} # 2 {3/8} # 10 {3/4} # 4 {3/8} # 14 {3/4} # 6 {3/8} # 18 {3/4} # 8 {3/8} # 22 {3/4} # 10 {3/8}
3 # {1/2} # 7 # 2 {1/2} # 11 # 4 {1/2} # 15 # 6 {1/2} # 19 # 8 {1/2} # 23 # 10 {1/2}
3 {1/4} # {5/8} # 7 {1/4} # 2 {5/8} # 11 {1/4} # 4 {5/8} # 15 {1/4} # 6 {5/8} # 19 {1/4} # 8 {5/8} # 23 {1/4} # 10 {5/8}
3 {1/2} # {3/4} # 7 {1/2} # 2 {3/4} # 11 {1/2} # 4 {3/4} # 15 {1/2} # 6 {3/4} # 19 {1/2} # 8 {3/4} # 23 {1/2} # 10 {3/4}
3 {3/4} # {7/8} # 7 {3/4} # 2 {7/8} # 11 {3/4} # 4 {7/8} # 15 {3/4} # 6 {7/8} # 19 {3/4} # 8 {7/8} # 23 {3/4} # 10 {7/8}
4 # I # 8 # III # 12 # V # 16 # VII # 20 # IX # 24 # XI
</note>
<p style="it">
  <s xml:id="echoid-s4011" xml:space="preserve">In horologio, quod circulo horæ 22. </s>
  <s xml:id="echoid-s4012" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumlibet duarum horarum huius ta-<lb/>bulæ ſunt parallelæ, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s4013" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4014" xml:space="preserve">probatum est.</s>
  <s xml:id="echoid-s4015" xml:space="preserve"/>
</p>
<pb o="62" file="0082" n="82" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div223" type="section" level="1" n="71">
<head xml:id="echoid-head74" xml:space="preserve">Linea horæ 21. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 10 {5/8} # 4 {1/4} # {5/8} # 8 {1/4} # 2 {5/8} # 12 {1/4} # 4 {5/8} # 16 {1/4} # 6 {5/8} # 20 {1/4} # 8 {5/8}
{1/2} # 10 {3/4} # 4 {1/2} # {3/4} # 8 {1/2} # 2 {3/4} # 12 {1/2} # 4 {3/4} # 16 {1/2} # 6 {3/4} # 20 {1/2} # 8 {3/4}
{3/4} # 10 {7/8} # 4 {3/4} # {7/8} # 8 {3/4} # 2 {7/8} # 12 {3/4} # 4 {7/8} # 16 {3/4} # 6 {7/8} # 20 {3/4} # 8 {7/8}
1 # XI # 5 # I # 9 # III # 13 # V # 17 # VII # 21 # IX
1 {1/4} # 11 {1/8} # 5 {1/4} # 1 {1/8} # 9 {1/4} # 3 {1/8} # 13 {1/4} # 5 {1/8} # 17 {1/4} # 7 {1/8} # 21 {1/4} # 9 {1/8}
1 {1/2} # 11 {1/4} # 5 {1/2} # 1 {1/4} # 9 {1/2} # 3 {1/4} # 13 {1/2} # 5 {1/4} # 17 {1/2} # 7 {1/4} # 21 {1/2} # 9 {1/4}
1 {3/4} # 11 {3/8} # 5 {3/4} # 1 {3/8} # 9 {3/4} # 3 {3/8} # 13 {3/4} # 5 {3/8} # 17 {3/4} # 7 {3/8} # 21 {3/4} # 9 {3/8}
2 # 11 {1/2} # 6 # 1 {1/2} # 10 # 3 {1/2} # 14 # 5 {1/2} # 18 # 7 {1/2} # 22 # 9 {1/2}
2 {1/4} # 11 {5/8} # 6 {1/4} # 1 {5/8} # 10 {1/4} # 3 {5/8} # 14 {1/4} # 5 {5/8} # 18 {1/4} # 7 {5/8} # 22 {1/4} # 9 {5/8}
2 {1/2} # 11 {3/4} # 6 {1/2} # 1 {3/4} # 10 {1/2} # 3 {3/4} # 14 {1/2} # 5 {3/4} # 18 {1/2} # 7 {3/4} # 22 {1/2} # 9 {3/4}
2 {3/4} # 11 {7/8} # 6 {3/4} # 1 {7/8} # 10 {3/4} # 3 {7/8} # 14 {3/4} # 5 {7/8} # 18 {3/4} # 7 {7/8} # 22 {3/4} # 9 {7/8}
3 # XII # 7 # II # 11 # IIII # 15 # VI # 19 # VIII # 23 # X
3 {1/4} # {1/8} # 7 {1/4} # 2 {1/8} # 11 {1/4} # 4 {1/8} # 15 {1/4} # 6 {1/8} # 19 {1/4} # 8 {1/8} # 23 {1/4} # 10 {1/8}
3 {1/2} # {1/4} # 7 {1/2} # 2 {1/4} # 11 {1/2} # 4 {1/4} # 15 {1/2} # 6 {1/4} # 19 {1/2} # 8 {1/4} # 23 {1/2} # 10 {1/4}
3 {3/4} # {3/8} # 7 {3/4} # 2 {3/8} # 11 {3/4} # 4 {3/8} # 15 {3/4} # 6 {3/8} # 19 {3/4} # 8 {3/8} # 23 {3/4} # 10 {3/8}
4 # {1/2} # 8 # 2 {1/2} # 12 # 4 {1/2} # 16 # 6 {1/2} # 20 # 8 {1/2} # 24 # 10 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4016" xml:space="preserve">In horologio, quod cir culo horæ 21. </s>
  <s xml:id="echoid-s4017" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumuis duarum horarum huius tabu-<lb/>læ ſunt, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s4018" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4019" xml:space="preserve">demonſtrauimus, parallclæ.</s>
  <s xml:id="echoid-s4020" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div224" type="section" level="1" n="72">
<head xml:id="echoid-head75" xml:space="preserve">Linea horæ 20. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 10 {1/8} # 4 {1/4} # {1/8} # 8 {1/4} # 2 {1/8} # 12 {1/4} # 4 {1/8} # 16 {1/4} # 6 {1/8} # 20 {1/4} # 8 {1/8}
{1/2} # 10 {1/4} # 4 {1/2} # {1/4} # 8 {1/2} # 2 {1/4} # 12 {1/2} # 4 {1/4} # 16 {1/2} # 6 {1/4} # 20 {1/2} # 8 {1/4}
{3/4} # 10 {3/8} # 4 {3/4} # {3/8} # 8 {3/4} # 2 {3/8} # 12 {3/4} # 4 {3/8} # 16 {3/4} # 6 {3/8} # 20 {3/4} # 8 {3/8}
1 # 10 {1/2} # 5 # {1/2} # 9 # 2 {1/2} # 13 # 4 {1/2} # 17 # 6 {1/2} # 21 # 8 {1/2}
1 {1/4} # 10 {5/8} # 5 {1/4} # {5/8} # 9 {1/4} # 2 {5/8} # 13 {1/4} # 4 {5/8} # 17 {1/4} # 6 {5/8} # 21 {1/4} # 8 {5/8}
1 {1/2} # 10 {3/4} # 5 {1/2} # {3/4} # 9 {1/2} # 2 {3/4} # 13 {1/2} # 4 {3/4} # 17 {1/2} # 6 {3/4} # 21 {1/2} # 8 {3/4}
1 {3/4} # 10 {7/8} # 5 {3/4} # {7/8} # 9 {3/4} # 2 {7/8} # 13 {3/4} # 4 {7/8} # 17 {3/4} # 6 {7/8} # 21 {3/4} # 8 {7/8}
2 # XI # 6 # I # 10 # III # 14 # V # 18 # VII # 22 # IX
2 {1/4} # 11 {1/8} # 6 {1/4} # 1 {1/8} # 10 {1/4} # 3 {1/8} # 14 {1/4} # 5 {1/8} # 18 {1/4} # 7 {1/8} # 22 {1/4} # 9 {1/8}
2 {1/2} # 11 {1/4} # 6 {1/2} # 1 {1/4} # 10 {1/2} # 3 {1/4} # 14 {1/2} # 5 {1/4} # 18 {1/2} # 7 {1/4} # 22 {1/2} # 9 {1/4}
2 {3/4} # 11 {3/8} # 6 {2/4} # 1 {3/8} # 10 {3/4} # 3 {3/8} # 14 {3/4} # 5 {3/8} # 18 {3/4} # 7 {3/8} # 22 {3/4} # 9 {3/8}
3 # 11 {1/2} # 7 # 1 {1/2} # 11 # 3 {1/2} # 15 # 5 {1/2} # 19 # 7 {1/2} # 23 # 9 {1/2}
3 {1/4} # 11 {5/8} # 7 {1/4} # 1 {5/8} # 11 {1/4} # 3 {5/8} # 15 {1/4} # 5 {5/8} # 19 {1/4} # 7 {5/8} # 23 {1/4} # 9 {5/8}
3 {1/2} # 11 {3/4} # 7 {1/2} # 1 {3/4} # 11 {1/2} # 3 {3/4} # 15 {1/2} # 5 {3/4} # 19 {1/2} # 7 {3/4} # 23 {1/2} # 9 {3/4}
3 {3/4} # 11 {7/8} # 7 {3/4} # 1 {7/8} # 11 {3/4} # 3 {7/8} # 15 {3/4} # 5 {7/8} # 19 {3/4} # 7 {7/8} # 23 {3/4} # 9 {7/8}
4 # XII # 8 # II # 12 # IIII # 16 # VI # 20 # VIII # 24 # X
</note>
<p style="it">
  <s xml:id="echoid-s4021" xml:space="preserve">In horologio, quod circulo horæ 20. </s>
  <s xml:id="echoid-s4022" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumlibet duarum horarum huius ta-<lb/>bulæ ſunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4023" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4024" xml:space="preserve">parallelæ inter ſe.</s>
  <s xml:id="echoid-s4025" xml:space="preserve"/>
</p>
<pb o="63" file="0083" n="83" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div225" type="section" level="1" n="73">
<head xml:id="echoid-head76" xml:space="preserve">Linea horæ 19. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 9 {5/8} # 4 {1/4} # 11 {5/8} # 8 {1/4} # 1 {5/8} # 12 {1/4} # 3 {5/8} # 16 {1/4} # 5 {5/8} # 20 {1/4} # 7 {5/8}
{1/2} # 9 {3/4} # 4 {1/2} # 11 {3/4} # 8 {1/2} # 1 {3/4} # 12 {1/2} # 3 {3/4} # 16 {1/2} # 5 {3/4} # 20 {1/2} # 7 {3/4}
{3/4} # 9 {7/8} # 4 {3/4} # 11 {7/8} # 8 {3/4} # 1 {7/8} # 12 {3/4} # 3 {7/8} # 16 {3/4} # 5 {7/8} # 20 {3/4} # 7 {7/8}
1 # X # 5 # XII # 9 # 11 # 13 # IIII # 17 # VI # 21 # VIII
1 {1/4} # 10 {1/8} # 5 {1/4} # {1/8} # 9 {1/4} # 2 {1/8} # 13 {1/4} # 4 {1/8} # 17 {1/4} # 6 {1/8} # 21 {1/4} # 8 {1/8}
1 {1/2} # 10 {1/4} # 5 {1/2} # {1/4} # 9 {1/2} # 2 {1/4} # 13 {1/2} # 4 {1/4} # 17 {1/2} # 6 {1/4} # 21 {1/2} # 8 {1/4}
1 {3/4} # 10 {3/8} # 5 {3/4} # {3/8} # 9 {3/4} # 2 {3/8} # 13 {3/4} # 4 {3/8} # 17 {3/4} # 6 {3/8} # 21 {3/4} # 8 {3/8}
2 # 10 {1/2} # 6 # {1/2} # 10 # 2 {1/2} # 14 # 4 {1/2} # 18 # 6 {1/2} # 22 # 8 {1/2}
2 {1/4} # 10 {5/8} # 6 {1/4} # {5/8} # 10 {1/4} # 2 {5/8} # 14 {1/4} # 4 {5/8} # 18 {1/4} # 6 {5/8} # 22 {1/4} # 8 {5/8}
2 {1/2} # 10 {3/4} # 6 {1/2} # {3/4} # 10 {1/2} # 2 {3/4} # 14 {1/2} # 4 {3/4} # 18 {1/2} # 6 {3/4} # 22 {1/2} # 8 {3/4}
2 {3/4} # 10 {7/8} # 6 {3/4} # {7/8} # 10 {3/4} # 2 {7/8} # 14 {3/4} # 4 {7/8} # 18 {3/4} # 6 {7/8} # 22 {3/4} # 8 {7/8}
3 # XI # 7 # I # 11 # III # 15 # V # 19 # VII # 23 # IX
3 {1/4} # 11 {1/8} # 7 {1/4} # 1 {1/8} # 11 {1/4} # 3 {1/8} # 15 {1/4} # 5 {1/8} # 19 {1/4} # 7 {1/8} # 23 {1/4} # 9 {1/8}
3 {1/2} # 11 {1/4} # 7 {1/2} # 1 {1/4} # 11 {1/2} # 3 {1/4} # 15 {1/2} # 5 {1/4} # 19 {1/2} # 7 {1/4} # 23 {1/2} # 9 {1/4}
3 {3/4} # 11 {3/8} # 7 {3/4} # 1 {3/8} # 11 {3/4} # 3 {3/8} # 15 {3/4} # 5 {3/8} # 19 {3/4} # 7 {3/8} # 23 {3/4} # 9 {3/8}
4 # 11 {1/2} # 8 # 1 {1/2} # 12 # 3 {1/2} # 16 # 5 {1/2} # 20 # 7 {1/2} # 24 # 9 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4026" xml:space="preserve">In horologio, quod circulo horæ 19. </s>
  <s xml:id="echoid-s4027" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumcunque duarum horarum huius ta-<lb/>bulæ ſunt parallelæ, vt patet ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4028" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4029" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div226" type="section" level="1" n="74">
<head xml:id="echoid-head77" xml:space="preserve">Linea horæ 18. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 9 {1/8} # 4 {1/4} # 11 {1/8} # 8 {1/4} # 1 {1/8} # 12 {1/4} # 3 {1/8} # 16 {1/4} # 5 {1/8} # 20 {1/4} # 7 {1/8}
{1/2} # 9 {1/4} # 4 {1/2} # 11 {1/4} # 8 {1/2} # 1 {1/4} # 12 {1/2} # 3 {1/4} # 16 {1/2} # 5 {1/4} # 20 {1/2} # 7 {1/4}
{3/4} # 9 {3/8} # 4 {3/4} # 11 {3/8} # 8 {3/4} # 1 {3/8} # 12 {3/4} # 3 {3/8} # 16 {3/4} # 5 {3/8} # 20 {3/4} # 7 {3/8}
1 # 9 {1/2} # 5 # 11 {1/2} # 9 # 1 {1/2} # 13 # 3 {1/2} # 17 # 5 {1/2} # 21 # 7 {1/2}
1 {1/4} # 9 {5/8} # 5 {1/4} # 11 {5/8} # 9 {1/4} # 1 {5/8} # 13 {1/4} # 3 {5/8} # 17 {1/4} # 5 {5/8} # 21 {1/4} # 7 {5/8}
1 {1/2} # 9 {3/4} # 5 {1/2} # 11 {3/4} # 9 {1/2} # 1 {3/4} # 13 {1/2} # 3 {3/4} # 17 {1/2} # 5 {3/4} # 21 {1/2} # 7 {3/4}
1 {3/4} # 9 {7/8} # 5 {3/4} # 11 {7/8} # 9 {3/4} # 1 {7/8} # 13 {3/4} # 3 {7/8} # 17 {3/4} # 5 {7/8} # 21 {3/4} # 7 {7/8}
2 # X # 6 # XII # 10 # II # 14 # IIII # 18 # VI # 22 # VIII
2 {1/4} # 10 {1/8} # 6 {1/4} # {1/8} # 10 {1/4} # 2 {1/8} # 14 {1/4} # 4 {1/8} # 18 {1/4} # 6 {1/8} # 22 {1/4} # 8 {1/8}
2 {1/2} # 10 {1/4} # 6 {1/2} # {1/4} # 10 {1/2} # 2 {1/4} # 14 {1/2} # 4 {1/4} # 18 {1/2} # 6 {1/4} # 22 {1/2} # 8 {1/4}
2 {3/4} # 10 {3/8} # 6 {2<unsure/>/4} # {3/8} # 10 {3/4} # 2 {3/8} # 14 {3/4} # 4 {3/8} # 18 {3/4} # 6 {3/8} # 22 {3/4} # 8 {3/8}
3 # 10 {1/2} # 7 # {1/2} # 11 # 2 {1/2} # 15 # 4 {1/2} # 19 # 6 {1/2} # 23 # 8 {1/2}
3 {1/4} # 10 {5/8} # 7 {1/4} # {5/8} # 11 {1/4} # 2 {5/8} # 15 {1/4} # 4 {5/8} # 19 {1/4} # 6 {5/8} # 23 {1/4} # 8 {5/8}
3 {1/2} # 10 {3/4} # 7 {1/2} # {3/4} # 11 {1/2} # 2 {3/4} # 15 {1/2} # 4 {3/4} # 19 {1/2} # 6 {3/4} # 23 {1/2} # 8 {3/4}
3 {3/4} # 10 {7/8} # 7 {3/4} # {7/8} # 11 {3/4} # 2 {7/8} # 15 {3/4} # 4 {7/8} # 19 {3/4} # 6 {7/8} # 23 {3/4} # 8 {7/8}
4 # XI # 8 # I # 12 # III # 16 # V # 20 # VII # 24 # IX
</note>
<p style="it">
  <s xml:id="echoid-s4030" xml:space="preserve">In horologio, quod circulo horæ 18. </s>
  <s xml:id="echoid-s4031" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumlibet duarum borarum huius ta-<lb/>bulæ parallelæ ſunt, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4032" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4033" xml:space="preserve">patet.</s>
  <s xml:id="echoid-s4034" xml:space="preserve"/>
</p>
<pb o="64" file="0084" n="84" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div227" type="section" level="1" n="75">
<head xml:id="echoid-head78" xml:space="preserve">Linea horæ 17. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 8 {5/8} # 4 {1/4} # 10 {5/8} # 8 {1/4} # {5/8} # 12 {1/4} # 2 {5/8} # 16 {1/4} # 4 {5/8} # 20 {1/4} # 6 {5/8}
{1/2} # 8 {3/4} # 4 {1/2} # 10 {3/4} # 8 {1/2} # {3/4} # 12 {1/2} # 2 {3/4} # 16 {1/2} # 4 {3/4} # 20 {1/2} # 6 {3/4}
{3/4} # 8 {7/8} # 4 {3/4} # 10 {7/8} # 8 {3/4} # {7/8} # 12 {3/4} # 2 {7/8} # 16 {3/4} # 4 {7/8} # 20 {3/4} # 6 {7/8}
1 # IX # 5 # XI # 9 # I # 13 # III # 17 # V # 21 # VII
1 {1/4} # 9 {1/8} # 5 {1/4} # 11 {1/8} # 9 {1/4} # 1 {1/8} # 1 {1/4} # 3 {1/8} # 17 {1/4} # 5 {1/8} # 21 {1/4} # 7 {1/8}
1 {1/2} # 9 {1/4} # 5 {1/2} # 11 {1/4} # 9 {1/2} # 1 {1/4} # 1 {1/2} # 3 {1/4} # 17 {1/2} # 5 {1/4} # 21 {1/2} # 7 {1/4}
1 {3/4} # 9 {3/8} # 5 {3/4} # 11 {3/8} # 9 {3/4} # 1 {3/8} # 1 {3/4} # 3 {3/8} # 17 {3/4} # 5 {3/8} # 21 {3/4} # 7 {3/8}
2 # 9 {1/2} # 6 # 11 {1/2} # 10 # 1 {1/2} # 14 # 3 {1/2} # 18 # 5 {1/2} # 22 # 7 {1/2}
2 {1/4} # 9 {5/8} # 6 {1/4} # 11 {5/8} # 10 {1/4} # 1 {5/8} # 14 {1/4} # 3 {5/8} # 18 {1/4} # 5 {5/8} # 22 {1/4} # 7 {5/8}
2 {1/2} # 9 {3/4} # 6 {1/2} # 11 {3/4} # 10 {1/2} # 1 {3/4} # 14 {1/2} # 3 {3/4} # 18 {1/2} # 5 {3/4} # 22 {1/2} # 7 {3/4}
2 {3/4} # 9 {7/8} # 6 {3/4} # 11 {7/8} # 10 {3/4} # 1 {7/8} # 14 {3/4} # 3 {7/8} # 18 {3/4} # 5 {7/8} # 22 {3/4} # 7 {7/8}
3 # X # 7 # XII # 11 # II # 15 # IIII # 19 # VI # 23 # VIII
3 {1/4} # 10 {1/8} # 7 {1/4} # {1/8} # 11 {1/4} # 2 {1/8} # 15 {1/4} # 4 {1/8} # 19 {1/4} # 6 {1/8} # 23 {1/4} # 8 {1/8}
3 {1/2} # 10 {1/4} # 7 {1/2} # {1/4} # 11 {1/2} # 2 {1/4} # 15 {1/2} # 4 {1/4} # 19 {1/2} # 6 {1/4} # 23 {1/2} # 8 {1/4}
3 {3/4} # 10 {3/8} # 7 {3/4} # {3/8} # 11 {3/4} # 2 {3/8} # 15 {3/4} # 4 {3/8} # 19 {3/4} # 6 {3/8} # 23 {3/4} # 8 {3/8}
4 # 10 {1/2} # 8 # {1/2} # 12 # 2 {1/2} # 16 # 4 {1/2} # 20 # 6 {1/2} # 24 # 8 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4035" xml:space="preserve">In horologio, quod circulo horæ 17. </s>
  <s xml:id="echoid-s4036" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumuis duarum horarum huius tabulæ<unsure/> <lb/>ſunt parallclæ, vt manifestum eſt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4037" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4038" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div228" type="section" level="1" n="76">
<head xml:id="echoid-head79" xml:space="preserve">Linea horæ 16. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 8 {1/8} # 4 {1/4} # 10 {1/8} # 8 {1/4} # {1/8} # 12 {1/4} # 2 {1/8} # 16 {1/4} # 4 {1/8} # 20 {1/4} # 6 {1/8}
{1/2} # 8 {1/4} # 4 {1/2} # 10 {1/4} # 8 {1/2} # {1/4} # 12 {1/2} # 2 {1/4} # 16 {1/2} # 4 {1/4} # 20 {1/2} # 6 {1/4}
{3/4} # 8 {3/8} # 4 {3/4} # 10 {3/8} # 8 {3/4} # {3/8} # 12 {3/4} # 2 {3/8} # 16 {3/4} # 4 {3/8} # 20 {3/4} # 6 {3/8}
1 # 8 {1/2} # 5 # 10 {1/2} # 9 # {1/2} # 13 # 2 {1/2} # 17 # 4 {1/2} # 21 # 6 {1/2}
1 {1/4} # 8 {5/8} # 5 {1/4} # 10 {5/8} # 9 {1/4} # {5/8} # 13 {1/4} # 2 {5/8} # 17 {1/4} # 4 {5/8} # 21 {1/4} # 6 {5/8}
1 {1/2} # 8 {3/4} # 5 {1/2} # 10 {3/4} # 9 {1/2} # {3/4} # 13 {1/2} # 2 {3/4} # 17 {1/2} # 4 {3/4} # 21 {1/2} # 6 {3/4}
1 {3/4} # 8 {7/8} # 5 {3/4} # 10 {7/8} # 9 {3/4} # {7/8} # 13 {3/4} # 2 {7/8} # 17 {3/4} # 4 {7/8} # 21 {3/4} # 6 {7/8}
2 # IX # 6 # XI # 10 # I # 14 # III # 18 # V # 22 # VII
2 {1/4} # 9 {1/8} # 6 {1/4} # 11 {1/8} # 10 {1/4} # 1 {1/8} # 14 {1/4} # 3 {1/8} # 18 {1/4} # 5 {1/8} # 22 {1/4} # 7 {1/8}
2 {1/2} # 9 {1/4} # 6 {1/2} # 11 {1/4} # 10 {1/2} # 1 {1/4} # 14 {1/2} # 3 {1/4} # 18 {1/2} # 5 {1/4} # 22 {1/2} # 7 {1/4}
2 {3/4} # 9 {3/8} # 6 {3/4} # 11 {3/8} # 10 {3/4} # 1 {3/8} # 14 {3/4} # 3 {3/8} # 18 {3/4} # 5 {3/8} # 22 {3/4} # 7 {3/8}
3 # 9 {1/2} # 7 # 11 {1/2} # 11 # 1 {1/2} # 15 # 3 {1/2} # 19 # 5 {1/2} # 23 # 7 {1/2}
3 {1/4} # 9 {5/8} # 7 {1/4} # 11 {5/8} # 11 {1/4} # 1 {5/8} # 15 {1/4} # 3 {5/8} # 19 {1/4} # 5 {5/8} # 23 {1/4} # 7 {5/8}
3 {1/2} # 9 {3/4} # 7 {1/2} # 11 {3/4} # 11 {1/2} # 1 {3/4} # 15 {1/2} # 3 {3/4} # 19 {1/2} # 5 {3/4} # 23 {1/2} # 7 {3/4}
3 {3/4} # 9 {7/8} # 7 {3/4} # 11 {7/8} # 11 {3/4} # 1 {7/8} # 15 {3/4} # 3 {7/8} # 19 {3/4} # 5 {7/8} # 23 {3/4} # 7 {7/8}
4 # X # 8 # XII # 12 # II # 16 # IIII # 20 # VI # 24 # VIII
</note>
<p style="it">
  <s xml:id="echoid-s4039" xml:space="preserve">In horologio, quod circulo horæ 16. </s>
  <s xml:id="echoid-s4040" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumlibet duarum horarum huius ta-<lb/>bulæ parallelæ ſunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4041" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4042" xml:space="preserve"/>
</p>
<pb o="65" file="0085" n="85" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div229" type="section" level="1" n="77">
<head xml:id="echoid-head80" xml:space="preserve">Linea horæ 15. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 7 {5/8} # 4 {1/4} # 9 {5/8} # 8 {1/4} # 11 {5/8} # 12 {1/4} # 1 {5/8} # 16 {1/4} # 3 {5/8} # 20 {1/4} # 5 {5/8}
{1/2} # 7 {3/4} # 4 {1/2} # 9 {3/4} # 8 {1/2} # 11 {3/4} # 12 {1/2} # 1 {3/4} # 16 {1/2} # 3 {3/4} # 20 {1/2} # 5 {3/4}
{3/4} # 7 {7/8} # 4 {3/4} # 9 {7/8} # 8 {3/4} # 11 {7/8} # 12 {3/4} # 1 {7/8} # 16 {3/4} # 3 {7/8} # 20 {3/4} # 5 {7/8}
1 # VIII # 5 # X # 9 # XII # 13 # II # 17 # IIII # 21 # VI
1 {1/4} # 8 {1/8} # 5 {1/4} # 10 {1/8} # 9 {1/4} # {1/8} # 13 {1/4} # 2 {1/8} # 17 {1/4} # 4 {1/8} # 21 {1/4} # 6 {1/8}
1 {1/2} # 8 {1/4} # 5 {1/2} # 10 {1/4} # 9 {1/2} # {1/4} # 13 {1/2} # 2 {1/4} # 17 {1/2} # 4 {1/4} # 21 {1/2} # 6 {1/4}
1 {3/4} # 8 {3/8} # 5 {3/4} # 10 {3/8} # 9 {3/4} # {3/8} # 13 {3/4} # 2 {3/8} # 17 {3/4} # 4 {3/8} # 21 {3/4} # 6 {3/8}
2 # 8 {1/2} # 6 # 10 {1/2} # 10 # {1/2} # 14 # 2 {1/2} # 18 # 4 {1/2} # 22 # 6 {1/2}
2 {1/4} # 8 {5/8} # 6 {1/4} # 10 {5/8} # 10 {1/4} # {5/8} # 14 {1/4} # 2 {5/8} # 18 {1/4} # 4 {5/8} # 22 {1/4} # 6 {5/8}
2 {1/2} # 8 {3/4} # 6 {1/2} # 10 {3/4} # 10 {1/2} # {3/4} # 14 {1/2} # 2 {3/4} # 18 {1/2} # 4 {3/4} # 22 {1/2} # 6 {3/4}
2 {3/4} # 8 {7/8} # 6 {3/4} # 10 {7/8} # 10 {3/4} # {7/8} # 14 {3/4} # 2 {7/8} # 18 {3/4} # 4 {7/8} # 22 {3/4} # 6 {7/8}
3 # IX # 7 # XI # 11 # I # 15 # III # 19 # V # 23 # VII
3 {1/4} # 9 {1/8} # 7 {1/4} # 11 {1/8} # 11 {1/4} # 1 {1/8} # 15 {1/4} # 3 {1/8} # 19 {1/4} # 5 {1/8} # 23 {1/4} # 7 {1/8}
3 {1/2} # 9 {1/4} # 7 {1/2} # 11 {1/4} # 11 {1/2} # 1 {1/4} # 15 {1/2} # 3 {1/4} # 19 {1/2} # 5 {1/4} # 23 {1/2} # 7 {1/4}
3 {3/4} # 9 {3/8} # 7 {3/4} # 11 {3/8} # 11 {3/4} # 1 {3/8} # 15 {3/4} # 3 {3/8} # 19 {3/4} # 5 {3/8} # 23 {3/4} # 7 {3/8}
4 # 9 {1/2} # 8 # 11 {1/2} # 12 # 1 {1/2} # 16 # 3 {1/2} # 20 # 5 {1/2} # 24 # 7 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4043" xml:space="preserve">In horologio, quod circulo horæ 15. </s>
  <s xml:id="echoid-s4044" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumlibet duarum horarum huius tabu <lb/>læ ſunt parallelæ, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4045" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4046" xml:space="preserve">perſpicuum eſt.</s>
  <s xml:id="echoid-s4047" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div230" type="section" level="1" n="78">
<head xml:id="echoid-head81" xml:space="preserve">Linea horæ 14. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 7 {1/8} # 4 {1/4} # 9 {1/8} # 8 {1/4} # 11 {1/8} # 12 {1/4} # 1 {1/8} # 16 {1/4} # 3 {1/8} # 20 {1/4} # 5 {1/8}
{1/2} # 7 {1/4} # 4 {1/2} # 9 {1/4} # 8 {1/2} # 11 {1/4} # 12 {1/2} # 1 {1/4} # 16 {1/2} # 3 {1/4} # 20 {1/2} # 5 {1/4}
{3/4} # 7 {3/8} # 4 {3/4} # 9 {3/8} # 8 {3/4} # 11 {3/8} # 12 {3/4} # 1 {3/8} # 16 {3/4} # 3 {3/8} # 20 {3/4} # 5 {3/8}
1 # 7 {1/2} # 5 # 9 {1/2} # 9 # 11 {1/2} # 13 # 1 {1/2} # 17 # 3 {1/2} # 21 # 5 {1/2}
1 {1/4} # 7 {5/8} # 5 {1/4} # 9 {5/8} # 9 {1/4} # 11 {5/8} # 13 {1/4} # 1 {5/8} # 17 {1/4} # 3 {5/8} # 21 {1/4} # 5 {5/8}
1 {1/2} # 7 {3/4} # 5 {1/2} # 9 {3/4} # 9 {1/2} # 11 {3/4} # 13 {1/2} # 1 {3/4} # 17 {1/2} # 3 {3/4} # 21 {1/2} # 5 {3/4}
1 {3/4} # 7 {7/8} # 5 {3/4} # 9 {7/8} # 9 {3/4} # 11 {7/8} # 13 {3/4} # 1 {7/8} # 17 {3/4} # 3 {7/8} # 21 {3/4} # 5 {7/8}
2 # VIII # 6 # X # 10 # XII # 14 # II # 18 # IIII # 22 # VI
2 {1/4} # 8 {1/8} # 6 {1/4} # 10 {1/8} # 10 {1/4} # {1/8} # 14 {1/4} # 2 {1/8} # 18 {1/4} # 4 {1/8} # 22 {1/4} # 6 {1/8}
2 {1/2} # 8 {1/4} # 6 {1/2} # 10 {1/4} # 10 {1/2} # {1/4} # 14 {1/2} # 2 {1/4} # 18 {1/2} # 4 {1/4} # 22 {1/2} # 6 {1/4}
2 {3/4} # 8 {3/8} # 6 {3/4} # 10 {3/8} # 10 {3/4} # {3/8} # 14 {3/4} # 2 {3/8} # 18 {3/4} # 4 {3/8} # 22 {3/4} # 6 {3/8}
3 # 8 {1/2} # 7 # 10 {1/2} # 11 # {1/2} # 15 # 2 {1/2} # 19 # 4 {1/2} # 23 # 6 {1/2}
3 {1/4} # 8 {5/8} # 7 {1/4} # 10 {5/8} # 11 {1/4} # {5/8} # 15 {1/4} # 2 {5/8} # 19 {1/4} # 4 {5/8} # 23 {1/4} # 6 {5/8}
3 {1/2} # 8 {3/4} # 7 {1/2} # 10 {3/4} # 11 {1/2} # {3/4} # 15 {1/2} # 2 {3/4} # 19 {1/2} # 4 {3/4} # 23 {1/2} # 6 {3/4}
3 {3/4} # 8 {7/8} # 7 {3/4} # 10 {7/8} # 11 {3/4} # {7/8} # 15 {3/4} # 2 {7/8} # 19 {3/4} # 4 {7/8} # 23 {3/4} # 6 {7/8}
4 # IX # 8 # XI # 12 # I # 16 # III # 20 # V # 24 # VII
</note>
<p style="it">
  <s xml:id="echoid-s4048" xml:space="preserve">In horologio, quod circulo horæ 14. </s>
  <s xml:id="echoid-s4049" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumuis duarum horarum huius ta-<unsure/> <lb/>bulæ parallelæ ſunt, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s4050" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4051" xml:space="preserve">docuimus.</s>
  <s xml:id="echoid-s4052" xml:space="preserve"/>
</p>
<pb o="66" file="0086" n="86" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div231" type="section" level="1" n="79">
<head xml:id="echoid-head82" xml:space="preserve">Linea horæ 13. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridi \\ vel media noct@ # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu@ \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 6 {5/8} # 4 {1/4} # 8 {5/8} # 8 {1/4} # 10 {5/8} # 12 {1/4} # {5/8} # 16 {1/4} # 2 {5/8} # 20 {1/4} # 4 {5/8}
{1/2} # 6 {3/4} # 4 {1/2} # 8 {3/4} # 8 {1/2} # 10 {3/4} # 12 {1/2} # {3/4} # 16 {1/2} # 2 {3/4} # 20 {1/2} # 4 {3/4}
{3/4} # 6 {7/8} # 4 {3/4} # 8 {7/8} # 8 {3/4} # 10 {7/8} # 12 {3/4} # {7/8} # 16 {3/4} # 2 {7/8} # 20 {3/4} # 4 {7/8}
1 # VII # 5 # IX # 9 # XI # 13 # I # 17 # III # 21 # V
1 {1/4} # 7 {1/8} # 5 {1/4} # 9 {1/8} # 9 {1/4} # 11 {1/8} # 13 {1/4} # 1 {1/8} # 17 {1/4} # 3 {1/8} # 21 {1/4} # 5 {1/8}
1 {1/2} # 7 {1/4} # 5 {1/2} # 9 {1/4} # 9 {1/2} # 11 {1/4} # 13 {1/2} # 1 {1/4} # 17 {1/2} # 3 {1/4} # 21 {1/2} # 5 {1/4}
1 {3/4} # 7 {3/8} # 5 {3/4} # 9 {3/8} # 9 {3/4} # 11 {3/8} # 13 {3/4} # 1 {3/8} # 17 {3/4} # 3 {3/8} # 21 {3/4} # 5 {3/8}
2 # 7 {1/2} # 0 # 9 {1/2} # 10 # 11 {1/2} # 14 # 1 {1/2} # 18 # 3 {1/2} # 22 # 5 {1/2}
2 {1/4} # 7 {5/8} # 6 {1/4} # 9 {5/8} # 10 {1/4} # 11 {5/8} # 14 {1/4} # 1 {5/8} # 10 {1/4} # 3 {5/8} # 22 {1/4} # 5 {5/8}
2 {1/2} # 7 {3/4} # 6 {1/2} # 9 {3/4} # 10 {1/2} # 11 {3/4} # 14 {1/2} # 1 {3/4} # 18 {1/2} # 3 {3/4} # 22 {1/2} # 5 {3/4}
2 {3/4} # 7 {7/8} # 6 {3/4} # 9 {7/8} # 10 {3/4} # 11 {7/8} # 14 {3/4} # 1 {7/8} # 18 {3/4} # 3 {7/8} # 22 {3/4} # 5 {7/8}
3 # VIII # 7 # X # 11 # XII # 15 # II # 19 # IIII # 23 # VI
3 {1/4} # 8 {1/8} # 7 {1/4} # 10 {1/8} # 11 {1/4} # {1/8} # 15 {1/4} # 2 {1/8} # 19 {1/4} # 4 {1/8} # 23 {1/4} # 6 {1/8}
3 {1/2} # 8 {1/4} # 7 {1/2} # 10 {1/4} # 11 {1/2} # {1/4} # 15 {1/2} # 2 {1/4} # 19 {1/2} # 4 {1/4} # 23 {1/2} # 6 {1/4}
3 {3/4} # 8 {3/8} # 7 {3/4} # 10 {3/8} # 11 {3/4} # {3/8} # 15 {3/4} # 2 {3/8} # 19 {3/4} # 4 {3/8} # 23 {3/4} # 6 {3/8}
4 # 8 {1/2} # 8 # 10 {1/2} # 12 # {1/2} # 16 # 2 {1/2} # 20 # 4 {1/2} # 24 # 6 {1/2}</note>
</div>
<div xml:id="echoid-div232" type="section" level="1" n="80">
<head xml:id="echoid-head83" xml:space="preserve">In horologio, quod circulo horæ 13. ab ortu vel occaſu æquidiſtat, lineæ quarumlibet duarum horarum huius tabu <lb/>læ ſunt, ex ſcholio propoſ. 22. parallelæ.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div233" type="section" level="1" n="81">
<head xml:id="echoid-head84" xml:space="preserve">Linea horæ 11. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 5 {5/8} # 4 {1/4} # 7 {5/8} # 8 {1/4} # 9 {5/8} # 12 {1/4} # 11 {5/8} # 16 {1/4} # 1 {5/8} # 20 {1/4} # 3 {5/8}
{1/2} # 5 {3/4} # 4 {1/2} # 7 {3/4} # 8 {1/2} # 9 {3/4} # 12 {1/2} # 11 {3/4} # 16 {1/2} # 1 {3/4} # 20 {1/2} # 3 {3/4}
{3/4} # 5 {7/8} # 4 {3/4} # 7 {7/8} # 8 {3/4} # 9 {7/8} # 12 {3/4} # 11 {7/8} # 16 {3/4} # 1 {7/8} # 20 {3/4} # 3 {7/8}
1 # VI # 5 # VIII # 9 # X # 13 # XII # 17 # II # 21 # IIII
1 {1/4} # 6 {1/8} # 5 {1/4} # 8 {1/8} # 9 {1/4} # 10 {1/8} # 1 {1/4} # {1/8} # 17 {1/4} # 2 {1/8} # 21 {1/4} # 4 {1/8}
1 {1/2} # 6 {1/4} # 5 {1/2} # 8 {1/4} # 9 {1/2} # 10 {1/4} # 13 {1/2} # {1/4} # 17 {1/2} # 2 {1/4} # 21 {1/2} # 4 {1/4}
1 {3/4} # 6 {3/8} # 5 {3/4} # 8 {3/8} # 9 {3/4} # 10 {3/8} # 13 {3/4} # {3/8} # 17 {3/4} # 2 {3/8} # 21 {3/4} # 4 {3/8}
2 # 6 {1/2} # 6 # 8 {1/2} # 10 # 10 {1/2} # 14 # {1/2} # 18 # 2 {1/3} # 22 # 4 {1/2}
2 {1/4} # 6 {5/8} # 6 {1/4} # 8 {5/8} # 10 {1/4} # 10 {5/8} # 14 {1/4} # {5/8} # 10 {1/4} # 2 {5/8} # 22 {1/4} # 4 {5/8}
2 {1/2} # 6 {3/4} # 6 {1/2} # 8 {3/4} # 10 {1/2} # 10 {3/4} # 14 {1/2} # {3/4} # 18 {1/2} # 2 {3/4} # 22 {1/2} # 4 {3/4}
2 {3/4} # 6 {7/8} # 6 {3/4} # 8 {7/8} # 10 {3/4} # 10 {7/8} # 14 {3/4} # {7/8} # 18 {3/4} # 2 {7/8} # 22 {3/4} # 4 {7/8}
3 # VII # 7 # IX # 11 # XI # 15 # I # 19 # III # 23 # V
3 {1/4} # 7 {1/8} # 7 {1/4} # 9 {1/8} # 11 {1/4} # 11 {1/8} # 15 {1/4} # 1 {1/8} # 19 {1/4} # 3 {1/8} # 23 {1/4} # 5 {1/8}
3 {1/2} # 7 {1/4} # 7 {1/2} # 9 {1/4} # 11 {1/2} # 11 {1/4} # 15 {1/2} # 1 {1/4} # 19 {1/2} # 3 {1/4} # 23 {1/2} # 5 {1/4}
3 {3/4} # 7 {3/8} # 7 {3/4} # 9 {3/8} # 11 {3/4} # 11 {3/8} # 15 {3/4} # 1 {3/8} # 19 {3/4} # 3 {3/8} # 23 {3/4} # 5 {3/8}
4 # 7 {1/2} # 8 # 9 {1/2} # 12 # 11 {1/2} # 16 # 1 {1/2} # 20 # 3 {1/2} # 24 # 5 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4053" xml:space="preserve">In horologio, quod circulo horæ 14. </s>
  <s xml:id="echoid-s4054" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumuis duarum horarum huius ta-<lb/>bulæſunt parallelæ, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4055" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4056" xml:space="preserve">manifeſtum eſt.</s>
  <s xml:id="echoid-s4057" xml:space="preserve"/>
</p>
<pb o="67" file="0087" n="87" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div234" type="section" level="1" n="82">
<head xml:id="echoid-head85" xml:space="preserve">Linea horæ 10. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media noct@ # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 5 {1/8} # 4 {1/4} # 7 {1/8} # 8 {1/4} # 9 {1/8} # 12 {1/4} # 11 {1/8} # 16 {1/4} # 1 {1/8} # 20 {1/4} # 3 {1/8}
{1/2} # 5 {1/4} # 4 {1/2} # 7 {1/4} # 8 {1/2} # 9 {1/4} # 12 {1/2} # 11 {1/4} # 16 {1/2} # 1 {1/4} # 20 {1/2} # 3 {1/4}
{3/4} # 5 {3/8} # 4 {3/4} # 7 {3/8} # 8 {3/4} # 9 {3/8} # 12 {3/4} # 11 {3/8} # 16 {3/4} # 1 {3/8} # 20 {3/4} # 3 {3/8}
1 # 5 {1/2} # 5 # 7 {1/2} # 9 # 9 {1/2} # 13 # 11 {1/2} # 17 # 1 {1/2} # 21 # 3 {1/2}
1 {1/4} # 5 {5/8} # 5 {1/4} # 7 {5/8} # 9 {1/4} # 9 {5/8} # 13 {1/@} # 11 {5/8} # 17 {1/4} # 1 {5/8} # 21 {1/4} # 3 {5/8}
1 {1/2} # 5 {3/4} # 5 {1/2} # 7 {3/4} # 9 {1/2} # 9 {3/4} # 13 {1/2} # 11 {3/4} # 17 {1/2} # 1 {3/4} # 21 {1/2} # 3 {3/4}
1 {3/4} # 5 {7/8} # 5 {3/4} # 7 {7/8} # 9 {3/4} # 9 {7/8} # 13 {3/4} # 11 {7/8} # 17 {3/4} # 1 {7/8} # 21 {3/4} # 3 {7/8}
2 # VI # 6 # VIII # 10 # X # 14 # XII # 18 # II # 22 # IIII
2 {1/4} # 6 {1/8} # 6 {1/4} # 8 {1/8} # 10 {1/4} # 10 {1/8} # 14 {1/4} # {1/8} # 18 {1/4} # 2 {1/8} # 22 {1/4} # 4 {1/8}
2 {1/2} # 6 {1/4} # 6 {1/2} # 8 {1/4} # 10 {1/2} # 10 {1/4} # 14 {1/2} # {1/4} # 18 {1/2} # 2 {1/4} # 22 {1/2} # 4 {1/4}
2 {3/4} # 6 {3/8} # 6 {3/4} # 8 {3/8} # 10 {3/4} # 10 {3/8} # 14 {3/4} # {3/8} # 18 {3/4} # 2 {3/8} # 22 {3/4} # 4 {3/8}
3 # 6 {1/2} # 7 # 8 {1/2} # 11 # 10 {1/2} # 15 # {1/2} # 19 # 2 {1/2} # 23 # 4 {1/2}
3 {1/4} # 6 {5/8} # 7 {1/4} # 8 {5/8} # 11 {1/4} # 10 {5/8} # 15 {1/4} # {5/8} # 19 {1/4} # 2 {5/8} # 23 {1/4} # 4 {5/8}
3 {1/2} # 6 {3/4} # 7 {1/2} # 8 {3/4} # 11 {1/2} # 10 {3/4} # 15 {1/2} # {3/4} # 19 {1/2} # 2 {3/4} # 23 {1/2} # 4 {3/4}
3 {3/4} # 6 {7/8} # 7 {3/4} # 8 {7/8} # 11 {3/4} # 10 {7/8} # 15 {3/4} # {7/8} # 19 {3/4} # 2 {7/8} # 23 {3/4} # 4 {7/8}
4 # VII # 8 # IX # 12 # XI # 16 # I # 20 # III # 24 # V</note>
</div>
<div xml:id="echoid-div235" type="section" level="1" n="83">
<head xml:id="echoid-head86" xml:space="preserve">In horologio, quod circulo horæ 10. ab ortu vel occaſu æquidiſtat, lineæ quarumcunque duarum horarum huius <lb/>tabulæ, ſunt parallelæ, vt conſtat ex ſcho io propoſ. 22.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div236" type="section" level="1" n="84">
<head xml:id="echoid-head87" xml:space="preserve">Linea horæ 9. ab ortu vel occaſu.</head>
<note position="left" xml:space="preserve">
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 4 {5/8} # 4 {1/4} # 6 {5/8} # 8 {1/4} # 8 {5/8} # 12 {1/4} # 10 {5/8} # 16 {1/4} # {5/8} # 20 {1/4} # 2 {5/8}
{1/2} # 4 {3/4} # 4 {1/2} # 6 {3/4} # 8 {1/2} # 8 {3/4} # 12 {1/2} # 10 {3/4} # 16 {1/2} # {3/4} # 20 {1/2} # 2 {3/4}
{3/4} # 4 {7/8} # 4 {3/4} # 6 {7/8} # 8 {3/4} # 8 {7/8} # 12 {3/4} # 10 {7/8} # 16 {3/4} # {7/8} # 20 {3/4} # 2 {7/8}
1 # V # 5 # VII # 9 # IX # 13 # XI # 17 # I # 21 # III
1 {1/4} # 5 {1/8} # 5 {1/4} # 7 {1/8} # 9 {1/4} # 9 {1/8} # 13 {1/4} # 11 {1/8} # 17 {1/4} # 1 {1/8} # 21 {1/4} # 3 {1/8}
1 {1/2} # 5 {1/4} # 5 {1/2} # 7 {1/4} # 9 {1/2} # 9 {1/4} # 13 {1/2} # 11 {1/4} # 17 {1/2} # 1 {1/4} # 21 {1/2} # 3 {1/4}
1 {3/4} # 5 {3/8} # 5 {3/4} # 7 {3/8} # 9 {3/4} # 9 {3/8} # 13 {3/4} # 11 {3/8} # 17 {3/4} # 1 {3/8} # 21 {3/4} # 3 {3/8}
2 # 5 {1/2} # 6 # 7 {1/2} # 10 # 9 {1/2} # 14 # 11 {1/2} # 18 # 1 {1/2} # 22 # 3 {1/2}
2 {1/4} # 5 {5/8} # 6 {1/4} # 7 {5/8} # 10 {1/4} # 9 {5/8} # 14 {1/4} # 11 {5/8} # 18 {1/4} # 1 {5/8} # 22 {1/4} # 3 {5/8}
2 {1/2} # 5 {3/4} # 6 {1/2} # 7 {3/4} # 10 {1/2} # 9 {3/4} # 14 {1/2} # 11 {3/4} # 18 {1/2} # 1 {3/4} # 22 {1/2} # 3 {3/4}
2 {3/4} # 5 {7/8} # 6 {3/4} # 7 {7/8} # 10 {3/4} # 9 {7/8} # 14 {3/4} # 11 {7/8} # 18 {3/4} # 1 {7/8} # 22 {3/4} # 3 {7/8}
3 # VI # 7 # VIII # 11 # X # 15 # XII # 19 # II # 23 # IIII
3 {1/4} # 6 {1/8} # 7 {1/4} # 8 {1/8} # 11 {1/4} # 10 {1/8} # 15 {1/4} # {1/8} # 19 {1/4} # 2 {1/8} # 23 {1/4} # 4 {1/8}
3 {1/2} # 6 {1/4} # 7 {1/2} # 8 {1/4} # 11 {1/2} # 10 {1/4} # 15 {1/2} # {1/4} # 19 {1/2} # 2 {1/4} # 23 {1/2} # 4 {1/4}
3 {3/4} # 6 {3/8} # 7 {3/4} # 8 {3/8} # 11 {3/4} # 10 {3/8} # 15 {3/4} # {3/8} # 19 {3/4} # 2 {3/8} # 23 {3/4} # 4 {3/8}
4 # 6 {1/2} # 8 # 8 {1/2} # 12 # 10 {1/2} # 16 # {1/2} # 20 # 2 {1/2} # 24 # 4 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4058" xml:space="preserve">In horologio, quod circulo horæ 9. </s>
  <s xml:id="echoid-s4059" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quarumlibet duarum horarum huius ta-<lb/>bulæ ſunt parallelæ, vt conſtat ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4060" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4061" xml:space="preserve"/>
</p>
<pb o="68" file="0088" n="88" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div237" type="section" level="1" n="85">
<head xml:id="echoid-head88" xml:space="preserve">Linea horæ 8. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte
{1/4} # 4 {1/8} # 4 {1/4} # 6 {1/8} # 8 {1/4} # 8 {1/8} # 12 {1/4} # 10 {1/8} # 16 {1/4} # {1/8} # 20 {1/4} # 2 {1/8}
{1/2} # 4 {1/4} # 4 {1/2} # 6 {1/4} # 8 {1/2} # 8 {1/4} # 12 {1/2} # 10 {1/4} # 16 {1/2} # {1/4} # 20 {1/2} # 2 {1/4}
{3/4} # 4 {3/8} # 4 {3/4} # 6 {3/8} # 8 {3/4} # 8 {3/8} # 12 {3/4} # 10 {3/8} # 16 {3/4} # {3/8} # 20 {3/4} # 2 {3/8}
1 # 4 {1/2} # 5 # {1/2} # 9 # 8 {1/2} # 13 # 10 {1/2} # 17 # {1/2} # 21 # 2 {1/2}
1 {1/4} # 4 {5/8} # 5 {1/4} # 6 {5/8} # 9 {1/4} # 8 {5/8} # 13 {1/4} # 10 {5/8} # 17 {1/4} # {5/8} # 21 {1/4} # 2 {5/8}
1 {1/2} # 4 {3/4} # 5 {1/2} # 6 {3/4} # 9 {1/2} # 8 {3/4} # 13 {1/2} # 10 {3/4} # 17 {1/2} # {3/4} # 21 {1/2} # 2 {3/4}
1 {3/4} # 4 {7/8} # 5 {3/4} # 6 {7/8} # 9 {3/4} # 8 {7/8} # 13 {3/4} # 10 {7/8} # 17 {3/4} # {7/8} # 21 {3/4} # 2 {7/8}
2 # V # 6 # VII # 10 # IX # 14 # XI # 18 # I # 22 # III
2 {1/4} # 5 {1/8} # 6 {1/4} # 7 {1/8} # 10 {1/4} # 9 {1/8} # 14 {1/4} # 11 {1/8} # 18 {1/4} # 1 {1/8} # 22 {1/4} # 3 {1/8}
2 {1/2} # 5 {1/4} # 6 {1/2} # 7 {1/4} # 10 {1/2} # 9 {1/4} # 14 {1/2} # 11 {1/4} # 18 {1/2} # 1 {1/4} # 22 {1/2} # 3 {1/4}
2 {3/4} # 5 {3/8} # 6 {3/4} # 7 {3/8} # 10 {3/4} # 9 {3/8} # 14 {3/4} # 11 {3/8} # 10 {3/4} # 1 {3/8} # 22 {3/4} # 3 {3/8}
3 # 5 {1/2} # 7 # 7 {1/2} # 11 # 9 {1/2} # 15 # 11 {1/2} # 19 # 1 {1/2} # 23 # 3 {1/2}
3 {1/4} # 5 {5/8} # 7 {1/4} # 7 {5/8} # 11 {1/4} # 9 {5/8} # 15 {1/4} # 11 {5/8} # 19 {1/4} # 1 {5/8} # 23 {1/4} # 3 {5/8}
3 {1/2} # 5 {3/4} # 7 {1/2} # 7 {3/4} # 11 {1/2} # 9 {3/4} # 15 {1/2} # 11 {3/4} # 19 {1/2} # 1 {3/4} # 23 {1/2} # 3 {3/4}
3 {3/4} # 5 {7/8} # 7 {3/4} # 7 {7/8} # 11 {3/4} # 9 {7/8} # 15 {3/4} # 11 {7/8} # 19 {3/4} # 1 {7/8} # 23 {3/4} # 3 {7/8}
4 # VI # 8 # VIII # 12 # X # 16 # XII # 20 # II # 24 # IIII
</note>
<p style="it">
  <s xml:id="echoid-s4062" xml:space="preserve">In horologio, quod circulo horæ 8. </s>
  <s xml:id="echoid-s4063" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quar umlibet duarum horarum huius ta-<lb/>bulæ parallelæ ſunt, vt patet ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4064" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4065" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div238" type="section" level="1" n="86">
<head xml:id="echoid-head89" xml:space="preserve">Linea horæ 7. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte
{1/4} # 3 {5/8} # 4 {1/4} # 5 {5/8} # 8 {1/4} # 7 {5/8} # 12 {1/4} # 9 {5/8} # 16 {1/4} # 11 {5/8} # 20 {1/4} # 1 {5/8}
{1/2} # 3 {3/4} # 4 {1/2} # 5 {3/4} # 8 {1/2} # 7 {3/4} # 12 {1/2} # 9 {3/4} # 16 {1/2} # 11 {3/4} # 20 {1/2} # 1 {3/4}
{3/4} # 3 {7/8} # 4 {3/4} # 5 {7/8} # 8 {3/4} # 7 {7/8} # 12 {3/4} # 9 {7/8} # 16 {3/4} # 11 {7/8} # 20 {3/4} # 1 {7/8}
1 # IIII # 5 # VI # 9 # VIII # 13 # X # 17 # XII # 21 # II
1 {1/4} # 4 {1/8} # 5 {1/4} # 6 {1/8} # 9 {1/4} # 8 {1/8} # 13 {1/4} # 10 {1/8} # 17 {1/4} # {1/8} # 21 {1/4} # 2 {1/8}
1 {1/2} # 4 {1/4} # 5 {1/2} # 6 {1/4} # 9 {1/2} # 8 {1/4} # 13 {1/2} # 10 {1/4} # 17 {1/2} # {1/4} # 21 {1/2} # 2 {1/4}
1 {3/4} # 4 {3/8} # 5 {3/4} # 6 {3/8} # 9 {3/4} # 8 {3/8} # 13 {3/4} # 10 {3/8} # 17 {3/4} # {3/8} # 21 {3/4} # 2 {3/8}
2 # 4 {1/2} # 6 # 6 {1/2} # 10 # 8 {1/2} # 14 # 10 {1/2} # 18 # {1/2} # 22 # 2 {1/2}
2 {1/4} # 4 {5/8} # 6 {1/4} # 6 {5/8} # 10 {1/4} # 8 {5/8} # 14 {1/4} # 10 {5/8} # 18 {1/4} # {5/8} # 22 {1/4} # 2 {5/8}
2 {1/2} # 4 {3/4} # 6 {1/2} # 6 {3/4} # 10 {1/2} # 8 {3/4} # 14 {1/2} # 10 {3/4} # 18 {1/2} # {3/4} # 22 {1/2} # 2 {3/4}
2 {3/4} # 4 {7/8} # 6 {3/4} # 6 {7/8} # 10 {3/4} # 8 {7/8} # 14 {3/4} # 10 {7/8} # 18 {3/4} # {7/8} # 22 {3/4} # 2 {7/8}
3 # V # 7 # VII # 11 # IX # 15 # XI # 19 # I # 23 # III
3 {1/4} # 5 {1/8} # 7 {1/4} # 7 {1/8} # 11 {1/4} # 9 {1/8} # 15 {1/4} # 11 {1/8} # 19 {1/4} # 1 {1/8} # 23 {1/4} # 3 {1/8}
3 {1/2} # 5 {1/4} # 7 {1/2} # 7 {1/4} # 11 {1/2} # 9 {1/4} # 15 {1/2} # 11 {1/4} # 19 {1/2} # 1 {1/4} # 23 {1/2} # 3 {1/4}
3 {3/4} # 5 {3/8} # 7 {3/4} # 7 {3/8} # 11 {3/4} # 9 {3/8} # 15 {3/4} # 11 {3/8} # 19 {3/4} # 1 {3/8} # 23 {3/4} # 3 {3/8}
4 # 5 {1/2} # 8 # 7 {1/2} # 12 # 9 {1/2} # 16 # 11 {1/2} # 20 # 1 {1/2} # 24 # 3 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4066" xml:space="preserve">In horologio, quod circulo horæ 7. </s>
  <s xml:id="echoid-s4067" xml:space="preserve">ab ortu vel occaſu æquidistat, lineæ quarumuis duarum horarum huius <lb/>tabulæ ſunt parallelæ, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s4068" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4069" xml:space="preserve">dcmonſtr auimus.</s>
  <s xml:id="echoid-s4070" xml:space="preserve"/>
</p>
<pb o="69" file="0089" n="89" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div239" type="section" level="1" n="87">
<head xml:id="echoid-head90" xml:space="preserve">Linea horæ 6. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridi \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 3 {1/8} # 4 {1/4} # 5 {1/8} # 8 {1/4} # 7 {1/8} # 12 {1/4} # 9 {1/8} # 16 {1/4} # 11 {1/8} # 20 {1/4} # 1 {1/8}
{1/2} # 3 {1/4} # 4 {1/2} # 5 {1/4} # 8 {1/2} # 7 {1/4} # 12 {1/2} # 9 {1/4} # 16 {1/2} # 11 {1/4} # 20 {1/2} # 1 {1/4}
{3/4} # 3 {3/8} # 4 {3/4} # 5 {3/8} # 8 {3/4} # 7 {3/8} # 12 {3/4} # 9 {3/8} # 16 {3/4} # 11 {3/8} # 20 {3/4} # 1 {3/8}
1 # 3 {1/2} # 5 # 5 {1/2} # 9 # 7 {1/2} # 13 # 9 {1/2} # 17 # 11 {1/2} # 21 # 1 {1/2}
1 {1/4} # 3 {5/8} # 5 {1/4} # 5 {5/8} # 9 {1/4} # 7 {5/8} # 13 {1/4} # 9 {5/8} # 17 {1/4} # 11 {5/8} # 21 {1/4} # 1 {5/8}
1 {1/2} # 3 {3/4} # 5 {1/2} # 5 {3/4} # 9 {1/2} # 7 {3/4} # 13 {1/2} # 9 {3/4} # 17 {1/2} # 11 {3/4} # 21 {1/2} # 1 {3/4}
1 {3/4} # 3 {7/8} # 5 {3/4} # 5 {7/8} # 9 {3/4} # 7 {7/8} # 13 {3/4} # 9 {7/8} # 17 {3/4} # 11 {7/8} # 21 {3/4} # 1 {7/8}
2 # IIII # 6 # VI # 10 # VIII # 14 # X # 18 # XII # 22 # II
2 {1/4} # 4 {1/8} # 6 {1/4} # 6 {1/8} # 10 {1/4} # 8 {1/8} # 14 {1/4} # 10 {1/8} # 18 {1/4} # {1/8} # 22 {1/4} # 2 {1/8}
2 {1/2} # 4 {1/4} # 6 {1/2} # 6 {1/4} # 10 {1/2} # 8 {1/4} # 14 {1/2} # 10 {1/4} # 18 {1/2} # {1/4} # 22 {1/2} # 2 {1/4}
2 {3/4} # 4 {3/8} # 6 {3/4} # 6 {3/8} # 10 {3/4} # 8 {3/8} # 14 {3/4} # 10 {3/8} # 18 {3/4} # {3/8} # 22 {3/4} # 2 {3/8}
3 # 4 {1/2} # 7 # 6 {1/2} # 11 # 8 {1/2} # 15 # 10 {1/2} # 19 # {1/2} # 23 # 2 {1/2}
3 {1/4} # 4 {5/8} # 7 {1/4} # 6 {5/8} # 11 {1/4} # 8 {5/8} # 15 {1/4} # 10 {5/8} # 19 {1/4} # {5/8} # 23 {1/4} # 2 {5/8}
3 {1/2} # 4 {3/4} # 7 {1/2} # 6 {3/4} # 11 {1/2} # 8 {3/4} # 15 {1/2} # 10 {3/4} # 19 {1/2} # {3/4} # 23 {1/2} # 2 {3/4}
3 {3/4} # 4 {7/8} # 7 {3/4} # 6 {7/8} # 11 {3/4} # 8 {7/8} # 15 {3/4} # 10 {7/8} # 19 {3/4} # {7/8} # 23 {3/4} # 2 {7/8}
4 # V # 8 # VII # 12 # IX # 16 # XI # 20 # I # 24 # III
</note>
<p style="it">
  <s xml:id="echoid-s4071" xml:space="preserve">In horologio, quod circulo horæ 10. </s>
  <s xml:id="echoid-s4072" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumuis duarum horarum huius ta-<lb/>bulæ, ſunt parallelæ, vt patet ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4073" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4074" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div240" type="section" level="1" n="88">
<head xml:id="echoid-head91" xml:space="preserve">Linea horæ 5. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horę ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte
{1/4} # 2 {5/8} # 4 {1/4} # 4 {5/8} # 8 {1/4} # 6 {5/8} # 12 {1/4} # 8 {5/8} # 16 {1/4} # 10 {5/8} # 20 {1/4} # {5/8}
{1/2} # 2 {3/4} # 4 {1/2} # 4 {3/4} # 8 {1/2} # 6 {3/4} # 12 {1/2} # 8 {3/4} # 16 {1/2} # 10 {3/4} # 20 {1/2} # {3/4}
{3/4} # 2 {7/8} # 4 {3/4} # 4 {7/8} # 8 {3/4} # 6 {7/8} # 12 {3/4} # 8 {7/8} # 16 {3/4} # 10 {7/8} # 20 {3/4} # {7/8}
1 # III # 5 # V # 9 # VII # 13 # IX # 17 # XI # 21 # I
1 {1/4} # 3 {1/8} # 5 {1/4} # 5 {1/8} # 9 {1/4} # 7 {1/8} # 13 {1/4} # 9 {1/8} # 17 {1/4} # 11 {1/8} # 21 {1/4} # 1 {1/8}
1 {1/2} # 3 {1/4} # 5 {1/2} # 5 {1/4} # 9 {1/2} # 7 {1/4} # 13 {1/2} # 9 {1/4} # 17 {1/2} # 11 {1/4} # 21 {1/2} # 1 {1/4}
1 {3/4} # 3 {3/8} # 5 {3/4} # 5 {3/8} # 9 {3/4} # 7 {3/8} # 13 {3/4} # 9 {3/8} # 17 {3/4} # 11 {3/8} # 21 {3/4} # 1 {3/8}
2 # 3 {1/2} # 6 # 5 {1/2} # 10 # 7 {1/2} # 14 # 9 {1/2} # 18 # 11 {1/2} # 22 # 1 {1/2}
2 {1/4} # 3 {5/8} # 6 {1/4} # 5 {5/8} # 10 {1/4} # 7 {5/8} # 14 {1/4} # 9 {5/8} # 18 {1/4} # 11 {5/8} # 22 {1/4} # 1 {5/8}
2 {1/2} # 3 {3/4} # 6 {1/2} # 5 {3/4} # 10 {1/2} # 7 {3/4} # 14 {1/2} # 9 {3/4} # 18 {1/2} # 11 {3/4} # 22 {1/2} # 1 {3/4}
2 {3/4} # 3 {7/8} # 6 {3/4} # 5 {7/8} # 10 {3/4} # 7 {7/8} # 14 {3/4} # 9 {7/8} # 18 {3/4} # 11 {7/8} # 22 {3/4} # 1 {7/8}
3 # IIII # 7 # VI # 11 # VIII # 15 # X # 19 # XII # 23 # II
3 {1/4} # 4 {1/8} # 7 {1/4} # 6 {1/8} # 11 {1/4} # 8 {1/8} # 15 {1/4} # 10 {1/8} # 19 {1/4} # {1/8} # 23 {1/4} # 2 {1/8}
3 {1/2} # 4 {1/4} # 7 {1/2} # 6 {1/4} # 11 {1/2} # 8 {1/4} # 15 {1/2} # 10 {1/4} # 19 {1/2} # {1/4} # 23 {1/2} # 2 {1/4}
3 {3/4} # 4 {3/8} # 7 {3/4} # 6 {3/8} # 11 {3/4} # 8 {3/8} # 15 {3/4} # 10 {3/8} # 19 {3/4} # {3/8} # 23 {3/4} # 2 {3/8}
4 # 4 {1/2} # 8 # 6 {1/2} # 12 # 8 {1/2} # 16 # 10 {1/2} # 20 # {1/2} # 24 # 2 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4075" xml:space="preserve">In horologio, quod circulo boræ 5. </s>
  <s xml:id="echoid-s4076" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineę quar umlibet duarum horarum huius ta-<lb/>bulæ ſunt parallelæ, exĳs, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s4077" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4078" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s4079" xml:space="preserve"/>
</p>
<pb o="70" file="0090" n="90" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div241" type="section" level="1" n="89">
<head xml:id="echoid-head92" xml:space="preserve">Linea horæ 4. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte
{1/4} # 2 {1/8} # 4 {1/4} # 4 {1/8} # 8 {1/4} # 6 {1/8} # 12 {1/4} # 8 {1/8} # 16 {1/4} # 10 {1/8} # 20 {1/4} # {1/8}
{1/2} # 2 {1/4} # 4 {1/2} # 4 {1/4} # 8 {1/2} # 6 {1/4} # 12 {1/2} # 8 {1/4} # 16 {1/2} # 10 {1/4} # 20 {1/2} # {1/4}
{3/4} # 2 {3/8} # 4 {3/4} # 4 {3/8} # 8 {3/4} # 6 {3/8} # 12 {3/4} # 8 {3/8} # 16 {3/4} # 10 {3/8} # 20 {3/4} # {3/8}
1 # 2 {1/2} # 5 # 4 {1/2} # 9 # 6 {1/2} # 13 # 8 {1/2} # 17 # 10 {1/2} # 21 # {1/2}
1 {1/4} # 2 {5/8} # 5 {1/4} # 4 {3/8} # 9 {1/4} # 6 {3/8} # 13 {1/4} # 8 {5/8} # 17 {1/4} # 10 {5/8} # 21 {1/4} # {5/8}
1 {1/2} # 2 {3/4} # 5 {1/2} # 4 {3/4} # 9 {1/2} # 6 {3/4} # 13 {1/2} # 8 {3/4} # 17 {1/2} # 10 {3/4} # 21 {1/2} # {3/4}
1 {3/4} # 2 {7/8} # 5 {3/4} # 4 {7/8} # 9 {3/4} # 6 {7/8} # 13 {3/4} # 8 {7/8} # 17 {3/4} # 10 {7/8} # 21 {3/4} # {7/8}
2 # III # 6 # V # 10 # VII # 14 # IX # 18 # XI # 22 # I
2 {1/4} # 3 {1/8} # 6 {1/4} # 5 {1/8} # 10 {1/4} # 7 {1/8} # 14 {1/4} # 9 {1/8} # 18 {1/4} # 11 {1/8} # 22 {1/4} # 1 {1/8}
2 {1/2} # 3 {1/4} # 6 {1/2} # 5 {1/4} # 10 {1/2} # 7 {1/4} # 14 {1/2} # 9 {1/4} # 18 {1/2} # 11 {1/4} # 22 {1/2} # 1 {1/4}
2 {3/4} # 3 {3/8} # 6 {3/4} # 5 {3/8} # 10 {3/4} # 7 {3/8} # 14 {3/4} # 9 {3/8} # 18 {3/4} # 11 {3/8} # 22 {3/4} # 1 {3/8}
3 # 3 {1/2} # 7 # 5 {1/2} # 11 # 7 {1/2} # 15 # 9 {1/2} # 19 # 11 {1/2} # 23 # 1 {1/2}
3 {1/4} # 3 {5/8} # 7 {1/4} # 5 {5/8} # 11 {1/4} # 7 {5/8} # 15 {1/4} # 9 {5/8} # 19 {1/4} # 11 {5/8} # 23 {1/4} # 1 {5/8}
3 {1/2} # 3 {3/4} # 7 {1/2} # 5 {3/4} # 11 {1/2} # 7 {3/4} # 15 {1/2} # 9 {3/4} # 19 {1/2} # 11 {3/4} # 23 {1/2} # 1 {3/4}
3 {3/4} # 3 {7/8} # 7 {3/4} # 5 {7/8} # 11 {3/4} # 7 {7/8} # 15 {3/4} # 9 {7/8} # 19 {3/4} # 11 {7/8} # 23 {3/4} # 1 {7/8}
4 # IIII # 8 # VI # 12 # VIII # 16 # X # 20 # XII # 24 # II
</note>
<p style="it">
  <s xml:id="echoid-s4080" xml:space="preserve">In horologio, quod circulo horæ 4. </s>
  <s xml:id="echoid-s4081" xml:space="preserve">ab ortu vel occaſu æquidiſtat, lineæ quarumlibet duarum horarum huius ta-<lb/>bulæ parallelæ ſunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4082" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4083" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div242" type="section" level="1" n="90">
<head xml:id="echoid-head93" xml:space="preserve">Linea horæ 3. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte
{1/4} # 1 {5/8} # 4 {1/4} # 3 {5/8} # 8 {1/4} # 5 {5/8} # 12 {1/4} # 7 {5/8} # 16 {1/4} # 9 {5/8} # 20 {1/4} # 11 {5/8}
{1/2} # 1 {3/4} # 4 {1/2} # 3 {3/4} # 8 {1/2} # 5 {3/4} # 12 {1/2} # 7 {3/4} # 16 {1/2} # 9 {3/4} # 20 {1/2} # 11 {3/4}
{3/4} # 1 {7/8} # 4 {3/4} # 3 {7/8} # 8 {3/4} # 5 {7/8} # 12 {3/4} # 7 {7/8} # 16 {3/4} # 9 {7/8} # 20 {3/4} # 11 {7/8}
I # II # 5 # II II # 9 # VI # 13 # VIII # 17 # X # 21 # XII
1 {1/4} # 2 {1/8} # 5 {1/4} # 4 {1/8} # 9 {1/4} # 6 {1/8} # 13 {1/4} # 8 {1/8} # 17 {1/4} # 10 {1/8} # 21 {1/4} # {1/8}
1 {1/2} # 2 {1/4} # 5 {1/2} # 4 {1/4} # 9 {1/2} # 6 {1/4} # 13 {1/2} # 8 {1/4} # 17 {1/2} # 10 {1/4} # 21 {1/2} # {1/4}
1 {3/4} # 2 {3/8} # 5 {3/4} # 4 {3/8} # 9 {3/4} # 6 {3/8} # 13 {3/4} # 8 {3/8} # 17 {3/4} # 10 {3/8} # 21 {3/4} # {3/8}
2 # 2 {1/2} # 6 # 4 {1/2} # 10 # 6 {1/2} # 14 # 8 {1/2} # 18 # 10 {1/2} # 22 # {1/2}
2 {1/4} # 2 {5/8} # 6 {1/4} # 4 {5/8} # 10 {1/4} # 6 {5/8} # 14 {1/4} # 8 {5/8} # 18 {1/4} # 10 {5/8} # 22 {1/4} # {5/8}
2 {1/2} # 2 {3/4} # 6 {1/2} # 4 {3/4} # 10 {1/2} # 6 {3/4} # 14 {1/2} # 8 {3/4} # 18 {1/2} # 10 {3/4} # 22 {1/2} # {3/4}
2 {3/4} # 2 {7/8} # 6 {3/4} # 4 {7/8} # 10 {3/4} # 6 {7/8} # 14 {3/4} # 8 {7/8} # 18 {3/4} # 10 {7/8} # 22 {3/4} # {7/8}
3 # III # 7 # V # 11 # VII # 15 # IX # 19 # XI # 23 # I
3 {1/4} # 3 {1/8} # 7 {1/4} # 5 {1/8} # 11 {1/4} # 7 {1/8} # 15 {1/4} # 9 {1/8} # 19 {1/4} # 11 {1/8} # 23 {1/4} # 1 {1/8}
3 {1/2} # 3 {1/4} # 7 {1/2} # 5 {1/4} # 11 {1/2} # 7 {1/4} # 15 {1/2} # 9 {1/4} # 19 {1/2} # 11 {1/4} # 23 {1/2} # 1 {1/4}
3 {3/4} # 3 {3/8} # 7 {3/4} # 5 {3/8} # 11 {3/4} # 7 {3/8} # 15 {3/4} # 9 {3/8} # 19 {3/4} # 11 {3/8} # 23 {3/4} # 1 {3/8}
4 # 3 {1/2} # 8 # 5 {1/2} # 12 # 7 {1/2} # 16 # 9 {1/2} # 20 # 11 {1/2} # 24 # 1 {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4084" xml:space="preserve">In horologio, quod circulo horæ 3. </s>
  <s xml:id="echoid-s4085" xml:space="preserve">ab ortu vel occaſu æquidistat, lineæ quarumlibet duarum horarum huius <lb/>tabulæ ſunt parallelæ, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4086" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4087" xml:space="preserve"/>
</p>
<pb o="71" file="0091" n="91" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div243" type="section" level="1" n="91">
<head xml:id="echoid-head94" xml:space="preserve">Linea horæ 2. ab ortu vel occaſu.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte
{1/4} # 1 {1/8} # 4 {1/4} # 3 {1/8} # 8 {1/4} # 5 {1/8} # 12 {1/4} # 7 {1/8} # 16 {1/4} # 9 {1/8} # 20 {1/4} # 11 {1/8}
{1/2} # 1 {1/4} # 4 {1/2} # 3 {1/4} # 8 {1/2} # 5 {1/4} # 12 {1/2} # 7 {1/4} # 16 {1/2} # 9 {1/4} # 20 {1/2} # 11 {1/4}
{3/4} # 1 {3/5} # 4 {3/4} # 3 {3/8} # 8 {3/4} # 5 {3/8} # 12 {3/4} # 7 {3/8} # 16 {3/4} # 9 {3/8} # 20 {3/4} # 11 {3/8}
1 # 1 {1/2} # 5 # 3 {1/2} # 9 # 5 {1/2} # 13 # 7 {1/2} # 17 # 9 {1/2} # 21 # 11 {1/2}
1 {1/4} # 1 {5/8} # 5 {1/4} # 3 {5/8} # 9 {1/4} # 5 {5/8} # 13 {1/4} # 7 {5/8} # 17 {1/4} # 9 {5/8} # 21 {1/4} # 11 {5/8}
1 {1/2} # 1 {3/4} # 5 {1/2} # 3 {3/4} # 9 {1/2} # 5 {3/4} # 13 {1/2} # 7 {3/4} # 17 {1/2} # 9 {3/4} # 21 {1/2} # 11 {3/4}
1 {3/4} # 1 {7/8} # 5 {3/4} # 3 {7/8} # 9 {3/4} # 5 {7/8} # 13 {3/4} # 7 {7/8} # 17 {3/4} # 9 {7/8} # 21 {3/4} # 11 {7/8}
2 # II # 6 # IIII # 10 # VI # 14 # VIII # 18 # X # 22 # XII
2 {1/4} # 2 {1/8} # 6 {1/4} # 4 {1/8} # 10 {1/4} # 6 {1/8} # 14 {1/4} # 8 {1/8} # 18 {1/4} # 10 {1/8} # 22 {1/4} # 12 {1/8}
2 {1/2} # 2 {1/4} # 6 {1/2} # 4 {1/4} # 10 {1/2} # 6 {1/4} # 14 {1/2} # 8 {1/4} # 18 {1/2} # 10 {1/4} # 22 {1/2} # 12 {1/4}
2 {3/4} # 2 {3/8} # 6 {3/4} # 4 {3/8} # 10 {3/4} # 6 {3/8} # 14 {3/4} # 8 {3/8} # 18 {3/4} # 10 {3/8} # 22 {3/4} # 12 {3/8}
3 # 2 {1/2} # 7 # 4 {1/2} # 11 # 6 {1/2} # 15 # 8 {1/2} # 19 # 10 {1/2} # 23 # 12 {1/2}
3 {1/4} # 2 {5/8} # 7 {1/4} # 4 {5/8} # 11 {1/4} # 6 {5/8} # 15 {1/4} # 8 {5/8} # 19 {1/4} # 10 {5/8} # 23 {1/4} # 12 {5/8}
3 {1/2} # 2 {3/4} # 7 {1/2} # 4 {3/4} # 11 {1/2} # 6 {3/4} # 15 {1/2} # 8 {3/4} # 19 {1/2} # 10 {3/4} # 23 {1/2} # 1 {3/4}
3 {3/4} # 2 {7/8} # 7 {3/4} # 4 {7/8} # 11 {3/4} # 6 {7/8} # 15 {3/4} # 8 {7/8} # 19 {3/4} # 10 {7/8} # 23 {3/4} # 1 {7/8}
4 # III # 8 # V # 12 # VII # 16 # IX # 20 # XI # 24 {4/4}<unsure/> # I</note>
</div>
<div xml:id="echoid-div244" type="section" level="1" n="92">
<head xml:id="echoid-head95" xml:space="preserve">In horologio, quod circulo horæ 2. ab ortu vel occaſu æquidiſtat, lineæ quarumlibet duarum horarum huius ta- \\ bulæ ſunt parallelæ, vt ex ſcholio propoſ. 22. patet.</head>
</div>
<div xml:id="echoid-div245" type="section" level="1" n="93">
<head xml:id="echoid-head96" xml:space="preserve">Linea horæ 1. ab ortu vel occaſu.</head>
  <note position="left" xml:space="preserve">
Horæ ab ortu \\ vel occaſu. # Horę à meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte<unsure/> # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horę a meridie \\ vel media nocte # Horæ ab ortu \\ vel occaſu. # Horæ a meridie \\ vel media nocte
{1/4} # {5/8} # 4 {1/4} # 2 {5/8} # 8 {1/4} # 4 {5/8} # 12 {1/4} # 6 {5/8} # 16 {1/4} # 8 {5/8} # 20 {1/4} # 10 {5/8}
{1/2} # {3/4} # 4 {1/2} # 2 {3/4} # 8 {1/2} # 4 {3/4} # 12 {1/2} # 6 {3/4} # 16 {1/2} # 8 {3/4} # 20 {1/2} # 10 {3/4}
{3/4} # {7/8} # 4 {3/4} # 2 {7/8} # 8 {3/4} # 4 {7/8} # 12 {3/4} # 6 {7/8} # 16 {3/4} # 8 {7/8} # 20 {3/4} # 10 {7/8}
1 # I # 5 # III # 9 # V # 13 # VII # 17 # IX # 21 # XI
1 {1/4} # 1 {1/8} # 5 {1/4} # 3 {1/8} # 9 {1/4} # 5 {1/8} # 13 {1/4} # 7 {1/8} # 17 {1/4} # 9 {1/8} # 21 {1/4} # 11 {1/8}
1 {1/2} # 1 {1/4} # 5 {1/2} # 3 {1/4} # 9 {1/2} # 5 {1/4} # 13 {1/2} # 7 {1/4} # 17 {1/2} # 9 {1/4} # 21 {1/2} # 11 {1/4}
1 {3/4} # 1 {3/8} # 5 {3/4} # 3 {3/8} # 9 {3/4} # 5 {3/8} # 13 {3/4} # 7 {3/8} # 17 {3/4} # 9 {3/8} # 21 {3/4} # 11 {3/8}
2 # 1 {1/2} # 6 # 3 {1/2} # 10 # 5 {1/2} # 14 # 7 {1/2} # 18 # 9 {1/2} # 22 # 11 {1/2}
2 {1/4} # 1 {5/8} # 6 {1/4} # 3 {5/8} # 10 {1/4} # 5 {5/8} # 14 {1/4} # 7 {5/8} # 18 {1/4} # 9 {5/8} # 22 {1/4} # 11 {5/8}
2 {1/2} # 1 {3/4} # 6 {1/2} # 3 {3/4} # 10 {1/2} # 5 {3/4} # 14 {1/2} # 7 {3/4} # 18 {1/2} # 9 {3/4} # 22 {1/2} # 11 {3/4}
2 {3/4} # 1 {7/8} # 6 {3/4} # 3 {7/8} # 10 {3/4} # 5 {7/8} # 14 {3/4} # 7 {7/8} # 18 {3/4} # 9 {7/8} # 22 {3/4} # 11 {7/8}
3 # II # 7 # IIII # 11 # VI # 15 # VIII # 19 # X # 23 # XII
3 {1/4} # 2 {1/8} # 7 {1/4} # 4 {1/8} # 11 {1/4} # 6 {1/8} # 15 {1/4} # 8 {1/8} # 19 {1/4} # 10 {1/8} # 23 {1/4} # {1/8}
3 {1/2} # 2 {1/4} # 7 {1/2} # 4 {1/4} # 11 {1/2} # 6 {1/4} # 15 {1/2} # 8 {1/4} # 19 {1/2} # 10 {1/4} # 23 {1/2} # {1/4}
3 {3/4} # 2 {3/8} # 7 {3/4} # 4 {3/8} # 11 {3/4} # 6 {3/8} # 15 {3/4} # 8 {3/8} # 19 {3/4} # 10 {3/8} # 23 {3/4} # {3/8}
4 # 2 {1/2} # 8 # 4 {1/2} # 12 # 6 {1/2} # 16 # 8 {1/2} # 20 # 10 {1/2} # 24 # {1/2}
</note>
<p style="it">
  <s xml:id="echoid-s4088" xml:space="preserve">In horologio, quod circulo horæ 1. </s>
  <s xml:id="echoid-s4089" xml:space="preserve">ab ortu vel occaſu æquidistat, lineæ quarumlibet duarum horarum huius <lb/>tabulæ ſunt parallelæ, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s4090" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4091" xml:space="preserve">demonstratum eſt à nobis.</s>
  <s xml:id="echoid-s4092" xml:space="preserve"/>
</p>
<pb o="72" file="0092" n="92" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div246" type="section" level="1" n="94">
<head xml:id="echoid-head97" xml:space="preserve">Linea horæ 11. a meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 21 {3/4} # 4 {1/4} # 17 {3/4} # 8 {1/4} # 13 {3/4} # 12 {1/4} # 9 {3/4} # 16 {1/4} # 5 {3/4} # 20 {1/4} # 1 {3/4}
{1/2} # 21 {1/2} # 4 {1/2} # 17 {1/2} # 8 {1/2} # 13 {1/2} # 12 {1/2} # 9 {1/2} # 16 {1/2} # 5 {1/2} # 20 {1/2} # 1 {1/2}
{3/4} # 21 {1/4} # 4 {3/4} # 17 {1/4} # 8 {3/4} # 13 {1/4} # 12 {3/4} # 9 {1/4} # 16 {3/4} # 5 {1/4} # 20 {3/4} # 1 {1/4}
1 # 21 # 5 # 17 # 9 # 13 # 13 # 9 # 17 # 5 # 21 # 1
1 {1/4} # 20 {3/4} # 5 {1/4} # 16 {3/4} # 9 {1/4} # 12 {3/4} # 13 {1/4} # 8 {3/4} # 17 {1/4} # 4 {3/4} # 21 {1/4} # {3/4}
1 {1/2} # 20 {1/2} # 5 {1/2} # 16 {1/2} # 9 {1/2} # 12 {1/2} # 13 {1/2} # 8 {1/2} # 17 {1/2} # 4 {1/2} # 21 {1/2} # {1/2}
1 {3/4} # 20 {1/4} # 5 {3/4} # 16 {1/4} # 9 {3/4} # 12 {1/4} # 13 {3/4} # 8 {1/4} # 17 {3/4} # 4 {1/4} # 21 {3/4} # {1/4}
2 # 20 # 6 # 16 # 10 # 12 # 14 # 8 # 18 # 4 # 22 # 24
2 {1/4} # 19 {3/4} # 6 {1/4} # 15 {3/4} # 10 {1/4} # 11 {3/4} # 14 {1/4} # 7 {3/4} # 18 {1/4} # 3 {3/4} # 22 {1/4} # 23 {3/4}
2 {1/2} # 19 {1/2} # 6 {1/2} # 15 {1/2} # 10 {1/2} # 11 {1/2} # 14 {1/2} # 7 {1/2} # 18 {1/2} # 3 {1/2} # 22 {1/2} # 23 {1/2}
2 {3/4} # 19 {1/4} # 6 {3/4} # 15 {1/4} # 10 {3/4} # 11 {1/4} # 14 {3/4} # 7 {1/4} # 18 {3/4} # 3 {1/4} # 22 {3/4} # 23 {1/4}
3 # 19 # 7 # 15 # II # 11 # 15 # 7 # 19 # 3 # 23 # 23
3 {1/4} # 18 {3/4} # 7 {1/4} # 14 {3/4} # 11 {1/4} # 10 {3/4} # 15 {1/4} # 6 {3/4} # 19 {1/4} # 2 {3/4} # 23 {1/4} # 22 {3/4}
3 {1/2} # 18 {1/2} # 7 {1/2} # 14 {1/2} # 11 {1/2} # 10 {1/2} # 15 {1/2} # 6 {1/2} # 19 {1/2} # 2 {1/2} # 23 {1/2} # 22 {1/2}
3 {3/4} # 18 {1/4} # 7 {3/4} # 14 {1/4} # 11 {3/4} # 10 {1/4} # 15 {3/4} # 6 {1/4} # 19 {3/4} # 2 {1/4} # 23 {3/4} # 22 {1/4}
4 # 18 # 8 # 14 # 12 # 10 # 16 # 6 # 20 # 2 # 24 # 22</note>
</div>
<div xml:id="echoid-div247" type="section" level="1" n="95">
<head xml:id="echoid-head98" xml:space="preserve">In horologio, quod circulo horæ 11. à meridie vel media nocte æquidiſtat, lineæ quarumuis duarum horarum \\ huius tabulæ ſunt parallelæ, vt conſtat ex ſcholio propoſ. 22.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div248" type="section" level="1" n="96">
<head xml:id="echoid-head99" xml:space="preserve">Linea horæ 10. à meridie vel media nocte.</head>
<note position="left" xml:space="preserve">
Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 19 {3/4} # 4 {1/4} # 15 {3/4} # 8 {1/4} # 11 {3/4} # 12 {1/4} # 7 {3/4} # 16 {1/4} # 3 {3/4} # 20 {1/4} # 23 {3/4}
{1/2} # 19 {1/2} # 4 {1/2} # 15 {1/2} # 8 {1/2} # 11 {1/2} # 12 {1/2} # 7 {1/2} # 16 {1/2} # 3 {1/2} # 20 {1/2} # 23 {1/2}
{3/4} # 19 {1/4} # 4 {3/4} # 15 {1/4} # 8 {3/4} # 11 {1/4} # 12 {3/4} # 7 {1/4} # 16 {3/4} # 3 {1/4} # 20 {3/4} # 23 {1/4}
1 # 19 # 5 # 15 # 9 # 11 # 13 # 7 # 17 # 3 # 21 # 23
1 {1/4} # 18 {3/4} # 5 {1/4} # 14 {3/4} # 9 {1/4} # 10 {3/4} # 13 {1/4} # 6 {3/4} # 17 {1/4} # 2 {3/4} # 21 {1/4} # 22 {3/4}
1 {1/2} # 18 {1/2} # 5 {1/2} # 14 {1/2} # 9 {1/2} # 10 {1/2} # 13 {1/2} # 6 {1/2} # 17 {1/2} # 2 {1/2} # 21 {1/2} # 22 {1/2}
1 {3/4} # 18 {1/4} # 5 {3/4} # 14 {1/4} # 9 {3/4} # 10 {1/4} # 13 {3/4} # 6 {1/4} # 17 {3/4} # 2 {1/4} # 21 {3/4} # 22 {1/4}
2 # 18 # 6 # 14 # 10 # 10 # 14 # 6 # 18 # 2 # 22 # 22
2 {1/4} # 17 {3/4} # 6 {1/4} # 13 {3/4} # 10 {1/4} # 9 {3/4} # 14 {1/4} # 5 {3/4} # 18 {1/4} # 1 {3/4} # 22 {1/4} # 21 {3/4}
2 {1/2} # 17 {1/2} # 6 {1/2} # 13 {1/2} # 10 {1/2} # 9 {1/2} # 14 {1/2} # 5 {1/2} # 18 {1/2} # 1 {1/2} # 22 {1/2} # 21 {1/2}
2 {3/4} # 17 {1/4} # 6 {3/4} # 13 {1/4} # 10 {3/4} # 9 {1/4} # 14 {3/4} # 5 {1/4} # 18 {3/4} # 1 {1/4} # 22 {3/4} # 21 {1/4}
3 # 17 # 7 # 13 # 11 # 9 # 15 # 5 # 19 # 1 # 23 # 21
3 {1/4} # 16 {3/4} # 7 {1/4} # 12 {3/4} # 11 {1/4} # 8 {3/4} # 15 {1/4} # 4 {3/4} # 19 {1/4} # {3/4} # 23 {1/4} # 20 {3/4}
3 {1/2} # 16 {1/2} # 7 {1/2} # 12 {1/2} # 11 {1/2} # 8 {1/2} # 15 {1/2} # 4 {1/2} # 19 {1/2} # {1/2} # 23 {1/2} # 20 {1/2}
3 {3/4} # 16 {1/4} # 7 {3/4} # 12 {1/4} # 11 {3/4} # 8 {1/4} # 15 {3/4} # 4 {1/4} # 19 {3/4} # {1/4} # 23 {3/4} # 20 {1/4}
4 # 16 # 8 # 12 # 12 # 8 # 16 # 4 # 20 # 24 # 24 # 20
</note>
<p style="it">
  <s xml:id="echoid-s4093" xml:space="preserve">In horologio, quod circulo horæ 10. </s>
  <s xml:id="echoid-s4094" xml:space="preserve">à meridie vel media nocte æquidistat, lineæ quarumlibet duarum ho-<lb/>rarum huius tabulæ ſunt parallelæ, vt perſpicuum eſt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4095" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4096" xml:space="preserve"/>
</p>
<pb o="73" file="0093" n="93" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div249" type="section" level="1" n="97">
<head xml:id="echoid-head100" xml:space="preserve">Linea horæ 9. à meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 17 {3/4} # 4 {1/4} # 13 {3/4} # 8 {1/4} # 9 {3/4} # 12 {1/4} # 5 {3/4} # 16 {1/4} # 1 {3/4} # 20 {1/4} # 21 {3/4}
{1/2} # 17 {1/2} # 4 {1/2} # 13 {1/2} # 8 {1/2} # 9 {1/2} # 12 {1/2} # 5 {1/2} # 16 {1/2} # 1 {1/2} # 20 {1/2} # 21 {1/2}
{3/4} # 17 {1/4} # 4 {3/4} # 13 {1/4} # 8 {3/4} # 9 {1/4} # 12 {3/4} # 5 {1/4} # 16 {3/4} # 1 {1/4} # 20 {3/4} # 21 {1/4}
1 # 17 # 5 # 13 # 9 # 9 # 13 # 5 # 17 # 1 # 21 # 21
1 {1/4} # 16 {3/4} # 5 {1/4} # 12 {3/4} # 9 {1/4} # 8 {3/4} # 13 {1/4} # 4 {3/4} # 17 {1/4} # {3/4} # 21 {1/4} # 20 {3/4}
1 {1/2} # 16 {1/2} # 5 {1/2} # 12 {1/2} # 9 {1/2} # 8 {1/2} # 13 {1/2} # 4 {1/2} # 17 {1/2} # {1/2} # 21 {1/2} # 20 {1/2}
1 {3/4} # 16 {1/4} # 5 {3/4} # 12 {1/4} # 9 {3/4} # 8 {1/4} # 13 {3/4} # 4 {1/4} # 17 {3/4} # {1/4} # 21 {3/4} # 20 {1/4}
2 # 16 # 6 # 12 # 10 # 8 # 14 # 4 # 18 # 24 # 22 # 20
2 {1/4} # 15 {3/4} # 6 {1/4} # 11 {3/4} # 10 {1/4} # 7 {3/4} # 14 {1/4} # 3 {3/4} # 18 {1/4} # 23 {3/4} # 22 {1/4} # 19 {3/4}
2 {1/2} # 15 {1/2} # 6 {1/2} # 11 {1/2} # 10 {1/2} # 7 {1/2} # 14 {1/2} # 3 {1/2} # 18 {1/2} # 23 {1/2} # 22 {1/2} # 19 {1/2}
2 {3/4} # 15 {1/4} # 6 {3/4} # 11 {1/4} # 10 {3/4} # 7 {1/4} # 14 {3/4} # 3 {1/4} # 18 {3/4} # 23 {1/4} # 22 {3/4} # 19 {1/4}
3 # 15 # 7 # 11 # 11 # 7 # 15 # 3 # 19 # 23 # 23 # 19
3 {1/4} # 14 {3/4} # 7 {1/4} # 10 {3/4} # 11 {1/4} # 6 {3/4} # 15 {1/4} # 2 {3/4} # 19 {1/4} # 22 {3/4} # 23 {1/4} # 18 {3/4}
3 {1/2} # 14 {1/2} # 7 {1/2} # 10 {1/2} # 11 {1/2} # 6 {1/2} # 15 {1/2} # 2 {1/2} # 19 {1/2} # 22 {1/2} # 23 {1/2} # 18 {1/2}
3 {3/4} # 14 {1/4} # 7 {3/4} # 10 {1/4} # 11 {3/4} # 6 {1/4} # 15 {3/4} # 2 {1/4} # 19 {3/4} # 22 {1/4} # 23 {3/4} # 18 {1/4}
4 # 14 # 8 # 10 # 12 # 6 # 16 # 2 # 20 # 22 # 24 # 18</note>
</div>
<div xml:id="echoid-div250" type="section" level="1" n="98">
<head xml:id="echoid-head101" xml:space="preserve">In horologio, quod circulo horæ 9. à meridie vel media nocte æquidiſtat, lineæ quarumlibet duarum horarum \\ huius tabulæ ſunt parallelæ, ex ſcholio propoſ. 22.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div251" type="section" level="1" n="99">
<head xml:id="echoid-head102" xml:space="preserve">Linea horæ 8. a meridie vel media nocte.</head>
  <note position="left" xml:space="preserve">
Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu.
{1/4} # 15 {3/4} # 4 {1/4} # 11 {3/4} # 8 {1/4} # 7 {3/4} # 12 {1/4} # 3 {3/4} # 16 {1/4} # 23 {3/4} # 20 {1/4} # 19 {3/4}
{1/2} # 15 {1/2} # 4 {1/2} # 11 {1/2} # 8 {1/2} # 7 {1/2} # 12 {1/2} # 3 {1/2} # 16 {1/2} # 23 {1/2} # 20 {1/2} # 19 {1/2}
{3/4} # 15 {1/4} # 4 {3/4} # 11 {1/4} # 8 {3/4} # 7 {1/4} # 12 {3/4} # 3 {1/4} # 16 {3/4} # 23 {1/4} # 20 {3/4} # 19 {1/4}
1 # 15 # 5 # 11 # 9 # 7 # 13 # 3 # 17 # 23 # 21 # 19
1 {1/4} # 14 {3/4} # 5 {1/4} # 10 {3/4} # 9 {1/4} # 6 {3/4} # 13 {1/4} # 2 {3/4} # 17 {1/4} # 22 {3/4} # 21 {1/4} # 18 {3/4}
1 {1/2} # 14 {1/2} # 5 {1/2} # 10 {1/2} # 9 {1/2} # 6 {1/2} # 13 {1/2} # 2 {1/2} # 17 {1/2} # 22 {1/2} # 21 {1/2} # 18 {1/2}
1 {3/4} # 14 {1/4} # 5 {3/4} # 10 {1/4} # 9 {3/4} # 6 {1/4} # 13 {3/4} # 2 {1/4} # 17 {3/4} # 22 {1/4} # 21 {3/4} # 18 {1/4}
2 # 14 # 6 # 10 # 10 # 6 # 14 # 2 # 18 # 22 # 22 # 18
2 {1/4} # 13 {3/4} # 6 {1/4} # 9 {3/4} # 10 {1/4} # 5 {3/4} # 14 {1/4} # 1 {3/4} # 18 {1/4} # 21 {3/4} # 22 {1/4} # 17 {3/4}
2 {1/2} # 13 {1/2} # 6 {1/2} # 9 {1/2} # 10 {1/2} # 5 {1/2} # 14 {1/2} # 1 {1/2} # 18 {1/2} # 21 {1/2} # 22 {1/2} # 17 {1/2}
2 {3/4} # 13 {1/4} # 6 {3/4} # 9 {1/4} # 10 {3/4} # 5 {1/4} # 14 {3/4} # 1 {1/4} # 18 {3/4} # 21 {1/4} # 22 {3/4} # 17 {1/4}
3 # 13 # 7 # 9 # 11 # 5 # 15 # 1 # 19 # 21 # 23 # 17
3 {1/4} # 12 {3/4} # 7 {1/4} # 8 {3/4} # 11 {1/4} # 4 {3/4} # 15 {1/4} # {3/4} # 19 {1/4} # 20 {3/4} # 23 {1/4} # 16 {3/4}
3 {1/2} # 12 {1/2} # 7 {1/2} # 8 {1/2} # 11 {1/2} # 4 {1/2} # 15 {1/2} # {1/2} # 19 {1/2} # 20 {1/2} # 23 {1/2} # 16 {1/2}
3 {3/4} # 12 {1/4} # 7 {3/4} # 8 {1/4} # 11 {3/4} # 4 {1/4} # 15 {3/4} # {1/4} # 19 {3/4} # 20 {1/4} # 23 {3/4} # 16 {1/4}
4 # 12 # 8 # 8 # 12 # 4 # 16 # 24 # 20 # 20 # 24 # 16
</note>
<p style="it">
  <s xml:id="echoid-s4097" xml:space="preserve">In horologio, quod circulo horæ 8. </s>
  <s xml:id="echoid-s4098" xml:space="preserve">à meridie vel media nocte æquidistat, lineæ quarumcunque duarum ho-<lb/>rarum huius tabulæ ſunt parallelæ, vt constat ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4099" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4100" xml:space="preserve"/>
</p>
<pb o="74" file="0094" n="94" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div252" type="section" level="1" n="100">
<head xml:id="echoid-head103" xml:space="preserve">Linea horæ 7. a meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{3/4} # 13 {3/4} # 4 {1/4} # 9 {3/4} # 8 {1/4} # 5 {3/4} # 12 {1/4} # 1 {3/4} # 16 {1/4} # 21 {3/4} # 20 {1/4} # 17 {3/4}
{1/2} # 13 {1/2} # 4 {1/2} # 9 {1/2} # 8 {1/2} # 5 {1/2} # 12 {1/2} # 1 {1/2} # 16 {1/2} # 21 {1/2} # 20 {1/2} # 17 {1/2}
{3/4} # 13 {1/4} # 4 {3/4} # 9 {1/4} # 8 {3/4} # 5 {1/4} # 12 {3/4} # 1 {1/4} # 16 {3/4} # 21 {1/4} # 20 {3/4} # 17 {1/4}
1 # 13 # 5 # 9 # 9 # 5 # 13 # 1 # 17 # 21 # 21 # 17
1 {1/4} # 12 {3/4} # 5 {1/4} # 8 {3/4} # 9 {1/4} # 4 {3/4} # 13 {1/4} # {3/4} # 17 {1/4} # 20 {3/4} # 21 {1/4} # 16 {3/4}
1 {1/2} # 12 {1/2} # 5 {1/2} # 8 {1/2} # 9 {1/2} # 4 {1/2} # 13 {1/2} # {1/2} # 17 {1/2} # 20 {1/2} # 21 {1/2} # 16 {1/2}
1 {3/4} # 12 {1/4} # 5 {3/4} # 8 {1/4} # 9 {3/4} # 4 {1/4} # 13 {3/4} # {1/4} # 17 {3/4} # 20 {1/4} # 21 {3/4} # 16 {1/4}
2 # 12 # 6 # 8 # 10 # 4 # 14 # 24 # 18 # 20 # 22 # 16
2 {1/4} # 11 {3/4} # 6 {1/4} # 7 {3/4} # 10 {1/4} # 3 {3/4} # 14 {1/4} # 23 {3/4} # 18 {1/4} # 19 {3/4} # 22 {1/4} # 15 {3/4}
2 {1/2} # 11 {1/2} # 6 {1/2} # 7 {1/2} # 10 {1/2} # 3 {1/2} # 14 {1/2} # 23 {1/2} # 18 {1/2} # 19 {1/2} # 22 {1/2} # 15 {1/2}
2 {3/4} # 11 {1/4} # 6 {3/4} # 7 {1/4} # 10 {3/4} # 3 {1/4} # 14 {3/4} # 23 {1/4} # 18 {3/4} # 19 {1/4} # 22 {3/4} # 15 {1/4}
3 # 11 # 7 # 7 # 11 # 3 # 15 # 23 # 19 # 19 # 23 # 15
3 {1/4} # 10 {3/4} # 7 {1/4} # 6 {3/4} # 11 {1/4} # 2 {3/4} # 15 {1/4} # 22 {3/4} # 19 {1/4} # 18 {3/4} # 23 {1/4} # 14 {3/4}
3 {1/2} # 10 {1/2} # 7 {1/2} # 6 {1/2} # 11 {1/2} # 2 {1/2} # 15 {1/2} # 22 {1/2} # 19 {1/2} # 18 {1/2} # 23 {1/2} # 14 {1/2}
3 {3/4} # 10 {1/4} # 7 {3/4} # 6 {1/4} # 11 {3/4} # 2 {1/4} # 15 {3/4} # 22 {1/4} # 19 {3/4} # 18 {1/4} # 23 {3/4} # 14 {1/4}
4 # 10 # 8 # 6 # 12 # 2 # 16 # 22 # 20 # 18 # 24 # 14</note>
</div>
<div xml:id="echoid-div253" type="section" level="1" n="101">
<head xml:id="echoid-head104" xml:space="preserve">In horologio, quod circulo horæ 7. à meridie vel media nocte æquidiſtat, lineæ quarumlibet duarum horarum \\ huius tabulæ ſunt parallelæ, vt ex ſcholio propoſ. 22. liquido conſtat.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div254" type="section" level="1" n="102">
<head xml:id="echoid-head105" xml:space="preserve">Linea horæ 5. à meridie vel media nocte.</head>
<note position="left" xml:space="preserve">
  Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 9 {3/4} # 4 {1/4} # 5 {3/4} # 8 {1/4} # 1 {3/4} # 12 {1/4} # 21 {3/4} # 16 {1/4} # 17 {3/4} # 20 {1/4} # 13 {3/4}
{1/2} # 9 {1/2} # 4 {1/2} # 5 {1/2} # 8 {1/2} # 1 {1/2} # 12 {1/2} # 21 {1/2} # 16 {1/2} # 17 {1/2} # 20 {1/2} # 13 {1/2}
{3/4} # 9 {1/4} # 4 {3/4} # 5 {1/4} # 8 {3/4} # 1 {1/4} # 12 {3/4} # 21 {1/4} # 16 {3/4} # 17 {1/4} # 20 {3/4} # 13 {1/4}
1 # 9 # 5 # 5 # 9 # 1 # 13 # 21 # 17 # 17 # 21 # 13
1 {1/4} # 8 {3/4} # 5 {1/4} # 4 {3/4} # 9 {1/4} # {3/4} # 13 {1/4} # 20 {3/4} # 17 {1/4} # 16 {3/4} # 21 {1/4} # 12 {3/4}
1 {1/2} # 8 {1/2} # 5 {1/2} # 4 {1/2} # 9 {1/2} # {1/2} # 13 {1/2} # 20 {1/2} # 17 {1/2} # 16 {1/2} # 21 {1/2} # 12 {1/2}
1 {3/4} # 8 {1/4} # 5 {3/4} # 4 {1/4} # 9 {3/4} # {1/4} # 13 {3/4} # 20 {1/4} # 17 {3/4} # 16 {1/4} # 21 {3/4} # 12 {1/4}
2 # 8 # 6 # 4 # 10 # 24 # 14 # 20 # 18 # 16 # 22 # 12
2 {1/4} # 7 {3/4} # 6 {1/4} # 3 {3/4} # 10 {1/4} # 23 {3/4} # 14 {1/4} # 19 {3/4} # 18 {1/4} # 15 {3/4} # 22 {1/4} # 11 {3/4}
2 {1/2} # 7 {1/2} # 6 {1/2} # 3 {1/2} # 10 {1/2} # 23 {1/2} # 14 {1/2} # 19 {1/2} # 18 {1/2} # 15 {1/2} # 22 {1/2} # 11 {1/2}
2 {3/4} # 7 {1/4} # 6 {3/4} # 3 {1/4} # 10 {3/4} # 23 {1/4} # 14 {3/4} # 19 {1/4} # 18 {3/4} # 15 {1/4} # 22 {3/4} # 11 {1/4}
3 # 7 # 7 # 3 # 11 # 23 # 15 # 19 # 19 # 15 # 23 # 11
3 {1/4} # 6 {3/4} # 7 {1/4} # 2 {3/4} # 11 {1/4} # 22 {3/4} # 15 {1/4} # 18 {3/4} # 19 {1/4} # 14 {3/4} # 23 {1/4} # 10 {3/4}
3 {1/2} # 6 {1/2} # 7 {1/2} # 2 {1/2} # 11 {1/2} # 22 {1/2} # 15 {1/2} # 18 {1/2} # 19 {1/2} # 14 {1/2} # 23 {1/2} # 10 {1/2}
3 {3/4} # 6 {1/4} # 7 {3/4} # 2 {1/4} # 11 {3/4} # 22 {1/4} # 15 {3/4} # 18 {1/4} # 19 {3/4} # 14 {1/4} # 23 {3/4} # 10 {1/4}
4 # 6 # 8 # 2 # 12 # 22 # 16 # 18 # 20 # 14 # 24 # 10
</note>
<p style="it">
  <s xml:id="echoid-s4101" xml:space="preserve">In horologio, quod circulo horæ tertiæ à meridie vel media nocte æquidistat, lineæ quarumlibet duarum ho-<lb/>rarum huius tabulæ ſunt parallelæ, vt patet ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4102" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4103" xml:space="preserve"/>
</p>
<pb o="75" file="0095" n="95" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div255" type="section" level="1" n="103">
<head xml:id="echoid-head106" xml:space="preserve">Linea horæ quartæ à meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 7 {3/4} # 4 {1/4} # 3 {3/4} # 8 {1/4} # 23 {3/4} # 12 {1/4} # 19 {3/4} # 16 {1/4} # 15 {3/4} # 20 {1/4} # 11 {3/4}
{1/2} # 7 {1/2} # 4 {1/2} # 3 {1/2} # 8 {1/2} # 23 {1/2} # 12 {1/2} # 19 {1/2} # 16 {1/2} # 15 {1/2} # 20 {1/2} # 11 {1/2}
{3/4} # 7 {1/4} # 4 {3/4} # 3 {1/4} # 8 {3/4} # 23 {1/4} # 12 {3/4} # 19 {1/4} # 16 {3/4} # 15 {1/4} # 20 {3/4} # 11 {1/4}
1 # 7 # 5 # 3 # 9 # 23 # 13 # 19 # 17 # 15 # 21 # 11
1 {1/4} # 6 {3/4} # 5 {1/4} # 2 {3/4} # 9 {1/4} # 22 {3/4} # 13 {1/4} # 18 {3/4} # 17 {1/4} # 14 {3/4} # 21 {1/4} # 10 {3/4}
1 {1/2} # 6 {1/2} # 5 {1/2} # 2 {1/2} # 9 {1/2} # 22 {1/2} # 13 {1/2} # 18 {1/2} # 17 {1/2} # 14 {1/2} # 21 {1/2} # 10 {1/2}
1 {3/4} # 6 {1/4} # 5 {3/4} # 2 {1/4} # 9 {3/4} # 22 {1/4} # 13 {3/4} # 18 {1/4} # 17 {3/4} # 14 {1/4} # 21 {3/4} # 10 {1/4}
2 # 6 # 6 # 2 # 10 # 22 # 14 # 18 # 18 # 14 # 22 # 10
2 {1/4} # 5 {3/4} # 6 {1/4} # 1 {3/4} # 10 {1/4} # 21 {3/4} # 14 {1/4} # 17 {3/4} # 18 {1/4} # 13 {3/4} # 22 {1/4} # 9 {3/4}
2 {1/2} # 5 {1/2} # 6 {1/2} # 1 {1/2} # 10 {1/2} # 21 {1/2} # 14 {1/2} # 17 {1/2} # 18 {1/2} # 13 {1/2} # 22 {1/2} # 9 {1/2}
2 {3/4} # 5 {1/4} # 6 {3/4} # 1 {1/4} # 10 {3/4} # 21 {1/4} # 14 {3/4} # 17 {1/4} # 18 {3/4} # 13 {1/4} # 22 {3/4} # 9 {1/4}
3 # 5 # 7 # 1 # 11 # 21 # 15 # 17 # 19 # 13 # 23 # 9
3 {1/4} # 4 {3/4} # 7 {1/4} # {3/4} # 11 {1/4} # 20 {3/4} # 15 {1/4} # 16 {3/4} # 19 {1/4} # 12 {3/4} # 23 {1/4} # 8 {3/4}
3 {1/2} # 4 {1/2} # 7 {1/2} # {1/2} # 11 {1/2} # 20 {1/2} # 15 {1/2} # 16 {1/2} # 19 {1/2} # 12 {1/2} # 23 {1/2} # 8 {1/2}
3 {3/4} # 4 {1/4} # 7 {3/4} # {1/4} # 11 {3/4} # 20 {1/4} # 15 {3/4} # 16 {1/4} # 19 {3/4} # 12 {1/4} # 23 {3/4} # 8 {1/4}
4 # 4 # 8 # 24 # 12 # 20 # 16 # 16 # 20 # 12 # 24 # 8</note>
</div>
<div xml:id="echoid-div256" type="section" level="1" n="104">
<head xml:id="echoid-head107" xml:space="preserve">In horologio, quod circulo horæ quartæ à merdie vel media nocte æquidiſtat, lineæ quarumlibet duarum hora- \\ rum huius tabulæ ſunt parallelæ, vt ex ſcholio propoſ. 22. manifeſte colligitur.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div257" type="section" level="1" n="105">
<head xml:id="echoid-head108" xml:space="preserve">Linea horæ tertiæ à meridie vel media nocte.</head>
<note position="left" xml:space="preserve">
Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horę ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 5 {3/4} # 4 {1/4} # 1 {3/4} # 8 {1/4} # 21 {3/4} # 12 {1/4} # 17 {3/4} # 16 {1/4} # 13 {3/4} # 20 {1/4} # 9 {3/4}
{1/2} # 5 {1/2} # 4 {1/2} # 1 {1/2} # 8 {1/2} # 21 {1/2} # 12 {1/2} # 17 {1/2} # 16 {1/2} # 13 {1/2} # 20 {1/2} # 9 {1/2}
{3/4} # 5 {1/4} # 4 {3/4} # 1 {1/4} # 8 {3/4} # 21 {1/4} # 12 {3/4} # 17 {1/4} # 16 {3/4} # 13 {1/4} # 20 {3/4} # 9 {1/4}
1 # 5 # 5 # 1 # 9 # 21 # 13 # 17 # 17 # 13 # 21 # 9
1 {1/4} # 4 {3/4} # 5 {1/4} # {3/4} # 9 {1/4} # 20 {3/4} # 13 {1/4} # 16 {3/4} # 17 {1/4} # 12 {3/4} # 21 {1/4} # 8 {3/4}
1 {1/2} # 4 {1/2} # 5 {1/2} # {1/2} # 9 {1/2} # 20 {1/2} # 13 {1/2} # 16 {1/2} # 17 {1/2} # 12 {1/2} # 21 {1/2} # 8 {1/2}
1 {3/4} # 4 {1/4} # 5 {3/4} # {1/4} # 9 {3/4} # 20 {1/4} # 13 {3/4} # 16 {1/4} # 17 {3/4} # 12 {1/4} # 21 {3/4} # 8 {1/4}
2 # 4 # 6 # 24 # 10 # 20 # 14 # 16 # 18 # 12 # 22 # 8
2 {1/4} # 3 {3/4} # 6 {1/4} # 23 {3/4} # 10 {1/4} # 19 {3/4} # 14 {1/4} # 15 {3/4} # 18 {1/4} # 11 {3/4} # 22 {1/4} # 7 {3/4}
2 {1/2} # 3 {1/2} # 6 {1/2} # 23 {1/2} # 10 {1/2} # 19 {1/2} # 14 {1/2} # 15 {1/2} # 18 {1/2} # 11 {1/2} # 22 {1/2} # 7 {1/2}
2 {3/4} # 3 {1/4} # 6 {3/4} # 23 {1/4} # 10 {3/4} # 19 {1/4} # 14 {3/4} # 15 {1/4} # 18 {3/4} # 11 {1/4} # 22 {3/4} # 7 {1/4}
3 # 3 # 7 # 23 # 11 # 19 # 15 # 15 # 19 # 11 # 23 # 7
3 {1/4} # 2 {3/4} # 7 {1/4} # 22 {3/4} # 11 {1/4} # 18 {3/4} # 15 {1/4} # 14 {3/4} # 19 {1/4} # 10 {3/4} # 23 {1/4} # 6 {3/4}
3 {1/2} # 2 {1/2} # 7 {1/2} # 22 {1/2} # 11 {1/2} # 18 {1/2} # 15 {1/2} # 14 {1/2} # 19 {1/2} # 10 {1/2} # 23 {1/2} # 6 {1/2}
3 {3/4} # 2 {1/4} # 7 {3/4} # 22 {1/4} # 11 {3/4} # 18 {1/4} # 15 {3/4} # 14 {1/4} # 19 {3/4} # 10 {1/4} # 23 {3/4} # 6 {1/4}
4 # 2 # 8 # 22 # 12 # 18 # 16 # 14 # 20 # 10 # 24 # 6
</note>
<p style="it">
  <s xml:id="echoid-s4104" xml:space="preserve">In horologio, quod circulo horæ tertiæ à meridie vel media nocte æquidistat, lineæ quarumlibet duarum ho-<lb/>rarum huius tabulæ ſunt parallelæ, vt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4105" xml:space="preserve">22. </s>
  <s xml:id="echoid-s4106" xml:space="preserve">patet.</s>
  <s xml:id="echoid-s4107" xml:space="preserve"/>
</p>
<pb o="76" file="0096" n="96" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div258" type="section" level="1" n="106">
<head xml:id="echoid-head109" xml:space="preserve">Linea horæ ſ cundæ à meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab
ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 3 {3/4} # 4 {1/4} # 23 {3/4} # 8 {1/4} # 19 {3/4} # 12 {1/4} # 15 {3/4} # 16 {1/4} # 11 {3/4} # 20 {1/4} # 7 {3/4}
{1/2} # 3 {1/2} # 4 {1/2} # 23 {1/2} # 8 {1/2} # 19 {1/2} # 12 {1/2} # 15 {1/2} # 16 {1/2} # 11 {1/2} # 20 {1/2} # 7 {1/2}
{3/4} # 3 {1/4} # 4 {3/4} # 23 {1/4} # 8 {3/4} # 19 {1/4} # 12 {3/4} # 15 {1/4} # 16 {3/4} # 11 {1/4} # 20 {3/4} # 7 {1/4}
1 # 3 # 5 # 23 # 9 # 19 # 13 # 15 # 17 # 11 # 21 # 7
1 {1/4} # 2 {3/4} # 5 {1/4} # 22 {3/4} # 9 {1/4} # 18 {3/4} # 13 {1/4} # 14 {3/4} # 17 {1/4} # 10 {3/4} # 21 {1/4} # 6 {3/4}
1 {1/2} # 2 {1/2} # 5 {1/2} # 22 {1/2} # 9 {1/2} # 18 {1/2} # 13 {1/2} # 14 {1/2} # 17 {1/2} # 10 {1/2} # 21 {1/2} # 6 {1/2}
1 {3/4} # 2 {1/4} # 5 {3/4} # 22 {1/4} # 9 {3/4} # 18 {1/4} # 13 {3/4} # 14 {1/4} # 17 {3/4} # 10 {1/4} # 21 {3/4} # 6 {1/4}
2 # 2 # 6 # 22 # 10 # 18 # 14 # 14 # 18 # 10 # 22 # 6
2 {1/4} # 1 {3/4} # 6 {1/4} # 21 {3/4} # 10 {1/4} # 17 {3/4} # 14 {1/4} # 13 {3/4} # 18 {1/4} # 9 {3/4} # 22 {1/4} # 5 {3/4}
2 {1/2} # 1 {1/2} # 6 {1/2} # 21 {1/2} # 10 {1/2} # 17 {1/2} # 14 {1/2} # 13 {1/2} # 18 {1/2} # 9 {1/2} # 22 {1/2} # 5 {1/2}
2 {3/4} # 1 {1/4} # 6 {3/4} # 21 {1/4} # 10 {3/4} # 17 {1/4} # 14 {3/4} # 13 {1/4} # 18 {3/4} # 9 {1/4} # 22 {3/4} # 5 {1/4}
3 # 1 # 7 # 21 # 11 # 17 # 15 # 13 # 19 # 9 # 23 # 5
3 {1/4} # {3/4} # 7 {1/4} # 20 {3/4} # 11 {1/4} # 16 {3/4} # 15 {1/4} # 12 {3/4} # 19 {1/4} # 8 {3/4} # 23 {1/4} # 4 {3/4}
3 {1/2} # {1/2} # 7 {1/2} # 20 {1/2} # 11 {1/2} # 16 {1/2} # 15 {1/2} # 12 {1/2} # 19 {1/2} # 8 {1/2} # 23 {1/2} # 4 {1/2}
3 {3/4} # {1/4} # 7 {3/4} # 20 {1/4} # 11 {3/4} # 16 {1/4} # 15 {3/4} # 12 {1/4} # 19 {3/4} # 8 {1/4} # 23 {3/4} # 4 {1/4}
4 # 24 # 8 # 20 # 12 # 16 # 16 # 12 # 20 # 8 # 24 # 4
</note>
<p style="it">
  <s xml:id="echoid-s4108" xml:space="preserve">In horologio, quod circulo horæ ſecundæ à meridie vel media nocte æquidiſtat, lineæ quarumlibet duarum hora-<lb/>rum huius tabulæ ſunt parallelæ, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4109" xml:space="preserve">22.</s>
  <s xml:id="echoid-s4110" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div259" type="section" level="1" n="107">
<head xml:id="echoid-head110" xml:space="preserve">Linea horæ primæ a meridie vel media nocte.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab
ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu. # Horæ ab ortu \\ vel occaſu.
{1/4} # 1 {3/4} # 4 {1/4} # 21 {3/4} # 8 {1/4} # 17 {3/4} # 12 {1/4} # 13 {3/4} # 16 {1/4} # 9 {3/4} # 20 {1/4} # 5 {3/4}
{1/2} # 1 {1/2} # 4 {1/2} # 21 {1/2} # 8 {1/2} # 17 {1/2} # 12 {1/2} # 13 {1/2} # 16 {1/2} # 9 {1/2} # 20 {1/2} # 5 {1/2}
{3/4} # 1 {1/4} # 4 {3/4} # 21 {1/4} # 8 {3/4} # 17 {1/4} # 12 {3/4} # 13 {1/4} # 16 {3/4} # 9 {1/4} # 20 {3/4} # 5 {1/4}
1 # 1 # 5 # 21 # 9 # 17 # 13 # 13 # 17 # 9 # 21 # 5
1 {1/4} # {3/4} # 5 {1/4} # 20 {3/4} # 9 {1/4} # 16 {3/4} # 13 {1/4} # 12 {3/4} # 17 {1/4} # 8 {3/4} # 21 {1/4} # 4 {3/4}
1 {1/2} # {1/2} # 5 {1/2} # 20 {1/2} # 9 {1/2} # 16 {1/2} # 13 {1/2} # 12 {1/2} # 17 {1/2} # 8 {1/2} # 21 {1/2} # 4 {1/2}
1 {3/4} # {1/4} # 5 {3/4} # 20 {1/4} # 9 {3/4} # 16 {1/4} # 13 {3/4} # 12 {1/4} # 17 {3/4} # 8 {1/4} # 21 {3/4} # 4 {1/4}
2 # 24 # 6 # 20 # 10 # 16 # 14 # 12 # 18 # 8 # 22 # 4
2 {1/4} # 23 {3/4} # 6 {1/4} # 19 {3/4} # 10 {1/4} # 15 {3/4} # 14 {1/4} # 11 {3/4} # 18 {1/4} # 7 {3/4} # 22 {1/4} # 3 {3/4}
2 {1/2} # 23 {1/2} # 6 {1/2} # 19 {1/2} # 10 {1/2} # 15 {1/2} # 14 {1/2} # 11 {1/2} # 18 {1/2} # 7 {1/2} # 22 {1/2} # 3 {1/2}
2 {3/4} # 23 {1/4} # 6 {3/4} # 19 {1/4} # 10 {3/4} # 15 {1/4} # 14 {3/4} # 11 {1/4} # 18 {3/4} # 7 {1/4} # 22 {3/4} # 3 {1/4}
3 # 23 # 7 # 19 # 11 # 15 # 15 # 11 # 19 # 7 # 23 # 3
3 {1/4} # 22 {3/4} # 7 {1/4} # 18 {3/4} # 11 {1/4} # 14 {3/4} # 15 {1/4} # 10 {3/4} # 19 {1/4} # 6 {3/4} # 23 {1/4} # 2 {3/4}
3 {1/2} # 22 {1/2} # 7 {1/2} # 18 {1/2} # 11 {1/2} # 14 {1/2} # 15 {1/2} # 10 {1/2} # 19 {1/2} # 6 {1/2} # 23 {1/2} # 2 {1/2}
3 {3/4} # 22 {1/4} # 7 {3/4} # 18 {1/4} # 11 {3/4} # 14 {1/4} # 15 {3/4} # 10 {1/4} # 19 {3/4} # 6 {1/4} # 23 {3/4} # 2 {1/4}
4 # 22 # 8 # 18 # 12 # 14 # 16 # 10 # 20 # 6 # 24 # 2
</note>
<p style="it">
  <s xml:id="echoid-s4111" xml:space="preserve">In horologio, quod circulo horæ primæ à meridie vel media nocte æquidistat, lineæ quarumcunque duarum <lb/>horarum huius tabulæ ſunt parallelæ, vt exĳs, quæ à nobis in ſcholio propoſ. </s>
  <s xml:id="echoid-s4112" xml:space="preserve">vigeſimæ ſecundæ ſunt demonſtrata, <lb/>colligitur.</s>
  <s xml:id="echoid-s4113" xml:space="preserve"/>
</p>
<pb o="77" file="0097" n="97" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div260" type="section" level="1" n="108">
<head xml:id="echoid-head111" xml:space="preserve">THEOREMA 19. PROPOSITIO 21.</head>
<note position="right" xml:space="preserve">@ Omnes lineæ <lb/>horaiũ à mer. <lb/>vel med. noc. <lb/>in quocunque <lb/>horologio axẽ <lb/>mundi ſecante <lb/>ſe mutuo inter. <lb/>ſecant in illo <lb/>puncto axis, in <lb/>quo axis plano <lb/>horologii occur <lb/>@it.</note>
<p>
  <s xml:id="echoid-s4114" xml:space="preserve">LINEAE omnium horarum à meridie vel media nocte in quo-<lb/>cunque horologio, cuius planum axem mundi ſecat, ſe mutuo interſe-<lb/>cant in illo puncto axis, in quo horologii plano ipſe axis occurrit.</s>
  <s xml:id="echoid-s4115" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4116" xml:space="preserve">CVM enim omnes circuli horas à meridie vel media nocte monſtrantes incedant per mun-<lb/>di polos, ex propoſ. </s>
  <s xml:id="echoid-s4117" xml:space="preserve">9. </s>
  <s xml:id="echoid-s4118" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4119" xml:space="preserve">vbi ſe mutuo eorum circunferentiæ interſecant, erit axis mundi <lb/>
<anchor type="note" xlink:label="note-0097-02a" xlink:href="note-0097-02"/>
<anchor type="note" xlink:label="note-0097-03a" xlink:href="note-0097-03"/>
eorum planorum communis ſectio. </s>
  <s xml:id="echoid-s4120" xml:space="preserve">In quo igitur puncto occurrit axis plano horologii, in eo-<lb/>dem coibunt, per propoſ. </s>
  <s xml:id="echoid-s4121" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4122" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4123" xml:space="preserve">omnium illorum, &amp; </s>
  <s xml:id="echoid-s4124" xml:space="preserve">plani horologii communes ſectio-<lb/>nes, hoc eſt, lineæ horariæ à meridie vel media nocte. </s>
  <s xml:id="echoid-s4125" xml:space="preserve">Quapropter lineæ omnium horarum à <lb/>meridie, vel media nocte, &amp;</s>
  <s xml:id="echoid-s4126" xml:space="preserve">c. </s>
  <s xml:id="echoid-s4127" xml:space="preserve">Quod erat demonſtrandum.</s>
  <s xml:id="echoid-s4128" xml:space="preserve"/>
</p>
<div xml:id="echoid-div260" type="float" level="2" n="1">
<note position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">Lineæ horarú <lb/>à mer uel med. <lb/>noc. in horolo-<lb/>gio Aequino-<lb/>ctiali, Horizon-<lb/>ta’i, Verticaliq́ <lb/>ſphærę obliquę, <lb/>conueniunt om <lb/>nes in @ pun-<lb/>cto, in quo axis <lb/>mundi planum <lb/>horologij ſecat, <lb/>excepto Vertica <lb/>li horologio il-<lb/>lius ſphærę ob-<lb/>liquæ, vbi po-<lb/>lus eſt in verti-<lb/>ce capitis.</note>
<note position="left" xlink:label="note-0097-03" xlink:href="note-0097-03a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div262" type="section" level="1" n="109">
<head xml:id="echoid-head112" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s4129" xml:space="preserve">ITAQVE in horologio Aequinoctiali, &amp; </s>
  <s xml:id="echoid-s4130" xml:space="preserve">Horizontali, Verticaliq́; </s>
  <s xml:id="echoid-s4131" xml:space="preserve">quocunq; </s>
  <s xml:id="echoid-s4132" xml:space="preserve">ſphæræ obliquæ ſecant <lb/>ſe mutuo lineæ oẽs horariæ à meridie vel media nocte in uno eodemq; </s>
  <s xml:id="echoid-s4133" xml:space="preserve">axis pũcto, in quo nimirũ axis ipſe <lb/>planis dictorum horologiorum occurrit: </s>
  <s xml:id="echoid-s4134" xml:space="preserve">quia plana horum horologiorum ſecant axem, quemadmodum <lb/>&amp; </s>
  <s xml:id="echoid-s4135" xml:space="preserve">circuli maximi, quibus ipſa æquidiſtant, videlicet Aequator, Horizon, Verticalisq́; </s>
  <s xml:id="echoid-s4136" xml:space="preserve">ſphærę obliquæ <lb/>
<anchor type="note" xlink:label="note-0097-04a" xlink:href="note-0097-04"/>
cuiuſuis eundem interſecant, vt maniſeſtum eſt. </s>
  <s xml:id="echoid-s4137" xml:space="preserve">Excipe tamen Verticale horologium illius ſphæræ obli-<lb/>
<anchor type="note" xlink:label="note-0097-05a" xlink:href="note-0097-05"/>
quæ, in qua vertex eſt polus mundi. </s>
  <s xml:id="echoid-s4138" xml:space="preserve">Ibi enim Verticalis circulus per mundi polos, &amp; </s>
  <s xml:id="echoid-s4139" xml:space="preserve">axem incedit, atque <lb/>adeò axem non ſecat. </s>
  <s xml:id="echoid-s4140" xml:space="preserve">Igitur neque planum horologii ei æquidiſtans eundem ſecare poteſt.</s>
  <s xml:id="echoid-s4141" xml:space="preserve"/>
</p>
<div xml:id="echoid-div262" type="float" level="2" n="1">
<note position="left" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0097-05" xlink:href="note-0097-05a" xml:space="preserve">In omni horo-<lb/>logio, quodæ-<lb/>quidiſta@ circu-<lb/>lo maximo per <lb/>polos mũ<unsure/>di nõ <lb/>ducto, lincæ ho-<lb/>rarum 2 mer. <lb/>vel med. noc. ſe <lb/>mutuo interſe-<lb/>cant in vno eo-<lb/>demq́; puncto, <lb/>in quo nimirũ <lb/>axis mundi ho <lb/>rologio occur-<lb/>rit.</note>
</div>
<p>
  <s xml:id="echoid-s4142" xml:space="preserve">DENIQVE, vt vno verbo omnia comprehendamus, lineæ horarię à meridie vel media nocte om-<lb/>nes in horologio quolibet, cuius planum non æquidiſtat alicui circulo per polos mundi tranſeunti, vel axi <lb/>mundi, (cuiuſmodi ſunt ferè omnia horologia declinantia, &amp; </s>
  <s xml:id="echoid-s4143" xml:space="preserve">inclinata,) ſecant axem mundi in vno eo-<lb/>demq́; </s>
  <s xml:id="echoid-s4144" xml:space="preserve">puncto, in quo ſcilicet axis ipſe plano horologij occurrit: </s>
  <s xml:id="echoid-s4145" xml:space="preserve">quia horologium eiuſmodi quodcunque <lb/>axem mundi ſecat, cum circulus maximus, cui ęquidiſtat, non per polos mundi ponatur tranſire.</s>
  <s xml:id="echoid-s4146" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4147" xml:space="preserve">APPELLATVR autem punctum illud, in quo axis mundi plano horologii occurrit, centrum <lb/>horologii.</s>
  <s xml:id="echoid-s4148" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div264" type="section" level="1" n="110">
<head xml:id="echoid-head113" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve">Centrum horo <lb/>logii quid.</note>
<p style="it">
  <s xml:id="echoid-s4149" xml:space="preserve">PARI ratione, lineæ quælibet horariæ tam à meridie vel media nocte, quàm ab ortu vel occaſu, <lb/>
<anchor type="note" xlink:label="note-0097-08a" xlink:href="note-0097-08"/>
quarum circuli horarĳ eandem habent communem ſectionem, in quouis horologio, cuius planum commu-<lb/>ni illi ſectioni non æquidiſtat, ſed ipſam ſecat, quamuis communis illa ſectio non ſit axis mundi, ſe mutuo <lb/>ſecant in illo puncto communis ſectionis, in quo ipſa plano horologĳ occurrit. </s>
  <s xml:id="echoid-s4150" xml:space="preserve">Eadem enim prorſus eſt <lb/>demonſtr atio, ex propoſ. </s>
  <s xml:id="echoid-s4151" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4152" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4153" xml:space="preserve">deſumpta. </s>
  <s xml:id="echoid-s4154" xml:space="preserve">Huiuſmodi ſunt ternæ quælibet horæ poſitæ in tabula <lb/>
<anchor type="note" xlink:label="note-0097-09a" xlink:href="note-0097-09"/>
propoſ. </s>
  <s xml:id="echoid-s4155" xml:space="preserve">19. </s>
  <s xml:id="echoid-s4156" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4157" xml:space="preserve">vnà cum linea æquinoctiali; </s>
  <s xml:id="echoid-s4158" xml:space="preserve">nec non &amp; </s>
  <s xml:id="echoid-s4159" xml:space="preserve">binæ quæuis in tabulis triginta ſex præ-<lb/>cedentis propoſ. </s>
  <s xml:id="echoid-s4160" xml:space="preserve">poſitæ, vnà cum hora, quæ in tit@lo cuiuſque tabulæ deſcripta eſt.</s>
  <s xml:id="echoid-s4161" xml:space="preserve"/>
</p>
<div xml:id="echoid-div264" type="float" level="2" n="1">
<note position="right" xlink:label="note-0097-08" xlink:href="note-0097-08a" xml:space="preserve">Quænam horæ <lb/>ab or. vel occ. &amp; <lb/>à mer. vel med. <lb/>noc. in quouis <lb/>horologio pa-<lb/>rallelæ ſint.</note>
<note position="right" xlink:label="note-0097-09" xlink:href="note-0097-09a" xml:space="preserve">Quælibet horæ <lb/>in tabulis præ-<lb/>cedentium dua <lb/>rum propoſ. de-<lb/>ſcriptæ, vna cũ <lb/>hora, vel linea, <lb/>quæ in titulo <lb/>tabulæ eſt poſi-<lb/>@a, ſe mutuo ſe-<lb/>cant in vno pũ-<lb/>cto.</note>
</div>
</div>
<div xml:id="echoid-div266" type="section" level="1" n="111">
<head xml:id="echoid-head114" xml:space="preserve">THEOREMA 20. PROPOSITIO 22.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s4162" xml:space="preserve">LINEAE omnium horarum à meridie vel media nocte in quo-<lb/>
<anchor type="note" xlink:label="note-0097-11a" xlink:href="note-0097-11"/>
cunque horologio, cuius planum circulo cuipiam per polos mundi de-<lb/>ſcripto, vel axi mundi æquidiſtat, ſunt parallelæ.</s>
  <s xml:id="echoid-s4163" xml:space="preserve"/>
</p>
<div xml:id="echoid-div266" type="float" level="2" n="1">
<note position="right" xlink:label="note-0097-11" xlink:href="note-0097-11a" xml:space="preserve">Lineæ horarũ <lb/>à mer. vel med. <lb/>nocte oẽs ſunt <lb/>parallelę in ho-<lb/>@ologio, q@ cir-<lb/>culo maximo p@ <lb/>polos mũdi du-<lb/>cto æquidiſtat.</note>
</div>
<p>
  <s xml:id="echoid-s4164" xml:space="preserve">NAM cum omnes circuli horarii à meridie vel media nocte deſcribantur, ex propoſ. </s>
  <s xml:id="echoid-s4165" xml:space="preserve">9. </s>
  <s xml:id="echoid-s4166" xml:space="preserve">hu-<lb/>ius lib. </s>
  <s xml:id="echoid-s4167" xml:space="preserve">per polos mundi, vbi eorum circunferentiæ mutuo ſe interſecant, erit axis mundi commu <lb/>nis eorum planorum ſectio. </s>
  <s xml:id="echoid-s4168" xml:space="preserve">Quare, ſi planum horologii ipſos circulos horarios ſecans æquidi-<lb/>
<anchor type="note" xlink:label="note-0097-12a" xlink:href="note-0097-12"/>
ſtet alicui circulo per polos mundi, atque adeo per axem, communem eorum ſectionem, ducto, <lb/>vel ipſi axi, erunt per propoſ. </s>
  <s xml:id="echoid-s4169" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4170" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4171" xml:space="preserve">illorum omnium circulorum, &amp; </s>
  <s xml:id="echoid-s4172" xml:space="preserve">plani horologii ipſos <lb/>
<anchor type="note" xlink:label="note-0097-13a" xlink:href="note-0097-13"/>
ſecantis, communes ſectiones, hoc eſt, lineæ horariæ à meridie vel media nocte, parallelæ. </s>
  <s xml:id="echoid-s4173" xml:space="preserve">Quo <lb/>circa lineæ omnium horarum à meridie, vel media nocte, &amp;</s>
  <s xml:id="echoid-s4174" xml:space="preserve">c. </s>
  <s xml:id="echoid-s4175" xml:space="preserve">Quod demonſtrandum erat.</s>
  <s xml:id="echoid-s4176" xml:space="preserve"/>
</p>
<div xml:id="echoid-div267" type="float" level="2" n="2">
<note position="right" xlink:label="note-0097-12" xlink:href="note-0097-12a" xml:space="preserve">Lineæ horarũ à <lb/>mer. vel med. <lb/>noc. in hori@on <lb/>tali horologio <lb/>ſphęræ rectæ, &amp; <lb/>in quolibet Me <lb/>ridiano a@que <lb/>Polari, ſunt oẽs <lb/>inter ſeæquidi-<lb/>ſtantes.</note>
<note position="left" xlink:label="note-0097-13" xlink:href="note-0097-13a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div269" type="section" level="1" n="112">
<head xml:id="echoid-head115" xml:space="preserve">COROLLARIVM.</head>
<note position="right" xml:space="preserve">In omni horo-<lb/>logio, quod æ-<lb/>quidiſta: circu-<lb/>lo maximo per <lb/>polos mũdi du-<lb/>cto, lineæ hora <lb/>rum à mer. vel <lb/>med. noc. om-<lb/>nes ſunt paral-<lb/>lelę.</note>
<p>
  <s xml:id="echoid-s4177" xml:space="preserve">SEQVITVR ex his, in horologio Horizontali ſphæræ rectæ, Meridiano, atque polari quolibet, li-<lb/>neas omnes horarias à meridie vel media nocte parallelas eſſe: </s>
  <s xml:id="echoid-s4178" xml:space="preserve">quoniam horum horologiorum plana <lb/>ęquidiſtant circulis, nempe Horizonti recto, Meridiano, &amp; </s>
  <s xml:id="echoid-s4179" xml:space="preserve">circulo horæ ſextæ à meridie vel media no-<lb/>cte, per polos, &amp; </s>
  <s xml:id="echoid-s4180" xml:space="preserve">axem mundi ductis, vt conſtat.</s>
  <s xml:id="echoid-s4181" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4182" xml:space="preserve">VT denique paucis multa complectar, lineæ omnes horarię à meridie vel media nocte in horologio <lb/>quouis, cuius planum alicui circulo horario à meridie uel media nocte, vel certè axi muudi æquidiſtat, <lb/>per hanc propoſ. </s>
  <s xml:id="echoid-s4183" xml:space="preserve">parallelę ſunt.</s>
  <s xml:id="echoid-s4184" xml:space="preserve"/>
</p>
<pb o="78" file="0098" n="98" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div270" type="section" level="1" n="113">
<head xml:id="echoid-head116" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s4185" xml:space="preserve">SIMILI modo, lineæ quælibet horariæ tam à meridie, vel media nocte, quàm ab ortu, vel occaſu, <lb/>
<anchor type="note" xlink:label="note-0098-01a" xlink:href="note-0098-01"/>
quarum circuli horarĳ eandem habent communem ſectionem, parallelæ ſunt in quouis horologio, cuius pla <lb/>num alicui circulo maximo per illam communem ſectionem ducto, vel ipſi communi ſectioni æquidiſtat, <lb/>quamuis communis illa ſectio non ſit axis mundi. </s>
  <s xml:id="echoid-s4186" xml:space="preserve">Eadem enim prorſus eſt demonſtr atio ex propoſ. </s>
  <s xml:id="echoid-s4187" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s4188" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4189" xml:space="preserve">deprompta.</s>
  <s xml:id="echoid-s4190" xml:space="preserve"/>
</p>
<div xml:id="echoid-div270" type="float" level="2" n="1">
<note position="left" xlink:label="note-0098-01" xlink:href="note-0098-01a" xml:space="preserve">Quænam horæ <lb/>abor. uel occ. &amp; <lb/>à mer. uel med. <lb/>noc. parallelæ <lb/>ſint in quouis <lb/>horologio.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4191" xml:space="preserve">HINC fit, ternas quaslibet horas in tabula propoſ. </s>
  <s xml:id="echoid-s4192" xml:space="preserve">19. </s>
  <s xml:id="echoid-s4193" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4194" xml:space="preserve">poſitas, quarum vna ſemper à <lb/>
<anchor type="note" xlink:label="note-0098-02a" xlink:href="note-0098-02"/>
meridie, vel media no cte, reliquæ ab ortu, vel occaſu ſumuntur, parallelas eſſe in horologio Aequinoctia-<lb/>li: </s>
  <s xml:id="echoid-s4195" xml:space="preserve">quia circuli illarum horarĳ, &amp; </s>
  <s xml:id="echoid-s4196" xml:space="preserve">Aequator eandem habent communem ſectionem, per propoſ. </s>
  <s xml:id="echoid-s4197" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4198" xml:space="preserve">hu-<lb/>
<anchor type="note" xlink:label="note-0098-03a" xlink:href="note-0098-03"/>
ius lib. </s>
  <s xml:id="echoid-s4199" xml:space="preserve">Quare cum planum horologĳ Aequinoctialis circulos illos horarios ſecans æquidiſtet vni illorum, <lb/>nimirum Aequatori, erunt communes ſectiones illorum, &amp; </s>
  <s xml:id="echoid-s4200" xml:space="preserve">plani horologĳ, hoc eſt, lineæ horariæ <lb/>parallelæ.</s>
  <s xml:id="echoid-s4201" xml:space="preserve"/>
</p>
<div xml:id="echoid-div271" type="float" level="2" n="2">
<note position="left" xlink:label="note-0098-02" xlink:href="note-0098-02a" xml:space="preserve">In horologio <lb/>Aequinoctiali <lb/>parallelæ ſunt <lb/>inter ſe ternæ <lb/>horæ quælibet <lb/>in tabula pro-<lb/>poſ. 19. huius <lb/>lib poſitæ.</note>
<note position="left" xlink:label="note-0098-03" xlink:href="note-0098-03a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">In horologio <lb/>horizontali pa-<lb/>rallelæ ſunt in-<lb/>ter ſe quæuis bi <lb/>næ horæ in ta-<lb/>bula prima pro <lb/>poſ. 29. huius <lb/>lib. poſitæ.</note>
<p style="it">
  <s xml:id="echoid-s4202" xml:space="preserve">PARI ratione, parallelæ erunt in horologio Horizontali quæuis binæ horę in tabula prima pro-<lb/>poſ. </s>
  <s xml:id="echoid-s4203" xml:space="preserve">20 huius lib. </s>
  <s xml:id="echoid-s4204" xml:space="preserve">poſitæ: </s>
  <s xml:id="echoid-s4205" xml:space="preserve">quia earum circuli horarĳ, &amp; </s>
  <s xml:id="echoid-s4206" xml:space="preserve">circul{us} horę 24. </s>
  <s xml:id="echoid-s4207" xml:space="preserve">ab ortu, vel occaſu, ſiue Ho-<lb/>rizon, eandem habent, per propoſ. </s>
  <s xml:id="echoid-s4208" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4209" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4210" xml:space="preserve">communem ſectionem, &amp; </s>
  <s xml:id="echoid-s4211" xml:space="preserve">planum horologĳ æquidiſtat <lb/>vni illorum, nempe circulo horæ 24. </s>
  <s xml:id="echoid-s4212" xml:space="preserve">ab ortu, vel occaſu, ſiue Horizonti.</s>
  <s xml:id="echoid-s4213" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4214" xml:space="preserve">RVRSVS inhorologio Verticali ad latitudinem grad. </s>
  <s xml:id="echoid-s4215" xml:space="preserve">45. </s>
  <s xml:id="echoid-s4216" xml:space="preserve">vel in horologio, quod circulo horæ <lb/>
<anchor type="note" xlink:label="note-0098-05a" xlink:href="note-0098-05"/>
12. </s>
  <s xml:id="echoid-s4217" xml:space="preserve">ab ortu, vel occaſu æquidiſtat, (qui circulus idem eſt, qui Verticalis ad latitudinem grad. </s>
  <s xml:id="echoid-s4218" xml:space="preserve">45. </s>
  <s xml:id="echoid-s4219" xml:space="preserve">vt con-<lb/>ctat ex Sphær a materiali) parallelæ erunt quæuis binæ horę in tabula ſecunda propoſ. </s>
  <s xml:id="echoid-s4220" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4221" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4222" xml:space="preserve">poſi-<lb/>
<anchor type="note" xlink:label="note-0098-06a" xlink:href="note-0098-06"/>
tę. </s>
  <s xml:id="echoid-s4223" xml:space="preserve">Habent enim illarum circuli horarĳ, &amp; </s>
  <s xml:id="echoid-s4224" xml:space="preserve">circulus horę 12. </s>
  <s xml:id="echoid-s4225" xml:space="preserve">ab ortu, vel occaſu, ſiue Verticalis ad la-<lb/>titudinem grad. </s>
  <s xml:id="echoid-s4226" xml:space="preserve">45. </s>
  <s xml:id="echoid-s4227" xml:space="preserve">eandem ſectionem communem, per propoſ. </s>
  <s xml:id="echoid-s4228" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4229" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4230" xml:space="preserve">planum{q́ue} horologĳ vni il-<lb/>lorum, vtpote circulo horę 12. </s>
  <s xml:id="echoid-s4231" xml:space="preserve">ab ortu, vel occaſu, ſiue Verticali ad latitudinem grad. </s>
  <s xml:id="echoid-s4232" xml:space="preserve">45. </s>
  <s xml:id="echoid-s4233" xml:space="preserve">æquidiſtat.</s>
  <s xml:id="echoid-s4234" xml:space="preserve"/>
</p>
<div xml:id="echoid-div272" type="float" level="2" n="3">
<note position="left" xlink:label="note-0098-05" xlink:href="note-0098-05a" xml:space="preserve">In horologio <lb/>Verticali ad la-<lb/>titudinẽgr. 45. <lb/>parallelæ inter <lb/>ſe ſunt quæuis <lb/>binæ horę in ta <lb/>bula ſecunda <lb/>propoſ. 20. hu-<lb/>ius lib. deſcri-<lb/>ptæ.</note>
<note position="left" xlink:label="note-0098-06" xlink:href="note-0098-06a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s4235" xml:space="preserve">PRAETEREA in horologio polari parallelę erunt binę quæuis horæ poſitæ in tabula tertia pro-<lb/>
<anchor type="note" xlink:label="note-0098-07a" xlink:href="note-0098-07"/>
poſ. </s>
  <s xml:id="echoid-s4236" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4237" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4238" xml:space="preserve">quia earum circuli, &amp; </s>
  <s xml:id="echoid-s4239" xml:space="preserve">circulus horæ ſextæ à meridie, vel media nocte, cui planum horo-<lb/>logĳ æquidiſtat, habent per propoſ. </s>
  <s xml:id="echoid-s4240" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4241" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4242" xml:space="preserve">communem eandem ſectionem, &amp; </s>
  <s xml:id="echoid-s4243" xml:space="preserve">c.</s>
  <s xml:id="echoid-s4244" xml:space="preserve"/>
</p>
<div xml:id="echoid-div273" type="float" level="2" n="4">
<note position="left" xlink:label="note-0098-07" xlink:href="note-0098-07a" xml:space="preserve">In horologio <lb/>polari paralle <lb/>læ ſunt binæ <lb/>horæ quæcun-<lb/>que in tabula <lb/>tertia ꝓpoſ<unsure/>. 20. <lb/>huius lib. poſi-<lb/>tæ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4245" xml:space="preserve">POSTREMO, erunt parallelę in horologio Meridiano binæ quęlibet horę in tabula quarta pro-<lb/>poſ. </s>
  <s xml:id="echoid-s4246" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4247" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4248" xml:space="preserve">deſcriptæ: </s>
  <s xml:id="echoid-s4249" xml:space="preserve">propterea quòd earum horarĳ circuli, &amp; </s>
  <s xml:id="echoid-s4250" xml:space="preserve">circulus horæ 12. </s>
  <s xml:id="echoid-s4251" xml:space="preserve">à meridie, vel <lb/>media nocte, ſiue Meridianus, cui horologĳ planum æquidiſtat, eandem habent, per propoſ. </s>
  <s xml:id="echoid-s4252" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4253" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s4254" xml:space="preserve">ſectionem communem, &amp; </s>
  <s xml:id="echoid-s4255" xml:space="preserve">c.</s>
  <s xml:id="echoid-s4256" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">In horologio <lb/>Meridiano pa-<lb/>rallelæ ſunt <lb/>quælibet binæ <lb/>horæ in tabula <lb/>quarta propoſ. <lb/>20. huius lib, <lb/>collocatæ.</note>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s4257" xml:space="preserve">IAM verò, quoniam quinque horum circulorum, Horizontis, ſiue circulihorę 24. </s>
  <s xml:id="echoid-s4258" xml:space="preserve">ab ortu vel <lb/>occaſu, circuli horæ ſextæ à meridievel media nocte, circuli horæ 12. </s>
  <s xml:id="echoid-s4259" xml:space="preserve">ab ortu vel occaſu, Verticalis <lb/>circuli, &amp; </s>
  <s xml:id="echoid-s4260" xml:space="preserve">Aequinoctialis, priores tres, vt Horizon, circulus horæ 6. </s>
  <s xml:id="echoid-s4261" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s4262" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s4263" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s4264" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4265" xml:space="preserve">circulus <lb/>horę 12. </s>
  <s xml:id="echoid-s4266" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s4267" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s4268" xml:space="preserve">eandem habent communem ſectionem, per propoſ. </s>
  <s xml:id="echoid-s4269" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4270" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4271" xml:space="preserve">Habent autem <lb/>per propoſ. </s>
  <s xml:id="echoid-s4272" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4273" xml:space="preserve">eandem quoque primus, tertius, &amp; </s>
  <s xml:id="echoid-s4274" xml:space="preserve">quintus, nempe Horizon, circulus horę 12. </s>
  <s xml:id="echoid-s4275" xml:space="preserve">ab or. <lb/></s>
  <s xml:id="echoid-s4276" xml:space="preserve">
<anchor type="note" xlink:label="note-0098-10a" xlink:href="note-0098-10"/>
vel occ. </s>
  <s xml:id="echoid-s4277" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4278" xml:space="preserve">Aequator: </s>
  <s xml:id="echoid-s4279" xml:space="preserve">Item eandem etiam primus, quartus, &amp; </s>
  <s xml:id="echoid-s4280" xml:space="preserve">quintus, puta Horizon, Verticalis, &amp; </s>
  <s xml:id="echoid-s4281" xml:space="preserve"><lb/>Aequator, quòd recti exiſtentes ad Meridianum tranſeant per polos eiuſdem Meridiani, per propoſ. </s>
  <s xml:id="echoid-s4282" xml:space="preserve">13. <lb/></s>
  <s xml:id="echoid-s4283" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4284" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4285" xml:space="preserve">Theodoſii, ibi{q́ue} ſe mutuo interſecent; </s>
  <s xml:id="echoid-s4286" xml:space="preserve">fit, vt omnes quinque vnam &amp; </s>
  <s xml:id="echoid-s4287" xml:space="preserve">eandem habeant ſectionem <lb/>communem. </s>
  <s xml:id="echoid-s4288" xml:space="preserve">Quare in horologio illo, cuius planum vni eorum æquidiſtat, parallelæ erunt, per propoſ. </s>
  <s xml:id="echoid-s4289" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4290" xml:space="preserve"><lb/>huius lib. </s>
  <s xml:id="echoid-s4291" xml:space="preserve">communes ſectiones reliquorum quatuor, &amp; </s>
  <s xml:id="echoid-s4292" xml:space="preserve">plani horologĳ. </s>
  <s xml:id="echoid-s4293" xml:space="preserve">Quòd ſi horologĳ planum omnes <lb/>
<anchor type="note" xlink:label="note-0098-11a" xlink:href="note-0098-11"/>
quinque circulos ſecet, æquidistet tamen communi eorum ſectioni, erunt per eandem propoſ. </s>
  <s xml:id="echoid-s4294" xml:space="preserve">18. </s>
  <s xml:id="echoid-s4295" xml:space="preserve">omnium <lb/>illorum, &amp; </s>
  <s xml:id="echoid-s4296" xml:space="preserve">plani horologĳ ſectiones communes, parallelæ.</s>
  <s xml:id="echoid-s4297" xml:space="preserve"/>
</p>
<div xml:id="echoid-div274" type="float" level="2" n="5">
<note position="left" xlink:label="note-0098-10" xlink:href="note-0098-10a" xml:space="preserve">Horizon, circu-<lb/>lus horæ ſextæ à <lb/>mer vel med. <lb/>noc. circulus ho <lb/>ræ 12 ab or, vel <lb/>occ. Verticalis, <lb/>átque Aequa-<lb/>tor, vnam ean-<lb/>demq́; habent <lb/>ſectionem com <lb/>munem.</note>
<note position="left" xlink:label="note-0098-11" xlink:href="note-0098-11a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">In horologio <lb/>Aequinoct@ali <lb/>Iinea horizonta <lb/>lis, ſeu horæ <lb/>24. ab or. uel <lb/>Occ. linea horæ <lb/>12. ab or. uel <lb/>Occ. linea hotæ <lb/>6. à mer. uel <lb/>med. nocte, &amp; li <lb/>nea Verticalis <lb/>ſunt parallelæ. <lb/>Eædemq́; lineæ <lb/>in horologio ho <lb/>rizõtali atq; Ver <lb/>ticali ſunt pa-<lb/>rallelæ.</note>
<p style="it">
  <s xml:id="echoid-s4298" xml:space="preserve">IT AQVE in horologio Aequinoctiali, cum eius planum Aequatori ſit æquidiſtans, parallelę <lb/>ſunt linea horizontalis, ſeuhoræ 24. </s>
  <s xml:id="echoid-s4299" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s4300" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s4301" xml:space="preserve">linea horæ 12. </s>
  <s xml:id="echoid-s4302" xml:space="preserve">ab ortu vel occaſu, linea horę ſextę <lb/>à meridie vel media nocte, &amp; </s>
  <s xml:id="echoid-s4303" xml:space="preserve">linea Verticalis.</s>
  <s xml:id="echoid-s4304" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4305" xml:space="preserve">SIC quoque eędem lineę, &amp; </s>
  <s xml:id="echoid-s4306" xml:space="preserve">adhuc æquinoctialis linea, parallelæ ſunt in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s4307" xml:space="preserve"><lb/>Verticali, cum illius planum Horizonti, huius verò Verticali circulo æquidiſtet. </s>
  <s xml:id="echoid-s4308" xml:space="preserve">Veruntamen in illo <lb/>linea horizont alis, in hoc vero Verticalis deſcribi nequit, vt ex ĳs, quę inſcholio propoſ. </s>
  <s xml:id="echoid-s4309" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4310" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s4311" xml:space="preserve">ſcripſim{us}, perſpicuum eſt.</s>
  <s xml:id="echoid-s4312" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4313" xml:space="preserve">SIMILITER in horologio polari parallelę ſunt, linea ęquinoctialis, Verticalis, &amp; </s>
  <s xml:id="echoid-s4314" xml:space="preserve">lineę ho-<lb/>
<anchor type="note" xlink:label="note-0098-13a" xlink:href="note-0098-13"/>
rarum 24. </s>
  <s xml:id="echoid-s4315" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4316" xml:space="preserve">12. </s>
  <s xml:id="echoid-s4317" xml:space="preserve">ab ortu vel occaſu. </s>
  <s xml:id="echoid-s4318" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s4319" xml:space="preserve">eius planum circulo ſextę horę à meridie vel media <lb/>nocte ęquidiſtat.</s>
  <s xml:id="echoid-s4320" xml:space="preserve"/>
</p>
<div xml:id="echoid-div275" type="float" level="2" n="6">
<note position="left" xlink:label="note-0098-13" xlink:href="note-0098-13a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s4321" xml:space="preserve">EANDEM denique ob cauſam, parallelę ſunt in horologio Meridiano lineę horarum ſextę, &amp; </s>
  <s xml:id="echoid-s4322" xml:space="preserve"><lb/>18. </s>
  <s xml:id="echoid-s4323" xml:space="preserve">ab ortu vel occaſu, &amp; </s>
  <s xml:id="echoid-s4324" xml:space="preserve">linea ęquinoctialis. </s>
  <s xml:id="echoid-s4325" xml:space="preserve">Habent enim, per propoſ. </s>
  <s xml:id="echoid-s4326" xml:space="preserve">17. </s>
  <s xml:id="echoid-s4327" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4328" xml:space="preserve">circuli ea-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s4329" xml:space="preserve">Meridianus, ſiue circulus horę 12. </s>
  <s xml:id="echoid-s4330" xml:space="preserve">à meridie vel media nocte, nec non, per propoſ. </s>
  <s xml:id="echoid-s4331" xml:space="preserve">16. <lb/></s>
  <s xml:id="echoid-s4332" xml:space="preserve">earundem circuli, &amp; </s>
  <s xml:id="echoid-s4333" xml:space="preserve">Aequator candem ſectionem communem, ęquidiſtat{q́ue} planum horologĳ cir-<lb/>culo Meridiano.</s>
  <s xml:id="echoid-s4334" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4335" xml:space="preserve">HAEC autem omnia ideò dixerim, vt intelligas, aliquando lineas quarundam horarum in tabu-<lb/>lis propoſ. </s>
  <s xml:id="echoid-s4336" xml:space="preserve">19. </s>
  <s xml:id="echoid-s4337" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4338" xml:space="preserve">20. </s>
  <s xml:id="echoid-s4339" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4340" xml:space="preserve">poſitarum, eſſe parallelas in aliquibus horologĳs, cum tamen in <lb/>alĳs ſe mutuo in vno eodem{q́ue} puncto interſecent, vt ibidem diximus. </s>
  <s xml:id="echoid-s4341" xml:space="preserve">Huiuſmodi ſunt lineę horariæ pau <lb/>lo ante adductę,</s>
</p>
<pb o="79" file="0099" n="99" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div277" type="section" level="1" n="114">
<head xml:id="echoid-head117" xml:space="preserve">PROBLEMA 3. PROPOSITIO 23.</head>
<p>
  <s xml:id="echoid-s4342" xml:space="preserve">DECLINATIONEM cuiuſcunque plani à Verticali circulo, <lb/>&amp; </s>
  <s xml:id="echoid-s4343" xml:space="preserve">eiuſdem inclinationem ad Horizontem inueſtigare.</s>
  <s xml:id="echoid-s4344" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Inſtrumentum <lb/>pro declinatio-<lb/>nibus, inclina-<lb/>tionibusq́; pla-<lb/>norum inueſti-<lb/>gandis.</note>
<p>
  <s xml:id="echoid-s4345" xml:space="preserve">PARETVR exligno, vel alia materia ſolida, cuius una ſuperficies plana ſit, rectangulum <lb/>quodcunque A B C D, cuius lateribus A B, D C, diuiſis bifariam in E, &amp; </s>
  <s xml:id="echoid-s4346" xml:space="preserve">F, ducatur recta E F, quæ <lb/>parallela erit vtriq; </s>
  <s xml:id="echoid-s4347" xml:space="preserve">lateri A D, <lb/>
<anchor type="figure" xlink:label="fig-0099-01a" xlink:href="fig-0099-01"/>
<anchor type="note" xlink:label="note-0099-02a" xlink:href="note-0099-02"/>
<anchor type="note" xlink:label="note-0099-03a" xlink:href="note-0099-03"/>
<anchor type="note" xlink:label="note-0099-04a" xlink:href="note-0099-04"/>
B C, ac propterea anguli ad <lb/>E, recti. </s>
  <s xml:id="echoid-s4348" xml:space="preserve">Vel certe in extremo <lb/>ſuperficiei planæ ſit linea re-<lb/>cta A B, quam ad rectos an-<lb/>gulos ſecet recta E F, quid-<lb/>quid ſit de alijs lineis.</s>
  <s xml:id="echoid-s4349" xml:space="preserve"/>
</p>
<div xml:id="echoid-div277" type="float" level="2" n="1">
  <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a">
    <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0099-01"/>
  </figure>
<note position="left" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">33. primi.</note>
<note position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">29. primi.</note>
</div>
<p>
  <s xml:id="echoid-s4350" xml:space="preserve">HOC inſtrumento, etiãſi <lb/>non ſit rectangulum, declina-<lb/>tionẽ cuiuſque plani (Appel-<lb/>lo autem declinationem angu <lb/>
<anchor type="note" xlink:label="note-0099-05a" xlink:href="note-0099-05"/>
lum acutum, quem faciunt <lb/>cõmunes ſectiones Horizon-<lb/>tis cum plano propoſito, &amp; </s>
  <s xml:id="echoid-s4351" xml:space="preserve"><lb/>Verticali circulo) inueſtigabi-<lb/>
<anchor type="note" xlink:label="note-0099-06a" xlink:href="note-0099-06"/>
mus hoc modo. </s>
  <s xml:id="echoid-s4352" xml:space="preserve">In plano pro-<lb/>poſito, quod ſit vel rectum ad <lb/>Horizontem, vt eſt planum <lb/>cuiuſcunq; </s>
  <s xml:id="echoid-s4353" xml:space="preserve">muri ad perpendi-<lb/>culum ædificati, vel inclinatũ, <lb/>vt eſt planum cuiuslibet tecti, <lb/>
<anchor type="note" xlink:label="note-0099-07a" xlink:href="note-0099-07"/>
deſcribatur beneficio libellæ, <lb/>&amp; </s>
  <s xml:id="echoid-s4354" xml:space="preserve">perpendiculi, linea A B, <lb/>Horizonti æquidiſtans, com-<lb/>munis videlicet ſectio plani <lb/>propoſiti, &amp; </s>
  <s xml:id="echoid-s4355" xml:space="preserve">Hotizontis. </s>
  <s xml:id="echoid-s4356" xml:space="preserve">Vel <lb/>certè in plano ad Horizõtem <lb/>recto, per filum, cui adhæret <lb/>perpendiculum, libere demiſſum ducatur in muro linea reſpondens filo perpendiculi, quæ ad <lb/>Horizontẽ perpendicularis erit. </s>
  <s xml:id="echoid-s4357" xml:space="preserve">Deinde hãc ad rectos angulos ſecet alia linea recta AB. </s>
  <s xml:id="echoid-s4358" xml:space="preserve">Hæc enim <lb/>erit Horizonti æquidiſtans, vel ſi mauis, cõmunis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s4359" xml:space="preserve">muri. </s>
  <s xml:id="echoid-s4360" xml:space="preserve">Quoniã enim murus <lb/>
<anchor type="note" xlink:label="note-0099-08a" xlink:href="note-0099-08"/>
ad Horizontem rectus ponitur, &amp; </s>
  <s xml:id="echoid-s4361" xml:space="preserve">in muro per filum perpendiculi ducta eſt ad Horizontem linea <lb/>perpendicularis, erit hæc eadem, per defin. </s>
  <s xml:id="echoid-s4362" xml:space="preserve">4. </s>
  <s xml:id="echoid-s4363" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4364" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4365" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s4366" xml:space="preserve">ad communem ſectionem Horizontis <lb/>atq; </s>
  <s xml:id="echoid-s4367" xml:space="preserve">muri perpendicularis. </s>
  <s xml:id="echoid-s4368" xml:space="preserve">Recta ergo A B, ad hãc ducta perpendicularis, cõmunis erit ſectio muri <lb/>atq; </s>
  <s xml:id="echoid-s4369" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s4370" xml:space="preserve">Huic lineæ A B, latus inſtrumẽti A B, applicetur, ipſumq́; </s>
  <s xml:id="echoid-s4371" xml:space="preserve">inſtrumentũ Horizonti <lb/>æquidiſtãs beneficio libellæ, &amp; </s>
  <s xml:id="echoid-s4372" xml:space="preserve">perpendiculi ſtatuatur. </s>
  <s xml:id="echoid-s4373" xml:space="preserve">Deinde in inſtrumẽto inueniatur beneficio <lb/>acus Magnete illitæ, vel ea ratione, quam in cõmentariis in ſphæram, cũ de Meridiano circulo age <lb/>remus, tradidimus, vel quod magis probo, ex ſcholio ſequẽti, linea meridiana G H. </s>
  <s xml:id="echoid-s4374" xml:space="preserve">Ex hac enim <lb/>id, quod proponitur, abſoluemus hac ratione. </s>
  <s xml:id="echoid-s4375" xml:space="preserve">Si linea meridiana G H, æquidiſter rectæ E F, oc-<lb/>curratq́ muro, vel lineæ A B, quæ Horizonti æquidiſtat, ad angulos rectos, carebit murus decli-<lb/>natione, ſpectabitq́; </s>
  <s xml:id="echoid-s4376" xml:space="preserve">rectà ad meridiem, vel Septentrionem, ita vt, ſi rectus fuerit ad Horizontem, <lb/>
<anchor type="note" xlink:label="note-0099-09a" xlink:href="note-0099-09"/>
Verticali circulo proprie dicto æquidiſter; </s>
  <s xml:id="echoid-s4377" xml:space="preserve">Si vero ad Horizontem fuerit inclinatus, rectus ſitad <lb/>Meridianum, æquidiſtetq́; </s>
  <s xml:id="echoid-s4378" xml:space="preserve">circulo maximo per puncta ortus &amp; </s>
  <s xml:id="echoid-s4379" xml:space="preserve">occaſus æquinoctialis tranſeunti; <lb/></s>
  <s xml:id="echoid-s4380" xml:space="preserve">quale eſt planum æquinoctialis circuli, circuli horæ ſextæ aſtronomicæ, circuli horæ 12. </s>
  <s xml:id="echoid-s4381" xml:space="preserve">ab ortu, <lb/>vel occaſu, &amp; </s>
  <s xml:id="echoid-s4382" xml:space="preserve">denique plana circulorum hectemoriorum, de quibus Prolemæus in Analemmate. </s>
  <s xml:id="echoid-s4383" xml:space="preserve"><lb/>At ſi meridiana linea G H, rectam E F, ſecet in I, ad angulos rectos, planum muri rectà in ortum, <lb/>vel occaſum verget, ita vt, ſi rectum ad Horizontem fuerit, parallelum ſit Meridiano circulo. </s>
  <s xml:id="echoid-s4384" xml:space="preserve">Si <lb/>verò inclinatum fuerit ad Horizontem, rectum ſit ad Verticalem circulum proprie dictum, æqui <lb/>diſtetq́; </s>
  <s xml:id="echoid-s4385" xml:space="preserve">maximo circulo per puncta, vbi circunferentia Meridiani circuli Horizontis circunferen <lb/>tiam interſecat, ducto; </s>
  <s xml:id="echoid-s4386" xml:space="preserve">qualia ſunt plana circulorum horariorum, de quibus Ptolemæus in A-<lb/>nalemmate. </s>
  <s xml:id="echoid-s4387" xml:space="preserve">Si denique linea meridiana G H, rectam E F, ſecet ad angulos inæquales in I, decli-<lb/>nabit planum &amp; </s>
  <s xml:id="echoid-s4388" xml:space="preserve">à Verticali circulo, &amp; </s>
  <s xml:id="echoid-s4389" xml:space="preserve">à Meridiano, ita vt neque rectà ad meridiem, Septentrio-<lb/>nemve, neque ad ortum, vel occaſum ſpectet. </s>
  <s xml:id="echoid-s4390" xml:space="preserve">Angulus autem E I G, ſemper erit angulus decli-
<pb o="80" file="0100" n="100" rhead="GNOMONICES"/>
nationis plani à Verticali circulo proprie dicto, ita vt tanta ſit declinatio plani, quantus eſt angu-<lb/>lus E I G, atque adeo arcus circuli ex centro I, deſcripti inter rectas I E, I G, comprehenſus conti-<lb/>neat gradus declinationis. </s>
  <s xml:id="echoid-s4391" xml:space="preserve">Ducatur enim G K, in plano inſtrumẽti A B C D, perpendicularis ad <lb/>G H, ita vt G K, ſit communis ſectio Verticalis circuli proprie dicti, &amp; </s>
  <s xml:id="echoid-s4392" xml:space="preserve">plani, in quo eſt inſtrumen <lb/>
<anchor type="figure" xlink:label="fig-0100-01a" xlink:href="fig-0100-01"/>
tum A B C D. </s>
  <s xml:id="echoid-s4393" xml:space="preserve">Erit igitur <lb/>E G K, angulus declinationis <lb/>plani propoſiti per rectã A B, <lb/>ducti à Verticali per rectam <lb/>G k, ducto. </s>
  <s xml:id="echoid-s4394" xml:space="preserve">Nam cum &amp; </s>
  <s xml:id="echoid-s4395" xml:space="preserve">Ver <lb/>ticalis circuli planũ per G K, <lb/>
<anchor type="note" xlink:label="note-0100-01a" xlink:href="note-0100-01"/>
&amp; </s>
  <s xml:id="echoid-s4396" xml:space="preserve">planum propoſitum per <lb/>A B, ductum, rectum ſit ad Ho <lb/>rizontem, erit quoque com-<lb/>munis ſectio Verticalis, &amp; </s>
  <s xml:id="echoid-s4397" xml:space="preserve">pla <lb/>ni propoſiti perpendicularis <lb/>
<anchor type="note" xlink:label="note-0100-02a" xlink:href="note-0100-02"/>
ad Horizontem, atque adeo <lb/>&amp; </s>
  <s xml:id="echoid-s4398" xml:space="preserve">ad rectas G k, A B, in Ho-<lb/>rizonte exiſtentes, ex deſin. <lb/></s>
  <s xml:id="echoid-s4399" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4400" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4401" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4402" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s4403" xml:space="preserve">Igitur ex <lb/>definitione 6. </s>
  <s xml:id="echoid-s4404" xml:space="preserve">eiuſdem libri, <lb/>
<anchor type="note" xlink:label="note-0100-03a" xlink:href="note-0100-03"/>
erit E G K, angulus decli-<lb/>nationis, ſiue inclinationis <lb/>plani propoſiti per A B, ducti <lb/>ad Verticalem circulum per <lb/>G k, ductum; </s>
  <s xml:id="echoid-s4405" xml:space="preserve">quandoquidem <lb/>rectæ G K, G E, ad idem pun <lb/>ctũ G, cõmunis ſectionis pla-<lb/>ni ꝓpoſiti, &amp; </s>
  <s xml:id="echoid-s4406" xml:space="preserve">Verticalis, rectos <lb/>cũ cõmuni ſectione angulos <lb/>efficiunt, vt dictum eſt. </s>
  <s xml:id="echoid-s4407" xml:space="preserve">Quòd <lb/>
<anchor type="note" xlink:label="note-0100-04a" xlink:href="note-0100-04"/>
ſi planum per A B, ductum <lb/>non ſit rectum ad Horizontẽ, <lb/>erit nihilominus E G K, angulus declinationis, licet impropriè. </s>
  <s xml:id="echoid-s4408" xml:space="preserve">oſtendit enim declinationem li-<lb/>neæ A B, quæ Horizonti æquidiſtat, à Verticali circulo. </s>
  <s xml:id="echoid-s4409" xml:space="preserve">Quamobrem, cum angulo E G K, ęqualis <lb/>ſit angulus E I G, (cum enim angulus I G K, rectus ęqualis ſit duobus angulis ſimul I G E, E I G, <lb/>quòd hi vhi angulo recto æquales ſint, ob rectum angulum G E I; </s>
  <s xml:id="echoid-s4410" xml:space="preserve">ſi dematur communis angu-<lb/>
<anchor type="note" xlink:label="note-0100-05a" xlink:href="note-0100-05"/>
lus I G E, remanebuntęquales anguli E G K, E I G.) </s>
  <s xml:id="echoid-s4411" xml:space="preserve">erit quoque E I G, angulus declinationis pla-<lb/>ni dati à Verticali circulo. </s>
  <s xml:id="echoid-s4412" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s4413" xml:space="preserve"/>
</p>
<div xml:id="echoid-div278" type="float" level="2" n="2">
<note position="left" xlink:label="note-0099-05" xlink:href="note-0099-05a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0099-06" xlink:href="note-0099-06a" xml:space="preserve">Declinatie pla-<lb/>ni p<unsure/>poſiti quo <lb/>modo@ inquira-<lb/>tur.</note>
<note position="left" xlink:label="note-0099-07" xlink:href="note-0099-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0099-08" xlink:href="note-0099-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0099-09" xlink:href="note-0099-09a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0100-01" xlink:href="fig-0100-01a">
    <image file="0100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0100-01"/>
  </figure>
<note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0100-03" xlink:href="note-0100-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0100-04" xlink:href="note-0100-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0100-05" xlink:href="note-0100-05a" xml:space="preserve">32. primi.</note>
</div>
<p>
  <s xml:id="echoid-s4414" xml:space="preserve">IAM vero, num planum propoſitum ad ortum declinet, an ad occaſum, ita cognoſcemus. </s>
  <s xml:id="echoid-s4415" xml:space="preserve">Si <lb/>
<anchor type="note" xlink:label="note-0100-06a" xlink:href="note-0100-06"/>
planum ad meridiem vergat, &amp; </s>
  <s xml:id="echoid-s4416" xml:space="preserve">meridiana linea ſecet rectam E B, ipſum declinabit à meridie in <lb/>
<anchor type="note" xlink:label="note-0100-07a" xlink:href="note-0100-07"/>
ortum: </s>
  <s xml:id="echoid-s4417" xml:space="preserve">ſi verò linea meridiana ſecet rectam E A, &amp; </s>
  <s xml:id="echoid-s4418" xml:space="preserve">planum ſpectet ad meridiem, ipſum à meri-<lb/>die in occaſum declinabit. </s>
  <s xml:id="echoid-s4419" xml:space="preserve">Contra verò, ſi planum ad Septentrionem vergat. </s>
  <s xml:id="echoid-s4420" xml:space="preserve">Nam linea meridia-<lb/>na ſecante rectam E B, planum à Septentrione in occaſum, ſecante autem recram E A, in ortum <lb/>declinabit, vt ex figura apparet. </s>
  <s xml:id="echoid-s4421" xml:space="preserve">Iam vero, ſi ex I, circulum deſcribas ad quodcunque interuallum, <lb/>dabit arcus inter rectas I E, I G, comprehenſus, gradus declinationis, vt etiam ante diximus.</s>
  <s xml:id="echoid-s4422" xml:space="preserve"/>
</p>
<div xml:id="echoid-div279" type="float" level="2" n="3">
<note position="left" xlink:label="note-0100-06" xlink:href="note-0100-06a" xml:space="preserve">An planũ pro-<lb/>poſitum in or-<lb/>tum, an uerò <lb/>in occaſum de-<lb/>clinet, qua ra-<lb/>tione cognoſca-<lb/>tur.</note>
<note position="left" xlink:label="note-0100-07" xlink:href="note-0100-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s4423" xml:space="preserve">IDEM hoc modo diſcemus. </s>
  <s xml:id="echoid-s4424" xml:space="preserve">Quoniam linea meridiana G H, dum ipſam E F, ſecat oblique, <lb/>cum recta A B, efficit angulum acutum, cui ſemper ſubtenditur recta I E, &amp; </s>
  <s xml:id="echoid-s4425" xml:space="preserve">reliquum obtuſum; <lb/></s>
  <s xml:id="echoid-s4426" xml:space="preserve">ex qua parte extiterit hic angulus obtuſus, in eam planũ declinabit, adeo vt ſi angulus obtuſus fue <lb/>rit verſus ortum, planũ à meridie vel Septẽtrione in ortũ, ſi vero in occaſum, in occaſum declinet.</s>
  <s xml:id="echoid-s4427" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4428" xml:space="preserve">CAETERVM tunc planum à meridie declinare in ortum vel occaſum, hoc eſt, ad meridiẽ <lb/>
<anchor type="note" xlink:label="note-0100-08a" xlink:href="note-0100-08"/>
ſpectare ſciemus, cum nobis ad planum conuerſis Sol à dextris oritur, &amp; </s>
  <s xml:id="echoid-s4429" xml:space="preserve">occidit à ſiniſtris; </s>
  <s xml:id="echoid-s4430" xml:space="preserve">à Se-<lb/>
<anchor type="note" xlink:label="note-0100-09a" xlink:href="note-0100-09"/>
ptentrione vero, cum ex parte ſiniſtra oritur, &amp; </s>
  <s xml:id="echoid-s4431" xml:space="preserve">ex parte dextra occidit. </s>
  <s xml:id="echoid-s4432" xml:space="preserve">Quòd ſi planum tantam <lb/>habeat declinationem à Verticali, vt parum à Meridiano circulo differat, proptereaq́; </s>
  <s xml:id="echoid-s4433" xml:space="preserve">difficile ad-<lb/>modum ſit dignoſcere, an ad meridiem ſpecter, an vero ad Septentrionem, vtemur hac arte. </s>
  <s xml:id="echoid-s4434" xml:space="preserve">Ad <lb/>muri planum, vel certe ad rectam, quę in eo parallela ducta eſt Horizõti, ducemus in plano, quod <lb/>Horizonti ęquidiſter, perpendicularem, &amp; </s>
  <s xml:id="echoid-s4435" xml:space="preserve">eius declinationem inueſtigabimus. </s>
  <s xml:id="echoid-s4436" xml:space="preserve">Si enim murus à <lb/>Meridiano circulo parum declinat, parum etiam declinabit dicta perpendicularis à Verticali cir-<lb/>culo proprie dicto, ac proinde ſacile intelligemus, num ea ad meridiem, vel ad Septentrionem <lb/>ſpectet, ſecundum regulam pręſcript@m: </s>
  <s xml:id="echoid-s4437" xml:space="preserve">quare &amp; </s>
  <s xml:id="echoid-s4438" xml:space="preserve">eius declinationem cognoſcemus. </s>
  <s xml:id="echoid-s4439" xml:space="preserve">Itaque ſi hęc <lb/>perpendicularis declinet à meridie in ortũ, vel à Septentrione in occaſum, declinabit murus pro-<lb/>poſitus à Septentrione in ortum, ſi ad ortum ſpectat, vel à meridie in occaſum, ſi ad occaſum per-
<pb o="81" file="0101" n="101" rhead="LIBER PRIMVS."/>
tinet. </s>
  <s xml:id="echoid-s4440" xml:space="preserve">Si vero dicta perpendicularis à meridie in <lb/>
<anchor type="figure" xlink:label="fig-0101-01a" xlink:href="fig-0101-01"/>
occaſum, vel à Septentrione in ortum declinet, <lb/>declinabit murus propoſitus à meridie in ortũ, ſi <lb/>ad ortum vergit, vel à Septentrione in occaſum, ſi <lb/>ad occaſum ſpectat. </s>
  <s xml:id="echoid-s4441" xml:space="preserve">Quę omnia ex hac figura per-<lb/>ſpicua ſunt, in qua linea meridiana eſt I k, &amp; </s>
  <s xml:id="echoid-s4442" xml:space="preserve">com-<lb/>munis ſectio Verticalis circuli &amp; </s>
  <s xml:id="echoid-s4443" xml:space="preserve">Horizontis L M, <lb/>illam in N, ad rectos angulos ſecans. </s>
  <s xml:id="echoid-s4444" xml:space="preserve">Nam propo-<lb/>ſito muro A B, qui ad ortum, &amp; </s>
  <s xml:id="echoid-s4445" xml:space="preserve">muro C D, qui ad <lb/>
<anchor type="note" xlink:label="note-0101-01a" xlink:href="note-0101-01"/>
occaſum ſpectat, quoniam perpendicularis B C, à <lb/>meridie in ortũ, &amp; </s>
  <s xml:id="echoid-s4446" xml:space="preserve">perpendicularis A D, à Septen-<lb/>trione in occaſum declinat, idcirco murus A B, à <lb/>Septentrione in ortum, &amp; </s>
  <s xml:id="echoid-s4447" xml:space="preserve">murus C D, à meridie <lb/>in occaſum declinat. </s>
  <s xml:id="echoid-s4448" xml:space="preserve">Similiter propoſito muro E F, <lb/>ad ortum, &amp; </s>
  <s xml:id="echoid-s4449" xml:space="preserve">muro G H, ad occaſum vergente, <lb/>quia perpendicularis F G, à meridie in occaſum, &amp; </s>
  <s xml:id="echoid-s4450" xml:space="preserve"><lb/>perpendicularis E H, à Septentrione in ortum de-<lb/>clinat, propterea murus E F, à meridie in ortũ, &amp; </s>
  <s xml:id="echoid-s4451" xml:space="preserve">murus G H, à Septentrione in occaſum declinat.</s>
  <s xml:id="echoid-s4452" xml:space="preserve"/>
</p>
<div xml:id="echoid-div280" type="float" level="2" n="4">
<note position="left" xlink:label="note-0100-08" xlink:href="note-0100-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0100-09" xlink:href="note-0100-09a" xml:space="preserve">An planũ pro-<lb/>poſitum ad me-<lb/>ridiem ſpectet, <lb/>an ad Septen-<lb/>trionem.</note>
  <figure xlink:label="fig-0101-01" xlink:href="fig-0101-01a">
    <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0101-01"/>
  </figure>
<note position="left" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s4453" xml:space="preserve">IDEM per ſolam lineam meridianam obtinere poſſumus. </s>
  <s xml:id="echoid-s4454" xml:space="preserve">Inuenta enim prope murum li-<lb/>
<anchor type="note" xlink:label="note-0101-02a" xlink:href="note-0101-02"/>
nea meridiana in plano, quod Horizonti ęquidiſtet, ſi hęc cum muro coeat ad partes Boreę, mu-<lb/>rusq́; </s>
  <s xml:id="echoid-s4455" xml:space="preserve">ad ortum ſpectet, declinabit murus à meridie in ortum, à meridie vero in occaſum, ſi ad <lb/>occaſum ſpectet murus. </s>
  <s xml:id="echoid-s4456" xml:space="preserve">Si autem linea meridiana cum muro coeat ad partes auſtrales, declinabit <lb/>murus à Septentrione in ortum vel occaſum, prout ad ortum, vel occaſum ſpectat, vt ex priori fi-<lb/>gura huius propoſ. </s>
  <s xml:id="echoid-s4457" xml:space="preserve">facile apparet. </s>
  <s xml:id="echoid-s4458" xml:space="preserve">Sed quoniam in planis, quæ parum à Meridiano circulo diffe-<lb/>runt, vix meridiana linea cum ipſis concurrit, idcirco priorem modum eligendũ eſſe iudicarem.</s>
  <s xml:id="echoid-s4459" xml:space="preserve"/>
</p>
<div xml:id="echoid-div281" type="float" level="2" n="5">
<note position="left" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s4460" xml:space="preserve">IN planis ad Horizontem rectis facilius idem hac ratione conſequemur. </s>
  <s xml:id="echoid-s4461" xml:space="preserve">Expectetur aliquo <lb/>die tempus meridiei, quod vel per horologium aliquod, vel per altitudinem meridianam Solis di-<lb/>ligenter diſcendum erit. </s>
  <s xml:id="echoid-s4462" xml:space="preserve">Nam ſi tunc planum propoſitum à Sole illuſtretur, dubitandum nullo <lb/>pacto erit, quin ad auſtrum uergat, ad boream uero, ſi non illuminetur a Sole. </s>
  <s xml:id="echoid-s4463" xml:space="preserve">Immo hoc etiam <lb/>
<anchor type="note" xlink:label="note-0101-03a" xlink:href="note-0101-03"/>
modo diſcemus, an planum propoſitũ in ortum declinet, an vero in occaſum. </s>
  <s xml:id="echoid-s4464" xml:space="preserve">Si enim ad meridiẽ <lb/>ſpectet, longiori autem tempore ante meridiem illuſtretur a ſole, quam poſt meridiem, declinabit <lb/>à meridie in ortum, in occaſum autem, ſi contra ſe res habeat. </s>
  <s xml:id="echoid-s4465" xml:space="preserve">Sic quoque, ſi planum ſpectet ad bo <lb/>ream, &amp; </s>
  <s xml:id="echoid-s4466" xml:space="preserve">pluribus horis matutino tempore, quam ueſpertino illuminetur à Sole, deflectet à Se-<lb/>ptentrione in ortum, ſi uero contrario modo ſe res habeat, in occaſum.</s>
  <s xml:id="echoid-s4467" xml:space="preserve"/>
</p>
<div xml:id="echoid-div282" type="float" level="2" n="6">
<note position="left" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s4468" xml:space="preserve">IDEM experiri licet in planis ad Horizontem inclinatis, ſi tempore meridiei ſupra lineam, <lb/>quæ in propoſito plano ducta eſt Horizõti æquidiſtãs, ſtatuatur tabella aliqua plana ex quacunque <lb/>materia ad Horizontem recta, &amp; </s>
  <s xml:id="echoid-s4469" xml:space="preserve">obſeruetur, utrum facies illa, quæ cum plano inclinato obtuſum <lb/>angulum conficit, illuſtretur tunc à Sole, nec ne. </s>
  <s xml:id="echoid-s4470" xml:space="preserve">Ex hoc enim cognoſcemus, ut de planis ad Hori-<lb/>zontem rectis diximus, an ea tabella, atque adeo &amp; </s>
  <s xml:id="echoid-s4471" xml:space="preserve">linea illa Horizonti æquidiſtans, uel potius pla-<lb/>
<anchor type="note" xlink:label="note-0101-04a" xlink:href="note-0101-04"/>
num ipſum inclinatum à meridie declinet, an a Septentrione.</s>
  <s xml:id="echoid-s4472" xml:space="preserve"/>
</p>
<div xml:id="echoid-div283" type="float" level="2" n="7">
<note position="left" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s4473" xml:space="preserve">HÆC autem omnia intelligẽda ſunt in ſphæra obliqua maiorem latitudinem habente, quam <lb/>gr. </s>
  <s xml:id="echoid-s4474" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4475" xml:space="preserve">min. </s>
  <s xml:id="echoid-s4476" xml:space="preserve">30. </s>
  <s xml:id="echoid-s4477" xml:space="preserve">quanta uidelicet eſt maxima declinatio Solis. </s>
  <s xml:id="echoid-s4478" xml:space="preserve">Nam in minori latitudine fieri poteſt <lb/>ut planum a Septentrione declinans illuſtretur à Sole in meridie, dum in principio ♋, exiſtit, uel <lb/>prope, vt ex ſphæra materiali conſtat. </s>
  <s xml:id="echoid-s4479" xml:space="preserve">Sed Sole exiſtente auſtraliore ipſo muro, ita ut umbræ om-<lb/>nes in Septentrionem proijciantur, locum etiam habebunt ea, quæ diximus, in ſphæra obliqua <lb/>minoris latitudinis, quàm gr. </s>
  <s xml:id="echoid-s4480" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4481" xml:space="preserve">min. </s>
  <s xml:id="echoid-s4482" xml:space="preserve">30.</s>
  <s xml:id="echoid-s4483" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4484" xml:space="preserve">QVOD ſi murus parum à Meridiano circulo abſit, &amp; </s>
  <s xml:id="echoid-s4485" xml:space="preserve">tectum ędificii ita promineat, vt in me-<lb/>ridie murus à Sole nõ poſſit illuſtrari, ducenda erit in ſolo procul à muro linea ipſi muro æqui-<lb/>diſtans, ita vt in meridie tota à Sole illuminetur. </s>
  <s xml:id="echoid-s4486" xml:space="preserve">Nam ſi ſtylus in ea linea poſitus, vel certe filum <lb/>
<anchor type="note" xlink:label="note-0101-05a" xlink:href="note-0101-05"/>
cum perpendiculo libere pendens proiiciat in meridie vmbram, quę illam lineam ſecet, ita vt ex <lb/>parte Septentrionali vmbra ſit inter murum, &amp; </s>
  <s xml:id="echoid-s4487" xml:space="preserve">dictam lineam, ſpectabit murus ad meridiem; </s>
  <s xml:id="echoid-s4488" xml:space="preserve">ad <lb/>boream vero, ſi contra linea illa ex parte boreali extiterit inter vmbram &amp; </s>
  <s xml:id="echoid-s4489" xml:space="preserve">murum. </s>
  <s xml:id="echoid-s4490" xml:space="preserve">Si autem vm-<lb/>bra in ipſam lineam cadet, æquidiſtabit murus Meridiano circulo.</s>
  <s xml:id="echoid-s4491" xml:space="preserve"/>
</p>
<div xml:id="echoid-div284" type="float" level="2" n="8">
<note position="left" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s4492" xml:space="preserve">INCLINATIONEM autẽ cuiuslibet plani ad Horizontem (voco autẽ inclinationem an-<lb/>
<anchor type="note" xlink:label="note-0101-06a" xlink:href="note-0101-06"/>
gulum acutum, quem faciunt cõmunes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s4493" xml:space="preserve">plani propoſiti cum alio plano ad <lb/>vtrumque recto) eodẽ inſtrumẽto A B C D, hac ratione inueſtigabimus. </s>
  <s xml:id="echoid-s4494" xml:space="preserve">Inuenta in plano propoſi-<lb/>to linea, quę Horizonti ęquidiſte@, nempe cõmuni ſectione plani propoſiti, &amp; </s>
  <s xml:id="echoid-s4495" xml:space="preserve">Horizõtis, ſecet eam <lb/>in M, ad angulos rectos recta N O; </s>
  <s xml:id="echoid-s4496" xml:space="preserve">cui inſtrumẽti latus A B, applicetur, ipſumq́; </s>
  <s xml:id="echoid-s4497" xml:space="preserve">inſtrumentũ be-<lb/>neficio perpendiculi ita erigatur, vt rectum ſit ad planum propoſitũ. </s>
  <s xml:id="echoid-s4498" xml:space="preserve">Deinde in inſtrumento ſic ere <lb/>cto ducatur eiuſdẽ perpendiculi beneficio ad Horizontẽ perpendicularis HG, ſecans E F, in I. </s>
  <s xml:id="echoid-s4499" xml:space="preserve">Dico <lb/>E I G, eſſe angulum inclinationis plani ad Horizontẽ. </s>
  <s xml:id="echoid-s4500" xml:space="preserve">Intelligatur enim G k, in plano inſtrumen-
<pb o="82" file="0102" n="102" rhead="GNOMONICES"/>
ti A B C D, perpendicularis ad G H, ita vt G K, communis ſit ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s4501" xml:space="preserve">plani, in que <lb/>eſt inſtrumentum A B C D. </s>
  <s xml:id="echoid-s4502" xml:space="preserve">Erit igitur E G K, angulus inclinationis plani propoſiti ad Horizon-<lb/>tem. </s>
  <s xml:id="echoid-s4503" xml:space="preserve">Nam cum &amp; </s>
  <s xml:id="echoid-s4504" xml:space="preserve">planum propoſitum ex conſtructione, &amp; </s>
  <s xml:id="echoid-s4505" xml:space="preserve">planum Horizontis rectum ſit ad <lb/>planum inſtrumẽti A B C D; </s>
  <s xml:id="echoid-s4506" xml:space="preserve">(cùm enim H G, per-<lb/>
<anchor type="figure" xlink:label="fig-0102-01a" xlink:href="fig-0102-01"/>
pendicularis ſit ad Horizontem, erit &amp; </s>
  <s xml:id="echoid-s4507" xml:space="preserve">planum <lb/>A B C D, per H G, ductum ad Horizontem rectum, <lb/>
<anchor type="note" xlink:label="note-0102-01a" xlink:href="note-0102-01"/>
&amp; </s>
  <s xml:id="echoid-s4508" xml:space="preserve">contra)<unsure/> erit quoque communis ſectio plani pro-<lb/>poſiti, ac Horizõtis ad idem planum A B C D, per-<lb/>
<anchor type="note" xlink:label="note-0102-02a" xlink:href="note-0102-02"/>
pendicularis, atque adeo &amp; </s>
  <s xml:id="echoid-s4509" xml:space="preserve">ad rectas E G, G K, in <lb/>dicto plano A B C D, exiſtentes, ex defin. </s>
  <s xml:id="echoid-s4510" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4511" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4512" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s4513" xml:space="preserve">
<anchor type="note" xlink:label="note-0102-03a" xlink:href="note-0102-03"/>
Euclidis, ſi Horizon in puncto G, ſecare intelligatur <lb/>planũ propoſitum. </s>
  <s xml:id="echoid-s4514" xml:space="preserve">Igitur ex definitione ſexta eiuſ-<lb/>dem libri, erit E G K, angulus inclinationis plani <lb/>propoſiti ad Horizontem, quandoquidem rectę <lb/>E G, G k, quarum illa in plano propoſito, hęc vero <lb/>in Horizonte exiſtit, ad idem punctum G, commu-<lb/>nis ſectionis plani propoſiti, &amp; </s>
  <s xml:id="echoid-s4515" xml:space="preserve">Horizontis, rectos <lb/>cum communi ſectione angulos efficiunt, vt dictũ <lb/>eſt. </s>
  <s xml:id="echoid-s4516" xml:space="preserve">Quamobrem, cum angulo E G K, ęqualis ſit an-<lb/>gulus E I G, (cum enim angulus I G k, rectus ęqua-<lb/>
<anchor type="note" xlink:label="note-0102-04a" xlink:href="note-0102-04"/>
lis ſit duobus angulis ſimul I G E, E I G, quòd hi vni angulo recto ęquales ſint, ob rectum angulũ <lb/>
<anchor type="note" xlink:label="note-0102-05a" xlink:href="note-0102-05"/>
G E I; </s>
  <s xml:id="echoid-s4517" xml:space="preserve">ſi tollatur communis E G I, reliqui erunt ęquales E G k, E I G) erit quoque E I G, angulus <lb/>inclinationis plani dati ad Horizontem. </s>
  <s xml:id="echoid-s4518" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s4519" xml:space="preserve"/>
</p>
<div xml:id="echoid-div285" type="float" level="2" n="9">
<note position="right" xlink:label="note-0101-06" xlink:href="note-0101-06a" xml:space="preserve">Inclinatio pla-<lb/>ni propoſiti ad <lb/>Horizontẽ qua <lb/>ratione inuefti <lb/>ganda ſit.</note>
  <figure xlink:label="fig-0102-01" xlink:href="fig-0102-01a">
    <image file="0102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0102-01"/>
  </figure>
<note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">32. primi.</note>
</div>
<p>
  <s xml:id="echoid-s4520" xml:space="preserve">QVOD ſi perpendicularis H G, ſecet rectam E F, in I, ad angulos rectos, carebit planum <lb/>propoſitum inclinatione ad Horizontem, rectumq́; </s>
  <s xml:id="echoid-s4521" xml:space="preserve">ad ipſum erit, vt patet.</s>
  <s xml:id="echoid-s4522" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s4523" xml:space="preserve">FACILE autẽ intelligemus, in quamnam partem planum inclinet, hoc eſt, an in partem he-<lb/>
<anchor type="note" xlink:label="note-0102-06a" xlink:href="note-0102-06"/>
miſphęrij ſuperioris Septen@rionalem, an in auſtralem, cogn ita declinatione eiuſdem plani à Ver-<lb/>ticali. </s>
  <s xml:id="echoid-s4524" xml:space="preserve">Nam ſi planum à Septentrione in ortum vel in occaſum declinet, cadet inclinatio in partẽ <lb/>hemiſphęrij auſtralem: </s>
  <s xml:id="echoid-s4525" xml:space="preserve">Si verò à meridie in ortum vel occaſum, cadet in partem hemiſphęrij <lb/>Septentrionalẽ, vt ex Sphęra materiali perſpicuum eſt. </s>
  <s xml:id="echoid-s4526" xml:space="preserve">Iam verò ſi ex I, circulus deſcribatur ad in-<lb/>
<anchor type="note" xlink:label="note-0102-07a" xlink:href="note-0102-07"/>
teruallum quodcunque, dabit arcus inter rectas I E, I G, comprehenſus, gradus inclinationis. </s>
  <s xml:id="echoid-s4527" xml:space="preserve">De-<lb/>clinationem igitur cuiuſcunque plani à Verticali circulo, &amp; </s>
  <s xml:id="echoid-s4528" xml:space="preserve">eiuſdem inclinationem ad Horizon-<lb/>tem inueſtigauimus. </s>
  <s xml:id="echoid-s4529" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s4530" xml:space="preserve"/>
</p>
<div xml:id="echoid-div286" type="float" level="2" n="10">
<note position="left" xlink:label="note-0102-06" xlink:href="note-0102-06a" xml:space="preserve">Quam in par-<lb/>tem cadat incli <lb/>natio plani pro <lb/>poſiti ad Hori-<lb/>zont@m.</note>
<note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div288" type="section" level="1" n="115">
<head xml:id="echoid-head118" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s4531" xml:space="preserve">PRAETER modum illum, quem in comment arĳs in ſphær am tradidimus, inueniendæ lineæ me-<lb/>ridianæ, viſum est alium hoc loco ſubiungere, ad vſum fortaſſis magis accommodatum, propterea quòd <lb/>neque duabus obſeruationibus, quarum vna ante meridiem, &amp; </s>
  <s xml:id="echoid-s4532" xml:space="preserve">post meridiem alter a facienda eſt, in hoc <lb/>modo opus eſt, vt in illo, neque puncta in extremit atibus vmbr arum ſignanda, quod non admodum facile <lb/>
<anchor type="note" xlink:label="note-0102-08a" xlink:href="note-0102-08"/>
eſt, cum vix in plano extremit as vmbræ poſſit diſcerni.</s>
  <s xml:id="echoid-s4533" xml:space="preserve"/>
</p>
<div xml:id="echoid-div288" type="float" level="2" n="1">
<note position="left" xlink:label="note-0102-08" xlink:href="note-0102-08a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">Linea meridia-<lb/>na quo pacto <lb/>per Aſtrolabiũ <lb/>in plano deſcri <lb/>ptũ reperiatur.</note>
<p style="it">
  <s xml:id="echoid-s4534" xml:space="preserve">INVENTVRVS igitur li-<lb/>
<anchor type="figure" xlink:label="fig-0102-02a" xlink:href="fig-0102-02"/>
neam meridianam quolibet die, ad-<lb/>diſce prius ex Ephemeride aliqualo <lb/>cum Solis. </s>
  <s xml:id="echoid-s4535" xml:space="preserve">Deinde in plano, quod <lb/>Horizonti æquidistet, obſeruetur <lb/>vmbra alicuius fili liberè pendentis, <lb/>vel certè alicuius regulę rectiſſimę <lb/>cum plano propoſito angulos rectos <lb/>facientis. </s>
  <s xml:id="echoid-s4536" xml:space="preserve">Ego vti ſolco ad hanc rem <lb/>
<anchor type="note" xlink:label="note-0102-10a" xlink:href="note-0102-10"/>
inſtrumento, quod hic depictum vi-<lb/>des, in quo norma C D E, ad angulos <lb/>rectos affixa eſt regulæ planę A B, <lb/>in recta D I, quę vni lateri regulæ <lb/>A B, ſit parallela, ita vt normæ la-<lb/>tus DH, ſit inſtar gnomonis cuiuſ-<lb/>dam ad Horizontem recti, vel fili <lb/>libere pendentis, dum regula A B, ſupra planum Horizonti parallelum collocatum eſt. </s>
  <s xml:id="echoid-s4537" xml:space="preserve">Hac enim ra-<lb/>tione facili negotio in extremitate vmbrę, quam latus H D, proĳcit, duo puncta ſine errore ſenſibili nota <lb/>bimus. </s>
  <s xml:id="echoid-s4538" xml:space="preserve">Quòd ſi in plano C D, ducatur linea F G, parallela lateri H D, &amp; </s>
  <s xml:id="echoid-s4539" xml:space="preserve">foramen fiat prope punctum <lb/>G, ita vt perpendiculum filo tenui ex foramine F, pendenti appenſum libere in eo poſſit moueri, erit idẽ
<pb o="83" file="0103" n="103" rhead="LIBER PRIMVS."/>
hoc inſtrumentum percommodum ad examinandum quodcunque planum propoſitum, ſit ne Horizonti <lb/>parallelum nec ne. </s>
  <s xml:id="echoid-s4540" xml:space="preserve">Filo enim radente planum C D, per rectam F G, erit planim, in quo iacet regula <lb/>A B, Horizonti æquidiſtans. </s>
  <s xml:id="echoid-s4541" xml:space="preserve">I am in vmbra ſiue fili, ſiue lateris H D, duo pur cta A, B, aliquantulum <lb/>inter ſe distantia notentur, quę recta linea A B, iungantur. </s>
  <s xml:id="echoid-s4542" xml:space="preserve">Erit hęc communis ſectio plani ſubiecti, &amp; </s>
  <s xml:id="echoid-s4543" xml:space="preserve"><lb/>Verticalis circuli, qui tempore obſeruatio-<lb/>
<anchor type="figure" xlink:label="fig-0103-01a" xlink:href="fig-0103-01"/>
nis per centrum Solis deſcribicur. </s>
  <s xml:id="echoid-s4544" xml:space="preserve">Obſerua-<lb/>ta autem vmbra, accipiatur ſine mora qua-<lb/>drante, vel Aſtrolabio, altitudo Solis; </s>
  <s xml:id="echoid-s4545" xml:space="preserve">quæ <lb/>quidem altitudo Solis obſeruanda eſt ſta-<lb/>tim poſt ſignationem duorum punctorum in <lb/>
<anchor type="note" xlink:label="note-0103-01a" xlink:href="note-0103-01"/>
vmbra, antequam recta linea per illa duca-<lb/>tur, ne periculum ſit in mora, quòd propter <lb/>aſcenſum Solis ante meridiem, vel deſcen-<lb/>ſum poſt meridiem, hoc eſt, propter motum <lb/>Solis diurnum, vmbra neceſſario mutetur, <lb/>at que Sol in alio statim Verticali exiſtat. <lb/></s>
  <s xml:id="echoid-s4546" xml:space="preserve">Poſt hęc in Aſtrolabio, in quo Aequator <lb/>C D E F, circa centrum G, vbi duę dia-<lb/>metri C E, D F, ſeſe ad angulos rectos ſe-<lb/>cant, &amp; </s>
  <s xml:id="echoid-s4547" xml:space="preserve">Verticalis proprie dictus HIKL, <lb/>
<anchor type="note" xlink:label="note-0103-02a" xlink:href="note-0103-02"/>
circa centrum M, per quod recta I L, du-<lb/>cta rectam C E, ad angulos rectos ſecat, <lb/>deſcribatur parallelus Solis N O, quem <lb/>exempli gratia ponamus tranſire per grad. <lb/></s>
  <s xml:id="echoid-s4548" xml:space="preserve">15. </s>
  <s xml:id="echoid-s4549" xml:space="preserve">♌, habereq́, declinationem grad. </s>
  <s xml:id="echoid-s4550" xml:space="preserve">16. </s>
  <s xml:id="echoid-s4551" xml:space="preserve"><lb/>min. </s>
  <s xml:id="echoid-s4552" xml:space="preserve">23. </s>
  <s xml:id="echoid-s4553" xml:space="preserve">quem in puncto O, ex parte orien-<lb/>tis (ponamus enim nunc obſeruationem fie-<lb/>ri ante meridiem) ſecet parallelus Horizon <lb/>tis P O, per altitudinem Solis, quam nunc <lb/>ponamus eſſe grad. </s>
  <s xml:id="echoid-s4554" xml:space="preserve">30. </s>
  <s xml:id="echoid-s4555" xml:space="preserve">tranſiens. </s>
  <s xml:id="echoid-s4556" xml:space="preserve">Per hoc <lb/>
<anchor type="note" xlink:label="note-0103-03a" xlink:href="note-0103-03"/>
enim punctum O, deſcribendus eſt Vertica-<lb/>lis eo tempore per centrum Solis incedens. <lb/></s>
  <s xml:id="echoid-s4557" xml:space="preserve">Huius autem centrum, quod in recta I L, existit, vt in Aſtrolabio à nobis demonſtratum eſt, ita inue-<lb/>niemus. </s>
  <s xml:id="echoid-s4558" xml:space="preserve">Ex H, &amp; </s>
  <s xml:id="echoid-s4559" xml:space="preserve">O, bini arcus tam ſupra puncta H, &amp; </s>
  <s xml:id="echoid-s4560" xml:space="preserve">O, quàm infra, deſcribantur ad quodcunque <lb/>interuallum ſeſe interſecantes in duobus punctis, per quę recta ducatur ſecans I L, in Q. </s>
  <s xml:id="echoid-s4561" xml:space="preserve">Erit enim Q, <lb/>centrum Verticalis per H, &amp; </s>
  <s xml:id="echoid-s4562" xml:space="preserve">O, deſcribendi. </s>
  <s xml:id="echoid-s4563" xml:space="preserve">Nam vt conſtat exĳs, quę in ſcholio propoſ. </s>
  <s xml:id="echoid-s4564" xml:space="preserve">25. </s>
  <s xml:id="echoid-s4565" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4566" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4567" xml:space="preserve"><lb/>Euclidis demonſtrauimas, recta coniungens illa puncta tranſit per centrum circuli deſcribendi per H, O. </s>
  <s xml:id="echoid-s4568" xml:space="preserve"><lb/>Si igitur ex Q, &amp; </s>
  <s xml:id="echoid-s4569" xml:space="preserve">ad interuallum Q H, vel Q O, circulus deſcribatur, erit hic Verticalis per centrũ <lb/>Solis incedens tempore obſeruationis, qui quidem à Verticali proprie dicto H I K L, ex parte orient ali <lb/>deflectet in Auſtrum, ſi centrum Q, in rectam E I, ceciderit, &amp; </s>
  <s xml:id="echoid-s4570" xml:space="preserve">obſeruatio fiat ante meridiem; </s>
  <s xml:id="echoid-s4571" xml:space="preserve">in Bo-<lb/>
<anchor type="note" xlink:label="note-0103-04a" xlink:href="note-0103-04"/>
ream verò, ſi extiterit in E L, &amp; </s>
  <s xml:id="echoid-s4572" xml:space="preserve">ante meridiem fiat obſeruatio. </s>
  <s xml:id="echoid-s4573" xml:space="preserve">At ſi obſeruatio fiat poſt meridiem, <lb/>quoniam tunc punctum O, ſumendũ eſt ex parte occidentis, ſi cẽtrum Q, extiterit in recta E L, deflectet <lb/>Verticalis H O, à proprio Verticali in Auſtrum ex parte occidentali, in boream vero, ſi centrum Q, in <lb/>rectam E I, ceciderit. </s>
  <s xml:id="echoid-s4574" xml:space="preserve">Sed quantum deflectat, ita deprehendemus. </s>
  <s xml:id="echoid-s4575" xml:space="preserve">Ex H, vertice per Q, recta duca-<lb/>tur ſecans Verticalem H I k L, in R. </s>
  <s xml:id="echoid-s4576" xml:space="preserve">Nam K S, dimidium arcus K R, erit declinatio Verticalis H O, <lb/>à Verticali propriè dicto H I K L, vt perſpicuum eſt ex ĳs, quæ in Aſtrolabio demonſtrauimus. </s>
  <s xml:id="echoid-s4577" xml:space="preserve">Comple-<lb/>mentum igitur I S, erit declinatio eiuſdem à Meridiano circulo. </s>
  <s xml:id="echoid-s4578" xml:space="preserve">Itaque ſi ex quocunque puncto A, lineę <lb/>vmbrę circulus deſeribatur B T, ęqualis Verticali H I K L, ſumatur{q́ue} arcus B T, ęqualis arcui I S, ab <lb/>ortu quidem verſus auſtrum, ſi obſeruatio fiat ante meridiem, &amp; </s>
  <s xml:id="echoid-s4579" xml:space="preserve">Verticalis H O, deftectat verſus au-<lb/>ſtrum ex parte orientali, vt in exemplo; </s>
  <s xml:id="echoid-s4580" xml:space="preserve">vel ab ortu verſus boream, ſi obſeruatio ante meridiem fiat, &amp; </s>
  <s xml:id="echoid-s4581" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0103-05a" xlink:href="note-0103-05"/>
Verticalis H O, ex parte orient ali deflectat verſus boream: </s>
  <s xml:id="echoid-s4582" xml:space="preserve">Ab occaſu vero eodem modo verſus au-<lb/>ſtrum vel boream, ſi obſeruatio poſt meridiem fiat, &amp; </s>
  <s xml:id="echoid-s4583" xml:space="preserve">c. </s>
  <s xml:id="echoid-s4584" xml:space="preserve">crit recta ducta A T, linea meridiana, nimirum <lb/>communis ſectio plani propoſiti, &amp; </s>
  <s xml:id="echoid-s4585" xml:space="preserve">Meridiani circuli.</s>
  <s xml:id="echoid-s4586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div289" type="float" level="2" n="2">
  <figure xlink:label="fig-0102-02" xlink:href="fig-0102-02a">
    <image file="0102-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0102-02"/>
  </figure>
<note position="left" xlink:label="note-0102-10" xlink:href="note-0102-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a">
    <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/>
  </figure>
<note position="left" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0103-04" xlink:href="note-0103-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0103-05" xlink:href="note-0103-05a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s4587" xml:space="preserve">EADEM hęc declinatio K S, Verticalis H O, à Verticali proprie dicto H I K L, ex calculo ſi-<lb/>
<anchor type="note" xlink:label="note-0103-06a" xlink:href="note-0103-06"/>
nuum inueniri, atque adeo &amp; </s>
  <s xml:id="echoid-s4588" xml:space="preserve">ipſa linea meridiana duci poteſt. </s>
  <s xml:id="echoid-s4589" xml:space="preserve">Si enim ex declinatione Solis, &amp; </s>
  <s xml:id="echoid-s4590" xml:space="preserve">altitu-<lb/>dine, quam habet Sol tempore obſeruationis, ex ſinubus inueniatur diſtantia Solis à Meridiano circulo, <lb/>vt propoſ. </s>
  <s xml:id="echoid-s4591" xml:space="preserve">36. </s>
  <s xml:id="echoid-s4592" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4593" xml:space="preserve">docebimus, &amp; </s>
  <s xml:id="echoid-s4594" xml:space="preserve">per hanc diſtantiam, ex eiſdem ſinubus inueſtigetur circunferen-<lb/>tia horizontalis, id eſt, arcus Horizontis interiectus inter Verticalem propriè dictum, &amp; </s>
  <s xml:id="echoid-s4595" xml:space="preserve">Verticalem <lb/>qui per centrum Solis tempore obſeruationis tranſit, vt propoſ. </s>
  <s xml:id="echoid-s4596" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4597" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4598" xml:space="preserve">5. </s>
  <s xml:id="echoid-s4599" xml:space="preserve">oſtendemus, erit hæc circunfe-<lb/>rentia circunferentiæ K S, æqualis, &amp; </s>
  <s xml:id="echoid-s4600" xml:space="preserve">c.</s>
  <s xml:id="echoid-s4601" xml:space="preserve"/>
</p>
<div xml:id="echoid-div290" type="float" level="2" n="3">
<note position="right" xlink:label="note-0103-06" xlink:href="note-0103-06a" xml:space="preserve">Inuentio lineæ <lb/>meridianæ per <lb/>ſinus.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4602" xml:space="preserve">IMMO ſine deſcriptione Aſtrolabĳ per ſolum Analemma eandem meridianam lineam reperie-
<pb o="84" file="0104" n="104" rhead="GNOMONICES"/>
mus, vt etiam Ioannes Baptiſta Benedictus facit in libro de gnomonum, vmbrarum{q́ue} ſolarium vſu, hoc <lb/>
<anchor type="note" xlink:label="note-0104-01a" xlink:href="note-0104-01"/>
modo. </s>
  <s xml:id="echoid-s4603" xml:space="preserve">Inuenta, vt prius, per vmbram recta A B, communi ſectione plani Horizonti æquidiſtantis, &amp; </s>
  <s xml:id="echoid-s4604" xml:space="preserve"><lb/>Verticalis circuli tempore obſeruationis per Solis centrum tranſeuntis; </s>
  <s xml:id="echoid-s4605" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4606" xml:space="preserve">eodem tempore accepta alti-<lb/>
<anchor type="figure" xlink:label="fig-0104-01a" xlink:href="fig-0104-01"/>
<anchor type="note" xlink:label="note-0104-02a" xlink:href="note-0104-02"/>
<anchor type="note" xlink:label="note-0104-03a" xlink:href="note-0104-03"/>
<anchor type="note" xlink:label="note-0104-04a" xlink:href="note-0104-04"/>
tudine Solis, loco Astrolabĳ deſcribemus Analemma, in quo Meridianus ſit F G H I; </s>
  <s xml:id="echoid-s4607" xml:space="preserve">Horizontis, &amp; </s>
  <s xml:id="echoid-s4608" xml:space="preserve"><lb/>Meridiani communis ſectio G I; </s>
  <s xml:id="echoid-s4609" xml:space="preserve">Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s4610" xml:space="preserve">eiuſdem Meridiani communis ſectio F H; <lb/></s>
  <s xml:id="echoid-s4611" xml:space="preserve">eiuſdem &amp; </s>
  <s xml:id="echoid-s4612" xml:space="preserve">Aequatoris communis ſectio L M; </s>
  <s xml:id="echoid-s4613" xml:space="preserve">communis denique ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s4614" xml:space="preserve">paralleli Solis <lb/>illo die, quo fit obſeruatio, recta N O; </s>
  <s xml:id="echoid-s4615" xml:space="preserve">quæ quidem beneficio declinationis Solis ducetur, quemadmodum <lb/>propoſ. </s>
  <s xml:id="echoid-s4616" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4617" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4618" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s4619" xml:space="preserve">Deinde ſupputata altitudine Solis inuenta ex I, vſque ad P, &amp; </s>
  <s xml:id="echoid-s4620" xml:space="preserve">ex G, vſ-<lb/>
<anchor type="note" xlink:label="note-0104-05a" xlink:href="note-0104-05"/>
que ad Q, ducemus rectam P Q, quæ ex ſcholio propoſ. </s>
  <s xml:id="echoid-s4621" xml:space="preserve">27. </s>
  <s xml:id="echoid-s4622" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4623" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4624" xml:space="preserve">Euclidis parallela erit ipſi G I, atque <lb/>adeo communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s4625" xml:space="preserve">paralleli Horizontis per centrum Solis tranſeuntis, ſecabit{q́ue} Verti-<lb/>calem lineam F H, in R, &amp; </s>
  <s xml:id="echoid-s4626" xml:space="preserve">diametrum paralleli Solis N O, in S. </s>
  <s xml:id="echoid-s4627" xml:space="preserve">Deſcripto autem ex R, centro circa <lb/>P Q, ſemicirculo P T Q, ducemus ex S, ad P Q, perpendicularem S T, vſque ad circunferentiam ſe-<lb/>micirculi P T Q, &amp; </s>
  <s xml:id="echoid-s4628" xml:space="preserve">rectam adiungemus T R. </s>
  <s xml:id="echoid-s4629" xml:space="preserve">Si igitur punctum S, fuerit inter Q, &amp; </s>
  <s xml:id="echoid-s4630" xml:space="preserve">R, &amp; </s>
  <s xml:id="echoid-s4631" xml:space="preserve">obſerua-<lb/>tio fiat ante meridiem, conſtituemus in centro C, (ex quo vt cunque aſſumpto in linea vmbræ A B, circu-<lb/>lum cuiuſcunque magnitudinis deſcribimus,) angulum A C D, angulo acuto T R Q, æqualem, ab ortu <lb/>verſus auſtrum, id eſt, à puncto A, verſus punctum D, vt in figura A, cernitur. </s>
  <s xml:id="echoid-s4632" xml:space="preserve">Si vero obſeruatio fiat <lb/>poſt meridiem, eidem angulo faciemus æqualem A C D, ab occaſu verſus auſtrum, hoc est, à puncto A, <lb/>verſus punctum D, vt in figura B, apparet. </s>
  <s xml:id="echoid-s4633" xml:space="preserve">Quòd ſi punctum S, in punctum R, cadat, ſiue obſeruatio fiat <lb/>
<anchor type="note" xlink:label="note-0104-06a" xlink:href="note-0104-06"/>
ante meridiem, ſiue poſt, ducemus ad A B, per C, perpendicularem D E, vt perſpicuum eſt in figura C. <lb/></s>
  <s xml:id="echoid-s4634" xml:space="preserve">Si denique punctum S, extiterit inter R, &amp; </s>
  <s xml:id="echoid-s4635" xml:space="preserve">P, &amp; </s>
  <s xml:id="echoid-s4636" xml:space="preserve">obſeruatio fiat ante meridiem, efficiemus angulo acuto <lb/>T R P, ęqualem A C E, ab ortu verſus boream, id est, à puncto A, verſus punctum E, vt videre eſt <lb/>in figura D. </s>
  <s xml:id="echoid-s4637" xml:space="preserve">Si verò fiat obſeruatio pomeridiano tempore, eidem angulo ęqualem faciemus A C E, ab <lb/>occaſu verſus boream, hoc eſt, à puncto A, verſus E, vt exfigura E, manifeſtum est. </s>
  <s xml:id="echoid-s4638" xml:space="preserve">Semper enim recta <lb/>D E, erit linea meridiana. </s>
  <s xml:id="echoid-s4639" xml:space="preserve">Quod hunc in modum confirmabimus. </s>
  <s xml:id="echoid-s4640" xml:space="preserve">Quoniã parallelus Horizontis P T Q, <lb/>&amp; </s>
  <s xml:id="echoid-s4641" xml:space="preserve">parallelus Solis recti ſunt ad Meridianum, erit quoque communis eorum ſectio ad eundem perpen-<lb/>
<anchor type="note" xlink:label="note-0104-07a" xlink:href="note-0104-07"/>
dicularis, at que adeo, per definitionem 3. </s>
  <s xml:id="echoid-s4642" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4643" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4644" xml:space="preserve">Euclidis, &amp; </s>
  <s xml:id="echoid-s4645" xml:space="preserve">ad rectam P Q, in puncto S, vbi mutuo ſe <lb/>diuidunt diametri dictorum parallelorum. </s>
  <s xml:id="echoid-s4646" xml:space="preserve">Igitur ST, perpendicularis exiſtens ad P Q, communis ſe-<lb/>ctio erit parallelorum dictorum, ac proinde tempore obſeruationis centrum Solis in puncto T, erit, ſi <lb/>parallelus Horizontis P T Q, vna cum Meridiano Analemmatis propriam poſitionem habeat. </s>
  <s xml:id="echoid-s4647" xml:space="preserve">Quare
<pb o="85" file="0105" n="105" rhead="LIBER PRIMVS."/>
verticalis tunc temporis per centrum Solis tranſiens per punctum T, tranſibit. </s>
  <s xml:id="echoid-s4648" xml:space="preserve">Et quia tranſit etiam <lb/>per rectam F H, communem ſectionem omnium verticalium, at que adeo per punctum R, erit T R, com-<lb/>munis ſectio dicti Verticalis, &amp; </s>
  <s xml:id="echoid-s4649" xml:space="preserve">paralleli Horizontis P T Q. </s>
  <s xml:id="echoid-s4650" xml:space="preserve">Quare cum recta Q R, vel P R, perpen-<lb/>dicularis ſit ad F H, communem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s4651" xml:space="preserve">Verticalis per T R, ducti, nec non &amp; </s>
  <s xml:id="echoid-s4652" xml:space="preserve">T R, ad <lb/>eandem F H, perpendicularis, (cum enim F H, axis paralleli Horizontis P T Q, rectus ſit ad circulũ <lb/>P T Q, ex propoſ. </s>
  <s xml:id="echoid-s4653" xml:space="preserve">10. </s>
  <s xml:id="echoid-s4654" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4655" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4656" xml:space="preserve">Theodoſii, erit per definitionem 3. </s>
  <s xml:id="echoid-s4657" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4658" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4659" xml:space="preserve">Euclidis, angulus F R T, rectus) <lb/>erit per definitionem 6. </s>
  <s xml:id="echoid-s4660" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4661" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4662" xml:space="preserve">Euclidis, angulus acutus T R Q, vel T R P, angulus inclinationis Ver-<lb/>ticalis per T R, ducti ad Meridianum F G H I; </s>
  <s xml:id="echoid-s4663" xml:space="preserve">ac propterea ſi dicto angulo fiat æqualis in centro C, <lb/>ad A B, communem ſectionem verticalis illius, &amp; </s>
  <s xml:id="echoid-s4664" xml:space="preserve">plani A D B E, erit recta D E, linea meridiana, id <lb/>eſt, communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s4665" xml:space="preserve">eiuſdem plani A D B E; </s>
  <s xml:id="echoid-s4666" xml:space="preserve">quandoquidem cum recta A B, conſtituit <lb/>
<anchor type="note" xlink:label="note-0105-01a" xlink:href="note-0105-01"/>
angulum inclinationis dicti Verticalis, &amp; </s>
  <s xml:id="echoid-s4667" xml:space="preserve">Meridiani. </s>
  <s xml:id="echoid-s4668" xml:space="preserve">Quoniam autem Verticalis proprie dictus per F H, <lb/>ductus ad Meridianum F G H I, rectus eſt, ſeparat{q́ue} partem hemiſphærĳſuperni boream ab auſtrali, ita <lb/>vt pars ad G, vergens ſit auſtralis, reliqua verò verſus I, borealis; </s>
  <s xml:id="echoid-s4669" xml:space="preserve">fit vt Sol, cum punctum S, vbi dia-<lb/>metri N O, P Q, ſe interſecant, fuerit inter Q, &amp; </s>
  <s xml:id="echoid-s4670" xml:space="preserve">R, ſit australis, hoc eſt, vltra verticalem circulũ <lb/>propriè dictum verſus auſtrum; </s>
  <s xml:id="echoid-s4671" xml:space="preserve">In Verticali verò circulo proprie dicto, cum punctum S, idem fuerit, <lb/>quod R, in quo diameter paralleli Solis N O, Verticalis diametrum F H, diuidit; </s>
  <s xml:id="echoid-s4672" xml:space="preserve">Borealis denique, quan <lb/>do punctum S, inter R, &amp; </s>
  <s xml:id="echoid-s4673" xml:space="preserve">P, extiterit. </s>
  <s xml:id="echoid-s4674" xml:space="preserve">Hinc factum eſt, vt præceptum à nobis ſit, angulo acuto, quem <lb/>recta T R, cum P Q, facit, æqualem eſſe conſtituendum in C, ad rectam A B, modo ab ortu, vel occaſu <lb/>Austrum verſus, modo verſus boream, &amp; </s>
  <s xml:id="echoid-s4675" xml:space="preserve">c.</s>
  <s xml:id="echoid-s4676" xml:space="preserve"/>
</p>
<div xml:id="echoid-div291" type="float" level="2" n="4">
<note position="left" xlink:label="note-0104-01" xlink:href="note-0104-01a" xml:space="preserve">Linea meridia-<lb/>na qua atte per <lb/>Analemma in-<lb/>Menia@@r.</note>
  <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a">
    <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0104-01"/>
  </figure>
<note position="left" xlink:label="note-0104-02" xlink:href="note-0104-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0104-03" xlink:href="note-0104-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0104-04" xlink:href="note-0104-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0104-05" xlink:href="note-0104-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0104-06" xlink:href="note-0104-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0104-07" xlink:href="note-0104-07a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s4677" xml:space="preserve">VT autẽ videas etiam hoc loco, quàm egregiũ vſum Analemma habeat, nõ ab re<unsure/>erit, ſi paucis declare <lb/>
<anchor type="note" xlink:label="note-0105-02a" xlink:href="note-0105-02"/>
<anchor type="note" xlink:label="note-0105-03a" xlink:href="note-0105-03"/>
mus, qua ratione ex Analẽmate hora diei, cognita Solis declinatione, &amp; </s>
  <s xml:id="echoid-s4678" xml:space="preserve">eiuſdẽ altitudine ſupra Horizon-<lb/>tẽ, cognſcatur. </s>
  <s xml:id="echoid-s4679" xml:space="preserve">Deſcripto enim circa N O, diametrũ paralleli Solis circulo, cuius centrũ est in d, puncto, <lb/>vbi axis mundi ab, diametrum N O, interſecat, eo{q́ue} diuiſo in 24. </s>
  <s xml:id="echoid-s4680" xml:space="preserve">horas æquales, initio facto à diametro <lb/>N O; </s>
  <s xml:id="echoid-s4681" xml:space="preserve">ſi ex z, vbi diameter N O, Horizontis diametrum G I, ſecat, ad N O, perpendicularis ducatur <lb/>X Y, erit hæc communis ſectio paralleli Solis &amp; </s>
  <s xml:id="echoid-s4682" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s4683" xml:space="preserve">Quoniam enim Horizon, &amp; </s>
  <s xml:id="echoid-s4684" xml:space="preserve">Solis paralle-<lb/>lus ad Meridianum recti ſunt, erit quoque eorum communis ſectio ad eundem recta, atque adeo per defi-<lb/>
<anchor type="note" xlink:label="note-0105-04a" xlink:href="note-0105-04"/>
nitionem 3. </s>
  <s xml:id="echoid-s4685" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4686" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4687" xml:space="preserve">Euclidis ad N O, perpendicularis. </s>
  <s xml:id="echoid-s4688" xml:space="preserve">Ex quo fit rectam X Y, quæ ad N O, perpen-<lb/>dicularis eſt in puncto z, vbi diametri G I, N O, ſe mutuo diuidunt, eſſe communem ſectionem paralle-<lb/>li Solis, &amp; </s>
  <s xml:id="echoid-s4689" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s4690" xml:space="preserve">Igitur arcus diurnus erit X N Y, &amp; </s>
  <s xml:id="echoid-s4691" xml:space="preserve">nocturnus Y O X, ac proinde numerus <lb/>horarum in his arcubus incluſus indicabit quantitatem diei, &amp; </s>
  <s xml:id="echoid-s4692" xml:space="preserve">noctis. </s>
  <s xml:id="echoid-s4693" xml:space="preserve">Id quod etiam in ſcholio propoſ. <lb/></s>
  <s xml:id="echoid-s4694" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4695" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s4696" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s4697" xml:space="preserve"/>
</p>
<div xml:id="echoid-div292" type="float" level="2" n="5">
<note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">Hora quo pa-<lb/>cto per Analem <lb/>ma ex cognita <lb/>declinatione So <lb/>lis, &amp; eiuſdem <lb/>altitudine ſu <lb/>pra Horizontẽ <lb/>ſit inquirenda.</note>
<note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">19. vndec.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s4698" xml:space="preserve">IAM verò ſi ex puncto S, ducatur S V, ad N O, perpendicularis, erit hæc communis ſectio paral-<lb/>leli Solis, &amp; </s>
  <s xml:id="echoid-s4699" xml:space="preserve">paralleli Horizontis, in quo tunc Sol exiſtit. </s>
  <s xml:id="echoid-s4700" xml:space="preserve">Cum enim vterque parallelus ad Meridianũ <lb/>rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s4701" xml:space="preserve">communis illorum ſectio ad eundem recta, &amp; </s>
  <s xml:id="echoid-s4702" xml:space="preserve">propterca per definitionem 3. </s>
  <s xml:id="echoid-s4703" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4704" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4705" xml:space="preserve">Eu-<lb/>
<anchor type="note" xlink:label="note-0105-06a" xlink:href="note-0105-06"/>
clidis, ad N O, perpendicularis. </s>
  <s xml:id="echoid-s4706" xml:space="preserve">Perpendicularis ergo V S, communis ſectio dictorum parallelorum erit, <lb/>ac idcirco Sol in puncto V, existet, (poſito parallelo Solis N X O Y, vna cum Meridiano, in propria po-<lb/>ſitione) cum altitudinem ſupra Horizontem habuerit I P, vel G Q. </s>
  <s xml:id="echoid-s4707" xml:space="preserve">Quare horæ repertæ in arcu N V, <lb/>indicabunt, quot horis Sol diſtet vel ante meridiem, vel poſt, prout obſeruatio ante vel poſt meri-<lb/>diem fit.</s>
  <s xml:id="echoid-s4708" xml:space="preserve"/>
</p>
<div xml:id="echoid-div293" type="float" level="2" n="6">
<note position="right" xlink:label="note-0105-06" xlink:href="note-0105-06a" xml:space="preserve">19. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4709" xml:space="preserve">QVOD ſi deſideretur hora ab occaſu Solis, more Italorum, &amp; </s>
  <s xml:id="echoid-s4710" xml:space="preserve">Bohemorum; </s>
  <s xml:id="echoid-s4711" xml:space="preserve">ſi quidem obſeruatio fit <lb/>
<anchor type="note" xlink:label="note-0105-07a" xlink:href="note-0105-07"/>
ante meridiem, inchoanda eſt diuiſio circuli N X O Y, in horas 24. </s>
  <s xml:id="echoid-s4712" xml:space="preserve">æquales à puncto Y, &amp; </s>
  <s xml:id="echoid-s4713" xml:space="preserve">continuanda <lb/>per punctum O. </s>
  <s xml:id="echoid-s4714" xml:space="preserve">Illico enim punctum V, indicabit horam ab occaſu elapſam. </s>
  <s xml:id="echoid-s4715" xml:space="preserve">Si verò obſeruatio fit poſt <lb/>meridiem, incipienda erit diuiſio dicta à puncto X, &amp; </s>
  <s xml:id="echoid-s4716" xml:space="preserve">continuanda per O, punctum. </s>
  <s xml:id="echoid-s4717" xml:space="preserve">Eodem modo ſi quæ-<lb/>ratur hora ab ortu Solis, more Babyloniorum, &amp; </s>
  <s xml:id="echoid-s4718" xml:space="preserve">inſularum Balearium, inchoanda erit diuiſio circu-<lb/>li N X O Y, à puncto X, et per N, continuanda, ſi obſeruatio fit ante meridiem, ſi vero poſt meridiem, <lb/>à puncto Y. </s>
  <s xml:id="echoid-s4719" xml:space="preserve">Eadem ratione quouis momento temporis horam cognoſcemus tam à mer. </s>
  <s xml:id="echoid-s4720" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s4721" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s4722" xml:space="preserve">quàm <lb/>ab or. </s>
  <s xml:id="echoid-s4723" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s4724" xml:space="preserve">ſi declinatio Solis cognita fuerit vnà cum altitudine, quam ſupra Horizontem ha-<lb/>bet tempore obſeruationis.</s>
  <s xml:id="echoid-s4725" xml:space="preserve"/>
</p>
<div xml:id="echoid-div294" type="float" level="2" n="7">
<note position="left" xlink:label="note-0105-07" xlink:href="note-0105-07a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Altitudo Solis <lb/>per Analẽma, <lb/>ex ho@a cogni-<lb/>ta, &amp; declina-<lb/>tione Solis, quo <lb/>modo indagan <lb/>da.</note>
<p style="it">
  <s xml:id="echoid-s4726" xml:space="preserve">VICISSIM ex hora cognita peruenire poſſumus in notitiam altitudinis Solis per Analemma, <lb/>ſi eiuſdem declinatio ignota non fuerit. </s>
  <s xml:id="echoid-s4727" xml:space="preserve">Si enim habita ratione declinationis, deſcribatur diameter pa-<lb/>
<anchor type="note" xlink:label="note-0105-09a" xlink:href="note-0105-09"/>
ralleli Solis N O, &amp; </s>
  <s xml:id="echoid-s4728" xml:space="preserve">circa ipſam circulus N X O Y, ducatur{q́ue} ex V, hora cognita ad N O, perpendicu-<lb/>laris V S, &amp; </s>
  <s xml:id="echoid-s4729" xml:space="preserve">per S, denique agatur recta P Q, Horizontis diametro G I, parallela, erit tam G Q, <lb/>quàm I P, arcus altitudinis Solis ſupra Horizontem, propterea quòd P Q, diameter eſt paralleli Ho-<lb/>rizontis, qui tunc per Solem ducitur, vt perſpicuum est.</s>
  <s xml:id="echoid-s4730" xml:space="preserve"/>
</p>
<div xml:id="echoid-div295" type="float" level="2" n="8">
<note position="left" xlink:label="note-0105-09" xlink:href="note-0105-09a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Altitudo Solis <lb/>per Analemm@, <lb/>ex longitudine <lb/>vmbræ cuiuſcũ <lb/>que ſtyli in pla-<lb/>no, quod Hori-<lb/>zonti æquidi-<lb/>f@et, a d angulos <lb/>rectos collocati, <lb/>quo pacto inue-<lb/>nienda ſit.</note>
<p style="it">
  <s xml:id="echoid-s4731" xml:space="preserve">NEQVE verò hoc omittendum eſt, ſi forte inſtrumento careamus, quo altitudinem Solis inueſtige-<lb/>mus, nos eandem poſſe habere in hunc modum. </s>
  <s xml:id="echoid-s4732" xml:space="preserve">In plano A D B E, quod Horizonti æquidiſtet, figatur <lb/>ſtylus ad angulos rectos, &amp; </s>
  <s xml:id="echoid-s4733" xml:space="preserve">tempore obſeruationis extremitas vmbræ notetur. </s>
  <s xml:id="echoid-s4734" xml:space="preserve">Si enim in An@lemmate <lb/>ſumatur K e, æqualis gnomoni, &amp; </s>
  <s xml:id="echoid-s4735" xml:space="preserve">per e, ducatur ad K e, perpendicularis e f, in qua ſumatur e f, æqua-<lb/>lis vmbræ notatæ, cadet recta ducta per f, &amp; </s>
  <s xml:id="echoid-s4736" xml:space="preserve">K, in punctũ P, altitudinis Solis. </s>
  <s xml:id="echoid-s4737" xml:space="preserve">Si enim circulus F G H I, <lb/>concipiatur eſſe Verticalis per centrum Solis tranſiens, erit recta e f, cõmunis ſectio huius Verticalis, &amp; </s>
  <s xml:id="echoid-s4738" xml:space="preserve"><lb/>plani, quòd Horizonti æquidiſtat. </s>
  <s xml:id="echoid-s4739" xml:space="preserve">Cum ergo extremitas vmbræ ſit f, erit f K P, radius Solis, ac proinde
<pb o="86" file="0106" n="106" rhead="GNOMONICES"/>
Sol in P, exiſtet, altitudo{q́ue} Solis erit arcus I P, vt ex ĳs, quæ propoſ. </s>
  <s xml:id="echoid-s4740" xml:space="preserve">2. </s>
  <s xml:id="echoid-s4741" xml:space="preserve">hui{us} lib. </s>
  <s xml:id="echoid-s4742" xml:space="preserve">ſcripſimus, facile col-<lb/>ligi poteſt.</s>
  <s xml:id="echoid-s4743" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4744" xml:space="preserve">QVOD ſi quando recta P Q, ceciderit in punctum N, hoc est, ſi altitudo Solis inuenta fuerit æqua <lb/>lis meridianæ altitudini Solis illius diei, exiſtet Sol in Meridiano circulo, ac propterea vmbra ipſa A B, <lb/>erit linea meridiana.</s>
  <s xml:id="echoid-s4745" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4746" xml:space="preserve">PER idem Analemma eadem ferè ratione explorare nobis licebit declinationem cuiuſcunque plani <lb/>propoſiti, etiamſi in plano Horizonti parallelo lineam meridianam non inueniamus, quemadmodum <lb/>&amp; </s>
  <s xml:id="echoid-s4747" xml:space="preserve">à Ioan. </s>
  <s xml:id="echoid-s4748" xml:space="preserve">Baptiſta Benedicto traditur in Gnomonica. </s>
  <s xml:id="echoid-s4749" xml:space="preserve">Quod vt fiat, ſit murus ad Horizontem rectus <lb/>A B, in quo ducta recta C D, <lb/>
<anchor type="note" xlink:label="note-0106-01a" xlink:href="note-0106-01"/>
<anchor type="figure" xlink:label="fig-0106-01a" xlink:href="fig-0106-01"/>
Horizonti parallela, figatur <lb/>
<anchor type="note" xlink:label="note-0106-02a" xlink:href="note-0106-02"/>
in ea ſtylus C E, cuiusuis longi-<lb/>tudinis ad murum rectus in <lb/>puncto C, obſeruetur{q́ue} quo-<lb/>cunque tempore, cum Sol pla-<lb/>num muri illuminat, ſiue ante <lb/>meridiem, ſiue poſt, extremitas <lb/>vmbræ E F, quam ſtylus proĳ-<lb/>cit, nempe punctũ F, per quod <lb/>ad rectam C D, perpendicula-<lb/>ris ducatur F D; </s>
  <s xml:id="echoid-s4750" xml:space="preserve">quæ dicto ci-<lb/>
<anchor type="note" xlink:label="note-0106-03a" xlink:href="note-0106-03"/>
tius ducetur hoc modo. </s>
  <s xml:id="echoid-s4751" xml:space="preserve">Ap-<lb/>plicetur muro filum cum per-<lb/>pendiculo, ita vt per punctum <lb/>F, tranſeat, ſignetur in mu-<lb/>ro punctum quodcunque D. <lb/></s>
  <s xml:id="echoid-s4752" xml:space="preserve">Nam linea recta per F, &amp; </s>
  <s xml:id="echoid-s4753" xml:space="preserve">D, ducta perpendicularis erit ad C D, cum filum ad Horizontẽ ſit rectũ. </s>
  <s xml:id="echoid-s4754" xml:space="preserve">Hinc <lb/>enim fit, vt &amp; </s>
  <s xml:id="echoid-s4755" xml:space="preserve">recta F D, quæ à filo perpendiculi non differt, vel certe ei parallela eſt, ad Horizontem, <lb/>qui per rectam C D, ducitur, ſit perpendicularis; </s>
  <s xml:id="echoid-s4756" xml:space="preserve">atque adeo per definitionem 3. </s>
  <s xml:id="echoid-s4757" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4758" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4759" xml:space="preserve">Euclidis, cum <lb/>recta C D, in Horizonte rectos conſtituat angulos. </s>
  <s xml:id="echoid-s4760" xml:space="preserve">Ego loco ſtyli vtor hic quoque inſtrumento illo, quod <lb/>ad initium huius ſcholĳ deſcripſimus. </s>
  <s xml:id="echoid-s4761" xml:space="preserve">Si enim applicetur muro A B, ita vt punctum D, in punctum C, <lb/>
<anchor type="note" xlink:label="note-0106-04a" xlink:href="note-0106-04"/>
cadat, &amp; </s>
  <s xml:id="echoid-s4762" xml:space="preserve">latus D A, in rectam C D, recta D I, vergente deorſum verſus, fungetur latus D H, mune-<lb/>re ſtyli ad murum recti. </s>
  <s xml:id="echoid-s4763" xml:space="preserve">Quare obſeruata extremitate vmbræ illius in puncto F, amouendum erit instru <lb/>mentum, &amp; </s>
  <s xml:id="echoid-s4764" xml:space="preserve">punctum C, diligenter notandum. </s>
  <s xml:id="echoid-s4765" xml:space="preserve">Itaque quoniam radius Solis E F, per E, verticem ſtyli, <lb/>qui in centro mundi eſt, per propoſ. </s>
  <s xml:id="echoid-s4766" xml:space="preserve">2. </s>
  <s xml:id="echoid-s4767" xml:space="preserve">huius libri, in plano illius Verticalis exiſtit, qui tempore obſerua-<lb/>tionis per centrum Solis ducitur, occurret hic Verticalis muro A B, in puncto F. </s>
  <s xml:id="echoid-s4768" xml:space="preserve">Quia verò tam planũ <lb/>muri, quàm huius Verticalis rectum eſt ad Horizontem, erit quoque communis eorum ſectio ad Horizon-<lb/>
<anchor type="note" xlink:label="note-0106-05a" xlink:href="note-0106-05"/>
tem recta, atque adeo, per defin. </s>
  <s xml:id="echoid-s4769" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4770" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4771" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4772" xml:space="preserve">Euclidis, perpendicularis ad rectam C D, in Horizonte exiſten <lb/>tem. </s>
  <s xml:id="echoid-s4773" xml:space="preserve">Cum ergo F D, ſit ad C D, perpendicularis, erit F D, communis ſectio muri A B, &amp; </s>
  <s xml:id="echoid-s4774" xml:space="preserve">Verticalis <lb/>tunc temporis per centrum Solis ducti, atque adeo idem Verticalis per punctum D, tranſibit. </s>
  <s xml:id="echoid-s4775" xml:space="preserve">Ducta igi-<lb/>tur recta E D, erit communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s4776" xml:space="preserve">eiuſdem Verticalis, cum vterque circulus per pun-<lb/>
<anchor type="note" xlink:label="note-0106-06a" xlink:href="note-0106-06"/>
cta E, D, tranſeat; </s>
  <s xml:id="echoid-s4777" xml:space="preserve">atque adeo linea F D, ad Horizontem recta, perpendicularis erit, per defin. </s>
  <s xml:id="echoid-s4778" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4779" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4780" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s4781" xml:space="preserve">Euclidis, ad rectam E D, in Horizonte exiſtentem: </s>
  <s xml:id="echoid-s4782" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s4783" xml:space="preserve">ad C D, perpendicularis oſtenſa. </s>
  <s xml:id="echoid-s4784" xml:space="preserve">Igi-<lb/>tur cum vtraque linea C D, E D, quarum illa in muro, hæc autem in Verticali per Solem tranſeunte exi-<lb/>ſtit, ad F D, communem ſectionem muri, &amp; </s>
  <s xml:id="echoid-s4785" xml:space="preserve">dicti Verticalis ſit perpendicularis, erit per defin. </s>
  <s xml:id="echoid-s4786" xml:space="preserve">6. </s>
  <s xml:id="echoid-s4787" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4788" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4789" xml:space="preserve"><lb/>Euclidis, C D E, angulus inclinationis muri ad dictum Verticalem. </s>
  <s xml:id="echoid-s4790" xml:space="preserve">Cui in plano muri æqualem exhibe-<lb/>bimus hoc modo. </s>
  <s xml:id="echoid-s4791" xml:space="preserve">Ducta recta C G, ad C D, perpendiculari, fiat C G, ſtylo, vel lateri D H, inſtrumenti <lb/>ad initium huius ſcholĳ deſcripti, æqualis, iungatur{q́ue} recta G D. </s>
  <s xml:id="echoid-s4792" xml:space="preserve">Dico angulum C D G, angulo C D E, <lb/>æqualem eſſe. </s>
  <s xml:id="echoid-s4793" xml:space="preserve">Quoniam enim duo latera C E, C D, trianguli C D E, duobus lateribus C G, C D, trian-<lb/>guli C D G, æqualia ſunt, angulosq́, comprehendunt æquales, vtpote rectos, (Eſt enim angulus E C D, <lb/>rectus, per d@fin. </s>
  <s xml:id="echoid-s4794" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4795" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4796" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4797" xml:space="preserve">Euclidis, angulus verò G C D, ex conſtructione) erit quoque baſis E D, baſi <lb/>
<anchor type="note" xlink:label="note-0106-07a" xlink:href="note-0106-07"/>
G D, &amp; </s>
  <s xml:id="echoid-s4798" xml:space="preserve">angulus C D E, angulo C D G, æqualis. </s>
  <s xml:id="echoid-s4799" xml:space="preserve">Ex hoc autem angulo C D G, cognito inuestigabimus de-<lb/>
<anchor type="note" xlink:label="note-0106-08a" xlink:href="note-0106-08"/>
clinationem muri propoſiti à Verticali proprie dicto, hac ratione.</s>
  <s xml:id="echoid-s4800" xml:space="preserve"/>
</p>
<div xml:id="echoid-div296" type="float" level="2" n="9">
<note position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">Declinatio pla-<lb/>ni propoſiti, per <lb/>Analẽma qua <lb/>arte ſit exqui-<lb/>renda.</note>
  <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a">
    <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-01"/>
  </figure>
<note position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0106-03" xlink:href="note-0106-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0106-04" xlink:href="note-0106-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0106-05" xlink:href="note-0106-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0106-06" xlink:href="note-0106-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0106-07" xlink:href="note-0106-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0106-08" xlink:href="note-0106-08a" xml:space="preserve">4. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4801" xml:space="preserve">POST QVAM vmbræ extremitas F, notata eſt, inquiratur ſtatim, antequã recta F D, ducatur, <lb/>(quoniã ſi mora aliqua interceſſerit, vmbra mutabitur, &amp; </s>
  <s xml:id="echoid-s4802" xml:space="preserve">Sol alium Verticalẽ occupabit, propter motum <lb/>diurnũ) altitudo Solis, quæ in Analemmate ſuperiori, quod hic repetiuimus, ſupputetur ex punctis G, I, <lb/>vſq;</s>
  <s xml:id="echoid-s4803" xml:space="preserve"><unsure/> ad puncta Q, P. </s>
  <s xml:id="echoid-s4804" xml:space="preserve">Iuncta enim recta PQ, erit diameter paralleli Horizõtis per centrũ Solis tempore <lb/>obſeruationis ducti, vt ſupra demonſtrauimus, ſecans diametrum paralleli Solis in S, &amp; </s>
  <s xml:id="echoid-s4805" xml:space="preserve">diametrum <lb/>Verticalis proprie dicti in R. </s>
  <s xml:id="echoid-s4806" xml:space="preserve">Deſcripto autem circa P Q, ex centro R, ſemicirculo P T Q, ducatur <lb/>ex S, ad P Q, perpendicularis S T, ſecans circunferentiam ſemicirculi P T Q, in T, iungatur{q́ue}<unsure/> re-<lb/>cta T R, quæ communis ſectio erit paralleli Horizontis, &amp; </s>
  <s xml:id="echoid-s4807" xml:space="preserve">Verticalis circuli, quorum vterque tunc per <lb/>Solis centrum ducitur; </s>
  <s xml:id="echoid-s4808" xml:space="preserve">adeo vt angulus acutus Q R T, vel P R T, ſit angulus declinationis dicti Verti-
<pb o="87" file="0107" n="107" rhead="LIBER PRIMVS."/>
calis à Meria<unsure/>iano, vt ſupra oſtendimus; </s>
  <s xml:id="echoid-s4809" xml:space="preserve">ac proinde reliquus T R H, angulus declinationis eiuſdem Ver-<lb/>ticalis à Verticali proprie dicto.</s>
  <s xml:id="echoid-s4810" xml:space="preserve"/>
</p>
  <figure>
    <image file="0107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0107-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s4811" xml:space="preserve">IT AQVE ſimurus ſpectet in meridiem, (quod ex ĳs diſcemus, quæ ſupra in hac propoſitione tra-<lb/>
<anchor type="note" xlink:label="note-0107-04a" xlink:href="note-0107-04"/>
didimus) &amp; </s>
  <s xml:id="echoid-s4812" xml:space="preserve">punctum S, extiterit inter Q, &amp; </s>
  <s xml:id="echoid-s4813" xml:space="preserve">R, hoc eſt, ſi Sol vltra Verticalem circulum proprie di-<lb/>ctum repertus fuerit, ita vt tam murum, quàm Verticalem proprie dictum ex parte auſtrali illuminet, <lb/>atque obſeruatio fiat ante meridiem, conferemus angulum T R H, cum angulo C D G, quem in muro in-<lb/>uenimus. </s>
  <s xml:id="echoid-s4814" xml:space="preserve">Si enim ille fuerit huic ęqualis, carebit murus declinatione, recta{q́ue} in meridiem verget, <lb/>cum eadem inuenta ſit declinatio Verticalis per Solem tranſeuntis à muro, &amp; </s>
  <s xml:id="echoid-s4815" xml:space="preserve">à Verticali proprie dicto, <lb/>
<anchor type="note" xlink:label="note-0107-05a" xlink:href="note-0107-05"/>
Si autem angulus T R H, deprehenſus fuerit maior angulo C D G, erit murus ex parte Orientali inter <lb/>Verticalem proprie dictum &amp; </s>
  <s xml:id="echoid-s4816" xml:space="preserve">Verticalem per centrum Solis ductum poſitus, propterea quòd ex parte <lb/>auſtr ali magis tunc diſtet Verticalis per Solem ductus à Verticali proprie dicto, quàm à muro. </s>
  <s xml:id="echoid-s4817" xml:space="preserve">Quare ſi <lb/>angulum C D G, id eſt, declinationem, quam Verticalis per Solem ductus habet à muro, demamus ex an-<lb/>gulo T R H, hoc est, à declinatione, quam idem Verticalis per Solem ductus habet à Verticali proprie <lb/>dicto, reliquus erit angulus declinationis muri à Verticali proprie dicto, &amp; </s>
  <s xml:id="echoid-s4818" xml:space="preserve">à meridie in occaſum. </s>
  <s xml:id="echoid-s4819" xml:space="preserve">Si <lb/>denique angulus T R H, angulo C D G, minor fuerit, erit Verticalis propriè dictus ex parte orientali <lb/>inter murum &amp; </s>
  <s xml:id="echoid-s4820" xml:space="preserve">Verticalem, qui per Solem ducitur, propterea quòd ex parte auſtrali magis tunc diſtet <lb/>Verticalis per Solem ductus à muro, quàm à Verticali proprie dicto. </s>
  <s xml:id="echoid-s4821" xml:space="preserve">Si igitur angulum T R H, ex angu-<lb/>lo C D G, auferamus, remanebit angulus declinationis muri à Verticali propriè dicto, &amp; </s>
  <s xml:id="echoid-s4822" xml:space="preserve">à meridie <lb/>
<anchor type="note" xlink:label="note-0107-06a" xlink:href="note-0107-06"/>
in ortum.</s>
  <s xml:id="echoid-s4823" xml:space="preserve"/>
</p>
<div xml:id="echoid-div297" type="float" level="2" n="10">
<note position="right" xlink:label="note-0107-04" xlink:href="note-0107-04a" xml:space="preserve">Quando muru@ <lb/>in meridiẽ ſpe-<lb/>ctat, &amp; Sol au-<lb/>ſtralior eſt quá <lb/>Verticalis pro-<lb/>prie dictus, ob-<lb/>@eruatioq; fit a@ <lb/>te meridiem.</note>
<note position="left" xlink:label="note-0107-05" xlink:href="note-0107-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0107-06" xlink:href="note-0107-06a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Quãdo mur<unsure/>us <lb/>in meridiẽ ſpe-<lb/>ctat, &amp; Sol in <lb/>Verticali pro-<lb/>priè dicto exi-<lb/>ſtit, obſerua-<lb/>tioque fit ante <lb/>meridiem.</note>
<p style="it">
  <s xml:id="echoid-s4824" xml:space="preserve">SI autem punctum S, idem fuerit, quod R, hoc eſt, ſi Sol in Verticali propriè dicto extiterit, ita vt <lb/>adhuc murum illuminet ex parte auſtrali, Verticalem autem proprie dictum nullo modo, erit angulus <lb/>inuentus C D G, angulus declinationis muri à Verticali propriè dicto, &amp; </s>
  <s xml:id="echoid-s4825" xml:space="preserve">à meridie in ortum; </s>
  <s xml:id="echoid-s4826" xml:space="preserve">quia tunc <lb/>ex parte orientis auſtralior eſt Verticalis propriè dictus, in quo nimirum Sol existit, quàm murus.</s>
  <s xml:id="echoid-s4827" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4828" xml:space="preserve">DENIQVE ſi fuerit punctum S, inter P, &amp; </s>
  <s xml:id="echoid-s4829" xml:space="preserve">R, id est, ſi Sol citra Verticalem circulum propriè <lb/>
<anchor type="note" xlink:label="note-0107-08a" xlink:href="note-0107-08"/>
dictum ſit conſtitutus, ita vt murum quidem illuminet ex parte auſtrali, Verticalem verò propriè di-<lb/>ctum ex boreali, exiſtet Verticalis, in quo Sol eſt, inter murum, &amp; </s>
  <s xml:id="echoid-s4830" xml:space="preserve">Verticalem primarium ex parte <lb/>orientis, quia ille Verticalis auſtralior tunc eſt, quàm murus, &amp; </s>
  <s xml:id="echoid-s4831" xml:space="preserve">borealior, quàm Verticalis primarius. <lb/></s>
  <s xml:id="echoid-s4832" xml:space="preserve">Quamobrem ſi angulus T R H, angulo C D G, addatur, conflabitur angulus declinationis muri à Verti-<lb/>cali primario, &amp; </s>
  <s xml:id="echoid-s4833" xml:space="preserve">à meridie in ortum.</s>
  <s xml:id="echoid-s4834" xml:space="preserve"/>
</p>
<div xml:id="echoid-div298" type="float" level="2" n="11">
<note position="right" xlink:label="note-0107-08" xlink:href="note-0107-08a" xml:space="preserve">Quãdo murus<unsure/> <lb/>in meridiẽ ſpe-<lb/>ctat, &amp; Sol bo-<lb/>realior eſt, quã <lb/>Verticalis pro-<lb/>prie dictus, ob-<lb/>ſeruatioq́; fit an<unsure/> <lb/>te meridiem.</note>
</div>
<pb o="88" file="0108" n="108" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s4835" xml:space="preserve">QVOD ſi murus in meridiem ſpectet, ſed obſeruatio fiat pomeridiano tempore, &amp; </s>
  <s xml:id="echoid-s4836" xml:space="preserve">punctum qui-<lb/>
<anchor type="note" xlink:label="note-0108-01a" xlink:href="note-0108-01"/>
dem S, inter Q, &amp; </s>
  <s xml:id="echoid-s4837" xml:space="preserve">R, extiterit, ita vt Sol &amp; </s>
  <s xml:id="echoid-s4838" xml:space="preserve">murum, &amp; </s>
  <s xml:id="echoid-s4839" xml:space="preserve">Verticalem primarium ex auſtrali parteil-<lb/>luminet, angulus{q́ue} T R H, angulo C D G, deprehenſus fuerit æqualis, carebit rurſum murus declina-<lb/>tione. </s>
  <s xml:id="echoid-s4840" xml:space="preserve">Si verò angulus T R H, maior inueniatur angulo C D G, erit murus ex parte occidentis inter <lb/>Verticalem primarium, &amp; </s>
  <s xml:id="echoid-s4841" xml:space="preserve">Verticalem per centrum Solis ductum poſitus. </s>
  <s xml:id="echoid-s4842" xml:space="preserve">Quocirca dempto angulo <lb/>C D G, ex angulo T R H, remane<unsure/>bit angulus declinationis muri à Verticali primario, &amp; </s>
  <s xml:id="echoid-s4843" xml:space="preserve">à meridie in <lb/>ortum. </s>
  <s xml:id="echoid-s4844" xml:space="preserve">Si denique angulus T R H, minor angulo C D G, fuerit, exiſtet Verticalis primarius ex parte oc-<lb/>cidentis inter murum, &amp; </s>
  <s xml:id="echoid-s4845" xml:space="preserve">verticalem, qui per Solem ducitur. </s>
  <s xml:id="echoid-s4846" xml:space="preserve">Ablato ergo illo ex hoc, reliquus erit an-<lb/>gulus declinationis muri à Verticali primario, &amp; </s>
  <s xml:id="echoid-s4847" xml:space="preserve">à meridie in occaſum.</s>
  <s xml:id="echoid-s4848" xml:space="preserve"/>
</p>
<div xml:id="echoid-div299" type="float" level="2" n="12">
<note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">Quãdo murus <lb/>in meridiẽ ſpe-<lb/>ctat, &amp; Sol au-<lb/>ſtralior eſt, quã <lb/>Verticalis pro-<lb/>priè dictus, ob-<lb/>ſeruatioq́ue fit <lb/>poſt meridiem.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4849" xml:space="preserve">PVNCTO autem S, cadente in R, ita vt Sol illuminet quidem murum ex parte auſtrali, Vertica <lb/>
<anchor type="note" xlink:label="note-0108-02a" xlink:href="note-0108-02"/>
<anchor type="note" xlink:label="note-0108-03a" xlink:href="note-0108-03"/>
lem verò primarium nullo modo, declinabit murus à Verticali, &amp; </s>
  <s xml:id="echoid-s4850" xml:space="preserve">à meridie in occaſum, angulo inuento <lb/>C D G; </s>
  <s xml:id="echoid-s4851" xml:space="preserve">quia tunc Sol in Verticali primario exiſtet, qui ex parte occidentis auſtralior eſt ipſo muro.</s>
  <s xml:id="echoid-s4852" xml:space="preserve"/>
</p>
<div xml:id="echoid-div300" type="float" level="2" n="13">
<note position="left" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">Quãdo murus <lb/>in meridiẽ ſpe-<lb/>ctat, &amp; Sol in <lb/>Verticali pro-<lb/>priè dicto exi-<lb/>ſtit, vel borea-<lb/>lior eſt, quàm <lb/>Verticalis pro-<lb/>ptiè dictus, ob-<lb/>ſeruati@q́ue fit <lb/>poſt meridiem.</note>
<note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s4853" xml:space="preserve">CADENTE denique puncto S, inter P, &amp; </s>
  <s xml:id="echoid-s4854" xml:space="preserve">R, ita vt Sol murum quidem illuminet ex parte au-<lb/>ſtrali, Verticalem vero primarium ex parte boreali, conſtitutus erit Verticalis, in quo eſt Sol, inter mu-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s4855" xml:space="preserve">Verticalem primarium ex parte occidentis. </s>
  <s xml:id="echoid-s4856" xml:space="preserve">Quapropter ſi angulus T R H, addatur angulo <lb/>C D G, componetur angulus, quo murus à Verticali primario, &amp; </s>
  <s xml:id="echoid-s4857" xml:space="preserve">à meridie in occaſum deflectit.</s>
  <s xml:id="echoid-s4858" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4859" xml:space="preserve">AT verò ſi murus in Septentrionem vergat, obſeruatio autem fiat ante meridiem, &amp; </s>
  <s xml:id="echoid-s4860" xml:space="preserve">punctum S, <lb/>
<anchor type="note" xlink:label="note-0108-04a" xlink:href="note-0108-04"/>
inter Q, &amp; </s>
  <s xml:id="echoid-s4861" xml:space="preserve">R, extiterit, ita vt Sol illuminet murum ex parte Septentrionali, &amp; </s>
  <s xml:id="echoid-s4862" xml:space="preserve">Verticalem propriè <lb/>dictum ex parte auſtrali, poſitus erit Verticalis per Solem ductus inter murum, &amp; </s>
  <s xml:id="echoid-s4863" xml:space="preserve">Verticalem prima-<lb/>rium, ex parte orientis. </s>
  <s xml:id="echoid-s4864" xml:space="preserve">Igitur ſi angulus T R H, angulo C D G, addatur, conficietur angulus declina-<lb/>
<anchor type="note" xlink:label="note-0108-05a" xlink:href="note-0108-05"/>
tionis muri à Verticali primario, &amp; </s>
  <s xml:id="echoid-s4865" xml:space="preserve">à Septentrione in ortum.</s>
  <s xml:id="echoid-s4866" xml:space="preserve"/>
</p>
<div xml:id="echoid-div301" type="float" level="2" n="14">
<note position="left" xlink:label="note-0108-04" xlink:href="note-0108-04a" xml:space="preserve">Quãdo murus <lb/>ſpectat in bo-<lb/>ream, &amp; Sol au-<lb/>ſtralior eſt, quã <lb/>Verticalis pro-<lb/>priè dictus, vel <lb/>in Verticali pro <lb/>priè dicto exi-<lb/>ſtit, obſerua-<lb/>tioq́ue fit ante <lb/>meridiem.</note>
<note position="left" xlink:label="note-0108-05" xlink:href="note-0108-05a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s4867" xml:space="preserve">SI verò punctum S, idem fuerit, quod R, ita vt Sol adhuc murum illuminet ex parte boreali, Ver-<lb/>ticalem autem propriè dictum nullo modo, erit angulus inuentus C D G, angulus declinationis muri à <lb/>Verticali propriè dicto, &amp; </s>
  <s xml:id="echoid-s4868" xml:space="preserve">à Septentrione in ortum.</s>
  <s xml:id="echoid-s4869" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4870" xml:space="preserve">SI denique fuerit punctum S, inter P, &amp; </s>
  <s xml:id="echoid-s4871" xml:space="preserve">R, ita vt Sol &amp; </s>
  <s xml:id="echoid-s4872" xml:space="preserve">murum, &amp; </s>
  <s xml:id="echoid-s4873" xml:space="preserve">Verticalem propriè dictum ex <lb/>
<anchor type="note" xlink:label="note-0108-06a" xlink:href="note-0108-06"/>
parte boreali illuminet, cõferendus erit angulus T R H, cum angulo C D G. </s>
  <s xml:id="echoid-s4874" xml:space="preserve">Si enim ille huic fuerit ęqua-<lb/>lis, nullam habebit murus declinationem, propter cauſam ante dictam. </s>
  <s xml:id="echoid-s4875" xml:space="preserve">Si verò angulus T R H, angulũ <lb/>C D G, ſuperauerit, ſi hic ab illo ſubducatur, relinquetur angulus, quo murus à Verticali primario decli-<lb/>nat, &amp; </s>
  <s xml:id="echoid-s4876" xml:space="preserve">à Septentrione in occaſum; </s>
  <s xml:id="echoid-s4877" xml:space="preserve">propterea quòd tunc murus ex parte orientis collocatus erit inter <lb/>Verticalem primarium, &amp; </s>
  <s xml:id="echoid-s4878" xml:space="preserve">illum, qui per Solem incedit. </s>
  <s xml:id="echoid-s4879" xml:space="preserve">Si denique angulus T R H, angulo C D G, fue-<lb/>
<anchor type="note" xlink:label="note-0108-07a" xlink:href="note-0108-07"/>
rit minor, exiſtet Verticalis primarius inter murum, &amp; </s>
  <s xml:id="echoid-s4880" xml:space="preserve">Verticalem, qui per Solem tranſit, ex parte <lb/>Orientis. </s>
  <s xml:id="echoid-s4881" xml:space="preserve">Quamobrem ſi illum ex hoc detrahamus, reliquum faciemus angulum, quo murus à Verticali <lb/>primario, &amp; </s>
  <s xml:id="echoid-s4882" xml:space="preserve">à Septentrione in ortum declinat.</s>
  <s xml:id="echoid-s4883" xml:space="preserve"/>
</p>
<div xml:id="echoid-div302" type="float" level="2" n="15">
<note position="left" xlink:label="note-0108-06" xlink:href="note-0108-06a" xml:space="preserve">Quando murus <lb/>in boream ſpe-<lb/>ctat, &amp; Sol bo-<lb/>realior eſt, quã <lb/>Verticalis pro-<lb/>priè dictus, ob-<lb/>ſeruatioq́ue fit <lb/>ante meridiem.</note>
<note position="left" xlink:label="note-0108-07" xlink:href="note-0108-07a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s4884" xml:space="preserve">MVRO autem in Septentrionem ſpectante, ſi obſeruatio tempore pomeridiano fiat, punctum{q́ue} S, <lb/>
<anchor type="note" xlink:label="note-0108-08a" xlink:href="note-0108-08"/>
existat inter Q, &amp; </s>
  <s xml:id="echoid-s4885" xml:space="preserve">R, ita vt Sol murum quidem ex parte boreali, Verticalem autẽ propriè dictum ex <lb/>auſtrali illuminet, poſitus erit Verticalis per Solem ductus, ex parte occidentali, inter murum, &amp; </s>
  <s xml:id="echoid-s4886" xml:space="preserve">Ver <lb/>ticalem primarium. </s>
  <s xml:id="echoid-s4887" xml:space="preserve">Quare ſi addatur angulus T R H, angulo C D G, conficietur angulus declinationis <lb/>muri à Verticali propriè dicto, &amp; </s>
  <s xml:id="echoid-s4888" xml:space="preserve">à Septentrione in occaſum.</s>
  <s xml:id="echoid-s4889" xml:space="preserve"/>
</p>
<div xml:id="echoid-div303" type="float" level="2" n="16">
<note position="left" xlink:label="note-0108-08" xlink:href="note-0108-08a" xml:space="preserve">Quando murus <lb/>in boream ſpe-<lb/>ctat, &amp; Sol au-<lb/>ſtralior eſt, quã <lb/>Verticalis pro-<lb/>priè dict<emph style="sub">9</emph>, vel in <lb/>Verticali ꝓpriè <lb/>dicto exiſtit, vel <lb/>borealior eſt, <lb/>quàm Vertica-<lb/>lis propriè di-<lb/>ctus, obſeruatio-<lb/>q́ue fit poſt me-<lb/>ridiem.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4890" xml:space="preserve">CADENTE autem puncto S, in punctum R, ita vt Sol illuminet quidem murum ex parte borea-<lb/>li, Verticalem vero primarium nullo modo, dabit angulus inuentus C D G, declinationem muri à Ver-<lb/>
<anchor type="note" xlink:label="note-0108-09a" xlink:href="note-0108-09"/>
ticali primario, &amp; </s>
  <s xml:id="echoid-s4891" xml:space="preserve">à Septentrione in occaſum; </s>
  <s xml:id="echoid-s4892" xml:space="preserve">quoniam tunc Verticalis primarius per Solem incedit, <lb/>eſt{q́ue} ipſo muro borealior.</s>
  <s xml:id="echoid-s4893" xml:space="preserve"/>
</p>
<div xml:id="echoid-div304" type="float" level="2" n="17">
<note position="left" xlink:label="note-0108-09" xlink:href="note-0108-09a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s4894" xml:space="preserve">PVNCTO denique S, inter P, &amp; </s>
  <s xml:id="echoid-s4895" xml:space="preserve">R, exiſtente’, ita vt Sol tam murum, quàm Verticalem pro-<lb/>priè dictum ex parte boreali illuminet, ſi quidem angulus T R H, æqualis fuerit angulo C D G, æquidi-<lb/>ſtabit murus Verticali primario, nullam{q́ue} habebit declinationem. </s>
  <s xml:id="echoid-s4896" xml:space="preserve">Si vero ille maior hoc fuerit, exiſtet <lb/>murus ex parte occidentali inter Verticalem primarium, &amp; </s>
  <s xml:id="echoid-s4897" xml:space="preserve">illum, qui per Solem tranſit. </s>
  <s xml:id="echoid-s4898" xml:space="preserve">Quocirca <lb/>dempto angulo C D G, ex angulo T R H, reliquus erit angulus declinationis muri à Verticali propriè di-<lb/>cto, &amp; </s>
  <s xml:id="echoid-s4899" xml:space="preserve">à Septentrione in ortum. </s>
  <s xml:id="echoid-s4900" xml:space="preserve">Si denique angulus T R H, angulo C D G, fuerit minor, collocatus erit <lb/>Verticalis primarius inter murum, &amp; </s>
  <s xml:id="echoid-s4901" xml:space="preserve">Verticalem, in quo Sol exiſtit, ex parte occidentali. </s>
  <s xml:id="echoid-s4902" xml:space="preserve">Quare dem-<lb/>pto illo ex hoc, remanebit angulus declinationis muri à Verticali primario, &amp; </s>
  <s xml:id="echoid-s4903" xml:space="preserve">à Septentrione in occa-<lb/>
<anchor type="note" xlink:label="note-0108-10a" xlink:href="note-0108-10"/>
ſum. </s>
  <s xml:id="echoid-s4904" xml:space="preserve">Quæ omnia perſpicua ſunt, ſi attentè diligenterq́, ſitus circulorum, &amp; </s>
  <s xml:id="echoid-s4905" xml:space="preserve">muri perpendatur.</s>
  <s xml:id="echoid-s4906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div305" type="float" level="2" n="18">
<note position="left" xlink:label="note-0108-10" xlink:href="note-0108-10a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">Quando altitu-<lb/>do Solis æqua-<lb/>lis fuerit altitu-<lb/>dini eiuſdem <lb/>meridianæ.</note>
<p style="it">
  <s xml:id="echoid-s4907" xml:space="preserve">QVOD ſi quando recta P Q, in Analemmate ceciderit in punctum N, hoc eſt, ſi altitudo Solis in-<lb/>uenta fuerit æqualis altitudini Meridianę Solis illius diei, exiſtet Sol in Meridiano circulo; </s>
  <s xml:id="echoid-s4908" xml:space="preserve">ac propterea <lb/>recta F D, in muro communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s4909" xml:space="preserve">muri; </s>
  <s xml:id="echoid-s4910" xml:space="preserve">cùm Meridianus tunc per E, centrũ mundi, <lb/>&amp; </s>
  <s xml:id="echoid-s4911" xml:space="preserve">per radium Solis E F, ducatur, murus{q́ue} ipſe in meridiem verget. </s>
  <s xml:id="echoid-s4912" xml:space="preserve">Igitur angulus C D G, in muro in-<lb/>uentus dabit declinationem muri à Meridiano, ac propterea eius complementum declinationem muri à <lb/>Verticali propriè dicto oſtendet, à meridie quidem in ortum, ſi vmbra F, cadat nobis ad murum conuer-<lb/>ſis ad dexteram, à meridie verò in occaſum, ſi ad ſiniſtram cadat vmbra. <lb/></s>
  <s xml:id="echoid-s4913" xml:space="preserve">
<anchor type="note" xlink:label="note-0108-12a" xlink:href="note-0108-12"/>
</s>
</p>
<div xml:id="echoid-div306" type="float" level="2" n="19">
<note position="left" xlink:label="note-0108-12" xlink:href="note-0108-12a" xml:space="preserve">Inuentio facili <lb/>ma declinatio-<lb/>nis muri in me <lb/>ridiem vergen-<lb/>tis in ipſo meri-<lb/>die.</note>
</div>
<p style="it">
  <s xml:id="echoid-s4914" xml:space="preserve">QVOCIRCA ſi in meridie fiat obſeruatio, qui in plano Horizonti parallelo ex vmbra ſtyli in li-<lb/>neam meridian<unsure/>am cadente cognoſcitur, (quod quidem tempus, ſi commode fieri poſſit, ego ſemper elige-<lb/>rem) dicto citius declinatio reperietur. </s>
  <s xml:id="echoid-s4915" xml:space="preserve">Nam complementum anguli C D G, in muro inuenti dabit decli-
<pb o="89" file="0109" n="109" rhead="LIBER PRIMVS."/>
nationem muri à Verticali propriè dicto, &amp; </s>
  <s xml:id="echoid-s4916" xml:space="preserve">à meridie in ortum, vel occaſum, prout vmbra nobis ad mu-<lb/>rum conuerſis ad dextram, vel ad ſiniſtram ceciderit, vt proxime dictum eſt. </s>
  <s xml:id="echoid-s4917" xml:space="preserve">Quod intelligendum eſt <lb/>de muro ad meridiem vergente. </s>
  <s xml:id="echoid-s4918" xml:space="preserve">Nam murus ad Boream ſpectans in meridie non illuminatur à Sole, niſi <lb/>Sol borealior ipſo muro fuerit, quod in Zona torrida contingere poteſt. </s>
  <s xml:id="echoid-s4919" xml:space="preserve">Quod cum acciderit, &amp; </s>
  <s xml:id="echoid-s4920" xml:space="preserve">vmbra <lb/>nobis ad murum conuerſis ceciderit ad ſiniſtram, declinabit murus à Septentrione in ortum, ſi verò ad <lb/>dextram, à Septentrione in occaſum.</s>
  <s xml:id="echoid-s4921" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s4922" xml:space="preserve">HAEC omnia accommodari poſſunt etiam planis inclinatis ad Horizontem, ſi ſupra lineam, quæ <lb/>
<anchor type="note" xlink:label="note-0109-01a" xlink:href="note-0109-01"/>
in eiuſinodi planis Horizonti ducitur parallela, ſtatuatur planum rectum ad Horizontem, obſeruatio{q́ue} <lb/>fiat in facie huius plani, quæ cum plano inclinato angulum obtuſum constituit. <lb/></s>
  <s xml:id="echoid-s4923" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div308" type="section" level="1" n="116">
<head xml:id="echoid-head119" xml:space="preserve">THEOREMA 21. PROPOSITIO 24.</head>
<p>
  <s xml:id="echoid-s4924" xml:space="preserve">SI à circunferentia circuli maximi in ſphęra ſuper alium circulum <lb/>
<anchor type="note" xlink:label="note-0109-03a" xlink:href="note-0109-03"/>
maximum inclinati perpendiculares ad eiuſdem circuli maximi planũ <lb/>ducantur, cadent omnes in lineam, quæ Ellipſis appellatur; </s>
  <s xml:id="echoid-s4925" xml:space="preserve">cuius qui-<lb/>dem diameter maior eadem eſt, quæ communis ſectio ipſorum circulo-<lb/>rum, nempe eorum diameter, minor verò determinatur interuallo per-<lb/>
<anchor type="note" xlink:label="note-0109-04a" xlink:href="note-0109-04"/>
pendicularium cadentium ab extremitate alterius diametri circuli incli <lb/>nati, quæ priorem diametrum, hoc eſt, communem ſectionem, ad re-<lb/>ctos angulos diuidit.</s>
  <s xml:id="echoid-s4926" xml:space="preserve"/>
</p>
<div xml:id="echoid-div308" type="float" level="2" n="1">
<note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">Declinatio<unsure/> pla-<lb/>norum, quæ ad <lb/>Horizontẽ ſunt <lb/>inclinata, qua <lb/>tatione repert@a-<lb/>tur.</note>
<note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">Perpendicula-<lb/>res cadentes à <lb/>circunferentia <lb/>maximi circuli <lb/>in ſphæra in pla <lb/>num alterius <lb/>circuli maximi, <lb/>ad quem ille in <lb/>clinatus eſt, fa-<lb/>ciunt in poſte-<lb/>riori circulo ma <lb/>ximo Ellipſina<unsure/>.</note>
<note position="left" xlink:label="note-0109-04" xlink:href="note-0109-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s4927" xml:space="preserve">SIT in ſphæra circulus maximus A B C D, cuius centrum E, ad circulum maximum AFCG, <lb/>inclinatus, &amp; </s>
  <s xml:id="echoid-s4928" xml:space="preserve">circulus A F C G, ſecet circulum A B C D, in centro E, vt ſit diameter A C, commu <lb/>nis ſectio circulorum A B C D, A F C G, ducaturq́; <lb/></s>
  <s xml:id="echoid-s4929" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0109-01a" xlink:href="fig-0109-01"/>
in circulo A B C D, alia diameter B D, ſecans A C, <lb/>ad rectos angulos: </s>
  <s xml:id="echoid-s4930" xml:space="preserve">ducatur quoque in plano circu-<lb/>li A F C G, alia diameter F G, ad eandem A G, per-<lb/>
<anchor type="note" xlink:label="note-0109-05a" xlink:href="note-0109-05"/>
pendicularis. </s>
  <s xml:id="echoid-s4931" xml:space="preserve">Quoniam igitur recta C E, rectis <lb/>B E, F E, ſeſe in E, ſecantibus inſiſtit ad rectos an-<lb/>gulos, erit eadem C E, ad planum per B E, F E, du-<lb/>
<anchor type="note" xlink:label="note-0109-06a" xlink:href="note-0109-06"/>
ctum ad angulos rectos. </s>
  <s xml:id="echoid-s4932" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s4933" xml:space="preserve">plana circulo-<lb/>rum A F C G, A B C D, per C E, tranſeuntia ad idẽ <lb/>
<anchor type="note" xlink:label="note-0109-07a" xlink:href="note-0109-07"/>
planum per B E, F E, ductum erunt recta, eritq́ue <lb/>F G, communis ſectio plani per B E, F E, ducti, &amp; </s>
  <s xml:id="echoid-s4934" xml:space="preserve"><lb/>plani circuli A F C G, quod ad illud rectum eſt <lb/>oſtenſum; </s>
  <s xml:id="echoid-s4935" xml:space="preserve">atque adeò ſi ex puncto B, quod in pla-<lb/>no per B E, F E, ducto exiſtit, linea perpendicularis ducatur ad planum A F C G, nempe B H, <lb/>
<anchor type="note" xlink:label="note-0109-08a" xlink:href="note-0109-08"/>
ipſa in F E, communem ſectionem plani per B E, F E, ducti, &amp; </s>
  <s xml:id="echoid-s4936" xml:space="preserve">plani A F C G, cadet. </s>
  <s xml:id="echoid-s4937" xml:space="preserve">Cadat ergo <lb/>
<anchor type="note" xlink:label="note-0109-09a" xlink:href="note-0109-09"/>
in H. </s>
  <s xml:id="echoid-s4938" xml:space="preserve">Eodem modo perpendicularis ex D, ad idem planum A F C G, ducta in rectam F G, cadet, <lb/>vt in I: </s>
  <s xml:id="echoid-s4939" xml:space="preserve">eruntq́; </s>
  <s xml:id="echoid-s4940" xml:space="preserve">rectæ E H, E I, inter ſe æquales. </s>
  <s xml:id="echoid-s4941" xml:space="preserve">Cum enim in triangulis E B H, E D I, anguli ad <lb/>H, I, recti ſint, ex defin. </s>
  <s xml:id="echoid-s4942" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4943" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4944" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4945" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s4946" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4947" xml:space="preserve">anguli ad verticẽ E, ęquales, Item &amp; </s>
  <s xml:id="echoid-s4948" xml:space="preserve">latera E B, E D, ęqua-<lb/>
<anchor type="note" xlink:label="note-0109-10a" xlink:href="note-0109-10"/>
lia, erunt quoque latc<unsure/>ra E H, E I, ęqualia. </s>
  <s xml:id="echoid-s4949" xml:space="preserve">Sumpto autem quouis alio puncto K, in circunferentia <lb/>
<anchor type="note" xlink:label="note-0109-11a" xlink:href="note-0109-11"/>
circuli A B C D, ab eodem ad idem planum A F C G, perpendicularis demittatur K L. </s>
  <s xml:id="echoid-s4950" xml:space="preserve">Dico pun <lb/>ctum L, cadere in Ellipſim, cuius quidem diameter maior eſt A C, circulorum diameter, &amp; </s>
  <s xml:id="echoid-s4951" xml:space="preserve">mi-<lb/>nor recta H I. </s>
  <s xml:id="echoid-s4952" xml:space="preserve">Ducta enim in plano A F C G, ex L, ad A C, perpendiculari L M, cum &amp; </s>
  <s xml:id="echoid-s4953" xml:space="preserve">H E, ad <lb/>eandẽ A C, ſit perpendicularis, erunt H E, L M, inter ſe parallelæ: </s>
  <s xml:id="echoid-s4954" xml:space="preserve">Sed &amp; </s>
  <s xml:id="echoid-s4955" xml:space="preserve">B H, K L, ſunt inter ſe <lb/>
<anchor type="note" xlink:label="note-0109-12a" xlink:href="note-0109-12"/>
parallelę, quòd ad idem planũ A F C G, ſint perpendiculares. </s>
  <s xml:id="echoid-s4956" xml:space="preserve">Ergo planũ per B H, H E, ductum <lb/>
<anchor type="note" xlink:label="note-0109-13a" xlink:href="note-0109-13"/>
<anchor type="note" xlink:label="note-0109-14a" xlink:href="note-0109-14"/>
plano per k L, L M, ducto parallelũ erit: </s>
  <s xml:id="echoid-s4957" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4958" xml:space="preserve">propterea ipſorũ planorũ, &amp; </s>
  <s xml:id="echoid-s4959" xml:space="preserve">circuli A B C D, cõmu-<lb/>
<anchor type="note" xlink:label="note-0109-15a" xlink:href="note-0109-15"/>
nes ſectiones, nempe rectæ B E, k M, parallelæ erunt. </s>
  <s xml:id="echoid-s4960" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s4961" xml:space="preserve">quoniã B E, E H, ſeſe in E, tangentes, re-<lb/>
<anchor type="note" xlink:label="note-0109-16a" xlink:href="note-0109-16"/>
ctis k M, M L, in M, ſeſe tangentibus ſunt parallelæ, non ſunt autem in eodem plano, ſed in planis <lb/>parallelis, vt dictũ eſt, erit angulus B E H, angulo K M L, æqualis: </s>
  <s xml:id="echoid-s4962" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s4963" xml:space="preserve">H, L, æquales, vt-<lb/>
<anchor type="note" xlink:label="note-0109-17a" xlink:href="note-0109-17"/>
potè recti, ex defin. </s>
  <s xml:id="echoid-s4964" xml:space="preserve">3. </s>
  <s xml:id="echoid-s4965" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4966" xml:space="preserve">11. </s>
  <s xml:id="echoid-s4967" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s4968" xml:space="preserve">Ergo &amp; </s>
  <s xml:id="echoid-s4969" xml:space="preserve">reliquus E B H, reliquo M k L, ęqualis erit, ex coroll. </s>
  <s xml:id="echoid-s4970" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s4971" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s4972" xml:space="preserve">32. </s>
  <s xml:id="echoid-s4973" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4974" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4975" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s4976" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s4977" xml:space="preserve">triangulũ B E H, triangulo k M L, æquiangulũ. </s>
  <s xml:id="echoid-s4978" xml:space="preserve">Quare erit vt B E, ad EH, <lb/>
<anchor type="note" xlink:label="note-0109-18a" xlink:href="note-0109-18"/>
ita K M, ad M L, permutandoq́;</s>
  <s xml:id="echoid-s4979" xml:space="preserve">, vt B E, ad K M, ita E H, ad M L. </s>
  <s xml:id="echoid-s4980" xml:space="preserve">Igitur vt quadratum ex B E, <lb/>ad quadratum ex k M, ita quadratum ex E H, ad quadratũ ex M L: </s>
  <s xml:id="echoid-s4981" xml:space="preserve">Vt autẽ quadratũ ex B E, ad qua-<lb/>
<anchor type="note" xlink:label="note-0109-19a" xlink:href="note-0109-19"/>
dratum ex K M, ita eſt, ex propoſ. </s>
  <s xml:id="echoid-s4982" xml:space="preserve">21. </s>
  <s xml:id="echoid-s4983" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4984" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4985" xml:space="preserve">Apollonij, rectangulum ſub C E, E A, ad rectangulũ <lb/>ſub C M, M A, propterea quòd B E, k M, in circulo A B C D, ad diametrum A C, ſint ductæ or-<lb/>dinatim, nempe perpendiculares. </s>
  <s xml:id="echoid-s4986" xml:space="preserve">Eſt igitur quoque, vt quadratum ex E H, ad quadratum ex
<pb o="90" file="0110" n="110" rhead="GNOMONICES"/>
M L, ita rectangulum ſub C E, E A, ad rectangulum ſub C M, M A. </s>
  <s xml:id="echoid-s4987" xml:space="preserve">Sed ex eadem propoſ. </s>
  <s xml:id="echoid-s4988" xml:space="preserve">21. <lb/></s>
  <s xml:id="echoid-s4989" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s4990" xml:space="preserve">1. </s>
  <s xml:id="echoid-s4991" xml:space="preserve">Apollonij, ſi circa diametrum maiorem AC, &amp; </s>
  <s xml:id="echoid-s4992" xml:space="preserve">minorem H I, (Eſt enim A C, maior quàm <lb/>H I, cum A C, diameter circuli A F C G, ęqualis ſit diametro F G, eiuſdem circuli) ellipſis deſcri-<lb/>batur, &amp; </s>
  <s xml:id="echoid-s4993" xml:space="preserve">ex quouis puncto ipſi H E, parallela du-<lb/>
<anchor type="figure" xlink:label="fig-0110-01a" xlink:href="fig-0110-01"/>
catur, hoc eſt, ordinatim applicata ad diametrũ <lb/>A C, quadratum ex H E, ad quadratum illius pa-<lb/>rallelæ eſt, vt rectangulum ſub C E, E A, ad re-<lb/>ctangulum ſub partibus diametri A C, quas pa-<lb/>rallela illa facit. </s>
  <s xml:id="echoid-s4994" xml:space="preserve">Igitur punctum L, in illam El-<lb/>lipſim cadet, cuius maior diameter A C, &amp; </s>
  <s xml:id="echoid-s4995" xml:space="preserve">mi-<lb/>
<anchor type="note" xlink:label="note-0110-01a" xlink:href="note-0110-01"/>
nor HI; </s>
  <s xml:id="echoid-s4996" xml:space="preserve">quandoquidem eſt, vt quadratum ex <lb/>H E, ad quadratum ex L M, ita rectangulum ſub <lb/>C E, E A, ad rectangulum ſub C M, M A; </s>
  <s xml:id="echoid-s4997" xml:space="preserve">alias <lb/>pars foret ęqualis toti. </s>
  <s xml:id="echoid-s4998" xml:space="preserve">Si enim illa Ellipſis non <lb/>tranſit per punctum L, tranſeat ſi fieri poteſt, per <lb/>N. </s>
  <s xml:id="echoid-s4999" xml:space="preserve">Erit igitur per propoſ. </s>
  <s xml:id="echoid-s5000" xml:space="preserve">21. </s>
  <s xml:id="echoid-s5001" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5002" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5003" xml:space="preserve">Apollonij, <lb/>vt rectangulum CE, E A, ad rectangulum ſub C M, M A, hoc eſt, vt quadratum ex H E, ad qua-<lb/>dratum ex L M, ita quadaatum ex H E, ad quadratum ex N M. </s>
  <s xml:id="echoid-s5004" xml:space="preserve">Aequalia ſunt igitur quadrata ex <lb/>
<anchor type="note" xlink:label="note-0110-02a" xlink:href="note-0110-02"/>
L M, &amp; </s>
  <s xml:id="echoid-s5005" xml:space="preserve">N M, atque adeò &amp; </s>
  <s xml:id="echoid-s5006" xml:space="preserve">rectę L M, N M, ęquales, totum &amp; </s>
  <s xml:id="echoid-s5007" xml:space="preserve">pars. </s>
  <s xml:id="echoid-s5008" xml:space="preserve">Quod eſt abſurdum. <lb/></s>
  <s xml:id="echoid-s5009" xml:space="preserve">Tranſit ergo Ellipſis illa per punctum L, ac proinde punctum L, in Ellipſim cadit, cuius maior <lb/>
<anchor type="note" xlink:label="note-0110-03a" xlink:href="note-0110-03"/>
diameter A C, &amp; </s>
  <s xml:id="echoid-s5010" xml:space="preserve">minor HI. </s>
  <s xml:id="echoid-s5011" xml:space="preserve">Eodem modo oſtendemus &amp; </s>
  <s xml:id="echoid-s5012" xml:space="preserve">alia puncta, in quæ à circunferentia <lb/>circuli. </s>
  <s xml:id="echoid-s5013" xml:space="preserve">A B C D, perpendiculares cadunt, in eadem Ellipſi eſſe. </s>
  <s xml:id="echoid-s5014" xml:space="preserve">Quocirca ſi à circunferentia cir-<lb/>culi maximi in ſphæra, &amp;</s>
  <s xml:id="echoid-s5015" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5016" xml:space="preserve">Quod erat demon ſtrandum.</s>
  <s xml:id="echoid-s5017" xml:space="preserve"/>
</p>
<div xml:id="echoid-div309" type="float" level="2" n="2">
  <figure xlink:label="fig-0109-01" xlink:href="fig-0109-01a">
    <image file="0109-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0109-01"/>
  </figure>
<note position="left" xlink:label="note-0109-05" xlink:href="note-0109-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0109-06" xlink:href="note-0109-06a" xml:space="preserve">4. vndec.</note>
<note position="right" xlink:label="note-0109-07" xlink:href="note-0109-07a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0109-08" xlink:href="note-0109-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0109-09" xlink:href="note-0109-09a" xml:space="preserve">38. vndec.</note>
<note position="right" xlink:label="note-0109-10" xlink:href="note-0109-10a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0109-11" xlink:href="note-0109-11a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0109-12" xlink:href="note-0109-12a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0109-13" xlink:href="note-0109-13a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0109-14" xlink:href="note-0109-14a" xml:space="preserve">6. vndec.</note>
<note position="right" xlink:label="note-0109-15" xlink:href="note-0109-15a" xml:space="preserve">15. vndec.</note>
<note position="right" xlink:label="note-0109-16" xlink:href="note-0109-16a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0109-17" xlink:href="note-0109-17a" xml:space="preserve">10. vndec.</note>
<note position="right" xlink:label="note-0109-18" xlink:href="note-0109-18a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0109-19" xlink:href="note-0109-19a" xml:space="preserve">22. ſexti.</note>
  <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a">
    <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-01"/>
  </figure>
<note position="left" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">9. quinti.</note>
<note position="left" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div311" type="section" level="1" n="117">
<head xml:id="echoid-head120" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s5018" xml:space="preserve">HOC theorema proponitur à Federico Commandino vniuer ſalius in libello de horologiorum deſcri-<lb/>ptione; </s>
  <s xml:id="echoid-s5019" xml:space="preserve">adeo vt etiamſi planum, in quo circulus A F C G, non ſecet circulum inclinatum A B C D, per <lb/>centrum, vel nullo modo, &amp; </s>
  <s xml:id="echoid-s5020" xml:space="preserve">ſiue A B C D, ſit maximus circulus in ſphæra, ſiue quicunque, tamen per-<lb/>pendiculares ductæ à circunferentia circuli A B C D, ad planum A F C G, cadant in Ellipſim. </s>
  <s xml:id="echoid-s5021" xml:space="preserve">Nam ſi <lb/>
<anchor type="note" xlink:label="note-0110-04a" xlink:href="note-0110-04"/>
planum, in quo circulus A F C G, non ſecet circulum A B C D, per centrum, vel nullo modo, ita propo-<lb/>ſitum colligit. </s>
  <s xml:id="echoid-s5022" xml:space="preserve">Ducto alio plano ipſi A F C G, æquidiſtante, quod circulum A B C D, ſecet in centro E, ſi-<lb/>militer demonſtrabitur, vt prius, perpendiculares à circuli A B C D, circunferentia ad planum illud de-<lb/>miſſas in Ellipſim cadere: </s>
  <s xml:id="echoid-s5023" xml:space="preserve">quæ quidem lineæ, cum vlterius productæ ad planum A F C G, quod illi æqui-<lb/>diſtat, eandem poſitionem habeant, cadent &amp; </s>
  <s xml:id="echoid-s5024" xml:space="preserve">eoloco in Ellipſim, cuius maior diameter æqualis erit dia-<lb/>metro A C, circuli A B C D, minor vero æqualis interuallo H I, perpendicularium B H, D I, quæ ab ex-<lb/>tremitatibus alteri{us} diametri B D, ducuntur.</s>
  <s xml:id="echoid-s5025" xml:space="preserve"/>
</p>
<div xml:id="echoid-div311" type="float" level="2" n="1">
<note position="left" xlink:label="note-0110-04" xlink:href="note-0110-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s5026" xml:space="preserve">NOS autem propoſuimus theorema de circulis maximis in ſphæra duntaxat, quia in his ſolis appare <lb/>bit eius vſus in noſtra hac Gnomonica.</s>
  <s xml:id="echoid-s5027" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div313" type="section" level="1" n="118">
<head xml:id="echoid-head121" xml:space="preserve">PROBLEMA 4. PROPOSITIO 25.</head>
<p>
  <s xml:id="echoid-s5028" xml:space="preserve">IN circunferentia circuli maximi in ſphęra ad alium circulum ma-<lb/>ximum inclinati ſumptis duobus punctis extremis diametri commu-<lb/>nem eorum ſectionem ad rectos angulos ſecantis, quo loco perpendi-<lb/>culares ab his ductæ ad alium circulum cadant, ſi nota fuerit inclina-<lb/>tio, inueſtigare.</s>
  <s xml:id="echoid-s5029" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s5030" xml:space="preserve">SIT in ſphęra circulus maximus A B C D, ad circulum maximum A F C E, inclinatus, ſitq́; <lb/></s>
  <s xml:id="echoid-s5031" xml:space="preserve">eorum ſectio communis diameter A C, ad quam in plano circuli A B C D, per centrum G, alia <lb/>diameter ducatur perpendicularis B D. </s>
  <s xml:id="echoid-s5032" xml:space="preserve">Oportet igitur inueſtigare, quo loco perpendiculares à <lb/>punctis D, B, in planum circuli A F C E, demiſſę cadant. </s>
  <s xml:id="echoid-s5033" xml:space="preserve">In plano circuli A F C E, ducatur alia <lb/>
<anchor type="note" xlink:label="note-0110-07a" xlink:href="note-0110-07"/>
diameter E F, ad A C, perpendicularis, ſitq́; </s>
  <s xml:id="echoid-s5034" xml:space="preserve">angulus inclinationis, quę nota ponitur E G H, ita vt <lb/>arcus E H, æqualis ſitarcui inclinationis circuli A B C D, ad circulum A F C E; </s>
  <s xml:id="echoid-s5035" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5036" xml:space="preserve">ab H, ducatur <lb/>HI, ad EF, perpendicularis. </s>
  <s xml:id="echoid-s5037" xml:space="preserve">Dico perpendicularem à D, ad planum circuli A F C E, demiſſam <lb/>cadere in punctum I. </s>
  <s xml:id="echoid-s5038" xml:space="preserve">Ducto enim per E G, D G, plano faciente in ſphæra ſemicirculum E D F, ex <lb/>propoſ. </s>
  <s xml:id="echoid-s5039" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5040" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5041" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5042" xml:space="preserve">Theodoſii, erit hicad circulos A F C E, A B C D, rectus. </s>
  <s xml:id="echoid-s5043" xml:space="preserve">(Nam cum C G, per-<lb/>pendicularis ſit ad E G, D G, erit eadem quoque ad planum per E G, D G, ductum, id eſt, ad ſe-<lb/>
<anchor type="note" xlink:label="note-0110-08a" xlink:href="note-0110-08"/>
micirculum E D F, recta, atque adeo &amp; </s>
  <s xml:id="echoid-s5044" xml:space="preserve">plana circulorum A F C E, A B C D, per C G, ducta ad
<pb o="91" file="0111" n="111" rhead="LIBER PRIMVS."/>
c<unsure/>undem ſemicirculũ E D F, recta erunt, atque idcirco &amp; </s>
  <s xml:id="echoid-s5045" xml:space="preserve">viciſſim hic ſemicirculus ad illa plana re-<lb/>ctus erit.) </s>
  <s xml:id="echoid-s5046" xml:space="preserve">Quare D E, arcus erit inclinationis circuli A B C D, ad circulum A F C E, proptereaq́; <lb/></s>
  <s xml:id="echoid-s5047" xml:space="preserve">arcui E H, æqualis: </s>
  <s xml:id="echoid-s5048" xml:space="preserve">cadetq́ue perpendicularis ex <lb/>
<anchor type="figure" xlink:label="fig-0111-01a" xlink:href="fig-0111-01"/>
D, ad planum A F C E, demiſſa in E F, communem <lb/>
<anchor type="note" xlink:label="note-0111-01a" xlink:href="note-0111-01"/>
ſectionem planorum A F C E, E D F; </s>
  <s xml:id="echoid-s5049" xml:space="preserve">quam dico <lb/>in I, cadere. </s>
  <s xml:id="echoid-s5050" xml:space="preserve">Si enim alio cadat, vt in k, erunt duo <lb/>anguli H I G, I G H, trianguli G H I, duobus an-<lb/>gulis D K G, K G D, trianguli G D K, ęquales; <lb/></s>
  <s xml:id="echoid-s5051" xml:space="preserve">(Nam I G H, K G D, ęquales ſunt, ob æqualitatem <lb/>
<anchor type="note" xlink:label="note-0111-02a" xlink:href="note-0111-02"/>
arcuum E H, E D, &amp; </s>
  <s xml:id="echoid-s5052" xml:space="preserve">H I G, D K G, recti ſunt, ex <lb/>
<anchor type="note" xlink:label="note-0111-03a" xlink:href="note-0111-03"/>
conſtructione, &amp; </s>
  <s xml:id="echoid-s5053" xml:space="preserve">definitione 3. </s>
  <s xml:id="echoid-s5054" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5055" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5056" xml:space="preserve">Euclidis) <lb/>ſuntautem &amp; </s>
  <s xml:id="echoid-s5057" xml:space="preserve">latera G H, G D, ducta à centro ſphę-<lb/>rę ad eius ſuperficiem, ęquales. </s>
  <s xml:id="echoid-s5058" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s5059" xml:space="preserve">latera G I, <lb/>
<anchor type="note" xlink:label="note-0111-04a" xlink:href="note-0111-04"/>
G K, æqualia erunt, pars, &amp; </s>
  <s xml:id="echoid-s5060" xml:space="preserve">totum. </s>
  <s xml:id="echoid-s5061" xml:space="preserve">Quod eſt abſur-<lb/>dum. </s>
  <s xml:id="echoid-s5062" xml:space="preserve">Non ergo perpendicularis à puncto D, de-<lb/>miſſa ad planum A F C E, alio cadit, quàm in I. </s>
  <s xml:id="echoid-s5063" xml:space="preserve">Eo-<lb/>dem modo reperiemus punctum, in quod cadit <lb/>perpendicularis ex B, demiſſa. </s>
  <s xml:id="echoid-s5064" xml:space="preserve">Cadet autem ſem-<lb/>per in punctum, puta M, quod tantum à centro <lb/>G, abeſt, quantum I, ab eodem diſtat. </s>
  <s xml:id="echoid-s5065" xml:space="preserve">Quoniam enim in triangulis D G I, B G M, anguli ad I, M, <lb/>
<anchor type="note" xlink:label="note-0111-05a" xlink:href="note-0111-05"/>
ex defin. </s>
  <s xml:id="echoid-s5066" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5067" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5068" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5069" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s5070" xml:space="preserve">recti ſunt, anguliq́; </s>
  <s xml:id="echoid-s5071" xml:space="preserve">ad verticem G, æquales; </s>
  <s xml:id="echoid-s5072" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s5073" xml:space="preserve">latera D G, B G, æqua <lb/>
<anchor type="note" xlink:label="note-0111-06a" xlink:href="note-0111-06"/>
lia, cum ſint ſpheræ ſemidiametri; </s>
  <s xml:id="echoid-s5074" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s5075" xml:space="preserve">latera G I, G M, inter ſe ęqualia. </s>
  <s xml:id="echoid-s5076" xml:space="preserve">In circunferentia igi-<lb/>
<anchor type="note" xlink:label="note-0111-07a" xlink:href="note-0111-07"/>
tur circuli maximi in ſphæra, &amp;</s>
  <s xml:id="echoid-s5077" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5078" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s5079" xml:space="preserve"/>
</p>
<div xml:id="echoid-div313" type="float" level="2" n="1">
<note position="left" xlink:label="note-0110-07" xlink:href="note-0110-07a" xml:space="preserve">Inuentio pun-<lb/>ctorum, in quæ <lb/>cadunt perpen-<lb/>diculares ab ex-<lb/>tremitatibus, <lb/>diametri circu-<lb/>li ad alium cir-<lb/>culum inclina-<lb/>ti<unsure/>.</note>
<note position="left" xlink:label="note-0110-08" xlink:href="note-0110-08a" xml:space="preserve">4. vndec.</note>
  <figure xlink:label="fig-0111-01" xlink:href="fig-0111-01a">
    <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0111-01"/>
  </figure>
<note position="right" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">38. vndec.</note>
<note position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0111-04" xlink:href="note-0111-04a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0111-05" xlink:href="note-0111-05a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0111-06" xlink:href="note-0111-06a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0111-07" xlink:href="note-0111-07a" xml:space="preserve">26. primi.</note>
</div>
</div>
<div xml:id="echoid-div315" type="section" level="1" n="119">
<head xml:id="echoid-head122" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s5080" xml:space="preserve">EX his eadem via inueniemus diametrum minorem ellipſis illius, in quam perpendiculares à circun-<lb/>
<anchor type="note" xlink:label="note-0111-08a" xlink:href="note-0111-08"/>
ferentia circuli inclinati in alium circulum demiſſæ cadunt. </s>
  <s xml:id="echoid-s5081" xml:space="preserve">Nam recta I M, inter puncta I, M, in quæ <lb/>dictæ perpendiculares cadunt, minor diameter eſt, per antecedentem propoſitionem.</s>
  <s xml:id="echoid-s5082" xml:space="preserve"/>
</p>
<div xml:id="echoid-div315" type="float" level="2" n="1">
<note position="right" xlink:label="note-0111-08" xlink:href="note-0111-08a" xml:space="preserve">Inuentio min@ <lb/>tis diametri El-<lb/>lipſis, quæ fit à <lb/>perpendiculari-<lb/>bus cadenubus <lb/>à circunferẽria <lb/>circuli inclinati <lb/>ad alium circu-<lb/>lum.</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div317" type="section" level="1" n="120">
<head xml:id="echoid-head123" xml:space="preserve">PROBLEMA 5. PROPOSITIO 26.</head>
<p>
  <s xml:id="echoid-s5083" xml:space="preserve">IN circunferentia circuli maximi in ſphæra ad alium circulum ma-<lb/>ximum inclinati ſumptis quibuslibet punctis, quo loco perpendicula-<lb/>res ab his ductæ in alium circulum cadant, ſi inclinatio fuerit nota, <lb/>inquirere.</s>
  <s xml:id="echoid-s5084" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5085" xml:space="preserve">SIT in ſphæra circulus maximus A B C D, ad maximum D E B F, inclinatus, &amp; </s>
  <s xml:id="echoid-s5086" xml:space="preserve">nota inclina-<lb/>tio, ſitq́; </s>
  <s xml:id="echoid-s5087" xml:space="preserve">eorum fectio communis diameter D B, per centrum G, tranſiens, ad quam ad angulos <lb/>
<anchor type="note" xlink:label="note-0111-10a" xlink:href="note-0111-10"/>
rectos ducatur in circulo quidem A B C D, diame-<lb/>
<anchor type="figure" xlink:label="fig-0111-02a" xlink:href="fig-0111-02"/>
rer A C, in circulo verò D E B F, diameter E F, in <lb/>quam cadent perpendiculares ex A, C, in circulum <lb/>D E B F, demiſſæ, vt in propoſitione præcedenti eſt <lb/>oſtenſum. </s>
  <s xml:id="echoid-s5088" xml:space="preserve">Cadant ergo in H, I, vt ſit D B, diame-<lb/>ter maior, &amp; </s>
  <s xml:id="echoid-s5089" xml:space="preserve">H I, minor eius Ellipſis, quam perpen <lb/>diculares à circunferentia circuli A B C D, in pla-<lb/>num circuli D E B F, demiſſę faciunt, vt demonſtra <lb/>tum eſt. </s>
  <s xml:id="echoid-s5090" xml:space="preserve">Sumatur autem quodcunque punctum K, <lb/>in circunferentia A B C D. </s>
  <s xml:id="echoid-s5091" xml:space="preserve">Oportet igitur inquire-<lb/>
<anchor type="note" xlink:label="note-0111-11a" xlink:href="note-0111-11"/>
re, quo loco perpendicularis à K, in planum D E-<lb/>B F, deducta cadat. </s>
  <s xml:id="echoid-s5092" xml:space="preserve">Sumatur arcui A K, æqualis ar-<lb/>cus E L, &amp; </s>
  <s xml:id="echoid-s5093" xml:space="preserve">ducatur recta G L, quæ circulum H I, <lb/>circa minorem Ellipſis diametrum H I, deſcriptũ <lb/>
<anchor type="note" xlink:label="note-0111-12a" xlink:href="note-0111-12"/>
ſecet in M. </s>
  <s xml:id="echoid-s5094" xml:space="preserve">Deinde per L, ducatur L N, parallela <lb/>minori diametro H I, quæ ſecet D B, in O; </s>
  <s xml:id="echoid-s5095" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5096" xml:space="preserve">per <lb/>M, ducatur P M, parallela maiori Ellipſis diame-<lb/>tro D B, ſecans L N, in Q. </s>
  <s xml:id="echoid-s5097" xml:space="preserve">Dico perpendicularem à K, in planum D E B F, demiſſam cadere in <lb/>punctum Q. </s>
  <s xml:id="echoid-s5098" xml:space="preserve">Quòd enim cadat in lineam L N, ita oſtendetur. </s>
  <s xml:id="echoid-s5099" xml:space="preserve">Ducta recta K O, erit hæc ipſi <lb/>A G, parallela. </s>
  <s xml:id="echoid-s5100" xml:space="preserve">Ductis enim L S, k T, ad E G, A G, perpendicularibus, cum G O, æqualis ſit ipſi <lb/>
<anchor type="note" xlink:label="note-0111-13a" xlink:href="note-0111-13"/>
L S, ſinui recto arcus E L; </s>
  <s xml:id="echoid-s5101" xml:space="preserve">ſit autem L S, ſinus æqualis ipſi k T, ſinui recto arcus A K, qui æqua-
<pb o="92" file="0112" n="112" rhead="GNOMONICES"/>
lis ponitur arcui E L; </s>
  <s xml:id="echoid-s5102" xml:space="preserve">crit quoque G O, ipſi k T, æqualis. </s>
  <s xml:id="echoid-s5103" xml:space="preserve">Cum ergo G O, K T, ſint etiam paral-<lb/>
<anchor type="note" xlink:label="note-0112-01a" xlink:href="note-0112-01"/>
lelæ, propterea quòd anguli O G T, k T G, recti ſint, ex conſtructione; </s>
  <s xml:id="echoid-s5104" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s5105" xml:space="preserve">G T, O K, æqua-<lb/>
<anchor type="note" xlink:label="note-0112-02a" xlink:href="note-0112-02"/>
les, &amp; </s>
  <s xml:id="echoid-s5106" xml:space="preserve">parallelæ. </s>
  <s xml:id="echoid-s5107" xml:space="preserve">Quare cum angulus A G O, rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s5108" xml:space="preserve">angulus G O k, rectus. </s>
  <s xml:id="echoid-s5109" xml:space="preserve">Quoniam igi <lb/>
<anchor type="note" xlink:label="note-0112-03a" xlink:href="note-0112-03"/>
<anchor type="figure" xlink:label="fig-0112-01a" xlink:href="fig-0112-01"/>
tur recta G O, ad rectas O L, O k, perpendicula-<lb/>ris eſt, erit eadem G O, ad planum per O L, O k, du-<lb/>
<anchor type="note" xlink:label="note-0112-04a" xlink:href="note-0112-04"/>
<anchor type="figure" xlink:label="fig-0112-02a" xlink:href="fig-0112-02"/>
ctum perpendicularis: </s>
  <s xml:id="echoid-s5110" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s5111" xml:space="preserve">planum cir-<lb/>culi D E B F, per G O, ductum, ad idem planum <lb/>
<anchor type="note" xlink:label="note-0112-05a" xlink:href="note-0112-05"/>
per O L, O K, ductum erit rectum. </s>
  <s xml:id="echoid-s5112" xml:space="preserve">Quare perpen-<lb/>dicularis ex k, in planum D E B F, demiſſa cidet <lb/>in rectam L N, communem ſectionem plani DE-<lb/>
<anchor type="note" xlink:label="note-0112-06a" xlink:href="note-0112-06"/>
<anchor type="note" xlink:label="note-0112-07a" xlink:href="note-0112-07"/>
B F, &amp; </s>
  <s xml:id="echoid-s5113" xml:space="preserve">eius, quod per O L, O k, ducitur. </s>
  <s xml:id="echoid-s5114" xml:space="preserve">Quòd au-<lb/>tem in Q, cadat, ita demonſtrabitur. </s>
  <s xml:id="echoid-s5115" xml:space="preserve">Cadat, ſi he-<lb/>ri poteſt, in aliud punctum, vt in R. </s>
  <s xml:id="echoid-s5116" xml:space="preserve">Quoniam igi <lb/>tur L S, M P, parallelæ ſunt, erit vt L M, ad M G, <lb/>
<anchor type="note" xlink:label="note-0112-08a" xlink:href="note-0112-08"/>
ita S P, ad P G; </s>
  <s xml:id="echoid-s5117" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5118" xml:space="preserve">componendo, vt L G, ad M G, ita <lb/>S G, ad P G: </s>
  <s xml:id="echoid-s5119" xml:space="preserve">Sed L G, M G, ipſis E G, H G, æqua-<lb/>les ſunt, per definitionem circuli; </s>
  <s xml:id="echoid-s5120" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5121" xml:space="preserve">S G, P G, ipſis <lb/>
<anchor type="note" xlink:label="note-0112-09a" xlink:href="note-0112-09"/>
L O, Q O, æquales, ob rectangula S O, P O. </s>
  <s xml:id="echoid-s5122" xml:space="preserve">Ergo <lb/>erit quoque, vt E G, ad H G, ita L O, ad Q O; </s>
  <s xml:id="echoid-s5123" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5124" xml:space="preserve"><lb/>permutando, vt E G, ad L O, ita H G, ad Q O; </s>
  <s xml:id="echoid-s5125" xml:space="preserve">atq; <lb/></s>
  <s xml:id="echoid-s5126" xml:space="preserve">
<anchor type="note" xlink:label="note-0112-10a" xlink:href="note-0112-10"/>
adeò vt quadratum ex E G, ad quadratum ex L O, ita quadratum ex H G, ad quadratum ex Q O: <lb/></s>
  <s xml:id="echoid-s5127" xml:space="preserve">
<anchor type="note" xlink:label="note-0112-11a" xlink:href="note-0112-11"/>
Sed eſt, ex propoſ. </s>
  <s xml:id="echoid-s5128" xml:space="preserve">21. </s>
  <s xml:id="echoid-s5129" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5130" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5131" xml:space="preserve">Apollonij, vt quadratum ex E G, ad quadratum ex L O, ita rectangu-<lb/>gulum ſub B G, GD, ad rectangulum ſub B O, O D, quòd E G, L O, ſint ordinatim ductæ ad B D, <lb/>diametrum circuli D E B F, nempe perpendiculares. </s>
  <s xml:id="echoid-s5132" xml:space="preserve">Erit ergo quoque vt rectangulum ſub B G, <lb/>G D, ad rectangulum ſub B O, O D, ita quadratum ex H G, ad quadratum ex Q O. </s>
  <s xml:id="echoid-s5133" xml:space="preserve">Et quoniam, cũ <lb/>Ellipſis diametrorum D B, HI, ponatur tranſire per R, (eò quod in R, dicatur cadere perpendicu <lb/>laris ex K, demiſſa,) eſt quoque, per eandem propoſitionem 21. </s>
  <s xml:id="echoid-s5134" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5135" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5136" xml:space="preserve">Apollonii, vt rectangulum <lb/>ſub B G, G D, ad rectangulum ſub B O, O D, ita quadratum ex H G, ad quadratum ex R O, quòd <lb/>H G, R O, ſint ordinatim applicatę ad diametrum BD. </s>
  <s xml:id="echoid-s5137" xml:space="preserve">Erit igitur vt quadratum ex H G, ad qua-<lb/>dratum ex Q O, ita idem quadratum ex H G, ad quadratum ex R O. </s>
  <s xml:id="echoid-s5138" xml:space="preserve">Quare quadrata ex Q O, <lb/>
<anchor type="note" xlink:label="note-0112-12a" xlink:href="note-0112-12"/>
<anchor type="note" xlink:label="note-0112-13a" xlink:href="note-0112-13"/>
R O, ęqualia ſunt, ac propterea &amp; </s>
  <s xml:id="echoid-s5139" xml:space="preserve">lineę Q O, R O, ęquales, totum &amp; </s>
  <s xml:id="echoid-s5140" xml:space="preserve">pars. </s>
  <s xml:id="echoid-s5141" xml:space="preserve">Quod eſt abſurdum. <lb/></s>
  <s xml:id="echoid-s5142" xml:space="preserve">Perpendicularis ergo à k, demiſſa non cadit in aliud punctum, quàm in Q. </s>
  <s xml:id="echoid-s5143" xml:space="preserve">Eodem modo ſum-<lb/>ptis alijs punctis in circunferentia circuli A B C D, inueniemus, quo loco perpendicutares ab ip-<lb/>ſis ductę in planum circuli D E B F, cadant. </s>
  <s xml:id="echoid-s5144" xml:space="preserve">Quapropter in circunferentia circuli maximi in ſphę <lb/>ra ad alium circulum, &amp;</s>
  <s xml:id="echoid-s5145" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5146" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s5147" xml:space="preserve"/>
</p>
<div xml:id="echoid-div317" type="float" level="2" n="1">
<note position="left" xlink:label="note-0111-10" xlink:href="note-0111-10a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0111-02" xlink:href="fig-0111-02a">
    <image file="0111-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0111-02"/>
  </figure>
<note position="left" xlink:label="note-0111-11" xlink:href="note-0111-11a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0111-12" xlink:href="note-0111-12a" xml:space="preserve">Inuenti@ pun-<lb/>ctorum, in quæ <lb/>cadunt perpen-<lb/>diculares à quo <lb/>cunque puncto <lb/>circuli inclinati <lb/>ad alium circu-<lb/>lum.</note>
<note position="right" xlink:label="note-0111-13" xlink:href="note-0111-13a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0112-01" xlink:href="note-0112-01a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0112-02" xlink:href="note-0112-02a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0112-03" xlink:href="note-0112-03a" xml:space="preserve">29. primi.</note>
  <figure xlink:label="fig-0112-01" xlink:href="fig-0112-01a">
    <image file="0112-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0112-01"/>
  </figure>
<note position="left" xlink:label="note-0112-04" xlink:href="note-0112-04a" xml:space="preserve">4. vndec.</note>
  <figure xlink:label="fig-0112-02" xlink:href="fig-0112-02a">
    <image file="0112-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0112-02"/>
  </figure>
<note position="left" xlink:label="note-0112-05" xlink:href="note-0112-05a" xml:space="preserve">38. vndec.</note>
<note position="left" xlink:label="note-0112-06" xlink:href="note-0112-06a" xml:space="preserve">38. vndec.</note>
<note position="left" xlink:label="note-0112-07" xlink:href="note-0112-07a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0112-08" xlink:href="note-0112-08a" xml:space="preserve">@. ſe@t@.</note>
<note position="left" xlink:label="note-0112-09" xlink:href="note-0112-09a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0112-10" xlink:href="note-0112-10a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0112-11" xlink:href="note-0112-11a" xml:space="preserve">@@. ſex@@.</note>
<note position="left" xlink:label="note-0112-12" xlink:href="note-0112-12a" xml:space="preserve">9. quar@@.</note>
<note position="left" xlink:label="note-0112-13" xlink:href="note-0112-13a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div319" type="section" level="1" n="121">
<head xml:id="echoid-head124" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s5148" xml:space="preserve">EX his manifeſtè patet modus deſcribendæ Ellipſis, cuius diametri datæ ſint. </s>
  <s xml:id="echoid-s5149" xml:space="preserve">Si enim duę diametri <lb/>D B, H I, ita aptentur, vt ſeſe bifariam in G, &amp; </s>
  <s xml:id="echoid-s5150" xml:space="preserve">ad angulos rectos ſecent; </s>
  <s xml:id="echoid-s5151" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5152" xml:space="preserve">ex centro G, &amp; </s>
  <s xml:id="echoid-s5153" xml:space="preserve">interuallis <lb/>
<anchor type="note" xlink:label="note-0112-14a" xlink:href="note-0112-14"/>
<anchor type="figure" xlink:label="fig-0112-03a" xlink:href="fig-0112-03"/>
G D, G H, circuli deſcribantur: </s>
  <s xml:id="echoid-s5154" xml:space="preserve">producta autem H I, <lb/>
<anchor type="note" xlink:label="note-0112-15a" xlink:href="note-0112-15"/>
vtrinque, ſumantur arcus ęquales E L, L A, A B, B C, <lb/>quotcunque, &amp; </s>
  <s xml:id="echoid-s5155" xml:space="preserve">his æquales F N, N k, k P, P R; </s>
  <s xml:id="echoid-s5156" xml:space="preserve">idemq́ <lb/>@@<unsure/>at in altero ſemicirculo E B F; </s>
  <s xml:id="echoid-s5157" xml:space="preserve">iunganturq́ue puncta <lb/>L, A, B, &amp;</s>
  <s xml:id="echoid-s5158" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5159" xml:space="preserve">cum centro G, rectis ſecantibus circulum <lb/>H M I, in partes, quæ ſimiles erunt partibus E L, L A, <lb/>&amp;</s>
  <s xml:id="echoid-s5160" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5161" xml:space="preserve">exijs, quę in commentarijs in ſphæram ad finem <lb/>capitis 1. </s>
  <s xml:id="echoid-s5162" xml:space="preserve">ſcripſimus. </s>
  <s xml:id="echoid-s5163" xml:space="preserve">Deinde bina quælibet puncta cir <lb/>culi maioris à D, vel B, hinc inde remota æqualiter <lb/>connectantur lineis rectis; </s>
  <s xml:id="echoid-s5164" xml:space="preserve">itemq́; </s>
  <s xml:id="echoid-s5165" xml:space="preserve">bina quælibet pun-<lb/>cta circuli minoris ab H, vel I, hinc inde ęqualiter quo-<lb/>que remota alijs lineis rectis; </s>
  <s xml:id="echoid-s5166" xml:space="preserve">ac poſtremo puncta, vbi <lb/>coierint quęque duæ lineæ, quę per diuiſiones ſibi re-<lb/>
<anchor type="note" xlink:label="note-0112-16a" xlink:href="note-0112-16"/>
ſpondentes tranſeunt, notentur, cadẽt ea omnia in El-<lb/>lipſim, cuius diametri D B, H I, vt demonſtratum eſt. <lb/></s>
  <s xml:id="echoid-s5167" xml:space="preserve">Nam in ſuperiori figura oſtendimus punctum Q, vbi <lb/>coeuntrectæ L N, P M, quarum illa minori diametro <lb/>H I, hæc verò maiori D B, parallela eſt, cadere in El-<lb/>lipſim, quæ quidem parallelæ ducuntur per puncta L, <lb/>M, interſe reſpondentia, hoc eſt, auferentia arcus ſimiles E L, H M. </s>
  <s xml:id="echoid-s5168" xml:space="preserve">Cum ergo hic idem fiat, propterea <lb/>quòd lineę omnes puncta correſpondentia connectentes parallelæ ſunt diametris H I, D B, ex ijs, quę in <lb/>ſcholio propoſ. </s>
  <s xml:id="echoid-s5169" xml:space="preserve">27. </s>
  <s xml:id="echoid-s5170" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5171" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5172" xml:space="preserve">Euclidis demonſtrauimus, perſpicuum eſt, omnia illa puncta in Ellipſim cadere. </s>
  <s xml:id="echoid-s5173" xml:space="preserve"><lb/>Idẽ fiet, etiã ſi arcus E L, L A, &amp;</s>
  <s xml:id="echoid-s5174" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5175" xml:space="preserve">nõ fint æquales, dummodo per puncta reſpondentia L, M, &amp;</s>
  <s xml:id="echoid-s5176" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5177" xml:space="preserve">ducant@r <lb/>parallelæ diametris Ellipſis, &amp;</s>
  <s xml:id="echoid-s5178" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5179" xml:space="preserve">Quare ſi lineam appoſitè, congruenterq́; </s>
  <s xml:id="echoid-s5180" xml:space="preserve">eiu@modi puncta<unsure/> coniungentem <lb/>duxerimus, Ellipſis deſcripta erit. </s>
  <s xml:id="echoid-s5181" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s5182" xml:space="preserve"/>
</p>
<div xml:id="echoid-div319" type="float" level="2" n="1">
<note position="left" xlink:label="note-0112-14" xlink:href="note-0112-14a" xml:space="preserve">Quo mode de-<lb/>ſcribenda fit El <lb/>lipſis, cuius dia-<lb/>@@etri datæ ſint@</note>
  <figure xlink:label="fig-0112-03" xlink:href="fig-0112-03a">
    <image file="0112-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0112-03"/>
  </figure>
<note position="left" xlink:label="note-0112-15" xlink:href="note-0112-15a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0112-16" xlink:href="note-0112-16a" xml:space="preserve">50</note>
</div>
<pb o="93" file="0113" n="113" rhead="LIBER PRIMVS."/>
<p style="it">
  <s xml:id="echoid-s5183" xml:space="preserve">FEDER@CVS Commandinus hoc quoque problema proponit generalius, vt &amp; </s>
  <s xml:id="echoid-s5184" xml:space="preserve">illud, quod ſupra <lb/>demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s5185" xml:space="preserve">24. </s>
  <s xml:id="echoid-s5186" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s5187" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div321" type="section" level="1" n="122">
<head xml:id="echoid-head125" xml:space="preserve">PROBLEMA 6. PROPOSITIO 27.</head>
<p>
  <s xml:id="echoid-s5188" xml:space="preserve">PLANI cuiuslibet inclinationem ad Meridianum circulum in-<lb/>ueſtigare.</s>
  <s xml:id="echoid-s5189" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5190" xml:space="preserve">SIT Horizon A B C D, Meridianus A C G, planum ad Meridianũ inclinatũ E F, ecans Meri <lb/>
<anchor type="note" xlink:label="note-0113-01a" xlink:href="note-0113-01"/>
dianũ in G, ſiue infra Horizontẽ, ſiue ſupra. </s>
  <s xml:id="echoid-s5191" xml:space="preserve">Intelligimus autẽ hic, &amp; </s>
  <s xml:id="echoid-s5192" xml:space="preserve">in ſequẽtibus quinque proble <lb/>
<anchor type="note" xlink:label="note-0113-02a" xlink:href="note-0113-02"/>
<anchor type="figure" xlink:label="fig-0113-01a" xlink:href="fig-0113-01"/>
matibus, planum inclinatũ, quod <lb/>per centrũ ſphærę ducitur, ac pro-<lb/>inde in ſphera, ꝑ propoſ. </s>
  <s xml:id="echoid-s5193" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5194" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5195" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s5196" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s5197" xml:space="preserve">circulũ maximũ facit. </s>
  <s xml:id="echoid-s5198" xml:space="preserve">Quo <lb/>niam igitur in triangulo ſphærico <lb/>C F G, cuius angulus C, rectus eſt. </s>
  <s xml:id="echoid-s5199" xml:space="preserve"><lb/>(Nam Meridianus ad Horizõtem <lb/>rectus eſt) vt ſinus anguli F, inclina <lb/>tionis plani dati EF, ad Horizontẽ, <lb/>ad ſinũ anguli C, recti, hoc eſt, ad <lb/>
<anchor type="note" xlink:label="note-0113-03a" xlink:href="note-0113-03"/>
ſinũ totũ, ita eſt, ꝑ propoſ. </s>
  <s xml:id="echoid-s5200" xml:space="preserve">18. </s>
  <s xml:id="echoid-s5201" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s5202" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5203" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s5204" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s5205" xml:space="preserve">de triangulis, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s5206" xml:space="preserve">14. </s>
  <s xml:id="echoid-s5207" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5208" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5209" xml:space="preserve">Gebri, vel cer <lb/>tè ex propoſ. </s>
  <s xml:id="echoid-s5210" xml:space="preserve">42. </s>
  <s xml:id="echoid-s5211" xml:space="preserve">noſtrorum trian-<lb/>gulotum ſphæricorum, ſinus com-<lb/>plementi anguli G, inclinationis eiuſdem plani E F, ad Meridianum, ad ſinum complementi ar-<lb/>cus CF, hoc eſt, ad ſinum arcus D F, vel B F, declinationem à Verticali circulo metientis: </s>
  <s xml:id="echoid-s5212" xml:space="preserve">Erit quo <lb/>que conuertendo, vt ſinus totus anguli recti C, ad ſinum anguli F, inclinationis plani E F, ad Ho <lb/>rizontem, ita ſinus complementi arcus C F, hoc eſt, ſinus arcus D F, vel B F, declinationem à Ver <lb/>ticali metientis, ad ſinum complementi anguli G, inclinationis eiuſdem plani E F, ad Meridia-<lb/>
<anchor type="note" xlink:label="note-0113-04a" xlink:href="note-0113-04"/>
num. </s>
  <s xml:id="echoid-s5213" xml:space="preserve">Quamobrem, inuenta per propoſ. </s>
  <s xml:id="echoid-s5214" xml:space="preserve">23. </s>
  <s xml:id="echoid-s5215" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5216" xml:space="preserve">declinatione plani propoſiti à Verticali cir-<lb/>culo, nec non eiuſdem inclinationead Horizontem; </s>
  <s xml:id="echoid-s5217" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum inclinationis ad <lb/>Horizontem, ita ſinus declinationis à Verticali ad aliud, habebitur ſinus complementi inclinatio-<lb/>nis ad Meridianũ; </s>
  <s xml:id="echoid-s5218" xml:space="preserve">quo cõplemento detracto ex quadrante, inclinatio ad Meridianum nota fiet.</s>
  <s xml:id="echoid-s5219" xml:space="preserve"/>
</p>
<div xml:id="echoid-div321" type="float" level="2" n="1">
<note position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve">Inclinatio pla-<lb/>ni propoſiti ad <lb/>Meridianum. <lb/>qua rati@one d@-<lb/>pr@hendatut.</note>
<note position="left" xlink:label="note-0113-02" xlink:href="note-0113-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0113-01" xlink:href="fig-0113-01a">
    <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/>
  </figure>
<note position="left" xlink:label="note-0113-03" xlink:href="note-0113-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0113-04" xlink:href="note-0113-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s5220" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s5221" xml:space="preserve">Ponatur declinatio plani à Verticali circulo grad. </s>
  <s xml:id="echoid-s5222" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5223" xml:space="preserve">inclinatio verò ad Ho <lb/>rizontem grad. </s>
  <s xml:id="echoid-s5224" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5225" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5226" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5227" xml:space="preserve">Si igitur fiat, vt 100000. </s>
  <s xml:id="echoid-s5228" xml:space="preserve">ſinus totus ad 78854. </s>
  <s xml:id="echoid-s5229" xml:space="preserve">ſinum inclinationis ad <lb/>Horizontem, nempead ſinum grad. </s>
  <s xml:id="echoid-s5230" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5231" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5232" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5233" xml:space="preserve">ita 50000. </s>
  <s xml:id="echoid-s5234" xml:space="preserve">ſinus declinationis à Verticali, hoc eſt, <lb/>ſinus grad. </s>
  <s xml:id="echoid-s5235" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5236" xml:space="preserve">ad aliud, inuenietur hic ſinus 39427. </s>
  <s xml:id="echoid-s5237" xml:space="preserve">cuius arcus continet gradus 23. </s>
  <s xml:id="echoid-s5238" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5239" xml:space="preserve">13. </s>
  <s xml:id="echoid-s5240" xml:space="preserve">quo <lb/>detracto ex quadrante, remanebit inclinatio ad Meridianũ grad. </s>
  <s xml:id="echoid-s5241" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5242" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5243" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5244" xml:space="preserve">Quod eſt propoſitũ.</s>
  <s xml:id="echoid-s5245" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Quando planũ <lb/>r@ctũ eſt ad Ver <lb/>ticalem.</note>
<p>
  <s xml:id="echoid-s5246" xml:space="preserve">QVOD ſi planum inclinatum directè ad ortum, vel occaſum ſpectet, hoc eſt, ſi ad Vertica-<lb/>
<anchor type="note" xlink:label="note-0113-06a" xlink:href="note-0113-06"/>
lem circulum ſit rectum, tranſeatque per communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s5247" xml:space="preserve">Meridiani, erit cõ-<lb/>plementum inclinationis ipſius ad Horizontẽ, inclinatio eiuſdem ad Meridianũ, vt perſpicuũ eſt.</s>
  <s xml:id="echoid-s5248" xml:space="preserve"/>
</p>
<div xml:id="echoid-div322" type="float" level="2" n="2">
<note position="left" xlink:label="note-0113-06" xlink:href="note-0113-06a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Quando planũ <lb/>inclinatum ad <lb/>Horizontem di <lb/>recto ſpectat ad <lb/>auſtrum, vel bo <lb/>ream.</note>
<p>
  <s xml:id="echoid-s5249" xml:space="preserve">SI verò planum ad Horizontem inclinatum careat declinatione, hoc eſt, ſi tranſeat per com-<lb/>munes ſectiones Verticalis circuli &amp; </s>
  <s xml:id="echoid-s5250" xml:space="preserve">Horizontis, vergatq́ue directò ad auſtrum, vel ſeptentrionẽ, <lb/>carebit huiuſmodi planum inclinationead Meridianum, hoc eſt, rectum erit ad Meridianum, <lb/>vt patet.</s>
  <s xml:id="echoid-s5251" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Quando planũ <lb/>rectũ eſt ad Ho <lb/>rizontem.</note>
<p>
  <s xml:id="echoid-s5252" xml:space="preserve">SI deniqueplanum ad Horizontem ſit rectum, hoc eſt, ſi tranſeat per verticem, erit comple-<lb/>mentum declinationis ipſius à Verticali circulo, inclinatio eiuſdem ad Meridianum, vt manife-<lb/>ſtum eſt. </s>
  <s xml:id="echoid-s5253" xml:space="preserve">Plani igitur cuiuslibet inclinationem ad Meridianum circulum inueſtigauimus. </s>
  <s xml:id="echoid-s5254" xml:space="preserve">Quod <lb/>erat faciendum.</s>
  <s xml:id="echoid-s5255" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div324" type="section" level="1" n="123">
<head xml:id="echoid-head126" xml:space="preserve">PROBLEMA. 7. PROPOSITIO 28.</head>
<p>
  <s xml:id="echoid-s5256" xml:space="preserve">DATO plano ad Horizontem &amp; </s>
  <s xml:id="echoid-s5257" xml:space="preserve">Meridianum, vel ad Meridia-<lb/>num tantum, vel ad Horizontem tantum inclinato, quantus ſit arcus <lb/>
<anchor type="note" xlink:label="note-0113-10a" xlink:href="note-0113-10"/>
Meridiani circuli interipſum, &amp; </s>
  <s xml:id="echoid-s5258" xml:space="preserve">Horizontem poſitus, inuenire.</s>
  <s xml:id="echoid-s5259" xml:space="preserve"/>
</p>
<div xml:id="echoid-div324" type="float" level="2" n="1">
<note position="right" xlink:label="note-0113-10" xlink:href="note-0113-10a" xml:space="preserve">Arcus Meridia <lb/>ni inter Hori-<lb/>zontem &amp; pla-<lb/>nũ inclinatum <lb/>poſitus, qua ar-<lb/>te ſit inueſti<unsure/>-<lb/>gandus.</note>
</div>
<p>
  <s xml:id="echoid-s5260" xml:space="preserve">SIT Horizon A B C D, cuius centrum E, communis ſectio ipſius, ac Meridiani A C; </s>
  <s xml:id="echoid-s5261" xml:space="preserve">eiuſdẽ <lb/>&amp; </s>
  <s xml:id="echoid-s5262" xml:space="preserve">Verticalis B D; </s>
  <s xml:id="echoid-s5263" xml:space="preserve">declinatio plani tam ad Horizontem, quàm ad Meridianum inclinati, à Ver-<lb/>ticali circulo D F, vt recta F G, communis ſectio ſit Horizontis, ac plani inclinati. </s>
  <s xml:id="echoid-s5264" xml:space="preserve">Inuẽta autem,
<pb o="94" file="0114" n="114" rhead="GNOMONICES"/>
per propoſ. </s>
  <s xml:id="echoid-s5265" xml:space="preserve">23. </s>
  <s xml:id="echoid-s5266" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5267" xml:space="preserve">eiuſdem plani inclinatione ad Horizontem, inueniatur ex propoſ. </s>
  <s xml:id="echoid-s5268" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5269" xml:space="preserve">hu <lb/>ius lib. </s>
  <s xml:id="echoid-s5270" xml:space="preserve">minor diameter Ellipſis, quam perpendiculares à circunferentia plani inclinati (quod in <lb/>
<anchor type="figure" xlink:label="fig-0114-01a" xlink:href="fig-0114-01"/>
ſphæra circulũ facit, ex propoſ. </s>
  <s xml:id="echoid-s5271" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5272" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5273" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5274" xml:space="preserve">Theod.) <lb/></s>
  <s xml:id="echoid-s5275" xml:space="preserve">ad Horizontis planum demiſſę, ex propoſ. </s>
  <s xml:id="echoid-s5276" xml:space="preserve">24. </s>
  <s xml:id="echoid-s5277" xml:space="preserve"><lb/>huius lib. </s>
  <s xml:id="echoid-s5278" xml:space="preserve">faciunt, quæ ſit HI, maiorem diame-<lb/>trum F G, ſecans in centro E, ad angulos rectos. </s>
  <s xml:id="echoid-s5279" xml:space="preserve"><lb/>lam ex coroll. </s>
  <s xml:id="echoid-s5280" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s5281" xml:space="preserve">26. </s>
  <s xml:id="echoid-s5282" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5283" xml:space="preserve">circa dia-<lb/>metros F G, H I, datas deſcribatur Ellipſis, vel <lb/>certè eius pars, ſecans A C, communem ſectio-<lb/>nem Horizontis, ac Meridiani in K, puncto, per <lb/>
<anchor type="note" xlink:label="note-0114-01a" xlink:href="note-0114-01"/>
quod ipſi A C, perpendicularis ducatur K L, ſe-<lb/>cãs Horizontis circunferentiã in L. </s>
  <s xml:id="echoid-s5284" xml:space="preserve">Dico arcum <lb/>C L, æqualẽ eſſe arcui Meridiani circuli inter <lb/>Horizontem, &amp; </s>
  <s xml:id="echoid-s5285" xml:space="preserve">planum inclinatum interpoſito. <lb/></s>
  <s xml:id="echoid-s5286" xml:space="preserve">Intelligatur enim ſemicirculus Meridiani AMC, <lb/>ad Horizontẽ A B C D, rectus; </s>
  <s xml:id="echoid-s5287" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5288" xml:space="preserve">M, punctum, <lb/>in quo planum inclinatum ſecat Meridianum, <lb/>ita vt arcus C M, ſit inter Horizontem, &amp; </s>
  <s xml:id="echoid-s5289" xml:space="preserve">pla-<lb/>num ipſum. </s>
  <s xml:id="echoid-s5290" xml:space="preserve">Ducantur quoque rectæ E L, <lb/>E M, C L, C M. </s>
  <s xml:id="echoid-s5291" xml:space="preserve">Quoniam igitur perpendicularis ex M, ad Horizontem demiſſa cadit in rectam <lb/>
<anchor type="note" xlink:label="note-0114-02a" xlink:href="note-0114-02"/>
<anchor type="note" xlink:label="note-0114-03a" xlink:href="note-0114-03"/>
A C, communem ſectionem Horizontis, ac Meridiani, quòd Meridianus ad Horizontem rectus <lb/>ſit; </s>
  <s xml:id="echoid-s5292" xml:space="preserve">cadit autem, per propoſ. </s>
  <s xml:id="echoid-s5293" xml:space="preserve">24. </s>
  <s xml:id="echoid-s5294" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5295" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5296" xml:space="preserve">in Ellipſim, quam perpendiculares à punctis circunfe <lb/>rentiæ plani inclinati, quorum vnum eſt M, in planum Horizontis cadentes efficiunt; </s>
  <s xml:id="echoid-s5297" xml:space="preserve">perſpicuũ <lb/>eſt, perpendicularem ex M, cadere in punctum K, vbi Ellipſis rectam A C, ſecat. </s>
  <s xml:id="echoid-s5298" xml:space="preserve">Cadat ergo, &amp; </s>
  <s xml:id="echoid-s5299" xml:space="preserve"><lb/>ſit M K, eritq́ue propterea tam angulus E K M, quàm C K M, rectus, per definitionem 3. </s>
  <s xml:id="echoid-s5300" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5301" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s5302" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s5303" xml:space="preserve">Quare tam quadratum ex E L, quadratis ex E K, K L, quàm quadratum ex E M, quadra <lb/>
<anchor type="note" xlink:label="note-0114-04a" xlink:href="note-0114-04"/>
tis ex E K, K M, æquale erit: </s>
  <s xml:id="echoid-s5304" xml:space="preserve">Ac propterea, cum quadrata rectarum æqualium E L, E M, (Ducun-<lb/>tur enim ex centro ſphæræ ad eius ſuperficiem.) </s>
  <s xml:id="echoid-s5305" xml:space="preserve">æqualia ſint; </s>
  <s xml:id="echoid-s5306" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s5307" xml:space="preserve">quadrata ex E K, K L, qua-<lb/>dratis ex E K, K M, æqualia; </s>
  <s xml:id="echoid-s5308" xml:space="preserve">Et dempto quadrato ex E K, cõmuni, æquale erit quadratum ex K L, <lb/>quadrato ex K M, atq; </s>
  <s xml:id="echoid-s5309" xml:space="preserve">adeò &amp; </s>
  <s xml:id="echoid-s5310" xml:space="preserve">recta K L, rectæ K M, æqualis erit. </s>
  <s xml:id="echoid-s5311" xml:space="preserve">Itaque cum in triangulis C K L, <lb/>
<anchor type="note" xlink:label="note-0114-05a" xlink:href="note-0114-05"/>
C K M, latera K L, K C, lateribus K M, K C, ſint ęqualia, angulosq́ue contineant ęquales, vtpo-<lb/>
<anchor type="note" xlink:label="note-0114-06a" xlink:href="note-0114-06"/>
te rectos; </s>
  <s xml:id="echoid-s5312" xml:space="preserve">ęqualis erit baſis C L, baſi C M, ac idcirco &amp; </s>
  <s xml:id="echoid-s5313" xml:space="preserve">arcus C L, arcui C M, Meridiani inter Ho <lb/>
<anchor type="note" xlink:label="note-0114-07a" xlink:href="note-0114-07"/>
rizontem, &amp; </s>
  <s xml:id="echoid-s5314" xml:space="preserve">planum inclinatum poſito ęqualis erit. </s>
  <s xml:id="echoid-s5315" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s5316" xml:space="preserve"/>
</p>
<div xml:id="echoid-div325" type="float" level="2" n="2">
  <figure xlink:label="fig-0114-01" xlink:href="fig-0114-01a">
    <image file="0114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0114-01"/>
  </figure>
<note position="left" xlink:label="note-0114-01" xlink:href="note-0114-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0114-02" xlink:href="note-0114-02a" xml:space="preserve">38. vndec.</note>
<note position="left" xlink:label="note-0114-03" xlink:href="note-0114-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0114-04" xlink:href="note-0114-04a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0114-05" xlink:href="note-0114-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0114-06" xlink:href="note-0114-06a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0114-07" xlink:href="note-0114-07a" xml:space="preserve">28. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s5317" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s5318" xml:space="preserve">Sit Horizon A B C D, Meridianus A C G, planum &amp; </s>
  <s xml:id="echoid-s5319" xml:space="preserve">ad Horizontem, &amp; </s>
  <s xml:id="echoid-s5320" xml:space="preserve">ad <lb/>
<anchor type="note" xlink:label="note-0114-08a" xlink:href="note-0114-08"/>
Meridianum inclinatum E F, ſecans Meridianum in G, ſiue infra Horizontem, ſiue ſupra, vt C G, <lb/>
<anchor type="figure" xlink:label="fig-0114-02a" xlink:href="fig-0114-02"/>
arcus ſit inter Horizontem, &amp; </s>
  <s xml:id="echoid-s5321" xml:space="preserve">pla-<lb/>num inclinatum interpoſitus. </s>
  <s xml:id="echoid-s5322" xml:space="preserve">Quo <lb/>niam igitur in ſphęrico triangulo <lb/>C F G, cuius angulus C, rectus eſt, <lb/>quòd Meridianus rectus ſit ad Ho-<lb/>
<anchor type="note" xlink:label="note-0114-09a" xlink:href="note-0114-09"/>
rizontem; </s>
  <s xml:id="echoid-s5323" xml:space="preserve">vt ſinus arcus C F, nem-<lb/>pe cõplementi declinationis D F, <lb/>à Verticali circulo, ad ſinum angu-<lb/>li G, inclinationis plani E F, ad Me <lb/>ridianum, ita eſt, per propoſ. </s>
  <s xml:id="echoid-s5324" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5325" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s5326" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5327" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s5328" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s5329" xml:space="preserve">de triangulis, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s5330" xml:space="preserve">13. </s>
  <s xml:id="echoid-s5331" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5332" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5333" xml:space="preserve">Gebri, vel cer-<lb/>tè ex propoſ. </s>
  <s xml:id="echoid-s5334" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5335" xml:space="preserve">noſtrorum trian-<lb/>gulorum ſphęricorum, ſinus arcus <lb/>C G, inter Horizontem, &amp; </s>
  <s xml:id="echoid-s5336" xml:space="preserve">planũ <lb/>
<anchor type="note" xlink:label="note-0114-10a" xlink:href="note-0114-10"/>
inclinatum, ad ſinũ anguli F, inclinationis plani ad Horizontẽ; </s>
  <s xml:id="echoid-s5337" xml:space="preserve">erit quoque conuertendo, vt ſinus <lb/>anguli G, inclinationis ad Meridianũ, ad ſinum arcus C F, complementi declinationis à Verticali, <lb/>ita ſinus anguli F, inclinationis ad Horizontẽ, ad ſinum arcus Meridiani C G, inter Horizontem, <lb/>&amp; </s>
  <s xml:id="echoid-s5338" xml:space="preserve">planum inclinatum intercepti. </s>
  <s xml:id="echoid-s5339" xml:space="preserve">Quamobrem, inuenta per propoſ. </s>
  <s xml:id="echoid-s5340" xml:space="preserve">23, huius lib. </s>
  <s xml:id="echoid-s5341" xml:space="preserve">declinatione pla <lb/>ni propoſiti à circulo Verticali, atque inclinatione eiuſdem ad Horizontem. </s>
  <s xml:id="echoid-s5342" xml:space="preserve">Item inclinatione <lb/>eiuſdem ad Meridianum, ex propoſ. </s>
  <s xml:id="echoid-s5343" xml:space="preserve">antecedente; </s>
  <s xml:id="echoid-s5344" xml:space="preserve">ſi fiat, vt ſinus inclinationis ad Meridianum ad <lb/>ſinum cõplementi declinationis à Verticali, ita ſinus inclinationis ad Horizontem, ad aliud, habe-<lb/>bitur ſinus illius arcus Meridiani, qui inter Horizontem, &amp; </s>
  <s xml:id="echoid-s5345" xml:space="preserve">planum inclinatum interiicitur.</s>
  <s xml:id="echoid-s5346" xml:space="preserve"/>
</p>
<div xml:id="echoid-div326" type="float" level="2" n="3">
<note position="left" xlink:label="note-0114-08" xlink:href="note-0114-08a" xml:space="preserve">Arcus Metidia <lb/>ni inter Hori-<lb/>zontẽ &amp; planũ <lb/>inclinatum po-<lb/>ſitus, quomodo <lb/>inquiratur per <lb/>ſinus.</note>
  <figure xlink:label="fig-0114-02" xlink:href="fig-0114-02a">
    <image file="0114-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0114-02"/>
  </figure>
<note position="left" xlink:label="note-0114-09" xlink:href="note-0114-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0114-10" xlink:href="note-0114-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s5347" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s5348" xml:space="preserve">Ponatur inclinatio ad Meridianum grad. </s>
  <s xml:id="echoid-s5349" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5350" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5351" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5352" xml:space="preserve">Declinatio à Vertica-<lb/>li grad. </s>
  <s xml:id="echoid-s5353" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5354" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5355" xml:space="preserve">inclinatio ad Horizontem grad. </s>
  <s xml:id="echoid-s5356" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5357" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5358" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5359" xml:space="preserve">Si igitur fiat, vt 91902. </s>
  <s xml:id="echoid-s5360" xml:space="preserve">ſinus inclinatio-<lb/>nis ad Meridianum ad 86602. </s>
  <s xml:id="echoid-s5361" xml:space="preserve">ſinum complementi declinationis à Verticali, ita 78854. </s>
  <s xml:id="echoid-s5362" xml:space="preserve">ſinus incli
<pb o="95" file="0115" n="115" rhead="LIBER PRIMVS."/>
nationis ad Horizontem, ad aliud, inuenietur hic ferè ſinus 74306. </s>
  <s xml:id="echoid-s5363" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s5364" xml:space="preserve">48. </s>
  <s xml:id="echoid-s5365" xml:space="preserve">ferè inter <lb/>Horizontem, &amp; </s>
  <s xml:id="echoid-s5366" xml:space="preserve">planum inclinatum eſt poſitus. </s>
  <s xml:id="echoid-s5367" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s5368" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5369" xml:space="preserve">QVOD ſi planum tam ad Horizontem, quàm ad Meridianum inclinatum directo ad ortũ <lb/>
<anchor type="note" xlink:label="note-0115-01a" xlink:href="note-0115-01"/>
vel occaſum ſpectet, hoc eſt, ſi ad Verticalem ſit rectum, nullus intercipietur arcus Meridiani inter <lb/>ipſum planum, &amp; </s>
  <s xml:id="echoid-s5370" xml:space="preserve">Horizontem, quia tunc planum per communes ſectiones Meridiani, &amp; </s>
  <s xml:id="echoid-s5371" xml:space="preserve">Hori-<lb/>zontis incedit, vt conſtat.</s>
  <s xml:id="echoid-s5372" xml:space="preserve"/>
</p>
<div xml:id="echoid-div327" type="float" level="2" n="4">
<note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">Quando planũ <lb/>rectũ eſt ad Ver <lb/>ticalem.</note>
</div>
<p>
  <s xml:id="echoid-s5373" xml:space="preserve">SI verò planum ad Horizontem tantum inclinatum fuerit, hoc eſt, ſi per communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0115-02a" xlink:href="note-0115-02"/>
nes Horizontis, ac Verticalis, ſeu polos Meridiani tranſierit, atque adeo ad Meridianum ſuerit re-<lb/>ctum, erit ipſa inclinatio ad Horizontem arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5374" xml:space="preserve">Horizontem poſitus: <lb/></s>
  <s xml:id="echoid-s5375" xml:space="preserve">quia tunc Meridianus inclinationem metitur, vt patet.</s>
  <s xml:id="echoid-s5376" xml:space="preserve"/>
</p>
<div xml:id="echoid-div328" type="float" level="2" n="5">
<note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">Quando planũ <lb/>rectũ eſt ad Me <lb/>tidianum.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s5377" xml:space="preserve">SI denique planum inclinatum tantum fuerit ad Meridianum, hoc eſt, ſi per verticem, ſeu <lb/>
<anchor type="note" xlink:label="note-0115-04a" xlink:href="note-0115-04"/>
polum Horizontis tranſierit, ideoq́uead Horizontem fuerit rectum, intercipietur inter ipſum pla <lb/>num, &amp; </s>
  <s xml:id="echoid-s5378" xml:space="preserve">Horizontem quarta pars Meridiani circuli, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s5379" xml:space="preserve">Dato ergo plano velad Ho <lb/>rizontem &amp; </s>
  <s xml:id="echoid-s5380" xml:space="preserve">Meridianum, vel ad Meridianum tantum, &amp;</s>
  <s xml:id="echoid-s5381" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5382" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s5383" xml:space="preserve"/>
</p>
<div xml:id="echoid-div329" type="float" level="2" n="6">
<note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">Quando planũ <lb/>rectũ eſt ad Ho <lb/>rizontem.</note>
</div>
</div>
<div xml:id="echoid-div331" type="section" level="1" n="124">
<head xml:id="echoid-head127" xml:space="preserve">SCHOLIVM I.</head>
<note position="right" xml:space="preserve">Quando arcus <lb/>Meridiani in-<lb/>ter Horizontẽ <lb/>&amp; planũ incli-<lb/>natũ reperiatur <lb/>ſupra Horizon <lb/>tem, &amp; quando <lb/>infra.</note>
<p style="it">
  <s xml:id="echoid-s5384" xml:space="preserve">SI inclinatio plani ad Horizontem cadat in partem hemiſphærĳ ſuperni Borealem, iuxta ea, quæ <lb/>propoſitione 23. </s>
  <s xml:id="echoid-s5385" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5386" xml:space="preserve">docuimus, ſecabitur Meridianus ex parte poli arctici ſupra Horizontem, at-<lb/>que arcus inter Horizontem &amp; </s>
  <s xml:id="echoid-s5387" xml:space="preserve">planum poſitus ſupra Horizontem extabit ex parte poli arctici. </s>
  <s xml:id="echoid-s5388" xml:space="preserve">Si ve-<lb/>
<anchor type="note" xlink:label="note-0115-06a" xlink:href="note-0115-06"/>
ro inclinatio in partem eiuſdem hemiſphærĳ auſtralem cadat, ſecabit planum circulum Meridianum ex <lb/>parte poli arctici infra Horizontem, arcus{q́ue} propterea Meridiani inter planum, ac Horizontem interie-<lb/>ctus ſub Horizonte occultabitur. </s>
  <s xml:id="echoid-s5389" xml:space="preserve">Ratio hui{us} rei eſt, quia cum inter circulum maximum metientem in-<lb/>clinationem plani, &amp; </s>
  <s xml:id="echoid-s5390" xml:space="preserve">planum ipſum intercipiatur quadrans Horizontis, quòd dictus circulus ſegmentum <lb/>Horizontis inter planum inclinatum, quod quidem ſemicirculus est, ſecet bifariam, per propoſ. </s>
  <s xml:id="echoid-s5391" xml:space="preserve">9. </s>
  <s xml:id="echoid-s5392" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5393" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s5394" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s5395" xml:space="preserve">fit vt cadente inclinatione in partem borealem, Meridianus ex eadem parte boreali ſecet planum <lb/>inclinatum ſupra Horizontem. </s>
  <s xml:id="echoid-s5396" xml:space="preserve">Eodem modo, cadente inclinatione ad partes auſtrales, ſecabit Meridia-<lb/>nus ex eadem parte australi planum inclinatum ſupra Horizontem, ac proinde ſub Horizonte ex parte <lb/>boreali. </s>
  <s xml:id="echoid-s5397" xml:space="preserve">Id quod facile intelligetur, ſi diligenter expendatur ſitus ac poſitio circulorum in ſphæra.</s>
  <s xml:id="echoid-s5398" xml:space="preserve"/>
</p>
<div xml:id="echoid-div331" type="float" level="2" n="1">
<note position="left" xlink:label="note-0115-06" xlink:href="note-0115-06a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div333" type="section" level="1" n="125">
<head xml:id="echoid-head128" xml:space="preserve">COROLLARIVM.</head>
<note position="right" xml:space="preserve">Arcus Meridia <lb/>ni inter planũ <lb/>inclinatũ, &amp; po <lb/>lum arcticũ po-<lb/>ſitus, quo pacto <lb/>cognoſcat@@.</note>
<p>
  <s xml:id="echoid-s5399" xml:space="preserve">EX his non difficile erit, quantus ſit arcus Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5400" xml:space="preserve">polum mundi ar-<lb/>cticum interpoſitus, inuenire. </s>
  <s xml:id="echoid-s5401" xml:space="preserve">Nam ſi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5402" xml:space="preserve">Horizontem fuerit ſub Horizon-<lb/>te ex parte poli arctici, erit arcus, qui ex ipſo, &amp; </s>
  <s xml:id="echoid-s5403" xml:space="preserve">arcu altitudinem poli ſupra Horizontem metiente com-<lb/>
<anchor type="figure" xlink:label="fig-0115-01a" xlink:href="fig-0115-01"/>
ponitur, interiectus inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5404" xml:space="preserve">polum mundi arcti-<lb/>cum, ſi quadratem non exceſſerit; </s>
  <s xml:id="echoid-s5405" xml:space="preserve">ſi enim exceſſerit quadrantem, <lb/>erit eius cõplementum ad ſemicirculũ dictus arcus, qui quidem ſupra <lb/>Horizontẽ cõtinetur verſus auſtrũ, quemadmodum ille partim ſupra <lb/>Horizontẽ &amp; </s>
  <s xml:id="echoid-s5406" xml:space="preserve">partim infra. </s>
  <s xml:id="echoid-s5407" xml:space="preserve">Si verò ſupra Horizontẽ extiterit, erit ar-<lb/>cus, quo ipſe differt ab arcu altitudinẽ poli ſupra Horizõtem metien <lb/>te, inter planũ ipſum, &amp; </s>
  <s xml:id="echoid-s5408" xml:space="preserve">polum mundi arcticũ interceptus, cõtinebi-<lb/>turq́; </s>
  <s xml:id="echoid-s5409" xml:space="preserve">ſupra Horizontem modo verſus boream, modo verſus auſtrum. <lb/></s>
  <s xml:id="echoid-s5410" xml:space="preserve">Quę quidem omnia ex hac appoſita figura perſpicua fient, in qua <lb/>Meridianus A B C D; </s>
  <s xml:id="echoid-s5411" xml:space="preserve">axis mundi E F; </s>
  <s xml:id="echoid-s5412" xml:space="preserve">polus arcticus E, antarcti-<lb/>cus F; </s>
  <s xml:id="echoid-s5413" xml:space="preserve">communis ſectio Horizontis ac Meridiani<unsure/> B D; </s>
  <s xml:id="echoid-s5414" xml:space="preserve">communis ſe-<lb/>
<anchor type="note" xlink:label="note-0115-09a" xlink:href="note-0115-09"/>
ctio Verticalis, &amp; </s>
  <s xml:id="echoid-s5415" xml:space="preserve">Meridiani A C; </s>
  <s xml:id="echoid-s5416" xml:space="preserve">communis ſectio plani inclinati, <lb/>&amp; </s>
  <s xml:id="echoid-s5417" xml:space="preserve">Meridiani G H, vel I k, vel L M, vel N O. </s>
  <s xml:id="echoid-s5418" xml:space="preserve">Vides igitur arcum <lb/>G E, compoſitum ex arcu G D, inter planum inclinatum, ac Horizon <lb/>tem ſub Horizonte, &amp; </s>
  <s xml:id="echoid-s5419" xml:space="preserve">arcu D E, altitudinis poli ſupra Horizontem; </s>
  <s xml:id="echoid-s5420" xml:space="preserve">arcum item I E, vel L E, quo differt <lb/>arcus D I, vel D L, inter planum inclinatum &amp; </s>
  <s xml:id="echoid-s5421" xml:space="preserve">Horizontem ſupra Horizontẽ ab arcu D E, altitudinis <lb/>poli ſupra Horizontem, interceptum eſſe inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5422" xml:space="preserve">polum arcticum E. </s>
  <s xml:id="echoid-s5423" xml:space="preserve">Item arcum <lb/>E N, inter planum N O, &amp; </s>
  <s xml:id="echoid-s5424" xml:space="preserve">polum eſſe ſumendum, quamuis arcus D O, inter planum, &amp; </s>
  <s xml:id="echoid-s5425" xml:space="preserve">Horizontem ſit <lb/>
<anchor type="note" xlink:label="note-0115-10a" xlink:href="note-0115-10"/>
ſub Horizonte, quia totus arcus E O, quadrantem ſuperat.</s>
  <s xml:id="echoid-s5426" xml:space="preserve"/>
</p>
<div xml:id="echoid-div333" type="float" level="2" n="1">
  <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a">
    <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01"/>
  </figure>
<note position="left" xlink:label="note-0115-09" xlink:href="note-0115-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0115-10" xlink:href="note-0115-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s5427" xml:space="preserve">QVOD ſi planum inclinatum, fuerit rectum ad Verticalem circulum, hoc eſt, ſi directè ad ortum, <lb/>
<anchor type="note" xlink:label="note-0115-11a" xlink:href="note-0115-11"/>
vel occaſum ſpectet, tranſeatq́; </s>
  <s xml:id="echoid-s5428" xml:space="preserve">per communes ſectiones Horizontis ac Meridiani, ita vt eius, &amp; </s>
  <s xml:id="echoid-s5429" xml:space="preserve">Meridia-<lb/>ni communis ſectio ſit recta B D, non differet arcus inter planum ipſum, &amp; </s>
  <s xml:id="echoid-s5430" xml:space="preserve">polum E, ab arcu D E, altitu <lb/>dinem poli ſupra Horizontem metiente, vt conſtat.</s>
  <s xml:id="echoid-s5431" xml:space="preserve"/>
</p>
<div xml:id="echoid-div334" type="float" level="2" n="2">
<note position="right" xlink:label="note-0115-11" xlink:href="note-0115-11a" xml:space="preserve">Quando planũ <lb/>rectũ eſt ad Ver <lb/>ticalem.</note>
</div>
<p>
  <s xml:id="echoid-s5432" xml:space="preserve">SI verò planum inclinatum rectum fuerit ad Horizontem, hoc eſt, ſi per verticem A, tranſierit, ita vt <lb/>
<anchor type="note" xlink:label="note-0115-12a" xlink:href="note-0115-12"/>
communis ſectio ipſius, ac Meridiani ſit recta A C, non differet arcus inter ipſum planum, &amp; </s>
  <s xml:id="echoid-s5433" xml:space="preserve">polum E, <lb/>ab arcu A E, qui complementum altitudinis poli ſupra Horizontem dimetitur, vt manifeſtum eſt.</s>
  <s xml:id="echoid-s5434" xml:space="preserve"/>
</p>
<div xml:id="echoid-div335" type="float" level="2" n="3">
<note position="right" xlink:label="note-0115-12" xlink:href="note-0115-12a" xml:space="preserve">Quando planũ <lb/>recũ eſt ad Ho <lb/>rizontem.</note>
</div>
<p>
  <s xml:id="echoid-s5435" xml:space="preserve">PARI ratione comperiemus, quantus ſit arcus Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5436" xml:space="preserve">verticem ca-<lb/>
<anchor type="note" xlink:label="note-0115-13a" xlink:href="note-0115-13"/>
pitis interiectus. </s>
  <s xml:id="echoid-s5437" xml:space="preserve">Nam ſi arcum Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s5438" xml:space="preserve">Horizontem auſeramus ex quadrante, reli-<lb/>quus erit arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5439" xml:space="preserve">verticem capitis; </s>
  <s xml:id="echoid-s5440" xml:space="preserve">continebiturq́ arcus hic in parte boreali, <lb/>ſi arcus inter planum, &amp; </s>
  <s xml:id="echoid-s5441" xml:space="preserve">Horizontem fuerit ſupra Horizontem ex eadem parte boreali; </s>
  <s xml:id="echoid-s5442" xml:space="preserve">in parte autem
<pb o="96" file="0116" n="116" rhead="GNOMONICES"/>
auſtrali, ſi arcus inter planum, &amp; </s>
  <s xml:id="echoid-s5443" xml:space="preserve">Horizontem ad partes boreales fuerit ſub Horizonte. </s>
  <s xml:id="echoid-s5444" xml:space="preserve">In ea<unsure/>dem enim fi-<lb/>gura cernis, arcum D I, vel D L, ex quadrante D A, ablatum relinquere arcum I A, vel L A, inter planum, <lb/>&amp; </s>
  <s xml:id="echoid-s5445" xml:space="preserve">verticem ad partes boreales. </s>
  <s xml:id="echoid-s5446" xml:space="preserve">Item arcum B H, vel B N, (Eſt autem arcus B H, arcui G D, &amp; </s>
  <s xml:id="echoid-s5447" xml:space="preserve">arcus <lb/>B N, arcui O D, inter planum &amp; </s>
  <s xml:id="echoid-s5448" xml:space="preserve">Horizontem ſub Horizonte æqualis) ex quadrante B A, detractum re-<lb/>
<anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/>
linquere arcum H A, uel N A, inter planum, &amp; </s>
  <s xml:id="echoid-s5449" xml:space="preserve">verticem ex parte auſtrali.</s>
  <s xml:id="echoid-s5450" xml:space="preserve"/>
</p>
<div xml:id="echoid-div336" type="float" level="2" n="4">
<note position="right" xlink:label="note-0115-13" xlink:href="note-0115-13a" xml:space="preserve">Quantus ſit ar-<lb/>cus Meridiani <lb/>inter planũ in-<lb/>clinatũ, &amp; ver-<lb/>ticem capitis.</note>
<note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">26. tertĳ.</note>
</div>
</div>
<div xml:id="echoid-div338" type="section" level="1" n="126">
<head xml:id="echoid-head129" xml:space="preserve">SCHOLIVM II.</head>
<p style="it">
  <s xml:id="echoid-s5451" xml:space="preserve">SED tradamus iam modum illum inueniendæ altitudinis poli ſupra Horizontem per Analemma, <lb/>quem in ſcholio propoſ. </s>
  <s xml:id="echoid-s5452" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5453" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5454" xml:space="preserve">polliciti ſumus, quem quidem ex Ioanne Baptiſta Benedicto in lib. <lb/></s>
  <s xml:id="echoid-s5455" xml:space="preserve">
<anchor type="note" xlink:label="note-0116-02a" xlink:href="note-0116-02"/>
de Gnomonum, vmbrarum ſolarium vſu accepimus. </s>
  <s xml:id="echoid-s5456" xml:space="preserve">Eum tamen clarius nos proponentes ad talem for-<lb/>mam redegimus.</s>
  <s xml:id="echoid-s5457" xml:space="preserve"/>
</p>
<div xml:id="echoid-div338" type="float" level="2" n="1">
<note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">Altitudo poli <lb/>ſupta Horizon-<lb/>ze@, quo artifi-<lb/>c@@ per Analem <lb/>c@a<unsure/> ieperiatur.</note>
<p style="it">
  <s xml:id="echoid-s5458" xml:space="preserve">IN plano, quod Horizonti æquidiſtet, deſcribatur circulus A B C D, cuius centrum E, in quo linea <lb/>meridiana ſit B D, id est, communis ſectio Meridiani circuli, &amp; </s>
  <s xml:id="echoid-s5459" xml:space="preserve">circuli A B C D, ita vt B, ad auſtrũ, <lb/>
<anchor type="figure" xlink:label="fig-0116-01a" xlink:href="fig-0116-01"/>
&amp; </s>
  <s xml:id="echoid-s5460" xml:space="preserve">D, ad Boream vergat; </s>
  <s xml:id="echoid-s5461" xml:space="preserve">AC, <lb/>communis ſectio Verticalis, et <lb/>eiuſdem circuli. </s>
  <s xml:id="echoid-s5462" xml:space="preserve">Infixo autem <lb/>ſtylo cuiuſcunque magnitu<unsure/>di-<lb/>nis in centro E, ad planum cir-<lb/>culi A B C D, recto, obſeruc-<lb/>
<anchor type="note" xlink:label="note-0116-04a" xlink:href="note-0116-04"/>
tur vel antemeridiẽ, vel poſt, <lb/>vmbra ſtyli, in cuius medio pro <lb/>pe extremitatem (nam punctũ <lb/>extremum uix in plano depre-<lb/>hendi poteſt ſine errore) pun-<lb/>ctum notetur, per quod &amp; </s>
  <s xml:id="echoid-s5463" xml:space="preserve">per <lb/>centrum E, ducatur recta F G. <lb/></s>
  <s xml:id="echoid-s5464" xml:space="preserve">Commode etiam hic vti pote-<lb/>rimus inſtrumento, quod ad <lb/>principium ſcholĳ propoſ. </s>
  <s xml:id="echoid-s5465" xml:space="preserve">23. </s>
  <s xml:id="echoid-s5466" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0116-05a" xlink:href="note-0116-05"/>
huius lib. </s>
  <s xml:id="echoid-s5467" xml:space="preserve">conſtruxim{us}. </s>
  <s xml:id="echoid-s5468" xml:space="preserve">Nam <lb/>ſi regula A B, in plano circuli <lb/>A B C D, collocetur, ita vt <lb/>punctum D, in centro E, pona-<lb/>tur, obſeruabimus vmbram la-<lb/>teris H D, loco vmbrę styli, <lb/>in qua punctum not abimus, <lb/>per quod &amp; </s>
  <s xml:id="echoid-s5469" xml:space="preserve">per centrum E, <lb/>(amoto prius inſtrumento,) <lb/>rectam ducem{us} F G. </s>
  <s xml:id="echoid-s5470" xml:space="preserve">Hoc eo-<lb/>
<anchor type="note" xlink:label="note-0116-06a" xlink:href="note-0116-06"/>
dem instrumento vtemur in a-<lb/>lĳs quoque obſeruationibus, in <lb/>quibus ſtyl{us} ad proiectionem vmbræ aſſumi ſolet. </s>
  <s xml:id="echoid-s5471" xml:space="preserve">Sumpta autem tunc altitudine Solis ſine mora, an-<lb/>tequam recta F G, ducatur, ſumatur ei è regione vmbræ arcus æqualis G H, &amp; </s>
  <s xml:id="echoid-s5472" xml:space="preserve">ex H, ad F G, perpen-<lb/>dicularis demittatur H I. </s>
  <s xml:id="echoid-s5473" xml:space="preserve">Deinde ex I, ad B D, perpendicularis ducatur I O Q, vel ipſi A C, paral-<lb/>lela, abſcindatur{q́ue}, O Q, ipſi H I, æqualis. </s>
  <s xml:id="echoid-s5474" xml:space="preserve">Rurſus poſt aliquod ſpatium temporis elapſis<unsure/>m obſeruetur ite-<lb/>rum vmbra ſtyli, in cuius medio prope extremitatem aliud punctum ſignetur, ex quo per centrum E, <lb/>emittatur recta K L; </s>
  <s xml:id="echoid-s5475" xml:space="preserve">ſumptaq́, eo tempore altitudine Solis, accipiatur ei è regione vmbræ arcus L M, <lb/>æqualis, &amp; </s>
  <s xml:id="echoid-s5476" xml:space="preserve">ex M, ad K L, deducatur perpendicularis M N; </s>
  <s xml:id="echoid-s5477" xml:space="preserve">atque ex N, ad B D, excitetur perpendicu-<lb/>laris N P R, vel ipſi AC, parallela, auferaturq́, P R, ipſi M N, æqualis. </s>
  <s xml:id="echoid-s5478" xml:space="preserve">Poſtremo per puncta R, Q, <lb/>
<anchor type="note" xlink:label="note-0116-07a" xlink:href="note-0116-07"/>
ducatur recta R Q. </s>
  <s xml:id="echoid-s5479" xml:space="preserve">Dico angulum P R Q, angulum eſſe altitudinis poli, &amp; </s>
  <s xml:id="echoid-s5480" xml:space="preserve">arcum π ρ, ex R, deſcri-<lb/>ptum continere gradus eiuſdem altitudinis. </s>
  <s xml:id="echoid-s5481" xml:space="preserve">Quod nos hac ratione demonſtr abimus. </s>
  <s xml:id="echoid-s5482" xml:space="preserve">Quoniam tempore <lb/>primæ obſeruationis extremum vmbræ cadit in rectam E F, erit recta F G, communis ſectio circuli <lb/>A B C D, &amp; </s>
  <s xml:id="echoid-s5483" xml:space="preserve">Verticalis illius, in quo tunc Sol exiſtit, vt ex propoſitione 11. </s>
  <s xml:id="echoid-s5484" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5485" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s5486" xml:space="preserve">Vnde <lb/>cum Verticalis propriè dictus per rectam A C, ductus, &amp; </s>
  <s xml:id="echoid-s5487" xml:space="preserve">Verticalis per centrum Solis, &amp; </s>
  <s xml:id="echoid-s5488" xml:space="preserve">per rectam <lb/>F G, tranſiens, auferant ex Horizonte, &amp; </s>
  <s xml:id="echoid-s5489" xml:space="preserve">circulo A B C D, (qui Horizonti æquidiſtat tanto interual-<lb/>lo ab eo remotus, quanta eſt ſtyli longitudo, vt ex propoſ. </s>
  <s xml:id="echoid-s5490" xml:space="preserve">2. </s>
  <s xml:id="echoid-s5491" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5492" xml:space="preserve">perſpicuum eſt) arcus ſimiles, ex <lb/>propoſ. </s>
  <s xml:id="echoid-s5493" xml:space="preserve">10. </s>
  <s xml:id="echoid-s5494" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5495" xml:space="preserve">2. </s>
  <s xml:id="echoid-s5496" xml:space="preserve">Theodoſii, quòd per eorum polos ducantur; </s>
  <s xml:id="echoid-s5497" xml:space="preserve">fit vt ſi circulus A B C D, pro Horizonte <lb/>accipiatur, recta F G, ſit quoque communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s5498" xml:space="preserve">Verticalis per centrum Solis tranſeun-<lb/>tis. </s>
  <s xml:id="echoid-s5499" xml:space="preserve">Quia verò G H, arcus eſt altitudinis Solis; </s>
  <s xml:id="echoid-s5500" xml:space="preserve">ſi ſemicircul{us} F H G, intelligatur circa diametrum <lb/>F G, moueri, donec rect{us} ſit ad Horizontem, &amp; </s>
  <s xml:id="echoid-s5501" xml:space="preserve">ideo recta, H I, ad eundem perpendicularis, ex deſini-
<pb o="97" file="0117" n="117" rhead="LIBER PRIMVS."/>
tione 4. </s>
  <s xml:id="echoid-s5502" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5503" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5504" xml:space="preserve">Euclidis, erit centrum Solis in puncto H. </s>
  <s xml:id="echoid-s5505" xml:space="preserve">Quare parallelus Solis tunc temporis per pun-<lb/>ctum H, tranſibit. </s>
  <s xml:id="echoid-s5506" xml:space="preserve">Quoniam verò, ſi in illa poſitione ſemicirculi F H G, per H, ducatur in plano paralle-<lb/>li Solis linea parallela ipſi I Q, (Poſſe enim per H, in plano paralleli Solis ipſi I Q, duci parallelam, <lb/>ita perſpicuum fiet. </s>
  <s xml:id="echoid-s5507" xml:space="preserve">Quoniam parallelus Solis, &amp; </s>
  <s xml:id="echoid-s5508" xml:space="preserve">Horizon ad Meridianum recti ſunt, crit communis <lb/>ſectio illorum ad eundem Meridianum per pendicularis, atque adeo &amp; </s>
  <s xml:id="echoid-s5509" xml:space="preserve">ad rectam B D, in Meridiano exi-<lb/>
<anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/>
ſtentem, cum ſit cõmunis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s5510" xml:space="preserve">Horizontis, perpendicularis erit, per d@fin. </s>
  <s xml:id="echoid-s5511" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5512" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5513" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5514" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s5515" xml:space="preserve">ac propterea ipſi I Q, parallela. </s>
  <s xml:id="echoid-s5516" xml:space="preserve">Si igitur in plano paralleli ſolis per H, agatur parallola communi ſectio <lb/>
<anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/>
ni paralleli, &amp; </s>
  <s xml:id="echoid-s5517" xml:space="preserve">Horizontis, erit eadem &amp; </s>
  <s xml:id="echoid-s5518" xml:space="preserve">ipſi I Q, parallela. </s>
  <s xml:id="echoid-s5519" xml:space="preserve">Duci ergo poterit per H, in plano paralle <lb/>
<anchor type="note" xlink:label="note-0117-03a" xlink:href="note-0117-03"/>
li ſolis ipſi I Q, linea parallela.) </s>
  <s xml:id="echoid-s5520" xml:space="preserve">linea recta ex O, ducta perpendicula<unsure/>ris ad Horizontem, atque adeo per <lb/>definitionem 3. </s>
  <s xml:id="echoid-s5521" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5522" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5523" xml:space="preserve">Euclidis ad rectam B D, &amp; </s>
  <s xml:id="echoid-s5524" xml:space="preserve">ipſi H I, ęqualis, cadit in illam parallelam in paralle-<lb/>
<anchor type="note" xlink:label="note-0117-04a" xlink:href="note-0117-04"/>
lo ſolis per punctũ H, ductam; </s>
  <s xml:id="echoid-s5525" xml:space="preserve">(Cum enim H I, &amp; </s>
  <s xml:id="echoid-s5526" xml:space="preserve">dicta perpendicularis ex O, ducta, rectæ ſint ad planũ <lb/>Horizontis, ipſæ erunt inter ſe par allelę. </s>
  <s xml:id="echoid-s5527" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s5528" xml:space="preserve">ęquales ſint ex hypotheſi, erit quoque recta ex H, <lb/>
<anchor type="note" xlink:label="note-0117-05a" xlink:href="note-0117-05"/>
ducta per extremũ punctũ perpendicularis ex O, eductę, ipſi I O, parallela; </s>
  <s xml:id="echoid-s5529" xml:space="preserve">atq; </s>
  <s xml:id="echoid-s5530" xml:space="preserve">adeo dicta perpendicula <lb/>
<anchor type="note" xlink:label="note-0117-06a" xlink:href="note-0117-06"/>
ris ex O, ducta cadet in parallelam illam per H, ductã in parallelo Solis: </s>
  <s xml:id="echoid-s5531" xml:space="preserve">alioquin ex eodẽ puncto H, duce-<lb/>rentur duæ parallelæ ipſi I O, nempe illa, quã per H, diximus debere duci, &amp; </s>
  <s xml:id="echoid-s5532" xml:space="preserve">illa, quæ ex H, per extre-<lb/>mitatẽ perpendicularis ex O, ductę tranſit, &amp; </s>
  <s xml:id="echoid-s5533" xml:space="preserve">quã ipſi I O, demonſtrauimus eſſe parallelam: </s>
  <s xml:id="echoid-s5534" xml:space="preserve">quod eſt ab-<lb/>ſurdum. </s>
  <s xml:id="echoid-s5535" xml:space="preserve">Eſſent enim &amp; </s>
  <s xml:id="echoid-s5536" xml:space="preserve">duę illæ ex H, emiſſę inter ſeparallelę, cum tamen in H, coeant.) </s>
  <s xml:id="echoid-s5537" xml:space="preserve">fit, vt cum <lb/>
<anchor type="note" xlink:label="note-0117-07a" xlink:href="note-0117-07"/>
O Q, ſumpta ſit æqualis ipſi H I, &amp; </s>
  <s xml:id="echoid-s5538" xml:space="preserve">perpendicularis ad B D, ſi ſemicirculus B A D, concipiatur mo-<lb/>@eri circadiametrum B D, donec rectus ſit ad Horizontem, idern<unsure/>{q́ue} ſit, qui Meridianus, ita vt Q O, <lb/>perpendicularis ſit ad eundem Horizontem, ex definitione 4. </s>
  <s xml:id="echoid-s5539" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5540" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5541" xml:space="preserve">Euclidis, punctum Q, cadat in illam <lb/>
<anchor type="note" xlink:label="note-0117-08a" xlink:href="note-0117-08"/>
parallelam per H, ductãin plano paralleli Solis; </s>
  <s xml:id="echoid-s5542" xml:space="preserve">ac idcirco planum paralleli per punctum Q, tranſeat, <lb/>manente ſemicirculo B A D, in eapoſitione, vt rectus ſit ad Horizontem, inſtar Meridiani. </s>
  <s xml:id="echoid-s5543" xml:space="preserve">Eodem mo-<lb/>do demonstrabimus idem planum paralleli ſolis per punctum R, tranſire in illa poſitione ſemicirculi <lb/>B A D. </s>
  <s xml:id="echoid-s5544" xml:space="preserve">Quare recta R Q, communis ſectio erit paralleli Solis, &amp; </s>
  <s xml:id="echoid-s5545" xml:space="preserve">Meridiani A B C D, (Sumimus enim <lb/>iam hunc cir culum pro Meridiano.) </s>
  <s xml:id="echoid-s5546" xml:space="preserve">ac propterea angulus P R Q, erit angulus altitudinis poli, quod ita <lb/>maniſeſtum fiet. </s>
  <s xml:id="echoid-s5547" xml:space="preserve">Ducta recta μ ξ, per centrum E, ipſi R Q, parallela, erit μ ξ, communis ſectio Aequa-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s5548" xml:space="preserve">Meridiani. </s>
  <s xml:id="echoid-s5549" xml:space="preserve">Quare angulus B E μ, erit angulus altitudinis Aequatoris, vel complementi altitis<unsure/> <lb/>dinis poli, ac propterea reliquus angulus ex recto A E μ, erit angulus altitudinis poli. </s>
  <s xml:id="echoid-s5550" xml:space="preserve">Cum igitur hic ſit <lb/>oppoſito P R Q, æqualis in parallelogrammo E R, erit quoque P R Q, angulus eleuationis poli ſupra <lb/>
<anchor type="note" xlink:label="note-0117-09a" xlink:href="note-0117-09"/>
Horizontem. </s>
  <s xml:id="echoid-s5551" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s5552" xml:space="preserve"/>
</p>
<div xml:id="echoid-div339" type="float" level="2" n="2">
  <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a">
    <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0116-01"/>
  </figure>
<note position="left" xlink:label="note-0116-04" xlink:href="note-0116-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0116-05" xlink:href="note-0116-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0116-06" xlink:href="note-0116-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0116-07" xlink:href="note-0116-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">28. primi.</note>
<note position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">9. undec.</note>
<note position="left" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">6. vndec.</note>
<note position="right" xlink:label="note-0117-06" xlink:href="note-0117-06a" xml:space="preserve">33. primi.</note>
<note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0117-08" xlink:href="note-0117-08a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0117-09" xlink:href="note-0117-09a" xml:space="preserve">34. primi.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s5553" xml:space="preserve">VERVM quoniam facile error aliquis committi poteſt in ducendarecta R Q, quando perpendi-<lb/>culares P R, O Q, atque adeo puncta R, Q, perexiguam inter ſe diſtantiam habent, vt in dato exemplo <lb/>contingit, accu@atius rem peragemus, ſi duas obſeruationes vmbrarum Solis elegerim{us}, in quibus dicta <lb/>puncta R, Q, notabili aliquo ſpatio inter ſe diſtent. </s>
  <s xml:id="echoid-s5554" xml:space="preserve">Immo rectius idem exequemur, ſole exiſtẽte in ſignis <lb/>Borealibus, ſi vmbram ſl<unsure/>yli obſeruemus, cum in ipſam A C, communem ſectionem verticalis propriè di <lb/>cti, &amp; </s>
  <s xml:id="echoid-s5555" xml:space="preserve">circuli A B C D, cadit, vel cum eidem rectæ A C, propinqua fuerit, ſiue ad partes B, ſiue ad par <lb/>tes D,. </s>
  <s xml:id="echoid-s5556" xml:space="preserve">Ita in præcedenti figur a uides, Sole in ipſo Verticali cir culo existente, vmbraq́, ſtyli in rectam <lb/>A C, ſiue ante meridiem, ſiue poſt, cadente, rectam E <anchor type="note" xlink:href="" symbol="a"/>, ſumptam eſſe æqualem perpendiculari Y Z, po
ſita tunc Solis altitudine A Y. </s>
  <s xml:id="echoid-s5557" xml:space="preserve">Sic etiam veſpertino tempore, cadente vmbra ſtyli in rectam E ß, <lb/>&amp; </s>
  <s xml:id="echoid-s5558" xml:space="preserve">Solis altituà<unsure/>ine existente γ δ<unsure/>, ſumpta eſt in perpendiculari ε θ, recta θ λ, æqualis perpendicu-<lb/>
<anchor type="note" xlink:label="note-0117-11a" xlink:href="note-0117-11"/>
lari δ ε, &amp; </s>
  <s xml:id="echoid-s5559" xml:space="preserve">c.</s>
  <s xml:id="echoid-s5560" xml:space="preserve"/>
</p>
<div xml:id="echoid-div340" type="float" level="2" n="3">
<note position="left" xlink:label="note-0117-11" xlink:href="note-0117-11a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s5561" xml:space="preserve">QVOD ſi obſeruatio commodè fieri poſſit in Horizonte patenti, &amp; </s>
  <s xml:id="echoid-s5562" xml:space="preserve">expedito, vel in loco aliquo edi <lb/>to, vbi Sol oriens, vel occidens conſpici queat, eligendus erit eiuſmodi locus. </s>
  <s xml:id="echoid-s5563" xml:space="preserve">Nam ſi Sole oriente, vel occi <lb/>dente, vmbra ſtyli obſeruetur, &amp; </s>
  <s xml:id="echoid-s5564" xml:space="preserve">ducatur iterum S E, communis ſectio circuli A B C D, &amp; </s>
  <s xml:id="echoid-s5565" xml:space="preserve">verticalis <lb/>per centrum Solis tunc temporis incedentis, ita vt C S, vel A S, arcus ſit amplitudinis ortiuæ, vel occi <lb/>duæ; </s>
  <s xml:id="echoid-s5566" xml:space="preserve">Item ducatur ad B D, perpendicularis S T, habebimus in recta B D, punctum T, per quod paralle-<lb/>lus Solis ducend{us}<unsure/> eſt, cum recta S T, ſit communis ſectio paralleli Solis, &amp; </s>
  <s xml:id="echoid-s5567" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s5568" xml:space="preserve">I am verò ſi in <lb/>meridie, vmbra ſtyli cadente in rectam B D, obſeruetur altitudo Solis, ea{q́ue} ſupputetur à B, vſque ad V, <lb/>tranſibit quoq; </s>
  <s xml:id="echoid-s5569" xml:space="preserve">parallelus tunctemporis per punctum V, in Meridiano. </s>
  <s xml:id="echoid-s5570" xml:space="preserve">Quare recta V T, communis ſe-<lb/>ctio erit paralleli Solis, &amp; </s>
  <s xml:id="echoid-s5571" xml:space="preserve">Meridiani, vt prius. </s>
  <s xml:id="echoid-s5572" xml:space="preserve">Denique ſi pręter duo puncta Q, R, tertium adhuc inue-<lb/>
<anchor type="note" xlink:label="note-0117-12a" xlink:href="note-0117-12"/>
niamus, vt α<unsure/>, vel T, facilius rectam V T, ſine errore per tria puncta ducemus.</s>
  <s xml:id="echoid-s5573" xml:space="preserve"/>
</p>
<div xml:id="echoid-div341" type="float" level="2" n="4">
<note position="left" xlink:label="note-0117-12" xlink:href="note-0117-12a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s5574" xml:space="preserve">CAETERVM, quia Sole oriente, vel occidente, vix vmbra styli depręhendi poteſt in plano circuli <lb/>
<anchor type="note" xlink:label="note-0117-13a" xlink:href="note-0117-13"/>
A B C D, vtemur hoc artificio in amplitudine Solis ortiua, occiduave explorãda. </s>
  <s xml:id="echoid-s5575" xml:space="preserve">In tabula aliqua plana, <lb/>&amp; </s>
  <s xml:id="echoid-s5576" xml:space="preserve">rectangula ducemus rectã A B, infimo lateri C D, parallelã, in ea{q́ue} ſtylum cui{us}vis longitudinis ad an <lb/>gulos rectos infigemus A E, vel certe, vt ſupra, latus H D, inſtrumenti, quod in principio ſcholĳ propoſ-<lb/>23. </s>
  <s xml:id="echoid-s5577" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5578" xml:space="preserve">poſitum eſt, in puncto A, statuemus. </s>
  <s xml:id="echoid-s5579" xml:space="preserve">Deinde Sole oriente, vel occidente latus infimũ tabu-<lb/>læ C D, meridianæ lineę B D, præcedentis figurę Horizonti æquidiſtantis adaptabimus, it a vt ipſa tabula <lb/>recta ſit ad planum circuli A B C D, quod facile fiet beneficio perpendiculi ex puncto F, demiſſi. </s>
  <s xml:id="echoid-s5580" xml:space="preserve">Perpen <lb/>diculo enim adbærente ipſi tabellæ, recta erit tabella ad circulum A B C D. </s>
  <s xml:id="echoid-s5581" xml:space="preserve">Deinde vmbram notabim{us} <lb/>in recta A B, quæ cad at in punctum B, ita vt radius Solis ſit E B. </s>
  <s xml:id="echoid-s5582" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s5583" xml:space="preserve">ſi in precedenti figura in Ver-<lb/>ticali linea A C, ſumamus rectam E φ, gnomoni A E, vel lateri H D, dicti inſtrumenti æqualem, &amp;</s>
  <s xml:id="echoid-s5584" xml:space="preserve">
<pb o="98" file="0118" n="118" rhead="GNOMONICES"/>
per Φ, ducamus ad A E, perpendicularem φ χ, accipiamuſ{q́ue} φ χ, vmbræ A B, æqualem, dabit recta <lb/>χ E, producta ad S, amplitudinem Solis ortiuam, vel occiduam C S. </s>
  <s xml:id="echoid-s5585" xml:space="preserve">Cum enim planum F D, ſit in plano <lb/>Meridiani, erit gnomon A E, pars communis ſectionis verticalis proprie dicti, &amp; </s>
  <s xml:id="echoid-s5586" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s5587" xml:space="preserve">Si igitur <lb/>circulus A B C D, pro Horizonte ſumatur, intelligatur{q́ue} tabulæ F D, applicari, ita vt punctum φ, in <lb/>
<anchor type="figure" xlink:label="fig-0118-01a" xlink:href="fig-0118-01"/>
A, &amp; </s>
  <s xml:id="echoid-s5588" xml:space="preserve">χ, in B, cadat, ob æqua <lb/>litatẽ rectarum A B, φ χ, ca-<lb/>det centrũ E, in extremũ ſtyli <lb/>E, propter æqualitatẽ rectarũ <lb/>A E, φ E. </s>
  <s xml:id="echoid-s5589" xml:space="preserve">Quare linea recta <lb/>χ E, cõgruet radio Solis B<unsure/> E, <lb/>
<anchor type="note" xlink:label="note-0118-01a" xlink:href="note-0118-01"/>
ac propterea producta cadet <lb/>in S, punctum ortus, vel occa-<lb/>ſus in Horizonte. </s>
  <s xml:id="echoid-s5590" xml:space="preserve">Igitur arcus <lb/>C S, amplitudo erit ortiua, <lb/>vel occidua. </s>
  <s xml:id="echoid-s5591" xml:space="preserve">Aduertendum ta <lb/>men est, ſi matutino tempore <lb/>obſeruatio fiat, vmbra{q́ue} cadat <lb/>in rectam A F, ſolem eſſe bo-<lb/>realẽ. </s>
  <s xml:id="echoid-s5592" xml:space="preserve">vnde amplitudo ſumen-<lb/>da tunc erit à C, verſus par-<lb/>
<anchor type="note" xlink:label="note-0118-02a" xlink:href="note-0118-02"/>
tes ſeptentrionales, nempe ver <lb/>ſus D: </s>
  <s xml:id="echoid-s5593" xml:space="preserve">Si autem vmbra cadat <lb/>in rectam A G, Solem eſſe au <lb/>ſtralẽ. </s>
  <s xml:id="echoid-s5594" xml:space="preserve">Quare amplitudo nume <lb/>rãda erit à C, verſus auſtrales <lb/>partes, hoc eſt, uerſus B. </s>
  <s xml:id="echoid-s5595" xml:space="preserve">Con-<lb/>trariũ intelligatur, ſi obſerua-<lb/>tio fiat tẽpore veſpertino. </s>
  <s xml:id="echoid-s5596" xml:space="preserve">Vm-<lb/>bra enim cadẽte in rectã AG, <lb/>Sol borealis eſt, auſtralis vero, <lb/>
<anchor type="note" xlink:label="note-0118-03a" xlink:href="note-0118-03"/>
umbra cadente in rectã A F, <lb/>vt perſpicuum eſt.</s>
  <s xml:id="echoid-s5597" xml:space="preserve"/>
</p>
<div xml:id="echoid-div342" type="float" level="2" n="5">
<note position="right" xlink:label="note-0117-13" xlink:href="note-0117-13a" xml:space="preserve">Amplitudo oc-<lb/>tiua, occiduaue, <lb/>qua uia per ſty-<lb/>lum in muro <lb/>affixum explo-<lb/>retur.</note>
  <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a">
    <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/>
  </figure>
<note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s5598" xml:space="preserve">POSTREMO, vt omnia hæc facili{us}, &amp; </s>
  <s xml:id="echoid-s5599" xml:space="preserve">rectius fiant, ducendæ erunt in circulo A B C D, ante-<lb/>quam ſtylus infigatur, aliquot rectę lineæ pro communibus ſectionibus Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s5600" xml:space="preserve">cir-<lb/>culi A B C D. </s>
  <s xml:id="echoid-s5601" xml:space="preserve">Vt in figura ducta eſt F G, diſtans ab A C, grad. </s>
  <s xml:id="echoid-s5602" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5603" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5604" xml:space="preserve">K L, grad. </s>
  <s xml:id="echoid-s5605" xml:space="preserve">50. </s>
  <s xml:id="echoid-s5606" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5607" xml:space="preserve">γβ, grad. </s>
  <s xml:id="echoid-s5608" xml:space="preserve">6. <lb/></s>
  <s xml:id="echoid-s5609" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5610" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5611" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5612" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5613" xml:space="preserve">Nam cadente vmbrę extremitate in aliquam dictarum linearum, ſciemus, in quonam Ver-<lb/>ticali circulo Sol ſit. </s>
  <s xml:id="echoid-s5614" xml:space="preserve">Vnde accepta tunc eius altitudine, progrediemur vt prius. </s>
  <s xml:id="echoid-s5615" xml:space="preserve">Hoc autem idcirco <lb/>fieri debet, quoniam ſtylus, ſi prius infigatur, antequàm lineæ per centrum ducantur ex puncto extremo in <lb/>vmbra notato, impedimento eſt, ne per centrum dictæ lineæ rectę duci poſſint. </s>
  <s xml:id="echoid-s5616" xml:space="preserve">At vero ſi pro ſtylo vſur-<lb/>pemus inſtrumentum in principio ſcholĳ propoſ. </s>
  <s xml:id="echoid-s5617" xml:space="preserve">23. </s>
  <s xml:id="echoid-s5618" xml:space="preserve">hui{us} lib. </s>
  <s xml:id="echoid-s5619" xml:space="preserve">deſcriptum, hac cautione opus non erit, <lb/>
<anchor type="note" xlink:label="note-0118-04a" xlink:href="note-0118-04"/>
cum illud instrumentum poſt obſeruationem vmbrę amoueri queat, vt lineæ per centrum E, poſſint duci <lb/>ſine impedimento.</s>
  <s xml:id="echoid-s5620" xml:space="preserve"/>
</p>
<div xml:id="echoid-div343" type="float" level="2" n="6">
<note position="left" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s5621" xml:space="preserve">IAM verò ſi per doctrinam ſinuum quantitatem anguli P R Q, altitudinis poli metiri volueri-<lb/>
<anchor type="note" xlink:label="note-0118-05a" xlink:href="note-0118-05"/>
mus, efficiemus id hoc modo. </s>
  <s xml:id="echoid-s5622" xml:space="preserve">Quoniam arcus G H, altitudinis Solis notus eſt, cognitus erit eius comple-<lb/>menti ſinus E I. </s>
  <s xml:id="echoid-s5623" xml:space="preserve">Quia verò &amp; </s>
  <s xml:id="echoid-s5624" xml:space="preserve">angulus C E G, notus eſt, ex vmbræ obſeruatione, (Cum enim vmbra ca-<lb/>dat in E F, metientur gradus arcus A F, angulum A E F, hoc eſt, C E G,) erit &amp; </s>
  <s xml:id="echoid-s5625" xml:space="preserve">alternus E I O, il <lb/>
<anchor type="note" xlink:label="note-0118-06a" xlink:href="note-0118-06"/>
li æqualis, in triangulo rectangulo E I O, notus. </s>
  <s xml:id="echoid-s5626" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s5627" xml:space="preserve">E O, ſinus anguli E I O, notus erit in parti-<lb/>bus ſinus totius E I. </s>
  <s xml:id="echoid-s5628" xml:space="preserve">Quòd ſi fiat, vt E I, ſinus totus ad E I, quatenus nota eſt in partibus ſinus totius <lb/>E G, ita E O, quatenus ſinus eſt anguli E I O, ad aliud, nota fiet E O, in partibus ſinus totius E G, vel <lb/>E B. </s>
  <s xml:id="echoid-s5629" xml:space="preserve">Eadem ratione in eiſdem partibus not a fiet E P. </s>
  <s xml:id="echoid-s5630" xml:space="preserve">Detracta ergo E O, ex E P, nota fiet O P, in eiſ-<lb/>
<anchor type="note" xlink:label="note-0118-07a" xlink:href="note-0118-07"/>
dem partibus. </s>
  <s xml:id="echoid-s5631" xml:space="preserve">Ducta autem recta Q ω, ex Q, ad P R, perpendiculari, erit tam Q ω, ipſi O P, quàm <lb/>
<anchor type="note" xlink:label="note-0118-08a" xlink:href="note-0118-08"/>
P ω, ipſi O Q, æqualis. </s>
  <s xml:id="echoid-s5632" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s5633" xml:space="preserve">Q ω, in partibus ſinus totius E B, not a erit. </s>
  <s xml:id="echoid-s5634" xml:space="preserve">Sunt autem in eiſdem par <lb/>tibus notæ rectæ O Q, hoc eſt, P ω, &amp; </s>
  <s xml:id="echoid-s5635" xml:space="preserve">P R, cum ſint æquales ſinubus rectis I H, N M, altitudinum So-<lb/>lis notarum. </s>
  <s xml:id="echoid-s5636" xml:space="preserve">Detracta ergo recta P ω, ex P R, erit &amp; </s>
  <s xml:id="echoid-s5637" xml:space="preserve">reliqua ω R, in eiſdem partib{us} nota. </s>
  <s xml:id="echoid-s5638" xml:space="preserve">Cum igi-<lb/>tur quadrata rectarum ω Q, ω R, æqualia ſint quadrato rectæ Q R, fiet quoque Q R, in eiſdem parti-<lb/>
<anchor type="note" xlink:label="note-0118-09a" xlink:href="note-0118-09"/>
bus nota. </s>
  <s xml:id="echoid-s5639" xml:space="preserve">Quapropter ſi fiat, vt Q R, quatenus nota in partibus ſinus totius E B, ad ſe ipſam, quatenus <lb/>eſt ſinus totus, ita Q ω, quatenus nota in partibus ſinus totius E B, ad aliud, nota fiet Q ω, in partibus <lb/>ſinus totius Q R, hoc eſt, quatenus ſinus est anguli Q R ω, altitudinis poli quæſitæ, &amp; </s>
  <s xml:id="echoid-s5640" xml:space="preserve">c.</s>
  <s xml:id="echoid-s5641" xml:space="preserve"/>
</p>
<div xml:id="echoid-div344" type="float" level="2" n="7">
<note position="left" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">Altitudo poli <lb/>ſupra Horizon-<lb/>tem qua ratio-<lb/>ne ſupputetur <lb/>per ſinus</note>
<note position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0118-07" xlink:href="note-0118-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0118-08" xlink:href="note-0118-08a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0118-09" xlink:href="note-0118-09a" xml:space="preserve">47. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s5642" xml:space="preserve">QVOD ſi vnum punctum inuentum ſit ex vmbra in recta E B, vt P, alterum autem in recta <lb/>E D, vt θ, addenda erit E θ, ipſi E P, vt tota θ P, not a fiat. </s>
  <s xml:id="echoid-s5643" xml:space="preserve">Hinc enim &amp; </s>
  <s xml:id="echoid-s5644" xml:space="preserve">λ a, ipſi θ P, æqualis not a <lb/>
<anchor type="note" xlink:label="note-0118-10a" xlink:href="note-0118-10"/>
erit. </s>
  <s xml:id="echoid-s5645" xml:space="preserve">Ex θ λ, autem vel P a, nota erit a R. </s>
  <s xml:id="echoid-s5646" xml:space="preserve">Igitur vt prius, angulus a R λ, in triangulo a R λ, notus
<pb o="99" file="0119" n="119" rhead="LIBER PRIMVS."/>
fiet, &amp; </s>
  <s xml:id="echoid-s5647" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5648" xml:space="preserve">Eadem ratione ex E P, &amp; </s>
  <s xml:id="echoid-s5649" xml:space="preserve">E T, notis nota fiet P T. </s>
  <s xml:id="echoid-s5650" xml:space="preserve">Igitur vt antea, iterum notus erit angu-<lb/>lus P R T, altitudinis poli, &amp; </s>
  <s xml:id="echoid-s5651" xml:space="preserve">c.</s>
  <s xml:id="echoid-s5652" xml:space="preserve"/>
</p>
<div xml:id="echoid-div345" type="float" level="2" n="8">
<note position="left" xlink:label="note-0118-10" xlink:href="note-0118-10a" xml:space="preserve">34. primi.</note>
</div>
</div>
<div xml:id="echoid-div347" type="section" level="1" n="127">
<head xml:id="echoid-head130" xml:space="preserve">PROBLEMA 8. PROPOSITIO 29.</head>
<p>
  <s xml:id="echoid-s5653" xml:space="preserve">DATO plano vel ad Meridianum, &amp; </s>
  <s xml:id="echoid-s5654" xml:space="preserve">Horizontem, vel ad Meri-<lb/>dianum tantum, vel ad Horizontem tantum inclinato, quanta ſit poli <lb/>altitudo ſupra ipſum, deprehendere.</s>
  <s xml:id="echoid-s5655" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s5656" xml:space="preserve">SIT planum circuli A B C D, cuius centrum E, &amp; </s>
  <s xml:id="echoid-s5657" xml:space="preserve">ad Meridianum, &amp; </s>
  <s xml:id="echoid-s5658" xml:space="preserve">ad Horizontem, vel ad <lb/>
<anchor type="note" xlink:label="note-0119-02a" xlink:href="note-0119-02"/>
Meridianum tantum inclinatum, &amp; </s>
  <s xml:id="echoid-s5659" xml:space="preserve">communis ipſius, ac Meridiani ſectio B D. </s>
  <s xml:id="echoid-s5660" xml:space="preserve">Inuento autem, <lb/>ex coroll. </s>
  <s xml:id="echoid-s5661" xml:space="preserve">propoſitionis præcedentis, arcu Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5662" xml:space="preserve">polum mun-<lb/>
<anchor type="figure" xlink:label="fig-0119-01a" xlink:href="fig-0119-01"/>
di arcticum, ſumatur illi ęqualis D F. </s>
  <s xml:id="echoid-s5663" xml:space="preserve">Inueniatur <lb/>quoque per coroll. </s>
  <s xml:id="echoid-s5664" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s5665" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5666" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5667" xml:space="preserve">minor <lb/>diameter Ellipſis, quam perpendiculares ex cir-<lb/>cunferentia Meridiani in planum inclinatum de-<lb/>miſſæ faciunt, quæ ſit G H, ſecans maiorem B D, <lb/>ad angulos rectos, &amp; </s>
  <s xml:id="echoid-s5668" xml:space="preserve">circa G H, circulus deſcri-<lb/>batur, cuius circunferentiam ſecet recta ducta E F, <lb/>
<anchor type="note" xlink:label="note-0119-03a" xlink:href="note-0119-03"/>
in I. </s>
  <s xml:id="echoid-s5669" xml:space="preserve">Deinde per F, agatur minori diametro paral-<lb/>lela F K; </s>
  <s xml:id="echoid-s5670" xml:space="preserve">per I, autem maiori diametro parallela <lb/>I K, ſecans priorem in K, puncto, per quod dia-<lb/>meter ducatur A C, ad quam ex K, perpendicula-<lb/>ris erigatur K L, ſecans circulum A B C D, in L. <lb/></s>
  <s xml:id="echoid-s5671" xml:space="preserve">Dico arcum C L, æqualem eſſe arcui, qui altitudi-<lb/>nem poli ſupra planum A B C D, metitur. </s>
  <s xml:id="echoid-s5672" xml:space="preserve">Quo-<lb/>niam enim arcus D F, ęqualis eſt ar cui Meridiani <lb/>inter planum A B C D, &amp; </s>
  <s xml:id="echoid-s5673" xml:space="preserve">polum mundi, erit &amp; </s>
  <s xml:id="echoid-s5674" xml:space="preserve"><lb/>reliquus F O, reliquo in Meridiano à polo vſque <lb/>
<anchor type="note" xlink:label="note-0119-04a" xlink:href="note-0119-04"/>
ad diametrum, quæ ipſam B D, ſecat ad angulos rectos, &amp; </s>
  <s xml:id="echoid-s5675" xml:space="preserve">à qua perpendiculares cadunt in puncta <lb/>G, H, æqualis. </s>
  <s xml:id="echoid-s5676" xml:space="preserve">Quare per ea, quæ propoſ. </s>
  <s xml:id="echoid-s5677" xml:space="preserve">26. </s>
  <s xml:id="echoid-s5678" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5679" xml:space="preserve">demonſtrata ſunt, cadet perpendicularis <lb/>ex polo in planum A B C D, demiſſa in punctum K, ellipſis diametrorum B D, G H. </s>
  <s xml:id="echoid-s5680" xml:space="preserve">Sicut enim in <lb/>figura illius propoſitionis ſe habent arcus D L, L E, quibus in circulo inclinato ęquales ſunt ar-<lb/>cus D K, K A, ita hic ſe habent arcus D F, F O, quibus in Meridiano ad circulum A B C D, incli-<lb/>nato reſpondent arcus ęquales à D, vſque ad polum arcticum, &amp; </s>
  <s xml:id="echoid-s5681" xml:space="preserve">à polo vſque ad diametrum, quę <lb/>ipſam B D, ad angulos rectos ſecat. </s>
  <s xml:id="echoid-s5682" xml:space="preserve">Quare vt ibi demonſtratum eſt, perpendicularem ex K, demiſ-<lb/>ſam cadere in punctum Q, vbi ſe interſecant rectæ L Q, M Q, diametris H I, B D, ellipſis æqui <lb/>diſtantes, ita quoque hic oſtendetur, perpendicularem ex polo demiſſam cadere in punctum K, <lb/>vbi ſe interſecant rectæ F K, I K, diametris G H, B D, ellipſis æquidiſtantes. </s>
  <s xml:id="echoid-s5683" xml:space="preserve">Sit igitur perpendi-<lb/>
<anchor type="note" xlink:label="note-0119-05a" xlink:href="note-0119-05"/>
cularis à polo cadens K M, &amp; </s>
  <s xml:id="echoid-s5684" xml:space="preserve">polus M; </s>
  <s xml:id="echoid-s5685" xml:space="preserve">intelligaturq́; </s>
  <s xml:id="echoid-s5686" xml:space="preserve">circulus maximus A M C, duci per rectas <lb/>A E K C, K M, qui neceſſario ad planum A B C D, rectus erit; </s>
  <s xml:id="echoid-s5687" xml:space="preserve">ac propterea cum per polum mun <lb/>
<anchor type="note" xlink:label="note-0119-06a" xlink:href="note-0119-06"/>
di M, tranſeat, inſtar Meridiani erit ipſius plani inclinati, recta autẽ A C, linea erit meridiana, &amp; </s>
  <s xml:id="echoid-s5688" xml:space="preserve"><lb/>arcus C M, altitudinẽ poli ſupra idem planum metietur. </s>
  <s xml:id="echoid-s5689" xml:space="preserve">Ducantur quoque rectæ E L, E M, C L, <lb/>C M. </s>
  <s xml:id="echoid-s5690" xml:space="preserve">Quoniam igitur tam quadratum ex E L, quadratis ex E K, K L, quam quadratum ex E M, <lb/>
<anchor type="note" xlink:label="note-0119-07a" xlink:href="note-0119-07"/>
quadratis ex E K, K M, æquale eſt; </s>
  <s xml:id="echoid-s5691" xml:space="preserve">propterea quòd anguli E K L, E KM, recti ſunt, ex conſtru-<lb/>ctione, &amp; </s>
  <s xml:id="echoid-s5692" xml:space="preserve">ex defin. </s>
  <s xml:id="echoid-s5693" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5694" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5695" xml:space="preserve">11. </s>
  <s xml:id="echoid-s5696" xml:space="preserve">Euclidis: </s>
  <s xml:id="echoid-s5697" xml:space="preserve">Sunt autem quadrata rectarum E L, E M, æqualium ex cen-<lb/>tro ſphæræad eius ſuperficiem ductarum ęqualia; </s>
  <s xml:id="echoid-s5698" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s5699" xml:space="preserve">quadrata ex E K, K L, quadratis ex E K, <lb/>K M, ęqualia. </s>
  <s xml:id="echoid-s5700" xml:space="preserve">Dempto ergo communi quadrato ex E K, æquale erit quadratum ex K L, quadrato <lb/>ex K M, &amp; </s>
  <s xml:id="echoid-s5701" xml:space="preserve">recta K L, rectæ K M, æqualis. </s>
  <s xml:id="echoid-s5702" xml:space="preserve">Itaque cum latera K L, K C, lateribus K M, K C, ſint <lb/>
<anchor type="note" xlink:label="note-0119-08a" xlink:href="note-0119-08"/>
æqualia, angulosq́; </s>
  <s xml:id="echoid-s5703" xml:space="preserve">æquales cõprehendant, vtpote rectos, æqualis erit baſis C L, baſi C M; </s>
  <s xml:id="echoid-s5704" xml:space="preserve">ac proin <lb/>
<anchor type="note" xlink:label="note-0119-09a" xlink:href="note-0119-09"/>
de &amp; </s>
  <s xml:id="echoid-s5705" xml:space="preserve">arcus C L, æqualis erit arcui C M, qui altitudinẽ poli ſupra planũ A B C D, metitur. </s>
  <s xml:id="echoid-s5706" xml:space="preserve">Quod <lb/>
<anchor type="note" xlink:label="note-0119-10a" xlink:href="note-0119-10"/>
eſt propoſitum: </s>
  <s xml:id="echoid-s5707" xml:space="preserve">Atque hoc modo Federicus Cõmandinus ferè propoſitum exequitur, quanquã <lb/>de plano ad Horizontem tantum inclinato nihil dicat. </s>
  <s xml:id="echoid-s5708" xml:space="preserve">Quod idẽ nos ex ſinubus ita abſoluemus.</s>
  <s xml:id="echoid-s5709" xml:space="preserve"/>
</p>
<div xml:id="echoid-div347" type="float" level="2" n="1">
<note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">Altitudo poli <lb/>ſupra planum <lb/>inclinatum ad <lb/>Meridianum, <lb/>&amp; Horizontem, <lb/>vel ad Meridia-<lb/>num t<unsure/>antum, <lb/>quomodo inue <lb/>miatur.</note>
  <figure xlink:label="fig-0119-01" xlink:href="fig-0119-01a">
    <image file="0119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0119-01"/>
  </figure>
<note position="left" xlink:label="note-0119-03" xlink:href="note-0119-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0119-04" xlink:href="note-0119-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0119-05" xlink:href="note-0119-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0119-06" xlink:href="note-0119-06a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0119-07" xlink:href="note-0119-07a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0119-08" xlink:href="note-0119-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0119-09" xlink:href="note-0119-09a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0119-10" xlink:href="note-0119-10a" xml:space="preserve">28. tertĳ.</note>
</div>
<note position="right" xml:space="preserve">Altitudo poli <lb/>ſupra planum <lb/>inclinatum ad <lb/>Meridianum, &amp; <lb/>Horizon@ẽ qua <lb/>uia per ſinu@ in <lb/>quiratur.</note>
<p>
  <s xml:id="echoid-s5710" xml:space="preserve">SIT Horizon A B C D, Meridianus A C; </s>
  <s xml:id="echoid-s5711" xml:space="preserve">planum ad Meridianum &amp; </s>
  <s xml:id="echoid-s5712" xml:space="preserve">ad Horizontem inclina <lb/>tum E F, ſec<unsure/>ans Meridianum in G, vbicunque hoc contingat; </s>
  <s xml:id="echoid-s5713" xml:space="preserve">Polus mundi H, per quem &amp; </s>
  <s xml:id="echoid-s5714" xml:space="preserve">polũ <lb/>plani inclinati E F, circulus maximus deſcribatur B D, ſecans planum inclinatum in I, atque adeo <lb/>per propoſ. </s>
  <s xml:id="echoid-s5715" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5716" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5717" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5718" xml:space="preserve">Theodoſij, ad angulos rectos; </s>
  <s xml:id="echoid-s5719" xml:space="preserve">metieturq́; </s>
  <s xml:id="echoid-s5720" xml:space="preserve">propterea arcus HI, altitudinem <lb/>poli ſupra planum E F. </s>
  <s xml:id="echoid-s5721" xml:space="preserve">Quoniam igitur in triangulo ſphęrico G H I, cuius angulus I, rectus eſt, <lb/>vt ſinus arcus Meridiani G H, qui inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5722" xml:space="preserve">polum interijcitur, ad ſinum angu <lb/>li recti I, hoc eſt, ad ſinum totum, ita eſt, per propoſ. </s>
  <s xml:id="echoid-s5723" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5724" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5725" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5726" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s5727" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s5728" xml:space="preserve">de triangulis, vel per
<pb o="100" file="0120" n="120" rhead="GNOMONICES"/>
propoſ. </s>
  <s xml:id="echoid-s5729" xml:space="preserve">13. </s>
  <s xml:id="echoid-s5730" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5731" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5732" xml:space="preserve">Gebri, vel certè ex propoſ. </s>
  <s xml:id="echoid-s5733" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5734" xml:space="preserve">noſtrorum triangulorum ſphæricorum, ſinus ar-<lb/>cus H I, altitudinis poli ſupra planum, ad ſinum anguli G, inclinationis plani ad Meridianum; </s>
  <s xml:id="echoid-s5735" xml:space="preserve">erit <lb/>quoque conuertendo, vt ſinus totus anguli recti I, ad ſinum arcus Meridiani G H, inter planum, &amp; </s>
  <s xml:id="echoid-s5736" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0120-01a" xlink:href="fig-0120-01"/>
<anchor type="note" xlink:label="note-0120-01a" xlink:href="note-0120-01"/>
polum intercepti, ita ſinus anguli G, inclinationis plani ad Meridianum, ad ſinum arcus H I, alti-<lb/>tudinis poli ſupra planum. </s>
  <s xml:id="echoid-s5737" xml:space="preserve">Itaque inuento per corollarium præcedentis propoſ. </s>
  <s xml:id="echoid-s5738" xml:space="preserve">arcu Meridiani <lb/>inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s5739" xml:space="preserve">polum mundi intercepto, nec non per propoſ. </s>
  <s xml:id="echoid-s5740" xml:space="preserve">27. </s>
  <s xml:id="echoid-s5741" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s5742" xml:space="preserve">inclina-<lb/>
<anchor type="note" xlink:label="note-0120-02a" xlink:href="note-0120-02"/>
tione plani ad Meridianum; </s>
  <s xml:id="echoid-s5743" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5744" xml:space="preserve">po-<lb/>lum interiecti; </s>
  <s xml:id="echoid-s5745" xml:space="preserve">ita ſinus inclinationis plani ad Meridianum, ad aliud, habebitur ſinus altitudinis <lb/>
<anchor type="note" xlink:label="note-0120-03a" xlink:href="note-0120-03"/>
poli ſupra planum propoſitum. </s>
  <s xml:id="echoid-s5746" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s5747" xml:space="preserve">Ponatur arcus Meridiani inter planũ, &amp; </s>
  <s xml:id="echoid-s5748" xml:space="preserve">polum grad. <lb/></s>
  <s xml:id="echoid-s5749" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5750" xml:space="preserve">inclinatio verò plani ad Meridianũ grad. </s>
  <s xml:id="echoid-s5751" xml:space="preserve">35. </s>
  <s xml:id="echoid-s5752" xml:space="preserve">Si igitur fiat, vt 100000. </s>
  <s xml:id="echoid-s5753" xml:space="preserve">ſinus totus ad 50000. </s>
  <s xml:id="echoid-s5754" xml:space="preserve"><lb/>ſinum arcus inter planum, &amp; </s>
  <s xml:id="echoid-s5755" xml:space="preserve">polum poſiti, ita 57357. </s>
  <s xml:id="echoid-s5756" xml:space="preserve">ſinus grad. </s>
  <s xml:id="echoid-s5757" xml:space="preserve">35. </s>
  <s xml:id="echoid-s5758" xml:space="preserve">hoc eſt, inclinationis ad Me-<lb/>ridianum, ad aliud, inuenietur hic ferè ſinus 28678 {1/2}, cuius arcus grad. </s>
  <s xml:id="echoid-s5759" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5760" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5761" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5762" xml:space="preserve">altitudinem <lb/>poli ſupra planum propoſitum dimetitur.</s>
  <s xml:id="echoid-s5763" xml:space="preserve"/>
</p>
<div xml:id="echoid-div348" type="float" level="2" n="2">
  <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a">
    <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-01"/>
  </figure>
<note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">Exem plum pri-<lb/>mum.</note>
</div>
<p>
  <s xml:id="echoid-s5764" xml:space="preserve">SIMILITER ponatur arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5765" xml:space="preserve">polum poſitus grad. </s>
  <s xml:id="echoid-s5766" xml:space="preserve">90. </s>
  <s xml:id="echoid-s5767" xml:space="preserve">vt contin <lb/>
<anchor type="note" xlink:label="note-0120-04a" xlink:href="note-0120-04"/>
git, quando planum &amp; </s>
  <s xml:id="echoid-s5768" xml:space="preserve">Aequator in vno eodemq́; </s>
  <s xml:id="echoid-s5769" xml:space="preserve">puncto Meridianum interſecant: </s>
  <s xml:id="echoid-s5770" xml:space="preserve">Inclinatio ve-<lb/>rò plani ad Meridianum grad. </s>
  <s xml:id="echoid-s5771" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5772" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5773" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5774" xml:space="preserve">Itaque ſi fiat vt 100000. </s>
  <s xml:id="echoid-s5775" xml:space="preserve">ſinus totus ad 100000. </s>
  <s xml:id="echoid-s5776" xml:space="preserve">ſinũ <lb/>
<anchor type="note" xlink:label="note-0120-05a" xlink:href="note-0120-05"/>
arcus inter planum, &amp; </s>
  <s xml:id="echoid-s5777" xml:space="preserve">polum, ita 91902. </s>
  <s xml:id="echoid-s5778" xml:space="preserve">ſinus inclinationis ad Meridianum, ad aliud, inuenietur <lb/>idem ſinus 91902. </s>
  <s xml:id="echoid-s5779" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s5780" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5781" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5782" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5783" xml:space="preserve">altitudinem poli ſupra planum propoſitum con <lb/>tinet. </s>
  <s xml:id="echoid-s5784" xml:space="preserve">Vbi vides altitudinem poli ſupra planum ęqualem eſſe inclinationi eius ad Meridianum: <lb/></s>
  <s xml:id="echoid-s5785" xml:space="preserve">quoniam quando planum, &amp; </s>
  <s xml:id="echoid-s5786" xml:space="preserve">Aequator in eodem puncto Meridianum interſecant, idem arcus <lb/>circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s5787" xml:space="preserve">per polos plani ducti metitur &amp; </s>
  <s xml:id="echoid-s5788" xml:space="preserve">altitudinem poli ſupra pla-<lb/>num, &amp; </s>
  <s xml:id="echoid-s5789" xml:space="preserve">inclinationem eiuſdem plani ad Meridianum, vt perſpicuum eſt, cum per propoſ. </s>
  <s xml:id="echoid-s5790" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5791" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5792" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s5793" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s5794" xml:space="preserve">ſit rectus ad planum inclinatum. </s>
  <s xml:id="echoid-s5795" xml:space="preserve">Hinc enim fit, vt metiatur altitudinem poli ſupra pla-<lb/>num, veluti proprius quidam Meridianus ipſius plani inclinati. </s>
  <s xml:id="echoid-s5796" xml:space="preserve">Idem quoque circulus maximus <lb/>menſurat inclinationem eiuſdem plani ad Meridianum, quia rectus quoque eſt ad Meridianum; </s>
  <s xml:id="echoid-s5797" xml:space="preserve"><lb/>quod ita planum fiet. </s>
  <s xml:id="echoid-s5798" xml:space="preserve">Quoniam enim tranſit per polos plani, &amp; </s>
  <s xml:id="echoid-s5799" xml:space="preserve">per polos Aequatoris, tranſibunt <lb/>
<anchor type="note" xlink:label="note-0120-06a" xlink:href="note-0120-06"/>
quoque viciſsim planum propoſitum, &amp; </s>
  <s xml:id="echoid-s5800" xml:space="preserve">Aequator per illius polos, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s5801" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5802" xml:space="preserve">libri 1. <lb/></s>
  <s xml:id="echoid-s5803" xml:space="preserve">Theodoſij. </s>
  <s xml:id="echoid-s5804" xml:space="preserve">Quare puncta, vbi ſe interſecant planum, &amp; </s>
  <s xml:id="echoid-s5805" xml:space="preserve">Aequator in Meridiano, poli ſunt illius <lb/>circuli, ac proinde Meridianus per hos polos ductus, erit per propoſ. </s>
  <s xml:id="echoid-s5806" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5807" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5808" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5809" xml:space="preserve">Theodoſij, ad illum <lb/>rectus. </s>
  <s xml:id="echoid-s5810" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s5811" xml:space="preserve">viciſſim ille ad Meridianum rectus erit, quod erat oſtendendum.</s>
  <s xml:id="echoid-s5812" xml:space="preserve"/>
</p>
<div xml:id="echoid-div349" type="float" level="2" n="3">
<note position="left" xlink:label="note-0120-04" xlink:href="note-0120-04a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
<note position="left" xlink:label="note-0120-05" xlink:href="note-0120-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0120-06" xlink:href="note-0120-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s5813" xml:space="preserve">EODEM modo ſupra planum ad Meridianum tantum inclinatum, quod nimirum per ver <lb/>
<anchor type="note" xlink:label="note-0120-07a" xlink:href="note-0120-07"/>
<anchor type="figure" xlink:label="fig-0120-02a" xlink:href="fig-0120-02"/>
ticem loci tranſit, altitudo poli in-<lb/>uenietur, nec non ſupra planum, <lb/>quod ad Verticalem circulum eſt <lb/>rectum, &amp; </s>
  <s xml:id="echoid-s5814" xml:space="preserve">tam ad Meridianum, <lb/>quam ad Horizõtem inclinatum. <lb/></s>
  <s xml:id="echoid-s5815" xml:space="preserve">
<anchor type="note" xlink:label="note-0120-08a" xlink:href="note-0120-08"/>
Cuiuſmodi eſt planum, quod per <lb/>communes ſectiones Horizontis, <lb/>ac Meridiani incedit. </s>
  <s xml:id="echoid-s5816" xml:space="preserve">Id quod faci <lb/>le intelligi poteſt ex his duabus ſi-<lb/>guris, in quarum priori Verticalis <lb/>eſt k L, planum ad Meridianum <lb/>tantum inclinatum E F, tranſiens <lb/>per verticem G, ſiue polum Hori <lb/>zontis, ac propterea rectum exi-<lb/>ſtens ad Horizontem, ita vtarcus <lb/>Meridiani G H, inter planum &amp; </s>
  <s xml:id="echoid-s5817" xml:space="preserve">polum æqualis ſit complemento altitudinis poli ſupra Horizon
<pb o="101" file="0121" n="121" rhead="LIBER PRIMVS."/>
tem; </s>
  <s xml:id="echoid-s5818" xml:space="preserve">inclinatio verò ad Meridianum ſit complementum declinationis eiuſdem plani à Vertica-<lb/>li circulo. </s>
  <s xml:id="echoid-s5819" xml:space="preserve">In poſteriori autem planum inclinatum E F, tranſit per communes ſectiones A, C, Ho-<lb/>rizontis, &amp; </s>
  <s xml:id="echoid-s5820" xml:space="preserve">Meridiani, hoc eſt, per polos Verticalis, rectumq́; </s>
  <s xml:id="echoid-s5821" xml:space="preserve">eſt propterea ad Verticalem. </s>
  <s xml:id="echoid-s5822" xml:space="preserve">Vnde <lb/>ſi loco C, ſumatur litera G, vbi planum inclinatum ſecat Meridianũ, (ita vtarcus Meridiani G H, <lb/>inter planum &amp; </s>
  <s xml:id="echoid-s5823" xml:space="preserve">polum æqualis ſit altitudini poli ſupra Horizontem, inclinatio verò plani ad <lb/>Meridianum ſit complementum inclinationis einſdem plani ad Horizontem) erit ſemper eadem <lb/>proportio ſinus totius, ſeu anguli recti I, ad ſinum arcus G H, quæ ſinus anguli G, ad ſinum arcus <lb/>H I, &amp;</s>
  <s xml:id="echoid-s5824" xml:space="preserve">c. </s>
  <s xml:id="echoid-s5825" xml:space="preserve">vt demonſtratum eſt.</s>
  <s xml:id="echoid-s5826" xml:space="preserve"/>
</p>
<div xml:id="echoid-div350" type="float" level="2" n="4">
<note position="left" xlink:label="note-0120-07" xlink:href="note-0120-07a" xml:space="preserve">Quando planũ <lb/>ad Meridianũ <lb/>tan tum inclina <lb/>tum eſt. Vel ad <lb/>Meridianum &amp; <lb/>Horizõtem, re-<lb/>ctum autem ad <lb/>Verti@alem.</note>
  <figure xlink:label="fig-0120-02" xlink:href="fig-0120-02a">
    <image file="0120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-02"/>
  </figure>
<note position="left" xlink:label="note-0120-08" xlink:href="note-0120-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s5827" xml:space="preserve">EXEMPLVM prioris. </s>
  <s xml:id="echoid-s5828" xml:space="preserve">Ponatur planum per verticem tranſiens declinare à Verticali circu <lb/>
<anchor type="note" xlink:label="note-0121-01a" xlink:href="note-0121-01"/>
lo grad. </s>
  <s xml:id="echoid-s5829" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5830" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5831" xml:space="preserve">idcirco à Meridiano grad. </s>
  <s xml:id="echoid-s5832" xml:space="preserve">60. </s>
  <s xml:id="echoid-s5833" xml:space="preserve">Si igitur fiat vt 100000. </s>
  <s xml:id="echoid-s5834" xml:space="preserve">ſinus totus ad 74314. </s>
  <s xml:id="echoid-s5835" xml:space="preserve">ſinum <lb/>
<anchor type="note" xlink:label="note-0121-02a" xlink:href="note-0121-02"/>
arcus G H, inter planum, &amp; </s>
  <s xml:id="echoid-s5836" xml:space="preserve">polum interiecti, ita 86602. </s>
  <s xml:id="echoid-s5837" xml:space="preserve">ſinus inclinationis ad Meridianum, ad <lb/>aliud, inuenietur hic ferè ſinus 64357. </s>
  <s xml:id="echoid-s5838" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s5839" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5840" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5841" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5842" xml:space="preserve">paulo amplius, oſtendet altitu <lb/>dinem poli ſupra planum propoſitum. </s>
  <s xml:id="echoid-s5843" xml:space="preserve">Rurſus pro exemplo poſterioris, ponatur planum trãſiens <lb/>per communes ſectiones Horizontis, ac Meridiani declinare ab Horizonte grad. </s>
  <s xml:id="echoid-s5844" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5845" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s5846" xml:space="preserve">idcirco à <lb/>Meridiano grad. </s>
  <s xml:id="echoid-s5847" xml:space="preserve">60. </s>
  <s xml:id="echoid-s5848" xml:space="preserve">Itaque ſi fiat, vt 100000. </s>
  <s xml:id="echoid-s5849" xml:space="preserve">ſinus totus, ad 66913. </s>
  <s xml:id="echoid-s5850" xml:space="preserve">ſinum arcus G H, inter pla <lb/>num, &amp; </s>
  <s xml:id="echoid-s5851" xml:space="preserve">polum interpoſiti, ita 86602. </s>
  <s xml:id="echoid-s5852" xml:space="preserve">ſinus inclinationis ad Meridianum, ad aliud, inuenietur <lb/>hic propemodum ſinus 57948, cuius arcus grad. </s>
  <s xml:id="echoid-s5853" xml:space="preserve">35. </s>
  <s xml:id="echoid-s5854" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5855" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5856" xml:space="preserve">altitudinem poli ſupra propoſitum <lb/>planum indicabit.</s>
  <s xml:id="echoid-s5857" xml:space="preserve"/>
</p>
<div xml:id="echoid-div351" type="float" level="2" n="5">
<note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s5858" xml:space="preserve">QVOD ſi planum ad Horizontem tantum ſit inclinatum, hoc eſt, ſi tranſeat per communes <lb/>
<anchor type="note" xlink:label="note-0121-03a" xlink:href="note-0121-03"/>
ſectiones Horizontis, ac Verticalis, rectumq́; </s>
  <s xml:id="echoid-s5859" xml:space="preserve">ſit ad Meridianum, erit ipſe arcus Meridiani inter <lb/>
<anchor type="note" xlink:label="note-0121-04a" xlink:href="note-0121-04"/>
planum, &amp; </s>
  <s xml:id="echoid-s5860" xml:space="preserve">polum poſitus, altitudo poli ſupra Horizontem, vt ap paret ex figura corollarij propoſ. <lb/></s>
  <s xml:id="echoid-s5861" xml:space="preserve">præcedentis. </s>
  <s xml:id="echoid-s5862" xml:space="preserve">Dato igitur plano vel ad Meridianum, vel ad Horizontem inclinato, quanta ſit poli <lb/>altitudo ſupra ipſum, deprehendimus. </s>
  <s xml:id="echoid-s5863" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s5864" xml:space="preserve"/>
</p>
<div xml:id="echoid-div352" type="float" level="2" n="6">
<note position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">Quando planũ <lb/>ad Horizon@em <lb/>tantum eſt incli <lb/>na@um.</note>
<note position="left" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div354" type="section" level="1" n="128">
<head xml:id="echoid-head131" xml:space="preserve">PROBLEMA. 9. PROPOSITIO 30.</head>
<p>
  <s xml:id="echoid-s5865" xml:space="preserve">DATO plano ad Meridianum inclinato, quantus ſit interceptus <lb/>arcus ipſius inter Meridianum, &amp; </s>
  <s xml:id="echoid-s5866" xml:space="preserve">circulum maximum, qui per polos <lb/>
<anchor type="note" xlink:label="note-0121-05a" xlink:href="note-0121-05"/>
ipſius, &amp; </s>
  <s xml:id="echoid-s5867" xml:space="preserve">per polos mundi ducitur, altitudinemq́; </s>
  <s xml:id="echoid-s5868" xml:space="preserve">poli ſupra ipſum di-<lb/>metitur, tanquam proprius eius Meridianus: </s>
  <s xml:id="echoid-s5869" xml:space="preserve">Et quantum circulus hic <lb/>maximus ad Meridianum Horizontis, ſeu loci, in quo planum inclina-<lb/>tum conſideratur, in clinatus ſit, inuenire.</s>
  <s xml:id="echoid-s5870" xml:space="preserve"/>
</p>
<div xml:id="echoid-div354" type="float" level="2" n="1">
<note position="left" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">30</note>
</div>
  <figure>
    <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0121-01"/>
  </figure>
<note position="left" xml:space="preserve">40</note>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s5871" xml:space="preserve">SIT Horizon A B C D; </s>
  <s xml:id="echoid-s5872" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s5873" xml:space="preserve">planum inclinatum ad Meridianum E F, ſecans <lb/>Meridianum in G; </s>
  <s xml:id="echoid-s5874" xml:space="preserve">polus mundi H, per quem &amp; </s>
  <s xml:id="echoid-s5875" xml:space="preserve">polum plani inclinati E F, circulus maximus de-<lb/>ſcribatur B D, ſecans planum inclinatum in I, qui cum per propoſ. </s>
  <s xml:id="echoid-s5876" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5877" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5878" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5879" xml:space="preserve">Theodoſij, rectus ſit <lb/>ad ipſum planum inclinatum, metietur altitudinem poli H, ſupra ipſum, per arcum H I. </s>
  <s xml:id="echoid-s5880" xml:space="preserve">Oporter <lb/>
<anchor type="note" xlink:label="note-0121-08a" xlink:href="note-0121-08"/>
igitur inuenire quantitatem arcus G I, &amp; </s>
  <s xml:id="echoid-s5881" xml:space="preserve">anguli G H I. </s>
  <s xml:id="echoid-s5882" xml:space="preserve">Quod ita exequemur. </s>
  <s xml:id="echoid-s5883" xml:space="preserve">Quoniam in trian-<lb/>gulo ſphærico G H I, angulus I, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s5884" xml:space="preserve">19. </s>
  <s xml:id="echoid-s5885" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5886" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5887" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s5888" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s5889" xml:space="preserve">vel per propoſ. <lb/></s>
  <s xml:id="echoid-s5890" xml:space="preserve">15. </s>
  <s xml:id="echoid-s5891" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5892" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5893" xml:space="preserve">Gebri, vel certè ex propoſ. </s>
  <s xml:id="echoid-s5894" xml:space="preserve">43. </s>
  <s xml:id="echoid-s5895" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple <lb/>menti arcus Meridiani G H, inter planum &amp; </s>
  <s xml:id="echoid-s5896" xml:space="preserve">polum intercepti, ad ſinum complementiarcus H I, <lb/>altitudinem poli ſupra planum E F, metientis, ita ſinus complementi arcus G I, ad ſinum totum; </s>
  <s xml:id="echoid-s5897" xml:space="preserve"><lb/>ac propterea &amp; </s>
  <s xml:id="echoid-s5898" xml:space="preserve">conuertendo, vt ſinus complementiarcus H I, altitudinis poli ſupra planum E F, <lb/>ad ſinum complementi arcus Meridiani G H, inter planum &amp; </s>
  <s xml:id="echoid-s5899" xml:space="preserve">polum, ita ſinus totus ad ſinum cõ-
<pb o="102" file="0122" n="122" rhead="GNOMONICES"/>
plementi arcus G I. </s>
  <s xml:id="echoid-s5900" xml:space="preserve">Quare ſi fiat, vt ſinus complementi altitudinis poli ſupra planum inclina-<lb/>tum, ad ſinum complementi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5901" xml:space="preserve">polum, ita ſinus totus ad aliud, ha-<lb/>bebitur ſinus complementi arcus plani G I, qui angulo H, inclinationis Meridiani B D, ipſius pla-<lb/>
<anchor type="figure" xlink:label="fig-0122-01a" xlink:href="fig-0122-01"/>
<anchor type="note" xlink:label="note-0122-01a" xlink:href="note-0122-01"/>
ni inclinati ad Meridianum A C, ipſius Horizontis opponitur in triangulo G H I, eſtq́; </s>
  <s xml:id="echoid-s5902" xml:space="preserve">arcus pla <lb/>ni inclinati, qui interijcitur inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s5903" xml:space="preserve">dictum circulum maximum, hoc <lb/>
<anchor type="note" xlink:label="note-0122-02a" xlink:href="note-0122-02"/>
eſt, Meridianum plani inclinati; </s>
  <s xml:id="echoid-s5904" xml:space="preserve">atque adeo &amp; </s>
  <s xml:id="echoid-s5905" xml:space="preserve">arcus ipſe G I, cognitus erit.</s>
  <s xml:id="echoid-s5906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div355" type="float" level="2" n="2">
<note position="right" xlink:label="note-0121-08" xlink:href="note-0121-08a" xml:space="preserve">Arcus plani in-<lb/>clinati iter eius <lb/>Meridianum &amp; <lb/>Meridianũ Ho <lb/>rizontis quo ar-<lb/>uficio deprehẽ-<lb/>dacur.</note>
  <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a">
    <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-01"/>
  </figure>
<note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s5907" xml:space="preserve">IDEM &amp; </s>
  <s xml:id="echoid-s5908" xml:space="preserve">facilius conſequemur, ſi planum inclinatum E F, tranſierit per verticem G, ita vt ſit <lb/>vnus ex circulis Verticalibus, velut in ſecunda figura apparet: </s>
  <s xml:id="echoid-s5909" xml:space="preserve">quia tunc arcus G H, Meridiani <lb/>inter planum, &amp; </s>
  <s xml:id="echoid-s5910" xml:space="preserve">polum eſt complementum altitudinis poli ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s5911" xml:space="preserve">complementũ <lb/>ipſius arcus G H, eſt ipſamet altitudo poli ſupra Horizontem, nempe arcus H C.</s>
  <s xml:id="echoid-s5912" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5913" xml:space="preserve">SIMILITER res facilis erit, ſi planum inclinatum E F, tranſierit per puncta A, C, vbi Ho-<lb/>rizon, &amp; </s>
  <s xml:id="echoid-s5914" xml:space="preserve">Meridianus ſe mutuo interſecant, ita vt ſit vnus ex circulis poſitionum, velut in figura <lb/>tertia apparet: </s>
  <s xml:id="echoid-s5915" xml:space="preserve">quia tunc arcus Meridiani G H, inter planum, &amp; </s>
  <s xml:id="echoid-s5916" xml:space="preserve">polum eſt altitudo poli ſupra Ho-<lb/>rizontem, nempe arcus H C. </s>
  <s xml:id="echoid-s5917" xml:space="preserve">Conſtat ergo id quod primo loco propoſitum eſt.</s>
  <s xml:id="echoid-s5918" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s5919" xml:space="preserve">DEINDE quoniam eſt, per propoſ. </s>
  <s xml:id="echoid-s5920" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5921" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s5922" xml:space="preserve">4. </s>
  <s xml:id="echoid-s5923" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s5924" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s5925" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s5926" xml:space="preserve">13. <lb/></s>
  <s xml:id="echoid-s5927" xml:space="preserve">
<anchor type="note" xlink:label="note-0122-03a" xlink:href="note-0122-03"/>
<anchor type="note" xlink:label="note-0122-04a" xlink:href="note-0122-04"/>
lib. </s>
  <s xml:id="echoid-s5928" xml:space="preserve">1. </s>
  <s xml:id="echoid-s5929" xml:space="preserve">Gebri, vel certè per propoſ. </s>
  <s xml:id="echoid-s5930" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5931" xml:space="preserve">noſtrorum triangulorum ſphęricorum, vt ſinus arcus G H, <lb/>Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5932" xml:space="preserve">polum, ad ſinum anguli recti I, hoc eſt, ad ſinum totum, ita ſinus ar-<lb/>cus G I, ipſius plani inter duos Meridianos, quem iam inuenimus, ad ſinum anguli H, inclinatio-<lb/>nis circuli maximi B D, (qui eſt inſtar Meridiani ipſius plani) ad Horizontis Meridianum A C; </s>
  <s xml:id="echoid-s5933" xml:space="preserve">ſi <lb/>fiat, vt ſinus arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5934" xml:space="preserve">polum, ad ſinum totum, ita ſinus arcus G I, ipſius pla <lb/>ni inter duos Meridianos inuenti ad aliud, habebitur ſinus anguli H, inclinationis quęſitæ. <lb/></s>
  <s xml:id="echoid-s5935" xml:space="preserve">Quod eſt ſecundum.</s>
  <s xml:id="echoid-s5936" xml:space="preserve"/>
</p>
<div xml:id="echoid-div356" type="float" level="2" n="3">
<note position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">Inclinatio, quã <lb/>habet Meridia-<lb/>nus plani incli-<lb/>nati ad Meri-<lb/>dianũ Horizon <lb/>tis quo pacto re <lb/>per@atur.</note>
<note position="left" xlink:label="note-0122-04" xlink:href="note-0122-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s5937" xml:space="preserve">EXEMPLVM vtriuſque. </s>
  <s xml:id="echoid-s5938" xml:space="preserve">Ponatur altitudo poli ſupra planum grad. </s>
  <s xml:id="echoid-s5939" xml:space="preserve">16. </s>
  <s xml:id="echoid-s5940" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5941" xml:space="preserve">40. </s>
  <s xml:id="echoid-s5942" xml:space="preserve">Arcus ve-<lb/>
<anchor type="note" xlink:label="note-0122-05a" xlink:href="note-0122-05"/>
rò Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5943" xml:space="preserve">polum grad. </s>
  <s xml:id="echoid-s5944" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5945" xml:space="preserve">Si igitur fiat, vt 9579 S. </s>
  <s xml:id="echoid-s5946" xml:space="preserve">ſinus complementi altitu-<lb/>dinis poli ſupra planum ad 86602. </s>
  <s xml:id="echoid-s5947" xml:space="preserve">ſinum complementi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5948" xml:space="preserve">polum, <lb/>
<anchor type="note" xlink:label="note-0122-06a" xlink:href="note-0122-06"/>
ita 100000. </s>
  <s xml:id="echoid-s5949" xml:space="preserve">ſinus totus ad aliud, habebitur hic ferè ſinus 90401. </s>
  <s xml:id="echoid-s5950" xml:space="preserve">cuius arcus continet grad. </s>
  <s xml:id="echoid-s5951" xml:space="preserve">64. <lb/></s>
  <s xml:id="echoid-s5952" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5953" xml:space="preserve">41. </s>
  <s xml:id="echoid-s5954" xml:space="preserve">quo detracto ex quadrante, remanebit arcus ipſius plani inter duos Meridianos, grad. </s>
  <s xml:id="echoid-s5955" xml:space="preserve">25. </s>
  <s xml:id="echoid-s5956" xml:space="preserve"><lb/>min. </s>
  <s xml:id="echoid-s5957" xml:space="preserve">19. </s>
  <s xml:id="echoid-s5958" xml:space="preserve">quod eſt primum. </s>
  <s xml:id="echoid-s5959" xml:space="preserve">Poſt hęc, ſi fiat, vt 50000. </s>
  <s xml:id="echoid-s5960" xml:space="preserve">ſinus arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5961" xml:space="preserve">po-<lb/>lum, ad 100000. </s>
  <s xml:id="echoid-s5962" xml:space="preserve">ſinum totum, ita 42762. </s>
  <s xml:id="echoid-s5963" xml:space="preserve">ſinus arcus inter duos Meridianos inuenti ad aliud, in-<lb/>uenietur hic ſinus 85524. </s>
  <s xml:id="echoid-s5964" xml:space="preserve">cuius arcus, nempe inclinatio Meridiani ipſius plani ad Meridianum <lb/>Horizontis, continet grad. </s>
  <s xml:id="echoid-s5965" xml:space="preserve">58. </s>
  <s xml:id="echoid-s5966" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5967" xml:space="preserve">47. </s>
  <s xml:id="echoid-s5968" xml:space="preserve">quod eſt ſecundum.</s>
  <s xml:id="echoid-s5969" xml:space="preserve"/>
</p>
<div xml:id="echoid-div357" type="float" level="2" n="4">
<note position="left" xlink:label="note-0122-05" xlink:href="note-0122-05a" xml:space="preserve">Exemplum pri-<lb/>mum.</note>
<note position="left" xlink:label="note-0122-06" xlink:href="note-0122-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s5970" xml:space="preserve">RVRSVS ponatur altitudo poli ſupra planum grad. </s>
  <s xml:id="echoid-s5971" xml:space="preserve">66. </s>
  <s xml:id="echoid-s5972" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5973" xml:space="preserve">47 arcus verò Meridiani inter <lb/>planum &amp; </s>
  <s xml:id="echoid-s5974" xml:space="preserve">polum grad. </s>
  <s xml:id="echoid-s5975" xml:space="preserve">90. </s>
  <s xml:id="echoid-s5976" xml:space="preserve">vt contingit in plano declinante à Verticali, à ſeptentrione in ortum <lb/>grad. </s>
  <s xml:id="echoid-s5977" xml:space="preserve">30. </s>
  <s xml:id="echoid-s5978" xml:space="preserve">inclinato verò ad Horizontem grad. </s>
  <s xml:id="echoid-s5979" xml:space="preserve">52. </s>
  <s xml:id="echoid-s5980" xml:space="preserve">min. </s>
  <s xml:id="echoid-s5981" xml:space="preserve">3. </s>
  <s xml:id="echoid-s5982" xml:space="preserve">ex parte auſtrali, in latitudine grad. </s>
  <s xml:id="echoid-s5983" xml:space="preserve">42. </s>
  <s xml:id="echoid-s5984" xml:space="preserve">vt <lb/>ex præcedentibus colligi poteſt. </s>
  <s xml:id="echoid-s5985" xml:space="preserve">Si igitur fiat, vt 39420. </s>
  <s xml:id="echoid-s5986" xml:space="preserve">ſinus complementi altitudinis poli ſupra <lb/>
<anchor type="note" xlink:label="note-0122-07a" xlink:href="note-0122-07"/>
planum inclinatum ad ſinum complementi arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s5987" xml:space="preserve">polum, quod nul <lb/>lum eſt, ita 100000. </s>
  <s xml:id="echoid-s5988" xml:space="preserve">ſinus totus ad aliud, habebitur hic ſinus o, cuius arcus grad. </s>
  <s xml:id="echoid-s5989" xml:space="preserve">0. </s>
  <s xml:id="echoid-s5990" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s5991" xml:space="preserve">0. </s>
  <s xml:id="echoid-s5992" xml:space="preserve">detra-<lb/>ctus ex grad. </s>
  <s xml:id="echoid-s5993" xml:space="preserve">90. </s>
  <s xml:id="echoid-s5994" xml:space="preserve">relinquit arcum ipſius plani inter duos Meridianos grad. </s>
  <s xml:id="echoid-s5995" xml:space="preserve">90. </s>
  <s xml:id="echoid-s5996" xml:space="preserve">quod eſt primum. <lb/></s>
  <s xml:id="echoid-s5997" xml:space="preserve">Rurſus ſi fiat, vt 100000. </s>
  <s xml:id="echoid-s5998" xml:space="preserve">ſinus arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s5999" xml:space="preserve">polum, ad 100000. </s>
  <s xml:id="echoid-s6000" xml:space="preserve">ſinum totum, <lb/>ita 100000. </s>
  <s xml:id="echoid-s6001" xml:space="preserve">ſinus arcus plani inter duos Meridianos inuẽti, ad aliud, reperietur ſinus hic 100000. </s>
  <s xml:id="echoid-s6002" xml:space="preserve"><lb/>cuius arcus grad. </s>
  <s xml:id="echoid-s6003" xml:space="preserve">90. </s>
  <s xml:id="echoid-s6004" xml:space="preserve">erit inclinatio Meridiani ipſius ad Meridianum Horizontis. </s>
  <s xml:id="echoid-s6005" xml:space="preserve">quæ res cum ſu-<lb/>perioribus conſentit. </s>
  <s xml:id="echoid-s6006" xml:space="preserve">Quia enim polus Meridiani ipſius plani inclinati eſt punctum, vbi Aequa-<lb/>tor Meridianum interſecat, vt in pręcedenti propoſ. </s>
  <s xml:id="echoid-s6007" xml:space="preserve">diximus, neceſſe eſt ex coroll. </s>
  <s xml:id="echoid-s6008" xml:space="preserve">propoſitionis <lb/>16. </s>
  <s xml:id="echoid-s6009" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6010" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6011" xml:space="preserve">Theodoſij, arcum ipſius plani à polo dicto vſq; </s>
  <s xml:id="echoid-s6012" xml:space="preserve">ad Meridianũ ipſius eſſe quadrantẽ, &amp;</s>
  <s xml:id="echoid-s6013" xml:space="preserve">c.</s>
  <s xml:id="echoid-s6014" xml:space="preserve"/>
</p>
<div xml:id="echoid-div358" type="float" level="2" n="5">
<note position="left" xlink:label="note-0122-07" xlink:href="note-0122-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s6015" xml:space="preserve">ALIVD exemplũ pro ſecunda figura. </s>
  <s xml:id="echoid-s6016" xml:space="preserve">Ponatur planũ E F, declinare à meridie in ortum, vel à <lb/>
<anchor type="note" xlink:label="note-0122-08a" xlink:href="note-0122-08"/>
ſeptentrione in occaſum, grad. </s>
  <s xml:id="echoid-s6017" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6018" xml:space="preserve">in Horizonte Romano, vel vbi polus ſupra Horizõtem eleuatur
<pb o="103" file="0123" n="123" rhead="LIBER PRIMVS."/>
gradibus 42. </s>
  <s xml:id="echoid-s6019" xml:space="preserve">Erit altitudo poli ſupra planum E F, per propoſ. </s>
  <s xml:id="echoid-s6020" xml:space="preserve">pręcedentem inuẽta grad. </s>
  <s xml:id="echoid-s6021" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6022" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s6023" xml:space="preserve">3, ferè. </s>
  <s xml:id="echoid-s6024" xml:space="preserve">Arcus verò Meridiani inter idem planum, &amp; </s>
  <s xml:id="echoid-s6025" xml:space="preserve">polum continebit grad. </s>
  <s xml:id="echoid-s6026" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6027" xml:space="preserve">quantum nimirũ <lb/>eſt complementum altitudinis poli ſupra Horizontem. </s>
  <s xml:id="echoid-s6028" xml:space="preserve">Igitur ſi fiat, vt 76548. </s>
  <s xml:id="echoid-s6029" xml:space="preserve">ſinus complemen-<lb/>ti altitudinis poli ſupra planum, ad 66913. </s>
  <s xml:id="echoid-s6030" xml:space="preserve">ſinum complementi arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s6031" xml:space="preserve"><lb/>polum, (quod complementum in huiuſmodi planis inclinatis eſt ipſamet poli altitudo ſupra Ho <lb/>rizontem,) ita 100000. </s>
  <s xml:id="echoid-s6032" xml:space="preserve">ſinus totus ad, aliud, rep erietur hic ferè ſinus 87413. </s>
  <s xml:id="echoid-s6033" xml:space="preserve">cuius arcus continet <lb/>gradus 60. </s>
  <s xml:id="echoid-s6034" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6035" xml:space="preserve">57. </s>
  <s xml:id="echoid-s6036" xml:space="preserve">quo detracto ex quadrante, reliquus erit arcus grad. </s>
  <s xml:id="echoid-s6037" xml:space="preserve">29. </s>
  <s xml:id="echoid-s6038" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6039" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6040" xml:space="preserve">ipſius plani, <lb/>qui inter Meridianum ipſius, &amp; </s>
  <s xml:id="echoid-s6041" xml:space="preserve">Meridianum Horizontis interiicitut. </s>
  <s xml:id="echoid-s6042" xml:space="preserve">Quod eſt primum. </s>
  <s xml:id="echoid-s6043" xml:space="preserve">Rurſus <lb/>ſi fiat, vt 74314. </s>
  <s xml:id="echoid-s6044" xml:space="preserve">ſinus arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s6045" xml:space="preserve">polum, ad 100000. </s>
  <s xml:id="echoid-s6046" xml:space="preserve">ſinũ totum, ita 48557. </s>
  <s xml:id="echoid-s6047" xml:space="preserve"><lb/>ſinus arcus inter duos Meridianos inuenti ad aliud, inuenietur hic ferè ſinus 65340. </s>
  <s xml:id="echoid-s6048" xml:space="preserve">cuius arcus <lb/>
<anchor type="note" xlink:label="note-0123-01a" xlink:href="note-0123-01"/>
complectitur grad. </s>
  <s xml:id="echoid-s6049" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6050" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6051" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6052" xml:space="preserve">Tanta eſt inclinatio Meridiani ipſius plani ad Meridianum Hori-<lb/>zontis. </s>
  <s xml:id="echoid-s6053" xml:space="preserve">quod eſt ſecundum.</s>
  <s xml:id="echoid-s6054" xml:space="preserve"/>
</p>
<div xml:id="echoid-div359" type="float" level="2" n="6">
<note position="left" xlink:label="note-0122-08" xlink:href="note-0122-08a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
<note position="left" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s6055" xml:space="preserve">PRO figura autem tertia hoc ſume exemplum. </s>
  <s xml:id="echoid-s6056" xml:space="preserve">Ponatur planum E F, declinare à Meridiano <lb/>
<anchor type="note" xlink:label="note-0123-02a" xlink:href="note-0123-02"/>
grad. </s>
  <s xml:id="echoid-s6057" xml:space="preserve">60. </s>
  <s xml:id="echoid-s6058" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6059" xml:space="preserve">idcirco ab Horizonte grad. </s>
  <s xml:id="echoid-s6060" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6061" xml:space="preserve">Erit altitudo poli ſupra ipſum (nempe arcus H I,) per <lb/>pręcedentem propoſ. </s>
  <s xml:id="echoid-s6062" xml:space="preserve">inuenta, grad. </s>
  <s xml:id="echoid-s6063" xml:space="preserve">35. </s>
  <s xml:id="echoid-s6064" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6065" xml:space="preserve">25. </s>
  <s xml:id="echoid-s6066" xml:space="preserve">Itaque ſi fiat, vt 81495. </s>
  <s xml:id="echoid-s6067" xml:space="preserve">ſinus complementi altitu <lb/>dinis poli ſupra planum, ad 74314. </s>
  <s xml:id="echoid-s6068" xml:space="preserve">ſinum complementi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s6069" xml:space="preserve">polũ, <lb/>hoc eſt, ad ſinum complementi altitudinis poli ſupra Horizontem in hoc exemplo, ita 100000. </s>
  <s xml:id="echoid-s6070" xml:space="preserve">ſi-<lb/>nus totus ad aliud, reperietur hic ferè ſinus 91188. </s>
  <s xml:id="echoid-s6071" xml:space="preserve">cuius arcus continet gradus 65. </s>
  <s xml:id="echoid-s6072" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6073" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6074" xml:space="preserve">quo <lb/>detracto ex quadrante, reliquus erit arcus grad. </s>
  <s xml:id="echoid-s6075" xml:space="preserve">24. </s>
  <s xml:id="echoid-s6076" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6077" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6078" xml:space="preserve">ipſius plani inter Meridianum ipſius, <lb/>&amp; </s>
  <s xml:id="echoid-s6079" xml:space="preserve">Meridianum Horizontis interiecti, nempe arcus G I. </s>
  <s xml:id="echoid-s6080" xml:space="preserve">Quod eſt primũ. </s>
  <s xml:id="echoid-s6081" xml:space="preserve">Rurſus ſi fiat, vt 66913. <lb/></s>
  <s xml:id="echoid-s6082" xml:space="preserve">
<anchor type="note" xlink:label="note-0123-03a" xlink:href="note-0123-03"/>
ſinus arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s6083" xml:space="preserve">polum, nempe in hoc exemplo, vt ſinus altitudinis poli ſu-<lb/>pra Horizontem, ad 100000. </s>
  <s xml:id="echoid-s6084" xml:space="preserve">ſinum totum, ita 41045. </s>
  <s xml:id="echoid-s6085" xml:space="preserve">ſinus arcus G I, inter duos Meridianos in-<lb/>uenti ad aliud, inuenietur hic fere ſinus 61341. </s>
  <s xml:id="echoid-s6086" xml:space="preserve">cuius arcus complectitur grad. </s>
  <s xml:id="echoid-s6087" xml:space="preserve">37. </s>
  <s xml:id="echoid-s6088" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6089" xml:space="preserve">50. </s>
  <s xml:id="echoid-s6090" xml:space="preserve">Tan-<lb/>ta eſt inclinatio Meridiani ipſius plani ad Meridianum Horizontis, hoc eſt, tantus eſt angulus <lb/>G H I, ſeu arcus Aequatoris inter duos Meridianos poſitus. </s>
  <s xml:id="echoid-s6091" xml:space="preserve">Quod eſt ſecundum.</s>
  <s xml:id="echoid-s6092" xml:space="preserve"/>
</p>
<div xml:id="echoid-div360" type="float" level="2" n="7">
<note position="right" xlink:label="note-0123-02" xlink:href="note-0123-02a" xml:space="preserve">Exemplum ter-<lb/>tium.</note>
<note position="left" xlink:label="note-0123-03" xlink:href="note-0123-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s6093" xml:space="preserve">SI planum inclinatum per polum trãſeat, nullus erit arcus ipſius interpoſitus inter Meridianũ <lb/>
<anchor type="note" xlink:label="note-0123-04a" xlink:href="note-0123-04"/>
Horizontis, &amp; </s>
  <s xml:id="echoid-s6094" xml:space="preserve">Meridianum plani inclinati; </s>
  <s xml:id="echoid-s6095" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6096" xml:space="preserve">cõplementum inclinationis plani ad Meridianum, <lb/>erit inclinatio Meridiani ipſius ad Horizontis Meridianum, vt patet in ſphæra materiali. </s>
  <s xml:id="echoid-s6097" xml:space="preserve">Dato <lb/>igitur plano ad Meridianum inclinato, quantus ſit interceptus arcus, &amp;</s>
  <s xml:id="echoid-s6098" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6099" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s6100" xml:space="preserve"/>
</p>
<div xml:id="echoid-div361" type="float" level="2" n="8">
<note position="right" xlink:label="note-0123-04" xlink:href="note-0123-04a" xml:space="preserve">Quando plan@ <lb/>inclinarum per <lb/>polos mundi <lb/>tranſit.</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div363" type="section" level="1" n="129">
<head xml:id="echoid-head132" xml:space="preserve">PROBLEMA 10. PROPOSITIO 31.</head>
<p>
  <s xml:id="echoid-s6101" xml:space="preserve">DATO plano ad Meridianum inclinato, quantus ſit arcus ipſius in-<lb/>terceptus inter circulum maximum, qui per polos ipſius, &amp; </s>
  <s xml:id="echoid-s6102" xml:space="preserve">polos Hori-<lb/>zontis tranſit, metiturq́; </s>
  <s xml:id="echoid-s6103" xml:space="preserve">eius inclinationem ad Horizontem, &amp; </s>
  <s xml:id="echoid-s6104" xml:space="preserve">tam Me <lb/>ridianum proprium ipſius, (nempe circulum maximum, qui per eius <lb/>polos, &amp; </s>
  <s xml:id="echoid-s6105" xml:space="preserve">polos mundi ducitur, altitudinemq́; </s>
  <s xml:id="echoid-s6106" xml:space="preserve">poli ſupra ipſum dimeti-<lb/>
<anchor type="note" xlink:label="note-0123-06a" xlink:href="note-0123-06"/>
tur, inſtar proprij Meridiani) quàm Meridianum Horizontis, reperire.</s>
  <s xml:id="echoid-s6107" xml:space="preserve"/>
</p>
<div xml:id="echoid-div363" type="float" level="2" n="1">
<note position="left" xlink:label="note-0123-06" xlink:href="note-0123-06a" xml:space="preserve">40</note>
</div>
  <figure>
    <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01"/>
  </figure>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Arcus plani in-<lb/>clinati inter <lb/>maximum cir-<lb/>culum per eius <lb/>polos, &amp; per po-<lb/>los Horizontis <lb/>ductum, &amp; Me-<lb/>ridianum eius <lb/>proprium in-<lb/>teriectus, qua <lb/>uia cognoſca-<lb/>tur.</note>
<p>
  <s xml:id="echoid-s6108" xml:space="preserve">SIT Horizon A B C D; </s>
  <s xml:id="echoid-s6109" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s6110" xml:space="preserve">Verticalis k L; </s>
  <s xml:id="echoid-s6111" xml:space="preserve">planum inclinatum E F, ſecans Me-<lb/>ridianum in G; </s>
  <s xml:id="echoid-s6112" xml:space="preserve">eius Meridianus B D, per eius polum P, &amp; </s>
  <s xml:id="echoid-s6113" xml:space="preserve">per polum mundi H, tranſiens; </s>
  <s xml:id="echoid-s6114" xml:space="preserve">Cir-<lb/>culus maximus inclinationem plani ad Horizontem metiens, hoc eſt, per verticem M, ſeu polum <lb/>Horizontis, &amp; </s>
  <s xml:id="echoid-s6115" xml:space="preserve">per P, polum plani inclinati deſcriptus N O, ſecans planum inclinatum in Q; </s>
  <s xml:id="echoid-s6116" xml:space="preserve">opor-<lb/>teatq́; </s>
  <s xml:id="echoid-s6117" xml:space="preserve">inuenire tam arcum I Q, quàm arcum G Q. </s>
  <s xml:id="echoid-s6118" xml:space="preserve">Quoniam arcus M N, P Q, quadrantes ſunt,
<pb o="104" file="0124" n="124" rhead="GNOMONICES"/>
ex coroll. </s>
  <s xml:id="echoid-s6119" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6120" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6121" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6122" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6123" xml:space="preserve">Theodoſii, quôd M, polus ſit Horizõtis A B C D, &amp; </s>
  <s xml:id="echoid-s6124" xml:space="preserve">P, polus plani E F; <lb/></s>
  <s xml:id="echoid-s6125" xml:space="preserve">ablato communi arcu M Q, erit P M, arcus æqualis arcui Q N, inclinationem plani ad Horizon-<lb/>tem metienti. </s>
  <s xml:id="echoid-s6126" xml:space="preserve">Quare cum in ſphęrico triangulo H P M, per propoſ. </s>
  <s xml:id="echoid-s6127" xml:space="preserve">17. </s>
  <s xml:id="echoid-s6128" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6129" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6130" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6131" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6132" xml:space="preserve">de <lb/>
<anchor type="figure" xlink:label="fig-0124-01a" xlink:href="fig-0124-01"/>
<anchor type="note" xlink:label="note-0124-01a" xlink:href="note-0124-01"/>
triangulis, vel per propoſitionem 13. </s>
  <s xml:id="echoid-s6133" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6134" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6135" xml:space="preserve">Gebri, vel certè per propoſ. </s>
  <s xml:id="echoid-s6136" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6137" xml:space="preserve">noſtrorum triangulorũ <lb/>
<anchor type="note" xlink:label="note-0124-02a" xlink:href="note-0124-02"/>
ſphæricorum, ſit vt ſinus arcus P M, qui inclinationi plani ad Horizontem æqualis eſt, ad ſinum <lb/>anguli H, inclinationis Meridiani ipſius plani inclinati ad Meridianum Horizontis, ita ſinus arcus <lb/>H M, complementi altitudinis poli ſupra Horizontem, ad ſinum anguli P, hoc eſt, ad ſinum ar-<lb/>cus I Q; </s>
  <s xml:id="echoid-s6138" xml:space="preserve">Si fiat, vt ſinus inclinationis ad Horizontem, ad ſinum inclinationis Meridiani ipſius pla <lb/>ni inclinati ad Meridianum Horizontis, per propoſ. </s>
  <s xml:id="echoid-s6139" xml:space="preserve">pręcedentem inuentę, ita ſinus complementi <lb/>altitudinis poli ſupra Horizontem ad aliud, habebitur ſinus arcus primi I Q, quæſiti.</s>
  <s xml:id="echoid-s6140" xml:space="preserve"/>
</p>
<div xml:id="echoid-div364" type="float" level="2" n="2">
  <figure xlink:label="fig-0124-01" xlink:href="fig-0124-01a">
    <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01"/>
  </figure>
<note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0124-02" xlink:href="note-0124-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s6141" xml:space="preserve">RVRSVS ducto arcu circuli maximi per puncta G, P, erunt duo arcus G P, G M, trianguli <lb/>
<anchor type="note" xlink:label="note-0124-03a" xlink:href="note-0124-03"/>
ſphærici G M P, noti; </s>
  <s xml:id="echoid-s6142" xml:space="preserve">quoniam G P, quadrans eſt, per coroll. </s>
  <s xml:id="echoid-s6143" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6144" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6145" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6146" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6147" xml:space="preserve">Theodoſii, quòd <lb/>P, polus ſit circuli E F, arcus vero G M, notus eſt, quia interijcitur inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s6148" xml:space="preserve"><lb/>verticem M, ac proinde, per coroll. </s>
  <s xml:id="echoid-s6149" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6150" xml:space="preserve">28. </s>
  <s xml:id="echoid-s6151" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s6152" xml:space="preserve">notus eſt, cum ſit complementum arcus <lb/>Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s6153" xml:space="preserve">Horizontem. </s>
  <s xml:id="echoid-s6154" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s6155" xml:space="preserve">angulus G M P, notus eſt. </s>
  <s xml:id="echoid-s6156" xml:space="preserve">quoniam <lb/>
<anchor type="note" xlink:label="note-0124-04a" xlink:href="note-0124-04"/>
enim circulus O N, ductus per polos P, M, circulorum E F, E B F, ſecat arcus E F, E B F, per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s6157" xml:space="preserve">9. </s>
  <s xml:id="echoid-s6158" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6159" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6160" xml:space="preserve">Theodoſii, bifariam; </s>
  <s xml:id="echoid-s6161" xml:space="preserve">eſtq́; </s>
  <s xml:id="echoid-s6162" xml:space="preserve">E B F, per propoſ. </s>
  <s xml:id="echoid-s6163" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6164" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6165" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6166" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s6167" xml:space="preserve">ſemicirculus, erit E N, <lb/>quadrans, atque adeò quadranti k C, ęqualis. </s>
  <s xml:id="echoid-s6168" xml:space="preserve">ablato ergo communi arcu k N, relinquetur arcus <lb/>E k, declinationis plani E F, à Verticali, arcui N C, ęqualis, atque adeo arcus N C, notus erit. </s>
  <s xml:id="echoid-s6169" xml:space="preserve">quare <lb/>&amp; </s>
  <s xml:id="echoid-s6170" xml:space="preserve">angulus N M C, ac proinde &amp; </s>
  <s xml:id="echoid-s6171" xml:space="preserve">reliquus ex duobus rectis G M P, notus erit. </s>
  <s xml:id="echoid-s6172" xml:space="preserve">Quoniam autem <lb/>eſt in triangulo ſphęrico G P M, per propoſ. </s>
  <s xml:id="echoid-s6173" xml:space="preserve">17. </s>
  <s xml:id="echoid-s6174" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6175" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6176" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6177" xml:space="preserve">Regiom de triangulis, vel per propoſ. <lb/></s>
  <s xml:id="echoid-s6178" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6179" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6180" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6181" xml:space="preserve">Gebri, vel certè per propoſ. </s>
  <s xml:id="echoid-s6182" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6183" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus <lb/>G P, nempe ſinus totus, ad ſinum anguli G M P, nempe ad ſinum declinationis plani à Verticali, <lb/>(habent enim arcus N C, C O, angulorum N M C, C M O, vel G M P, cũ ſemicirculum cõficiant, <lb/>eundem ſinum) ita ſinus arcus G M, Meridiani, qui inter planum, &amp; </s>
  <s xml:id="echoid-s6184" xml:space="preserve">verticem M, interponitur, ad <lb/>
<anchor type="note" xlink:label="note-0124-05a" xlink:href="note-0124-05"/>
ſinum anguli G P M, hoc eſt, ad ſinum arcus G Q; </s>
  <s xml:id="echoid-s6185" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum declinationis, ita <lb/>ſinus arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s6186" xml:space="preserve">verticem collocati ad aliud, habebitur ſinus arcus ſecun-<lb/>di G Q, qui quæritur.</s>
  <s xml:id="echoid-s6187" xml:space="preserve"/>
</p>
<div xml:id="echoid-div365" type="float" level="2" n="3">
<note position="left" xlink:label="note-0124-03" xlink:href="note-0124-03a" xml:space="preserve">Arcus plani in-<lb/>clinati inter ma <lb/>ximum circulũ <lb/>per eius polos, <lb/>&amp; per polos Ho <lb/>@zontis ductũ, <lb/>&amp; Meridianum <lb/>Horizontis in-<lb/>tercep us, quo <lb/>artificio explo-<lb/>retur.</note>
<note position="left" xlink:label="note-0124-04" xlink:href="note-0124-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0124-05" xlink:href="note-0124-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s6188" xml:space="preserve">EXEMPLVM vtriuſque. </s>
  <s xml:id="echoid-s6189" xml:space="preserve">Ponatur inclinatio ad Horizontem grad. </s>
  <s xml:id="echoid-s6190" xml:space="preserve">52. </s>
  <s xml:id="echoid-s6191" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6192" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6193" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6194" xml:space="preserve">inclina-<lb/>
<anchor type="note" xlink:label="note-0124-06a" xlink:href="note-0124-06"/>
tio Meridiani B D, ipſius plani inclinati E F, ad Meridianum Horizontis A C, grad. </s>
  <s xml:id="echoid-s6195" xml:space="preserve">90. </s>
  <s xml:id="echoid-s6196" xml:space="preserve">Si igitur <lb/>fiat vt 78854. </s>
  <s xml:id="echoid-s6197" xml:space="preserve">ſinus inclinationis ad Horizontem ad 100000. </s>
  <s xml:id="echoid-s6198" xml:space="preserve">ſinũ totum, nempe ad ſinum incli-<lb/>nationis Meridianorũ, ita 74314. </s>
  <s xml:id="echoid-s6199" xml:space="preserve">ſinus complementi altitudinis poli ſupra Horizontẽ ad aliud, <lb/>inuenietur hic ferè ſinus 94242. </s>
  <s xml:id="echoid-s6200" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s6201" xml:space="preserve">70. </s>
  <s xml:id="echoid-s6202" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6203" xml:space="preserve">28. </s>
  <s xml:id="echoid-s6204" xml:space="preserve">ferè inter Meridianum plani incli-<lb/>nati, &amp; </s>
  <s xml:id="echoid-s6205" xml:space="preserve">circulum maximum interijcitur, qui inclinationem plani ad Horizontem metitur.</s>
  <s xml:id="echoid-s6206" xml:space="preserve"/>
</p>
<div xml:id="echoid-div366" type="float" level="2" n="4">
<note position="left" xlink:label="note-0124-06" xlink:href="note-0124-06a" xml:space="preserve">Exemplum.</note>
</div>
<p>
  <s xml:id="echoid-s6207" xml:space="preserve">RVRSVS ſi fiat, vt 100000. </s>
  <s xml:id="echoid-s6208" xml:space="preserve">ſinus totus ad 50000. </s>
  <s xml:id="echoid-s6209" xml:space="preserve">ſinum declinationis plani à Verticali (po-<lb/>
<anchor type="note" xlink:label="note-0124-07a" xlink:href="note-0124-07"/>
nimus enim idem planum, de quo proximè egimus, declinare à Verticali à Septentrione in ortũ, <lb/>grad. </s>
  <s xml:id="echoid-s6210" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6211" xml:space="preserve">ita vt inclinatio cadat in partem auſtralem) ita 66913. </s>
  <s xml:id="echoid-s6212" xml:space="preserve">ſinus arcus Meridiani inter pla-<lb/>num, &amp; </s>
  <s xml:id="echoid-s6213" xml:space="preserve">verticem intercepti (qui quidem arcus complectitur grad. </s>
  <s xml:id="echoid-s6214" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6215" xml:space="preserve">Nam arcus inter planum, <lb/>&amp; </s>
  <s xml:id="echoid-s6216" xml:space="preserve">Horizontem continet, per propoſ. </s>
  <s xml:id="echoid-s6217" xml:space="preserve">28. </s>
  <s xml:id="echoid-s6218" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s6219" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s6220" xml:space="preserve">48. </s>
  <s xml:id="echoid-s6221" xml:space="preserve">ſub Horizonte ad partes boreales, qui <lb/>ablatus ex quadrante relinquit arcum inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s6222" xml:space="preserve">verticem ad partes auſtrales <lb/>grad. </s>
  <s xml:id="echoid-s6223" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6224" xml:space="preserve">ex coroll. </s>
  <s xml:id="echoid-s6225" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6226" xml:space="preserve">28. </s>
  <s xml:id="echoid-s6227" xml:space="preserve">huius lib.) </s>
  <s xml:id="echoid-s6228" xml:space="preserve">ad aliud, reperietur hic propemodum ſinus 33456. </s>
  <s xml:id="echoid-s6229" xml:space="preserve">cui <lb/>reſpondet arcus ferme grad. </s>
  <s xml:id="echoid-s6230" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6231" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6232" xml:space="preserve">33. </s>
  <s xml:id="echoid-s6233" xml:space="preserve">inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s6234" xml:space="preserve">circulum maximum in-<lb/>reriectus, qui inclinationem plani ad Horizontem dimetitur. </s>
  <s xml:id="echoid-s6235" xml:space="preserve">Dato ergo plano ad Meridianum <lb/>inclinato, quãtus ſit arcus ipſins interceptus inter circulum maximum, qui per polos ipſius, &amp; </s>
  <s xml:id="echoid-s6236" xml:space="preserve">per <lb/>polos Horizontis tranſit, metiturq́; </s>
  <s xml:id="echoid-s6237" xml:space="preserve">eius inclinationem ad Horizontem, &amp; </s>
  <s xml:id="echoid-s6238" xml:space="preserve">tam Meridianum pro-<lb/>prium ipſius, &amp;</s>
  <s xml:id="echoid-s6239" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6240" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s6241" xml:space="preserve"/>
</p>
<div xml:id="echoid-div367" type="float" level="2" n="5">
<note position="left" xlink:label="note-0124-07" xlink:href="note-0124-07a" xml:space="preserve">50</note>
</div>
<pb o="105" file="0125" n="125" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div369" type="section" level="1" n="130">
<head xml:id="echoid-head133" xml:space="preserve">PROBLEMA 11. PROPOSITIO 32.</head>
<p>
  <s xml:id="echoid-s6242" xml:space="preserve">DATO plano ad Horizontem inclinato, &amp; </s>
  <s xml:id="echoid-s6243" xml:space="preserve">declinante à Verticali, <lb/>quantus ſit arcus circuli maximi inclinationem ipſius ad Horizontem <lb/>metientis inter Horizontem, &amp; </s>
  <s xml:id="echoid-s6244" xml:space="preserve">circulum horæ ſextæ à meridie, vel me-<lb/>dia nocte poſitus, explorare.</s>
  <s xml:id="echoid-s6245" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6246" xml:space="preserve">SIT Horizon A B C D; </s>
  <s xml:id="echoid-s6247" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s6248" xml:space="preserve">Verticalis B I D; </s>
  <s xml:id="echoid-s6249" xml:space="preserve">planum inclinatum ad Horizon-<lb/>
<anchor type="note" xlink:label="note-0125-01a" xlink:href="note-0125-01"/>
<anchor type="note" xlink:label="note-0125-02a" xlink:href="note-0125-02"/>
tem, &amp; </s>
  <s xml:id="echoid-s6250" xml:space="preserve">à Verticali declinans E F; </s>
  <s xml:id="echoid-s6251" xml:space="preserve">circulus maximus eius inclinationem ſupra Horizontem metiẽs <lb/>G H, tranſiens per verticem, I, ſeu polum Horizontis, &amp; </s>
  <s xml:id="echoid-s6252" xml:space="preserve">per polum plani inclinati M; </s>
  <s xml:id="echoid-s6253" xml:space="preserve">Circulus <lb/>denique horæ ſextæ à meridie, vel media nocte B K D, ductus <lb/>
<anchor type="figure" xlink:label="fig-0125-01a" xlink:href="fig-0125-01"/>
per polum mundi K, &amp; </s>
  <s xml:id="echoid-s6254" xml:space="preserve">per B, D, communes ſectiones Hori-<lb/>zontis, &amp; </s>
  <s xml:id="echoid-s6255" xml:space="preserve">Verticalis, ſecanſq́ue circulum G H, in L; </s>
  <s xml:id="echoid-s6256" xml:space="preserve">oporteatq́; <lb/></s>
  <s xml:id="echoid-s6257" xml:space="preserve">arcum L H, explorare. </s>
  <s xml:id="echoid-s6258" xml:space="preserve">Quoniam in triangulo ſphærico D H L, <lb/>cuius angulus H, per propoſ. </s>
  <s xml:id="echoid-s6259" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6260" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6261" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6262" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s6263" xml:space="preserve">rectus eſt, quòd <lb/>circulus G H, per I, polum Horizontis A B C D, ducatur; </s>
  <s xml:id="echoid-s6264" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6265" xml:space="preserve">an-<lb/>gulus D, angulus altitudinis poli, cum D, polus ſit Meridiani, <lb/>
<anchor type="note" xlink:label="note-0125-03a" xlink:href="note-0125-03"/>
(Hinc enim fit, vt per corol. </s>
  <s xml:id="echoid-s6266" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6267" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6268" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6269" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6270" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s6271" xml:space="preserve">arcus DC, <lb/>D k, quadrantes ſint, ac proinde arcus C k, altitudinis poli ſu-<lb/>pra Horizontem metiatut angulum C D k) eſt per propoſ. </s>
  <s xml:id="echoid-s6272" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s6273" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6274" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6275" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6276" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6277" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s6278" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6279" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6280" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6281" xml:space="preserve">Ge-<lb/>bri, vel certè per propoſ. </s>
  <s xml:id="echoid-s6282" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6283" xml:space="preserve">noſtrorum triangulorum ſphęri-<lb/>corum, vt ſinus anguli H D L, altitudinis poli, ad ſinum totum, ita ſinus complementi anguli L, <lb/>ad ſinum complementi arcus D H, hoc eſt, ad ſinum arcus C H, qui æqualis eſt declinationi pla <lb/>ni à Verticali; </s>
  <s xml:id="echoid-s6284" xml:space="preserve">(quoniam enim circulus G H, per polos Horizontis, &amp; </s>
  <s xml:id="echoid-s6285" xml:space="preserve">circuli E F, ductus ſecat ar-<lb/>cus E N F, E H F, per propoſ. </s>
  <s xml:id="echoid-s6286" xml:space="preserve">9. </s>
  <s xml:id="echoid-s6287" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6288" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6289" xml:space="preserve">Theodoſij, bifariam; </s>
  <s xml:id="echoid-s6290" xml:space="preserve">Eſt autem arcus E H F, ſemicirculus, <lb/>per propoſ. </s>
  <s xml:id="echoid-s6291" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6292" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6293" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6294" xml:space="preserve">Theodoſij, erit E H, quadrans, atque adeò quadranti D C, æqualis. </s>
  <s xml:id="echoid-s6295" xml:space="preserve">Ablato <lb/>
<anchor type="note" xlink:label="note-0125-04a" xlink:href="note-0125-04"/>
ergo communiarcu D H, erit reliquus arcus D E, declinationis plani à Verticali, æqualis arcui <lb/>reliquo C H.) </s>
  <s xml:id="echoid-s6296" xml:space="preserve">Erit conuertendo vt ſinus totus ad ſinum anguli H D L, altitudinis poli, ita ſinus <lb/>complementi arcus D H, hoc eſt, ſinus declinationis plani à Verticali, ad ſinum complementi an-<lb/>guli L. </s>
  <s xml:id="echoid-s6297" xml:space="preserve">Igitur ſi fiat, vt ſinus torus ad ſinum altitudinis poli ſupra Horizontem, ita ſinus declina-<lb/>tionis ad aliud, habebitur ſinus, cuius arcus ex quadrante ſubtractus relinquit angulum L, notũ. <lb/></s>
  <s xml:id="echoid-s6298" xml:space="preserve">Quia verò per propoſ. </s>
  <s xml:id="echoid-s6299" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6300" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6301" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6302" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6303" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6304" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s6305" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6306" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6307" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6308" xml:space="preserve">Gebri, vel cer <lb/>tè per propoſ. </s>
  <s xml:id="echoid-s6309" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6310" xml:space="preserve">noſtrorum triangulorum ſphęricorum, in eodem triangulo eſt, vt ſinus anguli <lb/>L, proximè inuenti, ad ſinum arcus D H, complementi declinationis, ita ſinus anguli H D L, al-<lb/>titudinis poli, ad ſinum arcus L H; </s>
  <s xml:id="echoid-s6311" xml:space="preserve">Si fiat, vt ſinus anguli L, inuenti ad ſinum complementi decli <lb/>nationis, ita ſinus altitudinis poli ſupra Horizontem ad aliud, habebitur ſinus arcus L H, quæſiti.</s>
  <s xml:id="echoid-s6312" xml:space="preserve"/>
</p>
<div xml:id="echoid-div369" type="float" level="2" n="1">
<note position="left" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">Arcus circuli <lb/>maximi, qui pla <lb/>ni à Verticali <lb/>declinantis in-<lb/>clinationem ad <lb/>Horizontẽ me-<lb/>titur, inter Ho-<lb/>rizon@ẽ. &amp; circu <lb/>lum horæ 6. à <lb/>mer. uel med. <lb/>noc. poſitus, quo <lb/>pacto inueſtigã-<lb/>dus.</note>
  <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a">
    <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-01"/>
  </figure>
<note position="left" xlink:label="note-0125-03" xlink:href="note-0125-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0125-04" xlink:href="note-0125-04a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Exemplum pri-<lb/>mum.</note>
<p>
  <s xml:id="echoid-s6313" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s6314" xml:space="preserve">Ponatur planum inclinatum ad Horizontem grad. </s>
  <s xml:id="echoid-s6315" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6316" xml:space="preserve">declinãs verò à Ver-<lb/>
<anchor type="note" xlink:label="note-0125-06a" xlink:href="note-0125-06"/>
ticali grad. </s>
  <s xml:id="echoid-s6317" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6318" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s6319" xml:space="preserve">ſinus totus, ad 66913. </s>
  <s xml:id="echoid-s6320" xml:space="preserve">ſinum altitudinis poli, ita 34202. </s>
  <s xml:id="echoid-s6321" xml:space="preserve">ſinus de-<lb/>clinationis ad aliud, reperietur hic ferè ſinus 22885 cuius arcus grad. </s>
  <s xml:id="echoid-s6322" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6323" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6324" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6325" xml:space="preserve">à quadrante <lb/>demptus relinquit angulum L, grad. </s>
  <s xml:id="echoid-s6326" xml:space="preserve">76. </s>
  <s xml:id="echoid-s6327" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6328" xml:space="preserve">46. </s>
  <s xml:id="echoid-s6329" xml:space="preserve">Rurſus fiat, vt 97344. </s>
  <s xml:id="echoid-s6330" xml:space="preserve">ſinus anguli L, inuenti, <lb/>ad 93969. </s>
  <s xml:id="echoid-s6331" xml:space="preserve">ſinum complementi declinationis, ita 66913. </s>
  <s xml:id="echoid-s6332" xml:space="preserve">ſinus altitudinis poliad aliud, habebi-<lb/>turq́ue hic propemodum ſinus 64593. </s>
  <s xml:id="echoid-s6333" xml:space="preserve">cui reſpondent grad. </s>
  <s xml:id="echoid-s6334" xml:space="preserve">40. </s>
  <s xml:id="echoid-s6335" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6336" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6337" xml:space="preserve">pro arcu L H. </s>
  <s xml:id="echoid-s6338" xml:space="preserve">quęſito.</s>
  <s xml:id="echoid-s6339" xml:space="preserve"/>
</p>
<div xml:id="echoid-div370" type="float" level="2" n="2">
<note position="left" xlink:label="note-0125-06" xlink:href="note-0125-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s6340" xml:space="preserve">RVRSVS ponatur planum inclinatum ad Horizontem grad. </s>
  <s xml:id="echoid-s6341" xml:space="preserve">52. </s>
  <s xml:id="echoid-s6342" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6343" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6344" xml:space="preserve">declinans autem à <lb/>
<anchor type="note" xlink:label="note-0125-07a" xlink:href="note-0125-07"/>
Verticali grad. </s>
  <s xml:id="echoid-s6345" xml:space="preserve">30. </s>
  <s xml:id="echoid-s6346" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s6347" xml:space="preserve">ſinus totus ad 66913. </s>
  <s xml:id="echoid-s6348" xml:space="preserve">ſinum altitudinis poli, ita 50000. </s>
  <s xml:id="echoid-s6349" xml:space="preserve">ſinus <lb/>declinationis ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s6350" xml:space="preserve">hic fermè ſinus 33456. </s>
  <s xml:id="echoid-s6351" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s6352" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6353" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6354" xml:space="preserve">33. </s>
  <s xml:id="echoid-s6355" xml:space="preserve">à qua-<lb/>drante ablatus relinquit angulum L, quem circulus maximus inclinationem plani ad Horizontẽ <lb/>metiens facit cum circulo horæ ſextæ à meridie, vel media nocte, grad. </s>
  <s xml:id="echoid-s6356" xml:space="preserve">70. </s>
  <s xml:id="echoid-s6357" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6358" xml:space="preserve">27.</s>
  <s xml:id="echoid-s6359" xml:space="preserve"/>
</p>
<div xml:id="echoid-div371" type="float" level="2" n="3">
<note position="right" xlink:label="note-0125-07" xlink:href="note-0125-07a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s6360" xml:space="preserve">FIAT rurſus, vt 94234. </s>
  <s xml:id="echoid-s6361" xml:space="preserve">ſinus anguli L, inuenti, ad 86602. </s>
  <s xml:id="echoid-s6362" xml:space="preserve">ſinum complementi declinatio-<lb/>nis, ita 66913. </s>
  <s xml:id="echoid-s6363" xml:space="preserve">ſinus altitudinis poli ad aliud, habebiturq́; </s>
  <s xml:id="echoid-s6364" xml:space="preserve">hic ferè ſinus 61493. </s>
  <s xml:id="echoid-s6365" xml:space="preserve">cui reſpondent <lb/>grad. </s>
  <s xml:id="echoid-s6366" xml:space="preserve">37. </s>
  <s xml:id="echoid-s6367" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6368" xml:space="preserve">57. </s>
  <s xml:id="echoid-s6369" xml:space="preserve">pro arcu LH, qui quęritur. </s>
  <s xml:id="echoid-s6370" xml:space="preserve">Dato ergo plano ad Horizontem inclinato &amp;</s>
  <s xml:id="echoid-s6371" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6372" xml:space="preserve">Quod <lb/>erat faciendum.</s>
  <s xml:id="echoid-s6373" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div373" type="section" level="1" n="131">
<head xml:id="echoid-head134" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s6374" xml:space="preserve">PROPOSVIMVS proxima ſex Problemata, quoniam eorum mirificus vſus apparebit in ho-<lb/>
<anchor type="note" xlink:label="note-0125-09a" xlink:href="note-0125-09"/>
rologĳs, quorum plana, in quibus deſcribuntur, parallela ſunt circulis maximis, qui vel à Verticali decli <lb/>nant, &amp; </s>
  <s xml:id="echoid-s6375" xml:space="preserve">ad Horizontem ſunt recti; </s>
  <s xml:id="echoid-s6376" xml:space="preserve">vel ab Horizonte declinant, rectiq́, ſunt ad Verticalem; </s>
  <s xml:id="echoid-s6377" xml:space="preserve">vel deniq; <lb/></s>
  <s xml:id="echoid-s6378" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6379" xml:space="preserve">à Verticali declinant, &amp; </s>
  <s xml:id="echoid-s6380" xml:space="preserve">ad Horizontem ſunt inclinati, vt ex ſequentibus fiet perſpicuum.</s>
  <s xml:id="echoid-s6381" xml:space="preserve"/>
</p>
<div xml:id="echoid-div373" type="float" level="2" n="1">
<note position="right" xlink:label="note-0125-09" xlink:href="note-0125-09a" xml:space="preserve">Ad quid condu <lb/>cant ſex antece-<lb/>dentes propoſi-<lb/>tiones.</note>
</div>
<pb o="106" file="0126" n="126" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div375" type="section" level="1" n="132">
<head xml:id="echoid-head135" xml:space="preserve">PROBLEMA 12. PROPOSITIO 33.</head>
<p>
  <s xml:id="echoid-s6382" xml:space="preserve">DATO arcu diurno, nocturnove, &amp; </s>
  <s xml:id="echoid-s6383" xml:space="preserve">latitudine loci, declinationem <lb/>paralleli illius arcus ab Aequatore inquirere.</s>
  <s xml:id="echoid-s6384" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6385" xml:space="preserve">DIVIDATVR circulus quicunque A B C D, cuius centrũ P, &amp; </s>
  <s xml:id="echoid-s6386" xml:space="preserve">in quo duæ diametri A C, <lb/>
<anchor type="note" xlink:label="note-0126-01a" xlink:href="note-0126-01"/>
B D, ſe mutuo ad angulos rectos ſecantes, in horas vigintiquatuor æquales vnà cum ſemihoris, <lb/>
<anchor type="figure" xlink:label="fig-0126-01a" xlink:href="fig-0126-01"/>
&amp; </s>
  <s xml:id="echoid-s6387" xml:space="preserve">quadrantibus, ſi placuerit, initio <lb/>facto à quouis punctorum A, B, C, D. <lb/></s>
  <s xml:id="echoid-s6388" xml:space="preserve">Numerato autẽ à puncto B, hinc in-<lb/>
<anchor type="note" xlink:label="note-0126-02a" xlink:href="note-0126-02"/>
de arcu ſemidiurno B E, B F, vel à D, <lb/>hinc inde arcu ſeminocturno D E, <lb/>D F, vt totus arcus E B F, ſit verbi gra-<lb/>tia arcus diurnus horarum 14. </s>
  <s xml:id="echoid-s6389" xml:space="preserve">vel <lb/>E D F, arcus nocturnus horarum 10. <lb/></s>
  <s xml:id="echoid-s6390" xml:space="preserve">datus, ducatur recta E F, ſecans B D, <lb/>in G, quæ ipſi A C, ob æquales arcus <lb/>A E, C F, parallela erit, per ea, quæ ad <lb/>propoſ. </s>
  <s xml:id="echoid-s6391" xml:space="preserve">27. </s>
  <s xml:id="echoid-s6392" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6393" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6394" xml:space="preserve">Euclidis, demonſtra <lb/>uimus; </s>
  <s xml:id="echoid-s6395" xml:space="preserve">atque adeo ad B D, perpendi-<lb/>
<anchor type="note" xlink:label="note-0126-03a" xlink:href="note-0126-03"/>
cularis. </s>
  <s xml:id="echoid-s6396" xml:space="preserve">Conſtituatur iam angulus <lb/>
<anchor type="note" xlink:label="note-0126-04a" xlink:href="note-0126-04"/>
P G k, æqualis angulo altitudinis Ae-<lb/>quatoris, ſeu complementi altítudi-<lb/>nis poli; </s>
  <s xml:id="echoid-s6397" xml:space="preserve">ſecetq́; </s>
  <s xml:id="echoid-s6398" xml:space="preserve">recta G k, rectã A C, <lb/>in k, puncto, ex quo recta ducatur <lb/>K B. </s>
  <s xml:id="echoid-s6399" xml:space="preserve">Dico P B k, æqualem eſſe angu-<lb/>lo declinationis paralleli illius, cuius <lb/>arcus diurnus tot horas cõplectitur, <lb/>quot ſunt in arcu E B F, nempe 14. </s>
  <s xml:id="echoid-s6400" xml:space="preserve">Ducta enim recta K D, deſcribatur circulus B O M N, ex cen-<lb/>tro K, interualloq́; </s>
  <s xml:id="echoid-s6401" xml:space="preserve">k B, vel K D. </s>
  <s xml:id="echoid-s6402" xml:space="preserve">Sunt enim rectæ K B, K D, inter ſe æquales. </s>
  <s xml:id="echoid-s6403" xml:space="preserve">Nam cum latera <lb/>
<anchor type="note" xlink:label="note-0126-05a" xlink:href="note-0126-05"/>
B P, P K, lateribus D P, P K, in triangulis B P K, D P K, ęqualia ſint, angulosq́; </s>
  <s xml:id="echoid-s6404" xml:space="preserve">contineant æqua-<lb/>les, vtpote rectos, ęquales erunt rectæ K B, K D. </s>
  <s xml:id="echoid-s6405" xml:space="preserve">Deinde per K, ipſi B D, parallela agatur diame-<lb/>
<anchor type="note" xlink:label="note-0126-06a" xlink:href="note-0126-06"/>
ter L M. </s>
  <s xml:id="echoid-s6406" xml:space="preserve">Extendatur quoque recta G K, hinc inde. </s>
  <s xml:id="echoid-s6407" xml:space="preserve">Quoniam igitur P G K, ex conſtructione, an-<lb/>gulus eſt complementi altitudinis poli, erit P <emph style="sc">K</emph> G, angulus altitudinis poli. </s>
  <s xml:id="echoid-s6408" xml:space="preserve">Quare arcus I N, alti-<lb/>tudinem poli ſupra Horizontem metietur, atque adeo ſi circulus N L O M, ponatur eſſe Meridia <lb/>nus, erit recta HI, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s6409" xml:space="preserve">Horizontis; </s>
  <s xml:id="echoid-s6410" xml:space="preserve">N O, axis mundi; </s>
  <s xml:id="echoid-s6411" xml:space="preserve">L M, commu-<lb/>nis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s6412" xml:space="preserve">Acquatoris; </s>
  <s xml:id="echoid-s6413" xml:space="preserve">B D, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s6414" xml:space="preserve">paralleli A B C D, cuius <lb/>arcus diurnus E B F, datus. </s>
  <s xml:id="echoid-s6415" xml:space="preserve">Eſt enim E F, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s6416" xml:space="preserve">paralleli A B C D, quod <lb/>ita planum fiet. </s>
  <s xml:id="echoid-s6417" xml:space="preserve">Quoniam tam Horizon per HI, ductus, quàm parallelus A B C D, ad Meridianũ <lb/>N L O M, rectus eſt, ſi hi circuli propriã cõcipiantur habere poſitionẽ in ſphæra, erit quoque com <lb/>
<anchor type="note" xlink:label="note-0126-07a" xlink:href="note-0126-07"/>
munis eorũ ſectio, quæ quidẽ in G, cadit, vbi ſe interſecãt Horizon &amp; </s>
  <s xml:id="echoid-s6418" xml:space="preserve">dictus parallelus, ad Meridia <lb/>
<anchor type="note" xlink:label="note-0126-08a" xlink:href="note-0126-08"/>
num recta, atque adeo per defin. </s>
  <s xml:id="echoid-s6419" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6420" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6421" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6422" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s6423" xml:space="preserve">perpendicularis ad rectam B D, in Meridiano exi-<lb/>ftentem. </s>
  <s xml:id="echoid-s6424" xml:space="preserve">Cum ergo E F, per G, ducta, ſit oſtenſa perpendicularis ad B D, erit E F, communis ſectio <lb/>Horizontis &amp; </s>
  <s xml:id="echoid-s6425" xml:space="preserve">paralleli A B C D. </s>
  <s xml:id="echoid-s6426" xml:space="preserve">Eſt ergo B L, in Meridiano N L O M, arcus declinationis paral-<lb/>leli A B C D, ab Aequatore, atque adeo B K L, angulus eiuſdem declinationis, cui quidem æqua-<lb/>lis eſt angulus P B K, alternus, quod eſt propoſitum.</s>
  <s xml:id="echoid-s6427" xml:space="preserve"/>
</p>
<div xml:id="echoid-div375" type="float" level="2" n="1">
<note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">Declinatio pa-<lb/>talleli, cuius <lb/>arcus di@@nus <lb/>contineat quot-<lb/>cunque quis @@@ <lb/>ras propoſu@ri@ <lb/>quo artificio in <lb/>ueniatur per <lb/>Analemma.</note>
  <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a">
    <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01"/>
  </figure>
<note position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0126-03" xlink:href="note-0126-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0126-05" xlink:href="note-0126-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0126-06" xlink:href="note-0126-06a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0126-07" xlink:href="note-0126-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0126-08" xlink:href="note-0126-08a" xml:space="preserve">19. vndec.</note>
</div>
<note position="left" xml:space="preserve">29. primi.</note>
<p>
  <s xml:id="echoid-s6428" xml:space="preserve">EODEM modo inueniemus Q B P, angulum declinationis paralleli, cuius arcus diurnus con <lb/>tinet horas 13. </s>
  <s xml:id="echoid-s6429" xml:space="preserve">Item R B P, angulum declinationis paralleli, cuius arcus diurnus horas 15. </s>
  <s xml:id="echoid-s6430" xml:space="preserve">comple <lb/>ctitur, &amp;</s>
  <s xml:id="echoid-s6431" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6432" xml:space="preserve">Simili ratione reperiemus angulum declinationis paralleli auſtralis, cuius arcus diur-<lb/>nus continet pauciores hotas, quàm 12. </s>
  <s xml:id="echoid-s6433" xml:space="preserve">nempe 9, vel 8, &amp;</s>
  <s xml:id="echoid-s6434" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6435" xml:space="preserve">Nam in eadem figura, ſi à puncto D, <lb/>
<anchor type="note" xlink:label="note-0126-10a" xlink:href="note-0126-10"/>
vtrinque numeretur exempli gratia arcus ſemidiurnus D E, D F, horarum 5. </s>
  <s xml:id="echoid-s6436" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6437" xml:space="preserve">cætera fiant, vt <lb/>prius, erit HI, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s6438" xml:space="preserve">Meridiani, arcusq́; </s>
  <s xml:id="echoid-s6439" xml:space="preserve">H O, numerabit altitudinẽ po-<lb/>li ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s6440" xml:space="preserve">B D, erit parallelus auſtralis; </s>
  <s xml:id="echoid-s6441" xml:space="preserve">angulus declinationis P D K, vel D K M, &amp; </s>
  <s xml:id="echoid-s6442" xml:space="preserve"><lb/>ſic de reliquis.</s>
  <s xml:id="echoid-s6443" xml:space="preserve"/>
</p>
<div xml:id="echoid-div376" type="float" level="2" n="2">
<note position="left" xlink:label="note-0126-10" xlink:href="note-0126-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s6444" xml:space="preserve">IDEM parallelus auſtralis, cuius arcus diurnus datus eſt, nempe horarũ 10. </s>
  <s xml:id="echoid-s6445" xml:space="preserve">inuenietur hac ra-<lb/>tione. </s>
  <s xml:id="echoid-s6446" xml:space="preserve">Numeretur à puncto B, in vtramque partẽ arcus ſemidiurnus, nimirũ hor. </s>
  <s xml:id="echoid-s6447" xml:space="preserve">5. </s>
  <s xml:id="echoid-s6448" xml:space="preserve">in dato exem <lb/>plo. </s>
  <s xml:id="echoid-s6449" xml:space="preserve">Deinde per extremitates horum arcuum ſemidiurnorum ducatur recta linea ſecans rectam <lb/>B D, in puncto, per quod ſi agatur ipſi H I, parallela, conſtituens nimirum cum B D, angulum cõ-<lb/>plementi altitudinis poli angulo B G H, æqualem, ſecabitur recta A P, in puncto, ad quod ducta <lb/>recta ex B, continebit cum recta B D, angulum declinationis quæſitum, qui omnino æqualis erit <lb/>angulo P D K, vel P B K. </s>
  <s xml:id="echoid-s6450" xml:space="preserve">Atque ſic de cæteris. </s>
  <s xml:id="echoid-s6451" xml:space="preserve">Exemplum huius inuenies in ſecunda figura ſcho-
<pb o="107" file="0127" n="127" rhead="LIBER PRIMVS."/>
lij ſequentis. </s>
  <s xml:id="echoid-s6452" xml:space="preserve">Sed tamen præſtat inuenire declinationes parallelorum Borealium. </s>
  <s xml:id="echoid-s6453" xml:space="preserve">Nam horũ de-<lb/>clinationes æquales ſunt declinationibus reſpondentium parallelorum auſtralium. </s>
  <s xml:id="echoid-s6454" xml:space="preserve">Vt declinatio <lb/>paralleli borealis, cuius arcus diurnus continet horas 14. </s>
  <s xml:id="echoid-s6455" xml:space="preserve">æqualis eſt declinationi paralleli auſtra-<lb/>lis, cuius arcus diurnus horas 10. </s>
  <s xml:id="echoid-s6456" xml:space="preserve">complectitur, nempe qui cum illo horas 24. </s>
  <s xml:id="echoid-s6457" xml:space="preserve">conſtituit. </s>
  <s xml:id="echoid-s6458" xml:space="preserve">Nam ar-<lb/>cus nocturnus E D F, paralleli borealis, cuius diameter B D, declinationemq́; </s>
  <s xml:id="echoid-s6459" xml:space="preserve">habens D M, æqua-<lb/>lis eſt, per propoſ. </s>
  <s xml:id="echoid-s6460" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6461" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6462" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6463" xml:space="preserve">Theodoſii, arcui diurno paralleli auſtralis, qui priori ęqnalis eſt, &amp; </s>
  <s xml:id="echoid-s6464" xml:space="preserve">op-<lb/>poſitus, hoc eſt, qui declinationem habet æqualem. </s>
  <s xml:id="echoid-s6465" xml:space="preserve">Vnde inuenta declinatione paralleli borealis, <lb/>habetur etiam declinatio paralleli auſtralis oppoſiti, &amp; </s>
  <s xml:id="echoid-s6466" xml:space="preserve">æqualis, cuius arcus diurnus cum arcu <lb/>diurno illius complet horas 24.</s>
  <s xml:id="echoid-s6467" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s6468" xml:space="preserve">QVONIAM verò modus proxime deſcriptus requirit accuratam diuiſionẽ circuli ABCD, <lb/>
<anchor type="note" xlink:label="note-0127-01a" xlink:href="note-0127-01"/>
in horas, ſemiſſes horarũ, &amp; </s>
  <s xml:id="echoid-s6469" xml:space="preserve">quadrantes, poterimus ex ſinubus idem conſequi ſine vlla diuiſione <lb/>circuli, hac arte. </s>
  <s xml:id="echoid-s6470" xml:space="preserve">Sit Analemma A B C D, cuius centrum E; </s>
  <s xml:id="echoid-s6471" xml:space="preserve">Horizon B D; </s>
  <s xml:id="echoid-s6472" xml:space="preserve">Aequator A C; </s>
  <s xml:id="echoid-s6473" xml:space="preserve">paralle-<lb/>
<anchor type="note" xlink:label="note-0127-02a" xlink:href="note-0127-02"/>
lus ſiue boreus, ſiue auſtrinus H I; </s>
  <s xml:id="echoid-s6474" xml:space="preserve">axis mundi F G, ſecans parallelum in K. </s>
  <s xml:id="echoid-s6475" xml:space="preserve">Deſcribatur ex K, circa <lb/>H I, ſen@icirculus paralleli H M I, cui occurrat axis productus in M. </s>
  <s xml:id="echoid-s6476" xml:space="preserve">Ducatur quoque ex L, ad H I, <lb/>perpendicularis L N, quæ erit communis ſectio paralleli H M I, &amp; </s>
  <s xml:id="echoid-s6477" xml:space="preserve">Horizontis; </s>
  <s xml:id="echoid-s6478" xml:space="preserve">(Quoniã enim tam <lb/>Horizon, quàm parallelus rectus eſt ad Meridianum, erit quoque cõmunis eorum ſectio ad eun-<lb/>
<anchor type="note" xlink:label="note-0127-03a" xlink:href="note-0127-03"/>
dem perpendicularis in puncto L, <lb/>
<anchor type="figure" xlink:label="fig-0127-01a" xlink:href="fig-0127-01"/>
vbi ſe mutuo ſecant, ac proinde &amp; </s>
  <s xml:id="echoid-s6479" xml:space="preserve">ad <lb/>rectam H I, per defin. </s>
  <s xml:id="echoid-s6480" xml:space="preserve">3. </s>
  <s xml:id="echoid-s6481" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6482" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6483" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s6484" xml:space="preserve">Ergo L N, perpendicularis ad H I, <lb/>
<anchor type="note" xlink:label="note-0127-04a" xlink:href="note-0127-04"/>
cõmunis ſectio erit Horizontis &amp; </s>
  <s xml:id="echoid-s6485" xml:space="preserve">pa <lb/>ralleli) atque adeo H N, erit arcus ſe-<lb/>midiurnus dicti paralleli, qui poni-<lb/>tur notus. </s>
  <s xml:id="echoid-s6486" xml:space="preserve">Tandem iungatur recta <lb/>E H. </s>
  <s xml:id="echoid-s6487" xml:space="preserve">Quoniam igitur in triangulo <lb/>E <emph style="sc">K</emph> L, ſi recta E L, ponatur ſinus to-<lb/>tus, recta K L, ſinus eſt anguli K E L, <lb/>altitudinis poli, &amp; </s>
  <s xml:id="echoid-s6488" xml:space="preserve">E K, ſinus anguli <lb/>E L k, complementi altitudinis poli; <lb/></s>
  <s xml:id="echoid-s6489" xml:space="preserve">ſi fiat, vt K L, ſinus altitudinis poli, <lb/>
<anchor type="note" xlink:label="note-0127-05a" xlink:href="note-0127-05"/>
ad E K, ſinum complementi altitudi-<lb/>nis poli, ita K L, quatenus ſinus re-<lb/>ctus arcus M N, quo arcus ſemidiur-<lb/>nus H N, notus, &amp; </s>
  <s xml:id="echoid-s6490" xml:space="preserve">quadrans H M, <lb/>inter ſe differunt, ad aliud, nota fiet <lb/>recta E k, in partibus ſinus totius <lb/>K H, reſpectu cuius K L, ſinus rectus <lb/>eſt arcus M N. </s>
  <s xml:id="echoid-s6491" xml:space="preserve">Quia igitur duo qua-<lb/>drata rectarum E K, k H, quadrato rectæ E H, æqualia ſunt; </s>
  <s xml:id="echoid-s6492" xml:space="preserve">ſi ſimul addantur quadratum ſinus to-<lb/>
<anchor type="note" xlink:label="note-0127-06a" xlink:href="note-0127-06"/>
tius K H, &amp; </s>
  <s xml:id="echoid-s6493" xml:space="preserve">quadratum rectæ E K, notæ iam factæ in partibus ſinus totius K H, notum erit qua-<lb/>
<anchor type="note" xlink:label="note-0127-07a" xlink:href="note-0127-07"/>
dratum rectæ E H, cuius radix quadrata dabit rectam E H, notam in ijſdem partibus ſinus to-<lb/>tius k H. </s>
  <s xml:id="echoid-s6494" xml:space="preserve">Itaque ſi fiat, vt E H, quatenus nota in partibus ſinus totius K H, ad E K, quatenus <lb/>nota eſt in ijſdem partibus, ita E H, quatenus ſinus totus, ad aliud, nota fiet E K, in partibus <lb/>ſinus totius E H. </s>
  <s xml:id="echoid-s6495" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s6496" xml:space="preserve">A H, arcus reſpondens ſinui E k, ex tabula ſinuum cognitus <lb/>erit, nempe declinatio paralleli, cuius arcus diurnus, ac proinde &amp; </s>
  <s xml:id="echoid-s6497" xml:space="preserve">ſemidiurnus H N, no-<lb/>tus ponitur.</s>
  <s xml:id="echoid-s6498" xml:space="preserve"/>
</p>
<div xml:id="echoid-div377" type="float" level="2" n="3">
<note position="left" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">Declinatio pa-<lb/>ralleli, cuius ar-<lb/>cus diutnus ſit <lb/>notus, qua arte <lb/>per ſinus per-<lb/>quiratur.</note>
<note position="right" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0127-01" xlink:href="fig-0127-01a">
    <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0127-01"/>
  </figure>
<note position="left" xlink:label="note-0127-04" xlink:href="note-0127-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0127-05" xlink:href="note-0127-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0127-06" xlink:href="note-0127-06a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0127-07" xlink:href="note-0127-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s6499" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s6500" xml:space="preserve">Sit datus arcus diurnus horarum 14. </s>
  <s xml:id="echoid-s6501" xml:space="preserve">vel 10. </s>
  <s xml:id="echoid-s6502" xml:space="preserve">atque adeo ſemidiurnus arcus <lb/>
<anchor type="note" xlink:label="note-0127-08a" xlink:href="note-0127-08"/>
H N, horarum 7. </s>
  <s xml:id="echoid-s6503" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s6504" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s6505" xml:space="preserve">105. </s>
  <s xml:id="echoid-s6506" xml:space="preserve">vel 75. </s>
  <s xml:id="echoid-s6507" xml:space="preserve">ex quo fiet arcus M N, horæ vnius, nempe grad. <lb/></s>
  <s xml:id="echoid-s6508" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6509" xml:space="preserve">cum quadrans H M, contineat horas 6. </s>
  <s xml:id="echoid-s6510" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s6511" xml:space="preserve">90. </s>
  <s xml:id="echoid-s6512" xml:space="preserve">Si igitur fiat, vt k L, ſinus altitudinis <lb/>poli 66913. </s>
  <s xml:id="echoid-s6513" xml:space="preserve">ad E K, ſinum complementi altitudinis poli 74314. </s>
  <s xml:id="echoid-s6514" xml:space="preserve">ita K L, ſinus arcus M N, quo <lb/>
<anchor type="note" xlink:label="note-0127-09a" xlink:href="note-0127-09"/>
differt arcus ſemidiurnus à quadrãte, nempe in dato exemplo, ſinus arcus grad. </s>
  <s xml:id="echoid-s6515" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6516" xml:space="preserve">qui eſt 25881. <lb/></s>
  <s xml:id="echoid-s6517" xml:space="preserve">ad aliud, inuenietur E K, partium ferè 28744, qualium K L, eſt 25881. </s>
  <s xml:id="echoid-s6518" xml:space="preserve">Quia verò K H, ſinus totus <lb/>earundem partium eſt 100000. </s>
  <s xml:id="echoid-s6519" xml:space="preserve">ſi quadrati numeri ſinuum E K, KH, ſimul addantur, fiet quadra-<lb/>tum rectę E H, partium ferè 10826217536. </s>
  <s xml:id="echoid-s6520" xml:space="preserve">atque adeò recta E H, erit quaſi partium 104049. </s>
  <s xml:id="echoid-s6521" xml:space="preserve"><lb/>reſpectu ſinus totius K H. </s>
  <s xml:id="echoid-s6522" xml:space="preserve">Igitur ſi fiat, vt E H, 104049. </s>
  <s xml:id="echoid-s6523" xml:space="preserve">ad E K, 28744. </s>
  <s xml:id="echoid-s6524" xml:space="preserve">ita E H, ſinus to-<lb/>tus 100000. </s>
  <s xml:id="echoid-s6525" xml:space="preserve">ad aliud, reperietur E K, ſinus declinationis paralleli H I, reſpectu ſinus totius <lb/>E H, partium ferè 27625. </s>
  <s xml:id="echoid-s6526" xml:space="preserve">cuius arcus eſt grad. </s>
  <s xml:id="echoid-s6527" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6528" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6529" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6530" xml:space="preserve">Tanta eſt declinatio paralle-<lb/>
<anchor type="note" xlink:label="note-0127-10a" xlink:href="note-0127-10"/>
li <emph style="sc">H</emph> I, borealis quidem, ſi dies maior eſt 12. </s>
  <s xml:id="echoid-s6531" xml:space="preserve">horis, auſtralis autem, ſi minor. </s>
  <s xml:id="echoid-s6532" xml:space="preserve">Eadem ratio eſt <lb/>in cæteris.</s>
  <s xml:id="echoid-s6533" xml:space="preserve"/>
</p>
<div xml:id="echoid-div378" type="float" level="2" n="4">
<note position="right" xlink:label="note-0127-08" xlink:href="note-0127-08a" xml:space="preserve">Exemplu@.</note>
<note position="left" xlink:label="note-0127-09" xlink:href="note-0127-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0127-10" xlink:href="note-0127-10a" xml:space="preserve">Declinatio pa-<lb/>ralleli, cuius ar-<lb/>cus. diurnus da-<lb/>tus ſit, quo pa-<lb/>cto aliter per ſi-<lb/>nus ſit inuefti-<lb/>gandus.</note>
</div>
<p>
  <s xml:id="echoid-s6534" xml:space="preserve">FACILIVS idem obtinebimus per triangula ſphęrica hoc modo. </s>
  <s xml:id="echoid-s6535" xml:space="preserve">Sit <emph style="sc">H</emph>orizon A B C D; <lb/></s>
  <s xml:id="echoid-s6536" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s6537" xml:space="preserve">Aequator B D, Meridianum ſecans in E; </s>
  <s xml:id="echoid-s6538" xml:space="preserve">parallelus ſiue borealis, ſiue au-
<pb o="108" file="0128" n="128" rhead="GNOMONICES"/>
ſtralis F G, ſecans Meridianum in K, vt ſit arcus ſemidiurnus datus F k. </s>
  <s xml:id="echoid-s6539" xml:space="preserve">Per puncta <emph style="sc">H</emph>, &amp; </s>
  <s xml:id="echoid-s6540" xml:space="preserve">F, quorũ <lb/><emph style="sc">H</emph>, ſit polus arcticus, ducatur per propoſ. </s>
  <s xml:id="echoid-s6541" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6542" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6543" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6544" xml:space="preserve">Theodoſii, circulus maximus <emph style="sc">H</emph> F, ſecans Ae-<lb/>quatorem in I. </s>
  <s xml:id="echoid-s6545" xml:space="preserve">Erit arcus Aequatoris I E, ſimilis arcui ſemidiurno dato F K, ex propoſ. </s>
  <s xml:id="echoid-s6546" xml:space="preserve">10. </s>
  <s xml:id="echoid-s6547" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6548" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s6549" xml:space="preserve">Theodoſij, ac propterea notus, totidem videlicet graduum, quot arcus F K, cõplectitur. </s>
  <s xml:id="echoid-s6550" xml:space="preserve">Et quoniã <lb/>I E, arcus eſt anguli I <emph style="sc">H</emph> E, quòd arcus <emph style="sc">H</emph> E, <emph style="sc">H</emph> I, ex coroll. </s>
  <s xml:id="echoid-s6551" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s6552" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6553" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6554" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6555" xml:space="preserve">Theodoſij quadrantes <lb/>ſint; </s>
  <s xml:id="echoid-s6556" xml:space="preserve">erit angulus I <emph style="sc">H</emph> E, totidem graduum, quot arcus ſemidiurnus datus continet. </s>
  <s xml:id="echoid-s6557" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s6558" xml:space="preserve"><lb/>reliquus duorum rectorum (qui grad. </s>
  <s xml:id="echoid-s6559" xml:space="preserve">180. </s>
  <s xml:id="echoid-s6560" xml:space="preserve">continent) I <emph style="sc">H</emph> C, notus erit. </s>
  <s xml:id="echoid-s6561" xml:space="preserve">Quoniam igitur in <lb/>triangulo ſphærico C F <emph style="sc">H</emph>, angulus C, rectus eſt; </s>
  <s xml:id="echoid-s6562" xml:space="preserve">(Meridianus enim A C, per polum Hori-<lb/>zontis ductus ad Horizontem rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s6563" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6564" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6565" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6566" xml:space="preserve">Theodoſii) &amp; </s>
  <s xml:id="echoid-s6567" xml:space="preserve">nullus arcuum <lb/>quadrans eſt; </s>
  <s xml:id="echoid-s6568" xml:space="preserve">(propterea quòd C <emph style="sc">H</emph>, arcus altitudinis poli minor ſemper eſt quadrante; </s>
  <s xml:id="echoid-s6569" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6570" xml:space="preserve">C B, <lb/>
<anchor type="note" xlink:label="note-0128-01a" xlink:href="note-0128-01"/>
arcus Horizontis inter Meridianum, &amp; </s>
  <s xml:id="echoid-s6571" xml:space="preserve">Aequatorem quadrans, ac proinde, ſi parallelus eſt Septen <lb/>trionalis, arcus C F, minor quadrãte, vel ſi parallelus eſt auſtralis, quadrante maior; </s>
  <s xml:id="echoid-s6572" xml:space="preserve">ſimiliter arcus <lb/>H I, inter polum, &amp; </s>
  <s xml:id="echoid-s6573" xml:space="preserve">Aequatorem quadrans, &amp; </s>
  <s xml:id="echoid-s6574" xml:space="preserve">idcirco H F, in parallelo boreali quadrante minor, <lb/>
<anchor type="figure" xlink:label="fig-0128-01a" xlink:href="fig-0128-01"/>
in auſtrali verò maior quadrante) erit per propoſ. <lb/></s>
  <s xml:id="echoid-s6575" xml:space="preserve">18. </s>
  <s xml:id="echoid-s6576" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6577" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6578" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6579" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6580" xml:space="preserve">de triangulis, vel per pro <lb/>poſ. </s>
  <s xml:id="echoid-s6581" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6582" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6583" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6584" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s6585" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6586" xml:space="preserve">noſtrorum <lb/>triangulorum ſphęricorum, vt ſinus anguli C H F, <lb/>noti ad ſinum totum, ita ſinus complementi an-<lb/>guli C F H, ad ſinum complementi arcus C H: </s>
  <s xml:id="echoid-s6587" xml:space="preserve"><lb/>Et conuertendo, vt ſinus totus ad ſinum anguli <lb/>
<anchor type="note" xlink:label="note-0128-02a" xlink:href="note-0128-02"/>
C H F, noti, ita ſinus complementi arcus C H, al-<lb/>titudinis poli, ad ſinum cõplementi anguli C F H. <lb/></s>
  <s xml:id="echoid-s6588" xml:space="preserve">Cum ergo priora tria ſint cognita, cognoſcetur &amp; </s>
  <s xml:id="echoid-s6589" xml:space="preserve"><lb/>quartum, nempe ſinus complementi anguli CFH, <lb/>ex regula proportionum; </s>
  <s xml:id="echoid-s6590" xml:space="preserve">atque adeo &amp; </s>
  <s xml:id="echoid-s6591" xml:space="preserve">comple-<lb/>mentum anguli ex tabula ſinuum, &amp; </s>
  <s xml:id="echoid-s6592" xml:space="preserve">angulus ipſe <lb/>C F H, &amp; </s>
  <s xml:id="echoid-s6593" xml:space="preserve">ei oppoſitus (ſi parallelus eſt borealis) <lb/>I F B, notus erit. </s>
  <s xml:id="echoid-s6594" xml:space="preserve">Rurſus cum in triangulo ſphæri-<lb/>co B F I, angulus B F I, notus ſit, &amp; </s>
  <s xml:id="echoid-s6595" xml:space="preserve">angulus F B I, <lb/>altitudini Aequatoris ſupra Horizontem æqualis, <lb/>
<anchor type="note" xlink:label="note-0128-03a" xlink:href="note-0128-03"/>
hoc eſt, complemento altitudinis poli; </s>
  <s xml:id="echoid-s6596" xml:space="preserve">ſitq́; </s>
  <s xml:id="echoid-s6597" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s6598" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6599" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6600" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6601" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6602" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6603" xml:space="preserve">de triangulis, <lb/>vel per propoſ. </s>
  <s xml:id="echoid-s6604" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6605" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6606" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6607" xml:space="preserve">Gebri, vel certè per propoſ. </s>
  <s xml:id="echoid-s6608" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6609" xml:space="preserve">noſtrorum triangulorum ſphæricorum, <lb/>vt ſinus arcus I B, noti (eſt enim I B, differen tia inter arcum ſemidiurnum I E, datum, &amp; </s>
  <s xml:id="echoid-s6610" xml:space="preserve">quadran <lb/>tem B E) ad ſinum anguli B F I, noti, ita ſinus arcus I F, ad ſinum anguli I B F, altitudinis Aequa-<lb/>toris: </s>
  <s xml:id="echoid-s6611" xml:space="preserve">Et conuertendo, vt ſinus anguli B F I, noti ad ſinum arcus I B, noti, ita ſinus anguli I B F, <lb/>noti ad ſinum arcus I F; </s>
  <s xml:id="echoid-s6612" xml:space="preserve">fiet ex tribus prioribus notis etiam quartum notum, ex regula proportio-<lb/>num, nimirum ſinus arcus I F, declinationis paralleli propoſiti; </s>
  <s xml:id="echoid-s6613" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s6614" xml:space="preserve">ipſe arcus decli-<lb/>nationis I F, notus fiet.</s>
  <s xml:id="echoid-s6615" xml:space="preserve"/>
</p>
<div xml:id="echoid-div379" type="float" level="2" n="5">
<note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0128-01" xlink:href="fig-0128-01a">
    <image file="0128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0128-01"/>
  </figure>
<note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0128-03" xlink:href="note-0128-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s6616" xml:space="preserve">ITAQVE ſi fiat, vt ſinus totus ad ſinum arcus, quo arcus ſemidiurnus datus à ſemicirculo <lb/>differt, hoc eſt, ad ſinum anguli C H F, (qui cum E H I, angulo arcus ſemidiurni duos rectos an-<lb/>
<anchor type="note" xlink:label="note-0128-04a" xlink:href="note-0128-04"/>
gulos conficit) ita ſinus complementi arcus C H, altitudinis poli ad aliud, inuenietur ſinus com-<lb/>plementi anguli C F H, vel I F B; </s>
  <s xml:id="echoid-s6617" xml:space="preserve">ac idcirco complementum ipſius anguli notum erit, &amp; </s>
  <s xml:id="echoid-s6618" xml:space="preserve">ex hoc an <lb/>gulus ipſe I F B. </s>
  <s xml:id="echoid-s6619" xml:space="preserve">Quòd ſi rurſus fiat, vt ſinus anguli I F B, iam noti, ad ſinum arcus I B, quo arcus <lb/>ſemidiurnus à quadrante differt, ita ſinus altitudinis Aequatoris, vel complementi altitudinis po <lb/>li, nempe anguli I B F, ad aliud, notus efficietur ſinus arcus I F, declinationis paralleli F G, quæſi-<lb/>tæ; </s>
  <s xml:id="echoid-s6620" xml:space="preserve">ac proinde ex tabula ſinuum, &amp; </s>
  <s xml:id="echoid-s6621" xml:space="preserve">ipſa declinatio nota euadet.</s>
  <s xml:id="echoid-s6622" xml:space="preserve"/>
</p>
<div xml:id="echoid-div380" type="float" level="2" n="6">
<note position="left" xlink:label="note-0128-04" xlink:href="note-0128-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s6623" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s6624" xml:space="preserve">Sit rurſus datus arcus diurnus horarum 14. </s>
  <s xml:id="echoid-s6625" xml:space="preserve">vel 10. </s>
  <s xml:id="echoid-s6626" xml:space="preserve">ac proinde ſemidiurnus <lb/>
<anchor type="note" xlink:label="note-0128-05a" xlink:href="note-0128-05"/>
I E, horarum 7. </s>
  <s xml:id="echoid-s6627" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s6628" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s6629" xml:space="preserve">105. </s>
  <s xml:id="echoid-s6630" xml:space="preserve">vel 75. </s>
  <s xml:id="echoid-s6631" xml:space="preserve">Vnde arcus I B, continebit vnam horam, hoc eſt, <lb/>grad. </s>
  <s xml:id="echoid-s6632" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6633" xml:space="preserve">Si igitur fiat, vt 100000. </s>
  <s xml:id="echoid-s6634" xml:space="preserve">ſinus totus, ad 96592. </s>
  <s xml:id="echoid-s6635" xml:space="preserve">ſinum anguli C H F, (cum enim arcus <lb/>I E, comprehendat horas 7. </s>
  <s xml:id="echoid-s6636" xml:space="preserve">ſiue grad. </s>
  <s xml:id="echoid-s6637" xml:space="preserve">105. </s>
  <s xml:id="echoid-s6638" xml:space="preserve">loquimur enim de parallelo boreali, comprehendet re-<lb/>
<anchor type="note" xlink:label="note-0128-06a" xlink:href="note-0128-06"/>
liquus arcus ſemicirculi horas quinque, hoc eſt, grad. </s>
  <s xml:id="echoid-s6639" xml:space="preserve">75. </s>
  <s xml:id="echoid-s6640" xml:space="preserve">quibus predictus ſinus 96592. </s>
  <s xml:id="echoid-s6641" xml:space="preserve">debetur. <lb/></s>
  <s xml:id="echoid-s6642" xml:space="preserve">Quòd ſi de parallelo auſtrali ſit ſermo, erit arcus I E, horarum 5. </s>
  <s xml:id="echoid-s6643" xml:space="preserve">ſiue grad. </s>
  <s xml:id="echoid-s6644" xml:space="preserve">75. </s>
  <s xml:id="echoid-s6645" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6646" xml:space="preserve">reliquus ex ſemi-<lb/>circulo horatum 7. </s>
  <s xml:id="echoid-s6647" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s6648" xml:space="preserve">105. </s>
  <s xml:id="echoid-s6649" xml:space="preserve">quibus idem ſinus reſpondet) ita 74314. </s>
  <s xml:id="echoid-s6650" xml:space="preserve">ſinus complemen-<lb/>ti arcus C H, altitudinis poli, ad aliud, inuenietur ſinus complementi anguli C F H, vel I F B, <lb/>71781. </s>
  <s xml:id="echoid-s6651" xml:space="preserve">cui reſpondet arcus grad. </s>
  <s xml:id="echoid-s6652" xml:space="preserve">45. </s>
  <s xml:id="echoid-s6653" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6654" xml:space="preserve">52. </s>
  <s xml:id="echoid-s6655" xml:space="preserve">Huius complementum grad. </s>
  <s xml:id="echoid-s6656" xml:space="preserve">44. </s>
  <s xml:id="echoid-s6657" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6658" xml:space="preserve">8. </s>
  <s xml:id="echoid-s6659" xml:space="preserve">erit quan-<lb/>titas anguli I F B. </s>
  <s xml:id="echoid-s6660" xml:space="preserve">Si ergo rurſus fiat, vt 69633. </s>
  <s xml:id="echoid-s6661" xml:space="preserve">ſinus anguli I F B, ad 25881, ſinum arcus I B, grad. </s>
  <s xml:id="echoid-s6662" xml:space="preserve"><lb/>15. </s>
  <s xml:id="echoid-s6663" xml:space="preserve">ita 74314. </s>
  <s xml:id="echoid-s6664" xml:space="preserve">ſinus anguli IBF, vel altitudinis Aequatoris, ad aliud, reperietur ſinus arcus decli-<lb/>nationis I F, 27621. </s>
  <s xml:id="echoid-s6665" xml:space="preserve">ferè. </s>
  <s xml:id="echoid-s6666" xml:space="preserve">Quare arcus ipſe declinationis I F, continebit grad. </s>
  <s xml:id="echoid-s6667" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6668" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6669" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6670" xml:space="preserve">ferè, ſicu-<lb/>ti prius. </s>
  <s xml:id="echoid-s6671" xml:space="preserve">Eodem pacto deprehendemus parallelum, cuius arcus diurnus contineat horas 15. </s>
  <s xml:id="echoid-s6672" xml:space="preserve">vel <lb/>9. </s>
  <s xml:id="echoid-s6673" xml:space="preserve">declinationẽ habere grad. </s>
  <s xml:id="echoid-s6674" xml:space="preserve">23. </s>
  <s xml:id="echoid-s6675" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6676" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6677" xml:space="preserve">ferè, &amp; </s>
  <s xml:id="echoid-s6678" xml:space="preserve">ſic de cęteris. </s>
  <s xml:id="echoid-s6679" xml:space="preserve">Quocirca dato arcu diurno, &amp; </s>
  <s xml:id="echoid-s6680" xml:space="preserve">lati <lb/>tudine loci, declinationẽ paralleli illius arcus ab Aequatore inquiſiuimus. </s>
  <s xml:id="echoid-s6681" xml:space="preserve">Quod faciendũ erat.</s>
  <s xml:id="echoid-s6682" xml:space="preserve"/>
</p>
<div xml:id="echoid-div381" type="float" level="2" n="7">
<note position="left" xlink:label="note-0128-05" xlink:href="note-0128-05a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0128-06" xlink:href="note-0128-06a" xml:space="preserve">50</note>
</div>
<pb o="109" file="0129" n="129" rhead="LIBER PRIMVS."/>
</div>
<div xml:id="echoid-div383" type="section" level="1" n="133">
<head xml:id="echoid-head136" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s6683" xml:space="preserve">ANDREAS Schonerus in opere, quod Gnomonicen inſcripſit, inueſtigat declinationes datorum <lb/>
<anchor type="note" xlink:label="note-0129-01a" xlink:href="note-0129-01"/>
arcuum diurnorum hoc modo. </s>
  <s xml:id="echoid-s6684" xml:space="preserve">Ex centro A, interualloq́, cuiuslibet rectę<unsure/> A B, circulus deſcribatur, vel <lb/>certè eius portio, ſumantur{q́ue} duo arcus B C, B D, ęquales complemento altitudinis poli, ita vt ſi A B, <lb/>ponatur communis ſectio Aequatoris, <lb/>
<anchor type="figure" xlink:label="fig-0129-01a" xlink:href="fig-0129-01"/>
&amp; </s>
  <s xml:id="echoid-s6685" xml:space="preserve">Meridiani C B D, arcus B C, B D, <lb/>ſint declinationes duorũ parallelorum, <lb/>@uorum alter maximus eſt eorum, qui <lb/>
<anchor type="note" xlink:label="note-0129-02a" xlink:href="note-0129-02"/>
ſemper apparent, habet{q́ue} arcum diur-<lb/>num horarum 24. </s>
  <s xml:id="echoid-s6686" xml:space="preserve">cum totus extet ſupra <lb/>Horizontem, alter verò maximus ec-<lb/>rum, qui ſemper occultantur, habet{q́ue} <lb/>arcum diurnum boræ o. </s>
  <s xml:id="echoid-s6687" xml:space="preserve">cum totus ſub <lb/>Horizonte lateat. </s>
  <s xml:id="echoid-s6688" xml:space="preserve">Ducta iam recta C D, <lb/>quæ ipſam A B, ſecet in E, erunt rectæ <lb/>E C, E D, æquales, &amp; </s>
  <s xml:id="echoid-s6689" xml:space="preserve">anguli ad E, re-<lb/>cti. </s>
  <s xml:id="echoid-s6690" xml:space="preserve">quod oſtendemus ea demonſtratione <lb/>qua in propoſ. </s>
  <s xml:id="echoid-s6691" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6692" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s6693" xml:space="preserve">vſi ſumus ad <lb/>probandum, rectam M N, in Analem-<lb/>
<anchor type="note" xlink:label="note-0129-03a" xlink:href="note-0129-03"/>
mate ſecari bifariam, anguloſ{q́ue} ad O, <lb/>rectos eſſe. </s>
  <s xml:id="echoid-s6694" xml:space="preserve">Deſcripto deinde ex centro <lb/>F, interuallo{q́ue} E C, vel E D, circulo, <lb/>eo{q́ue} diuiſo in partes 48. </s>
  <s xml:id="echoid-s6695" xml:space="preserve">æquales, con-<lb/>nectantur quælibet duo puncta a puncto C, vel D, æquè remota lineis rectis, &amp; </s>
  <s xml:id="echoid-s6696" xml:space="preserve">per puncta, qui-<lb/>bus illæ rectam C D, ſecant, ex A, rectæ educantur vſque ad circunferentiam C B D. </s>
  <s xml:id="echoid-s6697" xml:space="preserve">Hæ enim abſc<unsure/>in-<lb/>dent arcus declinationum omnium arcuum diurnorum, initio ſumpto ab arcu horarum 24. </s>
  <s xml:id="echoid-s6698" xml:space="preserve">vſque ad ar <lb/>cum horæ o. </s>
  <s xml:id="echoid-s6699" xml:space="preserve">vt numeri in figura deſcripti indicant. </s>
  <s xml:id="echoid-s6700" xml:space="preserve">Huius praxis demonſtrationem Andre{as} Schonerus <lb/>non affert, multis tamen experimentis comprobaui, angulos declinationum hac arte inuentos æquales eſſe <lb/>angulis declinationum ex noſtra demonſtratione repertis</s>
</p>
<div xml:id="echoid-div383" type="float" level="2" n="1">
<note position="right" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">Declinationes <lb/>omnium arcuũ <lb/>diurnorũ, qua <lb/>ratione ab An-<lb/>drea Schonero <lb/>inquirantur.</note>
  <figure xlink:label="fig-0129-01" xlink:href="fig-0129-01a">
    <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-01"/>
  </figure>
<note position="left" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s6701" xml:space="preserve">APPELLABIMVS autẽ in ſequentibus lineas in figura hac Andreæ Schoneri ex A, e<unsure/>miſſ{as}, <lb/>vel ex B, cadentes in ſequenti noſtra figura, radios arcuum diurnorũ; </s>
  <s xml:id="echoid-s6702" xml:space="preserve">quoniam exiſtente Sole in parallelis, <lb/>quorum declinationes indicantur à dictis rectis, repreſentant radios, quos Sol per centrum mundi proĳ-<lb/>cit, qucmadmodum propoſ. </s>
  <s xml:id="echoid-s6703" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6704" xml:space="preserve">de radĳs ſignorum diximus, qui quidem declinationes eorundem ſignorum <lb/>commonſtrant. </s>
  <s xml:id="echoid-s6705" xml:space="preserve">Radius autem arc{us} diurni horarum 12. </s>
  <s xml:id="echoid-s6706" xml:space="preserve">idem eſt, qui radius Aequatoris, vt patet.</s>
  <s xml:id="echoid-s6707" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s6708" xml:space="preserve">CAETERVM ſatis erit vt plurimum, ſi inueſtigentur declinationes illorum arcuum diurnorum, <lb/>qui inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s6709" xml:space="preserve">parallelum ♋, cõtinentur; </s>
  <s xml:id="echoid-s6710" xml:space="preserve">vt Romæ arcuũ horarum 13. </s>
  <s xml:id="echoid-s6711" xml:space="preserve">14. </s>
  <s xml:id="echoid-s6712" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6713" xml:space="preserve">Nam hæ decli <lb/>nationes æquales ſunt declinationibus arcuum diurnorum, qui inter Aequatorem &amp; </s>
  <s xml:id="echoid-s6714" xml:space="preserve">parallelum ♑, collo <lb/>cantur, nimirum horarum 11. </s>
  <s xml:id="echoid-s6715" xml:space="preserve">10. </s>
  <s xml:id="echoid-s6716" xml:space="preserve">9. </s>
  <s xml:id="echoid-s6717" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6718" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6719" xml:space="preserve">Reliquorum autem arcuum diurnorum, qui extra tropicos po-<lb/>nuntur, nullus eſt vſ{us} in horologĳs, exceptis paucis quibuſdam, qui ad deſcriptionem linearum horaria-<lb/>
<anchor type="note" xlink:label="note-0129-05a" xlink:href="note-0129-05"/>
rum ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s6720" xml:space="preserve">horarum inæqualium requiruntur, cuiuſmodi ſunt maximè radĳ arcuum diur <lb/>norum, qui hor{as} 24. </s>
  <s xml:id="echoid-s6721" xml:space="preserve">0. </s>
  <s xml:id="echoid-s6722" xml:space="preserve">18. </s>
  <s xml:id="echoid-s6723" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6724" xml:space="preserve">6. </s>
  <s xml:id="echoid-s6725" xml:space="preserve">complectuntur, vt ſuo loco monebimus.</s>
  <s xml:id="echoid-s6726" xml:space="preserve"/>
</p>
<div xml:id="echoid-div384" type="float" level="2" n="2">
<note position="left" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s6727" xml:space="preserve">QVOD ſi fortè ſuſpecta cuipiam videatur hęc Andreæ Schoneri operatio, tropterea quòd, licet bre-<lb/>uis illa quidem ſit, ac facilis, nulla tamen Geometrica ratione ſtabiliatur, poterimus ex noſtra demonſtra <lb/>tione, eadem fere breuitate, ac facilitate figuram construere ſimilem illi, quam ipſe deſcripſit, quæ nimi-<lb/>rum contineat declinationes omnium ar cuum diurnorum, hac ratione. </s>
  <s xml:id="echoid-s6728" xml:space="preserve">Deſcribatur ex centro P, circulus <lb/>
<anchor type="note" xlink:label="note-0129-06a" xlink:href="note-0129-06"/>
A B C D, cuiuſcũ magnitudinis, qui, ductis prius in eo duabus diametris A C, B D, ſeſe in centro P, ad <lb/>angulos rectos ſecantibus, diuidatur in 48. </s>
  <s xml:id="echoid-s6729" xml:space="preserve">partes ęquales, initio facto a puncto B. </s>
  <s xml:id="echoid-s6730" xml:space="preserve">Deinde bina puncta æ-<lb/>qualiter a puncto B, remota lineis rectis iungantur, quæ diametrum C D, ſecabunt in punctis, @er quæ ſi <lb/>rectæ ducantur conſtituentes cum B D, angulos complemento altitudinis poli æquales, ſecabitur diame-<lb/>
<anchor type="note" xlink:label="note-0129-07a" xlink:href="note-0129-07"/>
ter A C, (producenda autem ea erit, cum comolementum alritudinis poli maius est, quàm grad. </s>
  <s xml:id="echoid-s6731" xml:space="preserve">45.) </s>
  <s xml:id="echoid-s6732" xml:space="preserve">in <lb/>punctis, per quæ ſi ex B, rectæ emittantur, auferent hæ ex arcu ex centro B, deſcripto arcus declinatio-<lb/>num omnium arcuum diurnorum, vt in figura Andreæ Schoneri, ita vt anguli, qu{as} eædem rectæ cum <lb/>B D, ad B, constituunt, ſint anguli declinationum: </s>
  <s xml:id="echoid-s6733" xml:space="preserve">quemadmodum in prima figura huius propoſ. </s>
  <s xml:id="echoid-s6734" xml:space="preserve">de-<lb/>monſtratum eſt.</s>
  <s xml:id="echoid-s6735" xml:space="preserve"/>
</p>
<div xml:id="echoid-div385" type="float" level="2" n="3">
<note position="right" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">Declinationes <lb/>omnium arcuũ <lb/>diurnorũ, quo <lb/>modo ex noſt@a <lb/>demonſtratio-<lb/>ne reperiantur.</note>
<note position="left" xlink:label="note-0129-07" xlink:href="note-0129-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s6736" xml:space="preserve">ITA autem ſine magno labore rectas ill{as} per puncta rectæ B D, ducemus, quæ cum ea angulos cõ <lb/>plemento altitudinis poli conſtituant æquales. </s>
  <s xml:id="echoid-s6737" xml:space="preserve">Ex D, ad ſiniſtram rectæ B D, deſcribatur arcus circuli, in <lb/>quo arecta B D, complementum altitudinis poli computetur, &amp; </s>
  <s xml:id="echoid-s6738" xml:space="preserve">per finẽ ſupput ationis ducta recta D E, <lb/>agatur per quodcunq; </s>
  <s xml:id="echoid-s6739" xml:space="preserve">ei{us} punctũ E, ipſi B D, parallela E O, in quam omnia puncta rectę D B, transferan <lb/>tur, initio facto a recta D E. </s>
  <s xml:id="echoid-s6740" xml:space="preserve">Nam ſi puncta in vtraque linea D B, E O, reſpondentia, quæ nimirum ęqua <lb/>liter diſtant a punctis D, E, coniungantur rectis occultis, erunt hæ omnes ipſi D E, parallelæ; </s>
  <s xml:id="echoid-s6741" xml:space="preserve">atque adeo <lb/>
<anchor type="note" xlink:label="note-0129-08a" xlink:href="note-0129-08"/>
<pb o="110" file="0130" n="130" rhead="GNOMONICES"/>
<anchor type="figure" xlink:label="fig-0130-01a" xlink:href="fig-0130-01"/>
<anchor type="note" xlink:label="note-0130-01a" xlink:href="note-0130-01"/>
<anchor type="note" xlink:label="note-0130-02a" xlink:href="note-0130-02"/>
<anchor type="note" xlink:label="note-0130-03a" xlink:href="note-0130-03"/>
cum B D, angulos angulo B D E, hoc eſt, cõplemento altitudinis poli ęquales conſtituent. </s>
  <s xml:id="echoid-s6742" xml:space="preserve">Numeri in no-<lb/>
<anchor type="note" xlink:label="note-0130-04a" xlink:href="note-0130-04"/>
ſtra hac figura ĳdem ſunt, qui in figura Andreę Schoneri. </s>
  <s xml:id="echoid-s6743" xml:space="preserve">Satis autẽ eſt, ſi recta E O, æqualis ſumatur ipſi <lb/>D P. </s>
  <s xml:id="echoid-s6744" xml:space="preserve">Nam puncta inuenta in recta P C, translata in rectam P A, initio ſemper facto a puncto P, dabunt <lb/>etiam puncta in recta P A, per quæ lineę declinationum ducendę ſunt; </s>
  <s xml:id="echoid-s6745" xml:space="preserve">propterea quòd dictæ parallelæ ais <lb/>ferunt ex P A, ſegmenta æqualia reſpondentibus ſegmentis rectæ P C: </s>
  <s xml:id="echoid-s6746" xml:space="preserve">nempe rectam P I, æqualem re-<lb/>ctæ P K, &amp; </s>
  <s xml:id="echoid-s6747" xml:space="preserve">c. </s>
  <s xml:id="echoid-s6748" xml:space="preserve">Quoniam enim in triangulis I L P, K G P, anguli alterni L, G, inter parallelas I L, G K, <lb/>
<anchor type="note" xlink:label="note-0130-05a" xlink:href="note-0130-05"/>
æquales ſunt, &amp; </s>
  <s xml:id="echoid-s6749" xml:space="preserve">anguli ad P, recti; </s>
  <s xml:id="echoid-s6750" xml:space="preserve">ſunt autem &amp; </s>
  <s xml:id="echoid-s6751" xml:space="preserve">latera P L, P G, æqualia; </s>
  <s xml:id="echoid-s6752" xml:space="preserve">(Nam recta ducta M E, <lb/>
<anchor type="note" xlink:label="note-0130-06a" xlink:href="note-0130-06"/>
ſecabitur in N, bifariam, propter æquales arcus A M, A E: </s>
  <s xml:id="echoid-s6753" xml:space="preserve">quod eadem demonſtratione probari po-<lb/>teſt, qua vſi ſumus in propoſ. </s>
  <s xml:id="echoid-s6754" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6755" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s6756" xml:space="preserve">ad oſtendendum, rectam M N, in Analemmate bifariam ſecari <lb/>in O. </s>
  <s xml:id="echoid-s6757" xml:space="preserve">Cum ergo in parallelogrammis P M, P E, latera P L, P G, oppoſitis lateribus N M, N E, ęqua <lb/>
<anchor type="note" xlink:label="note-0130-07a" xlink:href="note-0130-07"/>
lia ſint, æquales erunt etiam rectæ P L, P G.) </s>
  <s xml:id="echoid-s6758" xml:space="preserve">erunt quoque latera P I, P K, inter ſe æqualia.</s>
  <s xml:id="echoid-s6759" xml:space="preserve"/>
</p>
<div xml:id="echoid-div386" type="float" level="2" n="4">
<note position="right" xlink:label="note-0129-08" xlink:href="note-0129-08a" xml:space="preserve">33. primi.</note>
  <figure xlink:label="fig-0130-01" xlink:href="fig-0130-01a">
    <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0130-01"/>
  </figure>
<note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0130-03" xlink:href="note-0130-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0130-04" xlink:href="note-0130-04a" xml:space="preserve">2@. primi.</note>
<note position="left" xlink:label="note-0130-05" xlink:href="note-0130-05a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0130-06" xlink:href="note-0130-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0130-07" xlink:href="note-0130-07a" xml:space="preserve">34. primi.</note>
</div>
<note position="left" xml:space="preserve">26. primi.</note>
<p style="it">
  <s xml:id="echoid-s6760" xml:space="preserve">QVEMADMODVM autem propoſ. </s>
  <s xml:id="echoid-s6761" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6762" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6763" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6764" xml:space="preserve">hui{us} lib. </s>
  <s xml:id="echoid-s6765" xml:space="preserve">tabul{as} cõfecimus AEQVINO-<lb/>CTIALIS LINEAE, LINEAE XXIIII. </s>
  <s xml:id="echoid-s6766" xml:space="preserve">ABORTV, VEL OCC ASV, &amp; </s>
  <s xml:id="echoid-s6767" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s6768" xml:space="preserve">vt intelligeremus, quænam horæ ab ortu uel occaſu, &amp; </s>
  <s xml:id="echoid-s6769" xml:space="preserve">à meridie vel media nocte ſe mutuo ſecent in vno <lb/>
<anchor type="note" xlink:label="note-0130-09a" xlink:href="note-0130-09"/>
eodem{q́ue} puncto illarum linearũ, ita hic proponemus octo alias tabulas arcuũ diurnorum, &amp; </s>
  <s xml:id="echoid-s6770" xml:space="preserve">nocturnorũ, <lb/>vt ſciamus, quænam horæ ab ortu vel occaſu, et à meridic vel media nocte ſe mutuo ſecent in vno eodem{q́ue} <lb/>puncto illorum ar cuum in quouis horologio deſcriptorum. </s>
  <s xml:id="echoid-s6771" xml:space="preserve">Plurimum enim hæc res conducet ad deſcriptio <lb/>
<anchor type="note" xlink:label="note-0130-10a" xlink:href="note-0130-10"/>
nem tam horarum ab ortu, &amp; </s>
  <s xml:id="echoid-s6772" xml:space="preserve">occaſu, quàm inęqualium, vt ſuo loco manifestum erit. </s>
  <s xml:id="echoid-s6773" xml:space="preserve">Constructio autem <lb/>barum tabularũ ex arcubus diurnis, nocturniſq́, depromitur, vt ex ĳs, quę mox dicemus, colligi poteſt. </s>
  <s xml:id="echoid-s6774" xml:space="preserve">In <lb/>hiſce. </s>
  <s xml:id="echoid-s6775" xml:space="preserve">n. </s>
  <s xml:id="echoid-s6776" xml:space="preserve">tabulis quelibet horæ vel ternæ vel binæ ſe mutuo ſecant in vno eodem{q́ue} puncto arcus illius diur-<lb/>ni, vel nocturni, quitabulę, in qua deſcriptæ ſunt, præponitur; </s>
  <s xml:id="echoid-s6777" xml:space="preserve">ita vt in quibus punctis horę aſtronomicæ, <lb/>ſiue a mer. </s>
  <s xml:id="echoid-s6778" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s6779" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s6780" xml:space="preserve">arcum diurnum, nocturnumue cuiuſuis tabulæ ſecant, in ĳſdem omnino eundẽ ſe-<lb/>cent horę ab ortu, vel occaſu, quę illis horis aſtronomicis, ſiue a mer. </s>
  <s xml:id="echoid-s6781" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s6782" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s6783" xml:space="preserve">poſitę ſunt ad dexterã, <lb/>vel ſiniſtram. </s>
  <s xml:id="echoid-s6784" xml:space="preserve">Quod facile quiuis intelliget, ſi diligenter conſideret, qua hora à meridie, vel media nocte, <lb/>&amp; </s>
  <s xml:id="echoid-s6785" xml:space="preserve">ab ortu, vel occaſu Sol oriatur in propoſito arcu diurno, aut in nocturno occidat. </s>
  <s xml:id="echoid-s6786" xml:space="preserve">Quoniam enim (vt <lb/>paucis aperiam, quo artificio ex ar cubus diurnis, nocturniſq́, huiuſmodi tabulæ ſint compoſitæ.) </s>
  <s xml:id="echoid-s6787" xml:space="preserve">die conti-<lb/>nente horas 10. </s>
  <s xml:id="echoid-s6788" xml:space="preserve">Sol oritur hora 7. </s>
  <s xml:id="echoid-s6789" xml:space="preserve">à media nocte, vt ſuperſint horæ 5. </s>
  <s xml:id="echoid-s6790" xml:space="preserve">vſque ad horam 12. </s>
  <s xml:id="echoid-s6791" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s6792" xml:space="preserve"><lb/>aliæ quinqu<unsure/>e ad occaſum Solis vſque; </s>
  <s xml:id="echoid-s6793" xml:space="preserve">Item hora 14. </s>
  <s xml:id="echoid-s6794" xml:space="preserve">ab occaſu, vt decem hore ſuperſint vſque ad horam
<pb o="111" file="0131" n="131" rhead="LIBER PRIMVS."/>
24. </s>
  <s xml:id="echoid-s6795" xml:space="preserve">qua Sol occidit; </s>
  <s xml:id="echoid-s6796" xml:space="preserve">Et tandem hora 24. </s>
  <s xml:id="echoid-s6797" xml:space="preserve">ab ortu Solis, cum dies vnus naturalis ab ortu Solis inchoat{us} <lb/>
<anchor type="note" xlink:label="note-0131-01a" xlink:href="note-0131-01"/>
tunc perfectus ſit, &amp; </s>
  <s xml:id="echoid-s6798" xml:space="preserve">aiter incipiat; </s>
  <s xml:id="echoid-s6799" xml:space="preserve">liquido constat, has tres hor{as} cõuenire in eodem puncto arcus diur-<lb/>ni hor arum 10. </s>
  <s xml:id="echoid-s6800" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6801" xml:space="preserve">proinde &amp; </s>
  <s xml:id="echoid-s6802" xml:space="preserve">ſequentes tres in tabula arcus diurni hor arum 10. </s>
  <s xml:id="echoid-s6803" xml:space="preserve">videlicet horam 8. </s>
  <s xml:id="echoid-s6804" xml:space="preserve">à <lb/>media nocte, &amp; </s>
  <s xml:id="echoid-s6805" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6806" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s6807" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6808" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s6809" xml:space="preserve">ſic de cęteris. </s>
  <s xml:id="echoid-s6810" xml:space="preserve">Item quia, cum nox complectitur horas <lb/>14. </s>
  <s xml:id="echoid-s6811" xml:space="preserve">Sol occidit hor a quinta à meridie, vt ſeptem horæ ſuperſint vſque ad horam 12. </s>
  <s xml:id="echoid-s6812" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s6813" xml:space="preserve">alię <lb/>ſeptem vſque ad ortum Solis; </s>
  <s xml:id="echoid-s6814" xml:space="preserve">Item hora 24. </s>
  <s xml:id="echoid-s6815" xml:space="preserve">ab occaſu, cum dies vnus naturalis ab occaſu Solis inchoa-<lb/>tus tunc abſolutus ſit, &amp; </s>
  <s xml:id="echoid-s6816" xml:space="preserve">alter incipiat; </s>
  <s xml:id="echoid-s6817" xml:space="preserve">Et denique hora 10. </s>
  <s xml:id="echoid-s6818" xml:space="preserve">ab ortu, vt ſuperſint horæ 14. </s>
  <s xml:id="echoid-s6819" xml:space="preserve">vſque ad ho-<lb/>ram 24. </s>
  <s xml:id="echoid-s6820" xml:space="preserve">qua Sol oritur; </s>
  <s xml:id="echoid-s6821" xml:space="preserve">coibunt quoque hæ tres horæ in eodem puncto arcus nocturni hor arum 14. </s>
  <s xml:id="echoid-s6822" xml:space="preserve">nec nõ <lb/>&amp; </s>
  <s xml:id="echoid-s6823" xml:space="preserve">tres, quæillas ſequuntur in tabula arcus nocturni horarum 14. </s>
  <s xml:id="echoid-s6824" xml:space="preserve">nimirum hora 6. </s>
  <s xml:id="echoid-s6825" xml:space="preserve">à meridie, 1. </s>
  <s xml:id="echoid-s6826" xml:space="preserve">ab oc-<lb/>caſu, &amp; </s>
  <s xml:id="echoid-s6827" xml:space="preserve">11. </s>
  <s xml:id="echoid-s6828" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s6829" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6830" xml:space="preserve">c.</s>
  <s xml:id="echoid-s6831" xml:space="preserve"/>
</p>
<div xml:id="echoid-div387" type="float" level="2" n="5">
<note position="left" xlink:label="note-0130-09" xlink:href="note-0130-09a" xml:space="preserve">Tabulæ areuũ <lb/>diurnorum, &amp; <lb/>nocturnorum, <lb/>ex quibus co-<lb/>guoſcitur, quæ-<lb/>n@ horæ à mer. <lb/>uel med noc. &amp; <lb/>ab or uel occ ſe <lb/>mu uo interſe-<lb/>@ent in propo-<lb/>ſito arcu diur-<lb/>no, aut noctur-<lb/>@@.</note>
<note position="left" xlink:label="note-0130-10" xlink:href="note-0130-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">Quo artificio <lb/>tabulæ arcuum <lb/>diurnorum, no <lb/>cturnorumq́ue <lb/>compoſitæ ſint.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s6832" xml:space="preserve">HAC arte conficipoterunt tabulæ pro ſingulis arcubus diurnis, atque nocturnis, ſi prius diligenter <lb/>conſideretur horatam à meridie, vel media nocte, quàm ab ortu, &amp; </s>
  <s xml:id="echoid-s6833" xml:space="preserve">occaſu, qua Sol oritur, vel occidit; <lb/></s>
  <s xml:id="echoid-s6834" xml:space="preserve">quod difficile non eſt. </s>
  <s xml:id="echoid-s6835" xml:space="preserve">Sed tabulæ hic propoſitæ ad deſcriptionem horarum ab ortu, vel occaſu ſufficiunt, <lb/>vt ex ſequentibus conſtabit.</s>
  <s xml:id="echoid-s6836" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">
14 # VII # 24
15 # VIII # 1
16 # IX # 2
17 # X # 3
18 # XI # 4
19 # XII # 5
# Horę à merid.
20 # I # 6
21 # II # 7
22 # III # 8
23 # IIII # 9
24 # V # 10
### Arcus nocturnus horarum 14. in quo Sol oc- \\ cidit hora 5. à meridie, &amp; hora 24. ab \\ occaſu, &amp; hora 10. ab ortu.
Horæ ab occ. # Horæ à merid. # Horæ ab ortu.
24 # V # 10
1 # VI # 11
2 # VII # 12
3 # VIII # 13
4 # IX # 14
5 # X # 15
6 # XI # 16
7 # XII # 17
# Horę à me. noc.
8 # I # 18
9 # II # 19
10 # III # 20
11 # IIII # 21
12 # V # 22
13 # VI # 23
14 # VII # 24
</note>
<note position="right" xml:space="preserve"> <lb/>### Arcus diurnus horarum 14. in quo Sol ori- \\ tur hora 5. à media nocte, &amp; hora 10. \\ aboccaſu, &amp; hora 24. ab ortu. <lb/>Horæ ab occ. # Horę à me. noc. # Horę ab ortu. <lb/>10 # V # 24 <lb/>11 # VI # 1 <lb/>12 # VII # 2 <lb/>13 # VIII # 3 <lb/>14 # IX # 4 <lb/>15 # X # 5 <lb/>16 # XI # 6 <lb/>17 # XII # 7 <lb/># Horę à merid. <lb/>18 # I # 8 <lb/>19 # II # 9 <lb/>20 # III # 10 <lb/>21 # IIII # 11 <lb/>22 # V # 12 <lb/>23 # VI # 13 <lb/>24 # VII # 14 <lb/>### Arcus nocturnus horarum 10. in quo Sol oc- \\ cidit hora 7. à meridie, &amp; hora 24. ab \\ occaſu, &amp; hora 14. ab ortu. <lb/>Horæ ab occ. # Horę à merid # Horæ ab ortu. <lb/>24 # VII # 14 <lb/>1 # VIII # 15 <lb/>2 # IX # 16 <lb/>3 # X # 17 <lb/>4 # XI # 18 <lb/>5 # XII # 19 <lb/># Horę à me. noc. <lb/>6 # I # 20 <lb/>7 # II # 21 <lb/>8 # III # 22 <lb/>9 # IIII # 23 <lb/>10 # V # 24 <lb/></note>
<pb o="112" file="0132" n="132" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>### Arcus diurnus horarum 12. in quo Sol ori- \\ tur hora 6. à med. noct. &amp; hora 12. ab \\ occaſu, &amp; hora 24. ab ortu. <lb/>Horæ ab occ. # Horę à me. noc. # Horæ ab ortu. <lb/>12 # VI # 24 <lb/>13 # VII # 1 <lb/>14 # VIII # 2 <lb/>15 # IX # 3 <lb/>16 # X # 4 <lb/>17 # XI # 5 <lb/>18 # XII # 6 <lb/># Horę à merid. <lb/>19 # I # 7 <lb/>20 # II # 8 <lb/>21 # III # 9 <lb/>22 # IIII # 10 <lb/>23 # V # 11 <lb/>24 # VI # 12 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>### Arcus nocturnus horarum 12. in quo Sol oc- \\ cidit hora 6. à meridie, &amp; hora 24. ab \\ occaſu, &amp; hora 12. ab ortu. <lb/>Horæ ab occ. # Horę à merid. # Horę ab ortu. <lb/>24 # VI # 12 <lb/>1 # VII # 13 <lb/>2 # VIII # 14 <lb/>3 # IX # 15 <lb/>
4 # X # 16
5 # XI # 17
6 # XII # 18
# Horę à me. noc.
7 # I # 19
8 # II # 20
9 # III # 21
10 # IIII # 22
11 # V # 23
12 # VI # 24
</note>
<note position="right" xml:space="preserve"> <lb/>## Arcus diurnus horarum 24. in \\ quo Sol oritur hora 12. à \\ meridie, &amp; hora 24. ab \\ ortu uel occaſu. <lb/>Quod <lb/>dictum <lb/>eſt in ta <lb/>bulis ar <lb/>cuũ di-<lb/>urnorũ, <lb/>noctur-<lb/>norũq́; <lb/>de horis <lb/>ĩtegris, <lb/>idẽ in-<lb/>telligen <lb/>dum eſt <lb/>de parti <lb/>bus ho-<lb/>rarum.
Horæ ab ortu \\ uel occaſu. # Horæ à me- \\ ridie.
24 # XII
# Horę à me. noc.
1 # I
2 # II
3 # III
4 # IIII
5 # V
6 # VI
7 # VII
8 # VIII
9 # IX
10 # X
11 # XI
12 # XII
# Horę à merid.
13 # I
14 # II
15 # III
16 # IIII
17 # V
18 # VI
19 # VII
20 # VIII
21 # IX
22 # X
23 # XI
</note>
<note position="right" xml:space="preserve"> <lb/>## Arcus nocturnus horarum 24. \\ in quo Sol occidit hora 12. \\ à media nocte, &amp; hora \\ 24. ab or. uel occ. # QVAECVNQVE au \\ tem horæ à meridie, vel me- \\ dia nocte, &amp; ab ortu, vel oc \\ caſu ſe mutuo interſecant in \\ vno puncto cuiuſcunque ar- \\ cus diurni, vel nocturni, in \\ eodem ſe interſecabunt mu- \\ tuo partes earundem hor a- \\ rum, quales ſunt quadr antes, \\ &amp; ſemiſſes horarum, &amp; c. \\ Vt quia hora 17. ab occaſu, \\ hora 10. à media nocte, &amp; \\ hora 3. ab ortu, per vnum \\ idem{q́ue} punctum tranſeunt in \\ arcu diurno horarum 10. fit \\ vt earum partes, quæ inter ſe \\ reſpõdent, nimirũ hora 17 {1/2}. \\ ab occaſu, hora 10 {1/2}. à med. \\ noc. &amp; hora 3 {1/2}. ab ortu in- \\ cedant quoque per vnũ et idẽ \\ punctum eiuſdem arcus, &amp; \\ſic de cæteris, vt conſtat, ſi \\ tabulæ per dictas partes ho- \\ rarum extendantur. <lb/>Horæ ab ortu \\ uel occaſu. # Horę à media \\ nocte. <lb/>
24 # XII
# Horæ à merid.
1 # I
2 # II
3 # III
4 # IIII
5 # V
6 # VI
7 # VII
8 # VIII
9 # IX
10 # X
11 # XI
12 # XII
# Horę à me noc.
13 # I
14 # II
15 # III
16 # IIII
17 # V
18 # VI
19 # VII
20 # VIII
21 # IX
22 # X
23 # XI
</note>
<pb o="113" file="0133" n="133" rhead="LIBER PRIMVS."/>
<p style="it">
  <s xml:id="echoid-s6837" xml:space="preserve">EADEM induſtria conſtruximus ſex ali{as} tabul{as}, vt earum inſcriptiones indicant, vt cognoſca-<lb/>
<anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/>
tur, quęnam horę<unsure/> à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s6838" xml:space="preserve">quæ inæquales ſe mutuo ſecent in vno eodem{q́ue} puncto ar <lb/>cus diurni, vel nocturni hor arum 6. </s>
  <s xml:id="echoid-s6839" xml:space="preserve">vel 18. </s>
  <s xml:id="echoid-s6840" xml:space="preserve">Item arcus diurni nocturniue horarũ 12. </s>
  <s xml:id="echoid-s6841" xml:space="preserve">quem linea æquino-<lb/>ctialis in quolibet horologio nobis exhibet. </s>
  <s xml:id="echoid-s6842" xml:space="preserve">In prioribus quatuor continentur horæ inæquales integræ cum <lb/>ſemiſſibus, &amp; </s>
  <s xml:id="echoid-s6843" xml:space="preserve">quadr antibus; </s>
  <s xml:id="echoid-s6844" xml:space="preserve">in poſterioribus verò duabus integræ tantum horæ, ſed intelligendæ ſunt <lb/>etiam earum partes, quemadmodum in ſuperioribus octo tabulis horarum æqualium dictum est. </s>
  <s xml:id="echoid-s6845" xml:space="preserve">Nam <lb/>quemadmodum v.</s>
  <s xml:id="echoid-s6846" xml:space="preserve">g. </s>
  <s xml:id="echoid-s6847" xml:space="preserve">in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s6848" xml:space="preserve">ſe mutuo inter ſecant hora 3. </s>
  <s xml:id="echoid-s6849" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s6850" xml:space="preserve">hora 9. </s>
  <s xml:id="echoid-s6851" xml:space="preserve">in-<lb/>ęqualis diurna, ita quoque hora 3 {3/4}. </s>
  <s xml:id="echoid-s6852" xml:space="preserve">a meridie, &amp; </s>
  <s xml:id="echoid-s6853" xml:space="preserve">hora inæqualis 9 {3/4}. </s>
  <s xml:id="echoid-s6854" xml:space="preserve">eundem ar cum in vno eodem{q́ue} <lb/>puncto interſecabunt, at que ita de cæteris dicendum eſt.</s>
  <s xml:id="echoid-s6855" xml:space="preserve"/>
</p>
<div xml:id="echoid-div388" type="float" level="2" n="6">
<note position="right" xlink:label="note-0133-01" xlink:href="note-0133-01a" xml:space="preserve">Tabulæ arcuu<unsure/> <lb/>diurnorum, no <lb/>cturnorumq́ue <lb/>horarum 6, 18. <lb/>&amp; 12 ex qu@bus <lb/>intelligitur, quę <lb/>nã horæ à mer. <lb/>uel med. noc &amp; <lb/>quæ inęquales <lb/>ſe mut<unsure/>uo in his <lb/>arcubus diurnis <lb/>interſecent.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>## Arcus diurnus \\ horarũ 6. in quo \\ oritur Sol hora \\ 9. poſt med. noc. \\ &amp; hora 12. in- \\ ęquali matutina, \\ &amp; ſingulæ ſemi- \\ horę à mer. vel \\ med. noc. reſpon \\ dent ſingulis ho \\ ris inequalibus \\ diurnis.
Horę in \\ ęquales \\ diurnę. # Horę à \\ med. no \\ cte.
XII # IX
{1/4} # 9 {1/8}
{1/2} # 9 {1/4}
{3/4} # 9 {3/8}
1 # 9 {1/2}
1 {1/4} # 9 {5/8}
1 {1/2} # 9 {3/4}
1 {3/4} # 9 {7/8}
II # X
2 {1/4} # 10 {1/8}
2 {1/2} # 10 {1/4}
2 {3/4} # 10 {3/8}
III # 10 {1/2}
3 {1/4} # 10 {5/8}
3 {1/2} # 10 {3/4}
3 {3/4} # 10 {7/8}
IIII # XI
4 {1/4} # 11 {1/8}
4 {1/2} # 11 {1/4}
4 {3/4} # 11 {3/8}
V # 11 {1/2}
5 {1/4} # 11 {5/8}
5 {1/2} # 11 {3/4}
5 {3/4} # 11 {7/8}
VI # XII
</note>
<note position="right" xml:space="preserve"> <lb/>## Arcus nocturnus \\ horarum 18. in \\ quo Sol occidit \\ hora 3. à meri- \\ die, &amp; hora 12. \\ inęquali veſper- \\ tina, &amp; ſingula \\ ſpatia hor. 1 {1/2}. à \\ merid. vel med. \\ noc. rñdẽt ſingu \\ lis horis inęqua- \\ libus nocturnis. <lb/>Horę in \\ ęquales \\ noctur. # Horæ à \\ meri- \\ die. <lb/>IX # III <lb/>{1/4} # 3 {3/8} <lb/>{1/2} # 3 {3/4} <lb/>{3/4} # 4 {1/8} <lb/>1 # 4 {1/2} <lb/>1 {1/4} # 4 {7/8} <lb/>1 {1/2} # 5 {1/4} <lb/>1 {3/4} # 5 {5/8} <lb/>II # VI <lb/>2 {1/4} # 6 {3/8} <lb/>2 {1/2} # 6 {3/4} <lb/>2 {3/4} # 7 {1/8} <lb/>III # 7 {1/2} <lb/>3 {1/4} # 7 {7/8} <lb/>3 {1/2} # 8 {1/4} <lb/>3 {3/4} # 8 {5/8} <lb/>IIII # IX <lb/>4 {1/4} # 9 {3/8} <lb/>4 {1/2} # 9 {3/4} <lb/>4 {3/4} # 10 {1/8} <lb/>V # 10 {1/2} <lb/>5 {1/4} # 10 {7/8} <lb/>5 {1/2} # 11 {1/4} <lb/>5 {3/4} # 11 {5/8} <lb/>VI # XII <lb/></note>
<note position="right" xml:space="preserve"> <lb/>## Arcus diurnus \\ horarum 18. in \\ quo Sol oritur \\ hora 3. à med. \\ noc. &amp; hora 12. \\ inę quali matuti- \\ na, &amp; ſingula ſpa \\ tia hor. 1 {1/2}. à \\ merid. vel med. \\ noc. rñdẽt ſingu \\ lis horis inęqua- \\ libus diurnis. <lb/>Horę in \\ ęqual es \\ diurnę. # Horæ à \\ med. no \\ cte. <lb/>XII # III <lb/>{1/4} # 3 {3/8} <lb/>{1/2} # 3 {3/4} <lb/>{3/4} # 4 {1/8} <lb/>I # 4 {1/2} <lb/>1 {1/4} # 4 {7/8} <lb/>1 {1/2} # 5 {1/4} <lb/>1 {3/4} # 5 {5/8} <lb/>II # VI <lb/>2 {1/4} # 6 {3/8} <lb/>2 {1/2} # 6 {3/4} <lb/>2 {3/4} # 7 {1/8} <lb/>III # 7 {1/2} <lb/>3 {1/4} # 7 {7/8} <lb/>3 {1/2} # 8 {1/4} <lb/>3 {3/4} # 8 {5/8} <lb/>IIII # IX <lb/>4 {1/4} # 9 {3/8} <lb/>4 {1/2} # 9 {3/4} <lb/>4 {3/4} # 10 {1/8} <lb/>V # 10 {1/2} <lb/>5 {1/4} # 10 {7/8} <lb/>5 {1/2} # 11 {1/4} <lb/>5 {3/4} # 11 {5/8} <lb/>VI # XII <lb/></note>
<note position="right" xml:space="preserve"> <lb/>## Arcus nocturnus \\ horarum 6. in \\ quo Sol occidit \\ hora 9, poſt me- \\ ridiem, &amp; hora \\ 12. inæquali ve- \\ ſpertina, &amp; ſingu \\ læ ſemihoræ à \\ merid. vel med. \\ noc. rñdẽt ſingu \\ lis horis inęqua- \\ lib<emph style="sub">9</emph> nocturnis. <lb/>Horę in \\ ęquales \\ noctur. # Horæ à \\ meri- \\ die. <lb/>XII # IX <lb/>{1/4} # 9 {1/8} <lb/>{1/2} # 9 {1/4} <lb/>{3/4} # 9 {3/8} <lb/>I # 9 {1/2} <lb/>1 {1/4} # 9 {5/8} <lb/>1 {1/2} # 9 {3/4} <lb/>1 {3/4} # 9 {7/8} <lb/>II # X <lb/>2 {1/4} # 10 {1/8} <lb/>2 {1/2} # 10 {1/4} <lb/>2 {3/4} # 10 {3/8} <lb/>III # 10 {1/2} <lb/>3 {1/4} # 10 {5/8} <lb/>3 {1/2} # 10 {3/4} <lb/>3 {3/4} # 10 {7/8} <lb/>IIII # XI <lb/>4 {1/4} # 11 {1/8} <lb/>4 {1/2} # 11 {1/4} <lb/>4 {3/4} # 11 {3/8} <lb/>V # 11 {1/2} <lb/>5 {1/4} # 11 {5/8} <lb/>5 {1/2} # 11 {3/4} <lb/>5 {3/4} # 11 {7/8} <lb/>VI # XII <lb/></note>
<pb o="114" file="0134" n="134" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>## Reliquum arcus \\ diurni horarum \\ 6. &amp; c. <lb/>Horę in \\ ęquales \\ diurnę. # Horæ à \\ meri- \\ die. <lb/>6 {1/4} # {1/8} <lb/>6 {1/2} # {1/4} <lb/>6 {3/4} # {3/8} <lb/>VII # {1/2} <lb/>7 {1/4} # {5/8} <lb/>7 {1/2} # {3/4} <lb/>7 {3/4} # {7/8} <lb/>VIII # I <lb/>8 {1/4} # 1 {1/8} <lb/>8 {1/2} # 1 {1/4} <lb/>8 {3/4} # 1 {3/8} <lb/>IX # 1 {1/2} <lb/>9 {1/4} # 1 {5/8} <lb/>9 {1/2} # 1 {3/4} <lb/>9 {3/4} # 1 {7/8} <lb/>X # II <lb/>10 {1/4} # 2 {1/8} <lb/>10 {1/2} # 2 {1/4} <lb/>10 {3/4} # 2 {3/8} <lb/>XI # 2 {1/2} <lb/>11 {1/4} # 2 {5/8} <lb/>11 {1/2} # 2 {3/4} <lb/>11 {3/4} # 2 {7/8} <lb/>XII # III <lb/></note>
<note position="right" xml:space="preserve"> <lb/>## Reliquum arcus \\ nocturni horarũ \\ 18. &amp; c. <lb/>Horę in \\ ęquales \\ noctur. # Horæ à \\ med. no \\ cte. <lb/>6 {1/4} # {3/8} <lb/>6 {1/2} # {3/4} <lb/>6 {3/4} # 1 {1/8} <lb/>VII # 1 {1/2} <lb/>7 {1/4} # 1 {7/8} <lb/>7 {1/2} # 2 {1/4} <lb/>7 {3/4} # 2 {5/8} <lb/>VIII # III <lb/>8 {1/4} # 3 {3/8} <lb/>8 {1/2} # 3 {3/4} <lb/>8 {3/4} # 4 {1/8} <lb/>IX # 4 {1/2} <lb/>9 {1/4} # 4 {7/8} <lb/>9 {1/2} # 5 {1/4} <lb/>9 {3/4} # 5 {5/8} <lb/>X # VI <lb/>10 {1/4} # 6 {3/8} <lb/>10 {1/2} # 6 {3/4} <lb/>10 {3/4} # 7 {1/8} <lb/>XI # 7 {1/2} <lb/>11 {1/4} # 7 {7/8} <lb/>11 {1/2} # 8 {1/4} <lb/>11 {3/4} # 8 {5/8} <lb/>XII # IX <lb/></note>
<note position="right" xml:space="preserve"> <lb/>## Reliquum arcus \\ diurni horarum \\ 18. &amp; c. <lb/>Horę in \\ ęquales \\ diurnę. # Horæ à \\ meri- \\ die. <lb/>6 {1/4} # {3/8} <lb/>6 {1/2} # {3/4} <lb/>6 {3/4} # 1 {1/8} <lb/>VII # 1 {1/2} <lb/>7 {1/4} # 1 {7/8} <lb/>7 {1/2} # 2 {1/4} <lb/>7 {3/4} # 2 {5/8} <lb/>VIII # III <lb/>8 {1/4} # 3 {3/8} <lb/>8 {1/2} # 3 {3/4} <lb/>8 {3/4} # 4 {1/8} <lb/>IX # 4 {1/2} <lb/>9 {1/4} # 4 {7/8} <lb/>9 {1/2} # 5 {1/4} <lb/>9 {3/4} # 5 {5/8} <lb/>X # VI <lb/>10 {1/4} # 6 {3/8} <lb/>10 {1/2} # 6 {3/4} <lb/>10 {3/4} # 7 {1/8} <lb/>XI # 7 {1/2} <lb/>11 {1/4} # 7 {7/8} <lb/>11 {1/2} # 8 {1/4} <lb/>11 {3/4} # 8 {5/8} <lb/>XII # IX <lb/></note>
<note position="right" xml:space="preserve"> <lb/>## Reliquum arcus \\ nocturni horarũ \\ 6. &amp; c. <lb/>Horę in \\ ęquales \\ noctur. # Horę à \\ med. no \\ cte. <lb/>6 {1/4} # {1/8} <lb/>6 {1/2} # {1/4} <lb/>6 {3/4} # {3/8} <lb/>
VII # {1/2}
7 {1/4} # {5/8}
7 {1/2} # {3/4}
7 {3/4} # {7/8}
VIII # I
8 {1/4} # 1 {1/8}
8 {1/2} # 1 {1/4}
8 {3/4} # 1 {3/8}
IX # 1 {1/2}
9 {1/4} # 1 {5/8}
9 {1/2} # 1 {3/4}
9 {3/4} # 1 {7/8}
X # II
10 {1/4} # 2 {1/8}
10 {1/2} # 2 {1/4}
10 {3/4} # 2 {3/8}
XI # 2 {1/2}
11 {1/4} # 2 {5/8}
11 {1/2} # 2 {3/4}
11 {3/4} # 2 {7/8}
XII # III
</note>
<note position="right" xml:space="preserve"> <lb/>#### Arcus diurnus horarũ 12. in quo Sol ori- \\ tur hora 6 à med. noc. &amp; hora 12. inæqua \\ li matutina, &amp; ſingulę horę à mer. vel me- \\ dia noc. ſingulis horis inęqualibus diur- \\ nis reſpondent. <lb/>Horę in \\ ę quales \\ diurnæ. # Horæ \\ poſt me \\ diã noc. <lb/># Horę in \\ æquales \\ diurnæ. # Horæ \\ poſt me \\ ridiem. <lb/>XII # VI # VII # I <lb/>I # VII # VIII # II <lb/>II # VIII # IX # III <lb/>III # IX # X # IIII <lb/>IIII # X # XI # V <lb/>V # XI # XII # VI <lb/>VI # XII <lb/></note>
<note position="right" xml:space="preserve"> <lb/>#### Arcus nocturnus horarum 12. in quo Sol \\ occidit hora 6. poſt merid. &amp; hora 12. in- \\ ęquali veſpertina, &amp; ſingulę horę à merid. \\ vel med. noc. ſingulis horis inęqualibus \\ nocturnis reſpondent. <lb/>
Horę in \\ æquales \\ noctur. # Horæ \\ poſt me \\ ridiem. # Horę in \\ æquales \\ noctur. # Horæ \\ poſt me \\ diãnoc.
XII # VI # VII # I
I # VII # VIII # II
II # VIII # IX # III
III # IX # X # IIII
IIII # X # XI # V
V # XI # XII # VI
VI # XII
</note>
</div>
<div xml:id="echoid-div390" type="section" level="1" n="134">
<head xml:id="echoid-head137" xml:space="preserve">PROBLEMA 13. PROPOSITIO 34.</head>
<p>
  <s xml:id="echoid-s6856" xml:space="preserve">AMPLITVDINEM ortiuam, occiduamve, &amp; </s>
  <s xml:id="echoid-s6857" xml:space="preserve">arcum ſemidiur-<lb/>num cuiuſuis paralleli, ad datam poli altitudinem in ueſtigare.</s>
  <s xml:id="echoid-s6858" xml:space="preserve"/>
</p>
<pb o="115" file="0135" n="135" rhead="LIBER PRIMVS."/>
<p>
  <s xml:id="echoid-s6859" xml:space="preserve">QVONIAM plerique parallelis, vel arcubus ſignorum Zodiaci in horologijs (quos in quo-<lb/>libet horologio deſcribere docebimus in ſequentibus duobus libris) aſcribere ſolent quantitates <lb/>dierum, &amp; </s>
  <s xml:id="echoid-s6860" xml:space="preserve">crepuſculorum longitudines, non omnino ab re erit, breuiter hoc loco (licet alicui <lb/>videri poſsit quodammodo eſſe pręter inſtitutum, cum ad alium locum hęc res pertineat) demon <lb/>ſtrare, quo pacto &amp; </s>
  <s xml:id="echoid-s6861" xml:space="preserve">quantitates dierum, &amp; </s>
  <s xml:id="echoid-s6862" xml:space="preserve">crepuſculorum longitudines ad quamcunque latitudi-<lb/>nem loci, cognita declinatione Solis, ſupputentur, vt &amp; </s>
  <s xml:id="echoid-s6863" xml:space="preserve">nos in horologio quocunque, ſi viſum <lb/>ſuerit, parallelis ſignorum Zodiaci eas apponere poſſimus. </s>
  <s xml:id="echoid-s6864" xml:space="preserve">Pro quantitatibus igitur dierum in-<lb/>quirendis indagabimus arcus ſemidiurnos. </s>
  <s xml:id="echoid-s6865" xml:space="preserve">Hi namque duplicati totos arcus diurnos conſiciunt. <lb/></s>
  <s xml:id="echoid-s6866" xml:space="preserve">Præ omnibus autem vijs (multis enim modis diei magnitudo reperiri poteſt) hanc in primis dele-<lb/>gimus, quę parum ab ea differre videtur, qua in pręcedenti propoſ. </s>
  <s xml:id="echoid-s6867" xml:space="preserve">vſi ſumus in declinatione pa-<lb/>
<anchor type="note" xlink:label="note-0135-01a" xlink:href="note-0135-01"/>
ralleli, cuius arcus diurnus datus ſit, ſupputanda. </s>
  <s xml:id="echoid-s6868" xml:space="preserve">Hic enim è contrario ex data declinatione pa-<lb/>ralleli eius diurnus arcus proponitur perueſtigandus. </s>
  <s xml:id="echoid-s6869" xml:space="preserve">Sed prius amplitudo ortiua, occiduaue ex-<lb/>ploranda erit. </s>
  <s xml:id="echoid-s6870" xml:space="preserve">Ex hac enim ſtatim arcus ſemidiurnus colligetur.</s>
  <s xml:id="echoid-s6871" xml:space="preserve"/>
</p>
<div xml:id="echoid-div390" type="float" level="2" n="1">
<note position="left" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s6872" xml:space="preserve">REPETATVR ergo poſtrema ſigurat<unsure/> præcedentis propoſ. </s>
  <s xml:id="echoid-s6873" xml:space="preserve">in qua Horizon eſt A B C D; <lb/></s>
  <s xml:id="echoid-s6874" xml:space="preserve">
<anchor type="note" xlink:label="note-0135-02a" xlink:href="note-0135-02"/>
Meridianus A C; </s>
  <s xml:id="echoid-s6875" xml:space="preserve">Aequator B D, Meridianum ſe-<lb/>
<anchor type="figure" xlink:label="fig-0135-01a" xlink:href="fig-0135-01"/>
cans in E; </s>
  <s xml:id="echoid-s6876" xml:space="preserve">parallelus ſiue borealis, ſiue auſtralis <lb/>F G, ſecans Meridianum in k, vt ſit arcus ſemidiur-<lb/>nus inquirendus F K, vel G K. </s>
  <s xml:id="echoid-s6877" xml:space="preserve">Meridianus enim <lb/>A C, tranſiens per polos Horizontis, &amp; </s>
  <s xml:id="echoid-s6878" xml:space="preserve">paralleli <lb/>FG, ſecat ſegmentũ FG, per propoſ. </s>
  <s xml:id="echoid-s6879" xml:space="preserve">9. </s>
  <s xml:id="echoid-s6880" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6881" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6882" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s6883" xml:space="preserve">
<anchor type="note" xlink:label="note-0135-03a" xlink:href="note-0135-03"/>
bifariam. </s>
  <s xml:id="echoid-s6884" xml:space="preserve">Suſcipiatur polus arcticus H, per quem, <lb/>&amp; </s>
  <s xml:id="echoid-s6885" xml:space="preserve">per punctum F, ducatur, per propoſ. </s>
  <s xml:id="echoid-s6886" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6887" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6888" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s6889" xml:space="preserve">Theodoſii, circulus maximus declinationem pa-<lb/>ralleli ab Aequatore metiens H F, ſecans Aequato-<lb/>rem in 1. </s>
  <s xml:id="echoid-s6890" xml:space="preserve">Erit arcus Aequatoris I E, per propoſ. </s>
  <s xml:id="echoid-s6891" xml:space="preserve">10. </s>
  <s xml:id="echoid-s6892" xml:space="preserve"><lb/>lib. </s>
  <s xml:id="echoid-s6893" xml:space="preserve">2. </s>
  <s xml:id="echoid-s6894" xml:space="preserve">Theodoſii, ſimilis arcui diurno I E; </s>
  <s xml:id="echoid-s6895" xml:space="preserve">atque <lb/>adeo in uento arcu I E, cognitus erit &amp; </s>
  <s xml:id="echoid-s6896" xml:space="preserve">arcus ſemi-<lb/>diurnus F k, qui quæritur; </s>
  <s xml:id="echoid-s6897" xml:space="preserve">cũ tot gradus, horæve <lb/>in arcu I E, contineantur, quot in F k, propter ho-<lb/>rum arcuũ ſimilitudinẽ. </s>
  <s xml:id="echoid-s6898" xml:space="preserve">Arcum autem I E, ita in-<lb/>
<anchor type="note" xlink:label="note-0135-04a" xlink:href="note-0135-04"/>
ueniemus. </s>
  <s xml:id="echoid-s6899" xml:space="preserve">Quoniã in triãgulo ſphærico rectangu <lb/>lo C F H, (Eſt enim angulus C, rectus, cum Meridianus A C, per polũ Horizõtis ductus rectus ſit, <lb/>per propoſ. </s>
  <s xml:id="echoid-s6900" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6901" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6902" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6903" xml:space="preserve">Theodoſii, ad Horizontẽ) nullus arcuũ quadrãs eſt, vt in præcedenti propoſ. <lb/></s>
  <s xml:id="echoid-s6904" xml:space="preserve">oſtenſum eſt, erit per propoſ. </s>
  <s xml:id="echoid-s6905" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6906" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6907" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6908" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6909" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6910" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s6911" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6912" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6913" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6914" xml:space="preserve">Gebri, <lb/>vel certè per propoſ. </s>
  <s xml:id="echoid-s6915" xml:space="preserve">43. </s>
  <s xml:id="echoid-s6916" xml:space="preserve">noſtrorũ triangulorũ ſphæricorũ, vt ſinus cõplementi arcus H F, hoc eſt, <lb/>vt ſinus arcus declinationis I F, (Tam enim iu parallelo auſtrali, quàm boreali, arcus declinationis <lb/>I F, cõplementum eſt arcus H F, cũ H I, per coroll propoſ. </s>
  <s xml:id="echoid-s6917" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6918" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6919" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6920" xml:space="preserve">Theod quadrans ſit) ad ſinũ <lb/>cõplementi arcus altitudinis poli C H, ita ſinus cõplementi arcus C F, id eſt, ita ſinus arcus B F, <lb/>(qui eſt cõplementũ arcus C F, cum C B, quadrans ſit; </s>
  <s xml:id="echoid-s6921" xml:space="preserve">metiturq́; </s>
  <s xml:id="echoid-s6922" xml:space="preserve">amplitudinẽ ortiuã, occiduam ve <lb/>paralleli F G) ad ſinum totum. </s>
  <s xml:id="echoid-s6923" xml:space="preserve">Quocirca &amp; </s>
  <s xml:id="echoid-s6924" xml:space="preserve">conuertendo erit, vt ſinus complementi altitudinis <lb/>
<anchor type="note" xlink:label="note-0135-05a" xlink:href="note-0135-05"/>
poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad ſinum arcus B F, latitudinis or-<lb/>tiuæ, vel occiduæ. </s>
  <s xml:id="echoid-s6925" xml:space="preserve">Quod etiam hoc modo, &amp; </s>
  <s xml:id="echoid-s6926" xml:space="preserve">fortaſſis commodius, demonſtrabitur. </s>
  <s xml:id="echoid-s6927" xml:space="preserve">Quia in trian <lb/>gulo ſphærico B I F, angulus I, rectus eſt, cum circulus maximus H I, per polos mundi, ſeu Aequa <lb/>toris B D, ductus rectus ſit, per propoſ. </s>
  <s xml:id="echoid-s6928" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6929" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6930" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6931" xml:space="preserve">Theodoſii, ad Aequatorem; </s>
  <s xml:id="echoid-s6932" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s6933" xml:space="preserve">angulus B, incli-<lb/>nationem Aequatoris ad Horizontem, vel, quod idem eſt, altitudinem Aequatoris ſupra Horizon <lb/>tem metitur, id eſt, arcum Meridiani A E, cum B, polus ſit Meridiani A C; </s>
  <s xml:id="echoid-s6934" xml:space="preserve">erunt duo anguli I, <lb/>&amp; </s>
  <s xml:id="echoid-s6935" xml:space="preserve">B, trianguli B I F, noti. </s>
  <s xml:id="echoid-s6936" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s6937" xml:space="preserve">arcus I F, declinationis cognitus. </s>
  <s xml:id="echoid-s6938" xml:space="preserve">Cum ergo, per propoſ. <lb/></s>
  <s xml:id="echoid-s6939" xml:space="preserve">16. </s>
  <s xml:id="echoid-s6940" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6941" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6942" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6943" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6944" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s6945" xml:space="preserve">13. </s>
  <s xml:id="echoid-s6946" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6947" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6948" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s6949" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6950" xml:space="preserve">noſtrorum <lb/>triangulorum ſphæricorum, ſit vt ſinus anguli B, altitudinis Aequatoris, vel complementi altitu-<lb/>dinis poli, ad ſinum arcus I F, declinationis paralleli propoſiti, ita ſinus anguli recti I, hoc eſt, ita <lb/>
<anchor type="note" xlink:label="note-0135-06a" xlink:href="note-0135-06"/>
ſinus totus ad ſinum arcus B F, latitudinis ortiuę, vel occiduæ. </s>
  <s xml:id="echoid-s6951" xml:space="preserve">Igitur ex tribus cognitis &amp; </s>
  <s xml:id="echoid-s6952" xml:space="preserve">quar-<lb/>tum, nempe arcus latitudinis ortiuę, cognoſcetur. </s>
  <s xml:id="echoid-s6953" xml:space="preserve">Itaque ſi ſiat, vt ſinus complementi altitudinis <lb/>poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad aliud, reperietur ſinus latitudinis <lb/>ortiuæ, ſiue occidue, ex quo ipſa latitudo ortiua, occiduave cognita erit.</s>
  <s xml:id="echoid-s6954" xml:space="preserve"/>
</p>
<div xml:id="echoid-div391" type="float" level="2" n="2">
<note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">A mplitudo or-<lb/>tiua, occiduaue, <lb/>qua ratione in-<lb/>@eſtigetur.</note>
  <figure xlink:label="fig-0135-01" xlink:href="fig-0135-01a">
    <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01"/>
  </figure>
<note position="left" xlink:label="note-0135-03" xlink:href="note-0135-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0135-05" xlink:href="note-0135-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0135-06" xlink:href="note-0135-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s6955" xml:space="preserve">RVRSVS quia in triangulo eodem rectangulo B I F, angulus I, rectus eſt, vt proximè di-<lb/>
<anchor type="note" xlink:label="note-0135-07a" xlink:href="note-0135-07"/>
ctum eſt, &amp; </s>
  <s xml:id="echoid-s6956" xml:space="preserve">nullus arcuum quadrãs eſt, cum omnes ſint partes quadrantum; </s>
  <s xml:id="echoid-s6957" xml:space="preserve">(Nam I F, in triangu-<lb/>lo boreali pars eſt quadrantis H I, in auſtrali verò pars illius quadrantis, qui ex I, per F, vſque ad <lb/>polum antarcticum ducitur. </s>
  <s xml:id="echoid-s6958" xml:space="preserve">Item I B, in auſtrali triangulo pars eſt quadrantis B E, in boreali au-<lb/>tem portio illius quadrantis, qui ex B, per I, vſque ad Meridianum infra Horizontem extenditur. <lb/></s>
  <s xml:id="echoid-s6959" xml:space="preserve">B F, tandem pars eſt quadrantis B C, vel B A) erit per propoſ. </s>
  <s xml:id="echoid-s6960" xml:space="preserve">19. </s>
  <s xml:id="echoid-s6961" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6962" xml:space="preserve">4. </s>
  <s xml:id="echoid-s6963" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s6964" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s6965" xml:space="preserve">de triangu-<lb/>lis, vel per propoſ. </s>
  <s xml:id="echoid-s6966" xml:space="preserve">15. </s>
  <s xml:id="echoid-s6967" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s6968" xml:space="preserve">1. </s>
  <s xml:id="echoid-s6969" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s6970" xml:space="preserve">43. </s>
  <s xml:id="echoid-s6971" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt
<pb o="116" file="0136" n="136" rhead="GNOMONICES"/>
ſinus cõplementi arcus I F, declinationis paralleli propoſiti ad ſinũ totum, ita ſinus cõplementiar-<lb/>cus BF, latitudinis ortiuæ, occiduęve proximè inuentæ ad ſinũ cõplemẽti arcus B I, hoc eſt, ad ſinũ <lb/>arcus ſemidiurni I E, in parallelo aultrali, vel arcus ſeminocturni in parallelo boreali. </s>
  <s xml:id="echoid-s6972" xml:space="preserve">Nam arcus <lb/>
<anchor type="figure" xlink:label="fig-0136-01a" xlink:href="fig-0136-01"/>
Aequatoris inter I, &amp; </s>
  <s xml:id="echoid-s6973" xml:space="preserve">Meridianum ſub Horizonte <lb/>complementũ eſt arcus B I, in triangulo boreali, cũ <lb/>arcus Aequatoris ex B, per I, vſque ad Meridianum <lb/>infra Horizontem porrectus ſit quadrans. </s>
  <s xml:id="echoid-s6974" xml:space="preserve">Igitur <lb/>ſi fiat, vt ſinus complementi declinationis propoſi-<lb/>ti paralleli ad ſinum totum, ita ſinus compleinen-<lb/>ti latitudinis ortiuæ proxime inuentæ in priori di-<lb/>
<anchor type="note" xlink:label="note-0136-01a" xlink:href="note-0136-01"/>
ſcurſu, ad aliud, inuenietur ſinus arcus ſemidiur-<lb/>ni auſtralis, vel ſeminocturni borealis. </s>
  <s xml:id="echoid-s6975" xml:space="preserve">Dempto au-<lb/>tem arcu ſeminocturno boreali ex ſemicirculo Ae-<lb/>quatoris, qui inter Meridianum ſupra, &amp; </s>
  <s xml:id="echoid-s6976" xml:space="preserve">infra Ho-<lb/>rizontem interijcitur, re@iquus erit arcus diurnus <lb/>borealis I B E.</s>
  <s xml:id="echoid-s6977" xml:space="preserve"/>
</p>
<div xml:id="echoid-div392" type="float" level="2" n="3">
<note position="right" xlink:label="note-0135-07" xlink:href="note-0135-07a" xml:space="preserve">Arcus ſemidiu@ <lb/>nus, quo modo <lb/>ex latitudine or <lb/>tiua, occiduaue <lb/>ſit exquitend@@</note>
  <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a">
    <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0136-01"/>
  </figure>
<note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s6978" xml:space="preserve">PONATVR exempli gratia inquirendus ar-<lb/>
<anchor type="note" xlink:label="note-0136-02a" xlink:href="note-0136-02"/>
cus ſemidiurnus ad latitudinem grad. </s>
  <s xml:id="echoid-s6979" xml:space="preserve">42. </s>
  <s xml:id="echoid-s6980" xml:space="preserve">Sole exi-<lb/>ſtente in principio ♊, vel ♐, vbi declinationem <lb/>habet grad. </s>
  <s xml:id="echoid-s6981" xml:space="preserve">20. </s>
  <s xml:id="echoid-s6982" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6983" xml:space="preserve">12. </s>
  <s xml:id="echoid-s6984" xml:space="preserve">Fiat vt 74314. </s>
  <s xml:id="echoid-s6985" xml:space="preserve">ſinus com <lb/>
<anchor type="note" xlink:label="note-0136-03a" xlink:href="note-0136-03"/>
plementi altitudinis poli, ad 34529. </s>
  <s xml:id="echoid-s6986" xml:space="preserve">ſinũ declinationis paralleli ♊, vel ♐, ita 100000. </s>
  <s xml:id="echoid-s6987" xml:space="preserve">ſinus to-<lb/>tus ad aliud, inuenieturq́ hic ferè ſinus 46464. </s>
  <s xml:id="echoid-s6988" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s6989" xml:space="preserve">27. </s>
  <s xml:id="echoid-s6990" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s6991" xml:space="preserve">41. </s>
  <s xml:id="echoid-s6992" xml:space="preserve">dabit latitudinem <lb/>ortiuam, occiduamve, borealem quidem paralleli ♊, auſtralem verò paralleli ♐. </s>
  <s xml:id="echoid-s6993" xml:space="preserve">Rurſus fiat, vt <lb/>93849. </s>
  <s xml:id="echoid-s6994" xml:space="preserve">ſinus complementi declinationis eiuſdem paralleli ♊, vel ♐, ad 100000, ſinum totum, <lb/>ita 88552. </s>
  <s xml:id="echoid-s6995" xml:space="preserve">ſinus complementi latitudinis ortiuæ proximè inuentæ ad aliud, conſurgetq́; </s>
  <s xml:id="echoid-s6996" xml:space="preserve">quaſi hic <lb/>ſinus 94355. </s>
  <s xml:id="echoid-s6997" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s6998" xml:space="preserve">70. </s>
  <s xml:id="echoid-s6999" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7000" xml:space="preserve">39. </s>
  <s xml:id="echoid-s7001" xml:space="preserve">exhibebit arcum ſemidiurnum paralleli ♐, &amp; </s>
  <s xml:id="echoid-s7002" xml:space="preserve">ſemi-<lb/>nocturnum paralleli ♊, quo dempto ex ſemicirculo, id eſt, ex grad. </s>
  <s xml:id="echoid-s7003" xml:space="preserve">180. </s>
  <s xml:id="echoid-s7004" xml:space="preserve">reliquus erit arcus ſemi-<lb/>diurnus paralleli ♊, grad. </s>
  <s xml:id="echoid-s7005" xml:space="preserve">109. </s>
  <s xml:id="echoid-s7006" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7007" xml:space="preserve">21. </s>
  <s xml:id="echoid-s7008" xml:space="preserve">Quòd ſi gradus horum arcuum reducantur ad horas, tri <lb/>buendo ſingulis horis grad. </s>
  <s xml:id="echoid-s7009" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7010" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7011" xml:space="preserve">quaternis minutis horæ ſingulos gradus, continebit arcus ſemi-<lb/>diurnus paralleli ♐, Hor. </s>
  <s xml:id="echoid-s7012" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7013" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7014" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7015" xml:space="preserve">paralleli autem ♊, Hor. </s>
  <s xml:id="echoid-s7016" xml:space="preserve">7. </s>
  <s xml:id="echoid-s7017" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7018" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7019" xml:space="preserve">paulo amplius. </s>
  <s xml:id="echoid-s7020" xml:space="preserve">Si au-<lb/>
<anchor type="note" xlink:label="note-0136-04a" xlink:href="note-0136-04"/>
tem eoſdem arcus ſemidiutnos duplicemus, habebimus totos arcus diurnos, nempe arcum diur-<lb/>num paralleli ♐, grad. </s>
  <s xml:id="echoid-s7021" xml:space="preserve">141. </s>
  <s xml:id="echoid-s7022" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7023" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7024" xml:space="preserve">vel Hor. </s>
  <s xml:id="echoid-s7025" xml:space="preserve">9. </s>
  <s xml:id="echoid-s7026" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7027" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7028" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7029" xml:space="preserve">arcum diurnum paralleli ♊, grad. <lb/></s>
  <s xml:id="echoid-s7030" xml:space="preserve">21 8, Min. </s>
  <s xml:id="echoid-s7031" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7032" xml:space="preserve">vel Hor. </s>
  <s xml:id="echoid-s7033" xml:space="preserve">14. </s>
  <s xml:id="echoid-s7034" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7035" xml:space="preserve">35. </s>
  <s xml:id="echoid-s7036" xml:space="preserve">paulo minus.</s>
  <s xml:id="echoid-s7037" xml:space="preserve"/>
</p>
<div xml:id="echoid-div393" type="float" level="2" n="4">
<note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0136-04" xlink:href="note-0136-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Arcus ſemidiur <lb/>nus, qua ratio-<lb/>ne aliter inue-<lb/>ſtigetur per triã <lb/>gula ſphærica.</note>
<p>
  <s xml:id="echoid-s7038" xml:space="preserve">POSSVMVS autem arcum ſemidiurnum cuiuſuis paralleli per eadem triangula ſphærica <lb/>inuenire etiam hoc modo. </s>
  <s xml:id="echoid-s7039" xml:space="preserve">Quoniam in triangulo ſphærico C F H, angulus C, rectus eſt, erit per <lb/>propoſ. </s>
  <s xml:id="echoid-s7040" xml:space="preserve">16 lib. </s>
  <s xml:id="echoid-s7041" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7042" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s7043" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s7044" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s7045" xml:space="preserve">13 lib. </s>
  <s xml:id="echoid-s7046" xml:space="preserve">1. </s>
  <s xml:id="echoid-s7047" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s7048" xml:space="preserve">41. <lb/></s>
  <s xml:id="echoid-s7049" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus F H, complementi declinationis paralleli <lb/>propoſiti (Nam F H, in parallelo boreali complementum eſt declinationis F I, in auſtrali verò <lb/>arcus F H, eundem ſinum habet, quem complementum arcus F I, declinationis cum eo ſemicir-<lb/>culum conſtituens, quod quidem complementum interijcitur inter F, &amp; </s>
  <s xml:id="echoid-s7050" xml:space="preserve">alterum polum, cum ar-<lb/>
<anchor type="note" xlink:label="note-0136-06a" xlink:href="note-0136-06"/>
cus ex I, per F, vſque ad alterum polum tendens ſit quadrans) ad ſinum anguli recti C, id eſt, ad ſi-<lb/>num totum, ita ſinus arcus C H, altitudinis poli, ad ſinum anguli F. </s>
  <s xml:id="echoid-s7051" xml:space="preserve">Ex tribus ergo prioribus co-<lb/>gnitis cognoſcetur &amp; </s>
  <s xml:id="echoid-s7052" xml:space="preserve">angulus F. </s>
  <s xml:id="echoid-s7053" xml:space="preserve">Rurſus quia in triangulo ſphærico B I F, angulus I, rectus eſt, erit <lb/>per eaſdem propoſitiones, vt ſinus anguli B, complementi altitudinis poli, quem Aequator facit <lb/>cum Horizonte, ad ſinum arcus F I, declinationis dati paralleli, ita ſinus anguli F, proxime co-<lb/>gniti ad ſinum arcus B I. </s>
  <s xml:id="echoid-s7054" xml:space="preserve">Igitur ex tribus notis cognitus fiet arcus B I, qui in ſignis borealibus ad-<lb/>ditus quadranti conficit arcum ſemidiurnum E I, in ſignis autem auſtralibus ex quadrante ſub-<lb/>latus relinquit arcum ſemidiurnum E I. </s>
  <s xml:id="echoid-s7055" xml:space="preserve">Itaque ſi fiat, vt ſinus complementi declinationis paral-<lb/>leli propoſiti ad ſinum totum, ita ſinus altitudinis poli ad aliud, habebitur ſinus quidam, quem <lb/>Primum Inuentum licebit appellare. </s>
  <s xml:id="echoid-s7056" xml:space="preserve">Deinde ſi fiat, vt ſinus complementi altitudinis poli ad ſi-<lb/>
<anchor type="note" xlink:label="note-0136-07a" xlink:href="note-0136-07"/>
num declinationis, ita ſinus, quem diximus Primum Inuentum, ad aliud, inuenietur ſinus, cuius <lb/>arcus, Sole exiſtente boreali, additus quadranti, vel Sole auſtrali exiſtente, ex quadrante demptus, <lb/>dabit arcum ſemidiurnum.</s>
  <s xml:id="echoid-s7057" xml:space="preserve"/>
</p>
<div xml:id="echoid-div394" type="float" level="2" n="5">
<note position="left" xlink:label="note-0136-06" xlink:href="note-0136-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0136-07" xlink:href="note-0136-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s7058" xml:space="preserve">COMMODISSIME etiam ſine triangulis ſphæricis latitudines ortiuas, occiduasue, atq; <lb/></s>
  <s xml:id="echoid-s7059" xml:space="preserve">
<anchor type="note" xlink:label="note-0136-08a" xlink:href="note-0136-08"/>
arcus ſemidiurnos reperiemus hac ratione. </s>
  <s xml:id="echoid-s7060" xml:space="preserve">Repetatur Analemma, hoc eſt, figura ſecunda præ-<lb/>cedentis propoſ. </s>
  <s xml:id="echoid-s7061" xml:space="preserve">vbi H N, tam in parallelo boreali, quàm in auſtrali oſtenſus eſt eſſe arcus ſemi-<lb/>diurnus; </s>
  <s xml:id="echoid-s7062" xml:space="preserve">Item E L, ſinus rectus eſt amplitudinis ortiuæ, occiduæue: </s>
  <s xml:id="echoid-s7063" xml:space="preserve">Nam vt in ſcholio propoſ. <lb/></s>
  <s xml:id="echoid-s7064" xml:space="preserve">1. </s>
  <s xml:id="echoid-s7065" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s7066" xml:space="preserve">demonſtrauimus recta, ex L, ducta ad B D, perpendicularis, cum ſit commu-<lb/>nis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s7067" xml:space="preserve">paralleli, aufert ex circulo A B C D, arcum latitudinis ortiuæ, ſiue occi-<lb/>duæ, cuius quidem ſinus eſt E L. </s>
  <s xml:id="echoid-s7068" xml:space="preserve">Quoniam igitur in triangulo rectangulo E k L, ſi E L, ponatur <lb/>ſinus totus, recta E K, eſt ſinus anguli E L <emph style="sc">K</emph>, complementi altitudinis poli, vt in tractatione ſinuũ
<pb o="117" file="0137" n="137" rhead="LIBER PRIMVS."/>
oſtendimus: </s>
  <s xml:id="echoid-s7069" xml:space="preserve">Si ſiat vt E k, ſinus complementi altitudinis poli ad E L, ſinum totum, ita E k, ſinus <lb/>declinationis paralleli dati reſpectu ſinus totius E F, ad aliud, inuenietur E L, ſinus amplitudinis <lb/>ortiuę, occiduæue, reſpectu eiuſdem <lb/>
<anchor type="figure" xlink:label="fig-0137-01a" xlink:href="fig-0137-01"/>
ſinus totius E F. </s>
  <s xml:id="echoid-s7070" xml:space="preserve">Ex ſinu autem E L, <lb/>amplitudo ipſa ortiua, occiduaue no-<lb/>ta fiet.</s>
  <s xml:id="echoid-s7071" xml:space="preserve"/>
</p>
<div xml:id="echoid-div395" type="float" level="2" n="6">
<note position="left" xlink:label="note-0136-08" xlink:href="note-0136-08a" xml:space="preserve">Amplitudo or. <lb/>tiua uel occi-<lb/>dua, quo modo <lb/>ſuppu@etur pe@ <lb/>ſinus ex Ana-<lb/>@emmate.</note>
  <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a">
    <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/>
  </figure>
</div>
<p>
  <s xml:id="echoid-s7072" xml:space="preserve">RVRSVS quia in eodem trian-<lb/>
<anchor type="note" xlink:label="note-0137-01a" xlink:href="note-0137-01"/>
gulo E K L, ſi E L, ponatur ſinus to-<lb/>tus, recta k L, eſt ſinus anguli k E L, <lb/>altitudinis poli, vt ex eadem tracta-<lb/>
<anchor type="note" xlink:label="note-0137-02a" xlink:href="note-0137-02"/>
tione ſinuum conſtat: </s>
  <s xml:id="echoid-s7073" xml:space="preserve">ſi fiat vt E K, <lb/>ſinus complementi altitudinis poli <lb/>ad K L, ſinum altitudinis poli, ita E K, <lb/>ſinus declinationis reſpectu ſinus to-<lb/>tius E F, ad aliud, cognita erit K L, in <lb/>partibus eiuſdem ſinus totius E F. <lb/></s>
  <s xml:id="echoid-s7074" xml:space="preserve">Deinde quoniam H K, eſt ſinus com-<lb/>plemẽti declinationis reſpectu ſinus <lb/>totius E F: </s>
  <s xml:id="echoid-s7075" xml:space="preserve">Si fiat, vt H K, ſinus com-<lb/>plementi declinationis reſpectu ſi-<lb/>
<anchor type="note" xlink:label="note-0137-03a" xlink:href="note-0137-03"/>
nus totius E F, ad K L, quatenus nota <lb/>facta eſt in partibus eiuſdem ſinus to <lb/>rius E F, ita H k, quatenus ſinus to-<lb/>rus in parallelo Solis, ad aliud, efficie <lb/>tur K L, nota in partibus eiuſdem ſi-<lb/>nus totius H k; </s>
  <s xml:id="echoid-s7076" xml:space="preserve">ac propterea eius arcus M N, notus erit, qui in parallelo boreali additus quadran <lb/>ti H M, complet arcum ſemidiurnum H N, in auſtrali vero ex quadrante H M, deductus relinquit <lb/>arcum ſemidiurnum H N. </s>
  <s xml:id="echoid-s7077" xml:space="preserve">Itaque ſi fiat, vt ſinus complementi altitudinis poli ad ſinum altitudi-<lb/>nis poli, ita ſinus declinationis propoſiti paralleliad aliud, reperietur ſinus quidam, quem Pri-<lb/>mum Inuẽtum nominemus. </s>
  <s xml:id="echoid-s7078" xml:space="preserve">Deinde ſi fiat, vt ſinus cõplementi declinationis ad ſinum, quem ap-<lb/>
<anchor type="note" xlink:label="note-0137-04a" xlink:href="note-0137-04"/>
pellaumus Primum Inuẽntum, ita ſinus totus ad aliud, inuentus erit ſinus cuiuſdam arcus, qui <lb/>Sole in ſignis borealibus commorante, adiectus ad quadrantem, vel Sole auſtralia percurrente ſi-<lb/>gna, ex quadrante detractus, dabit arcum ſemidiurnum. </s>
  <s xml:id="echoid-s7079" xml:space="preserve">Amplitudinẽ ergo ortiuam, occiduamve, <lb/>&amp; </s>
  <s xml:id="echoid-s7080" xml:space="preserve">arcnm ſemidiurnum cuiuſuis paralleli, ad datam poli altitudinem inueſtigauimus. </s>
  <s xml:id="echoid-s7081" xml:space="preserve">Quod fa-<lb/>ciendum erat.</s>
  <s xml:id="echoid-s7082" xml:space="preserve"/>
</p>
<div xml:id="echoid-div396" type="float" level="2" n="7">
<note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">Arcus ſemidiur <lb/>nus, qua uia per <lb/>ſinus eliciatur <lb/>ex Analẽmate.</note>
<note position="left" xlink:label="note-0137-02" xlink:href="note-0137-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0137-03" xlink:href="note-0137-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0137-04" xlink:href="note-0137-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div398" type="section" level="1" n="135">
<head xml:id="echoid-head138" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s7083" xml:space="preserve">DVOS alios modos inueniendi arcus ſemidiurni ſine triangulis quoque ſphæricis, Sole in quocunque <lb/>parallelo exiſtente, trademus in ſcholio propoſ. </s>
  <s xml:id="echoid-s7084" xml:space="preserve">ſequentis, quos lectori non ingratos fore confidimus.</s>
  <s xml:id="echoid-s7085" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s7086" xml:space="preserve">CAETERM arcus ſemidiurni parallelorum auftr alium, vt ex demonstratis conſtat, æquales <lb/>
<anchor type="note" xlink:label="note-0137-05a" xlink:href="note-0137-05"/>
<anchor type="note" xlink:label="note-0137-06a" xlink:href="note-0137-06"/>
ſunt ſeminocturnis arcubus parallelorum borealium oppoſitorum. </s>
  <s xml:id="echoid-s7087" xml:space="preserve">Eadem enim operatione in priori mo-<lb/>do inuentus eſt &amp; </s>
  <s xml:id="echoid-s7088" xml:space="preserve">arcus ſemidiurnus auſtr alis paralleli, &amp; </s>
  <s xml:id="echoid-s7089" xml:space="preserve">ſeminocturnus paralleli borealis oppoſiti. <lb/></s>
  <s xml:id="echoid-s7090" xml:space="preserve">Quod etiarn non obſcure ex propoſ. </s>
  <s xml:id="echoid-s7091" xml:space="preserve">19. </s>
  <s xml:id="echoid-s7092" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s7093" xml:space="preserve">2. </s>
  <s xml:id="echoid-s7094" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s7095" xml:space="preserve">elicitur. </s>
  <s xml:id="echoid-s7096" xml:space="preserve">Cùm enim ibi demonstretur, alterna ſeg-<lb/>menta oppoſitorum &amp; </s>
  <s xml:id="echoid-s7097" xml:space="preserve">æqualium parallelorum, in quæ ab Horizonte diuiduntur, &amp; </s>
  <s xml:id="echoid-s7098" xml:space="preserve">cuiuſmodi ſunt ar-<lb/>cus diurnus vnius paralleli, &amp; </s>
  <s xml:id="echoid-s7099" xml:space="preserve">arcus nocturnus alterius paralleli oppoſiti &amp; </s>
  <s xml:id="echoid-s7100" xml:space="preserve">æqualis, eſſe æqualia inter <lb/>ſe, erunt quoque eorum dimidia inter ſe æqualia, nempe arcus ſemidiurnus paralleli vnius, &amp; </s>
  <s xml:id="echoid-s7101" xml:space="preserve">ſemino-<lb/>cturnus alterius. </s>
  <s xml:id="echoid-s7102" xml:space="preserve">Igitur ſi omnium punctorum Eclipticæ arcus ſemidiurni deſiderentur, ſatis erit, vt ar-<lb/>
<anchor type="note" xlink:label="note-0137-07a" xlink:href="note-0137-07"/>
cus ſemidiurni inueſtigentur in par allelis auſtr alibus: </s>
  <s xml:id="echoid-s7103" xml:space="preserve">hienim, cũ æquales ſint arcubus ſeminocturnis pa-<lb/>rallelorum borealium oppoſitorum, vt dictum eſt, ſubducti ex ſemicirculo relinquent arcus etiam ſemi-<lb/>diurnos parallelorum borealium oppoſitorum.</s>
  <s xml:id="echoid-s7104" xml:space="preserve"/>
</p>
<div xml:id="echoid-div398" type="float" level="2" n="1">
<note position="left" xlink:label="note-0137-05" xlink:href="note-0137-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0137-06" xlink:href="note-0137-06a" xml:space="preserve">Arcus ſemidiu@ <lb/>ni parallelorũ <lb/>auſtraliũ æqua-<lb/>les ſunt arcu-<lb/>bus ſeminoctur <lb/>nis parallelorũ <lb/>borealium op-<lb/>poſitorum.</note>
<note position="right" xlink:label="note-0137-07" xlink:href="note-0137-07a" xml:space="preserve">Satis eſt, ſi inne <lb/>ſtigentur arcus <lb/>ſemidiurni pa-<lb/>rallelorum au-<lb/>ſtralium. Ex his <lb/>enim facili ne-<lb/>gotio elicientur <lb/>quoque arcus ſe <lb/>midiurni paral <lb/>lelorũ borealiũ <lb/>oppoſitorum.</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s7105" xml:space="preserve">HOC etiam ex poſteriori modo liquido conſtat. </s>
  <s xml:id="echoid-s7106" xml:space="preserve">Quoniam enim in Analemmate eadem operatione <lb/>inuentus est &amp; </s>
  <s xml:id="echoid-s7107" xml:space="preserve">arcus M N, in parallelo boreali, &amp; </s>
  <s xml:id="echoid-s7108" xml:space="preserve">in auſtrali, quo quidem &amp; </s>
  <s xml:id="echoid-s7109" xml:space="preserve">quadrans M I, arcum ſe-<lb/>minocturnum N I, paralleli borealis, &amp; </s>
  <s xml:id="echoid-s7110" xml:space="preserve">quadrans M H, arcum ſemidiurnum H N, paralleli auſtr alis <lb/>ſuperat, perſpicuum eſt, arcum ſeminocturnum N I, paralleli borealis æqualem eſſe ſemidiurno arcui <lb/>
<anchor type="note" xlink:label="note-0137-09a" xlink:href="note-0137-09"/>
N H, paralleli auſtralis. </s>
  <s xml:id="echoid-s7111" xml:space="preserve">Et ſic de cæteris. </s>
  <s xml:id="echoid-s7112" xml:space="preserve">Vbi etiam manifeſte cernis, arcum ſeminocturnum N I, ex <lb/>ſemicirculo H N I, ſubtractum relinquere arcum ſemidiurnum H N.</s>
  <s xml:id="echoid-s7113" xml:space="preserve"/>
</p>
<div xml:id="echoid-div399" type="float" level="2" n="2">
<note position="right" xlink:label="note-0137-09" xlink:href="note-0137-09a" xml:space="preserve">Satis eſt, ſi ſup-<lb/>putcn@ur arcus <lb/>ſemidiutni v-<lb/>nius quadrãtis <lb/>auſtralis Eclipti <lb/>cæ: quia ex his <lb/>arcus ſcmidiur <lb/>ni aliorũ pun-<lb/>ctorũ Eclipticæ <lb/>facile colligun-<lb/>tur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7114" xml:space="preserve">IMMO quia arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, qui interĳcitur inter Aequato-<lb/>rem, &amp; </s>
  <s xml:id="echoid-s7115" xml:space="preserve">colurum Solſtitiorum, æquales ſunt ſemidiurnis arcubus alterius quadrantis auſtralis, ſuppu-<lb/>tandi erunt duntaxat arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, nempe eius, qui inter prin <lb/>c<unsure/>ipium ♎, &amp; </s>
  <s xml:id="echoid-s7116" xml:space="preserve">principium ♑, interĳeitur. </s>
  <s xml:id="echoid-s7117" xml:space="preserve">Nam hi æquales erunt ſemidiurnis arcubus alterius quadran <lb/>tis auſiralis inter principium ♈, &amp; </s>
  <s xml:id="echoid-s7118" xml:space="preserve">principium ♑, intercepti. </s>
  <s xml:id="echoid-s7119" xml:space="preserve">Iidem verò ex ſemicir culo detracti re-
<pb o="118" file="0138" n="138" rhead="GNOMONICES"/>
linquunt arcus ſemidiurnos quadrantis Eclipticæ borealis inter principium ♈, &amp; </s>
  <s xml:id="echoid-s7120" xml:space="preserve">principium ♋, inter-<lb/>poſiti; </s>
  <s xml:id="echoid-s7121" xml:space="preserve">quirurſum æquales ſunt arcubus ſemidiurnis reliqui quadrantis borealis inter principium ♎, &amp; </s>
  <s xml:id="echoid-s7122" xml:space="preserve"><lb/>principium ♋, interiecti.</s>
  <s xml:id="echoid-s7123" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s7124" xml:space="preserve">IDEM prorſus dicendum eſt de latitudine ortiua, occiduave: </s>
  <s xml:id="echoid-s7125" xml:space="preserve">quia ſi ſupputentur pro vno quadran <lb/>tc<unsure/> Eclipticę ſiue auſtralis, ſiue borealis, omnes amplitudines ortiuę occiduęve, habebuntur etiam latitu-<lb/>dines ortiuæ, ſiue occiduę pro omnibus punctis Eclipticę, vt ex demonſtr atione patet: </s>
  <s xml:id="echoid-s7126" xml:space="preserve">quia nimirum de-<lb/>clinationes punctorum vnius quadrantis Eclipticæ, ex quibus latitudines ortiuę &amp; </s>
  <s xml:id="echoid-s7127" xml:space="preserve">occiduę ſupputantur, <lb/>æquales ſunt declinationibus reliquorum punctorum Eclipticæ, vt alibi ostenſum eſt à nobis.</s>
  <s xml:id="echoid-s7128" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div401" type="section" level="1" n="136">
<head xml:id="echoid-head139" xml:space="preserve">PROBLEMA 14. PROPOSITIO 35.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s7129" xml:space="preserve">CREPVSCVLORVM magnitudines in quocunque parallelo <lb/>ad datam poli altitudinem inuenire.</s>
  <s xml:id="echoid-s7130" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7131" xml:space="preserve">QVAMVIS problema hoc per triangula ſphærica poſſit abſolui, vt in ſcholio ſequenti de-<lb/>monſtrabimus, multo tamen breuius, &amp; </s>
  <s xml:id="echoid-s7132" xml:space="preserve">facilius idem per triangula plana rectilinea expediemus. <lb/></s>
  <s xml:id="echoid-s7133" xml:space="preserve">Sit enim Meridianus Analemmatis A B C D, cuius centrum E; </s>
  <s xml:id="echoid-s7134" xml:space="preserve">diameter Horizontis A C; </s>
  <s xml:id="echoid-s7135" xml:space="preserve">Ver-<lb/>ticalis B D; </s>
  <s xml:id="echoid-s7136" xml:space="preserve">axis mundi F G; </s>
  <s xml:id="echoid-s7137" xml:space="preserve">diameter Aequatoris H I; </s>
  <s xml:id="echoid-s7138" xml:space="preserve">diameter paralleli Solis K L, ſiue borealis, <lb/>ſiue auſtralis, circa quam ſemicirculus paralleli deſcribatur K P L, cuius centrum erit punctum <lb/>
<anchor type="note" xlink:label="note-0138-02a" xlink:href="note-0138-02"/>
M, vbi axis, &amp; </s>
  <s xml:id="echoid-s7139" xml:space="preserve">paralleli diameter ſe interſecant; </s>
  <s xml:id="echoid-s7140" xml:space="preserve">quandoquidem recta E M, perpendicularis ad <lb/>K L, ipſam K L, bifariam diuidit. </s>
  <s xml:id="echoid-s7141" xml:space="preserve">Ex puncto autem S, vbi diameter paralleli diametrum Hori-<lb/>
<anchor type="note" xlink:label="note-0138-03a" xlink:href="note-0138-03"/>
zontis ſecat, erigatur ad K L, perpendicularis S Q, quæ communis ſectio erit Horizontis, &amp; </s>
  <s xml:id="echoid-s7142" xml:space="preserve">paral-<lb/>leli. </s>
  <s xml:id="echoid-s7143" xml:space="preserve">Quoniam enim tam Horizon, quàm parallelus ad Meridianum rectus eſt, erit eorum com-<lb/>munis ſectio ad eundem perpendicularis; </s>
  <s xml:id="echoid-s7144" xml:space="preserve">atque adeo, per defin. </s>
  <s xml:id="echoid-s7145" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7146" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s7147" xml:space="preserve">11. </s>
  <s xml:id="echoid-s7148" xml:space="preserve">Euclidis, &amp; </s>
  <s xml:id="echoid-s7149" xml:space="preserve">ad diametrũ <lb/>
<anchor type="note" xlink:label="note-0138-04a" xlink:href="note-0138-04"/>
paralleli K L. </s>
  <s xml:id="echoid-s7150" xml:space="preserve">Cum ergo communis illa ſectio per punctum S, vbi ſe mutuo ſecant Horizon, &amp; </s>
  <s xml:id="echoid-s7151" xml:space="preserve"><lb/>parallelus in Meridiano, tranſeat, erit S Q, perpendicularis exiſtens ad k L, communis ſectio Ho-<lb/>rizontis, &amp; </s>
  <s xml:id="echoid-s7152" xml:space="preserve">paralleli. </s>
  <s xml:id="echoid-s7153" xml:space="preserve">Igitur K Q, arcus erit ſemidiurnus paralleli, cum intercipiatur inter Hori-<lb/>zontem, qui per punctum Q, tranſit, &amp; </s>
  <s xml:id="echoid-s7154" xml:space="preserve">Meridianum, qui in k, parallelum ſecat. </s>
  <s xml:id="echoid-s7155" xml:space="preserve">Ducatur quoque <lb/>diameter paralleli Horizontis X Y, infra Horizontem, in quo exiſtit Sol, cum crepuſculum matu-<lb/>
<anchor type="note" xlink:label="note-0138-05a" xlink:href="note-0138-05"/>
tinum incipit, vel veſpertinum deſinit, ita vt tam arcus A X, quàm C Y, comprehendat grad. </s>
  <s xml:id="echoid-s7156" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s7157" xml:space="preserve">Tot enim gradibus ab Horizonte abeſt Sol in initio matutini crepuſculi, vel in fine veſpertini, <lb/>vt communis eſt opinio, licet aliqui auctores minorem faciant hanc diſtantiam, &amp; </s>
  <s xml:id="echoid-s7158" xml:space="preserve">alij maiorem, <lb/>vt refert Petrus Nonius in parte ſecunda libri de crepuſculis propoſ. </s>
  <s xml:id="echoid-s7159" xml:space="preserve">1. </s>
  <s xml:id="echoid-s7160" xml:space="preserve">Secet autem diameter X Y, <lb/>paralleli Solis diametrum K L, in T, puncto, à quo ad K L, educatur perpendicularis T R, quæ <lb/>communis ſectio erit paralleli Solis, &amp; </s>
  <s xml:id="echoid-s7161" xml:space="preserve">paralleli Horizontis, in quo principium eſt, vel finis crepu-<lb/>ſculi. </s>
  <s xml:id="echoid-s7162" xml:space="preserve">Quoniam enim tam parallelus Solis, quà parallelus Horizontis ad Meridianum rectus <lb/>eſt, erit &amp; </s>
  <s xml:id="echoid-s7163" xml:space="preserve">eorum ſectio communis ad eundem, atque adeò per definitionem 3. </s>
  <s xml:id="echoid-s7164" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s7165" xml:space="preserve">11. </s>
  <s xml:id="echoid-s7166" xml:space="preserve">Euclidis, <lb/>
<anchor type="note" xlink:label="note-0138-06a" xlink:href="note-0138-06"/>
&amp; </s>
  <s xml:id="echoid-s7167" xml:space="preserve">ad rectam K L, in Meridiani plano exiſtentem perpendicularis, qualis eſt recta T R. </s>
  <s xml:id="echoid-s7168" xml:space="preserve">Erit ergo <lb/>longitudo crepuſculi arcus Q R, quandoquidem Sol in puncto R, exiſtit, quando occupat Hori-<lb/>
<anchor type="note" xlink:label="note-0138-07a" xlink:href="note-0138-07"/>
zontis parallelum X Y, in quo principium eſt crepuſculi matutini, vel finis veſpertini; </s>
  <s xml:id="echoid-s7169" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7170" xml:space="preserve">in pun-<lb/>cto Q, oritur, vel occidit. </s>
  <s xml:id="echoid-s7171" xml:space="preserve">Cum enim T R, ſit communis ſectio paralleli Solis, &amp; </s>
  <s xml:id="echoid-s7172" xml:space="preserve">Horizontis pa-<lb/>ralleli X Y, ſecabunt ſeſe mutuo hi paralleli in R, atque adeò Sol in puncto R, exiſtens vtrumque <lb/>parallelum poſſidebit. </s>
  <s xml:id="echoid-s7173" xml:space="preserve">Eodem pacto in puncto Q, exiſtens Horizontem tenebit, cum vt paulo <lb/>ante diximus, S Q, ſit communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s7174" xml:space="preserve">paralleli Solis. </s>
  <s xml:id="echoid-s7175" xml:space="preserve">Demittatur tandem ex K, <lb/>ad A C, perpendicularis K N, ſecans X Y, in O, eritq́; </s>
  <s xml:id="echoid-s7176" xml:space="preserve">K N, ſinus altitudinis meridianæ Solis in pa <lb/>rallelo K L, exiſtentis, hoc eſt, ſinus arcus K A; </s>
  <s xml:id="echoid-s7177" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7178" xml:space="preserve">recta K O, compoſita ex K N, ſinu altitudinis <lb/>meridianæ, &amp; </s>
  <s xml:id="echoid-s7179" xml:space="preserve">N O, ſinu diſtantię Solis ſub Horizonte in principio crepuſculi matutini, uel fine <lb/>veſpertini. </s>
  <s xml:id="echoid-s7180" xml:space="preserve">Sic etiam erit K S, ſinus verſus arcus ſemidiurni K Q; </s>
  <s xml:id="echoid-s7181" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7182" xml:space="preserve">K T, ſinus verſus arcus K R, <lb/>ex arcu ſemidiurno k Q, &amp; </s>
  <s xml:id="echoid-s7183" xml:space="preserve">arcu crepuſculi Q R, quem videlicer Sol in ſuo parallelo percurrit, <lb/>
<anchor type="note" xlink:label="note-0138-08a" xlink:href="note-0138-08"/>
<anchor type="note" xlink:label="note-0138-09a" xlink:href="note-0138-09"/>
dum crepuſculum durat, compoſitus.</s>
  <s xml:id="echoid-s7184" xml:space="preserve"/>
</p>
<div xml:id="echoid-div401" type="float" level="2" n="1">
<note position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0138-03" xlink:href="note-0138-03a" xml:space="preserve">3. tertĳ.</note>
<note position="left" xlink:label="note-0138-04" xlink:href="note-0138-04a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0138-05" xlink:href="note-0138-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0138-06" xlink:href="note-0138-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0138-07" xlink:href="note-0138-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0138-08" xlink:href="note-0138-08a" xml:space="preserve">Crepuſeuli ma <lb/>gnitudo, quo <lb/>modo inueſtige <lb/>tur, Sole exi-<lb/>ſtente in quo-<lb/>cunque paralle <lb/>10.</note>
<note position="left" xlink:label="note-0138-09" xlink:href="note-0138-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s7185" xml:space="preserve">ITAQVE quoniam in triangulo K O T, recta S N, baſi O T, parallela eſt, erit vt k N, ſinus <lb/>altitudinis Meridianæ ad K O, rectam compoſitam ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7186" xml:space="preserve">ex N O, ſinu <lb/>diſtantiæ Solis ſub Horizonte in principio crepuſculi matutini, vel fine veſpertini, ita K S, ſinus <lb/>verſus ſemidiurni arcus ad K T, ſinum verſum arcus compoſiti ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7187" xml:space="preserve">arcu crepu-<lb/>
<anchor type="note" xlink:label="note-0138-10a" xlink:href="note-0138-10"/>
ſculi. </s>
  <s xml:id="echoid-s7188" xml:space="preserve">Quamobrem ſi fiat, vt ſinus altitudinis meridianæ (quo pacto autem meridiana altitudo in-<lb/>ueniatur ex cognita declinatione Solis, in ſequenti ſcholio exponemus) ad rectam compoſitam <lb/>ex ſinu altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s7189" xml:space="preserve">ſinu grad. </s>
  <s xml:id="echoid-s7190" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7191" xml:space="preserve">(tot enim gradibus ſecundum communem ſenten-<lb/>tiam Sol infra Horizontem deprimitur in Verticali per centrum Solis tunc tranſeuntis) ita ſinus <lb/>verſus arcus ſemidiurni ad aliud, habebitur ſinus verſus arcus compoſiti ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7192" xml:space="preserve"><lb/>arcu crepuſculi. </s>
  <s xml:id="echoid-s7193" xml:space="preserve">Ex hoc ergo ſinu verſo ita inueniemus quantitatem crepuſculi. </s>
  <s xml:id="echoid-s7194" xml:space="preserve">Si ſinus verſus in-
<pb o="119" file="0139" n="139" rhead="LIBER PRIMVS."/>
uentus k T, maior fuerit ſinu toto, vt contingit in prioribus duabus figuris, detrahemus ex eo ſi-<lb/>
<anchor type="note" xlink:label="note-0139-01a" xlink:href="note-0139-01"/>
num totum K M, &amp; </s>
  <s xml:id="echoid-s7195" xml:space="preserve">reliqui ſinus T M, arcum P R, accipiemus. </s>
  <s xml:id="echoid-s7196" xml:space="preserve">Hic enim arcus P R, additus <lb/>quadranti k P, conficiet arcum k R, compoſitum ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7197" xml:space="preserve">arcu crepuſculi. </s>
  <s xml:id="echoid-s7198" xml:space="preserve">Quare <lb/>
<anchor type="figure" xlink:label="fig-0139-01a" xlink:href="fig-0139-01"/>
<anchor type="note" xlink:label="note-0139-02a" xlink:href="note-0139-02"/>
<anchor type="note" xlink:label="note-0139-03a" xlink:href="note-0139-03"/>
<anchor type="note" xlink:label="note-0139-04a" xlink:href="note-0139-04"/>
<anchor type="note" xlink:label="note-0139-05a" xlink:href="note-0139-05"/>
ablato arcu ſemidiurno k Q, reliquus erit arcus crepuſculi Q R. </s>
  <s xml:id="echoid-s7199" xml:space="preserve">Si verò dictus ſinus verſus K T, <lb/>fuerit minor ſinu toto, vt in tertia figura accidit, auferemus eum ex ſinu toto K M, &amp; </s>
  <s xml:id="echoid-s7200" xml:space="preserve">reliqui ſinus <lb/>T M, arcum P R, accipiemus. </s>
  <s xml:id="echoid-s7201" xml:space="preserve">Hic enim arcus P R, ex quadrante K P, ablatus reliquum faciet ar-<lb/>
<anchor type="note" xlink:label="note-0139-06a" xlink:href="note-0139-06"/>
cum k R, ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7202" xml:space="preserve">arcu crepuſculi compoſitum. </s>
  <s xml:id="echoid-s7203" xml:space="preserve">Si igitur ex hoc rurſum detraha-<lb/>mus arcum ſemidiurnum K Q, remanebit arcus crepuſculi Q R. </s>
  <s xml:id="echoid-s7204" xml:space="preserve">Si denique ſinus verſus prædi-<lb/>ctus k T, inuentus æqualis fuerit ſinui toti, vt in quarta figura euenit, erit ipſemet quadrans k P, <lb/>
<anchor type="note" xlink:label="note-0139-07a" xlink:href="note-0139-07"/>
arcus ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7205" xml:space="preserve">arcu crepuſculi compoſitus. </s>
  <s xml:id="echoid-s7206" xml:space="preserve">Ab hoc ergo quadrante ſi ſubtrahamus <lb/>arcum ſemidiutnum K Q, reliquus erit arcus crepuſculi Q R, vel Q P.</s>
  <s xml:id="echoid-s7207" xml:space="preserve"/>
</p>
<div xml:id="echoid-div402" type="float" level="2" n="2">
<note position="left" xlink:label="note-0138-10" xlink:href="note-0138-10a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Quando. finus <lb/>ve ſus inuen@us <lb/>fuent maior ſi-<lb/>nu toto, quom o <lb/>do per eum in-<lb/>veniatur @epu-<lb/>@@ulum.</note>
  <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a">
    <image file="0139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0139-01"/>
  </figure>
<note position="left" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0139-05" xlink:href="note-0139-05a" xml:space="preserve">Quando ſinus <lb/>uer us inuen tus <lb/>fuerit mi<unsure/>nor ſi-<lb/>nu to@o, qua ta-<lb/>@one ex eo cre-<lb/>puſculum elicia <lb/>@ur.</note>
<note position="right" xlink:label="note-0139-06" xlink:href="note-0139-06a" xml:space="preserve">Quando ſinus <lb/>uerſus inuẽrus <lb/>fuerit æqualis <lb/>ſinui toti, quo <lb/>pacto ex eo in <lb/>cognitionẽ<unsure/> cre-<lb/>puſculi uen@a-<lb/>mus.</note>
<note position="left" xlink:label="note-0139-07" xlink:href="note-0139-07a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Crepuſculum <lb/>quo modo ali-<lb/>ter explorandũ <lb/>ſit.</note>
<p>
  <s xml:id="echoid-s7208" xml:space="preserve">IDEM obtinebimus quoque hac ratione. </s>
  <s xml:id="echoid-s7209" xml:space="preserve">Quoniam in eiſdem figuris eſt, vt K N, ſinus alti-<lb/>tudinis meridianæ ad N O, ſinum occultationis Solis ſub Horizonte in principio crepuſculi ma-<lb/>tutini, vel fine veſpertini, quam occultationem ponimus grad. </s>
  <s xml:id="echoid-s7210" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7211" xml:space="preserve">ita K S, ſinus verſus arcus ſemi-<lb/>
<anchor type="note" xlink:label="note-0139-09a" xlink:href="note-0139-09"/>
diurni ad S T; </s>
  <s xml:id="echoid-s7212" xml:space="preserve">Si fiat, ut ſinus altitudinis meridianæ ad ſinum grad. </s>
  <s xml:id="echoid-s7213" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7214" xml:space="preserve">ita ſinus verſus arcus ſemi <lb/>diurni ad aliud, inuenietur numerus rectę S T, qui additus ſinui verſo arcus ſemidiurni conficit <lb/>ſinum uerſum arcus compoſiti ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7215" xml:space="preserve">arcu crepuſculi. </s>
  <s xml:id="echoid-s7216" xml:space="preserve">Ex quo ſinu verſo inuenie-<lb/>niemus, vt prius, crepuſculi longitudinem. </s>
  <s xml:id="echoid-s7217" xml:space="preserve">Exemplum nullum ponimus, quia ex figuris ipſis res <lb/>manifeſta per ſe exiſtit.</s>
  <s xml:id="echoid-s7218" xml:space="preserve"/>
</p>
<div xml:id="echoid-div403" type="float" level="2" n="3">
<note position="right" xlink:label="note-0139-09" xlink:href="note-0139-09a" xml:space="preserve">2. ſexti.</note>
</div>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Crepuſculum <lb/>qua tatione in <lb/>æquinoctus in-<lb/>ueſtigetur.</note>
<p>
  <s xml:id="echoid-s7219" xml:space="preserve">SOLE æquinoctialia puncta, ideſt, principium ♈, uel ♎, poſſidente, multo facilius crepu-<lb/>ſculorum magnitudines inuenientur hac ratione. </s>
  <s xml:id="echoid-s7220" xml:space="preserve">Ducta in prima figura ex H, ad A C, &amp; </s>
  <s xml:id="echoid-s7221" xml:space="preserve">X Y, <lb/>perpendiculari H α β, erit ut H α, ſinus altitudinis Aequatoris, ſiue complementi altitudinis po-<lb/>
<anchor type="note" xlink:label="note-0139-12a" xlink:href="note-0139-12"/>
li, ad α β, ſinum grad. </s>
  <s xml:id="echoid-s7222" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7223" xml:space="preserve">(quot nimirum graduum poſuimus arcum A X) ita H E, ſinus totus <lb/>ad E γ, ſinum rectum arcus crepuſculi δ G. </s>
  <s xml:id="echoid-s7224" xml:space="preserve">Si igitur fiat, ut ſinus complementi altitudinis poli <lb/>ad ſinum grad. </s>
  <s xml:id="echoid-s7225" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7226" xml:space="preserve">ita ſinus totus ad aliud, proueniet ſinus, cuius arcus dabit crepuſculum, Sole <lb/>in ęquinoctijs exiſtente.</s>
  <s xml:id="echoid-s7227" xml:space="preserve"/>
</p>
<div xml:id="echoid-div404" type="float" level="2" n="4">
<note position="right" xlink:label="note-0139-12" xlink:href="note-0139-12a" xml:space="preserve">2. ſexti.</note>
</div>
<note position="right" xml:space="preserve">Crepuſcula om <lb/>nia, qua ratione <lb/>facilime ſuppu-<lb/>te@tur.</note>
<p>
  <s xml:id="echoid-s7228" xml:space="preserve">CAETERVM inuenta hac ratione, quam proxime expoſuimus, quantitate rectæ E γ, inue-<lb/>niemus per eam crepuſcula omnium parallelorum, ſiue punctorum Eclipticæ, hoc modo. </s>
  <s xml:id="echoid-s7229" xml:space="preserve">Quo-<lb/>niam E γ, æqualis eſt ſingulis ſegmentis S T, diametrorum parallelorum in@er A C, X Y, interce-<lb/>
<anchor type="note" xlink:label="note-0139-14a" xlink:href="note-0139-14"/>
ptis, cognita erunt huiuſmodi ſegmenta in partibus ſinus totius maximi circuli in ſphæra. </s>
  <s xml:id="echoid-s7230" xml:space="preserve">Tanta
<pb o="120" file="0140" n="140" rhead="GNOMONICES"/>
enim erunt ſingula, quanta inuenta eſt recta E γ, Sole in ęquinoctijs exiſtente. </s>
  <s xml:id="echoid-s7231" xml:space="preserve">Hinc cognoſce-<lb/>mus eadem ſegmenta in partibus ſinus totius propriorum parallelorum, hac arte. </s>
  <s xml:id="echoid-s7232" xml:space="preserve">Fiat ut k M, ſi-<lb/>nus complementi declinationis paralleli cuiuſuis ad K M, quatenus ſinus totus proprii paralleli, <lb/>ita S T, quatenus nota in partibus ſinus totius in circulo maximo, ad aliud. </s>
  <s xml:id="echoid-s7233" xml:space="preserve">Prodibit enim nota <lb/>eadem S T, in partibus ſinus totius K M, proprii paralleli. </s>
  <s xml:id="echoid-s7234" xml:space="preserve">Vnde ſi S T, nota in partibus ſinus to-<lb/>tius proprii paralleli addatur ſinui verſo K S, arcus ſemidiurni, notus erit ſinus verſus K T, arcus <lb/>K R, compoſiti ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7235" xml:space="preserve">arcu crepuſculi. </s>
  <s xml:id="echoid-s7236" xml:space="preserve">Quare, ut prius, ex hoc ſinu uerſo quanti-<lb/>tatem crȩpuſculi inueniemus.</s>
  <s xml:id="echoid-s7237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div405" type="float" level="2" n="5">
<note position="right" xlink:label="note-0139-14" xlink:href="note-0139-14a" xml:space="preserve">34. primi.</note>
</div>
<p>
  <s xml:id="echoid-s7238" xml:space="preserve">HAEC autem ratio<unsure/> inueſtigandorum crepuſculorum videtur omnium facilima, &amp; </s>
  <s xml:id="echoid-s7239" xml:space="preserve">expedi-<lb/>tiſſima, quoniam in eadem poli altitudine recta E γ, ſemel inuenta in partibus ſinus totius circu-<lb/>
<anchor type="note" xlink:label="note-0140-01a" xlink:href="note-0140-01"/>
li maximi, eadem ſemper manet in omnibus parallelis Solis, ita vt nunquam mutetur: </s>
  <s xml:id="echoid-s7240" xml:space="preserve">cuius qui-<lb/>dem inuentio perfacilis eſt, cum in ea perueſtiganda ſinus totus uſurpetur, qui facilimam reddit <lb/>multiplicationem, ut ex demonſtratis conſtat. </s>
  <s xml:id="echoid-s7241" xml:space="preserve">Hac autem inuenta, reperitur arte proxime tradita <lb/>eadem E. </s>
  <s xml:id="echoid-s7242" xml:space="preserve">γ, uel S T, quatenus pars eſt ſinus totius proprii paralleli: </s>
  <s xml:id="echoid-s7243" xml:space="preserve">quę inuentio difficilis etiam <lb/>non eſt, propterea quòd ad eam in quirendam ſinus totus quoque adhibeatur, qui operationem <lb/>minus difficilem reddit, ut diximus. </s>
  <s xml:id="echoid-s7244" xml:space="preserve">Quod in prioribus præceptis non contingit. </s>
  <s xml:id="echoid-s7245" xml:space="preserve">Nun quam enim <lb/>in illis ſinus totus aſſumitur, ut recta K T, inueniatur. </s>
  <s xml:id="echoid-s7246" xml:space="preserve">Vnde multiplicatio difficilior aliquanto <lb/>redditur, vt pater. </s>
  <s xml:id="echoid-s7247" xml:space="preserve">Crepuſculorum ergo magnitudines, &amp; </s>
  <s xml:id="echoid-s7248" xml:space="preserve">c. </s>
  <s xml:id="echoid-s7249" xml:space="preserve">inuenimus. </s>
  <s xml:id="echoid-s7250" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s7251" xml:space="preserve"/>
</p>
<div xml:id="echoid-div406" type="float" level="2" n="6">
<note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div408" type="section" level="1" n="137">
<head xml:id="echoid-head140" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s7252" xml:space="preserve">ALTITVDO meridiana Solis ita reperitur, vt communiter omnes tradunt. </s>
  <s xml:id="echoid-s7253" xml:space="preserve">Sole in borealibus <lb/>
<anchor type="note" xlink:label="note-0140-03a" xlink:href="note-0140-03"/>
ſignis exiſtente, adĳciatur eius declinatio altitudini Aequatoris, ſeu complemento altitudinis poli: </s>
  <s xml:id="echoid-s7254" xml:space="preserve">Eo-<lb/>dem verò auſtr alia per currente ſigna, dematur eius declinatio ab altitudine Aequatoris, ſcu à comple-<lb/>mento altitudinis poli. </s>
  <s xml:id="echoid-s7255" xml:space="preserve">Numerus enim ex illa additione conflatus, vel ex hac ſubtr actione relictus da-<lb/>bit altitudinem meridianam quæſitam. </s>
  <s xml:id="echoid-s7256" xml:space="preserve">Vt Sole exiſtente in principio ♋, ſi eius declinatio, quæ continet <lb/>
<anchor type="note" xlink:label="note-0140-04a" xlink:href="note-0140-04"/>
grad. </s>
  <s xml:id="echoid-s7257" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7258" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7259" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7260" xml:space="preserve">addatur complemento altitudinis poli, ſiue eleuationi Aequatoris Romæ, quæ gradus <lb/>48. </s>
  <s xml:id="echoid-s7261" xml:space="preserve">complectitur, conficitur altitudo meridiana grad. </s>
  <s xml:id="echoid-s7262" xml:space="preserve">71. </s>
  <s xml:id="echoid-s7263" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7264" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7265" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s7266" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7267" xml:space="preserve">qualis Ro-<lb/>mæreperitur. </s>
  <s xml:id="echoid-s7268" xml:space="preserve">Sole verò in principio ♑, exiſtente, ſi eius declinatio, quæ eſt grad. </s>
  <s xml:id="echoid-s7269" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7270" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7271" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7272" xml:space="preserve">ab eleua-<lb/>tione Aequatoris, hoc est, à complemento altitudinis poli, nimirum à grad. </s>
  <s xml:id="echoid-s7273" xml:space="preserve">48. </s>
  <s xml:id="echoid-s7274" xml:space="preserve">detrabatur, reliqua erit <lb/>
<anchor type="note" xlink:label="note-0140-05a" xlink:href="note-0140-05"/>
altitudo meridiana grad. </s>
  <s xml:id="echoid-s7275" xml:space="preserve">24. </s>
  <s xml:id="echoid-s7276" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7277" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7278" xml:space="preserve">Huius operationis ratio perſpicua eſt ex ſuperioribus figuris. <lb/></s>
  <s xml:id="echoid-s7279" xml:space="preserve">Nam in prima, vbi parallelus diametri K L, borealis eſt, componitur altitudo meridiana A K, ex de-<lb/>clinatione K H, &amp; </s>
  <s xml:id="echoid-s7280" xml:space="preserve">altitudine Aequatoris H A. </s>
  <s xml:id="echoid-s7281" xml:space="preserve">In alĳs verò, in quibus parallelus diametri K L, au-<lb/>ſtralis eſt, prouenit altitudo meridiana A K, ſi declinatio K H, ab altitudine Aequatoris H A, <lb/>deducatur.</s>
  <s xml:id="echoid-s7282" xml:space="preserve"/>
</p>
<div xml:id="echoid-div408" type="float" level="2" n="1">
<note position="left" xlink:label="note-0140-03" xlink:href="note-0140-03a" xml:space="preserve">Meridiana alti <lb/>tudo Solis quo <lb/>pacto reperiat.</note>
<note position="left" xlink:label="note-0140-04" xlink:href="note-0140-04a" xml:space="preserve">Quando nume <lb/>rus conflatus ex <lb/>declinatione bo <lb/>reali &amp; altitudi <lb/>ne Aequatoris <lb/>ſuperat gra. 90. <lb/>Quando altitu <lb/>do poli minor <lb/>eſt declinatione <lb/>borealis paralle <lb/>li Solis, verteæ <lb/>loci eſt inter pa <lb/>ralielum Solis <lb/>&amp; Aȩquatorem, <lb/>altitudoq́; meri <lb/>diana solis eſt <lb/>borealis.</note>
<note position="left" xlink:label="note-0140-05" xlink:href="note-0140-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s7283" xml:space="preserve">SED hic nonulla obſeruanda ſunt. </s>
  <s xml:id="echoid-s7284" xml:space="preserve">Primum, quando in ſignis borealibus ex additione declina-<lb/>tionis ad eleuationem Aequatoris maior numerus conflatur, quàm grad. </s>
  <s xml:id="echoid-s7285" xml:space="preserve">90. </s>
  <s xml:id="echoid-s7286" xml:space="preserve">auferendus eſt numer us <lb/>
<anchor type="note" xlink:label="note-0140-06a" xlink:href="note-0140-06"/>
conflatus ex ſemicir culo, vt altitudo meridiana babeatur. </s>
  <s xml:id="echoid-s7287" xml:space="preserve">Tunc enim Sol inter verticem B, &amp; </s>
  <s xml:id="echoid-s7288" xml:space="preserve">polum <lb/>arcticum F, exiſtet, vel (quod idem eſt) vertex B, inter Solem &amp; </s>
  <s xml:id="echoid-s7289" xml:space="preserve">Aequatorem: </s>
  <s xml:id="echoid-s7290" xml:space="preserve">vt in priori figura hu-<lb/>ius ſcholĳ cernitur, vbi arcus A K, inter Horizontem, &amp; </s>
  <s xml:id="echoid-s7291" xml:space="preserve">parallelum borealem, quadr antem A B, ſupe-<lb/>
<anchor type="note" xlink:label="note-0140-07a" xlink:href="note-0140-07"/>
rat, &amp; </s>
  <s xml:id="echoid-s7292" xml:space="preserve">altitudo meridiana eſt arcus C k, ex parte boreali, vertex{q́ue}, B, inter parallelum Solis, &amp; </s>
  <s xml:id="echoid-s7293" xml:space="preserve">Ae-<lb/>quatorem conſtitutus eſt. </s>
  <s xml:id="echoid-s7294" xml:space="preserve">Quod quidem accidit, cum altitudo poli minor eſt declinatione propoſiti pa-<lb/>ralleli, vt bic contingit. </s>
  <s xml:id="echoid-s7295" xml:space="preserve">Arcus enim B H, qui arcui altitudinis poli C F, ęqualis eſt, vt in ſphæra ostendi-<lb/>mus, &amp; </s>
  <s xml:id="echoid-s7296" xml:space="preserve">ex fig ur a facile colligitur, (Nam ſi ex ęqualibus quadr antibus C B, F H, dematur communis <lb/>
<anchor type="note" xlink:label="note-0140-08a" xlink:href="note-0140-08"/>
arous F B, æquales remanent arcus C F, B H,) minor est declinatione H K. </s>
  <s xml:id="echoid-s7297" xml:space="preserve">Quòd ſi altitudo poli <lb/>B H, æqualis quandoque fuerit declinationi paralleli, tanget parallelus Verticalem in B, vertice, erit{q́ue} <lb/>altitudo meridiana quadrans, nempe C B, vel A B, grad. </s>
  <s xml:id="echoid-s7298" xml:space="preserve">90.</s>
  <s xml:id="echoid-s7299" xml:space="preserve"/>
</p>
<div xml:id="echoid-div409" type="float" level="2" n="2">
<note position="left" xlink:label="note-0140-06" xlink:href="note-0140-06a" xml:space="preserve">Quando altitu-<lb/>do poli æqualis <lb/>eſt declinationi <lb/>borealis paralle <lb/>li Solis, tangit <lb/>parallelus Solis <lb/>Verticalem cir-<lb/>culum in B, uer <lb/>tice, altitudoq́ue <lb/>meridiana Solis <lb/>eſt quadrans.</note>
<note position="left" xlink:label="note-0140-07" xlink:href="note-0140-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0140-08" xlink:href="note-0140-08a" xml:space="preserve">Quando com-<lb/>plemen tum al-<lb/>titudinis poli <lb/>minus eſt decli-<lb/>natione borea-<lb/>lis paralleli So-<lb/>lis, extat totus <lb/>parallelus ſupra <lb/>Horizontẽ, nul <lb/>lumq́; crepuſcu <lb/>lunt ht. Sol au-<lb/>tem duas habet <lb/>altitudines me-<lb/>ridianas in eo <lb/>parallelo.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7300" xml:space="preserve">DEINDE, quando complementum altitudinis poli minus eſt declinatione paralleli borealis, exta-<lb/>bit parallelus totus ſupra Horizontem, habebitq́, duas altitudines meridianas, auſtralem vnam, quæ ma-<lb/>ior cſt, &amp; </s>
  <s xml:id="echoid-s7301" xml:space="preserve">alteram Septentrionalem, quæ minor eſt. </s>
  <s xml:id="echoid-s7302" xml:space="preserve">Prior inuenitur per regulam ſupra traditam; </s>
  <s xml:id="echoid-s7303" xml:space="preserve">poſte-<lb/>
<anchor type="note" xlink:label="note-0140-09a" xlink:href="note-0140-09"/>
rior autem babetur, ſi complementum altitudinis poli ex declinatione dematur. </s>
  <s xml:id="echoid-s7304" xml:space="preserve">Perſpicuum hoc eſt in <lb/>ſecunda figura huius ſcholĳ, vbi C I, complementum altitudinis poli minus eſt declinatione I L, &amp; </s>
  <s xml:id="echoid-s7305" xml:space="preserve">pa-<lb/>rallelus borealis K L, totus eſt ſupra Horizontem; </s>
  <s xml:id="echoid-s7306" xml:space="preserve">altitudo meridiana auſtr alis &amp; </s>
  <s xml:id="echoid-s7307" xml:space="preserve">maior, arcus A K; <lb/></s>
  <s xml:id="echoid-s7308" xml:space="preserve">
<anchor type="note" xlink:label="note-0140-10a" xlink:href="note-0140-10"/>
borealis verò &amp; </s>
  <s xml:id="echoid-s7309" xml:space="preserve">minor, arcus C L, quæ babetur, ſi ex declinatione I L, auferatur complementum altitu-<lb/>dinis poli I C. </s>
  <s xml:id="echoid-s7310" xml:space="preserve">Sole autem in hoc parallelo exiſtente nullum crepuſculum eſt, cum continua dies exiſtat. <lb/></s>
  <s xml:id="echoid-s7311" xml:space="preserve">Quòd ſi complementum altitudinis poli I C, fuerit quandoque ęquale declinationi paralleli, tanget pa-<lb/>rallelus Horizontem in C, totusq́, ſupra Horizontem extabit, vnde nec tunc crepuſculum quæren-<lb/>dum erit.</s>
  <s xml:id="echoid-s7312" xml:space="preserve"/>
</p>
<div xml:id="echoid-div410" type="float" level="2" n="3">
<note position="left" xlink:label="note-0140-09" xlink:href="note-0140-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0140-10" xlink:href="note-0140-10a" xml:space="preserve">Quando com-<lb/>plementũ altitu <lb/>dinis poli æqua <lb/>le eſt declinatio <lb/>ni borealis pa-<lb/>ralleli Solis, tan <lb/>git parallelus <lb/>Horizontẽ, nul <lb/>lumq́; eſt crepu <lb/>ſculum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7313" xml:space="preserve">TERTIO quando in ſignis austr alibus declinatio paralleli alicuius maior fuerit complemento <lb/>altitudinis poli, &amp; </s>
  <s xml:id="echoid-s7314" xml:space="preserve">propterea auferri non poſſit à dicto complemento, vt altitudo meridiana habeatur, <lb/>
<anchor type="note" xlink:label="note-0140-11a" xlink:href="note-0140-11"/>
nullam habebit Sol in illo parallelo altitudinem meridianam, ſed totus parallelus ſub Horizonte late-
<pb o="121" file="0141" n="141" rhead="LIBER PRIMVS."/>
bit, vt patet in eadem ſecunda figura, in qua declinatio auſtralis H K, maior eſt complemento altitudinis <lb/>
<anchor type="note" xlink:label="note-0141-01a" xlink:href="note-0141-01"/>
poli A H. </s>
  <s xml:id="echoid-s7315" xml:space="preserve">Quòd ſi a<unsure/>rcus A K, differentia inter complementum altitudinis poli A H, &amp; </s>
  <s xml:id="echoid-s7316" xml:space="preserve">declinationem <lb/>auſtralem H K, minor fuerit arcu A X, qui inter Horizontem &amp; </s>
  <s xml:id="echoid-s7317" xml:space="preserve">parallelum, qui incedit per initium <lb/>
<anchor type="figure" xlink:label="fig-0141-01a" xlink:href="fig-0141-01"/>
<anchor type="note" xlink:label="note-0141-02a" xlink:href="note-0141-02"/>
<anchor type="note" xlink:label="note-0141-03a" xlink:href="note-0141-03"/>
<anchor type="note" xlink:label="note-0141-04a" xlink:href="note-0141-04"/>
crepuſculi matutini, &amp; </s>
  <s xml:id="echoid-s7318" xml:space="preserve">per finem veſpertini, interĳcitur, erit crepuſculum, dum @ol arcum k R, &amp; </s>
  <s xml:id="echoid-s7319" xml:space="preserve">alte-<lb/>rum ſibi æqualem percurrit, ita vt K R, ſit crepuſculi dimidium; </s>
  <s xml:id="echoid-s7320" xml:space="preserve">quia in arcu K R, &amp; </s>
  <s xml:id="echoid-s7321" xml:space="preserve">in alio ſibi æqua-<lb/>
<anchor type="note" xlink:label="note-0141-05a" xlink:href="note-0141-05"/>
li Sol minus diſtat ab Horizonte, quàm grad. </s>
  <s xml:id="echoid-s7322" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7323" xml:space="preserve">Huius autem arcus quantitatem it a inueniemus. </s>
  <s xml:id="echoid-s7324" xml:space="preserve">Ex <lb/>puncto L, paralleli auſtralis in posteriori figura huius ſcholĳ, ducatur ad A C, perpendicularis L N, ſe-<lb/>cans X Y, in O. </s>
  <s xml:id="echoid-s7325" xml:space="preserve">Item per K, &amp; </s>
  <s xml:id="echoid-s7326" xml:space="preserve">M, agantur ipſi A C, parallelæ K θ, M λ, ſecantes L N, in θ, &amp; </s>
  <s xml:id="echoid-s7327" xml:space="preserve">λ. </s>
  <s xml:id="echoid-s7328" xml:space="preserve">An-<lb/>te omnia veniemus in cognitionem rectarum L λ, L O, hoc pacto. </s>
  <s xml:id="echoid-s7329" xml:space="preserve">Totus arcus C L, quem appellare poſ-<lb/>ſumus depreſſionem Solis ſub Horizonte, hoc eſt, distantiam ipſius in Meridiano ſub Horizonte maio-<lb/>
<anchor type="note" xlink:label="note-0141-06a" xlink:href="note-0141-06"/>
<anchor type="note" xlink:label="note-0141-07a" xlink:href="note-0141-07"/>
rem, (Habet enim Sol in illo parallelo duas depreſſiones ſub Horizonte, maiorem C L, &amp; </s>
  <s xml:id="echoid-s7330" xml:space="preserve">minorẽ A K, <lb/>quarum illa ad ſeptentrionem, hæc verò ad auſtrum vergit) compoſitus ex C I, complemento altitudinis <lb/>poli, &amp; </s>
  <s xml:id="echoid-s7331" xml:space="preserve">I L, declinatione auſtrali, notus eſt. </s>
  <s xml:id="echoid-s7332" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s7333" xml:space="preserve">eius ſinus L N, notus erit. </s>
  <s xml:id="echoid-s7334" xml:space="preserve">Rurſus arcus A K, <lb/>depreſſionis minoris notus eſt, cum ſit differentia inter arcum declinationis auſtralis H K, &amp; </s>
  <s xml:id="echoid-s7335" xml:space="preserve">arcum <lb/>complementi altitudinis poli A H. </s>
  <s xml:id="echoid-s7336" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s7337" xml:space="preserve">eius ſinus θ N, cognitus erit. </s>
  <s xml:id="echoid-s7338" xml:space="preserve">Ablato ergo ſinu θ N, ex <lb/>L N, ſinu, qui iam cognitus eſt, remanebit &amp; </s>
  <s xml:id="echoid-s7339" xml:space="preserve">L θ, nota, quæ differentia eſt inter ſinum maioris depreſ-<lb/>ſionis, &amp; </s>
  <s xml:id="echoid-s7340" xml:space="preserve">ſinum minoris depreſſionis ſub Horizonte. </s>
  <s xml:id="echoid-s7341" xml:space="preserve">Quoniam verò eſt vt L M, ad M K, it a L λ, ad λ θ; <lb/></s>
  <s xml:id="echoid-s7342" xml:space="preserve">
<anchor type="note" xlink:label="note-0141-08a" xlink:href="note-0141-08"/>
eſt autem L M, æqualis ipſi M K; </s>
  <s xml:id="echoid-s7343" xml:space="preserve">erit quoque L λ, ipſi λ θ, æqualis. </s>
  <s xml:id="echoid-s7344" xml:space="preserve">Cum ergo L θ, recta nota ſit, erit <lb/>&amp; </s>
  <s xml:id="echoid-s7345" xml:space="preserve">eius medietas L λ, nota. </s>
  <s xml:id="echoid-s7346" xml:space="preserve">At vero L O, nota eſt, cum ſit differentia inter L N, ſinum maioris depreſ-<lb/>ſionis, &amp; </s>
  <s xml:id="echoid-s7347" xml:space="preserve">O N, ſinum grad. </s>
  <s xml:id="echoid-s7348" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7349" xml:space="preserve">nempe arcus A X, vel C Y. </s>
  <s xml:id="echoid-s7350" xml:space="preserve">Vtraque ergo L λ, L O, nota eſt.</s>
  <s xml:id="echoid-s7351" xml:space="preserve"/>
</p>
<div xml:id="echoid-div411" type="float" level="2" n="4">
<note position="left" xlink:label="note-0140-11" xlink:href="note-0140-11a" xml:space="preserve">Quando decli-<lb/>nauo paralleli</note>
<note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">auſtralis maior <lb/>eſt complemen <lb/>to altitudinis <lb/>poli, exiſtit to-<lb/>tus parallelus <lb/>ſub Horizonte, <lb/>nullamq́; habet <lb/>altitudinẽ meri <lb/>dianam.</note>
  <figure xlink:label="fig-0141-01" xlink:href="fig-0141-01a">
    <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0141-01"/>
  </figure>
<note position="left" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">Crepuſculum <lb/>quantum ſit, <lb/>dum parallelus <lb/>auſtralis totus <lb/>ſub Horizont<unsure/>e <lb/>la@er.</note>
<note position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">Crepuſeulum, <lb/>quando paralle <lb/>lus auſtralis to-<lb/>tus ſub Horizõ-<lb/>te latet, quo pa-<lb/>cto in@eniatur.</note>
<note position="left" xlink:label="note-0141-06" xlink:href="note-0141-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0141-07" xlink:href="note-0141-07a" xml:space="preserve">Depreſſio Solis <lb/>quid.</note>
<note position="right" xlink:label="note-0141-08" xlink:href="note-0141-08a" xml:space="preserve">2. ſexti.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s7352" xml:space="preserve">IAM verò quoniam eſt, vt L λ, ad L O, ita L M, ad L T; </s>
  <s xml:id="echoid-s7353" xml:space="preserve">ſi fiat, vt L λ, medietas differentiæ in-<lb/>
<anchor type="note" xlink:label="note-0141-10a" xlink:href="note-0141-10"/>
ter ſinum maioris depreſſionis &amp; </s>
  <s xml:id="echoid-s7354" xml:space="preserve">ſinũ minoris, ad L O, differentiam inter ſinum maioris depreſſionis, &amp; </s>
  <s xml:id="echoid-s7355" xml:space="preserve"><lb/>ſinum grad. </s>
  <s xml:id="echoid-s7356" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7357" xml:space="preserve">it a L M, ſinus totus ad aliud, inuenietur L T, ſinus verſus arcus L R. </s>
  <s xml:id="echoid-s7358" xml:space="preserve">Ex quo ſinu verſo <lb/>L T, ita perueſtigabimus arcum K R, dimidiati crepuſculi. </s>
  <s xml:id="echoid-s7359" xml:space="preserve">Quando ſinus verſus L T, inuentus maior <lb/>eſt ſinu toto L M, auferemus ex eo ſinum totum, vt habeamus ſinum rectum M T, cuius arcum P R, ex <lb/>tabula ſinuum acceptum auferemus ex quadrante K P, remanebitq́, arcus K R, dimidĳ crepuſculinotus. <lb/></s>
  <s xml:id="echoid-s7360" xml:space="preserve">Si verò ſinus verſus L T, fuerit repertus æqualis ſinui toti, erit arcus dimidĳ crepuſculi quadrans inte-<lb/>ger, quia tunc diameter K L, tranſit per punctum, vbi axis diametrum X Y, interſecat, ac proinde pun <lb/>ctum T, in punctum M, cadet. </s>
  <s xml:id="echoid-s7361" xml:space="preserve">Si denique deprehenſus fuerit ſinus verſus L T, minor ſinu toto, aufere-<lb/>mus eum ex ſin@ toto, &amp; </s>
  <s xml:id="echoid-s7362" xml:space="preserve">reliqui ſinus recti arcum ex tabula ſinuum acceptum adĳciemus ad quadran-<lb/>
<anchor type="note" xlink:label="note-0141-11a" xlink:href="note-0141-11"/>
tem, vt habeamus arcum dimidĳ crepuſculi: </s>
  <s xml:id="echoid-s7363" xml:space="preserve">quia tunc diameter K L, ſecat axem inter E, centrum, <lb/>Analemmatis &amp; </s>
  <s xml:id="echoid-s7364" xml:space="preserve">diametrum X Y, at que adeo punctum T, cadet inter M, centrum paralleli, &amp; </s>
  <s xml:id="echoid-s7365" xml:space="preserve">pun-<lb/>ctum L, vt patet.</s>
  <s xml:id="echoid-s7366" xml:space="preserve"/>
</p>
<div xml:id="echoid-div412" type="float" level="2" n="5">
<note position="right" xlink:label="note-0141-10" xlink:href="note-0141-10a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0141-11" xlink:href="note-0141-11a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s7367" xml:space="preserve">SI verò arcus A K, infra Horizontem, nempe differentia inter cõplementum altitudinis poli A H, <lb/>
<anchor type="note" xlink:label="note-0141-12a" xlink:href="note-0141-12"/>
&amp; </s>
  <s xml:id="echoid-s7368" xml:space="preserve">declinationem auſtralem H K, (quando in ſignis auſtralibus declinatio maior eſt, quàm complemen-<lb/>tum altitudinis poli) æqualis fuerit, vel maior arcu A X, nullum erit crepuſculum, Sole illum paralle-<lb/>lum auſtralem percurrente; </s>
  <s xml:id="echoid-s7369" xml:space="preserve">quia tunc Sol ſub Horizonte ſemper plus diſtat ab Horizonte, quàm grad. </s>
  <s xml:id="echoid-s7370" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s7371" xml:space="preserve">niſi dicere velimus crepuſculum, punctum illud temporis, in quo Sol in puncto X, existit in media nocte, <lb/>quando nimirum arcus A K, æqualis eſt arcui A X.</s>
  <s xml:id="echoid-s7372" xml:space="preserve"/>
</p>
<div xml:id="echoid-div413" type="float" level="2" n="6">
<note position="right" xlink:label="note-0141-12" xlink:href="note-0141-12a" xml:space="preserve">Crepuſeulum <lb/>quãdo nu llum <lb/>ſit, Sole exiſten <lb/>te in auſtrali-<lb/>bus ſignis.</note>
</div>
<note position="right" xml:space="preserve">Crepuſculum <lb/>quãdo nullum <lb/>ſit, Sole in æqui <lb/>noctijs exiſtẽte.</note>
<p style="it">
  <s xml:id="echoid-s7373" xml:space="preserve">QVOD ſi complementum altitudinis poli minus fuerit arcu grad. </s>
  <s xml:id="echoid-s7374" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7375" xml:space="preserve">vt in ſecunda figura huius <lb/>ſcholĳ contingit, (eſt enim arcus C I, complementi altitudinis poli minor arcu C Y, grad. </s>
  <s xml:id="echoid-s7376" xml:space="preserve">18.) </s>
  <s xml:id="echoid-s7377" xml:space="preserve">erit, So-
<pb o="122" file="0142" n="142" rhead="GNOMONICES"/>
le exiſtente in æquinoctĳs, per totam noctem crepuſculum, quia minus tunc ab Horizonte ſemper Sol d@@ <lb/>ſtat, quàm grad. </s>
  <s xml:id="echoid-s7378" xml:space="preserve">18.</s>
  <s xml:id="echoid-s7379" xml:space="preserve"/>
</p>
  <figure>
    <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s7380" xml:space="preserve">PORRO ſi quis nolit vti ſinubus verſis, poterit alio modo crepuſculorum magnitudines indagare, <lb/>&amp; </s>
  <s xml:id="echoid-s7381" xml:space="preserve">fortaſſis commodius. </s>
  <s xml:id="echoid-s7382" xml:space="preserve">Quod vt declaremus, docebimus prius inucſtigare depreſſionem meridianam So-<lb/>lis, hoc eſt, diſtantiam eius ſub Horizonte in Meridiano. </s>
  <s xml:id="echoid-s7383" xml:space="preserve">Hæc autem ita reperietur. </s>
  <s xml:id="echoid-s7384" xml:space="preserve">In ſignis borealibus <lb/>
<anchor type="note" xlink:label="note-0142-03a" xlink:href="note-0142-03"/>
detrahatur declinatio paralleli propoſiti ex complemento altitudinis poli; </s>
  <s xml:id="echoid-s7385" xml:space="preserve">In ſignis verò auſtralibus <lb/>eadem declinatio ad complementum altitudinis poli addatur. </s>
  <s xml:id="echoid-s7386" xml:space="preserve">Numerus enim ex illa ſubtractione reli-<lb/>
<anchor type="note" xlink:label="note-0142-04a" xlink:href="note-0142-04"/>
ctus, vel ex hac additione compoſitus, dabit depreſſionem meridianam, vt perſpicuum eſt ex quatuor fi-<lb/>guris huius propoſ. </s>
  <s xml:id="echoid-s7387" xml:space="preserve">in quibus perpetuò depreſſio meridiana eſt arcus C L. </s>
  <s xml:id="echoid-s7388" xml:space="preserve">Eſt autem depreſſio cuiuslibet <lb/>paralleli æqualis altitudini meridianæ paralleli oppoſiti. </s>
  <s xml:id="echoid-s7389" xml:space="preserve">Si enim ex L, per centrum E, duceretur diame <lb/>ter, caderet hæc in quadrante A B, in punctum, per quod diameter paralleli oppoſiti eſſet ducendus, vt <lb/>
<anchor type="note" xlink:label="note-0142-05a" xlink:href="note-0142-05"/>
patet. </s>
  <s xml:id="echoid-s7390" xml:space="preserve">Cum ergo huiuſmodi diameter vna cum diametro Horizontis A C, ad verticem E, angulos æqua-<lb/>
<anchor type="note" xlink:label="note-0142-06a" xlink:href="note-0142-06"/>
les faciat, erunt arcus, quibus inſiſtunt dicti æquales anguli ad centrum E, inter ſe æquales; </s>
  <s xml:id="echoid-s7391" xml:space="preserve">nempe ar-<lb/>
<anchor type="note" xlink:label="note-0142-07a" xlink:href="note-0142-07"/>
cus depreſſionis meridianæ C L, &amp; </s>
  <s xml:id="echoid-s7392" xml:space="preserve">arcus altitudinis meridianæ paralleli oppoſiti. </s>
  <s xml:id="echoid-s7393" xml:space="preserve">Vnde ſi quæratur de-<lb/>
<anchor type="note" xlink:label="note-0142-08a" xlink:href="note-0142-08"/>
preſſio meridiana alicuius paralleli, poterit pro ea aſſumi altitudo meridiana paralleli oppoſiti.</s>
  <s xml:id="echoid-s7394" xml:space="preserve"/>
</p>
<div xml:id="echoid-div414" type="float" level="2" n="7">
<note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">Depreſſio meri <lb/>dſana So ´is quo <lb/>modo reperia-<lb/>tur.</note>
<note position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">Depreſſio meri-<lb/>diana cuiusli-<lb/>bet paralleli æ-<lb/>qualis eſt altitu <lb/>dini meridianæ <lb/>paralleli oppo-<lb/>ſiti.</note>
<note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0142-07" xlink:href="note-0142-07a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0142-08" xlink:href="note-0142-08a" xml:space="preserve">Quando nume <lb/>rus compoſitus <lb/>ex complemen-<lb/>to altitudinis <lb/>poli, &amp; declina-<lb/>tione auſtrali <lb/>quadrãrem ex-<lb/>ceſſerit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7395" xml:space="preserve">VERVM hic quoque obſeruanda nonnulla ſunt. </s>
  <s xml:id="echoid-s7396" xml:space="preserve">Si enim in ſignis auſtralibus numerus ex comple-<lb/>mento altitudinis poli, &amp; </s>
  <s xml:id="echoid-s7397" xml:space="preserve">declinatione conflatus maior fuerit quadrante, numerus conflatus ex ſemicir-<lb/>culo erit auferendus, vt depreſſio meridiana habeatur, ceu videre eſt in prima figura huius ſcholĳ. </s>
  <s xml:id="echoid-s7398" xml:space="preserve">Simi-<lb/>liter@ ſi in ſignis borealibus declinatio paralleli fuerit maior complemento altitudinis poli, ita vt illa ab <lb/>
<anchor type="note" xlink:label="note-0142-09a" xlink:href="note-0142-09"/>
hoc detrahi nequeat, extabit totus parallelus ſupra Horizontem, vt in ſecunda figura huius ſcholĳ appa-<lb/>ret. </s>
  <s xml:id="echoid-s7399" xml:space="preserve">Quare nulla erit tunc depreſſio meridiana, ſed parallelus duas meridianas altitudines habebit, vt <lb/>
<anchor type="note" xlink:label="note-0142-10a" xlink:href="note-0142-10"/>
paulo ante dictum eſt. </s>
  <s xml:id="echoid-s7400" xml:space="preserve">Quando denique in ſignis auſtralibus declinatio paralleli maior fuerit comple-<lb/>mento altitudinis poli, vt in eadem ſecunda figura huius ſcholĳ apparet, dictum iam eſt paulo ante, pa-<lb/>rallelum tunc eſſe totum ſub Horizonte, habereq́, duas depreſſiones meridianas, quas ibidem inueſtiga-<lb/>uimus; </s>
  <s xml:id="echoid-s7401" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7402" xml:space="preserve">aliquando poſſe eſſe crepuſculum, aliquando autem non; </s>
  <s xml:id="echoid-s7403" xml:space="preserve">Item quo pacto illud crepuſculum <lb/>inueſtigari debeat.</s>
  <s xml:id="echoid-s7404" xml:space="preserve"/>
</p>
<div xml:id="echoid-div415" type="float" level="2" n="8">
<note position="left" xlink:label="note-0142-09" xlink:href="note-0142-09a" xml:space="preserve">Quando decli-<lb/>natio borealis <lb/>maior fuerit cõ<unsure/> <lb/>plemento altitu <lb/>dinis poli, nulla <lb/>eſt depreſſio me <lb/>ridiana, ſed to-<lb/>tus parallelus <lb/>ſupra Horizon-<lb/>@em extat.</note>
<note position="left" xlink:label="note-0142-10" xlink:href="note-0142-10a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">Quando decli-<lb/>natio aũ<unsure/>ſtralis <lb/>maior fuerit cõ <lb/>plemento altitu <lb/>dinis poli, totus <lb/>parallelus au-<lb/>ſtralis ſub Hori <lb/>zonte latet, ha-<lb/>betq́; duas de-<lb/>preſſiones meri <lb/>dianas.</note>
<p style="it">
  <s xml:id="echoid-s7405" xml:space="preserve">HIS ita poſitis, ducatur ex L, ad rectam K O, productam in omnibus figuris (excepta ſecunda figu-<lb/>ra huius ſcholĳ) perpendicularis L θ; </s>
  <s xml:id="echoid-s7406" xml:space="preserve">Item ex M, centro paralleli alia perpendicularis M λ. </s>
  <s xml:id="echoid-s7407" xml:space="preserve">Et quo-<lb/>niam eſt in triangulo K θ L, vt K M, ad M L, ita K λ, ad λ θ: </s>
  <s xml:id="echoid-s7408" xml:space="preserve">Eſt autem K M, ipſi M L, æqualis; </s>
  <s xml:id="echoid-s7409" xml:space="preserve">erit <lb/>quoque k λ, ipſi λ θ, æqualis. </s>
  <s xml:id="echoid-s7410" xml:space="preserve">Cum ergo K N, ſinus ſit altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7411" xml:space="preserve">θ N, ſinus depreſſio-<lb/>nis meridianæ, (quia θ N, æqualis est ſinui depreſſionis, qui ex L, ad A C, duceretur perpendicularis) <lb/>
<anchor type="note" xlink:label="note-0142-12a" xlink:href="note-0142-12"/>
erit K λ, medietas rectæ compoſitæ ex ſinubus altitudinis, &amp; </s>
  <s xml:id="echoid-s7412" xml:space="preserve">depreſſionis meridianæ. </s>
  <s xml:id="echoid-s7413" xml:space="preserve">At vero λ O, dif-<lb/>ferentia erit inter dictam medietatem, &amp; </s>
  <s xml:id="echoid-s7414" xml:space="preserve">rectam compoſitam ex ſinubus altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7415" xml:space="preserve">grad. <lb/></s>
  <s xml:id="echoid-s7416" xml:space="preserve">
<anchor type="note" xlink:label="note-0142-13a" xlink:href="note-0142-13"/>
18. </s>
  <s xml:id="echoid-s7417" xml:space="preserve">Quia verò eſt, vt K λ, ad λ O, ita K M, ad M T; </s>
  <s xml:id="echoid-s7418" xml:space="preserve">Si fiat, vt K λ, medietas rectæ compoſitæ ex ſinu <lb/>
<anchor type="note" xlink:label="note-0142-14a" xlink:href="note-0142-14"/>
<anchor type="note" xlink:label="note-0142-15a" xlink:href="note-0142-15"/>
altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7419" xml:space="preserve">ſinu depreſſionis meridianæ, ad λ O, differentiam inter medietatem prædictam, <lb/>
<anchor type="note" xlink:label="note-0142-16a" xlink:href="note-0142-16"/>
&amp; </s>
  <s xml:id="echoid-s7420" xml:space="preserve">rectam compoſitam ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7421" xml:space="preserve">ſinu grad. </s>
  <s xml:id="echoid-s7422" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7423" xml:space="preserve">ita K M, ſinus totus ad aliud, <lb/>prodibit M T, ſinus rectus arcus P R, qui quidem arcus additus quadranti conſtituit arcum K R, ex ar-<lb/>cu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7424" xml:space="preserve">arcu crepuſculi compoſito, ſi videlicet prædicta medietas K λ, minor deprehc<unsure/>nſa fue-<lb/>rit, quàm recta compoſita ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7425" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s7426" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7427" xml:space="preserve">vt in ſignis borealibus ſemper con-<lb/>tingit, &amp; </s>
  <s xml:id="echoid-s7428" xml:space="preserve">nonnunquam in auſtralibus, ceu videre licet in duabus prioribus figuris huius propoſ. </s>
  <s xml:id="echoid-s7429" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7430" xml:space="preserve">in prio-<lb/>vi huius ſcholĳ, vel ſubtractus ex quadrante relinquit arcum K R, compoſitum ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7431" xml:space="preserve"><lb/>@@rcu crepuſculi, ſi nimir@m medietas dicta deprehenſa ſuerit maior, quàm recta ex ſinu meridianę alti-
<pb o="123" file="0143" n="143" rhead="LIBER PRIMVS."/>
tudinis, &amp; </s>
  <s xml:id="echoid-s7432" xml:space="preserve">ſinu grad. </s>
  <s xml:id="echoid-s7433" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7434" xml:space="preserve">compoſita, vt accidit in tertia figura huius propoſ. </s>
  <s xml:id="echoid-s7435" xml:space="preserve">Subtracto autem arcu ſe-<lb/>midiurno K Q, ex arcu K R, inuento, perſpicuum eſt, arcum crepuſculi Q R, relinqui. </s>
  <s xml:id="echoid-s7436" xml:space="preserve">Quòd ſi dicta me-<lb/>dietas K λ, æqualis fuerit dictæ rectę K O, erit arcus compoſitus ex arcu ſemidiurno, &amp; </s>
  <s xml:id="echoid-s7437" xml:space="preserve">arcu crepuſcu-<lb/>li quadrans, vt in quarta figura huius propoſ. </s>
  <s xml:id="echoid-s7438" xml:space="preserve">apparet.</s>
  <s xml:id="echoid-s7439" xml:space="preserve"/>
</p>
<div xml:id="echoid-div416" type="float" level="2" n="9">
<note position="left" xlink:label="note-0142-12" xlink:href="note-0142-12a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0142-13" xlink:href="note-0142-13a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0142-14" xlink:href="note-0142-14a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0142-15" xlink:href="note-0142-15a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0142-16" xlink:href="note-0142-16a" xml:space="preserve">Crepuſculum <lb/>qua ratione ali <lb/>ter, quàm ſu-<lb/>pra, inueſtigan-<lb/>@um.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7440" xml:space="preserve">QVIN etiam beneficio altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7441" xml:space="preserve">depreſſionis meridianæ, breui admodum calculo <lb/>arcus ſemidiurnos ſupputabimus, licet eoſdem alio modo in præcedenti propoſ. </s>
  <s xml:id="echoid-s7442" xml:space="preserve">inuenerimus. </s>
  <s xml:id="echoid-s7443" xml:space="preserve">Quoniam <lb/>enim in omnibus figuris huius propoſ. </s>
  <s xml:id="echoid-s7444" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7445" xml:space="preserve">etiam in priori, quę in ſcholio ponitur, eſt vt K λ, medietas re-<lb/>
<anchor type="note" xlink:label="note-0143-01a" xlink:href="note-0143-01"/>
<anchor type="note" xlink:label="note-0143-02a" xlink:href="note-0143-02"/>
ctæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7446" xml:space="preserve">ſinu depreſſionis meridianæ ad λ N, differentiam inter <lb/>prædictam medietatem, &amp; </s>
  <s xml:id="echoid-s7447" xml:space="preserve">ſinum altitudinis meridianæ, ita K M, ſinus totus ad M S: </s>
  <s xml:id="echoid-s7448" xml:space="preserve">Si fiat vt K λ, <lb/>medietas rectę ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7449" xml:space="preserve">ſinu depreſſionis meridianæ compoſitæ, ad λ N, differen-<lb/>
<anchor type="note" xlink:label="note-0143-03a" xlink:href="note-0143-03"/>
tiam inter dictam medietatem, &amp; </s>
  <s xml:id="echoid-s7450" xml:space="preserve">ſinum meridianæ altitudinis, ita K M, ſinus totus ad aliud, inuenietur <lb/>ſinus rectus M S, cuius arcus P Q, in ſignis borealibus additus quadranti, in auſtralibus verò à qua-<lb/>drante ſubtractus, dabit arcum ſemidiurnum K Q.</s>
  <s xml:id="echoid-s7451" xml:space="preserve"/>
</p>
<div xml:id="echoid-div417" type="float" level="2" n="10">
<note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">2. vel 4. ſexti</note>
<note position="right" xlink:label="note-0143-02" xlink:href="note-0143-02a" xml:space="preserve">Arcus ſemidiur <lb/>nus qua ratio-<lb/>ne ſupputandus <lb/>aliter quàm ſ@-<lb/>pra.</note>
<note position="left" xlink:label="note-0143-03" xlink:href="note-0143-03a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s7452" xml:space="preserve">IDEM hac ratione conſequemur. </s>
  <s xml:id="echoid-s7453" xml:space="preserve">Quoniam in eiſdem figuris eſt, vt K λ, medietas prædicta ad <lb/>
<anchor type="note" xlink:label="note-0143-04a" xlink:href="note-0143-04"/>
K N, ſinum altitudinis meridianæ, ita K M, ſinus totus ad K S, ſinum verſum arcus ſemidiurni <lb/>K Q: </s>
  <s xml:id="echoid-s7454" xml:space="preserve">Si fiat vt K λ, medietas rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7455" xml:space="preserve">ſinu depreſſionis meri-<lb/>dianę ad K N, ſinum altitudinis meridianæ, ita K M, ſinus totus ad aliud, obtinebimus K S, ſinum ver-<lb/>ſum arcus ſemidiurni K Q. </s>
  <s xml:id="echoid-s7456" xml:space="preserve">Ex quo ſinu verſo ita adipiſcemur arcum ſemidiurnum K Q. </s>
  <s xml:id="echoid-s7457" xml:space="preserve">In ſignis borea-<lb/>libus dematur ex ſinu verſo inuento ſinus totus, &amp; </s>
  <s xml:id="echoid-s7458" xml:space="preserve">reſidui ſinus recti arcus P Q, ad quadrantem adĳ-<lb/>ciatur; </s>
  <s xml:id="echoid-s7459" xml:space="preserve">In ſignis verò auſtralib{us} contra, ſin{us} verſ{us} inuentus ex ſinu toto auferatur, &amp; </s>
  <s xml:id="echoid-s7460" xml:space="preserve">reſidui ſinus <lb/>
<anchor type="note" xlink:label="note-0143-05a" xlink:href="note-0143-05"/>
recti arcus P Q, ex quadrante rurſus ſubtrahatur. </s>
  <s xml:id="echoid-s7461" xml:space="preserve">Exurget enim ſemper ſiue ex illa additione, ſiue ex <lb/>hac ſubtractione arcus ſemidiurnus.</s>
  <s xml:id="echoid-s7462" xml:space="preserve"/>
</p>
<div xml:id="echoid-div418" type="float" level="2" n="11">
<note position="right" xlink:label="note-0143-04" xlink:href="note-0143-04a" xml:space="preserve">Arcus ſemidiur <lb/>nus quomodo <lb/>aliter inueſtige-<lb/>tur.</note>
<note position="left" xlink:label="note-0143-05" xlink:href="note-0143-05a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s7463" xml:space="preserve">HAEC autem omnia intelligenda ſunt, quando complementum altitudinis poli maius eſt declina-<lb/>
<anchor type="note" xlink:label="note-0143-06a" xlink:href="note-0143-06"/>
tione paralleli illius, cuius arcus ſemidiurnus inueſtigatur. </s>
  <s xml:id="echoid-s7464" xml:space="preserve">Nam quando complementum illud non eſt ma-<lb/>ius, tanget vel parallelus Horizontem, at que ita eius arcus diurnus, ſi borealis eſt, continebit horas 24. <lb/></s>
  <s xml:id="echoid-s7465" xml:space="preserve">vel ſi auſiralis, hor. </s>
  <s xml:id="echoid-s7466" xml:space="preserve">0. </s>
  <s xml:id="echoid-s7467" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7468" xml:space="preserve">0. </s>
  <s xml:id="echoid-s7469" xml:space="preserve">Vel totus parallelus borealis ſupra Horizontem extat, &amp; </s>
  <s xml:id="echoid-s7470" xml:space="preserve">auſtralis infra, <lb/>atque ita nullus erit arcus diurnus, ſed continua dies in parallelo boreali, &amp; </s>
  <s xml:id="echoid-s7471" xml:space="preserve">continua nox in auſtrali erit. </s>
  <s xml:id="echoid-s7472" xml:space="preserve"><lb/>Quæ omnia in ſecunda figura ſcholĳ huius propoſ. </s>
  <s xml:id="echoid-s7473" xml:space="preserve">apparent, vbi complementum altitudinis poli C I, mi-<lb/>nus eſt declinatione I L, paralleli borealis, &amp; </s>
  <s xml:id="echoid-s7474" xml:space="preserve">rurſus idem complementum A H, minus declinatione <lb/>H K, paralleli auſtralis. </s>
  <s xml:id="echoid-s7475" xml:space="preserve">Quòd ſi complementum illud declinationi foret æquale, tangeret parallelus bo-<lb/>
<anchor type="note" xlink:label="note-0143-07a" xlink:href="note-0143-07"/>
realis Horizontem in C, &amp; </s>
  <s xml:id="echoid-s7476" xml:space="preserve">australis in A, vt manifeſtum eſt.</s>
  <s xml:id="echoid-s7477" xml:space="preserve"/>
</p>
<div xml:id="echoid-div419" type="float" level="2" n="12">
<note position="right" xlink:label="note-0143-06" xlink:href="note-0143-06a" xml:space="preserve">Arcus diurnus <lb/>quoniodo ſe ha <lb/>beat, quando cõ <lb/>plementum al-<lb/>titudinis poli <lb/>maius non fue-<lb/>rit declinatione <lb/>propoſiti paral-<lb/>leli.</note>
<note position="left" xlink:label="note-0143-07" xlink:href="note-0143-07a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s7478" xml:space="preserve">VT autem omnibus numeris abſoluta ſit demonſtratio huius propoſ. </s>
  <s xml:id="echoid-s7479" xml:space="preserve">trademus etiam inuentionem <lb/>crepuſculorum in ſphærarecta, vbi multo facilius inueniuntur. </s>
  <s xml:id="echoid-s7480" xml:space="preserve">Sit Meridianus Analemmatis A B C D; <lb/></s>
  <s xml:id="echoid-s7481" xml:space="preserve">Horizontis recti diameter A C, per polos A, C, tranſiens; </s>
  <s xml:id="echoid-s7482" xml:space="preserve">Paral-<lb/>
<anchor type="figure" xlink:label="fig-0143-01a" xlink:href="fig-0143-01"/>
leli Horizontis, in quo principium, vel terminus crepuſculi ponitur, <lb/>
<anchor type="note" xlink:label="note-0143-08a" xlink:href="note-0143-08"/>
diameter F G; </s>
  <s xml:id="echoid-s7483" xml:space="preserve">Aequatoris diameter B D, ſecans F G, in H; </s>
  <s xml:id="echoid-s7484" xml:space="preserve">diame <lb/>ter paralleli Solis c<unsure/>uiuſcunque I K, ſecans A C, F G, in L, &amp; </s>
  <s xml:id="echoid-s7485" xml:space="preserve">M. <lb/></s>
  <s xml:id="echoid-s7486" xml:space="preserve">Ex L, centro paralleli deſcribatur ſemicirculus ipſius I N K, exten <lb/>danturq́, A C, F G, vſque ad N, &amp; </s>
  <s xml:id="echoid-s7487" xml:space="preserve">O.</s>
  <s xml:id="echoid-s7488" xml:space="preserve"/>
</p>
<div xml:id="echoid-div420" type="float" level="2" n="13">
  <figure xlink:label="fig-0143-01" xlink:href="fig-0143-01a">
    <image file="0143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0143-01"/>
  </figure>
<note position="right" xlink:label="note-0143-08" xlink:href="note-0143-08a" xml:space="preserve">Crepuſculum <lb/>in ſphæra recta, <lb/>quo pacto in-<lb/>dagandum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s7489" xml:space="preserve">ERIT igitur A F, vel C G, arcus crepuſculi, Sole in Aequa-<lb/>
<anchor type="note" xlink:label="note-0143-09a" xlink:href="note-0143-09"/>
tore exiſtente, cuius ſinus eſt recta E H, reſpondens arcui grad. </s>
  <s xml:id="echoid-s7490" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s7491" xml:space="preserve">Igitur ſi ſumatur arcus grad. </s>
  <s xml:id="echoid-s7492" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7493" xml:space="preserve">habebitur arcus crepuſculi in ſphæ-<lb/>rarecta, Sole in æquinoctĳs exiſtente.</s>
  <s xml:id="echoid-s7494" xml:space="preserve"/>
</p>
<div xml:id="echoid-div421" type="float" level="2" n="14">
<note position="left" xlink:label="note-0143-09" xlink:href="note-0143-09a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s7495" xml:space="preserve">SOLE verò in quouis parallelo exiſtente, vt in parallelo INK, <lb/>erit arcus O N, longitudo crepuſculi. </s>
  <s xml:id="echoid-s7496" xml:space="preserve">Si igitur fiat, vt I L, quatenus <lb/>pars eſt ſinus totius B E, maximi circuli, hoc eſt, quatenus ſinus eſt complementi declinationis, (eſt <lb/>enim arcus I C, vel I A, complementum declinationis) ad L M, ſinum grad. </s>
  <s xml:id="echoid-s7497" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7498" xml:space="preserve">eiuſdem circuli maximi, <lb/>ita I L, quatenus ſinus totus in parallelo I N K, ad aliud, c<unsure/>ognita erit L M, in partibus ſinus totius I L; <lb/></s>
  <s xml:id="echoid-s7499" xml:space="preserve">atque adeò @ius arcus N O, qui crepuſculum metitur, notus erit. </s>
  <s xml:id="echoid-s7500" xml:space="preserve">Atque hoc verum eſt, ſiue I K, ſit dia-<lb/>meter paralleli auſtralis, ſiue borealis, vt ex figura manifeſtum eſt.</s>
  <s xml:id="echoid-s7501" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s7502" xml:space="preserve">NON eſt autem prætereundum, vno fere nos labore peruestigare poſſe crepuſcula duorum paralle-<lb/>
<anchor type="note" xlink:label="note-0143-11a" xlink:href="note-0143-11"/>
lorum oppoſitorum, ſi primo modo vtamur. </s>
  <s xml:id="echoid-s7503" xml:space="preserve">Quoniam enim arcus ſemidiurnus cuiuſuis paralleli æqualis <lb/>eſt ar cui ſeminocturno, vt in ſcholio antecedentis propoſ. </s>
  <s xml:id="echoid-s7504" xml:space="preserve">oſtendimus, erit ſinus verſus K S, arcus ſemi-<lb/>diurni paralleli australis æqualis ſinui verſo L S, arcus ſeminocturni paralleli borealis oppoſiti, vt in <lb/>ſequẽti prima figura apparet. </s>
  <s xml:id="echoid-s7505" xml:space="preserve">Est autẽ &amp; </s>
  <s xml:id="echoid-s7506" xml:space="preserve">S T, portio diametri paralleli auſtralis portioni S T, diametri <lb/>
<anchor type="note" xlink:label="note-0143-12a" xlink:href="note-0143-12"/>
paralleli borealis æqualis. </s>
  <s xml:id="echoid-s7507" xml:space="preserve">Igitur ſi fiat, vt K N, ſinus altitudinis meridianæ paralleli auſtralis ad <lb/>N O, ſinum grad. </s>
  <s xml:id="echoid-s7508" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7509" xml:space="preserve">ita K S, ſinus verſus arcus ſemidiurni paralleli auſtralis, ad aliud, nota erit re-<lb/>cta S T; </s>
  <s xml:id="echoid-s7510" xml:space="preserve">cum eandem proportionem habeat K N, ad N O, quam k S, ad S T. </s>
  <s xml:id="echoid-s7511" xml:space="preserve">Hæc autem S T, nota, <lb/>
<anchor type="note" xlink:label="note-0143-13a" xlink:href="note-0143-13"/>
(quam fortaſſis facilius inuenies ratione ad finem huius propoſ. </s>
  <s xml:id="echoid-s7512" xml:space="preserve">præſcripta) ſi adĳciatur ad ſinum ver-<lb/>ſum K S, arcus ſemidiurni paralleli auſtralis, conflabitur K T, ſinus verſus arcus K R, compoſiti ex ar-<lb/>@u ſemidiurno K Q, &amp; </s>
  <s xml:id="echoid-s7513" xml:space="preserve">arcu crepuſculi Q R. </s>
  <s xml:id="echoid-s7514" xml:space="preserve">Dempto ergo ſemidiurno arcu K Q, remanebit ar-
<pb o="124" file="0144" n="144" rhead="GNOMONICES"/>
cus Q R, crepuſculinota. </s>
  <s xml:id="echoid-s7515" xml:space="preserve">Eadem autem S T, ablata ex L S, ſinu verſo arcus ſeminocturni paralleli bo-<lb/>realis oppoſiti, qui ſinui verſo K S, arcus ſemidiurni æqualis eſt in parallelo auſtrali, vt diximus, relinquet <lb/>
<anchor type="figure" xlink:label="fig-0144-01a" xlink:href="fig-0144-01"/>
<anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/>
T L, ſinum verſum arcus L R, qui ablatus ex arcu ſeminocturno L Q, paralleli borealis, quem arcui ſe-<lb/>midiurno k Q, paralleli auſtralis æqualem eſſe tradidimus, relinquet arcum crepuſculi Q R. </s>
  <s xml:id="echoid-s7516" xml:space="preserve">Itaque vt <lb/>vides, vnica multiplicatione, &amp; </s>
  <s xml:id="echoid-s7517" xml:space="preserve">diuiſione inuenitur recta S T, in vtroque parallelo, beneficio cuius cre-<lb/>
<anchor type="note" xlink:label="note-0144-02a" xlink:href="note-0144-02"/>
puſculum vtrumque elicitur, vt expoſuimus. </s>
  <s xml:id="echoid-s7518" xml:space="preserve">Malumus autem reperire prædictam rectam S T, in paral-<lb/>lelo auſtrali, quàm in boreali; </s>
  <s xml:id="echoid-s7519" xml:space="preserve">quia &amp; </s>
  <s xml:id="echoid-s7520" xml:space="preserve">ſinus rectus k N, altitudinis meridianæ paralleli auſtralis minor <lb/>eſt ſinu recto altitudinis meridianæ paralleli borealis, &amp; </s>
  <s xml:id="echoid-s7521" xml:space="preserve">ſinus verſus K S, arcus ſemidiurni paralleli au-<lb/>stralis ſinu verſo arcus ſemidiurni paralleli ſeptentrionalis. </s>
  <s xml:id="echoid-s7522" xml:space="preserve">Vnde facilior efficitur multiplicatio, atque <lb/>diuiſio per numeros minores.</s>
  <s xml:id="echoid-s7523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div422" type="float" level="2" n="15">
<note position="right" xlink:label="note-0143-11" xlink:href="note-0143-11a" xml:space="preserve">Crepuſcula duo <lb/>rum parallclo-<lb/>rum oppoſito-<lb/>rum, qua ratio-<lb/>ne vnico labore<unsure/> <lb/>inueniantur.</note>
<note position="right" xlink:label="note-0143-12" xlink:href="note-0143-12a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0143-13" xlink:href="note-0143-13a" xml:space="preserve">2. ſ@nti.</note>
  <figure xlink:label="fig-0144-01" xlink:href="fig-0144-01a">
    <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0144-01"/>
  </figure>
<note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0144-02" xlink:href="note-0144-02a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">Crepuſculum <lb/>pontinuum in <lb/>parallelo borea <lb/>li quando.</note>
<p style="it">
  <s xml:id="echoid-s7524" xml:space="preserve">ADVERTENDVM autem eſt hic, quando recta S T, in parallelo auſtrali inuenta fuerit ma-<lb/>ior ſinu verſo K S, arcus ſemidiurni, (quod quidem accidit, cum ſinus altitudinis meridianæ K N, minor <lb/>eſt ſinu grad. </s>
  <s xml:id="echoid-s7525" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7526" xml:space="preserve">vt in ſecunda figura contingit) perpetuum eſſe crepuſculum in parallelo boreali oppoſi-<lb/>to: </s>
  <s xml:id="echoid-s7527" xml:space="preserve">quia tunc recta S T, in parallelo boreali auferri nequit ex L S, ſinu verſo arcus ſeminocturni, qui ſi-<lb/>nui verſo K S, arcus ſeminocturni paralleli auſtralis æqualis eſt, atqu@ adeo minor quoque quàm recta <lb/>
<anchor type="note" xlink:label="note-0144-04a" xlink:href="note-0144-04"/>
S T. </s>
  <s xml:id="echoid-s7528" xml:space="preserve">Quare nunquam illa nocte Sol ad parallelum Horizontis, cuius diameter X Y, perueniet, &amp; </s>
  <s xml:id="echoid-s7529" xml:space="preserve">c.</s>
  <s xml:id="echoid-s7530" xml:space="preserve"/>
</p>
<div xml:id="echoid-div423" type="float" level="2" n="16">
<note position="left" xlink:label="note-0144-04" xlink:href="note-0144-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s7531" xml:space="preserve">DENIQVE vt nihil prætermittamus, quod ad rem, in qua verſamur, pertineat, placet quoque <lb/>
<anchor type="note" xlink:label="note-0144-05a" xlink:href="note-0144-05"/>
viam præſcribere, qua per triangula ſphęrica poſſint crepuſcula ſupputari. </s>
  <s xml:id="echoid-s7532" xml:space="preserve">Sit ergo, vt in tertia figura, <lb/>Horizon A B C D; </s>
  <s xml:id="echoid-s7533" xml:space="preserve">Meridianus B D; </s>
  <s xml:id="echoid-s7534" xml:space="preserve">Aequator A F C; </s>
  <s xml:id="echoid-s7535" xml:space="preserve">Verticalis proprie dictus A E C; </s>
  <s xml:id="echoid-s7536" xml:space="preserve">parallelus <lb/>ſiue borealis, ſiue auſtralis G I H; </s>
  <s xml:id="echoid-s7537" xml:space="preserve">parallelus Horizontis infra Horizontem K P, in quo Sol exiſtit in <lb/>principio matutini crepuſculi, vel in fine veſpertini, ita vt diſtet ab Horizonte grad. </s>
  <s xml:id="echoid-s7538" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7539" xml:space="preserve">ſecundum magis <lb/>receptam ſententiam, ſecet{q́ue} parallelum Solis in puncto K; </s>
  <s xml:id="echoid-s7540" xml:space="preserve">eritq́<unsure/>, K G, arcus crepuſculi, quem nimirum <lb/>Sol in ſuo parallelo percurrit à principio crepuſculi vſque ad finem, &amp; </s>
  <s xml:id="echoid-s7541" xml:space="preserve">G I, arcus ſemidiurnus. </s>
  <s xml:id="echoid-s7542" xml:space="preserve">Ducatur <lb/>ex M, polo arctico per G, K, duo circuli maximi M G, M K, ſecantes Aequatorem in O, &amp; </s>
  <s xml:id="echoid-s7543" xml:space="preserve">N. </s>
  <s xml:id="echoid-s7544" xml:space="preserve">Et quia <lb/>per propoſ. </s>
  <s xml:id="echoid-s7545" xml:space="preserve">10. </s>
  <s xml:id="echoid-s7546" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s7547" xml:space="preserve">2. </s>
  <s xml:id="echoid-s7548" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s7549" xml:space="preserve">arcus F O, arcui I G, &amp; </s>
  <s xml:id="echoid-s7550" xml:space="preserve">arcus O N, arcui G K, ſimilis eſt, erit F O, ar-<lb/>cus ſemidiurnus paralleli G H, &amp; </s>
  <s xml:id="echoid-s7551" xml:space="preserve">O N, arcus crepuſculi, quem ita notum efficiemus. </s>
  <s xml:id="echoid-s7552" xml:space="preserve">Ducto per verticem <lb/>
<anchor type="note" xlink:label="note-0144-06a" xlink:href="note-0144-06"/>
E, &amp; </s>
  <s xml:id="echoid-s7553" xml:space="preserve">per K, locum Solis in principio crepuſculi matutini, vel in fine veſpertini, circulo maximo E K, qui <lb/>ſecet Horizontem in L, erit arcus K L, grad. </s>
  <s xml:id="echoid-s7554" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7555" xml:space="preserve">Quoniam igitur in triangulo ſphærico E K M, omnia <lb/>latera nota ſunt, (Est enim E M, arcus complementi altitudinis poli; </s>
  <s xml:id="echoid-s7556" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7557" xml:space="preserve">arcus E K, compoſitus ex qua-<lb/>drante E L, &amp; </s>
  <s xml:id="echoid-s7558" xml:space="preserve">arcu L K, grad. </s>
  <s xml:id="echoid-s7559" xml:space="preserve">18. </s>
  <s xml:id="echoid-s7560" xml:space="preserve">ita vt totus arcus E K, contineat grad. </s>
  <s xml:id="echoid-s7561" xml:space="preserve">108. </s>
  <s xml:id="echoid-s7562" xml:space="preserve">Denique arcus M K, in <lb/>parallelo boreali complementum eſt declinationis paralleli propoſiti, in auſtrali vero compoſitus ex qua <lb/>drante M N, &amp; </s>
  <s xml:id="echoid-s7563" xml:space="preserve">arcu N k, declinationis) cognitus erit, per propoſ. </s>
  <s xml:id="echoid-s7564" xml:space="preserve">vltimam lib. </s>
  <s xml:id="echoid-s7565" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7566" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s7567" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s7568" xml:space="preserve">de <lb/>triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s7569" xml:space="preserve">45. </s>
  <s xml:id="echoid-s7570" xml:space="preserve">noſtrorum triangulorum ſphæricorum, angulus E M K. </s>
  <s xml:id="echoid-s7571" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s7572" xml:space="preserve">eius <lb/>arcus F N; </s>
  <s xml:id="echoid-s7573" xml:space="preserve">à quo ſi detrabatur arcus ſemidiurnus F O, reliquus erit arcus crepuſculi N O. </s>
  <s xml:id="echoid-s7574" xml:space="preserve">Quod <lb/>eſt propoſitum.</s>
  <s xml:id="echoid-s7575" xml:space="preserve"/>
</p>
<div xml:id="echoid-div424" type="float" level="2" n="17">
<note position="left" xlink:label="note-0144-05" xlink:href="note-0144-05a" xml:space="preserve">Crepuſcula per <lb/>triangula ſphæ-<lb/>rica, quo modo <lb/>ſupputanda.</note>
<note position="left" xlink:label="note-0144-06" xlink:href="note-0144-06a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div426" type="section" level="1" n="138">
<head xml:id="echoid-head141" xml:space="preserve">PROBLEMA 15. PROPOSITIO 36.</head>
<p>
  <s xml:id="echoid-s7576" xml:space="preserve">EX cognita diei hora altitudinem Solis ſupra Horizontem; </s>
  <s xml:id="echoid-s7577" xml:space="preserve">Et con-<lb/>tra ex altitudine Solis nota horam diei cognoſcere.</s>
  <s xml:id="echoid-s7578" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7579" xml:space="preserve">QVONIAM in ſequentibus libris horologia ſumus deſcripturi, ex quibus horas diei cogno <lb/>ſcamus, rem gratam me facturum multis arbitror, ſi in vltima hac propol. </s>
  <s xml:id="echoid-s7580" xml:space="preserve">huius libri modum o-<lb/>ſtendam, quo ſine horologio ex ſola altitudine ſolis cognita eaſdem horas, &amp; </s>
  <s xml:id="echoid-s7581" xml:space="preserve">viciſſim ex hora co-<lb/>gnita altitudinem Solis inuenire poſſimus: </s>
  <s xml:id="echoid-s7582" xml:space="preserve">Vel ob eam præcipue cauſam, quòd magno vſui hæc <lb/>res ſit tũ ad horologia deſcribenda, tum maxime ad quadrantes, Cylindros horarios, &amp; </s>
  <s xml:id="echoid-s7583" xml:space="preserve">alia id ge
<pb o="125" file="0145" n="145" rhead="LIBER PRIMVS."/>
nus inſtrum@ta, quibus horæ depingũtur, conficienda, vt proprijs in locis explicabimus.</s>
  <s xml:id="echoid-s7584" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7585" xml:space="preserve">SINT igitur eædem figuræ, quæ in præcedenti propoſ. </s>
  <s xml:id="echoid-s7586" xml:space="preserve">ponaturq́; </s>
  <s xml:id="echoid-s7587" xml:space="preserve">Sol in puncto O, in ſuo pa <lb/>rallelo, ducaturq́; </s>
  <s xml:id="echoid-s7588" xml:space="preserve">ex O, ad K L, diametrum paralleli perpendicularis O R, &amp; </s>
  <s xml:id="echoid-s7589" xml:space="preserve">per R, diametro Ho <lb/>
<anchor type="figure" xlink:label="fig-0145-01a" xlink:href="fig-0145-01"/>
<anchor type="note" xlink:label="note-0145-01a" xlink:href="note-0145-01"/>
<anchor type="note" xlink:label="note-0145-02a" xlink:href="note-0145-02"/>
<anchor type="figure" xlink:label="fig-0145-02a" xlink:href="fig-0145-02"/>
<anchor type="note" xlink:label="note-0145-03a" xlink:href="note-0145-03"/>
rizontis A C, parallela agatur ſecans K N, ſinum altitudinis meridianæ in T. </s>
  <s xml:id="echoid-s7590" xml:space="preserve">Erit O R, commu-<lb/>nis ſectio paralleli Solis, &amp; </s>
  <s xml:id="echoid-s7591" xml:space="preserve">paralleli Horizontis, in quo Sol exiſtit tempore obſeruationis. </s>
  <s xml:id="echoid-s7592" xml:space="preserve">Quia <lb/>enim vterq; </s>
  <s xml:id="echoid-s7593" xml:space="preserve">parallelus ad Meridianum rectus eſt, erit quoq; </s>
  <s xml:id="echoid-s7594" xml:space="preserve">communis eorum ſectio ad eundem <lb/>
<anchor type="note" xlink:label="note-0145-04a" xlink:href="note-0145-04"/>
recta, &amp; </s>
  <s xml:id="echoid-s7595" xml:space="preserve">ob id per defin. </s>
  <s xml:id="echoid-s7596" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7597" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s7598" xml:space="preserve">11. </s>
  <s xml:id="echoid-s7599" xml:space="preserve">Euclidis, ad rectam K L, perpendicularis. </s>
  <s xml:id="echoid-s7600" xml:space="preserve">Cum igitur tunc Sol <lb/>in communi illa ſectione exiſtat, ponaturq́; </s>
  <s xml:id="echoid-s7601" xml:space="preserve">in puncto O, erit O R, perpendicularis ducta ad K L, <lb/>communis ſectio dictorum parallelorum. </s>
  <s xml:id="echoid-s7602" xml:space="preserve">Quare parallelus Horizontis per centrum Solis tunc <lb/>ductus ſecabit Meridianum in R, ac proinde parallela R T, communis ſectio erit Meridiani &amp; </s>
  <s xml:id="echoid-s7603" xml:space="preserve">pa <lb/>ralleli Horizontis. </s>
  <s xml:id="echoid-s7604" xml:space="preserve">Meridianus enim in Horizonte, &amp; </s>
  <s xml:id="echoid-s7605" xml:space="preserve">eius parallelo quocunq; </s>
  <s xml:id="echoid-s7606" xml:space="preserve">facit duas ſectiones <lb/>
<anchor type="note" xlink:label="note-0145-05a" xlink:href="note-0145-05"/>
parallelas. </s>
  <s xml:id="echoid-s7607" xml:space="preserve">Erit ergo T N, ſinus rectus altitudinis Solis, hoc eſt, illius arcus, qui inter A C, &amp; </s>
  <s xml:id="echoid-s7608" xml:space="preserve">paral-<lb/>
<anchor type="note" xlink:label="note-0145-06a" xlink:href="note-0145-06"/>
lelam R T, interijcitur in Verticali circulo per centrum Solis ducto, pro quo accipi poteſt Meri-<lb/>dianus A B C D. </s>
  <s xml:id="echoid-s7609" xml:space="preserve">Si enim circa B D, axem Horizontis circumferatur, fungetur munere omnium <lb/>Verticalium, vt patet.</s>
  <s xml:id="echoid-s7610" xml:space="preserve"/>
</p>
<div xml:id="echoid-div426" type="float" level="2" n="1">
  <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a">
    <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-01"/>
  </figure>
<note position="left" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0145-02" xlink:href="fig-0145-02a">
    <image file="0145-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-02"/>
  </figure>
<note position="left" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0145-05" xlink:href="note-0145-05a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0145-06" xlink:href="note-0145-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s7611" xml:space="preserve">ANTE omnia igitur explorãda eſt diſtãtia Solis à meridie quo ad gradus, quã data hora quæ-<lb/>
<anchor type="note" xlink:label="note-0145-07a" xlink:href="note-0145-07"/>
cunq; </s>
  <s xml:id="echoid-s7612" xml:space="preserve">manifeſtabit hac ratione. </s>
  <s xml:id="echoid-s7613" xml:space="preserve">Si de horis aſtronomicis loquamur, diſtabit hora 1. </s>
  <s xml:id="echoid-s7614" xml:space="preserve">à meridie v. </s>
  <s xml:id="echoid-s7615" xml:space="preserve">g. <lb/></s>
  <s xml:id="echoid-s7616" xml:space="preserve">vel 11. </s>
  <s xml:id="echoid-s7617" xml:space="preserve">à media nocte à Meridiano ſupra Horizontẽ, hoc eſt, à meridie, grad. </s>
  <s xml:id="echoid-s7618" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7619" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7620" xml:space="preserve">hora 2. </s>
  <s xml:id="echoid-s7621" xml:space="preserve">à meri-<lb/>die, vel 10. </s>
  <s xml:id="echoid-s7622" xml:space="preserve">à media nocte, grad. </s>
  <s xml:id="echoid-s7623" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7624" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s7625" xml:space="preserve">c. </s>
  <s xml:id="echoid-s7626" xml:space="preserve">cùm ſingulæ horę cõplectãtur grad. </s>
  <s xml:id="echoid-s7627" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7628" xml:space="preserve">Si vero de horis Ita-<lb/>licis ſermo habeatur, vel Babylonicis, cognoſcendũ eſt prius tẽpus meridiei in die propoſito, vt in <lb/>cap. </s>
  <s xml:id="echoid-s7629" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7630" xml:space="preserve">Sphæræ docuimus, cũ de arcubus ſemidiurnis ageremus. </s>
  <s xml:id="echoid-s7631" xml:space="preserve">Hoc namq; </s>
  <s xml:id="echoid-s7632" xml:space="preserve">cognito, non difficile <lb/>erit intelligere, quãta ſit diſtãtia horæ datæ à meridiano tẽpore. </s>
  <s xml:id="echoid-s7633" xml:space="preserve">Quãdo enim v.</s>
  <s xml:id="echoid-s7634" xml:space="preserve">g. </s>
  <s xml:id="echoid-s7635" xml:space="preserve">meridies fit hora <lb/>
<anchor type="note" xlink:label="note-0145-08a" xlink:href="note-0145-08"/>
17 {1/2}. </s>
  <s xml:id="echoid-s7636" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s7637" xml:space="preserve">6 {1/2}. </s>
  <s xml:id="echoid-s7638" xml:space="preserve">ab ortu, quod quidẽ euenit, quãdo dies continet horas 13. </s>
  <s xml:id="echoid-s7639" xml:space="preserve">perſpicuũ eſt, <lb/>horam 20. </s>
  <s xml:id="echoid-s7640" xml:space="preserve">vel 15. </s>
  <s xml:id="echoid-s7641" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s7642" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7643" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s7644" xml:space="preserve">ab ortu, diſtare à meridie hor. </s>
  <s xml:id="echoid-s7645" xml:space="preserve">2 {1/2}. </s>
  <s xml:id="echoid-s7646" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s7647" xml:space="preserve">37. </s>
  <s xml:id="echoid-s7648" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s7649" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7650" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s7651" xml:space="preserve">c. </s>
  <s xml:id="echoid-s7652" xml:space="preserve">Si deniq; </s>
  <s xml:id="echoid-s7653" xml:space="preserve">horæ antiquæ, ſiue inæquales fuerint propoſitæ, diuidẽdus erit arcus diurnus per <lb/>12. </s>
  <s xml:id="echoid-s7654" xml:space="preserve">vt ſciamus quantitatem vnius horæ inæqualis. </s>
  <s xml:id="echoid-s7655" xml:space="preserve">Hinc enim facile diſtantiã Solis à meridie ex da <lb/>ta hora inæquali cognoſcemus. </s>
  <s xml:id="echoid-s7656" xml:space="preserve">Vt in principio ♋, arcus diurnus ad latitudinem grad. </s>
  <s xml:id="echoid-s7657" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7658" xml:space="preserve">conti-<lb/>net horas 15. </s>
  <s xml:id="echoid-s7659" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7660" xml:space="preserve">4. </s>
  <s xml:id="echoid-s7661" xml:space="preserve">quo diuiſo per 12. </s>
  <s xml:id="echoid-s7662" xml:space="preserve">reperiemus vnam horam inæqualẽ comprehendere hor. </s>
  <s xml:id="echoid-s7663" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s7664" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7665" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7666" xml:space="preserve">Sec. </s>
  <s xml:id="echoid-s7667" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7668" xml:space="preserve">ex horis æqualibus. </s>
  <s xml:id="echoid-s7669" xml:space="preserve">Quam ob rem hora 4. </s>
  <s xml:id="echoid-s7670" xml:space="preserve">inæqualis v.</s>
  <s xml:id="echoid-s7671" xml:space="preserve">g. </s>
  <s xml:id="echoid-s7672" xml:space="preserve">vel 8. </s>
  <s xml:id="echoid-s7673" xml:space="preserve">diſtabit à meri-<lb/>die, ſiue ab hora 6. </s>
  <s xml:id="echoid-s7674" xml:space="preserve">inæquali, hor. </s>
  <s xml:id="echoid-s7675" xml:space="preserve">2. </s>
  <s xml:id="echoid-s7676" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7677" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7678" xml:space="preserve">Sec. </s>
  <s xml:id="echoid-s7679" xml:space="preserve">40. </s>
  <s xml:id="echoid-s7680" xml:space="preserve">At hora 3. </s>
  <s xml:id="echoid-s7681" xml:space="preserve">inæqualis vel 9. </s>
  <s xml:id="echoid-s7682" xml:space="preserve">aberit à meridie <lb/>hor. </s>
  <s xml:id="echoid-s7683" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7684" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7685" xml:space="preserve">46. </s>
  <s xml:id="echoid-s7686" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7687" xml:space="preserve">ſic de cęteris. </s>
  <s xml:id="echoid-s7688" xml:space="preserve">Ex quibus horis æqualibus reperiemus diſtantiam Solis à meridie <lb/>quo ad gradus, vt prius. </s>
  <s xml:id="echoid-s7689" xml:space="preserve">Cognita porro diſtantia Solis à meridie, cognitum etiam erit eius com-<lb/>plementum, nempe differentia inter quadrantem, &amp; </s>
  <s xml:id="echoid-s7690" xml:space="preserve">dictam diſtantiam.</s>
  <s xml:id="echoid-s7691" xml:space="preserve"/>
</p>
<div xml:id="echoid-div427" type="float" level="2" n="2">
<note position="right" xlink:label="note-0145-07" xlink:href="note-0145-07a" xml:space="preserve">Diſtantia Solis <lb/>à meridie quo <lb/>ad gradus, quo <lb/>modo ex data <lb/>hora cognoſca-<lb/>tur.</note>
<note position="left" xlink:label="note-0145-08" xlink:href="note-0145-08a" xml:space="preserve">50</note>
</div>
<pb o="126" file="0146" n="146" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s7692" xml:space="preserve">QVONIAM igitur eſt, vt k M, ſinus totus ad MR, ſinũ cõplementi diſtã<unsure/>tiæ Soli<unsure/>s à meridie, <lb/>
<anchor type="note" xlink:label="note-0146-01a" xlink:href="note-0146-01"/>
ita K λ, medieras rectæ cõpoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7693" xml:space="preserve">ſinu meridianæ depreſſionis, ad <lb/>rectã λ T: </s>
  <s xml:id="echoid-s7694" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum cõplementi diſtãtiæ Solis à meridie, ita k λ, medietas re-<lb/>
<anchor type="figure" xlink:label="fig-0146-01a" xlink:href="fig-0146-01"/>
<anchor type="note" xlink:label="note-0146-02a" xlink:href="note-0146-02"/>
<anchor type="figure" xlink:label="fig-0146-02a" xlink:href="fig-0146-02"/>
<anchor type="note" xlink:label="note-0146-03a" xlink:href="note-0146-03"/>
<anchor type="note" xlink:label="note-0146-04a" xlink:href="note-0146-04"/>
ctæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7695" xml:space="preserve">ſinu depreſſionis meridianæ, ad aliud, inuenietur <lb/>recta λ T, differentia nimirum inter T N, ſinum altitudinis Solis tempore obſeruationis, &amp; </s>
  <s xml:id="echoid-s7696" xml:space="preserve">re-<lb/>ctam λ N, quæ differentia eſt inter prædictam medietatem K λ, &amp; </s>
  <s xml:id="echoid-s7697" xml:space="preserve">K N, ſinum altitudinis meri-<lb/>dianæ. </s>
  <s xml:id="echoid-s7698" xml:space="preserve">Ex hac autem recta λ T, reperiemus ſinum altitudinis Solis T N, atque adeo &amp; </s>
  <s xml:id="echoid-s7699" xml:space="preserve">altitudinẽ <lb/>
<anchor type="note" xlink:label="note-0146-05a" xlink:href="note-0146-05"/>
ipſam Solis, hoc modo. </s>
  <s xml:id="echoid-s7700" xml:space="preserve">In parallelis borealibus, quando diſtantia Solis à meridie minor eſt qua-<lb/>drante, ſeu ſex horis, addatur recta inuenta λ T, ad λ N, differentiam inter medietatem prædi-<lb/>ctam, &amp; </s>
  <s xml:id="echoid-s7701" xml:space="preserve">ſinum altitudinis meridianæ. </s>
  <s xml:id="echoid-s7702" xml:space="preserve">Componetur enim hac ratione ſinus altitudinis Solis T N, <lb/>vt in prima figura, &amp; </s>
  <s xml:id="echoid-s7703" xml:space="preserve">tertia apparet.</s>
  <s xml:id="echoid-s7704" xml:space="preserve"/>
</p>
<div xml:id="echoid-div428" type="float" level="2" n="3">
<note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">Altitudo Solis <lb/>ſupra Horizon-<lb/>tem quomodo <lb/>ex hora cognita <lb/>ſupputetur.</note>
  <figure xlink:label="fig-0146-01" xlink:href="fig-0146-01a">
    <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-01"/>
  </figure>
<note position="left" xlink:label="note-0146-02" xlink:href="note-0146-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0146-02" xlink:href="fig-0146-02a">
    <image file="0146-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-02"/>
  </figure>
<note position="left" xlink:label="note-0146-03" xlink:href="note-0146-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0146-04" xlink:href="note-0146-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0146-05" xlink:href="note-0146-05a" xml:space="preserve">Quando diſtan <lb/>tia Solis à meri <lb/>die in parallelo <lb/>boreali minor <lb/>eſt quadrante.</note>
</div>
<note position="left" xml:space="preserve">Quando diſtan <lb/>tia Solis à meri <lb/>die in parallelo <lb/>boreali quadrãs <lb/>eſt.</note>
<p>
  <s xml:id="echoid-s7705" xml:space="preserve">QVOD ſi diſtantia Solis à meridie contineat quadrantem, ſiue 6 horas, erit differentia inter-<lb/>
<anchor type="note" xlink:label="note-0146-07a" xlink:href="note-0146-07"/>
dictam merietatem, &amp; </s>
  <s xml:id="echoid-s7706" xml:space="preserve">ſinum altitudinis meridianæ, nempe recta λ N, ſinus altitudinis Solis, vt <lb/>ex eiſdem figuris patet: </s>
  <s xml:id="echoid-s7707" xml:space="preserve">quia tunc Sol in puncto P, ſui paralleli exiſtet, atq; </s>
  <s xml:id="echoid-s7708" xml:space="preserve">adeo recta λ M, erit <lb/>portio diametri paralleli Horizontis, &amp;</s>
  <s xml:id="echoid-s7709" xml:space="preserve">c. </s>
  <s xml:id="echoid-s7710" xml:space="preserve">Vnde ſi medietas prædicta auferatur ex ſinu altitudinis <lb/>meridianæ, relinquetur ſinus altitudinis Solis.</s>
  <s xml:id="echoid-s7711" xml:space="preserve"/>
</p>
<div xml:id="echoid-div429" type="float" level="2" n="4">
<note position="left" xlink:label="note-0146-07" xlink:href="note-0146-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s7712" xml:space="preserve">ALITER quoq; </s>
  <s xml:id="echoid-s7713" xml:space="preserve">inueniemus altitudinem Solis, cum ſex horis à meridie abeſt. </s>
  <s xml:id="echoid-s7714" xml:space="preserve">Ductis enim <lb/>in prima ſigura ex M, F, ad A C, duabus perpendicularibus M α, F β; </s>
  <s xml:id="echoid-s7715" xml:space="preserve">quoniã eſt, vt E F, ſinus to-<lb/>tus ad F β, ſinum altitudinis poli, ita E M, ſinus declinationis ad M α, ſinum altitudinis Solis: <lb/></s>
  <s xml:id="echoid-s7716" xml:space="preserve">
<anchor type="note" xlink:label="note-0146-08a" xlink:href="note-0146-08"/>
<anchor type="note" xlink:label="note-0146-09a" xlink:href="note-0146-09"/>
(Eſt namq; </s>
  <s xml:id="echoid-s7717" xml:space="preserve">M α, æqualis ſinui altitudinis Solis λ N.) </s>
  <s xml:id="echoid-s7718" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum altitudinis <lb/>poli, ita ſinus declinationis ad aliud, inuenietur ſinus altitudinis Solis.</s>
  <s xml:id="echoid-s7719" xml:space="preserve"/>
</p>
<div xml:id="echoid-div430" type="float" level="2" n="5">
<note position="left" xlink:label="note-0146-08" xlink:href="note-0146-08a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0146-09" xlink:href="note-0146-09a" xml:space="preserve">34. primi.</note>
</div>
<p>
  <s xml:id="echoid-s7720" xml:space="preserve">SI autẽ diſtantia Solis à meridie quadrantẽ vel 6. </s>
  <s xml:id="echoid-s7721" xml:space="preserve">horas ſuperet, vt in ſecunda figura cernitur, <lb/>
<anchor type="note" xlink:label="note-0146-10a" xlink:href="note-0146-10"/>
<anchor type="note" xlink:label="note-0146-11a" xlink:href="note-0146-11"/>
auferenda eſt recta inuenta λ T, ex λ N, differentia inter dictam medietatem, &amp; </s>
  <s xml:id="echoid-s7722" xml:space="preserve">ſinum altitudi-<lb/>nis meridianæ, vt habeatur T N, ſinus altitudinis Solis.</s>
  <s xml:id="echoid-s7723" xml:space="preserve"/>
</p>
<div xml:id="echoid-div431" type="float" level="2" n="6">
<note position="left" xlink:label="note-0146-10" xlink:href="note-0146-10a" xml:space="preserve">Quando diſtan <lb/>tia Solis à meri <lb/>die in parallelo <lb/>boreali maior <lb/>eſt quadrante.</note>
<note position="left" xlink:label="note-0146-11" xlink:href="note-0146-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s7724" xml:space="preserve">IN ſignis deniq; </s>
  <s xml:id="echoid-s7725" xml:space="preserve">auſtralibus ſemper auferenda eſt differentia inter medietatem dictam, &amp; </s>
  <s xml:id="echoid-s7726" xml:space="preserve">ſi-<lb/>
<anchor type="note" xlink:label="note-0146-12a" xlink:href="note-0146-12"/>
num altitudinis meridianæ, hoc eſt, recta λ N, ex recta λ T, inuenta, vt relinquatur T N, ſinus <lb/>altitudinis Solis, vt perſpicuum eſt ex figura quarta, &amp; </s>
  <s xml:id="echoid-s7727" xml:space="preserve">quinta.</s>
  <s xml:id="echoid-s7728" xml:space="preserve"><unsure/></s>
</p>
<div xml:id="echoid-div432" type="float" level="2" n="7">
<note position="left" xlink:label="note-0146-12" xlink:href="note-0146-12a" xml:space="preserve">Qua<unsure/>ndo Solin <lb/>parallelo auſtra <lb/>li exiſtit.</note>
</div>
<p>
  <s xml:id="echoid-s7729" xml:space="preserve">CÆTERVM Sole exiſtente in æquinoctijs, multo breuius altitudinem Solis conſequemur <lb/>
<anchor type="note" xlink:label="note-0146-13a" xlink:href="note-0146-13"/>
ex data hora. </s>
  <s xml:id="echoid-s7730" xml:space="preserve">Quoniam enim in ſexta figura eſt, vt H E, ſinus totus ad R E, ſinum cõplementi di-<lb/>ſtantiæ Solis à meridie, ita H N, ſinus complementi altitudinis poli ad T N, ſinum altitudinis So-<lb/>lis: </s>
  <s xml:id="echoid-s7731" xml:space="preserve">Si fiat vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus complementi <lb/>altitudinis poliad aliud, habebitur ſinus altitudinis Solis tempore obſeruationis.</s>
  <s xml:id="echoid-s7732" xml:space="preserve"/>
</p>
<div xml:id="echoid-div433" type="float" level="2" n="8">
<note position="left" xlink:label="note-0146-13" xlink:href="note-0146-13a" xml:space="preserve">Altitudo Solis <lb/>ſupra Horizon <lb/>tem quomodo <lb/>in æquinoctiis <lb/>ex data hora nu <lb/>meranda ſit.</note>
</div>
<note position="left" xml:space="preserve">2. vel 4. ſexti</note>
<p>
  <s xml:id="echoid-s7733" xml:space="preserve">SIMILITER altitudinem Solis in Verticali circulo proprie dicto exiſtentis, ſine magno la-
<pb o="127" file="0147" n="147" rhead="LIBER PRIMVS."/>
bore inuenimus, etiamſi horam ignoremus. </s>
  <s xml:id="echoid-s7734" xml:space="preserve">In quarta enim figura ducatur diameter paralleli bo@ <lb/>
<anchor type="note" xlink:label="note-0147-01a" xlink:href="note-0147-01"/>
realis V X, (In borealibus enim duntaxat parallelis Sol ſupra Horizontem in Verticali poteſt exi-<lb/>ſtere.) </s>
  <s xml:id="echoid-s7735" xml:space="preserve">ſecans axem in Y, &amp; </s>
  <s xml:id="echoid-s7736" xml:space="preserve">Verticalis diametrum in Z, puncto, per quod ducatur diameter paral <lb/>lè<unsure/>li Horizontis, ita vt Z E, ſit ſinus altitudinis Solis in Verticali exiſtentis. </s>
  <s xml:id="echoid-s7737" xml:space="preserve">Ducta autem D γ, ad <lb/>H E, perpendiculari, quæ ſecet V X, in δ; </s>
  <s xml:id="echoid-s7738" xml:space="preserve">quoniam eſt, vt D γ, ſinus alitudinis poli ad γ δ, ſinum <lb/>
<anchor type="note" xlink:label="note-0147-02a" xlink:href="note-0147-02"/>
declinationis paralleli propoſiti, ita D E, ſinus totus ad EZ, ſinum altitudinis Solis: </s>
  <s xml:id="echoid-s7739" xml:space="preserve">Si fiat, vt ſinus <lb/>altitudinis poli ad ſinum declinationis, ita ſinus totus ad aliud, inueniemus ſinum altitudinis So-<lb/>lis in Verticali. </s>
  <s xml:id="echoid-s7740" xml:space="preserve">Huius rei hoc ſit exemplum. </s>
  <s xml:id="echoid-s7741" xml:space="preserve">Sole exiſtẽte in principio ♋, in Horizonte Romano, <lb/>vel ad latitudinem grad. </s>
  <s xml:id="echoid-s7742" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7743" xml:space="preserve">Fiat vt 66913, ſinus altitudinis poli ad 39874. </s>
  <s xml:id="echoid-s7744" xml:space="preserve">ſinum declinationis, <lb/>quæ cõtinet grad. </s>
  <s xml:id="echoid-s7745" xml:space="preserve">23. </s>
  <s xml:id="echoid-s7746" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7747" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7748" xml:space="preserve">ita 100000 ſinus totus ad aliud, inueniemusq́; </s>
  <s xml:id="echoid-s7749" xml:space="preserve">ferè 59591. </s>
  <s xml:id="echoid-s7750" xml:space="preserve">ſinum <lb/>
<anchor type="note" xlink:label="note-0147-03a" xlink:href="note-0147-03"/>
altitudinis quæſitæ, cui reſpondet arcus grad. </s>
  <s xml:id="echoid-s7751" xml:space="preserve">36. </s>
  <s xml:id="echoid-s7752" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7753" xml:space="preserve">35. </s>
  <s xml:id="echoid-s7754" xml:space="preserve">pro altitudine Solis in Verticali circulo <lb/>ad datam latitudinem.</s>
  <s xml:id="echoid-s7755" xml:space="preserve"/>
</p>
<div xml:id="echoid-div434" type="float" level="2" n="9">
<note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">Altitudo Solis <lb/>in Verticali cit <lb/>culo qua ratio-<lb/>ne inueniatur, <lb/>etiamſi hora <lb/>ignoretur.</note>
<note position="right" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0147-03" xlink:href="note-0147-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s7756" xml:space="preserve">QVOD ſi declinatio paralleli borealis æqualis fuerit altitudini poli, hoc eſt, arcui B H, tan-<lb/>get parallelus Verticalem in B, Z enith, vt paté<unsure/>t. </s>
  <s xml:id="echoid-s7757" xml:space="preserve">Vnde altitudo Solis in Verticali comprehendet <lb/>tunc grad. </s>
  <s xml:id="echoid-s7758" xml:space="preserve">90. </s>
  <s xml:id="echoid-s7759" xml:space="preserve">Si vero maior fuerit declinatio altitudine poli, non ſecabit parallelus Verticalem, vt <lb/>ex tertia ſigura manifeſtũ eſt. </s>
  <s xml:id="echoid-s7760" xml:space="preserve">Quare tunc ſol nunquam ad Verticalẽ perueniet. </s>
  <s xml:id="echoid-s7761" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s7762" xml:space="preserve">hæc de prima <lb/>parte huius problematis. </s>
  <s xml:id="echoid-s7763" xml:space="preserve">Sed antequam ad ſecundam partem problematis accedamus, rem totam <lb/>nonnullis exemplis illuſtremus.</s>
  <s xml:id="echoid-s7764" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Exemplum pri-<lb/>mum.</note>
<p>
  <s xml:id="echoid-s7765" xml:space="preserve">SOLE igitur exiſtente in principio ♊, vel ♌, quando nimirum altitudo meridiana continet <lb/>grad. </s>
  <s xml:id="echoid-s7766" xml:space="preserve">68. </s>
  <s xml:id="echoid-s7767" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7768" xml:space="preserve">12. </s>
  <s xml:id="echoid-s7769" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s7770" xml:space="preserve">depreſſio meridiana grad. </s>
  <s xml:id="echoid-s7771" xml:space="preserve">27. </s>
  <s xml:id="echoid-s7772" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7773" xml:space="preserve">48. </s>
  <s xml:id="echoid-s7774" xml:space="preserve">dies autem continet horas 14. </s>
  <s xml:id="echoid-s7775" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s7776" xml:space="preserve">
<anchor type="note" xlink:label="note-0147-05a" xlink:href="note-0147-05"/>
35. </s>
  <s xml:id="echoid-s7777" xml:space="preserve">fere; </s>
  <s xml:id="echoid-s7778" xml:space="preserve">adeo vt meridies fiat more ſtalorum horá<unsure/> 16. </s>
  <s xml:id="echoid-s7779" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7780" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7781" xml:space="preserve">more autem Babyloniorum hora <lb/>7. </s>
  <s xml:id="echoid-s7782" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7783" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7784" xml:space="preserve">inquirenda ſit in Horizonte Romano, hoc eſt, ad latitudinem grad. </s>
  <s xml:id="echoid-s7785" xml:space="preserve">42. </s>
  <s xml:id="echoid-s7786" xml:space="preserve">altitudo Solis <lb/>ad horam 20. </s>
  <s xml:id="echoid-s7787" xml:space="preserve">ab occaſu, vel ad horam 4. </s>
  <s xml:id="echoid-s7788" xml:space="preserve">ab ortu, quarum vtraq; </s>
  <s xml:id="echoid-s7789" xml:space="preserve">diſtat à meridie horis 3. </s>
  <s xml:id="echoid-s7790" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7791" xml:space="preserve">17. <lb/></s>
  <s xml:id="echoid-s7792" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s7793" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7794" xml:space="preserve">min. </s>
  <s xml:id="echoid-s7795" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7796" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s7797" xml:space="preserve">ſinus totus ad 65275. </s>
  <s xml:id="echoid-s7798" xml:space="preserve">ſinum cõplementi diſtantiæ So-<lb/>lis à meridie, ita 69743. </s>
  <s xml:id="echoid-s7799" xml:space="preserve">medietas rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7800" xml:space="preserve">ſinu depreſ-<lb/>ſionis meridianæ, ad aliud, inuenieturq; </s>
  <s xml:id="echoid-s7801" xml:space="preserve">hic ferè numerus 45524. </s>
  <s xml:id="echoid-s7802" xml:space="preserve">qui additus ad 23105. </s>
  <s xml:id="echoid-s7803" xml:space="preserve">differen <lb/>tiam inter medietatem rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7804" xml:space="preserve">ſinu depreſſionis meri-<lb/>dianæ, &amp; </s>
  <s xml:id="echoid-s7805" xml:space="preserve">ſinum altitudinis meridianæ, (quia Sol ponitur in parallelo boreali, &amp; </s>
  <s xml:id="echoid-s7806" xml:space="preserve">diſtantia Solis à <lb/>meridie minor quàm hor. </s>
  <s xml:id="echoid-s7807" xml:space="preserve">6.) </s>
  <s xml:id="echoid-s7808" xml:space="preserve">facit 68629. </s>
  <s xml:id="echoid-s7809" xml:space="preserve">Cuius arcus grad. </s>
  <s xml:id="echoid-s7810" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7811" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7812" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7813" xml:space="preserve">dabit altitudinem Solis <lb/>ad oblatam horam.</s>
  <s xml:id="echoid-s7814" xml:space="preserve"/>
</p>
<div xml:id="echoid-div435" type="float" level="2" n="10">
<note position="left" xlink:label="note-0147-05" xlink:href="note-0147-05a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s7815" xml:space="preserve">RVRSVS Sole in eodem parallelo exiſtente, inquirenda ſit altitudo Solis ad horam 6. </s>
  <s xml:id="echoid-s7816" xml:space="preserve">à me-<lb/>
<anchor type="note" xlink:label="note-0147-07a" xlink:href="note-0147-07"/>
ridie, vel media nocte. </s>
  <s xml:id="echoid-s7817" xml:space="preserve">Differentia inter 69743. </s>
  <s xml:id="echoid-s7818" xml:space="preserve">medietatem rectæ compoſitæ ex ſinu altitudinis <lb/>meridianæ, &amp; </s>
  <s xml:id="echoid-s7819" xml:space="preserve">ſinu depreſſionis meridianæ, &amp; </s>
  <s xml:id="echoid-s7820" xml:space="preserve">92848. </s>
  <s xml:id="echoid-s7821" xml:space="preserve">ſinũ altitudinis meridianę<unsure/>, nẽpe 23105. </s>
  <s xml:id="echoid-s7822" xml:space="preserve">erit <lb/>ſinus altitudinis Solis quæſitæ; </s>
  <s xml:id="echoid-s7823" xml:space="preserve">quia tunc Sol eſt borealis, habetq́ue diſtantiam à meridie æqualem <lb/>quadranti, ſiue 6. </s>
  <s xml:id="echoid-s7824" xml:space="preserve">horis. </s>
  <s xml:id="echoid-s7825" xml:space="preserve">Quare Solis altitudo tunc erit grad. </s>
  <s xml:id="echoid-s7826" xml:space="preserve">13. </s>
  <s xml:id="echoid-s7827" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7828" xml:space="preserve">22. </s>
  <s xml:id="echoid-s7829" xml:space="preserve">ferè. </s>
  <s xml:id="echoid-s7830" xml:space="preserve">Quæ etiã hoc modo <lb/>inuenietur, vt ante demonſtrauimus. </s>
  <s xml:id="echoid-s7831" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s7832" xml:space="preserve">ſinus totus ad 66913. </s>
  <s xml:id="echoid-s7833" xml:space="preserve">ſinũ altitudinis poli, ita <lb/>34529. </s>
  <s xml:id="echoid-s7834" xml:space="preserve">ſinus declinationis ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s7835" xml:space="preserve">hic ferèſinus 23104. </s>
  <s xml:id="echoid-s7836" xml:space="preserve">altitudinis Solis, vt ſupra.</s>
  <s xml:id="echoid-s7837" xml:space="preserve"/>
</p>
<div xml:id="echoid-div436" type="float" level="2" n="11">
<note position="right" xlink:label="note-0147-07" xlink:href="note-0147-07a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
</div>
<note position="right" xml:space="preserve">Exemplum t@@-<lb/>tium.</note>
<p>
  <s xml:id="echoid-s7838" xml:space="preserve">PRÆTEREA Sole eundem parallelum deſcribente, inueſtiganda ſit altitudo Solis ad ho-<lb/>ram 23. </s>
  <s xml:id="echoid-s7839" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7840" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7841" xml:space="preserve">ab occaſu, vel ad horam 0. </s>
  <s xml:id="echoid-s7842" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7843" xml:space="preserve">30. </s>
  <s xml:id="echoid-s7844" xml:space="preserve">ab ortu, ita vt diſtantia à meridie ſit hor. </s>
  <s xml:id="echoid-s7845" xml:space="preserve">6. <lb/></s>
  <s xml:id="echoid-s7846" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7847" xml:space="preserve">47. </s>
  <s xml:id="echoid-s7848" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s7849" xml:space="preserve">101. </s>
  <s xml:id="echoid-s7850" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7851" xml:space="preserve">45. </s>
  <s xml:id="echoid-s7852" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s7853" xml:space="preserve">ſinus totus ad 20364. </s>
  <s xml:id="echoid-s7854" xml:space="preserve">ſinum complementi di-<lb/>
<anchor type="note" xlink:label="note-0147-09a" xlink:href="note-0147-09"/>
ſtantiæ Solis à meridie;</s>
  <s xml:id="echoid-s7855" xml:space="preserve"><unsure/> ita 69743. </s>
  <s xml:id="echoid-s7856" xml:space="preserve">medietas rectæ compoſitæ ex ſinu altitudinis meridiane,<unsure/> &amp; </s>
  <s xml:id="echoid-s7857" xml:space="preserve">ſinu <lb/>depreſſionis meridianæ, ad aliud, inuenieturq; </s>
  <s xml:id="echoid-s7858" xml:space="preserve">hic quaſi numerus 14202. </s>
  <s xml:id="echoid-s7859" xml:space="preserve">qui ablatus ex 23105. <lb/></s>
  <s xml:id="echoid-s7860" xml:space="preserve">differe@@ia inter medietatem prædictam, &amp; </s>
  <s xml:id="echoid-s7861" xml:space="preserve">ſinum altitudinis meridianæ, (quia Sol in parallelo <lb/>boreali exiſtens ponitur habere maiorem diſtãtiam à meridie, quà m 6. </s>
  <s xml:id="echoid-s7862" xml:space="preserve">hor.) </s>
  <s xml:id="echoid-s7863" xml:space="preserve">relinquit 8903. </s>
  <s xml:id="echoid-s7864" xml:space="preserve">ſinũ <lb/>altitudinis Solis illa hora, atque adeo Solis altitudo complectetur grad. </s>
  <s xml:id="echoid-s7865" xml:space="preserve">5. </s>
  <s xml:id="echoid-s7866" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7867" xml:space="preserve">7.</s>
  <s xml:id="echoid-s7868" xml:space="preserve"/>
</p>
<div xml:id="echoid-div437" type="float" level="2" n="12">
<note position="left" xlink:label="note-0147-09" xlink:href="note-0147-09a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s7869" xml:space="preserve">POSTREMO altitudo Solis inuenienda ſit hora 3. </s>
  <s xml:id="echoid-s7870" xml:space="preserve">poſt meridiem, vel hora 9. </s>
  <s xml:id="echoid-s7871" xml:space="preserve">poſt mediam <lb/>
<anchor type="note" xlink:label="note-0147-10a" xlink:href="note-0147-10"/>
noctem, Sole in principio ♐, vel ♒, exiſte<unsure/>nte. </s>
  <s xml:id="echoid-s7872" xml:space="preserve">Fiat, vt 100000. </s>
  <s xml:id="echoid-s7873" xml:space="preserve">ſinus totus ad 70710. </s>
  <s xml:id="echoid-s7874" xml:space="preserve">ſinum com-<lb/>plementi diſtantiæ Solis à meridie, ita 69743. </s>
  <s xml:id="echoid-s7875" xml:space="preserve">medietas rectæ compoſitę ex ſinu altitudinis meri-<lb/>dianæ, &amp; </s>
  <s xml:id="echoid-s7876" xml:space="preserve">ſinu depreſſionis meridianę, (Erit autem hæc eadem, quę prius, cum ♐, &amp; </s>
  <s xml:id="echoid-s7877" xml:space="preserve">♒, ſint ſigna <lb/>oppoſita ſignis ♊, &amp; </s>
  <s xml:id="echoid-s7878" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s7879" xml:space="preserve">Conſtat autẽ ex dictis; </s>
  <s xml:id="echoid-s7880" xml:space="preserve">altitudinẽ meridianã vnius ſigni eſſe depreſſionem <lb/>
<anchor type="note" xlink:label="note-0147-11a" xlink:href="note-0147-11"/>
alterius, &amp; </s>
  <s xml:id="echoid-s7881" xml:space="preserve">contra.) </s>
  <s xml:id="echoid-s7882" xml:space="preserve">ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s7883" xml:space="preserve">propemodũ hic numerus 49315. </s>
  <s xml:id="echoid-s7884" xml:space="preserve">à quo ſi auferatur <lb/>23105. </s>
  <s xml:id="echoid-s7885" xml:space="preserve">differentia inter medietatem ptædictam, &amp; </s>
  <s xml:id="echoid-s7886" xml:space="preserve">ſinum altitudinis meridianæ, (quia Sol in au-<lb/>ſtrali parallelo ponitur.) </s>
  <s xml:id="echoid-s7887" xml:space="preserve">relinquetur ſinus altitudinis Solis 26210. </s>
  <s xml:id="echoid-s7888" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s7889" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7890" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7891" xml:space="preserve">12. <lb/></s>
  <s xml:id="echoid-s7892" xml:space="preserve">dabit Solis altitudinem tunc temporis. </s>
  <s xml:id="echoid-s7893" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s7894" xml:space="preserve">ita manifeſte patet ratio, qua ex hora cognita in noti-<lb/>tiam altitudinis Solis poſſimus peruenire. </s>
  <s xml:id="echoid-s7895" xml:space="preserve">Explicemus nunc alteram propoſitionis partem, qua ra <lb/>tione videlicet ex Solis altitudine cognita horam cognoſcamus; </s>
  <s xml:id="echoid-s7896" xml:space="preserve">quod ita exequemur.</s>
  <s xml:id="echoid-s7897" xml:space="preserve"/>
</p>
<div xml:id="echoid-div438" type="float" level="2" n="13">
<note position="right" xlink:label="note-0147-10" xlink:href="note-0147-10a" xml:space="preserve">Exemplũ quar-<lb/>tum.</note>
<note position="left" xlink:label="note-0147-11" xlink:href="note-0147-11a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Qua ratione <lb/>hora ex altitudi <lb/>ne Solis ſupra <lb/>Horizontem co <lb/>gnita reperia-<lb/>tur.</note>
<p>
  <s xml:id="echoid-s7898" xml:space="preserve">CVM in eiſdem figuris ſit, vt K λ, medietas rectæ compoſitæ ex ſinu altitudinis meridianę, <lb/>&amp; </s>
  <s xml:id="echoid-s7899" xml:space="preserve">ſinu depreſſionis meridianę, ad λ T, differẽtiam inter T N, ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s7900" xml:space="preserve">λ N, dif-<lb/>ferentiam inter medietatem prędictam, &amp; </s>
  <s xml:id="echoid-s7901" xml:space="preserve">ſinum altitudinis meridianę, ita K M, ſinus totus ad <lb/>M R, ſinum complementi diſtantie Solis à meridie: </s>
  <s xml:id="echoid-s7902" xml:space="preserve">Si fiat vt medietas rectę compoſitę ex ſinu al-<lb/>
<anchor type="note" xlink:label="note-0147-13a" xlink:href="note-0147-13"/>
titudinis meridianę, &amp; </s>
  <s xml:id="echoid-s7903" xml:space="preserve">ſinu depreſſionis meridianę, a differentiam, quam inter ſe habent ſinus
<pb o="128" file="0148" n="148" rhead="GNOMONICES"/>
altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s7904" xml:space="preserve">differẽtia inter dictam medietatem, &amp; </s>
  <s xml:id="echoid-s7905" xml:space="preserve">ſinum altitudinis meridianę<unsure/>, ita ſinus <lb/>totus ad aliud, habebitur ſinus complementi diſtantię Solis à meridie, atq; </s>
  <s xml:id="echoid-s7906" xml:space="preserve">adeo &amp; </s>
  <s xml:id="echoid-s7907" xml:space="preserve">ipſum comple <lb/>mentum diſtantię Solis à meridie notum erit, beneficio cuius diſtantiam Solis à meridie, ac proin <lb/>de &amp; </s>
  <s xml:id="echoid-s7908" xml:space="preserve">horam tempore obſeruationis cognoſcemus hoc modo. </s>
  <s xml:id="echoid-s7909" xml:space="preserve">Quando Sol ſeptentrionalis eſt, &amp; </s>
  <s xml:id="echoid-s7910" xml:space="preserve"><lb/>ſinus altitudinis Solis ſuperat differentiam inter medietatem dictam, &amp; </s>
  <s xml:id="echoid-s7911" xml:space="preserve">ſinum altitudinis meri-<lb/>dianę, vt in figura prima &amp; </s>
  <s xml:id="echoid-s7912" xml:space="preserve">tertia apparet, ſubtrahatur complementum diſtautię Solis à meridie <lb/>inuentum ex quadrante, reman ebitq́; </s>
  <s xml:id="echoid-s7913" xml:space="preserve">Solis diſtan<unsure/>tia à meridie, quo ad gradus.</s>
  <s xml:id="echoid-s7914" xml:space="preserve"/>
</p>
<div xml:id="echoid-div439" type="float" level="2" n="14">
<note position="right" xlink:label="note-0147-13" xlink:href="note-0147-13a" xml:space="preserve">2. ſexti.</note>
</div>
<p>
  <s xml:id="echoid-s7915" xml:space="preserve">QVOD ſi ſinus altitudinis Solis fuerit ęqualis differentię inter prędictam medietatem, &amp; </s>
  <s xml:id="echoid-s7916" xml:space="preserve">ſi-<lb/>num altitudinis meridianę, diſtabit Sol quadrante i<unsure/>ntegro, ſiue ſex horis à meridie, vt in tribus <lb/>figuris prioribus manifeſtum eſſe poteſt. </s>
  <s xml:id="echoid-s7917" xml:space="preserve">Si enim λ N, differentia inter K N, ſinum altitudinis <lb/>
<anchor type="note" xlink:label="note-0148-01a" xlink:href="note-0148-01"/>
meridianæ, &amp; </s>
  <s xml:id="echoid-s7918" xml:space="preserve">K λ, medietatem prædictam, ponatur ſinus altitudinis Solis, ita vt λ M, ſit por-<lb/>tio diametri paralleli Horizontis per Solem tranſeuntis, dabit quadrans K P, diſtantiam Solis <lb/>à meridie.</s>
  <s xml:id="echoid-s7919" xml:space="preserve"/>
</p>
<div xml:id="echoid-div440" type="float" level="2" n="15">
<note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s7920" xml:space="preserve">SI vero Sole exiſtente boreali, ſinus altitudinis ſolis minor extiterit, quam differentia inter me <lb/>dietatem prędictam, &amp; </s>
  <s xml:id="echoid-s7921" xml:space="preserve">ſinum altitudinis meridianæ, vt in ſecun da figura cõtingit, adiungatur cõ-<lb/>plementum diſtantię Solis à meridie inuentum quadranti, conflabiturq́; </s>
  <s xml:id="echoid-s7922" xml:space="preserve">diſtantia Solis à meri-<lb/>die, quo ad gradus.</s>
  <s xml:id="echoid-s7923" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s7924" xml:space="preserve">SOLE deniq; </s>
  <s xml:id="echoid-s7925" xml:space="preserve">auſtrali exiſtente, complementum diſtantiæ Solis à meridie inuentum perpe-<lb/>
<anchor type="note" xlink:label="note-0148-02a" xlink:href="note-0148-02"/>
tuo ex quadrante deducendum eſt, vt diſtantia Solis à meridie quoad gradus remaneat, vt ex figu-<lb/>ra quarta &amp; </s>
  <s xml:id="echoid-s7926" xml:space="preserve">quinta conſtat. </s>
  <s xml:id="echoid-s7927" xml:space="preserve">Nam ſi ex quadrante K P, ſubtrahatur O P, complementum diſtantiæ <lb/>
<anchor type="note" xlink:label="note-0148-03a" xlink:href="note-0148-03"/>
Solis à meridie, relinquetur K O, diſtantia Solis à meridie.</s>
  <s xml:id="echoid-s7928" xml:space="preserve"/>
</p>
<div xml:id="echoid-div441" type="float" level="2" n="16">
<note position="left" xlink:label="note-0148-02" xlink:href="note-0148-02a" xml:space="preserve">Qua ratione tẽ <lb/>pore æquinoctii <lb/>hora ex altitu-<lb/>dine Solis ſu-<lb/>pra Horizontẽ <lb/>cognita depre-<lb/>hendatur.</note>
<note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s7929" xml:space="preserve">HANC autem diſtãtiam Solis à meridie ex altitudine Solis cognita facilius comperiemus, <lb/>Sole Æquatorem percurrente. </s>
  <s xml:id="echoid-s7930" xml:space="preserve">Vt enim ex ſexta figura liquet, eſt vt H N, ſinus complementi alti-<lb/>
<anchor type="note" xlink:label="note-0148-04a" xlink:href="note-0148-04"/>
tudinis poli ad T N, ſinum altitudinis Solis tempore obſeruationis, ita H E, ſinus totus ad R E, ſi-<lb/>num complementi diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s7931" xml:space="preserve">Quapropter ſi fiat, vt ſinus complementi altitudi-<lb/>nis poli ad ſinum altitudinis Solis tempore obſeruationis inuentæ, ita ſinus totus ad aliud, <lb/>inuenietur ſinus complementi diſtantiæ Solis à meridie, ac proinde &amp; </s>
  <s xml:id="echoid-s7932" xml:space="preserve">ipſamet diſtantia latere <lb/>non poterit.</s>
  <s xml:id="echoid-s7933" xml:space="preserve"/>
</p>
<div xml:id="echoid-div442" type="float" level="2" n="17">
<note position="left" xlink:label="note-0148-04" xlink:href="note-0148-04a" xml:space="preserve">2. vel 4. ſexti</note>
</div>
<p>
  <s xml:id="echoid-s7934" xml:space="preserve">VNO exemplo rem explicemus. </s>
  <s xml:id="echoid-s7935" xml:space="preserve">Ponamus Sole exiſtente in principio ♊, vel ♌ nos ante meri-<lb/>
<anchor type="note" xlink:label="note-0148-05a" xlink:href="note-0148-05"/>
diem inueniſſe altitudinem Solis grad, 43. </s>
  <s xml:id="echoid-s7936" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7937" xml:space="preserve">20. </s>
  <s xml:id="echoid-s7938" xml:space="preserve">ex quo exploranda ſit hora tempore illius ob-<lb/>
<anchor type="note" xlink:label="note-0148-06a" xlink:href="note-0148-06"/>
ſeruationis. </s>
  <s xml:id="echoid-s7939" xml:space="preserve">Fiat vt 69743. </s>
  <s xml:id="echoid-s7940" xml:space="preserve">medietas rectæ cõpoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s7941" xml:space="preserve">ſinu depreſ-<lb/>ſionis meridianæ, ad 45519 differentiam inter ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s7942" xml:space="preserve">inter differentiam præ-<lb/>dictæ medietatis, &amp; </s>
  <s xml:id="echoid-s7943" xml:space="preserve">ſinus altitudinis meridianæ, ita 100000. </s>
  <s xml:id="echoid-s7944" xml:space="preserve">ſinus totus ad aliud. </s>
  <s xml:id="echoid-s7945" xml:space="preserve">Prodibit enim <lb/>ſinus ferè hic 65267. </s>
  <s xml:id="echoid-s7946" xml:space="preserve">complementi diſtantiæ Solis à meridie, cuius arcus grad. </s>
  <s xml:id="echoid-s7947" xml:space="preserve">40. </s>
  <s xml:id="echoid-s7948" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7949" xml:space="preserve">45. </s>
  <s xml:id="echoid-s7950" xml:space="preserve">ſubtra <lb/>tractus ex quadrante, (quia Sol borealis eſt, &amp; </s>
  <s xml:id="echoid-s7951" xml:space="preserve">ſinus altitudinis Solis, nempe 68624. </s>
  <s xml:id="echoid-s7952" xml:space="preserve">ſuperat diffe-<lb/>rentiã, quæ inter medietatem ſæpius dictam, &amp; </s>
  <s xml:id="echoid-s7953" xml:space="preserve">ſinum altitudinis meridianæ reperitur, nimirum <lb/>23105.) </s>
  <s xml:id="echoid-s7954" xml:space="preserve">relinquet grad. </s>
  <s xml:id="echoid-s7955" xml:space="preserve">49. </s>
  <s xml:id="echoid-s7956" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7957" xml:space="preserve">15. </s>
  <s xml:id="echoid-s7958" xml:space="preserve">pro diſtantia Solis à meridie, quæ complectitur horas 3. <lb/></s>
  <s xml:id="echoid-s7959" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7960" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7961" xml:space="preserve">Cum igitur obſeruatio fiat ante meridiem, inſtabit tunc hora 8. </s>
  <s xml:id="echoid-s7962" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7963" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7964" xml:space="preserve">poſt mediam <lb/>noctem, more Aſtronomorum. </s>
  <s xml:id="echoid-s7965" xml:space="preserve">Et ſi poſt meridiem facta eſſet obſeruatio, inſtaret hora 3. </s>
  <s xml:id="echoid-s7966" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7967" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7968" xml:space="preserve"><lb/>à meridie. </s>
  <s xml:id="echoid-s7969" xml:space="preserve">At ſecundum Italos erit hora 13. </s>
  <s xml:id="echoid-s7970" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7971" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7972" xml:space="preserve">ab occaſu, quia illo die meridies fit hora 16. </s>
  <s xml:id="echoid-s7973" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0148-07a" xlink:href="note-0148-07"/>
Min. </s>
  <s xml:id="echoid-s7974" xml:space="preserve">43. </s>
  <s xml:id="echoid-s7975" xml:space="preserve">à quo meridie ſi auferatur diſtantia Solis à meridie proximè inuenta, nempe hor. </s>
  <s xml:id="echoid-s7976" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7977" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s7978" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7979" xml:space="preserve">remanebunt horæ 13. </s>
  <s xml:id="echoid-s7980" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7981" xml:space="preserve">26. </s>
  <s xml:id="echoid-s7982" xml:space="preserve">Si vero obſeruatio fieret poſt meridiem, addenda eſſet hęc di-<lb/>ſtantia, vt hora ab occaſu Solis nota euaderet. </s>
  <s xml:id="echoid-s7983" xml:space="preserve">Inueniretur autem hora 20. </s>
  <s xml:id="echoid-s7984" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s7985" xml:space="preserve">Secundum <lb/>denique Babylonios erit hora 4. </s>
  <s xml:id="echoid-s7986" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7987" xml:space="preserve">o. </s>
  <s xml:id="echoid-s7988" xml:space="preserve">ab ortu Solis. </s>
  <s xml:id="echoid-s7989" xml:space="preserve">Cum enim illo die meridies fiat ſecundum <lb/>has horas, hora 7. </s>
  <s xml:id="echoid-s7990" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7991" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7992" xml:space="preserve">ſi ex hoc meridiano tempore detrahatur diſtantia Solis à meridie in-<lb/>uenta, nempe hor. </s>
  <s xml:id="echoid-s7993" xml:space="preserve">3. </s>
  <s xml:id="echoid-s7994" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s7995" xml:space="preserve">17. </s>
  <s xml:id="echoid-s7996" xml:space="preserve">remanet hora 4. </s>
  <s xml:id="echoid-s7997" xml:space="preserve">Quòd ſi obſeruatio poſt meridiem fieret, addenda <lb/>eſſet hęc diſtantia, atq; </s>
  <s xml:id="echoid-s7998" xml:space="preserve">ita inueniretur hora 10. </s>
  <s xml:id="echoid-s7999" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8000" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8001" xml:space="preserve">ab ortu Solis. </s>
  <s xml:id="echoid-s8002" xml:space="preserve">Ex hoc exemplo cętera ſine <lb/>labore intelligentur.</s>
  <s xml:id="echoid-s8003" xml:space="preserve"/>
</p>
<div xml:id="echoid-div443" type="float" level="2" n="18">
<note position="left" xlink:label="note-0148-05" xlink:href="note-0148-05a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0148-06" xlink:href="note-0148-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0148-07" xlink:href="note-0148-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s8004" xml:space="preserve">IN Verticali ci@culo Sole exiſtente, ita quoque pręter artem hactenus traditam ex eius altitu-<lb/>
<anchor type="note" xlink:label="note-0148-08a" xlink:href="note-0148-08"/>
dine horam offendemus. </s>
  <s xml:id="echoid-s8005" xml:space="preserve">Ducta in quarta figura ex puncto Z, vbi parallelus Solis Verticalẽ inter-<lb/>
<anchor type="note" xlink:label="note-0148-09a" xlink:href="note-0148-09"/>
ſecat, ad V X, perpendiculari Z β, vſque ad circunferentiam paralleli Solis ex centro Y, deſcripti <lb/>circa diametrum V X, erit Z β, cõmunis ſectio paralleli Solis, &amp; </s>
  <s xml:id="echoid-s8006" xml:space="preserve">paralleli Horizontis, cuius dia-<lb/>meter μ Z: </s>
  <s xml:id="echoid-s8007" xml:space="preserve">quod ita perſpicuũ fiet. </s>
  <s xml:id="echoid-s8008" xml:space="preserve">Quoniã vterq; </s>
  <s xml:id="echoid-s8009" xml:space="preserve">parallelus ad Meridianũ rectus eſt, erit &amp; </s>
  <s xml:id="echoid-s8010" xml:space="preserve">eorũ <lb/>
<anchor type="note" xlink:label="note-0148-10a" xlink:href="note-0148-10"/>
cõmunis ſectio ad eandẽ recta, ac proinde per defin. </s>
  <s xml:id="echoid-s8011" xml:space="preserve">3. </s>
  <s xml:id="echoid-s8012" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8013" xml:space="preserve">11. </s>
  <s xml:id="echoid-s8014" xml:space="preserve">Euclidis, ad V X, perpendicularis in <lb/>Z, puncto, vbi ſe mutuo ſecant dicti paralleli in Meridiano. </s>
  <s xml:id="echoid-s8015" xml:space="preserve">Igitur Z β, perpendicularis ad V X, in <lb/>Z, communis ſectio erit illorum parallelorum. </s>
  <s xml:id="echoid-s8016" xml:space="preserve">Ex quo ſequitur, cum Z, ſit centrum paralleli Ho <lb/>rizontis, cuius diameter μ Z, rectam Z β, ę<unsure/>qualem eſſe ſemidiametro μ Z, quan<unsure/>doquidem om-<lb/>nes lineæ ductæ ex Z, ad circunferentiam paralleli, cuius diameter μ Z, (qualis etiam eſt Z β, <lb/>communis eius ſectio cum parallelo Solis, vt oſtenſum eſt) ęquales ſunt ſemidiametro μ Z. </s>
  <s xml:id="echoid-s8017" xml:space="preserve">Quo-<lb/>niam verò μ Z, ſinus eſt complementi altitudinis Solis in Verticali circulo exiſtentis, nempe ſi-<lb/>nus arcus B μ, erit vt V Y, ſinus complementi declinationis paralleli V X, (quatenus ni@nirum
<pb o="129" file="0149" n="149" rhead="LIBER PRIMVS."/>
V Y, pars eſt ſinus totius A E, circuli maximi) ad V Y, quatenus ſinus totus eſt in ſu<unsure/>o parallelo, <lb/>ita β Z, quatenus pars eſt eiuſdem ſinus totius A E, maximi circuli (quæ quidem ęqualis eſt ſi-<lb/>nui μ Z, complementi altitudinis Solis in Verticali, vt demõſtrauimus) ad β Z, quatenus pars eſt <lb/>ſinus totius V Y. </s>
  <s xml:id="echoid-s8018" xml:space="preserve">Quapropter ſi fiat, ut ſinus complementi declinationis paralleli propoſiti ad <lb/>ſinum totum, ita ſinus complementi altitudinis Solis in Verticali exiſtentis ad aliud, cognita fiet <lb/>Z β, nempe ſinus diſtantię Solis à meridie. </s>
  <s xml:id="echoid-s8019" xml:space="preserve">Hac arte, Sole parallelum ♋, percurrente, inuenimus <lb/>hor. </s>
  <s xml:id="echoid-s8020" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8021" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8022" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8023" xml:space="preserve">paulo amplius ante, &amp; </s>
  <s xml:id="echoid-s8024" xml:space="preserve">poſt meridiem, dum in Verticali circulo exiſtit, ad latitudi-<lb/>nem grad. </s>
  <s xml:id="echoid-s8025" xml:space="preserve">42. </s>
  <s xml:id="echoid-s8026" xml:space="preserve">Ex quibus horis facile conijcies, quota hora ſit poſt mediam noctem, uel ab occa-<lb/>ſu, aut ortu Solis, cum Sol Verticalem obtinet, ſi prius tempus meridiei cognoſcatur more Italo-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s8027" xml:space="preserve">Babyloniorum. </s>
  <s xml:id="echoid-s8028" xml:space="preserve">Rurſus colliges ex hora cognita ante, uel p<unsure/>oſt meridiem quolibet die, <lb/>
<anchor type="note" xlink:label="note-0149-01a" xlink:href="note-0149-01"/>
<anchor type="note" xlink:label="note-0149-02a" xlink:href="note-0149-02"/>
Sole in ſignis borealibus exiſtente, an Sol attigerit Verticalem circulum, an uerò nondum ad eum <lb/>peruenerit, uel certe<unsure/> num eundem pertranſierit. </s>
  <s xml:id="echoid-s8029" xml:space="preserve">Quando enim antemeridiano tempore hora co-<lb/>gnita indicauerit maiorem diſtantiam à meridie, quàm inuenta eſt in Verticali circulo (ut ſi in <lb/>noſtro exemplo maiorem indicet, quàm hor. </s>
  <s xml:id="echoid-s8030" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8031" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8032" xml:space="preserve">4.) </s>
  <s xml:id="echoid-s8033" xml:space="preserve">perſpicuum eſt, eum nondum ad Vertica-<lb/>lem motu primi mobilis perueniſſe, quando autem ęqualem diſtantiam monſtrauerit, in Verticali <lb/>
<anchor type="note" xlink:label="note-0149-03a" xlink:href="note-0149-03"/>
eum exiſtere, quando denique minorem ſignificauerit, eundem iam pertranſiiſſe Verticalẽ, atque <lb/>inter Verticalem, &amp; </s>
  <s xml:id="echoid-s8034" xml:space="preserve">Meridianum ex parte auſtrali eſſe poſitum. </s>
  <s xml:id="echoid-s8035" xml:space="preserve">Contrarium intelligas tempore <lb/>pomeridiano.</s>
  <s xml:id="echoid-s8036" xml:space="preserve"/>
</p>
<div xml:id="echoid-div444" type="float" level="2" n="19">
<note position="left" xlink:label="note-0148-08" xlink:href="note-0148-08a" xml:space="preserve">Hora quanta <lb/>ſit, cum @ol in <lb/>Verticali circu <lb/>lo @xiſtit, qua <lb/>ratione explorã <lb/>dum.</note>
<note position="left" xlink:label="note-0148-09" xlink:href="note-0148-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0148-10" xlink:href="note-0148-10a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">Num Sol in fi-<lb/>gnis borealibus <lb/>exiſtens Verti-<lb/>calem at@@gerit, <lb/>necne, quo pa-<lb/>cto cognoſcat<unsure/>.</note>
<note position="left" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">Altitudo Soli@ <lb/>ſupra Horizon-<lb/>tem ex hora co <lb/>gnita quomodo <lb/>aliter, quàm ſu-<lb/>pra, inueſtige-<lb/>tur.</note>
</div>
<p>
  <s xml:id="echoid-s8037" xml:space="preserve">TOTVM hoc problema expedire poſſumus hoc etiam modo. </s>
  <s xml:id="echoid-s8038" xml:space="preserve">Quia in eiſdem figuris om-<lb/>nibus ſuprapoſitis eſt, ut K S, ſinus verſus arcus ſemidiurni ad R S, differentiam inter ſinum <lb/>
<anchor type="note" xlink:label="note-0149-04a" xlink:href="note-0149-04"/>
uerſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8039" xml:space="preserve">ſinum verſum diſtantię Solis à meridie, ita K N, ſinus altitudinis me <lb/>
<anchor type="note" xlink:label="note-0149-05a" xlink:href="note-0149-05"/>
ridianę ad T N, ſinum altitudinis Solis: </s>
  <s xml:id="echoid-s8040" xml:space="preserve">Si fiat, vt ſinus uerſus arcus ſemidiurni ad differentiam <lb/>inter ſinum uerſum ſemidiurni arcus, &amp; </s>
  <s xml:id="echoid-s8041" xml:space="preserve">ſinum uerſum diſtantię Solis à meridie, ita ſinus al-<lb/>titudinis meridianę ad aliud, inuenietur finus altitudinis Solis quæſitę, atque adeò altitudo ipſa <lb/>maniſeſta erit.</s>
  <s xml:id="echoid-s8042" xml:space="preserve"/>
</p>
<div xml:id="echoid-div445" type="float" level="2" n="20">
<note position="left" xlink:label="note-0149-04" xlink:href="note-0149-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0149-05" xlink:href="note-0149-05a" xml:space="preserve">2. vel 4. ſexti</note>
</div>
<note position="right" xml:space="preserve">Altitudo Solis <lb/>in æquinoctiis <lb/>quo modo ex <lb/>hora nota co-<lb/>gnoſcatur.</note>
<p>
  <s xml:id="echoid-s8043" xml:space="preserve">IN Aequatore autem, vt ex ſexta figura apparet, ſinus uerſus arcus ſemidiurni eſt ſinus totus <lb/>H E, &amp; </s>
  <s xml:id="echoid-s8044" xml:space="preserve">differentia inter ipſum, &amp; </s>
  <s xml:id="echoid-s8045" xml:space="preserve">ſinum uerſum diſtantię Solis à meridie eſt R E, ſinus cõplemen-<lb/>ti diſtantię Solis à meridie, &amp; </s>
  <s xml:id="echoid-s8046" xml:space="preserve">ſinus altitudinis meridianę eſt ſinus complementi altitudinis po-<lb/>li. </s>
  <s xml:id="echoid-s8047" xml:space="preserve">Vnde ſi tunc fiat, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus <lb/>complementi altitudinis poli ad aliud, habebitur ſinus altitudinis Solis tempore obſeruationis, <lb/>
<anchor type="note" xlink:label="note-0149-07a" xlink:href="note-0149-07"/>
<anchor type="note" xlink:label="note-0149-08a" xlink:href="note-0149-08"/>
ut &amp; </s>
  <s xml:id="echoid-s8048" xml:space="preserve">ſupra demonſtratum eſt.</s>
  <s xml:id="echoid-s8049" xml:space="preserve"/>
</p>
<div xml:id="echoid-div446" type="float" level="2" n="21">
<note position="left" xlink:label="note-0149-07" xlink:href="note-0149-07a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0149-08" xlink:href="note-0149-08a" xml:space="preserve">Qua ratio ne. ex <lb/>altitudine Solis <lb/>ſupra Horizon-<lb/>tem cognita in-<lb/>ueſtige. u@ ho-<lb/>ra.</note>
</div>
<p>
  <s xml:id="echoid-s8050" xml:space="preserve">RVRSVS quia eſt, ut k N, ſinus altitud nis meridianę ad T N, ſinum altitudinis Solis, <lb/>ita K S, ſinus uerſus arcus ſemidiurni ad R S, differentiam inter ſinum uerſum arcus ſemidiur-<lb/>ni, &amp; </s>
  <s xml:id="echoid-s8051" xml:space="preserve">ſinum uerſum diſtantiæ Solis à meridie: </s>
  <s xml:id="echoid-s8052" xml:space="preserve">Si ſiat, ut ſinus altitudinis meridianę ad ſinum <lb/>
<anchor type="note" xlink:label="note-0149-09a" xlink:href="note-0149-09"/>
altitudinis Solis tempore obſeruationis inuentę, ita ſinus uerſus arcus ſemidiurni ad aliud, re-<lb/>perietur numerus, qui ex ſinu uerſo arcus ſemidiurni ſublatus relinquit ſinum uerſum diſtan-<lb/>tiæ Solis à meridie. </s>
  <s xml:id="echoid-s8053" xml:space="preserve">Ex hoc autem ſinu uerſo diſtantiam Solis à meridie, atque adeò horam in-<lb/>ueniemus hac ratione. </s>
  <s xml:id="echoid-s8054" xml:space="preserve">Quando ſinus uerſus diſtantiæ Solis à meridie inuentus minor fuerit ſi-<lb/>nu toto, vt contingit ſemper in ſignis auſtralibus, &amp; </s>
  <s xml:id="echoid-s8055" xml:space="preserve">in ſignis etiam borealibus, cum diſtantia So-<lb/>lis à meridie minor eſt quadrante, auferemus @um ex ſinu toto, &amp; </s>
  <s xml:id="echoid-s8056" xml:space="preserve">reſidui ſinus recti arcum ex <lb/>
<anchor type="note" xlink:label="note-0149-10a" xlink:href="note-0149-10"/>
quadrante auferemus, remanebitq́ue diſtantia Solis à meridie. </s>
  <s xml:id="echoid-s8057" xml:space="preserve">Si autem dictus ſinus verſus <lb/>ęqualis fuerit ſinui toti, quod bis duntaxat in quolibet arcu diurno parallelorum borealium eue-<lb/>nire poteſt, erit diſtantia Solis à meridie quadrans complectens ſex horas. </s>
  <s xml:id="echoid-s8058" xml:space="preserve">Si denique ſinus ver-<lb/>ſus inuentus extiterit maior ſinu toto, auferemus ex eo ſinum totum, &amp; </s>
  <s xml:id="echoid-s8059" xml:space="preserve">reſidui ſinus recti arcum <lb/>ad quadrantem adijciemus, conficiemusq́; </s>
  <s xml:id="echoid-s8060" xml:space="preserve">diſtantiam Solis à meridie.</s>
  <s xml:id="echoid-s8061" xml:space="preserve"/>
</p>
<div xml:id="echoid-div447" type="float" level="2" n="22">
<note position="right" xlink:label="note-0149-09" xlink:href="note-0149-09a" xml:space="preserve">2. vel 4. ſexti</note>
<note position="left" xlink:label="note-0149-10" xlink:href="note-0149-10a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Quota hora ſi@, <lb/>quo modo in <lb/>æquinoctiis ex <lb/>data altitudine <lb/>Solis cognoſce@. <lb/>dum.</note>
<p>
  <s xml:id="echoid-s8062" xml:space="preserve">SOLE in æquinoctiis exiſtente, vt ex ſexta figura eſt manifeſtum, ſinus altitudinis meri-<lb/>dianæ eſt ſinus complementi altitudinis poli, &amp; </s>
  <s xml:id="echoid-s8063" xml:space="preserve">ſinus uerſus arcus ſemidiurni eſt ſinus totus <lb/>H E, &amp; </s>
  <s xml:id="echoid-s8064" xml:space="preserve">differentia inter ſinum uerſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8065" xml:space="preserve">ſinum verſum diſtantiæ Solis à me-<lb/>ridie, eſt ſinus complementi diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8066" xml:space="preserve">Quamobrem, ſi tunc ſiat, vt ſinus com-<lb/>plementi altitudinis poli ad ſinum altitudinis Solis tempore obſeruationis, ita ſinus totus ad <lb/>
<anchor type="note" xlink:label="note-0149-12a" xlink:href="note-0149-12"/>
aliud, habebitur ſinus complementi diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8067" xml:space="preserve">Id quod ſupra quoque demon-<lb/>ſtratum eſt.</s>
  <s xml:id="echoid-s8068" xml:space="preserve"/>
</p>
<div xml:id="echoid-div448" type="float" level="2" n="23">
<note position="left" xlink:label="note-0149-12" xlink:href="note-0149-12a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s8069" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s8070" xml:space="preserve">Ponamus Solem in parallelo ♐, uel ♒, habere poſt meridiem altitudinẽ <lb/>
<anchor type="note" xlink:label="note-0149-13a" xlink:href="note-0149-13"/>
ſupra Horizontem grad. </s>
  <s xml:id="echoid-s8071" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8072" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8073" xml:space="preserve">45. </s>
  <s xml:id="echoid-s8074" xml:space="preserve">Fiat ut 46638. </s>
  <s xml:id="echoid-s8075" xml:space="preserve">ſinus altitudinis meridianę ad 11753. </s>
  <s xml:id="echoid-s8076" xml:space="preserve">ſinum <lb/>altitudinis Solis inuentę<unsure/>, ita 66867. </s>
  <s xml:id="echoid-s8077" xml:space="preserve">ſinus uerſus arcus ſemidiurni ad aliud, prodibitq́; </s>
  <s xml:id="echoid-s8078" xml:space="preserve">hic fermè <lb/>numerus 16851. </s>
  <s xml:id="echoid-s8079" xml:space="preserve">qui ex 66867. </s>
  <s xml:id="echoid-s8080" xml:space="preserve">ſinu uerfo arcus ſemidiurni ſubtractus relinquet 50016. </s>
  <s xml:id="echoid-s8081" xml:space="preserve">ſinum <lb/>uerſum diſtantię Solis à meridie. </s>
  <s xml:id="echoid-s8082" xml:space="preserve">Hunc ergo quia minor eſt ſinu toto, ex 100000. </s>
  <s xml:id="echoid-s8083" xml:space="preserve">ſinu toto ſubdu-<lb/>cemus, &amp; </s>
  <s xml:id="echoid-s8084" xml:space="preserve">reſidui ſinus recti 49984. </s>
  <s xml:id="echoid-s8085" xml:space="preserve">arcũ grad. </s>
  <s xml:id="echoid-s8086" xml:space="preserve">29. </s>
  <s xml:id="echoid-s8087" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8088" xml:space="preserve">59. </s>
  <s xml:id="echoid-s8089" xml:space="preserve">ex quadrante dememus, habebimusq́; <lb/></s>
  <s xml:id="echoid-s8090" xml:space="preserve">diſtantiam Solis à meridie grad. </s>
  <s xml:id="echoid-s8091" xml:space="preserve">60. </s>
  <s xml:id="echoid-s8092" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8093" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8094" xml:space="preserve">hoc eſt, hor. </s>
  <s xml:id="echoid-s8095" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8096" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8097" xml:space="preserve">o, poſt meridiẽ, quia obſeruatio <lb/>ponitur facta poſt meridiem. </s>
  <s xml:id="echoid-s8098" xml:space="preserve">Ante meridiem eſſet hora 8. </s>
  <s xml:id="echoid-s8099" xml:space="preserve">poſt med. </s>
  <s xml:id="echoid-s8100" xml:space="preserve">noct. </s>
  <s xml:id="echoid-s8101" xml:space="preserve">Cognita autem hora <lb/>meridiei more Italorũ, &amp; </s>
  <s xml:id="echoid-s8102" xml:space="preserve">Babyloniorum ex quantitate diei, facile comperiemus, quęnam hora ab
<pb o="130" file="0150" n="150" rhead="GNOMONICES"/>
occaſu, vel ab ortu congruat horę quartę à meridie, vel octauę poſt mediam noctem, hoc eſt, <lb/>quartę ante meridiem, &amp;</s>
  <s xml:id="echoid-s8103" xml:space="preserve">c.</s>
  <s xml:id="echoid-s8104" xml:space="preserve"/>
</p>
<div xml:id="echoid-div449" type="float" level="2" n="24">
<note position="right" xlink:label="note-0149-13" xlink:href="note-0149-13a" xml:space="preserve">Exemplum.</note>
</div>
<p>
  <s xml:id="echoid-s8105" xml:space="preserve">CAETERVM in ſphęra recta totum problema hoc perfacile erit. </s>
  <s xml:id="echoid-s8106" xml:space="preserve">Sit enim Meridianus <lb/>A B C D, cuius centrum E; </s>
  <s xml:id="echoid-s8107" xml:space="preserve">Horizontis recti diameter A C, per polos A, C, tranſiens; </s>
  <s xml:id="echoid-s8108" xml:space="preserve">Aequatoris <lb/>diameter B D; </s>
  <s xml:id="echoid-s8109" xml:space="preserve">diameter cuiusuis paralleli Solis F G, ſecans Ho <lb/>rizontis diametrum in H; </s>
  <s xml:id="echoid-s8110" xml:space="preserve">paralleli Horizontis diameter I k, ſe-<lb/>
<anchor type="figure" xlink:label="fig-0150-01a" xlink:href="fig-0150-01"/>
cans B D, F G, in L, &amp; </s>
  <s xml:id="echoid-s8111" xml:space="preserve">M, qui quidem parallelus tempore ob-<lb/>ſeruationis per centrum Solis tranſeat; </s>
  <s xml:id="echoid-s8112" xml:space="preserve">Ac tandem ex H, cen-<lb/>tro paralleli Solis ſemicirculus deſcribatur F N O G, quem I K, <lb/>A C, productæ ſecent in N, &amp; </s>
  <s xml:id="echoid-s8113" xml:space="preserve">O.</s>
  <s xml:id="echoid-s8114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div450" type="float" level="2" n="25">
  <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a">
    <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0150-01"/>
  </figure>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s8115" xml:space="preserve">ERIT igitur arcus A I, vel C K, altitudo Solis in Aequato-<lb/>
<anchor type="note" xlink:label="note-0150-02a" xlink:href="note-0150-02"/>
re, &amp; </s>
  <s xml:id="echoid-s8116" xml:space="preserve">parallelo Horizontis diametri I K, exiſtentis, hoc eſt, in <lb/>puncto I, vel k, vt perſpicuum eſt, ſi Meridianus A B C D, circa <lb/>axem Horizontis B D, circumuertatur, ita vt cum Aequatore <lb/>ſphęrę rectę, &amp; </s>
  <s xml:id="echoid-s8117" xml:space="preserve">Verticali coniungatur. </s>
  <s xml:id="echoid-s8118" xml:space="preserve">Aequator enim in ſphę-<lb/>ra recta eſt tunc circulus etiam Verticalis altitudines Solis me-<lb/>tiens in ęquinoctiis. </s>
  <s xml:id="echoid-s8119" xml:space="preserve">Quocirca cum F I, vel F K, ſit diſtantia So-<lb/>lis à meridie, erit arcus I A, vel k C, hoc eſt, complementum diſtantię Solis à meridie, altitudo So-<lb/>lis. </s>
  <s xml:id="echoid-s8120" xml:space="preserve">Vnde ſi Solis altitudo quęratur ex hora cognita in ſphęra recta, Sole exiſtente in ęquinoctijs, <lb/>accipiendum erit complementum diſtantię Solis à meridie pro altitudine Solis.</s>
  <s xml:id="echoid-s8121" xml:space="preserve"/>
</p>
<div xml:id="echoid-div451" type="float" level="2" n="26">
<note position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">Altitudo Solis <lb/>in ſphæra recta, <lb/>quo modo in <lb/>æquinoctiis ex <lb/>data hora elicia <lb/>tur.</note>
</div>
<note position="left" xml:space="preserve">Altitudo Solis <lb/>in quouis paral <lb/>lelo exiſtentis, <lb/>quo pacto in <lb/>ſphæra recta ex <lb/>data hora de-<lb/>prehendatur.</note>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s8122" xml:space="preserve">SOLE vero exiſtente in parallelo F N O G, &amp; </s>
  <s xml:id="echoid-s8123" xml:space="preserve">in parallelo Horizontis diametri I K, hoc eſt, in <lb/>puncto N, in eadem ſphęra recta, erit arcus F N, diſtantia Solis à meridie, &amp; </s>
  <s xml:id="echoid-s8124" xml:space="preserve">H M, ęqualis ſinui <lb/>arcus A I, vel C k, qui altitudinem Solis tempore obſeruationis metitur, vt conſtat, ſi Meridianus <lb/>A B C D, circa axem Horizontis B D, circumuoluatur, vt vices obeat omnium Verticalium. </s>
  <s xml:id="echoid-s8125" xml:space="preserve">Si <lb/>igitur fiat, vt F H, ſinus totus paralleli Solis ad M H, ſinum complementi diſtantię Solis à meri-<lb/>die, ita F H, quatenus pars eſt ſinus totius B E, in maximo circulo, hoc eſt, quatenus ſinus eſt com <lb/>plementi declinationis paralleli Solis, ad aliud, inuenietur H M, in partibus eiuſdem ſinus totius <lb/>B E, atque adeò quatenus ſinus eſt altitudinis Solis A I, vel C K. </s>
  <s xml:id="echoid-s8126" xml:space="preserve">Solis ergo altitudo A I, vel C K, <lb/>nota euadet, Atque ita prima pars problematis explicata eſt.</s>
  <s xml:id="echoid-s8127" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8128" xml:space="preserve">IAM vero ex altitudine Solis cognita horam conſequemur in eadem ſphęra recta hoc modo. <lb/></s>
  <s xml:id="echoid-s8129" xml:space="preserve">
<anchor type="note" xlink:label="note-0150-05a" xlink:href="note-0150-05"/>
<anchor type="note" xlink:label="note-0150-06a" xlink:href="note-0150-06"/>
Sole exiſtente in æquinoctijs, accipiemus complementum altitudinis Solis pro diſtantia eius à <lb/>meridie, &amp;</s>
  <s xml:id="echoid-s8130" xml:space="preserve">c. </s>
  <s xml:id="echoid-s8131" xml:space="preserve">vt ex figura conſtat. </s>
  <s xml:id="echoid-s8132" xml:space="preserve">Eſt enim F I, vel F k, diſtantia Solis à meridie, complementum <lb/>altitudinis Solis A I, vel C K.</s>
  <s xml:id="echoid-s8133" xml:space="preserve"/>
</p>
<div xml:id="echoid-div452" type="float" level="2" n="27">
<note position="left" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">Hora diei qua <lb/>uia tepore æqui <lb/>noctiorum in <lb/>ſphæra recta ex <lb/>nota altitudine <lb/>Solis inueſtigan <lb/>da.</note>
<note position="left" xlink:label="note-0150-06" xlink:href="note-0150-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s8134" xml:space="preserve">SOLE autem poſito extra Aequatorem in quoliber parallelo F N O G; </s>
  <s xml:id="echoid-s8135" xml:space="preserve">Fiat vt F H, ſinus com-<lb/>
<anchor type="note" xlink:label="note-0150-07a" xlink:href="note-0150-07"/>
plementi declinationis ad H M, ſinum altitudinis Solis, ita F H, quatenus ſinus totus in paralle-<lb/>lo Solis, ad aliud; </s>
  <s xml:id="echoid-s8136" xml:space="preserve">habebiturq́; </s>
  <s xml:id="echoid-s8137" xml:space="preserve">M H, in partibus eiuſdem ſinus totius, quatenus videlicet eſt ſi-<lb/>nus complementi diſtantiæ Solis à meridie; </s>
  <s xml:id="echoid-s8138" xml:space="preserve">atque adeo complementum huiuſce diſtantiæ N O, <lb/>notum erit. </s>
  <s xml:id="echoid-s8139" xml:space="preserve">Ablato ergo complemento hoc N O, ex quadrante, reliqua erit diſtantia Solis à <lb/>meridie F N.</s>
  <s xml:id="echoid-s8140" xml:space="preserve"/>
</p>
<div xml:id="echoid-div453" type="float" level="2" n="28">
<note position="left" xlink:label="note-0150-07" xlink:href="note-0150-07a" xml:space="preserve">Hora diei qua <lb/>rõne extra tẽpu@ <lb/>æquinoctiorum <lb/>in ſphæra recta <lb/>ex cognita alti-<lb/>tudine Solis in-<lb/>quirenda.</note>
</div>
<note position="left" xml:space="preserve">Altitudo Solis <lb/>quomodo aliter <lb/>adhuc ex hora <lb/>eliciatur ĩ<unsure/> ſphę-<lb/>ra obliqua.</note>
<p>
  <s xml:id="echoid-s8141" xml:space="preserve">VERVM hac etiam ratione, ſi placet, totum problema expediemus in ſphæra obliqua. </s>
  <s xml:id="echoid-s8142" xml:space="preserve">Ducta <lb/>
<anchor type="note" xlink:label="note-0150-09a" xlink:href="note-0150-09"/>
in prima figura huius propoſ, ex puncto R, vbi parallelus Solis, &amp; </s>
  <s xml:id="echoid-s8143" xml:space="preserve">parallelus Horizontis ſe mutuo <lb/>interſecant, ad Horizontis diametrum A C, perpendiculari R ε, erit in triangulo R S ε, recta <lb/>R ε, ſinus complementi altitudinis poli, nempe anguli R S ε, (qui æqualis eſt angulo A E H) ſi <lb/>
<anchor type="note" xlink:label="note-0150-10a" xlink:href="note-0150-10"/>
R S, ponatur eſſe ſinus totus. </s>
  <s xml:id="echoid-s8144" xml:space="preserve">Inueniemus ergo prius rectam R S, in partibus ſinus totius circuli <lb/>maximi in ſphæra, hoc modo. </s>
  <s xml:id="echoid-s8145" xml:space="preserve">Fiat vt K M, ſinus totus in parallelo Solis ad K M, quatenus ſinus <lb/>eſt complementi declinationis paralleli K L, ita R S, differentia inter K S, ſinum verſum arcus ſe-<lb/>midiurni, &amp; </s>
  <s xml:id="echoid-s8146" xml:space="preserve">K R, ſinum verſum diſtantię Solis à meridie ad aliud. </s>
  <s xml:id="echoid-s8147" xml:space="preserve">Inuenietur enim hac ratione <lb/>R S, nota in partibus ſinus totius maximi circuli. </s>
  <s xml:id="echoid-s8148" xml:space="preserve">Deinde fiat, vt R S, ſinus totus ad R ε, ſinum <lb/>complementi altitudinis poli, ita R S, quatenus facta eſt nota in partibus ſinus totius maximi cir-<lb/>culi, ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s8149" xml:space="preserve">R ε, nota in partibus eiuſdem ſinus totius maximi circuli. </s>
  <s xml:id="echoid-s8150" xml:space="preserve">Cum ergo <lb/>
<anchor type="note" xlink:label="note-0150-11a" xlink:href="note-0150-11"/>
R ε, ſit ſinus altitudinis Solis, cognita erit ipſa Solis altitudo.</s>
  <s xml:id="echoid-s8151" xml:space="preserve"/>
</p>
<div xml:id="echoid-div454" type="float" level="2" n="29">
<note position="left" xlink:label="note-0150-09" xlink:href="note-0150-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0150-10" xlink:href="note-0150-10a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0150-11" xlink:href="note-0150-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s8152" xml:space="preserve">AD hæc; </s>
  <s xml:id="echoid-s8153" xml:space="preserve">Fiat vt R ε, ſinus complementi altitudinis poli ad R S, ſinum totum, ita R ε, quate-<lb/>
<anchor type="note" xlink:label="note-0150-12a" xlink:href="note-0150-12"/>
nus ſinus eſt altitudinis Solis cognitæ, ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s8154" xml:space="preserve">R S, nota in partibus ſinus totius cir-<lb/>culi maximi. </s>
  <s xml:id="echoid-s8155" xml:space="preserve">Quare eandẽ inueniemus etiam in partibus ſinus to tius K M, in parallelo propoſito <lb/>Solis, quatenus videlicet R S, differentia eſt inter K S, ſinũ verſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8156" xml:space="preserve">K R, ſinum <lb/>verſum diſtantiæ Solis à meridie, hoc modo. </s>
  <s xml:id="echoid-s8157" xml:space="preserve">Fiat vt K M, ſinus complementi declinationis paral-<lb/>leli k L, ad K M, ſinum totum in parallelo, ita R S, quatenus nota facta eſt in partibus ſinus totius <lb/>circuli maximi, ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8158" xml:space="preserve">R S, nota, quatenus differentia eſt inter ſinum verſum arcus <lb/>ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8159" xml:space="preserve">ſinum verſum diſtantię Solis à meridie. </s>
  <s xml:id="echoid-s8160" xml:space="preserve">Quamobrem &amp; </s>
  <s xml:id="echoid-s8161" xml:space="preserve">ſinus verſus diſtantiæ So-<lb/>lis à meridie, (ſi nimirum R S, hoc modo inuenta detrahatur ex K S@ ſinu verſo arcus ſemidiurni) <lb/>&amp; </s>
  <s xml:id="echoid-s8162" xml:space="preserve">ipſa propterea diſtantia Solis à meridie cognoſcetur.</s>
  <s xml:id="echoid-s8163" xml:space="preserve"/>
</p>
<div xml:id="echoid-div455" type="float" level="2" n="30">
<note position="left" xlink:label="note-0150-12" xlink:href="note-0150-12a" xml:space="preserve">Quomodo co-<lb/>gnoſcatur hora <lb/>ex altitudine <lb/>Solis nota.</note>
</div>
<pb o="131" file="0151" n="151" rhead="LIBER PRIMVS."/>
<p>
  <s xml:id="echoid-s8164" xml:space="preserve">SED inter omnes modos fortaſſe commodiſſimus hic erit. </s>
  <s xml:id="echoid-s8165" xml:space="preserve">Quoniam in prioribus quinque <lb/>figuris ad initiũ huius propoſ. </s>
  <s xml:id="echoid-s8166" xml:space="preserve">poſitis eſt, vt k M, ſinus totus in parallelo Solis ad K R, ita K λ, me-<lb/>
<anchor type="note" xlink:label="note-0151-01a" xlink:href="note-0151-01"/>
dietas rectę compoſitę ex ſinu altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s8167" xml:space="preserve">ſinu depreſſionis meridianæ ad <emph style="sc">K</emph> T: </s>
  <s xml:id="echoid-s8168" xml:space="preserve">Et <lb/>vt k R, ad R S, differentiam inter K S, ſinum verſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8169" xml:space="preserve">K R, ſinum verſum di-<lb/>
<anchor type="note" xlink:label="note-0151-02a" xlink:href="note-0151-02"/>
ſtantię Solis à meridie, ita K T, ad T N, ſinum rectum altitudinis Solis; </s>
  <s xml:id="echoid-s8170" xml:space="preserve">Erit ex æquo, vt <emph style="sc">K</emph> M, ſinus <lb/>totus in parallelo Solis ad R S, differentiam inter ſinum verſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8171" xml:space="preserve">ſinũ verſum <lb/>diſtantię Solis à meridie, ita K λ, medietas rectę compoſitę ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s8172" xml:space="preserve">ſinu <lb/>depreſſionis meridianę ad T N, ſinum rectum altitudinis Solis. </s>
  <s xml:id="echoid-s8173" xml:space="preserve">Quapropter ſi fiat, vt ſinus totus <lb/>
<anchor type="note" xlink:label="note-0151-03a" xlink:href="note-0151-03"/>
ad differentiam inter ſinum verſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8174" xml:space="preserve">ſinum verſum diſtantiæ Solis à meridie, <lb/>ita medietas rectæ compoſitę ex ſinu altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s8175" xml:space="preserve">ſinu depreſſionis meridianę, ad <lb/>
<anchor type="note" xlink:label="note-0151-04a" xlink:href="note-0151-04"/>
aliud, inuentus erit ſinus rectus altitudinis Solis, qui inquiritur; </s>
  <s xml:id="echoid-s8176" xml:space="preserve">atque adeo altitudo ipſa no-<lb/>ta euadet.</s>
  <s xml:id="echoid-s8177" xml:space="preserve"/>
</p>
<div xml:id="echoid-div456" type="float" level="2" n="31">
<note position="right" xlink:label="note-0151-01" xlink:href="note-0151-01a" xml:space="preserve">2. vel 4. ſexti</note>
<note position="right" xlink:label="note-0151-02" xlink:href="note-0151-02a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0151-03" xlink:href="note-0151-03a" xml:space="preserve">Altitudo Solis <lb/>quo pacto ex ho <lb/>ra aliter inue-<lb/>nienda.</note>
<note position="left" xlink:label="note-0151-04" xlink:href="note-0151-04a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8178" xml:space="preserve">QVOD ſi viciſſim fiat, vt K λ, medietas prędicta ad T N, ſinum altitudinis Solis, ita <emph style="sc">K</emph> M, ſinus <lb/>
<anchor type="note" xlink:label="note-0151-05a" xlink:href="note-0151-05"/>
totus ad aliud, inuenietur R S, differentia inter ſinum verſum arcus ſemidiurni, &amp; </s>
  <s xml:id="echoid-s8179" xml:space="preserve">ſinum verſum <lb/>diſtantię Solis à meridie; </s>
  <s xml:id="echoid-s8180" xml:space="preserve">qua differentia ſublata à ſinu verſo arcus ſemidiurni, reliquus erit k R, <lb/>ſinus verſus diſtantię Solis à meridie, &amp;</s>
  <s xml:id="echoid-s8181" xml:space="preserve">c.</s>
  <s xml:id="echoid-s8182" xml:space="preserve"/>
</p>
<div xml:id="echoid-div457" type="float" level="2" n="32">
<note position="right" xlink:label="note-0151-05" xlink:href="note-0151-05a" xml:space="preserve">Quomodo ho-<lb/>ra ex altitudine <lb/>Solis ſupputan <lb/>da ſit aliter ꝗ̃ <lb/>ſupra traditum <lb/>eſt.</note>
</div>
<p>
  <s xml:id="echoid-s8183" xml:space="preserve">AVT certe hoc modo (qui mihi magis probatur) idem negotium conficiemus. </s>
  <s xml:id="echoid-s8184" xml:space="preserve">Quoniam eſt <lb/>vt K M, ſinus totus in parallelo Solis, ad K R, ſinum verſum diſtantię Solis à meridie, ita K λ, me-<lb/>
<anchor type="note" xlink:label="note-0151-06a" xlink:href="note-0151-06"/>
dietas rectę compoſitę ex ſinu altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s8185" xml:space="preserve">ſinu depreſſionis meridianę ad K T, diffe-<lb/>rentiam inter k N, ſinum altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s8186" xml:space="preserve">T N, ſinum altitudinis Solis tempore obſerua-<lb/>
<anchor type="note" xlink:label="note-0151-07a" xlink:href="note-0151-07"/>
tionis: </s>
  <s xml:id="echoid-s8187" xml:space="preserve">Si fiat vt ſinus totus ad ſinum verſum diſtantię Solis à meridie, ita medietas rectæ compo-<lb/>
<anchor type="note" xlink:label="note-0151-08a" xlink:href="note-0151-08"/>
ſitę ex ſinu altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s8188" xml:space="preserve">ſinu depreſſionis meridianæ ad aliud, reperietur numerus <lb/>rectę k T, qui ex ſinu altitudinis meridianæ detractus relinquet ſinum altitudinis Solis.</s>
  <s xml:id="echoid-s8189" xml:space="preserve"/>
</p>
<div xml:id="echoid-div458" type="float" level="2" n="33">
<note position="right" xlink:label="note-0151-06" xlink:href="note-0151-06a" xml:space="preserve">2. vel 4. ſexti</note>
<note position="left" xlink:label="note-0151-07" xlink:href="note-0151-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0151-08" xlink:href="note-0151-08a" xml:space="preserve">Altitudo Solis <lb/>qua ratione ex <lb/>hora aliter inue <lb/>nienda.</note>
</div>
<p>
  <s xml:id="echoid-s8190" xml:space="preserve">ITEM, ſi viciſſim fiat, vt k λ, medietas prædicta ad K T, differentiam inter ſinum altitudinis <lb/>
<anchor type="note" xlink:label="note-0151-09a" xlink:href="note-0151-09"/>
meridianę, &amp; </s>
  <s xml:id="echoid-s8191" xml:space="preserve">ſinum altitudinis Solis, quę nota ponitur, ita k M, ſinus totus ad aliud, cognitus erit <lb/>K R, ſinus verſus diſtantiæ Solis à meridie, &amp;</s>
  <s xml:id="echoid-s8192" xml:space="preserve">c.</s>
  <s xml:id="echoid-s8193" xml:space="preserve"/>
</p>
<div xml:id="echoid-div459" type="float" level="2" n="34">
<note position="right" xlink:label="note-0151-09" xlink:href="note-0151-09a" xml:space="preserve">Hora qua ratio <lb/>ne aliter ex alti <lb/>tudine Solis nu <lb/>meranda.</note>
</div>
<p>
  <s xml:id="echoid-s8194" xml:space="preserve">HIC modus poſtremus latiſſime patet. </s>
  <s xml:id="echoid-s8195" xml:space="preserve">Pertinet enim etiam ad illum parallelum Solis, qui <lb/>
<anchor type="note" xlink:label="note-0151-10a" xlink:href="note-0151-10"/>
vel Horizontem tangit, vel totus ſupra eundem extat, vt ad finem ſcholij huius propoſ. </s>
  <s xml:id="echoid-s8196" xml:space="preserve">dicemus. <lb/></s>
  <s xml:id="echoid-s8197" xml:space="preserve">Adde quòd conuenit non ſolum in Horizontem, ſed in alia etiã omnia plana, quæ vel recta ſint ad <lb/>Horizontem, vel inclinata, vt ex propoſ. </s>
  <s xml:id="echoid-s8198" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8199" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8200" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8201" xml:space="preserve">perſpicuum erit. </s>
  <s xml:id="echoid-s8202" xml:space="preserve">Ibi enim eadem hac rationealti-<lb/>
<anchor type="note" xlink:label="note-0151-11a" xlink:href="note-0151-11"/>
iudinem Solis ſupra quodcunque planum ex data hora inueſtigabimus. </s>
  <s xml:id="echoid-s8203" xml:space="preserve">Quare præ cæter is omni-<lb/>bus modus hic memorię commendandus erit.</s>
  <s xml:id="echoid-s8204" xml:space="preserve"/>
</p>
<div xml:id="echoid-div460" type="float" level="2" n="35">
<note position="right" xlink:label="note-0151-10" xlink:href="note-0151-10a" xml:space="preserve">Quis modus <lb/>inuenieudæ al-<lb/>titudinis Solis <lb/>ſit præſtantior.</note>
<note position="left" xlink:label="note-0151-11" xlink:href="note-0151-11a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s8205" xml:space="preserve">LIBET iam per triangula ſphęrica idem hoc problema explicare. </s>
  <s xml:id="echoid-s8206" xml:space="preserve">Sit ergo Horizon ABCD; <lb/></s>
  <s xml:id="echoid-s8207" xml:space="preserve">
<anchor type="note" xlink:label="note-0151-12a" xlink:href="note-0151-12"/>
Meridianus B E D; </s>
  <s xml:id="echoid-s8208" xml:space="preserve">Aequator AFC; </s>
  <s xml:id="echoid-s8209" xml:space="preserve">Verticalis A E C; </s>
  <s xml:id="echoid-s8210" xml:space="preserve">parallelus Solis ſiue borealis, ſiue auſtralis <lb/>G H I, ita vt borealis Verticalem ſecet in K; </s>
  <s xml:id="echoid-s8211" xml:space="preserve">quod quidem contingit, quando arcus F H, declina-<lb/>
<anchor type="figure" xlink:label="fig-0151-01a" xlink:href="fig-0151-01"/>
<anchor type="note" xlink:label="note-0151-13a" xlink:href="note-0151-13"/>
tionis parallelli minor fuerit arcu E F, altitudinis poli, qui inter verticem, &amp; </s>
  <s xml:id="echoid-s8212" xml:space="preserve">Aequatorem interpo <lb/>
<anchor type="note" xlink:label="note-0151-14a" xlink:href="note-0151-14"/>
nitur; </s>
  <s xml:id="echoid-s8213" xml:space="preserve">ponaturq́; </s>
  <s xml:id="echoid-s8214" xml:space="preserve">Sol in puncto L, ſui paralleli, ita vt H L, ſit diſtantia Solis à meridie, cui ſimilis <lb/>erit arcus Aequatoris F M, per propoſ. </s>
  <s xml:id="echoid-s8215" xml:space="preserve">10. </s>
  <s xml:id="echoid-s8216" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8217" xml:space="preserve">2. </s>
  <s xml:id="echoid-s8218" xml:space="preserve">Theodoſii, quem aufert circulus declinationis ex <lb/>polo N, per centrum Solis L, ductus. </s>
  <s xml:id="echoid-s8219" xml:space="preserve">Ex vertice E, per Solem L, deſcendat Verticalis E L O, ita vt <lb/>arcus altitudinis Solis ſit L O, quem inueſtigare oportet, ſi diſtantia Solis à meridie ex hora data <lb/>cognita ſit, vt prior pars problematis pręcipit. </s>
  <s xml:id="echoid-s8220" xml:space="preserve">Deſcribatur alius circulus maximus per A, polum <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s8221" xml:space="preserve">per Solem in L, conſtitutum, ſecans Meridianum in P.</s>
  <s xml:id="echoid-s8222" xml:space="preserve"/>
</p>
<div xml:id="echoid-div461" type="float" level="2" n="36">
<note position="right" xlink:label="note-0151-12" xlink:href="note-0151-12a" xml:space="preserve">Altitudo Solis <lb/>qua uia ex co-<lb/>gn@a hora per <lb/>triangula ſphæ-<lb/>rica ſit explotã-<lb/>da, Sole in quo-<lb/>cunque pa@all@ <lb/>lo exiſtente.</note>
  <figure xlink:label="fig-0151-01" xlink:href="fig-0151-01a">
    <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151-01"/>
  </figure>
<note position="left" xlink:label="note-0151-13" xlink:href="note-0151-13a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0151-14" xlink:href="note-0151-14a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s8223" xml:space="preserve">QVONIAM igitur in triangulo ſphęrico A L M, priorum quatuor figurarum, angulus M, <lb/>rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s8224" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8225" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8226" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8227" xml:space="preserve">Theodoſii, cum circulus maximus N M, per N, polum Aequatoris <lb/>A F C, ductus ſit; </s>
  <s xml:id="echoid-s8228" xml:space="preserve">erit per propoſ. </s>
  <s xml:id="echoid-s8229" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8230" xml:space="preserve">lib: </s>
  <s xml:id="echoid-s8231" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8232" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8233" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8234" xml:space="preserve">de triangulis, uel per propoſ. </s>
  <s xml:id="echoid-s8235" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8236" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8237" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s8238" xml:space="preserve">Gebri, uel per propoſ. </s>
  <s xml:id="echoid-s8239" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8240" xml:space="preserve">noſtrorum triangulorum ſphęricorum, ut ſinus complementiarcus <lb/>A M, hoc eſt, ut ſinus diſtantię Solis à meridie (eſt enim F M, diſtantia Solis à meridie, comple-
<pb o="132" file="0152" n="152" rhead="GNOMONICES"/>
mentum arcus A M. </s>
  <s xml:id="echoid-s8241" xml:space="preserve">Solum quando diſtantia Solis à meridie in ſignis borealibus excedit ſex ho-<lb/>ras, vt in tertia figura contingit, complementum arcus A M, eſt diſtantia Solis à media nocte, nem-<lb/>pearcus Aequatoris inſra Horizontem inter M, &amp; </s>
  <s xml:id="echoid-s8242" xml:space="preserve">Meridianum; </s>
  <s xml:id="echoid-s8243" xml:space="preserve">ſed hic arcus eundem ſinum ha-<lb/>
<anchor type="figure" xlink:label="fig-0152-01a" xlink:href="fig-0152-01"/>
<anchor type="note" xlink:label="note-0152-01a" xlink:href="note-0152-01"/>
<anchor type="note" xlink:label="note-0152-02a" xlink:href="note-0152-02"/>
bet, quem arcus F M, diſtantiæ Solis à meridie, vt in tractatu ſinuũ explicauimus. </s>
  <s xml:id="echoid-s8244" xml:space="preserve">Conficiunt enim <lb/>
<anchor type="note" xlink:label="note-0152-03a" xlink:href="note-0152-03"/>
hi duo arcus ſemicirculum) ad ſinum totum, ita ſinus complementi arcus A L, ad ſinum comple <lb/>menti arcus L M, declinationis paralleli. </s>
  <s xml:id="echoid-s8245" xml:space="preserve">Conuertendo ergo erit quoque vt ſinus totus ad ſinum <lb/>diſtantiæ Solis à meridie, ita ſinus complementi declinationis propoſiti paralleli ad ſinum <lb/>complementi arcus A L; </s>
  <s xml:id="echoid-s8246" xml:space="preserve">atque adeò ex tribus primis notis quartum cognoſcetur, nempe com-<lb/>plementum arcus A L, hoc eſt, ipſe arcus L P; </s>
  <s xml:id="echoid-s8247" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s8248" xml:space="preserve">arcus A L, cognitus erit, qui dicatur <lb/>Primum Inuentum.</s>
  <s xml:id="echoid-s8249" xml:space="preserve"/>
</p>
<div xml:id="echoid-div462" type="float" level="2" n="37">
  <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a">
    <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0152-01"/>
  </figure>
<note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Pri@um inuen <lb/>@m.</note>
<p>
  <s xml:id="echoid-s8250" xml:space="preserve">RVRSVS quia in triangulo ſphærico N L P, earundem quatuor priorum ſigurarum, angu-<lb/>lus P, rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s8251" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8252" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8253" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8254" xml:space="preserve">Theodoſij, quòd circulus maximus A P, ductus eſt per A, po-<lb/>lum Meridiani B E D; </s>
  <s xml:id="echoid-s8255" xml:space="preserve">erit per eandem propoſ. </s>
  <s xml:id="echoid-s8256" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8257" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8258" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8259" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8260" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8261" xml:space="preserve">de triangulis, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8262" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8263" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8264" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8265" xml:space="preserve">Gebri, uel per propoſ. </s>
  <s xml:id="echoid-s8266" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8267" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple-<lb/>
<anchor type="note" xlink:label="note-0152-05a" xlink:href="note-0152-05"/>
menti arcus N L, hoc eſt, vt ſinus arcus L M, declinationis paralleli, ad ſinum complementi arcus <lb/>L P, hoc eſt, ad ſinum arcus A L, quem diximus Primum inuentum, ita ſinus complementi arcus <lb/>N P, ad ſinum totum. </s>
  <s xml:id="echoid-s8268" xml:space="preserve">Conuertendo igitur erit quoque, vt ſinus arcus, quem diximus Primum <lb/>inuentum, ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad ſinum complementi arcus <lb/>N P, atque adeò ex primis tribus notis quartum cognoſcetur, ńempe complementum arcus NP, <lb/>id eſt, ipſe arcus F P, in prima, ſecunda, &amp; </s>
  <s xml:id="echoid-s8269" xml:space="preserve">quarta figura, cum N F, quadrans ſit. </s>
  <s xml:id="echoid-s8270" xml:space="preserve">Solum quando di-<lb/>ſtantia Solis à meridie in borealibus ſignis ſuperat ſex horas, vt in tertia figura accidit, cõplementũ <lb/>arcus N P, eſt arcus à P, tendens per D, vſque ad Aequatorem ſub Horizonte; </s>
  <s xml:id="echoid-s8271" xml:space="preserve">(Quia enim tunc <lb/>P, cadit inter N, polum, &amp; </s>
  <s xml:id="echoid-s8272" xml:space="preserve">Horizontẽ, propterea quòd circulus A L P, ſecat circulum declinationis <lb/>N M, in L, cum N L M, ſecet Aequatorem in M, vltra punctum A, ſub Horizonte, propter arcum <lb/>
<anchor type="note" xlink:label="note-0152-06a" xlink:href="note-0152-06"/>
F M, diſtantiæ Solis à meridie, quæ maior ponitur quàm 6. </s>
  <s xml:id="echoid-s8273" xml:space="preserve">horarum, ſeu quàm quadrans F A; <lb/></s>
  <s xml:id="echoid-s8274" xml:space="preserve">efficitur, vt cum arcus ex polo N, per D, tendens vſque ad Aequatorẽ ſub Horizonte ſit quadrans, <lb/>dictus arcus tendens ex P, per D, vſque ad Aequatorem ſub Horizonte, complementum exiſtat ip-<lb/>ſius arcus N P,) quo complemento cognito cognoſcetur quoque arcus F P, reliquus ex ſemicircu-<lb/>lo. </s>
  <s xml:id="echoid-s8275" xml:space="preserve">Iam verò ſi arcus F P, inuentus, Sole exiſtente boreali, vt in prima, ſecunda, &amp; </s>
  <s xml:id="echoid-s8276" xml:space="preserve">tertia figura ap-<lb/>paret, adijciatur ad arcũ F B, altitudinis Aequatoris, vel cõplementi altitudinis poli, cognitus erit <lb/>totus arcus B P: </s>
  <s xml:id="echoid-s8277" xml:space="preserve">Sole autem auſtralia ſigna percurrente, ſi idem arcus inuentus F P, detrahatur ex <lb/>arcu F B, complementi altitudin is poli, idem arcus B P, notus relinquetur, vt in quarta figura eſt <lb/>manifeſtum. </s>
  <s xml:id="echoid-s8278" xml:space="preserve">Hic autem arcus B P, dicatur ſecundum Inuentum.</s>
  <s xml:id="echoid-s8279" xml:space="preserve"/>
</p>
<div xml:id="echoid-div463" type="float" level="2" n="38">
<note position="left" xlink:label="note-0152-05" xlink:href="note-0152-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0152-06" xlink:href="note-0152-06a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">Secundum in-<lb/>uentum.</note>
<p>
  <s xml:id="echoid-s8280" xml:space="preserve">POSTREMO, quoniam in triangulo ſphærico E L P, angulus P, rectus eſt, vt proximè di-<lb/>ximus, erit per eandem propoſ. </s>
  <s xml:id="echoid-s8281" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8282" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8283" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8284" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8285" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8286" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8287" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8288" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8289" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8290" xml:space="preserve">Ge-
<pb o="133" file="0153" n="153" rhead="LIBER PRIMVS."/>
bri, vel per propoſ. </s>
  <s xml:id="echoid-s8291" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8292" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus complementi arcus P L, <lb/>hoc eſt, vt ſinus arcus A L, quem diximus Primum inuentum, ad ſinum totum, ita ſinus comple-<lb/>menti arcus E L, hoc eſt, ita ſinus arcus L O, altitudinis Solis tempore obſeruationis, ad ſinum <lb/>complementi arcus E P, hoc eſt, ad ſinum arcus B P, quem appellauimus Inuentum ſecundum. <lb/></s>
  <s xml:id="echoid-s8293" xml:space="preserve">Nam in prima, &amp; </s>
  <s xml:id="echoid-s8294" xml:space="preserve">quarta figura arcus B P, complementum eſt arcus E P, cum E B, ſit quadrans: </s>
  <s xml:id="echoid-s8295" xml:space="preserve"><lb/>At vero in ſecunda, &amp; </s>
  <s xml:id="echoid-s8296" xml:space="preserve">tertia figura arcus P D, eſt complementum arcus E P, cum E D, ſit quadrans; </s>
  <s xml:id="echoid-s8297" xml:space="preserve"><lb/>eſt tamen idem ſinus arcus P D, qui arcui B P, debetur; </s>
  <s xml:id="echoid-s8298" xml:space="preserve">propterea quòd hi arcus ſemicirculum <lb/>complent. </s>
  <s xml:id="echoid-s8299" xml:space="preserve">Conuertendo igitur erit quoque vt ſinus totus ad ſinum atcus, quem diximus Primum <lb/>inuentum, ita ſinus arcus, quem appellauimus Inuentum ſecundum, ad ſinum altitudinis Solis <lb/>tempore obſeruationis. </s>
  <s xml:id="echoid-s8300" xml:space="preserve">Quare ex tribus prioribus cognitis cognoſcemus &amp; </s>
  <s xml:id="echoid-s8301" xml:space="preserve">quartum, nempe ſinũ <lb/>
<anchor type="note" xlink:label="note-0153-01a" xlink:href="note-0153-01"/>
altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s8302" xml:space="preserve">proinde &amp; </s>
  <s xml:id="echoid-s8303" xml:space="preserve">altitudinem ipſam.</s>
  <s xml:id="echoid-s8304" xml:space="preserve"/>
</p>
<div xml:id="echoid-div464" type="float" level="2" n="39">
<note position="left" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8305" xml:space="preserve">ITAQVE ſi fiat, vt ſinus totus ad ſinum diſtantię Solis à meridie, ita ſinus complementi de-<lb/>clinationis paralleli propoſiti ad aliud, inuenietur ſinus cuiuſdam arcus, qui ex quadrante ſubla-<lb/>tus relin quet arcum, qui Primum inuentum dici poteſt.</s>
  <s xml:id="echoid-s8306" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8307" xml:space="preserve">DEINDE ſi fiat, vt ſinus arcus, quem diximus Primum inuentum, ad ſinum declinationis <lb/>paralleli propoſiti, ita ſinus totus ad aliud, exurget ſinus, cuius areus, vel certè, (ſi diſtantia à meri-<lb/>die quadrantem, ſeu ſex horas exceſſerit) reliquus ex ſemicirculo, (ſi ille ex ſemicirculo detrahatur) <lb/>additus complemento altitudinis poli, quando nimirum Sol borealis eſt; </s>
  <s xml:id="echoid-s8308" xml:space="preserve">vel ſi auſtralis exiſtit, ex <lb/>complemento altitudinis poli ſubtractus, exhibebit arcum, qui Inuentum ſecundum poteſt appel <lb/>lari, Quòd ſi hic arcus Inuenti ſecundi quadrante fuerit maior, detrahendus erit à ſemicirculo, vt <lb/>
<anchor type="note" xlink:label="note-0153-02a" xlink:href="note-0153-02"/>
arcus relinquatur, quem Inuentum ſecundum nominauimus, vt in ſecunda, &amp; </s>
  <s xml:id="echoid-s8309" xml:space="preserve">tertia figura euenit.</s>
  <s xml:id="echoid-s8310" xml:space="preserve"/>
</p>
<div xml:id="echoid-div465" type="float" level="2" n="40">
<note position="left" xlink:label="note-0153-02" xlink:href="note-0153-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s8311" xml:space="preserve">AD extremum ſi fiat, vt ſinus totus ad ſinum arcus, quem appellauimus Primum inuentum, <lb/>ita ſinus arcus, quem Inuentum ſecundum uocauimus, ad aliud, reperietur ſinus altitudinis Solis <lb/>rempore obſeruationis. </s>
  <s xml:id="echoid-s8312" xml:space="preserve">Exemplis aliquot rem totam magis illuſtrem reddemns.</s>
  <s xml:id="echoid-s8313" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8314" xml:space="preserve">PONAMVS Solem in principio ♋, diſtantiamq́; </s>
  <s xml:id="echoid-s8315" xml:space="preserve">ipſius à meridie grad. </s>
  <s xml:id="echoid-s8316" xml:space="preserve">45. </s>
  <s xml:id="echoid-s8317" xml:space="preserve">nempe 3. </s>
  <s xml:id="echoid-s8318" xml:space="preserve">hor. <lb/></s>
  <s xml:id="echoid-s8319" xml:space="preserve">
<anchor type="note" xlink:label="note-0153-03a" xlink:href="note-0153-03"/>
Hoc ergo modo inueſtigabimus eo tempore altitudinem Solis ad latitudinem grad. </s>
  <s xml:id="echoid-s8320" xml:space="preserve">42. </s>
  <s xml:id="echoid-s8321" xml:space="preserve">Fiat vt <lb/>100000. </s>
  <s xml:id="echoid-s8322" xml:space="preserve">ſinus totus ad 70710. </s>
  <s xml:id="echoid-s8323" xml:space="preserve">ſinum diſtantiæ Solis à meridie, ita 91706. </s>
  <s xml:id="echoid-s8324" xml:space="preserve">ſinus complementi de-<lb/>clinationis ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8325" xml:space="preserve">fermè hic ſinus 64845. </s>
  <s xml:id="echoid-s8326" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8327" xml:space="preserve">40. </s>
  <s xml:id="echoid-s8328" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8329" xml:space="preserve">25. </s>
  <s xml:id="echoid-s8330" xml:space="preserve">ex quadrã-<lb/>ta deductus relinquet grad. </s>
  <s xml:id="echoid-s8331" xml:space="preserve">49. </s>
  <s xml:id="echoid-s8332" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8333" xml:space="preserve">35. </s>
  <s xml:id="echoid-s8334" xml:space="preserve">pro Primo Inuento.</s>
  <s xml:id="echoid-s8335" xml:space="preserve"/>
</p>
<div xml:id="echoid-div466" type="float" level="2" n="41">
<note position="right" xlink:label="note-0153-03" xlink:href="note-0153-03a" xml:space="preserve">Exemplum pri-<lb/>mum.</note>
</div>
<p>
  <s xml:id="echoid-s8336" xml:space="preserve">RVRSVS fiat, vt 76134. </s>
  <s xml:id="echoid-s8337" xml:space="preserve">ſinus arcus Primi Inuenti ad 39874. </s>
  <s xml:id="echoid-s8338" xml:space="preserve">ſinũ declinationis, ita 100000. <lb/></s>
  <s xml:id="echoid-s8339" xml:space="preserve">
<anchor type="note" xlink:label="note-0153-04a" xlink:href="note-0153-04"/>
ſinus totus ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8340" xml:space="preserve">hic propemodum ſinus 52373. </s>
  <s xml:id="echoid-s8341" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8342" xml:space="preserve">31. </s>
  <s xml:id="echoid-s8343" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8344" xml:space="preserve">35. <lb/></s>
  <s xml:id="echoid-s8345" xml:space="preserve">additus ad grad. </s>
  <s xml:id="echoid-s8346" xml:space="preserve">48. </s>
  <s xml:id="echoid-s8347" xml:space="preserve">nempe ad complementum altitudinis poli, quia Sol borealis eſt, conficiet ar-<lb/>cum grad. </s>
  <s xml:id="echoid-s8348" xml:space="preserve">79. </s>
  <s xml:id="echoid-s8349" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8350" xml:space="preserve">35. </s>
  <s xml:id="echoid-s8351" xml:space="preserve">pro Inuento ſecundo.</s>
  <s xml:id="echoid-s8352" xml:space="preserve"/>
</p>
<div xml:id="echoid-div467" type="float" level="2" n="42">
<note position="left" xlink:label="note-0153-04" xlink:href="note-0153-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s8353" xml:space="preserve">TANDEM fiat, vt 100000. </s>
  <s xml:id="echoid-s8354" xml:space="preserve">ſinus totus ad 76134. </s>
  <s xml:id="echoid-s8355" xml:space="preserve">ſinum arcus Primi Inuenti, ita 98351. </s>
  <s xml:id="echoid-s8356" xml:space="preserve">ſi-<lb/>nus arcus Inuenti ſecundi ad aliud, prodibitq́; </s>
  <s xml:id="echoid-s8357" xml:space="preserve">in lucem hic quaſi ſinus 74878. </s>
  <s xml:id="echoid-s8358" xml:space="preserve">cui reſpondet ar-<lb/>cus grad. </s>
  <s xml:id="echoid-s8359" xml:space="preserve">48. </s>
  <s xml:id="echoid-s8360" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8361" xml:space="preserve">29. </s>
  <s xml:id="echoid-s8362" xml:space="preserve">pro Solis altitudine tempore obſeruation is.</s>
  <s xml:id="echoid-s8363" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8364" xml:space="preserve">PONAMVS rurſus Solem in eodem parallelo habere diſtantiam à meridie grad. </s>
  <s xml:id="echoid-s8365" xml:space="preserve">75. </s>
  <s xml:id="echoid-s8366" xml:space="preserve">nem-<lb/>
<anchor type="note" xlink:label="note-0153-05a" xlink:href="note-0153-05"/>
pe hor. </s>
  <s xml:id="echoid-s8367" xml:space="preserve">5. </s>
  <s xml:id="echoid-s8368" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s8369" xml:space="preserve">ſinus totus ad 96592. </s>
  <s xml:id="echoid-s8370" xml:space="preserve">ſinum diſtantię Solis à meridie, ita 91706. </s>
  <s xml:id="echoid-s8371" xml:space="preserve">ſinus <lb/>complementi declinationis ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s8372" xml:space="preserve">hic ſinus ferè 88580. </s>
  <s xml:id="echoid-s8373" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8374" xml:space="preserve">62. </s>
  <s xml:id="echoid-s8375" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s8376" xml:space="preserve">21. </s>
  <s xml:id="echoid-s8377" xml:space="preserve">detractus ex quadrante relinquet grad. </s>
  <s xml:id="echoid-s8378" xml:space="preserve">27. </s>
  <s xml:id="echoid-s8379" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8380" xml:space="preserve">39. </s>
  <s xml:id="echoid-s8381" xml:space="preserve">pro Primo Inuento.</s>
  <s xml:id="echoid-s8382" xml:space="preserve"/>
</p>
<div xml:id="echoid-div468" type="float" level="2" n="43">
<note position="right" xlink:label="note-0153-05" xlink:href="note-0153-05a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s8383" xml:space="preserve">POST hæc fiat, vt 46406. </s>
  <s xml:id="echoid-s8384" xml:space="preserve">ſinus arcus, quem nominauimus Inuentum Primum, ad 39874. <lb/></s>
  <s xml:id="echoid-s8385" xml:space="preserve">ſinum declinationis, ita 100000. </s>
  <s xml:id="echoid-s8386" xml:space="preserve">ſinus totus ad aliud, prouenietq́; </s>
  <s xml:id="echoid-s8387" xml:space="preserve">ferè hic ſinus 85924. </s>
  <s xml:id="echoid-s8388" xml:space="preserve">cuius ar-<lb/>cus grad. </s>
  <s xml:id="echoid-s8389" xml:space="preserve">59. </s>
  <s xml:id="echoid-s8390" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8391" xml:space="preserve">14. </s>
  <s xml:id="echoid-s8392" xml:space="preserve">adiunctus complemento altitudinis poli grad. </s>
  <s xml:id="echoid-s8393" xml:space="preserve">48. </s>
  <s xml:id="echoid-s8394" xml:space="preserve">facietarcum grad. </s>
  <s xml:id="echoid-s8395" xml:space="preserve">107. </s>
  <s xml:id="echoid-s8396" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s8397" xml:space="preserve">14. </s>
  <s xml:id="echoid-s8398" xml:space="preserve">qui quoniam quadrantem ſuperat, detractus exſemicirculo, vt ex grad. </s>
  <s xml:id="echoid-s8399" xml:space="preserve">180. </s>
  <s xml:id="echoid-s8400" xml:space="preserve">relinquet ar-<lb/>cum grad. </s>
  <s xml:id="echoid-s8401" xml:space="preserve">72. </s>
  <s xml:id="echoid-s8402" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8403" xml:space="preserve">46. </s>
  <s xml:id="echoid-s8404" xml:space="preserve">pro Inuento ſecundo.</s>
  <s xml:id="echoid-s8405" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8406" xml:space="preserve">FIAT deniq; </s>
  <s xml:id="echoid-s8407" xml:space="preserve">vt 100000, ſinus totus ad 46406. </s>
  <s xml:id="echoid-s8408" xml:space="preserve">ſinum Inuenti primi, ita 95510. </s>
  <s xml:id="echoid-s8409" xml:space="preserve">ſinus Inuenti <lb/>ſecundi ad aliud, prodibitq́; </s>
  <s xml:id="echoid-s8410" xml:space="preserve">ſinus ferè hic 44322. </s>
  <s xml:id="echoid-s8411" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8412" xml:space="preserve">26. </s>
  <s xml:id="echoid-s8413" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8414" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8415" xml:space="preserve">dabit altitudinem <lb/>Solis quæſitam.</s>
  <s xml:id="echoid-s8416" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8417" xml:space="preserve">PRÆTEREA Sol exiſtens in eodem parallelo habeat diſtantiam à meridie horas 7, id eſt, <lb/>
<anchor type="note" xlink:label="note-0153-07a" xlink:href="note-0153-07"/>
grad. </s>
  <s xml:id="echoid-s8418" xml:space="preserve">105. </s>
  <s xml:id="echoid-s8419" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s8420" xml:space="preserve">ſinus totus ad 96592. </s>
  <s xml:id="echoid-s8421" xml:space="preserve">ſinum diſtantiæ Solis à meridie, (qui quidem ſi-<lb/>
<anchor type="note" xlink:label="note-0153-08a" xlink:href="note-0153-08"/>
nus debetur arcui grad. </s>
  <s xml:id="echoid-s8422" xml:space="preserve">75. </s>
  <s xml:id="echoid-s8423" xml:space="preserve">atq; </s>
  <s xml:id="echoid-s8424" xml:space="preserve">adeo &amp; </s>
  <s xml:id="echoid-s8425" xml:space="preserve">arcui grad. </s>
  <s xml:id="echoid-s8426" xml:space="preserve">105. </s>
  <s xml:id="echoid-s8427" xml:space="preserve">reliquo ex ſemicirculo) ita 91706. </s>
  <s xml:id="echoid-s8428" xml:space="preserve">ſinus <lb/>complemẽti declinationis ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s8429" xml:space="preserve">ſinus ferè hic 88580. </s>
  <s xml:id="echoid-s8430" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8431" xml:space="preserve">62. </s>
  <s xml:id="echoid-s8432" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s8433" xml:space="preserve">21. </s>
  <s xml:id="echoid-s8434" xml:space="preserve">detractus ex quadrante relinquet grad. </s>
  <s xml:id="echoid-s8435" xml:space="preserve">27. </s>
  <s xml:id="echoid-s8436" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8437" xml:space="preserve">39. </s>
  <s xml:id="echoid-s8438" xml:space="preserve">pro Inuento primo.</s>
  <s xml:id="echoid-s8439" xml:space="preserve"/>
</p>
<div xml:id="echoid-div469" type="float" level="2" n="44">
<note position="right" xlink:label="note-0153-07" xlink:href="note-0153-07a" xml:space="preserve">Exemplum @e@-<lb/>tium.</note>
<note position="left" xlink:label="note-0153-08" xlink:href="note-0153-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s8440" xml:space="preserve">FIAT quoque, vt 46406. </s>
  <s xml:id="echoid-s8441" xml:space="preserve">ſinus Inuenti primi ad 39874. </s>
  <s xml:id="echoid-s8442" xml:space="preserve">ſinum declinationis, ita 100000. </s>
  <s xml:id="echoid-s8443" xml:space="preserve">ſi-<lb/>nus totus ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8444" xml:space="preserve">hic quaſi ſinus 85924. </s>
  <s xml:id="echoid-s8445" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8446" xml:space="preserve">59. </s>
  <s xml:id="echoid-s8447" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8448" xml:space="preserve">14. </s>
  <s xml:id="echoid-s8449" xml:space="preserve">ex ſemicircu <lb/>lo detractus, quia diſtantia Solis à meridie ſuperat ſex horas, relinquet arcũ grad. </s>
  <s xml:id="echoid-s8450" xml:space="preserve">120. </s>
  <s xml:id="echoid-s8451" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8452" xml:space="preserve">46. </s>
  <s xml:id="echoid-s8453" xml:space="preserve">qui <lb/>adiectus ad complementũ alitudinis Poli grad. </s>
  <s xml:id="echoid-s8454" xml:space="preserve">48. </s>
  <s xml:id="echoid-s8455" xml:space="preserve">conficiet arcũ grad. </s>
  <s xml:id="echoid-s8456" xml:space="preserve">168. </s>
  <s xml:id="echoid-s8457" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8458" xml:space="preserve">46. </s>
  <s xml:id="echoid-s8459" xml:space="preserve">qui tandem, <lb/>quoniã quadrãte maior eſt, detractus ex ſemicirculo relinquet grad. </s>
  <s xml:id="echoid-s8460" xml:space="preserve">11. </s>
  <s xml:id="echoid-s8461" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8462" xml:space="preserve">14. </s>
  <s xml:id="echoid-s8463" xml:space="preserve">pro Inuẽto ſecũdo.</s>
  <s xml:id="echoid-s8464" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8465" xml:space="preserve">AD hęc, fiat vt 100000. </s>
  <s xml:id="echoid-s8466" xml:space="preserve">ſinus totus ad 46406. </s>
  <s xml:id="echoid-s8467" xml:space="preserve">ſinum Inuenti primi, ita 19480. </s>
  <s xml:id="echoid-s8468" xml:space="preserve">ſinus Inuenti ſe-<lb/>cundi ad aliud, habebiturq́; </s>
  <s xml:id="echoid-s8469" xml:space="preserve">fermè hic ſinus 9039. </s>
  <s xml:id="echoid-s8470" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8471" xml:space="preserve">5. </s>
  <s xml:id="echoid-s8472" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8473" xml:space="preserve">11. </s>
  <s xml:id="echoid-s8474" xml:space="preserve">offeret altitudi-<lb/>nem Solis, quam quærebamus.</s>
  <s xml:id="echoid-s8475" xml:space="preserve"/>
</p>
<pb o="134" file="0154" n="154" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s8476" xml:space="preserve">POSTREMO exiſtat Sol in parallelo quocunq; </s>
  <s xml:id="echoid-s8477" xml:space="preserve">auſtrali, vt in principio ♑, habeatq́; </s>
  <s xml:id="echoid-s8478" xml:space="preserve">díſtan-<lb/>
<anchor type="note" xlink:label="note-0154-01a" xlink:href="note-0154-01"/>
tiam à meridie hor. </s>
  <s xml:id="echoid-s8479" xml:space="preserve">2. </s>
  <s xml:id="echoid-s8480" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s8481" xml:space="preserve">30. </s>
  <s xml:id="echoid-s8482" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s8483" xml:space="preserve">ad 50000. </s>
  <s xml:id="echoid-s8484" xml:space="preserve">ſinum diſtantiæ Solis à meri-<lb/>die, ita 91706. </s>
  <s xml:id="echoid-s8485" xml:space="preserve">ſinus complementi declinationis ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8486" xml:space="preserve">hic ſinus 45853. </s>
  <s xml:id="echoid-s8487" xml:space="preserve">cuius ar <lb/>cus grad. </s>
  <s xml:id="echoid-s8488" xml:space="preserve">27. </s>
  <s xml:id="echoid-s8489" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8490" xml:space="preserve">18. </s>
  <s xml:id="echoid-s8491" xml:space="preserve">ablatus ex quadrante relinquet arcũ grad. </s>
  <s xml:id="echoid-s8492" xml:space="preserve">62. </s>
  <s xml:id="echoid-s8493" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8494" xml:space="preserve">42. </s>
  <s xml:id="echoid-s8495" xml:space="preserve">pro Inuẽto primo.</s>
  <s xml:id="echoid-s8496" xml:space="preserve"/>
</p>
<div xml:id="echoid-div470" type="float" level="2" n="45">
<note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">Exemplũ quar-<lb/>tum.</note>
</div>
<p>
  <s xml:id="echoid-s8497" xml:space="preserve">DEINDE fiat, vt 88861. </s>
  <s xml:id="echoid-s8498" xml:space="preserve">ſinus Inuenti primi ad 39874. </s>
  <s xml:id="echoid-s8499" xml:space="preserve">ſinum declinationis, ita 100000. <lb/></s>
  <s xml:id="echoid-s8500" xml:space="preserve">ſinus totus ad aliud, habebiturq́; </s>
  <s xml:id="echoid-s8501" xml:space="preserve">ferè ſinus hic 44872. </s>
  <s xml:id="echoid-s8502" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8503" xml:space="preserve">26. </s>
  <s xml:id="echoid-s8504" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8505" xml:space="preserve">40. </s>
  <s xml:id="echoid-s8506" xml:space="preserve">ſublatus <lb/>ex complemento altitudinis poli grad. </s>
  <s xml:id="echoid-s8507" xml:space="preserve">48. </s>
  <s xml:id="echoid-s8508" xml:space="preserve">quia ſol auſtralis eſt, relinquet arcum grad. </s>
  <s xml:id="echoid-s8509" xml:space="preserve">21. </s>
  <s xml:id="echoid-s8510" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8511" xml:space="preserve"><lb/>20. </s>
  <s xml:id="echoid-s8512" xml:space="preserve">pro Inuento ſecundo.</s>
  <s xml:id="echoid-s8513" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8514" xml:space="preserve">FIAT tandem, vt 100000. </s>
  <s xml:id="echoid-s8515" xml:space="preserve">ſinus totus ad 88861. </s>
  <s xml:id="echoid-s8516" xml:space="preserve">ſinum Inuenti primi, ita 36379. </s>
  <s xml:id="echoid-s8517" xml:space="preserve">ſinus In-<lb/>uenti ſecundi ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8518" xml:space="preserve">hic propemodum ſinus 32327. </s>
  <s xml:id="echoid-s8519" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8520" xml:space="preserve">18. </s>
  <s xml:id="echoid-s8521" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s8522" xml:space="preserve">
<anchor type="note" xlink:label="note-0154-02a" xlink:href="note-0154-02"/>
52. </s>
  <s xml:id="echoid-s8523" xml:space="preserve">exhibebit quæſitam Solis altitudinem.</s>
  <s xml:id="echoid-s8524" xml:space="preserve"/>
</p>
<div xml:id="echoid-div471" type="float" level="2" n="46">
<note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8525" xml:space="preserve">SOLE exiſtente in Verticali circulo, vt in puncto K, veluti in figura quinta apparet, multo <lb/>
<anchor type="note" xlink:label="note-0154-03a" xlink:href="note-0154-03"/>
<anchor type="figure" xlink:label="fig-0154-01a" xlink:href="fig-0154-01"/>
<anchor type="note" xlink:label="note-0154-04a" xlink:href="note-0154-04"/>
<anchor type="note" xlink:label="note-0154-05a" xlink:href="note-0154-05"/>
expeditius ex diſtantia Solis à meridie cognita altitudinem per ſphęrica triangula venabimur, <lb/>hac ratione. </s>
  <s xml:id="echoid-s8526" xml:space="preserve">Quoniam in triangulo ſphærico A k M, angulus M, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s8527" xml:space="preserve">19. <lb/></s>
  <s xml:id="echoid-s8528" xml:space="preserve">
<anchor type="note" xlink:label="note-0154-06a" xlink:href="note-0154-06"/>
lib. </s>
  <s xml:id="echoid-s8529" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8530" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8531" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8532" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8533" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8534" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8535" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8536" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8537" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8538" xml:space="preserve">noſtrorũ <lb/>triangulorum ſphæricorum, vt ſinus complementi arcus A M, hoc eſt, vt ſinus diſtantiæ Solis à <lb/>meridie, id eſt, vt ſinus arcus F M, ad ſinum totum, ita ſinus complementi arcus A <emph style="sc">K</emph>, ad ſinum <lb/>complementi arcus K M, hoc eſt, ad ſinum complementi declinationis. </s>
  <s xml:id="echoid-s8539" xml:space="preserve">Conuertendo ergo erit <lb/>quoque, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis pa-<lb/>ralleli propoſiti ad ſinum complementi arcus A K, vnde ex prioribus tribus cognitis cognoſce-<lb/>@ur &amp; </s>
  <s xml:id="echoid-s8540" xml:space="preserve">quartum, nempe complementum arcus A K, atque adeò &amp; </s>
  <s xml:id="echoid-s8541" xml:space="preserve">ipſemet arcus A <emph style="sc">K</emph>, altitudinem <lb/>Solis metiens. </s>
  <s xml:id="echoid-s8542" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s8543" xml:space="preserve">Sole in Verticali circulo exiſtente, ſi fiat vt ſinus totus ad ſinum diſtantiæ Solis <lb/>à meridie, ita ſinus complementi declinationis ad aliud, inuenietur ſinus complementi altitudinis <lb/>Solis, ac proinde &amp; </s>
  <s xml:id="echoid-s8544" xml:space="preserve">ipſa altitudo manifeſta erit.</s>
  <s xml:id="echoid-s8545" xml:space="preserve"/>
</p>
<div xml:id="echoid-div472" type="float" level="2" n="47">
<note position="left" xlink:label="note-0154-03" xlink:href="note-0154-03a" xml:space="preserve">Altitudo Solis <lb/>in circulo Ver-<lb/>ticali quomodo <lb/>ex data hora p <lb/>triangula ſphæ <lb/>tica ſupputetur.</note>
  <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a">
    <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0154-01"/>
  </figure>
<note position="left" xlink:label="note-0154-04" xlink:href="note-0154-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0154-05" xlink:href="note-0154-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0154-06" xlink:href="note-0154-06a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s8546" xml:space="preserve">SED ſi diſtantia Solis à meridie ignota fuerit, inueniemus nihilominus altitudinem Solis in <lb/>
<anchor type="note" xlink:label="note-0154-08a" xlink:href="note-0154-08"/>
Verticali exiſtentis hoc modo. </s>
  <s xml:id="echoid-s8547" xml:space="preserve">Quoniam in triangulo ſphærico E K N, angulus E, rectus eſt; </s>
  <s xml:id="echoid-s8548" xml:space="preserve">erit <lb/>per propoſ. </s>
  <s xml:id="echoid-s8549" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8550" xml:space="preserve">l b. </s>
  <s xml:id="echoid-s8551" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8552" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8553" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8554" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8555" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8556" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8557" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8558" xml:space="preserve">Gebri, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8559" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8560" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus complementi arcus E N, hoc eſt, vt ſi-<lb/>nus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus N k, id eſt, ita ſinus <lb/>arcus K M, declinationis paralleli propoſiti, ad ſinum complementi arcus E K, hoc eſt, ad ſinum <lb/>arcus A K, altitudinis Solis. </s>
  <s xml:id="echoid-s8561" xml:space="preserve">Igitur ſi fiat, vt ſinus altitudinis poli ad ſinum totum, ita ſinus decli-<lb/>nationis ad aliud, inuenietur ſinus altitudinis Solis. </s>
  <s xml:id="echoid-s8562" xml:space="preserve">Quod etiam clarius ita poterit demonſtrari. <lb/></s>
  <s xml:id="echoid-s8563" xml:space="preserve">Quoniam in triangulo ſphærico A K M, eiuſdem figuræ quintę angulus M, rectus eſt, erit per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8564" xml:space="preserve">16. </s>
  <s xml:id="echoid-s8565" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8566" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8567" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8568" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8569" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8570" xml:space="preserve">13. </s>
  <s xml:id="echoid-s8571" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8572" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8573" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8574" xml:space="preserve">41. </s>
  <s xml:id="echoid-s8575" xml:space="preserve"><lb/>noſtrorum triangulorum ſphæricorum, vt ſinus anguli A, altitudinis poli, (eſt enim E F, &amp; </s>
  <s xml:id="echoid-s8576" xml:space="preserve">arcus
<pb o="135" file="0155" n="155" rhead="LIBER PRIMVS."/>
altitudinis poli, &amp; </s>
  <s xml:id="echoid-s8577" xml:space="preserve">arcus anguli A.) </s>
  <s xml:id="echoid-s8578" xml:space="preserve">ad ſinum arcus k M, declinationis, ita ſinus anguli recti M, <lb/>hoc eſt, ita ſinus totus ad ſinum arcus A K, altitudinis poli. </s>
  <s xml:id="echoid-s8579" xml:space="preserve">Quare ſi fiat, vt ſinus altitudinis poli <lb/>ad ſinum declinationis, ita ſinus totus ad aliud, reperietur rurſus ſinus altitudinis Solis in Vertica-<lb/>li circulo. </s>
  <s xml:id="echoid-s8580" xml:space="preserve">Quod etiam ſupra demonſtrauimus ſine triangulis ſphæricis.</s>
  <s xml:id="echoid-s8581" xml:space="preserve"/>
</p>
<div xml:id="echoid-div473" type="float" level="2" n="48">
<note position="left" xlink:label="note-0154-08" xlink:href="note-0154-08a" xml:space="preserve">Altitudo Solis <lb/>in Verticali quo <lb/>modo ſuppute-<lb/>tur per ſphæti-<lb/>ca triangula, <lb/>etiãſi hora igno <lb/>retur.</note>
</div>
<p>
  <s xml:id="echoid-s8582" xml:space="preserve">INSVPER cum Sol in parallelis borealibus diſtat à meridie ſex horis, vt in ſexta figura, nul <lb/>
<anchor type="note" xlink:label="note-0155-01a" xlink:href="note-0155-01"/>
lius erit negotij altitudinem eius in ueſtigare. </s>
  <s xml:id="echoid-s8583" xml:space="preserve">Quia enim in ſphærico triangulo E L N, figuræ <lb/>ſextæ angulus N, rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s8584" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8585" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8586" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8587" xml:space="preserve">Theodoſij, quòd maximus circulus N A, per A, <lb/>polum Meridiani ductus ſit; </s>
  <s xml:id="echoid-s8588" xml:space="preserve">erit per propoſ. </s>
  <s xml:id="echoid-s8589" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8590" xml:space="preserve">lib 4. </s>
  <s xml:id="echoid-s8591" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8592" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8593" xml:space="preserve">de triangulis, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8594" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8595" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8596" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8597" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8598" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8599" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple-<lb/>menti arcus E N, hoc eſt, vt ſinus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus comple-<lb/>
<anchor type="note" xlink:label="note-0155-02a" xlink:href="note-0155-02"/>
menti arcus E L, hoc eſt, ita ſinus arcus L O, altitudinis Solis, ad ſinum complementi arcus N L, <lb/>id eſt, ad ſinum arcus L A, declinationis. </s>
  <s xml:id="echoid-s8600" xml:space="preserve">Conuertendo ergo erit quoque, vt ſinus totus ad ſinum <lb/>altitudinis poli, ita ſinus declinationis ad ſinum altitudinis Solis. </s>
  <s xml:id="echoid-s8601" xml:space="preserve">Quocirca ſi fiat, vt ſinus totus ad <lb/>ſinum altitudinis poli, ita ſinus declinationis ad aliud, habebitur linus altitudinis Solis. </s>
  <s xml:id="echoid-s8602" xml:space="preserve">Quod <lb/>etiam ſupra demonſtrauimus ſine triangulis ſphęricis.</s>
  <s xml:id="echoid-s8603" xml:space="preserve"/>
</p>
<div xml:id="echoid-div474" type="float" level="2" n="49">
<note position="right" xlink:label="note-0155-01" xlink:href="note-0155-01a" xml:space="preserve">Altitudo Solis, <lb/>cum Sol ſex ho-<lb/>ris abeſt à meri-<lb/>die in parallelis <lb/>borealibus, qua <lb/>rati one per ſphę <lb/>rica triangula <lb/>inueſtiganda.</note>
<note position="left" xlink:label="note-0155-02" xlink:href="note-0155-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8604" xml:space="preserve">ADHVC ſole puncta æquinoctiorũ poſſidente, ſine magno labore ex hora cognita, ſiue ex <lb/>
<anchor type="note" xlink:label="note-0155-03a" xlink:href="note-0155-03"/>
diſtantia Solis à meridie, altitudinem Solis eliciemus per ſphęrica triãgula hoc modo. </s>
  <s xml:id="echoid-s8605" xml:space="preserve">Intelligatur <lb/>in quinta figura Aequator eſle G H I, &amp; </s>
  <s xml:id="echoid-s8606" xml:space="preserve">Sol exiſtere in k, ne cogamur nouam figurã deſcribere. <lb/></s>
  <s xml:id="echoid-s8607" xml:space="preserve">Quia igitur in triangulo ſphærico E H K, angulus H, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s8608" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8609" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8610" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8611" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8612" xml:space="preserve"><lb/>Regiom. </s>
  <s xml:id="echoid-s8613" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s8614" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8615" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8616" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8617" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8618" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8619" xml:space="preserve">noſtrorum triangulorum ſphærico-<lb/>
<anchor type="note" xlink:label="note-0155-04a" xlink:href="note-0155-04"/>
rum, vt ſinus complementiarcus E H, hoc eſt, vt ſinus arcus H B, altitudinis Aequatoris, vel com <lb/>plementi altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K, id eſt, ita ſinus arcus <lb/>K A, altitudinis Solis, ad ſinum complementi arcus H K, diſtantie Solis à meridie. </s>
  <s xml:id="echoid-s8620" xml:space="preserve">Quare erit etiã <lb/>conuertendo, vt ſinus totus ad ſinum complementi altitndinis poli, ita ſinus complementi diſtan-<lb/>tię Solis à meridie, ad ſinum altitudinis Solis; </s>
  <s xml:id="echoid-s8621" xml:space="preserve">Ac propterea ſi fiat, vt ſinus totus ad ſinum com-<lb/>plementi altitudinis poli, ita ſinus complementi diſtantię Solis à meridiead aliud, cognitus erit <lb/>ſinus altitudinis Solis.</s>
  <s xml:id="echoid-s8622" xml:space="preserve"/>
</p>
<div xml:id="echoid-div475" type="float" level="2" n="50">
<note position="right" xlink:label="note-0155-03" xlink:href="note-0155-03a" xml:space="preserve">Altitudo Solis <lb/>in ęquiuoctiis, <lb/>quo pacto ex da <lb/>ta hora per triã <lb/>gula ſphęrica in <lb/>daganda.</note>
<note position="left" xlink:label="note-0155-04" xlink:href="note-0155-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s8623" xml:space="preserve">ALIA quoque ratione per triangula ſphęrica, &amp; </s>
  <s xml:id="echoid-s8624" xml:space="preserve">commodius fortaſſe, ſine circulo A L P, repe <lb/>
<anchor type="note" xlink:label="note-0155-05a" xlink:href="note-0155-05"/>
riemus altitudinem Solis ex hora cognita, quæ eiuſmodi eſt. </s>
  <s xml:id="echoid-s8625" xml:space="preserve">Producatur circulus declinationis <lb/>N L, ad partes L, donec Horizontem ſecet in Q. </s>
  <s xml:id="echoid-s8626" xml:space="preserve">Et quoniam angulus F N M, diſtantiæ Solis à <lb/>
<anchor type="note" xlink:label="note-0155-06a" xlink:href="note-0155-06"/>
meridie cognitus eſt, erit &amp; </s>
  <s xml:id="echoid-s8627" xml:space="preserve">Q N D, reliquus duorum rectorum notus. </s>
  <s xml:id="echoid-s8628" xml:space="preserve">Cum ergo in triangulo <lb/>ſphęrico D N Q, cuius angulus D, rectus, &amp; </s>
  <s xml:id="echoid-s8629" xml:space="preserve">D N Q, notus eſt, vnà cum arcu D N, altitudinis po-<lb/>li, ſit per propoſ. </s>
  <s xml:id="echoid-s8630" xml:space="preserve">18 lib. </s>
  <s xml:id="echoid-s8631" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8632" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8633" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8634" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8635" xml:space="preserve">14. </s>
  <s xml:id="echoid-s8636" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8637" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8638" xml:space="preserve">Gebri, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8639" xml:space="preserve">42. </s>
  <s xml:id="echoid-s8640" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus anguli D N Q, ad ſinum totum, ita ſinus <lb/>complementi anguli D Q N, ad ſinum complementi arcus D N, altitudinis poli; </s>
  <s xml:id="echoid-s8641" xml:space="preserve">erit conuerten-<lb/>do, vt ſinus totus ad ſinum anguli D N Q, ita ſinus complementi arcus D N, altitudinis poli <lb/>ad ſinum complementi anguli D Q N: </s>
  <s xml:id="echoid-s8642" xml:space="preserve">atque adeo angulus ipſe D Q N, cognitus erit. </s>
  <s xml:id="echoid-s8643" xml:space="preserve">Rurſus <lb/>quia in eodem triangulo ſphęrico D N Q, eſt per propoſ. </s>
  <s xml:id="echoid-s8644" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8645" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8646" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8647" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8648" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8649" xml:space="preserve">de triangulis, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s8650" xml:space="preserve">13. </s>
  <s xml:id="echoid-s8651" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8652" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8653" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8654" xml:space="preserve">41. </s>
  <s xml:id="echoid-s8655" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus an-<lb/>guli D Q N, noti iam facti ad ſinum arcus D N, altitudinis poli, ita ſinus totus anguli recti D, ad <lb/>
<anchor type="note" xlink:label="note-0155-07a" xlink:href="note-0155-07"/>
ſinum arcus N Q; </s>
  <s xml:id="echoid-s8656" xml:space="preserve">cognitus erit ſinus arcus N Q, ex quo perueſtig@bimus arcũ ipſum N Q, hac <lb/>ratione. </s>
  <s xml:id="echoid-s8657" xml:space="preserve">Quando in ſignis borealibus diſtantia Solis à meridie maior fuerit, quàm hor. </s>
  <s xml:id="echoid-s8658" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8659" xml:space="preserve">vt in <lb/>tertia figura accidit, dabit arcus ex tabula ſinum erutus arcum N Q; </s>
  <s xml:id="echoid-s8660" xml:space="preserve">quia arcus N Q, minor <lb/>quadrante tunc eſt, propterea quòd arcus ex polo N, per Q, vſque ad Aequatorem productus qua-<lb/>drans eſt. </s>
  <s xml:id="echoid-s8661" xml:space="preserve">Quando vero diſtantia Solis à meridie minor fuerit, quàm hor. </s>
  <s xml:id="echoid-s8662" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8663" xml:space="preserve">vt in figura prima, ſe-<lb/>cunda, &amp; </s>
  <s xml:id="echoid-s8664" xml:space="preserve">quarta apparet, in quocunque parallelo ſiue boreali, ſiue auſtrali Sol commoretur, erit <lb/>arcus N Q, quadrante maior: </s>
  <s xml:id="echoid-s8665" xml:space="preserve">quoniam vero, vt in tractatu ſinuum oſtendimus, idem ſinus eſt ar-<lb/>cus N Q, &amp; </s>
  <s xml:id="echoid-s8666" xml:space="preserve">reliqui ex ſemicirculo, auferemus arcum ſinus inuenti ex ſemicirculo, vt habeamus <lb/>arcum N Q. </s>
  <s xml:id="echoid-s8667" xml:space="preserve">Quando denique diſtantia Solis à meridie comprehendit hor. </s>
  <s xml:id="echoid-s8668" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8669" xml:space="preserve">nihil hic pręcipi-<lb/>mus, quia tunc, vt in fra docebimus, multo facilius altitudo Solis inquiritur: </s>
  <s xml:id="echoid-s8670" xml:space="preserve">Eſſet tamen tuncarcus <lb/>
<anchor type="note" xlink:label="note-0155-08a" xlink:href="note-0155-08"/>
NQ, quadrans, quia punctũ Q, caderet in punctũ A Inuento autem hac ratione arcu N Q, repe <lb/>riendus eſt ex eo arcus L Q, hoc modo. </s>
  <s xml:id="echoid-s8671" xml:space="preserve">In parallelis borealibus ex arcu inuento N Q, detrahatur <lb/>arcus N L, cõplementi declinationis; </s>
  <s xml:id="echoid-s8672" xml:space="preserve">In auſtralibus autem parallelis ex eodem arcu inuento N Q, <lb/>auferatur arcus N L, compoſitus ex quadrante N M, &amp; </s>
  <s xml:id="echoid-s8673" xml:space="preserve">arcu declinationis M L, vt in quarta figura <lb/>apparet. </s>
  <s xml:id="echoid-s8674" xml:space="preserve">Semper enim reliquus erit arcus L Q. </s>
  <s xml:id="echoid-s8675" xml:space="preserve">Iam vero quoniam in triangulo ſphærico L O Q, <lb/>angulus O, rectus eſt, &amp; </s>
  <s xml:id="echoid-s8676" xml:space="preserve">L Q O, notus paulo ante factus, vna cum arcu L Q; </s>
  <s xml:id="echoid-s8677" xml:space="preserve">eſtq́; </s>
  <s xml:id="echoid-s8678" xml:space="preserve">per propoſ. <lb/></s>
  <s xml:id="echoid-s8679" xml:space="preserve">16. </s>
  <s xml:id="echoid-s8680" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8681" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8682" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8683" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8684" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8685" xml:space="preserve">13. </s>
  <s xml:id="echoid-s8686" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8687" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8688" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8689" xml:space="preserve">41. </s>
  <s xml:id="echoid-s8690" xml:space="preserve">noſtrorũ <lb/>triangulorum ſphæricorum, vt ſinus totus anguli recti O, ad ſinum arcus L Q, noti, ita ſinus an-<lb/>guli L Q O. </s>
  <s xml:id="echoid-s8691" xml:space="preserve">noti ad ſinum arcus L O, altitudinis Solis; </s>
  <s xml:id="echoid-s8692" xml:space="preserve">cognita fiet Solis altitudo. </s>
  <s xml:id="echoid-s8693" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0155-09a" xlink:href="note-0155-09"/>
</s>
</p>
<div xml:id="echoid-div476" type="float" level="2" n="51">
<note position="right" xlink:label="note-0155-05" xlink:href="note-0155-05a" xml:space="preserve">Altitudo Solis <lb/>quomodo aliter <lb/>per ſphærica <lb/>triangula ex da-<lb/>ta hora inueſti-<lb/>ganda.</note>
<note position="left" xlink:label="note-0155-06" xlink:href="note-0155-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0155-07" xlink:href="note-0155-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0155-08" xlink:href="note-0155-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0155-09" xlink:href="note-0155-09a" xml:space="preserve">Inuentum pri-<lb/>mum.</note>
</div>
<p>
  <s xml:id="echoid-s8694" xml:space="preserve">ITAQVE ſi fiat, vt ſinus totus ad ſinum anguli D N Q, qui relinquitur, ablato angulo di-<lb/>ſtantiæ Solis à meridie ex duobus rectis, ita ſinus complementi altitudinis poli ad aliud, inuenie-
<pb o="136" file="0156" n="156" rhead="GNOMONICES"/>
tur ſinus arcus cuiuſdam, qui ex quadrante ſublatus dabit arcum, quem vocabimus Inuen-<lb/>tum primum.</s>
  <s xml:id="echoid-s8695" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8696" xml:space="preserve">DEINDE ſi fiat, vt ſinus illius arcus, quem Inuentum primum diximus, ad ſinum altitudinis <lb/>poli, ita ſinus totus ad aliud, reperietur ſinus arcus alterius, ex quo, ſi Sol fuerit borealis, habueritq́ <lb/>diſtantiam à meridie maiorem, quàm hor. </s>
  <s xml:id="echoid-s8697" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8698" xml:space="preserve">ſubtractus arcus complementi declinationis dabit <lb/>
<anchor type="note" xlink:label="note-0156-01a" xlink:href="note-0156-01"/>
arcum quendam, quem Inuentum ſecundum appellabimus. </s>
  <s xml:id="echoid-s8699" xml:space="preserve">Quòd ſi diſtantia Solis à meridie <lb/>minor fuerit quàm hor. </s>
  <s xml:id="echoid-s8700" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8701" xml:space="preserve">in quocunque parallelo extiterit Sol, detrahendus erit arcus per Inuen-<lb/>tum primum compertus ex ſemicirculo, &amp; </s>
  <s xml:id="echoid-s8702" xml:space="preserve">ex reliquo arcu, ſi Sol eſt borealis, ſubtrahendus rur-<lb/>ſus arcus complementi declinationis, vel ſi auſtralis Sol eſt, auferendus arcus compoſitus ex qua-<lb/>drante, &amp; </s>
  <s xml:id="echoid-s8703" xml:space="preserve">arcu declinationis, vt arcus inueniatur, quem Inuentum ſecundum vocemus.</s>
  <s xml:id="echoid-s8704" xml:space="preserve"/>
</p>
<div xml:id="echoid-div477" type="float" level="2" n="52">
<note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">Inuen@@ ſe-<lb/>cundum.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s8705" xml:space="preserve">POSTREMO ſi fiat, vt ſinus totus ad ſinumarcus, quem ſecundum Inuentum nominaui-<lb/>mus, ita ſinus arcus, quem diximus Inuentum primum, ad aliud, inuentus erit ſinus altitudinis <lb/>Solis quæſitæ. </s>
  <s xml:id="echoid-s8706" xml:space="preserve">Quod vt planius fiat, duobus exemplis rem totam explicabimus.</s>
  <s xml:id="echoid-s8707" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8708" xml:space="preserve">PONATVR Sol in principio ♋, habere diſtantiam à meridie hor. </s>
  <s xml:id="echoid-s8709" xml:space="preserve">7. </s>
  <s xml:id="echoid-s8710" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s8711" xml:space="preserve">105. </s>
  <s xml:id="echoid-s8712" xml:space="preserve">ita <lb/>
<anchor type="note" xlink:label="note-0156-03a" xlink:href="note-0156-03"/>
vt angulus BNQ, totidem gradus complectatur, atque adeo reliquus ex duobus rectis DNQ, <lb/>grad. </s>
  <s xml:id="echoid-s8713" xml:space="preserve">75. </s>
  <s xml:id="echoid-s8714" xml:space="preserve">Fiat ergo, vt 100000. </s>
  <s xml:id="echoid-s8715" xml:space="preserve">ſinus totus ad 96592. </s>
  <s xml:id="echoid-s8716" xml:space="preserve">ſinum anguli DNQ, ita 74314. </s>
  <s xml:id="echoid-s8717" xml:space="preserve">ſinus cõ-<lb/>plementi altitudinis poli ad aliud, inueniemusq́; </s>
  <s xml:id="echoid-s8718" xml:space="preserve">hunc propemodum ſinum 71781. </s>
  <s xml:id="echoid-s8719" xml:space="preserve">cuius arcus <lb/>grad. </s>
  <s xml:id="echoid-s8720" xml:space="preserve">45. </s>
  <s xml:id="echoid-s8721" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8722" xml:space="preserve">52. </s>
  <s xml:id="echoid-s8723" xml:space="preserve">ex quadrante detractus relinquet arcum grad. </s>
  <s xml:id="echoid-s8724" xml:space="preserve">44. </s>
  <s xml:id="echoid-s8725" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8726" xml:space="preserve">8. </s>
  <s xml:id="echoid-s8727" xml:space="preserve">pro Inuento primo.</s>
  <s xml:id="echoid-s8728" xml:space="preserve"/>
</p>
<div xml:id="echoid-div478" type="float" level="2" n="53">
<note position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">Exemplum pri-<lb/>num.</note>
</div>
<p>
  <s xml:id="echoid-s8729" xml:space="preserve">RVRSVS fiat, vt 69633. </s>
  <s xml:id="echoid-s8730" xml:space="preserve">ſinus arcus Primi Inuenti ad 66913. </s>
  <s xml:id="echoid-s8731" xml:space="preserve">ſinum altitudinis poli, ita <lb/>100000. </s>
  <s xml:id="echoid-s8732" xml:space="preserve">ſinus totus ad aliud, reperiemus q́; </s>
  <s xml:id="echoid-s8733" xml:space="preserve">fere hunc ſinum 96093. </s>
  <s xml:id="echoid-s8734" xml:space="preserve">ex cuius arcu grad. </s>
  <s xml:id="echoid-s8735" xml:space="preserve">73. </s>
  <s xml:id="echoid-s8736" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s8737" xml:space="preserve">
<anchor type="note" xlink:label="note-0156-04a" xlink:href="note-0156-04"/>
56. </s>
  <s xml:id="echoid-s8738" xml:space="preserve">(quoniam Sol borealis ponitur, eiuſq́; </s>
  <s xml:id="echoid-s8739" xml:space="preserve">diſtantia à meridie maior, quàm hor. </s>
  <s xml:id="echoid-s8740" xml:space="preserve">6.) </s>
  <s xml:id="echoid-s8741" xml:space="preserve">ſi detrahatur <lb/>complementum declinationis paralleli ♋, nempe grad. </s>
  <s xml:id="echoid-s8742" xml:space="preserve">66. </s>
  <s xml:id="echoid-s8743" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8744" xml:space="preserve">30. </s>
  <s xml:id="echoid-s8745" xml:space="preserve">relinquetur arcus grad. </s>
  <s xml:id="echoid-s8746" xml:space="preserve">7. <lb/></s>
  <s xml:id="echoid-s8747" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8748" xml:space="preserve">26. </s>
  <s xml:id="echoid-s8749" xml:space="preserve">pro Inuento ſecundo.</s>
  <s xml:id="echoid-s8750" xml:space="preserve"/>
</p>
<div xml:id="echoid-div479" type="float" level="2" n="54">
<note position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s8751" xml:space="preserve">TANDEM fiat, vt 100000. </s>
  <s xml:id="echoid-s8752" xml:space="preserve">ſinus totus ad 12937. </s>
  <s xml:id="echoid-s8753" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita 69633. <lb/></s>
  <s xml:id="echoid-s8754" xml:space="preserve">ſinus arcus Inuenti primi ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8755" xml:space="preserve">hic ferme ſinus 9008. </s>
  <s xml:id="echoid-s8756" xml:space="preserve">altitudinis Solis. </s>
  <s xml:id="echoid-s8757" xml:space="preserve">Quare <lb/>altitudo Solis comprehendet grad. </s>
  <s xml:id="echoid-s8758" xml:space="preserve">5. </s>
  <s xml:id="echoid-s8759" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8760" xml:space="preserve">10.</s>
  <s xml:id="echoid-s8761" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8762" xml:space="preserve">STATVATVR rurſus Sol in principio ♑, &amp; </s>
  <s xml:id="echoid-s8763" xml:space="preserve">diſtantia eius à meridie hor. </s>
  <s xml:id="echoid-s8764" xml:space="preserve">2. </s>
  <s xml:id="echoid-s8765" xml:space="preserve">hoc eſt, grad. <lb/></s>
  <s xml:id="echoid-s8766" xml:space="preserve">
<anchor type="note" xlink:label="note-0156-05a" xlink:href="note-0156-05"/>
30. </s>
  <s xml:id="echoid-s8767" xml:space="preserve">ita vt angulus BNQ, totidem gradus cõtineat, ac proinde reliquus ex duobus rectis DNQ, <lb/>grad. </s>
  <s xml:id="echoid-s8768" xml:space="preserve">150. </s>
  <s xml:id="echoid-s8769" xml:space="preserve">Fiat igitur, vt 100000. </s>
  <s xml:id="echoid-s8770" xml:space="preserve">ſinus totus ad 50000. </s>
  <s xml:id="echoid-s8771" xml:space="preserve">ſinum anguli DNQ, (eſt enim idem ſi-<lb/>nus arcus grad. </s>
  <s xml:id="echoid-s8772" xml:space="preserve">150. </s>
  <s xml:id="echoid-s8773" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s8774" xml:space="preserve">arcus grad. </s>
  <s xml:id="echoid-s8775" xml:space="preserve">30. </s>
  <s xml:id="echoid-s8776" xml:space="preserve">qui cum illo ſemicirculum conficit, vt in tractatu ſinuum <lb/>
<anchor type="note" xlink:label="note-0156-06a" xlink:href="note-0156-06"/>
docuimus) ita 74314. </s>
  <s xml:id="echoid-s8777" xml:space="preserve">ſinus complementi altitudinis poliad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8778" xml:space="preserve">ferme ſinus hic, <lb/>37157. </s>
  <s xml:id="echoid-s8779" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8780" xml:space="preserve">21. </s>
  <s xml:id="echoid-s8781" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8782" xml:space="preserve">49. </s>
  <s xml:id="echoid-s8783" xml:space="preserve">ex quadrante detractus relinquet pro Inuento primo arcum <lb/>grad. </s>
  <s xml:id="echoid-s8784" xml:space="preserve">68. </s>
  <s xml:id="echoid-s8785" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8786" xml:space="preserve">11.</s>
  <s xml:id="echoid-s8787" xml:space="preserve"/>
</p>
<div xml:id="echoid-div480" type="float" level="2" n="55">
<note position="left" xlink:label="note-0156-05" xlink:href="note-0156-05a" xml:space="preserve">Exemplum ſe-<lb/>cundum.</note>
<note position="left" xlink:label="note-0156-06" xlink:href="note-0156-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s8788" xml:space="preserve">DEINDE fiat, vt 92837. </s>
  <s xml:id="echoid-s8789" xml:space="preserve">ſinus arcus Primi Inuenti, ad 66913. </s>
  <s xml:id="echoid-s8790" xml:space="preserve">ſinum altitudinis poli, ita <lb/>100000. </s>
  <s xml:id="echoid-s8791" xml:space="preserve">ad aliud, inuenieturq́; </s>
  <s xml:id="echoid-s8792" xml:space="preserve">hic quaſi ſinus 72075. </s>
  <s xml:id="echoid-s8793" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s8794" xml:space="preserve">46. </s>
  <s xml:id="echoid-s8795" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8796" xml:space="preserve">7. </s>
  <s xml:id="echoid-s8797" xml:space="preserve">ex ſemicirculo <lb/>grad. </s>
  <s xml:id="echoid-s8798" xml:space="preserve">180. </s>
  <s xml:id="echoid-s8799" xml:space="preserve">deductus (quoniam diſtantia Solis à meridie ad hor. </s>
  <s xml:id="echoid-s8800" xml:space="preserve">6. </s>
  <s xml:id="echoid-s8801" xml:space="preserve">non peruenit) dabit arcum NQ, <lb/>grad. </s>
  <s xml:id="echoid-s8802" xml:space="preserve">133. </s>
  <s xml:id="echoid-s8803" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8804" xml:space="preserve">53. </s>
  <s xml:id="echoid-s8805" xml:space="preserve">ex quo, quia Sol auſtralis ponitur, ſi detrahatur arcus NL, compoſitus ex ſinu <lb/>toto, &amp; </s>
  <s xml:id="echoid-s8806" xml:space="preserve">ſinu declinationis, nempe grad. </s>
  <s xml:id="echoid-s8807" xml:space="preserve">113. </s>
  <s xml:id="echoid-s8808" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8809" xml:space="preserve">30. </s>
  <s xml:id="echoid-s8810" xml:space="preserve">relinquetur pro Inuento ſecundo arcus grad. <lb/></s>
  <s xml:id="echoid-s8811" xml:space="preserve">20. </s>
  <s xml:id="echoid-s8812" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8813" xml:space="preserve">23.</s>
  <s xml:id="echoid-s8814" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8815" xml:space="preserve">POSTREMO fiat, vt 100000. </s>
  <s xml:id="echoid-s8816" xml:space="preserve">ſinus totus ad 34829. </s>
  <s xml:id="echoid-s8817" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita <lb/>
<anchor type="note" xlink:label="note-0156-07a" xlink:href="note-0156-07"/>
92837. </s>
  <s xml:id="echoid-s8818" xml:space="preserve">ſinus Inuenti primi ad aliud, reperieturq́; </s>
  <s xml:id="echoid-s8819" xml:space="preserve">hic fere ſinus 32334. </s>
  <s xml:id="echoid-s8820" xml:space="preserve">altitudinis Solis, atq; </s>
  <s xml:id="echoid-s8821" xml:space="preserve">adeo <lb/>altitudo ipſa Solis complectetur grad. </s>
  <s xml:id="echoid-s8822" xml:space="preserve">18. </s>
  <s xml:id="echoid-s8823" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s8824" xml:space="preserve">52.</s>
  <s xml:id="echoid-s8825" xml:space="preserve"/>
</p>
<div xml:id="echoid-div481" type="float" level="2" n="56">
<note position="left" xlink:label="note-0156-07" xlink:href="note-0156-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s8826" xml:space="preserve">PORRO quando Sol exiſtit in Verticali circulo, vel abeſt à meridie horis ſex, aut denique in <lb/>Aequatore conſtitutus eſt, expediemus rem, vt paulo ante tradidimus.</s>
  <s xml:id="echoid-s8827" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8828" xml:space="preserve">AD extremum abſoluemus idem hoc proble-<lb/>
<anchor type="note" xlink:label="note-0156-08a" xlink:href="note-0156-08"/>
<anchor type="figure" xlink:label="fig-0156-01a" xlink:href="fig-0156-01"/>
ma per triangula ſphærica in ſphæra recta, hac ra-<lb/>tione. </s>
  <s xml:id="echoid-s8829" xml:space="preserve">Sole Aequatorem percurrente, erit comple <lb/>mentum diſtantiæ ipſius à meridie, altitudo Solis <lb/>ſupra Horizontem: </s>
  <s xml:id="echoid-s8830" xml:space="preserve">quia in ſphæra recta Aequator <lb/>idem eſt, quod Verticalis circulus per centrum Solis <lb/>
<anchor type="note" xlink:label="note-0156-09a" xlink:href="note-0156-09"/>
tranſiens. </s>
  <s xml:id="echoid-s8831" xml:space="preserve">Vt in ſubiecta figura, ſi poli mundi intelli <lb/>gantur B, D, erit Verticalis AEC, &amp; </s>
  <s xml:id="echoid-s8832" xml:space="preserve">idẽ ipſe Aequa <lb/>tor. </s>
  <s xml:id="echoid-s8833" xml:space="preserve">Poſito ergo Sole in I, erit arcus AI, complemen <lb/>ti diſtantiæ Solis à meridie, arcus etiam altitudinis <lb/>Solis, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s8834" xml:space="preserve"/>
</p>
<div xml:id="echoid-div482" type="float" level="2" n="57">
<note position="left" xlink:label="note-0156-08" xlink:href="note-0156-08a" xml:space="preserve">Altitudo Solis <lb/>in ęquinoctiis, <lb/>quomodo in <lb/>ſphęra recta ex <lb/>data hora depre <lb/>hendatur.</note>
  <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a">
    <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-01"/>
  </figure>
<note position="left" xlink:label="note-0156-09" xlink:href="note-0156-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s8835" xml:space="preserve">SOLE autem occupante quemcunque paral-<lb/>
<anchor type="note" xlink:label="note-0156-10a" xlink:href="note-0156-10"/>
lelum FG, ſiue borealem, ſiue auſtralem, ita rem <lb/>exequemur. </s>
  <s xml:id="echoid-s8836" xml:space="preserve">Ponatur Sol in k, ducaturq́ Vertica-<lb/>lis EL, ex E, vertice per centrum Solis k: </s>
  <s xml:id="echoid-s8837" xml:space="preserve">Item <lb/>circulus declinationis D <emph style="sc">K</emph> B, per polos mundi, &amp; </s>
  <s xml:id="echoid-s8838" xml:space="preserve"><lb/>per centrum Solis ductus ſit, ſecans Aequatorem
<pb o="137" file="0157" n="157" rhead="LIBER PRIMVS."/>
in I; </s>
  <s xml:id="echoid-s8839" xml:space="preserve">eritq́ arcus EI, ſimilis arcui HK, diſtantię Solis à meridie, per propoſ. </s>
  <s xml:id="echoid-s8840" xml:space="preserve">10. </s>
  <s xml:id="echoid-s8841" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8842" xml:space="preserve">2. </s>
  <s xml:id="echoid-s8843" xml:space="preserve">Theo-<lb/>doſii. </s>
  <s xml:id="echoid-s8844" xml:space="preserve">Quoniam igitur in triangulo ſphęrico EIK, angulus I, rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s8845" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8846" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8847" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s8848" xml:space="preserve">Theodoſii, erit per propoſ. </s>
  <s xml:id="echoid-s8849" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8850" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8851" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8852" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8853" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8854" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8855" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8856" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8857" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8858" xml:space="preserve">Gebri, <lb/>vel per propoſ. </s>
  <s xml:id="echoid-s8859" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8860" xml:space="preserve">noſtrorum triangulorum ſphęricorum, vt ſinus complementi arcus IK, decli-<lb/>nationis paralleli ad ſinum totum, ita ſinus complemen ti arcus Ek, hoc eſt, ita ſinus arcus KL, <lb/>altitudinis Solis, ad ſinum complementi arcus EI, diſtantię Solis à meridie. </s>
  <s xml:id="echoid-s8861" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s8862" xml:space="preserve">conuer-<lb/>tendo erit, vt ſinus totus ad ſinum complementi declinationis propoſiti paralleli, ita ſinus com-<lb/>plementi diſtantię Solis à meridie ad ſinum altitudinis Solis. </s>
  <s xml:id="echoid-s8863" xml:space="preserve">Quamobrem ſi fiat, vt ſinus totus <lb/>ad ſinum complementi declinationis, ita ſinus complementi diſtantię Solis à meridie ad aliud, <lb/>notus euadet ſinus altitudinis Solis. </s>
  <s xml:id="echoid-s8864" xml:space="preserve">Id quod etiam ſupra oſtendimus ſine triangulis ſphæricis. </s>
  <s xml:id="echoid-s8865" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0157-01a" xlink:href="note-0157-01"/>
Atque hac ratione perſ picuum eſt, vt ex hora cognita per triangula ſphæri ca altitudo Solis erua-<lb/>tur, quod prior problematis pars præcipit.</s>
  <s xml:id="echoid-s8866" xml:space="preserve"/>
</p>
<div xml:id="echoid-div483" type="float" level="2" n="58">
<note position="left" xlink:label="note-0156-10" xlink:href="note-0156-10a" xml:space="preserve">Altitudo Solis <lb/>in quocunque <lb/>parallelo exiſtẽ-<lb/>tis, quo pacto <lb/>per triangula <lb/>ſphęrica in ſphę <lb/>ra recta ex data <lb/>hora colligatur.</note>
<note position="left" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8867" xml:space="preserve">VT autem vice verſa ex cogmita Solis altitudine ſupra Horizontem per triangula ſphærica ho <lb/>
<anchor type="note" xlink:label="note-0157-02a" xlink:href="note-0157-02"/>
ram, ſiue diſtantiam Solis à meridie perdiſcamus, hanc viam ſequemur. </s>
  <s xml:id="echoid-s8868" xml:space="preserve">Repetitis ſuperioribus <lb/>
<anchor type="figure" xlink:label="fig-0157-01a" xlink:href="fig-0157-01"/>
<anchor type="note" xlink:label="note-0157-03a" xlink:href="note-0157-03"/>
<anchor type="note" xlink:label="note-0157-04a" xlink:href="note-0157-04"/>
<anchor type="note" xlink:label="note-0157-05a" xlink:href="note-0157-05"/>
figuris, quoniam in prima, ſecunda, tertia &amp; </s>
  <s xml:id="echoid-s8869" xml:space="preserve">quarta triangulum ELN, tria latera habet nota, (Nam <lb/>EL, eſt complementum altitudinis Solis, quæ nota ponitur; </s>
  <s xml:id="echoid-s8870" xml:space="preserve">EN, verò eſt complementum altitu-<lb/>dinis poli, &amp; </s>
  <s xml:id="echoid-s8871" xml:space="preserve">LN, in parallelis borealibus eſt complementum declinationis paralleli propoſiti, in <lb/>auſtralibus verò parallelis arcus LN, compoſitus eſt ex declinationis arcu LM, &amp; </s>
  <s xml:id="echoid-s8872" xml:space="preserve">quadrãte MN,) <lb/>cognoſcetur quoque angulus ENL, per propoſ. </s>
  <s xml:id="echoid-s8873" xml:space="preserve">34. </s>
  <s xml:id="echoid-s8874" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8875" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8876" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8877" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8878" xml:space="preserve">de triangulis, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s8879" xml:space="preserve">45. </s>
  <s xml:id="echoid-s8880" xml:space="preserve">noſtrorum triangulorum ſphæricorum, atque adeo &amp; </s>
  <s xml:id="echoid-s8881" xml:space="preserve">eius arcus FM, diſtantiam Solis à <lb/>meridie metiens notus er it. </s>
  <s xml:id="echoid-s8882" xml:space="preserve">Sed quoniam in parallelis borealibus angulus ENL, poteſt eſſe re-<lb/>ctus, vel minor, vel maior recto; </s>
  <s xml:id="echoid-s8883" xml:space="preserve">Quandocunque deprehenſus fuerit rectus, diſtantia Solis à meri-<lb/>die 6. </s>
  <s xml:id="echoid-s8884" xml:space="preserve">horas comprehendet; </s>
  <s xml:id="echoid-s8885" xml:space="preserve">ſi minor, pauciores horas quàm 6. </s>
  <s xml:id="echoid-s8886" xml:space="preserve">ſi denique maior, plures quàm ſex <lb/>continebit. </s>
  <s xml:id="echoid-s8887" xml:space="preserve">Vt autem ſciamus, quando dictus angulus rectus ſit, &amp; </s>
  <s xml:id="echoid-s8888" xml:space="preserve">quando minor, vel maior, in-<lb/>
<anchor type="note" xlink:label="note-0157-06a" xlink:href="note-0157-06"/>
quirenda eſt altitudo Solis, quam habet, cum ſex horis à meridie abeſt. </s>
  <s xml:id="echoid-s8889" xml:space="preserve">Nam quando altitudo So-<lb/>lis tempore obſeruationis, quæ nota ponitur, fuerit æqualis altitudini, quam habet, cum ſex horis <lb/>abeſt à meridie, angulus dictus rectus erit; </s>
  <s xml:id="echoid-s8890" xml:space="preserve">exiſtet enim tunc Sol in circulo ſextæ horæ, qui cum <lb/>Meridiano angulum rectum conſtituit: </s>
  <s xml:id="echoid-s8891" xml:space="preserve">Si verò reperta fuerit altitudo Solis maior, quàm ea, quam <lb/>habet, cum ſex horis diſtat à meridie, erit idem angulus recto minor; </s>
  <s xml:id="echoid-s8892" xml:space="preserve">quia Solis diſtantia à meri-<lb/>die minor tunc eſt quadrante: </s>
  <s xml:id="echoid-s8893" xml:space="preserve">Si denique altitudo Solis minor extiterit, quàm ca, quam habet, <lb/>cum abeſt à meridie ſex horis, idem angulus maior erit recto; </s>
  <s xml:id="echoid-s8894" xml:space="preserve">proprerea quòd Solis diſtantia à <lb/>meridie tunc temporis maior eſt quadrante. <lb/></s>
  <s xml:id="echoid-s8895" xml:space="preserve">
<anchor type="note" xlink:label="note-0157-07a" xlink:href="note-0157-07"/>
</s>
</p>
<div xml:id="echoid-div484" type="float" level="2" n="59">
<note position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">Hora qua ratio <lb/>ne ex altitudine <lb/>Solis cognita ꝑ <lb/>triangula ſphæ-<lb/>rica colliga@r.</note>
  <figure xlink:label="fig-0157-01" xlink:href="fig-0157-01a">
    <image file="0157-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0157-01"/>
  </figure>
<note position="left" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0157-04" xlink:href="note-0157-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0157-05" xlink:href="note-0157-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0157-06" xlink:href="note-0157-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0157-07" xlink:href="note-0157-07a" xml:space="preserve">Hora quo pacto <lb/>inueniatur, So-<lb/>le conſtituto in <lb/>Verticali circu-<lb/>lo.</note>
</div>
<p>
  <s xml:id="echoid-s8896" xml:space="preserve">QVANDO autem Solis altitudo inuenta fuerit æqualis ei, quam habet in Verticali cir-<lb/>culo, quam ſupra, etiam diſtantia Solis à meridie ignorata, inuenimus, exiſter Sol in Verticali <lb/>circulo. </s>
  <s xml:id="echoid-s8897" xml:space="preserve">Vnde facilis admodum erit inuentio diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8898" xml:space="preserve">Quoniam enim in trian-
<pb o="138" file="0158" n="158" rhead="GNOMONICES"/>
gulo E k N, figuræ quintæ angulus E, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s8899" xml:space="preserve">16. </s>
  <s xml:id="echoid-s8900" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8901" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8902" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8903" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8904" xml:space="preserve">de triangu <lb/>lis, vel per Propoſ. </s>
  <s xml:id="echoid-s8905" xml:space="preserve">13. </s>
  <s xml:id="echoid-s8906" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8907" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8908" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8909" xml:space="preserve">41. </s>
  <s xml:id="echoid-s8910" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt <lb/>ſinusarcus N k, complementi declinationis ad ſinum anguli recti E, id eſt, ad ſinum totum, ita ſi-<lb/>nus arcus E K, complementi altitudinis Solis ad ſinum anguli N, diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8911" xml:space="preserve">Itaque <lb/>ſi fiat, vt ſinus complementi declinationis ad ſinum to@um, ita ſinus complementi altitudinis So-<lb/>lis in Verticali circulo ad aliud, inueniet ur ſinus diſtantiæ Solis à meridie.</s>
  <s xml:id="echoid-s8912" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s8913" xml:space="preserve">VNDE ſi quæratur, qua hora Sol in Verticali circulo reperiatur, inuenienda primum erit al-<lb/>
<anchor type="note" xlink:label="note-0158-01a" xlink:href="note-0158-01"/>
titudo Solis in Verticali circulo, vt ſupra docuimus, etiamſi ignota ſit diſtantia Solis à meridie: <lb/></s>
  <s xml:id="echoid-s8914" xml:space="preserve">Deinde ex hac altitudine exploranda diſtantia Solis à meridie, vt proxime oſtendimus.</s>
  <s xml:id="echoid-s8915" xml:space="preserve"/>
</p>
<div xml:id="echoid-div485" type="float" level="2" n="60">
<note position="left" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">Qua hora Sol <lb/>in Verticali cir <lb/>culo exiſtat.</note>
</div>
<p>
  <s xml:id="echoid-s8916" xml:space="preserve">SOLE in Aequatore exiſtente, facili etiam negotio ex altitudine Solis horam inquiremus. <lb/></s>
  <s xml:id="echoid-s8917" xml:space="preserve">
<anchor type="note" xlink:label="note-0158-02a" xlink:href="note-0158-02"/>
<anchor type="note" xlink:label="note-0158-03a" xlink:href="note-0158-03"/>
Quoniam enim in ſphærico triangulo E H K, quintæ figurę, ſi intelligatur Aequator eſſe G H I, &amp; </s>
  <s xml:id="echoid-s8918" xml:space="preserve"><lb/>Sol in K, vt ſupra diximus, angulus H, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s8919" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8920" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8921" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8922" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8923" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8924" xml:space="preserve">de trian-<lb/>gulis, vel per propoſ. </s>
  <s xml:id="echoid-s8925" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8926" xml:space="preserve">hb. </s>
  <s xml:id="echoid-s8927" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8928" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s8929" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8930" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt <lb/>ſmus complementi arcus EH, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K, <lb/>hoc eſt, ita ſinus arcus A K, altitudinis Solis, ad ſinum complementi arcus H K, diſtantię Solis à <lb/>meridie. </s>
  <s xml:id="echoid-s8931" xml:space="preserve">Quare ſi hat, vt ſinus complementi altitudinis poli ad ſinum totum, ita ſinus altitudinis <lb/>Solis ad aliud, inuenietur ſinus complementi diſtantię Solis à meridie.</s>
  <s xml:id="echoid-s8932" xml:space="preserve"/>
</p>
<div xml:id="echoid-div486" type="float" level="2" n="61">
<note position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">Hora qua via <lb/>in æquinoctijs <lb/>ex altiuidine <lb/>Solis nota explo <lb/>ianda.</note>
<note position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s8933" xml:space="preserve">IDEM quoque aliter demonſtrabimus. </s>
  <s xml:id="echoid-s8934" xml:space="preserve">Quia enim in triangulo ſphærico A G K, angulus A, <lb/>rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s8935" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8936" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8937" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8938" xml:space="preserve">Theodoſii, quòd circulus maximus E A, per polum Horizontis E, <lb/>ductus ſit, erit per propoſ. </s>
  <s xml:id="echoid-s8939" xml:space="preserve">16. </s>
  <s xml:id="echoid-s8940" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8941" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8942" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s8943" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8944" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8945" xml:space="preserve">13. </s>
  <s xml:id="echoid-s8946" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8947" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8948" xml:space="preserve">Gebri, <lb/>
<anchor type="note" xlink:label="note-0158-04a" xlink:href="note-0158-04"/>
vel per propoſ. </s>
  <s xml:id="echoid-s8949" xml:space="preserve">41. </s>
  <s xml:id="echoid-s8950" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus anguli G, complementi altitu-<lb/>dinis poli, (Si enim Aequator ponatur G H I, erit angulus G, reſpondens arcui H B, altitudinis <lb/>Aequatoris, ſeu complementi altitudinis poli) ad ſinum arcus A k, altitudinis Solis, ita ſinus an-<lb/>guli A, recti, id eſt, ita ſinus totus, ad ſinum arcus Gk, altitudinis Solis, ita ſinus an-<lb/>Si igitur fiat, vt ſinus complementi altitudinis poli, ad ſinum altitudinis Solis, ita ſinus totusad <lb/>aliud, notus fiet ſinus complementi diſtantiæ Solis à meridie.</s>
  <s xml:id="echoid-s8951" xml:space="preserve"/>
</p>
<div xml:id="echoid-div487" type="float" level="2" n="62">
<note position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s8952" xml:space="preserve">POSTREMO in ſphæra recta ita procedemus. </s>
  <s xml:id="echoid-s8953" xml:space="preserve">Sole exiſtente in æquinoctiis, accipiemus <lb/>
<anchor type="note" xlink:label="note-0158-05a" xlink:href="note-0158-05"/>
<anchor type="figure" xlink:label="fig-0158-01a" xlink:href="fig-0158-01"/>
cõplementum altitudinis Solis pro diſtantia eiuſdẽ <lb/>à meridie. </s>
  <s xml:id="echoid-s8954" xml:space="preserve">Nã in appoſita figura, quam pro ſphæra <lb/>recta conſtruximus, arcus EI, diſtantiæ Solis à meri <lb/>
<anchor type="note" xlink:label="note-0158-06a" xlink:href="note-0158-06"/>
die, complementũ eſt arcus A I, altitudinis Solis.</s>
  <s xml:id="echoid-s8955" xml:space="preserve"/>
</p>
<div xml:id="echoid-div488" type="float" level="2" n="63">
<note position="left" xlink:label="note-0158-05" xlink:href="note-0158-05a" xml:space="preserve">Quo pacto in <lb/>ſphæra recta rẽ-<lb/>pore ęquinoctio <lb/>rum reperienda <lb/>ſit hora ex alti-<lb/>dine Solis.</note>
  <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a">
    <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0158-01"/>
  </figure>
<note position="left" xlink:label="note-0158-06" xlink:href="note-0158-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s8956" xml:space="preserve">QVANDO verò Sol in aliquo alio parallelo <lb/>
<anchor type="note" xlink:label="note-0158-07a" xlink:href="note-0158-07"/>
exiſtit, vt in K; </s>
  <s xml:id="echoid-s8957" xml:space="preserve">quoniã in triangulo ſphærico E I K, <lb/>angulus I, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s8958" xml:space="preserve">19. </s>
  <s xml:id="echoid-s8959" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8960" xml:space="preserve">4. </s>
  <s xml:id="echoid-s8961" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s8962" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s8963" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s8964" xml:space="preserve">15. </s>
  <s xml:id="echoid-s8965" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s8966" xml:space="preserve">1. </s>
  <s xml:id="echoid-s8967" xml:space="preserve">Ge-<lb/>bri, vel per propoſ. </s>
  <s xml:id="echoid-s8968" xml:space="preserve">43. </s>
  <s xml:id="echoid-s8969" xml:space="preserve">noſtrorum triangulorũ ſphæ <lb/>ricorum, vt ſinus complemẽti arcus Ik, declinatio-<lb/>nis paralleli propoſiti, ad ſinum totum, ita ſinus cõ-<lb/>plementi arcus E K, hoc eſt, ita ſinus arcus K L, alti <lb/>tudinis Solis, ad ſinum complementi arcus E I, di-<lb/>
<anchor type="note" xlink:label="note-0158-08a" xlink:href="note-0158-08"/>
ſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8970" xml:space="preserve">Quamobrem ſi fiat, vt ſinus <lb/>complementi declinationis Solis ad ſinum totum, <lb/>ita ſinus altitudinis Solis ad aliud, notus fiet ſinus <lb/>cõplementi diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s8971" xml:space="preserve">Igitur ex co-<lb/>gnita diei hora altitudinem Solis ſupra Horizontem: </s>
  <s xml:id="echoid-s8972" xml:space="preserve">Et contra ex altitudine Solis nota horam dioi <lb/>cognouimus. </s>
  <s xml:id="echoid-s8973" xml:space="preserve">Quod erar faciendum.</s>
  <s xml:id="echoid-s8974" xml:space="preserve"/>
</p>
<div xml:id="echoid-div489" type="float" level="2" n="64">
<note position="left" xlink:label="note-0158-07" xlink:href="note-0158-07a" xml:space="preserve">Qua ratione in <lb/>ſphæra recta ſit <lb/>indaganda ho-<lb/>ra ex al titudine <lb/>Solis in quocũ-<lb/>que parallelo <lb/>exiſtentis.</note>
<note position="left" xlink:label="note-0158-08" xlink:href="note-0158-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div491" type="section" level="1" n="139">
<head xml:id="echoid-head142" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s8975" xml:space="preserve">QVANDO inueniendæ ſunt altitudines Solis pro ſingulis horis duorum parallelorum oppoſito-<lb/>
<anchor type="note" xlink:label="note-0158-09a" xlink:href="note-0158-09"/>
rum, quales ſunt v. </s>
  <s xml:id="echoid-s8976" xml:space="preserve">g. </s>
  <s xml:id="echoid-s8977" xml:space="preserve">duo tropici à principĳs ♋, &amp; </s>
  <s xml:id="echoid-s8978" xml:space="preserve">♑, deſcripti, quod non rarò vſu venit in conſtruen-<lb/>dis inſtrumentis horarĳs, &amp; </s>
  <s xml:id="echoid-s8979" xml:space="preserve">in deſcriptionibus horologiorum, perfacile reddetur totum negotium, ſi ea, <lb/>quæ iamiam explicabimus, attentè conſiderentur.</s>
  <s xml:id="echoid-s8980" xml:space="preserve"/>
</p>
<div xml:id="echoid-div491" type="float" level="2" n="1">
<note position="left" xlink:label="note-0158-09" xlink:href="note-0158-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s8981" xml:space="preserve">NAM ſi primo velimus modo vti, permanebit pro ſingulis horis vtriuſque paralleli eadem medietas <lb/>
<anchor type="note" xlink:label="note-0158-10a" xlink:href="note-0158-10"/>
rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s8982" xml:space="preserve">ſinu depreſſionis meridianæ, ita vt ſemel inuenta huiuſ-<lb/>modi medietas adbibeatur ad omnium horarum altitudines perueſtigandas in duobus parallelis oppoſi-<lb/>tis. </s>
  <s xml:id="echoid-s8983" xml:space="preserve">Quia enim, vt in ſcholio antecedentis propoſ. </s>
  <s xml:id="echoid-s8984" xml:space="preserve">oſtendimus, depreſſio meridiana cuiuſcunque paralleli <lb/>æqualis eſt altitudini meridianæ paralleli oppoſiti, fit vt recta compoſita ex ſinu altitudinis meridianæ, et <lb/>ſinu depreſſionis meridianæ vnius paralleli, ſit æqualis rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s8985" xml:space="preserve"><lb/>ſinu depreſſionis meridianæ alterius paralleli oppoſiti, quandoquidem depreſſio meridiana illius æqualis <lb/>eſt altitudini meridianæ huius, &amp; </s>
  <s xml:id="echoid-s8986" xml:space="preserve">huius meridiana depreſſio ęqualis illius altitudini meridianæ. </s>
  <s xml:id="echoid-s8987" xml:space="preserve">Vnde &amp;</s>
  <s xml:id="echoid-s8988" xml:space="preserve">
<pb o="139" file="0159" n="159" rhead="LIBER PRIMVS."/>
mediet ates harum rectarum compoſitarum æquales erunt. </s>
  <s xml:id="echoid-s8989" xml:space="preserve">Vt in duob{us} tropicis mediet as rectæ compo-<lb/>ſię ex ſinu altitudinis meridianæ ♋, &amp; </s>
  <s xml:id="echoid-s8990" xml:space="preserve">ſinu depreſſionis meridianę ♋, vel ex ſinu altitudinis meridia-<lb/>næ ♑, &amp; </s>
  <s xml:id="echoid-s8991" xml:space="preserve">ſinu depreſſionis ♑, erit 68151. </s>
  <s xml:id="echoid-s8992" xml:space="preserve">eadem permanens, &amp; </s>
  <s xml:id="echoid-s8993" xml:space="preserve">vtilis ad omnium horarum altitudines, <lb/>Sole in principio ♋, vel ♑, exiſtente, inuestigandas.</s>
  <s xml:id="echoid-s8994" xml:space="preserve"/>
</p>
<div xml:id="echoid-div492" type="float" level="2" n="2">
<note position="left" xlink:label="note-0158-10" xlink:href="note-0158-10a" xml:space="preserve">Qui numeti nõ <lb/>mutentur un-<lb/>quam, ſi per pri <lb/>mum modum <lb/>traditum inue-<lb/>ſtigentur altitu <lb/>dines S olis pro <lb/>ſingulis. horis <lb/>duorum paralle <lb/>lotum oppoſito <lb/>rum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s8995" xml:space="preserve">RVRVS in omnibus parallelis ſemper vſurpatur idem ſinus totus 100000. </s>
  <s xml:id="echoid-s8996" xml:space="preserve">in Solis altitudini-<lb/>bus perquirendis.</s>
  <s xml:id="echoid-s8997" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s8998" xml:space="preserve">POSTREMO recta λ N, hoc eſt, differentia inter ſinum altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s8999" xml:space="preserve">medietatem <lb/>prædictam K λ, nunquam mutatur in duobus parallelis oppoſitis: </s>
  <s xml:id="echoid-s9000" xml:space="preserve">quia eadem differentia est omnino in-<lb/>ter ſinum depreſſionis meridianæ, &amp; </s>
  <s xml:id="echoid-s9001" xml:space="preserve">medietatem alteram θ λ, vt ex figuris manifeſtum eſt. </s>
  <s xml:id="echoid-s9002" xml:space="preserve">Conſtat autẽ <lb/>ex demonſtratis, ſinum depreſſionis meridianę paralleli borealis æqualem eſſe ſinui altitudinis meridianæ <lb/>
<anchor type="note" xlink:label="note-0159-01a" xlink:href="note-0159-01"/>
paralleli auſtralis oppoſiti: </s>
  <s xml:id="echoid-s9003" xml:space="preserve">Vnde ſemper eadem differentia erit inter medietatem prædictam, &amp; </s>
  <s xml:id="echoid-s9004" xml:space="preserve">ſinum <lb/>altitudinis meridianæ tam paralleli borealis, quàm oppoſiti auſtralis. </s>
  <s xml:id="echoid-s9005" xml:space="preserve">Vt in duobus tropicis erit huiuſmo <lb/>di differentia hic numerus ferè 26681. </s>
  <s xml:id="echoid-s9006" xml:space="preserve">qui nunquam mutãdus erit, donec omnes altitudines inuentæ ſint <lb/>in duobus tropicis, &amp; </s>
  <s xml:id="echoid-s9007" xml:space="preserve">ad quem numerum modo adĳcienda eſt recta T λ, inuenta, modo ex eodem detra-<lb/>
<anchor type="note" xlink:label="note-0159-02a" xlink:href="note-0159-02"/>
henda in ſignis borealibus, vel certè in australibus ſignis ipſemet numerus 26681. </s>
  <s xml:id="echoid-s9008" xml:space="preserve">ſubducendus eſt ex re-<lb/>cta T λ, inuenta, vt habeatur ſinus T N, altitudinis Solis, vt ex ſuperioribus patet.</s>
  <s xml:id="echoid-s9009" xml:space="preserve"/>
</p>
<div xml:id="echoid-div493" type="float" level="2" n="3">
<note position="left" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve"><gap/></note>
</div>
<p style="it">
  <s xml:id="echoid-s9010" xml:space="preserve">QVOD ſi per alterum modum altitudines Solis inueſtigare placuerit in duobus oppoſitis parallelis, <lb/>
<anchor type="note" xlink:label="note-0159-03a" xlink:href="note-0159-03"/>
permanebit quidem in vno eodem parallelo &amp; </s>
  <s xml:id="echoid-s9011" xml:space="preserve">ſinus verſus arcus ſemidiurni, et ſinus rectus altitudinis <lb/>meridianæ ſmeper idẽ ſed ad altitudi@es inquir endas in altero parallelo, qui ei opponitur, proprius ſinus <lb/>tam verſus arcus ſemidiurni, quàm rectus altitudinis meridianę accipiendus crit. </s>
  <s xml:id="echoid-s9012" xml:space="preserve">Solum id commodi ha-<lb/>
<anchor type="note" xlink:label="note-0159-04a" xlink:href="note-0159-04"/>
bebimus, quòd detr acto ſinu verſo arcus ſemidiurni vnius paralleli ex tota diametro, hoc eſt, ex 200000. <lb/></s>
  <s xml:id="echoid-s9013" xml:space="preserve">ſtatim habeamus ſinum verſam arcus ſemidiurni paralleli oppoſiti: </s>
  <s xml:id="echoid-s9014" xml:space="preserve">quia ſinus verſus arcus ſemidiurni <lb/>vnius paralleli eſt æqualis ſinui verſo arcus ſeminocturni alterius paralleli oppoſiti: </s>
  <s xml:id="echoid-s9015" xml:space="preserve">Perſpicuum autem <lb/>eſt, ſinum verſum arcus ſeminocturni ex tota diametro ſubductum relinq@ere arcum verſum arcus ſemi-<lb/>diurni, &amp; </s>
  <s xml:id="echoid-s9016" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s9017" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0159-05a" xlink:href="note-0159-05"/>
</s>
</p>
<div xml:id="echoid-div494" type="float" level="2" n="4">
<note position="right" xlink:label="note-0159-03" xlink:href="note-0159-03a" xml:space="preserve">Qui numeri ij-<lb/>dẽ permaneãt, ſi <lb/>altitudines So-<lb/>lis indagen tur <lb/>per ſecundum <lb/>modũ pro ſingu <lb/>lis horis cuiuſ-<lb/>uis paralleli.</note>
<note position="left" xlink:label="note-0159-04" xlink:href="note-0159-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0159-05" xlink:href="note-0159-05a" xml:space="preserve">Qui numeri nũ <lb/>quam mutẽtur, <lb/>ſi per vltimam <lb/>viam, quam an-<lb/>te rationẽ trian <lb/>gulorũ ſphæri-<lb/>corum tradidi-<lb/>mus, @nueſtigen <lb/>tur altitudines <lb/>Solis pro ſingu <lb/>lis hotis duorũ <lb/>parallelorũ op-<lb/>poſitorum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9018" xml:space="preserve">AT vero in vltimailla via, quam proxime ante rationem ex triangulis ſphæricis depromptam ſcri-<lb/>pſimus, habebimus in oppoſitis parallelis non ſolum eandem ſemper medietatem rectę compoſitæ ex ſinu <lb/>altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s9019" xml:space="preserve">ſinu meridianę depreſſionis, atque ſinum totum, verum etiam eoſaem ſinus ver <lb/>ſos diſtantiarum Solis à meridie in horis ęqualiter à Meridiano diſtantibus, vt ſunt horæ prima, &amp; </s>
  <s xml:id="echoid-s9020" xml:space="preserve">vnde-<lb/>cima. </s>
  <s xml:id="echoid-s9021" xml:space="preserve">Item ſecunda &amp; </s>
  <s xml:id="echoid-s9022" xml:space="preserve">decima, &amp; </s>
  <s xml:id="echoid-s9023" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9024" xml:space="preserve">tam in parallelo ♋, quàm in parallelo ♑. </s>
  <s xml:id="echoid-s9025" xml:space="preserve">Vnde in eiſdem horis ea-<lb/>
<anchor type="note" xlink:label="note-0159-06a" xlink:href="note-0159-06"/>
dem recta K T, inuenictur, adeo vt in parallelo oppoſito non opus ſit inueſtigare rurſus rectam K T, pro <lb/>illa hora, pro qua inuenta eſt eadem K T, in altero parallelo, ſed eadem omnino aſſumenda, vt detraha-<lb/>tur à ſinu altitudinis meridianæ propoſiti paralleli, &amp; </s>
  <s xml:id="echoid-s9026" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s9027" xml:space="preserve">
<anchor type="note" xlink:label="note-0159-07a" xlink:href="note-0159-07"/>
</s>
</p>
<div xml:id="echoid-div495" type="float" level="2" n="5">
<note position="left" xlink:label="note-0159-06" xlink:href="note-0159-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0159-07" xlink:href="note-0159-07a" xml:space="preserve">Qui ſinus ijdẽ <lb/>ſemper maneãt, <lb/>ſi per triangula <lb/>ſphærica altitu-<lb/>dines Solis in-<lb/>quirantur pro <lb/>ſingulis horis <lb/>duorum paral-<lb/>lelorum oppoſi <lb/>torum,</note>
</div>
<p style="it">
  <s xml:id="echoid-s9028" xml:space="preserve">DENIQVE ſi quis altitudines Solis in duobus oppoſitis parallelis maluerit per triangula ſphęri <lb/>ca indagare, negotium etiam perfacile reddetur, quia idem ſemper ſinus totus, idemq́, ſinus declinationis <lb/>vtriuſq; </s>
  <s xml:id="echoid-s9029" xml:space="preserve">paralleli in omniũ horarũ altitudinibus perueſtigandis ret inendus eſt, vt ex dictis liquido cõſtat.</s>
  <s xml:id="echoid-s9030" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s9031" xml:space="preserve">CÆTERVM vbi tanta eſt poli altitudo, vt totus parallelus aliquis borealis ſupra Horizontem <lb/>extet, ſiue illum tangat, vt in prima hac figura ſubiecta, ſiue non, vt in ſecunda, nihilo ſecius per priorem <lb/>modum in hac propoſ. </s>
  <s xml:id="echoid-s9032" xml:space="preserve">traditum altitudo Solis ex hora cognita, &amp; </s>
  <s xml:id="echoid-s9033" xml:space="preserve">viciſſim ex altitudine Solis hora inue-<lb/>
<anchor type="note" xlink:label="note-0159-08a" xlink:href="note-0159-08"/>
nietur, dummodo in vtr aque figura meridies intelligatur eſſe in K, vbi Sol in Meridiano exiſtens maxi-<lb/>
<anchor type="note" xlink:label="note-0159-09a" xlink:href="note-0159-09"/>
mam habet altitudinẽ, quæ ex decli-<lb/>
<anchor type="figure" xlink:label="fig-0159-01a" xlink:href="fig-0159-01"/>
natione paralleli inueſtiganda eſt, vt <lb/>ſupra in ſcholio propoſ. </s>
  <s xml:id="echoid-s9034" xml:space="preserve">præcedentis <lb/>declarauimus. </s>
  <s xml:id="echoid-s9035" xml:space="preserve">Verum nulla hic erit <lb/>depreſſio Meridiana, ſed in priori fi-<lb/>gura quidẽ recta K λ, erit medietas <lb/>ſinus altitudinis meridianę; </s>
  <s xml:id="echoid-s9036" xml:space="preserve">In poſte <lb/>riori verò eadem K λ, medietas erit <lb/>rectę K θ, quæ differentia eſt inter <lb/>K N, ſinum maioris altitudinis me-<lb/>
<anchor type="note" xlink:label="note-0159-10a" xlink:href="note-0159-10"/>
ridianę K A, &amp; </s>
  <s xml:id="echoid-s9037" xml:space="preserve">θ N, ſinum minoris <lb/>altitudinis meridianę L C: </s>
  <s xml:id="echoid-s9038" xml:space="preserve">quę qui-<lb/>dem minor altitudo C L, habebitur, <lb/>ſi ex arcu I L, declinationis detraha <lb/>tur arcus I C, complementi altitudi <lb/>nis poli. </s>
  <s xml:id="echoid-s9039" xml:space="preserve">Quòd ſi declinatio ęqualis fuerit complemento altitudinis poli, tanget parallelus Horizontem, <lb/>vt in priori figura accidit. </s>
  <s xml:id="echoid-s9040" xml:space="preserve">Quòd autem K λ, ſit medietas dictarum rectarum, ita probabitur. </s>
  <s xml:id="echoid-s9041" xml:space="preserve">Quoniam in <lb/>priori figur a eſt, vt k M, ad M C, ita K λ, ad λ N; </s>
  <s xml:id="echoid-s9042" xml:space="preserve">In poſteriori verò vt K M, ad M L, ita K λ, ad λ θ Eſt <lb/>
<anchor type="note" xlink:label="note-0159-11a" xlink:href="note-0159-11"/>
autemtam K M, ipſi M C, quàm K M, ipſi M L, æqualis, quòd hæ rectę ſint ſemidiametri ipſius paralle-<lb/>li; </s>
  <s xml:id="echoid-s9043" xml:space="preserve">erit quoque K λ, ipſi λ N, in priori figura, &amp; </s>
  <s xml:id="echoid-s9044" xml:space="preserve">ipſi λ θ, in poſteriori ęqualis.</s>
  <s xml:id="echoid-s9045" xml:space="preserve"/>
</p>
<div xml:id="echoid-div496" type="float" level="2" n="6">
<note position="right" xlink:label="note-0159-08" xlink:href="note-0159-08a" xml:space="preserve">Quando paral-<lb/>lelus borealis to <lb/>tus eſt ſupra Ho <lb/>rizontem, qua <lb/>ratio ne altitu-<lb/>do Solis ex no-<lb/>ta hora, &amp; uiciſ-<lb/>ſim ex altitudi-<lb/>ne Solis cogni-<lb/>ta exploranda <lb/>ſit hora.</note>
<note position="left" xlink:label="note-0159-09" xlink:href="note-0159-09a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a">
    <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0159-01"/>
  </figure>
<note position="left" xlink:label="note-0159-10" xlink:href="note-0159-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0159-11" xlink:href="note-0159-11a" xml:space="preserve">2. ſex@@.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9046" xml:space="preserve">ITAQVE quoniam in priori figura, vbi parallelus Horizontem tangit, eſt vt K M, ſinus totus ad <lb/>
<anchor type="note" xlink:label="note-0159-12a" xlink:href="note-0159-12"/>
<pb o="140" file="0160" n="160" rhead="GNOMONICES"/>
M R, ſinum complementi diſtantię Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ ad <lb/>λT, differentiam inter T N, ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s9047" xml:space="preserve">rectam λ N, medietatem ſinus altitudinis me-<lb/>ridianæ: </s>
  <s xml:id="echoid-s9048" xml:space="preserve">Sifiat vt ſinus totus adſinum complementi diſtantię Solis à meridie, ita medietas ſinus altitu-<lb/>
<anchor type="figure" xlink:label="fig-0160-01a" xlink:href="fig-0160-01"/>
dinis meridianæ ad aliud, inuenietur <lb/>recta, quæ addita medietati prędi-<lb/>ctę, ſi diſtantia à meridie minor eſt <lb/>quadrante, vel ab eadem medietate <lb/>ablata, ſi maior eſt diſtantia à meri <lb/>die quadrante, dabit ſinum altitudi-<lb/>nis Solis tempore obſeruationis. </s>
  <s xml:id="echoid-s9049" xml:space="preserve">Si <lb/>
<anchor type="note" xlink:label="note-0160-01a" xlink:href="note-0160-01"/>
autem distantia Solis à meridie qua-<lb/>dranti fuerit ęqualis, erit ipſamet <lb/>medietas λ N, ſinus altitudinis So <lb/>lis tempore obſeruationis. </s>
  <s xml:id="echoid-s9050" xml:space="preserve">Rurſus <lb/>
<anchor type="note" xlink:label="note-0160-02a" xlink:href="note-0160-02"/>
quoniam in ſecunda figura, vbi pa-<lb/>rallelus totus ſupra Horizontem ex-<lb/>tat, &amp; </s>
  <s xml:id="echoid-s9051" xml:space="preserve">illum non tangit, eſt vt K M, <lb/>ſinus totus ad M R, ſinum complemẽ <lb/>ti diſtantiæ Solis à meridie K, ita K λ, medietas differentiæ K θ, inter ſinum maioris altitudinis meridia <lb/>næ, &amp; </s>
  <s xml:id="echoid-s9052" xml:space="preserve">ſinum minoris altitudinis meridianæ ad λ T, differentiam inter T N, ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s9053" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0160-03a" xlink:href="note-0160-03"/>
rectam λ N, compoſitam ex dictamedietate λ θ, ac ſinu θ N, minoris altitudinis meridianæ: </s>
  <s xml:id="echoid-s9054" xml:space="preserve">Si fiat, <lb/>vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita medietas differentiæ inter ſinum maio-<lb/>ris altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s9055" xml:space="preserve">ſinum minoris altitudinis meridianæ ad aliud, reperietur recta, quæ ablata <lb/>ex recta compoſita ex dicta medietate, ac ſinu minoris altitudinis meridianæ, ſi diſtantia Solis à meridie <lb/>fuerit quadrante maior, vel eidem rectæ compoſitæ addita, ſi diſtantia quadrante fuerit minor, dabit ſinũ <lb/>altitudinis Solis tempore obſeruationis, Si autem diſtantia quadranti æ qualis extiterit, erit ipſamet re-<lb/>cta compoſita ex dicta medietate, &amp; </s>
  <s xml:id="echoid-s9056" xml:space="preserve">ſinu altitudinis meridianæ minoris, ſinus altitudinis Solis tempore <lb/>obſeruationis. </s>
  <s xml:id="echoid-s9057" xml:space="preserve">Quę omnia ex hiſce duabus appoſitis figuris facile colligi poſſunt.</s>
  <s xml:id="echoid-s9058" xml:space="preserve"/>
</p>
<div xml:id="echoid-div497" type="float" level="2" n="7">
<note position="right" xlink:label="note-0159-12" xlink:href="note-0159-12a" xml:space="preserve">2. vel 4. ſexti</note>
  <figure xlink:label="fig-0160-01" xlink:href="fig-0160-01a">
    <image file="0160-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0160-01"/>
  </figure>
<note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">2. vel 4. ſexti</note>
<note position="left" xlink:label="note-0160-03" xlink:href="note-0160-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s9059" xml:space="preserve">VICISSIM, ſi fiat, vt K λ, medietas ſinus altitudinis meridianæ in priori figura, vel medietas <lb/>rectæ K θ, in poſteriori, quæ differentia eſt inter ſinum maioris altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s9060" xml:space="preserve">ſinum minoris al-<lb/>
<anchor type="note" xlink:label="note-0160-04a" xlink:href="note-0160-04"/>
titudinis meridianæ, ad λ T, differentiam inter ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s9061" xml:space="preserve">medietatem ſinus altitudinis <lb/>meridianæ in priori figura, vel inter ſinum altitudinis Solis, &amp; </s>
  <s xml:id="echoid-s9062" xml:space="preserve">rectam λ N, quę componitur ex medieta-<lb/>te differentiæ inter ſinum maioris altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s9063" xml:space="preserve">ſinum minoris altitudinis meridianæ, atque <lb/>ſinu minoris altitudinis meridianæ, vt in poſteriori figura apparet, ita ſinus totus ad aliud, reperietur ſi-<lb/>nus complementi diſtantiæ Solis à meridie K. </s>
  <s xml:id="echoid-s9064" xml:space="preserve">Quod complementum additum quadranti, quando ſinus al-<lb/>titudinis Solis minor eſt, quàm recta λ N, hoc eſt, quàm medietas ſinus altitudinis meridianæ in priori <lb/>figura, vel quàm recta compoſita ex ſinus minoris altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s9065" xml:space="preserve">medietate differentiæ inter ſi-<lb/>num maioris altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s9066" xml:space="preserve">ſinum minoris altitudinis meridianæ in figur a poſteriori, dabit di-<lb/>stantiam Solis à meridie, vt in poſteriori figura apparet. </s>
  <s xml:id="echoid-s9067" xml:space="preserve">Idem vero complementum à quadrante ſublatũ, <lb/>quando ſinus altitudinis Solis maior eſt, quàm dicta recta λ N, relinquet diſtantiam Solis à meridie. <lb/></s>
</p>
<p style="it">
  <s xml:id="echoid-s9068" xml:space="preserve">SED facilius hęc res conficietur illo modo, quem vltimo loco tractauimus, antequàm problema hoc <lb/>propoſitum per triangula ſphærica explicaremus. </s>
  <s xml:id="echoid-s9069" xml:space="preserve">Nam ſi fiat, vt K M, ſinus totus ad K R, ſinum verſum <lb/>diſtantiæ Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ in priori figura, vel in poſterio-<lb/>ri ita medietas differentiæ inter ſinum maioris altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s9070" xml:space="preserve">ſinum minoris altitudinis meri-<lb/>dianę, ad aliud, nota euadet K T, differentia inter ſinum maioris altitudinis meridianæ, vel certe in prio-<lb/>ri figura ipſius altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s9071" xml:space="preserve">ſinum altitudinis Solis quæſitę.</s>
  <s xml:id="echoid-s9072" xml:space="preserve"/>
</p>
<div xml:id="echoid-div498" type="float" level="2" n="8">
<note position="left" xlink:label="note-0160-04" xlink:href="note-0160-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s9073" xml:space="preserve">ITEM ſi fiat, vt medietas præ dicta ad differentiam inter ſinum maioris altitudinis meridianæ, vel <lb/>certe in priori figura ipſius altitudinis meridianę, &amp; </s>
  <s xml:id="echoid-s9074" xml:space="preserve">ſinum altitudinis Solis, ita ſinus totus ad aliud, pro-<lb/>ueniet ſinus verſus distantiæ Solis à meridie K. </s>
  <s xml:id="echoid-s9075" xml:space="preserve">Vt ex ĳſdem figuris manifeſtum eſt.</s>
  <s xml:id="echoid-s9076" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s9077" xml:space="preserve">QVOD ſi polus mundi in vertice, ſeu polo Horizontis extiterit, erit in quolibet die Solis alti-<lb/>
<anchor type="note" xlink:label="note-0160-06a" xlink:href="note-0160-06"/>
tudo perpetuo æqualis declinationi paralleli, quem tunc Sol deſcribit motu primi mo-<lb/>bilis: </s>
  <s xml:id="echoid-s9078" xml:space="preserve">Quia tunc Aequator idem est, qui Horizon, &amp; </s>
  <s xml:id="echoid-s9079" xml:space="preserve">paralleli Hori-<lb/>zontis à parallelis Solis, vel Aequatoris non diffc-<lb/>runt, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s9080" xml:space="preserve"/>
</p>
<div xml:id="echoid-div499" type="float" level="2" n="9">
<note position="left" xlink:label="note-0160-06" xlink:href="note-0160-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div501" type="section" level="1" n="140">
<head xml:id="echoid-head143" style="it" xml:space="preserve">FINIS PRIMI LIBRI.</head>
<pb o="141" file="0161" n="161"/>
</div>
<div xml:id="echoid-div502" type="section" level="1" n="141">
<head xml:id="echoid-head144" xml:space="preserve">GNOMONICES <lb/>LIBER SECVNDVS.</head>
  <figure>
    <image file="0161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0161-01"/>
  </figure>
</div>
<div xml:id="echoid-div503" type="section" level="1" n="142">
<head xml:id="echoid-head145" xml:space="preserve">AVCTORE <lb/>
CHRISTOPHORO CLAVIO BAMBER GENSI
SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s9081" xml:space="preserve">PRAEMISSIS ſuperiore libro theorematibus varijs, ac <lb/>problematibus, quæ vel neceſſaria, vel vtilia fore iudicaui-<lb/>mus, vt eſſent veluti baſis, ac fundamentum omnium demon <lb/>ſtrationum, quas ad horologiorum deſcriptiones adhibituri <lb/>ſumus, aggrediemur iam ſecundo hoc libro ad deſcriptionein <lb/>
<anchor type="note" xlink:label="note-0161-02a" xlink:href="note-0161-02"/>
horologiorum, quæ in ſuperficiebus planis ſolent depingi: </s>
  <s xml:id="echoid-s9082" xml:space="preserve">In <lb/>quarum ſingulis, quæ quidem multæ ſunt, vt in principio dixi-<lb/>
<anchor type="note" xlink:label="note-0161-03a" xlink:href="note-0161-03"/>
mus, non ſolum horas (quod cæteri fere omnes ſcriptores tan <lb/>tum fecerunt) deſcribemus, ſed vt, quoad eius fieri poteſt, no-<lb/>ſtra hæc Gnomonica reddatur quàm abſolutiſſima, duodecim problemata demon-<lb/>ſtrabimus, quibus explicentur, quæcunque ferme ex gnomonis vmbra cognoſci <lb/>poſſe videantur, hoc ſemper ordine, qui ſequitur, ſeruato.</s>
  <s xml:id="echoid-s9083" xml:space="preserve"/>
</p>
<div xml:id="echoid-div503" type="float" level="2" n="1">
<note position="left" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0161-03" xlink:href="note-0161-03a" xml:space="preserve">Quid in ſingu-<lb/>lis planis horo-<lb/>logiorũ deſcri-<lb/>batur in hoc e<unsure/>-<lb/>per@.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9084" xml:space="preserve">PRIMVM docebimus, quanam ratione in plano propoſito quocunque borologiũ Aſtro <lb/>
<anchor type="note" xlink:label="note-0161-04a" xlink:href="note-0161-04"/>
nomicum, continens nimirum lineas horarum à meridie, vel media nocte (quæ nihil ſunt <lb/>
<anchor type="note" xlink:label="note-0161-05a" xlink:href="note-0161-05"/>
aliud, quàm communes ſectiones plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9085" xml:space="preserve">circulorum maximorum, qui per po-<lb/>los mundi ducuntur, diuidunt{q́ue} Aequatorem, &amp; </s>
  <s xml:id="echoid-s9086" xml:space="preserve">reliquos parallelos, in 24. </s>
  <s xml:id="echoid-s9087" xml:space="preserve">partes <lb/>æquales) deſcribatur.</s>
  <s xml:id="echoid-s9088" xml:space="preserve"/>
</p>
<div xml:id="echoid-div504" type="float" level="2" n="2">
<note position="right" xlink:label="note-0161-04" xlink:href="note-0161-04a" xml:space="preserve">Horæ à mer. <lb/>uel med. noc.</note>
<note position="left" xlink:label="note-0161-05" xlink:href="note-0161-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s9089" xml:space="preserve">DEINDE, quaratione in eodem plano paralleliper initia ſignorum Zodiaci, vel <lb/>
<anchor type="note" xlink:label="note-0161-06a" xlink:href="note-0161-06"/>
per quę cunque alia puncta tranſeuntes delineentur, trademus: </s>
  <s xml:id="echoid-s9090" xml:space="preserve">qui quidem paralleli ab artificibus arcus <lb/>ſignorum dicuntur, ſunt{q́ue} in plano dato vel circuli, vel parabolę, vel hyperbolæ, vel Ellipſes, nempe ſe-<lb/>ctiones communes plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9091" xml:space="preserve">ſuperficierum conicarum, quarum baſes ſunt dicti paralleli ſignorũ <lb/>Zodiaci, vertex autem centrum mundi, excepto parallelo per principia ♈, &amp; </s>
  <s xml:id="echoid-s9092" xml:space="preserve">♎, ducto, qui cum ab <lb/>Aequatore non differat, efficit lineam rectam in plano propoſito, vt libro ſuperiore demonſtr auimus.</s>
  <s xml:id="echoid-s9093" xml:space="preserve"/>
</p>
<div xml:id="echoid-div505" type="float" level="2" n="3">
<note position="right" xlink:label="note-0161-06" xlink:href="note-0161-06a" xml:space="preserve">Paralleli, ſiue <lb/>arcus ſignorum <lb/>Zodiaci.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9094" xml:space="preserve">POSTEA deſcribemus in eodem plano parallelos arcuum diurnorum, qui ſunt quidem &amp; </s>
  <s xml:id="echoid-s9095" xml:space="preserve">ipſi <lb/>
<anchor type="note" xlink:label="note-0161-07a" xlink:href="note-0161-07"/>
<anchor type="note" xlink:label="note-0161-08a" xlink:href="note-0161-08"/>
paralleli à punctis Zodiaci ad motum primi mobilis deſcripti, non tamen neceſſario per initia ſignorum <lb/>ducuntur, quamuis hoc poſſit aliquando contingere, ſed per illa puncta Eclipticæ, in quibus Sol exiſtens <lb/>efficit diem datarum horarum, vt 12. </s>
  <s xml:id="echoid-s9096" xml:space="preserve">vel 13. </s>
  <s xml:id="echoid-s9097" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s9098" xml:space="preserve">vel 8. </s>
  <s xml:id="echoid-s9099" xml:space="preserve">vel denique quotcunque quis voluerit, dummo <lb/>do numerum 24. </s>
  <s xml:id="echoid-s9100" xml:space="preserve">horarum non ſuperent. </s>
  <s xml:id="echoid-s9101" xml:space="preserve">Sunt autem hi quoque paralleli in propoſito plano vel cir culi, <lb/>vel parabolæ, vel hyperbolæ, vel ellipſes, excepto parallelo horarum 12. </s>
  <s xml:id="echoid-s9102" xml:space="preserve">qui cum ſit Aequator ipſe, effi-<lb/>cit in horologĳ plano lineam rectam, vt diximus.</s>
  <s xml:id="echoid-s9103" xml:space="preserve"/>
</p>
<div xml:id="echoid-div506" type="float" level="2" n="4">
<note position="left" xlink:label="note-0161-07" xlink:href="note-0161-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0161-08" xlink:href="note-0161-08a" xml:space="preserve">Paralleii arcu@ <lb/>diurnorum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9104" xml:space="preserve">RVRSVS in quarto problemate circulos Verticales, quos Azimuth dicunt, id eſt, communes ſe-<lb/>
<anchor type="note" xlink:label="note-0161-09a" xlink:href="note-0161-09"/>
ctiones plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9105" xml:space="preserve">Verticalium circulorum, in eodem plano depingemus.</s>
  <s xml:id="echoid-s9106" xml:space="preserve"/>
</p>
<div xml:id="echoid-div507" type="float" level="2" n="5">
<note position="right" xlink:label="note-0161-09" xlink:href="note-0161-09a" xml:space="preserve">Verticales cir-<lb/>euli.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9107" xml:space="preserve">IN quinto autem problemate collocabimus in eodem dato plano parallelos Horizontis, quos Almu-<lb/>
<anchor type="note" xlink:label="note-0161-10a" xlink:href="note-0161-10"/>
cantarath vocant, qui in plano propoſito (vt de parallelis ſignorum Zodiaci, &amp; </s>
  <s xml:id="echoid-s9108" xml:space="preserve">arcuum diurnorum di-<lb/>
<anchor type="note" xlink:label="note-0161-11a" xlink:href="note-0161-11"/>
ctum eſt) ſunt communes ſectiones plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9109" xml:space="preserve">conicarum ſuperficierum, quarum baſes ſunt dicti <lb/>paralleli Horizontis, vertex autem centrum mundi, nimirum vel circuli, vel parabolæ, vel hyperbolæ, <lb/>vel ellipſes, excepto Horizonte, qui cum ſit circulus maximus, rectam lineam in plano efficit.</s>
  <s xml:id="echoid-s9110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div508" type="float" level="2" n="6">
<note position="right" xlink:label="note-0161-10" xlink:href="note-0161-10a" xml:space="preserve">Paralleli Hori <lb/>zontis, quos Al <lb/>mucãtarath di-<lb/>cunt.</note>
<note position="left" xlink:label="note-0161-11" xlink:href="note-0161-11a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s9111" xml:space="preserve">PROBLEMA ſextum continebit in plano eodem deſcriptionem circulorum Meridianorum to-<lb/>
<anchor type="note" xlink:label="note-0161-12a" xlink:href="note-0161-12"/>
tius mundi, qui ſunt in plano lineæ rectæ inſtar linearum horarum à meridie, vel media nocte.</s>
  <s xml:id="echoid-s9112" xml:space="preserve"/>
</p>
<div xml:id="echoid-div509" type="float" level="2" n="7">
<note position="right" xlink:label="note-0161-12" xlink:href="note-0161-12a" xml:space="preserve">Meridiani cir-<lb/>culi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9113" xml:space="preserve">SEPTIMVM autem problema exhibebit lineamenta parallelorum ciuitatum, ſiue circulos la-<lb/>
<anchor type="note" xlink:label="note-0161-13a" xlink:href="note-0161-13"/>
titudinum, in eodem plano, qui videlicet per locorum vertices ducuntur, efficiunt{q́ue} in plano horologĳ <lb/>vel circulos, vel parabolas, vel hyperbolas, vel Ellipſes, vt paralleli ſignorum Zodiaci, vel arcuum <lb/>diurnorum.</s>
  <s xml:id="echoid-s9114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div510" type="float" level="2" n="8">
<note position="right" xlink:label="note-0161-13" xlink:href="note-0161-13a" xml:space="preserve">Paralleli latitu <lb/>dinum, ſeu ciui <lb/>tatum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9115" xml:space="preserve">AD hæc, in octauo problemate deſignabimus domos cęleſtes, id eſt, lineas rectas, quę ſunt communes <lb/>
<anchor type="note" xlink:label="note-0161-14a" xlink:href="note-0161-14"/>
ſectiones plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9116" xml:space="preserve">circulorum cæleſtium domorum tam ſecundum doctrinam Ioan. </s>
  <s xml:id="echoid-s9117" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s9118" xml:space="preserve">qui
<pb o="142" file="0162" n="162" rhead="GNOMONICES"/>
eos ducit per partes æquales Aequatoris, quàm ſecundum Campani ſententiam, qui eoſdem per partes <lb/>æquales Verticalis circuli primarĳ ducendos eſſe cenſet.</s>
  <s xml:id="echoid-s9119" xml:space="preserve"/>
</p>
<div xml:id="echoid-div511" type="float" level="2" n="9">
<note position="right" xlink:label="note-0161-14" xlink:href="note-0161-14a" xml:space="preserve">Domus c@@@-<lb/>ſtes.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9120" xml:space="preserve">PRAETEREA in problemate nono trademus modum, quo in eodem plano propoſito deſcribere <lb/>
<anchor type="note" xlink:label="note-0162-01a" xlink:href="note-0162-01"/>
poſſimus aſcendentia ſigna Zodiaci, hoc eſt, lineas rectas, quæ communes ſectiones ſunt plani horologĳ, &amp; </s>
  <s xml:id="echoid-s9121" xml:space="preserve"><lb/>Eclipticæ, prout varios ſitus, ac poſitiones habet in Horizonte, dum initia ſignorum Zodiaci ſupra Hori-<lb/>zontem emergunt.</s>
  <s xml:id="echoid-s9122" xml:space="preserve"/>
</p>
<div xml:id="echoid-div512" type="float" level="2" n="10">
<note position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">Signa aſcenden <lb/>tia.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9123" xml:space="preserve">DECIMO loco horologium Italicum, continens nimirum horas ab occaſu Solis, quarum vſus ho-<lb/>
<anchor type="note" xlink:label="note-0162-02a" xlink:href="note-0162-02"/>
die in Italia maxime &amp; </s>
  <s xml:id="echoid-s9124" xml:space="preserve">Bohemia viget, in dato plano conſtruemus.</s>
  <s xml:id="echoid-s9125" xml:space="preserve"/>
</p>
<div xml:id="echoid-div513" type="float" level="2" n="11">
<note position="left" xlink:label="note-0162-02" xlink:href="note-0162-02a" xml:space="preserve">Horæ ab occaſu <lb/>Solis.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9126" xml:space="preserve">IN ſequenti verò problemate vndecimo conſtituemus horologium Babylonicum in eodem plano, com <lb/>
<anchor type="note" xlink:label="note-0162-03a" xlink:href="note-0162-03"/>
plectens videlicet horas ab ortu Solis, quibus nostra tempeſtate inſulæ Baleares vtuntur.</s>
  <s xml:id="echoid-s9127" xml:space="preserve"/>
</p>
<div xml:id="echoid-div514" type="float" level="2" n="12">
<note position="left" xlink:label="note-0162-03" xlink:href="note-0162-03a" xml:space="preserve">Horæ ab ortu <lb/>Solis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s9128" xml:space="preserve">AD extremum in plano eodem horologium Antiquum depingemus, comprehendens horas inæquales, <lb/>
<anchor type="note" xlink:label="note-0162-05a" xlink:href="note-0162-05"/>
quæ olim apud Veteres vbique fere gentium in vſu fuerunt.</s>
  <s xml:id="echoid-s9129" xml:space="preserve"/>
</p>
<div xml:id="echoid-div515" type="float" level="2" n="13">
<note position="left" xlink:label="note-0162-05" xlink:href="note-0162-05a" xml:space="preserve">Horæ antiquæ, <lb/>ſiue inæquales.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9130" xml:space="preserve">IN hiſce autem duodecim rebus in omni plano propoſito deſcribendis, vtemur ſemper demonſtra-<lb/>tionibus Geometricis, ne in deſcriptione ipſa quicquam in dubium quæſtionem{q́ue} horologiographus vocare <lb/>poſſit. </s>
  <s xml:id="echoid-s9131" xml:space="preserve">Vſus quoque omnium explicabitur in proprĳs propoſitionibus horologiorũ horizontalium, de qui-<lb/>bus primo loco dicturi ſumus, qui in omnibus alĳs horologĳs eodem modo intelligendus erit.</s>
  <s xml:id="echoid-s9132" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s9133" xml:space="preserve">ITAQVE ſecundus hic liber complectetur omnia illa horologia, quæ in plano, quod vel Horizon-<lb/>
<anchor type="note" xlink:label="note-0162-06a" xlink:href="note-0162-06"/>
tis, vel Verticali propriè dicto, vel Meridiano, vel circulo horæ ſextæ à meridie vel media nocte, vel de-<lb/>nique Aequatori æquidiſtat, deſcribi ſolent: </s>
  <s xml:id="echoid-s9134" xml:space="preserve">quod quidem planum, cuicunque maximo circulo ex nomina-<lb/>tis æquidiſtet, perpetuo vnum, &amp; </s>
  <s xml:id="echoid-s9135" xml:space="preserve">idem eſt, nunquam ſitum mutans in eodem climate. </s>
  <s xml:id="echoid-s9136" xml:space="preserve">Reliqua vero ho-<lb/>
<anchor type="note" xlink:label="note-0162-07a" xlink:href="note-0162-07"/>
rologia, quorum plana circulis maximis æquidiſtant, qui vel declinant à Verticali, vel ab Horizonte, vel <lb/>ad Horizontẽ ſunt inclinati, vel denique &amp; </s>
  <s xml:id="echoid-s9137" xml:space="preserve">à Verticali deflectunt, &amp; </s>
  <s xml:id="echoid-s9138" xml:space="preserve">ſimul inclinati ſunt ad Horizon-<lb/>tem, intertium librum reĳciemus: </s>
  <s xml:id="echoid-s9139" xml:space="preserve">quæ quidem in eodem climate ſexcentis modis variari poſſunt. </s>
  <s xml:id="echoid-s9140" xml:space="preserve">Nam <lb/>verbi gratia, circulus maximus à Verticali declinans, cui horologium æquidiſtat, declinare poteſt in ortũ <lb/>vel occaſum, vno duntaxat gradu, vel duobus, vel tribus, quatuor, quinque, ſex, &amp; </s>
  <s xml:id="echoid-s9141" xml:space="preserve">ita deinceps vſque ad <lb/>90. </s>
  <s xml:id="echoid-s9142" xml:space="preserve">Vnde &amp; </s>
  <s xml:id="echoid-s9143" xml:space="preserve">horologium illi æquidiſtans tot modis etiam variabitur, licet in eodem ſemper climate, ſiue <lb/>eadem altitudine poli permaneamus. </s>
  <s xml:id="echoid-s9144" xml:space="preserve">Idem{q́ue} de alĳs dicendum eſt.</s>
  <s xml:id="echoid-s9145" xml:space="preserve"/>
</p>
<div xml:id="echoid-div516" type="float" level="2" n="14">
<note position="left" xlink:label="note-0162-06" xlink:href="note-0162-06a" xml:space="preserve">Argumentum <lb/>libri ſecundi.</note>
<note position="left" xlink:label="note-0162-07" xlink:href="note-0162-07a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s9146" xml:space="preserve">QVONIAM vero pluribus vĳs horologium Aſtronomicum in quolibet plano deſcripturi ſumus, <lb/>
<anchor type="note" xlink:label="note-0162-08a" xlink:href="note-0162-08"/>
inter omnes illa ratio magis mihi probatur, (vt etiã hac in parte ſtudioſo Lectori ſignificem, qua potiſſi-<lb/>mum via in horologiorum deſcriptionibus progrediendum eſſe cenſeam) quæ longitudinem ſtyli datam, <lb/>
<anchor type="note" xlink:label="note-0162-09a" xlink:href="note-0162-09"/>
eius{q́ue} locum datum accipit, vt horologium deſcribat; </s>
  <s xml:id="echoid-s9147" xml:space="preserve">adiuncta etiam illa, quæ per Ellipſim fit in plano <lb/>horologĳ deſcriptam. </s>
  <s xml:id="echoid-s9148" xml:space="preserve">Id quod à nemine hactenus (quod ſciam) factum eſſe, nedum demonſtratum, obſer <lb/>uauimus. </s>
  <s xml:id="echoid-s9149" xml:space="preserve">Priorem rationem explicatam, demonſtratam{q́ue} in ſcholĳs ſingulorum Aſtronomicorum horo-<lb/>logiorum, quæ deſcribuntur propoſ. </s>
  <s xml:id="echoid-s9150" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9151" xml:space="preserve">13. </s>
  <s xml:id="echoid-s9152" xml:space="preserve">25. </s>
  <s xml:id="echoid-s9153" xml:space="preserve">37. </s>
  <s xml:id="echoid-s9154" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9155" xml:space="preserve">49. </s>
  <s xml:id="echoid-s9156" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s9157" xml:space="preserve">at que propoſ. </s>
  <s xml:id="echoid-s9158" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9159" xml:space="preserve">13. </s>
  <s xml:id="echoid-s9160" xml:space="preserve">25. </s>
  <s xml:id="echoid-s9161" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9162" xml:space="preserve">37. </s>
  <s xml:id="echoid-s9163" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9164" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s9165" xml:space="preserve">eandem{q́ue} libro 7. </s>
  <s xml:id="echoid-s9166" xml:space="preserve">repetitam inuenies. </s>
  <s xml:id="echoid-s9167" xml:space="preserve">Posteriorem vero in ſcholĳs propoſitionum 1. </s>
  <s xml:id="echoid-s9168" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9169" xml:space="preserve">13. </s>
  <s xml:id="echoid-s9170" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s9171" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9172" xml:space="preserve"><lb/>in ſcholĳs propoſitionum 1. </s>
  <s xml:id="echoid-s9173" xml:space="preserve">13. </s>
  <s xml:id="echoid-s9174" xml:space="preserve">25. </s>
  <s xml:id="echoid-s9175" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9176" xml:space="preserve">37. </s>
  <s xml:id="echoid-s9177" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9178" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9179" xml:space="preserve">quia Ellipſis illa locum non habet in ſcholĳs propoſitio-<lb/>num 25. </s>
  <s xml:id="echoid-s9180" xml:space="preserve">37. </s>
  <s xml:id="echoid-s9181" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9182" xml:space="preserve">49. </s>
  <s xml:id="echoid-s9183" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s9184" xml:space="preserve">Quod vero attinet ad horas ab ortu, &amp; </s>
  <s xml:id="echoid-s9185" xml:space="preserve">occaſu Solis deſcribendas, eligerem <lb/>ſemper modum illum, quem libro 5. </s>
  <s xml:id="echoid-s9186" xml:space="preserve">explicabimus; </s>
  <s xml:id="echoid-s9187" xml:space="preserve">ſi tamen tabulæ, quæ ad hanc rem neceſſariæ ſunt, ha-<lb/>beantur in promptu, quas quidem in eodem lib. </s>
  <s xml:id="echoid-s9188" xml:space="preserve">ſupputare docebimus. </s>
  <s xml:id="echoid-s9189" xml:space="preserve">Hic enim modus uidctur eſſe om-<lb/>nium facillimus, &amp; </s>
  <s xml:id="echoid-s9190" xml:space="preserve">minus obnoxius errori, vt ſuo loco planum faciemus.</s>
  <s xml:id="echoid-s9191" xml:space="preserve"/>
</p>
<div xml:id="echoid-div517" type="float" level="2" n="15">
<note position="left" xlink:label="note-0162-08" xlink:href="note-0162-08a" xml:space="preserve">Quæ ra tio de-<lb/>ſctibendi horo-<lb/>logij Aſtrono-<lb/>mici in quoli-<lb/>bet plano ma-<lb/>gis probetur.</note>
<note position="left" xlink:label="note-0162-09" xlink:href="note-0162-09a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s9192" xml:space="preserve">NON explicauimus autem duas illas rationes deſcribendi horologĳ Aſtronomici in ipſis propoſitio-<lb/>nibus, ſed eas in ſcholia reiecimus; </s>
  <s xml:id="echoid-s9193" xml:space="preserve">quoniam deſcriptiones in propoſitionibus expoſitę ab omnibus fere ar-<lb/>tificibus vſurpantur, licet in illis etiam aliqua immutauerimus. </s>
  <s xml:id="echoid-s9194" xml:space="preserve">Vnde viſum eſt, priori loco illas Geome <lb/>tricis demonstrationibus corroborare. </s>
  <s xml:id="echoid-s9195" xml:space="preserve">quod quidem neminem ante nos perfecte, plene{q́ue} præſtitiſ-<lb/>ſe inuenimus.</s>
  <s xml:id="echoid-s9196" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div519" type="section" level="1" n="143">
<head xml:id="echoid-head146" xml:space="preserve">DE HOROLOGIIS HORIZONTALIBVS. <lb/>PROBLEMA 1. PROPOSITIO 1.</head>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s9197" xml:space="preserve">HOROLOGIVM Aſtronomicum Horizontale conſtituere. <lb/></s>
  <s xml:id="echoid-s9198" xml:space="preserve">Hoc eſt, lineas horarum à meridie, vel media nocte inchoatarum in pla <lb/>no, quod Horizonti æquidiſtat, deſcribere.</s>
  <s xml:id="echoid-s9199" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s9200" xml:space="preserve">SIT Meridiani ſemicirculus A B C, cuius centrum D, ſitq́; </s>
  <s xml:id="echoid-s9201" xml:space="preserve">B C, communis ſectio ipſius &amp; </s>
  <s xml:id="echoid-s9202" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0162-12a" xlink:href="note-0162-12"/>
Horizontis; </s>
  <s xml:id="echoid-s9203" xml:space="preserve">A D, communis eiuſdem ac Verticalis ſectio; </s>
  <s xml:id="echoid-s9204" xml:space="preserve">F D, ſectio cõmunis eiuſdem &amp; </s>
  <s xml:id="echoid-s9205" xml:space="preserve">Aequa <lb/>toris; </s>
  <s xml:id="echoid-s9206" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9207" xml:space="preserve">E D, axis mundi, vt propoſ. </s>
  <s xml:id="echoid-s9208" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9209" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9210" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s9211" xml:space="preserve">Productis autem rectis A D, E D, <lb/>FD, ad partes D, ſumatur in A D, producta gnomoni horologij futuri, cuiuſcunque is magnitu-<lb/>dinis fuerit, æqualis recta D G, &amp; </s>
  <s xml:id="echoid-s9212" xml:space="preserve">per G, agatur ipſi B C, parallela H I, ſecans E D, F D, productas
<pb o="143" file="0163" n="163" rhead="LIBER SECVNDVS."/>
in H, &amp; </s>
  <s xml:id="echoid-s9213" xml:space="preserve">I. </s>
  <s xml:id="echoid-s9214" xml:space="preserve">Si igitur per B C, duci intelligatur Horizon ad Meridianum rectus, &amp; </s>
  <s xml:id="echoid-s9215" xml:space="preserve">per HI, planum <lb/>horologij Horizonti æquidiſtans; </s>
  <s xml:id="echoid-s9216" xml:space="preserve">cum &amp; </s>
  <s xml:id="echoid-s9217" xml:space="preserve">Meridianus, &amp; </s>
  <s xml:id="echoid-s9218" xml:space="preserve">Verticalis ad Horizontem rectus ſit, erit <lb/>ad eundem communis eorum ſectio A D, perpendicularis, atque adeo &amp; </s>
  <s xml:id="echoid-s9219" xml:space="preserve">ad planum horologij per <lb/>
<anchor type="note" xlink:label="note-0163-01a" xlink:href="note-0163-01"/>
H I, ductum Horizonti parallelum, ex iis, quæ ad pro-<lb/>
<anchor type="figure" xlink:label="fig-0163-01a" xlink:href="fig-0163-01"/>
poſ. </s>
  <s xml:id="echoid-s9220" xml:space="preserve">14. </s>
  <s xml:id="echoid-s9221" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9222" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9223" xml:space="preserve">Euclidis demonſtrauimus, perpendicu-<lb/>laris erit. </s>
  <s xml:id="echoid-s9224" xml:space="preserve">Erit ergo H I, in plano horologij linea me-<lb/>ridiana, ſiue horæ 12. </s>
  <s xml:id="echoid-s9225" xml:space="preserve">vtpote communis ſectio Meri-<lb/>diani, &amp; </s>
  <s xml:id="echoid-s9226" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s9227" xml:space="preserve">Eſt enim recta H I, in plano <lb/>rectarum H D, I D, hoc eſt, in plano Meridiani; </s>
  <s xml:id="echoid-s9228" xml:space="preserve">D G, <lb/>
<anchor type="note" xlink:label="note-0163-02a" xlink:href="note-0163-02"/>
gnomon erit, ſiue ſtylus ad planum horologij rectus, <lb/>
<anchor type="note" xlink:label="note-0163-03a" xlink:href="note-0163-03"/>
atque adeò &amp; </s>
  <s xml:id="echoid-s9229" xml:space="preserve">ad H I, lineam meridianam, per defini-<lb/>tionem 3. </s>
  <s xml:id="echoid-s9230" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9231" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9232" xml:space="preserve">Euclidis, perpendicularis, cuius ver-<lb/>tex D, idem eſt, quod centrum mundi, per propoſ. </s>
  <s xml:id="echoid-s9233" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s9234" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9235" xml:space="preserve">Locus ſtyli punctum G, in linea meri-<lb/>diana diſtans à puncto H, in quo axis mundi plano <lb/>horologij occurrit, &amp; </s>
  <s xml:id="echoid-s9236" xml:space="preserve">quod centrum dicitur horolo-<lb/>gij, interuallo G H, vel à puncto I, in quo planũ Aequa <lb/>toris lineam meridianam ſecat interuallo G I. </s>
  <s xml:id="echoid-s9237" xml:space="preserve">Quæ omnia perſpicua ſunt &amp; </s>
  <s xml:id="echoid-s9238" xml:space="preserve">manifeſta, ſi Meridia <lb/>nus in proprio ſitu intelligatur eſſe poſitus, vt nimirum punctum E, ad polum arcticum ſpectet, &amp; </s>
  <s xml:id="echoid-s9239" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0163-04a" xlink:href="note-0163-04"/>
F, vergat in auſtrum. </s>
  <s xml:id="echoid-s9240" xml:space="preserve">Hanc autem figuram appellabimus doctrinæ cauſa portionem Analemma-<lb/>
<anchor type="note" xlink:label="note-0163-05a" xlink:href="note-0163-05"/>
tis, cum verè pars ſit Analemmatis propoſ. </s>
  <s xml:id="echoid-s9241" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9242" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s9243" xml:space="preserve">deſcripti, continens nimirum com-<lb/>munes ſectiones Meridiani, &amp; </s>
  <s xml:id="echoid-s9244" xml:space="preserve">aliquot circulorum ſphæræ.</s>
  <s xml:id="echoid-s9245" xml:space="preserve"/>
</p>
<div xml:id="echoid-div519" type="float" level="2" n="1">
<note position="left" xlink:label="note-0162-12" xlink:href="note-0162-12a" xml:space="preserve">Deſcriptio pot-<lb/>tionis Analem-<lb/>matis.</note>
<note position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0163-01" xlink:href="fig-0163-01a">
    <image file="0163-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0163-01"/>
  </figure>
<note position="right" xlink:label="note-0163-02" xlink:href="note-0163-02a" xml:space="preserve">2. vndec.</note>
<note position="left" xlink:label="note-0163-03" xlink:href="note-0163-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0163-04" xlink:href="note-0163-04a" xml:space="preserve">Portio Analem <lb/>matis quid di-<lb/>catur.</note>
<note position="left" xlink:label="note-0163-05" xlink:href="note-0163-05a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s9246" xml:space="preserve">IAM vero beneficio trianguli D H I, conſtruemus horologium Aſtronomicum horizontale, <lb/>
<anchor type="note" xlink:label="note-0163-06a" xlink:href="note-0163-06"/>
hoc modo. </s>
  <s xml:id="echoid-s9247" xml:space="preserve">In lineam rectam H E, ductam vtcunque pro linea meridiana in plano horologij, <lb/>transferatur H I, linea meridiana portionis Analemmatis, &amp; </s>
  <s xml:id="echoid-s9248" xml:space="preserve">abſcindatur I E, ex recta H E, rectæ <lb/>
<anchor type="figure" xlink:label="fig-0163-02a" xlink:href="fig-0163-02"/>
<anchor type="note" xlink:label="note-0163-07a" xlink:href="note-0163-07"/>
<anchor type="note" xlink:label="note-0163-08a" xlink:href="note-0163-08"/>
<anchor type="note" xlink:label="note-0163-09a" xlink:href="note-0163-09"/>
DI, in eadem portione Analemmatis æqualis. </s>
  <s xml:id="echoid-s9249" xml:space="preserve">Deinde per I, in plano horologij educatur ad H E, <lb/>perpendicularis F k: </s>
  <s xml:id="echoid-s9250" xml:space="preserve">Et ex E, deſcribatur circulus ad quodcunque interuallum, quo diuiſo in 24. <lb/></s>
  <s xml:id="echoid-s9251" xml:space="preserve">partes æquales, initio facto à linea meridiana H E, producta, ducantur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s9252" xml:space="preserve"><lb/>centrum E, rectæ occultę ſecantes rectam F K, in punctis, per quæ &amp; </s>
  <s xml:id="echoid-s9253" xml:space="preserve">punctum H, emiſſæ lineę re-<lb/>ctę dabunt lineas horarias à meridie, vel media nocte in plano, quod Horizonti æquidiſtat; </s>
  <s xml:id="echoid-s9254" xml:space="preserve">ita vt <lb/>H E, det horam duodecimam meridiei, &amp; </s>
  <s xml:id="echoid-s9255" xml:space="preserve">lineę nobis conuerſis ad horologium poſitæ ad ſini-<lb/>
<anchor type="note" xlink:label="note-0163-10a" xlink:href="note-0163-10"/>
ſtram (Appello autem ſiniſtram partem, in qua punctum F, dextram vero, in qua punctum k) <lb/>oſtendant horas à meridie, &amp; </s>
  <s xml:id="echoid-s9256" xml:space="preserve">lineę ad dextram poſitæ horas ante meridiem, vel poſt mediam no-<lb/>ctem, vt numeri ipſi indicant. </s>
  <s xml:id="echoid-s9257" xml:space="preserve">Pro hora verò ſexta eſt ducenda per H, linea C L, ad H E, perpen-<lb/>dicularis, vel æquidiſtans ipſi F K, monſtrabitq́; </s>
  <s xml:id="echoid-s9258" xml:space="preserve">H C, horam ſextam à meridie, &amp; </s>
  <s xml:id="echoid-s9259" xml:space="preserve">H L, horam <lb/>ſextam à media nocte.</s>
  <s xml:id="echoid-s9260" xml:space="preserve"/>
</p>
<div xml:id="echoid-div520" type="float" level="2" n="2">
<note position="right" xlink:label="note-0163-06" xlink:href="note-0163-06a" xml:space="preserve">Horizontalis <lb/>horologij Aſtro <lb/>nomici deſcri-<lb/>ptio.</note>
  <figure xlink:label="fig-0163-02" xlink:href="fig-0163-02a">
    <image file="0163-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0163-02"/>
  </figure>
<note position="left" xlink:label="note-0163-07" xlink:href="note-0163-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0163-08" xlink:href="note-0163-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0163-09" xlink:href="note-0163-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0163-10" xlink:href="note-0163-10a" xml:space="preserve">Ordo horaruæ <lb/>in horologio <lb/>horizontali.</note>
</div>
<pb o="144" file="0164" n="164" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s9261" xml:space="preserve">CONSTRVCTIONIS autẽ huius hęc erit demonſtratio. </s>
  <s xml:id="echoid-s9262" xml:space="preserve">Intelligatur portio Analem-<lb/>
<anchor type="note" xlink:label="note-0164-01a" xlink:href="note-0164-01"/>
matis horologio ſuperpoſita, ita vt punctũ H, puncto H, &amp; </s>
  <s xml:id="echoid-s9263" xml:space="preserve">punctũ I, puncto I, atq; </s>
  <s xml:id="echoid-s9264" xml:space="preserve">recta H I, re-<lb/>ctę H I, congruat, (congruet autem ei propter æqualitatem rectarum HI, HI,) ipſaq́; </s>
  <s xml:id="echoid-s9265" xml:space="preserve">porti@ <lb/>
<anchor type="figure" xlink:label="fig-0164-01a" xlink:href="fig-0164-01"/>
<anchor type="note" xlink:label="note-0164-02a" xlink:href="note-0164-02"/>
<anchor type="note" xlink:label="note-0164-03a" xlink:href="note-0164-03"/>
Analemmatis animo concipiatur recta ad planum horologii, &amp; </s>
  <s xml:id="echoid-s9266" xml:space="preserve">meridiana linea H E, habeat pro-<lb/>prium ſitum, ita vt ſit communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s9267" xml:space="preserve">plani horologij, punctumq́; </s>
  <s xml:id="echoid-s9268" xml:space="preserve">H, ad auſtrum, <lb/>
<anchor type="note" xlink:label="note-0164-04a" xlink:href="note-0164-04"/>
&amp; </s>
  <s xml:id="echoid-s9269" xml:space="preserve">E, ad boream vergat; </s>
  <s xml:id="echoid-s9270" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9271" xml:space="preserve">denique recta B C, plano horologij æquidiſtet, ita vt ſit communis ſe-<lb/>ctio Meridiani &amp; </s>
  <s xml:id="echoid-s9272" xml:space="preserve">Horizontis, cum D, vertex ſtyli ſit centrum mundi, vt propoſ. </s>
  <s xml:id="echoid-s9273" xml:space="preserve">2. </s>
  <s xml:id="echoid-s9274" xml:space="preserve">præcedentis lib. <lb/></s>
  <s xml:id="echoid-s9275" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s9276" xml:space="preserve">Vel potius loco portionis Analemmatis intelligatur duntaxat triangulum D H I, ea <lb/>ratione, vt diximus, ſuperpoſitum eſſe horologio, ita vt D H, referat axem mundi, &amp; </s>
  <s xml:id="echoid-s9277" xml:space="preserve">D I, commu-<lb/>nem ſectionem Meridiani &amp; </s>
  <s xml:id="echoid-s9278" xml:space="preserve">Aequatoris, &amp; </s>
  <s xml:id="echoid-s9279" xml:space="preserve">tandem D G, ſtylus communem ſectionem Meridia-<lb/>ni, ac Verticalis circuli per D, centrum mundi ducti. </s>
  <s xml:id="echoid-s9280" xml:space="preserve">quod quidem triangulum D H I, vna cum <lb/>ſtylo D G, in horologio deſcriptum eſt. </s>
  <s xml:id="echoid-s9281" xml:space="preserve">His ita poſitis, occurret axis D H, plano horologij in H, &amp; </s>
  <s xml:id="echoid-s9282" xml:space="preserve"><lb/>Aequatoris diameter D I, in I; </s>
  <s xml:id="echoid-s9283" xml:space="preserve">Verticalis autem diameter D G, in G. </s>
  <s xml:id="echoid-s9284" xml:space="preserve">Quoniam igitur tam planum <lb/>Aequatoris, quàm planũ horologij Horizonti æquidiſtãs rectũ eſt ad Meridiani planũ, erit &amp; </s>
  <s xml:id="echoid-s9285" xml:space="preserve">cõ <lb/>munis ſectio Aequatoris; </s>
  <s xml:id="echoid-s9286" xml:space="preserve">ac plani horologij ad idẽ planum Meridiani, ideoq́; </s>
  <s xml:id="echoid-s9287" xml:space="preserve">per defin. </s>
  <s xml:id="echoid-s9288" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9289" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9290" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9291" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0164-05a" xlink:href="note-0164-05"/>
<anchor type="note" xlink:label="note-0164-06a" xlink:href="note-0164-06"/>
Euclidis, &amp; </s>
  <s xml:id="echoid-s9292" xml:space="preserve">ad lineã meridianã H E, in plano Meridiani exiſtentẽ perpendicularis in puncto I, in <lb/>quo Aequator per rectam D I, ductus lineæ meridianę in horologio occurrit, vt dictum eſt. </s>
  <s xml:id="echoid-s9293" xml:space="preserve">Re-<lb/>cta igitur F K, quæ in horologio per I, ad meridianam lineam H I, perpendicularis educta eſt, <lb/>communis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s9294" xml:space="preserve">plani horologij, nempe linea æquinoctialis: </s>
  <s xml:id="echoid-s9295" xml:space="preserve">Circa quam ſi mo <lb/>ueri intelligatur planum circuli ex centro E, deſcripti, donec cum mundi centro D, in triangulo <lb/>D H I, (quod rectum eſſe diximus, vna cum tota portione Analemmatis, ad planum horologij, <lb/>quamuis ſolum triangulum deſcriptum ſit in horologio, &amp; </s>
  <s xml:id="echoid-s9296" xml:space="preserve">in plano Meridiani exiſtere) con-<lb/>iungatur E, centrum circuli, propterea quòd rectæ D I, I E, ęquales ſunt ex conſtructione, &amp; </s>
  <s xml:id="echoid-s9297" xml:space="preserve">in <lb/>illo motu circuli ex E, deſcripti recta I E, ſemper maneat in plano Meridiani, in quo exiſtit recta <lb/>D I; </s>
  <s xml:id="echoid-s9298" xml:space="preserve">erit ipſe circulus circa centrum mũdi D, ſeu Aequatoris deſcriptus, &amp; </s>
  <s xml:id="echoid-s9299" xml:space="preserve">in plano eiuſdẽ Aequa-<lb/>
<anchor type="note" xlink:label="note-0164-07a" xlink:href="note-0164-07"/>
toris exiſtens, cum Aequatoris planum per rectas D I, I k, ducatur, quemadmodum &amp; </s>
  <s xml:id="echoid-s9300" xml:space="preserve">circulus di-<lb/>crus in tali poſitione per eaſdem eſt ductus; </s>
  <s xml:id="echoid-s9301" xml:space="preserve">ita vt circulus hic, &amp; </s>
  <s xml:id="echoid-s9302" xml:space="preserve">Aequator in eodem exiſtant pla-<lb/>no, idemq́; </s>
  <s xml:id="echoid-s9303" xml:space="preserve">habeant centrum, nimirum D, centrum mundi. </s>
  <s xml:id="echoid-s9304" xml:space="preserve">Intelligatur quoque I E, protracta in <lb/>vtramque partem in eadem poſitione, quippe quę ſimul cum circulo moueatur, tanquam commu-<lb/>nis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s9305" xml:space="preserve">Aequatoris, cum tam Meridianus, quàm Aequator, in huiuſmodi poſitio-<lb/>ne per réctam D I, vel I E, (quæ eadem eſt in eo ſitu, que D I) tranſeat. </s>
  <s xml:id="echoid-s9306" xml:space="preserve">Quoniam verò ex ijs, quæ <lb/>in commentarijs in ſphęram ad finem capitis 1. </s>
  <s xml:id="echoid-s9307" xml:space="preserve">ſcripſimus, circuli in eodem plano, &amp; </s>
  <s xml:id="echoid-s9308" xml:space="preserve">circa idem <lb/>centrum deſcripti ſecantur in partes ſimiles à lineis è centro egredientibus, ſit vt rectę illę occultę <lb/>per centrum E, quod iam cum puncto D, hoc eſt, cum centro mundi eſt coniunctum, ductę, quę <lb/>quidem circumferentiam circuli ſecant in partes 24. </s>
  <s xml:id="echoid-s9309" xml:space="preserve">æquales, occurruntq́; </s>
  <s xml:id="echoid-s9310" xml:space="preserve">rectæ F K, communi <lb/>ſectioni Aequatoris, &amp; </s>
  <s xml:id="echoid-s9311" xml:space="preserve">plani horologii, in punctis I, A, B, &amp;</s>
  <s xml:id="echoid-s9312" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9313" xml:space="preserve">ſecent quoque, ſi producantur, cir-
<pb o="145" file="0165" n="165" rhead="LIBER SECVNDVS."/>
cumferentiam Aequatoris, initio facto à Meridiano, in totidem partes æquales: </s>
  <s xml:id="echoid-s9314" xml:space="preserve">Ac propterea, cũ <lb/>circuli horarum à meridie, vel media nocte eundem Aequatorem diuidant in partes 24. </s>
  <s xml:id="echoid-s9315" xml:space="preserve">æquales, <lb/>initio quoque facto à Meridiano, vt patet ex propoſ. </s>
  <s xml:id="echoid-s9316" xml:space="preserve">9. </s>
  <s xml:id="echoid-s9317" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9318" xml:space="preserve">efficitur, vt eędem rectę oc-<lb/>cultę è centro E, egredientes ſint communes ſectiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s9319" xml:space="preserve">circulorum horariorũ, qui <lb/>horas à mer. </s>
  <s xml:id="echoid-s9320" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9321" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9322" xml:space="preserve">indicant; </s>
  <s xml:id="echoid-s9323" xml:space="preserve">nempe N M, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s9324" xml:space="preserve">circuli horę 12. <lb/></s>
  <s xml:id="echoid-s9325" xml:space="preserve">hoc eſt, Meridiani; </s>
  <s xml:id="echoid-s9326" xml:space="preserve">O P, Aequatoris, &amp; </s>
  <s xml:id="echoid-s9327" xml:space="preserve">circuli horę primę à meridie, vel media nocte; </s>
  <s xml:id="echoid-s9328" xml:space="preserve">Q R, Aequa <lb/>toris, &amp; </s>
  <s xml:id="echoid-s9329" xml:space="preserve">circuli horę 2. </s>
  <s xml:id="echoid-s9330" xml:space="preserve">à meridie vel media nocte; </s>
  <s xml:id="echoid-s9331" xml:space="preserve">S T, Aequatoris, &amp; </s>
  <s xml:id="echoid-s9332" xml:space="preserve">circuli horę 3. </s>
  <s xml:id="echoid-s9333" xml:space="preserve">à meridie, <lb/>vel media nocte, &amp;</s>
  <s xml:id="echoid-s9334" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9335" xml:space="preserve">vt patet, ſi circulus ex E, deſcriptus in propria poſitione intelligatur. </s>
  <s xml:id="echoid-s9336" xml:space="preserve">Vergent <lb/>enim puncta O, Q, S, in hemiſphærio ſupero ad partes occidentales, ſeu pomeridianas, &amp;</s>
  <s xml:id="echoid-s9337" xml:space="preserve">c.</s>
  <s xml:id="echoid-s9338" xml:space="preserve"/>
</p>
<div xml:id="echoid-div521" type="float" level="2" n="3">
<note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">Demonſtratio <lb/>conſtructionis <lb/>horologij hori-<lb/>zontalis.</note>
  <figure xlink:label="fig-0164-01" xlink:href="fig-0164-01a">
    <image file="0164-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0164-01"/>
  </figure>
<note position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0164-03" xlink:href="note-0164-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0164-04" xlink:href="note-0164-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0164-05" xlink:href="note-0164-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0164-06" xlink:href="note-0164-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0164-07" xlink:href="note-0164-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s9339" xml:space="preserve">QVARE circuli horarij à meridie, vel media nocte ſecant in plano horologii rectam F K, <lb/>
<anchor type="note" xlink:label="note-0165-01a" xlink:href="note-0165-01"/>
in punctis I, A, B, &amp;</s>
  <s xml:id="echoid-s9340" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9341" xml:space="preserve">(quæ quidem puncta non variantur, etiamſi planum circuli circa E, deſcri <lb/>pti aliam poſitionem habeat, nempe in plano horologii, in quo ipſum deſcripſimus, exiſtat. </s>
  <s xml:id="echoid-s9342" xml:space="preserve">Nam <lb/>ſi planum huius circuli circumuertatur circa rectam F K, tanguam cardinem immobilem, ita vt <lb/>recta I E, ſemper perpendicularis ſit ad F K, occurrent recte N E, O E, Q E, &amp; </s>
  <s xml:id="echoid-s9343" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9344" xml:space="preserve">in eiſdem ſemper <lb/>punctis ęquinoctiali lineę F K, vt perſpicuum eſt) ac idcirco per hęc puncta incedent communes <lb/>ſectiones illorum circulorum horariorum, &amp; </s>
  <s xml:id="echoid-s9345" xml:space="preserve">plani horologij, quæ quidem ſunt lineę horarię à <lb/>meridie, vel media nocte; </s>
  <s xml:id="echoid-s9346" xml:space="preserve">Atqui per corollar. </s>
  <s xml:id="echoid-s9347" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s9348" xml:space="preserve">21. </s>
  <s xml:id="echoid-s9349" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s9350" xml:space="preserve">eędem communes ſe-<lb/>ctiones, ſeu lineæ horarię, ſecant ſe mutuo in horologij centro H, in quo axis D H, plano horolo-<lb/>gij occurrit. </s>
  <s xml:id="echoid-s9351" xml:space="preserve">Igitur rectę per puncta I, A, B, &amp;</s>
  <s xml:id="echoid-s9352" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9353" xml:space="preserve">æquinoctialis lineę F k, &amp; </s>
  <s xml:id="echoid-s9354" xml:space="preserve">per punctum H, ſeu cen <lb/>trum horologij, emiſſę ſunt lineę horarũ à meridie, vel media nocte, ita vt meridiana linea H I E, <lb/>
<anchor type="note" xlink:label="note-0165-02a" xlink:href="note-0165-02"/>
indicet horam 12. </s>
  <s xml:id="echoid-s9355" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s9356" xml:space="preserve">lineę ad ſiniſtram illius monſtrent horas à meridie; </s>
  <s xml:id="echoid-s9357" xml:space="preserve">lineę verò ad <lb/>dexteram horas à media nocte, vt in ſigura apparet, &amp; </s>
  <s xml:id="echoid-s9358" xml:space="preserve">in ſcholio ſequenti declarabimus.</s>
  <s xml:id="echoid-s9359" xml:space="preserve"/>
</p>
<div xml:id="echoid-div522" type="float" level="2" n="4">
<note position="left" xlink:label="note-0165-01" xlink:href="note-0165-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0165-02" xlink:href="note-0165-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s9360" xml:space="preserve">SOLA linea horę 6. </s>
  <s xml:id="echoid-s9361" xml:space="preserve">ducenda eſt per H, perpendicularis ad H I, vel ęquidiſtans ipſi F k, qua-<lb/>lis eſt C L. </s>
  <s xml:id="echoid-s9362" xml:space="preserve">Cum enim, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s9363" xml:space="preserve">22. </s>
  <s xml:id="echoid-s9364" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9365" xml:space="preserve">docuimus, in horologio horizon-<lb/>tali parallelæ ſint linea ęquinoctialis, &amp; </s>
  <s xml:id="echoid-s9366" xml:space="preserve">linea horę ſextę à meridie, vel media nocte, perſpicuum <lb/>eſt, rectam C L, lineam eſſe horę ſextę à meridie, vel media nocte, quandoquidem parallela eſt <lb/>ęquinoctiali lineę F K, tranſitq́; </s>
  <s xml:id="echoid-s9367" xml:space="preserve">per punctum H, vbi omnes horarię lineę à meridie, vel media <lb/>nocte ſe interſecant. </s>
  <s xml:id="echoid-s9368" xml:space="preserve">Horologium igitur Aſtronomicum horizontale conſtituimus, &amp;</s>
  <s xml:id="echoid-s9369" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9370" xml:space="preserve">Quod <lb/>faciendum erat.</s>
  <s xml:id="echoid-s9371" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div524" type="section" level="1" n="144">
<head xml:id="echoid-head147" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve">Alia deſcriptio <lb/>horologii Aſtro <lb/>nomici horizõ-<lb/>talis, commodiſ <lb/>ſima pro horis <lb/>deli@eãdis, quæ <lb/>propinquæ ſunt <lb/>hotæ 6. à mer. <lb/>vel med. noc.</note>
<p style="it">
  <s xml:id="echoid-s9372" xml:space="preserve">ANDREAS Schonerus proponit aliam rationem horarum à meridie, vel media nocte deſcriben-<lb/>darum, quæ per commoda eſt pro illis horis delineandis, quæ æquinoctialem lineam in punctis valde remo <lb/>tis ſecant, quales ſunt horæ, quæ propinquæ ſunt horæ ſextæ à mer. </s>
  <s xml:id="echoid-s9373" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9374" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9375" xml:space="preserve">Ea autem est huiuſmodi. <lb/></s>
  <s xml:id="echoid-s9376" xml:space="preserve">In æquinoctiali linea F k, ſumatur recta I a, æqualis rectæ I E, vel I D, &amp; </s>
  <s xml:id="echoid-s9377" xml:space="preserve">per a, ducatur ad ęquinoctia-<lb/>lem lineam perpendicularis a b, vel ipſi H I, parallela ſecans lineam horæ ſextæ C L, (quæ ſemper ex <lb/>H, centro horologĳ ducitur perpendicularis ad H I, vel parallela lineæ ęquinoctiali, vt oſtenſum eſt) in b. </s>
  <s xml:id="echoid-s9378" xml:space="preserve"><lb/>Sumpta deinde b d, æquali ipſi a b, ducatur per d, ad b d, perpendicularis e f, vel parallela ipſi H I. </s>
  <s xml:id="echoid-s9379" xml:space="preserve"><lb/>Poſtremo ex d, centro deſcripto circulo, eo{q́ue} in partes 24. </s>
  <s xml:id="echoid-s9380" xml:space="preserve">diuiſo, initio facto à recta b d, ducantur ex d, <lb/>
<anchor type="note" xlink:label="note-0165-05a" xlink:href="note-0165-05"/>
centro per diuiſionum puncta lineæ occultæ. </s>
  <s xml:id="echoid-s9381" xml:space="preserve">Hæ enim rectam a b, ſecabunt in punctis, per quæ ſi ex H, <lb/>
<anchor type="note" xlink:label="note-0165-06a" xlink:href="note-0165-06"/>
centro horologĳ rectæ emittantur, dabunt hæ, vt prius, horas à meridie, vel media nocte.</s>
  <s xml:id="echoid-s9382" xml:space="preserve"/>
</p>
<div xml:id="echoid-div524" type="float" level="2" n="1">
<note position="right" xlink:label="note-0165-05" xlink:href="note-0165-05a" xml:space="preserve">Segmenta æqui <lb/>noctialis lineæ <lb/>in horologio ho <lb/>rizontali inter <lb/>lineam meridia <lb/>nam, &amp; binas <lb/>horas vtrinque <lb/>à meridie æqua <lb/>li temporis ſpa-<lb/>lio diſtãtes, ſunt <lb/>æqualia.</note>
<note position="left" xlink:label="note-0165-06" xlink:href="note-0165-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s9383" xml:space="preserve">IN horologio porrò quouis horizontali binæ lineæ quęcunque horariæ hinc inde à meridiana linea <lb/>æquali temporis ſpatio remotæ auferunt ex linea ęquinoctiali F K, lineas æquales, illas nimirum, quæ in-<lb/>ter lineas borarias, &amp; </s>
  <s xml:id="echoid-s9384" xml:space="preserve">meridianam lineam interĳciuntur. </s>
  <s xml:id="echoid-s9385" xml:space="preserve">Vt lineæ H F, H K, quarum vtraque quin-<lb/>que horis à meridiana linea diſtat, auferunt lineas I F, I K, æquales. </s>
  <s xml:id="echoid-s9386" xml:space="preserve">Cum enim anguli I E F, I E k, qui <lb/>continentur ſub linea meridiana, &amp; </s>
  <s xml:id="echoid-s9387" xml:space="preserve">rectis occultis ex E, ad F, K, ductis, (licet enim E F, ducta non <lb/>ſit, eam tamen ductam eſſe concipiendum eſt) æquales ſint, quòd in centro E, ab æqualibus arcubus circuli <lb/>
<anchor type="note" xlink:label="note-0165-07a" xlink:href="note-0165-07"/>
ex E, deſcripti ſubtendantur, &amp; </s>
  <s xml:id="echoid-s9388" xml:space="preserve">anguli ad I, recti, erunt duo anguli I E F, E I F, trianguli E I F, æqua-<lb/>les duobus angulis I E K, E I K, trianguli E I K; </s>
  <s xml:id="echoid-s9389" xml:space="preserve">ac propterea cum habeant latus I E, commune, erunt <lb/>
<anchor type="note" xlink:label="note-0165-08a" xlink:href="note-0165-08"/>
reliqua later a vnius æqualia reliquis lateribus alterius, nempe I F, ipſi I K, quod eſt propoſitũ. </s>
  <s xml:id="echoid-s9390" xml:space="preserve">Eadem <lb/>
<anchor type="note" xlink:label="note-0165-09a" xlink:href="note-0165-09"/>
<anchor type="note" xlink:label="note-0165-10a" xlink:href="note-0165-10"/>
eſt ratio de cęteris. </s>
  <s xml:id="echoid-s9391" xml:space="preserve">Itaque ſpatia horaria ante meridiem æqualia ſunt ſpatĳs horarĳs poſt meridiem, ſin-<lb/>gula ſingulis, in linea æquinoctiali horologĳ horizontalis.</s>
  <s xml:id="echoid-s9392" xml:space="preserve"/>
</p>
<div xml:id="echoid-div525" type="float" level="2" n="2">
<note position="right" xlink:label="note-0165-07" xlink:href="note-0165-07a" xml:space="preserve">27. tertĳ.</note>
<note position="right" xlink:label="note-0165-08" xlink:href="note-0165-08a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0165-09" xlink:href="note-0165-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0165-10" xlink:href="note-0165-10a" xml:space="preserve">Arcus circuli ex <lb/>H, centro horo <lb/>logij horizon@a <lb/>lis deſcripti, in-<lb/>ter metidianã <lb/>lineam &amp; binas <lb/>horas vtrinque <lb/>à metidie æqua <lb/>liter diſtantes <lb/>interiecti ſunt <lb/>æquales.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9393" xml:space="preserve">EX hoc ſequitur, arcus circuli cuiuſuis ex H, deſcripti in horologio horizontali inter ceptos inter li-<lb/>neam meridianam, &amp; </s>
  <s xml:id="echoid-s9394" xml:space="preserve">binas quaſcunque lineas horarias æquali ſpatio temporis à meridie diſtantes, qua-<lb/>les ſunt v. </s>
  <s xml:id="echoid-s9395" xml:space="preserve">g. </s>
  <s xml:id="echoid-s9396" xml:space="preserve">arcus circuli ex H, deſcripti inter meridianam lineam H I, &amp; </s>
  <s xml:id="echoid-s9397" xml:space="preserve">lineas H F, H K, interiecti, <lb/>æquales eſſe. </s>
  <s xml:id="echoid-s9398" xml:space="preserve">Nam cum latera I H, I F, trianguli I H F, lateribus I H, I K, trianguli I H K, ęqualia <lb/>ſint, angulos{q́ue} comprehendant æquales, nempe rectos, erunt &amp; </s>
  <s xml:id="echoid-s9399" xml:space="preserve">anguli I H F, I H K, æquales, ac propte-<lb/>
<anchor type="note" xlink:label="note-0165-11a" xlink:href="note-0165-11"/>
rea in circulo ex H, deſcripto ab arcubus ęqualibus ſubtendentur, &amp; </s>
  <s xml:id="echoid-s9400" xml:space="preserve">ſic de cęteris. <lb/></s>
  <s xml:id="echoid-s9401" xml:space="preserve">
<anchor type="note" xlink:label="note-0165-12a" xlink:href="note-0165-12"/>
</s>
</p>
<div xml:id="echoid-div526" type="float" level="2" n="3">
<note position="right" xlink:label="note-0165-11" xlink:href="note-0165-11a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0165-12" xlink:href="note-0165-12a" xml:space="preserve">26. tertĳ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9402" xml:space="preserve">SEQVITVR rurſus, interualla inter centrum E, Aequatoris, &amp; </s>
  <s xml:id="echoid-s9403" xml:space="preserve">binas horas quaſcunque in ęqui <lb/>
<anchor type="note" xlink:label="note-0165-13a" xlink:href="note-0165-13"/>
noctiali linea F K, ęquali temporis interuallo à linea meridiana diſtantes, qualia ſunt interualla E F, <lb/>E K, eſſe ę<unsure/>qualia. </s>
  <s xml:id="echoid-s9404" xml:space="preserve">Cum enim ęqualia ſint latera I E, I F, trianguli I E F, lateribus I E, I K, trian-
<pb o="146" file="0166" n="166" rhead="GNOMONICES"/>
guli I E K, angulos{q́ue} contineant ęquales, erunt &amp; </s>
  <s xml:id="echoid-s9405" xml:space="preserve">baſes E F, E K, æquales, &amp; </s>
  <s xml:id="echoid-s9406" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s9407" xml:space="preserve"/>
</p>
<div xml:id="echoid-div527" type="float" level="2" n="4">
<note position="right" xlink:label="note-0165-13" xlink:href="note-0165-13a" xml:space="preserve">Interualla in-<lb/>ter E, centrum <lb/>Aequatoris &amp; <lb/>binas horas v<unsure/>-</note>
</div>
<note position="left" xml:space="preserve">trinque à meri-<lb/>die æquali tem <lb/>poris @patio di-<lb/>ſtant es in horo <lb/>logio hori@on-<lb/>tali, ſunt aqua-<lb/>lia.</note>
<p style="it">
  <s xml:id="echoid-s9408" xml:space="preserve">POSTREMO ſequitur, ſatis eſſe ad deſcriptionem horologĳ Aſtronomici horizontalis, ſi vnus <lb/>quadrans circuli ex E, deſcripti, qualis eſt v.</s>
  <s xml:id="echoid-s9409" xml:space="preserve">g. </s>
  <s xml:id="echoid-s9410" xml:space="preserve">quadrans Mg, in ſex partes æquales diſtribuatur. </s>
  <s xml:id="echoid-s9411" xml:space="preserve">Nam du <lb/>
<anchor type="figure" xlink:label="fig-0166-01a" xlink:href="fig-0166-01"/>
<anchor type="note" xlink:label="note-0166-02a" xlink:href="note-0166-02"/>
<anchor type="note" xlink:label="note-0166-03a" xlink:href="note-0166-03"/>
ctis rectis occultis per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s9412" xml:space="preserve">centrum E, ſecantibus rectam F I, in punctis, per quę hora-<lb/>
<anchor type="note" xlink:label="note-0166-04a" xlink:href="note-0166-04"/>
riæ lineæ ſunt ducendæ ex H; </s>
  <s xml:id="echoid-s9413" xml:space="preserve">ſi hæc puncta ex I, transferantur ad alteram partem lineę ęquinoctialis, <lb/>
<anchor type="note" xlink:label="note-0166-05a" xlink:href="note-0166-05"/>
verſus K, habebuntur alia puncta, per quæ horariæ lineę ducendæ ſunt: </s>
  <s xml:id="echoid-s9414" xml:space="preserve">quandoquidem ſingula ſpatia ho-<lb/>raria in recta I F, æqualia ſunt ſingulis ſpatĳs horarĳs in recta I K, vt demonſtratum est. </s>
  <s xml:id="echoid-s9415" xml:space="preserve">Rurſus ductis <lb/>lineis horarĳs ex H, per puncta rectæ I F, vel I K, vt reliquę altera ex parte accuratius ducãtur, tranſ-<lb/>ferenda erunt puncta circumferentiæ circuli ex H, deſcripti ex puncto, vbi linea meridiana, &amp; </s>
  <s xml:id="echoid-s9416" xml:space="preserve">dicta cir-<lb/>cumferentia ſe mutuo interſecant, in partem alteram eiuſdem circumferentię. </s>
  <s xml:id="echoid-s9417" xml:space="preserve">Nam per hęctranſire de-<lb/>bent omnino horariæ lineę ex H, per puncta rectæ F K, eductę, cum arcus dicti circuli ex vna parte ęqua <lb/>les ſint ar cubus eiuſdem ex altera parte, vt oſtenſum eſt.</s>
  <s xml:id="echoid-s9418" xml:space="preserve"/>
</p>
<div xml:id="echoid-div528" type="float" level="2" n="5">
  <figure xlink:label="fig-0166-01" xlink:href="fig-0166-01a">
    <image file="0166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0166-01"/>
  </figure>
<note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0166-03" xlink:href="note-0166-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0166-04" xlink:href="note-0166-04a" xml:space="preserve">Satis eſt ad de-<lb/>ſoriptionẽ horo <lb/>logij horizonta <lb/>lis Aſtronomi-<lb/>ci, ſi unus dun-<lb/>taxat quadrans <lb/>circuli ex E, de-<lb/>ſcripti ſecetur <lb/>in 6. partes æ-<lb/>quales.</note>
<note position="left" xlink:label="note-0166-05" xlink:href="note-0166-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s9419" xml:space="preserve">QVOD ſi axis H D, in triangulo D H I, ad planum horologĳ recto, intelligatur eſſe filum exten-<lb/>
<anchor type="note" xlink:label="note-0166-06a" xlink:href="note-0166-06"/>
tum, vel etiam ferrum aliquod tenue, faciens in H, cum linea meridiana angulum æqualẽ angulo D H I, <lb/>&amp; </s>
  <s xml:id="echoid-s9420" xml:space="preserve">cum recta C L, angulos rectos, vel certè ipſum triangulum D H I, conſtruatur ex materia aliqua ſoli-<lb/>
<anchor type="note" xlink:label="note-0166-07a" xlink:href="note-0166-07"/>
da, statuaturq́, rectum ad planum horologĳ, indicabit vmbra axis D I, ſingulas horas à meridie, vel me-<lb/>dia nocte, ſi horologium in plano, quòd Horizonti æquidiſtet, ita statuatur, vt recta H I, lineam meridia-<lb/>nam (cuius inuentionem in plano, quod æquidiſtet Horizonti, tradidimus &amp; </s>
  <s xml:id="echoid-s9421" xml:space="preserve">in commentarĳs in ſphæram, <lb/>cum de Meridiano circulo ageremus, &amp; </s>
  <s xml:id="echoid-s9422" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s9423" xml:space="preserve">23. </s>
  <s xml:id="echoid-s9424" xml:space="preserve">ſuperioris lib.) </s>
  <s xml:id="echoid-s9425" xml:space="preserve">referat, punctum{q́ue} H, ad <lb/>auſtrum, at que I, ad boream vergat. </s>
  <s xml:id="echoid-s9426" xml:space="preserve">Cum enim omnes circuli horarum à meridie, vel media nocte ducan-<lb/>tur per axem mundi, fit vt radius Solis in quocunque illorum exiſtentis non recedat ab axe, &amp; </s>
  <s xml:id="echoid-s9427" xml:space="preserve">communi <lb/>ſectione illius, ac plani horologĳ, cum &amp; </s>
  <s xml:id="echoid-s9428" xml:space="preserve">axis, &amp; </s>
  <s xml:id="echoid-s9429" xml:space="preserve">communis hęc ſectio, nempe linea eius horaria, in eodem <lb/>
<anchor type="note" xlink:label="note-0166-08a" xlink:href="note-0166-08"/>
circulo horario existant. </s>
  <s xml:id="echoid-s9430" xml:space="preserve">Quare vmbra axis in lineam horariam illius circuli proĳcietur. </s>
  <s xml:id="echoid-s9431" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9432" xml:space="preserve">ſic de cęte-<lb/>ris. </s>
  <s xml:id="echoid-s9433" xml:space="preserve">Hinc fit, vt &amp; </s>
  <s xml:id="echoid-s9434" xml:space="preserve">vmbra verticis D, ſtyli D G, recti ad planum horologĳ in puncto G, hoc eſt, vmbra cen <lb/>tri mundi (eſt enim vertex ſtyli idem, quod centrum mundi, per propoſ. </s>
  <s xml:id="echoid-s9435" xml:space="preserve">2. </s>
  <s xml:id="echoid-s9436" xml:space="preserve">libri ſuperioris) in eaſdem li-<lb/>
<anchor type="note" xlink:label="note-0166-09a" xlink:href="note-0166-09"/>
neas horarias proĳciatur, quia &amp; </s>
  <s xml:id="echoid-s9437" xml:space="preserve">vertex D, in axe exiſtit, cuius quidem omnium punctorum vmbrę in li-<lb/>neas horarias cadunt, vt dictum eſt: </s>
  <s xml:id="echoid-s9438" xml:space="preserve">quod etiam propoſ. </s>
  <s xml:id="echoid-s9439" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9440" xml:space="preserve">pręcedentis lib. </s>
  <s xml:id="echoid-s9441" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s9442" xml:space="preserve">Itaque vſus <lb/>
<anchor type="note" xlink:label="note-0166-10a" xlink:href="note-0166-10"/>
borologĳ Aſtronomici eſt, vt ex vmbra ſtyli in eius lineas horarias cadente intelligamus, quot horę tran-<lb/>ſactæ ſint à meridie, vel media nocte proxima, &amp; </s>
  <s xml:id="echoid-s9443" xml:space="preserve">quot ſuperſint ad ſequentem meridiem, vel mediam no-<lb/>ctem. </s>
  <s xml:id="echoid-s9444" xml:space="preserve">Matutino enim tempore, ſi vmbra cadat v.</s>
  <s xml:id="echoid-s9445" xml:space="preserve">g. </s>
  <s xml:id="echoid-s9446" xml:space="preserve">in lineam horæ 7. </s>
  <s xml:id="echoid-s9447" xml:space="preserve">pro comperto habebimus, elapſas <lb/>eſſeſeptem horas à med. </s>
  <s xml:id="echoid-s9448" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9449" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9450" xml:space="preserve">ſupcreſſe quinque vſque ad proximum meridiem, &amp; </s>
  <s xml:id="echoid-s9451" xml:space="preserve">c.</s>
  <s xml:id="echoid-s9452" xml:space="preserve"/>
</p>
<div xml:id="echoid-div529" type="float" level="2" n="6">
<note position="left" xlink:label="note-0166-06" xlink:href="note-0166-06a" xml:space="preserve">Quomodo ho-<lb/>rologiũ hotizõ <lb/>tale una cũ axe <lb/>mundi collocã <lb/>dum ſit, ut ho-<lb/>ras monſtret à <lb/>mer. vel med. <lb/>noc.</note>
<note position="left" xlink:label="note-0166-07" xlink:href="note-0166-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0166-08" xlink:href="note-0166-08a" xml:space="preserve">Si ſtylus D G, <lb/>in G, rectus ſit <lb/>ad planum ho-<lb/>rologit, indica-<lb/>bit umbra ſo-<lb/>lius uerticis D, <lb/>horas à mer. uel <lb/>med. noc.</note>
<note position="left" xlink:label="note-0166-09" xlink:href="note-0166-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0166-10" xlink:href="note-0166-10a" xml:space="preserve">Vſus horologij <lb/>Aſtronomici.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9453" xml:space="preserve">IAM verò ſi &amp; </s>
  <s xml:id="echoid-s9454" xml:space="preserve">dimidiatas horas, &amp; </s>
  <s xml:id="echoid-s9455" xml:space="preserve">earum quartas partes, immo &amp; </s>
  <s xml:id="echoid-s9456" xml:space="preserve">octauas, vel quaſuis alias in <lb/>
<anchor type="note" xlink:label="note-0166-11a" xlink:href="note-0166-11"/>
horologio deſcribere placuerit, diuidendę erunt ſingulæ partes circuli ex E, deſcripti in dictas partes, vt <lb/>in duas, quatuor, octo, &amp; </s>
  <s xml:id="echoid-s9457" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9458" xml:space="preserve">reliqua autem peragenda, vt prius. </s>
  <s xml:id="echoid-s9459" xml:space="preserve">Quod etiam, in alĳs horologĳs, quę ſequu@ <lb/>tur, obſeruandum erit.</s>
  <s xml:id="echoid-s9460" xml:space="preserve"/>
</p>
<div xml:id="echoid-div530" type="float" level="2" n="7">
<note position="left" xlink:label="note-0166-11" xlink:href="note-0166-11a" xml:space="preserve">Qua ratione di <lb/>midia@æ horæ, <lb/>&amp; earum quar-<lb/>tæ pattes, vel <lb/>quæcunque alię <lb/>in horologio de <lb/>ſeribantur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9461" xml:space="preserve">HIC autem, &amp; </s>
  <s xml:id="echoid-s9462" xml:space="preserve">in ſequentibus omnibus, magnopere obſeruandum eſt, lineam quamcunque in horolo-
<pb o="147" file="0167" n="167" rhead="LIBER SECVNDVS."/>
gio, quę æquinoctialem lineam ſecat, eum ſemicirculũ cœleſtem referre, cuius communis ſectio facta in cir-<lb/>
<anchor type="note" xlink:label="note-0167-01a" xlink:href="note-0167-01"/>
culo, quem ex E, centro Aequatoris, atque in eius plano deſcripſimus, (ſi nimirum eius centrum E, cum <lb/>centro mundi D, coniungatur) per centrum E, tranſit, antequam æquinoctiali lineę in horologio oc-<lb/>currat: </s>
  <s xml:id="echoid-s9463" xml:space="preserve">nimirum rectam H A, eſſe horam primam à meridie, hoc eſt, referre ſemicirculum illum cœle-<lb/>ſtem, in quo Sol hora prima à meridie exiſtit; </s>
  <s xml:id="echoid-s9464" xml:space="preserve">quia in A, cadit O E, per centrum E, ducta, quæ quidẽ O E, <lb/>communis ſectio eſt ſemicirculi horæ 1. </s>
  <s xml:id="echoid-s9465" xml:space="preserve">à meridie per punctum O, ducti, tranſit{q́ue} per centrũ E, priuſquam <lb/>ęquinoctialem lineam ſecat in A; </s>
  <s xml:id="echoid-s9466" xml:space="preserve">vt conſtat, ſi circulus ex E, deſcriptus concipiatur eſſe in plano Aequa <lb/>toris, centrum{q́ue} E, cum centro mundi D, coniunctum. </s>
  <s xml:id="echoid-s9467" xml:space="preserve">Cauſa huius rei eſt, quia Sol proĳcit radium ſuum <lb/>prius ad centrum mundi, ſeu verticem ſtyli, antequam vmbra ſtyli in horologĳ planum cadat, vt perſpi-<lb/>cuum eſt. </s>
  <s xml:id="echoid-s9468" xml:space="preserve">Hac rationc erit quoque recta H K, hora 7. </s>
  <s xml:id="echoid-s9469" xml:space="preserve">à media nocte, hoc eſt, illum ſemicirculum cœle-<lb/>
<anchor type="note" xlink:label="note-0167-02a" xlink:href="note-0167-02"/>
ſtem repræſentabit, in quo Sol exiſtit hora 7. </s>
  <s xml:id="echoid-s9470" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s9471" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9472" xml:space="preserve">quia in K, cadit V E, per centrum E, ducta, quæ <lb/>quidem V E, communis ſectio eſt ſemicir culi horæ 7. </s>
  <s xml:id="echoid-s9473" xml:space="preserve">à media nocte, per punctum V, ducti, tranſit{q́ue} per <lb/>centrum E, antequam lineam ęquinoctialem ſecat in k, vt perſpicuum eſt; </s>
  <s xml:id="echoid-s9474" xml:space="preserve">atque ita de cęteris.</s>
  <s xml:id="echoid-s9475" xml:space="preserve"/>
</p>
<div xml:id="echoid-div531" type="float" level="2" n="8">
<note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">Quem ſemicir-<lb/>culum cęleſtem <lb/>quælibet linea <lb/>in horologio <lb/>repræſentet.</note>
<note position="left" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s9476" xml:space="preserve">NON eſt etiam omittendum, lineam cuiuſcunque horę à meridie vltra centrum horologĳ productam <lb/>
<anchor type="note" xlink:label="note-0167-03a" xlink:href="note-0167-03"/>
monſtrare eiuſdem numeri horam à media nocte, &amp; </s>
  <s xml:id="echoid-s9477" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s9478" xml:space="preserve">Quod ita demonſtrabimus. </s>
  <s xml:id="echoid-s9479" xml:space="preserve">Sumatur exem-<lb/>pli gratia, circulus horæ quintæ à mer. </s>
  <s xml:id="echoid-s9480" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9481" xml:space="preserve">med. </s>
  <s xml:id="echoid-s9482" xml:space="preserve">nocte faciens in horologio lineam eiuſdem horæ per centrũ <lb/>H, ductam. </s>
  <s xml:id="echoid-s9483" xml:space="preserve">Quoniam igitur, ſi Sol in polo arctico poneretur, vmbra ſtyli caderet in punctum H, cum ra-<lb/>dius Solis tunc idem eſſet, qui axis mundi, qui quidem per verticem ſtyli ductus in puncto H, occurrit pla <lb/>no horologĳ, efficitur, vt Sole existente in ſemicirculo dicti circuli, qui oceidentalior eſt, quàm Meridia-<lb/>nus, vmbra ſtyli cadat in partem oppoſitam, nempe in eam partem lineæ horę quintæ, quæ orientalior eſt <lb/>
<anchor type="note" xlink:label="note-0167-04a" xlink:href="note-0167-04"/>
in horologio, quàm linea meridiana; </s>
  <s xml:id="echoid-s9484" xml:space="preserve">exiſtente autem Sole in eiuſdem circuli altero ſemicirculo, quiorien <lb/>talior eſt Meridiano, vmbra ſtyli in partem eiuſdem lineę horę quintæ, quæ occidentalior eſt, quàm linea <lb/>meridiana, cadat. </s>
  <s xml:id="echoid-s9485" xml:space="preserve">Semper enim vmbra in dictam lineam cadit, dum Sol in dicto circulo exiſtit, vt pro-<lb/>poſ. </s>
  <s xml:id="echoid-s9486" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9487" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9488" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s9489" xml:space="preserve">Cum ergo ſemicirculus occidentalis pertineat ad horam quintam pome <lb/>ridianam, &amp; </s>
  <s xml:id="echoid-s9490" xml:space="preserve">orientalis ad quintam poſt mediam noctem, indicabit orientalis portio illius lineæ, quæni-<lb/>mirum ex centro H, tendit ad partem orienta lem horologĳ, (Diuidit porrò linea meridiana horologium <lb/>totum in partem orientalem, &amp; </s>
  <s xml:id="echoid-s9491" xml:space="preserve">occidentalem, quemadmodum &amp; </s>
  <s xml:id="echoid-s9492" xml:space="preserve">Meridianus totam ſphęram cœleſtem <lb/>in hemiſphærium orientale, &amp; </s>
  <s xml:id="echoid-s9493" xml:space="preserve">occidentale partitur) horam quintam à meridie, reliqua autem portio eiuſ-<lb/>dem lineæ in partem occidentalem vergens, horam quintam à media nocte. </s>
  <s xml:id="echoid-s9494" xml:space="preserve">Eadem{q́ue} ratio eſt de cęteris <lb/>lineis, in alĳs etiam horologĳs, quæ non ſunt horizontalia.</s>
  <s xml:id="echoid-s9495" xml:space="preserve"/>
</p>
<div xml:id="echoid-div532" type="float" level="2" n="9">
<note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">Linea cuiuſuis <lb/>horę à meridie <lb/>vltra centrum <lb/>horologij pro-<lb/>ducta indicat <lb/>eiuſdem nume-<lb/>ri horã à med. <lb/>noc. &amp; contra.</note>
<note position="left" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s9496" xml:space="preserve">IDEM hac etiam ratione oſtendemus, &amp; </s>
  <s xml:id="echoid-s9497" xml:space="preserve">breuius. </s>
  <s xml:id="echoid-s9498" xml:space="preserve">Quoniam vmbra styli ante meridiem cadit in par <lb/>tem occidentalem horologĳ, poſt meridiem verò in orientalem, cum in contrariam ſemper partem Solis <lb/>proĳciatur, pertinebunt omnes lineæ horariæ in parte occidentali (quam quidem linea meridiana ab <lb/>orientali dirimit in omni horologio) in centro H, terminatæ, ad horas antemeridianas, ſiue poſt mediam <lb/>noctem, reliquæ verò in orientali parte ad pomeridianas. </s>
  <s xml:id="echoid-s9499" xml:space="preserve">Cum ergo horariæ lineæ in parte orientali horo-<lb/>logĳ productæ vltra centrum exhibeant lineas earundem horarum in parte occidentali, &amp; </s>
  <s xml:id="echoid-s9500" xml:space="preserve">econtrario, <lb/>perſpicuum eſt, quod proponitur.</s>
  <s xml:id="echoid-s9501" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s9502" xml:space="preserve">HINC colligitur quemcunque circulum maximum per polos mundi tranſeuntem facere in horologio <lb/>
<anchor type="note" xlink:label="note-0167-06a" xlink:href="note-0167-06"/>
ſectionem, lineam rectam, cuius vna portio in centro terminata pertinet ad vnum ſemicirculum, &amp; </s>
  <s xml:id="echoid-s9503" xml:space="preserve">al-<lb/>tera ad alterum. </s>
  <s xml:id="echoid-s9504" xml:space="preserve">Hoc enim demonſtratum eſt in circulis horarum à meridie &amp; </s>
  <s xml:id="echoid-s9505" xml:space="preserve">media nocte. </s>
  <s xml:id="echoid-s9506" xml:space="preserve">Idem{q́ue} ve-<lb/>
<anchor type="note" xlink:label="note-0167-07a" xlink:href="note-0167-07"/>
rum eſt de circulis Meridianis, de quibus agemus propoſ. </s>
  <s xml:id="echoid-s9507" xml:space="preserve">6. </s>
  <s xml:id="echoid-s9508" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s9509" xml:space="preserve">Item de Verticalibus circulis, de <lb/>quibus propoſ. </s>
  <s xml:id="echoid-s9510" xml:space="preserve">4. </s>
  <s xml:id="echoid-s9511" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s9512" xml:space="preserve">diſputabimus, dummodo loco poli mundi accipiamus verticem capitis, ſeu Ze-<lb/>nith, hoc eſt, polum Horizontis, &amp; </s>
  <s xml:id="echoid-s9513" xml:space="preserve">in horologio loco centri horologĳ ſumamus punctũ verticale, in quod <lb/>cadit axis Horizontis, cuiuſmodi eſt in horizontali horologio, quod deſcripſimus, punctum G.</s>
  <s xml:id="echoid-s9514" xml:space="preserve"/>
</p>
<div xml:id="echoid-div533" type="float" level="2" n="10">
<note position="right" xlink:label="note-0167-06" xlink:href="note-0167-06a" xml:space="preserve">Quilibet circu-<lb/>lus maximus P <lb/>polos mũdi du-<lb/>ctus facit in ho <lb/>rologio rectam <lb/>lineã, cuius una <lb/>portio in cen-<lb/>tro terminata <lb/>pertinet ad vnũ <lb/>ſemicirculũ, &amp; <lb/>altera ad alterũ.</note>
<note position="left" xlink:label="note-0167-07" xlink:href="note-0167-07a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s9515" xml:space="preserve">EX his perfacile iudicare poterimus, quęnam lineæ horarię ad horas à meridie pertineant, &amp; </s>
  <s xml:id="echoid-s9516" xml:space="preserve">quæ <lb/>ad horas à media nocte. </s>
  <s xml:id="echoid-s9517" xml:space="preserve">Quoniam enim, ſi circulus ex E, deſcriptus in proprio ſitu collocetur, punctum <lb/>
<anchor type="note" xlink:label="note-0167-08a" xlink:href="note-0167-08"/>
N, Meridianum ſecat ſupra Horizontem, pertinebit illud ad horam 12. </s>
  <s xml:id="echoid-s9518" xml:space="preserve">meridiei, ita vt recta NE, ſit <lb/>communis ſectio Meridiani, ſeu circuli horæ 12. </s>
  <s xml:id="echoid-s9519" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s9520" xml:space="preserve">Cum ergo NE, per centrum E, tranſeat, at-<lb/>que æquinoctialem lineam ſecet in I, indicabit recta H I E, horam 12. </s>
  <s xml:id="echoid-s9521" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s9522" xml:space="preserve">reliqua eius portio <lb/>vltra centrum horologĳ H, horam 12. </s>
  <s xml:id="echoid-s9523" xml:space="preserve">mediæ noctis. </s>
  <s xml:id="echoid-s9524" xml:space="preserve">Eadem ratione pertinebunt rectę H A, H B, &amp; </s>
  <s xml:id="echoid-s9525" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0167-09a" xlink:href="note-0167-09"/>
cæteræ in parte orientali horologĳ poſitæ, ad horas poſt meridiem: </s>
  <s xml:id="echoid-s9526" xml:space="preserve">quia referunt ſemicirculos horarios <lb/>ſectionum O E, Q E, &amp; </s>
  <s xml:id="echoid-s9527" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9528" xml:space="preserve">qui quidem horas à meridie indicant in circulo ex E, deſcripto. </s>
  <s xml:id="echoid-s9529" xml:space="preserve">Denique li-<lb/>neę in parte occidentali horologĳ poſitæ, id eſt, ad dextram lineæ ipſius meridianæ, horas à media nocte ſi-<lb/>gnificabunt: </s>
  <s xml:id="echoid-s9530" xml:space="preserve">quoniam referunt ſemicirculos horarios, quorum ſectiones in circulo ex E, deſcripto rece-<lb/>dunt à recta N E, verſus orientalem plagam, monſtrant{q́ue} horas ante meridiem, vel à@media nocte.</s>
  <s xml:id="echoid-s9531" xml:space="preserve"/>
</p>
<div xml:id="echoid-div534" type="float" level="2" n="11">
<note position="right" xlink:label="note-0167-08" xlink:href="note-0167-08a" xml:space="preserve">Qua ratione iu <lb/>dicandum ſit, <lb/>quæ lineæ hora <lb/>riæ pertineant <lb/>ad horas à mer. <lb/>&amp; quæ ad horas <lb/>à med. noc. in <lb/>horologio de-<lb/>ſcripto.</note>
<note position="left" xlink:label="note-0167-09" xlink:href="note-0167-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s9532" xml:space="preserve">HOC ſi attentè conſideretur, cognoſcemus facillimè etiam in omnibus alĳs horologĳs, de quibus in <lb/>
<anchor type="note" xlink:label="note-0167-10a" xlink:href="note-0167-10"/>
ſequentibus agemus, quęnam horæ ſint à meridie numerandæ, &amp; </s>
  <s xml:id="echoid-s9533" xml:space="preserve">quæ à media nocte.</s>
  <s xml:id="echoid-s9534" xml:space="preserve"/>
</p>
<div xml:id="echoid-div535" type="float" level="2" n="12">
<note position="right" xlink:label="note-0167-10" xlink:href="note-0167-10a" xml:space="preserve">Quomodo indi <lb/>candum ſit in <lb/>omni horolo-<lb/>gio, quæ lineæ <lb/>horariæ ad ho-<lb/>ras à mer. &amp; quę <lb/>ad horas à med. <lb/>noc. pertinean@.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9535" xml:space="preserve">MONENDVS quoque lector eſt, nos hactenus horologium horizontale conſtruxiſſe in plana qua-<lb/>cunque ſuperficie, vt illud poſtea in proprio ſitu collocetur, vel in planum aliquod ſtabile, quod Horizonti <lb/>ſit parallelum, transferatur, ita vt recta H E, ſit linea meridiana, &amp; </s>
  <s xml:id="echoid-s9536" xml:space="preserve">punctum H, ad auſtrum, punctum <lb/>verò E, ad boream vergat, velut in hoc ſcholio tradidimus. </s>
  <s xml:id="echoid-s9537" xml:space="preserve">Quòd ſiplanum aliquod ſtabile, quod Hori-
<pb o="148" file="0168" n="168" rhead="GNOMONICES"/>
zonti æquidiſtat, nobis offeratur, vt in eo horologium depingamus, efficiemus illud hac arte. </s>
  <s xml:id="echoid-s9538" xml:space="preserve">Inuenta in <lb/>
<anchor type="note" xlink:label="note-0168-01a" xlink:href="note-0168-01"/>
plano linea meridiana H E, ſecabimus eam ad angulos rectos in I, per rectam F K, quæ linea æquinoctia-<lb/>lis erit. </s>
  <s xml:id="echoid-s9539" xml:space="preserve">Deinde ex I, verſus austrum vſque ad H, transferemus ex portione Analemmatis rectam I H, <lb/>&amp; </s>
  <s xml:id="echoid-s9540" xml:space="preserve">rectam I E, verſus boream accipiemus æqualem rectæ I E, ex portione eadem Analemmatis. </s>
  <s xml:id="echoid-s9541" xml:space="preserve">Po-<lb/>ſtremo ex E, deſcripto circulo, eo{q́ue} diuiſo in 24. </s>
  <s xml:id="echoid-s9542" xml:space="preserve">partes æquales, reliqua abſoluemus, vt prius.</s>
  <s xml:id="echoid-s9543" xml:space="preserve"/>
</p>
<div xml:id="echoid-div536" type="float" level="2" n="13">
<note position="left" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">Qua ratione in <lb/>plano ſtabili, qd <lb/>Horizonti æqui <lb/>diſtet, horolo-<lb/>gium deſcriben <lb/>dum ſit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9544" xml:space="preserve">SED ſi idem horologium deſcribere velimus in dato plano, ſine portione Analemmatis ſeorſum con <lb/>
<anchor type="note" xlink:label="note-0168-02a" xlink:href="note-0168-02"/>
ſtructa, ad quamcunque ſtyli longitudinem, cuius etiam locus datus ſit, efficiemus id hac ratione. </s>
  <s xml:id="echoid-s9545" xml:space="preserve">Sit lon-<lb/>gitudo ſtyli data D G, eius{q́ue} locus in plano horologĳ ſit punctum G. </s>
  <s xml:id="echoid-s9546" xml:space="preserve">Si igitur planum horologii fuerit <lb/>quodcunque, vt horologium in co deſcriptum in proprio deinde ſitu collocetur, vel in planum ſtabile, quod <lb/>Horizonti ſit parallelum, transferatur, vt proxime diximus, ducemus per G, locum ſtyli lineam rectam <lb/>
<anchor type="note" xlink:label="note-0168-03a" xlink:href="note-0168-03"/>
vtcunque M N, pro linea meridiana: </s>
  <s xml:id="echoid-s9547" xml:space="preserve">Si autem planum horologĳ ſtabile proponatur, Horizonti{q́ue} paral-<lb/>
<anchor type="figure" xlink:label="fig-0168-01a" xlink:href="fig-0168-01"/>
<anchor type="note" xlink:label="note-0168-04a" xlink:href="note-0168-04"/>
<anchor type="note" xlink:label="note-0168-05a" xlink:href="note-0168-05"/>
lelum, reperiemus, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s9548" xml:space="preserve">23. </s>
  <s xml:id="echoid-s9549" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9550" xml:space="preserve">ſcripſimus, vel alibi, lineam meridianã <lb/>in propoſito plano, cui (ſi forte non tranſit per G, locum ſtyli) per G, locũ ſtyli parallelam ducemus MN, <lb/>pro linea meridiana. </s>
  <s xml:id="echoid-s9551" xml:space="preserve">Ad hanc deinde meridianam lineam M N, excitabimus in G, perpendicularem <lb/>
<anchor type="note" xlink:label="note-0168-06a" xlink:href="note-0168-06"/>
B G D, abſcindemus{q́ue} G D, dato ſtylo ęqualem. </s>
  <s xml:id="echoid-s9552" xml:space="preserve">Ex centro autem D, arcum circuli deſcribemus A B C, <lb/>in quo à recta D G B, verſus partes auſtrales, quæ nunc ponantur vergere verſus M, numerabimus com-<lb/>plementum altitudinis poli B A, &amp; </s>
  <s xml:id="echoid-s9553" xml:space="preserve">verſus boreales partes, hoc eſt, verſus N, ipſam altitudinem poli <lb/>B C; </s>
  <s xml:id="echoid-s9554" xml:space="preserve">ductis{q́ue} rectis D A, D C, ſecabimus lineam meridianam in punctis H, &amp; </s>
  <s xml:id="echoid-s9555" xml:space="preserve">I. </s>
  <s xml:id="echoid-s9556" xml:space="preserve">Poſt hęc per I, excita-<lb/>bimus ad meridianam lineam per pendicularem F K, pro linea ęquinoctiali. </s>
  <s xml:id="echoid-s9557" xml:space="preserve">Poſtremo ſumpta recta I E, <lb/>æquali ipſi I D, deſcribemus ex E, circulum cuiuſcunque magnitudinis, quo diuiſo in partes 24. </s>
  <s xml:id="echoid-s9558" xml:space="preserve">æquales, <lb/>initio facto à linea meridiana, reliqua perficiemus, vt ante docuimus in hac propoſ.</s>
  <s xml:id="echoid-s9559" xml:space="preserve"/>
</p>
<div xml:id="echoid-div537" type="float" level="2" n="14">
<note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>ad datam ſtyli <lb/>longitudinem, <lb/>cuius etiam lo-<lb/>cus datus ſit, ſi-<lb/>ne portione A-<lb/>nalem matis ſe-<lb/>orſum conſtru-<lb/>@@@.</note>
<note position="left" xlink:label="note-0168-03" xlink:href="note-0168-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a">
    <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0168-01"/>
  </figure>
<note position="left" xlink:label="note-0168-04" xlink:href="note-0168-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0168-05" xlink:href="note-0168-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0168-06" xlink:href="note-0168-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s9560" xml:space="preserve">DEMONSTRATIO huius deſcriptionis facilis eſt. </s>
  <s xml:id="echoid-s9561" xml:space="preserve">Si enim linea meridiana M N, proprium <lb/>
<anchor type="note" xlink:label="note-0168-07a" xlink:href="note-0168-07"/>
habeat ſitum, it a vt M, ad auſtrum, &amp; </s>
  <s xml:id="echoid-s9562" xml:space="preserve">N, in boream vergat, triangulum{q́ue} H D I, rectum ſtatuatur ad <lb/>planum horologĳ, it a vt in plano Meridiani circuli ſitum habeat; </s>
  <s xml:id="echoid-s9563" xml:space="preserve">quoniam angulus H D G, per conſtru-<lb/>
<anchor type="note" xlink:label="note-0168-08a" xlink:href="note-0168-08"/>
ctionem, æqualis eſt complemento altitudinis poli, erit reliquus D H G, altitudini poli æqualis. </s>
  <s xml:id="echoid-s9564" xml:space="preserve">Rurſus <lb/>quia, per conſtructionem I D G, eſt angulus altitudinis poli, erit reliquus D I G, complemento altitudinis <lb/>poli æqualis. </s>
  <s xml:id="echoid-s9565" xml:space="preserve">Sumpto igitur D, vertice ſtyli pro centro mundi, erit D H, faciens cum linea meridiana in <lb/>H, angulum altitudinis poli, axis mundi occurrens plano horologĳ in H, centro horologĳ. </s>
  <s xml:id="echoid-s9566" xml:space="preserve">Recta autem <lb/>D I, conſtituens cum eadem linea meridiana in I, angulum complementi altitudinis poli, erit communis ſe <lb/>ctio Meridiani atque Aequatoris, cum eiuſmodi ſectio in ſphæra cum meridiana linea horizontali efficiat <lb/>ſemper angulum complemento altitudinis poli ęqualem; </s>
  <s xml:id="echoid-s9567" xml:space="preserve">cum axe vero angulum rectum, cuiuſinodi eſt an-<lb/>gulus H D I, conflatus ex angulo altitudinis poli, &amp; </s>
  <s xml:id="echoid-s9568" xml:space="preserve">angulo complementi eiuſdem altitudinis poli. </s>
  <s xml:id="echoid-s9569" xml:space="preserve">Occur-<lb/>rit igitur Aequator plano horologĳ in puncto I, ac proinde, vt ſupra demonſtratum est, erit recta F K, <lb/>linea æquinoctialis. </s>
  <s xml:id="echoid-s9570" xml:space="preserve">Recta autem D G, erit communis ſectio Meridiani ac Verticalis. </s>
  <s xml:id="echoid-s9571" xml:space="preserve">Reliqua omnia de-<lb/>monſtrabuntur, vt prius.</s>
  <s xml:id="echoid-s9572" xml:space="preserve"/>
</p>
<div xml:id="echoid-div538" type="float" level="2" n="15">
<note position="left" xlink:label="note-0168-07" xlink:href="note-0168-07a" xml:space="preserve">Demonſtratio <lb/>huius deſcriptio <lb/>ni@.</note>
<note position="left" xlink:label="note-0168-08" xlink:href="note-0168-08a" xml:space="preserve">50</note>
</div>
<pb o="149" file="0169" n="169" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s9573" xml:space="preserve">QVONIAM verò in omnibus modis, quibus hactenus horizontale horologium deſcripſimus, hoc <lb/>
<anchor type="note" xlink:label="note-0169-01a" xlink:href="note-0169-01"/>
incommodi accidit, vt vix lineæ illæ horariæ, quæ proximæ ſunt lineæ horæ 6. </s>
  <s xml:id="echoid-s9574" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9575" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9576" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9577" xml:space="preserve">duci poſ-<lb/>ſint, propterea quòd lineam æquinoctialem in remotiſſimis punctis interſecant, monſtrabo aliam viam, &amp; </s>
  <s xml:id="echoid-s9578" xml:space="preserve"><lb/>nouam illam quidem à nemine antea (quod ſciam) tentatam, qua horarias lineas omnes ducere poſſimus <lb/>per puncta cuiuſdam ellipſis in plano horologĳ deſcriptæ, etiamſi nulla puncta in æquinoctiali linea habea <lb/>mus: </s>
  <s xml:id="echoid-s9579" xml:space="preserve">quæ quidem via omnino neceſſaria eſt ad horologia declinantia à Verticali, ſiue ſimul ad Horizon-<lb/>tem inclinata ſint, ſiue non, recte delineanda: </s>
  <s xml:id="echoid-s9580" xml:space="preserve">quoniam in his linearũ horariarũ nonnullæ æquidiſtantes <lb/>ferè ſunt interdũ lineæ æquinoctiali, vt ſuo loco manifeſtum erit. </s>
  <s xml:id="echoid-s9581" xml:space="preserve">Quamuis enim hoc idem alia ratione <lb/>præstiterit Andreas Schonerus, vt ſupra diximus, nullam tamen eius deſcriptionis demonſtrationem <lb/>nec ipſe, nec vllus alius confecit. </s>
  <s xml:id="echoid-s9582" xml:space="preserve">Via autem à nobis inuenta eiuſmodi eſt.</s>
  <s xml:id="echoid-s9583" xml:space="preserve"/>
</p>
<div xml:id="echoid-div539" type="float" level="2" n="16">
<note position="right" xlink:label="note-0169-01" xlink:href="note-0169-01a" xml:space="preserve">Alia deſcriptio <lb/>horologij hori-<lb/>zontalis Aſtro-<lb/>nomici noua &amp; <lb/>pulcherrima be <lb/>neficio Ellipſis, <lb/>ſine punctis in <lb/>linea ęquino-<lb/>ctiali inuentis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s9584" xml:space="preserve">DATO ſtylo G D, eius{q́ue} loco in G, ducatur per G, linea meridiana H I. </s>
  <s xml:id="echoid-s9585" xml:space="preserve">Conſtituto rurſus ad ſty-<lb/>lum G D, qui perpendicularis ſit ad meridianam lineam, angulo complementi altitudinis poli G D H, &amp; </s>
  <s xml:id="echoid-s9586" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0169-01a" xlink:href="fig-0169-01"/>
<anchor type="note" xlink:label="note-0169-03a" xlink:href="note-0169-03"/>
<anchor type="note" xlink:label="note-0169-04a" xlink:href="note-0169-04"/>
<anchor type="note" xlink:label="note-0169-05a" xlink:href="note-0169-05"/>
angulo altitudinis poli G D I, ita vt H D, ſit axis mundi, &amp; </s>
  <s xml:id="echoid-s9587" xml:space="preserve">H, centrum horologĳ, punctum autem I, il-<lb/>lud, per quod linea æquinoctialis ducenda eſt ad HI, perpendicularis, veluti in præcedenti deſcriptione de-<lb/>monstrauimus; </s>
  <s xml:id="echoid-s9588" xml:space="preserve">ſumemus in axe H D, producto quodcunque punctum A, &amp; </s>
  <s xml:id="echoid-s9589" xml:space="preserve">ab eo ad H A, perpendicula <lb/>rem educemus AB, vt ſit A B, noua quædam communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s9590" xml:space="preserve">Aequatoris. </s>
  <s xml:id="echoid-s9591" xml:space="preserve">Quo autem re-<lb/>
<anchor type="note" xlink:label="note-0169-06a" xlink:href="note-0169-06"/>
motius ſumptum fuerit punctũ A, eò accur atius horologium deſcribetur: </s>
  <s xml:id="echoid-s9592" xml:space="preserve">Vnde ſi ſtylus datus tantus fue <lb/>rit, vt recta H I, notabilem habeat longitudinem, contenti erimus punctis D, &amp; </s>
  <s xml:id="echoid-s9593" xml:space="preserve">I. </s>
  <s xml:id="echoid-s9594" xml:space="preserve">Sed quoniam in exem-<lb/>plo præcedentis deſcriptionis recta H I, eſt nimis breuis, accepimus propterea alia puncta remotiora A, <lb/>&amp; </s>
  <s xml:id="echoid-s9595" xml:space="preserve">B. </s>
  <s xml:id="echoid-s9596" xml:space="preserve">Deinde abſciſſa recta H C, ipſi A B, æquali, deſcribantur ex centro H, ad interualla H B, H C, <lb/>(quorum illud eſt inter centrum horologĳ, &amp; </s>
  <s xml:id="echoid-s9597" xml:space="preserve">punctum B, per quod æquinoctialis linea in linea meridiana <lb/>ducitur, hoc vero æquale eſt communi ſectioni A B, Meridiani, &amp; </s>
  <s xml:id="echoid-s9598" xml:space="preserve">Aequatoris inter meridianam lineã, <lb/>&amp; </s>
  <s xml:id="echoid-s9599" xml:space="preserve">axem) duo circuli, qui (ducta prius diametro S T, ad meridianam lineam H B, perpendiculari) in 24. <lb/></s>
  <s xml:id="echoid-s9600" xml:space="preserve">partes æquales ſecentur, initio facto à meridiana linea H B, vel à diametro S T. </s>
  <s xml:id="echoid-s9601" xml:space="preserve">Satis autem eſt, ſi exte-<lb/>rior diuidatur. </s>
  <s xml:id="echoid-s9602" xml:space="preserve">Nam rectæ ex punctis diuiſionum ad centrum H, ductæ ſecabunt interiorem quoque in <lb/>24. </s>
  <s xml:id="echoid-s9603" xml:space="preserve">partes ęquales, vt ad finem commentariorum in ſphæram demonſtrauimus. </s>
  <s xml:id="echoid-s9604" xml:space="preserve">Poſt hæc ſumantur duo <lb/>puncta diuiſionum reſpondentia, qualia ſunt v. </s>
  <s xml:id="echoid-s9605" xml:space="preserve">g. </s>
  <s xml:id="echoid-s9606" xml:space="preserve">F, &amp; </s>
  <s xml:id="echoid-s9607" xml:space="preserve">K: </s>
  <s xml:id="echoid-s9608" xml:space="preserve">Sunt enim in eadem recta F k, ex F, ad cen-
<pb o="150" file="0170" n="170" rhead="GNOMONICES"/>
trum H, ducta, &amp; </s>
  <s xml:id="echoid-s9609" xml:space="preserve">vtrumque in ſuo circulo quatuor horis abeſt à linca meridiana) &amp; </s>
  <s xml:id="echoid-s9610" xml:space="preserve">per F, punctum ex-<lb/>terioris circuli ducatur diametro S T, quæ meridianam lineam ad rectos angulos ſecat, parallela occulta <lb/>F L; </s>
  <s xml:id="echoid-s9611" xml:space="preserve">quod facile fiet, ſi recta occulta ducatur ex F, ad punctum M, quod tanto interuallo abſit à punct@ <lb/>
<anchor type="figure" xlink:label="fig-0170-01a" xlink:href="fig-0170-01"/>
<anchor type="note" xlink:label="note-0170-01a" xlink:href="note-0170-01"/>
<anchor type="note" xlink:label="note-0170-02a" xlink:href="note-0170-02"/>
<anchor type="note" xlink:label="note-0170-03a" xlink:href="note-0170-03"/>
S, quanto punctum F, à puncto T, abeſt. </s>
  <s xml:id="echoid-s9612" xml:space="preserve">Rectæ enim F M, T S, parallelę erunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s9613" xml:space="preserve">27. <lb/></s>
  <s xml:id="echoid-s9614" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9615" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9616" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9617" xml:space="preserve">ob æqualitatem arcuum F T, M S: </s>
  <s xml:id="echoid-s9618" xml:space="preserve">Item per K, punctum circuli interioris agatur meridianæ <lb/>lineę H B, parallela occulta K L; </s>
  <s xml:id="echoid-s9619" xml:space="preserve">quod facile etiã fiet, ſi recta occulta ducatur ex K, ad punctum N, quod <lb/>
<anchor type="note" xlink:label="note-0170-04a" xlink:href="note-0170-04"/>
tanto ſpatio diſtet à puncto R, quanto abeſt ab eodem punctum K: </s>
  <s xml:id="echoid-s9620" xml:space="preserve">Secet autem recta K L, rectam F L, <lb/>in L. </s>
  <s xml:id="echoid-s9621" xml:space="preserve">Quod ſi idem fiat cum reliquis binis punctis diuiſionum reſpondentibus, vt in figura apparet, inuenta <lb/>erunt puncta ellipſis, cuius maior diameter eſt B V, &amp; </s>
  <s xml:id="echoid-s9622" xml:space="preserve">minor R X, centrum autem H, vt ex coroll. </s>
  <s xml:id="echoid-s9623" xml:space="preserve">propoſ. <lb/></s>
  <s xml:id="echoid-s9624" xml:space="preserve">26. </s>
  <s xml:id="echoid-s9625" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9626" xml:space="preserve">perſpicuum eſt. </s>
  <s xml:id="echoid-s9627" xml:space="preserve">Dico rectas ex H, per hæc puncta ellipſis inuenta ductas, eſſe lineas ho-<lb/>rarias, ita vt quælibet eam horam referat, quam puncta diuiſionum reſpondentia in circulis referunt. </s>
  <s xml:id="echoid-s9628" xml:space="preserve">Vt <lb/>quoniam punctum F, refert quartam horam poſt meridiem, idcirco recta H L, ducta dabit horam quar-<lb/>tam à meridie, &amp; </s>
  <s xml:id="echoid-s9629" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s9630" xml:space="preserve">Atque hac ratione commodiſſime horas ducemus, quia ſemper terna pun <lb/>cta pro ſingulis horis habemus, quorum duo ſunt oppoſita in ellipſi, qualia ſunt L, &amp; </s>
  <s xml:id="echoid-s9631" xml:space="preserve">a, tertium autem <lb/>eſt ipſum centrum H. </s>
  <s xml:id="echoid-s9632" xml:space="preserve">Inuenietur autem punctum oppoſitum a, in ellipſi hoc modo. </s>
  <s xml:id="echoid-s9633" xml:space="preserve">Sumantur arcus S β, <lb/>X γ, oppoſiti arcubus T F, R K, æquales, ducantur{q́ue} rectæ β α, γ α, diametris S T, B V, parallelæ ſe-<lb/>
<anchor type="note" xlink:label="note-0170-05a" xlink:href="note-0170-05"/>
cantes ſeſe in α. </s>
  <s xml:id="echoid-s9634" xml:space="preserve">Punctum enim α, oppoſitum erit puncto L. </s>
  <s xml:id="echoid-s9635" xml:space="preserve">Iam vero ſi dimidiatas horas, &amp; </s>
  <s xml:id="echoid-s9636" xml:space="preserve">quadran-<lb/>tes earundem deſcribere lubeat, diuidendæ erunt ſingulæ partes circulorum bifariam, &amp; </s>
  <s xml:id="echoid-s9637" xml:space="preserve">in quatuor par-<lb/>tes, &amp; </s>
  <s xml:id="echoid-s9638" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9639" xml:space="preserve">Hanc deſcriptionem, quæ omnium elegantiſſima eſt, hoc modo demonſtrabimus.</s>
  <s xml:id="echoid-s9640" xml:space="preserve"/>
</p>
<div xml:id="echoid-div540" type="float" level="2" n="17">
  <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a">
    <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0169-01"/>
  </figure>
<note position="left" xlink:label="note-0169-03" xlink:href="note-0169-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0169-04" xlink:href="note-0169-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0169-05" xlink:href="note-0169-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0169-06" xlink:href="note-0169-06a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a">
    <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-01"/>
  </figure>
<note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0170-02" xlink:href="note-0170-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0170-03" xlink:href="note-0170-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0170-04" xlink:href="note-0170-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0170-05" xlink:href="note-0170-05a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s9641" xml:space="preserve">INTELLIGATVR triangulum A B H, circa rectam B H, moueri, donec rectum ſit ad pla-<lb/>
<anchor type="note" xlink:label="note-0170-06a" xlink:href="note-0170-06"/>
num horologĳ, &amp; </s>
  <s xml:id="echoid-s9642" xml:space="preserve">cum plano Meridiani circuli coniunctum: </s>
  <s xml:id="echoid-s9643" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9644" xml:space="preserve">ex A, quod centrum mundi refert, ad <lb/>interuallum A B, concipiatur deſcriptus circulus θ Y B Z, Aequatori concentricus, &amp; </s>
  <s xml:id="echoid-s9645" xml:space="preserve">in plano Aequa <lb/>toris, qui propterea, vt Aequator, in 24. </s>
  <s xml:id="echoid-s9646" xml:space="preserve">partes æquales à communibus ſectionibus circulorum horariorũ <lb/>&amp; </s>
  <s xml:id="echoid-s9647" xml:space="preserve">Aequatoris diuidetur. </s>
  <s xml:id="echoid-s9648" xml:space="preserve">Diſtent quoque puncta O, P, quatuor horis à puncto B, meridiei, quemadmo-<lb/>dum &amp; </s>
  <s xml:id="echoid-s9649" xml:space="preserve">puncta F, K, M, δ, quatuor horis distant ab eodem puncto B, meridiei. </s>
  <s xml:id="echoid-s9650" xml:space="preserve">Quamuis enim punctum <lb/>P, in Aequatore pertineat ad horam 4. </s>
  <s xml:id="echoid-s9651" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s9652" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9653" xml:space="preserve">(vt conſtat, ſi circulus θ Y B Z, in proprio ſitu pona-<lb/>tur, ita vt ſemicirculus θ Y B, ſit occidentalis, &amp; </s>
  <s xml:id="echoid-s9654" xml:space="preserve">B Z θ, oriẽtalis) tamen quia A, ponitur centrum mun-
<pb o="151" file="0171" n="171" rhead="LIBER SECVNDVS."/>
di, neceſſe est, vt Sol exiſtens in @, hora 4. </s>
  <s xml:id="echoid-s9655" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9656" xml:space="preserve">proĳciat radium per centrum A, &amp; </s>
  <s xml:id="echoid-s9657" xml:space="preserve">punctũ P, vſq; </s>
  <s xml:id="echoid-s9658" xml:space="preserve">ad <lb/>planũ horologĳ, atq; </s>
  <s xml:id="echoid-s9659" xml:space="preserve">adeo ſectio, quã facit ſemicirculus horarius per P, ductus in plano horologĳ, indicet <lb/>horã 4. </s>
  <s xml:id="echoid-s9660" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9661" xml:space="preserve">vt perſpicuum eſt exĳs, quę ſupra in hoc ſcholio ſcripſimus. </s>
  <s xml:id="echoid-s9662" xml:space="preserve">Vnde non immerito punctum <lb/>P, pro hora 4. </s>
  <s xml:id="echoid-s9663" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9664" xml:space="preserve">ſumi poteſt, quandoquidem ſemicir culus horarius per ipſum ductus facit in horolo-<lb/>gio lineam horæ 4. </s>
  <s xml:id="echoid-s9665" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9666" xml:space="preserve">Eodem modo ſumi poterit punctum O, pro hora 8. </s>
  <s xml:id="echoid-s9667" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s9668" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9669" xml:space="preserve">quamuis reuera <lb/>in Aequatore indicet horam 8. </s>
  <s xml:id="echoid-s9670" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9671" xml:space="preserve">Intelligatur iam Cylindrus, cuius baſes ſint circulus θ Y B Z, &amp; </s>
  <s xml:id="echoid-s9672" xml:space="preserve"><lb/>alter a e b π, ei æqualis, &amp; </s>
  <s xml:id="echoid-s9673" xml:space="preserve">oppoſitus, axis autem idem, qui axis mundi A H λ. </s>
  <s xml:id="echoid-s9674" xml:space="preserve">Et quoniam omnes circu <lb/>li horarĳ à mer. </s>
  <s xml:id="echoid-s9675" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9676" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9677" xml:space="preserve">per axem mundi, ſiue Cylindri ducuntur, facient eorum plana in cylindro pa <lb/>rallelogrãma, ita vt duo latera cuiuſq; </s>
  <s xml:id="echoid-s9678" xml:space="preserve">ſint diametri baſium cylindri, reliqua vero duo in ſuperficie cylin <lb/>dri deſcribantur, vt à Sereno demonſtratur lib. </s>
  <s xml:id="echoid-s9679" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9680" xml:space="preserve">de ſectione cylindri, propoſ. </s>
  <s xml:id="echoid-s9681" xml:space="preserve">2. </s>
  <s xml:id="echoid-s9682" xml:space="preserve">Vt v. </s>
  <s xml:id="echoid-s9683" xml:space="preserve">g. </s>
  <s xml:id="echoid-s9684" xml:space="preserve">circulus horæ 4. <lb/></s>
  <s xml:id="echoid-s9685" xml:space="preserve">
<anchor type="note" xlink:label="note-0171-01a" xlink:href="note-0171-01"/>
à mer. </s>
  <s xml:id="echoid-s9686" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9687" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9688" xml:space="preserve">ductus per puncta ε, P, in circulo θ γ B Z, faciet parallelogrammum, cuius vnum la-<lb/>tus eſt ε P, diameter baſis cylindri, duo vero ducuntur ex punctis ε, P, in ſuperficie cylindri, &amp; </s>
  <s xml:id="echoid-s9689" xml:space="preserve">ita de <lb/>reliquis. </s>
  <s xml:id="echoid-s9690" xml:space="preserve">Dico latera hæc in ſuperficie cylindri deſcripta cadere in puncta ellipſis in plano horologĳ de-<lb/>ſcriptę nempe latera ex punctis Z, Y, circuli horæ 6. </s>
  <s xml:id="echoid-s9691" xml:space="preserve">àmer. </s>
  <s xml:id="echoid-s9692" xml:space="preserve">uel med. </s>
  <s xml:id="echoid-s9693" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9694" xml:space="preserve">ducta cadere in puncta R, X, <lb/>&amp; </s>
  <s xml:id="echoid-s9695" xml:space="preserve">latus ex puncto θ, Meridiani circuli ductum cadere in punctum V, &amp; </s>
  <s xml:id="echoid-s9696" xml:space="preserve">latera ex punctis ε, P, ducta <lb/>cadere in puncta α L, &amp; </s>
  <s xml:id="echoid-s9697" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s9698" xml:space="preserve">Ducatur enim per Y Z, diametrum, quæ diametrum θ B, ad an-<lb/>gulos rectos ſecet, &amp; </s>
  <s xml:id="echoid-s9699" xml:space="preserve">per axem A H, circulus horæ 6. </s>
  <s xml:id="echoid-s9700" xml:space="preserve">occurrens plano horologĳ in H. </s>
  <s xml:id="echoid-s9701" xml:space="preserve">Et quoniam tam <lb/>planum horologĳ, quàm planum huius circuli horę 6. </s>
  <s xml:id="echoid-s9702" xml:space="preserve">rectum eſt ad Meridianum, erit quoque eorum com-<lb/>munis ſectio, nempe linea horæ 6. </s>
  <s xml:id="echoid-s9703" xml:space="preserve">ad eundem recta, ac idcirco ad meridianam lineam H B, in Meridiano <lb/>
<anchor type="note" xlink:label="note-0171-02a" xlink:href="note-0171-02"/>
exiſtentẽ, per defin. </s>
  <s xml:id="echoid-s9704" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9705" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9706" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9707" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9708" xml:space="preserve">perpendicularis in puncto H. </s>
  <s xml:id="echoid-s9709" xml:space="preserve">Diameter igitur S T, quam ad meridia-<lb/>
<anchor type="note" xlink:label="note-0171-03a" xlink:href="note-0171-03"/>
nam lineam H B, duximus perpendicularem, communis ſectio eſt plani horologĳ &amp; </s>
  <s xml:id="echoid-s9710" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s9711" xml:space="preserve">hoc <lb/>eſt, linea horæ 6. </s>
  <s xml:id="echoid-s9712" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9713" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9714" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9715" xml:space="preserve">Ac propterea latera parallelogrammi, quod circulus horæ 6. </s>
  <s xml:id="echoid-s9716" xml:space="preserve">in cy-<lb/>lindro facit, ducta ex punctis Z, Y, cadent in rectam S T; </s>
  <s xml:id="echoid-s9717" xml:space="preserve">quandoquidem &amp; </s>
  <s xml:id="echoid-s9718" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s9719" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9720" xml:space="preserve">latera hæc <lb/>in plano circuli horę 6. </s>
  <s xml:id="echoid-s9721" xml:space="preserve">exiſtunt. </s>
  <s xml:id="echoid-s9722" xml:space="preserve">Quoniam vero recta S T, ad Meridianum oſtenſa perpendicularis, per-<lb/>pendicularis quoque eſt, per defin. </s>
  <s xml:id="echoid-s9723" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9724" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9725" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9726" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9727" xml:space="preserve">ad axem A H, in Meridiano exiſtentem; </s>
  <s xml:id="echoid-s9728" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s9729" xml:space="preserve"><lb/>diameter Z Y, ad eundem axem perpendicularis, (Cum enim &amp; </s>
  <s xml:id="echoid-s9730" xml:space="preserve">circulus horæ 6. </s>
  <s xml:id="echoid-s9731" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9732" xml:space="preserve">Aequator rectus ſit <lb/>ad Meridianum, erit quoque corum communis ſectio Z Y, ad eundem recta, ac proinde ad axem in Meri-<lb/>
<anchor type="note" xlink:label="note-0171-04a" xlink:href="note-0171-04"/>
diano exiſtentem, per defin. </s>
  <s xml:id="echoid-s9733" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9734" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9735" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9736" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9737" xml:space="preserve">perpendicularis) erunt rectæ S T, Z Y, in eodem plano circu <lb/>li horę 6. </s>
  <s xml:id="echoid-s9738" xml:space="preserve">exiſtentes, cum ad axem ſint perpendiculares, inter ſe parallelæ. </s>
  <s xml:id="echoid-s9739" xml:space="preserve">Quocirca parallelogrammum <lb/>
<anchor type="note" xlink:label="note-0171-05a" xlink:href="note-0171-05"/>
erit quadrilaterum, cuius latera ſunt axis A H, ſemidiameter A Z, latus cylindri ex Z, ductum, &amp; </s>
  <s xml:id="echoid-s9740" xml:space="preserve">por <lb/>
<anchor type="note" xlink:label="note-0171-06a" xlink:href="note-0171-06"/>
tio rectæ H T, inter H, &amp; </s>
  <s xml:id="echoid-s9741" xml:space="preserve">dictum latus ex Z, ductum. </s>
  <s xml:id="echoid-s9742" xml:space="preserve">Eſt enim &amp; </s>
  <s xml:id="echoid-s9743" xml:space="preserve">latus cylindri ex Z, ductum, axi A H, <lb/>
<anchor type="note" xlink:label="note-0171-07a" xlink:href="note-0171-07"/>
parallelum, quòd illud latus &amp; </s>
  <s xml:id="echoid-s9744" xml:space="preserve">axis, ſi producãtur, coniungant ſemidiametros æquales A Z, λ ξ, baſium <lb/>cylindri æqualium, quæ quidem ſemidiametri æquidiſtantes ſunt, vtpote ſectiones baſium æquidiſtantium <lb/>
<anchor type="note" xlink:label="note-0171-08a" xlink:href="note-0171-08"/>
factæ à plano circuli horæ 6. </s>
  <s xml:id="echoid-s9745" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9746" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9747" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9748" xml:space="preserve">Quare recta A Z, æqualis erit lateri oppoſito in dicto <lb/>parallelogrammo, hoc eſt, portioni rectæ H T, inter H, &amp; </s>
  <s xml:id="echoid-s9749" xml:space="preserve">latus cylindri ex Z, ductum. </s>
  <s xml:id="echoid-s9750" xml:space="preserve">Eſt autem H R, <lb/>ſemidiameter circuli C R X, ſemidiametro A Z, circuli θ Y B Z, æqualis: </s>
  <s xml:id="echoid-s9751" xml:space="preserve">poſita enim eſt H C, æqualis <lb/>ſemidiametro A B, vel A Z. </s>
  <s xml:id="echoid-s9752" xml:space="preserve">Igitur latus cylindri ex Z, ductum cadit in punctum R. </s>
  <s xml:id="echoid-s9753" xml:space="preserve">Eodem{q́ue} pacto <lb/>latus ex Y, ductum in punctum X, cadet.</s>
  <s xml:id="echoid-s9754" xml:space="preserve"/>
</p>
<div xml:id="echoid-div541" type="float" level="2" n="18">
<note position="left" xlink:label="note-0170-06" xlink:href="note-0170-06a" xml:space="preserve">Denion ſtratio <lb/>huius deſcri-<lb/>ptionis.</note>
<note position="left" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0171-02" xlink:href="note-0171-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0171-03" xlink:href="note-0171-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0171-04" xlink:href="note-0171-04a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0171-05" xlink:href="note-0171-05a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0171-06" xlink:href="note-0171-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0171-07" xlink:href="note-0171-07a" xml:space="preserve">33. primi.</note>
<note position="right" xlink:label="note-0171-08" xlink:href="note-0171-08a" xml:space="preserve">16. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9755" xml:space="preserve">RVRSVS, quia latus cylindri ex θ, ductum cadit in lineam meridianam, cum exiſtat in Meridia-<lb/>no, parallelum{q́ue} eſt axi A H; </s>
  <s xml:id="echoid-s9756" xml:space="preserve">quod demonſtr abitur ea ratione, qua paulo ante oſtendimus, latus ex Z, <lb/>
<anchor type="note" xlink:label="note-0171-09a" xlink:href="note-0171-09"/>
<anchor type="note" xlink:label="note-0171-10a" xlink:href="note-0171-10"/>
ductum eidem axi eſſe parallelum, quia nimirum latus illud ex θ, ductum, &amp; </s>
  <s xml:id="echoid-s9757" xml:space="preserve">axis coniungunt ſemidia-<lb/>metros. </s>
  <s xml:id="echoid-s9758" xml:space="preserve">A θ, λ π, æquales &amp; </s>
  <s xml:id="echoid-s9759" xml:space="preserve">æquidiſtantes; </s>
  <s xml:id="echoid-s9760" xml:space="preserve">erit vt B A, ad A θ, ita B H, ad portionem meridianæ lineæ <lb/>
<anchor type="note" xlink:label="note-0171-11a" xlink:href="note-0171-11"/>
inter H, &amp; </s>
  <s xml:id="echoid-s9761" xml:space="preserve">latus ex θ, ductum: </s>
  <s xml:id="echoid-s9762" xml:space="preserve">Eſt autem recta B A, rectæ A θ, æqualis. </s>
  <s xml:id="echoid-s9763" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s9764" xml:space="preserve">B H, portioni di-<lb/>ctæ meridianæ lineæ æqualis erit; </s>
  <s xml:id="echoid-s9765" xml:space="preserve">ac propterea, cum H V, ipſi B H, ſit æqualis, cadet latus cylindri ex <lb/>θ, ductum in punctum V.</s>
  <s xml:id="echoid-s9766" xml:space="preserve"/>
</p>
<div xml:id="echoid-div542" type="float" level="2" n="19">
<note position="left" xlink:label="note-0171-09" xlink:href="note-0171-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0171-10" xlink:href="note-0171-10a" xml:space="preserve">33. primi.</note>
<note position="right" xlink:label="note-0171-11" xlink:href="note-0171-11a" xml:space="preserve">2. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9767" xml:space="preserve">POSTREMO, quoniam iuncta recta O P, parallela eſt rectæ Y Z, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s9768" xml:space="preserve">27. </s>
  <s xml:id="echoid-s9769" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9770" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s9771" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9772" xml:space="preserve">Nam arcus Y O, Z P, æquales ſunt, quòd vtrumque punctum O, P, quatuor horis diſtare pona-<lb/>tur à puncto B, at que adeo duabus horis à punctis Y, Z; </s>
  <s xml:id="echoid-s9773" xml:space="preserve">ſi per P O, concipiatur duci planum æquidiſtans <lb/>parallelogrammo per Z Y, &amp; </s>
  <s xml:id="echoid-s9774" xml:space="preserve">axem ducto, faciet hoc planum in cylindro parallelogrammum, per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s9775" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9776" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9777" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9778" xml:space="preserve">Sereni de ſectione cylindri, cuius duo latera ſunt recta O P, &amp; </s>
  <s xml:id="echoid-s9779" xml:space="preserve">alia recta a b, in oppoſita <lb/>
<anchor type="note" xlink:label="note-0171-12a" xlink:href="note-0171-12"/>
baſi ei reſpondens, reliqua autẽ duo in ſuperficie cylindri ex punctis O, P, ducta, quorum illud, quod ex P, <lb/>demittitur, est etiam latus parallelogrammi per ε P, ducti, adeo vt per ipſum ducatur circulus horæ 4. <lb/></s>
  <s xml:id="echoid-s9780" xml:space="preserve">Nam ex vno puncto P, vnum tantum latus cylindri duci potest, vt facile probari poteſt ex propoſ. </s>
  <s xml:id="echoid-s9781" xml:space="preserve">8. </s>
  <s xml:id="echoid-s9782" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9783" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s9784" xml:space="preserve">Sereni de ſectione cylindri. </s>
  <s xml:id="echoid-s9785" xml:space="preserve">Nam recta quæcunque ducta ex puncto P, ad aliud punctum, quod in late <lb/>re cylindri non ſit, cadit, per dictam propoſ. </s>
  <s xml:id="echoid-s9786" xml:space="preserve">intra cylindrum. </s>
  <s xml:id="echoid-s9787" xml:space="preserve">Huius ergo parallelogrammi per O P, du <lb/>cti, &amp; </s>
  <s xml:id="echoid-s9788" xml:space="preserve">Meridiani cõmunis ſectio ſit recta E Q, quæ axi A H, parallela erit, propterea quòd E Q, A H, <lb/>
<anchor type="note" xlink:label="note-0171-13a" xlink:href="note-0171-13"/>
ſectiones ſunt planorum parallelorum, nempe illorum parallelogrammorum, quæper E Q, A H, ducun-<lb/>tur, factę à Meridiano. </s>
  <s xml:id="echoid-s9789" xml:space="preserve">Quocirca erit vt ſemidiameter B H, ad B A, ſemidiametrum, ita B Q, ad B E; <lb/></s>
  <s xml:id="echoid-s9790" xml:space="preserve">
<anchor type="note" xlink:label="note-0171-14a" xlink:href="note-0171-14"/>
ac proinde arcus circulorum θ Y B Z, B T V S, reſpondentes ſinubus verſis B Q, B E, ſimiles erunt, ex <lb/>lemmate propoſ. </s>
  <s xml:id="echoid-s9791" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9792" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9793" xml:space="preserve">Eſt autem arcus B F, ſimilis arcui B P, quòd vterq; </s>
  <s xml:id="echoid-s9794" xml:space="preserve">quatuor horas com-<lb/>plectatur; </s>
  <s xml:id="echoid-s9795" xml:space="preserve">eſt{q́ue} B E, ſinus verſus arcus B P. </s>
  <s xml:id="echoid-s9796" xml:space="preserve">Igitur B Q, ſinus quoque verſus erit arcus B F; </s>
  <s xml:id="echoid-s9797" xml:space="preserve">ac propte-
<pb o="152" file="0172" n="172" rhead="GNOMONICES"/>
rca ducta recta Q F, ſinus rectus erit eiuſdem arcus B F, (Sinus enim verſus cuiuſuis arcus terminatur <lb/>in ſinu recto eiuſdem arcus, vt conſtat ex tractatione ſinuum) &amp; </s>
  <s xml:id="echoid-s9798" xml:space="preserve">ad meridianam lineam B H, perpendi-<lb/>cularis. </s>
  <s xml:id="echoid-s9799" xml:space="preserve">Eſt autem recta F L M, ad eandem meridianam lineam perpendicularis; </s>
  <s xml:id="echoid-s9800" xml:space="preserve">propterea quòd, ex <lb/>
<anchor type="note" xlink:label="note-0172-01a" xlink:href="note-0172-01"/>
<anchor type="figure" xlink:label="fig-0172-01a" xlink:href="fig-0172-01"/>
<anchor type="note" xlink:label="note-0172-02a" xlink:href="note-0172-02"/>
<anchor type="note" xlink:label="note-0172-03a" xlink:href="note-0172-03"/>
<anchor type="note" xlink:label="note-0172-04a" xlink:href="note-0172-04"/>
ſcholio propoſ. </s>
  <s xml:id="echoid-s9801" xml:space="preserve">27. </s>
  <s xml:id="echoid-s9802" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9803" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9804" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9805" xml:space="preserve">parallela eſt ipſi S T, ob æquales arcus F T, M S. </s>
  <s xml:id="echoid-s9806" xml:space="preserve">Igitur recta F L M, per <lb/>punctum Q, tranſit. </s>
  <s xml:id="echoid-s9807" xml:space="preserve">Quoniam vero &amp; </s>
  <s xml:id="echoid-s9808" xml:space="preserve">planum horologĳ, &amp; </s>
  <s xml:id="echoid-s9809" xml:space="preserve">planum parallelogrammi per O P, E Q, <lb/>ductirectum eſt ad Meridianum, erit quoque communis eorum ſectio ad eundem recta in Q, ac propte-<lb/>
<anchor type="note" xlink:label="note-0172-05a" xlink:href="note-0172-05"/>
<anchor type="note" xlink:label="note-0172-06a" xlink:href="note-0172-06"/>
rea, per defin. </s>
  <s xml:id="echoid-s9810" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9811" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9812" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9813" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9814" xml:space="preserve">ad rectam B Q, in Meridiano exiſtentem perpendicularis in puncto Q. </s>
  <s xml:id="echoid-s9815" xml:space="preserve">Re-<lb/>cta igitur F Q, perpendicularis ad B Q, communis ſectio erit horologĳ &amp; </s>
  <s xml:id="echoid-s9816" xml:space="preserve">parallelogrammi per O P, <lb/>E Q, ducti: </s>
  <s xml:id="echoid-s9817" xml:space="preserve">ac proinde latus eiuſdem parallelogrammi ex P, ductum in rectam Q F, cadet; </s>
  <s xml:id="echoid-s9818" xml:space="preserve">quandoqui-<lb/>dem recta F Q, &amp; </s>
  <s xml:id="echoid-s9819" xml:space="preserve">latus dictum in plano illius parallelogrammi exiſtunt. </s>
  <s xml:id="echoid-s9820" xml:space="preserve">Et quoniam E P, E Q, <lb/>rectis A Z, A H, parallelæ ſunt oſtenſę, erit angulus P E Q, angulo Z A H, ęqualis: </s>
  <s xml:id="echoid-s9821" xml:space="preserve">Eſt autem angu-<lb/>
<anchor type="note" xlink:label="note-0172-07a" xlink:href="note-0172-07"/>
lus Z A H, rectus: </s>
  <s xml:id="echoid-s9822" xml:space="preserve">oſtendimus enim ſupra Z Y, perpendicularẽ eſſe ad axem. </s>
  <s xml:id="echoid-s9823" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s9824" xml:space="preserve">angulus P E Q, <lb/>rectus eſt. </s>
  <s xml:id="echoid-s9825" xml:space="preserve">At recta F Q, perpendicularis oſtenſa ad Meridianum, perpendicularis quoque eſt, per defin. <lb/></s>
  <s xml:id="echoid-s9826" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9827" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s9828" xml:space="preserve">11. </s>
  <s xml:id="echoid-s9829" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s9830" xml:space="preserve">ad rectam E Q, in Meridiano exiſtentem. </s>
  <s xml:id="echoid-s9831" xml:space="preserve">Igitur rectę Q F, E P, in eodem plano paral-<lb/>lelogrammi per O P, E Q, ducti exiſtentes, cum ad rectam E Q, ſint perpendiculares, parallelę inter <lb/>
<anchor type="note" xlink:label="note-0172-08a" xlink:href="note-0172-08"/>
ſe erunt. </s>
  <s xml:id="echoid-s9832" xml:space="preserve">Parallelogrammum ergo erit quadrilaterum, cuius latera ſunt E Q, E P, latus cylindri du-<lb/>
<anchor type="note" xlink:label="note-0172-09a" xlink:href="note-0172-09"/>
ctum ex P, &amp; </s>
  <s xml:id="echoid-s9833" xml:space="preserve">portio rectę Q F, inter Q, &amp; </s>
  <s xml:id="echoid-s9834" xml:space="preserve">dictũ latus ex P, ductum. </s>
  <s xml:id="echoid-s9835" xml:space="preserve">Eſt enim &amp; </s>
  <s xml:id="echoid-s9836" xml:space="preserve">latus ex P, ductum <lb/>rectę E Q, parallelum, quòd illud latus, &amp; </s>
  <s xml:id="echoid-s9837" xml:space="preserve">recta E Q, ſi producantur, coniungant rectasęquales in ba-<lb/>
<anchor type="note" xlink:label="note-0172-10a" xlink:href="note-0172-10"/>
ſibus cylindri ęqualibus, nempe rectam E P, &amp; </s>
  <s xml:id="echoid-s9838" xml:space="preserve">aliam rectam d b, in oppoſita baſi ei reſpondentem, quę <lb/>videlicet ſinus rectus eſt arcus b e, quatuor horarum, quemadmodum &amp; </s>
  <s xml:id="echoid-s9839" xml:space="preserve">E P, ſinus rectus eſt arcus B P, <lb/>quatuor horarum; </s>
  <s xml:id="echoid-s9840" xml:space="preserve">quę quidem rectæ ęquidiſtantes ſunt, cum ſint ſectiones baſium ęquidictantium factę <lb/>
<anchor type="note" xlink:label="note-0172-11a" xlink:href="note-0172-11"/>
à parallelogrammo per O P, E Q, ducto. </s>
  <s xml:id="echoid-s9841" xml:space="preserve">Quapropter recta E P, ęqualis erit oppoſito lateri prædicti <lb/>
<anchor type="note" xlink:label="note-0172-12a" xlink:href="note-0172-12"/>
parallelogrammi, hoc eſt, ſegmento rectę Q F, inter Q, &amp; </s>
  <s xml:id="echoid-s9842" xml:space="preserve">latus cylindri ex P, ductum. </s>
  <s xml:id="echoid-s9843" xml:space="preserve">Eſt autem E P, <lb/>ſinus rectus arcus B P, quatuor horarum ęqualis ſinui recto K μ, (qui ex K, ducitur perpendicularis ad <lb/>B H) arcus C K, quatuor quoque horarum, quòd circuli θ Y B Z, C R X, æquales ſint, ex conſtructione. <lb/></s>
  <s xml:id="echoid-s9844" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s9845" xml:space="preserve">portio rectæ Q F, intercepta inter Q, &amp; </s>
  <s xml:id="echoid-s9846" xml:space="preserve">latus cylindri ex P, ductum ęqualis erit ſinui recto <lb/>K μ. </s>
  <s xml:id="echoid-s9847" xml:space="preserve">Cum ergo Q L, ipſi K μ, ſit ęqualis, ob parallelogrammum L μ, tranſibit omnino latus cylindri ex <lb/>
<anchor type="note" xlink:label="note-0172-13a" xlink:href="note-0172-13"/>
<pb o="153" file="0173" n="173" rhead="LIBER SECVNDVS."/>
P, demiſſum per punctum L. </s>
  <s xml:id="echoid-s9848" xml:space="preserve">Quamobrem, cum per hoc latus cylindri ducatur circulus horę 4. </s>
  <s xml:id="echoid-s9849" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9850" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s9851" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9852" xml:space="preserve">vt ſupra diximus, occurret latus parallelogrammi ſacti à circulo horę 4. </s>
  <s xml:id="echoid-s9853" xml:space="preserve">ex P, demiſſurn pla-<lb/>no horologĳ in puncto L. </s>
  <s xml:id="echoid-s9854" xml:space="preserve">Eademq́, ratione alterum latus eiuſdem parallelogrammi ex ε, demiſſum plano <lb/>horologĳ occurret in puncto α Ac propterea circulus ipſe horæ 4. </s>
  <s xml:id="echoid-s9855" xml:space="preserve">planum horologĳ ſecabit in punctis L, <lb/>a. </s>
  <s xml:id="echoid-s9856" xml:space="preserve">Cum ergo tranſeat quoque per centrum H, dabit recta α H L, horam 4. </s>
  <s xml:id="echoid-s9857" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s9858" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s9859" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s9860" xml:space="preserve">Eadem <lb/>ratione demonſtrabimus reliqua latera cylindri à circulis horarĳs facta cadere in reliqua puncta Ellipſis <lb/>deſcriptæ in plano horologĳ, &amp; </s>
  <s xml:id="echoid-s9861" xml:space="preserve">c.</s>
  <s xml:id="echoid-s9862" xml:space="preserve"/>
</p>
<div xml:id="echoid-div543" type="float" level="2" n="20">
<note position="left" xlink:label="note-0171-12" xlink:href="note-0171-12a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0171-13" xlink:href="note-0171-13a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0171-14" xlink:href="note-0171-14a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">29. primi.</note>
  <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a">
    <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0172-01"/>
  </figure>
<note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0172-04" xlink:href="note-0172-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0172-05" xlink:href="note-0172-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0172-06" xlink:href="note-0172-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0172-07" xlink:href="note-0172-07a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0172-08" xlink:href="note-0172-08a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0172-09" xlink:href="note-0172-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0172-10" xlink:href="note-0172-10a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0172-11" xlink:href="note-0172-11a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0172-12" xlink:href="note-0172-12a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0172-13" xlink:href="note-0172-13a" xml:space="preserve">34. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9863" xml:space="preserve">QVAMVIS autem ſatis ſit ad deſcriptionem horologĳ, ſi dimidiata duntaxat Ellipſis R L B X, <lb/>deſcribatur, accur atius tamen horologium delineabitur, ſi tota Ellipſis deſcribatur; </s>
  <s xml:id="echoid-s9864" xml:space="preserve">vt ſingulę horæ ha-<lb/>beant terna puncta, per quæ ducantur.</s>
  <s xml:id="echoid-s9865" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s9866" xml:space="preserve">EX demonſtratis colligitur, ſi cylindrus rectus ſecetur plano, quod neque per axem ducatur, neque <lb/>
<anchor type="note" xlink:label="note-0173-02a" xlink:href="note-0173-02"/>
axi æquidiſtet, ſectionẽ factã eſſe Ellipſim. </s>
  <s xml:id="echoid-s9867" xml:space="preserve">Quẽadmodum enim oſtendimus, planũ horologĳ noſtri horizon <lb/>talis ad latitudinem grad. </s>
  <s xml:id="echoid-s9868" xml:space="preserve">42. </s>
  <s xml:id="echoid-s9869" xml:space="preserve">fabricati ſecans cylindrum rectum, cuius axis eſt axis mundi, facere El-<lb/>lipſim, propterea quòd omnia later a cylindri cadant in puncta Ellipſis, ita eodem modo demonſtrabimus <lb/>idem contingere, ſi maior fuerit, aut minor altitudo poli, quàm grad. </s>
  <s xml:id="echoid-s9870" xml:space="preserve">42. </s>
  <s xml:id="echoid-s9871" xml:space="preserve">ita vt planum horologĳ horizon <lb/>talis quomodocunque inclinatum ad axem, ſeu dictum cylindrum rectum, ſemper faciat Ellipſim. </s>
  <s xml:id="echoid-s9872" xml:space="preserve">Id quod <lb/>Serenus lib. </s>
  <s xml:id="echoid-s9873" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9874" xml:space="preserve">de ſectione cylindri in omni cylindro demonſtrat, quando planum ſecans neque ęquidiſtat <lb/>baſibus cylindri, aut axi, neque per axem tranſit, aut ſubcontrarie ponitur.</s>
  <s xml:id="echoid-s9875" xml:space="preserve"/>
</p>
<div xml:id="echoid-div544" type="float" level="2" n="21">
<note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">Planum ſecans <lb/>conum rectum, <lb/>per cuius axem <lb/>non ducitur, ne <lb/>que axi æquidi <lb/>ſtat, facit Elli-<lb/>pſim.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9876" xml:space="preserve">IAM verò, quando altitudo poli ſupra Horizontem perexigua eſt, puta grad. </s>
  <s xml:id="echoid-s9877" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9878" xml:space="preserve">2. </s>
  <s xml:id="echoid-s9879" xml:space="preserve">3. </s>
  <s xml:id="echoid-s9880" xml:space="preserve">vel 4. </s>
  <s xml:id="echoid-s9881" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9882" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s9883" xml:space="preserve">
<anchor type="note" xlink:label="note-0173-03a" xlink:href="note-0173-03"/>
difficilis aliquantulum, &amp; </s>
  <s xml:id="echoid-s9884" xml:space="preserve">laborioſa efficitur deſcriptio horologĳ horizontalis, propterea quòd tunc axis <lb/>
<anchor type="note" xlink:label="note-0173-04a" xlink:href="note-0173-04"/>
mundi E D, in portione Analemmatis huius propoſ. </s>
  <s xml:id="echoid-s9885" xml:space="preserve">nimis prope ad diamctrum Horizontis B C, accedit. <lb/></s>
  <s xml:id="echoid-s9886" xml:space="preserve">Ex quo fit, ſtylum D G, admodum breuem fore, niſi velimus punctum H, à puncto G, atque adeo à pun-<lb/>cto I, plus æquo recedere, quod incommodum ſanè eſt, tum quia nimis amplum planum ad deſcriptionem <lb/>horologĳ requireretur, propterea quòd centrum horologĳ H, vltra quàm ſatis est, ab ęquinoctiali linea <lb/>remoueretur, (Nam lineę horarię in remotiſſimo puncto conueniant, neceſſe eſt, cum in eo plano, quod <lb/>axi mundi æquidistat, à quo planum horologĳ parum abeſſe ponitur ſint parallelę, vt in coroll. </s>
  <s xml:id="echoid-s9887" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s9888" xml:space="preserve">22. </s>
  <s xml:id="echoid-s9889" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s9890" xml:space="preserve">demonſtrauimus, ac proinde in propoſito horologio horizontali ferè etiam paralle-<lb/>læ videantur) tum etiam, quia difficile admodum eſt, in tam remoto ſpatio diſcernere, atque diſtinguere <lb/>punctum H, ſine aliqua erroris ſuſpitione, eo qòd angulus D H I, acutiſſimus tunc efficitur.</s>
  <s xml:id="echoid-s9891" xml:space="preserve"/>
</p>
<div xml:id="echoid-div545" type="float" level="2" n="22">
<note position="right" xlink:label="note-0173-03" xlink:href="note-0173-03a" xml:space="preserve">Quando altitue <lb/>do poli ſupra <lb/>Horizonté val-<lb/>de exigua eſt, <lb/>difficilior red-<lb/>ditur deſcripero <lb/>horologii hori-<lb/>aontalis.</note>
<note position="left" xlink:label="note-0173-04" xlink:href="note-0173-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s9892" xml:space="preserve">IDEM quodammodo contingit, quando maxima eſt altitudo poli ſupra Horizontem, vt grad. </s>
  <s xml:id="echoid-s9893" xml:space="preserve">89. <lb/></s>
  <s xml:id="echoid-s9894" xml:space="preserve">
<anchor type="note" xlink:label="note-0173-05a" xlink:href="note-0173-05"/>
<anchor type="note" xlink:label="note-0173-06a" xlink:href="note-0173-06"/>
88. </s>
  <s xml:id="echoid-s9895" xml:space="preserve">87. </s>
  <s xml:id="echoid-s9896" xml:space="preserve">86. </s>
  <s xml:id="echoid-s9897" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s9898" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9899" xml:space="preserve">ita vt polus parum à vertice abſit: </s>
  <s xml:id="echoid-s9900" xml:space="preserve">quoniam tunc diameter Aequatoris F D, acutiſ-<lb/>ſimum quoque angulum conſtituit in I, cum recta H I, &amp; </s>
  <s xml:id="echoid-s9901" xml:space="preserve">cum eadem in puneto remotiſſimo conuenit, vt <lb/>non facile ſit diiudicare, vbi rectę F D, H I, ſe mutuo interſecent, propter anguſtiam anguli acuti HID. <lb/></s>
  <s xml:id="echoid-s9902" xml:space="preserve">Quamobrem ad duplex hoc incommodum vitandum, duplex etiam remcdium excogitauimus. </s>
  <s xml:id="echoid-s9903" xml:space="preserve">Priore <lb/>deſcribemus horarias lineas, etiamſi centrum, vbi omnes coeunt, non habeamus: </s>
  <s xml:id="echoid-s9904" xml:space="preserve">Poſteriore reperiemus <lb/>punctum in meridiana linea, per quod ęquinoctialis linea ducenda eſt, licet rectam D I, in portione Ana <lb/>lemmatis huius propoſ. </s>
  <s xml:id="echoid-s9905" xml:space="preserve">quę in illud punctum cadere debet, non ducamus.</s>
  <s xml:id="echoid-s9906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div546" type="float" level="2" n="23">
<note position="left" xlink:label="note-0173-05" xlink:href="note-0173-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0173-06" xlink:href="note-0173-06a" xml:space="preserve">Quando altitu-<lb/>do poli ſupra <lb/>Horizontem n@ <lb/>mis magna eſt, <lb/>difficilior etiã <lb/>efficitur deli <lb/>neatio horolo-<lb/>gii horizonia-<lb/>lis.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9907" xml:space="preserve">SIT ergo deſcribendum horologium horizontale ad latitudinem grad. </s>
  <s xml:id="echoid-s9908" xml:space="preserve">20. </s>
  <s xml:id="echoid-s9909" xml:space="preserve">(tantam autem latitudi-<lb/>
<anchor type="note" xlink:label="note-0173-07a" xlink:href="note-0173-07"/>
nem eligimus, vt ratio deſcriptionis fiat planior, quætamen in alias latitudines quamuis minimas qua-<lb/>drat) boc eſt, in ea regione, ſupra cuius Horizontem polus attollitur grad. </s>
  <s xml:id="echoid-s9910" xml:space="preserve">20. </s>
  <s xml:id="echoid-s9911" xml:space="preserve">In plano aliquo ducatur <lb/>
<anchor type="note" xlink:label="note-0173-08a" xlink:href="note-0173-08"/>
pro linea meridiana, recta vtcunque A B; </s>
  <s xml:id="echoid-s9912" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9913" xml:space="preserve">C D, eam ad angulos rectos ſecans in E, referat æquino ctia-<lb/>lem lineam. </s>
  <s xml:id="echoid-s9914" xml:space="preserve">Deinceps in E, puncto, ad rectam E D, vel E C, conſtituatur angulus altitudinis poli D E F, <lb/>atque in recta E F, aſſumpto quoquis puncto F, (quod quo remotius fuerit ab E, eo maius delineabitur ho <lb/>rologium) excitetur in F, ad rectam E F, perpendicularis F G. </s>
  <s xml:id="echoid-s9915" xml:space="preserve">Poſtea in recta A E, accepto quolibet pun <lb/>cto H, ducatur per illud recta H G, ipſi E F, parallela, vel ad F G, perpendicularis ſecans F G, in G; </s>
  <s xml:id="echoid-s9916" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s9917" xml:space="preserve"><lb/>rurſus per idem punctum H, recta I K, ad A B, perpendicularis. </s>
  <s xml:id="echoid-s9918" xml:space="preserve">Poſtremò ſumptis in recta A B, rectis <lb/>E B, H L, quæ rectis E F, H G, ſint æquales, deſcribantur ex B, L, circuli, vel potius quadrantes circulo <lb/>rum; </s>
  <s xml:id="echoid-s9919" xml:space="preserve">(quod ſatis eſt, ſi puncta per hos quadrantes in rectis E D, H K, inuenta transferantur in rectas <lb/>E C, H I) &amp; </s>
  <s xml:id="echoid-s9920" xml:space="preserve">circuli quidem, ſi deſcripti ſint, in partes 24. </s>
  <s xml:id="echoid-s9921" xml:space="preserve">quadrantes vero, ſi forte quadrantes tantum <lb/>ſint deſcripti, in 6. </s>
  <s xml:id="echoid-s9922" xml:space="preserve">partes ęquales diſtribuantur, initio ſemper facto à linea meridiana A B. </s>
  <s xml:id="echoid-s9923" xml:space="preserve">Nam rectæ <lb/>
<anchor type="note" xlink:label="note-0173-09a" xlink:href="note-0173-09"/>
ductæ, occultè tamen, per centra B, L, &amp; </s>
  <s xml:id="echoid-s9924" xml:space="preserve">per puncta diuiſionum circulorum, quadrantumve ſecabunt re <lb/>ctas C D, I K, vel ipſas E D, H K, ſi quadrantes tantum ſint deſcripti, in punctis, per quæ eductæ rectæ <lb/>lineæ (ſumendo ſemper bina puncta reſpondentia inter ſe, hoc eſt, primùm duo proxima punctis E, H, <lb/>deinde duo ſequentia, &amp; </s>
  <s xml:id="echoid-s9925" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s9926" xml:space="preserve">dabunt lineas horarias, quas deſideramus; </s>
  <s xml:id="echoid-s9927" xml:space="preserve">ita tamen, vt ſi quadrantes dun-<lb/>taxat ſint deſcripti, puncta rectarum E D, H K, transfer antur prius in rectas E C, H I, &amp; </s>
  <s xml:id="echoid-s9928" xml:space="preserve">poſtea lineæ <lb/>ducantur, vt dictum eſt. </s>
  <s xml:id="echoid-s9929" xml:space="preserve">Has autem producemus, quantum libuerit. </s>
  <s xml:id="echoid-s9930" xml:space="preserve">Nam arcus ſignorum, quos ſequenti <lb/>propoſ. </s>
  <s xml:id="echoid-s9931" xml:space="preserve">deſcribemus, terminabunt earum longitudines. </s>
  <s xml:id="echoid-s9932" xml:space="preserve">Longitude gnomonis erit F M, perpendicularis ad <lb/>A B, eiuſ{q́ue} locus in M, puncto. </s>
  <s xml:id="echoid-s9933" xml:space="preserve">Quod ita demonſtr abimus.</s>
  <s xml:id="echoid-s9934" xml:space="preserve"/>
</p>
<div xml:id="echoid-div547" type="float" level="2" n="24">
<note position="right" xlink:label="note-0173-07" xlink:href="note-0173-07a" xml:space="preserve">Deſcriptio ho-<lb/>rologii horizon <lb/>talis, cum poli <lb/>altitudo perexi <lb/>gua eſt.</note>
<note position="left" xlink:label="note-0173-08" xlink:href="note-0173-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0173-09" xlink:href="note-0173-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s9935" xml:space="preserve">QVONIAM angulus D E F, altitudini poli æqualis eſt, erit angulus A E F, complemento eiuſ-<lb/>
<anchor type="note" xlink:label="note-0173-10a" xlink:href="note-0173-10"/>
dem altitudinis æqualis; </s>
  <s xml:id="echoid-s9936" xml:space="preserve">ac proinde duo anguli A E F, E F G, duobus rectis erunt minores, ideo{q́ue} recta <lb/>F G, cum recta E A, ad partes A, tandem conueniet, vt in A, puncto, quod etiamſi in plano propter mo
<pb o="154" file="0174" n="174" rhead="GNOMONICES"/>
dicam eius quantit atem non contineatur, animo tamen ipſum concipere licebit, Igitur angulus E A F. <lb/></s>
  <s xml:id="echoid-s9937" xml:space="preserve">altitudini poli æqualis crit, cum E A F, A E F, vni recto ſint æquales, &amp; </s>
  <s xml:id="echoid-s9938" xml:space="preserve">A E F, ſit complemento al-<lb/>
<anchor type="note" xlink:label="note-0174-01a" xlink:href="note-0174-01"/>
titudinis poli æqualis; </s>
  <s xml:id="echoid-s9939" xml:space="preserve">ac propterea ſi triangulum E A F, intelligatur circa lineam meridianam A E, cir-<lb/>cumduci, quoad rectum ſit ad planum borologĳ, &amp; </s>
  <s xml:id="echoid-s9940" xml:space="preserve">in plano Meridiani exiſtat, erit A F, axis mundi; <lb/></s>
  <s xml:id="echoid-s9941" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0174-01a" xlink:href="fig-0174-01"/>
<anchor type="note" xlink:label="note-0174-02a" xlink:href="note-0174-02"/>
<anchor type="note" xlink:label="note-0174-03a" xlink:href="note-0174-03"/>
<anchor type="note" xlink:label="note-0174-04a" xlink:href="note-0174-04"/>
<anchor type="note" xlink:label="note-0174-05a" xlink:href="note-0174-05"/>
quia in plano Meridiani cum meridiana linea Horizontis, quæ ipſi A B, in plano horologĳ æquidiſt@t, <lb/>
<anchor type="note" xlink:label="note-0174-06a" xlink:href="note-0174-06"/>
(propterea quòd ambæ ſint ſectiones factæ à Meridiano in planis parallelis) angulum facit angulo E A F, <lb/>altitudinis poli æqualem, nempe externum interno. </s>
  <s xml:id="echoid-s9942" xml:space="preserve">Quocirca rectæ F E, G H, ad axem F G, perpendicu-<lb/>
<anchor type="note" xlink:label="note-0174-07a" xlink:href="note-0174-07"/>
<anchor type="note" xlink:label="note-0174-08a" xlink:href="note-0174-08"/>
lares, communes ſectiones erunt Meridiani, &amp; </s>
  <s xml:id="echoid-s9943" xml:space="preserve">Aequatoris, ita vt vtrumque punctorum F, G, pro cen-<lb/>tro mundi ſumatur. </s>
  <s xml:id="echoid-s9944" xml:space="preserve">Ac propterea, vt in hac propoſ. </s>
  <s xml:id="echoid-s9945" xml:space="preserve">oſtenſum eſt, circuli horarĳ occurrent plano horo-<lb/>logĳ in punctis, quæ in rectis C D, I K, reperimus, &amp; </s>
  <s xml:id="echoid-s9946" xml:space="preserve">F M, erit ſtylus, eiuſ{q́ue} locus in M. </s>
  <s xml:id="echoid-s9947" xml:space="preserve">Sunt enim triã-<lb/>gula A E F, A H G, ita conſtructa hoc loco, vt triangulum H I D, in ſuperiori horologio huius propoſ.</s>
  <s xml:id="echoid-s9948" xml:space="preserve"/>
</p>
<div xml:id="echoid-div548" type="float" level="2" n="25">
<note position="right" xlink:label="note-0173-10" xlink:href="note-0173-10a" xml:space="preserve">Demonſtr@ti@ <lb/>proximæ deſ@c@ <lb/>ptionis.</note>
<note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">82. primi.</note>
  <figure xlink:label="fig-0174-01" xlink:href="fig-0174-01a">
    <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0174-01"/>
  </figure>
<note position="left" xlink:label="note-0174-02" xlink:href="note-0174-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0174-03" xlink:href="note-0174-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0174-04" xlink:href="note-0174-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0174-05" xlink:href="note-0174-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0174-06" xlink:href="note-0174-06a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0174-07" xlink:href="note-0174-07a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0174-08" xlink:href="note-0174-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s9949" xml:space="preserve">IN hoc propoſito exemplo, quia altitudo poli eſt magna ſatis, continetur centrum horologĳ A, ad <lb/>quod omnes lineæ horariæ tendunt. </s>
  <s xml:id="echoid-s9950" xml:space="preserve">Quod eo conſilio factum eſt, vt experientia etiam diſceres, rectè hac <lb/>ratione horologia deſcribi. </s>
  <s xml:id="echoid-s9951" xml:space="preserve">Liquido verò conſtat, ſi centrum in planum horologĳ non cadit, ſextam horã, <lb/>quæ per centrum horologĳ neceſſario ducitur ad meridianam lineam perpendicularis, deſcribi non poſſe. <lb/></s>
  <s xml:id="echoid-s9952" xml:space="preserve">
<anchor type="note" xlink:label="note-0174-09a" xlink:href="note-0174-09"/>
Atque hæc de remedio prioris incommodi.</s>
  <s xml:id="echoid-s9953" xml:space="preserve"/>
</p>
<div xml:id="echoid-div549" type="float" level="2" n="26">
<note position="left" xlink:label="note-0174-09" xlink:href="note-0174-09a" xml:space="preserve">Deſctiptio hoto <lb/>logii horizonta <lb/>lis, cum polial-<lb/>titudovalde ma <lb/>gna eſt.</note>
</div>
<p style="it">
  <s xml:id="echoid-s9954" xml:space="preserve">QVOD autem attinet ad poſterius incommodum, illud ita leuabimus. </s>
  <s xml:id="echoid-s9955" xml:space="preserve">Sit rurſus in aliquo plano me <lb/>ridiana linea A B, &amp; </s>
  <s xml:id="echoid-s9956" xml:space="preserve">ſtatuatur A, centrum horologĳ. </s>
  <s xml:id="echoid-s9957" xml:space="preserve">Conſtituatur ad rectam A B, in A, angulus alti
<pb o="155" file="0175" n="175" rhead="LIBER SECVNDVS."/>
tudinis poli B A N, ita vt A N, ſit axis mundi, in quo ſumatur quodcunque punctum N, pro centro mun <lb/>di, ex quo ducta perpendicularis ad A N, referet ſectionem communem Meridiani, &amp; </s>
  <s xml:id="echoid-s9958" xml:space="preserve">Acquatoris, quem-<lb/>admodum paulo ante rectæ F E, G H. </s>
  <s xml:id="echoid-s9959" xml:space="preserve">Sed quoniam, ſi punctum N, longius aliquanto abfuerit à centro <lb/>horologĳ A, ad eum finem, vt ſtylus, qui ex N, ad A B, ducendus eſt perpendicularis, decentem, &amp; </s>
  <s xml:id="echoid-s9960" xml:space="preserve">con-<lb/>ſpicuam habere poſſit magnitudinem, perpendicularis ex N, ad A N, ducta in remotiſſimo puncto ipſi me <lb/>ridianæ lineę A B, occurrit, vt difficile ſit illud abſque crrore deprehendere, quòd perpendicularis illa fa-<lb/>cile hinc inde deflectere poſſit; </s>
  <s xml:id="echoid-s9961" xml:space="preserve">inueniemus punctum illius occurſus hac induſtria ſatis exquiſitè. </s>
  <s xml:id="echoid-s9962" xml:space="preserve">Diuiſa <lb/>recta A N, in quotcunque partes æquales, ita vt perpendicularis ex O, puncto diuiſionis ipſi A, proximo <lb/>ducta ad A N, commodè ſecare queat rectam A B, in P; </s>
  <s xml:id="echoid-s9963" xml:space="preserve">ſi in A B, producta acceperimus lineam tam <lb/>multiplicem ipſius A P, quàm eſt multiplex A N, ipſius A O, erit vltimum punctum illius multiplicis <lb/>
<anchor type="note" xlink:label="note-0175-01a" xlink:href="note-0175-01"/>
illud, in quod cadet neceſſario perpendicularis ex N, ad A N, ducta. </s>
  <s xml:id="echoid-s9964" xml:space="preserve">Quod hoc modo confirmabimus. <lb/></s>
  <s xml:id="echoid-s9965" xml:space="preserve">Quoniam quam proportionem habet A N, ad A O, talem habet multiplex illa in recta A B, ad A P; </s>
  <s xml:id="echoid-s9966" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0175-02a" xlink:href="note-0175-02"/>
erit recta ex N, ad extremum punctum illius multiplicis ducta, parallela ipſi O P; </s>
  <s xml:id="echoid-s9967" xml:space="preserve">ac proinde angulus <lb/>ad N, angulo ad O, ęqualis, vtpotèrectus. </s>
  <s xml:id="echoid-s9968" xml:space="preserve">Cadio ergo dicta perpendicularis ex N, in dictum punctum <lb/>
<anchor type="note" xlink:label="note-0175-03a" xlink:href="note-0175-03"/>
rectę A B: </s>
  <s xml:id="echoid-s9969" xml:space="preserve">alias ſi in aliud punctum caderet, ducerentur ex N, duæ perpendiculares ad A N, quod eſt <lb/>abſurdum, Vides ergo ingens valde planum requiri ad huiuſmodi horologium deſcribendum, ſi ſtylus me-<lb/>diocrem longitudinem haberc debeat. </s>
  <s xml:id="echoid-s9970" xml:space="preserve">Stylus enim ex O, ductus perpendicularis ad A B, nimis breuis <lb/>eſt. </s>
  <s xml:id="echoid-s9971" xml:space="preserve">Neque verò hic prius incommodum vit are poſſumus, ſed inuento prædicto puncto in recta A B, de-<lb/>ſcribendum erit horologium, vt in hac propoſ tradidimus, hoc eſt, ab illo puncto inuento abſcindenda eſt <lb/>recta ex A B, æqualis perpendiculari lineæ ex N, ad A N, ductæ, cadenti{q́ue} in dictum punctum, per quod <lb/>
<anchor type="note" xlink:label="note-0175-04a" xlink:href="note-0175-04"/>
ad A B, perpendicularis ducenda eſt pro ęquinoctiali linea. </s>
  <s xml:id="echoid-s9972" xml:space="preserve">Deinde ex puncto, quod terminat rectam il-<lb/>lam perpendiculari ex N, ductę ad A N, æqualem, circulus deſcribendus, &amp; </s>
  <s xml:id="echoid-s9973" xml:space="preserve">c. </s>
  <s xml:id="echoid-s9974" xml:space="preserve">In exemplo recta A N, <lb/>octupla eſt rectæ A O. </s>
  <s xml:id="echoid-s9975" xml:space="preserve">Vnde ipſius A P, octuplam rectam abſcindere nos oportebit ex A B. </s>
  <s xml:id="echoid-s9976" xml:space="preserve">Sed <lb/>ſi axem terminemus in Q, abſcindenda erit ex A B, recta ipſius A B, tripla, quia &amp; </s>
  <s xml:id="echoid-s9977" xml:space="preserve">A Q, ipſius A O, <lb/>tripla eſt.</s>
  <s xml:id="echoid-s9978" xml:space="preserve"/>
</p>
<div xml:id="echoid-div550" type="float" level="2" n="27">
<note position="left" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0175-02" xlink:href="note-0175-02a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0175-03" xlink:href="note-0175-03a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0175-04" xlink:href="note-0175-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s9979" xml:space="preserve">FORTASSIS autem id, quod proponitur, certius aſſequemur, (Nam quando maxima eſt altitu <lb/>do poli, ita vt axis A N, angulum ferèrectum cum A B, conficiat, non facile quoque eſt punctum P, di-<lb/>gnoſcere, quòd nimis acutus ſit angulus A P O) ſi prius in recta A B, punctum quodcunque eligamus, <lb/>puta P, &amp; </s>
  <s xml:id="echoid-s9980" xml:space="preserve">ex eo ad A N, perpendicularem excitemus P O. </s>
  <s xml:id="echoid-s9981" xml:space="preserve">Nam ſi ipſi A O, quotcunque portiones <lb/>æquales abſcindamus vſque ad N, vel Q, vel vſque ad quoduis aliud punctum, &amp; </s>
  <s xml:id="echoid-s9982" xml:space="preserve">in A B, ſumamus re-<lb/>
<anchor type="note" xlink:label="note-0175-05a" xlink:href="note-0175-05"/>
ctam it a multiplicem ipſius A P, vt multiplex eſt A N, vel A Q, vel alia aliqua portio aſſumpta in <lb/>axe A N, ipſius A O, ad eundem ſcopum, ad quem tendebamus antea, perueniemus, &amp; </s>
  <s xml:id="echoid-s9983" xml:space="preserve">certius <lb/>quidem multo. </s>
  <s xml:id="echoid-s9984" xml:space="preserve">Quis enim non videt, nos hac ratione in puncto P, aſſumendo, atque adeò inrecta <lb/>A P, minus poſſe hallucinari, quàm prius, cum idem punctum P, &amp; </s>
  <s xml:id="echoid-s9985" xml:space="preserve">rectam A P, quæreremus per <lb/>perpendicularem O P? </s>
  <s xml:id="echoid-s9986" xml:space="preserve">quippe cum anguſtię anguli acuti A P O, punctum illud valde ambiguum red-<lb/>dant, &amp; </s>
  <s xml:id="echoid-s9987" xml:space="preserve">incertum.</s>
  <s xml:id="echoid-s9988" xml:space="preserve"/>
</p>
<div xml:id="echoid-div551" type="float" level="2" n="28">
<note position="left" xlink:label="note-0175-05" xlink:href="note-0175-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s9989" xml:space="preserve">NEQVE vero prætereundum hoc loco videtur, Orontium Finęum inſigniter deceptum eſſe in de-<lb/>
<anchor type="note" xlink:label="note-0175-06a" xlink:href="note-0175-06"/>
ſcriptione horologĳ Aſtronomici tam horizontalis, quàm Verticalis. </s>
  <s xml:id="echoid-s9990" xml:space="preserve">Quod vt planum fiat, verba ipſius <lb/>in medium afferemus, errorem{q́ue} detegemus, ne ſimul cum eo in errorem quis inducatur, quod multis iam, <lb/>auctoritate forſan Orontĳ deceptis, contigiſſe animaduertimus. </s>
  <s xml:id="echoid-s9991" xml:space="preserve">Ita igitur libro 1. </s>
  <s xml:id="echoid-s9992" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s9993" xml:space="preserve">1. </s>
  <s xml:id="echoid-s9994" xml:space="preserve">horologiorũ <lb/>
<anchor type="note" xlink:label="note-0175-07a" xlink:href="note-0175-07"/>
Protypum (quem ipſe appellat) deſcribit, quo tam horizontalia, quàm Verticalia horologia, vt ipſe ait, <lb/>fabricantur. </s>
  <s xml:id="echoid-s9995" xml:space="preserve">Super oblato plano, &amp; </s>
  <s xml:id="echoid-s9996" xml:space="preserve">circa datum in eo centrum A, circulus deſcribatur B C D E, <lb/>
<anchor type="figure" xlink:label="fig-0175-01a" xlink:href="fig-0175-01"/>
<anchor type="note" xlink:label="note-0175-08a" xlink:href="note-0175-08"/>
binisq́; </s>
  <s xml:id="echoid-s9997" xml:space="preserve">diametris B D, &amp; </s>
  <s xml:id="echoid-s9998" xml:space="preserve">C E, in codem centro A, ſeſe ad rectos dirimentibus angulos, in quatuor <lb/>quadrantes ſolito more diuidatur; </s>
  <s xml:id="echoid-s9999" xml:space="preserve">Horum porro quadrantũ dexter &amp; </s>
  <s xml:id="echoid-s10000" xml:space="preserve">ſuperior B C, in 90. </s>
  <s xml:id="echoid-s10001" xml:space="preserve">partes <lb/>adinuicem æquales diſtribuatur: </s>
  <s xml:id="echoid-s10002" xml:space="preserve">primo quidem in tres, poſtea quælibet in 6. </s>
  <s xml:id="echoid-s10003" xml:space="preserve">tandem quælibet in <lb/>5. </s>
  <s xml:id="echoid-s10004" xml:space="preserve">Sumpta poſtmodum libera poli borealis ſublimitate, ſiue regionis latitudine, ad quam videli-<lb/>set iuuat horologia fabricare: </s>
  <s xml:id="echoid-s10005" xml:space="preserve">ca ſupputetur in quadrante B C, à ſigno quidem B, verſus C. </s>
  <s xml:id="echoid-s10006" xml:space="preserve">Finis
<pb o="156" file="0176" n="176" rhead="GNOMONICES"/>
autem ſupputationis obſignetur notula F: </s>
  <s xml:id="echoid-s10007" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10008" xml:space="preserve">à centro A, ad datum ſignum F, recta producatur li-<lb/>nea A F. </s>
  <s xml:id="echoid-s10009" xml:space="preserve">Dato inſuper arcu B F, æqualis eidem conſtituatur in quadrante B E, ſitq; </s>
  <s xml:id="echoid-s10010" xml:space="preserve">B G: </s>
  <s xml:id="echoid-s10011" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10012" xml:space="preserve">à ſi-<lb/>gno F, ad ſignum G, recta ducatur linea F G. </s>
  <s xml:id="echoid-s10013" xml:space="preserve">Hæc enim à ſemidiametro A B, bifariam diuidetur, <lb/>
<anchor type="figure" xlink:label="fig-0176-01a" xlink:href="fig-0176-01"/>
<anchor type="note" xlink:label="note-0176-01a" xlink:href="note-0176-01"/>
in ſigno quidem H: </s>
  <s xml:id="echoid-s10014" xml:space="preserve">quapropter &amp; </s>
  <s xml:id="echoid-s10015" xml:space="preserve">ad rectos angulos, per 3. </s>
  <s xml:id="echoid-s10016" xml:space="preserve">tertij elementorum Euclidis. </s>
  <s xml:id="echoid-s10017" xml:space="preserve">Erit itaq; <lb/></s>
  <s xml:id="echoid-s10018" xml:space="preserve">recta linea F H, perpendicularis ſuper A B: </s>
  <s xml:id="echoid-s10019" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10020" xml:space="preserve">triangulum A F H, rectangulum. </s>
  <s xml:id="echoid-s10021" xml:space="preserve">Ergo circulus B C-<lb/>D E, Meridianum, &amp; </s>
  <s xml:id="echoid-s10022" xml:space="preserve">B C, quadrantem eius ſeptentrionalem, A, vero centrum mundi repreſenta-<lb/>
<anchor type="note" xlink:label="note-0176-02a" xlink:href="note-0176-02"/>
bit: </s>
  <s xml:id="echoid-s10023" xml:space="preserve">recta porro B D, Horizontem, &amp; </s>
  <s xml:id="echoid-s10024" xml:space="preserve">C E, Verticalem circulum cum ipſo Meridiano ad rectos an <lb/>gulos incidentem. </s>
  <s xml:id="echoid-s10025" xml:space="preserve">Deinde paulo poſt ita rem proſequitur. </s>
  <s xml:id="echoid-s10026" xml:space="preserve">Data recta linea F H, æqualis eidem con <lb/>ſtituatur in ſemidiametro A C, ſitq́, illa A I: </s>
  <s xml:id="echoid-s10027" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10028" xml:space="preserve">à ſigno H, ad ſignum I, recta linea ducatur H I, di-<lb/>rimens rectam A F, in ſigno K. </s>
  <s xml:id="echoid-s10029" xml:space="preserve">Erit igitur triangulum A H I, ęqualeatque ſimile triangulo A F H: <lb/></s>
  <s xml:id="echoid-s10030" xml:space="preserve">quemadmodum ex 4. </s>
  <s xml:id="echoid-s10031" xml:space="preserve">primi ipſius Euclidis fit manifeſtum. </s>
  <s xml:id="echoid-s10032" xml:space="preserve">Hanc igitur deſcriptionem, generalem <lb/>protypum Orontius appellat pro horizontalibus, Verticalibus{q́ue}, horologĳs conſtruendis: </s>
  <s xml:id="echoid-s10033" xml:space="preserve">ita vt ipſe trian <lb/>gulo AHK, rtatur in horizontalibus horologĳs fabricandis ad datam altitudinem poli B F, non ſecus, <lb/>atq; </s>
  <s xml:id="echoid-s10034" xml:space="preserve">nos in hac propoſitione vſi ſumus triangulo D H I, in portione Analemmatis contento pro eiſdẽ ho-<lb/>rologĳs componendis ad datam poli altitudinem C E. </s>
  <s xml:id="echoid-s10035" xml:space="preserve">Nam ſtatim in propoſ. </s>
  <s xml:id="echoid-s10036" xml:space="preserve">2. </s>
  <s xml:id="echoid-s10037" xml:space="preserve">aſſumit in linea meridia-<lb/>narectam ęqualem lateri A H, pro linea Horizontis, quemadmodum nos accepimus rectam æqualem la <lb/>
<anchor type="note" xlink:label="note-0176-03a" xlink:href="note-0176-03"/>
tcri H I, in noſtro triangulo. </s>
  <s xml:id="echoid-s10038" xml:space="preserve">Deinde pro linea Aequatoris ſumit aliam rectam æqualem lateri A K, <lb/>quemadmodum nos ſumpſimus rectam æqualem rectæ D I, in noſtro triangulo. </s>
  <s xml:id="echoid-s10039" xml:space="preserve">Itaque vult in triangulo <lb/>A H K, rectam A H, eſſe lineam Horizontis; </s>
  <s xml:id="echoid-s10040" xml:space="preserve">H K, axem mundi; </s>
  <s xml:id="echoid-s10041" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10042" xml:space="preserve">A K, lineam Aequatoris, pro <lb/>horizontalibus horologĳs componendis. </s>
  <s xml:id="echoid-s10043" xml:space="preserve">Sic etiam in propoſ. </s>
  <s xml:id="echoid-s10044" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10045" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s10046" xml:space="preserve">pro V erticalibus horologĳs <lb/>conſtruendis accipit in triangulo F H K, rectam F H, pro linea V erticalis circuli; </s>
  <s xml:id="echoid-s10047" xml:space="preserve">H K, pro axe mundi; <lb/></s>
  <s xml:id="echoid-s10048" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10049" xml:space="preserve">F K, pro Aequatoris linea. </s>
  <s xml:id="echoid-s10050" xml:space="preserve">Qua in re ipſum eſſe mirum in modum hallucinatum, facile demonſtra-<lb/>bimus hoc modo.</s>
  <s xml:id="echoid-s10051" xml:space="preserve"/>
</p>
<div xml:id="echoid-div552" type="float" level="2" n="29">
<note position="right" xlink:label="note-0175-06" xlink:href="note-0175-06a" xml:space="preserve">Error Orontii <lb/>Finæi in deſcri-<lb/>ptione horolo-<lb/>gii Aſtronomi-<lb/>ci horizontalis <lb/>&amp; Verticalis.</note>
<note position="left" xlink:label="note-0175-07" xlink:href="note-0175-07a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a">
    <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0175-01"/>
  </figure>
<note position="left" xlink:label="note-0175-08" xlink:href="note-0175-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a">
    <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0176-01"/>
  </figure>
<note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0176-03" xlink:href="note-0176-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s10052" xml:space="preserve">QVONIAM latera I A, A H, trianguli I A H, æqualia ſunt lateribus F H, H A, trianguli <lb/>F H A, angulos{q́ue} continent æquales, vtpote rectos, erunt &amp; </s>
  <s xml:id="echoid-s10053" xml:space="preserve">baſes H I, A F, &amp; </s>
  <s xml:id="echoid-s10054" xml:space="preserve">anguli A H I, H A F, <lb/>
<anchor type="note" xlink:label="note-0176-04a" xlink:href="note-0176-04"/>
aquales. </s>
  <s xml:id="echoid-s10055" xml:space="preserve">Quare quemadmodum A F, axis eſt reſpectu Horizontis A H, ita quoque H I, pro axc ſumi <lb/>
<anchor type="note" xlink:label="note-0176-05a" xlink:href="note-0176-05"/>
potest reſpectu ciuſdem Horizontis A H, quandoquidem tam A F, quàm H I, cum A H, angulum alti-<lb/>tudinis poli conſtituit. </s>
  <s xml:id="echoid-s10056" xml:space="preserve">Atque hucuſque inter nos &amp; </s>
  <s xml:id="echoid-s10057" xml:space="preserve">Orontium nullum diſcrimen eſt: </s>
  <s xml:id="echoid-s10058" xml:space="preserve">Sed error ipſius cõ-<lb/>ſiſtit in linea Aequat oris duntaxat, quam nulla ratione eſſe poſſe rectam A K, vt ipſe putat, in regione, <lb/>cuius latitudo maior ſit, quàm grad. </s>
  <s xml:id="echoid-s10059" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10060" xml:space="preserve">ita perſpicuum faciemus. </s>
  <s xml:id="echoid-s10061" xml:space="preserve">Sit enim primum altitudo poli B F, <lb/>maior, quàm grad. </s>
  <s xml:id="echoid-s10062" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10063" xml:space="preserve">vt in eius figura. </s>
  <s xml:id="echoid-s10064" xml:space="preserve">Erit igitur angulus F A H, dimidio rectimaior; </s>
  <s xml:id="echoid-s10065" xml:space="preserve">ac proinde cum <lb/>ei æqualis ſit oſtenſus angulus A H I, erunt duo anguli K A H, K H A, in triangulo A H K, ſimul re-<lb/>cto maiores. </s>
  <s xml:id="echoid-s10066" xml:space="preserve">Igitur reliquus A K H, recto minor erit. </s>
  <s xml:id="echoid-s10067" xml:space="preserve">Quare cum linea Aequatoris cum axe in omni <lb/>
<anchor type="note" xlink:label="note-0176-06a" xlink:href="note-0176-06"/>
climate rectos faciat angnlos, vt ex portione Analemmatis huius propoſ. </s>
  <s xml:id="echoid-s10068" xml:space="preserve">vel ex ipſomet Analemmate <lb/>in propoſ. </s>
  <s xml:id="echoid-s10069" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10070" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10071" xml:space="preserve">conſtat, quis adhuc dubitabit, rectam A K, quæ cum axe H K, angulum acutũ <lb/>facit A K H, lineam Aequatoris eſſe non poſſe? </s>
  <s xml:id="echoid-s10072" xml:space="preserve">Itaque vt in triangulo A H K, linea Aequatoris ha-<lb/>
<anchor type="note" xlink:label="note-0176-07a" xlink:href="note-0176-07"/>
beatur, ducenda erit ex A, ad axem H K, perpendicularis A L, quæ neceſſario minor eſt quàm A K. <lb/></s>
  <s xml:id="echoid-s10073" xml:space="preserve">
<anchor type="note" xlink:label="note-0176-08a" xlink:href="note-0176-08"/>
Deinde ſit altitudo poli B F, minor, quàm grad. </s>
  <s xml:id="echoid-s10074" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10075" xml:space="preserve">vt in ſecunda figura apparet: </s>
  <s xml:id="echoid-s10076" xml:space="preserve">erit{q́ue} propterea <lb/>angulus F A H, recto minor. </s>
  <s xml:id="echoid-s10077" xml:space="preserve">Quare cum ei ęqualis ſit oſtenſus angulus A H I, erunt anguli H A F, <lb/>
<anchor type="note" xlink:label="note-0176-09a" xlink:href="note-0176-09"/>
A H I, ſimul vno recto minores; </s>
  <s xml:id="echoid-s10078" xml:space="preserve">ac proinde reliquus A K H, in triangulo A K H, rectum ſuperabit. <lb/></s>
  <s xml:id="echoid-s10079" xml:space="preserve">Non igitur recta A K, eſſe poteſt linea Aequatoris, cum non faciat cum axe H I, angulos rectos: </s>
  <s xml:id="echoid-s10080" xml:space="preserve">ſed du-<lb/>cta A L, ad axem H I, perpendicularis lineam Aequatoris dabit. </s>
  <s xml:id="echoid-s10081" xml:space="preserve">Solum in regione, vbi altitudo poli cõ-<lb/>plectitur grad. </s>
  <s xml:id="echoid-s10082" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10083" xml:space="preserve">recta A K, erit linea Aequatoris, quia ibi ſolum rectos angulos cum axe H I, conſti-<lb/>tuit. </s>
  <s xml:id="echoid-s10084" xml:space="preserve">Contineat enim altitudo poli B F, grad. </s>
  <s xml:id="echoid-s10085" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10086" xml:space="preserve">vt in tertia figura: </s>
  <s xml:id="echoid-s10087" xml:space="preserve">erit{q́ue} propterea angulus F A H, <lb/>ſemirectus. </s>
  <s xml:id="echoid-s10088" xml:space="preserve">Cum ergo ei æqualis oſtenſus ſit angulus A H I, erunt duo anguli H A K, A H K, ſimul vni <lb/>recto ęquales: </s>
  <s xml:id="echoid-s10089" xml:space="preserve">ac propterea reliquus angulus A K H, in triangulo A K H, rectus erit. </s>
  <s xml:id="echoid-s10090" xml:space="preserve">Igitur recta <lb/>
<anchor type="note" xlink:label="note-0176-10a" xlink:href="note-0176-10"/>
A K, fungetur munere lineę Aequatoris. </s>
  <s xml:id="echoid-s10091" xml:space="preserve">Manifeſtũ igitur eſt, Orontium pueriliter labi in linea Aequa@
<pb o="157" file="0177" n="177" rhead="LIBER SECVNDVS."/>
toris aſſignanda; </s>
  <s xml:id="echoid-s10092" xml:space="preserve">atque adeo horologia horizontalia ex eius Protypo deſcripta falſa eſſe, vbi poli altitu <lb/>do maior eſt, aut minor, quàm grad. </s>
  <s xml:id="echoid-s10093" xml:space="preserve">45. </s>
  <s xml:id="echoid-s10094" xml:space="preserve">Idem dicendum eſt de V erticalibus horologĳs. </s>
  <s xml:id="echoid-s10095" xml:space="preserve">Quamuis enim in <lb/>illis Orontius recte aſſumat lineam Verticalem F H, &amp; </s>
  <s xml:id="echoid-s10096" xml:space="preserve">axem mundi H K, errat tamen in linea F K, <lb/>quam pro linea Aequatoris accipit, propterea quòd ea ad axem H K, perpendicularis non eſt, vt <lb/>demonſtrauimus.</s>
  <s xml:id="echoid-s10097" xml:space="preserve"/>
</p>
<div xml:id="echoid-div553" type="float" level="2" n="30">
<note position="left" xlink:label="note-0176-04" xlink:href="note-0176-04a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0176-05" xlink:href="note-0176-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0176-06" xlink:href="note-0176-06a" xml:space="preserve">32. primi.</note>
<note position="left" xlink:label="note-0176-07" xlink:href="note-0176-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0176-08" xlink:href="note-0176-08a" xml:space="preserve">19. primi.</note>
<note position="left" xlink:label="note-0176-09" xlink:href="note-0176-09a" xml:space="preserve">32. primi.</note>
<note position="left" xlink:label="note-0176-10" xlink:href="note-0176-10a" xml:space="preserve">32. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10098" xml:space="preserve">TVRPIVS adhuc lapſus eſt Orontius in propoſ. </s>
  <s xml:id="echoid-s10099" xml:space="preserve">7. </s>
  <s xml:id="echoid-s10100" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s10101" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10102" xml:space="preserve">horologiorum, vbi totum axem <lb/>
<anchor type="note" xlink:label="note-0177-01a" xlink:href="note-0177-01"/>
A F, inter centrum A, &amp; </s>
  <s xml:id="echoid-s10103" xml:space="preserve">lineam Verticalis circuli F H, interiectũ pro linea Aequatoris accepit, quod <lb/>nullibi verum eſſe poteſt, cum recta A L, quæ valde inæqualis eſt rectæ A F, ſit linea Aequatoris, <lb/>vt diximus.</s>
  <s xml:id="echoid-s10104" xml:space="preserve"/>
</p>
<div xml:id="echoid-div554" type="float" level="2" n="31">
<note position="right" xlink:label="note-0177-01" xlink:href="note-0177-01a" xml:space="preserve">Maior errot <lb/>Orontii.</note>
</div>
</div>
<div xml:id="echoid-div556" type="section" level="1" n="145">
<head xml:id="echoid-head148" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s10105" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci, hoc eſt, commu <lb/>nes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s10106" xml:space="preserve">conorum, quorum baſes ſunt paral-<lb/>leli ſignorum Zodiaci, vertex autem centrum mundi, in prædicto horo <lb/>logio horizontali deſcribere.</s>
  <s xml:id="echoid-s10107" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s10108" xml:space="preserve">REPETATVR portio Analemmatis præcedentis propoſ. </s>
  <s xml:id="echoid-s10109" xml:space="preserve">perficiaturq; </s>
  <s xml:id="echoid-s10110" xml:space="preserve">Meridianus A B C, <lb/>
<anchor type="note" xlink:label="note-0177-03a" xlink:href="note-0177-03"/>
in quo ex Analemmate propoſ. </s>
  <s xml:id="echoid-s10111" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10112" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s10113" xml:space="preserve">conſtructo diametri parallelorum ducantur, <lb/>
<anchor type="note" xlink:label="note-0177-04a" xlink:href="note-0177-04"/>
vna cum diametris oppoſita ſigna connectentibus, <lb/>
<anchor type="figure" xlink:label="fig-0177-01a" xlink:href="fig-0177-01"/>
vt ſiant trianguia per axem in conis, quorum baſes <lb/>funt ipſi paralleli, vertex autem communis centrum <lb/>D. </s>
  <s xml:id="echoid-s10114" xml:space="preserve">Erit igitur ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s10115" xml:space="preserve">4. </s>
  <s xml:id="echoid-s10116" xml:space="preserve">5. </s>
  <s xml:id="echoid-s10117" xml:space="preserve">6. </s>
  <s xml:id="echoid-s10118" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10119" xml:space="preserve"><lb/>7. </s>
  <s xml:id="echoid-s10120" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10121" xml:space="preserve">KR, diameter conicæ ſectionis, quá <lb/>Sol in principio ♋, exiſtens deſcribit; </s>
  <s xml:id="echoid-s10122" xml:space="preserve">L R, diameter <lb/>
<anchor type="note" xlink:label="note-0177-05a" xlink:href="note-0177-05"/>
ſectionis, quam Sol in primo puncto ♊, &amp; </s>
  <s xml:id="echoid-s10123" xml:space="preserve">♌, de-<lb/>ſcribit; </s>
  <s xml:id="echoid-s10124" xml:space="preserve">M R, diameter ſectionis, quam Sol in initio <lb/>♉, &amp; </s>
  <s xml:id="echoid-s10125" xml:space="preserve">♍, deſcribit: </s>
  <s xml:id="echoid-s10126" xml:space="preserve">At verò NO, PO, QO, diame-<lb/>tri erunt ſectionum conicarum, quas Sol in oppo-<lb/>
<anchor type="note" xlink:label="note-0177-06a" xlink:href="note-0177-06"/>
ſitis parallelis, nempe in parallelis ♑; </s>
  <s xml:id="echoid-s10127" xml:space="preserve">♐ &amp; </s>
  <s xml:id="echoid-s10128" xml:space="preserve">♒; </s>
  <s xml:id="echoid-s10129" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s10130" xml:space="preserve"><lb/>♓, exiſtens deſcribit.</s>
  <s xml:id="echoid-s10131" xml:space="preserve"/>
</p>
<div xml:id="echoid-div556" type="float" level="2" n="1">
<note position="right" xlink:label="note-0177-03" xlink:href="note-0177-03a" xml:space="preserve">Deſcriptio at-<lb/>cuum ſignorũ <lb/>Zodiaci in prę-<lb/>dicto horologio <lb/>horizontali, ex <lb/>Analemmate.</note>
<note position="left" xlink:label="note-0177-04" xlink:href="note-0177-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a">
    <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01"/>
  </figure>
<note position="right" xlink:label="note-0177-05" xlink:href="note-0177-05a" xml:space="preserve">Diametri coni-<lb/>carũ ſectionũ, <lb/>Sole in princi-<lb/>pijs ſignorum <lb/>exiſtente.</note>
<note position="left" xlink:label="note-0177-06" xlink:href="note-0177-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s10132" xml:space="preserve">PORRO hæ diametri conicarum ſectionum <lb/>
<anchor type="note" xlink:label="note-0177-07a" xlink:href="note-0177-07"/>
inuenientur eodem pacto in quocunque alio Ana-<lb/>lemmate, quod vel maius ſit, vel minus hoc noſtro <lb/>propoſito, etiam ſi horologium ſine portione Ana-<lb/>lemmatis conſtructum ſit, vt in præcedenti ſcholio docuimus; </s>
  <s xml:id="echoid-s10133" xml:space="preserve">dummodo in alio illo Analem-<lb/>mate ex diametro Verticalis infra centrum abſcindatur recta gnomoni aſſumpto æqualis, produ-<lb/>cta ipſa diametro Verticalis, ſi id longitudo gnomonis requirat; </s>
  <s xml:id="echoid-s10134" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10135" xml:space="preserve">per extremum punctum re-<lb/>cta ducatur parallela diametro Horizontis, per quam planum horologij horizontalis duci conci-<lb/>
<anchor type="note" xlink:label="note-0177-08a" xlink:href="note-0177-08"/>
pitur. </s>
  <s xml:id="echoid-s10136" xml:space="preserve">Hæc enim recta in maiori, vel minori Analemmate à diametris ſignorum oppoſitorum ſe-<lb/>cabitur in partes æquales partibus rectæ R O, in noſtro hoc Analemmate: </s>
  <s xml:id="echoid-s10137" xml:space="preserve">Quod ita oſtendi po-<lb/>teſt. </s>
  <s xml:id="echoid-s10138" xml:space="preserve">Quoniam tam illa recta, quàm hæc R O, æqualiter à centro ſui Analemmatis diſtar, &amp; </s>
  <s xml:id="echoid-s10139" xml:space="preserve">angu-<lb/>li, quos diametri oppoſitorum ſignorum cum diametro Æquatoris faciunt, in quolibet Analem-<lb/>mate ſunt eiuſdem magnitudinis, cum ſemper eiſdem declinationibus eorundem ſignorum inſi-<lb/>
<anchor type="note" xlink:label="note-0177-09a" xlink:href="note-0177-09"/>
ſtant ad centra; </s>
  <s xml:id="echoid-s10140" xml:space="preserve">efficitur vt &amp; </s>
  <s xml:id="echoid-s10141" xml:space="preserve">anguli, quos eædem diametri cum diametro Verticalis circuli fa-<lb/>ciunt, (qui quidem vel componuntur ex illis, &amp; </s>
  <s xml:id="echoid-s10142" xml:space="preserve">ex angulo altitudinis poli contento ſub diametro <lb/>Æquatoris, &amp; </s>
  <s xml:id="echoid-s10143" xml:space="preserve">diametro Verticalis, vel relinquuntur poſt detractionem illorum ex eodem angulo <lb/>altitudinis poli) æquales inter ſe ſint, cum &amp; </s>
  <s xml:id="echoid-s10144" xml:space="preserve">anguli contenti ſub diamctro Verticalis, &amp; </s>
  <s xml:id="echoid-s10145" xml:space="preserve">diametro <lb/>Æquatoris æquales ſint. </s>
  <s xml:id="echoid-s10146" xml:space="preserve">Quare cum anguli, quos rectæ per extremitatem gnomonis (nempe per <lb/>
<anchor type="note" xlink:label="note-0177-10a" xlink:href="note-0177-10"/>
punctum G, in noſtro Analemmate, &amp; </s>
  <s xml:id="echoid-s10147" xml:space="preserve">per punctũ huic reſpondens in alio Analemmate.) </s>
  <s xml:id="echoid-s10148" xml:space="preserve">ductæ <lb/>diametro Horizontis æquidiſtantes cum diametro Verticalis faciunt, recti ſint, (qualis in noſtro <lb/>Analemmate eſtangulus G.) </s>
  <s xml:id="echoid-s10149" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10150" xml:space="preserve">anguli, quos in vtroq; </s>
  <s xml:id="echoid-s10151" xml:space="preserve">Analemmate radius cuiuſuis ſigni cum ea-<lb/>dem diametro Verticalis cóſtituit, æquales quoque, vt diximus; </s>
  <s xml:id="echoid-s10152" xml:space="preserve">(Sunt enim cũ illis, quos æquales <lb/>oſtendimus, ad verticem.) </s>
  <s xml:id="echoid-s10153" xml:space="preserve">reperientur ſemper bina triangula in vtroq; </s>
  <s xml:id="echoid-s10154" xml:space="preserve">Analemmate, nempe vnũ <lb/>in vno, &amp; </s>
  <s xml:id="echoid-s10155" xml:space="preserve">in altero alterum, habentia binos angulos æquales, vtrumq; </s>
  <s xml:id="echoid-s10156" xml:space="preserve">vtriq;</s>
  <s xml:id="echoid-s10157" xml:space="preserve">. Cum igitur &amp; </s>
  <s xml:id="echoid-s10158" xml:space="preserve">latus <lb/>habeant æquale, quod dictis angulis adiacet, nempe magnitudinem ſtyli; </s>
  <s xml:id="echoid-s10159" xml:space="preserve">habebunt quoq; </s>
  <s xml:id="echoid-s10160" xml:space="preserve">reliqua <lb/>latera æqualia, nimirum illa, quæ inter extremitatem ſtyli, &amp; </s>
  <s xml:id="echoid-s10161" xml:space="preserve">radium cuiuſq; </s>
  <s xml:id="echoid-s10162" xml:space="preserve">ſigni in vtroq; </s>
  <s xml:id="echoid-s10163" xml:space="preserve">Ana-<lb/>
<anchor type="note" xlink:label="note-0177-11a" xlink:href="note-0177-11"/>
lemmate interijciuntur, &amp;</s>
  <s xml:id="echoid-s10164" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10165" xml:space="preserve">Quod etiam inde patere poteſt; </s>
  <s xml:id="echoid-s10166" xml:space="preserve">quòd ſi Analemma illud maius ſuper-<lb/>poni intelligatur huic noſtro, ita vt centra, &amp; </s>
  <s xml:id="echoid-s10167" xml:space="preserve">diametri Horizontis, Verticalis, atq; </s>
  <s xml:id="echoid-s10168" xml:space="preserve">Æquatoris in-<lb/>ter ſe congruant, recta per extremitatem ſtyli in illo ducta congruat rectæ R O, in noſtro Analem
<pb o="158" file="0178" n="178" rhead="GNOMONICES"/>
mate, propter æqualitatem gnomonũ, &amp; </s>
  <s xml:id="echoid-s10169" xml:space="preserve">angulorum rectorum, quos gnomones cum dictis rectis <lb/>conſtituunt. </s>
  <s xml:id="echoid-s10170" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s10171" xml:space="preserve">diametri Eclipticæ oppoſita ſigna connectentes inter ſe congruant, <lb/>(quod eoſdem angulos in vtroq; </s>
  <s xml:id="echoid-s10172" xml:space="preserve">Analemmate cum diametro Æquatoris efficiant, propter eaſdẽ <lb/>declinationes in vtroq;</s>
  <s xml:id="echoid-s10173" xml:space="preserve">, vt ex cõſtructione Analemmatis manifeſtum eſt.) </s>
  <s xml:id="echoid-s10174" xml:space="preserve">liquido conſtat, rectas <lb/>inter extremitatem ſtyli G, &amp; </s>
  <s xml:id="echoid-s10175" xml:space="preserve">radios ſignorum in noſtro Analemmate æquales eſſe eiſdem rectis <lb/>in alio Analemmate; </s>
  <s xml:id="echoid-s10176" xml:space="preserve">propterea quòd illæ his congruant.</s>
  <s xml:id="echoid-s10177" xml:space="preserve"/>
</p>
<div xml:id="echoid-div557" type="float" level="2" n="2">
<note position="right" xlink:label="note-0177-07" xlink:href="note-0177-07a" xml:space="preserve">Qua ration@ <lb/>diametri coni-<lb/>carum ſectionũ <lb/>in quocunque <lb/>Analẽmate in-<lb/>ueniantur.</note>
<note position="left" xlink:label="note-0177-08" xlink:href="note-0177-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0177-09" xlink:href="note-0177-09a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0177-10" xlink:href="note-0177-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0177-11" xlink:href="note-0177-11a" xml:space="preserve">26. primi.</note>
</div>
<p>
  <s xml:id="echoid-s10178" xml:space="preserve">ITAQVE ſi in lineam meridianam horologij deſcripti ſiue ex centro H, ſiue ex I, puncto, <lb/>vbi Æquatoris planum plano horologij occurrit, transferãtur puncta G, K, L, M, I, Q, P, N, accepta <lb/>beneficio circini ex puncto, vbi in Analemmate axis mundi, vel diameter Æquatoris rectam, quæ <lb/>per extremitatem gnomonis ducta eſt diametro Horizontis æquidiſtans, interſecat; </s>
  <s xml:id="echoid-s10179" xml:space="preserve">erit G, locus <lb/>
<anchor type="note" xlink:label="note-0178-01a" xlink:href="note-0178-01"/>
<anchor type="figure" xlink:label="fig-0178-01a" xlink:href="fig-0178-01"/>
<anchor type="note" xlink:label="note-0178-02a" xlink:href="note-0178-02"/>
<anchor type="note" xlink:label="note-0178-03a" xlink:href="note-0178-03"/>
ſtyli D G; </s>
  <s xml:id="echoid-s10180" xml:space="preserve">reliqua vero puncta erunt illa, in quæ vmbra ſtyli proijcitur, Sole exiſtente in Meridia-<lb/>no circulo, &amp; </s>
  <s xml:id="echoid-s10181" xml:space="preserve">initijs ſignorum, &amp; </s>
  <s xml:id="echoid-s10182" xml:space="preserve">per quæ duci debent conicæ ſectiones ſignorum, quæ ſunt vel <lb/>circuli, vel parabolæ, vel hyperbolæ, vel ellipſes, vt ſuperiore lib. </s>
  <s xml:id="echoid-s10183" xml:space="preserve">demonſtratum eſt. </s>
  <s xml:id="echoid-s10184" xml:space="preserve">Per I, autem <lb/>ducenda eſt ad meridianam lineam perpendicularis. </s>
  <s xml:id="echoid-s10185" xml:space="preserve">Hæc enim erit linea æquinoctialis, in quam <lb/>vmbræ proijciuntur tẽpore æquinoctiorũ. </s>
  <s xml:id="echoid-s10186" xml:space="preserve">Iam vero ſi circa diametros KR, LR, MR, NO, PO, <lb/>QO, per propoſ. </s>
  <s xml:id="echoid-s10187" xml:space="preserve">8. </s>
  <s xml:id="echoid-s10188" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10189" xml:space="preserve">conicę ſectiones deſcribãtur iu aliqua materia ſolida, vt in ligno, <lb/>vel in chartis conglutinatis, excindanturq́ue, vt fiant quædã quaſi regulæ curuę, ſeu inflexę, quarũ <lb/>beneficio eędẽ ſectiones in horologiũ trãsferantur, ita vt per puncta k, L, M, Q, P, N, in lineã meri <lb/>dianã translata tranſeant, &amp; </s>
  <s xml:id="echoid-s10190" xml:space="preserve">axes earũ lineę meridianę congruant, deſcripti erunt paralleli ſignorũ <lb/>Zodiaci: </s>
  <s xml:id="echoid-s10191" xml:space="preserve">qui quidem in ipſomet etiam horologio circa diametros K H, L H, MH, N φ, P φ, Q φ, <lb/>
<anchor type="note" xlink:label="note-0178-04a" xlink:href="note-0178-04"/>
per propoſ. </s>
  <s xml:id="echoid-s10192" xml:space="preserve">8. </s>
  <s xml:id="echoid-s10193" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s10194" xml:space="preserve">deſcribi poterunt, non autem ſeorſum, vt poſtea in horologiũ tranſ <lb/>ferantur. </s>
  <s xml:id="echoid-s10195" xml:space="preserve">Tranſibit enim per k, parallelus ♋; </s>
  <s xml:id="echoid-s10196" xml:space="preserve">per L, parallelus ♊, &amp; </s>
  <s xml:id="echoid-s10197" xml:space="preserve">♌; </s>
  <s xml:id="echoid-s10198" xml:space="preserve">per M, parallelus ♉, &amp; </s>
  <s xml:id="echoid-s10199" xml:space="preserve"><lb/>♍; </s>
  <s xml:id="echoid-s10200" xml:space="preserve">per I, linea ęquinoctialis; </s>
  <s xml:id="echoid-s10201" xml:space="preserve">per Q, parallelus ♏, &amp; </s>
  <s xml:id="echoid-s10202" xml:space="preserve">♓; </s>
  <s xml:id="echoid-s10203" xml:space="preserve">per P, parallelus ♐, &amp; </s>
  <s xml:id="echoid-s10204" xml:space="preserve">♒; </s>
  <s xml:id="echoid-s10205" xml:space="preserve">per N, denique <lb/>parallelus ♑: </s>
  <s xml:id="echoid-s10206" xml:space="preserve">quos quidem omnes vmbra verticis ſtyli deſcribit, Sole in ſignorum initijs exiſten-<lb/>te, cum in illos vmbrę extremitas proijciatur, vt conſtat ex coroll. </s>
  <s xml:id="echoid-s10207" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s10208" xml:space="preserve">12. </s>
  <s xml:id="echoid-s10209" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10210" xml:space="preserve">Om-<lb/>nium autem horariarum linearum (linea meridiana excepta.) </s>
  <s xml:id="echoid-s10211" xml:space="preserve">portiones, quę extra ſectiones co-<lb/>
<anchor type="note" xlink:label="note-0178-05a" xlink:href="note-0178-05"/>
nicas ♋, &amp; </s>
  <s xml:id="echoid-s10212" xml:space="preserve">♑, reperiuntur, tam in horizontali horologio, quàm in quouis alio, delendæ ſunt, <lb/>quoniam illarum vſus nullus eſt, cum vmbra ſtyli extra tropicos non proiiciatur, quemadmodum <lb/>neque Sol extra ipſos vnquam in cœlo vagatur. </s>
  <s xml:id="echoid-s10213" xml:space="preserve">Vnde deſcribendæ erunt lineæ horariæ occultæ, <lb/>vt earum duntaxat partes intra tropicos ſignari queant, poſt deſcriptionem arcuum ſignorum Zo-<lb/>
<anchor type="note" xlink:label="note-0178-06a" xlink:href="note-0178-06"/>
diaci. </s>
  <s xml:id="echoid-s10214" xml:space="preserve">Satis eſt autem, ſi deſcribantur ſectiones conicæ ſignorũ duntaxat borealium, quando Hori-<lb/>zon omnes parallelos ſecat. </s>
  <s xml:id="echoid-s10215" xml:space="preserve">Hę enim æquales ſunt conicis ſectionibus ſignorum auſtralium oppo-<lb/>ſitorum, ſingulę ſingulis, cum tunc ſint hyperbolæ oppoſitę, &amp; </s>
  <s xml:id="echoid-s10216" xml:space="preserve">æquales, vt propoſ. </s>
  <s xml:id="echoid-s10217" xml:space="preserve">6. </s>
  <s xml:id="echoid-s10218" xml:space="preserve">ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s10219" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s10220" xml:space="preserve">Vnde facile ad ſigna auſtralia transferri poterunt, &amp; </s>
  <s xml:id="echoid-s10221" xml:space="preserve">circa puncta N, P, Q, deſcribi.</s>
  <s xml:id="echoid-s10222" xml:space="preserve"/>
</p>
<div xml:id="echoid-div558" type="float" level="2" n="3">
<note position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0178-01" xlink:href="fig-0178-01a">
    <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-01"/>
  </figure>
<note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0178-04" xlink:href="note-0178-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0178-05" xlink:href="note-0178-05a" xml:space="preserve">In quouis horo <lb/>logio ducendæ <lb/>ſunt portiones <lb/>duntaxat linea-<lb/>rum hotariarũ <lb/>inter tropicos <lb/>Cãcri, &amp; Capri-<lb/>corni, compre-<lb/>henſz.</note>
<note position="left" xlink:label="note-0178-06" xlink:href="note-0178-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s10223" xml:space="preserve">SECTIONES porrò conicæ, quarum diametri in Analemmate ſuntinter punctum R, &amp; </s>
  <s xml:id="echoid-s10224" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0178-07a" xlink:href="note-0178-07"/>
punctum I, vbi diameter Aequatoris rectam R O, ſecat, habent cornua verſus centrum horologii <lb/>H, conuerſa; </s>
  <s xml:id="echoid-s10225" xml:space="preserve">in oppoſitam verò partem conuertuntur cornua ſectionum illarum, quarum diame-<lb/>tri ſunt inter puncta O, &amp; </s>
  <s xml:id="echoid-s10226" xml:space="preserve">I; </s>
  <s xml:id="echoid-s10227" xml:space="preserve">Sic etiam in omnibus alijs horologiis, etiam declinantibus, &amp; </s>
  <s xml:id="echoid-s10228" xml:space="preserve">incli-<lb/>natis, ſectiones conicæ inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s10229" xml:space="preserve">lineam æquinoctialem porrigunt cornua ſua <lb/>verſus centrum, reliquæ verò in partem contrariam ea conuertunt: </s>
  <s xml:id="echoid-s10230" xml:space="preserve">Ita vt in vniuerſum cornua <lb/>omnium ſectionum à linea æquinoctiali magis ac magis recedant, &amp; </s>
  <s xml:id="echoid-s10231" xml:space="preserve">quodammodo fugiant. </s>
  <s xml:id="echoid-s10232" xml:space="preserve">Ra-
<pb o="159" file="0179" n="179" rhead="LIBER SECVNDVS."/>
tio huiuſce rei facilis eſt exconicis elementis Apollonii Pergęi, ſi rectè cõcipiantur coni in Analem <lb/>mate huius propoſ. </s>
  <s xml:id="echoid-s10233" xml:space="preserve">Nam ſectiones conicæ ſemper magis dilatantur verſus baſes conorum, vt ex <lb/>dictis elementis conicis patet.</s>
  <s xml:id="echoid-s10234" xml:space="preserve"/>
</p>
<div xml:id="echoid-div559" type="float" level="2" n="4">
<note position="left" xlink:label="note-0178-07" xlink:href="note-0178-07a" xml:space="preserve">Quam in partẽ <lb/>cornua ſectionũ <lb/>conicarũ in ho <lb/>tologiis vergãt.</note>
</div>
<p>
  <s xml:id="echoid-s10235" xml:space="preserve">QVOD ſi in Analemmate ſumatur longior ſtylus D M, &amp; </s>
  <s xml:id="echoid-s10236" xml:space="preserve">per M, parallela ipſi B C, agatur <lb/>
<anchor type="note" xlink:label="note-0179-01a" xlink:href="note-0179-01"/>
ſecans diametros oppoſitorum ſignorum, habebuntur diametri aliarum conicarum ſectionum, <lb/>circa quas eodem modo ſectiones ipſæ conicæ deſcribi poſſunt pro maiori horologio, in quo qui-<lb/>dem eædem lineę horariæ omnino manent: </s>
  <s xml:id="echoid-s10237" xml:space="preserve">ſed æquinoctialis linea tanto ſpatio diſtare debet in <lb/>linea meridiana à centro H, quanta eſt portio illius parallelæ per M, ductæ, intercepta inter pun-<lb/>ctum, vbi ab axe C D, ſecatur, &amp; </s>
  <s xml:id="echoid-s10238" xml:space="preserve">punctum, in quo eandem ſecat radius, ſiue diameter Aequatoris <lb/>F D. </s>
  <s xml:id="echoid-s10239" xml:space="preserve">Eadem ratione, ſi ſumatur minor ſtylus D M, minus horologium deſcribetur. </s>
  <s xml:id="echoid-s10240" xml:space="preserve">Itaque portio <lb/>
<anchor type="note" xlink:label="note-0179-02a" xlink:href="note-0179-02"/>
<anchor type="note" xlink:label="note-0179-03a" xlink:href="note-0179-03"/>
illa Analemmatis in propoſ. </s>
  <s xml:id="echoid-s10241" xml:space="preserve">præcedenti deſcripta, eſt veluti inſtrumentum quoddam ad deſcri-<lb/>benda horologia cuiuſcunque magnitudinis, quod ad ſtylum, centrum horologii, lineam æquino <lb/>ctialem, &amp; </s>
  <s xml:id="echoid-s10242" xml:space="preserve">ad lineas horarias attinet; </s>
  <s xml:id="echoid-s10243" xml:space="preserve">cum in ea aſſumi poſſit ſtylus cuiuſuis magnitudinis. </s>
  <s xml:id="echoid-s10244" xml:space="preserve">Quod <lb/>vero ſpectat ad arcus ſignorum, recurrendum erit ad Analemma in principio huius propoſ. </s>
  <s xml:id="echoid-s10245" xml:space="preserve">de-<lb/>ſcriptum, ex quo in horologio quocunque arcus ſignornm deſcribentur, vt dictum eſt.</s>
  <s xml:id="echoid-s10246" xml:space="preserve"/>
</p>
<div xml:id="echoid-div560" type="float" level="2" n="5">
<note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">Qua ratione ex <lb/>Analemmate <lb/>huius propoſ. in <lb/>horologio de <lb/>ſcribãtur arcus <lb/>ſignorũ ad ma-<lb/>iorem, vel m i-<lb/>norem longitu <lb/>dinem gnomo-<lb/>nis.</note>
<note position="left" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0179-03" xlink:href="note-0179-03a" xml:space="preserve">Portio Analem <lb/>matis inſtrumẽ <lb/>tum eſt ad ho-<lb/>rologia cuiuſuis <lb/>magnitudinis <lb/>deſcribenda.</note>
</div>
<p>
  <s xml:id="echoid-s10247" xml:space="preserve">PARALLELI iidem, ſiue arcus ſignorum Zodiaci, hac etiam ratione in horologio deſcri-<lb/>
<anchor type="note" xlink:label="note-0179-04a" xlink:href="note-0179-04"/>
bi poſſunt. </s>
  <s xml:id="echoid-s10248" xml:space="preserve">Circa rectam A λ, vtcunque ductam, quæ axem mundi referat, ex quolibet puncto D, <lb/>vt centro, ſemicircu <lb/>lus deſcribatur cuinſ <lb/>
<anchor type="figure" xlink:label="fig-0179-01a" xlink:href="fig-0179-01"/>
cunque magnitudi-<lb/>
<anchor type="note" xlink:label="note-0179-05a" xlink:href="note-0179-05"/>
nis; </s>
  <s xml:id="echoid-s10249" xml:space="preserve">ſitq́ D H, ex par <lb/>te ſiniſtra ipſius D, <lb/>æqualis aſſumpto axi <lb/>D H, in portione A-<lb/>nalemmatis præcedẽ <lb/>tis propoſ. </s>
  <s xml:id="echoid-s10250" xml:space="preserve">vel in triã <lb/>gulo H D I, ex quo in <lb/>ſcholio eiuſdem pro-<lb/>poſ. </s>
  <s xml:id="echoid-s10251" xml:space="preserve">horologium ſine <lb/>portione Analemma <lb/>
<anchor type="note" xlink:label="note-0179-06a" xlink:href="note-0179-06"/>
tis deſcripſimus; </s>
  <s xml:id="echoid-s10252" xml:space="preserve">du-<lb/>ctaq́; </s>
  <s xml:id="echoid-s10253" xml:space="preserve">D C, perpendi <lb/>culariad axem D H, <lb/>ſumatur D I, æquino <lb/>ctiali lineę D I, eiuſ-<lb/>dem portionis Ana-<lb/>lemmatis, vel dicti <lb/>trianguli, ęqualis, du-<lb/>caturq́; </s>
  <s xml:id="echoid-s10254" xml:space="preserve">recta H I, ad <lb/>partes I, quantumlibet; </s>
  <s xml:id="echoid-s10255" xml:space="preserve">vel certè (ne in ducenda linea H I, error committatur, quòd punctum H, <lb/>
<anchor type="note" xlink:label="note-0179-07a" xlink:href="note-0179-07"/>
fortaſſe nimis propinquum ſit puncto I) ex H, arcus deſcribatur ad partes D, in quo ſumatur A B, <lb/>verſus rectam D C, æqualis arcui altitudinis poli, &amp; </s>
  <s xml:id="echoid-s10256" xml:space="preserve">per B, recta H B, educatur, ſecans D C, æqui-<lb/>noctialem in I. </s>
  <s xml:id="echoid-s10257" xml:space="preserve">Erit triangulum D H I, æquale prorſus triangulo D H I, prędictę portionis Ana-<lb/>lemmatis, vel triangulo horologij ſine portione Analemmatis deſcripti, &amp; </s>
  <s xml:id="echoid-s10258" xml:space="preserve">H I, ęqualis lineę me-<lb/>ridianæ eiuſdem portionis Analemmatis, vel dicti horologij, vt ex conſtructione vtraque huius <lb/>trianguli in hac figura perſpicuum eſſe poteſt. </s>
  <s xml:id="echoid-s10259" xml:space="preserve">Ex priori enim conſtructione, ſunt duo latera D H, <lb/>D I, huius trianguli duobus lateribus D H, D I, illius ęqualia, angulosq́; </s>
  <s xml:id="echoid-s10260" xml:space="preserve">comprehendunt æqua-<lb/>les, vtpote rectos. </s>
  <s xml:id="echoid-s10261" xml:space="preserve">Igitur tota triangula ęqualia erunt. </s>
  <s xml:id="echoid-s10262" xml:space="preserve">Ex conſtructione autem poſteriori, ſunt duo <lb/>
<anchor type="note" xlink:label="note-0179-08a" xlink:href="note-0179-08"/>
anguli H D I, D H I, vnius trianguli duobus angulis H D I, D H I, alterius trianguli æquales, (quòd <lb/>in vtroque triangulo prior angulus rectus ſit, &amp; </s>
  <s xml:id="echoid-s10263" xml:space="preserve">poſterior æqualis altitudini poli) eſtq́; </s>
  <s xml:id="echoid-s10264" xml:space="preserve">latus D H, <lb/>
<anchor type="note" xlink:label="note-0179-09a" xlink:href="note-0179-09"/>
vnius lateri D H, alterius æquale. </s>
  <s xml:id="echoid-s10265" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s10266" xml:space="preserve">latera D I, H I, vnius æqualia ſunt lateribus D I, H I, al-<lb/>
<anchor type="note" xlink:label="note-0179-10a" xlink:href="note-0179-10"/>
terius, &amp;</s>
  <s xml:id="echoid-s10267" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10268" xml:space="preserve">Ex centro deinde E, Aequatoris in horologio, ex quo videlicet circulus fuit deſcriptus, <lb/>diuiſusq́; </s>
  <s xml:id="echoid-s10269" xml:space="preserve">in partes 24. </s>
  <s xml:id="echoid-s10270" xml:space="preserve">æquales, &amp;</s>
  <s xml:id="echoid-s10271" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10272" xml:space="preserve">transferantur omnia interualla inter centrum E, &amp; </s>
  <s xml:id="echoid-s10273" xml:space="preserve">lineas ho-<lb/>rarias in æquinoctiali linea F k, poſita in lineam D C, huius figuræ, quam nunc conſtruimus, à <lb/>puncto D; </s>
  <s xml:id="echoid-s10274" xml:space="preserve">nempe interuallo E F, vel E K, in horologio, quod ante hanc figuram proxime conſtru <lb/>ctum eſt, (Sunt enim rectæ E F, E K, in horologio dicto inter ſe æquales, vt in ſcholio præcedentis <lb/>propoſ. </s>
  <s xml:id="echoid-s10275" xml:space="preserve">demonſtratum eſt: </s>
  <s xml:id="echoid-s10276" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s10277" xml:space="preserve">reliqua interualla quæcunque inter E, &amp; </s>
  <s xml:id="echoid-s10278" xml:space="preserve">binas ho-<lb/>ras æquali temporis interuallo à linea meridiana remotas ęqualia oſtenſa ſunt) æqualis ſit in hac <lb/>figura recta D C; </s>
  <s xml:id="echoid-s10279" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10280" xml:space="preserve">interuallo E R, vel E S, eiuſdem horologij æqualis ſit recta D T, in hac fi-<lb/>gura, &amp;</s>
  <s xml:id="echoid-s10281" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10282" xml:space="preserve">Per puncta autem C, T, &amp; </s>
  <s xml:id="echoid-s10283" xml:space="preserve">reliqua in linea D C, notata, ex H, emittantur rectæ, qui-<lb/>bus aſcribantur numeri horarum reſpondentes translatis interuallis; </s>
  <s xml:id="echoid-s10284" xml:space="preserve">ita vt recta H C, ſit linea ho
<pb o="160" file="0180" n="180" rhead="GNOMONICES"/>
ræ quintæ poſt meridiem, &amp; </s>
  <s xml:id="echoid-s10285" xml:space="preserve">ſeptimæ poſt mediam noctem; </s>
  <s xml:id="echoid-s10286" xml:space="preserve">H T, horæ quartę poſt meridiem, &amp; </s>
  <s xml:id="echoid-s10287" xml:space="preserve"><lb/>@ctauę poſt mediam noctem, &amp;</s>
  <s xml:id="echoid-s10288" xml:space="preserve">c.</s>
  <s xml:id="echoid-s10289" xml:space="preserve"/>
</p>
<div xml:id="echoid-div561" type="float" level="2" n="6">
<note position="right" xlink:label="note-0179-04" xlink:href="note-0179-04a" xml:space="preserve">Alia deſcriptio <lb/>arcuum ſigno-<lb/>rum Zodiaci in <lb/>horologio hori-<lb/>zontali.</note>
  <figure xlink:label="fig-0179-01" xlink:href="fig-0179-01a">
    <image file="0179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179-01"/>
  </figure>
<note position="left" xlink:label="note-0179-05" xlink:href="note-0179-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0179-06" xlink:href="note-0179-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0179-07" xlink:href="note-0179-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0179-08" xlink:href="note-0179-08a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0179-09" xlink:href="note-0179-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0179-10" xlink:href="note-0179-10a" xml:space="preserve">26. primi.</note>
</div>
<p>
  <s xml:id="echoid-s10290" xml:space="preserve">EASDEM has lineas horarias ex H, per puncta lineę D C, emiſſas in hac figura obtinebimus <lb/>quoque, ſi interualla horarum in horologio inter centrum H, &amp; </s>
  <s xml:id="echoid-s10291" xml:space="preserve">ęquinoctialem lineam poſita <lb/>transferamus ex puncto H, huius figurę in rectam D C, beneficio circini, notando puncta in re-<lb/>cta D C, (quod quidem fiet, ſi ad dicta interualla horologij deſcribantur ex H, huius figurę arcus <lb/>quidam occulti ſecã-<lb/>
<anchor type="figure" xlink:label="fig-0180-01a" xlink:href="fig-0180-01"/>
tes rectã D C, in pun <lb/>ctis, quę notãda ſunt) <lb/>&amp; </s>
  <s xml:id="echoid-s10292" xml:space="preserve">per puncta in re-<lb/>
<anchor type="note" xlink:label="note-0180-01a" xlink:href="note-0180-01"/>
cta D C, hac ratione <lb/>inuenta rectas ex H, <lb/>emittamus. </s>
  <s xml:id="echoid-s10293" xml:space="preserve">Si enim <lb/>in horologio intelli-<lb/>gatur centrum E, in <lb/>propria poſitione cõ-<lb/>iunctum cum centro <lb/>mundi D, (vt in prę-<lb/>cedenti propoſ. </s>
  <s xml:id="echoid-s10294" xml:space="preserve">dixi-<lb/>mus, quando triangu <lb/>
<anchor type="note" xlink:label="note-0180-02a" xlink:href="note-0180-02"/>
lum DHI, rectũ ad <lb/>horologij planũ ſta-<lb/>tuebamus, &amp; </s>
  <s xml:id="echoid-s10295" xml:space="preserve">circulũ <lb/>ex E, deſcriptum ani-<lb/>mo concipiebamus <lb/>moueri circa lineam <lb/>ęquinoctialẽ F k, do-<lb/>nec eius centrum E, <lb/>cum D, centro mundi coniungeretur) intelligemus duo triangula, nempe H D F, vel H E F, <lb/>in horologio, &amp; </s>
  <s xml:id="echoid-s10296" xml:space="preserve">H D C, in hac propoſita figura. </s>
  <s xml:id="echoid-s10297" xml:space="preserve">Et quoniam latera illius H D, D F, ęqualia ſunt <lb/>
<anchor type="note" xlink:label="note-0180-03a" xlink:href="note-0180-03"/>
lateribus huius H D, D C; </s>
  <s xml:id="echoid-s10298" xml:space="preserve">(ſumpta enim eſt ipſi D F, vel E F, ęqualis D C, in priori con-<lb/>ſtructione huius figurę, &amp; </s>
  <s xml:id="echoid-s10299" xml:space="preserve">axis H D, hic idem eſt, qui ibi) ſuntq́; </s>
  <s xml:id="echoid-s10300" xml:space="preserve">anguli dictis lateribus contenti <lb/>æquales, nempe recti; </s>
  <s xml:id="echoid-s10301" xml:space="preserve">(Nam angulus H D C, in hac figura rectus eſt, ex conſtructione; </s>
  <s xml:id="echoid-s10302" xml:space="preserve">at verò <lb/>H D F, in horologio rectus eſt, eò quòd axis H D, ad planum Aequatoris rectus exiſtens, perpendi <lb/>cularis etiam eſt, per definitionem 3. </s>
  <s xml:id="echoid-s10303" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10304" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10305" xml:space="preserve">Euclidis, ad rectam D F, in plano Aequatoris exiſten-<lb/>tem) erunt &amp; </s>
  <s xml:id="echoid-s10306" xml:space="preserve">baſes HF, H C, ęquales. </s>
  <s xml:id="echoid-s10307" xml:space="preserve">Quare ſi rectam H F, in horologio ſumptam transferamus <lb/>
<anchor type="note" xlink:label="note-0180-04a" xlink:href="note-0180-04"/>
in hac figura ex puncto H, in rectam D C, vt dictum eſt in hac poſteriori conſtructione propoſitę <lb/>ſigurę, offendemus omnino punctum C, quod ante ex priori conſtructione eiuſdem figure inueni-<lb/>mus pro hora quinta, ac ſeptima. </s>
  <s xml:id="echoid-s10308" xml:space="preserve">Aliàs ſi recta H F, in horologio translata ex puncto H, huius fi-<lb/>gurę in rectam D C, caderet in aliud punctum, quàm in C, oſtenderemus, vt proximè, ductam re-<lb/>
<anchor type="note" xlink:label="note-0180-05a" xlink:href="note-0180-05"/>
ctam H C, fore ęqualem ipſi H F, in horologio, atque adeò &amp; </s>
  <s xml:id="echoid-s10309" xml:space="preserve">ipſi rectę ex H, in rectam <lb/>D C, quę ponitur cadere in aliud punctum, quàm in C; </s>
  <s xml:id="echoid-s10310" xml:space="preserve">cum hęc translata ſit ęqualis ſumpta eidẽ <lb/>H F, ex conſtructione. </s>
  <s xml:id="echoid-s10311" xml:space="preserve">Quare due rectæ æquales ducentur ex H, ad rectam D C, infra rectum an-<lb/>gulum D, quod eſt abſurdum. </s>
  <s xml:id="echoid-s10312" xml:space="preserve">Nam vt propoſ. </s>
  <s xml:id="echoid-s10313" xml:space="preserve">16. </s>
  <s xml:id="echoid-s10314" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10315" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10316" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s10317" xml:space="preserve">ex Proclo demonſtrauimus, ex H, ad <lb/>rectam D C, ſolum duæ rectæ inter ſe æquales duci poſſunt, vna infra punctum D, &amp; </s>
  <s xml:id="echoid-s10318" xml:space="preserve">ſupra idem <lb/>punctum altera; </s>
  <s xml:id="echoid-s10319" xml:space="preserve">non autem ambæ inſra punctum D, vt hic contingeret. </s>
  <s xml:id="echoid-s10320" xml:space="preserve">Cadet ergo recta H F, <lb/>translata ex H, in rectam D C, in punctum C. </s>
  <s xml:id="echoid-s10321" xml:space="preserve">Eadem ratione alia interualla horarum in horolo-<lb/>gio inter H, &amp; </s>
  <s xml:id="echoid-s10322" xml:space="preserve">lineam æquinoctialem tran slata ex puncto H, huius figurę in rectam D C, demon-<lb/>ſtrabimus cadere in puncta, quæ prius inuenta ſunt. </s>
  <s xml:id="echoid-s10323" xml:space="preserve">Atque hactenus in hac figura ductę ſunt ex <lb/>H, per puncta rectę D C, lineę horarię à duodecima hora meridiei vſq; </s>
  <s xml:id="echoid-s10324" xml:space="preserve">ad horam quintam à mer. <lb/></s>
  <s xml:id="echoid-s10325" xml:space="preserve">
<anchor type="note" xlink:label="note-0180-06a" xlink:href="note-0180-06"/>
&amp; </s>
  <s xml:id="echoid-s10326" xml:space="preserve">ab hora ſeptima à med. </s>
  <s xml:id="echoid-s10327" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10328" xml:space="preserve">vſque ad horam duodecimam meridiei, vt ex ipſa conſtructione <lb/>conſtat. </s>
  <s xml:id="echoid-s10329" xml:space="preserve">Dictę enim horę duntaxat ſecant ęquinoctialem lineam in horologio, quarum quidem <lb/>interualla translata ſunt. </s>
  <s xml:id="echoid-s10330" xml:space="preserve">Vnde aliarum horarum lineas ita ducemus.</s>
  <s xml:id="echoid-s10331" xml:space="preserve"/>
</p>
<div xml:id="echoid-div562" type="float" level="2" n="7">
  <figure xlink:label="fig-0180-01" xlink:href="fig-0180-01a">
    <image file="0180-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0180-01"/>
  </figure>
<note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0180-02" xlink:href="note-0180-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0180-03" xlink:href="note-0180-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0180-04" xlink:href="note-0180-04a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0180-05" xlink:href="note-0180-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0180-06" xlink:href="note-0180-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s10332" xml:space="preserve">PRO hora ſexta à mer. </s>
  <s xml:id="echoid-s10333" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s10334" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10335" xml:space="preserve">ducatur ex H, ipſi D C, patallela H V; </s>
  <s xml:id="echoid-s10336" xml:space="preserve">Et pro hora ſe-<lb/>ptima à mer. </s>
  <s xml:id="echoid-s10337" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10338" xml:space="preserve">quinta à med. </s>
  <s xml:id="echoid-s10339" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10340" xml:space="preserve">ducatur H X, angulum V H X, ęqualem faciens angulo V H C. <lb/></s>
  <s xml:id="echoid-s10341" xml:space="preserve">Similiter pro hora octaua à mer. </s>
  <s xml:id="echoid-s10342" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10343" xml:space="preserve">quarta à med. </s>
  <s xml:id="echoid-s10344" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10345" xml:space="preserve">ducatur H Y, angulũ V H Y, angulo VHT, <lb/>faciens ęqualem, &amp; </s>
  <s xml:id="echoid-s10346" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s10347" xml:space="preserve">Quod facile fiet, ſi ex H, arcus circuli deſcribatur. </s>
  <s xml:id="echoid-s10348" xml:space="preserve">Nam ſi cir-<lb/>eumferentiæ huius arcus interceptæ inter H V, &amp; </s>
  <s xml:id="echoid-s10349" xml:space="preserve">rectas ex H, ad dexterã ipſius H V, eductas, (quę <lb/>nimirum rectam D C, ſecant) transferantur ad ſiniſtram partem eiuſdem H V, in dictum arcum, <lb/>facient rectę ex H, per illas circumferentias translatas ad ſiniſtram ipſius H V, emiſſę cum H V, <lb/>angulos ęquales illis, qui ex parte dextra cum eadem H V, fiunt; </s>
  <s xml:id="echoid-s10350" xml:space="preserve">propterea quòd arcus, quibus illi <lb/>
<anchor type="note" xlink:label="note-0180-07a" xlink:href="note-0180-07"/>
<pb o="161" file="0181" n="181" rhead="LIBER SECVNDVS."/>
ad centrum H, inſiſtunt, æquales ſunt arcubus, quibus hi inſiſtunt ad idem centrum H.</s>
  <s xml:id="echoid-s10351" xml:space="preserve"/>
</p>
<div xml:id="echoid-div563" type="float" level="2" n="8">
<note position="left" xlink:label="note-0180-07" xlink:href="note-0180-07a" xml:space="preserve">27. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s10352" xml:space="preserve">POST hæc in ſemicirculo ex D, deſcripto ſupputentur declinationes ſignorum, initio facto <lb/>à recta D C, ad vtramque partem ipſius rectæ D C; </s>
  <s xml:id="echoid-s10353" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10354" xml:space="preserve">per fines ſupputationum ex D, egrediantur <lb/>rectæ, quę radij erunt ſignorum, Sole in principijs ipſorum exiſtente, ita vt recta D C, in medio <lb/>omnium aliarum rectarum ſit radius Aequatoris, ſiue ♈, &amp; </s>
  <s xml:id="echoid-s10355" xml:space="preserve">♎, vt perſpicuum eſt ex ijs, quæ in <lb/>Analemmate diximus propoſ. </s>
  <s xml:id="echoid-s10356" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10357" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10358" xml:space="preserve">Erunt autem arcus ſemicirculi ex D, deſcripti, in-<lb/>ter radium Aequatoris D C, &amp; </s>
  <s xml:id="echoid-s10359" xml:space="preserve">radios aliorum ſignorum poſiti, vel æquales omnino arcubus Ana-<lb/>lemmatis inter diametrum Aequatoris, &amp; </s>
  <s xml:id="echoid-s10360" xml:space="preserve">communes ſectiones Eclipticæ, &amp; </s>
  <s xml:id="echoid-s10361" xml:space="preserve">Meridiani poſitis, <lb/>quando nimirum ſemicirculus ex D, deſcriptus ęqualis fuerit circulo Analemmatis, vel certè ipſis <lb/>ſimiles exiſtent, quando ſcilicet dictus ſemicirculus circulo Analemmatis fuerit inæqualis. </s>
  <s xml:id="echoid-s10362" xml:space="preserve">Vnde <lb/>
<anchor type="note" xlink:label="note-0181-01a" xlink:href="note-0181-01"/>
vt ſacilius deſcribantur radij ſignorum per eorum declinationes in Analemmate inuentas, e re fo-<lb/>ret, ſi ſemicirculus ex D, deſcriptus haberet ſemidiametrum æqualem ſemidiametro Analemma-<lb/>tis, vt arcus declinationũ ex Analemmate in hunc ſemicirculũ beneficio circini poſſint transferri.</s>
  <s xml:id="echoid-s10363" xml:space="preserve"/>
</p>
<div xml:id="echoid-div564" type="float" level="2" n="9">
<note position="left" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s10364" xml:space="preserve">EX hac itaque figura in hunc modum conſtructa, quam in ſequentibus figuram radiorum Zo <lb/>diaci appellabimus, deſcribentur in horologio arcus ſignorum hac ratione. </s>
  <s xml:id="echoid-s10365" xml:space="preserve">Transferatur ex figu-<lb/>ra iam confecta linea H μ, horæ 12. </s>
  <s xml:id="echoid-s10366" xml:space="preserve">inter punctum H, &amp; </s>
  <s xml:id="echoid-s10367" xml:space="preserve">radium ♋, in lineam meridianam horo-<lb/>logij ex H, vel linea I μ, inter Aequatoris radium, &amp; </s>
  <s xml:id="echoid-s10368" xml:space="preserve">radium ♋, ex puncto I, æquinoctialis lineę <lb/>in horologio in lineam meridianam, punctum notando K. </s>
  <s xml:id="echoid-s10369" xml:space="preserve">Similiter linea horę primę, &amp; </s>
  <s xml:id="echoid-s10370" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10371" xml:space="preserve">eiuſ-<lb/>dem figuræ inter H, &amp; </s>
  <s xml:id="echoid-s10372" xml:space="preserve">eundem radium ♋, vel inter ęquinoctialem radium, &amp; </s>
  <s xml:id="echoid-s10373" xml:space="preserve">radium ♋, transfe-<lb/>ratur in lineas horę primæ, &amp; </s>
  <s xml:id="echoid-s10374" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10375" xml:space="preserve">horologij ex H, vel ex ξ, π, punctis æquinoctialis lineæ, pun-<lb/>
<anchor type="note" xlink:label="note-0181-02a" xlink:href="note-0181-02"/>
ctum quoque in qualibet notando: </s>
  <s xml:id="echoid-s10376" xml:space="preserve">Et ſic reliqua ſpatia inter H, &amp; </s>
  <s xml:id="echoid-s10377" xml:space="preserve">radium ♋, vel inter æquino-<lb/>ctialem radium, &amp; </s>
  <s xml:id="echoid-s10378" xml:space="preserve">radium ♋, transferantur in horologium in lineas horarum correſpondẽtium, <lb/>puncta notando in illis. </s>
  <s xml:id="echoid-s10379" xml:space="preserve">Deinde hæc puncta in horariis lineis horologii notata coniungantur ap-<lb/>poſitè linea quadam curua, &amp; </s>
  <s xml:id="echoid-s10380" xml:space="preserve">inflexa. </s>
  <s xml:id="echoid-s10381" xml:space="preserve">Hæc enim erit ſectio conica ♋, in horologio deſcripta. </s>
  <s xml:id="echoid-s10382" xml:space="preserve">Eo-<lb/>dem modo conicæ ſectiones aliorum ſignorum deſcribentur, ſi rectæ inter H, &amp; </s>
  <s xml:id="echoid-s10383" xml:space="preserve">radios ſignorum, <lb/>vel inter æquinoctialem radium, &amp; </s>
  <s xml:id="echoid-s10384" xml:space="preserve">radios ſignorum comprehenſæ in lineas horarias correſpon-<lb/>dentes horologij ex H, centro horologij, vel ex linea æquinoctiali transferantur, &amp;</s>
  <s xml:id="echoid-s10385" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10386" xml:space="preserve">hac tamen cõ <lb/>ditione, vt rectæ inter radium Aequatoris, &amp; </s>
  <s xml:id="echoid-s10387" xml:space="preserve">radios aliorum ſignorum verſus punctum H, exiſten <lb/>tes, transferantur à linea æquinoctiali in reſpondentes lineas horarias verſus centrum H; </s>
  <s xml:id="echoid-s10388" xml:space="preserve">aliæ autẽ <lb/>in contrariam partem: </s>
  <s xml:id="echoid-s10389" xml:space="preserve">Item interualla linearum ex H, cadentium verſus radium Aequatoris DC, <lb/>
<anchor type="note" xlink:label="note-0181-03a" xlink:href="note-0181-03"/>
transferantur ex centro horologij H, in eas lineas horarias, quæ ex H, centro horologii verſus li-<lb/>neam æquinoctialem tendunt; </s>
  <s xml:id="echoid-s10390" xml:space="preserve">Interualla verò linearum ex H, ductarum in alteram partem rectæ <lb/>H V, ita vt radium Aequatoris infra D, ſecare non poſſint, transferantur in lineas horarum horolo <lb/>gij ex centro H, in partem ſuperiorem, hoc eſt, in eas horas, quæ lineam æquinoctialem non ſecãt, <lb/>quales ſunt omnes horæ poſt horam ſextam à meridie vſque ad mediam noctem, &amp; </s>
  <s xml:id="echoid-s10391" xml:space="preserve">omnes horæ <lb/>à media nocte, vſque ad horam ſextam.</s>
  <s xml:id="echoid-s10392" xml:space="preserve"/>
</p>
<div xml:id="echoid-div565" type="float" level="2" n="10">
<note position="left" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0181-03" xlink:href="note-0181-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s10393" xml:space="preserve">COMMODVM etiam erit interdum in ſemiſſibus horarum, vel quadrantibus inquirere <lb/>puncta arcuum ſignorum. </s>
  <s xml:id="echoid-s10394" xml:space="preserve">Vt in propoſito exemplo, quia puncta in lineis horarum quintæ à me-<lb/>dia nocte, &amp; </s>
  <s xml:id="echoid-s10395" xml:space="preserve">ſeptimæ à meridie, per quæ duci debet arcus ♋, nimium diſtant à centro H, inuenien <lb/>da erunt huiuſmodi puncta in lineis horarum 5 {1/2}. </s>
  <s xml:id="echoid-s10396" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s10397" xml:space="preserve">6 {1/2}. </s>
  <s xml:id="echoid-s10398" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s10399" xml:space="preserve">Idem facien <lb/>
<anchor type="note" xlink:label="note-0181-04a" xlink:href="note-0181-04"/>
dum eſſet in lineis horarum 8 {1/2}. </s>
  <s xml:id="echoid-s10400" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s10401" xml:space="preserve">3 {1/2}. </s>
  <s xml:id="echoid-s10402" xml:space="preserve">à meridie pro punctis arcus ♑, inueſtigan <lb/>dis, &amp;</s>
  <s xml:id="echoid-s10403" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10404" xml:space="preserve">In proxima figura linea ex H, cadens ad ſiniſtram rectæ H V, punctis diſtincta pertinet ad <lb/>horas 5 {1/2}. </s>
  <s xml:id="echoid-s10405" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s10406" xml:space="preserve">6 {1/2}. </s>
  <s xml:id="echoid-s10407" xml:space="preserve">à meridie, &amp;</s>
  <s xml:id="echoid-s10408" xml:space="preserve">c.</s>
  <s xml:id="echoid-s10409" xml:space="preserve"/>
</p>
<div xml:id="echoid-div566" type="float" level="2" n="11">
<note position="left" xlink:label="note-0181-04" xlink:href="note-0181-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s10410" xml:space="preserve">SED demonſtremus iam Geometricè, rectè hac ratione deſcribi parallelos, arcusve ſignorũ. <lb/></s>
  <s xml:id="echoid-s10411" xml:space="preserve">Non enim deſunt, qui vel omnino negent, inter quos eſt Ioan. </s>
  <s xml:id="echoid-s10412" xml:space="preserve">B@ptiſta Benedictus in ſua Gnomo <lb/>nica cap. </s>
  <s xml:id="echoid-s10413" xml:space="preserve">70. </s>
  <s xml:id="echoid-s10414" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10415" xml:space="preserve">71. </s>
  <s xml:id="echoid-s10416" xml:space="preserve">vbi alia, &amp; </s>
  <s xml:id="echoid-s10417" xml:space="preserve">multo longiore ratione conatur arcus ſignorum deſcribere, vel certè <lb/>dubitent, hoc modo rectè poſſe deſcribi arcus ſignorum, cùm rationem non videant, qua hæc no-<lb/>
<anchor type="note" xlink:label="note-0181-05a" xlink:href="note-0181-05"/>
ſtra deſcriptio, quam quidem omnes ſcriptores ſine vlla demonſtratione tradunt, nitatur. </s>
  <s xml:id="echoid-s10418" xml:space="preserve">Intelli-<lb/>gatur ergo triangulum D H I, portionis Analemmatis præcedentis propoſ. </s>
  <s xml:id="echoid-s10419" xml:space="preserve">vel horologij in ſcho-<lb/>lio eiuſdem propoſ. </s>
  <s xml:id="echoid-s10420" xml:space="preserve">ſine por@ione Analemmatis deſcripti, rectum ad planum horologii, ac lineæ <lb/>
<anchor type="note" xlink:label="note-0181-06a" xlink:href="note-0181-06"/>
meridianæ inſiſtens, ita vt punctum H, in centro horologii, &amp; </s>
  <s xml:id="echoid-s10421" xml:space="preserve">I, in linea æquinoctiali ſtatuatur, vt <lb/>in horologio huius propoſ. </s>
  <s xml:id="echoid-s10422" xml:space="preserve">apparet. </s>
  <s xml:id="echoid-s10423" xml:space="preserve">Si igitur figura continens lineas horarias, &amp; </s>
  <s xml:id="echoid-s10424" xml:space="preserve">ſignorum ra-<lb/>dios proxime conſtructa axi H D, dicti trianguli ad horologium recti applicetur, &amp; </s>
  <s xml:id="echoid-s10425" xml:space="preserve">hinc inde cir-<lb/>cunducatur, ita tamen vt D C, radius Aequatoris rectum ſemper angulum in D, cum axe D H, con <lb/>ſtituat; </s>
  <s xml:id="echoid-s10426" xml:space="preserve">perſpicuum eſt, radios ſignorum, ſi eos planum horologii penetrare concipiamus animo, <lb/>in horologio deſcribere ſectiones conicas ſignorum, in quas nimirum ad motum diurnum ipſi <lb/>radii à Sole proiiciuntur; </s>
  <s xml:id="echoid-s10427" xml:space="preserve">quia in illa circunductione radii ſignorum efficientes cum radio Aequa <lb/>toris angulos declinationum, &amp; </s>
  <s xml:id="echoid-s10428" xml:space="preserve">cum axe angulos complementorum declinationum, à conicis ſu-<lb/>perficiebus à radiis Solis deſcriptis non recedunt, ſed producti ad cœlum vſque ad ipſos paralle-<lb/>los perueniunt. </s>
  <s xml:id="echoid-s10429" xml:space="preserve">Q<unsure/>uoniam verò latera H D, D C, trianguli H D C, proximè antecedentis figuræ <lb/>(vt à quinta hora à meridie, vel à ſeptima à med. </s>
  <s xml:id="echoid-s10430" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10431" xml:space="preserve">cui reſpondet linea H C@ incipiamus) æqua-
<pb o="162" file="0182" n="182" rhead="GNOMONICES"/>
lia ſunt lateribus H D, D F, trianguli H D F, in horologio, quòd D F, ipſi E F, cui æqualis eſt ſum <lb/>pta D C, in radio Aequatoris, æqualis ſit; </s>
  <s xml:id="echoid-s10432" xml:space="preserve">(Cum enim latera E I, I F, trianguli E I F, lateribus D I, <lb/>I F, trianguli D I F, æqualia ſint, angulosq́; </s>
  <s xml:id="echoid-s10433" xml:space="preserve">contineant æquales, nempe rectos; </s>
  <s xml:id="echoid-s10434" xml:space="preserve">Nam E I F, rectus eſt <lb/>ex conſtructione, at F I D, rectus eſt, ex defin. </s>
  <s xml:id="echoid-s10435" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10436" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10437" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10438" xml:space="preserve">Euclidis, quòd F I, communis ſectio Aequa <lb/>
<anchor type="figure" xlink:label="fig-0182-01a" xlink:href="fig-0182-01"/>
toris, &amp; </s>
  <s xml:id="echoid-s10439" xml:space="preserve">plani horolo <lb/>gii ad Meridianum, <lb/>
<anchor type="note" xlink:label="note-0182-01a" xlink:href="note-0182-01"/>
hoc eſt, ad triãgulum <lb/>D H I, in plano Meri-<lb/>diani ſitũ, atq; </s>
  <s xml:id="echoid-s10440" xml:space="preserve">adeo <lb/>ad rectã D I, perpen-<lb/>
<anchor type="note" xlink:label="note-0182-02a" xlink:href="note-0182-02"/>
dicularis eſt, in pun-<lb/>cto I; </s>
  <s xml:id="echoid-s10441" xml:space="preserve">æquales erunt <lb/>
<anchor type="note" xlink:label="note-0182-03a" xlink:href="note-0182-03"/>
baſes E F, D F,) angu <lb/>losq́, continent æqua <lb/>les, vtpote rectos; </s>
  <s xml:id="echoid-s10442" xml:space="preserve">Nã <lb/>H D C, in proxima <lb/>figura rectus eſt, ex <lb/>cõſtructione, at vero <lb/>&amp; </s>
  <s xml:id="echoid-s10443" xml:space="preserve">H D F, in horo-<lb/>logio rectus eſt, pro-<lb/>
<anchor type="note" xlink:label="note-0182-04a" xlink:href="note-0182-04"/>
pterea quòd axis HD, <lb/>rectus ad planũ Ae-<lb/>quatoris, ad rectam <lb/>F D, in eo exiſtentem <lb/>perpendicularis eſt, <lb/>in pũcto D, ex defin. <lb/></s>
  <s xml:id="echoid-s10444" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10445" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10446" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10447" xml:space="preserve">Euclidis; </s>
  <s xml:id="echoid-s10448" xml:space="preserve">æquales erunt baſes H C, H F, &amp; </s>
  <s xml:id="echoid-s10449" xml:space="preserve">anguli D H C, D H F. </s>
  <s xml:id="echoid-s10450" xml:space="preserve">Quare ſi triangulum <lb/>
<anchor type="note" xlink:label="note-0182-05a" xlink:href="note-0182-05"/>
H D C, circa axem H D, in horologio moueri concipiatur, donec cum triangulo H D F, coniun-<lb/>tur, &amp; </s>
  <s xml:id="echoid-s10451" xml:space="preserve">recta H C, rectæ H F, in plano horologij congruat, cadet radii æquinoctialis punctum C, in <lb/>punctum F, ob æqualitatem angulorum C H D; </s>
  <s xml:id="echoid-s10452" xml:space="preserve">F H D, &amp; </s>
  <s xml:id="echoid-s10453" xml:space="preserve">linearum H C, H F, &amp; </s>
  <s xml:id="echoid-s10454" xml:space="preserve">radii ♋, punctũ <lb/>
<anchor type="note" xlink:label="note-0182-06a" xlink:href="note-0182-06"/>
Z, cadet in punctum α, propterea quod &amp; </s>
  <s xml:id="echoid-s10455" xml:space="preserve">recta H α, æqualis ſumpta eſt rectæ H Z, per conſtru-<lb/>ctionem, vel F α, ipſi C Z. </s>
  <s xml:id="echoid-s10456" xml:space="preserve">Per punctum ergo α, horæ quintæ à meridie incedit ſectio conica ♋, <lb/>cum in ipſum radius cancri incidat in illa reuolutione trianguli D H C, circa axem D H, in horo-<lb/>logio, vt oſtendimus. </s>
  <s xml:id="echoid-s10457" xml:space="preserve">Non aliter probabimus &amp; </s>
  <s xml:id="echoid-s10458" xml:space="preserve">punctum T, in illa circumlatione radiorum Zo-<lb/>diaci cadere in R; </s>
  <s xml:id="echoid-s10459" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10460" xml:space="preserve">β, punctum radii ♋, in γ; </s>
  <s xml:id="echoid-s10461" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10462" xml:space="preserve">ſic de cæteris lineis horariis, quæ æquinoctia-<lb/>lem lineam interſecant, dicendum eſt.</s>
  <s xml:id="echoid-s10463" xml:space="preserve"/>
</p>
<div xml:id="echoid-div567" type="float" level="2" n="12">
<note position="right" xlink:label="note-0181-05" xlink:href="note-0181-05a" xml:space="preserve">Demonſtratio <lb/>poſterioris de-<lb/>ſcriptionis pa-<lb/>rallelorum, ſiue <lb/>arcuum ſigno-<lb/>rum. Vnde li-<lb/>quet, Ioan. Ba-<lb/>ptiſtam Benedi <lb/>ctum immerito <lb/>huiuſmodi de-<lb/>ſcriptionẽ dam <lb/>nare.</note>
<note position="left" xlink:label="note-0181-06" xlink:href="note-0181-06a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a">
    <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0182-01"/>
  </figure>
<note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0182-02" xlink:href="note-0182-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0182-03" xlink:href="note-0182-03a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0182-04" xlink:href="note-0182-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0182-05" xlink:href="note-0182-05a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0182-06" xlink:href="note-0182-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s10464" xml:space="preserve">PRO hora vero ſexta à mer. </s>
  <s xml:id="echoid-s10465" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s10466" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10467" xml:space="preserve">quæ lineam æquinoctialem non ſecat, ſed ei ęqui-<lb/>diſtat, ducenda eſt H V, ad axem H D, perpendicularis in figura radiorum Zodiaci, ſiue radio Ae-<lb/>quatoris D C, parallela; </s>
  <s xml:id="echoid-s10468" xml:space="preserve">quia hac ratione, in illa circumductione radiorum, recta H V, recte H δ, <lb/>in horologio congruet, propter æqualitatem angulorum rectorum D H V, D H δ; </s>
  <s xml:id="echoid-s10469" xml:space="preserve">Eſt enim angu <lb/>
<anchor type="note" xlink:label="note-0182-07a" xlink:href="note-0182-07"/>
lus D H V, rectus, ex conſtructione, angulus vero D H δ<unsure/>, ad axem conſtitutus rectus quoque eſt, <lb/>per defin. </s>
  <s xml:id="echoid-s10470" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10471" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10472" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10473" xml:space="preserve">Euclidis, propterea quòd H δ, linea ſextæ horæ, communis nimirum ſectio pla <lb/>ni horologii, &amp; </s>
  <s xml:id="echoid-s10474" xml:space="preserve">circuli horæ ſextæ, ad Meridianum, (ad quem vtrumque illorum rectum eſt) hoc <lb/>eſt, ad triangulum D H I, ac proinde &amp; </s>
  <s xml:id="echoid-s10475" xml:space="preserve">ad rectam D H, in puncto H, perpendicularis eſt. </s>
  <s xml:id="echoid-s10476" xml:space="preserve">Quam-<lb/>
<anchor type="note" xlink:label="note-0182-08a" xlink:href="note-0182-08"/>
obrem punctum θ, radij ♋, cadet in δ, ob ęqualitatem, ex conſtructione, rectarum H θ, H δ: <lb/></s>
  <s xml:id="echoid-s10477" xml:space="preserve">Sumpta enim eſt in horologio recta H δ, rectæ H θ, in figura radiorum æqualis. </s>
  <s xml:id="echoid-s10478" xml:space="preserve">Pro hora deni-<lb/>que ſeptima à meridie, vel quinta à med. </s>
  <s xml:id="echoid-s10479" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10480" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10481" xml:space="preserve">aliis, quæ æquinoctialem lineam nõ ſecant, ſi opus <lb/>fuerit, (In noſtro exemplo nulla alia hora indigemus, cum arcus ♋, ſecet lineas horarum ſeptimæ à <lb/>mer. </s>
  <s xml:id="echoid-s10482" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10483" xml:space="preserve">quintæ à med. </s>
  <s xml:id="echoid-s10484" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10485" xml:space="preserve">in punctis ualde remotis à centro H) ducendæ ſunt lineæ, quæ ex alte-<lb/>ra parte, nempe ſiniſtra, cum linea H V, horæ ſextæ angulos faciant æquales angulis, quos lineæ ra-<lb/>
<anchor type="note" xlink:label="note-0182-09a" xlink:href="note-0182-09"/>
dium Aequatoris ex parte dextra ſecantes, &amp; </s>
  <s xml:id="echoid-s10486" xml:space="preserve">quæ ad horas æquinoctialem lineam ſecantes in ho-<lb/>rologio pertinent, cum eadem linea horæ ſextæ faciunt, quales ſunt H X, H Y, &amp;</s>
  <s xml:id="echoid-s10487" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10488" xml:space="preserve">Nam hoc mo. <lb/></s>
  <s xml:id="echoid-s10489" xml:space="preserve">do facient huiuſmodi lineæ cum axe H D, in figura radiorum Zodiaci angulos X H D, Y H D, <lb/>æquales angulis, quos lineæ horariæ reſpondentes in horologio cum axe H D, faciunt: </s>
  <s xml:id="echoid-s10490" xml:space="preserve">nimirum <lb/>angulum X H D, in dicta figura æqualem angulo κ H D, in horologio. </s>
  <s xml:id="echoid-s10491" xml:space="preserve">Cum enim duo anguli <lb/>X H λ, X H D, in figura radiorum æquales ſint duobus angulis D H k, D H κ, in horologio; </s>
  <s xml:id="echoid-s10492" xml:space="preserve">quòd <lb/>tam hi, quàm illi duobus ſint rectis æquales: </s>
  <s xml:id="echoid-s10493" xml:space="preserve">Sit autem angulus X H λ, in dicta figura angulo <lb/>
<anchor type="note" xlink:label="note-0182-10a" xlink:href="note-0182-10"/>
D H K, in horologio æqualis; </s>
  <s xml:id="echoid-s10494" xml:space="preserve">(Nam angulus X H λ, in eadem figura æqualis eſt angulo C H D, <lb/>eiuſdem figuræ, per pronunciatum 3. </s>
  <s xml:id="echoid-s10495" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10496" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10497" xml:space="preserve">Euclidis, quòd &amp; </s>
  <s xml:id="echoid-s10498" xml:space="preserve">anguli toti recti V H λ, V H D, in-<lb/>ter ſe, &amp; </s>
  <s xml:id="echoid-s10499" xml:space="preserve">ablati V H X, V H C, inter ſe, per conſtructionem, æquales ſint; </s>
  <s xml:id="echoid-s10500" xml:space="preserve">angulus autem C H D, <lb/>dictæ figuræ æqualis eſt angulo D H F, in horologio, vt demõſtratũ eſt, atq; </s>
  <s xml:id="echoid-s10501" xml:space="preserve">adeò &amp; </s>
  <s xml:id="echoid-s10502" xml:space="preserve">angulo D H K,
<pb o="163" file="0183" n="183" rhead="LIBER SECVNDVS."/>
in eodem horologio, qui angulo D H F, æqualis eſt. </s>
  <s xml:id="echoid-s10503" xml:space="preserve">Quod hac ratione oſtendemus. </s>
  <s xml:id="echoid-s10504" xml:space="preserve">Ducta recta <lb/>D K, erit D K, ipſi D F, æqualis; </s>
  <s xml:id="echoid-s10505" xml:space="preserve">propterea quòd latera I D, I F, trianguli D I F, lateribus I D, I K, <lb/>
<anchor type="note" xlink:label="note-0183-01a" xlink:href="note-0183-01"/>
trianguli D I K, æqualia ſint, angulosq́; </s>
  <s xml:id="echoid-s10506" xml:space="preserve">contineant æquales, nimirum rectos. </s>
  <s xml:id="echoid-s10507" xml:space="preserve">Quoniam igitur la-<lb/>tera D H, D F, trianguli D H F, in horologio, lateribus D H, D k, trianguli D H k, in eodem horo-<lb/>logio æqualia ſunt, angulosq́; </s>
  <s xml:id="echoid-s10508" xml:space="preserve">continent æquales, vtpote rectos; </s>
  <s xml:id="echoid-s10509" xml:space="preserve">Eſt enim axis H D, rectus exiſtens <lb/>ad planum Aequatoris, ad rectas D F, D K, in plano eodem Aequatoris exiſtentes perpendicularis, <lb/>ex defin. </s>
  <s xml:id="echoid-s10510" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10511" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10512" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10513" xml:space="preserve">Euclidis; </s>
  <s xml:id="echoid-s10514" xml:space="preserve">æquales erunt anguli D H F, D H k) erit quoque reliquus X H D, in <lb/>dicta figura reliquo D H X, in horologio æqualis; </s>
  <s xml:id="echoid-s10515" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10516" xml:space="preserve">ſic de aliis. </s>
  <s xml:id="echoid-s10517" xml:space="preserve">Quæ cum ita ſint, coniungetur <lb/>recta H X, dictæ figuræ cum recta H X, horologii, in illa circumuolutione radiorum, propter an-<lb/>gulo rum æqualitatem, quos rectę H X, H X, faciunt cum axe H D, &amp;</s>
  <s xml:id="echoid-s10518" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10519" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s10520" xml:space="preserve">eſt ratio de cæte-<lb/>
<anchor type="note" xlink:label="note-0183-02a" xlink:href="note-0183-02"/>
ris. </s>
  <s xml:id="echoid-s10521" xml:space="preserve">Conſtat igitur Ioan. </s>
  <s xml:id="echoid-s10522" xml:space="preserve">Baptiſtam Benedictum in ſua Gnomonica immerito deſcriptionẽ hanc <lb/>arcuum ſignorum reprehendere.</s>
  <s xml:id="echoid-s10523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div568" type="float" level="2" n="13">
<note position="left" xlink:label="note-0182-07" xlink:href="note-0182-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0182-08" xlink:href="note-0182-08a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0182-09" xlink:href="note-0182-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0182-10" xlink:href="note-0182-10a" xml:space="preserve">13. primi.</note>
<note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0183-02" xlink:href="note-0183-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s10524" xml:space="preserve">PORRO deſcriptis hyperbolis borealium ſignorum, hoc eſt, quæ inter centrum H, &amp; </s>
  <s xml:id="echoid-s10525" xml:space="preserve">æqui-<lb/>
<anchor type="note" xlink:label="note-0183-03a" xlink:href="note-0183-03"/>
noctialem lineam continentur, deſcribemus accuratius hyperbolas oppoſitas ſignorum auſtraliũ, <lb/>id eſt, quæ ex altera parte lineæ æquinoctialis deſcribuntur, (quoniam hæ difficilius deſcribentur, <lb/>quòd puncta in lineis horarijs vltra lineam æquinoctialem, per quæ ducendæ ſunt, magis inter ſe <lb/>diſtent, quàm citra lineam æquinoctialem) hac ratione. </s>
  <s xml:id="echoid-s10526" xml:space="preserve">Inuenta diametro transuerſa oppoſita-<lb/>rum ſectionum in linea meridiana horologij, quæ quidem æqualis ſemper eſt portioni rectę H B, <lb/>in figura radiorum inter radios ſignorum oppoſitorum interceptæ, (quemadmodum in horolo-<lb/>gio recta K N, diameter eſt oppoſitarum ſectionum ♋, &amp; </s>
  <s xml:id="echoid-s10527" xml:space="preserve">♑, atque ęqualis portioni μ a, rectæ <lb/>
<anchor type="note" xlink:label="note-0183-04a" xlink:href="note-0183-04"/>
H B, in figura radiorum inter radios ♋, &amp; </s>
  <s xml:id="echoid-s10528" xml:space="preserve">♑, interiectæ) diuidemus eam bifariam, vt habeamus <lb/>centrum oppoſitarum ſectionum, ſecundum doctrinam Apollonii in ſecundis definitionibus lib. <lb/></s>
  <s xml:id="echoid-s10529" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10530" xml:space="preserve">conicorum elementorum. </s>
  <s xml:id="echoid-s10531" xml:space="preserve">Deinde quia per propoſ. </s>
  <s xml:id="echoid-s10532" xml:space="preserve">30. </s>
  <s xml:id="echoid-s10533" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10534" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10535" xml:space="preserve">Apollonii, recta linea quæcunque <lb/>per centrum oppoſitarum ſectionum ducta in centro ſecatur bifariam, ducemus ex punctis linea-<lb/>rum horariarum ſupra lineam ęquinoctialem, per quæ hyperbolæ boreales tranſeunt, per centrũ <lb/>inuentum lineas occultas. </s>
  <s xml:id="echoid-s10536" xml:space="preserve">Si enim ſegmentis illarum inter dicta puncta, &amp; </s>
  <s xml:id="echoid-s10537" xml:space="preserve">centrum poſitis ab-<lb/>ſcindamus infra centrum dictum lineas ęquales, habebimus in lineis illis occultis puncta, per quæ <lb/>hyperbolæ auſtrales ducendæ ſunt. </s>
  <s xml:id="echoid-s10538" xml:space="preserve">Qua arte, &amp; </s>
  <s xml:id="echoid-s10539" xml:space="preserve">induſtria vtemur quoque in ſequentibus horolo-<lb/>giis, in quibus oppoſitæ hyperbolæ deſcribendę erunt, ſiue illæ ſint parallelorum Æquatoris per <lb/>initia ſignorum Zodiaci ductorum, ſiue parallelorum Horizontis.</s>
  <s xml:id="echoid-s10540" xml:space="preserve"/>
</p>
<div xml:id="echoid-div569" type="float" level="2" n="14">
<note position="right" xlink:label="note-0183-03" xlink:href="note-0183-03a" xml:space="preserve">Quomodo ex <lb/>hyperbolis ſi-<lb/>gnorum borea-<lb/>lium deſcriban <lb/>tur hyperbolæ <lb/>auſtraliũ ſign@@ <lb/>ium.</note>
<note position="left" xlink:label="note-0183-04" xlink:href="note-0183-04a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s10541" xml:space="preserve">HÆC ratio deſcribendarum hyperbolarum auſtralium ſignorum ex hyperbolis ſignorũ bo-<lb/>realium planius intelligetur ex ſequenti figura: </s>
  <s xml:id="echoid-s10542" xml:space="preserve">In qua diameter oppoſitarum hyperbolarum eſt <lb/>D E, &amp; </s>
  <s xml:id="echoid-s10543" xml:space="preserve">centrum earum punctum F. </s>
  <s xml:id="echoid-s10544" xml:space="preserve">Si igitur ex puncto K, ſuperioris hyperbolæ ducatur per cen-<lb/>trum F, recta K F N, abſcindaturq́; </s>
  <s xml:id="echoid-s10545" xml:space="preserve">F N, ipſi F K, æqualis, ducenda erit per punctum N, hyperbola <lb/>oppoſita; </s>
  <s xml:id="echoid-s10546" xml:space="preserve">quandoquidem ex propoſ. </s>
  <s xml:id="echoid-s10547" xml:space="preserve">30. </s>
  <s xml:id="echoid-s10548" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10549" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10550" xml:space="preserve">Apolì. </s>
  <s xml:id="echoid-s10551" xml:space="preserve">recta F k, æqualis eſt ſegmento eiuſdem re-<lb/>ctæ vltra F, extenſæ inter F, centrum &amp; </s>
  <s xml:id="echoid-s10552" xml:space="preserve">oppoſitam hyperbolam comprehenſo. </s>
  <s xml:id="echoid-s10553" xml:space="preserve">Sic etiam, ducta <lb/>recta L F M, ſi rectæ F L, abſcindatur recta F M, ducenda erit oppoſita hyperbole per punctum M; <lb/></s>
  <s xml:id="echoid-s10554" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10555" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s10556" xml:space="preserve">Ducendæ porro erunt, meo iudicio, rectæ per centrum hyperbolarum oppoſita-<lb/>rum ex illis punctis borealium hyperbolarum, per quæ tranſeunt lineæ horariæ: </s>
  <s xml:id="echoid-s10557" xml:space="preserve">quoniã illa pun-<lb/>cta per conſtructionem ſunt inuenta. </s>
  <s xml:id="echoid-s10558" xml:space="preserve">Vnde accuratius per illa deſcribemus hyperbolam oppoſi-<lb/>
<anchor type="note" xlink:label="note-0183-06a" xlink:href="note-0183-06"/>
tam, quàm per alia puncta inter illa intermedia, quæ non ſunt per conſtructionem inuenta, ſed <lb/>per coniecturam.</s>
  <s xml:id="echoid-s10559" xml:space="preserve"/>
</p>
<div xml:id="echoid-div570" type="float" level="2" n="15">
<note position="left" xlink:label="note-0183-06" xlink:href="note-0183-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s10560" xml:space="preserve">FACILE autem ex propoſ. </s>
  <s xml:id="echoid-s10561" xml:space="preserve">6. </s>
  <s xml:id="echoid-s10562" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10563" xml:space="preserve">cognoſcemus, quinam paralleli faciant in ho-<lb/>rologio ſectiones oppoſitas, hoc eſt, hyperbolas, vel alias ſectiones. </s>
  <s xml:id="echoid-s10564" xml:space="preserve">In ſolas enim hyperbolas qua-<lb/>drat prædicta ratio. </s>
  <s xml:id="echoid-s10565" xml:space="preserve">Quod tamen etiam ex figura radiorum Zodiaci paulo ante deſcripta ita eli-<lb/>
<anchor type="note" xlink:label="note-0183-07a" xlink:href="note-0183-07"/>
ciemus. </s>
  <s xml:id="echoid-s10566" xml:space="preserve">Quotieſcunque recta H B, in dicta figura ſecat duos radios ſignorum oppoſitorum, hoc <lb/>eſt, radios æqualiter hinc inde à radio Æquatoris diſtantes, quales ſunt radij ♋, &amp; </s>
  <s xml:id="echoid-s10567" xml:space="preserve">♑; </s>
  <s xml:id="echoid-s10568" xml:space="preserve">♊, &amp; </s>
  <s xml:id="echoid-s10569" xml:space="preserve">♐; </s>
  <s xml:id="echoid-s10570" xml:space="preserve">♉, <lb/>&amp; </s>
  <s xml:id="echoid-s10571" xml:space="preserve">♏, &amp;</s>
  <s xml:id="echoid-s10572" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10573" xml:space="preserve">arcus, ſeu paralleli illorum oppoſitorum ſignorum ſunt hyperbolæ oppoſitæ. </s>
  <s xml:id="echoid-s10574" xml:space="preserve">Quoniam <lb/>enim in triangulo D H a, angulus externus A D a, maior eſt interno oppoſito D H a; </s>
  <s xml:id="echoid-s10575" xml:space="preserve">eſt autem an-<lb/>
<anchor type="note" xlink:label="note-0183-08a" xlink:href="note-0183-08"/>
gulus A D a, complemento declinationis paralleli, cuius radius D a, atque adeò &amp; </s>
  <s xml:id="echoid-s10576" xml:space="preserve">oppoſiti, cuius <lb/>
<anchor type="note" xlink:label="note-0183-09a" xlink:href="note-0183-09"/>
radius D μ, æqualis; </s>
  <s xml:id="echoid-s10577" xml:space="preserve">angulus autem D H a, altitudini poli ſupra Horizontem æqualis eſt, ſecabit <lb/>Horizon vtrumque parallelum radiorũ D a, D μ, vt in coroll propoſ. </s>
  <s xml:id="echoid-s10578" xml:space="preserve">6.</s>
  <s xml:id="echoid-s10579" xml:space="preserve"><unsure/> ſuperioris lib. </s>
  <s xml:id="echoid-s10580" xml:space="preserve">docuimus. <lb/></s>
  <s xml:id="echoid-s10581" xml:space="preserve">Quare per eandem@propoſ. </s>
  <s xml:id="echoid-s10582" xml:space="preserve">6. </s>
  <s xml:id="echoid-s10583" xml:space="preserve">arcus illorum ſignorum hyperbolæ ſunt oppoſitæ, &amp; </s>
  <s xml:id="echoid-s10584" xml:space="preserve">ęquales. </s>
  <s xml:id="echoid-s10585" xml:space="preserve">Quan-<lb/>do verò recta H B, non ſecat vtrumque radium ſignorum oppoſitorum, ſed vni æquidiſtat, &amp; </s>
  <s xml:id="echoid-s10586" xml:space="preserve">alte-<lb/>rum ſecat; </s>
  <s xml:id="echoid-s10587" xml:space="preserve">erit arcus illius ſigni, cuius radius ſecatur, Parabola. </s>
  <s xml:id="echoid-s10588" xml:space="preserve">Quoniam enim tunc externus <lb/>angulus A D a, cõplementi declinationis, æqualis eſt interno angulo D H μ, altitudinis poli, quòd <lb/>
<anchor type="note" xlink:label="note-0183-10a" xlink:href="note-0183-10"/>
H μ, D a, parallelæ ponantur; </s>
  <s xml:id="echoid-s10589" xml:space="preserve">tanget Horizon, ex coroll. </s>
  <s xml:id="echoid-s10590" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s10591" xml:space="preserve">5. </s>
  <s xml:id="echoid-s10592" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s10593" xml:space="preserve">vtrumque pa-<lb/>rallelorum oppoſitorum. </s>
  <s xml:id="echoid-s10594" xml:space="preserve">Quare per eandem propoſ. </s>
  <s xml:id="echoid-s10595" xml:space="preserve">5. </s>
  <s xml:id="echoid-s10596" xml:space="preserve">arcus alterius, cuius radius ſecatur, Para-<lb/>bole erit. </s>
  <s xml:id="echoid-s10597" xml:space="preserve">Quando denique recta H B, neque vtrumque radium oppoſitorum ſignorum ſecat, neq; <lb/></s>
  <s xml:id="echoid-s10598" xml:space="preserve">vni æquidiſtat, ſed vnum quidem ſecat, ab altero autem ſemper magis, ac magis recedit, erit arcus <lb/>illius ſigni, cuius radius ſecatur, Ellipſis. </s>
  <s xml:id="echoid-s10599" xml:space="preserve">Nam quia tunc angulus A D a, complementi declinatio-
<pb o="164" file="0184" n="184" rhead="GNOMONICES"/>
nis minor eſt angulo D H μ, altitudinis poli, (Si enim æquales eſſent anguli A D a, D H μ, exter-<lb/>nus, &amp; </s>
  <s xml:id="echoid-s10600" xml:space="preserve">internus, recta H B, foret radio D a, parallela; </s>
  <s xml:id="echoid-s10601" xml:space="preserve">ſi autem maior eſſet angulus A D a, angulo <lb/>
<anchor type="note" xlink:label="note-0184-01a" xlink:href="note-0184-01"/>
D H μ, coirent inter ſe rectæ H B, &amp; </s>
  <s xml:id="echoid-s10602" xml:space="preserve">D a, quod non ponitur) fit, vt Horizon parallelis illis oppoſi-<lb/>
<anchor type="note" xlink:label="note-0184-02a" xlink:href="note-0184-02"/>
tis neq; </s>
  <s xml:id="echoid-s10603" xml:space="preserve">æquidiſtet, neque eos tangat, neque ſecet, vt ex coroll. </s>
  <s xml:id="echoid-s10604" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s10605" xml:space="preserve">7. </s>
  <s xml:id="echoid-s10606" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s10607" xml:space="preserve">conſtat. <lb/></s>
  <s xml:id="echoid-s10608" xml:space="preserve">Quamobrem arcus ſigni illius, cuius radius ſecatur, erit per eandem propoſ. </s>
  <s xml:id="echoid-s10609" xml:space="preserve">7. </s>
  <s xml:id="echoid-s10610" xml:space="preserve">Ellipſis. </s>
  <s xml:id="echoid-s10611" xml:space="preserve">Manife-<lb/>ſtum autem eſt, quando alicuius ſigni arcus Parabola eſt, vel Ellipſis, oppoſiti ſigni arcum in horo-<lb/>logio deſcribi non poſſe; </s>
  <s xml:id="echoid-s10612" xml:space="preserve">propterea quòd rectæ ex H, emiſſę radium illius non ſecant, vt diximus.</s>
  <s xml:id="echoid-s10613" xml:space="preserve"/>
</p>
<div xml:id="echoid-div571" type="float" level="2" n="16">
<note position="right" xlink:label="note-0183-07" xlink:href="note-0183-07a" xml:space="preserve">Quomodo co-<lb/>gnoſcatur, an a@ <lb/>cus ſignorũ ſint <lb/>hyper@olæ, pa-<lb/>rabolæ, aut elli-<lb/>pſes.</note>
<note position="right" xlink:label="note-0183-08" xlink:href="note-0183-08a" xml:space="preserve">16. primi.</note>
<note position="left" xlink:label="note-0183-09" xlink:href="note-0183-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0183-10" xlink:href="note-0183-10a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">Quando alicu-<lb/>ius ſigni atcus <lb/>eſt Parabola, vel <lb/>Ellipſis, arcus ſi-<lb/>gni oppoſiti in <lb/>horologio de-<lb/>ſcribi nequit.</note>
</div>
<p>
  <s xml:id="echoid-s10614" xml:space="preserve">CÆTERVM ſatis erit, ſi ex poſteriori figura huius propoſ. </s>
  <s xml:id="echoid-s10615" xml:space="preserve">portionem arcus cuiuslibet ſi-<lb/>
<anchor type="note" xlink:label="note-0184-03a" xlink:href="note-0184-03"/>
gni vſque ad lineam meridianam ex vna duntaxat parte deſcribamus. </s>
  <s xml:id="echoid-s10616" xml:space="preserve">Ex hac enim &amp; </s>
  <s xml:id="echoid-s10617" xml:space="preserve">reliqua por-<lb/>tio ex alia parte, (atque in ſequentibus quidem horologiis multo accuratius, quàm ſi totum arcũ <lb/>
<anchor type="note" xlink:label="note-0184-04a" xlink:href="note-0184-04"/>
ex figura radiorum Zodiaci deſcriberemus, vt ſuo loco dicemus) immo &amp; </s>
  <s xml:id="echoid-s10618" xml:space="preserve">totus arcus ſigni oppo <lb/>ſiti (ſi tamen diameter arcuum, nempe recta H B, in figura radiorum radios ſignorum oppoſito-<lb/>rum ſecet. </s>
  <s xml:id="echoid-s10619" xml:space="preserve">Nam tunc ſolum, vt oſtendimus, illorum ſignorum arcus hyperbolæ oppoſitæ ſunt, &amp; </s>
  <s xml:id="echoid-s10620" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0184-01a" xlink:href="fig-0184-01"/>
<anchor type="note" xlink:label="note-0184-05a" xlink:href="note-0184-05"/>
<anchor type="note" xlink:label="note-0184-06a" xlink:href="note-0184-06"/>
ęquales) deſcribi poterit. </s>
  <s xml:id="echoid-s10621" xml:space="preserve">Ita autem propoſitum exequemur. </s>
  <s xml:id="echoid-s10622" xml:space="preserve">Sit hyperbolarum oppoſitarum, vel <lb/>Parabolæ, vel Ellipſis axis A B, qualis eſt meridiana linea in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s10623" xml:space="preserve">portio arcus <lb/>
<anchor type="note" xlink:label="note-0184-07a" xlink:href="note-0184-07"/>
illius, vel ſectionis conicæ vſque ad axem deſcripta ſit C D: </s>
  <s xml:id="echoid-s10624" xml:space="preserve">Inuento autem in axe A B, puncto E, <lb/>per quod arcus ſigni oppofiti tranſire debet, (quod quidem habetur, ſi D E, ſumatur æqualis dia-<lb/>metro tranſuerſæ arcuum oppoſiterum in figura radiorum, nempe ſegmento rectæ H B, inter ra-<lb/>dios illorum ſignorum oppoſitorum) &amp; </s>
  <s xml:id="echoid-s10625" xml:space="preserve">acceptis rectis D A, E B, inter ſe æqualibus cuiuſcunque <lb/>magnitudinis; </s>
  <s xml:id="echoid-s10626" xml:space="preserve">diuiſaq́; </s>
  <s xml:id="echoid-s10627" xml:space="preserve">diametro D E, bifariam in F, ponemus vnum pedem circini in F, &amp; </s>
  <s xml:id="echoid-s10628" xml:space="preserve">alterũ <lb/>extendemus ad quodlibet punctum arcus C D, vtpote vſque ad C, &amp; </s>
  <s xml:id="echoid-s10629" xml:space="preserve">circino non variato deſcribe-<lb/>mus ex F, ex altera parte axis arcũ occultum alicuius circuli; </s>
  <s xml:id="echoid-s10630" xml:space="preserve">Item alios duos ex vtraque parte eiuſ-<lb/>dem axis verſus partes E. </s>
  <s xml:id="echoid-s10631" xml:space="preserve">Rurſus vnum pedem circini ſtatuentes in A, extendemus alterum vſque <lb/>ad C, &amp; </s>
  <s xml:id="echoid-s10632" xml:space="preserve">ſic manentibus circini cruribus extenſis, deſcribemus ex A, arcum circuli, qui priorem ex <lb/>F, deſcriptum ex altera parte axis ſecet in G; </s>
  <s xml:id="echoid-s10633" xml:space="preserve">Item duos alios ex B, qui priores duos ex F, ex vtraq; <lb/></s>
  <s xml:id="echoid-s10634" xml:space="preserve">
<anchor type="note" xlink:label="note-0184-08a" xlink:href="note-0184-08"/>
parte eiuſdem axis verſus partes E, deſcriptos ſecent in H, I. </s>
  <s xml:id="echoid-s10635" xml:space="preserve">Nam per punctum G, tranſibit arcus <lb/>C D, productus, &amp; </s>
  <s xml:id="echoid-s10636" xml:space="preserve">per puncta H, I, incedet arcus oppoſitus, &amp; </s>
  <s xml:id="echoid-s10637" xml:space="preserve">æqualis, qui per punctum E, poſi-<lb/>tus eſt tranſire. </s>
  <s xml:id="echoid-s10638" xml:space="preserve">Eodem pacto, ſi circinum extendamus ex F, in K, &amp; </s>
  <s xml:id="echoid-s10639" xml:space="preserve">ex F, tres arcus deſcribamus ad <lb/>interuallum F K; </s>
  <s xml:id="echoid-s10640" xml:space="preserve">Item ex A, &amp; </s>
  <s xml:id="echoid-s10641" xml:space="preserve">B, alios tres ad interuallum A K, vnum quidem ex A, &amp; </s>
  <s xml:id="echoid-s10642" xml:space="preserve">duos ex B, <lb/>qui priores tres ſecent in L, M, N, tranſibunt ijdem arcus per puncta L, M, N; </s>
  <s xml:id="echoid-s10643" xml:space="preserve">Et ita alia atque alia <lb/>puncta, quotquot voluerimus, inueniemus. </s>
  <s xml:id="echoid-s10644" xml:space="preserve">Hortarer tamen, vt ex F, in portione arcus C D, acci <lb/>perentur puncta illa, vbi à lineis horarijs ſecatur. </s>
  <s xml:id="echoid-s10645" xml:space="preserve">Quòd ſi arcus ſignorum oppoſitorum non ſunt <lb/>hyperbolę oppoſitæ, &amp; </s>
  <s xml:id="echoid-s10646" xml:space="preserve">æquales, vt contingit, cum diameter arcuum, vel recta H B, in figura radio-<lb/>rum Zodiaci radios oppoſitos non ſecat, ſed vnum tantum, ſatis eſt, ſi bini duntaxat arcus ex alte-<lb/>ra parte axis D E, ſeſe ſecantes deſcribantur ex F, &amp; </s>
  <s xml:id="echoid-s10647" xml:space="preserve">A, ita vt F, ſumatur in quocunque loco diame-<lb/>tri A B, etiamſi illud non ſit centrum: </s>
  <s xml:id="echoid-s10648" xml:space="preserve">Nam tunc arcus oppoſiti ſigni deſcribi non poteſt, vt pau-
<pb o="165" file="0185" n="185" rhead="LIBER SECVNDVS."/>
lo ante diximus. </s>
  <s xml:id="echoid-s10649" xml:space="preserve">Verum hoc arti ficium tunc minus neceſſarium eſt in horizontali horologio, quia <lb/>vtraque portio arcus C D, G D, vno labore deſcribitur ſecundum poſteriorem modum, qui per fi-<lb/>guram radiorum Zodiaci abſoluitur, vt ex ſuperioribus patet. </s>
  <s xml:id="echoid-s10650" xml:space="preserve">Sed pro arcubus oppoſitis res erit <lb/>valde vtilis, &amp; </s>
  <s xml:id="echoid-s10651" xml:space="preserve">commoda. </s>
  <s xml:id="echoid-s10652" xml:space="preserve">In declinantibus quoque horologijs, &amp; </s>
  <s xml:id="echoid-s10653" xml:space="preserve">inclinatis magnam commodita-<lb/>tem afferet hæc praxis, ſiue vtriuſque ſigni oppoſiti arcus deſcribi poſſit in horologio, ſiue vnius <lb/>tantum, vt ſuo loco perſpicuum erit.</s>
  <s xml:id="echoid-s10654" xml:space="preserve"/>
</p>
<div xml:id="echoid-div572" type="float" level="2" n="17">
<note position="left" xlink:label="note-0184-03" xlink:href="note-0184-03a" xml:space="preserve">Quo pacto ex <lb/>portione vnius <lb/>arcus alicuius ſi <lb/>gni uſque ad li-<lb/>neam meridia-<lb/>nam deſcripti, <lb/>deſcribatur re <lb/>liqua portio, at-<lb/>que etĩam arcus <lb/>ſigni oppoſi ti, ſi <lb/>arcus ſignorum <lb/>õ<unsure/>ppoſitorũ ſue-<lb/>@int hyperbolę.</note>
<note position="left" xlink:label="note-0184-04" xlink:href="note-0184-04a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a">
    <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0184-01"/>
  </figure>
<note position="left" xlink:label="note-0184-05" xlink:href="note-0184-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0184-06" xlink:href="note-0184-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0184-07" xlink:href="note-0184-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0184-08" xlink:href="note-0184-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s10655" xml:space="preserve">SED praxim hanc Geometrice demonſtremus. </s>
  <s xml:id="echoid-s10656" xml:space="preserve">Ductis rectis A k, A L, K L, D K, D L, F K, <lb/>F L, F M, F N, B M, B N, E M, E N, quarum k L, ſecet rectam A D, in O; </s>
  <s xml:id="echoid-s10657" xml:space="preserve">quoniam duo latera F A, <lb/>F K, triãguli A F k, æqualia ſunt duobus lateribus F A, F L, trianguli A F L, &amp; </s>
  <s xml:id="echoid-s10658" xml:space="preserve">baſis A K, baſi A L, <lb/>æqualis, erunt anguli quoque A F k, A F L, æquales. </s>
  <s xml:id="echoid-s10659" xml:space="preserve">Rurſus quia latera F O, F K, trianguli O F k, <lb/>
<anchor type="note" xlink:label="note-0185-01a" xlink:href="note-0185-01"/>
<anchor type="note" xlink:label="note-0185-02a" xlink:href="note-0185-02"/>
æqualia ſunt lateribus F O, F L, trianguli O F L, continentq́; </s>
  <s xml:id="echoid-s10660" xml:space="preserve">angulos æquales, vt oſtendimus, erũt <lb/>&amp; </s>
  <s xml:id="echoid-s10661" xml:space="preserve">baſes O K, OL, &amp; </s>
  <s xml:id="echoid-s10662" xml:space="preserve">anguli ad O, æquales, ideoq́; </s>
  <s xml:id="echoid-s10663" xml:space="preserve">recti. </s>
  <s xml:id="echoid-s10664" xml:space="preserve">Et quoniam in cono recto, cuiuſmodi ſunt <lb/>
<anchor type="note" xlink:label="note-0185-03a" xlink:href="note-0185-03"/>
omnes, quorum baſes ſunt paralleli Solis, &amp; </s>
  <s xml:id="echoid-s10665" xml:space="preserve">communis vertex in centro mundi, diameter ſection-<lb/>nis cuiuſuis conicę ſecat omnes ordinatim applicatas bifariam, &amp; </s>
  <s xml:id="echoid-s10666" xml:space="preserve">ad angulos rectos, vt conſtat ex <lb/>propoſ. </s>
  <s xml:id="echoid-s10667" xml:space="preserve">7. </s>
  <s xml:id="echoid-s10668" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10669" xml:space="preserve">1 Apollonij, fit vt k L, ſit ordinatim applicata ad diametrum A D, conicæ ſectionis <lb/>C D. </s>
  <s xml:id="echoid-s10670" xml:space="preserve">Nulla enim alia recta ex K, ad A D, applicata ſecari poteſt ad angulos rectos, vt conſtat ex iis, <lb/>quę ad propoſ. </s>
  <s xml:id="echoid-s10671" xml:space="preserve">17. </s>
  <s xml:id="echoid-s10672" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10673" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10674" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s10675" xml:space="preserve">demonſtrauimus ex Proclo. </s>
  <s xml:id="echoid-s10676" xml:space="preserve">Tranſibit ergo ſectio conica C D, pro-<lb/>ducta per punctum L; </s>
  <s xml:id="echoid-s10677" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10678" xml:space="preserve">ſic de cæteris punctis. </s>
  <s xml:id="echoid-s10679" xml:space="preserve">Rurſus quia A D, B E, æquales ſunt, ſi addantur <lb/>æquales D F, E F, erunt quoque totæ A F, B F, æquales. </s>
  <s xml:id="echoid-s10680" xml:space="preserve">Cum ergo duo latera A F, F k, trianguli <lb/>A F K, æqualia ſint duobus lateribus B F, F N, trianguli B F N, &amp; </s>
  <s xml:id="echoid-s10681" xml:space="preserve">baſis A K, baſi B N, æqualis, erũt <lb/>
<anchor type="note" xlink:label="note-0185-04a" xlink:href="note-0185-04"/>
&amp; </s>
  <s xml:id="echoid-s10682" xml:space="preserve">anguli A F K, B F N, æquales. </s>
  <s xml:id="echoid-s10683" xml:space="preserve">Quare vt ex Proclo ad propoſ. </s>
  <s xml:id="echoid-s10684" xml:space="preserve">15. </s>
  <s xml:id="echoid-s10685" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10686" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10687" xml:space="preserve">Euclidis demonſtraui-<lb/>
<anchor type="note" xlink:label="note-0185-05a" xlink:href="note-0185-05"/>
mus, rectę F K, F N, vnam rectam lineam conſtituent, ac proinde in F, centro ſectionis diuiſam bi-<lb/>fariam. </s>
  <s xml:id="echoid-s10688" xml:space="preserve">Quocirca cum in hyperbolis oppoſitis, quarum diameter D E, recta ex k, per centrum F, <lb/>ducta ſecetur, per propoſ. </s>
  <s xml:id="echoid-s10689" xml:space="preserve">30. </s>
  <s xml:id="echoid-s10690" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10691" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10692" xml:space="preserve">Apollonij, in centro F, bifariam, tranſibit neceſſario oppoſita <lb/>hyperbola per punctum N. </s>
  <s xml:id="echoid-s10693" xml:space="preserve">Eodem pacto oſtendemus eandem tranſire per punctum M, &amp; </s>
  <s xml:id="echoid-s10694" xml:space="preserve">ſic de <lb/>reliquis punctis. </s>
  <s xml:id="echoid-s10695" xml:space="preserve">Quoniam verò in triangulis D O K, D O L, latera O D, O k, lateribus O D, O L, <lb/>æqualia ſunt, angulosq́; </s>
  <s xml:id="echoid-s10696" xml:space="preserve">comprehendunt ęquales, nempe rectos, vt demõſtra tum eſt, erunt &amp; </s>
  <s xml:id="echoid-s10697" xml:space="preserve">baſes <lb/>
<anchor type="note" xlink:label="note-0185-06a" xlink:href="note-0185-06"/>
D k, D L, æquales. </s>
  <s xml:id="echoid-s10698" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s10699" xml:space="preserve">ratione æquales inter ſe erunt E M, E N: </s>
  <s xml:id="echoid-s10700" xml:space="preserve">Et rurſus D k, ipſi E N, &amp; </s>
  <s xml:id="echoid-s10701" xml:space="preserve"><lb/>D L, ipſi E M, æqualis erit, ſi conſiderentur triangula D F K, E F N, &amp; </s>
  <s xml:id="echoid-s10702" xml:space="preserve">D F L, E F M; </s>
  <s xml:id="echoid-s10703" xml:space="preserve">Sunt enim la-<lb/>tera quoque F D, F K, lateribus F E, F N, æqualia, angulosq́; </s>
  <s xml:id="echoid-s10704" xml:space="preserve">continent æquales, &amp;</s>
  <s xml:id="echoid-s10705" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10706" xml:space="preserve">Quare ſi inter-<lb/>
<anchor type="note" xlink:label="note-0185-07a" xlink:href="note-0185-07"/>
uallo D K, deſcribatur ex D, arcus verſus L, &amp; </s>
  <s xml:id="echoid-s10707" xml:space="preserve">alii duo ex E, hincinde, tranſibunt hi arcus per pun-<lb/>cta L, M, N; </s>
  <s xml:id="echoid-s10708" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s10709" xml:space="preserve">ratione arcus ex eiſdẽ punctis D, E, deſcripti ad interualla inter D, &amp; </s>
  <s xml:id="echoid-s10710" xml:space="preserve">reliqua <lb/>puncta conicæ ſectionis C D, tranſibunt per alia puncta ſectionum D L G, E M H, E N I. </s>
  <s xml:id="echoid-s10711" xml:space="preserve">Vnde ſi <lb/>terni ſemper arcus ex A, F, D, Item ex B, F, E, deſcripti ſe mutuo interſecent, exquiſite valde inuen-<lb/>ta erunt puncta, per quæ duci debent ſectiones conicæ oppoſitæ; </s>
  <s xml:id="echoid-s10712" xml:space="preserve">adeò vt hac ratione facile exami-<lb/>nari poſſit deſcriptio arcuum ſignorum. </s>
  <s xml:id="echoid-s10713" xml:space="preserve">Quæ res magnam cõmoditatem prębet in arcubus ſigno-<lb/>rum delineandis in horologiis declinantibus, &amp; </s>
  <s xml:id="echoid-s10714" xml:space="preserve">inclinatis, vt infra manifeſtum erit.</s>
  <s xml:id="echoid-s10715" xml:space="preserve"/>
</p>
<div xml:id="echoid-div573" type="float" level="2" n="18">
<note position="left" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">8. primi.</note>
<note position="right" xlink:label="note-0185-03" xlink:href="note-0185-03a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0185-04" xlink:href="note-0185-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0185-05" xlink:href="note-0185-05a" xml:space="preserve">8. primi.</note>
<note position="right" xlink:label="note-0185-06" xlink:href="note-0185-06a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0185-07" xlink:href="note-0185-07a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s10716" xml:space="preserve">POSSVNT quoque hyperbolæ ſignorum oppoſitorum, (quando nimirum recta H B, in fi-<lb/>
<anchor type="note" xlink:label="note-0185-08a" xlink:href="note-0185-08"/>
gura radiorum radios oppoſitorum ſignorum ſecat) quæ quidem æquales inter ſe ſunt, &amp; </s>
  <s xml:id="echoid-s10717" xml:space="preserve">oppoſi-<lb/>tæ, vt ex propoſ. </s>
  <s xml:id="echoid-s10718" xml:space="preserve">14. </s>
  <s xml:id="echoid-s10719" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s10720" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10721" xml:space="preserve">Apollonij liquet, una opera commodiſſime deſcribi hoc modo. </s>
  <s xml:id="echoid-s10722" xml:space="preserve">Inuẽtis, <lb/>
<anchor type="note" xlink:label="note-0185-09a" xlink:href="note-0185-09"/>
vt prius, in linea meridiana horologij duobus punctis, per quæ arcus ſignorum oppoſitorum du-<lb/>ci debent, ſumatur in eadem linea meridiana extenſa punctum φ, tantum à puncto hyperbolę vl-<lb/>tra lineam ęquinoctialem deſcribendæ diſtans, quantum centrum horologii H, à puncto hyperbo <lb/>læ inter lineam ęquinoctialem, &amp; </s>
  <s xml:id="echoid-s10723" xml:space="preserve">centrum H, deſcribendæ, quæ illi opponitur, abeſt, &amp; </s>
  <s xml:id="echoid-s10724" xml:space="preserve">ex puncto <lb/>φ, egrediantur occultæ lineæ horarię inſtar earum, quæ ex centro H, eductæ ſunt. </s>
  <s xml:id="echoid-s10725" xml:space="preserve">Quod quidẽ fa-<lb/>cile fiet, ſi per punctum X, bifariam diuidens tranſuerſam diametrum hyperbolarum oppoſitarũ <lb/>ducatur linea æquinoctiali lineæ parallela, tanquam altera linea æquinoctialis reſpectu centri φ. <lb/></s>
  <s xml:id="echoid-s10726" xml:space="preserve">Vbi enim hęc ſecabit horarias lineas ex centro H, emiſſas, per ea puncta ducendæ ſunt occultę li-<lb/>neę horarię ex φ, vt patet: </s>
  <s xml:id="echoid-s10727" xml:space="preserve">quia hac ratione ęquales erunt anguli ad centra H, φ, contenti ſub li-<lb/>
<anchor type="note" xlink:label="note-0185-10a" xlink:href="note-0185-10"/>
neis horarijs, &amp; </s>
  <s xml:id="echoid-s10728" xml:space="preserve">linea meridiana. </s>
  <s xml:id="echoid-s10729" xml:space="preserve">Vel etiam hoc modo, &amp; </s>
  <s xml:id="echoid-s10730" xml:space="preserve">forſitan commodius. </s>
  <s xml:id="echoid-s10731" xml:space="preserve">Deſcripto ex H, ar-<lb/>
<anchor type="note" xlink:label="note-0185-11a" xlink:href="note-0185-11"/>
cu circuli occulto, deſcribatur ad idem interuallum alius arcus ex φ. </s>
  <s xml:id="echoid-s10732" xml:space="preserve">Si enim in priori arcu ſuman <lb/>tur interualla horarum, initio facto à linea meridiana, transferanturq́; </s>
  <s xml:id="echoid-s10733" xml:space="preserve">in poſteriorem arcum, à li-<lb/>nea quoque meridiana facto initio, habebuntur puncta in ſecundo hoc arcu, per quę ducendę rur <lb/>ſus ſunt lineę horarię ex φ. </s>
  <s xml:id="echoid-s10734" xml:space="preserve">Pro hora vero ſexta ducenda eſt per φ, linea ęquinoctiali lineę paralle-<lb/>la, vel ad lineam meridianam perpendicularis. </s>
  <s xml:id="echoid-s10735" xml:space="preserve">Itaque ſi omnia interualla, quę in poſteriori deſcri <lb/>ptione arcuum ſignorum Zodiaci (quę quidem ex figura radiorum Zodiaci abſoluitur) diximus <lb/>circino transferenda eſſe ex H, centro horologii in lineas horarias, vt deſcribatur quęcunque hy-<lb/>perbola inter centrum H, &amp; </s>
  <s xml:id="echoid-s10736" xml:space="preserve">lineam ęquinoctialem, transferantur ſimul eodem circino ex φ, in re <lb/>ſpondentes lineas horarias ex φ, egredientes, habebuntur vno labore vtrobique puncta, per quę du <lb/>cendę ſunt hyperbolę oppoſitæ, &amp; </s>
  <s xml:id="echoid-s10737" xml:space="preserve">ęquales. </s>
  <s xml:id="echoid-s10738" xml:space="preserve">Exemplum habes in hyperbolis ♋, &amp; </s>
  <s xml:id="echoid-s10739" xml:space="preserve">♑, ſuperioris ho <lb/>rologij. </s>
  <s xml:id="echoid-s10740" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s10741" xml:space="preserve">ratio eſt de alijs hyperbolis oppoſitis.</s>
  <s xml:id="echoid-s10742" xml:space="preserve"/>
</p>
<div xml:id="echoid-div574" type="float" level="2" n="19">
<note position="right" xlink:label="note-0185-08" xlink:href="note-0185-08a" xml:space="preserve">Qua ratione <lb/>hyperbolæ op-<lb/>poſitæ una ope-<lb/>ra in horologio <lb/>deſcribantur.</note>
<note position="left" xlink:label="note-0185-09" xlink:href="note-0185-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0185-10" xlink:href="note-0185-10a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0185-11" xlink:href="note-0185-11a" xml:space="preserve">50</note>
</div>
<pb o="166" file="0186" n="186" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s10743" xml:space="preserve">EODEM artificio in ſequentibus utemur, ſumendo in horologiis declinantibus, &amp; </s>
  <s xml:id="echoid-s10744" xml:space="preserve">inclinatis <lb/>lineam ſtyli loco lineę meridianæ; </s>
  <s xml:id="echoid-s10745" xml:space="preserve">ſimiliter &amp; </s>
  <s xml:id="echoid-s10746" xml:space="preserve">in figura, ex qua arcus ſignorum deſcribuntur, lineã <lb/>indicis pro linea H B, horę 12. </s>
  <s xml:id="echoid-s10747" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s10748" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10749" xml:space="preserve">vt ſuo loco monebimus. </s>
  <s xml:id="echoid-s10750" xml:space="preserve">Itaque parallelos, ſiue arcus ſignorum <lb/>Zodiaci, &amp;</s>
  <s xml:id="echoid-s10751" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10752" xml:space="preserve">in prędicto horologio horizontali deſcripſimus. </s>
  <s xml:id="echoid-s10753" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s10754" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div576" type="section" level="1" n="146">
<head xml:id="echoid-head149" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s10755" xml:space="preserve">LINEAS horarias in figura radiorum huius propoſ. </s>
  <s xml:id="echoid-s10756" xml:space="preserve">ex H, egredientes hoc modo deſcribit An-<lb/>
<anchor type="note" xlink:label="note-0186-01a" xlink:href="note-0186-01"/>
dreas Schonerus in opere ſuæ Gnomonices. </s>
  <s xml:id="echoid-s10757" xml:space="preserve">Ducta recta H I B, quæ conſtituat angulum altitudinis poli <lb/>A H B, quemadmodum &amp; </s>
  <s xml:id="echoid-s10758" xml:space="preserve">nos fecimus, ſumit in ea punctum quodcunque φ, per quod ipſi D H, parallelã <lb/>
<anchor type="note" xlink:label="note-0186-02a" xlink:href="note-0186-02"/>
agit φ V, quæ rectam <lb/>
<anchor type="figure" xlink:label="fig-0186-01a" xlink:href="fig-0186-01"/>
ductam ex H, ipſi D C, <lb/>parallelã, ſecet in V, <lb/>puncto, è quo, vt cen-<lb/>tro, interualloq́, V φ, <lb/>circulũ deſcribit. </s>
  <s xml:id="echoid-s10759" xml:space="preserve">Quo <lb/>diuiſo in partes 24. </s>
  <s xml:id="echoid-s10760" xml:space="preserve">ini <lb/>tio facto in φ, conne-<lb/>ctit quælibet duo pun-<lb/>cta à φ, æqualiter re-<lb/>
<anchor type="note" xlink:label="note-0186-03a" xlink:href="note-0186-03"/>
mota lineis rectis oc-<lb/>cultis, ſecantibus rectã <lb/>φ V, in pũctis, per quæ <lb/>ex H, rectas emittit <lb/>pro lineis horarĳs, quæ <lb/>omnino illis, quæ priori <lb/>modo inuentæ ſunt, re-<lb/>ſpondebunt. </s>
  <s xml:id="echoid-s10761" xml:space="preserve">Quòd ſi ſin <lb/>guli arcus circuli ex <lb/>V, deſcripti bifariã ſe-<lb/>
<anchor type="note" xlink:label="note-0186-04a" xlink:href="note-0186-04"/>
centur, vel in quatuor <lb/>partes, &amp; </s>
  <s xml:id="echoid-s10762" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10763" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10764" xml:space="preserve">eadem <lb/>fiant, habebuntur quoque lineæ pro ſemihoris, vel pro quartis horarum partibus, &amp; </s>
  <s xml:id="echoid-s10765" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10766" xml:space="preserve">ex H, egredientes. <lb/></s>
  <s xml:id="echoid-s10767" xml:space="preserve">Quamuis autem operationem hanc ipſe non demonstret, multis tamen experimentis didicimus, eam verã <lb/>eſſe, lineasq́, horarias per eam inuentas congruere illis, quas antea inuenimus.</s>
  <s xml:id="echoid-s10768" xml:space="preserve"/>
</p>
<div xml:id="echoid-div576" type="float" level="2" n="1">
<note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">Praxis pulcher-<lb/>rima pro lineis <lb/>horariis in figu <lb/>ra radiorũ du-<lb/>cendis ſine in-<lb/>teruallis hora-<lb/>tijs horologii.</note>
<note position="left" xlink:label="note-0186-02" xlink:href="note-0186-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a">
    <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-01"/>
  </figure>
<note position="left" xlink:label="note-0186-03" xlink:href="note-0186-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0186-04" xlink:href="note-0186-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s10769" xml:space="preserve">IAM vero, ſi certa eſt hæc praxis, poterit quis commodiſſime horologium horizontale Aſtronomi-<lb/>
<anchor type="note" xlink:label="note-0186-05a" xlink:href="note-0186-05"/>
cum, vnà cum arcubus ſignorum deſcribere, ad datam etiam ſtyli magnitudinem, hac ratione. </s>
  <s xml:id="echoid-s10770" xml:space="preserve">Deſcripto <lb/>radio Aequatoris D C, vnà cum aliorum ſignorum radĳs, ducatur per D, perpendicularis D H, pro axe <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s10771" xml:space="preserve">ex D, demittatur recta D ρ, faciens cum axe D H, angulum ρ D H, complemento altitudinis <lb/>poli æqualem. </s>
  <s xml:id="echoid-s10772" xml:space="preserve">Deinde ſumpta longitudine ſtyli data D ρ, ducatur per ρ, ad D ρ, perpendicularis H ρ I, ſe-<lb/>
<anchor type="note" xlink:label="note-0186-06a" xlink:href="note-0186-06"/>
cans axem D H, in H, &amp; </s>
  <s xml:id="echoid-s10773" xml:space="preserve">radium Aequatoris D C, in I. </s>
  <s xml:id="echoid-s10774" xml:space="preserve">Sumpto quoque in recta H I, producta puncto <lb/>quouis φ, per quod axi D H, parallela agatur φ V, deſcribatur ex V, centro, interuallo V φ, circulus, <lb/>at que tota figura abſoluatur, vt Andreas Schonerus docuit. </s>
  <s xml:id="echoid-s10775" xml:space="preserve">Poſt hæc in plano horologĳ ducta meridia-<lb/>na linea H E, quam in I, ſecet ad angulos rectos æquinoctialis linea F K, ſumatur ſurſum verſus recta I H, <lb/>æqualis rectæ H I, in hac figura proxime conſtructa, &amp; </s>
  <s xml:id="echoid-s10776" xml:space="preserve">recta I E, rectæ D I. </s>
  <s xml:id="echoid-s10777" xml:space="preserve">Si enim interualla in radio <lb/>Aequatoris inter D, &amp; </s>
  <s xml:id="echoid-s10778" xml:space="preserve">lineas horarias ex H, egredientes poſita transferantur in plano horologĳ ex E, <lb/>vtrinque in lineã æquinoctialem, impreſſis in ea punctis, dabunt rectæ ex H, per hæc puncta æquinoctialis <lb/>lineæ emiſſæ horas à mer. </s>
  <s xml:id="echoid-s10779" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s10780" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s10781" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10782" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10783" xml:space="preserve">vt prius. </s>
  <s xml:id="echoid-s10784" xml:space="preserve">Arcus vero ſignorum ex figura radiorum proxime <lb/>
<anchor type="note" xlink:label="note-0186-07a" xlink:href="note-0186-07"/>
conſtructa deſcribentur, vt ſupra.</s>
  <s xml:id="echoid-s10785" xml:space="preserve"/>
</p>
<div xml:id="echoid-div577" type="float" level="2" n="2">
<note position="left" xlink:label="note-0186-05" xlink:href="note-0186-05a" xml:space="preserve">Deſcriptio ho-<lb/>rologii horizon <lb/>talis ex figura <lb/>radiorum An-<lb/>dreæ Schoneri.</note>
<note position="left" xlink:label="note-0186-06" xlink:href="note-0186-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0186-07" xlink:href="note-0186-07a" xml:space="preserve">Quomodo per <lb/>figuram radio-<lb/>rum maius, aut <lb/>minus horo@o <lb/>gium deſcriba-<lb/>tur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10786" xml:space="preserve">DESCRIPTIS autem lineis horarĳs ex H, ſi per hunc modum, qui per figuram radiorum ab-<lb/>
<anchor type="note" xlink:label="note-0186-08a" xlink:href="note-0186-08"/>
ſoluitur, maius, aut minus horologium ſit conſtruendum, deſcribenda erit figura radiorum Zodiaci ex pun <lb/>cto D, egredientium magis distans à puncto H, vel minus, &amp; </s>
  <s xml:id="echoid-s10787" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10788" xml:space="preserve">Ita enim fiet, vt eadem proportio ſit linea-<lb/>rum inter H, &amp; </s>
  <s xml:id="echoid-s10789" xml:space="preserve">radium Aequatoris D C, poſitæ ad lineas eiuſdem radĳ Aequatoris inter D, &amp; </s>
  <s xml:id="echoid-s10790" xml:space="preserve">puncta, <lb/>
<anchor type="note" xlink:label="note-0186-09a" xlink:href="note-0186-09"/>
in quibus rectæ ex H, emiſſæ ſecant ipſam D C, interpoſitas, quæ linearum inter H, &amp; </s>
  <s xml:id="echoid-s10791" xml:space="preserve">radium Aequato-<lb/>ris remotiorẽ, vel propinquiorem, poſitæ ad lineas eiuſdem radĳ Aequatoris inter axem D H, &amp; </s>
  <s xml:id="echoid-s10792" xml:space="preserve">puncta, <lb/>in quibus rectæ ex H, emiſſæ ipſum radiũ Aequatoris interſecãt, propter triangulorum ſimilitudinẽ, &amp; </s>
  <s xml:id="echoid-s10793" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s10794" xml:space="preserve">Deſcriptio enim linearum horariarum ex H, emiſſarum eadem manet in eodẽ climate, ſiue horologiũ ma-<lb/>gnũ, ſiue paruũ deſcribendum ſit: </s>
  <s xml:id="echoid-s10795" xml:space="preserve">At deſcriptio radiorum Zodiaci in quocunque climate eadẽ ſemper eſt, <lb/>dummodo remotior ea ſit, vel propinquior puncto H, prout horologiũ maius, minus ve fuerit deſcribẽdum. </s>
  <s xml:id="echoid-s10796" xml:space="preserve"><lb/>Linea quoque æquinoctialis in maiori, aut minori horologio tantum abeſſe debet in meridiana linea à cen-<lb/>tro H, quanta eſt portio rectæ H B, infigura radiorum Zodiaci inter H, &amp; </s>
  <s xml:id="echoid-s10797" xml:space="preserve">radium Aequatoris magis,
<pb o="167" file="0187" n="187" rhead="LIBER SECVNDVS."/>
aut minus diſtantem à puncto H, intercepta.</s>
  <s xml:id="echoid-s10798" xml:space="preserve"/>
</p>
<div xml:id="echoid-div578" type="float" level="2" n="3">
<note position="left" xlink:label="note-0186-08" xlink:href="note-0186-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0186-09" xlink:href="note-0186-09a" xml:space="preserve">4. ſexti.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10799" xml:space="preserve">STYLVS ſiue gnomon ex poſteriori modo deſcribendi parallelos ſignorum, hoc eſt, ex figuraradio-<lb/>
<anchor type="note" xlink:label="note-0187-01a" xlink:href="note-0187-01"/>
rum, habetur, ſi e x puncto D, vbi radius Aequatoris axem A λ, ſecat, ad H I, perpendicularis ducatur, <lb/>D ρ, vel certè recta D ρ, faciens angulum ρ D I, æqualem angulo altitudinis poli. </s>
  <s xml:id="echoid-s10800" xml:space="preserve">Longitudo enim ſtyli <lb/>est ipſarecta D ρ: </s>
  <s xml:id="echoid-s10801" xml:space="preserve">Locus verò eius eſt punctum ρ, diſtans ab H, centro horologĳ interuallo H ρ, in linea <lb/>meridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana verſus centrum H.</s>
  <s xml:id="echoid-s10802" xml:space="preserve"/>
</p>
<div xml:id="echoid-div579" type="float" level="2" n="4">
<note position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">Quã ratione ex <lb/>figura radiorũ <lb/>longitudo ſtyli, <lb/>eiusq́; locus in <lb/>horologio explo <lb/>retur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10803" xml:space="preserve">QVOD ſi magnitudo gnomonis data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodia-<lb/>
<anchor type="note" xlink:label="note-0187-02a" xlink:href="note-0187-02"/>
ci à puncto H, in axe H D. </s>
  <s xml:id="echoid-s10804" xml:space="preserve">Nam horariæ lineæ ex H, procedentes eædem omnino manent, vt diximus, in <lb/>eadem altitudine poli. </s>
  <s xml:id="echoid-s10805" xml:space="preserve">In portione Analemmatis, quam propoſ. </s>
  <s xml:id="echoid-s10806" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10807" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s10808" xml:space="preserve">deſcripſimus, abſcindatur ex <lb/>A D, diametro Verticalis circuli protracta, recta D M, æqualis gnomoni dato, &amp; </s>
  <s xml:id="echoid-s10809" xml:space="preserve">per M, ipſi B C, diame <lb/>
<anchor type="note" xlink:label="note-0187-03a" xlink:href="note-0187-03"/>
tro Horizontis parallela agatur N O, ſecans axem E D, in N, &amp; </s>
  <s xml:id="echoid-s10810" xml:space="preserve">Aequatoris diametrũ F D, in O; </s>
  <s xml:id="echoid-s10811" xml:space="preserve">Pun <lb/>ctum ergo D, in figura radiorum Zodiaci huius propoſ. </s>
  <s xml:id="echoid-s10812" xml:space="preserve">in quo conueniunt omnes radĳ Zodiaci, diſtare de-<lb/>bet ab H, interuallo D N, cuiuſmodi eſt punctum D, prope A, in dicta figura radiorum Zodiaci huius pro-<lb/>poſ. </s>
  <s xml:id="echoid-s10813" xml:space="preserve">Si enim ex illo puncto D, demittatur perpendicularis ad H D, pro radio Aequatoris, &amp; </s>
  <s xml:id="echoid-s10814" xml:space="preserve">ſimul ex D, <lb/>aliorum ſignorum radĳ emittantur, vt in Analemmate propoſ. </s>
  <s xml:id="echoid-s10815" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10816" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10817" xml:space="preserve">deſcribemus beneficio li-<lb/>nearum horariarum inter hoſce radios, &amp; </s>
  <s xml:id="echoid-s10818" xml:space="preserve">punctum H, comprehenſarum parallelos ſignorum, vt prius; <lb/></s>
  <s xml:id="echoid-s10819" xml:space="preserve">quos percurret extremitas vmbræ à gnomone dato D M, proiectæ, vt ex demonſtratis conſtat. </s>
  <s xml:id="echoid-s10820" xml:space="preserve">Nam ſi ex <lb/>dicto puncto D, demittatur ad H I B, perpendicularis D K, erit hæc æqualis gnomoni dato D M. </s>
  <s xml:id="echoid-s10821" xml:space="preserve">Cum <lb/>enim angulus D H K, in triangulo D H K, figuræ radiorum Zodiaci huius propoſ. </s>
  <s xml:id="echoid-s10822" xml:space="preserve">æqualis ſit angulo <lb/>D N M, in triangulo D N M, portionis Analemmatis propoſ. </s>
  <s xml:id="echoid-s10823" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10824" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s10825" xml:space="preserve">(Vterque enim eſt angulus <lb/>
<anchor type="note" xlink:label="note-0187-04a" xlink:href="note-0187-04"/>
altitudinis poli) &amp; </s>
  <s xml:id="echoid-s10826" xml:space="preserve">recti anguli ad K, &amp; </s>
  <s xml:id="echoid-s10827" xml:space="preserve">M, æquales ſint; </s>
  <s xml:id="echoid-s10828" xml:space="preserve">ſit autem &amp; </s>
  <s xml:id="echoid-s10829" xml:space="preserve">latus H D, lateri D N, æquale, <lb/>ex constructione; </s>
  <s xml:id="echoid-s10830" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s10831" xml:space="preserve">reliqua latera, nempe D K, D M, inter ſe, &amp; </s>
  <s xml:id="echoid-s10832" xml:space="preserve">H K, N M, inter ſe æqualia. <lb/></s>
  <s xml:id="echoid-s10833" xml:space="preserve">
<anchor type="note" xlink:label="note-0187-05a" xlink:href="note-0187-05"/>
Quod est propoſitum. </s>
  <s xml:id="echoid-s10834" xml:space="preserve">Mutatis autem arcubus ſignorum, mutatur quoque ęquinoctialis linea, quæ tanto <lb/>
<anchor type="note" xlink:label="note-0187-06a" xlink:href="note-0187-06"/>
ſpatio in linea meridiana abeſt ſemper à centro H, quanta est portio rectæ H B, in figura radiorum huius <lb/>propoſ. </s>
  <s xml:id="echoid-s10835" xml:space="preserve">inter H, &amp; </s>
  <s xml:id="echoid-s10836" xml:space="preserve">radium Aequatoris inter cepta, vt &amp; </s>
  <s xml:id="echoid-s10837" xml:space="preserve">paulo ante diximus.</s>
  <s xml:id="echoid-s10838" xml:space="preserve"/>
</p>
<div xml:id="echoid-div580" type="float" level="2" n="5">
<note position="right" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">Quomodo cx <lb/>data ſtyli longi <lb/>tudine inuenia <lb/>tur diſtantia ra <lb/>diorum Zodia-<lb/>ci à puncto H, <lb/>in figura radio-<lb/>rum.</note>
<note position="left" xlink:label="note-0187-03" xlink:href="note-0187-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0187-04" xlink:href="note-0187-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0187-05" xlink:href="note-0187-05a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0187-06" xlink:href="note-0187-06a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum, qui <lb/>non per ſigno -<lb/>rum initia, ſed <lb/>per alia puncta <lb/>Zodiaci tran-<lb/>ſeunt, in eodem <lb/>horologio.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10839" xml:space="preserve">IAM verò ſi accipiamus declinationes aliorum punctorum Zodiaci, eorum{q́ue} parallelos in prima fi-<lb/>gura huius propoſ. </s>
  <s xml:id="echoid-s10840" xml:space="preserve">vel eorum radios ex D, in tertia figura ducamus, deſcribemus eodem modo eorum pa-<lb/>rallelos in prædicto horologio.</s>
  <s xml:id="echoid-s10841" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s10842" xml:space="preserve">IMMO propoſito die primo cuiuſque menſis, vel alio quouis, ſi quæratur locus Solis illo die in Zo-<lb/>
<anchor type="note" xlink:label="note-0187-07a" xlink:href="note-0187-07"/>
diaco, &amp; </s>
  <s xml:id="echoid-s10843" xml:space="preserve">declinatio, at que in prima figura huius propoſ. </s>
  <s xml:id="echoid-s10844" xml:space="preserve">eius parallelus, vel in figura radiorum eius ra-<lb/>
<anchor type="note" xlink:label="note-0187-08a" xlink:href="note-0187-08"/>
dius ex D, ducatur, deſcribetur eadem ratione in horologio linea quædam flexa, quam vmbræ extremitas <lb/>percurret die illo propoſito.</s>
  <s xml:id="echoid-s10845" xml:space="preserve"/>
</p>
<div xml:id="echoid-div581" type="float" level="2" n="6">
<note position="right" xlink:label="note-0187-07" xlink:href="note-0187-07a" xml:space="preserve">Deſcriptio pa-<lb/>ralleli, in quo <lb/>Sol exiſtit quo-<lb/>libet die propo <lb/>ſito, in eodẽ ho <lb/>rologio.</note>
<note position="left" xlink:label="note-0187-08" xlink:href="note-0187-08a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s10846" xml:space="preserve">HAC ratione deſcribi poſſunt in horologio dies feſti ſanctorum, hoc eſt, lineæ quædam inflexę, quas <lb/>
<anchor type="note" xlink:label="note-0187-09a" xlink:href="note-0187-09"/>
vmbra ſtyli percurrit illis diebus.</s>
  <s xml:id="echoid-s10847" xml:space="preserve"/>
</p>
<div xml:id="echoid-div582" type="float" level="2" n="7">
<note position="right" xlink:label="note-0187-09" xlink:href="note-0187-09a" xml:space="preserve">Deſcriptio die-<lb/>rum feſtorũ in <lb/>eodem horolo-<lb/>gio.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10848" xml:space="preserve">HIS autem omnibus parallelis ſignorum aſcribi poſſunt characteres ſignorum, dies menſium, qui-<lb/>
<anchor type="note" xlink:label="note-0187-10a" xlink:href="note-0187-10"/>
bus vmbrę extremitas illos percurrit; </s>
  <s xml:id="echoid-s10849" xml:space="preserve">tempus ortus Solis &amp; </s>
  <s xml:id="echoid-s10850" xml:space="preserve">occaſus, dierum &amp; </s>
  <s xml:id="echoid-s10851" xml:space="preserve">crepuſculorum magni-<lb/>tudines, &amp; </s>
  <s xml:id="echoid-s10852" xml:space="preserve">alia huiuſmodi, cuiuſmodi eſſet in horologio Italico, &amp; </s>
  <s xml:id="echoid-s10853" xml:space="preserve">Babylonico, de quibus propoſ. </s>
  <s xml:id="echoid-s10854" xml:space="preserve">10. </s>
  <s xml:id="echoid-s10855" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10856" xml:space="preserve"><lb/>11. </s>
  <s xml:id="echoid-s10857" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s10858" xml:space="preserve">agetur, tempus meridiei, &amp; </s>
  <s xml:id="echoid-s10859" xml:space="preserve">c.</s>
  <s xml:id="echoid-s10860" xml:space="preserve"/>
</p>
<div xml:id="echoid-div583" type="float" level="2" n="8">
<note position="right" xlink:label="note-0187-10" xlink:href="note-0187-10a" xml:space="preserve">Quid aſcriben-<lb/>du ſit arcubus <lb/>ſignorum in ho <lb/>rologĩo delinea <lb/>tis.</note>
</div>
<p style="it">
  <s xml:id="echoid-s10861" xml:space="preserve">IN huius verò rei gratiam ducendæ ſunt quædam lineæ parallelæ ipſi lineę meridianæ tam ad ſini-<lb/>ſtram, quàm ad dexteram, vt in ſecunda figur a huius propoſ. </s>
  <s xml:id="echoid-s10862" xml:space="preserve">apparet. </s>
  <s xml:id="echoid-s10863" xml:space="preserve">Hę autem parallelę, quo remo-<lb/>
<anchor type="note" xlink:label="note-0187-11a" xlink:href="note-0187-11"/>
tiores erunt à meridiana linea, eo maiori temporis ſpatio vmbra gnomonis in horologio excipietur.</s>
  <s xml:id="echoid-s10864" xml:space="preserve"/>
</p>
<div xml:id="echoid-div584" type="float" level="2" n="9">
<note position="left" xlink:label="note-0187-11" xlink:href="note-0187-11a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s10865" xml:space="preserve">RVRSVS quoniam Sol à ♑, per ♈, aſcendit vſque ad ♋; </s>
  <s xml:id="echoid-s10866" xml:space="preserve">à ♋, verò per ♎, vſque ad ♑, deſcen-<lb/>dit, aſcribenda erunt ad priora ſigna, hæc verba. </s>
  <s xml:id="echoid-s10867" xml:space="preserve">A S C E N S V S S O L I S; </s>
  <s xml:id="echoid-s10868" xml:space="preserve">ad poſteriora verò hæc. <lb/></s>
  <s xml:id="echoid-s10869" xml:space="preserve">D E S C E N S V S S O L I S. </s>
  <s xml:id="echoid-s10870" xml:space="preserve">Exemplum habes in horologio ſuperiori. </s>
  <s xml:id="echoid-s10871" xml:space="preserve">Quod etiam intelligendum <lb/>eſt in alĳs horologĳs, vt in Verticali, Meridiano Aequinoctiali, &amp; </s>
  <s xml:id="echoid-s10872" xml:space="preserve">c.</s>
  <s xml:id="echoid-s10873" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s10874" xml:space="preserve">POSTREMO eoſdem parallelos, arcusve ſignorum in horologio, quod in ſcholio pręcedentis pro-<lb/>
<anchor type="note" xlink:label="note-0187-12a" xlink:href="note-0187-12"/>
poſ. </s>
  <s xml:id="echoid-s10875" xml:space="preserve">etiamſi cent rum eius non haberemus, eiſdem ferè rationibus, quibus in hac propoſ. </s>
  <s xml:id="echoid-s10876" xml:space="preserve">vſi ſumus, deſcribe <lb/>mus. </s>
  <s xml:id="echoid-s10877" xml:space="preserve">Nam quòd ad priorem rationem attinet, ſi deſcribatur Analemma pro data altitudine poli, vt in <lb/>propoſito exemplo ad latitudinem grad. </s>
  <s xml:id="echoid-s10878" xml:space="preserve">20. </s>
  <s xml:id="echoid-s10879" xml:space="preserve">cum parallelis ſignorum, eorundem radĳs, vt in conis ha-<lb/>beantur triangula per axem, at que adeò in recta R O, (quæ Horizonti B C, æquidiſtare debet ſecundum <lb/>
<anchor type="note" xlink:label="note-0187-13a" xlink:href="note-0187-13"/>
diſtantiam rectæ D G, ſtylo F M, ęqualis) diametri ſectionum conicarum; </s>
  <s xml:id="echoid-s10880" xml:space="preserve">at que puncta K, L, M. </s>
  <s xml:id="echoid-s10881" xml:space="preserve">Q, P, <lb/>N, ex puncto I, (vbi Aequatoris diameter rectam. </s>
  <s xml:id="echoid-s10882" xml:space="preserve">R O, diuidit) accepta transferantur in lineam meri-<lb/>dianam A B, ex puncto E, vbi æquinoctialis linea, ac meridiana ſe interſecant; </s>
  <s xml:id="echoid-s10883" xml:space="preserve">postremo verò circa dia-<lb/>metros ſectionum conicarum deſcribantur ſectiones conicæ, ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s10884" xml:space="preserve">8. </s>
  <s xml:id="echoid-s10885" xml:space="preserve">ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s10886" xml:space="preserve">it a vt per illa puncta K, L, M, &amp; </s>
  <s xml:id="echoid-s10887" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10888" xml:space="preserve">in horologio tranſeant, deſcripti erunt paralleli ſignorum.</s>
  <s xml:id="echoid-s10889" xml:space="preserve"/>
</p>
<div xml:id="echoid-div585" type="float" level="2" n="10">
<note position="right" xlink:label="note-0187-12" xlink:href="note-0187-12a" xml:space="preserve">Qua atte arcus <lb/>ſignorum in ho <lb/>rologio, quod <lb/>centrum non <lb/>habear, deſcribẽ <lb/>di ſiut.</note>
<note position="left" xlink:label="note-0187-13" xlink:href="note-0187-13a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s10890" xml:space="preserve">QVOD verò attinet ad posteriorem rationem ex figura radiorum Zodiaci depromptam, it a rem <lb/>perficiemus. </s>
  <s xml:id="echoid-s10891" xml:space="preserve">Inradium Aequatoris D C, transferantur omnia interualla inter centrum B, (ex quo cir-<lb/>culus deſcriptus fuit, at que in partes 24. </s>
  <s xml:id="echoid-s10892" xml:space="preserve">æquales diuiſus) &amp; </s>
  <s xml:id="echoid-s10893" xml:space="preserve">horas in ęquinoctiali linea C D, interiecta, à <lb/>puncto D, imprimendo puncta in ipſo radio Aequatoris. </s>
  <s xml:id="echoid-s10894" xml:space="preserve">Deinde in axe D G, abſcindatur recta D G, <lb/>æqualis portioni axis F G, in horologio, ad finem ſcholĳ ant ecedentis propoſ. </s>
  <s xml:id="echoid-s10895" xml:space="preserve">deſcripto, &amp; </s>
  <s xml:id="echoid-s10896" xml:space="preserve">per G, radio <lb/>Aequatoris D C, parallela agatur G H, in quam eodem modo à puncto G, transferantur ſpatia compre-
<pb o="168" file="0188" n="188" rhead="GNOMONICES"/>
henſa inter aliud centrũ L, (ex quo nimirum alius circulus in prædicto horologio deſcriptus fuit, &amp; </s>
  <s xml:id="echoid-s10897" xml:space="preserve">in par <lb/>tes ęquales 24. </s>
  <s xml:id="echoid-s10898" xml:space="preserve">diſtributus) &amp; </s>
  <s xml:id="echoid-s10899" xml:space="preserve">horas in æquinoctiali linea I K, imprimẽdo puncta in ipſa G H. </s>
  <s xml:id="echoid-s10900" xml:space="preserve">Poſtremo <lb/>per bina ſemper puncta reſpondentia in rectis D C, C H, rectæ lineę ducantur, Hę etenim dabunt horarias <lb/>
<anchor type="figure" xlink:label="fig-0188-01a" xlink:href="fig-0188-01"/>
<anchor type="note" xlink:label="note-0188-01a" xlink:href="note-0188-01"/>
<anchor type="note" xlink:label="note-0188-02a" xlink:href="note-0188-02"/>
<anchor type="note" xlink:label="note-0188-03a" xlink:href="note-0188-03"/>
<anchor type="note" xlink:label="note-0188-04a" xlink:href="note-0188-04"/>
lineas, nõ aliter, at q; </s>
  <s xml:id="echoid-s10901" xml:space="preserve">in figura radiorum Zodiaci huius propoſ. </s>
  <s xml:id="echoid-s10902" xml:space="preserve">quarũ interualla inter radium Aequatoris <lb/>D C, &amp; </s>
  <s xml:id="echoid-s10903" xml:space="preserve">radios aliorum ſignorũ translat a in reſpondentes lineas horarias in horologio ab ipſa æquinoctiali <lb/>linea C D, dabunt in horarĳs lineis puncta, per quæ ſignorum arcus ducendi ſunt; </s>
  <s xml:id="echoid-s10904" xml:space="preserve">Vt ex ĳs, quæ ſupra de-<lb/>monſtrata ſunt, perſpicuũ eſt. </s>
  <s xml:id="echoid-s10905" xml:space="preserve">Nam recta G H, eſt alius radius Aequatoris pro minori horologio deſcriben <lb/>
<anchor type="note" xlink:label="note-0188-05a" xlink:href="note-0188-05"/>
do, cuius nimirum æquinoctialis linea I K, &amp; </s>
  <s xml:id="echoid-s10906" xml:space="preserve">axis A G. </s>
  <s xml:id="echoid-s10907" xml:space="preserve">Vnde ſi in axe D G, huius proximę figuræ ſume-<lb/>retur ex D, recta æqualis axi F A, in horologio, vel ex G, æqualis axi G A, terminaretur vtraque in eo-<lb/>dem puncto, ex quo rectæ ductæ per puncta tam radĳ Aequatoris D C, quàm G H, exhiberent lineas ho-<lb/>rarias, non ſecus, ac in figura radiorum Zodiaci huius propoſ. </s>
  <s xml:id="echoid-s10908" xml:space="preserve">Quare neceſſe eſt, haſce lineas horarias trã-<lb/>ſire per puncta inuenta in vtroque radio Aequatoris, &amp; </s>
  <s xml:id="echoid-s10909" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10910" xml:space="preserve">Quòd ſi ex D, ad proximam lineam horariam, <lb/>nempe ad lineam horæ 12. </s>
  <s xml:id="echoid-s10911" xml:space="preserve">ducatur perpendicularis linea, dabit hæc longitudinem ſtyli: </s>
  <s xml:id="echoid-s10912" xml:space="preserve">locus verò eius <lb/>erit punctum in meridiana linea tantum diſtans ab ęquinoctiali linea ſurſum verſus, quantum àradio <lb/>Aequatoris D C, remouetur punctum, in quod ſtylus ex D, cadit ad angulos rectos in lineam horę 12. <lb/></s>
  <s xml:id="echoid-s10913" xml:space="preserve">Cæterum in translatione interuallorum ex radio Aequatoris in horologium ſeruandus eſt hic ordo, vt in-<lb/>terualla linearum horariarum verſus illam partem, in quam cadit ſtylus ex D, transferantur à linea æqui <lb/>noctiali ſurſum verſus, &amp; </s>
  <s xml:id="echoid-s10914" xml:space="preserve">c.</s>
  <s xml:id="echoid-s10915" xml:space="preserve"/>
</p>
<div xml:id="echoid-div586" type="float" level="2" n="11">
  <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a">
    <image file="0188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0188-01"/>
  </figure>
<note position="left" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0188-02" xlink:href="note-0188-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0188-03" xlink:href="note-0188-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0188-04" xlink:href="note-0188-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0188-05" xlink:href="note-0188-05a" xml:space="preserve">50</note>
</div>
<pb o="169" file="0189" n="189" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s10916" xml:space="preserve">PORRO vſus parallelorum, ſiue arcuum ſignorum Zodiaci in omnibus horologĳs eſt, vt per eos ſcia <lb/>
<anchor type="note" xlink:label="note-0189-01a" xlink:href="note-0189-01"/>
mus, quonam in ſigno Zodiaci Sol quotidie verſetur. </s>
  <s xml:id="echoid-s10917" xml:space="preserve">Quotieſcunque enim vmbræ extremitas in aliquem <lb/>arcum in horologio deſcriptum cadit pręcisè, ac proinde toto illo die ab eo minimè recedit, exiſtet neceſ-<lb/>ſario tunc Sol in prineipio illius ſigni Zodiaci, quod arcus prędictus repræſent at. </s>
  <s xml:id="echoid-s10918" xml:space="preserve">Quando autem non prę-<lb/>cisè in aliquem arcum cadit vmbra, ſed in ſpatium inter duos arcus concluſum, non verſabitur tunc Sol <lb/>in principio alicuius ſigni, ſed vel iuxta princi@ium, vel in medio, vel prope finem, vel deniq; </s>
  <s xml:id="echoid-s10919" xml:space="preserve">in alia qua-<lb/>piam parte illius, pro proportione diſtantiæ vmbrę ab arcu illius ſigni. </s>
  <s xml:id="echoid-s10920" xml:space="preserve">Vt autem cognoſcamus, quodnam <lb/>duorum ſignorum, quæ cuilibet arcui, (exceptis duobus tropicis) ſunt aſcripta, accipiendum ſit, obſeruan <lb/>dum erit, quanam in parte anni verſemur. </s>
  <s xml:id="echoid-s10921" xml:space="preserve">Nam cum à duodecimo die Iunĳ vſque ad diem duodecimum <lb/>Decembris, percurr at hac tempeſtate Sol hæc ſex ſigna: </s>
  <s xml:id="echoid-s10922" xml:space="preserve">♋, ♌, ♍, ♎, ♏, &amp; </s>
  <s xml:id="echoid-s10923" xml:space="preserve">♐: </s>
  <s xml:id="echoid-s10924" xml:space="preserve">Alia autem ſex, vt ♑, <lb/>
<anchor type="note" xlink:label="note-0189-02a" xlink:href="note-0189-02"/>
♒, ♓, ♈, ♉, &amp; </s>
  <s xml:id="echoid-s10925" xml:space="preserve">♊, à die duodecimo Decembris vſque ad duodecimum diem Iunĳ, facile quibet iudica <lb/>re poterit, in quonam duorum ſignorum Sol existat. </s>
  <s xml:id="echoid-s10926" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s10927" xml:space="preserve">Si in aliquo die inter duodecimũ <lb/>Iunĳ, &amp; </s>
  <s xml:id="echoid-s10928" xml:space="preserve">duodecimum Decembris extremitas vmbræ præcisè cadat in arcum, cui appoſita ſunt duo hæc <lb/>ſigna ♊, &amp; </s>
  <s xml:id="echoid-s10929" xml:space="preserve">♌, exiſtet Sol in principio ♌, non autem in principio ♊: </s>
  <s xml:id="echoid-s10930" xml:space="preserve">Si autem vmbra cadat in ſpatium <lb/>inter dictum arcum, &amp; </s>
  <s xml:id="echoid-s10931" xml:space="preserve">arcum alium horum duorum ſignorum ♉, &amp; </s>
  <s xml:id="echoid-s10932" xml:space="preserve">♍, comprehenſum, verſabitur Sol <lb/>in aliquo gradu ♌, non autẽ ingradu aliquo ♊, vel ♍, vel ♉; </s>
  <s xml:id="echoid-s10933" xml:space="preserve">quia illo anni tempore non poteſt eſſe in ♊, <lb/>vel ♉, vt diximus, ſed vel in ♌, vel in ♍; </s>
  <s xml:id="echoid-s10934" xml:space="preserve">cum ergo Sol moueatur à ♌, in ♍, &amp; </s>
  <s xml:id="echoid-s10935" xml:space="preserve">non è contrario, effici-<lb/>tur, illum tunc exiſtere in gradu aliquo ♌, non autem ♍. </s>
  <s xml:id="echoid-s10936" xml:space="preserve">Contrarium eſſet intelligendum, ſi in ea parte <lb/>anni, quæ inter duodecimum diem Decembris, &amp; </s>
  <s xml:id="echoid-s10937" xml:space="preserve">duodecimum diem Iunĳ ponitur, verſaremur. </s>
  <s xml:id="echoid-s10938" xml:space="preserve">Nam tunc <lb/>vmbra cadente in arcum ♊, &amp; </s>
  <s xml:id="echoid-s10939" xml:space="preserve">♌, Sol existeret in principio ♊: </s>
  <s xml:id="echoid-s10940" xml:space="preserve">cadente autem vmbra in idem ſpatium <lb/>
<anchor type="note" xlink:label="note-0189-03a" xlink:href="note-0189-03"/>
inter dictum arcum, &amp; </s>
  <s xml:id="echoid-s10941" xml:space="preserve">arcum ♉, &amp; </s>
  <s xml:id="echoid-s10942" xml:space="preserve">♍, contentum, conſtitutus eſſet Sol in gradu aliquo ♉, quia à ♉, in <lb/>♊, proprio motu progreditur. </s>
  <s xml:id="echoid-s10943" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10944" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s10945" xml:space="preserve"/>
</p>
<div xml:id="echoid-div587" type="float" level="2" n="12">
<note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">Vſus arcuum <lb/>ſignorum in ho <lb/>rologio deſcri-<lb/>p@o@um, quibus <lb/>diſcimus, qua <lb/>in parte Zo-<lb/>diaci Sol exi-<lb/>ſtat.</note>
<note position="left" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0189-03" xlink:href="note-0189-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div589" type="section" level="1" n="147">
<head xml:id="echoid-head150" xml:space="preserve">PROBLEMA 3. PROPOSITIO 3.</head>
<p>
  <s xml:id="echoid-s10946" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio ho-<lb/>rizontali deſcribere.</s>
  <s xml:id="echoid-s10947" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s10948" xml:space="preserve">CVM paralleli arcuum diurnorum æquidiſtent Aequatori, quemadmodum &amp; </s>
  <s xml:id="echoid-s10949" xml:space="preserve">paralleli ſigno <lb/>
<anchor type="note" xlink:label="note-0189-04a" xlink:href="note-0189-04"/>
<anchor type="note" xlink:label="note-0189-05a" xlink:href="note-0189-05"/>
rum Zodiaci, perſpicuum eſt, eandem eſſe &amp; </s>
  <s xml:id="echoid-s10950" xml:space="preserve">illorum, &amp; </s>
  <s xml:id="echoid-s10951" xml:space="preserve">horum deſcribendorum rationem. </s>
  <s xml:id="echoid-s10952" xml:space="preserve">Itaque <lb/>ſi in priori modo deſcriptionis pręcedẽte propoſ. </s>
  <s xml:id="echoid-s10953" xml:space="preserve">tradito, loco parallelorum, qui per ſigna Zodia-<lb/>ci ducuntur, ſumantur paralleli arcuum diurnorum, quorum declinationes propoſ. </s>
  <s xml:id="echoid-s10954" xml:space="preserve">33. </s>
  <s xml:id="echoid-s10955" xml:space="preserve">præceden-<lb/>tis libri inuentę ſunt: </s>
  <s xml:id="echoid-s10956" xml:space="preserve">in poſteriori autem, loco radiorum Zodiaci ex puncto D, egredientium aſ-<lb/>ſumantur radii arcuum diurnorum, vt ex his figuris appoſitis patet, in quarum priore continen-<lb/>tur paralleli, quorum arcus diurni horas continent 8. </s>
  <s xml:id="echoid-s10957" xml:space="preserve">9. </s>
  <s xml:id="echoid-s10958" xml:space="preserve">10. </s>
  <s xml:id="echoid-s10959" xml:space="preserve">11. </s>
  <s xml:id="echoid-s10960" xml:space="preserve">12. </s>
  <s xml:id="echoid-s10961" xml:space="preserve">13. </s>
  <s xml:id="echoid-s10962" xml:space="preserve">14. </s>
  <s xml:id="echoid-s10963" xml:space="preserve">15. </s>
  <s xml:id="echoid-s10964" xml:space="preserve">16. </s>
  <s xml:id="echoid-s10965" xml:space="preserve">in poſteriori <lb/>
<anchor type="figure" xlink:label="fig-0189-01a" xlink:href="fig-0189-01"/>
<anchor type="note" xlink:label="note-0189-06a" xlink:href="note-0189-06"/>
<anchor type="note" xlink:label="note-0189-07a" xlink:href="note-0189-07"/>
<gap/> <lb/>verò radij parallelorum, quorum arcus diurni continent horas. </s>
  <s xml:id="echoid-s10966" xml:space="preserve">0. </s>
  <s xml:id="echoid-s10967" xml:space="preserve">1. </s>
  <s xml:id="echoid-s10968" xml:space="preserve">2. </s>
  <s xml:id="echoid-s10969" xml:space="preserve">3. </s>
  <s xml:id="echoid-s10970" xml:space="preserve">4. </s>
  <s xml:id="echoid-s10971" xml:space="preserve">5. </s>
  <s xml:id="echoid-s10972" xml:space="preserve">6. </s>
  <s xml:id="echoid-s10973" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s10974" xml:space="preserve">ſic deinceps <lb/>vſque ad 24. </s>
  <s xml:id="echoid-s10975" xml:space="preserve">vbi totus parallelus eſt arcus diurnus; </s>
  <s xml:id="echoid-s10976" xml:space="preserve">deſcribemus parallelos arcuum diurnorum ea-<lb/>dem prorſus arte, qua parallelos ſignorum pręcedente propoſ. </s>
  <s xml:id="echoid-s10977" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s10978" xml:space="preserve">Qui quidem omnes <lb/>conicæ ſectiones ſunt, quas vinbra ſtvli deſcribit, ex coroll. </s>
  <s xml:id="echoid-s10979" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s10980" xml:space="preserve">12. </s>
  <s xml:id="echoid-s10981" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10982" xml:space="preserve">Sole in illis <lb/>exiſtente. </s>
  <s xml:id="echoid-s10983" xml:space="preserve">Linea autem ęquinoctialis eſt arcus diurnus horarum 12.</s>
  <s xml:id="echoid-s10984" xml:space="preserve"/>
</p>
<div xml:id="echoid-div589" type="float" level="2" n="1">
<note position="left" xlink:label="note-0189-04" xlink:href="note-0189-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0189-05" xlink:href="note-0189-05a" xml:space="preserve">Deſcriptio ar-<lb/>cuum diurnorũ <lb/>in pradicto ho-<lb/>rologio norizon <lb/>tali.</note>
  <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a">
    <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-01"/>
  </figure>
<note position="left" xlink:label="note-0189-06" xlink:href="note-0189-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0189-07" xlink:href="note-0189-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s10985" xml:space="preserve">SVNT autem extrem@e lineę in figura radiorum ex H, eductę lineis extremis ex D, emiſſis pa-<lb/>
<anchor type="note" xlink:label="note-0189-08a" xlink:href="note-0189-08"/>
<pb o="170" file="0190" n="190" rhead="GNOMONICES"/>
rallelę, ſingulę ſingulis; </s>
  <s xml:id="echoid-s10986" xml:space="preserve">propterea quòd anguli H D A, D H I, æquales ſunt duobus rectis. </s>
  <s xml:id="echoid-s10987" xml:space="preserve">Eſt enim, <lb/>per conſtructionem angulus H D I, rectus, &amp; </s>
  <s xml:id="echoid-s10988" xml:space="preserve">D H I, angulus altitudinis poli, atque A D I, (qui ex <lb/>ſcholio propoſ. </s>
  <s xml:id="echoid-s10989" xml:space="preserve">33. </s>
  <s xml:id="echoid-s10990" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s10991" xml:space="preserve">angulus eſt complementi altitudinis poli) ſimul etiam æquales <lb/>vni recto, &amp;</s>
  <s xml:id="echoid-s10992" xml:space="preserve">c. </s>
  <s xml:id="echoid-s10993" xml:space="preserve">Itaque parallelos arcuum diurnorum in eodem horologio horizontali deſcripſi-<lb/>mus. </s>
  <s xml:id="echoid-s10994" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s10995" xml:space="preserve"/>
</p>
<div xml:id="echoid-div590" type="float" level="2" n="2">
<note position="right" xlink:label="note-0189-08" xlink:href="note-0189-08a" xml:space="preserve">28. primi.</note>
</div>
</div>
<div xml:id="echoid-div592" type="section" level="1" n="148">
<head xml:id="echoid-head151" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s10996" xml:space="preserve">HIC quoque parallelis arcuum diurnorum apponi poſſunt magnitudines dierum, &amp; </s>
  <s xml:id="echoid-s10997" xml:space="preserve">crepuſculorum, <lb/>
<anchor type="note" xlink:label="note-0190-01a" xlink:href="note-0190-01"/>
&amp; </s>
  <s xml:id="echoid-s10998" xml:space="preserve">alia huiuſmodi, vt dies menſium reſpondentes illis parallelis, &amp; </s>
  <s xml:id="echoid-s10999" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11000" xml:space="preserve"/>
</p>
<div xml:id="echoid-div592" type="float" level="2" n="1">
<note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">Quid aſeribe@-<lb/>dũ ſit arcubus <lb/>diurnis in horo <lb/>logio deſcriptis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s11001" xml:space="preserve">EST autem horum parallelorum vſus, vt per eos diſcamus, quotnam horas quilibet dies anni conti-<lb/>
<anchor type="note" xlink:label="note-0190-03a" xlink:href="note-0190-03"/>
neat. </s>
  <s xml:id="echoid-s11002" xml:space="preserve">Nam quando vmbra gnomonis cadit præcisè in arcum aliquem diurnum, comprehendet dies tunc <lb/>præcisè tothoras, quot illi arcui ſunt aſcriptæ. </s>
  <s xml:id="echoid-s11003" xml:space="preserve">Si autem vmbra ſtyli non præcisè in aliquem arcum ca-<lb/>dat, ſed in ſpatium inter duos arcus comprehenſum, iudicabimus plus minus, quot horarum tunc dies exi-<lb/>ſtat, habita ratione diſtantiæ vmbræ à propinquiore arcu, dummodo in memoriam reuocemus, dies à duo-<lb/>decimo Iunĳ vſque ad duodecimum Decembris decreſcere hac tempeſtate; </s>
  <s xml:id="echoid-s11004" xml:space="preserve">at verò eoſdem augeri à duo-<lb/>decimo Decembris vſque ad duodecimum Iunĳ. </s>
  <s xml:id="echoid-s11005" xml:space="preserve">Vnde ſi, verbi gratia, vmbra cadat in medium ſpatium <lb/>inter arcus horarum 13. </s>
  <s xml:id="echoid-s11006" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11007" xml:space="preserve">14. </s>
  <s xml:id="echoid-s11008" xml:space="preserve">ſi quidem hoc fiat eo anni tempore, quod inter duodecimum diem Iunĳ, <lb/>&amp; </s>
  <s xml:id="echoid-s11009" xml:space="preserve">duodecimum diẽ Decembris interĳcitur, continebit tunc dies horas ferè 13 {1/2}. </s>
  <s xml:id="echoid-s11010" xml:space="preserve">quia tunc Sol mouetur <lb/>proprio motu ab arcu diurno horarum 14. </s>
  <s xml:id="echoid-s11011" xml:space="preserve">ad arcũ diurnum horarum 13. </s>
  <s xml:id="echoid-s11012" xml:space="preserve">cum tunc dies deereſcant. </s>
  <s xml:id="echoid-s11013" xml:space="preserve">Si ve-<lb/>
<anchor type="note" xlink:label="note-0190-04a" xlink:href="note-0190-04"/>
rò idem accidat in reliquo anni tempore, erit rurſus dies horarum quaſi 13 {1/2}. </s>
  <s xml:id="echoid-s11014" xml:space="preserve">quia tunc dies incrementũ <lb/>ſumunt, at que adeo Sol proprio motu ab arcu diurno horarum 13. </s>
  <s xml:id="echoid-s11015" xml:space="preserve">ad arcum diurnum borarum 14. </s>
  <s xml:id="echoid-s11016" xml:space="preserve">moue-<lb/>tur. </s>
  <s xml:id="echoid-s11017" xml:space="preserve">Atque ita de ſingulis.</s>
  <s xml:id="echoid-s11018" xml:space="preserve"/>
</p>
<div xml:id="echoid-div593" type="float" level="2" n="2">
<note position="left" xlink:label="note-0190-03" xlink:href="note-0190-03a" xml:space="preserve">Vſus arcuum <lb/>diurnorũ in ho <lb/>rologio deſcri-<lb/>ptorum, quibus <lb/>cognoſcimus, <lb/>quot horas com <lb/>plectatur quili-<lb/>bet dies propo-<lb/>fit@@.</note>
<note position="left" xlink:label="note-0190-04" xlink:href="note-0190-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div595" type="section" level="1" n="149">
<head xml:id="echoid-head152" xml:space="preserve">PROBLEMA. 4. PROPOSITIO 4.</head>
<p>
  <s xml:id="echoid-s11019" xml:space="preserve">CIRCVLOS Verticales, quos Azimuth dicunt, in eodem hori-<lb/>zontali horologio deſcribere.</s>
  <s xml:id="echoid-s11020" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s11021" xml:space="preserve">DVCATVR per G, locum gnomonis in horologio recta A B, ad lineam meridianam H I, <lb/>
<anchor type="note" xlink:label="note-0190-06a" xlink:href="note-0190-06"/>
perpendicularis. </s>
  <s xml:id="echoid-s11022" xml:space="preserve">Deinde ex G, circulus quicunque deſcriptus diuidatur in partes 360. </s>
  <s xml:id="echoid-s11023" xml:space="preserve">æquales, <lb/>initio facto à recta A B. </s>
  <s xml:id="echoid-s11024" xml:space="preserve">(Nos ob loci anguſtias eum diſtribuimus tantum in 24. </s>
  <s xml:id="echoid-s11025" xml:space="preserve">vt quælibet con-<lb/>
<anchor type="figure" xlink:label="fig-0190-01a" xlink:href="fig-0190-01"/>
<anchor type="note" xlink:label="note-0190-07a" xlink:href="note-0190-07"/>
<anchor type="note" xlink:label="note-0190-08a" xlink:href="note-0190-08"/>
tineat gradus 15.) </s>
  <s xml:id="echoid-s11026" xml:space="preserve">Si enim ex centro G, per diuiſionum puncta rectę educantur, quę tamen intra <lb/>tropicos contineantur, vt in figura apparet, cum lineamenta extra ipſos ſuperuacanea ſint; </s>
  <s xml:id="echoid-s11027" xml:space="preserve">deſcri-<lb/>pti erunt circuli Verticales, ſiue Azimuth, hoc eſt, communes ſectiones circulorum Verticalium, <lb/>&amp; </s>
  <s xml:id="echoid-s11028" xml:space="preserve">plani horologii; </s>
  <s xml:id="echoid-s11029" xml:space="preserve">in quas quidem vmbra gnomonis, ex propoſ. </s>
  <s xml:id="echoid-s11030" xml:space="preserve">11. </s>
  <s xml:id="echoid-s11031" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11032" xml:space="preserve">proiicitur, So-<lb/>le in dictis circulis exiſtente. </s>
  <s xml:id="echoid-s11033" xml:space="preserve">Quod facile hoc modo demonſtrabitur.</s>
  <s xml:id="echoid-s11034" xml:space="preserve"/>
</p>
<div xml:id="echoid-div595" type="float" level="2" n="1">
<note position="left" xlink:label="note-0190-06" xlink:href="note-0190-06a" xml:space="preserve">Deſ@tiptio cir-<lb/>culorum Verti-<lb/>calium in eodẽ <lb/>horologio hori-<lb/>zontali.</note>
  <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a">
    <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0190-01"/>
  </figure>
<note position="left" xlink:label="note-0190-07" xlink:href="note-0190-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0190-08" xlink:href="note-0190-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s11035" xml:space="preserve">QVONIAM tam planum Verticalis propriè dicti, quod per G, tranſit, (Eſt enim gnomon <lb/>
<anchor type="note" xlink:label="note-0190-09a" xlink:href="note-0190-09"/>
horologij horizontalis pars ſectionis communis Meridiani, &amp; </s>
  <s xml:id="echoid-s11036" xml:space="preserve">Verticalis circuli propriè dicti, vt
<pb o="171" file="0191" n="191" rhead="LIBER SECVNDVS."/>
ex Analemmate conſtat) quàm planum horologii horizontalis, ad Meridianum rectum eſt, erit &amp; </s>
  <s xml:id="echoid-s11037" xml:space="preserve"><lb/>communis eorum ſectio ad eundem Meridianum recta; </s>
  <s xml:id="echoid-s11038" xml:space="preserve">atque adeò, per defin. </s>
  <s xml:id="echoid-s11039" xml:space="preserve">3. </s>
  <s xml:id="echoid-s11040" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s11041" xml:space="preserve">11. </s>
  <s xml:id="echoid-s11042" xml:space="preserve">Euclidis, <lb/>
<anchor type="note" xlink:label="note-0191-01a" xlink:href="note-0191-01"/>
ad lineam meridianam in puncto G, perpendicularis. </s>
  <s xml:id="echoid-s11043" xml:space="preserve">Recta igitur A B, quæ per G, ducta eſt ad <lb/>meridianam lineam perpendicularis, communis ſectio eſt plani horologii, &amp; </s>
  <s xml:id="echoid-s11044" xml:space="preserve">Verticalis propriè <lb/>dicti. </s>
  <s xml:id="echoid-s11045" xml:space="preserve">Et quia circuli omnes Verticales ſecant Horizontem in partes 360. </s>
  <s xml:id="echoid-s11046" xml:space="preserve">ęquales, atque adeo &amp; </s>
  <s xml:id="echoid-s11047" xml:space="preserve"><lb/>circulum, quem planum horologii Horizonti ęquidiſtans in ſphęra, per propoſ. </s>
  <s xml:id="echoid-s11048" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11049" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s11050" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11051" xml:space="preserve">Theodo-<lb/>ſii, facit; </s>
  <s xml:id="echoid-s11052" xml:space="preserve">propterea quòd per Zenith, ſeu polum Horizontis tranſeuntes diuidant, per propoſ. </s>
  <s xml:id="echoid-s11053" xml:space="preserve">10. <lb/></s>
  <s xml:id="echoid-s11054" xml:space="preserve">lib.</s>
  <s xml:id="echoid-s11055" xml:space="preserve"><unsure/> 2. </s>
  <s xml:id="echoid-s11056" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s11057" xml:space="preserve">Horizontem, &amp; </s>
  <s xml:id="echoid-s11058" xml:space="preserve">circulos Horizonti parallelos, in ſegmenta ſimilia; </s>
  <s xml:id="echoid-s11059" xml:space="preserve">fit vt omnes Ver-<lb/>ticales circuli, atque adeò &amp; </s>
  <s xml:id="echoid-s11060" xml:space="preserve">communes ipſorum, ac plani horologij ſectiones, tranſeant per pun-<lb/>cta, quibus dictus circulus à plano horologij in ſphęra factus in 360. </s>
  <s xml:id="echoid-s11061" xml:space="preserve">partes ęquales diuiditur. </s>
  <s xml:id="echoid-s11062" xml:space="preserve">Sed <lb/>
<anchor type="note" xlink:label="note-0191-02a" xlink:href="note-0191-02"/>
eędem ſectiones ducuntur quoque per punctum G, ex propoſ. </s>
  <s xml:id="echoid-s11063" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11064" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11065" xml:space="preserve">in quo nimirum <lb/>communis ſectio circulorum Verticalium plano horologij occurrit. </s>
  <s xml:id="echoid-s11066" xml:space="preserve">Igitur eędem ſectiones tran-<lb/>ſibunt quoque per puncta diuiſionum circuli ex G, deſcripti. </s>
  <s xml:id="echoid-s11067" xml:space="preserve">Cum enim G, punctum, in quod <lb/>cadit axis Horizontis, &amp; </s>
  <s xml:id="echoid-s11068" xml:space="preserve">circuli à plano horologii in ſphęra facti, centrum ſit, per propoſ. </s>
  <s xml:id="echoid-s11069" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11070" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s11071" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11072" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s11073" xml:space="preserve">dicti circuli ab horologij plano in ſphęra procreati, efficitur, vt circulus hic, &amp; </s>
  <s xml:id="echoid-s11074" xml:space="preserve">ille, quẽ <lb/>ex G, deſcripſimus, in arcus ſimiles diuidantur à rectis lineis è centro G, egredientibus, per ea, quę <lb/>in commentarijs in ſphæram ad finem cap. </s>
  <s xml:id="echoid-s11075" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11076" xml:space="preserve">demonſtrauimus: </s>
  <s xml:id="echoid-s11077" xml:space="preserve">Ac proinde cum prior ſecetur <lb/>in partes æquales, ſecabitur &amp; </s>
  <s xml:id="echoid-s11078" xml:space="preserve">poſterior, quem ex G, deſcripſimus, in æquales partes. </s>
  <s xml:id="echoid-s11079" xml:space="preserve">Sunt ergo re-<lb/>ctę illę ex G, emiſſæ per puncta, quibus circulus ex G, deſcriptus in partes ęquales eſt diuiſus, com <lb/>munes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s11080" xml:space="preserve">circulorum Verticalium. </s>
  <s xml:id="echoid-s11081" xml:space="preserve">Circulos igitur Verticales, &amp;</s>
  <s xml:id="echoid-s11082" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11083" xml:space="preserve">in eo-<lb/>
<anchor type="note" xlink:label="note-0191-03a" xlink:href="note-0191-03"/>
dem horizontali horologio deſcripſimus. </s>
  <s xml:id="echoid-s11084" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s11085" xml:space="preserve"/>
</p>
<div xml:id="echoid-div596" type="float" level="2" n="2">
<note position="left" xlink:label="note-0190-09" xlink:href="note-0190-09a" xml:space="preserve">Demonſtrat@o <lb/>deſcriptionis <lb/>Ver@calium.</note>
<note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0191-03" xlink:href="note-0191-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div598" type="section" level="1" n="150">
<head xml:id="echoid-head153" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Vſus Vertica-<lb/>lium circulor@ <lb/>in hotologio <lb/>deſcriptorum, <lb/>quibus cogno-<lb/>ſcimus, quonã <lb/>in quadrãte he-<lb/>miſphærii ſupe <lb/>ri Sol exiſtat.</note>
<p style="it">
  <s xml:id="echoid-s11086" xml:space="preserve">EX circulis Verticalibus addiſcimus quolibet momento temporis, quanam in parte ex quatuor illis, <lb/>in quas hemiſphærium ſuperum à Verticali proprio, ac Meridiano dirimitur, Sol verſetur. </s>
  <s xml:id="echoid-s11087" xml:space="preserve">Nam in eaſ-<lb/>dem quatuor partes diuiditur planum horologĳ à recta A B, quæ communis ſectio eſt ipſius plani horolo <lb/>gĳ, &amp; </s>
  <s xml:id="echoid-s11088" xml:space="preserve">Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s11089" xml:space="preserve">à linea meridiana, ſiue ſectione communi eiuſdem plani horologĳ, &amp; </s>
  <s xml:id="echoid-s11090" xml:space="preserve"><lb/>Meridiani; </s>
  <s xml:id="echoid-s11091" xml:space="preserve">ita vt pars contenta intra rectas G B, G C, dicatur Quarta occidentalis, &amp; </s>
  <s xml:id="echoid-s11092" xml:space="preserve">borea; </s>
  <s xml:id="echoid-s11093" xml:space="preserve">pars au-<lb/>
<anchor type="note" xlink:label="note-0191-05a" xlink:href="note-0191-05"/>
tem intra rectas G B, G H, comprehenſa, Quarta occidentalis, &amp; </s>
  <s xml:id="echoid-s11094" xml:space="preserve">auſtrina; </s>
  <s xml:id="echoid-s11095" xml:space="preserve">pars deinde, quam continẽt <lb/>
<anchor type="note" xlink:label="note-0191-06a" xlink:href="note-0191-06"/>
rectę G A, G C, Quarta orientalis, ac borea; </s>
  <s xml:id="echoid-s11096" xml:space="preserve">pars denique, quam rectæ G A, G H, complectuntur, Quar-<lb/>ta orientalis, &amp; </s>
  <s xml:id="echoid-s11097" xml:space="preserve">auſtrina. </s>
  <s xml:id="echoid-s11098" xml:space="preserve">Vnde cum Sol proĳciat ſemper vmbram ſtyli in contrariam partem ei, <lb/>in qua exiſtit, facile iudicabimus ex vmbra, quanam in Quarta hemiſphærĳ commoretur. </s>
  <s xml:id="echoid-s11099" xml:space="preserve">Nam ſi vm-<lb/>bra ſtyli cadat in Quartam occidentalem, boream{q́ue}, quam intra lineas G B, G C, contineri dixi-<lb/>mus, dicemus Solem tunc exiſtere in Quarta oppoſita, nempe in Quarta orientali, atque auſtrina, &amp; </s>
  <s xml:id="echoid-s11100" xml:space="preserve"><lb/>ſic de cæteris.</s>
  <s xml:id="echoid-s11101" xml:space="preserve"/>
</p>
<div xml:id="echoid-div598" type="float" level="2" n="1">
<note position="right" xlink:label="note-0191-05" xlink:href="note-0191-05a" xml:space="preserve">Quatuor qua-<lb/>drantes hemi-<lb/>ſphęrii ſuperi in <lb/>horologio hori-<lb/>zontali qui ſint.</note>
<note position="left" xlink:label="note-0191-06" xlink:href="note-0191-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s11102" xml:space="preserve">PRAETEREA ex eiſdem Verticalibus cognoſcimus, quanta ſit Solis diſtantia Verticalis, <lb/>
<anchor type="note" xlink:label="note-0191-07a" xlink:href="note-0191-07"/>
hoc eſi, quantum Verticalis ille circulus, in quo Sol quouis momento temporis exiſtit, recedat in Ho-<lb/>rizonte à Verticali proprie dicto, ſiue à puncto veri ortus, occaſusve. </s>
  <s xml:id="echoid-s11103" xml:space="preserve">Nam ſi, exempli gratia, Sol <lb/>deprehenſus fuerit, per ea, quæ proximè tradidimus, exiſtere in Quarta orientali, &amp; </s>
  <s xml:id="echoid-s11104" xml:space="preserve">auſtrina, cadat <lb/>
<anchor type="note" xlink:label="note-0191-08a" xlink:href="note-0191-08"/>
autem vmbra tunc temporis in Verticalem lineam, cui aſcriptus eſt numerus hic, 30. </s>
  <s xml:id="echoid-s11105" xml:space="preserve">diſtabit Vertica-<lb/>lis, in quo Sol tunc eſt, à puncto veri ortus verſus auſtrum grad. </s>
  <s xml:id="echoid-s11106" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11107" xml:space="preserve">hoc eſt, ar cus Horizontis inter Ver-<lb/>ticalem propriè dictum, &amp; </s>
  <s xml:id="echoid-s11108" xml:space="preserve">Verticalem, qui tunc per centrum Solis incedit, interpoſitus orientalis eſt, &amp; </s>
  <s xml:id="echoid-s11109" xml:space="preserve"><lb/>austrinus, complectitur{q́ue} grad. </s>
  <s xml:id="echoid-s11110" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11111" xml:space="preserve">atque ita de cæteris erit iudicandum.</s>
  <s xml:id="echoid-s11112" xml:space="preserve"/>
</p>
<div xml:id="echoid-div599" type="float" level="2" n="2">
<note position="right" xlink:label="note-0191-07" xlink:href="note-0191-07a" xml:space="preserve">Quo pacto e@ <lb/>circulis Vertica <lb/>libus cognoſca-<lb/>tur, quantus ſit <lb/>arcus Horizon-<lb/>tis inter Ver-<lb/>ticalem propriè <lb/>dictum, &amp; Ver-<lb/>ticalem, qui per <lb/>Solem ducitur:<unsure/> <lb/>qui quidem ar-<lb/>cus dici ſolet di <lb/>ſtantia Vertica <lb/>lis.</note>
<note position="left" xlink:label="note-0191-08" xlink:href="note-0191-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div601" type="section" level="1" n="151">
<head xml:id="echoid-head154" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
<p>
  <s xml:id="echoid-s11113" xml:space="preserve">PARALLELOS Horizontis, hoc eſt, circulos minores al-<lb/>titudinum aſtrorum, quos Almucantarath vocant, in eodem horolo-<lb/>
<anchor type="note" xlink:label="note-0191-09a" xlink:href="note-0191-09"/>
gio horizontali deſcribere.</s>
  <s xml:id="echoid-s11114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div601" type="float" level="2" n="1">
<note position="left" xlink:label="note-0191-09" xlink:href="note-0191-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s11115" xml:space="preserve">DESCRIBATVR quadrans circuli A B C, qui in 90. </s>
  <s xml:id="echoid-s11116" xml:space="preserve">partes ęquales diſtribuatur, initio <lb/>
<anchor type="note" xlink:label="note-0191-10a" xlink:href="note-0191-10"/>
facto à ſemidiametro A B. </s>
  <s xml:id="echoid-s11117" xml:space="preserve">(Nos eundem in 9. </s>
  <s xml:id="echoid-s11118" xml:space="preserve">partes tantum diuiſimus, ob ſpatii anguſtias, ita <lb/>vt ſingulæ denos complectantur gradus.) </s>
  <s xml:id="echoid-s11119" xml:space="preserve">Sumpta deinde A D, longitudine ſtyli in ſemidiametro <lb/>A C, ducatur per D, alteri ſemidiametro A B, parallela D E. </s>
  <s xml:id="echoid-s11120" xml:space="preserve">Poſtremo eductis è centro A, per <lb/>diuiſionum puncta rectis, ſi in horologio ex G, loco gnomonis, tanquam centro, ad interualla re-<lb/>ctarum inter D, &amp; </s>
  <s xml:id="echoid-s11121" xml:space="preserve">rectas ex A, emiſſas, comprehenſarum, circuli deſcribantur, vt in figura pręce-<lb/>dentis propoſ. </s>
  <s xml:id="echoid-s11122" xml:space="preserve">qui tamen tropicos horologii non tranſcendant, deſcripti erunt paralleli Hori-<lb/>zontis, ſeu circuli altitudinum; </s>
  <s xml:id="echoid-s11123" xml:space="preserve">qui quidem omnes conicę ſectiones ſunt, in quas, ex coroll. </s>
  <s xml:id="echoid-s11124" xml:space="preserve">pro-
<pb o="172" file="0192" n="192" rhead="GNOMONICES"/>
poſ. </s>
  <s xml:id="echoid-s11125" xml:space="preserve">12. </s>
  <s xml:id="echoid-s11126" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11127" xml:space="preserve">vmbra ſtyli cadit, Sole in dictis circulis altitudinum exiſtente. </s>
  <s xml:id="echoid-s11128" xml:space="preserve">Quod hune <lb/>in modum confirmabimus.</s>
  <s xml:id="echoid-s11129" xml:space="preserve"/>
</p>
<div xml:id="echoid-div602" type="float" level="2" n="2">
<note position="right" xlink:label="note-0191-10" xlink:href="note-0191-10a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis, qui Al <lb/>mucantarath di<unsure/> <lb/>cuntur, in eodẽ <lb/>horologio hori-<lb/>zon tali.</note>
</div>
<p>
  <s xml:id="echoid-s11130" xml:space="preserve">PERFICIATVR totus circulus G H C B, referens Meridianum, producanturq́ue ſemi-<lb/>
<anchor type="note" xlink:label="note-0192-01a" xlink:href="note-0192-01"/>
<anchor type="figure" xlink:label="fig-0192-01a" xlink:href="fig-0192-01"/>
diametri B A, A C, unà cum recta <lb/>E D, ad puncta H, G, L. </s>
  <s xml:id="echoid-s11131" xml:space="preserve">Poſita igi-<lb/>tur H B, communi ſectione Hori-<lb/>zontis, ac Meridiani, erit G C, com <lb/>munis ſectio eiuſdem Meridiani, <lb/>&amp; </s>
  <s xml:id="echoid-s11132" xml:space="preserve">Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s11133" xml:space="preserve">L E, commu <lb/>nis ſectio Meridiani eiuſdẽ, &amp; </s>
  <s xml:id="echoid-s11134" xml:space="preserve">pla-<lb/>
<anchor type="note" xlink:label="note-0192-02a" xlink:href="note-0192-02"/>
ni horologii. </s>
  <s xml:id="echoid-s11135" xml:space="preserve">Quoniam verò ſi re-<lb/>ctę ex A, per puncta diuiſionum <lb/>quadrantis B C, eductę, per cen-<lb/>trum producantur, anguli ad verti-<lb/>cem A, ęq́uales fiunt, erunt arcus <lb/>
<anchor type="note" xlink:label="note-0192-03a" xlink:href="note-0192-03"/>
<anchor type="note" xlink:label="note-0192-04a" xlink:href="note-0192-04"/>
in quadrante H G, ęquáles arcubus <lb/>in quadrante B C. </s>
  <s xml:id="echoid-s11136" xml:space="preserve">Rectæ igitur per <lb/>puncta quadrantis H G, ductę &amp; </s>
  <s xml:id="echoid-s11137" xml:space="preserve"><lb/>ipſi H B, æquidiſtantes, communes <lb/>ſectiones ſunt Meridiani, &amp; </s>
  <s xml:id="echoid-s11138" xml:space="preserve">circulo <lb/>
<anchor type="note" xlink:label="note-0192-05a" xlink:href="note-0192-05"/>
rum altitudinum, ſiue Almucanta-<lb/>rath, à quarum punctis extremis re <lb/>ctæ per centrum A, ductæ conſti-<lb/>tuent triãgula per axem conorum, <lb/>quorum baſes ſunt Horizontis pa-<lb/>ralleli, cuiuſinodi ſunt triangula A K I, A L E.</s>
  <s xml:id="echoid-s11139" xml:space="preserve"><unsure/> Et quia planum horologij per rectam L E, ductum <lb/>Horizonti, atque adeò &amp; </s>
  <s xml:id="echoid-s11140" xml:space="preserve">baſibus conorum æquidiſtans, facit, per propoſ. </s>
  <s xml:id="echoid-s11141" xml:space="preserve">4 ſuperioris lib. </s>
  <s xml:id="echoid-s11142" xml:space="preserve">ſectio-<lb/>nes communes conicarum illarum ſuperficierum, circulos centra habentes in axe conorum; </s>
  <s xml:id="echoid-s11143" xml:space="preserve">erit <lb/>D, locus ſtyli, centrum illorum circulorum, rectæ verò D E, D F, &amp;</s>
  <s xml:id="echoid-s11144" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11145" xml:space="preserve">quas latera triangulorum per <lb/>axem abrumpunt, eorundem ſemidiametri, vt ex dicta propoſ. </s>
  <s xml:id="echoid-s11146" xml:space="preserve">4. </s>
  <s xml:id="echoid-s11147" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s11148" xml:space="preserve">conſtat: </s>
  <s xml:id="echoid-s11149" xml:space="preserve">Ac pro-<lb/>
<anchor type="note" xlink:label="note-0192-06a" xlink:href="note-0192-06"/>
inde, ſi ex G, loco ſtyli in horologio ad interualla rectarum inter D, &amp; </s>
  <s xml:id="echoid-s11150" xml:space="preserve">rectas ex A, egredientes cõ-<lb/>prehenſarum circuli deſcribantur, erunt hi circuli altitudinum. </s>
  <s xml:id="echoid-s11151" xml:space="preserve">Quare parallelos Horizontis, &amp;</s>
  <s xml:id="echoid-s11152" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s11153" xml:space="preserve">in eodem horologio horizontali deſcripſimus. </s>
  <s xml:id="echoid-s11154" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s11155" xml:space="preserve"/>
</p>
<div xml:id="echoid-div603" type="float" level="2" n="3">
<note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis pa <lb/>rallelorum Ho-<lb/>rizontis.</note>
  <figure xlink:label="fig-0192-01" xlink:href="fig-0192-01a">
    <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0192-01"/>
  </figure>
<note position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0192-03" xlink:href="note-0192-03a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0192-04" xlink:href="note-0192-04a" xml:space="preserve">26. tertĳ.</note>
<note position="left" xlink:label="note-0192-05" xlink:href="note-0192-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0192-06" xlink:href="note-0192-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div605" type="section" level="1" n="152">
<head xml:id="echoid-head155" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s11156" xml:space="preserve">DVCVNT nos paralleli Horizontis in notitiam altitudinis Solis quouis tempore, quo vmbram <lb/>
<anchor type="note" xlink:label="note-0192-07a" xlink:href="note-0192-07"/>
ſtyli in horologio obſeruamus. </s>
  <s xml:id="echoid-s11157" xml:space="preserve">Quandocunque enim vmbra gnomonis cadit v. </s>
  <s xml:id="echoid-s11158" xml:space="preserve">g. </s>
  <s xml:id="echoid-s11159" xml:space="preserve">in parallelum, cui appo-<lb/>ſitus eſt numerus hic, 30. </s>
  <s xml:id="echoid-s11160" xml:space="preserve">continet Solis altitudo, hoc eſt, arcus circuli illius Verticalis, qui tunc temporis <lb/>per Solis centrum ducitur, inter centrum Solis, ſiue parallelum Horizontis per Solis centrum tunc <lb/>
<anchor type="note" xlink:label="note-0192-08a" xlink:href="note-0192-08"/>
etiam tranſeuntem, &amp; </s>
  <s xml:id="echoid-s11161" xml:space="preserve">Horizontem interiectus, grad. </s>
  <s xml:id="echoid-s11162" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11163" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s11164" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11165" xml:space="preserve"/>
</p>
<div xml:id="echoid-div605" type="float" level="2" n="1">
<note position="left" xlink:label="note-0192-07" xlink:href="note-0192-07a" xml:space="preserve">@ ſus parallelo-<lb/>rum Horizõtis <lb/>in horologio de <lb/>ſcriptorum eſt, <lb/>ut<unsure/> ex ipſis altitu <lb/>dinem Solis co <lb/>gnoſcamus.</note>
<note position="left" xlink:label="note-0192-08" xlink:href="note-0192-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div607" type="section" level="1" n="153">
<head xml:id="echoid-head156" xml:space="preserve">PROBLEMA 6. PROPOSITIO 6.</head>
<p>
  <s xml:id="echoid-s11166" xml:space="preserve">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in eo-<lb/>dem horologio horizontali deſcribere.</s>
  <s xml:id="echoid-s11167" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s11168" xml:space="preserve">QVONIAM circuli Meridiani per polos mundi incedunt, quemadmodum &amp; </s>
  <s xml:id="echoid-s11169" xml:space="preserve">circuli ho-<lb/>
<anchor type="note" xlink:label="note-0192-09a" xlink:href="note-0192-09"/>
rarij, qui horas à meridie, vel media nocte monſtrant, non differet Meridianorum deſcriptio à <lb/>
<anchor type="note" xlink:label="note-0192-10a" xlink:href="note-0192-10"/>
deſcriptione circulorum horariorum à meridie, vel media nocte. </s>
  <s xml:id="echoid-s11170" xml:space="preserve">Itaque circulus ex E, deſcriptus <lb/>propoſ. </s>
  <s xml:id="echoid-s11171" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11172" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s11173" xml:space="preserve">ſecetur in partes 360. </s>
  <s xml:id="echoid-s11174" xml:space="preserve">æquales vel in paueiores, vt in 24. </s>
  <s xml:id="echoid-s11175" xml:space="preserve">ita vt quælibet <lb/>complectatur grad. </s>
  <s xml:id="echoid-s11176" xml:space="preserve">15. </s>
  <s xml:id="echoid-s11177" xml:space="preserve">vt à nobis factum eſt, initio ſumpto non à linea meridiana, ſed ab eo <lb/>puncto, per quod tranſit Meridianus per Inſulas Fortunatas ductus, à quo videlicet longitudines <lb/>locorum, atque adeo Meridiani circuli, initium ſumunt, cuiuſmodi eſt punctum A; </s>
  <s xml:id="echoid-s11178" xml:space="preserve">quod quidem <lb/>habetur, numerando à linea meridiana longitudinem loci, in quo horologium deſcriptum eſt, à <lb/>puncto B, verſus occidentales partes, nimirum ad dexteram procedendo. </s>
  <s xml:id="echoid-s11179" xml:space="preserve">Hæc enim pars ad oc-<lb/>cidentem vergit, vt conſtat, ſi horologium in proprio ſitu collocetur, circulusq́; </s>
  <s xml:id="echoid-s11180" xml:space="preserve">ex E, deſcriptus <lb/>in plano Aequatoris intelligatur eſſe conſtitutus. </s>
  <s xml:id="echoid-s11181" xml:space="preserve">Nos numerauimus à puncto B, vſque ad A, grad. <lb/></s>
  <s xml:id="echoid-s11182" xml:space="preserve">36. </s>
  <s xml:id="echoid-s11183" xml:space="preserve">longitudinem ſcilicet Vrbis Romæ. </s>
  <s xml:id="echoid-s11184" xml:space="preserve">Reliqua fiant, vt de lineis horariis à meridie, vel <lb/>media nocte deſcribendis propoſ. </s>
  <s xml:id="echoid-s11185" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11186" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s11187" xml:space="preserve">dictum eſt, deſcriptiq́ue erunt circuli Meridiani,
<pb o="173" file="0193" n="193" rhead="LIBER SECVNDVS."/>
nempe communes corum, &amp; </s>
  <s xml:id="echoid-s11188" xml:space="preserve">plani horologii ſectiones, in quas vmbra ſtyli proiicitur, ex propoſ. <lb/></s>
  <s xml:id="echoid-s11189" xml:space="preserve">11. </s>
  <s xml:id="echoid-s11190" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11191" xml:space="preserve">Sole dictos Meridianos poſſidente. </s>
  <s xml:id="echoid-s11192" xml:space="preserve">Meridianos ergo, ſeu circulos longitudi-<lb/>num, &amp;</s>
  <s xml:id="echoid-s11193" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11194" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s11195" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s11196" xml:space="preserve"/>
</p>
<div xml:id="echoid-div607" type="float" level="2" n="1">
<note position="left" xlink:label="note-0192-09" xlink:href="note-0192-09a" xml:space="preserve">Deſcriptio Me-<lb/>ridianorum in <lb/>eodem horolo-<lb/>gio horizontali.</note>
<note position="left" xlink:label="note-0192-10" xlink:href="note-0192-10a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0193-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div609" type="section" level="1" n="154">
<head xml:id="echoid-head157" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s11197" xml:space="preserve">QVOD ſi longitudo loci ſit arcus B A C, grad. </s>
  <s xml:id="echoid-s11198" xml:space="preserve">v.</s>
  <s xml:id="echoid-s11199" xml:space="preserve">g. </s>
  <s xml:id="echoid-s11200" xml:space="preserve">216. </s>
  <s xml:id="echoid-s11201" xml:space="preserve">ita vt diuiſio circuli ex E, deſcripti initiũ <lb/>
<anchor type="note" xlink:label="note-0193-04a" xlink:href="note-0193-04"/>
ſumat à puncto C, &amp; </s>
  <s xml:id="echoid-s11202" xml:space="preserve">propterea punctum A, diſtet ſemicirculo, hoc eſt, grad. </s>
  <s xml:id="echoid-s11203" xml:space="preserve">180. </s>
  <s xml:id="echoid-s11204" xml:space="preserve">ab co, erit recta K L, <lb/>quæ in noſtro exemplo dat initium longitudinum, longitudo grad. </s>
  <s xml:id="echoid-s11205" xml:space="preserve">180. </s>
  <s xml:id="echoid-s11206" xml:space="preserve">nempe communis ſectio plani ho-<lb/>rologĳ, &amp; </s>
  <s xml:id="echoid-s11207" xml:space="preserve">ſemicirculi eiuſdem Meridiani, qui ſemicirculo per Inſulas Fortunatas tranſeunti opponitur. <lb/></s>
  <s xml:id="echoid-s11208" xml:space="preserve">In hoc enim Sol exiſtens proĳcit vmbram ſtyli per centrum mundi in rectam K L, &amp;</s>
  <s xml:id="echoid-s11209" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11210" xml:space="preserve">cum ſemicircu-<lb/>lus Aequatoris M B N, ſupra Horizontem exiſtat, reliquus verò infra; </s>
  <s xml:id="echoid-s11211" xml:space="preserve">atque adeo, Sole exiſtente in <lb/>Aequatore in puncto A, (quod tunc indicat ſemicir culum Meridiani grad. </s>
  <s xml:id="echoid-s11212" xml:space="preserve">180. </s>
  <s xml:id="echoid-s11213" xml:space="preserve">qui nimirum ſemicirculo <lb/>Inſularum Fortunatarum per C, tranſeunti opponitur) radius A E, cadat in planum horologĳ in punctũ <lb/>L, &amp;</s>
  <s xml:id="echoid-s11214" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11215" xml:space="preserve">Hæc autem luce clariora ſunt ex ĳs, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s11216" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11217" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s11218" xml:space="preserve">ſcripſimus; </s>
  <s xml:id="echoid-s11219" xml:space="preserve">nempe lineam <lb/>quamcunque in horologio, quæ æquinoctialem lineam ſecat, eum ſemicir culum cæleſtem referre, cuius com <lb/>
<anchor type="note" xlink:label="note-0193-05a" xlink:href="note-0193-05"/>
munis ſectio in circulo ex E, deſcripto per centrum E, tranſit, priuſquam æquinoctiali lineæ occurrat, cu-<lb/>iuſmodi eſt ſectio A E, &amp;</s>
  <s xml:id="echoid-s11220" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11221" xml:space="preserve"/>
</p>
<div xml:id="echoid-div609" type="float" level="2" n="1">
<note position="right" xlink:label="note-0193-04" xlink:href="note-0193-04a" xml:space="preserve">Not<unsure/>@, qu<unsure/>æ hi@ <lb/>dicun@ur.</note>
<note position="left" xlink:label="note-0193-05" xlink:href="note-0193-05a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s11222" xml:space="preserve">EADEM ratione recta, quæ in eodem noſtro exemplo dat longitudinem grad. </s>
  <s xml:id="echoid-s11223" xml:space="preserve">15. </s>
  <s xml:id="echoid-s11224" xml:space="preserve">erit longitudo <lb/>grad. </s>
  <s xml:id="echoid-s11225" xml:space="preserve">195. </s>
  <s xml:id="echoid-s11226" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s11227" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11228" xml:space="preserve">quia numeratio graduum in circulo incipiet tunc à puncto C, &amp; </s>
  <s xml:id="echoid-s11229" xml:space="preserve">procedet verſus N, quem-<lb/>admodum &amp; </s>
  <s xml:id="echoid-s11230" xml:space="preserve">prius à puncto A, incipiebat, &amp; </s>
  <s xml:id="echoid-s11231" xml:space="preserve">per B, C, &amp; </s>
  <s xml:id="echoid-s11232" xml:space="preserve">N, procedebat, nimirum per partes orienta-<lb/>les, vt ratio poſtulat.</s>
  <s xml:id="echoid-s11233" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s11234" xml:space="preserve">VSVS porrò Meridianorum circulorum pulcherrimus est. </s>
  <s xml:id="echoid-s11235" xml:space="preserve">Per eos enim dicto citius cognoſcimus, <lb/>
<anchor type="note" xlink:label="note-0193-06a" xlink:href="note-0193-06"/>
quibusnam populis meridies fiat quouis momento temporis, &amp; </s>
  <s xml:id="echoid-s11236" xml:space="preserve">quota hora ſit in qualibet ciuitate, cuius <lb/>longitudo ignota non fuerit. </s>
  <s xml:id="echoid-s11237" xml:space="preserve">Nam vmbra gnomonis cadente præcisè in aliquam lineam meridianam, (om-<lb/>nes enim rectæ ex H, egredientes ſunt variæ lineæ meridianæ variarum vrbium, cum ſint, vt oſtenſum eſt, <lb/>
<anchor type="note" xlink:label="note-0193-07a" xlink:href="note-0193-07"/>
ſectiones communes plani horologĳ, &amp; </s>
  <s xml:id="echoid-s11238" xml:space="preserve">circulorum Meridianorum) erit meridies in omnibus ciuitatibus, <lb/>quę habent longitudinem illam, quam numerus illi meridianæ lineæ affixus monſtrat. </s>
  <s xml:id="echoid-s11239" xml:space="preserve">Exempli gratia. <lb/></s>
  <s xml:id="echoid-s11240" xml:space="preserve">Gnomonis vmbra cadente quocunque anni tempore in meridianam lineam, cui aſc<unsure/>riptus est numerus hic, <lb/>60. </s>
  <s xml:id="echoid-s11241" xml:space="preserve">fiet meridies Alexandriæ Aegypti, quia longitudo huiuſce vrbis, vt ex tabulis Ptolemæi conſtat, con <lb/>tinet grad. </s>
  <s xml:id="echoid-s11242" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11243" xml:space="preserve">Idem{q́ue} continget in omni alio loco, vel ciuitate cuius longitudo totidem gradus comple-<lb/>ctitur. </s>
  <s xml:id="echoid-s11244" xml:space="preserve">Quòd ſi tunc temporis noſſe velim, quota hora ſit vbiuis gentium, vt v. </s>
  <s xml:id="echoid-s11245" xml:space="preserve">g. </s>
  <s xml:id="echoid-s11246" xml:space="preserve">in Inſulis Fortu-<lb/>natis. </s>
  <s xml:id="echoid-s11247" xml:space="preserve">Detraho longitudinem Inſularum Fortunatarum, quæ est grad. </s>
  <s xml:id="echoid-s11248" xml:space="preserve">o. </s>
  <s xml:id="echoid-s11249" xml:space="preserve">(Inde enim initium duci-<lb/>tur longitudinum omnium) ex longitudine illius Meridiani, in cuius lineam tunc vmbra cadit, nem-<lb/>pe ex grad. </s>
  <s xml:id="echoid-s11250" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11251" xml:space="preserve">remanent{q́ue} grad. </s>
  <s xml:id="echoid-s11252" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11253" xml:space="preserve">Hos gradus reuoco ad horas, tribuendo quindenis gradibus ſin-<lb/>gulas horas, &amp; </s>
  <s xml:id="echoid-s11254" xml:space="preserve">ſingulis gradibus quaterna horæ minuta, vel certè ex tabula, (quod quidem multo bre-<lb/>uius fit) quam in commentarĳs in ſphęram poſuimus, cum de Acquatore ageremus; </s>
  <s xml:id="echoid-s11255" xml:space="preserve">efficioq́,<unsure/> horas 4. </s>
  <s xml:id="echoid-s11256" xml:space="preserve">Et
<pb o="174" file="0194" n="194" rhead="GNOMONICES"/>
quoniam Sol nondum peruenit tunc ad Meridianum Fortunatarum Inſularum, quòd earum linea meri-<lb/>diana in horologio ſit orientalior, quàm meridiana linea grad. </s>
  <s xml:id="echoid-s11257" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11258" xml:space="preserve">diſtabit propterea Sol horis 4. </s>
  <s xml:id="echoid-s11259" xml:space="preserve">ante <lb/>meridiem illarum inſularum; </s>
  <s xml:id="echoid-s11260" xml:space="preserve">ac proinde erit tunc apud eaſdem hora octaua poſt mediam noctem. </s>
  <s xml:id="echoid-s11261" xml:space="preserve">Simi-<lb/>liter ſi ſcire lubet, quotatunc hora ſit in regione, cuius longitudo comprehendit grad. </s>
  <s xml:id="echoid-s11262" xml:space="preserve">300. </s>
  <s xml:id="echoid-s11263" xml:space="preserve">Aufero grad. <lb/></s>
  <s xml:id="echoid-s11264" xml:space="preserve">300. </s>
  <s xml:id="echoid-s11265" xml:space="preserve">ex grad. </s>
  <s xml:id="echoid-s11266" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11267" xml:space="preserve">adiecto prius, more Aſtronomorum, integro circulo grad. </s>
  <s xml:id="echoid-s11268" xml:space="preserve">360. </s>
  <s xml:id="echoid-s11269" xml:space="preserve">ita vt fiãt grad. </s>
  <s xml:id="echoid-s11270" xml:space="preserve">420. </s>
  <s xml:id="echoid-s11271" xml:space="preserve">re-<lb/>linquuntur{q́ue} grad. </s>
  <s xml:id="echoid-s11272" xml:space="preserve">120. </s>
  <s xml:id="echoid-s11273" xml:space="preserve">qui faciunt horas 8. </s>
  <s xml:id="echoid-s11274" xml:space="preserve">Tot ergo horis abest tunc Sol ante meridiem illius loci, ac <lb/>propterea habebunt illi tunc populi horam quartam post mediam noctem. </s>
  <s xml:id="echoid-s11275" xml:space="preserve">Rurſus idem cupio cognoſcere <lb/>in eo loco, vbi longitudo eſt grad. </s>
  <s xml:id="echoid-s11276" xml:space="preserve">110. </s>
  <s xml:id="echoid-s11277" xml:space="preserve">qualis fere eſt Calecutĳ in India orientali. </s>
  <s xml:id="echoid-s11278" xml:space="preserve">Demo grad. </s>
  <s xml:id="echoid-s11279" xml:space="preserve">110. </s>
  <s xml:id="echoid-s11280" xml:space="preserve">ex <lb/>grad. </s>
  <s xml:id="echoid-s11281" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11282" xml:space="preserve">adiecto prius integro circulo, remanent{q́ue} grad. </s>
  <s xml:id="echoid-s11283" xml:space="preserve">310. </s>
  <s xml:id="echoid-s11284" xml:space="preserve">qui complectuntur horas 20. </s>
  <s xml:id="echoid-s11285" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11286" xml:space="preserve">40. </s>
  <s xml:id="echoid-s11287" xml:space="preserve">atque <lb/>tot horæ deſunt in illo loco, vt ſit meridies. </s>
  <s xml:id="echoid-s11288" xml:space="preserve">Et quoniam à meridie ad meridiem effluunt horę 24. </s>
  <s xml:id="echoid-s11289" xml:space="preserve">neceſſe <lb/>
<anchor type="note" xlink:label="note-0194-01a" xlink:href="note-0194-01"/>
est, tunc elapſas eſſe horas 3. </s>
  <s xml:id="echoid-s11290" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11291" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11292" xml:space="preserve">poſt meridiem proximum. </s>
  <s xml:id="echoid-s11293" xml:space="preserve">Pariratione, ſi quæratur tunc <lb/>hora in eo loco, vbi longitudo continet grad. </s>
  <s xml:id="echoid-s11294" xml:space="preserve">240. </s>
  <s xml:id="echoid-s11295" xml:space="preserve">Deductis grad. </s>
  <s xml:id="echoid-s11296" xml:space="preserve">240. </s>
  <s xml:id="echoid-s11297" xml:space="preserve">ex grad. </s>
  <s xml:id="echoid-s11298" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11299" xml:space="preserve">(adiecto prius <lb/>integro circulo grad. </s>
  <s xml:id="echoid-s11300" xml:space="preserve">360. </s>
  <s xml:id="echoid-s11301" xml:space="preserve">vt fiant grad. </s>
  <s xml:id="echoid-s11302" xml:space="preserve">420.) </s>
  <s xml:id="echoid-s11303" xml:space="preserve">reliqui ſunt grad. </s>
  <s xml:id="echoid-s11304" xml:space="preserve">180. </s>
  <s xml:id="echoid-s11305" xml:space="preserve">qui continent horas 12. </s>
  <s xml:id="echoid-s11306" xml:space="preserve">Di-<lb/>cam ergo, Solem distare à meridie dicti loci horis 12. </s>
  <s xml:id="echoid-s11307" xml:space="preserve">ac proinde mediam noctem tunc eſſe. </s>
  <s xml:id="echoid-s11308" xml:space="preserve">Poſtremo <lb/>ſi idem deſideretur in regione longitudinis grad. </s>
  <s xml:id="echoid-s11309" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11310" xml:space="preserve">qualem habet fere Toletum Hiſpaniæ. </s>
  <s xml:id="echoid-s11311" xml:space="preserve">Aufero grad. <lb/></s>
  <s xml:id="echoid-s11312" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11313" xml:space="preserve">ex grad. </s>
  <s xml:id="echoid-s11314" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11315" xml:space="preserve">relinquuntur{q́ue} grad. </s>
  <s xml:id="echoid-s11316" xml:space="preserve">50. </s>
  <s xml:id="echoid-s11317" xml:space="preserve">qui dant horas 3. </s>
  <s xml:id="echoid-s11318" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11319" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11320" xml:space="preserve">Tot ergo horis diſtat tunc Sol ante <lb/>meridiem Toleti. </s>
  <s xml:id="echoid-s11321" xml:space="preserve">Vnde eo tempore habebunt incolæ dictæ vrbis horas 8. </s>
  <s xml:id="echoid-s11322" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11323" xml:space="preserve">40. </s>
  <s xml:id="echoid-s11324" xml:space="preserve">poſt mediam noctem. </s>
  <s xml:id="echoid-s11325" xml:space="preserve"><lb/>Idem iudicium de cæteris habendum eſt.</s>
  <s xml:id="echoid-s11326" xml:space="preserve"/>
</p>
<div xml:id="echoid-div610" type="float" level="2" n="2">
<note position="right" xlink:label="note-0193-06" xlink:href="note-0193-06a" xml:space="preserve">Per Meridia-<lb/>nos in horolo-<lb/>gio deſcriptos <lb/>cognoſcimus, <lb/>quibuſnam po-<lb/>pulis meridies <lb/>fiat quolibet tẽ <lb/>pore, &amp; quota <lb/>hora ſit in quo <lb/>uis loco, cuiu@ <lb/>longitudo ſit <lb/>nota.</note>
<note position="left" xlink:label="note-0193-07" xlink:href="note-0193-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s11327" xml:space="preserve">IDEM quoque aſſequemur, &amp; </s>
  <s xml:id="echoid-s11328" xml:space="preserve">fortaſſis commodius, hoc modo. </s>
  <s xml:id="echoid-s11329" xml:space="preserve">Si longitudo Meridiani, in cuius li-<lb/>neam vmbra tempore obſeruationis cadit, minor fuerit longitudine illius loci, pro quo hora quæritur, de-<lb/>
<anchor type="note" xlink:label="note-0194-02a" xlink:href="note-0194-02"/>
trahatur minor longitudo ex maiore. </s>
  <s xml:id="echoid-s11330" xml:space="preserve">Gradus enim reliqui ad horas reuocati dabunt tempus elapſum à <lb/>meridie dicti loci. </s>
  <s xml:id="echoid-s11331" xml:space="preserve">Vnde ſi horę pauciores fuerint, quàm 12. </s>
  <s xml:id="echoid-s11332" xml:space="preserve">cognitæ erunt horę à meridie; </s>
  <s xml:id="echoid-s11333" xml:space="preserve">ſi verò fue-<lb/>rint præcisè 12. </s>
  <s xml:id="echoid-s11334" xml:space="preserve">erunt præcisè horæ 12. </s>
  <s xml:id="echoid-s11335" xml:space="preserve">à meridie, nempe tempus mediæ noctis; </s>
  <s xml:id="echoid-s11336" xml:space="preserve">ſi denique plures fue-<lb/>rint, quàm 12. </s>
  <s xml:id="echoid-s11337" xml:space="preserve">ablatis 12. </s>
  <s xml:id="echoid-s11338" xml:space="preserve">ex ipſis, remanebunt horæ poſt mediam noctem. </s>
  <s xml:id="echoid-s11339" xml:space="preserve">Siautem longitudo Meri-<lb/>diani, in cuius lineam vmbra cadit, maior fuerit longitudine alterius loci propoſiti, detracta minore lon-<lb/>gitudine ex maiori, relinquentur gradus, qui ad horas reducti dabunt tempus ante meridiem dicti loci. <lb/></s>
  <s xml:id="echoid-s11340" xml:space="preserve">Vnde ſi pauciores fuerint, quàm 12. </s>
  <s xml:id="echoid-s11341" xml:space="preserve">detractis illis ex 12. </s>
  <s xml:id="echoid-s11342" xml:space="preserve">remanebunt horę poſt mediam noctem; </s>
  <s xml:id="echoid-s11343" xml:space="preserve">Si ve-<lb/>rò fuerint præcisè 12. </s>
  <s xml:id="echoid-s11344" xml:space="preserve">erunt omnino horæ 12. </s>
  <s xml:id="echoid-s11345" xml:space="preserve">ante meridiem, nempe tempus mediæ noctis; </s>
  <s xml:id="echoid-s11346" xml:space="preserve">ſi denique plu-<lb/>res fuerint, quàm 12. </s>
  <s xml:id="echoid-s11347" xml:space="preserve">detractis eis ex 24. </s>
  <s xml:id="echoid-s11348" xml:space="preserve">remanebunt horæ à meridie elapſæ. </s>
  <s xml:id="echoid-s11349" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s11350" xml:space="preserve">Cadat rurſum <lb/>quolibet anni tempore extremitas vmbræ ſtyli in lineam meridianam grad. </s>
  <s xml:id="echoid-s11351" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11352" xml:space="preserve">quanta nimirum longitu-<lb/>
<anchor type="note" xlink:label="note-0194-03a" xlink:href="note-0194-03"/>
do est Alexandriæ Vrbis Aegypti, operæ{q́ue} pretium ſit cognoſcere, quota tunc hora ſit in eo loco, cuius <lb/>longitudo complectitur grad. </s>
  <s xml:id="echoid-s11353" xml:space="preserve">300. </s>
  <s xml:id="echoid-s11354" xml:space="preserve">Aufero minorem longitudinem ex maiore, nimirum grad. </s>
  <s xml:id="echoid-s11355" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11356" xml:space="preserve">ex 300. <lb/></s>
  <s xml:id="echoid-s11357" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11358" xml:space="preserve">reliquos grad. </s>
  <s xml:id="echoid-s11359" xml:space="preserve">240. </s>
  <s xml:id="echoid-s11360" xml:space="preserve">reduco ad horas 16. </s>
  <s xml:id="echoid-s11361" xml:space="preserve">quæ elapſæ ſunt à meridie illius loci. </s>
  <s xml:id="echoid-s11362" xml:space="preserve">Vnde inſtat tunc hora <lb/>quarta poſt mediam noctem. </s>
  <s xml:id="echoid-s11363" xml:space="preserve">Rurſus idem inuestigetur in ciuitate longitudinis grad. </s>
  <s xml:id="echoid-s11364" xml:space="preserve">240. </s>
  <s xml:id="echoid-s11365" xml:space="preserve">Detractis grad. </s>
  <s xml:id="echoid-s11366" xml:space="preserve"><lb/>60. </s>
  <s xml:id="echoid-s11367" xml:space="preserve">ex grad. </s>
  <s xml:id="echoid-s11368" xml:space="preserve">240. </s>
  <s xml:id="echoid-s11369" xml:space="preserve">remanent grad. </s>
  <s xml:id="echoid-s11370" xml:space="preserve">180. </s>
  <s xml:id="echoid-s11371" xml:space="preserve">qui faciunt horas 12. </s>
  <s xml:id="echoid-s11372" xml:space="preserve">à meridie elapſas. </s>
  <s xml:id="echoid-s11373" xml:space="preserve">Eſt ergo pręcisè tunc tem <lb/>pus mediæ noctis. </s>
  <s xml:id="echoid-s11374" xml:space="preserve">Adhuc deſiderat quis idem noſſe in eo loco, qui ab Inſulis Fortunatis recedit grad. </s>
  <s xml:id="echoid-s11375" xml:space="preserve"><lb/>110. </s>
  <s xml:id="echoid-s11376" xml:space="preserve">verſus orientem, cuiuſmodi eſt Calecutium emporium Indiæ orientalis. </s>
  <s xml:id="echoid-s11377" xml:space="preserve">Subductis grad. </s>
  <s xml:id="echoid-s11378" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11379" xml:space="preserve">ex <lb/>grad. </s>
  <s xml:id="echoid-s11380" xml:space="preserve">110. </s>
  <s xml:id="echoid-s11381" xml:space="preserve">reliqui fiunt grad. </s>
  <s xml:id="echoid-s11382" xml:space="preserve">50. </s>
  <s xml:id="echoid-s11383" xml:space="preserve">qui exhibent horas 3. </s>
  <s xml:id="echoid-s11384" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11385" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11386" xml:space="preserve">poſt meridiem tranſactas. </s>
  <s xml:id="echoid-s11387" xml:space="preserve">Ad extremum <lb/>ſi optemus idem cognoſcere in loco, quilongitudinem habeat grad. </s>
  <s xml:id="echoid-s11388" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11389" xml:space="preserve">ſubtrahemus grad. </s>
  <s xml:id="echoid-s11390" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11391" xml:space="preserve">ex grad. </s>
  <s xml:id="echoid-s11392" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11393" xml:space="preserve"><lb/>Nam reliq@i grad. </s>
  <s xml:id="echoid-s11394" xml:space="preserve">50. </s>
  <s xml:id="echoid-s11395" xml:space="preserve">dabunt horas 3. </s>
  <s xml:id="echoid-s11396" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11397" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11398" xml:space="preserve">ante meridiem illius loci, hoc eſt, horas 8. </s>
  <s xml:id="echoid-s11399" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11400" xml:space="preserve">40. </s>
  <s xml:id="echoid-s11401" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0194-04a" xlink:href="note-0194-04"/>
poſt mediam noctem, &amp;</s>
  <s xml:id="echoid-s11402" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11403" xml:space="preserve"/>
</p>
<div xml:id="echoid-div611" type="float" level="2" n="3">
<note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0194-04" xlink:href="note-0194-04a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div613" type="section" level="1" n="155">
<head xml:id="echoid-head158" xml:space="preserve">PROBLEMA 7. PROPOSITIO 7.</head>
<p>
  <s xml:id="echoid-s11404" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in eo-<lb/>dem horologio horizontali deſcribere.</s>
  <s xml:id="echoid-s11405" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s11406" xml:space="preserve">HORVM deſcriptio à deſcriptione parallelorum Zodiaci, quam propoſ. </s>
  <s xml:id="echoid-s11407" xml:space="preserve">2. </s>
  <s xml:id="echoid-s11408" xml:space="preserve">huius libri tra-<lb/>
<anchor type="note" xlink:label="note-0194-05a" xlink:href="note-0194-05"/>
didimus, non differt, cum tam hi, quàm illi æquidiſtent Aequatori; </s>
  <s xml:id="echoid-s11409" xml:space="preserve">ſi modo loco declinationum <lb/>
<anchor type="note" xlink:label="note-0194-06a" xlink:href="note-0194-06"/>
ſignorum, quas ibi vſurpauimus, aſſumantur hic declinationes parallelorum, qui per vertices ci-<lb/>uitatum ducuntur, nempe ipſæmet latitudines ciuitatum. </s>
  <s xml:id="echoid-s11410" xml:space="preserve">Immo &amp; </s>
  <s xml:id="echoid-s11411" xml:space="preserve">paralleli ſignorum ſupra de-<lb/>ſcripti, circuli etiam ſunt latitudinum ciuitatum, vt tropicus ♋, eſt circulus latitudinis ciuitatum, <lb/>quæ ab Aequatore boream verſus abſunt grad. </s>
  <s xml:id="echoid-s11412" xml:space="preserve">23. </s>
  <s xml:id="echoid-s11413" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11414" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11415" xml:space="preserve">qualis eſt Syene vrbs Aegypti, &amp;</s>
  <s xml:id="echoid-s11416" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11417" xml:space="preserve">Pa-<lb/>rallelos ergo ciuitatum, &amp;</s>
  <s xml:id="echoid-s11418" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11419" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s11420" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s11421" xml:space="preserve"/>
</p>
<div xml:id="echoid-div613" type="float" level="2" n="1">
<note position="left" xlink:label="note-0194-05" xlink:href="note-0194-05a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ciui <lb/>ta um, ſiue cir <lb/>culorum latitu-<lb/>dinum, in eodẽ <lb/>horizontali ho-<lb/>rologio.</note>
<note position="left" xlink:label="note-0194-06" xlink:href="note-0194-06a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">Paralleli ciuita <lb/>tum. ſeu circuli <lb/>latitudinum in <lb/>horologio de-<lb/>ſctipti indicãt, <lb/>quæ gentes So-<lb/>lem habeant in <lb/>vertice capitis <lb/>tempore meri-<lb/>diano.</note>
</div>
<div xml:id="echoid-div615" type="section" level="1" n="156">
<head xml:id="echoid-head159" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s11422" xml:space="preserve">CIRCVLI latitudinum, ſeu paralleli ciuitatum hanc nobis afferunt vtilitatem, vt eorum benefi-<lb/>cio intelligamus, quinam populi Solem habeant in vertice capitis tempore meridiano. </s>
  <s xml:id="echoid-s11423" xml:space="preserve">Nam cum @ vmbra <lb/>gnomonis in aliquem horum parallelorum cadit, tranſibit illa die Sol per verticem omnium locorum, qui
<pb o="175" file="0195" n="195" rhead="LIBER SECVNDVS."/>
ab Aequatore abſunt tot gradibus verſus eandem partem ſiue borealem, ſiue auſtralem, (prout paral-<lb/>lelus ille comprehenſus fuerit in horologio inter boreales, auſtralesve parallelos) quot comprehendun-<lb/>tur in declinatione illius paralleli. </s>
  <s xml:id="echoid-s11424" xml:space="preserve">Vt ſi v. </s>
  <s xml:id="echoid-s11425" xml:space="preserve">g. </s>
  <s xml:id="echoid-s11426" xml:space="preserve">vmbra ſtyli cadat in parallelum, cuius declinatio comple <lb/>ctatur grad. </s>
  <s xml:id="echoid-s11427" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11428" xml:space="preserve">incedet Sol per verticem cuiuſcunque ciuitatis, cuius latitudo grad. </s>
  <s xml:id="echoid-s11429" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11430" xml:space="preserve">extiterit ſiue <lb/>verſus boream, ſiue verſus auſtrum, prout ille parallelus in boream quoque, vel auſtrum declinat in ho-<lb/>rologio. </s>
  <s xml:id="echoid-s11431" xml:space="preserve">Ita quoque vmbra ſtyli percurrente parallelum ♋, cuius declinatio eſt borealis, &amp; </s>
  <s xml:id="echoid-s11432" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s11433" xml:space="preserve">23. <lb/></s>
  <s xml:id="echoid-s11434" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11435" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11436" xml:space="preserve">perueniet Sol in meridie ad Zenith, verticemve vrbis Aegypti Syenes, propterea quòd eius la-<lb/>titudo borealis quoque eſt, atque gradus complectitur 23. </s>
  <s xml:id="echoid-s11437" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11438" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11439" xml:space="preserve">Et ſic de reliquis.</s>
  <s xml:id="echoid-s11440" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div616" type="section" level="1" n="157">
<head xml:id="echoid-head160" xml:space="preserve">PROBLEMA 8. PROPOSITIO 8.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s11441" xml:space="preserve">DOMOS cœleſtes, hoc eſt, communes ſectiones plani horolo-<lb/>gij, &amp; </s>
  <s xml:id="echoid-s11442" xml:space="preserve">circulorum poſitionum, qui per initia, vel quaſcunque partes <lb/>domorum cœleſtium ducuntur, in eodem horologio horizontali de-<lb/>ſcribere.</s>
  <s xml:id="echoid-s11443" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s11444" xml:space="preserve">SECVNDVM doctrinam Ioan. </s>
  <s xml:id="echoid-s11445" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11446" xml:space="preserve">qui docet, circulos domorum cœleſtium (qui <lb/>
<anchor type="note" xlink:label="note-0195-02a" xlink:href="note-0195-02"/>
quidem ſunt ex numero circulorum, quos poſitionum dicunt.) </s>
  <s xml:id="echoid-s11447" xml:space="preserve">Aequatorem ſecare in 12. </s>
  <s xml:id="echoid-s11448" xml:space="preserve">partes <lb/>
<anchor type="note" xlink:label="note-0195-03a" xlink:href="note-0195-03"/>
æquales, tranſireq́; </s>
  <s xml:id="echoid-s11449" xml:space="preserve">per communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s11450" xml:space="preserve">Meridiani, ita domos cœleſtes in ho-<lb/>rologio horizontali deſcribemus. </s>
  <s xml:id="echoid-s11451" xml:space="preserve">Circulus iam ſæpius ex E, deſcriptus in partes 360. </s>
  <s xml:id="echoid-s11452" xml:space="preserve">æquales di-<lb/>uidatur, initio facto à linea meridiana. </s>
  <s xml:id="echoid-s11453" xml:space="preserve">Nos illum diuiſimus in partes 12. </s>
  <s xml:id="echoid-s11454" xml:space="preserve">vt quælibet conſtet gra-<lb/>dibus 30. </s>
  <s xml:id="echoid-s11455" xml:space="preserve">vnamq́; </s>
  <s xml:id="echoid-s11456" xml:space="preserve">domum conſtituat. </s>
  <s xml:id="echoid-s11457" xml:space="preserve">Per centrum deinde, &amp; </s>
  <s xml:id="echoid-s11458" xml:space="preserve">puncta diuiſionum rectæ ducan-<lb/>tur ſecantes lineam æquinoctialem in punctis, per quæ ſi rectæ agantur ipſi lineæ meridianæ æqui <lb/>diſtantes; </s>
  <s xml:id="echoid-s11459" xml:space="preserve">(quod quidem facile fiet, ſi ducatur recta C D, lineæ æquinoctiali parallela ſecans meri-<lb/>
<anchor type="figure" xlink:label="fig-0195-01a" xlink:href="fig-0195-01"/>
<anchor type="note" xlink:label="note-0195-04a" xlink:href="note-0195-04"/>
<anchor type="note" xlink:label="note-0195-05a" xlink:href="note-0195-05"/>
dianam lineam in B; </s>
  <s xml:id="echoid-s11460" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11461" xml:space="preserve">omnia puncta lineæ æquinoctialis beneficio circini ex I, accepta trans-<lb/>ferantur in lineam C D, ex puncto B. </s>
  <s xml:id="echoid-s11462" xml:space="preserve">Nam hac ratione rectę connectentes bina puncta æqualite<unsure/>r <lb/>ab I, &amp; </s>
  <s xml:id="echoid-s11463" xml:space="preserve">B, remota, parallelæ erunt) deſcriptæ erunt domus cœleſtes, ſecundum Ioan. </s>
  <s xml:id="echoid-s11464" xml:space="preserve">Regiom. <lb/></s>
  <s xml:id="echoid-s11465" xml:space="preserve">
<anchor type="note" xlink:label="note-0195-06a" xlink:href="note-0195-06"/>
<anchor type="note" xlink:label="note-0195-07a" xlink:href="note-0195-07"/>
Quod ita oſtendi poteſt.</s>
  <s xml:id="echoid-s11466" xml:space="preserve"/>
</p>
<div xml:id="echoid-div616" type="float" level="2" n="1">
<note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium in eodem <lb/>horologio hori <lb/>zontali, ſecun-<lb/>dum Ioan, Re-<lb/>giom.</note>
<note position="left" xlink:label="note-0195-03" xlink:href="note-0195-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a">
    <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0195-01"/>
  </figure>
<note position="left" xlink:label="note-0195-04" xlink:href="note-0195-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0195-05" xlink:href="note-0195-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0195-06" xlink:href="note-0195-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0195-07" xlink:href="note-0195-07a" xml:space="preserve">33. primi.</note>
</div>
<p>
  <s xml:id="echoid-s11467" xml:space="preserve">QVONIAM iuxta Ioan. </s>
  <s xml:id="echoid-s11468" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11469" xml:space="preserve">circuli domorum cœleſtium tranſeunt per communes <lb/>
<anchor type="note" xlink:label="note-0195-08a" xlink:href="note-0195-08"/>
ſectiones Meridiani, atque Horizontis, diuiduntq́ Æquatorem in partes æquales, initio facto à Me <lb/>ridiano circulo, qui initium eſt domus decimæ cœleſtis, quam domus vndecima, &amp; </s>
  <s xml:id="echoid-s11470" xml:space="preserve">duodecima ſe-<lb/>quuntur verſus ortum; </s>
  <s xml:id="echoid-s11471" xml:space="preserve">prima autem incipit ab ipſo Horizonte ex parte orientis, latetq́; </s>
  <s xml:id="echoid-s11472" xml:space="preserve">tota ſub <lb/>Horizonte, &amp; </s>
  <s xml:id="echoid-s11473" xml:space="preserve">reliquæ deinceps eodem ordine ſub Horizonte ponuntur vſque ad initium ſeptimæ <lb/>domus, tribuendo ſingulis domibus grad. </s>
  <s xml:id="echoid-s11474" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11475" xml:space="preserve">fit, vt rectæ per puncta diuiſionum &amp; </s>
  <s xml:id="echoid-s11476" xml:space="preserve">centrum cir-<lb/>culi ex E, deſcripti, ſint communes ſectiones Æquatoris, &amp; </s>
  <s xml:id="echoid-s11477" xml:space="preserve">circulorum domorũ cœleſtium. </s>
  <s xml:id="echoid-s11478" xml:space="preserve">Nam <lb/>ſi dictus circulus ex E, deſcriptus circa æquinoctialem lineam circumuolui intelligatur, donec in <lb/>plano Æquinoctialis circuli poſitus ſit, atque adeò eius centrum in centro mundi, ducentur dicti <lb/>circuli domorum cœleſtium per illa diuiſionum puncta, &amp; </s>
  <s xml:id="echoid-s11479" xml:space="preserve">centrum mundi E. </s>
  <s xml:id="echoid-s11480" xml:space="preserve">Quare circuli do-
<pb o="176" file="0196" n="196" rhead="GNOMONICES"/>
morum cœleſtium occurrent lineæ æquinoctiali horologij in punctis, in quibus prædictæ rectæ <lb/>eandem ſecant; </s>
  <s xml:id="echoid-s11481" xml:space="preserve">atque adeo per hæc eadem puncta æquinoctialis lineæ tranſibunt communes ſe-<lb/>ctiones dictorum circulorum, &amp; </s>
  <s xml:id="echoid-s11482" xml:space="preserve">plani horologii, Cum ergo, per propoſ. </s>
  <s xml:id="echoid-s11483" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11484" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11485" xml:space="preserve">com-<lb/>munes hæ ſectiones parallelæ ſint inter ſe, immo &amp; </s>
  <s xml:id="echoid-s11486" xml:space="preserve">communi omnium circulorum domorũ cœ-<lb/>leſtium ſectioni æquidiſtent, vt ex demonſtratione dictę propoſ. </s>
  <s xml:id="echoid-s11487" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11488" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11489" xml:space="preserve">perſpicuum eſt; <lb/></s>
  <s xml:id="echoid-s11490" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0196-01a" xlink:href="fig-0196-01"/>
<anchor type="note" xlink:label="note-0196-01a" xlink:href="note-0196-01"/>
<anchor type="note" xlink:label="note-0196-02a" xlink:href="note-0196-02"/>
(propterea quòd planum horologij communi ſectioni dictorum circulorum æquidiſtat) ſit autẽ <lb/>
<anchor type="note" xlink:label="note-0196-03a" xlink:href="note-0196-03"/>
&amp; </s>
  <s xml:id="echoid-s11491" xml:space="preserve">linea meridiana communi illi ſectioni circulorum domorum cœleſtium parallela, quòd linea <lb/>meridiana, &amp; </s>
  <s xml:id="echoid-s11492" xml:space="preserve">illa ſectio ſint ſectiones planorum parallelorum, nempe Horizontis, &amp; </s>
  <s xml:id="echoid-s11493" xml:space="preserve">plani horolo-<lb/>
<anchor type="note" xlink:label="note-0196-04a" xlink:href="note-0196-04"/>
<anchor type="note" xlink:label="note-0196-05a" xlink:href="note-0196-05"/>
gii, factæ à Meridiano; </s>
  <s xml:id="echoid-s11494" xml:space="preserve">erunt quoque communes ſectiones circulorum domorum cœleſtium, &amp; </s>
  <s xml:id="echoid-s11495" xml:space="preserve"><lb/>plani horologii ipſi lineæ meridianæ æquidiſtantes. </s>
  <s xml:id="echoid-s11496" xml:space="preserve">Quocirca rectæ illæ, quæ per puncta æquino-<lb/>ctialis lineæ ſunt ductæ æquidiſtantes ipſi lineæ meridianæ, communes ſectiones erunt circulorũ <lb/>domorum cœleſtium, &amp; </s>
  <s xml:id="echoid-s11497" xml:space="preserve">plani horologij, in quas videlicet vmbra ſtyli, ex coroll. </s>
  <s xml:id="echoid-s11498" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s11499" xml:space="preserve">12. </s>
  <s xml:id="echoid-s11500" xml:space="preserve">ſupe-<lb/>rioris lib. </s>
  <s xml:id="echoid-s11501" xml:space="preserve">cadit, Sole exiſtente in prædictis domorum cœleſtium circulis.</s>
  <s xml:id="echoid-s11502" xml:space="preserve"/>
</p>
<div xml:id="echoid-div617" type="float" level="2" n="2">
<note position="right" xlink:label="note-0195-08" xlink:href="note-0195-08a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis d@ <lb/>morum cœle-<unsure/> <lb/>ſtium ſecundũ <lb/>Ioan. Regio@.</note>
  <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a">
    <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0196-01"/>
  </figure>
<note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0196-05" xlink:href="note-0196-05a" xml:space="preserve">9. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s11503" xml:space="preserve">AT ſecundum Campani ſententiam, qui præcipit, domorum cœleſtium circulos ita duci de-<lb/>
<anchor type="note" xlink:label="note-0196-06a" xlink:href="note-0196-06"/>
bere per communes ſectiones Meridiani, &amp; </s>
  <s xml:id="echoid-s11504" xml:space="preserve">Horizontis, vt Verticalem circulum, non autẽ Aequa-<lb/>torem, (vt vult Ioan. </s>
  <s xml:id="echoid-s11505" xml:space="preserve">Regiom.) </s>
  <s xml:id="echoid-s11506" xml:space="preserve">in partes 12. </s>
  <s xml:id="echoid-s11507" xml:space="preserve">ęquales partiantur, hac ratione domos cœleſtes deli-<lb/>neabimus. </s>
  <s xml:id="echoid-s11508" xml:space="preserve">In linea meridiana ſumatur à G, loco ſtyli ſiue ſurſum, ſiue deorſuin verſus recta æqua <lb/>lis ſtylo vſque ad punctum C, è quo circulus cuiuſuis magnitudinis deſcriptus ſecetur in 12. </s>
  <s xml:id="echoid-s11509" xml:space="preserve">par-<lb/>
<anchor type="note" xlink:label="note-0196-07a" xlink:href="note-0196-07"/>
tes æquales, pro duodecim domibus cœleſtibus, initio facto à linea meridiana. </s>
  <s xml:id="echoid-s11510" xml:space="preserve">Deinde per centrũ <lb/>C, &amp; </s>
  <s xml:id="echoid-s11511" xml:space="preserve">puncta diuiſionum rectæ ducantur ſecantes rectam A B, (quæ in hunc tantum finem per lo-<lb/>cum ſtvli ducaturad lineam meridianam perpendicularis, vel, quod idem eſt, æquinoctiali lineæ <lb/>parallela, vt ſecari poſſit à dictis rectis) in punctis, per quæ, ſi rectæ ducantur æquidiſtantes lineæ <lb/>ipſi meridianæ, deſcripti erunt circuli domorum cœleſtium ex doctrina Campani. </s>
  <s xml:id="echoid-s11512" xml:space="preserve">Cuius rei hanc <lb/>accipe demonſtrationem.</s>
  <s xml:id="echoid-s11513" xml:space="preserve"/>
</p>
<div xml:id="echoid-div618" type="float" level="2" n="3">
<note position="left" xlink:label="note-0196-06" xlink:href="note-0196-06a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium in eodem <lb/>horizontali ho <lb/>rologio, ſecun-<lb/>dũ Campanũ.</note>
<note position="left" xlink:label="note-0196-07" xlink:href="note-0196-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s11514" xml:space="preserve">SI dictus circulus ex C, deſcriptus, circa rectam A B, intelligatur moueri, donec in plano Ver-<lb/>
<anchor type="note" xlink:label="note-0196-08a" xlink:href="note-0196-08"/>
ticalis circuli iaceat, nempe rectus ſit ad planum horologij, atque eius centrum idem ſit, quod <lb/>mundi, ſeu vertex gnomonis; </s>
  <s xml:id="echoid-s11515" xml:space="preserve">erunt rectæ per centrum C, &amp; </s>
  <s xml:id="echoid-s11516" xml:space="preserve">diuiſionum puncta eductæ, commu-<lb/>nes ſectiones circulorum cœleſtium domorum, ac Verticalis circuli, atque idcirco cuiuſcunque al-<lb/>
<anchor type="note" xlink:label="note-0196-09a" xlink:href="note-0196-09"/>
terius, qui in eius plano ex centro mundi deſcribitur, qualis eſt dictus circulus ex C, deſcriptus; <lb/></s>
  <s xml:id="echoid-s11517" xml:space="preserve">propterea quòd hic, &amp; </s>
  <s xml:id="echoid-s11518" xml:space="preserve">Verticalis proprie dictus à rectis ex centro C, exeuntibus ſecantur in partes <lb/>ſimiles, vt ad finem cap. </s>
  <s xml:id="echoid-s11519" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11520" xml:space="preserve">ſphæræ demonſtrauimus. </s>
  <s xml:id="echoid-s11521" xml:space="preserve">Quamobrem circuli domorum cœleſtium <lb/>occurrent lineæ A B, in punctis, in quibus prædictæ rectæ eandem ſecant: </s>
  <s xml:id="echoid-s11522" xml:space="preserve">ac proinde per hæc ea-<lb/>dem puncta lineæ A B, incedent communes ſectiones dictorum circulorum, &amp; </s>
  <s xml:id="echoid-s11523" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s11524" xml:space="preserve"><lb/>Cum ergo hæ ſectiones parallelæ ſint &amp; </s>
  <s xml:id="echoid-s11525" xml:space="preserve">inter ſe, &amp; </s>
  <s xml:id="echoid-s11526" xml:space="preserve">communi eorundem circulorum ſectioni, atq; </s>
  <s xml:id="echoid-s11527" xml:space="preserve"><lb/>adeo &amp; </s>
  <s xml:id="echoid-s11528" xml:space="preserve">lineæ ipſi meridianæ, vt in ſuperiori deſcriptione oſtenſum eſt; </s>
  <s xml:id="echoid-s11529" xml:space="preserve">erunt rectæ illæ, quæ per <lb/>dicta puncta lineæ AB, ſunt ductæ æquidiſtantes lineæ meridianæ, communes ſectiones circulo-<lb/>rum cœleſtium domorum, &amp; </s>
  <s xml:id="echoid-s11530" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s11531" xml:space="preserve">Igitur domos cœleſtes, hoc eſt, communes ſectio-<lb/>nes, &amp;</s>
  <s xml:id="echoid-s11532" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11533" xml:space="preserve">in eodem horologio horizontali deſcripſimus. </s>
  <s xml:id="echoid-s11534" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s11535" xml:space="preserve"/>
</p>
<div xml:id="echoid-div619" type="float" level="2" n="4">
<note position="left" xlink:label="note-0196-08" xlink:href="note-0196-08a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domorum cœle <lb/>ſtium ſecundũ <lb/>Campanum.</note>
<note position="left" xlink:label="note-0196-09" xlink:href="note-0196-09a" xml:space="preserve">50</note>
</div>
<pb o="177" file="0197" n="197" rhead="LIBER SECVNDVS."/>
</div>
<div xml:id="echoid-div621" type="section" level="1" n="158">
<head xml:id="echoid-head161" xml:space="preserve">COROLLARIVM.</head>
<p>
  <s xml:id="echoid-s11536" xml:space="preserve">PERSPICVVM autem eſt, initia domorum cœleſtium ſecundum Ioan. </s>
  <s xml:id="echoid-s11537" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11538" xml:space="preserve">tranſire per ea <lb/>
<anchor type="note" xlink:label="note-0197-01a" xlink:href="note-0197-01"/>
puncta lineę ęquinoctia lis in horologio, per quæ lineæ horarię à meridiana linea duabus, &amp; </s>
  <s xml:id="echoid-s11539" xml:space="preserve">quatuor hc-<lb/>ris diſtantes ducuntur, cuiuſmodi ſunt hora ſecunda, &amp; </s>
  <s xml:id="echoid-s11540" xml:space="preserve">quarta poſt meridiem tranſeuntes per puncta <lb/>F, k; </s>
  <s xml:id="echoid-s11541" xml:space="preserve">Item 8. </s>
  <s xml:id="echoid-s11542" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11543" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11544" xml:space="preserve">poſt mediam noctem, tranſeuntes per M, L, quia huiuſmodi horæ in Æquatore diſtant <lb/>à Meridiano circalo grad. </s>
  <s xml:id="echoid-s11545" xml:space="preserve">30. </s>
  <s xml:id="echoid-s11546" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11547" xml:space="preserve">60. </s>
  <s xml:id="echoid-s11548" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s11549" xml:space="preserve">domorum cœleſtium initia. </s>
  <s xml:id="echoid-s11550" xml:space="preserve">Vnde ſi per dictas ho <lb/>ras in ęquinoctiali linea ducantur lineæ parallelæ ipſi lineæ meridianæ, dabunt hæ initia domorum cœ-<lb/>leſtium, ex doctrina Ioan. </s>
  <s xml:id="echoid-s11551" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11552" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s11553" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11554" xml:space="preserve">Quod quidem non ſolum in horizontali horologio, ſed etiam <lb/>in omnibus aliis intelligendum eſt.</s>
  <s xml:id="echoid-s11555" xml:space="preserve"/>
</p>
<div xml:id="echoid-div621" type="float" level="2" n="1">
<note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">Per quas horas <lb/>in æquinoctiali <lb/>linea tranſeant <lb/>domus cœleſtes <lb/>ſecundum 10. <lb/>Regiom.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div623" type="section" level="1" n="159">
<head xml:id="echoid-head162" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s11556" xml:space="preserve">CÆTERVM lineæ domorum cæleſtiumnon eodem modo cæleſtes domos indicant, quo horariæ <lb/>
<anchor type="note" xlink:label="note-0197-03a" xlink:href="note-0197-03"/>
lineæ horas. </s>
  <s xml:id="echoid-s11557" xml:space="preserve">Hæ enim terminos hor arum ſignificant, adeo vt vmbr a gnomonis in lineam aliquam hora-<lb/>riam cadens moneat nos, horam illam, cui linea horaria debetur, tranſactam eſſe, &amp; </s>
  <s xml:id="echoid-s11558" xml:space="preserve">aliam, quæ ſequitur, <lb/>incipere: </s>
  <s xml:id="echoid-s11559" xml:space="preserve">Illæ vero demonſtrant nobis initia domorum, non autem fines, adeo vt vmbra ſtyli in aliquam <lb/>dictarum linearum cadens monſtret, Solem in illo circulo poſitionis exiſtere, qui principium eſt illius do-<lb/>mus cœleſtis, quam numerus aſcriptus ſignificat. </s>
  <s xml:id="echoid-s11560" xml:space="preserve">Cauſa huius rei eſt, quòd Sol prius exiſtit in fine cuiusli-<lb/>bet domus, quàm in principio. </s>
  <s xml:id="echoid-s11561" xml:space="preserve">Domus enim cœleſtes numer antur ab occaſu in ortum; </s>
  <s xml:id="echoid-s11562" xml:space="preserve">Sol autem ab ortu <lb/>in occaſum fertur motu primi mobilis. </s>
  <s xml:id="echoid-s11563" xml:space="preserve">Vnde Sol prius exiſtit in fine cuiuſque domus, poſtea in medio, ac <lb/>
<anchor type="note" xlink:label="note-0197-04a" xlink:href="note-0197-04"/>
poſtremo in principio eiuſdem. </s>
  <s xml:id="echoid-s11564" xml:space="preserve">In horis autem alia ratio eſt, quia circuli horarum computantur etiam ab <lb/>ortu in occaſum. </s>
  <s xml:id="echoid-s11565" xml:space="preserve">Itaque quemadmodum vmbra ſtyli cadens in aliquam lineam horariam docet, illam ho-<lb/>ram eſſe tranſactam, Solem{q́ue} motum fuiſſe ab initio illi{us} horę vſque ad finem, ita eadem vmbra aliquã <lb/>domum cœlestem attingens oſtendit, Solem per totam illam domum iam delatum eſſe, à fine nimirum il-<lb/>lius vſque ad principium. </s>
  <s xml:id="echoid-s11566" xml:space="preserve">In exemplo, quoniam neque principium domus 7. </s>
  <s xml:id="echoid-s11567" xml:space="preserve">neque finis 12. </s>
  <s xml:id="echoid-s11568" xml:space="preserve">deſcribi poteſt <lb/>in horizontali horologio, delineauimus earum partes tertias, hoc eſt, lineas duximus tranſeuntes per <lb/>grad. </s>
  <s xml:id="echoid-s11569" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11570" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11571" xml:space="preserve">20. </s>
  <s xml:id="echoid-s11572" xml:space="preserve">ipſarum.</s>
  <s xml:id="echoid-s11573" xml:space="preserve"/>
</p>
<div xml:id="echoid-div623" type="float" level="2" n="1">
<note position="right" xlink:label="note-0197-03" xlink:href="note-0197-03a" xml:space="preserve">Lineæ domor@@ <lb/>cœleſtium indi <lb/>cant initia do-<lb/>morum cœle-<lb/>ſtium, horariæ <lb/>autem lineæ ter <lb/>minos, ſeu fines <lb/>horarum ſigni-<lb/>ficant.</note>
<note position="left" xlink:label="note-0197-04" xlink:href="note-0197-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s11574" xml:space="preserve">MVNVS autem domorum cœleſtium in horologio eſt, vt ex vmbra gnomonis comprehendamus, <lb/>
<anchor type="note" xlink:label="note-0197-05a" xlink:href="note-0197-05"/>
quanam in domo cœleſti Sol commoretur. </s>
  <s xml:id="echoid-s11575" xml:space="preserve">Quando enim, exempli gratia, vmbra ſtyli in lineam cadit, cui <lb/>aſcripta eſt domus nona, certum nobis erit, Solem tunc exiſtere in principio domus nonæ, &amp; </s>
  <s xml:id="echoid-s11576" xml:space="preserve">in fine octa-<lb/>
<anchor type="note" xlink:label="note-0197-06a" xlink:href="note-0197-06"/>
uæ<unsure/>; </s>
  <s xml:id="echoid-s11577" xml:space="preserve">adeò vt toto illo tempore, quo vmbra ſtyli ſpatium inter lineam domus nonæ, &amp; </s>
  <s xml:id="echoid-s11578" xml:space="preserve">lineam domus deci-<lb/>mæ<unsure/> interiectum percucurrit ab occaſu in ortum, Sol in domo nona ſit moratus, à cuius termino ad eiuſdem <lb/>principium motus eſt. </s>
  <s xml:id="echoid-s11579" xml:space="preserve">Et ita de cæteris.</s>
  <s xml:id="echoid-s11580" xml:space="preserve"/>
</p>
<div xml:id="echoid-div624" type="float" level="2" n="2">
<note position="right" xlink:label="note-0197-05" xlink:href="note-0197-05a" xml:space="preserve">Ex lineis, cœle-<lb/>ſtium domorũ <lb/>in hotologio de <lb/>ſcriptis percipi-<lb/>mus, quanam <lb/>in domo verſe-<lb/>tur Sol.</note>
<note position="left" xlink:label="note-0197-06" xlink:href="note-0197-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s11581" xml:space="preserve">SOLVM autem domos cœleſtes deſcripſimus ſecundum Ioan. </s>
  <s xml:id="echoid-s11582" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11583" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11584" xml:space="preserve">Campanum, non autem <lb/>ſecundum alios, quoniam frequentior apud Aſtronomos vſus reperitur domorum cœleſtium, prout ab his <lb/>auctoribus in cœlo conſtituuntur.</s>
  <s xml:id="echoid-s11585" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div626" type="section" level="1" n="160">
<head xml:id="echoid-head163" xml:space="preserve">PROBLEMA. 9. PROPOSITIO 9.</head>
<p>
  <s xml:id="echoid-s11586" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem Horizontali horolo-<lb/>
<anchor type="note" xlink:label="note-0197-07a" xlink:href="note-0197-07"/>
gio deſcribere.</s>
  <s xml:id="echoid-s11587" xml:space="preserve"/>
</p>
<div xml:id="echoid-div626" type="float" level="2" n="1">
<note position="left" xlink:label="note-0197-07" xlink:href="note-0197-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s11588" xml:space="preserve">SOLE exiſtente in principio ♈, quæratur, quota hora ante, vel poſt meridiem initia duode-<lb/>
<anchor type="note" xlink:label="note-0197-08a" xlink:href="note-0197-08"/>
cim ſignorum oriantur; </s>
  <s xml:id="echoid-s11589" xml:space="preserve">ad propoſitam latitudinem loci, initio facto à principio ♈. </s>
  <s xml:id="echoid-s11590" xml:space="preserve">Eodem verò <lb/>exiſtente in principio ♎, inueſtigetur idem de initijs duodecim ſignorum, incipiendo à princi-<lb/>pio ♎. </s>
  <s xml:id="echoid-s11591" xml:space="preserve">Rurſus eodem commorante in principio ♋, exploretur idem deinitijs eorundem 12. <lb/></s>
  <s xml:id="echoid-s11592" xml:space="preserve">ſignorum, facto initio à primo puncto ♋. </s>
  <s xml:id="echoid-s11593" xml:space="preserve">Poſtremo eodem manente in principio ♑, inquiratur <lb/>idem de initijs 12. </s>
  <s xml:id="echoid-s11594" xml:space="preserve">ſignorum, principio facto à primo puncto ♑. </s>
  <s xml:id="echoid-s11595" xml:space="preserve">Hæc autem hora facile inuenie-<lb/>
<anchor type="note" xlink:label="note-0197-09a" xlink:href="note-0197-09"/>
tur ex aſcenſione obliqua illius arcus Eclipticæ, qui inter principium ♈, vel ♎, vel ♋, vel ♑, &amp; </s>
  <s xml:id="echoid-s11596" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0197-10a" xlink:href="note-0197-10"/>
ſignum aſcendens propoſitum intercipitur. </s>
  <s xml:id="echoid-s11597" xml:space="preserve">Si enim aſcenſio huiuſmodi obliqua ad horas redi-<lb/>gatur, &amp; </s>
  <s xml:id="echoid-s11598" xml:space="preserve">horæ (ſi aſcenſio obliqua minor eſt arcu ſemidiurno) ab arcu ſemidiurno detrahantur, <lb/>relinquentur horæ, quæ ſuperſunt ad meridiem vſque, cum ſignum illud, cuius obliqua aſcenſio <lb/>ſumpta eſt, oriri incipit ſupra Horizontem; </s>
  <s xml:id="echoid-s11599" xml:space="preserve">Vel ſi è contrario à dictis horis (ſi nimirum aſcenſio <lb/>obliqua arcum ſemidiurnũ ſuperat) arcus ſemidiurnus ſubtrahatur, reliquæ erũt horæ poſt meri-<lb/>diem elapſæ, cum initiũ illius ſigni, cuius aſcenſio obliqua aſſumpta eſt, exoritur. </s>
  <s xml:id="echoid-s11600" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s11601" xml:space="preserve">Sole <lb/>
<anchor type="note" xlink:label="note-0197-11a" xlink:href="note-0197-11"/>
exiſtente in principio ♈, arcus ſemidiurnus continet horas 6. </s>
  <s xml:id="echoid-s11602" xml:space="preserve">quæriturq́; </s>
  <s xml:id="echoid-s11603" xml:space="preserve">quota ſit hora, cũ princi <lb/>pium ♋, aſcendit ſupra Horizontem Romanum, ad eleuationem nimirum grad. </s>
  <s xml:id="echoid-s11604" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11605" xml:space="preserve">Arcus inter <lb/>principium ♈, &amp; </s>
  <s xml:id="echoid-s11606" xml:space="preserve">primum gradum ♋, habet aſcenſionem obliquam, (vt conſtat ex tabulis aſcen <lb/>ſionum obliquarum in tabulis directionum Ioan. </s>
  <s xml:id="echoid-s11607" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s11608" xml:space="preserve">vel in commentariis noſtris in ſphæ-<lb/>ram contentis. </s>
  <s xml:id="echoid-s11609" xml:space="preserve">Quas tamen aſcenſiones ad finem ſcholii huius propoſ. </s>
  <s xml:id="echoid-s11610" xml:space="preserve">inuenire quoque docebi-
<pb o="178" file="0198" n="198" rhead="GNOMONICES"/>
mus ex doctrina ſinuum) grad. </s>
  <s xml:id="echoid-s11611" xml:space="preserve">66, min, 57. </s>
  <s xml:id="echoid-s11612" xml:space="preserve">quæ ad horas reducta continet horas 4. </s>
  <s xml:id="echoid-s11613" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11614" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11615" xml:space="preserve">Hæ <lb/>autem ſubtractæ ex horis 6. </s>
  <s xml:id="echoid-s11616" xml:space="preserve">hoc eſt, ex arcu ſemidiurno, relinquunt hor. </s>
  <s xml:id="echoid-s11617" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11618" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11619" xml:space="preserve">32. </s>
  <s xml:id="echoid-s11620" xml:space="preserve">ante meridiẽ. <lb/></s>
  <s xml:id="echoid-s11621" xml:space="preserve">Hac ergo hora principium ♋, aſcendit ſupra Horizontem, Sole in principio ♈, exiſtente; </s>
  <s xml:id="echoid-s11622" xml:space="preserve">quæ <lb/>quidem reſpondet horis 10. </s>
  <s xml:id="echoid-s11623" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11624" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11625" xml:space="preserve">poſt mediam noctem. </s>
  <s xml:id="echoid-s11626" xml:space="preserve">Rurſus Sole poſſidente principium <lb/>♋, arcus ſemidiurnus ad eleuationem grad. </s>
  <s xml:id="echoid-s11627" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11628" xml:space="preserve">complectitur horas 7. </s>
  <s xml:id="echoid-s11629" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11630" xml:space="preserve">32. </s>
  <s xml:id="echoid-s11631" xml:space="preserve">quæriturq́;</s>
  <s xml:id="echoid-s11632" xml:space="preserve">, qua <lb/>hora principium ♐, ſupra Horizontem aſcendat. </s>
  <s xml:id="echoid-s11633" xml:space="preserve">Aſcenſio obliqua arcus inter principium ♋, <lb/>&amp; </s>
  <s xml:id="echoid-s11634" xml:space="preserve">primum gradum ♐, interiecti continet grad. </s>
  <s xml:id="echoid-s11635" xml:space="preserve">190. </s>
  <s xml:id="echoid-s11636" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11637" xml:space="preserve">12. </s>
  <s xml:id="echoid-s11638" xml:space="preserve">quæ in horas conuerſa facit horas <lb/>12, min. </s>
  <s xml:id="echoid-s11639" xml:space="preserve">41. </s>
  <s xml:id="echoid-s11640" xml:space="preserve">a quibus ſi auferatur arcus ſemidiurnus horarum 7. </s>
  <s xml:id="echoid-s11641" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11642" xml:space="preserve">32. </s>
  <s xml:id="echoid-s11643" xml:space="preserve">relinquitur hora quinta <lb/>min. </s>
  <s xml:id="echoid-s11644" xml:space="preserve">9. </s>
  <s xml:id="echoid-s11645" xml:space="preserve">poſt meridiem, qua ſcilicet initium ♐, ſupra Horizontem tunc emergit. </s>
  <s xml:id="echoid-s11646" xml:space="preserve">Et ſic de cæt<unsure/>eris. </s>
  <s xml:id="echoid-s11647" xml:space="preserve"><lb/>Hac ratione ſequentes quatuor tabellas compoſuimus, in quibus horæ continentur, quibus ſigno-<lb/>
<anchor type="note" xlink:label="note-0198-01a" xlink:href="note-0198-01"/>
rum initia oriuntur in Horizonte Romano grad. </s>
  <s xml:id="echoid-s11648" xml:space="preserve">42.</s>
  <s xml:id="echoid-s11649" xml:space="preserve"/>
</p>
<div xml:id="echoid-div627" type="float" level="2" n="2">
<note position="right" xlink:label="note-0197-08" xlink:href="note-0197-08a" xml:space="preserve">Quid inquiren <lb/>dum, priuſquã <lb/>figna aſcenden <lb/>tia deſcriban-<lb/>tur.</note>
<note position="right" xlink:label="note-0197-09" xlink:href="note-0197-09a" xml:space="preserve">Qua ratione he <lb/>ra inueſtiganda <lb/>ſit, qua quodli-<lb/>bet ſi gnum Zo <lb/>diaci ſupra Ho-<lb/>rizontem inci-<lb/>pit aſcendere.</note>
<note position="left" xlink:label="note-0197-10" xlink:href="note-0197-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0197-11" xlink:href="note-0197-11a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0198-01" xlink:href="note-0198-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div629" type="section" level="1" n="161">
<head xml:id="echoid-head164" xml:space="preserve">I. Sole exiſtente in principio ♈.</head>
<note position="right" xml:space="preserve"> <lb/>
♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓
Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer.
H. M # H. M. # H. M. # H. M # H. M # H. M. # H. M. # H. M. # H. M. # H. M. # H. M # H. M.
6. 0 # 4. 51. # 5. 26. # 1. 32. # 0. 51. # 3. 26. # 6. 0. # 8. 34. # 11. 9. # 10. 28. # 8. 34. # 7. 9.
</note>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div630" type="section" level="1" n="162">
<head xml:id="echoid-head165" xml:space="preserve">II. Sole exiſtente in principio ♎.</head>
<note position="right" xml:space="preserve"> <lb/>
♎ # ♏ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍
Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Ante \\ mer. # Ante \\ mer.
H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M.
6. 0. # 3. 6. # 0. 51. # 1. 32. # 3. 26. # 4. 51. # 6. 0. # 7. 9. # 8. 34. # 10. 8. # 11. 9. # 8. 14.
</note>
</div>
<div xml:id="echoid-div631" type="section" level="1" n="163">
<head xml:id="echoid-head166" xml:space="preserve">III. Sole exiſtente in principio ♋.</head>
<note position="right" xml:space="preserve"> <lb/>
♋ # ♌ # ♍ # ♎ # ♉ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊
Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Añ vel \\ poſt m. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer.
H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M.
7. 32. # 5. 9. # 2. 34. # 0. 0. # 2. 34. # 5. 9. # 7. 32. # 9. 26. # 10. 51. # 12. 0. # 10. 50. # 8. 26.
</note>
</div>
<div xml:id="echoid-div632" type="section" level="1" n="164">
<head xml:id="echoid-head167" xml:space="preserve">IIII. Sole exiſtente in principio ♑.</head>
<note position="right" xml:space="preserve"> <lb/>
♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐
Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Añ vel \\ poſt m. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer.
H. M. # H. M. # H. M. # H. M. # H. M # H. M. # H. M. # H. M. # H. M. # H. M. # H. M # H. M.
4. 28. # 2. 34. # 1. 10. # 0. 0. # 1. 10. # 2. 34. # 4. 28. # 6. 51. # 9. 26. # 12. 0. # 9. 26. # 6. 51.
</note>
<p>
  <s xml:id="echoid-s11650" xml:space="preserve">EX his tabulis ita aſcendentia ſigna deſcribemus, hoc eſt, communes ſectiones plani horolo-<lb/>
<anchor type="note" xlink:label="note-0198-09a" xlink:href="note-0198-09"/>
gij, &amp; </s>
  <s xml:id="echoid-s11651" xml:space="preserve">Eclipticæ eo tempore, quo initia ſignorum ſupra Horizontem aſcendunt. </s>
  <s xml:id="echoid-s11652" xml:space="preserve">In has enim <lb/>communes ſectiones, quas planum horologii facit cum Ecliptica, prout varias poſitiones ſortitur <lb/>ad motum diurnum, cadit vmbra gnomonis, per propoſ. </s>
  <s xml:id="echoid-s11653" xml:space="preserve">11. </s>
  <s xml:id="echoid-s11654" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s11655" xml:space="preserve">Sole exiſtẽte in quo-<lb/>
<anchor type="note" xlink:label="note-0198-10a" xlink:href="note-0198-10"/>
cunque puncto Eclipticæ ſupra Horizontem, dum Ecliptica illos ſitus habet, quos communes ſe-<lb/>ctiones prædictæ referunt, hoc eſt, dum ſignorum initia ſupra Horizontem emergunt. </s>
  <s xml:id="echoid-s11656" xml:space="preserve">Suppute-<lb/>tur hora, qua initium ♉, Sole exiſtente in principio ♈, aſcendit, ſumpta ex prima tabella; </s>
  <s xml:id="echoid-s11657" xml:space="preserve">nem-<lb/>pe hor.</s>
  <s xml:id="echoid-s11658" xml:space="preserve">4 Min. </s>
  <s xml:id="echoid-s11659" xml:space="preserve">51. </s>
  <s xml:id="echoid-s11660" xml:space="preserve">ab A, in B, (quia principium ♉, ante meridiem tunc oritur, &amp; </s>
  <s xml:id="echoid-s11661" xml:space="preserve">ſemicirculus Æ-<lb/>quatoris ab A, verſus B, eſt orientalis, vt conſtat, ſi intelligatur circulus ex E, deſcriptus, hoc eſt, <lb/>Æquator, in propria poſitione) &amp; </s>
  <s xml:id="echoid-s11662" xml:space="preserve">ex B, per centrum E, ducatur recta occulta ſecans lineam æqui-<lb/>noctialem in C. </s>
  <s xml:id="echoid-s11663" xml:space="preserve">Nam punctum C, erit illud, in quod ſtyli vmbra cadit prædicta hora, qua princi-<lb/>pium ♉, aſcendit; </s>
  <s xml:id="echoid-s11664" xml:space="preserve">atque adeo per C, tranſibit communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s11665" xml:space="preserve">Eclipticæ eo <lb/>tempore. </s>
  <s xml:id="echoid-s11666" xml:space="preserve">Deinde ex quarta tabella ſumatur hora, qua idem initium ♉, aſcendit, Sole in princi-<lb/>pio ♑, exiſtente, nimirum hor. </s>
  <s xml:id="echoid-s11667" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11668" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11669" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11670" xml:space="preserve">quæ ab A, in D, partem Æquatoris occidentalem, quia <lb/>initium ♉, poſt meridiem tunc oritur, ſupputetur, &amp; </s>
  <s xml:id="echoid-s11671" xml:space="preserve">ex D, per E, recta ducatur ſecans æquino-
<pb o="179" file="0199" n="199" rhead="LIBER SECVNDVS."/>
ctialem lincam in F, per quod ex H, centro horologii recta emittatur ſecans tropicum ♑, in K. <lb/></s>
  <s xml:id="echoid-s11672" xml:space="preserve">Nam ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s11673" xml:space="preserve">prima huius lib. </s>
  <s xml:id="echoid-s11674" xml:space="preserve">punctum K, erit illud, in quod vmbra ſtyli cadit il. </s>
  <s xml:id="echoid-s11675" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0199-01a" xlink:href="fig-0199-01"/>
<anchor type="note" xlink:label="note-0199-01a" xlink:href="note-0199-01"/>
<anchor type="note" xlink:label="note-0199-02a" xlink:href="note-0199-02"/>
la hora, qua principium ♉, aſcendit, Sole exiſtente in principo ♑, atque adeò per K, tráſibit quo-<lb/>que communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s11676" xml:space="preserve">Eclipticæ eo tempore. </s>
  <s xml:id="echoid-s11677" xml:space="preserve">Quare recta per puncta C, &amp; </s>
  <s xml:id="echoid-s11678" xml:space="preserve">K, <lb/>ducta erit communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s11679" xml:space="preserve">Eclipticæ eo tempore, quo principium ♉, ſup ra <lb/>Horizontem aſcendit, &amp; </s>
  <s xml:id="echoid-s11680" xml:space="preserve">in quam tunc vmbra gnomonis cadit, ex propoſ. </s>
  <s xml:id="echoid-s11681" xml:space="preserve">11. </s>
  <s xml:id="echoid-s11682" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11683" xml:space="preserve">Sole <lb/>exiſtente ſupra Horizontem in quocunque puncto Eclipticæ. </s>
  <s xml:id="echoid-s11684" xml:space="preserve">Igitur recta C K, dabit ſignum ♉, <lb/>aſcendens. </s>
  <s xml:id="echoid-s11685" xml:space="preserve">Eodem modo reliqua ſigna aſcendentia deſcribemus, ſumendo ſingula ſigna vnà cum <lb/>
<anchor type="note" xlink:label="note-0199-03a" xlink:href="note-0199-03"/>
horis ex duabus tabellis, (primò quidem ex alterutra priorum duarum tabellarum, ſecundo autem <lb/>ex alterutra duarum poſteriorum) vt duo puncta inueniantur, vnum in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s11686" xml:space="preserve">in al-<lb/>terutro tropico alterum, per quæ communis ſectio Eclipticæ, &amp; </s>
  <s xml:id="echoid-s11687" xml:space="preserve">plani horologij incedat, &amp;</s>
  <s xml:id="echoid-s11688" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11689" xml:space="preserve"/>
</p>
<div xml:id="echoid-div632" type="float" level="2" n="1">
<note position="left" xlink:label="note-0198-09" xlink:href="note-0198-09a" xml:space="preserve">Deſc<unsure/>riptio ſi-<lb/>gnorum aſcen-<lb/>dentium in eo-<lb/>dem horologio <lb/>horizontali.</note>
<note position="left" xlink:label="note-0198-10" xlink:href="note-0198-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0199-01" xlink:href="fig-0199-01a">
    <image file="0199-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0199-01"/>
  </figure>
<note position="left" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0199-02" xlink:href="note-0199-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0199-03" xlink:href="note-0199-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s11690" xml:space="preserve">CÆTERVM, ex neutra duarum priorum tabellarum accipiendæ ſunt in horologio hori-<lb/>zontali horæ illorum ſignorum, quæ ſex horis, vel pluribus ante, vel poſt meridiem oriuntur. </s>
  <s xml:id="echoid-s11691" xml:space="preserve">Illæ <lb/>enim in æquinoctialem lineam non cadunt, vt patet. </s>
  <s xml:id="echoid-s11692" xml:space="preserve">Quare ex vtraque ſunt ſolum aſſumenda in <lb/>horizontali horologio priora quinque ſigna, quæ primum ſequuntur, qualia ſunt ♉, ♊, ♋, ♌, ♍, <lb/>♏, ♐, ♑, ♒, &amp; </s>
  <s xml:id="echoid-s11693" xml:space="preserve">♓. </s>
  <s xml:id="echoid-s11694" xml:space="preserve">Rurſus ex neutra duarum poſteriorum tabellarum ſumendæ ſunt in eodem <lb/>horologio horizontali horæ illorum ſignorum, quæ tot horis poſt, vel ante meridiem oriuntur, <lb/>quot in arcu ſemidiurno ♋, vel ♑, continentur, vel pluribus. </s>
  <s xml:id="echoid-s11695" xml:space="preserve">Nam illę horæ tropicos non ſecant, <lb/>
<anchor type="note" xlink:label="note-0199-04a" xlink:href="note-0199-04"/>
vt conſtat. </s>
  <s xml:id="echoid-s11696" xml:space="preserve">Vnde ex tertia tabella ſumentur tantummodo horæ priorum quinque ſignorum, ſimi <lb/>liter &amp; </s>
  <s xml:id="echoid-s11697" xml:space="preserve">ex quarta, relicto primo ſigno in vtraque tabella: </s>
  <s xml:id="echoid-s11698" xml:space="preserve">cuiuſmodi ſunt hæc ſigna. </s>
  <s xml:id="echoid-s11699" xml:space="preserve">♌, ♍, ♎, ♏, <lb/>♐, ♒, ♓, ♈, ♉, &amp; </s>
  <s xml:id="echoid-s11700" xml:space="preserve">♊. </s>
  <s xml:id="echoid-s11701" xml:space="preserve">Neque verò propterea ſuperuacanea cenſenda ſunt reliqua poſteriora ſex <lb/>ſigna harum tabularum, quoniam eorum vſus in alijs horologiis, quæ ſequuntur, vt in Meridia-<lb/>no vtroque, &amp; </s>
  <s xml:id="echoid-s11702" xml:space="preserve">in declinantibus, &amp; </s>
  <s xml:id="echoid-s11703" xml:space="preserve">inclinatis, neceſſarius omnino eſt, vt ex ſequentibus fiet <lb/>perſpicuum.</s>
  <s xml:id="echoid-s11704" xml:space="preserve"/>
</p>
<div xml:id="echoid-div633" type="float" level="2" n="2">
<note position="left" xlink:label="note-0199-04" xlink:href="note-0199-04a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio ſi-<lb/>gnorum @Arie-<lb/>tis, &amp; Libræ a-<lb/>ſcendentium.</note>
<p>
  <s xml:id="echoid-s11705" xml:space="preserve">VERVM lineæ ♈, &amp; </s>
  <s xml:id="echoid-s11706" xml:space="preserve">♎, ita deſcribentur. </s>
  <s xml:id="echoid-s11707" xml:space="preserve">Quoniam aſcendente principio ♈, &amp; </s>
  <s xml:id="echoid-s11708" xml:space="preserve">Sole exi-<lb/>ſtente in principio ♑, meridies inſtat, vt conſtat ex quarta tabella; </s>
  <s xml:id="echoid-s11709" xml:space="preserve">perſpicuum eſt, communem <lb/>tunc ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s11710" xml:space="preserve">Eclipticæ tranſire per illud punctum tropici ♑, per quod me-<lb/>ridiana linea ducitur. </s>
  <s xml:id="echoid-s11711" xml:space="preserve">Quoniam verò eo tempore Æquator, circulus horæ ſextæ à meridie vel me <lb/>
<anchor type="note" xlink:label="note-0199-06a" xlink:href="note-0199-06"/>
dia nocte, Ecliptica, &amp; </s>
  <s xml:id="echoid-s11712" xml:space="preserve">Horizon, eandem habent communem ſectionem, vt ex ſphæra materiali li-<lb/>quet, cui planum horologij æquidiſtat, cum parallelum ſit Horizonti; </s>
  <s xml:id="echoid-s11713" xml:space="preserve">parallelæ erunt, per propoſ. <lb/></s>
  <s xml:id="echoid-s11714" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11715" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s11716" xml:space="preserve">linea æquinoctialis, linea horæ ſextæ à mer. </s>
  <s xml:id="echoid-s11717" xml:space="preserve">vel med noc. </s>
  <s xml:id="echoid-s11718" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11719" xml:space="preserve">communis ſectio <lb/>Eclipticæ, ac plani horologii. </s>
  <s xml:id="echoid-s11720" xml:space="preserve">Recta igitur æquinoctiali lineæ, vel ipſi lineæ horæ ſextæ parallela <lb/>per punctum, in quo linea meridiana tropicum ♑, ſecat, educta dabit ſignum ♈, aſcendens. </s>
  <s xml:id="echoid-s11721" xml:space="preserve">Ea-<lb/>demq́ue ratione recta, quæ per punctum, in quo linea meridiana tropicum ♋, ſecat, lineæ æquino-<lb/>ctiali ducitur parallela, ſignum ♎, aſcendens dabit: </s>
  <s xml:id="echoid-s11722" xml:space="preserve">quoniam etiam hoc ſignum in meridie ori-<lb/>tur, Sole exiſtente in princ̃ipio ♋, vt ex tertia tabella manifeſtum eſt, &amp;</s>
  <s xml:id="echoid-s11723" xml:space="preserve">c.</s>
  <s xml:id="echoid-s11724" xml:space="preserve"/>
</p>
<div xml:id="echoid-div634" type="float" level="2" n="3">
<note position="left" xlink:label="note-0199-06" xlink:href="note-0199-06a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Deſctiptio fi-<lb/>gnorum Cácri, <lb/>&amp; Capricorni, <lb/>aſcendentium.</note>
<p>
  <s xml:id="echoid-s11725" xml:space="preserve">POSTREMO lineæ, ♋, &amp; </s>
  <s xml:id="echoid-s11726" xml:space="preserve">♑ hoc modo poterunt deſcribi. </s>
  <s xml:id="echoid-s11727" xml:space="preserve">Quia aſcendente principio ♋, <lb/>&amp; </s>
  <s xml:id="echoid-s11728" xml:space="preserve">Sole exiſtente in principio ♑, inſtat hora 4. </s>
  <s xml:id="echoid-s11729" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11730" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11731" xml:space="preserve">poſt meridiem, vt ex quarta tabella con-<lb/>ſt@t, hoc eſt, Sol tunc, vel principium ♑, occidit, ſecabunt Ecliptica, &amp; </s>
  <s xml:id="echoid-s11732" xml:space="preserve">circulus horæ 4.</s>
  <s xml:id="echoid-s11733" xml:space="preserve">
<pb o="180" file="0200" n="200" rhead="GNOMONIGES"/>
Min. </s>
  <s xml:id="echoid-s11734" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11735" xml:space="preserve">à metidie, in eodem puncto occaſus Horizontem; </s>
  <s xml:id="echoid-s11736" xml:space="preserve">atque adeo eandem habebunt ſectio-<lb/>nem communem Ecliptica, circulus ille horarius, &amp; </s>
  <s xml:id="echoid-s11737" xml:space="preserve">Horizon. </s>
  <s xml:id="echoid-s11738" xml:space="preserve">Quare cum planum horologii Ho-<lb/>rizonti, atque idcirco communi illi ſectioni æquidiſtet, parallelæ erunt, per propoſ. </s>
  <s xml:id="echoid-s11739" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11740" xml:space="preserve">præceden-<lb/>tis libri, linea hor. </s>
  <s xml:id="echoid-s11741" xml:space="preserve">4. </s>
  <s xml:id="echoid-s11742" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11743" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11744" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s11745" xml:space="preserve">communis ſectio Eclipticæ tunc temporis, ac pla-<lb/>ni horologii. </s>
  <s xml:id="echoid-s11746" xml:space="preserve">Si igitur ducatur linea hor. </s>
  <s xml:id="echoid-s11747" xml:space="preserve">4. </s>
  <s xml:id="echoid-s11748" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11749" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11750" xml:space="preserve">à meridie, cui per punctum in linea <lb/>æquinoctiali inuentum, per quod ſcilicet duci debet linea ♋, parallela agatur, dabit hæc ſi-<lb/>gnum ♋, aſcendens. </s>
  <s xml:id="echoid-s11751" xml:space="preserve">Eodemq́ue modo lineam ♑, aſcendentis ducemus. </s>
  <s xml:id="echoid-s11752" xml:space="preserve">Immo eadem hac <lb/>demonſtratione concludemus, lineam cuiuſque ſigni aſcendentis in horologio horizontali <lb/>æquidiſtare illi lineæ horariæ à meridie, vel media nocte, quæ indicat tempus occaſus ſigni op-<lb/>poſiti, nempe lineam ♏, æquidiſtare lineæ hor. </s>
  <s xml:id="echoid-s11753" xml:space="preserve">6. </s>
  <s xml:id="echoid-s11754" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11755" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11756" xml:space="preserve">à meridie, vel media nocte, qua <lb/>
<anchor type="note" xlink:label="note-0200-01a" xlink:href="note-0200-01"/>
videlicet hora principium ♉, ſigni oppoſiti occidit. </s>
  <s xml:id="echoid-s11757" xml:space="preserve">Tot enim horas arcus ſemidiurnus ♉, <lb/>continet. </s>
  <s xml:id="echoid-s11758" xml:space="preserve">Ratio verò eſt, quia Ecliptica illo tempore, &amp; </s>
  <s xml:id="echoid-s11759" xml:space="preserve">circulus horæ illius, &amp; </s>
  <s xml:id="echoid-s11760" xml:space="preserve">Horizon, eandem <lb/>communem habent ſectionem, vt patet, &amp;</s>
  <s xml:id="echoid-s11761" xml:space="preserve">c. </s>
  <s xml:id="echoid-s11762" xml:space="preserve">Itaque ſi ſumantur arcus ſemidiurni omniũ ſigno-<lb/>rum, vt in hac tabella, facile cognoſcemus, quibusnam lineis horariis à meridie, vel media nocte</s>
</p>
<div xml:id="echoid-div635" type="float" level="2" n="4">
<note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div637" type="section" level="1" n="165">
<head xml:id="echoid-head168" xml:space="preserve">Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>
♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓
H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M.
6. 0. # 6. 42. # 7. 17. # 7. 32. # 7. 17. # 6. 42. # 6. 0. # 5. 18. # 4. 43. # 4. 28. # 4. 43. # 5. 18.
</note>
<p>
  <s xml:id="echoid-s11763" xml:space="preserve">in horologio horizontali æquidiſtent lineæ ſignorum aſcendentium, ob rationem dictam. </s>
  <s xml:id="echoid-s11764" xml:space="preserve">Nam <lb/>lineæ ♈, &amp; </s>
  <s xml:id="echoid-s11765" xml:space="preserve">♎, æquidiſtant lineæ hor. </s>
  <s xml:id="echoid-s11766" xml:space="preserve">6.</s>
  <s xml:id="echoid-s11767" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11768" xml:space="preserve">o. </s>
  <s xml:id="echoid-s11769" xml:space="preserve">à meridie vel media nocte. </s>
  <s xml:id="echoid-s11770" xml:space="preserve">Lineæ ♉, &amp; </s>
  <s xml:id="echoid-s11771" xml:space="preserve">♍, æqui-<lb/>diſtant lineæ horæ 5. </s>
  <s xml:id="echoid-s11772" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11773" xml:space="preserve">18. </s>
  <s xml:id="echoid-s11774" xml:space="preserve">Lineæ ♊, &amp; </s>
  <s xml:id="echoid-s11775" xml:space="preserve">♌, æquidiſtant lineæ hor. </s>
  <s xml:id="echoid-s11776" xml:space="preserve">4. </s>
  <s xml:id="echoid-s11777" xml:space="preserve">min. </s>
  <s xml:id="echoid-s11778" xml:space="preserve">43. </s>
  <s xml:id="echoid-s11779" xml:space="preserve">Vnde &amp; </s>
  <s xml:id="echoid-s11780" xml:space="preserve">bi-<lb/>næ inter ſe æquidiſtantes erunt. </s>
  <s xml:id="echoid-s11781" xml:space="preserve">At vero linea ♋, æquidiſtat lineæ hor.</s>
  <s xml:id="echoid-s11782" xml:space="preserve">4. </s>
  <s xml:id="echoid-s11783" xml:space="preserve">min.</s>
  <s xml:id="echoid-s11784" xml:space="preserve">28. </s>
  <s xml:id="echoid-s11785" xml:space="preserve">Linea denique <lb/>
<anchor type="note" xlink:label="note-0200-04a" xlink:href="note-0200-04"/>
♑, æquidiſtat lineæ hor.</s>
  <s xml:id="echoid-s11786" xml:space="preserve">7.</s>
  <s xml:id="echoid-s11787" xml:space="preserve">min.</s>
  <s xml:id="echoid-s11788" xml:space="preserve">32.</s>
  <s xml:id="echoid-s11789" xml:space="preserve"/>
</p>
<div xml:id="echoid-div637" type="float" level="2" n="1">
<note position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">30. primi.</note>
</div>
<p>
  <s xml:id="echoid-s11790" xml:space="preserve">EST autem hic, &amp; </s>
  <s xml:id="echoid-s11791" xml:space="preserve">in ſequentibus horologijs diligenter notandum, nullam lineam aſcenden-<lb/>
<anchor type="note" xlink:label="note-0200-05a" xlink:href="note-0200-05"/>
<anchor type="note" xlink:label="note-0200-06a" xlink:href="note-0200-06"/>
tium ſignorum poſſe tropicos ſecare, ſed omnes contingere eos tantummodo in punctis illis, per <lb/>quæ ducendæ ſunt, ita vt omnes lineæ ſignorum aſcendentium intra limites tropicorum conti-<lb/>neantur. </s>
  <s xml:id="echoid-s11792" xml:space="preserve">Nam quemadmodum lineæ horarum ab ortu, vel occaſu tangunt ſectiones conicas pa-<lb/>rallelorum duorum, quorum vnus eſt ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s11793" xml:space="preserve">alter ſemper latentium maximus, <lb/>in illis punctis, in quibus lineæ horarum à meridie, vel media nocte eaſdem conicas ſectiones in-<lb/>terſecant, vt propoſ. </s>
  <s xml:id="echoid-s11794" xml:space="preserve">14. </s>
  <s xml:id="echoid-s11795" xml:space="preserve">præcedentis libri demonſtrauimus: </s>
  <s xml:id="echoid-s11796" xml:space="preserve">ita etiam communes ſectiones Ecli-<lb/>pticæ, &amp; </s>
  <s xml:id="echoid-s11797" xml:space="preserve">plani horologii, quæ ex variis poſitionibus, quas Ecliptica ad motum diurnum obtinet, <lb/>efficiuntur, tangent conicas ſectiones tropicorumin illis punctis, in quibus eædem ſectiones co-<lb/>nicæ ſecantur à lineis illarum horarum à meridie, vel media nocte, in quibus illas poſitiones ha-<lb/>bet Ecliptica. </s>
  <s xml:id="echoid-s11798" xml:space="preserve">Eadem enim eſt demonſtratio hic &amp; </s>
  <s xml:id="echoid-s11799" xml:space="preserve">ibi. </s>
  <s xml:id="echoid-s11800" xml:space="preserve">Quod ita perſpicuum faciemus. </s>
  <s xml:id="echoid-s11801" xml:space="preserve">Aſcen-<lb/>
<anchor type="note" xlink:label="note-0200-07a" xlink:href="note-0200-07"/>
dente v.</s>
  <s xml:id="echoid-s11802" xml:space="preserve">g. </s>
  <s xml:id="echoid-s11803" xml:space="preserve">ſigno ♉, cum Sol eſt in principio ♑, linea hor.</s>
  <s xml:id="echoid-s11804" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11805" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11806" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11807" xml:space="preserve">poſt meridiem ſecat in horo <lb/>logio tropicum ♑, in K. </s>
  <s xml:id="echoid-s11808" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s11809" xml:space="preserve">circulus dictæ horæ per polos mũdi ductus circulum ♑, in cœ-<lb/>lo ſecabit in eo puncto, in quo exiſtens Sol radium emittit per verticem ſtyli ad punctum K. </s>
  <s xml:id="echoid-s11810" xml:space="preserve">Cum <lb/>ergo Ecliptica tangat in cœlo circulum ♑, in principio ♑, in quo Sol ponitur, neceſſe eſt, eam <lb/>tunc temporis tangere dictum circulum ♑, in eodem illo puncto, in quo à prædicto circulo ho-<lb/>rario ſecatur, quandoquidẽ radius Solis tunc in punctum K, cadit. </s>
  <s xml:id="echoid-s11811" xml:space="preserve">Quare in quo puncto tropicus <lb/>♑, ſecatur tunc in horologio à linea hor. </s>
  <s xml:id="echoid-s11812" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11813" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11814" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11815" xml:space="preserve">poft meridiem, in eodem, nempe in K, tanget <lb/>eundem tropicum ♑, communis ſectio Eclipticæ, &amp; </s>
  <s xml:id="echoid-s11816" xml:space="preserve">plani horologii, vt ex propoſ. </s>
  <s xml:id="echoid-s11817" xml:space="preserve">13. </s>
  <s xml:id="echoid-s11818" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s11819" xml:space="preserve">14. </s>
  <s xml:id="echoid-s11820" xml:space="preserve">ſu-<lb/>perioris lib. </s>
  <s xml:id="echoid-s11821" xml:space="preserve">manifeſtum eſt. </s>
  <s xml:id="echoid-s11822" xml:space="preserve">Ita enim tunc ſe habent circulus dictæ horæ 1. </s>
  <s xml:id="echoid-s11823" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11824" xml:space="preserve">10. </s>
  <s xml:id="echoid-s11825" xml:space="preserve">poſt meridiẽ, <lb/>&amp; </s>
  <s xml:id="echoid-s11826" xml:space="preserve">Ecliptica, (cum ille ſuperficiem conicam ♑, ſecet per lineam rectam, hæc autem eandem ſu-<lb/>
<anchor type="note" xlink:label="note-0200-08a" xlink:href="note-0200-08"/>
perficiem in eadem linea tangat) quemadmodum ſe habent circulus quilibet horarius à meridie, <lb/>vel media nocte ſecans conicam ſuperficiem paralleli ſemper apparentium maximi per lineam re-<lb/>ctam, &amp; </s>
  <s xml:id="echoid-s11827" xml:space="preserve">circulus horarius ab ortu, vel occaſu in eadem linea recta tangens eandem ſuperficiẽ co-<lb/>nicam; </s>
  <s xml:id="echoid-s11828" xml:space="preserve">vt perſpicuum eſt, ſi rectè conſideretur poſitio Eclipticæ, &amp; </s>
  <s xml:id="echoid-s11829" xml:space="preserve">dicti circuli hor. </s>
  <s xml:id="echoid-s11830" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11831" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11832" xml:space="preserve">10. <lb/></s>
  <s xml:id="echoid-s11833" xml:space="preserve">dum principium ♉, aſcendit, &amp; </s>
  <s xml:id="echoid-s11834" xml:space="preserve">Sol in principio ♑, exiſtit. </s>
  <s xml:id="echoid-s11835" xml:space="preserve">Colurus enim Solſtitiorum fungitur <lb/>tunc officio illius circuli horarij ſecans tropicum ♑, in puncto, in quo eundem tropicum Eclipti <lb/>ca contingit, nempe in principio ♑. </s>
  <s xml:id="echoid-s11836" xml:space="preserve">Id quod luce clarius ex ſphæra materiali intelligi poteſt. </s>
  <s xml:id="echoid-s11837" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0200-09a" xlink:href="note-0200-09"/>
Eademq́ue ratio eſt de cæteris ſignis aſcendentibus, Sole exiſtente in principio ♑, vel ♋.</s>
  <s xml:id="echoid-s11838" xml:space="preserve"/>
</p>
<div xml:id="echoid-div638" type="float" level="2" n="2">
<note position="left" xlink:label="note-0200-05" xlink:href="note-0200-05a" xml:space="preserve">Lineę aſcenden <lb/>tiu m ſignorum <lb/>tangunt tropi-<lb/>cos in horolo-<lb/>gio quocunq;.</note>
<note position="left" xlink:label="note-0200-06" xlink:href="note-0200-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0200-07" xlink:href="note-0200-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0200-08" xlink:href="note-0200-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0200-09" xlink:href="note-0200-09a" xml:space="preserve">Qua ratione <lb/>ſigna aſcendẽ-<lb/>tia per doctri-<lb/>nam conicorũ <lb/>Apollonii de-<lb/>ſeribãtur in ho <lb/>rologio.</note>
</div>
<p>
  <s xml:id="echoid-s11839" xml:space="preserve">EX his colligitur alius modus deſcribendorum ſignorum aſcendentium. </s>
  <s xml:id="echoid-s11840" xml:space="preserve">Si enim ex punctis <lb/>tropicorum inuentis per tabellam tertiam, &amp; </s>
  <s xml:id="echoid-s11841" xml:space="preserve">quartam ducantur rectæ tangentes ipſos tropicos, <lb/>per ea, quæ in coroll. </s>
  <s xml:id="echoid-s11842" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s11843" xml:space="preserve">37. </s>
  <s xml:id="echoid-s11844" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s11845" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11846" xml:space="preserve">Apollonii ſcripſimus, (quod quidem hic perfacile eſt, cum
<pb o="181" file="0201" n="201" rhead="LIBER SECVNDVS."/>
ordinatim applicatæ ex dictis punctis tropicorum ſint ad diametrum, perpendiculares) deſcripta <lb/>erunt aſcendentia ſigna.</s>
  <s xml:id="echoid-s11847" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s11848" xml:space="preserve">ALITER deſcribentur aſcendentia ſigna hoc pacto. </s>
  <s xml:id="echoid-s11849" xml:space="preserve">Primum quęrantur puncta Eclipticæ in <lb/>circulo Meridiano exiſtentia, hoc eſt, mediationes cœli, cum principia ſignorum Zodiaci oriun-<lb/>tur, &amp; </s>
  <s xml:id="echoid-s11850" xml:space="preserve">eorundem punctorum declinationes. </s>
  <s xml:id="echoid-s11851" xml:space="preserve">Deindeiiſdem ſignorum initiis aſcen dentibus, inue-<lb/>ſtigentur puncta Eclipticæ in circulo horæ 6. </s>
  <s xml:id="echoid-s11852" xml:space="preserve">à meridie, vel media nocte conſtituta, vna cum eo-<lb/>rundem declinationibus. </s>
  <s xml:id="echoid-s11853" xml:space="preserve">Quæ omnia ita abſoluemus. </s>
  <s xml:id="echoid-s11854" xml:space="preserve">Ex aſcenſione obliqua principii cuiusli-<lb/>
<anchor type="note" xlink:label="note-0201-01a" xlink:href="note-0201-01"/>
bet ſigni (quę vel ex tabulis aſcenſionum obliquarum, quæ in tabulis Directionum Ioan. </s>
  <s xml:id="echoid-s11855" xml:space="preserve">Regiom. <lb/></s>
  <s xml:id="echoid-s11856" xml:space="preserve">vel in commentariis noſtris in ſphæram continentur, ſumenda eſt, vel certè ex doctrina ſinuum, vt <lb/>in cap. </s>
  <s xml:id="echoid-s11857" xml:space="preserve">3. </s>
  <s xml:id="echoid-s11858" xml:space="preserve">ſphęræ præcepimus, &amp; </s>
  <s xml:id="echoid-s11859" xml:space="preserve">ad finem ſcholii huius propoſ. </s>
  <s xml:id="echoid-s11860" xml:space="preserve">oſtendemus, eruenda) quadrans <lb/>
<anchor type="note" xlink:label="note-0201-02a" xlink:href="note-0201-02"/>
circuli auferatur, hoceſt, grad. </s>
  <s xml:id="echoid-s11861" xml:space="preserve">90. </s>
  <s xml:id="echoid-s11862" xml:space="preserve">adiecto prius integro circulo ad aſcenſionem obliquam, ſi de-<lb/>tractio fieri nequit, vt in calculo Aſtronomico ſieri ſolet. </s>
  <s xml:id="echoid-s11863" xml:space="preserve">Numerus en im reliquus erit aſcenſio <lb/>recta puncti Eclipticæ, quod tunc in Meridiano ſupra Horizontem reperitur, quodq́; </s>
  <s xml:id="echoid-s11864" xml:space="preserve">Mediatio-<lb/>nem cœli dicunt Aſtronomi. </s>
  <s xml:id="echoid-s11865" xml:space="preserve">Quare ex tabula aſcenſionum rectarum, vel ex doctrina, quam in <lb/>ſcholio ſequenti trademus, punctum illud Eclipticæ notum fiet, cuius punctum oppoſitum in eo-<lb/>dem Meridiano exiſter infra Horizontem, quod angulum terræ dicere poſſumus cum Aſtrono-<lb/>mis. </s>
  <s xml:id="echoid-s11866" xml:space="preserve">Huius operationis demonſtratio difficilis non eſt, ſi poſitio Horizontis, Meridiani, Zodiaci, <lb/>&amp; </s>
  <s xml:id="echoid-s11867" xml:space="preserve">Æ quatoris in ſphæra rectè concipiatur. </s>
  <s xml:id="echoid-s11868" xml:space="preserve">Nam quando aſcenſio obliqua maior fuerit quadran-<lb/>te, vel quadranti æqualis, perſpicuum eſt, ſi quadransÆ quatoris inter orientem, &amp; </s>
  <s xml:id="echoid-s11869" xml:space="preserve">meridiem poſi-<lb/>tus ex ea auferatur, relinqui aſcenſionem rectam puncti Eclipticæ cœlum mediantis, nempe di-<lb/>
<anchor type="note" xlink:label="note-0201-03a" xlink:href="note-0201-03"/>
ſtantiam principii ♈, à Meridiano circulo ſecundum ſignorum ſucceſſionem: </s>
  <s xml:id="echoid-s11870" xml:space="preserve">Quando vero aſcẽ-<lb/>ſio obliqua quadrante fuerit minor, liquido etiam conſtat, ſi quadrans Aequatoris inter orien-<lb/>tem, &amp; </s>
  <s xml:id="echoid-s11871" xml:space="preserve">meridiem conſtitutus ab integro circulo dematur, &amp; </s>
  <s xml:id="echoid-s11872" xml:space="preserve">reliquis tribus quadrantibus aſcen-<lb/>ſio obliqua apponatur, (quod perinde eſt, ac ſi quadrans ab aggregato, quod ex aſcenſione obli-<lb/>qua, &amp; </s>
  <s xml:id="echoid-s11873" xml:space="preserve">circulo integro fit, detrahatur) conflari aſcenſionem rectam puncti Eclipticæ cœlum me-<lb/>diantis. </s>
  <s xml:id="echoid-s11874" xml:space="preserve">In ſphæra quoquerecta eadem operatio locum habet, ſi loco aſcenſionis obliquæ aſcen-<lb/>dentis ſigni accipiatur aſcenſio recta eiuſdem.</s>
  <s xml:id="echoid-s11875" xml:space="preserve"/>
</p>
<div xml:id="echoid-div639" type="float" level="2" n="3">
<note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">Quomodo me-<lb/>diationes cœli, <lb/>cũ initia ſigno-<lb/>rum oriuntur, <lb/>inue ſtigandę <lb/>ſint.</note>
<note position="left" xlink:label="note-0201-02" xlink:href="note-0201-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0201-03" xlink:href="note-0201-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s11876" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s11877" xml:space="preserve">Ad latitudinem grad. </s>
  <s xml:id="echoid-s11878" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11879" xml:space="preserve">qualis ferè eſt Romæ, aſcenſio obliqua prine<unsure/>i-<lb/>
<anchor type="note" xlink:label="note-0201-04a" xlink:href="note-0201-04"/>
pii ♍, eſt grad. </s>
  <s xml:id="echoid-s11880" xml:space="preserve">141. </s>
  <s xml:id="echoid-s11881" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11882" xml:space="preserve">33. </s>
  <s xml:id="echoid-s11883" xml:space="preserve">ex qua ſi dematur quadrans, hoc eſt, grad. </s>
  <s xml:id="echoid-s11884" xml:space="preserve">90. </s>
  <s xml:id="echoid-s11885" xml:space="preserve">remanent grad. </s>
  <s xml:id="echoid-s11886" xml:space="preserve">51. <lb/></s>
  <s xml:id="echoid-s11887" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11888" xml:space="preserve">33. </s>
  <s xml:id="echoid-s11889" xml:space="preserve">pro aſcenſione recta puncti Eclipticæ cœlum mediantis, cum principium ♍, oritur. </s>
  <s xml:id="echoid-s11890" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0201-05a" xlink:href="note-0201-05"/>
Huic autem aſcenſioni rectæ reſpondet in tabula aſcenſionum rectarum (adhibita tamen parte <lb/>proportionali, vt fieri conſuea<unsure/>it, quando numerus non præcisè in tabula aliqua continetur) <lb/>gradus 23. </s>
  <s xml:id="echoid-s11891" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11892" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11893" xml:space="preserve">♉. </s>
  <s xml:id="echoid-s11894" xml:space="preserve">Hoc ergo punctum Eclipticæ in Meridiano tunc reperietur ſupra Ho-<lb/>rizontem, infra vero Horizontem in eodem Meridiano exiſtet gradus 23. </s>
  <s xml:id="echoid-s11895" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11896" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11897" xml:space="preserve">♏. </s>
  <s xml:id="echoid-s11898" xml:space="preserve">Rurſus <lb/>obliqua aſcenſio principii ♋, continet grad. </s>
  <s xml:id="echoid-s11899" xml:space="preserve">66. </s>
  <s xml:id="echoid-s11900" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11901" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11902" xml:space="preserve">Cui ſi addatur integer circulus, hoc <lb/>eſt, grad. </s>
  <s xml:id="echoid-s11903" xml:space="preserve">360. </s>
  <s xml:id="echoid-s11904" xml:space="preserve">fiunt grad. </s>
  <s xml:id="echoid-s11905" xml:space="preserve">426. </s>
  <s xml:id="echoid-s11906" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11907" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11908" xml:space="preserve">à quibus ſi deducantur grad. </s>
  <s xml:id="echoid-s11909" xml:space="preserve">90. </s>
  <s xml:id="echoid-s11910" xml:space="preserve">relinquuntur grad. </s>
  <s xml:id="echoid-s11911" xml:space="preserve">336. <lb/></s>
  <s xml:id="echoid-s11912" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11913" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11914" xml:space="preserve">pro aſcenſione recta puncti Eclipticæ mediantis tunc cœlum, cum initium ♋, aſcendit <lb/>ſupra Horizontem. </s>
  <s xml:id="echoid-s11915" xml:space="preserve">Huic rectæ aſcenſioni reſpondet in tabula aſcenſionum rectarum gradus <lb/>5. </s>
  <s xml:id="echoid-s11916" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11917" xml:space="preserve">6. </s>
  <s xml:id="echoid-s11918" xml:space="preserve">♓. </s>
  <s xml:id="echoid-s11919" xml:space="preserve">Quare hoc punctum eo tempore in Meridiano ſupra Horizontem exiſtet, angulus <lb/>autem terræ erit gradus 5. </s>
  <s xml:id="echoid-s11920" xml:space="preserve"><emph style="sc">M</emph>in. </s>
  <s xml:id="echoid-s11921" xml:space="preserve">6. </s>
  <s xml:id="echoid-s11922" xml:space="preserve">♍. </s>
  <s xml:id="echoid-s11923" xml:space="preserve">Poſtremo in ſphera recta, (vt de hac exemplum etiam af-<lb/>
<anchor type="note" xlink:label="note-0201-06a" xlink:href="note-0201-06"/>
feramus) aſcenſio recta ♐, complectitur grad. </s>
  <s xml:id="echoid-s11924" xml:space="preserve">237. </s>
  <s xml:id="echoid-s11925" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11926" xml:space="preserve">48. </s>
  <s xml:id="echoid-s11927" xml:space="preserve">Ex hac dempto quadrante, ſuper-<lb/>ſunt grad. </s>
  <s xml:id="echoid-s11928" xml:space="preserve">147. </s>
  <s xml:id="echoid-s11929" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11930" xml:space="preserve">48. </s>
  <s xml:id="echoid-s11931" xml:space="preserve">pro aſcenſione recta illius puncti Eclipticæ, quod tunc cœlum mediat. <lb/></s>
  <s xml:id="echoid-s11932" xml:space="preserve">Cui aſcenſioni conuenit gradus 25. </s>
  <s xml:id="echoid-s11933" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11934" xml:space="preserve">31. </s>
  <s xml:id="echoid-s11935" xml:space="preserve">♌, atque hoc punctum tuncin Meridiano exiſtet <lb/>ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s11936" xml:space="preserve">in angulo propterea terræ erit gradus 25. </s>
  <s xml:id="echoid-s11937" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11938" xml:space="preserve">31. </s>
  <s xml:id="echoid-s11939" xml:space="preserve">♒. </s>
  <s xml:id="echoid-s11940" xml:space="preserve">Hac arte compo-<lb/>ſuimus ſequentem tabellam mediationum cœli, &amp; </s>
  <s xml:id="echoid-s11941" xml:space="preserve">angulorum terræ, oriente principio cuiuſuis <lb/>ſigni Zodiaci, ad latitudinem grad. </s>
  <s xml:id="echoid-s11942" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11943" xml:space="preserve">in qua etiam adſcripſimus earundem mediationum, &amp; </s>
  <s xml:id="echoid-s11944" xml:space="preserve"><lb/>angulorum terræ declinationes per doctrinam ſinuum inuentas, vt in coroll. </s>
  <s xml:id="echoid-s11945" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s11946" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11947" xml:space="preserve">præce-<lb/>dentis libri tradidimus, licet eædem ex tabula declinationum, habita ratione partis proportiona-<lb/>lis, elici poſſint. </s>
  <s xml:id="echoid-s11948" xml:space="preserve">Perſpicuum autem eſt, declinationes punctorum ſeptentrionalium Eclipticæ <lb/>eſſe ſeptentrionales, auſtralium verò auſtrales. </s>
  <s xml:id="echoid-s11949" xml:space="preserve">Vnde facile iudicabis, quorumnam puncto-<lb/>
<anchor type="note" xlink:label="note-0201-07a" xlink:href="note-0201-07"/>
rum declinatio in dicta tabula ſit borealis, &amp; </s>
  <s xml:id="echoid-s11950" xml:space="preserve">quorum auſtralis: </s>
  <s xml:id="echoid-s11951" xml:space="preserve">quod quidem noſſe, magni re-<lb/>fert, vt ſigna aſcendentia deſcribantur.</s>
  <s xml:id="echoid-s11952" xml:space="preserve"/>
</p>
<div xml:id="echoid-div640" type="float" level="2" n="4">
<note position="right" xlink:label="note-0201-04" xlink:href="note-0201-04a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0201-05" xlink:href="note-0201-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0201-06" xlink:href="note-0201-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0201-07" xlink:href="note-0201-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div642" type="section" level="1" n="166">
<head xml:id="echoid-head169" xml:space="preserve">VI. Mediationes cœli, &amp; anguli terræ, eorumq́; declinationes, orientibus 12. <lb/>ſignorum Zodiaci initiis, ad latitudinem grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Mediationes # 0. 0. ♑. # 15. 59. ♑. # 6. 3. ♒. # 5. 6. ♓. # cœli <lb/>Anguli # 0. 0. ♋ # 15. 59. ♋. # 6. 3. ♌. # 5. 6. ♍. # terræ <lb/>Declina- # 23. 30. # 22. 32. # 18. 48. # 9. 40. # tiones <lb/></note>
<pb o="182" file="0202" n="202" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Mediationes # 13. 59. ♈. # 23. 57. ♉. # 0. 0. ♋. # 6. 3. ♌. # cœli <lb/>Anguli # 13. 59. ♎. # 23. 57. ♏. # 0. 0. ♑. # 6. 3. ♒. # terrę <lb/>Declina- # 5. 32. # 18. 48. # 23. 30. # 18. 48. # tiones <lb/>Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Mediationes # 16. 1. ♍ # 24. 54. ♎. # 23. 57. ♏. # 14. 1. ♐. # cœli <lb/>Anguli # 16. 1. ♓. # 24. 54. ♈. # 23. 57. ♉. # 14. 1. ♊. # terrę <lb/>Declina- # 5. 32. # 9. 40. # 18. 48. # 22. 32. # tiones <lb/></note>
<note position="left" xml:space="preserve">Qua arte inue-<lb/>niantur pun-<lb/>cta Eclipticæ in <lb/>circulo horæ <lb/>6. à merid. uel <lb/>med. noc. collo <lb/>cata, cum ſigno-<lb/>tum initia oriũ <lb/>tur.</note>
<p>
  <s xml:id="echoid-s11953" xml:space="preserve">RVRSVS, quoniam aſcenſio obliqua principii cuiuslibet ſigni eſt aſcenſio recta illius pun <lb/>cti Eclipticæ, quod tunc in circulo horæ 6. </s>
  <s xml:id="echoid-s11954" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s11955" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s11956" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s11957" xml:space="preserve">exiſtit ante meridiem, vt perſpi-<lb/>cuum eſt, ſi rectè conſideretur poſitio circuli horæ ſextæ à mer. </s>
  <s xml:id="echoid-s11958" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s11959" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s11960" xml:space="preserve">qui perperuo tranſit <lb/>per puncta veri ortus, hoc eſt, per finem aſcenſionis obliquæ, inſtar Horizontis cuiuſdam recti. <lb/></s>
  <s xml:id="echoid-s11961" xml:space="preserve">Hinc enim fit, vt arcus Æ quatoris metiens obliquam aſcenſionem puncti in Horizonte conſtitu-<lb/>
<anchor type="note" xlink:label="note-0202-03a" xlink:href="note-0202-03"/>
ti, metiatur quoque aſcenſionem rectam puncti Eclipticæ in circulo horæ ſextæ collocati illo tem <lb/>pore, aſcenſionem, inquam, rectam ſupra circulum horæ ſextæ, tanquam Horizontem quendam <lb/>rectum. </s>
  <s xml:id="echoid-s11962" xml:space="preserve">Hinc ex tabula aſcenſionum rectarum punctum illud Eclipticæ notum fiet. </s>
  <s xml:id="echoid-s11963" xml:space="preserve">Manifeſtum <lb/>autem eſt, punctum Eclipticæ oppoſitum in eodem tunc circulo horæ ſextæ exiſtere poſt meridiẽ.</s>
  <s xml:id="echoid-s11964" xml:space="preserve"/>
</p>
<div xml:id="echoid-div642" type="float" level="2" n="1">
<note position="left" xlink:label="note-0202-03" xlink:href="note-0202-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">Eremplum.</note>
<p>
  <s xml:id="echoid-s11965" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s11966" xml:space="preserve">Principio ♋, aſcendente, inuenio eius aſcenſionem obliquam, ad latitu-<lb/>dinem grad. </s>
  <s xml:id="echoid-s11967" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11968" xml:space="preserve">continere grad. </s>
  <s xml:id="echoid-s11969" xml:space="preserve">66. </s>
  <s xml:id="echoid-s11970" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11971" xml:space="preserve">57. </s>
  <s xml:id="echoid-s11972" xml:space="preserve">Tanta ergo eſt aſcenſio recta puncti Eclip@icæ tunc <lb/>in dicto circulo horæ ſextæ ante meridiem conſtituti. </s>
  <s xml:id="echoid-s11973" xml:space="preserve">Quod punctum ex tabula aſcenſionum re-<lb/>ctarum reperietur eſſe gradus 8. </s>
  <s xml:id="echoid-s11974" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11975" xml:space="preserve">41. </s>
  <s xml:id="echoid-s11976" xml:space="preserve">♊, habita ratione partis proportionalis; </s>
  <s xml:id="echoid-s11977" xml:space="preserve">ac proinde <lb/>in eodem circulo poſt meridiem exiſtet gradus 8. </s>
  <s xml:id="echoid-s11978" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s11979" xml:space="preserve">41. </s>
  <s xml:id="echoid-s11980" xml:space="preserve">♐. </s>
  <s xml:id="echoid-s11981" xml:space="preserve">In ſphæra recta idem punctum ſu-<lb/>pra Horizontem aſcendens eſt in circulo horæ ſextæ à mer. </s>
  <s xml:id="echoid-s11982" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s11983" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s11984" xml:space="preserve">ante meridiem, propte-<lb/>
<anchor type="note" xlink:label="note-0202-05a" xlink:href="note-0202-05"/>
rea quòd ibi dictus circulus horæ 6. </s>
  <s xml:id="echoid-s11985" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s11986" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s11987" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s11988" xml:space="preserve">idem ſit, qui Horizon. </s>
  <s xml:id="echoid-s11989" xml:space="preserve">Hac arte ſequen-<lb/>tem tabellam continentem puncta Eclipticæ in circulo horæ 6. </s>
  <s xml:id="echoid-s11990" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s11991" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s11992" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s11993" xml:space="preserve">conſtituta, <lb/>dum initia ſignorum oriuntur, ad latitudinem grad. </s>
  <s xml:id="echoid-s11994" xml:space="preserve">42. </s>
  <s xml:id="echoid-s11995" xml:space="preserve">conſtruximus, in qua etiam poſitæ ſunt <lb/>declinationes punctorum inuentorum, quas quidem ſupputauimus ex ſinuum ſcientia, vt in co-<lb/>roll. </s>
  <s xml:id="echoid-s11996" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s11997" xml:space="preserve">1. </s>
  <s xml:id="echoid-s11998" xml:space="preserve">pręcedentis libri docuimus, quamuis eædem colligi poſſint ex tabula declinationũ, <lb/>ſi partis proportionalis ratio hbeatur.</s>
  <s xml:id="echoid-s11999" xml:space="preserve"/>
</p>
<div xml:id="echoid-div643" type="float" level="2" n="2">
<note position="left" xlink:label="note-0202-05" xlink:href="note-0202-05a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div645" type="section" level="1" n="167">
<head xml:id="echoid-head170" xml:space="preserve">VII. Puncta Eclipticæ in circulo horę 6. conſtituta, eorumq́ue declinationes, <lb/>orientibus 12. ſignorum Zodiaci principijs, ad <lb/>latitudinem grad. 42.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Pũcta ĩ hora 6. # 0. 0. ♈. # 18. 49. ♈. # 10. 53. ♉. # 8. 41. ♊. # antemeridiana <lb/>Pũcta ĩ hora 6. # 0. 0. ♎. # 18. 49. ♎. # 10. 53. ♏. # 8. 41. ♐. # pomeridiana <lb/>Declina- # 0. 0. # 7. 23. # 15. 8. # 21. 48. # tiones <lb/>Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Pũcta ĩ hora 6. # 11. 49. ♋. # 19. 7. ♌. # 0. 0. ♎. # 10. 53. ♏. # antemeridiana <lb/>
Pũcta ĩ hora 6. # 11. 49. ♑. # 19. 7. ♒. # 0. 0. ♈. # 10. 53. ♉ # pomeridiana
Declina- # 22. 58. # 15. 8. # 0. 0. # 15. 8. # tiones
Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # minuta
Pũcta ĩ hora 6. # 18. 11. ♐. # 21. 19. ♑. # 19. 7. ♒. # 11. 11. ♓. # antemeridiana
Pũcta ĩ hora 6. # 18. 11. ♊. # 21. 19. ♋. # 19. 7. ♌. # 11. 11. ♍. # pomeridiana
Declina- # 22. 58. # 21. 48. # 15. 8. # 7. 23. # tiones
</note>
<pb o="183" file="0203" n="203" rhead="LIBER SECVNDVS."/>
<p>
  <s xml:id="echoid-s12000" xml:space="preserve">HIS ritè confectis, ita ſigna aſcendentia deſcribemus. </s>
  <s xml:id="echoid-s12001" xml:space="preserve">Declinationes mediationum cœli ſup-<lb/>
<anchor type="note" xlink:label="note-0203-01a" xlink:href="note-0203-01"/>
putentur in prima figura propoſ. </s>
  <s xml:id="echoid-s12002" xml:space="preserve">2. </s>
  <s xml:id="echoid-s12003" xml:space="preserve">huius libri, à puncto F, diametri Æ quatoris in boream, vel au-<lb/>ſtrum, prout puncta mediationum cœli borealia fuerint, vel auſtralia; </s>
  <s xml:id="echoid-s12004" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12005" xml:space="preserve">per fines ſupputationum, <lb/>centrumq́ue D, lineæ rectæ ducantur occultè, ſecantes rectam O R, in punctis, quorum interualla <lb/>à puncto G, nempe à loco ſtvli ſumpta, ſi in lineam meridianam horologii transferantur à G, loco <lb/>ſtyli, habebuntur in meridiana linea puncta, per quæ ducenda ſunt aſcendentia ſigna, illa nimirũ, <lb/>quorum mediationes cœli, &amp; </s>
  <s xml:id="echoid-s12006" xml:space="preserve">mediationum cœli declinationes ſumptæ ſunt. </s>
  <s xml:id="echoid-s12007" xml:space="preserve">Ratio huius eſt; <lb/></s>
  <s xml:id="echoid-s12008" xml:space="preserve">quia ſi v.</s>
  <s xml:id="echoid-s12009" xml:space="preserve">g. </s>
  <s xml:id="echoid-s12010" xml:space="preserve">oriente principio ♋, in Meridiano reperitur gradus 5. </s>
  <s xml:id="echoid-s12011" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12012" xml:space="preserve">6. </s>
  <s xml:id="echoid-s12013" xml:space="preserve">♓, ſupra Horizontem, <lb/>efficitur, vt Sole exiſtente in grad. </s>
  <s xml:id="echoid-s12014" xml:space="preserve">5. </s>
  <s xml:id="echoid-s12015" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12016" xml:space="preserve">6. </s>
  <s xml:id="echoid-s12017" xml:space="preserve">♓, &amp; </s>
  <s xml:id="echoid-s12018" xml:space="preserve">Meridianum circulum ſupra Horizontem poſ-<lb/>ſidente, principium ♋, oriatur. </s>
  <s xml:id="echoid-s12019" xml:space="preserve">Cum ergo tunc vmbra ſtyli in illud punctum meridianæ lineæ <lb/>
<anchor type="note" xlink:label="note-0203-02a" xlink:href="note-0203-02"/>
proiiciatur, quod per declinationem grad. </s>
  <s xml:id="echoid-s12020" xml:space="preserve">5. </s>
  <s xml:id="echoid-s12021" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12022" xml:space="preserve">6. </s>
  <s xml:id="echoid-s12023" xml:space="preserve">♓, inuenimus, nempe in ſectionem co-<lb/>nicam paralleli illius declinationis, vt ex coroll. </s>
  <s xml:id="echoid-s12024" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s12025" xml:space="preserve">12. </s>
  <s xml:id="echoid-s12026" xml:space="preserve">præcedentis libri conſtat, tranſibit <lb/>neceſſario communis ſectio Eclipticæ, &amp; </s>
  <s xml:id="echoid-s12027" xml:space="preserve">plani horologii illo tempore per idem punctum; </s>
  <s xml:id="echoid-s12028" xml:space="preserve">pro-<lb/>pterea quòd vmbra ſtyli, vt propoſ. </s>
  <s xml:id="echoid-s12029" xml:space="preserve">11. </s>
  <s xml:id="echoid-s12030" xml:space="preserve">eiuſdem præcedentis libri oſtendimus, ſemper in com-<lb/>munem ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s12031" xml:space="preserve">circuli maximi, in quo eſt Sol, qui quidem tunc Zodia-<lb/>cus eſt, proiiciatur. </s>
  <s xml:id="echoid-s12032" xml:space="preserve">Eademq́ue ratio eſt de cæteris. </s>
  <s xml:id="echoid-s12033" xml:space="preserve">Sed eadem puncta in linea meridiana re-<lb/>perientur ex tertia figura propoſ. </s>
  <s xml:id="echoid-s12034" xml:space="preserve">2. </s>
  <s xml:id="echoid-s12035" xml:space="preserve">huius libri, nempe ex figura radiorum Zodiaci, hoc pacto. </s>
  <s xml:id="echoid-s12036" xml:space="preserve">In <lb/>circulo ex D, deſcripto ſupputentur à radio Æ quatoris declinationes, vt prius, nempe verſus ra-<lb/>dium ♋, aut ♑, prout puncta mediationum cœli fuerint borealia, vel auſtralia; </s>
  <s xml:id="echoid-s12037" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12038" xml:space="preserve">earum declina-<lb/>tionum radii occultè ducantur ex D, ſecantes lineam H B, horæ 12. </s>
  <s xml:id="echoid-s12039" xml:space="preserve">in punctis, quæ ſi à puncto <lb/>
<anchor type="note" xlink:label="note-0203-03a" xlink:href="note-0203-03"/>
H, ſumpta in lineam meridianam horologii à centro horologii H, transferantur, reperientur in <lb/>linea meridiana puncta, vt prius.</s>
  <s xml:id="echoid-s12040" xml:space="preserve"/>
</p>
<div xml:id="echoid-div645" type="float" level="2" n="1">
<note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">Deſcriptio ſi-<lb/>gnorum aſcen-<lb/>dentium in ho-<lb/>tologio per cœ-<lb/>li mediationes, <lb/>&amp; puncta Ecli-<lb/>pticæ in circulo <lb/>horæ 6. à mer-<lb/>vel med. noc. cõ <lb/>ſtiruta, dum ini <lb/>tia ſignorum <lb/>oriuntur.</note>
<note position="left" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s12041" xml:space="preserve">SIMILITER declinationes punctorum Eclipticæ borealium in circulo horæ ſextæ à mer. <lb/></s>
  <s xml:id="echoid-s12042" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12043" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12044" xml:space="preserve">exiſtentium tam ante, quàm poſt meridiem, in tertia figura propoſ. </s>
  <s xml:id="echoid-s12045" xml:space="preserve">2. </s>
  <s xml:id="echoid-s12046" xml:space="preserve">huius libri, hoc <lb/>eſt, in figura radiorum Zodiaci, ſuppurentur in arcu circuli ex D, deſcripti, à radio Æquatoris ver-<lb/>ſus radium ♋. </s>
  <s xml:id="echoid-s12047" xml:space="preserve">(In horologio enim horizontali ſolum declinationes boreales ſumendæ ſunt, cum <lb/>hæ ſolæ in lineam horæ ſextæ, quæ tota in parte boreali horologii, quam æquinoctialis linea ab au <lb/>ſtrali ſeparant, cadere poſſint) &amp; </s>
  <s xml:id="echoid-s12048" xml:space="preserve">ex D, per fines ſupputationum ducantur occultè radii illarum de-<lb/>clinationum, ſecantes lineam ho æ ſextæ à mer. </s>
  <s xml:id="echoid-s12049" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12050" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12051" xml:space="preserve">in punctis, quæ ex H, in lineam ho-<lb/>ræ ſextæ horologij ex centro H, @translata ſiue ante, ſiue poſt meridiẽ, prout ex antecedenti tabella <lb/>
<anchor type="note" xlink:label="note-0203-04a" xlink:href="note-0203-04"/>
manifeſtum eſt, dabunt puncta in linea horæ ſextæ à mer. </s>
  <s xml:id="echoid-s12052" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12053" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12054" xml:space="preserve">per quæ aſcendentia ſigna <lb/>tranſibunt: </s>
  <s xml:id="echoid-s12055" xml:space="preserve">quod eodem modo demonſtrabitur. </s>
  <s xml:id="echoid-s12056" xml:space="preserve">Itaque ſi puncta reſpondentia in linea meridia-<lb/>na, &amp; </s>
  <s xml:id="echoid-s12057" xml:space="preserve">in linea horæ ſextæ à mer. </s>
  <s xml:id="echoid-s12058" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12059" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12060" xml:space="preserve">per lineas rectas copulentur, habebuntur ſigna aſcen <lb/>
<anchor type="note" xlink:label="note-0203-05a" xlink:href="note-0203-05"/>
dentia, vt prius. </s>
  <s xml:id="echoid-s12061" xml:space="preserve">Hic autem modus ſignorum aſcendentium deſcribendorum commodior vide-<lb/>tur, &amp; </s>
  <s xml:id="echoid-s12062" xml:space="preserve">certior, quàm præcedens, quia non indiget arcubus tropicorum, in quorum deſcriptione fa-<lb/>cile error committi poteſt, offertq́; </s>
  <s xml:id="echoid-s12063" xml:space="preserve">pro ſingulis ſignis bina puncta, vnum quidem in linea meri-<lb/>diana, alterum verò in linea horæ ſextæ à mer. </s>
  <s xml:id="echoid-s12064" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12065" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12066" xml:space="preserve">tanto ſpatio inter ſe diſtantia, vt facile <lb/>abſque errore lineæ ſignorum aſcendentium duci poſſint.</s>
  <s xml:id="echoid-s12067" xml:space="preserve"/>
</p>
<div xml:id="echoid-div646" type="float" level="2" n="2">
<note position="left" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0203-05" xlink:href="note-0203-05a" xml:space="preserve">Præfertur po-<lb/>ſterior hæc de-<lb/>ſcriptio priori.</note>
</div>
<p>
  <s xml:id="echoid-s12068" xml:space="preserve">IMMO ſi ex punctis in meridiana linea inuentis ducantur lineæ rectæ tangentes tropicos, vt <lb/>in coroll. </s>
  <s xml:id="echoid-s12069" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s12070" xml:space="preserve">37. </s>
  <s xml:id="echoid-s12071" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12072" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12073" xml:space="preserve">Apollonii docuimus, (quod quidem facile hic fiet, propterea quòd li-<lb/>
<anchor type="note" xlink:label="note-0203-06a" xlink:href="note-0203-06"/>
neæ ordinatim applicatæ ſunt ad diametrum perpendiculares) deſcripta erunt alio adhuc modo <lb/>ſigna aſcendentia.</s>
  <s xml:id="echoid-s12074" xml:space="preserve"/>
</p>
<div xml:id="echoid-div647" type="float" level="2" n="3">
<note position="left" xlink:label="note-0203-06" xlink:href="note-0203-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s12075" xml:space="preserve">VERVM cum docuerimus inuentionem punctorũ Eclipticæ in circulis horæ 12. </s>
  <s xml:id="echoid-s12076" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12077" xml:space="preserve">6. </s>
  <s xml:id="echoid-s12078" xml:space="preserve">à me-<lb/>ridie, vel media nocte exiſtentia, quis prohibet, quo minus doceamus, quo pacto puncta Eclipticæ <lb/>in aliarum etiam horarum circulis conſtituta, cum principia ſignorum oriuntur, inueniri poſſint, <lb/>præſertim cum illorum beneficio aſcendentia ſigna in quibuſdam horologiis deſcribantur com-<lb/>modiſſimè, non ſecus, ac proximè in horizontali horologio beneficio mediationum cœli, &amp; </s>
  <s xml:id="echoid-s12079" xml:space="preserve">pun-<lb/>ctorum Eclipticæ in circulo horæ 6. </s>
  <s xml:id="echoid-s12080" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s12081" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s12082" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s12083" xml:space="preserve">exiſtentium, eadem deſcripſimus? </s>
  <s xml:id="echoid-s12084" xml:space="preserve">Regu-<lb/>la ergo generalis hæc erit. </s>
  <s xml:id="echoid-s12085" xml:space="preserve">Ex aſcenſione obliqua prin cipii cuiuſcunque ſigni, ſeu quod idem eſt, <lb/>
<anchor type="note" xlink:label="note-0203-07a" xlink:href="note-0203-07"/>
ex aſcenſione recta illius puncti Eclipticæ, quod illo ſigno aſcendente in circulo horæ ſextæ ante <lb/>
<anchor type="note" xlink:label="note-0203-08a" xlink:href="note-0203-08"/>
meridiem reperitur, auferantur tot gradus Aequatoris, quot inter circulum horæ ſextæ ante meri-<lb/>diem, &amp; </s>
  <s xml:id="echoid-s12086" xml:space="preserve">circulum horæ propoſitæ interiiciuntur, numerando dictos gradus (initio facto à circu-<lb/>lo horæ 6.) </s>
  <s xml:id="echoid-s12087" xml:space="preserve">ab ortu in occaſum, nempe contra ſucceſſionem ſignorum, adiecto prius integro cir-<lb/>culo, ſi detractio fieri nequit. </s>
  <s xml:id="echoid-s12088" xml:space="preserve">Numerus enim, qui relinquitur, erit aſcenſio recta puncti illius Ecli <lb/>pticę, quod oriente principio ſigni propoſiti in circulo datæ horæ reperitur ſupra Horizontem. <lb/></s>
  <s xml:id="echoid-s12089" xml:space="preserve">Quare ex tabula aſcenſionum rectarum punctum illud notum euadet, atque adeò &amp; </s>
  <s xml:id="echoid-s12090" xml:space="preserve">punctum op-<lb/>poſitum in eodem circulo horæ propoſitæ ſub Horizonte exiſtens cognitum erit. </s>
  <s xml:id="echoid-s12091" xml:space="preserve">Demonſtratio <lb/>huius non differt ab ea, quam nuper confecimus ad inueniendam cœli mediationem, ſi loco qua-<lb/>drantis Aequatoris inter orientem, &amp; </s>
  <s xml:id="echoid-s12092" xml:space="preserve">meridiem, ſumatur arcus Æquatoris inter horam ſextam, <lb/>ſeu orientem, &amp; </s>
  <s xml:id="echoid-s12093" xml:space="preserve">horam oblatam ſupra Horizontem, procedendo ab ortu in occaſum; </s>
  <s xml:id="echoid-s12094" xml:space="preserve">vt liquido <lb/>conſtat, ſi rectè circuli in ſphæra concipiantur. </s>
  <s xml:id="echoid-s12095" xml:space="preserve">Perſpicuum autem eſt, has horas ſupra Horizon-
<pb o="184" file="0204" n="204" rhead="GNOMONICES"/>
tem, puta ſeptimam, octauam, nonam, decimam, &amp; </s>
  <s xml:id="echoid-s12096" xml:space="preserve">vndecimam, eſſe ante meridiem, has verò, nem <lb/>pe primam, ſecundam, tertiam, quartam, &amp; </s>
  <s xml:id="echoid-s12097" xml:space="preserve">quintam poſt meridiem. </s>
  <s xml:id="echoid-s12098" xml:space="preserve">Puncta enim in circulis iſta-<lb/>rum horarum exiſtentia tantum inquirimus. </s>
  <s xml:id="echoid-s12099" xml:space="preserve">Nam in horis oppoſitis conſtituuntur puncta il-<lb/>lis oppoſita.</s>
  <s xml:id="echoid-s12100" xml:space="preserve"/>
</p>
<div xml:id="echoid-div648" type="float" level="2" n="4">
<note position="right" xlink:label="note-0203-07" xlink:href="note-0203-07a" xml:space="preserve">Quomodo in-<lb/>quirantur pun-<lb/>cta Eclipticæ in <lb/>quouis circulo <lb/>horario à mer-<lb/>vel med. noc. cõ <lb/>ſtituta, cum ini-<lb/>tia ſignorum <lb/>oriuntur.</note>
<note position="left" xlink:label="note-0203-08" xlink:href="note-0203-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s12101" xml:space="preserve">EXEMPLVM. </s>
  <s xml:id="echoid-s12102" xml:space="preserve">Sit propoſitum inuenire punctum Eclipticæ in circulo horæ primæ poſt <lb/>
<anchor type="note" xlink:label="note-0204-01a" xlink:href="note-0204-01"/>
meridiem exiſtens, aſcendente principio ♋. </s>
  <s xml:id="echoid-s12103" xml:space="preserve">Arcus Aequatoris inter circulos horæ ſextæ ante me <lb/>ridiem, &amp; </s>
  <s xml:id="echoid-s12104" xml:space="preserve">primæ poſt meridiem, continet horas 7. </s>
  <s xml:id="echoid-s12105" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s12106" xml:space="preserve">105. </s>
  <s xml:id="echoid-s12107" xml:space="preserve">cum cuilibet horæ conue-<lb/>niant grad. </s>
  <s xml:id="echoid-s12108" xml:space="preserve">15. </s>
  <s xml:id="echoid-s12109" xml:space="preserve">Aſcenſio obliqua principij ♋, eſt grad. </s>
  <s xml:id="echoid-s12110" xml:space="preserve">66, Min. </s>
  <s xml:id="echoid-s12111" xml:space="preserve">57. </s>
  <s xml:id="echoid-s12112" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s12113" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12114" xml:space="preserve">Cui <lb/>ſi integer circulus addatur, fient grad. </s>
  <s xml:id="echoid-s12115" xml:space="preserve">426. </s>
  <s xml:id="echoid-s12116" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12117" xml:space="preserve">57. </s>
  <s xml:id="echoid-s12118" xml:space="preserve">à quibus ſi detrahantur grad. </s>
  <s xml:id="echoid-s12119" xml:space="preserve">105. </s>
  <s xml:id="echoid-s12120" xml:space="preserve">qui inter <lb/>circulos horæ 6. </s>
  <s xml:id="echoid-s12121" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12122" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12123" xml:space="preserve">interiecti ſunt, reliqui erunt grad, 321. </s>
  <s xml:id="echoid-s12124" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12125" xml:space="preserve">57. </s>
  <s xml:id="echoid-s12126" xml:space="preserve">pro aſcenſione recta puncti <lb/>
<anchor type="note" xlink:label="note-0204-02a" xlink:href="note-0204-02"/>
illius Eclipticæ, quod tunc circulum horæ 1. </s>
  <s xml:id="echoid-s12127" xml:space="preserve">poſt meridiem occupat. </s>
  <s xml:id="echoid-s12128" xml:space="preserve">Cuiaſcenſioni reſpondet in <lb/>tabula aſcenſionum rectarum (habita ratione partis proportionalis) gradus 19. </s>
  <s xml:id="echoid-s12129" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12130" xml:space="preserve">31. </s>
  <s xml:id="echoid-s12131" xml:space="preserve">♒, ferè. <lb/></s>
  <s xml:id="echoid-s12132" xml:space="preserve">Hoc igitur punctum Eclipticę, cum principium ♋, oritur, exiſtet in circulo horæ 1. </s>
  <s xml:id="echoid-s12133" xml:space="preserve">poſt meridiẽ, <lb/>punctum autem oppoſitum, hoc eſt, gradus 19. </s>
  <s xml:id="echoid-s12134" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12135" xml:space="preserve">31. </s>
  <s xml:id="echoid-s12136" xml:space="preserve">♌, in eodem circulo poſt mediam no-<lb/>ctem. </s>
  <s xml:id="echoid-s12137" xml:space="preserve">Hoc<unsure/> artificio conſtructæ ſunt ſequentes quatuor tabellæ continentes puncta Eclipticę in cir <lb/>culis hor. </s>
  <s xml:id="echoid-s12138" xml:space="preserve">11. </s>
  <s xml:id="echoid-s12139" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12140" xml:space="preserve">7. </s>
  <s xml:id="echoid-s12141" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12142" xml:space="preserve">5. </s>
  <s xml:id="echoid-s12143" xml:space="preserve">collocata, cum principia ſignorũ oriuntur, vnà cum declinationibus pun-<lb/>ctorum inuentorum. </s>
  <s xml:id="echoid-s12144" xml:space="preserve">He enim maxime conducent deſcriptionibus ſignorum aſcendentium in <lb/>vtroque horologio meridiano, &amp; </s>
  <s xml:id="echoid-s12145" xml:space="preserve">polari, vt ſuo loco docebimus. </s>
  <s xml:id="echoid-s12146" xml:space="preserve">Itaque ſigna Zodiaci aſcendentia <lb/>in eodem horizontali horologio deſcripſimus. </s>
  <s xml:id="echoid-s12147" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s12148" xml:space="preserve"/>
</p>
<div xml:id="echoid-div649" type="float" level="2" n="5">
<note position="left" xlink:label="note-0204-01" xlink:href="note-0204-01a" xml:space="preserve">Exemplum.</note>
<note position="left" xlink:label="note-0204-02" xlink:href="note-0204-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div651" type="section" level="1" n="168">
<head xml:id="echoid-head171" xml:space="preserve">VIII. Puncta Eclipticæ in circulo horę 11. exiſtentia, eorumq́; declinationes, <lb/>cum principia 12. ſignorum Zodiaci oriuntur, <lb/>ad latitudinem grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Puncta in hora # 13. 48. ♑. # 0. 9. ♒. # 21. 3. ♒. # 21. 6. ♓. # 11. antemerid. <lb/>Puncta in hora # 13. 48. ♋. # 0. 9. ♌. # 21. 3. ♌. # 21. 6. ♍. # 11. pomerid. <lb/>
Declina- # 22. 47. # 20. 10. # 14. 31. # 3. 32. # tiones
Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 29. 57. ♈. # 8. 19. ♊ # 13. 48. ♋. # 21. 3. ♌. # 11. antemerid.
Puncta in hora # 29. 57. ♎. # 8. 19. ♐. # 13. 48. ♑. # 21. 3. ♒. # 11. pomerid.
Declina- # 11. 29. # 21. 45. # 22. 47. # 14. 31. # tiones
Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 2. 21. ♎. # 10. 28. ♏. # 8. 19. ♐. # 27. 52. ♐. # 11. antemerid.
Puncta in hora # 2. 21. ♈. # 10. 28. ♉. # 8. 19. ♊. # 27. 52. ♊. # 11. pomerid.
Declina- # 0. 56. # 15. 0. # 21 45. # 23. 29. # tiones
###### IX. Puncta Eclipticę in circulo horæ 1. exiſtentia, eorumq́ue declinationes, \\ principiis 12. ſignorum aſcendentibus, ad \\ latitudinem grad. 42.
Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 16. 12. ♊. # 2. 8. ♋. # 21. 41. ♋. # 19. 32. ♌. # 1. antemerid.
Puncta in hora # 16. 12. ♐ # 2. 8. ♑. # 21. 41. ♑. # 19. 32. ♒. # 1. pomeridiana
Declina- # 22. 47. # 23. 29. # 21. 45. # 15. 0. # tiones
</note>
<pb o="185" file="0205" n="205" rhead="LIBER SECVNDVS."/>
<note position="right" xml:space="preserve"> <lb/>Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>Puncta in hora # 27. 39. ♍. # 8. 57. ♏. # 16. 12. ♐. # 21. 41. ♑. # 1. antemerid. <lb/>Puncta in hora # 27. 39. ♓. # 8. 57. ♉. # 16. 12. ♊. # 21. 41. ♋. # 1. pomeridiana. <lb/>Declina- # 0. 56. # 14. 31. # 22. 47. # 21. 45. # tiones <lb/>Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia <lb/>Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta <lb/>
Puncta in hora # 0. 3. ♓. # 8. 47. ♈. # 8. 57. ♉. # 0. 8. ♊. # 1. antemerid.
Puncta in hora # 0. 3. ♍. # 8. 47. ♎. # 8. 57. ♏. # 0. 8. ♐ # 1. pomeridiana.
Declina- # 11. 29. # 3. 30. # 14. 31. # 20. 14. # tiones
###### X. Puncta Eclipticæ in circulo horæ 7. exiſtentia, eorumq́; declinationes, cum principia \\ 12. ſignorum in Zodiaci oriuntur, ad latitudinem grad. 42.
Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 13. 42. ♓. # 2. 34. ♈. # 25. 19. ♈. # 24. 20. ♉. # 7. antemerid.
Puncta in hora # 13. 42. ♍. # 2. 34. ♎. # 25. 19. ♎. # 24. 20. ♏. # 7. pomerid.
Declina- # 6. 25. # 1. 2. # 9. 49. # 18. 54. # tiones
Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 28. 3. ♊. # 4. 12. ♌. # 13. 42. ♍. # 25. 19. ♎. # 7. antemerid.
Puncta in hora # 28. 3. ♐. # 4. 12. ♒. # 13. 42. ♓. # 25. 19. ♈. # 7. pomerid.
Declina- # 23. 29. # 19. 15. # 6. 25. # 9. 49. # tiones
Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 4. 9. ♐. # 7. 23. ♑. # 4. 12. ♒. # 25. 22. ♒. # 7. antemerid.
Puncta in hora # 4. 9. ♊. # 7. 23. ♋. # 4. 12. ♌. # 25. 22. ♌. # 7. pomerid.
Declina- # 21. 2. # 23. 18. # 19. 15. # 13. 6. # tiones
###### XI. Puncta Eclipticæ in circulo horæ 5. conſtituta, eorumq́; declinationes, cum principia \\ ſignorum Zodiaci oriuntur, ad latitudinem grad. 42.
Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 16. 18. ♈. # 4. 38. ♉. # 25. 47. ♉. # 22. 37. ♊. # 5. antemerid.
Puncta in hora # 16. 18. ♎ # 4. 38. ♏. # 25. 47. ♏. # 22 37. ♐. # 5. pomeridiana
Declina- # 6. 25. # 13. 6. # 19. 15. # 22. 18. # tiones
Signa aſcen- # ♌ # ♍ # ♎ # ♏ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 25. 51. ♋. # 4. 41. ♍. # 16. 18. ♎. # 25. 47. ♏. # 5. antemerid.
Puncta in hora # 25. 51. ♑. # 4. 41. ♓. # 16. 18. ♈. # 25. 47. ♉. # 5. pomerid.
Declina- # 21. 2. # 9. 49. # 6. 25. # 19. 15. # tiones.
Signa aſcen- # ♐ # ♑ # ♒ # ♓ # dentia
Gradus &amp; # G. M. # G. M. # G. M. # G. M. # Minuta
Puncta in hora # 1. 57. ♑. # 5. 40. ♒. # 4. 41. ♓. # 27. 26. ♓. # 5. antemerid.
Puncta in hora # 1. 57. ♋. # 5. 40. ♌. # 4. 41. ♍. # 27. 26. ♍. # 5. pomerid.
Declina- # 23. 29. # 18. 54. # 9. 49. # 1. 2. # tiones
</note>
<pb o="186" file="0206" n="206" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div652" type="section" level="1" n="169">
<head xml:id="echoid-head172" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s12149" xml:space="preserve">ALIOMODO ſigna aſcendentia e@ <lb/>
<anchor type="note" xlink:label="note-0206-01a" xlink:href="note-0206-01"/>
<anchor type="figure" xlink:label="fig-0206-01a" xlink:href="fig-0206-01"/>
Andrea Schonero deſcribemus hac ratione. <lb/></s>
  <s xml:id="echoid-s12150" xml:space="preserve">Deſcribatur circulus A B C D, cuius cen-<lb/>trum E, &amp; </s>
  <s xml:id="echoid-s12151" xml:space="preserve">duæ diametri ad rectos angu-<lb/>los ſe ſecantes A C, B D. </s>
  <s xml:id="echoid-s12152" xml:space="preserve">Sumantur de-<lb/>inde arcus A F, C G, maximæ declina-<lb/>tioni Solis æquales, &amp; </s>
  <s xml:id="echoid-s12153" xml:space="preserve">per F, G, ex B, <lb/>rectæ emiſſæ ſecent rectam AC, productam <lb/>
<anchor type="note" xlink:label="note-0206-02a" xlink:href="note-0206-02"/>
in H, I. </s>
  <s xml:id="echoid-s12154" xml:space="preserve">Sumantur rurſus arcus D K, B L, <lb/>declinationi maximæ Solis duplicatæ æqua-<lb/>les, &amp; </s>
  <s xml:id="echoid-s12155" xml:space="preserve">per K, L, rectæ ex B, eductæ ſecent <lb/>eandem A C, productam in M, N. </s>
  <s xml:id="echoid-s12156" xml:space="preserve">Atque <lb/>ex M, centro, interuallo M H, vel M I, <lb/>(Nam recta H I, in M, bifariam diuidi-<lb/>tur) circulus deſcribatur H B I D, qui per <lb/>B, D, tranſibit. </s>
  <s xml:id="echoid-s12157" xml:space="preserve">I am diuiſo circulo A B-<lb/>C D, in partes 12. </s>
  <s xml:id="echoid-s12158" xml:space="preserve">æquales, iungantur quæ-<lb/>libet bina puncta à D, vel B, æqualiter re-<lb/>
<anchor type="note" xlink:label="note-0206-03a" xlink:href="note-0206-03"/>
mota lineis rectis ſecantibus rectam B D, <lb/>in punctis, per quæ ſi ex N, rectæ ducantur <lb/>ſecantes circulum H B I D, in punctis, &amp; </s>
  <s xml:id="echoid-s12159" xml:space="preserve"><lb/>per hæc rurſus rectæ ex E, emittantur, erũt <lb/>hæ lineæ ſignorum, ita E D, ſit ♈; </s>
  <s xml:id="echoid-s12160" xml:space="preserve">E C, <lb/>♋; </s>
  <s xml:id="echoid-s12161" xml:space="preserve">E B, ♎ E A, ♑; </s>
  <s xml:id="echoid-s12162" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12163" xml:space="preserve">c. </s>
  <s xml:id="echoid-s12164" xml:space="preserve">Per hanc <lb/>igitur figuram inueniemus intropicis ♋, &amp; </s>
  <s xml:id="echoid-s12165" xml:space="preserve"><lb/>♑, puncta, per quæ lineæ ſignorum aſcen <lb/>dentium duci debent, vt docebimus.</s>
  <s xml:id="echoid-s12166" xml:space="preserve"/>
</p>
<div xml:id="echoid-div652" type="float" level="2" n="1">
<note position="left" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">Conſtructi@ <lb/>duatum figu-<lb/>rarum ex An-<lb/>drea Schonero@ <lb/>per quas ſigna<unsure/> <lb/>aſcendentia de<unsure/>-<lb/>ſcribuntur.<unsure/></note>
  <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a">
    <image file="0206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0206-01"/>
  </figure>
<note position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s12167" xml:space="preserve">DESCRIBATVR rurſum circulus <lb/>
<anchor type="note" xlink:label="note-0206-04a" xlink:href="note-0206-04"/>
A B C D, cuius centrum E, &amp; </s>
  <s xml:id="echoid-s12168" xml:space="preserve">duæ diame-<lb/>tri ſeſe ad angulos rectos ſecãtes A C, B D, <lb/>
<anchor type="figure" xlink:label="fig-0206-02a" xlink:href="fig-0206-02"/>
<anchor type="note" xlink:label="note-0206-05a" xlink:href="note-0206-05"/>
<anchor type="note" xlink:label="note-0206-06a" xlink:href="note-0206-06"/>
<pb o="187" file="0207" n="207" rhead="LIBER SECVNDVS."/>
vt in ſecunda figura apparet. </s>
  <s xml:id="echoid-s12169" xml:space="preserve">Sumantur autem arcus A F, C G, grad. </s>
  <s xml:id="echoid-s12170" xml:space="preserve">25 {3/4}. </s>
  <s xml:id="echoid-s12171" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12172" xml:space="preserve">puncta F, G, con-<lb/>nectantur recta linea ipſam B D, ſecante in H, puncto, è quo, vt centro, ar cus deſcribatur I K, ſit{q́ue} ar-<lb/>cus I K, æqualis altitudini poli; </s>
  <s xml:id="echoid-s12173" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12174" xml:space="preserve">ex H, per K, recta ducatur ſecans A C, in L, puncto, e quo circu-<lb/>lus deſcriptus diuidatur in partes 12. </s>
  <s xml:id="echoid-s12175" xml:space="preserve">æquales, initio facto à recta A C, &amp; </s>
  <s xml:id="echoid-s12176" xml:space="preserve">per diuiſionum puncta, ac <lb/>centrum L, rectæ ducantur ſecantes circulum A B C D, in 12. </s>
  <s xml:id="echoid-s12177" xml:space="preserve">punctis, ad quæ ex E, rectæ emiſſæ da-<lb/>bunt initia ſignorum. </s>
  <s xml:id="echoid-s12178" xml:space="preserve">Nam C, erit initium ♈; </s>
  <s xml:id="echoid-s12179" xml:space="preserve">primum deinde punctum verſus G, initium ♉; </s>
  <s xml:id="echoid-s12180" xml:space="preserve">ſe-<lb/>quens, initium ♊, &amp; </s>
  <s xml:id="echoid-s12181" xml:space="preserve">c. </s>
  <s xml:id="echoid-s12182" xml:space="preserve">Per hanc autem figuram inueſtigabimus in æquinoctiali linea puncta, per quæ <lb/>lineæ ſignorum aſcendentium debent duci, vt mox trademus. </s>
  <s xml:id="echoid-s12183" xml:space="preserve">Cæterum non eſt neceſſe hic, vt lineæ ſu-<lb/>pra rectam B D, reſpondeant lineis infra eandem B D, ſecundum lineam rectam, quemadmodum in ſu-<lb/>periori figura; </s>
  <s xml:id="echoid-s12184" xml:space="preserve">licet aliquando reſpondeant, vt in hac figura ad latitudinem grad. </s>
  <s xml:id="echoid-s12185" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12186" xml:space="preserve">conſtructa ac-<lb/>
<anchor type="note" xlink:label="note-0207-01a" xlink:href="note-0207-01"/>
cidit in lineis ♍, &amp; </s>
  <s xml:id="echoid-s12187" xml:space="preserve">♏. </s>
  <s xml:id="echoid-s12188" xml:space="preserve">Hæ enim rectas lineas conſtituunt cum lineis ♒, &amp; </s>
  <s xml:id="echoid-s12189" xml:space="preserve">♊; </s>
  <s xml:id="echoid-s12190" xml:space="preserve">ſunt tamen om-<lb/>nes aliæ vltra centrum producendæ, &amp; </s>
  <s xml:id="echoid-s12191" xml:space="preserve">productæ punctis diſtinguendæ, ne cum alĳs confundantur, at-<lb/>que eadem illis ſigna aſcribenda. </s>
  <s xml:id="echoid-s12192" xml:space="preserve">Vnde fit vt linea ♒, habeat etiam ſignum ♍; </s>
  <s xml:id="echoid-s12193" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12194" xml:space="preserve">linea ♊, ſignum <lb/>♏; </s>
  <s xml:id="echoid-s12195" xml:space="preserve">ſimiliter linea ♍, ſignum ♒; </s>
  <s xml:id="echoid-s12196" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12197" xml:space="preserve">linea ♏, ſignum ♊; </s>
  <s xml:id="echoid-s12198" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12199" xml:space="preserve">linea ♈, ſignum ♎; </s>
  <s xml:id="echoid-s12200" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12201" xml:space="preserve">linea ♎, <lb/>ſignum ♈; </s>
  <s xml:id="echoid-s12202" xml:space="preserve">atque ita quælibet linea habebit ſuum proprium ſignum ex deſcriptione, &amp; </s>
  <s xml:id="echoid-s12203" xml:space="preserve">adhuc ſignum il-<lb/>lius lineę, quæ producta rectam cum ea lineam conſtituit. </s>
  <s xml:id="echoid-s12204" xml:space="preserve">Quæres, quoniam ad deſcriptionem ſignorum <lb/>aſcendentium magnam affert vtilitatem, diligenter notanda eſt.</s>
  <s xml:id="echoid-s12205" xml:space="preserve"/>
</p>
<div xml:id="echoid-div653" type="float" level="2" n="2">
<note position="left" xlink:label="note-0206-04" xlink:href="note-0206-04a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0206-02" xlink:href="fig-0206-02a">
    <image file="0206-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0206-02"/>
  </figure>
<note position="left" xlink:label="note-0206-05" xlink:href="note-0206-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0206-06" xlink:href="note-0206-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s12206" xml:space="preserve">IT AQVE in recta linea E D, prioris figuræ ſumatur recta E O, æqualis meridianæ lineæ E I, <lb/>
<anchor type="note" xlink:label="note-0207-02a" xlink:href="note-0207-02"/>
horologĳ interceptæ inter E, centrum Aequatoris, &amp; </s>
  <s xml:id="echoid-s12207" xml:space="preserve">lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s12208" xml:space="preserve">per O, ipſi A C, pa-<lb/>rallela agatur ſecans lineas ſignorum ex E, emiſſas in P, Q, R, S; </s>
  <s xml:id="echoid-s12209" xml:space="preserve">adeò vt poſito centro E, huius <lb/>
<anchor type="note" xlink:label="note-0207-03a" xlink:href="note-0207-03"/>
figurę in centro E, Aequatoris horologĳ, &amp; </s>
  <s xml:id="echoid-s12210" xml:space="preserve">puncto O, in puncto I, parallela per O@, ducta congruat li-<lb/>neæ æquinoctiali. </s>
  <s xml:id="echoid-s12211" xml:space="preserve">Si igitur hæc puncta ex O, ſumpta in lineam æquinoctialem horologĳ ab I, hincinde <lb/>transferantur, per quæ ipſi lineæ meridianæ ducantur parallelæ, ſecabuntur tropici in punctis, per quę <lb/>lineæ ſignorum aſcendentium tranſeunt. </s>
  <s xml:id="echoid-s12212" xml:space="preserve">Nam per puncta tropici ♑, incedunt lineę ſignorum ſemi-<lb/>circuli A D C, nempe ♒, &amp; </s>
  <s xml:id="echoid-s12213" xml:space="preserve">♓, in horis ante meridiem, &amp; </s>
  <s xml:id="echoid-s12214" xml:space="preserve">♈, in ipſa hora meridiei, at ♉, &amp; </s>
  <s xml:id="echoid-s12215" xml:space="preserve">♊, in <lb/>horis poſt meridiem: </s>
  <s xml:id="echoid-s12216" xml:space="preserve">per puncta vero tropici ♋, lineæ ſignorum reliquorum his oppoſitorum, vt ♏, &amp; </s>
  <s xml:id="echoid-s12217" xml:space="preserve"><lb/>♐, in horis post meridiem, &amp; </s>
  <s xml:id="echoid-s12218" xml:space="preserve">♎, in ipſa hora meridiei, at ♌, &amp; </s>
  <s xml:id="echoid-s12219" xml:space="preserve">♍, in horis ante meridiem.</s>
  <s xml:id="echoid-s12220" xml:space="preserve"/>
</p>
<div xml:id="echoid-div654" type="float" level="2" n="3">
<note position="right" xlink:label="note-0207-02" xlink:href="note-0207-02a" xml:space="preserve">Deſcriptio aſcẽ <lb/>dentium ſigno-<lb/>rum in horolo <lb/>gio per proxi-<lb/>mas duas figu-<lb/>@as, ſ<unsure/>ecundum <lb/>praxim Andre@ <lb/>Schoneri.</note>
<note position="left" xlink:label="note-0207-03" xlink:href="note-0207-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s12221" xml:space="preserve">RVRSVS in recta E D, poſterioris figuræ ſumatur E M, eidem meridianæ E I, in horologio in-<lb/>terceptæ inter E, centrum Aequatoris, &amp; </s>
  <s xml:id="echoid-s12222" xml:space="preserve">lineam æquinoctialem, æqualis, &amp; </s>
  <s xml:id="echoid-s12223" xml:space="preserve">per M, ipſi A C, paralle-<lb/>la agatur; </s>
  <s xml:id="echoid-s12224" xml:space="preserve">adeo vt rurſus poſito centro E, huius figuræ in centro E, Aequatoris horologĳ, &amp; </s>
  <s xml:id="echoid-s12225" xml:space="preserve">puncto M, <lb/>
<anchor type="note" xlink:label="note-0207-04a" xlink:href="note-0207-04"/>
in puncto I, parallela per M, ducta æquinoctiali lineæ congruat. </s>
  <s xml:id="echoid-s12226" xml:space="preserve">ſecabit en<unsure/>im hæc parallela lineas ſigno-<lb/>rum ex E, emiſſas in punctis, quæ accepta ex M, &amp; </s>
  <s xml:id="echoid-s12227" xml:space="preserve">in lineam æquinoctialem horologĳ translata ex I, da-<lb/>bunt puncta, per quę lineæ aſcendentium ſignorum in linea æquinoctiali duci debent: </s>
  <s xml:id="echoid-s12228" xml:space="preserve">hac tamen lege, vt <lb/>puncta ſignorum ♉, ♊, ♋, ♏, &amp; </s>
  <s xml:id="echoid-s12229" xml:space="preserve">♐, transferantur in horas ante meridiem, puncta verò reliquorum <lb/>ſignorum in horas pomeridianas, eo nimirum ordine, quem habent ſigna in parallela per M, ducta, ſi ęqui <lb/>noctiali lineę horologĳ ſuperponeretur, ita vt centrum E, caderet ſurſum verſus, (quod contingeret, <lb/>ſi E, centrum Aequatoris in horologio acceptum fuiſſet verſus punctum H) &amp; </s>
  <s xml:id="echoid-s12230" xml:space="preserve">linea ♉, vel punctum A, <lb/>huius figuræ, ad partem dextram horologĳ, &amp; </s>
  <s xml:id="echoid-s12231" xml:space="preserve">c.</s>
  <s xml:id="echoid-s12232" xml:space="preserve"/>
</p>
<div xml:id="echoid-div655" type="float" level="2" n="4">
<note position="left" xlink:label="note-0207-04" xlink:href="note-0207-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s12233" xml:space="preserve">IAM ſi hæc puncta æquinoctialis lineæ cum punctis reſpondentibus in tropicis per lineas rectas <lb/>coniungantur, habebuntur lineæ ſignorum aſcendentium, vt prius. </s>
  <s xml:id="echoid-s12234" xml:space="preserve">Lineæ autem ♈, ♎, ♋, &amp; </s>
  <s xml:id="echoid-s12235" xml:space="preserve">♑, ducen-<lb/>
<anchor type="note" xlink:label="note-0207-05a" xlink:href="note-0207-05"/>
tur, vt ante diximus. </s>
  <s xml:id="echoid-s12236" xml:space="preserve">Huius operationis demonſtratio nulla adducitur ab Andrea Schonero, ſed ſola <lb/>praxi contentus, quæ ſine dubio pulcherrima eſt, eam ſcriptis mandauit.</s>
  <s xml:id="echoid-s12237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div656" type="float" level="2" n="5">
<note position="left" xlink:label="note-0207-05" xlink:href="note-0207-05a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s12238" xml:space="preserve">VTILITATEM porro habent ſigna aſcendentia in horologio deſcripta in ſignem valde, ac il-<lb/>
<anchor type="note" xlink:label="note-0207-06a" xlink:href="note-0207-06"/>
luſtrem: </s>
  <s xml:id="echoid-s12239" xml:space="preserve">quippe cum exipſis quolibet momento temporis totum propemodum cœli ſitum exploremus. <lb/></s>
  <s xml:id="echoid-s12240" xml:space="preserve">Nam ex vmbra gnomonis cadente in lineam aliquam ſignorum aſcendentium, confestim cognoſcimus, <lb/>quodnam ſignum tunc temporis ſupra Horizontem emergat, ac proinde, quodnam occidat, cùm neceſſe <lb/>ſit, oppoſitum tunc ſignum occidere. </s>
  <s xml:id="echoid-s12241" xml:space="preserve">Ex ſigno rurſus aſcendente facile in cognitionem ſigni, quod cœlum <lb/>tunc mediat, atque adeò &amp; </s>
  <s xml:id="echoid-s12242" xml:space="preserve">oppoſiti, quod angulum terræ oecupat, perueniemus ex ĳs, quæ paulo ante in <lb/>hac propoſ. </s>
  <s xml:id="echoid-s12243" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s12244" xml:space="preserve">Quod vt facilius aſſequamur, deſcribendæ erunt duæ tabellæ, vna ad ſiniſtram <lb/>partem horologĳ, &amp; </s>
  <s xml:id="echoid-s12245" xml:space="preserve">ad dextram altera, in quarum priore contineantur hæc ſex ſigna aſcendentia ♈, ♉, <lb/>
<anchor type="note" xlink:label="note-0207-07a" xlink:href="note-0207-07"/>
♊, ♋, ♌, &amp; </s>
  <s xml:id="echoid-s12246" xml:space="preserve">♍, vna cum ſex ſignis oppoſitis, quæ tunc ſub Horizontem deſcendunt, &amp; </s>
  <s xml:id="echoid-s12247" xml:space="preserve">cum alĳs ſex, <lb/>quæin Meridiano ſupra Horizontem reperiuntur illo tempore, &amp; </s>
  <s xml:id="echoid-s12248" xml:space="preserve">denique cum ſex, quæ hiſce vltimis op-<lb/>ponuntur, &amp; </s>
  <s xml:id="echoid-s12249" xml:space="preserve">in Meridiano infra Horizontem exiſtunt: </s>
  <s xml:id="echoid-s12250" xml:space="preserve">In poſteriore verò alia ſex ſigna aſcendentia ♎, <lb/>♏, ♐, ♑, ♒, &amp; </s>
  <s xml:id="echoid-s12251" xml:space="preserve">♓, vnà cum deſcendentibus, cœlum mediantibus, atque in angulo terræ exiſtentibus <lb/>collocentur, cuiuſm<unsure/>odi ſunt ſequentes duæ tabellæ ad latitudinem grad. </s>
  <s xml:id="echoid-s12252" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12253" xml:space="preserve">fabricatæ.</s>
  <s xml:id="echoid-s12254" xml:space="preserve"/>
</p>
<div xml:id="echoid-div657" type="float" level="2" n="6">
<note position="right" xlink:label="note-0207-06" xlink:href="note-0207-06a" xml:space="preserve">Per ſigna aſcẽ<unsure/>-<lb/>dentia in horo <lb/>logio deſcripta <lb/>exploratur ſitus <lb/>totius cœli quo <lb/>libet momento <lb/>temporis.</note>
<note position="left" xlink:label="note-0207-07" xlink:href="note-0207-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div659" type="section" level="1" n="170">
<head xml:id="echoid-head173" xml:space="preserve">SEQVVNTVR TABELLÆ.</head>
<pb o="188" file="0208" n="208" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Aſcen- \\ dentia. # Deſcen \\ dentia. # In medio \\ cœli. # In angulo \\ terrę. # Aſcen- \\ dentia. # Deſcen \\ dentia. # In medio \\ cœli. # In angulo \\ terræ. <lb/># # G. M. # G. M. # # # G. M. # G. M. <lb/>♈ # ♎ # o. o. ♑. # o. o. ♋. # ♎ # ♈ # o. o. ♋. # o. o. ♑. <lb/>♉ # ♏ # 15. 59. ♑. # 15. 59. ♋. # ♏ # ♉ # 6. 3. ♌. # 6. 3. ♒. <lb/>♊ # ♐ # 6. 3. ♒. # 6. 3. ♌. # ♐ # ♊ # 16. 1. ♍. # 16. 1. ♓. <lb/>♋ # ♑ # @. 6. ♓. # 5. 6. ♍. # ♑ # ♋ # 24. 54. ♎. # 24. 54. ♈. <lb/>♌ # ♒ # 13. 59. ♈. # 13. 59. ♎. # ♒ # ♌ # 23. 57. ♏. # 23. 57. ♉. <lb/>
♍ # ♓ # 23. 57. ♉. # 23. 57. ♏. # ♓ # ♍ # 14. 1. ♐. # 14. 1. ♊.
</note>
<p style="it">
  <s xml:id="echoid-s12255" xml:space="preserve">IT AQVE quotieſcunq; </s>
  <s xml:id="echoid-s12256" xml:space="preserve">ex vmbra gnomonis deprehendero v. </s>
  <s xml:id="echoid-s12257" xml:space="preserve">g. </s>
  <s xml:id="echoid-s12258" xml:space="preserve">aſcendere principiũ ♊, ſine vlla <lb/>mora intelligam, eodem momento temporis primum punctum ♐, deſcendere, in medio cæli exiſtere gr. </s>
  <s xml:id="echoid-s12259" xml:space="preserve">6. <lb/></s>
  <s xml:id="echoid-s12260" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12261" xml:space="preserve">3. </s>
  <s xml:id="echoid-s12262" xml:space="preserve">♒, &amp; </s>
  <s xml:id="echoid-s12263" xml:space="preserve">in angulo terræ cõſtitui gr. </s>
  <s xml:id="echoid-s12264" xml:space="preserve">6. </s>
  <s xml:id="echoid-s12265" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12266" xml:space="preserve">3. </s>
  <s xml:id="echoid-s12267" xml:space="preserve">♌, atq; </s>
  <s xml:id="echoid-s12268" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s12269" xml:space="preserve">Cognitis autẽ hoc modo quatuor <lb/>dictis punctis principalibus cæli, facile coniectura aſſequi cuiuis licebit, quibuſnam in partibus cæli cæte-<lb/>ra Zodiaci ſigna tunc poſita ſint, atq; </s>
  <s xml:id="echoid-s12270" xml:space="preserve">adeo ſi ſtellarum loca cognita fuerint in Zodiaco, vna cum earum <lb/>declinatione, vel latitudine, quænam ſtellæ in hac, vel in illa parte cæli exiſtant, etiamſi non cõpareant.</s>
  <s xml:id="echoid-s12271" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s12272" xml:space="preserve">CAETERVM quoniam ſex tantum ſigna in die artificiali quocunq; </s>
  <s xml:id="echoid-s12273" xml:space="preserve">oriuntur, fit vt ſex duntaxat <lb/>
<anchor type="note" xlink:label="note-0208-04a" xlink:href="note-0208-04"/>
lineæ ſignorum aſcendentium quolibet die propoſito monſtrent aſcendentia ſigna, lineæ nimirum illorum <lb/>ſex ſignorum, quæ inter diu oriuntur, quæ quidem computantur à loco Solis ſecundum ſucceſſionem ſigno-<lb/>rum: </s>
  <s xml:id="echoid-s12274" xml:space="preserve">quia Ecliptica ſolum illas poſitiones ſortitur eo die, quas lineæ illæ referunt, cũ reliqua ſigna inter-<lb/>diu tunc non oriantur. </s>
  <s xml:id="echoid-s12275" xml:space="preserve">Vnde licet vmbra ſtyli cadat in lineam alicuius ſigni, quod non continetur inter <lb/>
<anchor type="figure" xlink:label="fig-0208-01a" xlink:href="fig-0208-01"/>
ſex ſigna illo die orientia, non <lb/>tamen propterea illud tunc a-<lb/>ſcendere arbitrandum eſt, cum <lb/>nectota illa die poſſit oriri, nec <lb/>Ecliptica illum ſitum habere, <lb/>
<anchor type="note" xlink:label="note-0208-05a" xlink:href="note-0208-05"/>
quem linea illa exprimit. </s>
  <s xml:id="echoid-s12276" xml:space="preserve">Exem <lb/>plum. </s>
  <s xml:id="echoid-s12277" xml:space="preserve">Sole exiſtente in princi-<lb/>pio ♈, oriuntur interdiu hæc <lb/>tantum ſex ſigna ♈, ♉, ♊, <lb/>♋, ♌, &amp; </s>
  <s xml:id="echoid-s12278" xml:space="preserve">♍, occidente ver@ <lb/>Sole oritur principium ♎. </s>
  <s xml:id="echoid-s12279" xml:space="preserve">Q@@ <lb/>re tunc non aſcendent interdiu <lb/>ſupra Horizontem hæc ſex ſi-<lb/>gna, ♎, ♏, ♐, ♑, ♒, &amp; </s>
  <s xml:id="echoid-s12280" xml:space="preserve">♓, <lb/>quamuis vmbra gnomonis in il-<lb/>
<anchor type="note" xlink:label="note-0208-06a" xlink:href="note-0208-06"/>
lorum lineas cadat. </s>
  <s xml:id="echoid-s12281" xml:space="preserve">Eadem ra <lb/>tione Sole exiſtente circa me<unsure/>-<lb/>dium ♊, oriuntur in die hæc <lb/>dũtaxat ſex ſigna, reliqua pars <lb/>♊, ♋, ♌, ♍, ♎, ♏, &amp; </s>
  <s xml:id="echoid-s12282" xml:space="preserve">tan-<lb/>ta portio ♐, quãtam in ♊, pro-<lb/>prio motu Sol per ambulauit; <lb/></s>
  <s xml:id="echoid-s12283" xml:space="preserve">vt ſi Sol exiſtat in 18. </s>
  <s xml:id="echoid-s12284" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s12285" xml:space="preserve">♊, <lb/>orientur gr. </s>
  <s xml:id="echoid-s12286" xml:space="preserve">18. </s>
  <s xml:id="echoid-s12287" xml:space="preserve">♐. </s>
  <s xml:id="echoid-s12288" xml:space="preserve">Reliqua ve <lb/>ro ſex ſigna, nẽpe reliqui 12. </s>
  <s xml:id="echoid-s12289" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s12290" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0208-07a" xlink:href="note-0208-07"/>
♐, ♑, ♒, ♓, ♈, ♉, &amp; </s>
  <s xml:id="echoid-s12291" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s12292" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s12293" xml:space="preserve">♊, qui ante Solẽiam orti ſunt, <lb/>ſupra Horizontẽ illo die non e-<lb/>mergent; </s>
  <s xml:id="echoid-s12294" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12295" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s12296" xml:space="preserve">Quo-<lb/>libet ergo die propoſito, vt in-<lb/>telligamus, quænam ſigna exo-<lb/>riantur, &amp; </s>
  <s xml:id="echoid-s12297" xml:space="preserve">quæ non, ac proin-<lb/>de quaſnam lineas aſcerden-<lb/>tium ſignorum tunc obſeruare debeamus, inquirendum erit prius, vbi Sol verſetur in Zodiaco. </s>
  <s xml:id="echoid-s12298" xml:space="preserve">Nam <lb/>toto illo die obſeruanda ſolum erit vmbra ſtyli cadens in lineas ſex ſignorum, quæ oriri poſſunt ſu-<lb/>pra Horizontem. </s>
  <s xml:id="echoid-s12299" xml:space="preserve">Immo contingere ſolet, vt in eadem die bis vmbra ſtyli in eandem cadat lineam:</s>
  <s xml:id="echoid-s12300" xml:space="preserve">
<pb o="189" file="0209" n="209" rhead="LIBER SECVNDVS."/>
vt patet in linea ♈, &amp; </s>
  <s xml:id="echoid-s12301" xml:space="preserve">in linea ♓, quando Sol in Ecliptica non multum abcſt à principio ♑. </s>
  <s xml:id="echoid-s12302" xml:space="preserve">Vn-<lb/>de vt omnis occaſio errandi tollatur, deſcribenda erunt duo horologia ſignorũ aſcendentium, ita vt nullo <lb/>modo ſe mutuo interſecent ſignorum lineæ, veluti in duabus hic appoſitis figuris apparet. </s>
  <s xml:id="echoid-s12303" xml:space="preserve">Quarum prior <lb/>indicat ſigna aſcendentia, quàmdiu Sol deſcendentem ſemicirculum Eclipticæ à ♋, per ♎, vſque ad ♑, <lb/>percurrit; </s>
  <s xml:id="echoid-s12304" xml:space="preserve">voſterior verò, dum Sol in altero Eclipticæ ſemicir culo à ♑, per ♈, vſq; </s>
  <s xml:id="echoid-s12305" xml:space="preserve">ad ♋, qui aſcendens <lb/>dicitur, verſatur. </s>
  <s xml:id="echoid-s12306" xml:space="preserve">Ita enim fiet, vt vmbra gnomonis cadente in lineam alicuius ſigni illius figuræ, quæ illi <lb/>Eclipticæ ſemicirculo accommodatur, in quo Sol exiſtit, illud tunc ſignum neceſſari<unsure/>o oriatur ſine vlla ex-<lb/>ceptione; </s>
  <s xml:id="echoid-s12307" xml:space="preserve">dummodo obſeruatio ſiat eo anni tempore, quo Sol dictum Fclipticæ ſemicir culum percurrit.</s>
  <s xml:id="echoid-s12308" xml:space="preserve"/>
</p>
<div xml:id="echoid-div659" type="float" level="2" n="1">
<note position="left" xlink:label="note-0208-04" xlink:href="note-0208-04a" xml:space="preserve">Quolibet die <lb/>obſeruanda eſt, <lb/>vmbra gnomo-<lb/>nis in ſex dun-<lb/>taxat lineis il-<lb/>lorum ſex ſigno <lb/>rum, quæ illo <lb/>die oriuntur ſu <lb/>pra Horizontẽ.</note>
  <figure xlink:label="fig-0208-01" xlink:href="fig-0208-01a">
    <image file="0208-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0208-01"/>
  </figure>
<note position="left" xlink:label="note-0208-05" xlink:href="note-0208-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0208-06" xlink:href="note-0208-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0208-07" xlink:href="note-0208-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s12309" xml:space="preserve">VT autem in huiuſmodi figuris lineæ aſcendentium ſignorum ſe non interſecent, curandum erit, ne vl <lb/>
<anchor type="note" xlink:label="note-0209-01a" xlink:href="note-0209-01"/>
la linearum tropicos tangentium integra deſcribatur, ſed vna tantum portio vſque ad tropicum ex vna <lb/>
<anchor type="note" xlink:label="note-0209-02a" xlink:href="note-0209-02"/>
parte in prima figura, &amp; </s>
  <s xml:id="echoid-s12310" xml:space="preserve">altera portio ex alia parte ad eundem vſq; </s>
  <s xml:id="echoid-s12311" xml:space="preserve">tropicum ducatur in ſecunda figu-<lb/>ra, vt in figuris dictis cernitur. </s>
  <s xml:id="echoid-s12312" xml:space="preserve">Non erit porrò magni negotĳ dĳudicare, vtra figur arum ad eam anni par <lb/>tem pertineat, in qua Sol à ♋, per ♎, ad ♑, mouetur, vel ad reliquam, in qua Sol à ♑, per ♈, ad ♋, <lb/>vſq; </s>
  <s xml:id="echoid-s12313" xml:space="preserve">aſcendit, ſi diligenter attendatur, quęnam ſigna oriri poſſint, dum Sol in hac, vel illa parte Eclipti-<lb/>cæ verſatur. </s>
  <s xml:id="echoid-s12314" xml:space="preserve">Nam quoniam v.</s>
  <s xml:id="echoid-s12315" xml:space="preserve">g. </s>
  <s xml:id="echoid-s12316" xml:space="preserve">dum Sol in principio ♎, exiſtit, oriuntur inter diu hæc ſigna. </s>
  <s xml:id="echoid-s12317" xml:space="preserve">♎, ♏, ♐, <lb/>♑, ♒, &amp; </s>
  <s xml:id="echoid-s12318" xml:space="preserve">♓, quorum lineæ æquinoctialem lineam in priori figura eodem or dine ſecant, pertinebit pro-<lb/>pterea prior figura ad eam anni partem, quæ ſemicirculo Eclipticę deſcendenti reſpondet, in qua nimirũ <lb/>ſignum ♎, continetur. </s>
  <s xml:id="echoid-s12319" xml:space="preserve">Figura autem poſterior ad alter am partem anni pertinebit, in qua ſignum ♈, in-<lb/>cluditur; </s>
  <s xml:id="echoid-s12320" xml:space="preserve">quoniam Sole in principio ♈, exiſtente oriuntur hęc ſex ſigna. </s>
  <s xml:id="echoid-s12321" xml:space="preserve">♈, ♉, ♊, ♋, ♌, &amp; </s>
  <s xml:id="echoid-s12322" xml:space="preserve">♍, quo-<lb/>rum lineæ eodem ordine poſterioris figuræ lineam ęquinoctialem interſecant. </s>
  <s xml:id="echoid-s12323" xml:space="preserve">Idem quoq; </s>
  <s xml:id="echoid-s12324" xml:space="preserve">cognoſcemus, <lb/>
<anchor type="note" xlink:label="note-0209-03a" xlink:href="note-0209-03"/>
Sole exiſtente in quouis alio ſigno. </s>
  <s xml:id="echoid-s12325" xml:space="preserve">Quoniam enim Sole exiſtente v.</s>
  <s xml:id="echoid-s12326" xml:space="preserve">g. </s>
  <s xml:id="echoid-s12327" xml:space="preserve">in principio ♌, interdiu aſcendunt <lb/>hęc ſigna. </s>
  <s xml:id="echoid-s12328" xml:space="preserve">♌, ♍, ♎, ♏, ♐, &amp; </s>
  <s xml:id="echoid-s12329" xml:space="preserve">♑, percurrit{q́ue} vmbra ſtyli ſpatium inter tropicum ♋, &amp; </s>
  <s xml:id="echoid-s12330" xml:space="preserve">lineam ęqui-<lb/>noctialem: </s>
  <s xml:id="echoid-s12331" xml:space="preserve">Video autem, omnia hęc ſigna non contineri in poſteriori figura ſupra ęquinoctialem lineam, <lb/>hoc eſt, inter tropicum ♋, &amp; </s>
  <s xml:id="echoid-s12332" xml:space="preserve">lineam ęquinoctialem, ſed in priori, concludo idcirco, priorem figuram con-<lb/>uenire illi parti anni, in qua ſignum ♌, reperitur, nempe dum Sol à ♋, ad ♑, deſcendit. </s>
  <s xml:id="echoid-s12333" xml:space="preserve">Idem intelliges, <lb/>Sole in principio ♐, commorante. </s>
  <s xml:id="echoid-s12334" xml:space="preserve">Tunc enim hęc ſex ſigna oriuntur, ♐, ♑, ♒, ♓, ♈, &amp; </s>
  <s xml:id="echoid-s12335" xml:space="preserve">♉, quę omnia in <lb/>priori figura infra ęquinoctialem lineam continentur, nempe inter tropicum ♑, &amp; </s>
  <s xml:id="echoid-s12336" xml:space="preserve">lineam ęquinoctialẽ, <lb/>vbi vmbra gnomonis tunc verſatur; </s>
  <s xml:id="echoid-s12337" xml:space="preserve">atq; </s>
  <s xml:id="echoid-s12338" xml:space="preserve">ita de cęteris iudic andum erit. </s>
  <s xml:id="echoid-s12339" xml:space="preserve">Hęc omnia in ſequentium etiam <lb/>
<anchor type="note" xlink:label="note-0209-04a" xlink:href="note-0209-04"/>
horologiorum aſcendentibus ſignis intelligenda ſunt. </s>
  <s xml:id="echoid-s12340" xml:space="preserve">In ſingulis enim quatuor figurę deſcribi poſſunt, duę <lb/>pro vna facie plani horologĳ, &amp; </s>
  <s xml:id="echoid-s12341" xml:space="preserve">pro oppoſita facie alię duę. </s>
  <s xml:id="echoid-s12342" xml:space="preserve">Quę res non admodum difficilis erit, ſi ea, <lb/>
<anchor type="note" xlink:label="note-0209-05a" xlink:href="note-0209-05"/>
quę proximè à nobis dicta ſunt, rectè per cipiantur. </s>
  <s xml:id="echoid-s12343" xml:space="preserve">Nos breuitatis cauſa in ſequentibus vbiq; </s>
  <s xml:id="echoid-s12344" xml:space="preserve">vnicam f<unsure/>i-<lb/>guram depingemus continentem omnia ſigna aſcendentia, vt ea diſtrabi poſſit in quatuor particulares, vt <lb/>docuimus, ſi vſus ita poſtulauerit.</s>
  <s xml:id="echoid-s12345" xml:space="preserve"/>
</p>
<div xml:id="echoid-div660" type="float" level="2" n="2">
<note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">Quomodo due<unsure/> <lb/>horologia ſigno <lb/>rum aſcenden-<lb/>tium deſcriban <lb/>tur, in quibus li <lb/>neæ ſignorum <lb/>ſe non interſe-<lb/>cent, &amp; quorum <lb/>unum vni me-<lb/>dietati anni, &amp; <lb/>alterum alteri <lb/>medietati acco<unsure/> <lb/>modetur.</note>
<note position="left" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0209-04" xlink:href="note-0209-04a" xml:space="preserve">In horologiis<unsure/>@ <lb/>quæ horizonta-<lb/>lia nõ ſunt, de-<lb/>ſcribendæ ſ<unsure/>unt <lb/>quatuor figuræ <lb/>ſignorum aſce@ <lb/>dentiu@@.</note>
<note position="left" xlink:label="note-0209-05" xlink:href="note-0209-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s12346" xml:space="preserve">IAM verò quoniam ad deſcriptionem ſignorũ aſcendentium, &amp; </s>
  <s xml:id="echoid-s12347" xml:space="preserve">ad cęli mediationes perueſtigandas, <lb/>neceſſarię ſunt aſcenſiones rectę, &amp; </s>
  <s xml:id="echoid-s12348" xml:space="preserve">obliquę, quarum tabulas non omnes in promptu habent, operę pretiũ <lb/>me facturum arbitror, ſi breuiter hoc loco ostendam, qua ratione tam recta, quàm obliqua aſcenſio cuiuſ-<lb/>libet puncti Eclipticę ex ſinuum doctrina eruenda ſit. </s>
  <s xml:id="echoid-s12349" xml:space="preserve">Plura enim hac de re alio in lo co demonſtrata <lb/>ſunt à nobis.</s>
  <s xml:id="echoid-s12350" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s12351" xml:space="preserve">SIT igitur Horizon rectus, vel Meridianus, vel quiuis alius circulus maximus A B C D, per polos <lb/>
<anchor type="note" xlink:label="note-0209-06a" xlink:href="note-0209-06"/>
mundi A, C, ductus; </s>
  <s xml:id="echoid-s12352" xml:space="preserve">Aequator B G D; </s>
  <s xml:id="echoid-s12353" xml:space="preserve">Ecliptica E G F; </s>
  <s xml:id="echoid-s12354" xml:space="preserve">punctum G, principium ♈, &amp; </s>
  <s xml:id="echoid-s12355" xml:space="preserve">arcus Eclipti-<lb/>
<anchor type="note" xlink:label="note-0209-07a" xlink:href="note-0209-07"/>
cę G E, quadrante minor, ita vt eius aſcenſio recta, hoc eſt, in ſphęra recta, ſit arcus Aequatoris G B. <lb/></s>
  <s xml:id="echoid-s12356" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0209-01a" xlink:href="fig-0209-01"/>
<anchor type="note" xlink:label="note-0209-08a" xlink:href="note-0209-08"/>
Quoniam in ſphęrico triangulo E B G, angulus B, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s12357" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12358" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12359" xml:space="preserve">4. </s>
  <s xml:id="echoid-s12360" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s12361" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s12362" xml:space="preserve">de <lb/>
<anchor type="note" xlink:label="note-0209-09a" xlink:href="note-0209-09"/>
triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s12363" xml:space="preserve">15. </s>
  <s xml:id="echoid-s12364" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12365" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12366" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s12367" xml:space="preserve">43. </s>
  <s xml:id="echoid-s12368" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt <lb/>ſinus com@lementi arcus Eclipticæ E G, qui notus ponitur, quippe cum eius aſcenſio recta quæratur, ad ſi-<lb/>num complementi arcus B E, declinationis puncti E, propoſiti, ita ſinus complementi arcus B G, aſcen-<lb/>ſionis rectæ quæſitę ad ſinum totum: </s>
  <s xml:id="echoid-s12369" xml:space="preserve">Et conuertendo, vt ſinus complementi arcus B E, declinationis ad
<pb o="190" file="0210" n="210" rhead="GNOMONICES"/>
ſinum complementi arcus E G, Eclipticæ dati, ita ſinus totus ad ſinum complementi arcus B G, aſcenſio-<lb/>nis rectæ. </s>
  <s xml:id="echoid-s12370" xml:space="preserve">Quocirca ſi fiat, vt ſinus complementi declinationis puncti Eclipticæ propoſiti ad ſinum com-<lb/>plementi arcus Eclipticæ inter datum punctum, &amp; </s>
  <s xml:id="echoid-s12371" xml:space="preserve">principium ♈, ita ſinus totus ad aliud, proueniet ſi-<lb/>nus complementi aſcenſionis rectæ. </s>
  <s xml:id="echoid-s12372" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s12373" xml:space="preserve">Ponatur punctum E, grad. </s>
  <s xml:id="echoid-s12374" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12375" xml:space="preserve">♊, ita vt arcus Ecli-<lb/>
<anchor type="figure" xlink:label="fig-0210-01a" xlink:href="fig-0210-01"/>
<anchor type="note" xlink:label="note-0210-01a" xlink:href="note-0210-01"/>
pticæ G E, complectatur grad. </s>
  <s xml:id="echoid-s12376" xml:space="preserve">70. </s>
  <s xml:id="echoid-s12377" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12378" xml:space="preserve">arcus B E, declinationis, ex coroll. </s>
  <s xml:id="echoid-s12379" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s12380" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12381" xml:space="preserve">pręcedentis libri in-<lb/>
<anchor type="note" xlink:label="note-0210-02a" xlink:href="note-0210-02"/>
uentus, grad. </s>
  <s xml:id="echoid-s12382" xml:space="preserve">22. </s>
  <s xml:id="echoid-s12383" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12384" xml:space="preserve">0. </s>
  <s xml:id="echoid-s12385" xml:space="preserve">Itaque ſi fiat, vt 92718. </s>
  <s xml:id="echoid-s12386" xml:space="preserve">ſinus complementi declinationis ad 34202. </s>
  <s xml:id="echoid-s12387" xml:space="preserve">ſinum cõ-<lb/>plementi arcus Eclipticę B E, dati, ita 100000. </s>
  <s xml:id="echoid-s12388" xml:space="preserve">ſinus totus ad aliud, inuenietur hic ferme ſinus 36888. <lb/></s>
  <s xml:id="echoid-s12389" xml:space="preserve">cui reſpondet arcus grad. </s>
  <s xml:id="echoid-s12390" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12391" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12392" xml:space="preserve">39. </s>
  <s xml:id="echoid-s12393" xml:space="preserve">cuius complementum grad. </s>
  <s xml:id="echoid-s12394" xml:space="preserve">68. </s>
  <s xml:id="echoid-s12395" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12396" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12397" xml:space="preserve">dabit aſcenſionem rectam <lb/>grad. </s>
  <s xml:id="echoid-s12398" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12399" xml:space="preserve">♊. </s>
  <s xml:id="echoid-s12400" xml:space="preserve">atque ita de cęteris. </s>
  <s xml:id="echoid-s12401" xml:space="preserve">Hac arte ſupputari poſſunt aſcenſiones rectæ omnium arcuum Eclipti <lb/>cæ à principio ♈, vſque ad finem ♊.</s>
  <s xml:id="echoid-s12402" xml:space="preserve"/>
</p>
<div xml:id="echoid-div661" type="float" level="2" n="3">
<note position="right" xlink:label="note-0209-06" xlink:href="note-0209-06a" xml:space="preserve">A ſcenfio rect@ <lb/>cuiuſuis puncti <lb/>Eclipticæ quo-<lb/>modo inquir@@ <lb/>da<unsure/>.</note>
<note position="left" xlink:label="note-0209-07" xlink:href="note-0209-07a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0209-01" xlink:href="fig-0209-01a">
    <image file="0209-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0209-01"/>
  </figure>
<note position="left" xlink:label="note-0209-08" xlink:href="note-0209-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0209-09" xlink:href="note-0209-09a" xml:space="preserve">Quando arc@@ <lb/>Eclipticæ qua-<lb/>drante mino@ <lb/>e<unsure/>ſt.</note>
  <figure xlink:label="fig-0210-01" xlink:href="fig-0210-01a">
    <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0210-01"/>
  </figure>
<note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s12403" xml:space="preserve">QVOD ſi arcus Eclipticę G E, ſit quadrans, hoc eſt, E, ſit principium ♋, erit quoque eius aſcenſio <lb/>
<anchor type="note" xlink:label="note-0210-03a" xlink:href="note-0210-03"/>
recta G B, quadrans. </s>
  <s xml:id="echoid-s12404" xml:space="preserve">Quoniam enim in triangulo B E G, angulus B, rectus eſt, &amp; </s>
  <s xml:id="echoid-s12405" xml:space="preserve">arcus G E, quadrans, <lb/>erit per propoſ. </s>
  <s xml:id="echoid-s12406" xml:space="preserve">36. </s>
  <s xml:id="echoid-s12407" xml:space="preserve">noſtrorum triangulorum ſphęricorum, ſaltem alter reliquorum quadrans. </s>
  <s xml:id="echoid-s12408" xml:space="preserve">Cum ergo <lb/>B E, minor ſit quadrante, nempe declinationi maxime<unsure/> Solis æqualis, erit G B, quadrans. </s>
  <s xml:id="echoid-s12409" xml:space="preserve">Quod etiam ita <lb/>confirmari poteſt. </s>
  <s xml:id="echoid-s12410" xml:space="preserve">Quoniam arcus Eclipticæ G E, quadrans eſt, &amp; </s>
  <s xml:id="echoid-s12411" xml:space="preserve">G, principium ♈, tranſibit per punctũ <lb/>
<anchor type="note" xlink:label="note-0210-04a" xlink:href="note-0210-04"/>
E, colurus ſolſtitiorum, cum arcus Eclipticæ inter principium ♈, &amp; </s>
  <s xml:id="echoid-s12412" xml:space="preserve">colurum ſolstitiorum ſit quadrans. <lb/></s>
  <s xml:id="echoid-s12413" xml:space="preserve">Cum ergo idem colurus per polos mundi ducatur, non differet à circulo maximo A B C D; </s>
  <s xml:id="echoid-s12414" xml:space="preserve">ac proinde, <lb/>cum arcus Aequatoris inter principium ♈, &amp; </s>
  <s xml:id="echoid-s12415" xml:space="preserve">colurum ſolſtitiorum ſit quadrans, erit omnino arcus <lb/>G B, quadrans.</s>
  <s xml:id="echoid-s12416" xml:space="preserve"/>
</p>
<div xml:id="echoid-div662" type="float" level="2" n="4">
<note position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">Quando arcus <lb/>E<unsure/>c<unsure/>lipticæ eſt <lb/>@uadrans.</note>
<note position="left" xlink:label="note-0210-04" xlink:href="note-0210-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s12417" xml:space="preserve">SI arcus datus Eclipticæ ſit quadrante maior, minor autem ſemicirculo, ita vt v.</s>
  <s xml:id="echoid-s12418" xml:space="preserve">g. </s>
  <s xml:id="echoid-s12419" xml:space="preserve">punctum E, ſit <lb/>
<anchor type="note" xlink:label="note-0210-05a" xlink:href="note-0210-05"/>
grad. </s>
  <s xml:id="echoid-s12420" xml:space="preserve">20. </s>
  <s xml:id="echoid-s12421" xml:space="preserve">♋, &amp; </s>
  <s xml:id="echoid-s12422" xml:space="preserve">arcus datus comprehendat grad. </s>
  <s xml:id="echoid-s12423" xml:space="preserve">110. </s>
  <s xml:id="echoid-s12424" xml:space="preserve">Detrahemus ipſum ex ſemicirculo, &amp; </s>
  <s xml:id="echoid-s12425" xml:space="preserve">reliqui ar-<lb/>cus grad. </s>
  <s xml:id="echoid-s12426" xml:space="preserve">70. </s>
  <s xml:id="echoid-s12427" xml:space="preserve">ab altero ęquinoctio inchoati aſcenſionem rectam inuestigabimus, vt prius, eam{q́ue} ex ſemi-<lb/>circulo auferemus. </s>
  <s xml:id="echoid-s12428" xml:space="preserve">Remanebit enim aſcenſio recta arcus propoſiti, cum totus ſemicir culus ab ♈, vſque <lb/>ad ♎, habeat reſpondentem ſemicirculum Aequatoris pro aſcenſione recta. </s>
  <s xml:id="echoid-s12429" xml:space="preserve">Vt quoniam grad. </s>
  <s xml:id="echoid-s12430" xml:space="preserve">70. </s>
  <s xml:id="echoid-s12431" xml:space="preserve">ha-<lb/>bent aſcenſionem rectam grad. </s>
  <s xml:id="echoid-s12432" xml:space="preserve">68. </s>
  <s xml:id="echoid-s12433" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12434" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12435" xml:space="preserve">quę ablata ex grad. </s>
  <s xml:id="echoid-s12436" xml:space="preserve">180. </s>
  <s xml:id="echoid-s12437" xml:space="preserve">relinquit aſcenſionem rectam grad. <lb/></s>
  <s xml:id="echoid-s12438" xml:space="preserve">
<anchor type="note" xlink:label="note-0210-06a" xlink:href="note-0210-06"/>
111. </s>
  <s xml:id="echoid-s12439" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12440" xml:space="preserve">39. </s>
  <s xml:id="echoid-s12441" xml:space="preserve">reſpondentem arcui Eclipticæ grad. </s>
  <s xml:id="echoid-s12442" xml:space="preserve">110. </s>
  <s xml:id="echoid-s12443" xml:space="preserve">hoc eſt, gradui 20. </s>
  <s xml:id="echoid-s12444" xml:space="preserve">♋.</s>
  <s xml:id="echoid-s12445" xml:space="preserve"/>
</p>
<div xml:id="echoid-div663" type="float" level="2" n="5">
<note position="left" xlink:label="note-0210-05" xlink:href="note-0210-05a" xml:space="preserve">Quando arcus <lb/>Eclipticę maior <lb/>eſt quadrante, <lb/>at ſemicirculo <lb/>minor.</note>
<note position="left" xlink:label="note-0210-06" xlink:href="note-0210-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s12446" xml:space="preserve">AT ſi arcus Eclipticæ à principio ♈, inchoatus ſit ſemicirculus, ita vt in principio ♎, finiatur, erit <lb/>
<anchor type="note" xlink:label="note-0210-07a" xlink:href="note-0210-07"/>
quoque eius recta aſcenſio ſemicirculus, vt patet.</s>
  <s xml:id="echoid-s12447" xml:space="preserve"/>
</p>
<div xml:id="echoid-div664" type="float" level="2" n="6">
<note position="left" xlink:label="note-0210-07" xlink:href="note-0210-07a" xml:space="preserve">Quando arcus<unsure/> <lb/>Eclipticæ ſemi-<lb/>circulus eſt.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12448" xml:space="preserve">ARCV Eclipticę ſemicirculum ſuperante, ita tamen, vt tribus quadrantibus minor ſit, auferemus <lb/>
<anchor type="note" xlink:label="note-0210-08a" xlink:href="note-0210-08"/>
ex eo ſemicirculum, &amp; </s>
  <s xml:id="echoid-s12449" xml:space="preserve">reliqui arcus à principio ♎, inchoati aſcenſionem rectam inuentam, vt prius, ſe-<lb/>micirculo adĳciemus, vt habeamus aſcenſionem rectam dati arcus. </s>
  <s xml:id="echoid-s12450" xml:space="preserve">Vt ſi quęratur recta aſcenſio grad. <lb/></s>
  <s xml:id="echoid-s12451" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12452" xml:space="preserve">♐, ita vt totus arcus Eclipticę à principio ♈, computatus contineat grad. </s>
  <s xml:id="echoid-s12453" xml:space="preserve">250. </s>
  <s xml:id="echoid-s12454" xml:space="preserve">Detracto ſemicir-<lb/>culo ex grad. </s>
  <s xml:id="echoid-s12455" xml:space="preserve">250. </s>
  <s xml:id="echoid-s12456" xml:space="preserve">reliqui fiunt grad. </s>
  <s xml:id="echoid-s12457" xml:space="preserve">70. </s>
  <s xml:id="echoid-s12458" xml:space="preserve">huius arcus aſcenſio recta grad. </s>
  <s xml:id="echoid-s12459" xml:space="preserve">68. </s>
  <s xml:id="echoid-s12460" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12461" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12462" xml:space="preserve">inuenta, vt prius, ſi <lb/>addatur ſemicir culo, conficientur grad. </s>
  <s xml:id="echoid-s12463" xml:space="preserve">248. </s>
  <s xml:id="echoid-s12464" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12465" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12466" xml:space="preserve">pro aſcenſione recta oblati arcus.</s>
  <s xml:id="echoid-s12467" xml:space="preserve"/>
</p>
<div xml:id="echoid-div665" type="float" level="2" n="7">
<note position="left" xlink:label="note-0210-08" xlink:href="note-0210-08a" xml:space="preserve">Quando arcus <lb/>Eclipticæ ſemi-<lb/>circulo maior <lb/>eſt, minor autẽ <lb/>tribus quadran <lb/>tibus.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12468" xml:space="preserve">SI verò datus arcus comprehendat tres quadrantes, habebit eius aſcenſio recta tres ctiam qua-<lb/>
<anchor type="note" xlink:label="note-0210-09a" xlink:href="note-0210-09"/>
<anchor type="note" xlink:label="note-0210-10a" xlink:href="note-0210-10"/>
drantes, vt ex dictis patet. </s>
  <s xml:id="echoid-s12469" xml:space="preserve">Nam prior ſemicirculus habet ſemicirculum, &amp; </s>
  <s xml:id="echoid-s12470" xml:space="preserve">reliquus quadrans qua-<lb/>drantem, &amp; </s>
  <s xml:id="echoid-s12471" xml:space="preserve">c.</s>
  <s xml:id="echoid-s12472" xml:space="preserve"/>
</p>
<div xml:id="echoid-div666" type="float" level="2" n="8">
<note position="left" xlink:label="note-0210-09" xlink:href="note-0210-09a" xml:space="preserve">Quando arcus <lb/>Eclipticæ com-<lb/>plectitur tres <lb/>quadrantes.</note>
<note position="left" xlink:label="note-0210-10" xlink:href="note-0210-10a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s12473" xml:space="preserve">SI denique propoſitus arcus tres quadrantes ſuperauerit, auferendus erit ex toto circulo, &amp; </s>
  <s xml:id="echoid-s12474" xml:space="preserve">reliqui <lb/>
<anchor type="note" xlink:label="note-0210-11a" xlink:href="note-0210-11"/>
arcus ab ♈, inchoati aſcenſio recta inuenta, vt antea, ex toto circulo detrahenda. </s>
  <s xml:id="echoid-s12475" xml:space="preserve">Relinquetur enim re-<lb/>cta aſcenſio datiarcus, cum tota Ecliptica cum toto Aequatore aſcendat. </s>
  <s xml:id="echoid-s12476" xml:space="preserve">Vt ſidatus arcus contineat <lb/>grad. </s>
  <s xml:id="echoid-s12477" xml:space="preserve">290. </s>
  <s xml:id="echoid-s12478" xml:space="preserve">ita vt terminetur ingrad. </s>
  <s xml:id="echoid-s12479" xml:space="preserve">20. </s>
  <s xml:id="echoid-s12480" xml:space="preserve">♑, deducemus grad. </s>
  <s xml:id="echoid-s12481" xml:space="preserve">290. </s>
  <s xml:id="echoid-s12482" xml:space="preserve">ex 360. </s>
  <s xml:id="echoid-s12483" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12484" xml:space="preserve">reliqui arcus grad. </s>
  <s xml:id="echoid-s12485" xml:space="preserve">70. <lb/></s>
  <s xml:id="echoid-s12486" xml:space="preserve">aſcenſionem rectam grad. </s>
  <s xml:id="echoid-s12487" xml:space="preserve">68. </s>
  <s xml:id="echoid-s12488" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12489" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12490" xml:space="preserve">inuentam, vt prius, ex grad. </s>
  <s xml:id="echoid-s12491" xml:space="preserve">360. </s>
  <s xml:id="echoid-s12492" xml:space="preserve">ſubducemus, vt relinquantur <lb/>grad. </s>
  <s xml:id="echoid-s12493" xml:space="preserve">291. </s>
  <s xml:id="echoid-s12494" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12495" xml:space="preserve">39. </s>
  <s xml:id="echoid-s12496" xml:space="preserve">pro aſcenſione recta arcus propoſiti.</s>
  <s xml:id="echoid-s12497" xml:space="preserve"/>
</p>
<div xml:id="echoid-div667" type="float" level="2" n="9">
<note position="left" xlink:label="note-0210-11" xlink:href="note-0210-11a" xml:space="preserve">Quando arcus <lb/>Eclipticæ tribus <lb/>quadrantibus <lb/>maior eſt.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12498" xml:space="preserve">PERSPICVVM eſt ex his, qua ratione tabula aſcenſionum rectarum ſit conſtruenda. </s>
  <s xml:id="echoid-s12499" xml:space="preserve">Nam ſi <lb/>
<anchor type="note" xlink:label="note-0210-12a" xlink:href="note-0210-12"/>
aſcenſiones rectę inueſtigentur omnium ar cuum Eclipticę à principio ♈, vſque ad finem ♊, babebimus <lb/>aſcenſiones rectas omnium punctorum primi quadrantis Eclipticę. </s>
  <s xml:id="echoid-s12500" xml:space="preserve">Quod ſi ſingulas ex ſemicirculo de-
<pb o="191" file="0211" n="211" rhead="LIBER SECVNDVS."/>
trabamus, initio facto à maioribus, ſiue poſterioribus, reliquę erunt aſcenſiones rectę omnium punctorum <lb/>ſecundi quadrantis Eclipticę. </s>
  <s xml:id="echoid-s12501" xml:space="preserve">Rurſus ſi eaſdem ſemicir culo apponamus, facto initio à minoribus, ſiue prio <lb/>ribus, conficientur aſcenſiones rectæ omnium punctorum tertĳ quadrantis Eclipticę. </s>
  <s xml:id="echoid-s12502" xml:space="preserve">Si denique eaſdem <lb/>auferamus ex toto circulo, initio rurſus facto à maioribus, ſiue poſterioribus, remanebunt aſcenſiones re-<lb/>ctę omnium punctorum vltimi quadrantis Eclipticę. </s>
  <s xml:id="echoid-s12503" xml:space="preserve">Itaque totus labor poſitus eſt in perueſtigatione <lb/>aſcenſionum rectarum omnium punctorum primi quadrantis Eclipticæ inchoati à principio ♈, &amp; </s>
  <s xml:id="echoid-s12504" xml:space="preserve">in fi-<lb/>ne ♊, terminati.</s>
  <s xml:id="echoid-s12505" xml:space="preserve"/>
</p>
<div xml:id="echoid-div668" type="float" level="2" n="10">
<note position="left" xlink:label="note-0210-12" xlink:href="note-0210-12a" xml:space="preserve">Quo pacto tabu <lb/>la aſcenſionum <lb/>rectarum con-<lb/>ſtruenda.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12506" xml:space="preserve">SIT rurſum Horizon obliquus A B C D; </s>
  <s xml:id="echoid-s12507" xml:space="preserve">Aequator B D; </s>
  <s xml:id="echoid-s12508" xml:space="preserve">Ecliptica E F; </s>
  <s xml:id="echoid-s12509" xml:space="preserve">principium ♈, in ſecunda <lb/>
<anchor type="note" xlink:label="note-0211-01a" xlink:href="note-0211-01"/>
figura G; </s>
  <s xml:id="echoid-s12510" xml:space="preserve">in tertia verò principium ♎, idem punctum G; </s>
  <s xml:id="echoid-s12511" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s12512" xml:space="preserve">arcus Eclipticæ G E, à prin <lb/>cipio ♈, vel ♎, inchoatus qua drante minor, ita vt eius aſcenſio obliqua, hoc est, in obliqua ſphæra, ſit ar <lb/>
<anchor type="note" xlink:label="note-0211-02a" xlink:href="note-0211-02"/>
cus Aequatoris G B, quem inueſtigare oportet. </s>
  <s xml:id="echoid-s12513" xml:space="preserve">Ducatur ex polo mundi H, per E, circulus maximus ſe-<lb/>cans Aequatorem in I, ita vt G I, ſit aſcenſio recta eiuſdem arcus Eclipticæ G E. </s>
  <s xml:id="echoid-s12514" xml:space="preserve">Quoniam ergo in trian-<lb/>gulo ſphęrico C E H, in quo angulus C, rectus est, est per propoſ. </s>
  <s xml:id="echoid-s12515" xml:space="preserve">16. </s>
  <s xml:id="echoid-s12516" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12517" xml:space="preserve">4. </s>
  <s xml:id="echoid-s12518" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s12519" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s12520" xml:space="preserve">de triangulis, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s12521" xml:space="preserve">16. </s>
  <s xml:id="echoid-s12522" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12523" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12524" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s12525" xml:space="preserve">41. </s>
  <s xml:id="echoid-s12526" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus H E, <lb/>hoc eſt, vt ſinus complementi declinationis puncti Eclipticæ arcum G E, @terminantis (In tertia namque <lb/>figura idem ſinus eſt arcus H E, &amp; </s>
  <s xml:id="echoid-s12527" xml:space="preserve">complementi declinationis E I, propterea quòd arcus H E, cum com-<lb/>plemento declinationis E I, ſemicir culum conficit) ad ſinum anguli C, hoc eſt, ad ſinum totum, ita ſinus <lb/>arcus C H, altitudinis poli, ad ſinum anguli C E H, qui in ſecunda figura æqualis eſt angulo B E I. </s>
  <s xml:id="echoid-s12528" xml:space="preserve">Rurſus <lb/>eadem ratione, &amp; </s>
  <s xml:id="echoid-s12529" xml:space="preserve">conuertendo, intriangulo ſphærico B E I, eſt vt ſinus anguli E B I, complementi altitu <lb/>dinis poli, quem nimirum Aequator cum Horizonte conſtituit, ad ſinum arcus E I, declinationis, ita ſinus <lb/>
<anchor type="note" xlink:label="note-0211-03a" xlink:href="note-0211-03"/>
anguli B E I, proximè inuenti ad ſinum arcus B I, quo aſcenſio recta G I, ab aſcenſione obliqua G B, dif-<lb/>fert: </s>
  <s xml:id="echoid-s12530" xml:space="preserve">Si fiat, vt ſinus complementi declinationis puncti arcum Eclipticæ terminantis ad ſinum totum, ita <lb/>ſinus altitudinis poli ad aliud, inuenietur ſinus anguli B E I: </s>
  <s xml:id="echoid-s12531" xml:space="preserve">Et ſi rurſus fiat, vt ſinus complementi al-<lb/>titudinis poli ad ſinum declinationis eiuſdem arcus Eclipticę, ita ſinus anguli B E I, proximè inuentus ad <lb/>aliud, inuenietur ſinus arcus B I, differentiæ aſcenſionis rectę, &amp; </s>
  <s xml:id="echoid-s12532" xml:space="preserve">obliquę arcui Eelipticę G E, reſponden-<lb/>tis. </s>
  <s xml:id="echoid-s12533" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s12534" xml:space="preserve">Ponatur punctum E, in ſecunda figura grad. </s>
  <s xml:id="echoid-s12535" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12536" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s12537" xml:space="preserve">in tertia grad. </s>
  <s xml:id="echoid-s12538" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12539" xml:space="preserve">♏, ita vt <lb/>arcus G E, contineat grad. </s>
  <s xml:id="echoid-s12540" xml:space="preserve">59. </s>
  <s xml:id="echoid-s12541" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12542" xml:space="preserve">arcus E I, declinationis grad. </s>
  <s xml:id="echoid-s12543" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12544" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12545" xml:space="preserve">59. </s>
  <s xml:id="echoid-s12546" xml:space="preserve">Si igitur fiat, vt 93979. <lb/></s>
  <s xml:id="echoid-s12547" xml:space="preserve">ſinus complementi declinationis ad 100000. </s>
  <s xml:id="echoid-s12548" xml:space="preserve">ſinum totum, ita 66913. </s>
  <s xml:id="echoid-s12549" xml:space="preserve">ſinus altitudinis poli ad aliud, re-<lb/>perietur hic ferè ſinus 71199. </s>
  <s xml:id="echoid-s12550" xml:space="preserve">anguli E, qui ſeruetur. </s>
  <s xml:id="echoid-s12551" xml:space="preserve">Deinde ſi fiat, vt 74314. </s>
  <s xml:id="echoid-s12552" xml:space="preserve">ſinus complementi altitu <lb/>dinis poli ad 34174. </s>
  <s xml:id="echoid-s12553" xml:space="preserve">ſinum declinationis, ita 71199. </s>
  <s xml:id="echoid-s12554" xml:space="preserve">ſinus ſeruatus ad aliud, proueniet ferè hic ſinus <lb/>
<anchor type="note" xlink:label="note-0211-04a" xlink:href="note-0211-04"/>
32741. </s>
  <s xml:id="echoid-s12555" xml:space="preserve">cuius arcus continet grad. </s>
  <s xml:id="echoid-s12556" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12557" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12558" xml:space="preserve">7. </s>
  <s xml:id="echoid-s12559" xml:space="preserve">pro differentia aſcenſionis rectę, &amp; </s>
  <s xml:id="echoid-s12560" xml:space="preserve">obliquę arcus G E. <lb/></s>
  <s xml:id="echoid-s12561" xml:space="preserve">
<anchor type="note" xlink:label="note-0211-05a" xlink:href="note-0211-05"/>
Quę differentia ſi in ſecunda figura dematur ex aſcenſione recta G I, iam antea inuenta, (quia circulus ma <lb/>ximus H E, qui vices gerit recti Horizontis, Aequatorem ſecat infra Horizontem, cum medietas Zo-<lb/>diaci ab ♈, vſque ad ♎, ſit borealis) remanebit aſcenſio obliqua G B, grad. </s>
  <s xml:id="echoid-s12562" xml:space="preserve">37. </s>
  <s xml:id="echoid-s12563" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12564" xml:space="preserve">39. </s>
  <s xml:id="echoid-s12565" xml:space="preserve">arcui Eclipticę <lb/>boreali G E, debita: </s>
  <s xml:id="echoid-s12566" xml:space="preserve">Si verò eadem differentia in tertia figura rectæ aſcenſioni G I, addatur (quia <lb/>circulus maximus H E, ſecat Aequatorem ſupra Horizontem, propterea quòd medietas Zodiaci à ♎, <lb/>vſque ad ♈, australis eſt) conficietur aſcenſio obliqua G B, grad. </s>
  <s xml:id="echoid-s12567" xml:space="preserve">75. </s>
  <s xml:id="echoid-s12568" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12569" xml:space="preserve">53. </s>
  <s xml:id="echoid-s12570" xml:space="preserve">conueniens arcui Eclipticæ <lb/>auſtrali G E, à principio ♎, computato; </s>
  <s xml:id="echoid-s12571" xml:space="preserve">cui ſi apponatur ſemicirculus, conflabitur aſcenſio obliqua grad. <lb/></s>
  <s xml:id="echoid-s12572" xml:space="preserve">255. </s>
  <s xml:id="echoid-s12573" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12574" xml:space="preserve">53. </s>
  <s xml:id="echoid-s12575" xml:space="preserve">arcui Eclipticæ à principio ♈, vſque ad grad. </s>
  <s xml:id="echoid-s12576" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12577" xml:space="preserve">♏, inchoato debita.</s>
  <s xml:id="echoid-s12578" xml:space="preserve"/>
</p>
<div xml:id="echoid-div669" type="float" level="2" n="11">
<note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">Differentia in-<lb/>ter aſcẽſionem <lb/>rectam &amp; obli-<lb/>quam cuiusli <lb/>bet puncti Ecli <lb/>pticæ qua via <lb/>exploranda. ad <lb/>datam altitudi-<lb/>nem poli.</note>
<note position="left" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0211-03" xlink:href="note-0211-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0211-04" xlink:href="note-0211-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0211-05" xlink:href="note-0211-05a" xml:space="preserve">Aſcenſio obli-<lb/>qua cuiusuis pũ <lb/>cti Eclipticæ <lb/>qua ratione in-<lb/>ueniatur ex dif <lb/>ferentia aſcen-<lb/>ſionali.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12579" xml:space="preserve">ALITER quoque eadem differentia B I, inter aſcenſionem rectam, &amp; </s>
  <s xml:id="echoid-s12580" xml:space="preserve">obliquam inuenietur hac <lb/>
<anchor type="note" xlink:label="note-0211-06a" xlink:href="note-0211-06"/>
<anchor type="note" xlink:label="note-0211-07a" xlink:href="note-0211-07"/>
ratione. </s>
  <s xml:id="echoid-s12581" xml:space="preserve">Quoniam in triangulo ſphęrico B E I, angulus I, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s12582" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12583" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12584" xml:space="preserve">4. </s>
  <s xml:id="echoid-s12585" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s12586" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s12587" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s12588" xml:space="preserve">15. </s>
  <s xml:id="echoid-s12589" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12590" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12591" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s12592" xml:space="preserve">43. </s>
  <s xml:id="echoid-s12593" xml:space="preserve">noſtrorum triangulorum ſphęrico-<lb/>rum, vt ſinus complementi arcus B E, latitudinis ortiuę, cuius inuentionem in priori diſcurſu propoſ. </s>
  <s xml:id="echoid-s12594" xml:space="preserve">34. <lb/></s>
  <s xml:id="echoid-s12595" xml:space="preserve">pręcedentis libri tradidimus, ad ſinum complementi arcus E I, declinationis puncti Eclipticæ propoſiti, <lb/>ita ſinus complementi arcus B I, differentię quęſitæ ad ſinum totum: </s>
  <s xml:id="echoid-s12596" xml:space="preserve">Et conuertendo vt ſinus complemen <lb/>ti declinationis puncti Eclipticæ propoſiti ad ſinum complementi latitudinis ortiuæ eiuſdem puncti, ita <lb/>ſinus totus ad ſinum complementi differentiæ aſcenſionum. </s>
  <s xml:id="echoid-s12597" xml:space="preserve">Quamobrem ſi fiat, vt ſinus complementi de-<lb/>clinationis ad ſinum complementi latitudinis ortiuę, ita ſinus totus ad aliud, reperietur ſinus complemen-<lb/>ti differentię aſcenſionum quęſitę.</s>
  <s xml:id="echoid-s12598" xml:space="preserve"/>
</p>
<div xml:id="echoid-div670" type="float" level="2" n="12">
<note position="left" xlink:label="note-0211-06" xlink:href="note-0211-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0211-07" xlink:href="note-0211-07a" xml:space="preserve">Quomodo ea-<lb/>dem differẽtia <lb/>inter aſcenſio-<lb/>nem rectam &amp; <lb/>obliquam cu-<lb/>iuſuis puncti <lb/>Eclipticæ, ad da <lb/>tam latitudinẽ <lb/>loci aliter inue-<lb/>ſtigetur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12599" xml:space="preserve">QVONIAM autem declinationes omnium punctorum Eclipticę à principio ♈, vſque ad princi-<lb/>
<anchor type="note" xlink:label="note-0211-08a" xlink:href="note-0211-08"/>
<anchor type="note" xlink:label="note-0211-09a" xlink:href="note-0211-09"/>
pium ♋, ęquales ſunt declinationibus omnium punctorum Eclipticę à principio ♎, vſque ad principium <lb/>♋, contra ſucceſſionem ſignorum progrediendo, ſingulę ſingulis, cum huiuſmodi puncta eoſdem parallelos <lb/>deſcribant, bina nimirum ſingulos: </s>
  <s xml:id="echoid-s12600" xml:space="preserve">Rurſus declinationes omnium punctorum Eclipticę ab ♈, vſque ad <lb/>♎, æquales ſunt declinationibus omnium punctorum Eclipticæ à ♎, vſque ad ♈, ſecundum ſignorum ſe-<lb/>riem procedendo, ſingulæ ſingulis, cum hæc puncta illis ſint oppoſita, ac proinde æquales parallelos deſcri-<lb/>bant: </s>
  <s xml:id="echoid-s12601" xml:space="preserve">Fit, vt declinationes prioris quadrantis Eclipticæ ab ♈, vſque ad ♋, ęquales ſint declinationibus <lb/>poſteriorum trium quadrantum, vt in tabula declinationum apparet. </s>
  <s xml:id="echoid-s12602" xml:space="preserve">Quare cum latitudines ortiuæ in-<lb/>ueſtigentur beneficio declinationum, &amp; </s>
  <s xml:id="echoid-s12603" xml:space="preserve">altitudinis poli, vt ex propoſ. </s>
  <s xml:id="echoid-s12604" xml:space="preserve">34. </s>
  <s xml:id="echoid-s12605" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s12606" xml:space="preserve">liquet, manife-<lb/>ſtum eſt, latitudines ortiuas punctorum prioris quadrantis Eclipticæ ad quamcunque latitudinem inuen-<lb/>tas, æquales eſſe latitudinibus ortiuis poſteriorum trium quadrantum in eadem latitudine. </s>
  <s xml:id="echoid-s12607" xml:space="preserve">Ac proinde <lb/>eum differentiæ inter aſcenſiones rectas, &amp; </s>
  <s xml:id="echoid-s12608" xml:space="preserve">obliquas inquirantur, vt proximè demonſtrauimus, per decli-
<pb o="192" file="0212" n="212" rhead="GNOMONICES"/>
nationes, &amp; </s>
  <s xml:id="echoid-s12609" xml:space="preserve">latitudines ortiuas, liquido conſtat, differentias inter aſcenſiones rectas, &amp; </s>
  <s xml:id="echoid-s12610" xml:space="preserve">obliquas om-<lb/>nium punctorum prioris quadrantis Eclipticæ ad quamuis poli altitudinem compertas, æquales eſſe diffe-<lb/>rentĳs aſcenſionum omnium punctorum trium poſteriorum quadrantum Eclipticæ in eadem altitudine <lb/>poli. </s>
  <s xml:id="echoid-s12611" xml:space="preserve">Quocirca ſatis erit, ſi inquir antur differentiæ aſcenſionum conuenientes punctis prioris quadrantis <lb/>Eclipticæ à principio ♈, vſque ad principium ♋.</s>
  <s xml:id="echoid-s12612" xml:space="preserve"/>
</p>
<div xml:id="echoid-div671" type="float" level="2" n="13">
<note position="left" xlink:label="note-0211-08" xlink:href="note-0211-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0211-09" xlink:href="note-0211-09a" xml:space="preserve">Differentiæ a-<lb/>ſcenſionales pũ <lb/>ctorum prioris <lb/>quadrantis Ecli <lb/>pticæ ab A riet<unsure/>e <lb/>vſque ad Can-<lb/>crũ æquales sũt <lb/>differentijs aſcẽ <lb/>ſionalibus poſte <lb/>riorum trium <lb/>quadrantum <lb/>Eclipticæ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s12613" xml:space="preserve">EX his porrò differentĳs aſcenſionum prioris quadrantis Eclipticæ, ita tabulam aſcenſionum obli-<lb/>
<anchor type="note" xlink:label="note-0212-01a" xlink:href="note-0212-01"/>
quarum omnium punctorum Eclipticæ ad datam altitudinem poli, pro qua differentiæ perueſtigatæ ſunt, <lb/>componemus. </s>
  <s xml:id="echoid-s12614" xml:space="preserve">Quoniam in medietate Eclipticæ ab ♈, vſque ad ♎, perpetuo differentia aſcenſionum <lb/>detrahenda eſt ab aſcenſione recta, vt obliqua aſcenſio cognita fiat, propterea quòd hæc medietas borea-<lb/>lis eſt, ac proinde circulus maximus ex polo mundi, per punctum quodlibet illius ductus Aquatorem in-<lb/>
<anchor type="note" xlink:label="note-0212-02a" xlink:href="note-0212-02"/>
fra Horizontem ſecat, vt ex priori duarum proximarum figurarum patet, efficitur, vt differentiæ aſcen-<lb/>ſionum omnium punctorum prioris ſemicirculi ablata ex aſcenſionibus rectis eorundem punctorum re-<lb/>linquant illorum aſcenſiones obliquas. </s>
  <s xml:id="echoid-s12615" xml:space="preserve">Rurſus quia in altero Eclipticæ ſemicirculo à ♎, vſq; </s>
  <s xml:id="echoid-s12616" xml:space="preserve">ad ♈, diffe <lb/>rentia aſcenſionum ſemper adĳcienda est ad aſcenſionem rectam, vt aſcenſio obliqua cognoſcatur, propte-<lb/>rea quòd hic ſemicir culus auſtralis eſt, atque adeò circulus maximus ex polo mundi per quoduis punctum <lb/>illius ductus Aequatorem ſupra Horizontem ſecat, vt conſtat ex posteriori figura proxima, perſpicuum <lb/>eſt, differentias aſcenſionum omnium punctorum poſterioris huius ſemicirculi additas rectis aſcenſioni-<lb/>bus eorundem punctorum conficere illorum aſcenſiones obliquas. </s>
  <s xml:id="echoid-s12617" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s12618" xml:space="preserve">Differentia aſcenſionum <lb/>grad. </s>
  <s xml:id="echoid-s12619" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12620" xml:space="preserve">♉, quam inuenimus ad latitudinem grad. </s>
  <s xml:id="echoid-s12621" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12622" xml:space="preserve">eſſe grad. </s>
  <s xml:id="echoid-s12623" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12624" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12625" xml:space="preserve">7. </s>
  <s xml:id="echoid-s12626" xml:space="preserve">æqualis eſt differentię aſcen-<lb/>ſionum grad. </s>
  <s xml:id="echoid-s12627" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12628" xml:space="preserve">♌, &amp; </s>
  <s xml:id="echoid-s12629" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s12630" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12631" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s12632" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s12633" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12634" xml:space="preserve">♒. </s>
  <s xml:id="echoid-s12635" xml:space="preserve">Hæc enim quatuor puncta eandem habent declinatio-<lb/>
<anchor type="note" xlink:label="note-0212-03a" xlink:href="note-0212-03"/>
nem. </s>
  <s xml:id="echoid-s12636" xml:space="preserve">Siigitur eam detrabamus ex aſcenſione recta grad. </s>
  <s xml:id="echoid-s12637" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12638" xml:space="preserve">♉, hoc eſt, ex grad. </s>
  <s xml:id="echoid-s12639" xml:space="preserve">56. </s>
  <s xml:id="echoid-s12640" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12641" xml:space="preserve">46. </s>
  <s xml:id="echoid-s12642" xml:space="preserve">reliqua <lb/>erit aſcenſio obliqua grad. </s>
  <s xml:id="echoid-s12643" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12644" xml:space="preserve">♉, nempe grad. </s>
  <s xml:id="echoid-s12645" xml:space="preserve">37. </s>
  <s xml:id="echoid-s12646" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12647" xml:space="preserve">39. </s>
  <s xml:id="echoid-s12648" xml:space="preserve">Item ſi eandem differentiam ſubducamus ex <lb/>recta aſcenſione grad. </s>
  <s xml:id="echoid-s12649" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12650" xml:space="preserve">♌, nempe ex grad. </s>
  <s xml:id="echoid-s12651" xml:space="preserve">123. </s>
  <s xml:id="echoid-s12652" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12653" xml:space="preserve">14. </s>
  <s xml:id="echoid-s12654" xml:space="preserve">remanebunt grad. </s>
  <s xml:id="echoid-s12655" xml:space="preserve">104. </s>
  <s xml:id="echoid-s12656" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12657" xml:space="preserve">7. </s>
  <s xml:id="echoid-s12658" xml:space="preserve">pro aſcenſione <lb/>obliqua grad. </s>
  <s xml:id="echoid-s12659" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12660" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s12661" xml:space="preserve">Rurſus ſi eandem differentiam addamus aſcenſioni rectę grad. </s>
  <s xml:id="echoid-s12662" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12663" xml:space="preserve">♏, quæ continet <lb/>grad. </s>
  <s xml:id="echoid-s12664" xml:space="preserve">236. </s>
  <s xml:id="echoid-s12665" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12666" xml:space="preserve">46. </s>
  <s xml:id="echoid-s12667" xml:space="preserve">conficiemus grad. </s>
  <s xml:id="echoid-s12668" xml:space="preserve">255. </s>
  <s xml:id="echoid-s12669" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12670" xml:space="preserve">53. </s>
  <s xml:id="echoid-s12671" xml:space="preserve">pro aſcenſione obliqua grad. </s>
  <s xml:id="echoid-s12672" xml:space="preserve">29. </s>
  <s xml:id="echoid-s12673" xml:space="preserve">♏. </s>
  <s xml:id="echoid-s12674" xml:space="preserve">Ad extremum <lb/>ſi apponamus differentiam eandem ad aſcenſionem rectam grad. </s>
  <s xml:id="echoid-s12675" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12676" xml:space="preserve">♒, quæ grad. </s>
  <s xml:id="echoid-s12677" xml:space="preserve">303. </s>
  <s xml:id="echoid-s12678" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12679" xml:space="preserve">14. </s>
  <s xml:id="echoid-s12680" xml:space="preserve">complecti-<lb/>tur, conflabitur arcus grad. </s>
  <s xml:id="echoid-s12681" xml:space="preserve">322. </s>
  <s xml:id="echoid-s12682" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12683" xml:space="preserve">21. </s>
  <s xml:id="echoid-s12684" xml:space="preserve">pro obliqua aſcenſione grad. </s>
  <s xml:id="echoid-s12685" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12686" xml:space="preserve">♒. </s>
  <s xml:id="echoid-s12687" xml:space="preserve">Eadem{q́ue} de cæteris eſt ha-<lb/>benda ratio. </s>
  <s xml:id="echoid-s12688" xml:space="preserve">Hæc pauca libuit hocloco deguſtare ex aſcenſionibus rectis, &amp; </s>
  <s xml:id="echoid-s12689" xml:space="preserve">obliquis; </s>
  <s xml:id="echoid-s12690" xml:space="preserve">plura enim alio <lb/>in loco de eiſdem diſputauimus.</s>
  <s xml:id="echoid-s12691" xml:space="preserve"/>
</p>
<div xml:id="echoid-div672" type="float" level="2" n="14">
<note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">Quo pacto ta-<lb/>bula aſcenſio-<lb/>num obliqua-<lb/>rum ex differẽ-<lb/>tiis aſcenſio na-<lb/>libus compona <lb/>tu<unsure/>r<unsure/>.</note>
<note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div674" type="section" level="1" n="171">
<head xml:id="echoid-head174" xml:space="preserve">PROBLEMA. 10. PROPOSITIO 10.</head>
<p>
  <s xml:id="echoid-s12692" xml:space="preserve">HOROLOGIVM Italicum Horizontale conſtituere. </s>
  <s xml:id="echoid-s12693" xml:space="preserve">Hoc eſt <lb/>lineas horarum ab occaſu Solis in plano Horizonti æquidiſtanti de-<lb/>ſcribere.</s>
  <s xml:id="echoid-s12694" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s12695" xml:space="preserve">SECETVR circulus ex E, deſcriptus propoſ. </s>
  <s xml:id="echoid-s12696" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12697" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s12698" xml:space="preserve">in duas portiones, vt in ſcholio pro-<lb/>
<anchor type="note" xlink:label="note-0212-05a" xlink:href="note-0212-05"/>
poſ. </s>
  <s xml:id="echoid-s12699" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12700" xml:space="preserve">præcedentis libri tradidimus, quarum a N b, ſimilis ſit arcui diurno tropici ♋, &amp; </s>
  <s xml:id="echoid-s12701" xml:space="preserve">a M b, ar-<lb/>cui nocturno eiuſdem tropici. </s>
  <s xml:id="echoid-s12702" xml:space="preserve">Diuiſo autem circulo eodem ex E, deſcripto in partes 24. </s>
  <s xml:id="echoid-s12703" xml:space="preserve">æquales, <lb/>
<anchor type="note" xlink:label="note-0212-06a" xlink:href="note-0212-06"/>
initio facto à pũcto b, quod occidentale eſt in communi ſectione Horizontis, &amp; </s>
  <s xml:id="echoid-s12704" xml:space="preserve">paralleli a b, (vt <lb/>conſtat, ſi dictus circulus ex E, deſcriptus in propria poſitione concipiatur collocatus eſſe) tranſi-<lb/>bunt per hæc puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s12705" xml:space="preserve">per centrum E, ſi circulus in propria poſitione exiſtat, circuli <lb/>maximi per polos Mundi, &amp; </s>
  <s xml:id="echoid-s12706" xml:space="preserve">per horas ab occaſu in tropico ♋, ducti, inſtar horariorum circulo-<lb/>rum à meridie, vel media nocte. </s>
  <s xml:id="echoid-s12707" xml:space="preserve">Quoniam enim circuli maximi per polos mundi ducti diui-<lb/>dunt tropicum ♋, &amp; </s>
  <s xml:id="echoid-s12708" xml:space="preserve">Aequatorem, per propoſ. </s>
  <s xml:id="echoid-s12709" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12710" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12711" xml:space="preserve">2. </s>
  <s xml:id="echoid-s12712" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s12713" xml:space="preserve">in arcus ſimiles; </s>
  <s xml:id="echoid-s12714" xml:space="preserve">erit arcus Ae-<lb/>quatoris interceptus inter Meridianum, &amp; </s>
  <s xml:id="echoid-s12715" xml:space="preserve">circulum maximum per horam 24. </s>
  <s xml:id="echoid-s12716" xml:space="preserve">ab occaſu in tropi-<lb/>co ♋, hoc eſt, per punctum, vbi tropicus ♋, Horizontem ſecat, ductum, ſimilis arcui tropici ♋, <lb/>inter eoſdem circulos poſito, hoc eſt, arcui ſemidiurno tropici ♋. </s>
  <s xml:id="echoid-s12717" xml:space="preserve">Quoniam vero communes ſe-<lb/>ctiones, quas dicti circuli maximi cum Æquatore faciunt, per centrum Æquatoris E, ductæ ſe-<lb/>
<anchor type="note" xlink:label="note-0212-07a" xlink:href="note-0212-07"/>
cant quoque, per ea, quæ ad finem cap. </s>
  <s xml:id="echoid-s12718" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12719" xml:space="preserve">ſphæræ à nobis demonſtrata ſunt, Æquatorem, &amp; </s>
  <s xml:id="echoid-s12720" xml:space="preserve">circu-<lb/>lum M a N b, ex E, centro Aequatoris, in eiuſdemq́ue plano deſcriptum, in arcus ſimiles; </s>
  <s xml:id="echoid-s12721" xml:space="preserve">erit <lb/>quoque arcus circuli M a N b, inter dictas ſectiones communes poſitus, ſimilis arcui ſemidiurno <lb/>tropici ♋. </s>
  <s xml:id="echoid-s12722" xml:space="preserve">Cum ergo M N, ſit ſectio facta in Aequatore à Meridiano, atque adeo Meridianus per <lb/>punctum N, ducatur, arcusq́; </s>
  <s xml:id="echoid-s12723" xml:space="preserve">N b, ſimilis ſit arcui ſemidiurno tropici ♋, (Quoniam enim totus <lb/>arcus b N a, ſimilis eſt, per conſtructionem, toti arcui diurno tropici ♋, erit quoque b N, dimidia-<lb/>tus arcus ipſius b N a, ſemidiurno arcui tropici ♋, ſimilis) atque adeo &amp; </s>
  <s xml:id="echoid-s12724" xml:space="preserve">arcui Aequatoris inter <lb/>prædictas ſectiones interiecto, tranſibit neceſſario circulus alter maximus per horam 24. </s>
  <s xml:id="echoid-s12725" xml:space="preserve">ab occa-<lb/>ſu in tropico ♋, ductus, per punctum b. </s>
  <s xml:id="echoid-s12726" xml:space="preserve">Si enim per aliud punctum tranſiret, non auferrent dictæ <lb/>ſectiones ex Aequatore arcum ſimilem arcui b N, ſed illi, qui inter rectam E N, &amp; </s>
  <s xml:id="echoid-s12727" xml:space="preserve">aliud illud pun-<lb/>ctum interijceretur. </s>
  <s xml:id="echoid-s12728" xml:space="preserve">Quod eſt abſurdum. </s>
  <s xml:id="echoid-s12729" xml:space="preserve">Oſtendimus enim arcum ex Aequatore ablatum arcui
<pb o="193" file="0213" n="213" rhead="LIBER SECVNDVS."/>
b N, ſimilem eſſe, quòd hic ſimilis ſit arcui ſemidiurno tropici ♋. </s>
  <s xml:id="echoid-s12730" xml:space="preserve">Et quoniã arcus inter b, &amp; </s>
  <s xml:id="echoid-s12731" xml:space="preserve">pro-<lb/>ximum punctum diuiſionis verſus N, ſimilis eſt etiam arcui tropici ♋, inter duos maximos circu <lb/>los, qui per polos ducuntur, interiecto, quorum vnus per horam 24. </s>
  <s xml:id="echoid-s12732" xml:space="preserve">ab occaſu, id eſt, per pun-<lb/>
<anchor type="figure" xlink:label="fig-0213-01a" xlink:href="fig-0213-01"/>
<anchor type="note" xlink:label="note-0213-01a" xlink:href="note-0213-01"/>
<anchor type="note" xlink:label="note-0213-02a" xlink:href="note-0213-02"/>
ctum b, alter autem per horam 23. </s>
  <s xml:id="echoid-s12733" xml:space="preserve">aboccaſu in tropico ♋, ducitur, quòd vterque arcus ſit pars <lb/>
<anchor type="note" xlink:label="note-0213-03a" xlink:href="note-0213-03"/>
24. </s>
  <s xml:id="echoid-s12734" xml:space="preserve">ſui circuli; </s>
  <s xml:id="echoid-s12735" xml:space="preserve">tranſibit quoque per proximum punctum diuiſionis, à puncto b, verſus N, proce-<lb/>dendo, circulus maximus per polos mundi, &amp; </s>
  <s xml:id="echoid-s12736" xml:space="preserve">horam 23. </s>
  <s xml:id="echoid-s12737" xml:space="preserve">ab occaſu in tropico ♋, ductus: </s>
  <s xml:id="echoid-s12738" xml:space="preserve">qu ia <lb/>hac ratione rectæ ex centro E, ductæ per b, &amp; </s>
  <s xml:id="echoid-s12739" xml:space="preserve">per punctum proximum verſus N, hoc eſt, ſectiones <lb/>factę à duobus illis circulis maximis per polos, ac per horas 24. </s>
  <s xml:id="echoid-s12740" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12741" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12742" xml:space="preserve">ab occaſu in tropico ♋, du-<lb/>ctis, auferent ex Aequatore arcũ ſimilem arcui tropici inter horas 24. </s>
  <s xml:id="echoid-s12743" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12744" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12745" xml:space="preserve">poſito, vt vult Theod. <lb/></s>
  <s xml:id="echoid-s12746" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s12747" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12748" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12749" xml:space="preserve">2. </s>
  <s xml:id="echoid-s12750" xml:space="preserve">quod alioquin non contingeret, Si enim per aliud punctum tranſiret dictus cir-<lb/>culus, eſſet arcus circuli M a N b, inter b, &amp; </s>
  <s xml:id="echoid-s12751" xml:space="preserve">illud punctum, maior vel minor quàm vigeſimaquar <lb/>ta pars; </s>
  <s xml:id="echoid-s12752" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s12753" xml:space="preserve">arcus Aequatoris huic ſimilis, (vt conſtat ex demonſtratis à nobis ad finem <lb/>cap. </s>
  <s xml:id="echoid-s12754" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12755" xml:space="preserve">ſphæræ) foret maior, vel minor quàm pars vigeſimaquarta; </s>
  <s xml:id="echoid-s12756" xml:space="preserve">atque adeo non ſimilis prædi <lb/>cto arcui ttopici ♋. </s>
  <s xml:id="echoid-s12757" xml:space="preserve">Quod eſt abſurdum. </s>
  <s xml:id="echoid-s12758" xml:space="preserve">Eadem ratione ſequens punctum verſus N, horam 22. </s>
  <s xml:id="echoid-s12759" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0213-04a" xlink:href="note-0213-04"/>
&amp; </s>
  <s xml:id="echoid-s12760" xml:space="preserve">reliqua reliquas horas indicabunt.</s>
  <s xml:id="echoid-s12761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div674" type="float" level="2" n="1">
<note position="left" xlink:label="note-0212-05" xlink:href="note-0212-05a" xml:space="preserve">I<unsure/>talici horolo-<lb/>gii horizontalis<unsure/> <lb/>compoſitio.</note>
<note position="left" xlink:label="note-0212-06" xlink:href="note-0212-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0212-07" xlink:href="note-0212-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0213-01" xlink:href="fig-0213-01a">
    <image file="0213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0213-01"/>
  </figure>
<note position="left" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0213-03" xlink:href="note-0213-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0213-04" xlink:href="note-0213-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s12762" xml:space="preserve">IAM verò ex circulo M a N b, ita diuiſo, inueniemus in arcu ♋, puncta horarum ab occaſu, <lb/>hac ratione. </s>
  <s xml:id="echoid-s12763" xml:space="preserve">Per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s12764" xml:space="preserve">centrum E, rectas lineas occultas educemus ſecantes æqui-<lb/>noctialem lineam in punctis, per quæ ſi rectæ occultæ ducantur ex H, centro horologij, ſecabitur <lb/>tropicus ♋, in punctis horarum ab occaſu. </s>
  <s xml:id="echoid-s12765" xml:space="preserve">Verbi gratia, per punctum f, horæ 18. </s>
  <s xml:id="echoid-s12766" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s12767" xml:space="preserve">per <lb/>centrum E, ducta recta f E, ſecat lineam æquinoctialem in g; </s>
  <s xml:id="echoid-s12768" xml:space="preserve">Recta autem H g, ducta ſecat arcum <lb/>♋, in h, puncto, quod dico pertinere ad horam 18. </s>
  <s xml:id="echoid-s12769" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s12770" xml:space="preserve">Quoniam enim recta f g, commu <lb/>nis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s12771" xml:space="preserve">circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s12772" xml:space="preserve">horam 18. </s>
  <s xml:id="echoid-s12773" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12774" xml:space="preserve">in tropico ♋, <lb/>ducti; </s>
  <s xml:id="echoid-s12775" xml:space="preserve">propterea quòd, vt oſtendimus, dictus circulus maximus per punctum f, horę 18. </s>
  <s xml:id="echoid-s12776" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12777" xml:space="preserve">ſi <lb/>circulus M a N b, in proprio ſitu ſtatuatur, ac per centrum mundi E, tranſit; </s>
  <s xml:id="echoid-s12778" xml:space="preserve">occurret dictus cir-<lb/>
<anchor type="note" xlink:label="note-0213-05a" xlink:href="note-0213-05"/>
culus maximus plano horologii in puncto g. </s>
  <s xml:id="echoid-s12779" xml:space="preserve">Quia verò circulus idem per H, centrum horologij <lb/>tranſit, per propoſ. </s>
  <s xml:id="echoid-s12780" xml:space="preserve">18. </s>
  <s xml:id="echoid-s12781" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s12782" xml:space="preserve">quòd per axem ducatur, erit recta Hg, cõmunis ſectio eiuſ-<lb/>dem maximi circuli, &amp; </s>
  <s xml:id="echoid-s12783" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s12784" xml:space="preserve">Quare cum, Sole exiſtente in illo circulo maximo, vmbra <lb/>ſtyli, per propoſ. </s>
  <s xml:id="echoid-s12785" xml:space="preserve">11. </s>
  <s xml:id="echoid-s12786" xml:space="preserve">eiuſdem libri ſuperioris, cadat in rectam Hg, &amp; </s>
  <s xml:id="echoid-s12787" xml:space="preserve">eodem exiſtente in tropico <lb/>♋, proijciatur, per propoſ. </s>
  <s xml:id="echoid-s12788" xml:space="preserve">12. </s>
  <s xml:id="echoid-s12789" xml:space="preserve">eiuſdem ſuperioris libri, in arcum ♋; </s>
  <s xml:id="echoid-s12790" xml:space="preserve">fit vt Sole poſſidente punctũ <lb/>horæ 18. </s>
  <s xml:id="echoid-s12791" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12792" xml:space="preserve">in tropico ♋, vbi dictus circulus maximus, &amp; </s>
  <s xml:id="echoid-s12793" xml:space="preserve">tropicus ♋, ſe interſecant, vmbra <lb/>ſtyli proijciatur in punctum h, ac proinde per h, ducenda erit linea horæ 18. </s>
  <s xml:id="echoid-s12794" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s12795" xml:space="preserve">Eademq́; <lb/></s>
  <s xml:id="echoid-s12796" xml:space="preserve">de cæteris ratio eſt ha benda.</s>
  <s xml:id="echoid-s12797" xml:space="preserve"/>
</p>
<div xml:id="echoid-div675" type="float" level="2" n="2">
<note position="left" xlink:label="note-0213-05" xlink:href="note-0213-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s12798" xml:space="preserve">VERVM hac ratione, vt vides, inueniuntur in tropico ♋, puncta illarum duntaxat horarũ, <lb/>quæ in ſemicirculo t N u, continentur, propterea quòd communes ſectiones illorum maximorũ <lb/>circulorum, &amp; </s>
  <s xml:id="echoid-s12799" xml:space="preserve">Aequatoris, indicant in linea æquinoctiali illas horas, è quibus per centrum E, du-
<pb o="194" file="0214" n="214" rhead="GNOMONICES"/>
cuntur, antequam æquinoctiali lineæ occurrant, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s12800" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12801" xml:space="preserve">huius libri diximus: </s>
  <s xml:id="echoid-s12802" xml:space="preserve">cu-<lb/>iuſmodi ſunt ſolum illæ horæ, quæ in ſemicirculo t N u, reperiuntur, vt patet. </s>
  <s xml:id="echoid-s12803" xml:space="preserve">Vnde pro reliquis <lb/>horis, cuiuſmodi in noſtro exemplo ſunt 9. </s>
  <s xml:id="echoid-s12804" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12805" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12806" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12807" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12808" xml:space="preserve">vt in figura cernitur, inueniemus pun <lb/>cta in tropico ♋, hoc modo. </s>
  <s xml:id="echoid-s12809" xml:space="preserve">Ex horis quæ per diametrum opponuntur iſtis horis in circulo <lb/>
<anchor type="figure" xlink:label="fig-0214-01a" xlink:href="fig-0214-01"/>
<anchor type="note" xlink:label="note-0214-01a" xlink:href="note-0214-01"/>
<anchor type="note" xlink:label="note-0214-02a" xlink:href="note-0214-02"/>
M a N b, (habentur autem horæ oppoſitæ ex additione horarum 12. </s>
  <s xml:id="echoid-s12810" xml:space="preserve">ad horas illas, reiectis tamen <lb/>
<anchor type="note" xlink:label="note-0214-03a" xlink:href="note-0214-03"/>
24. </s>
  <s xml:id="echoid-s12811" xml:space="preserve">ſi numerus ex additione collectus maior fuerit, quàm 24. </s>
  <s xml:id="echoid-s12812" xml:space="preserve">Vt horæ 9. </s>
  <s xml:id="echoid-s12813" xml:space="preserve">opponitur hora 21. </s>
  <s xml:id="echoid-s12814" xml:space="preserve">quia <lb/>ex 9. </s>
  <s xml:id="echoid-s12815" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12816" xml:space="preserve">12. </s>
  <s xml:id="echoid-s12817" xml:space="preserve">fiunt 21. </s>
  <s xml:id="echoid-s12818" xml:space="preserve">Ita etiam horæ 23. </s>
  <s xml:id="echoid-s12819" xml:space="preserve">opponitur hora 11. </s>
  <s xml:id="echoid-s12820" xml:space="preserve">quia ex 23. </s>
  <s xml:id="echoid-s12821" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12822" xml:space="preserve">12. </s>
  <s xml:id="echoid-s12823" xml:space="preserve">fiunt 35. </s>
  <s xml:id="echoid-s12824" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12825" xml:space="preserve">abiectis <lb/>24. </s>
  <s xml:id="echoid-s12826" xml:space="preserve">remanent 11. </s>
  <s xml:id="echoid-s12827" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s12828" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s12829" xml:space="preserve">ducemus per centrum E, rectas ſecantes æquinoctialem lineam in punctis, <lb/>per quæ ſi ex H, ducantur rectæ, ſecabitur quidem tropicus ♋, in punctis, quæ horis illis oppoſitis <lb/>reſpondent, vt demonſtratum eſt: </s>
  <s xml:id="echoid-s12830" xml:space="preserve">Si verò illæ rectæ vltra centrum H, producantur, ſecabitur tro-<lb/>picus ♋, in punctis, quæ illis aliis horis reſpondent, quæ in ſemicirculo t N u, non continentur, &amp; </s>
  <s xml:id="echoid-s12831" xml:space="preserve"><lb/>quarum oppoſitæ acceptæ ſunt. </s>
  <s xml:id="echoid-s12832" xml:space="preserve">Vt ex m, puncto horæ 11. </s>
  <s xml:id="echoid-s12833" xml:space="preserve">quæ per diametrum opponitur horæ <lb/>23. </s>
  <s xml:id="echoid-s12834" xml:space="preserve">ducta recta per centrum E, ſecat æquinoctialem lineam in n: </s>
  <s xml:id="echoid-s12835" xml:space="preserve">ducta autem recta H n, ſecat tro-<lb/>picum ♋, in q, puncto horæ 11. </s>
  <s xml:id="echoid-s12836" xml:space="preserve">producta denique recta n H, vltra centrum ſecat tropicum ♋, in <lb/>puncto p, quod dico horæ 23. </s>
  <s xml:id="echoid-s12837" xml:space="preserve">deberi. </s>
  <s xml:id="echoid-s12838" xml:space="preserve">Quoniã enim circulus maximus per polos mundi ductus, <lb/>
<anchor type="note" xlink:label="note-0214-04a" xlink:href="note-0214-04"/>
&amp; </s>
  <s xml:id="echoid-s12839" xml:space="preserve">per horam vndecimam tropici ♋, ſecat, per propoſ. </s>
  <s xml:id="echoid-s12840" xml:space="preserve">15. </s>
  <s xml:id="echoid-s12841" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12842" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12843" xml:space="preserve">Theodoſii, tropicum ♋, atque <lb/>adeo &amp; </s>
  <s xml:id="echoid-s12844" xml:space="preserve">Aequatorem, ſiue circulum M a N b, bifariam, tranſibit omnino per horam 23. </s>
  <s xml:id="echoid-s12845" xml:space="preserve">quæ inte-<lb/>gro ſemicirculo, hoc eſt, horis 12. </s>
  <s xml:id="echoid-s12846" xml:space="preserve">abeſt ab hora vndecima, adeò vt vnus ſemicirculus eius monſtret <lb/>horam vndecimam, &amp; </s>
  <s xml:id="echoid-s12847" xml:space="preserve">alter 23. </s>
  <s xml:id="echoid-s12848" xml:space="preserve">Eſt ergo recta m E n, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s12849" xml:space="preserve">circuli ma <lb/>ximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s12850" xml:space="preserve">horam vndecimam, &amp; </s>
  <s xml:id="echoid-s12851" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12852" xml:space="preserve">tropici ♋, ducti. </s>
  <s xml:id="echoid-s12853" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s12854" xml:space="preserve">recta n H p, com-<lb/>munis ſectio eſt eiuſdem circuli maximi &amp; </s>
  <s xml:id="echoid-s12855" xml:space="preserve">plani horologij, quandoquidem dictus circulus plano <lb/>horologii occurrit in punctis n, &amp; </s>
  <s xml:id="echoid-s12856" xml:space="preserve">H; </s>
  <s xml:id="echoid-s12857" xml:space="preserve">hac tamen lege, vt portio H n, æquinoctialem lineam ſecans <lb/>referat ſemicirculum illius circuli maximi per horam vndecimam in tropico ♋, tranſeuntem, cu-<lb/>ius videlicet ſectio m E, per centrum E, ducitur, antequam lineæ æquinoctiali occurrat, vt in ſcho <lb/>lio propoſ. </s>
  <s xml:id="echoid-s12858" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12859" xml:space="preserve">huius libri ſcripſimus. </s>
  <s xml:id="echoid-s12860" xml:space="preserve">Ex quo fit, vt reliqua portio H p, vltra centrum horolo-<lb/>
<anchor type="note" xlink:label="note-0214-05a" xlink:href="note-0214-05"/>
gii producta, &amp; </s>
  <s xml:id="echoid-s12861" xml:space="preserve">æquinoctialem lineam non ſecans, referat alterum ſemicirculum per ho-<lb/>ram 23. </s>
  <s xml:id="echoid-s12862" xml:space="preserve">ductum, veluti in eodem ſcholio docuimus. </s>
  <s xml:id="echoid-s12863" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s12864" xml:space="preserve">ibi oſtendimus, lineam horariam, <lb/>quæ æquinoctialem lineam ſecat, indicare horam vnius ſemicirculi, portionem verò eius vltra cẽ-<lb/>trum productam, quæ lineam æquinoctialem non ſecat, monſtrare horam alterius ſemicirculi op-<lb/>poſiti; </s>
  <s xml:id="echoid-s12865" xml:space="preserve">ita vt duæ illæ horæ integro ſemicirculo, ſeu 12. </s>
  <s xml:id="echoid-s12866" xml:space="preserve">horis in Aequatore inter ſe diſtent, vt &amp; </s>
  <s xml:id="echoid-s12867" xml:space="preserve"><lb/>hic contingit. </s>
  <s xml:id="echoid-s12868" xml:space="preserve">Quare per punctum p, ducenda eſt linea horæ 23. </s>
  <s xml:id="echoid-s12869" xml:space="preserve">Idem de cæteris iudicium ha-<lb/>beatur. </s>
  <s xml:id="echoid-s12870" xml:space="preserve">Nam ita inueſtigabimus puncta in eodem tropico ♋, pro horis 9. </s>
  <s xml:id="echoid-s12871" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12872" xml:space="preserve">10. </s>
  <s xml:id="echoid-s12873" xml:space="preserve">ſi ex horis 21. </s>
  <s xml:id="echoid-s12874" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12875" xml:space="preserve"><lb/>22. </s>
  <s xml:id="echoid-s12876" xml:space="preserve">quæ illis opponuntur, per centrum E, rectas educamus, &amp;</s>
  <s xml:id="echoid-s12877" xml:space="preserve">c.</s>
  <s xml:id="echoid-s12878" xml:space="preserve"/>
</p>
<div xml:id="echoid-div676" type="float" level="2" n="3">
  <figure xlink:label="fig-0214-01" xlink:href="fig-0214-01a">
    <image file="0214-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0214-01"/>
  </figure>
<note position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0214-04" xlink:href="note-0214-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0214-05" xlink:href="note-0214-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s12879" xml:space="preserve">EODEM modo, ſi circulum ex E, deſcriptum ſecemus in duas portiones, quarum d N e, ſi-<lb/>milis ſit arcui diurno tropici ♑, &amp; </s>
  <s xml:id="echoid-s12880" xml:space="preserve">d M e, nocturno eiuſdem, (quod facile fiet, ſi arcubus M a, Mb, <lb/>æquales arcus ſumamus N d, N e, rectamq́; </s>
  <s xml:id="echoid-s12881" xml:space="preserve">d e, ducamus, ita vt rectæ a b, d e, ex diametro M N,
<pb o="195" file="0215" n="215" rhead="LIBER SECVNDVS."/>
æquales lineas abſcindant M α, N β, perpendicularesq́; </s>
  <s xml:id="echoid-s12882" xml:space="preserve">ſint ad M N) eumq́ue in partes 24. </s>
  <s xml:id="echoid-s12883" xml:space="preserve">æqua-<lb/>les diſtribuamus, initio facto à puncto e, occidentali; </s>
  <s xml:id="echoid-s12884" xml:space="preserve">reperiemus in arcu ♑, puncta, per quæ horæ <lb/>ab occaſu ducendæ erunt. </s>
  <s xml:id="echoid-s12885" xml:space="preserve">Vt ſi ex puncto δ, horæ 23. </s>
  <s xml:id="echoid-s12886" xml:space="preserve">tropici ♑, per centrum E, rectã ducamus, <lb/>quæ æquinoctialem lineam ſecet in ε, inueniemus per rectam H ε, productam in arcu ♑, punctũ <lb/>λ, pro hora 23. </s>
  <s xml:id="echoid-s12887" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12888" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s12889" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s12890" xml:space="preserve">QVOD ſi non lubeat circulum M a N b, ex E, deſcriptum ſecare in duas portiones, quarum <lb/>
<anchor type="note" xlink:label="note-0215-01a" xlink:href="note-0215-01"/>
vna ſimilis ſit arcui diurno tropici ♋, vel ♑, &amp; </s>
  <s xml:id="echoid-s12891" xml:space="preserve">nocturno altera, ea ratione, quam in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s12892" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12893" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s12894" xml:space="preserve">antecedentis tradidimus; </s>
  <s xml:id="echoid-s12895" xml:space="preserve">abſoluen dum erit negorium hoc modo. </s>
  <s xml:id="echoid-s12896" xml:space="preserve">Ex puncto N, numere <lb/>tur vtrinque arcus ſemidiurnus, tropici quidem ♋, vſque ad puncta a, &amp; </s>
  <s xml:id="echoid-s12897" xml:space="preserve">b, tropici vero ♑, vſque <lb/>ad puncta d, &amp; </s>
  <s xml:id="echoid-s12898" xml:space="preserve">e. </s>
  <s xml:id="echoid-s12899" xml:space="preserve">Quod quidem facile fiet, ſi circulus occulte diuidatur in 24. </s>
  <s xml:id="echoid-s12900" xml:space="preserve">horas æquales, ini-<lb/>
<anchor type="note" xlink:label="note-0215-02a" xlink:href="note-0215-02"/>
tio facto à puncto N, &amp; </s>
  <s xml:id="echoid-s12901" xml:space="preserve">ex vtraquè parte numerentur horæ in arcu ſemidiurno contentæ, &amp;</s>
  <s xml:id="echoid-s12902" xml:space="preserve">c. </s>
  <s xml:id="echoid-s12903" xml:space="preserve">Du-<lb/>ctis enim rectis a b, d e, habebimus eaſdem portiones, quas prius, reſpondentes arcui diurno tro-<lb/>pici ♋, vel ♑. </s>
  <s xml:id="echoid-s12904" xml:space="preserve">Vnde diuiſio circuli rurſus inchoanda erit à puncto b, vel à puncto e.</s>
  <s xml:id="echoid-s12905" xml:space="preserve"/>
</p>
<div xml:id="echoid-div677" type="float" level="2" n="4">
<note position="right" xlink:label="note-0215-01" xlink:href="note-0215-01a" xml:space="preserve">Quo pacto cir-<lb/>culus M a N b, <lb/>aliter diuida-<lb/>tur in arcum <lb/>diuinum tropi <lb/>ci Cancri, vel <lb/>Capricorni.</note>
<note position="left" xlink:label="note-0215-02" xlink:href="note-0215-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s12906" xml:space="preserve">POSSVMVS quoque initium huius diuiſionis ſtatuere in qualibet hora ab occaſu, etiamſi <lb/>
<anchor type="note" xlink:label="note-0215-03a" xlink:href="note-0215-03"/>
circulum non ſecemus in arcum diurnum tropici ♋, vel ♑, hac ratione. </s>
  <s xml:id="echoid-s12907" xml:space="preserve">Arcus ſemidiurnus au-<lb/>ferantur ex horis 24. </s>
  <s xml:id="echoid-s12908" xml:space="preserve">vt habeatur tempus meridiei more Italorũ. </s>
  <s xml:id="echoid-s12909" xml:space="preserve">Ex hoc tempore cognoſcemus, <lb/>quantum hora quælibet ab occ. </s>
  <s xml:id="echoid-s12910" xml:space="preserve">propoſita diſtet à meridie. </s>
  <s xml:id="echoid-s12911" xml:space="preserve">Vnde ſi à puncto N, numeretur hæc <lb/>diſtantia verſus b, ſi hora propoſita eſt pomeridiana, aut verſus a, ſi antemeridiana, habebimus <lb/>punctum propoſitæ horæ, à qua diuiſio circuli in 24. </s>
  <s xml:id="echoid-s12912" xml:space="preserve">partes æquales inchoanda erit. </s>
  <s xml:id="echoid-s12913" xml:space="preserve">Exempli <lb/>gratia, Sole exiſtente in principio ♋, arcus ſemidiurnus, ad latitudinem grad. </s>
  <s xml:id="echoid-s12914" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12915" xml:space="preserve">continet hor. </s>
  <s xml:id="echoid-s12916" xml:space="preserve">7. <lb/></s>
  <s xml:id="echoid-s12917" xml:space="preserve">
<anchor type="note" xlink:label="note-0215-04a" xlink:href="note-0215-04"/>
Min. </s>
  <s xml:id="echoid-s12918" xml:space="preserve">32. </s>
  <s xml:id="echoid-s12919" xml:space="preserve">quo ſublato ex horis 24. </s>
  <s xml:id="echoid-s12920" xml:space="preserve">remanent hor. </s>
  <s xml:id="echoid-s12921" xml:space="preserve">16. </s>
  <s xml:id="echoid-s12922" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12923" xml:space="preserve">28. </s>
  <s xml:id="echoid-s12924" xml:space="preserve">pro tempore meridiei: </s>
  <s xml:id="echoid-s12925" xml:space="preserve">ac proin-<lb/>de hora 18. </s>
  <s xml:id="echoid-s12926" xml:space="preserve">ab occaſu diſtabit à meridie verſus partes occidentales hora 1. </s>
  <s xml:id="echoid-s12927" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12928" xml:space="preserve">32. </s>
  <s xml:id="echoid-s12929" xml:space="preserve">hoc eſt, gra-<lb/>dibus 23. </s>
  <s xml:id="echoid-s12930" xml:space="preserve">Si igitur ex N, verſus b, numerentur grad. </s>
  <s xml:id="echoid-s12931" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12932" xml:space="preserve">vel hor. </s>
  <s xml:id="echoid-s12933" xml:space="preserve">1. </s>
  <s xml:id="echoid-s12934" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12935" xml:space="preserve">32. </s>
  <s xml:id="echoid-s12936" xml:space="preserve">reperietur punctum <lb/>f, horæ 18. </s>
  <s xml:id="echoid-s12937" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12938" xml:space="preserve">in tropico ♋, à quo diuiſio circuli principium habere poteſt, vt aliæ horæ ab <lb/>occ. </s>
  <s xml:id="echoid-s12939" xml:space="preserve">habeantut. </s>
  <s xml:id="echoid-s12940" xml:space="preserve">Rurſus ab eodem meridie diſtabit hora vndecima ab occ. </s>
  <s xml:id="echoid-s12941" xml:space="preserve">horis 5. </s>
  <s xml:id="echoid-s12942" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12943" xml:space="preserve">28. </s>
  <s xml:id="echoid-s12944" xml:space="preserve">hoc <lb/>eſt, gradibus 82. </s>
  <s xml:id="echoid-s12945" xml:space="preserve">quæ diſtantia ſi numeretur ex N, verſus a, quia hora vndecima eſt antemeridia-<lb/>na, inuenietur punctum m, horæ vndecimæ ab occ. </s>
  <s xml:id="echoid-s12946" xml:space="preserve">in tropico ♋, à quo etiam diuiſio circuli ini-<lb/>tium poteſt habere. </s>
  <s xml:id="echoid-s12947" xml:space="preserve">Poſtremo, Sole exiſtente in principio ♑, arcus ſemidiurnus comprehendit <lb/>hor. </s>
  <s xml:id="echoid-s12948" xml:space="preserve">4. </s>
  <s xml:id="echoid-s12949" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12950" xml:space="preserve">28. </s>
  <s xml:id="echoid-s12951" xml:space="preserve">ad eandem latitudinem grad. </s>
  <s xml:id="echoid-s12952" xml:space="preserve">42. </s>
  <s xml:id="echoid-s12953" xml:space="preserve">quo detracto ex 24. </s>
  <s xml:id="echoid-s12954" xml:space="preserve">remanent hor. </s>
  <s xml:id="echoid-s12955" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12956" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s12957" xml:space="preserve">32. <lb/></s>
  <s xml:id="echoid-s12958" xml:space="preserve">pro tempore meridiei: </s>
  <s xml:id="echoid-s12959" xml:space="preserve">atque adeo hora 23. </s>
  <s xml:id="echoid-s12960" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12961" xml:space="preserve">diſtabit à meridie verſus occidentem horis 3. </s>
  <s xml:id="echoid-s12962" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0215-05a" xlink:href="note-0215-05"/>
Min. </s>
  <s xml:id="echoid-s12963" xml:space="preserve">28. </s>
  <s xml:id="echoid-s12964" xml:space="preserve">id eſt, grad. </s>
  <s xml:id="echoid-s12965" xml:space="preserve">52. </s>
  <s xml:id="echoid-s12966" xml:space="preserve">quæ diſtantia ſi ſupputetur ex N, verſus e, inuenietur punctum δ, pro ho <lb/>ra 23. </s>
  <s xml:id="echoid-s12967" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s12968" xml:space="preserve">in tropico ♑, &amp;</s>
  <s xml:id="echoid-s12969" xml:space="preserve">c. </s>
  <s xml:id="echoid-s12970" xml:space="preserve">Hac ratione, cognito tempore meridiei, reperiemus punctum cu-<lb/>iuſcunque horæ ab occ. </s>
  <s xml:id="echoid-s12971" xml:space="preserve">Quod etiam de horis ab ortu intelligi volo. </s>
  <s xml:id="echoid-s12972" xml:space="preserve">Atque hoc non ſolum in <lb/>tropico ♋, vel ♑, verumetiam in quocunque parallelo. </s>
  <s xml:id="echoid-s12973" xml:space="preserve">Vnde ſi à puncto propoſitæ horæ ab occ. <lb/></s>
  <s xml:id="echoid-s12974" xml:space="preserve">in circulo M a N b, per centrum E, ducatur recta linea occulta ſecans æquinoctialem lineam in <lb/>puncto, per quod ex H, centro horologii recta ducatur, ſecabitur parallelus ♋, vel ♑, vel alius qui-<lb/>cunque in puncto propoſitæ horæ ab occ. </s>
  <s xml:id="echoid-s12975" xml:space="preserve">prout illa hora ſumpta fuerit in parallelo ♋, vel ♑, aut <lb/>in alio quouis parallelo.</s>
  <s xml:id="echoid-s12976" xml:space="preserve"/>
</p>
<div xml:id="echoid-div678" type="float" level="2" n="5">
<note position="right" xlink:label="note-0215-03" xlink:href="note-0215-03a" xml:space="preserve">Quomodo à <lb/>qualibet hora <lb/>ab occ. initium <lb/>diuiſionis habe <lb/>re poteſt circu-<lb/>lus M a N b, e-<lb/>tiamſi non diui <lb/>dat<unsure/>ur in arcum <lb/>diurnum tropi <lb/>ci Cancri, vel <lb/>Capricorni. Itẽ <lb/>qua ratione in <lb/>eodem circulo <lb/>inuenienda ſit <lb/>quęcunque ho-<lb/>ra propoſita ab <lb/>or. vel occ. in <lb/>quocunque pa-<lb/>rallelo.</note>
<note position="left" xlink:label="note-0215-04" xlink:href="note-0215-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0215-05" xlink:href="note-0215-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s12977" xml:space="preserve">ITAQVE ſi puncta horarum correſpondentia, quæ in tropicis inuenta ſunt, connectantur li-<lb/>neis rectis, deſcriptum erit horologium Italicum. </s>
  <s xml:id="echoid-s12978" xml:space="preserve">Tranſibunt autem lineæ horarum ab occaſu per <lb/>
<anchor type="note" xlink:label="note-0215-06a" xlink:href="note-0215-06"/>
puncta lineæ æquinoctialis, per quæ lineæ horarum à meridie, vel media nocte incedunt; </s>
  <s xml:id="echoid-s12979" xml:space="preserve">nimirũ <lb/>linea horæ 23. </s>
  <s xml:id="echoid-s12980" xml:space="preserve">ab occaſu per punctum horæ quintæ à meridie, vel media nocte; </s>
  <s xml:id="echoid-s12981" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s12982" xml:space="preserve">linea horæ 22. <lb/></s>
  <s xml:id="echoid-s12983" xml:space="preserve">per punctum horæ quartæ, &amp; </s>
  <s xml:id="echoid-s12984" xml:space="preserve">ſic deinceps, quemadmodum ex tabula propoſ. </s>
  <s xml:id="echoid-s12985" xml:space="preserve">19. </s>
  <s xml:id="echoid-s12986" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s12987" xml:space="preserve"><lb/>cui titulus eſt, AEQVINOCTIALIS LINEA, vel ex tabula arcus diurni horarũ 12. </s>
  <s xml:id="echoid-s12988" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s12989" xml:space="preserve">23. </s>
  <s xml:id="echoid-s12990" xml:space="preserve">eiuſdem ſuperioris lib. </s>
  <s xml:id="echoid-s12991" xml:space="preserve">manifeſtũ eſt. </s>
  <s xml:id="echoid-s12992" xml:space="preserve">Vnde ſatis erit inuenire tantummodo puncta hora-<lb/>rum in alterutro tropicorũ: </s>
  <s xml:id="echoid-s12993" xml:space="preserve">hæc enim cum punctis correſpõdentibus in linea ęquinoctiali cõnexa <lb/>lineis rectis, dabunt horarias lineas ab occaſu, vt prius. </s>
  <s xml:id="echoid-s12994" xml:space="preserve">Accuratius tamen has lineas ducemus, ſi in <lb/>vtroque tropico horaria puncta inueſtigentur, vt terna correſpondentia puncta habeantur, per quę <lb/>ſingulæ lineæ horariæ duci debeant. </s>
  <s xml:id="echoid-s12995" xml:space="preserve">Ita enim facilè omnis error, qui in lineis horariis ducendis <lb/>committi poteſt, vitabitur.</s>
  <s xml:id="echoid-s12996" xml:space="preserve"/>
</p>
<div xml:id="echoid-div679" type="float" level="2" n="6">
<note position="left" xlink:label="note-0215-06" xlink:href="note-0215-06a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s12997" xml:space="preserve">QVOD ſi puncta aliquarum horarum in tropico ♋, inuenta non habeant puncta reſponden <lb/>tia in tropico ♑, cuiuſmodi ſunt in noſtro exemplo omnes horæ ante 16. </s>
  <s xml:id="echoid-s12998" xml:space="preserve">horam, ducendæ erunt <lb/>lineæ horariæ per puncta illarum horarum in tropico ♋, inuenta, &amp; </s>
  <s xml:id="echoid-s12999" xml:space="preserve">per puncta reſpondentia in <lb/>linea æquinoctiali, quæ quidem ex dicta tabula propoſ. </s>
  <s xml:id="echoid-s13000" xml:space="preserve">19. </s>
  <s xml:id="echoid-s13001" xml:space="preserve">præcedentis libri, vel ex tabula ſcho-<lb/>lii propoſ. </s>
  <s xml:id="echoid-s13002" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13003" xml:space="preserve">eiuſdem libri reperiuntur. </s>
  <s xml:id="echoid-s13004" xml:space="preserve">Linea verò horæ duodecimæ ducenda erit per punctum <lb/>in tropico ♋, inuentum lineæ æquinoctiali, vel lineæ horæ ſextæ à meridie, vel media nocte ęqui <lb/>diſtans. </s>
  <s xml:id="echoid-s13005" xml:space="preserve">In omni enim horologio horizontali, linea æquinoctialis, linea horæ ſextæ à meridie, <lb/>vel media nocte, &amp; </s>
  <s xml:id="echoid-s13006" xml:space="preserve">linea horæ duodecimæ ab occaſu, parallelæ ſunt, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s13007" xml:space="preserve">22 præ-<lb/>cedentis libri demonſtrauimus. </s>
  <s xml:id="echoid-s13008" xml:space="preserve">At vero hora 11. </s>
  <s xml:id="echoid-s13009" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s13010" xml:space="preserve">ſi produceretur, tranſiret per horam quin <lb/>tam à mer. </s>
  <s xml:id="echoid-s13011" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s13012" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13013" xml:space="preserve">in linea æquinoctiali; </s>
  <s xml:id="echoid-s13014" xml:space="preserve">Hora autem 10. </s>
  <s xml:id="echoid-s13015" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s13016" xml:space="preserve">per horam quartam à mer. <lb/></s>
  <s xml:id="echoid-s13017" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s13018" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13019" xml:space="preserve">quemadmodum tabula propoſ. </s>
  <s xml:id="echoid-s13020" xml:space="preserve">19. </s>
  <s xml:id="echoid-s13021" xml:space="preserve">libri ſuperioris præcipit.</s>
  <s xml:id="echoid-s13022" xml:space="preserve"/>
</p>
<pb o="196" file="0216" n="216" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s13023" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s13024" xml:space="preserve">Deſcribantur in horologio Aſtronomico, per propoſ. </s>
  <s xml:id="echoid-s13025" xml:space="preserve">2. </s>
  <s xml:id="echoid-s13026" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s13027" xml:space="preserve">duo paralleli <lb/>
<anchor type="note" xlink:label="note-0216-01a" xlink:href="note-0216-01"/>
arcuum diurnorum, vnus horarum 14. </s>
  <s xml:id="echoid-s13028" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13029" xml:space="preserve">horarum 10. </s>
  <s xml:id="echoid-s13030" xml:space="preserve">alter; </s>
  <s xml:id="echoid-s13031" xml:space="preserve">Vel potius (quod quidem ſatis erit <lb/>ad propoſitum negotium) in horis à meridie, &amp; </s>
  <s xml:id="echoid-s13032" xml:space="preserve">à media nocte imprimantur puncta, per quæ di-<lb/>ctiarcus tranſire debent, etiamſi arcus ipſi non ducantur. </s>
  <s xml:id="echoid-s13033" xml:space="preserve">Deinde diligenter conſiderentur tabu-<lb/>læ arcuum diurnorum horarum 10. </s>
  <s xml:id="echoid-s13034" xml:space="preserve">12. </s>
  <s xml:id="echoid-s13035" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13036" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13037" xml:space="preserve">quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s13038" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13039" xml:space="preserve">præcedentis libri poſui-<lb/>mus. </s>
  <s xml:id="echoid-s13040" xml:space="preserve">In his enim ſtatim apparebit, per quasnam horas à meridie, vel media nocte dictorum ar-<lb/>cuum ducendæ ſint horæ ab occaſu Solis. </s>
  <s xml:id="echoid-s13041" xml:space="preserve">Ita namque vides, horam 23. </s>
  <s xml:id="echoid-s13042" xml:space="preserve">ab occaſu ducendam eſſe <lb/>per horam quartam à meridie in arcu horarum 10. </s>
  <s xml:id="echoid-s13043" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13044" xml:space="preserve">per horam quintam à meridie in arcu ho-<lb/>rarum 12. </s>
  <s xml:id="echoid-s13045" xml:space="preserve">(qui idem eſt hic, quod æquinoctialis linea) &amp; </s>
  <s xml:id="echoid-s13046" xml:space="preserve">per horam ſextam à meridie in arcu ho-<lb/>rarum 14. </s>
  <s xml:id="echoid-s13047" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13048" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s13049" xml:space="preserve">Horæ autem, quæ in arcu horarum 10. </s>
  <s xml:id="echoid-s13050" xml:space="preserve">non habent puncta reſponden-<lb/>
<anchor type="note" xlink:label="note-0216-02a" xlink:href="note-0216-02"/>
tia, quales ſunt omnes horæ ante horam 15. </s>
  <s xml:id="echoid-s13051" xml:space="preserve">in noſtro exemplo, ducendæ ſunt per puncta in arcu-<lb/>bus horarum 14. </s>
  <s xml:id="echoid-s13052" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13053" xml:space="preserve">12. </s>
  <s xml:id="echoid-s13054" xml:space="preserve">Hora verò duodecima ab occaſu ducenda eſt parallela lineæ æquinoctiali <lb/>(nam linea horæ duodecimæ ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s13055" xml:space="preserve">linea æquinoctialis, parallelæ ſunt in horolo-<lb/>gio horizontali, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s13056" xml:space="preserve">22. </s>
  <s xml:id="echoid-s13057" xml:space="preserve">præcedentis libri docuimus) per horam ſeptimam à me-<lb/>dia nocte in arcu horarum 14. </s>
  <s xml:id="echoid-s13058" xml:space="preserve">vt ex tabula dicti arcus conſtat. </s>
  <s xml:id="echoid-s13059" xml:space="preserve">Quoniam verò hora vndecima ab <lb/>occaſu ſolum in arcu horarum 14. </s>
  <s xml:id="echoid-s13060" xml:space="preserve">punctum habet, nempe horam ſextam à media nocte, ducemus <lb/>horam vndecimam ab ortu per horam quartam à meridie in arcu horarũ 14. </s>
  <s xml:id="echoid-s13061" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13062" xml:space="preserve">per horam quin-<lb/>tam à meridie in arcu horarum 12. </s>
  <s xml:id="echoid-s13063" xml:space="preserve">vt ex dictorum arcuum tabalis conſtat: </s>
  <s xml:id="echoid-s13064" xml:space="preserve">hæc enim producta <lb/>dabit horam vndecimam ab occaſu, cum cadat in alteram partem paralleli ſemper apparentium <lb/>maximi, vt conſtat, ſi hic parallelus deſcriberetur. </s>
  <s xml:id="echoid-s13065" xml:space="preserve">Nam hora quæcunque ab ortu vltra arcum, ſeu <lb/>
<anchor type="note" xlink:label="note-0216-03a" xlink:href="note-0216-03"/>
parallelum ſemper apparentium, vel latentium maximum producta, dat eandem numero horam <lb/>ab occaſu, &amp; </s>
  <s xml:id="echoid-s13066" xml:space="preserve">è contrario, vt in ſequenti ſcholio oſtendemus. </s>
  <s xml:id="echoid-s13067" xml:space="preserve">Tranſibit autem neceſſario hæc ho-<lb/>ra vndecima ab ortu producta, ſi erratum non fuerit, per horam ſextam à media nocte in arcus ho <lb/>rarum 14. </s>
  <s xml:id="echoid-s13068" xml:space="preserve">per quam nimirum hora vndecima ab occaſu ducenda eſt, ex tabula arcu diurni hora-<lb/>rum 14. </s>
  <s xml:id="echoid-s13069" xml:space="preserve">Simili ratione, quia hora decima ab occaſu nullum habet punctum in prædictis arcubus <lb/>diurnis, ducemus horam decimam ab ortu per horam tertiam à meridie in arcu horarum 14. </s>
  <s xml:id="echoid-s13070" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13071" xml:space="preserve"><lb/>per horam quartam à meridie in arcu horarum 12. </s>
  <s xml:id="echoid-s13072" xml:space="preserve">vt ex horum arcuum tabulis cõſtat. </s>
  <s xml:id="echoid-s13073" xml:space="preserve">Nam hęc <lb/>producta exhibebit horam decimam ab occaſu, ob cauſam prius dictam. </s>
  <s xml:id="echoid-s13074" xml:space="preserve">Atque ita procedemus in <lb/>aliis horis ante decimam, ſi in horologio ducendæ fuerint.</s>
  <s xml:id="echoid-s13075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div680" type="float" level="2" n="7">
<note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">Alia deſctiptio <lb/>horologii Itali-<lb/>ci horizonalis, <lb/>per arcus diur-<lb/>nos.</note>
<note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s13076" xml:space="preserve">COMMODISSIME quoque deſcribi poterunt horæ ab occaſu, ſi deſcribatur parallelus <lb/>
<anchor type="note" xlink:label="note-0216-04a" xlink:href="note-0216-04"/>
<anchor type="note" xlink:label="note-0216-05a" xlink:href="note-0216-05"/>
omnium ſemper apparentium maximus, ſiue arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s13077" xml:space="preserve">Nam rectæ ductæ per <lb/>horas à meridie, vel media nocte in arcu dicto, ſecundum tabulam arcus diurni horarum 24. </s>
  <s xml:id="echoid-s13078" xml:space="preserve">in <lb/>ſcholio propoſ. </s>
  <s xml:id="echoid-s13079" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13080" xml:space="preserve">præcedentis libri poſitam, &amp; </s>
  <s xml:id="echoid-s13081" xml:space="preserve">per horas à meridie, vel media nocte arcus diur-<lb/>ni horarum 12. </s>
  <s xml:id="echoid-s13082" xml:space="preserve">veluti tabula huius arcus in eodem ſcholio propoſ. </s>
  <s xml:id="echoid-s13083" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13084" xml:space="preserve">præcedentis libri poſita do <lb/>cet, dabunt horarias lineas ab occaſu. </s>
  <s xml:id="echoid-s13085" xml:space="preserve">Tranſit enim hora 23. </s>
  <s xml:id="echoid-s13086" xml:space="preserve">ab occaſu per horam vndecimam à <lb/>meridie illius paralleli, ſeu arcus diurni horarum 24. </s>
  <s xml:id="echoid-s13087" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13088" xml:space="preserve">per horam quintam à meridie lineæ ęqui <lb/>noctialis, vel arcus horarum 12. </s>
  <s xml:id="echoid-s13089" xml:space="preserve">Hora verò 22. </s>
  <s xml:id="echoid-s13090" xml:space="preserve">per horam decimam prioris arcus, &amp; </s>
  <s xml:id="echoid-s13091" xml:space="preserve">horam quar-<lb/>tam æquinoctialis lineæ, vel arcus poſterioris, &amp;</s>
  <s xml:id="echoid-s13092" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13093" xml:space="preserve">Vt manifeſtum eſt ex tabulis dictorum arcuum <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s13094" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13095" xml:space="preserve">præcedentis libri deſcriptis. </s>
  <s xml:id="echoid-s13096" xml:space="preserve">Hora autem duodecima ab occaſu ducitur pa-<lb/>rallela horæ ſextæ à meridie, vel media nocte, ſiue lineæ æquinoctiali, per punctum, quo linea me-<lb/>
<anchor type="note" xlink:label="note-0216-06a" xlink:href="note-0216-06"/>
ridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s13097" xml:space="preserve">à media nocte, quæ eſt hora meridiei, arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s13098" xml:space="preserve">id eſt, <lb/>parallelum ſemper apparentium maximum, interſecat: </s>
  <s xml:id="echoid-s13099" xml:space="preserve">quoniam linea horæ 12. </s>
  <s xml:id="echoid-s13100" xml:space="preserve">ab ortu, vel oc-<lb/>caſu, &amp; </s>
  <s xml:id="echoid-s13101" xml:space="preserve">linea horæ ſextæ à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s13102" xml:space="preserve">æquinoctialis linea, parallelæ ſunt, vt ex ijs, <lb/>quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s13103" xml:space="preserve">22. </s>
  <s xml:id="echoid-s13104" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s13105" xml:space="preserve">ſcripſimus, manifeſtum eſt; </s>
  <s xml:id="echoid-s13106" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13107" xml:space="preserve">linea horæ 12. </s>
  <s xml:id="echoid-s13108" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13109" xml:space="preserve">vel <lb/>occ. </s>
  <s xml:id="echoid-s13110" xml:space="preserve">tranſit per horam duodecimam à media nocte in arcu diurno horarum 24. </s>
  <s xml:id="echoid-s13111" xml:space="preserve">vt patet ex tabula <lb/>arcus diurni horarum 24. </s>
  <s xml:id="echoid-s13112" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s13113" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13114" xml:space="preserve">eiuſdem libri poſita. </s>
  <s xml:id="echoid-s13115" xml:space="preserve">Immo linea horæ duodeci-<lb/>mæ ab or. </s>
  <s xml:id="echoid-s13116" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13117" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13118" xml:space="preserve">reliquæ omnes ab or. </s>
  <s xml:id="echoid-s13119" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13120" xml:space="preserve">tangunt prædictum parallelum, ſeu arcum diur <lb/>num horarum 24. </s>
  <s xml:id="echoid-s13121" xml:space="preserve">in punctis, in quibus eundem lineæ horarum à mer. </s>
  <s xml:id="echoid-s13122" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s13123" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13124" xml:space="preserve">ſecant, vt <lb/>propoſ. </s>
  <s xml:id="echoid-s13125" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13126" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s13127" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s13128" xml:space="preserve">Vel etiam in quibuſdam horologiis ex iis, quæ ſe-<lb/>quuntur, arcum diurnum hor. </s>
  <s xml:id="echoid-s13129" xml:space="preserve">o. </s>
  <s xml:id="echoid-s13130" xml:space="preserve">vel nocturnum horarum 24. </s>
  <s xml:id="echoid-s13131" xml:space="preserve">hoc eſt, parallelum ſemper occul-<lb/>
<anchor type="note" xlink:label="note-0216-07a" xlink:href="note-0216-07"/>
torum maximum. </s>
  <s xml:id="echoid-s13132" xml:space="preserve">Vnde@, vt accuratius horæ ab ortu, vel occaſu ducantur, deſcribi poterunt <lb/>huiuſmodi arcus, vt propoſ. </s>
  <s xml:id="echoid-s13133" xml:space="preserve">34. </s>
  <s xml:id="echoid-s13134" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13135" xml:space="preserve">36. </s>
  <s xml:id="echoid-s13136" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s13137" xml:space="preserve">à nobis factum eſt in horologio Meridiano, <lb/>ac polari.</s>
  <s xml:id="echoid-s13138" xml:space="preserve"/>
</p>
<div xml:id="echoid-div681" type="float" level="2" n="8">
<note position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">Alia deſcriptio <lb/>horologii Itali-<lb/>ci hotizontalis, <lb/>per parallelum <lb/>@emper apparẽ-<lb/>tium maximũ, <lb/>ſiue pet arcum <lb/>diurnum hora-<lb/>@um 24.</note>
<note position="left" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0216-06" xlink:href="note-0216-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0216-07" xlink:href="note-0216-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s13139" xml:space="preserve">PORRO ducta vna aliqua hora ab occaſu, vel etiam ab ortu, vt in ſequenti propoſ. </s>
  <s xml:id="echoid-s13140" xml:space="preserve">dicemus, <lb/>
<anchor type="note" xlink:label="note-0216-08a" xlink:href="note-0216-08"/>
beneficio arcuum diurnorum, vel etiam nocturnorum, vt in ſequentibus horologiis patebit, duce-<lb/>mus alias facili negotio per ſequentia puncta, quę inter ſe reſpondent, nulla alia habita conſidera-<lb/>tione tabularum, quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s13141" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13142" xml:space="preserve">pręcedentis libri compoſuimus. </s>
  <s xml:id="echoid-s13143" xml:space="preserve">Vt ducta v g. </s>
  <s xml:id="echoid-s13144" xml:space="preserve">hora <lb/>23. </s>
  <s xml:id="echoid-s13145" xml:space="preserve">ducemus 22. </s>
  <s xml:id="echoid-s13146" xml:space="preserve">per proximum punctum in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s13147" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13148" xml:space="preserve">per proximum in arcu <lb/>diurno horarum 12. </s>
  <s xml:id="echoid-s13149" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13150" xml:space="preserve">per proximum in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s13151" xml:space="preserve">Item 21. </s>
  <s xml:id="echoid-s13152" xml:space="preserve">per alia ſequentia tria <lb/>puncta, &amp; </s>
  <s xml:id="echoid-s13153" xml:space="preserve">ſic de cæteris, vt in exemplo apparet.</s>
  <s xml:id="echoid-s13154" xml:space="preserve"/>
</p>
<div xml:id="echoid-div682" type="float" level="2" n="9">
<note position="left" xlink:label="note-0216-08" xlink:href="note-0216-08a" xml:space="preserve">Qua ratione, ſi <lb/>benefic<unsure/>io arcuũ <lb/>diurnorum, vcl <lb/>nocturnorum, <lb/>una aliqua ho <lb/>@a ab occaſu, <lb/>aut ab ortu du-<lb/>cta ſit<unsure/>, aliæ faci <lb/>li negotio de-<lb/>ſc<unsure/>ribi poſſint.</note>
</div>
<p>
  <s xml:id="echoid-s13155" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s13156" xml:space="preserve">Deſcribatur linea horæ duodecimę ab ortu, vel occaſu hac ratione. </s>
  <s xml:id="echoid-s13157" xml:space="preserve">In portion@
<pb o="197" file="0217" n="217" rhead="LIBER SECVNDVS."/>
Analemmatis propoſ. </s>
  <s xml:id="echoid-s13158" xml:space="preserve">1. </s>
  <s xml:id="echoid-s13159" xml:space="preserve">huius libri, ſumatur arcus E K, æqualis arcui C E, altitudinis poli, ita vt <lb/>
<anchor type="note" xlink:label="note-0217-01a" xlink:href="note-0217-01"/>
recta ducta C K, diameter ſit paralleli omnium ſemper apparentium maximi, nempe communis <lb/>eius, &amp; </s>
  <s xml:id="echoid-s13160" xml:space="preserve">Meridiani ſectio. </s>
  <s xml:id="echoid-s13161" xml:space="preserve">Et quoniam circulus horæ duodecimæ ab occaſu tangit dictum paral-<lb/>lelum in puncto K, quod in diametro eiuſdem paralleli opponitur puncto C, in quo eundem pa-<lb/>rallelum tangit Horizon, ſeu circulus horæ 24. </s>
  <s xml:id="echoid-s13162" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13163" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13164" xml:space="preserve">vt cõſtat ex figura propoſ. </s>
  <s xml:id="echoid-s13165" xml:space="preserve">9. </s>
  <s xml:id="echoid-s13166" xml:space="preserve">ſuperio-<lb/>ris lib. </s>
  <s xml:id="echoid-s13167" xml:space="preserve">tranſibit Meridianus per K, cõtactum dictorum circulorum. </s>
  <s xml:id="echoid-s13168" xml:space="preserve">Cum ergo trãſeat quoque per <lb/>polos dicti paralleli, tranſibit quoque per polos circuli horæ 12. </s>
  <s xml:id="echoid-s13169" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13170" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13171" xml:space="preserve">ex propoſ. </s>
  <s xml:id="echoid-s13172" xml:space="preserve">5. </s>
  <s xml:id="echoid-s13173" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s13174" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s13175" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s13176" xml:space="preserve">Igitur per propoſ. </s>
  <s xml:id="echoid-s13177" xml:space="preserve">15. </s>
  <s xml:id="echoid-s13178" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s13179" xml:space="preserve">1. </s>
  <s xml:id="echoid-s13180" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s13181" xml:space="preserve">Meridianus ad dictum circulum rectus erit, &amp; </s>
  <s xml:id="echoid-s13182" xml:space="preserve">hic vi-<lb/>ciſſim ad Meridianum rectus. </s>
  <s xml:id="echoid-s13183" xml:space="preserve">Rurſus quia dictus circulus horæ 12. </s>
  <s xml:id="echoid-s13184" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13185" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13186" xml:space="preserve">cum ſit maxi-<lb/>mus, tranſit per centrum mundi D, oſtenſumq́; </s>
  <s xml:id="echoid-s13187" xml:space="preserve">eſt, eundem tranſire per K, erit recta ex K, per D, <lb/>
<anchor type="note" xlink:label="note-0217-02a" xlink:href="note-0217-02"/>
educta communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s13188" xml:space="preserve">circuli horæ 12. </s>
  <s xml:id="echoid-s13189" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13190" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13191" xml:space="preserve">occurrens in plano horologii <lb/>lineæ meridianæ H I, in puncto L. </s>
  <s xml:id="echoid-s13192" xml:space="preserve">Dico iam rectam, quæ per L, ad lineam meridianam horologii <lb/>ducitur perpendicularis, eſſe lineam horæ 12. </s>
  <s xml:id="echoid-s13193" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13194" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13195" xml:space="preserve">Quoniam enim tam planum horolo-<lb/>gij horizontalis, quàm planum circuli horæ 12. </s>
  <s xml:id="echoid-s13196" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13197" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13198" xml:space="preserve">rectum eſt, vt proxime demonſtra-<lb/>uimus, ad Meridianum, erit quoque communis eorum ſectio, nimirum linea horæ 12. </s>
  <s xml:id="echoid-s13199" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13200" xml:space="preserve">vel <lb/>occ. </s>
  <s xml:id="echoid-s13201" xml:space="preserve">ad eundem Meridianum, atque adeo &amp; </s>
  <s xml:id="echoid-s13202" xml:space="preserve">ad lineam meridianam H I, in Meridiano exiſtentem, <lb/>
<anchor type="note" xlink:label="note-0217-03a" xlink:href="note-0217-03"/>
per defin. </s>
  <s xml:id="echoid-s13203" xml:space="preserve">3. </s>
  <s xml:id="echoid-s13204" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s13205" xml:space="preserve">11. </s>
  <s xml:id="echoid-s13206" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s13207" xml:space="preserve">perpendicularis in puncto L, in quo diximus communem ſectionem cir-<lb/>culi horæ 12. </s>
  <s xml:id="echoid-s13208" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13209" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13210" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13211" xml:space="preserve">Meridiani, ac proinde &amp; </s>
  <s xml:id="echoid-s13212" xml:space="preserve">ipſum circulum horæ 12 ab or. </s>
  <s xml:id="echoid-s13213" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13214" xml:space="preserve">pla <lb/>no horologii occurrere. </s>
  <s xml:id="echoid-s13215" xml:space="preserve">Recta igitur in plano horologii ducta per L, ad meridianam lineam per-<lb/>pendicularis, dabit lineam horæ 12. </s>
  <s xml:id="echoid-s13216" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13217" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13218" xml:space="preserve">Igitur ſi in lineam meridianam horologii ex <lb/>
<anchor type="note" xlink:label="note-0217-04a" xlink:href="note-0217-04"/>
centro H, transferatur punctum L, ſumptum beneficio circini ex puncto H, portionis Analemma <lb/>tis, ac per L, lin ea perpendicularis ad meridianam lineam, vel parallela lineę horę 6. </s>
  <s xml:id="echoid-s13219" xml:space="preserve">à meridie, vel <lb/>media nocte, ſeu linea æquinoctiali ducatur, erit hæc ipſa linea horæ 12. </s>
  <s xml:id="echoid-s13220" xml:space="preserve">ab ortu, vel occaſu. <lb/></s>
  <s xml:id="echoid-s13221" xml:space="preserve">
<anchor type="note" xlink:label="note-0217-05a" xlink:href="note-0217-05"/>
</s>
</p>
<div xml:id="echoid-div683" type="float" level="2" n="10">
<note position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">Quomodo li-<lb/>nea horæ 12. ab <lb/>or. vel occ. du-<lb/>cenda ſi@ in h@-<lb/>rologio ho@@zõ-<lb/>tali.</note>
<note position="left" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0217-04" xlink:href="note-0217-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0217-05" xlink:href="note-0217-05a" xml:space="preserve">Alia deſcriptio <lb/>horolog@i Itali-<lb/>ci horizontalis, <lb/>beneficio lineæ <lb/>horæ 12. ab or. <lb/>vel occ@ abſol-<lb/>uenda.</note>
</div>
<p>
  <s xml:id="echoid-s13222" xml:space="preserve">DESCRIPTA autem hoc modo linea horæ duodecimæ ab ortu, vel occaſu, facile reliquæ <lb/>horæ ab occaſu deſcribentur, ſi diligenter in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s13223" xml:space="preserve">linea horæ duodecimæ ab or. <lb/></s>
  <s xml:id="echoid-s13224" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13225" xml:space="preserve">notentur puncta ex tabula propoſ. </s>
  <s xml:id="echoid-s13226" xml:space="preserve">19. </s>
  <s xml:id="echoid-s13227" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13228" xml:space="preserve">tabula ſecunda propoſ. </s>
  <s xml:id="echoid-s13229" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13230" xml:space="preserve">præcedentis libri, per <lb/>quæ lineæ horarum ab occaſu tranſeunt. </s>
  <s xml:id="echoid-s13231" xml:space="preserve">Rectæ enim correſpondentia puncta connectentes da-<lb/>bunt horarias lineas ab occaſu. </s>
  <s xml:id="echoid-s13232" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s13233" xml:space="preserve">Hora 23. </s>
  <s xml:id="echoid-s13234" xml:space="preserve">ab occaſu tranſit in linea æquinoctiali per <lb/>punctum horæ quintæ à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s13235" xml:space="preserve">in linea horæ duodecimæ ab ortu, vel occaſu <lb/>per punctum horæ 5 {1/2}. </s>
  <s xml:id="echoid-s13236" xml:space="preserve">à meridie, vt ex dictis tabulis conſtat. </s>
  <s xml:id="echoid-s13237" xml:space="preserve">Igitur recta per illa duo puncta <lb/>
<anchor type="note" xlink:label="note-0217-06a" xlink:href="note-0217-06"/>
tranſiens dabit horariam lineam, quæ horam 23. </s>
  <s xml:id="echoid-s13238" xml:space="preserve">ab occaſu indicet. </s>
  <s xml:id="echoid-s13239" xml:space="preserve">Eodem modo tranſibit linea <lb/>horæ 22. </s>
  <s xml:id="echoid-s13240" xml:space="preserve">ab occaſu per punctum horæ quartæ à meridie in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s13241" xml:space="preserve">per punctum ho <lb/>ræ quintæ à meridie in linea horæ duodecimæ ab ortu, vel occaſu; </s>
  <s xml:id="echoid-s13242" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13243" xml:space="preserve">ſic de cæteris. <lb/></s>
  <s xml:id="echoid-s13244" xml:space="preserve">
<anchor type="note" xlink:label="note-0217-07a" xlink:href="note-0217-07"/>
</s>
</p>
<div xml:id="echoid-div684" type="float" level="2" n="11">
<note position="left" xlink:label="note-0217-06" xlink:href="note-0217-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0217-07" xlink:href="note-0217-07a" xml:space="preserve">Alia deſcriptio <lb/>horolog@i Itali-<lb/>ci horizontalis, <lb/>ex tabula pri-<lb/>ma propoſ. 20. <lb/>ſuperioris lib. <lb/>vbi quęlibet ho <lb/>ra ab occ. paral-<lb/>lela eſt alicui <lb/>horæ à mer. vel <lb/>med. noc.</note>
</div>
<p>
  <s xml:id="echoid-s13245" xml:space="preserve">POSSVNT etiam lineæ horarum ab occaſu facile ex tabula prima propoſ. </s>
  <s xml:id="echoid-s13246" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13247" xml:space="preserve">ſuperioris li-<lb/>bri deſcribi hoc modo. </s>
  <s xml:id="echoid-s13248" xml:space="preserve">Per punctum horæ quintæ à meridie, vel media nocte in linea æquino-<lb/>ctiali, per quod nimirum tranſit hora 23. </s>
  <s xml:id="echoid-s13249" xml:space="preserve">ab occaſu, vt ex tabula propoſ. </s>
  <s xml:id="echoid-s13250" xml:space="preserve">19@ eiuſdem libri conſtat, <lb/>agatur recta parallela lineæ horæ 11 {1/2}. </s>
  <s xml:id="echoid-s13251" xml:space="preserve">à meridie, vel media nocte. </s>
  <s xml:id="echoid-s13252" xml:space="preserve">Hæc enim erit linea horæ 23. <lb/></s>
  <s xml:id="echoid-s13253" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s13254" xml:space="preserve">Sic quoque linea horæ 22. </s>
  <s xml:id="echoid-s13255" xml:space="preserve">ab occaſu per punctum horæ quartæ à meridie tranſiens, <lb/>parallela erit lineæ horæ vndecimæ à meridie, vel media nocte, &amp;</s>
  <s xml:id="echoid-s13256" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13257" xml:space="preserve">vt perſpicuum eſt ex tabula pri <lb/>ma propoſ. </s>
  <s xml:id="echoid-s13258" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13259" xml:space="preserve">præcedentis libri, in qua quælibet binæ horæ parallelæ ſunt in horologio horizon <lb/>
<anchor type="note" xlink:label="note-0217-08a" xlink:href="note-0217-08"/>
tali, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s13260" xml:space="preserve">22. </s>
  <s xml:id="echoid-s13261" xml:space="preserve">eiuſdem lib demonſtrauimus. </s>
  <s xml:id="echoid-s13262" xml:space="preserve">Deſcribentur autem expeditè huiuſ-<lb/>modi parallelæ, ſi ſumantur rectæ in æquinoctiali linea interceptę inter puncta, per quæ horæ ab <lb/>occ. </s>
  <s xml:id="echoid-s13263" xml:space="preserve">duci debent, iuxta tabulam propoſ. </s>
  <s xml:id="echoid-s13264" xml:space="preserve">19. </s>
  <s xml:id="echoid-s13265" xml:space="preserve">libri antecedentis, &amp; </s>
  <s xml:id="echoid-s13266" xml:space="preserve">puncta horarum à meridie, vel <lb/>med noc. </s>
  <s xml:id="echoid-s13267" xml:space="preserve">quibus illæ, iuxta tabulam primam propoſ. </s>
  <s xml:id="echoid-s13268" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13269" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s13270" xml:space="preserve">æquidiſtantes ſunt, transfe <lb/>ranturq́ue ex H, centro horologii in lineam horæ ſextæ à meridie, vel media nocte. </s>
  <s xml:id="echoid-s13271" xml:space="preserve">Vt ſi lineæ in <lb/>æquinoctiali linea interiectæ inter punctum horæ vndecimæ à meridie@ cui æquidiſtat hora 22. </s>
  <s xml:id="echoid-s13272" xml:space="preserve">ab <lb/>occaſu, &amp; </s>
  <s xml:id="echoid-s13273" xml:space="preserve">punctum horæ quartæ à meridie, per quod tranſit eadem hora 22. </s>
  <s xml:id="echoid-s13274" xml:space="preserve">ſumatur in linea ho-<lb/>ræ ſextæ à meridie æqualis H X, erit recta per X, &amp; </s>
  <s xml:id="echoid-s13275" xml:space="preserve">punctum horæ quartæ à meridie ducta, lineę <lb/>horæ vndecimæ à meridie, vel media nocte paralle<unsure/>la, ac propterea horam 22. </s>
  <s xml:id="echoid-s13276" xml:space="preserve">ab occaſu indica-<lb/>
<anchor type="note" xlink:label="note-0217-09a" xlink:href="note-0217-09"/>
bit, &amp;</s>
  <s xml:id="echoid-s13277" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13278" xml:space="preserve">Quòd ſi lineæ æquinoctiali agatur parallela longius ab ea diſtans, in quam transferantur <lb/>
<anchor type="note" xlink:label="note-0217-10a" xlink:href="note-0217-10"/>
eędem rectę interceptę in linea æquinoctiali inter puncta, per quę duci debent horę ab occ. </s>
  <s xml:id="echoid-s13279" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13280" xml:space="preserve">pun <lb/>cta horarum à mer. </s>
  <s xml:id="echoid-s13281" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s13282" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13283" xml:space="preserve">quibus illę ęquidiſtant, initio ſemper facto ab horis à mer. </s>
  <s xml:id="echoid-s13284" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s13285" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13286" xml:space="preserve">quibus ęquidiſtare debent horę ab occ. </s>
  <s xml:id="echoid-s13287" xml:space="preserve">multo accuratius ducentur horę ab occ. </s>
  <s xml:id="echoid-s13288" xml:space="preserve">cum <lb/>quęlibet per tria puncta ducatur, quorum vnum eſt in linea horæ ſextæ à mer. </s>
  <s xml:id="echoid-s13289" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s13290" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13291" xml:space="preserve">alterũ <lb/>in æquinoctiali linea, &amp; </s>
  <s xml:id="echoid-s13292" xml:space="preserve">in parallela vltimò ducta tertium. <lb/></s>
  <s xml:id="echoid-s13293" xml:space="preserve">
<anchor type="note" xlink:label="note-0217-11a" xlink:href="note-0217-11"/>
</s>
</p>
<div xml:id="echoid-div685" type="float" level="2" n="12">
<note position="left" xlink:label="note-0217-08" xlink:href="note-0217-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0217-09" xlink:href="note-0217-09a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0217-10" xlink:href="note-0217-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0217-11" xlink:href="note-0217-11a" xml:space="preserve">Quæ horæ a@ <lb/>occ. ſe mutuo <lb/>ſecent in linea <lb/>horæ 6 à mer. <lb/>vel med. noc.</note>
</div>
<p>
  <s xml:id="echoid-s13294" xml:space="preserve">PRAETEREA hora 23. </s>
  <s xml:id="echoid-s13295" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13296" xml:space="preserve">13. </s>
  <s xml:id="echoid-s13297" xml:space="preserve">ab occaſu ſecant ſe mutuo, ſi rectę deſcriptę ſint, in linea <lb/>horę ſextę à meridie, vel med. </s>
  <s xml:id="echoid-s13298" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13299" xml:space="preserve">Item hora 22. </s>
  <s xml:id="echoid-s13300" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13301" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13302" xml:space="preserve">necnon 21. </s>
  <s xml:id="echoid-s13303" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13304" xml:space="preserve">15. </s>
  <s xml:id="echoid-s13305" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13306" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13307" xml:space="preserve">vt patet ex tabula <lb/>tertia propoſ. </s>
  <s xml:id="echoid-s13308" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13309" xml:space="preserve">pręcedentis libri. <lb/></s>
  <s xml:id="echoid-s13310" xml:space="preserve">
<anchor type="note" xlink:label="note-0217-12a" xlink:href="note-0217-12"/>
</s>
</p>
<div xml:id="echoid-div686" type="float" level="2" n="13">
<note position="right" xlink:label="note-0217-12" xlink:href="note-0217-12a" xml:space="preserve">Quæ lineæ ho-<lb/>ra@um ab occ. ſe <lb/>@@utu@ ſecẽt in <lb/>l@nea meridia-<lb/>na.</note>
</div>
<p>
  <s xml:id="echoid-s13311" xml:space="preserve">RVRSVS ex tabula quarta propoſ. </s>
  <s xml:id="echoid-s13312" xml:space="preserve">eiuſdem, hora decima, &amp; </s>
  <s xml:id="echoid-s13313" xml:space="preserve">decimaquarta ab occaſu ſe in-<lb/>terſecant in linea meridiana, ſeu horę duodecimę à meridie, vel med. </s>
  <s xml:id="echoid-s13314" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13315" xml:space="preserve">Item hora vndecima, <lb/>&amp; </s>
  <s xml:id="echoid-s13316" xml:space="preserve">decimatertia, &amp;</s>
  <s xml:id="echoid-s13317" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13318" xml:space="preserve">Denique ex propoſ. </s>
  <s xml:id="echoid-s13319" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13320" xml:space="preserve">ſuperioris libri, &amp; </s>
  <s xml:id="echoid-s13321" xml:space="preserve">figura propoſ. </s>
  <s xml:id="echoid-s13322" xml:space="preserve">9. </s>
  <s xml:id="echoid-s13323" xml:space="preserve">libri eiuſdem, vel
<pb o="198" file="0218" n="218" rhead="GNOMONICES"/>
certe ex tabulis, quas ad finem ſcholii propoſ. </s>
  <s xml:id="echoid-s13324" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13325" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s13326" xml:space="preserve">conſtruximus, facile cognoſcemus, <lb/>
<anchor type="note" xlink:label="note-0218-01a" xlink:href="note-0218-01"/>
quęnam horę ab ortu, vel occaſu horam quamcunque à meridie, vel media nocte in vno, &amp; </s>
  <s xml:id="echoid-s13327" xml:space="preserve">eodem <lb/>puncto ſecent. </s>
  <s xml:id="echoid-s13328" xml:space="preserve">Quæ res &amp; </s>
  <s xml:id="echoid-s13329" xml:space="preserve">facilem admodum reddit deſcriptionem linearum horarum ab occa-<lb/>ſu, &amp; </s>
  <s xml:id="echoid-s13330" xml:space="preserve">modum prębet, quo deſcriptio huiuſmodi poſſit examinari. </s>
  <s xml:id="echoid-s13331" xml:space="preserve">Horologium igitur Italicum <lb/>Horizontale conſtituimus, &amp;</s>
  <s xml:id="echoid-s13332" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13333" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s13334" xml:space="preserve"/>
</p>
<div xml:id="echoid-div687" type="float" level="2" n="14">
<note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Vſus poſterio-<lb/>r<unsure/>um tabularũ <lb/>propoſ. 20. præ-<lb/>cedentis lib. in <lb/>deſcribendis ho <lb/>@is ab occaſu.</note>
</div>
</div>
<div xml:id="echoid-div689" type="section" level="1" n="172">
<head xml:id="echoid-head175" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s13335" xml:space="preserve">HIC notatu dignum eſt, quamcunque horam ab occaſu productam vltra punctum illud, vbi paral-<lb/>
<anchor type="note" xlink:label="note-0218-02a" xlink:href="note-0218-02"/>
<anchor type="note" xlink:label="note-0218-03a" xlink:href="note-0218-03"/>
lelum ſemper apparentium maximum, ſiue arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s13336" xml:space="preserve">vel etiam nocturnum arcum, <lb/>qui eſt alter parallelus oppoſitus, &amp; </s>
  <s xml:id="echoid-s13337" xml:space="preserve">latentium maximus, tangit, indicare eandem numero horam ab or-<lb/>tu; </s>
  <s xml:id="echoid-s13338" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13339" xml:space="preserve">contra, quamuis horam ab ortu productam vltra illud punctum exhibere eandem numero horam <lb/>ab occaſu. </s>
  <s xml:id="echoid-s13340" xml:space="preserve">Id quod in propoſ. </s>
  <s xml:id="echoid-s13341" xml:space="preserve">hac, vt verũ, aſſumpſimus, nunc autem ita demonſtrabimus. </s>
  <s xml:id="echoid-s13342" xml:space="preserve">Si Sol ponere-<lb/>tur in illo puncto cœli, in quo circulus aliquis horarius ab ortu, vel occaſu parallelum ſemper apparẽtium <lb/>maximũ, vel ſemper latentium maximũ tangit, vmbra ſtyli caderet præcisè in punctũ illud horologĳ, vbi <lb/>linea horæ illius circuli arcum diurnum, vel nocturnum horarum 24. </s>
  <s xml:id="echoid-s13343" xml:space="preserve">tangit, vt facile ex demonſtratis in <lb/>præcedenti lib. </s>
  <s xml:id="echoid-s13344" xml:space="preserve">ostendi poteſt. </s>
  <s xml:id="echoid-s13345" xml:space="preserve">Quia enim, Sole in illo parallelo exiſtente, vmbra ſtyli proĳcitur in arcum <lb/>illius paralleli in horologio deſcriptum, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s13346" xml:space="preserve">12. </s>
  <s xml:id="echoid-s13347" xml:space="preserve">præcedentis libri. </s>
  <s xml:id="echoid-s13348" xml:space="preserve">Item Sole exiſtente in <lb/>illo circulo horario, eadem vmbra in communem ſectionem illius, &amp; </s>
  <s xml:id="echoid-s13349" xml:space="preserve">plani horologĳ, hoc est, in lineam ho <lb/>
<anchor type="note" xlink:label="note-0218-04a" xlink:href="note-0218-04"/>
rariam illius circuli proĳcitur, vt propoſ. </s>
  <s xml:id="echoid-s13350" xml:space="preserve">11. </s>
  <s xml:id="echoid-s13351" xml:space="preserve">eiuſdem libri oſtendimus; </s>
  <s xml:id="echoid-s13352" xml:space="preserve">fit vt vmbra cadat in dictum pun <lb/>ctum, quod commune eſt &amp; </s>
  <s xml:id="echoid-s13353" xml:space="preserve">arcui illius paralleli, &amp; </s>
  <s xml:id="echoid-s13354" xml:space="preserve">lineæ horariæ prædicti circuli. </s>
  <s xml:id="echoid-s13355" xml:space="preserve">Quod cum ita ſe ha-<lb/>beat, perſpicuum eſt, ſi nos in puncto illo contactus paralleli ſemper apparentium, vel latentium maxi-<lb/>mi poſiti eſſemus, ita vt vnus ſemicirculus circuli illius horarĳ foret nobis ad dexteram, &amp; </s>
  <s xml:id="echoid-s13356" xml:space="preserve">alter ad ſini <lb/>stram, Sol autem exiſteret in ſemicir culo dextro, vmbram ſtyli proĳci in partem ſiniſtram prædictæ li-<lb/>neę horariæ, nempe in oppoſitam partem; </s>
  <s xml:id="echoid-s13357" xml:space="preserve">Si autem Sol exiſteret in ſemicirculo ſiniſtro, eandem vmbrã <lb/>ſtyli cadere in partem dextram eiuſdem lineę, ſumendo partem dextram, &amp; </s>
  <s xml:id="echoid-s13358" xml:space="preserve">ſiniſtram reſpectu puncti con <lb/>tactus in arcu diurno, vel nocturno horarum 24. </s>
  <s xml:id="echoid-s13359" xml:space="preserve">in horologio. </s>
  <s xml:id="echoid-s13360" xml:space="preserve">Cum ergo Sole in diuerſis ſemicirculis il-<lb/>lius horarĳ circuli exiſtente, vmbra ſtyli cadat in diuerſas partes eius lineæ horariæ, nempè modo vltra <lb/>punctum contactus, modo citra idem; </s>
  <s xml:id="echoid-s13361" xml:space="preserve">eorum autem ſemicirculorum vnus indicet horam ab ortu So-<lb/>
<anchor type="note" xlink:label="note-0218-05a" xlink:href="note-0218-05"/>
lis, &amp; </s>
  <s xml:id="echoid-s13362" xml:space="preserve">alter ab occaſu, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s13363" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13364" xml:space="preserve">ſuperioris libri diximus; </s>
  <s xml:id="echoid-s13365" xml:space="preserve">pertinebit quoque vna <lb/>pars lineæ eius horariæ in puncto contactus terminata ad horas ab ortu, in quam nimirum proĳcitur <lb/>vmbra, Sole in ſemicirculo illo, qui horam ab ortu ſignificat, constituto, &amp; </s>
  <s xml:id="echoid-s13366" xml:space="preserve">altera ad horas ab occaſu. <lb/></s>
  <s xml:id="echoid-s13367" xml:space="preserve">Quod idem verum eſt in alĳs horologĳs, quæ non ſunt horizontalia, &amp; </s>
  <s xml:id="echoid-s13368" xml:space="preserve">in omnibus lineis horarĳs ab or-<lb/>tu, vel occaſu.</s>
  <s xml:id="echoid-s13369" xml:space="preserve"/>
</p>
<div xml:id="echoid-div689" type="float" level="2" n="1">
<note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">Quælibet hora <lb/>ab occaſu pro-<lb/>ducta vlt<unsure/>ra pun <lb/>ctum, vbi arcũ <lb/>diurnum, no-<lb/>cturnumve ho <lb/>rarum 24. tan-<lb/>git, pertinet ad <lb/>eandem horam <lb/>@umero ab or-<lb/>@u; &amp; contra.</note>
<note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0218-05" xlink:href="note-0218-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s13370" xml:space="preserve">IDEM quoque hac ratione perſpicuum fiet, etiamſi nec Solem, nec nos in illo puncto contactus con-<lb/>ſtituamus. </s>
  <s xml:id="echoid-s13371" xml:space="preserve">Quilibet ſemicirculus horarius à meridie, vel media nocte præciſe poſitus eſt in medio duo-<lb/>rum ſemicirculorum illius circuli horarĳ ab ortu, vel occaſu, qui in eodem puncto tangit parallelum ſem-<lb/>per apparentium, vel latentium maximum, in quo ſemicir culus ille horarius à meridie, vel media nocte <lb/>eundem parallelum ſecat, cum per polum illius tranſeat, ex propoſ. </s>
  <s xml:id="echoid-s13372" xml:space="preserve">5. </s>
  <s xml:id="echoid-s13373" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s13374" xml:space="preserve">Theodoſii; </s>
  <s xml:id="echoid-s13375" xml:space="preserve">ita vt vnum <lb/>
<anchor type="note" xlink:label="note-0218-06a" xlink:href="note-0218-06"/>
habeat ad dextram, &amp; </s>
  <s xml:id="echoid-s13376" xml:space="preserve">alterum ad ſinistram. </s>
  <s xml:id="echoid-s13377" xml:space="preserve">Quoniam autem, Sole exiſtente in ſemicirculo illo hora-<lb/>rio à meridie, vel media nocte, vmbra ſtyli cadit in lineam eius horariam, quæ arcum diurnum, vel noctur <lb/>num horarum 24. </s>
  <s xml:id="echoid-s13378" xml:space="preserve">ſecat; </s>
  <s xml:id="echoid-s13379" xml:space="preserve">perſpicuum eſt, Sole exiſtente in eo ſemicir ulo horario ab ortu, vel occaſu, qui <lb/>orientalis eſt reſpectu illius ſemicirculi horarĳ à meridie, vel media nocte, vmbram proĳci in partem op-<lb/>poſitam in plano horologĳ, nempe in partem occidentalem reſpectu lineæ illius horariæ à meridie, vel me-<lb/>dia nocte, in ipſam tamen lineam horariam ab ortu, vel occaſu, vt ex propoſ. </s>
  <s xml:id="echoid-s13380" xml:space="preserve">11. </s>
  <s xml:id="echoid-s13381" xml:space="preserve">præcedentis libri con-<lb/>ſtat: </s>
  <s xml:id="echoid-s13382" xml:space="preserve">Sole verò exiſtente in altero ſemicir culo occidentali, vmbram cadere in partem orientalem horolo-<lb/>gĳ reſpectu illius lineæ horariæ à meridie, vel media nocte, in ipſam tamen lineam horariam ab ortu, vel <lb/>occaſu, per eandem propoſ. </s>
  <s xml:id="echoid-s13383" xml:space="preserve">11. </s>
  <s xml:id="echoid-s13384" xml:space="preserve">antecedentis libri. </s>
  <s xml:id="echoid-s13385" xml:space="preserve">Cum ergo linea illa horaria à meridie, vel media no-<lb/>cte lineam horariam ab ortu, vel occaſu ſecet in puncto contactus arcus diurni, vel nocturni horarum <lb/>
<anchor type="note" xlink:label="note-0218-07a" xlink:href="note-0218-07"/>
24. </s>
  <s xml:id="echoid-s13386" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13387" xml:space="preserve">vnus ſemicir culus horarius ab ortu, vel occaſu monſtret horam ab ortu<gap/>er horam ab <lb/>occaſu, liquido conſtat, vnam portionem lineæ horariæ illius ab ortu, vel<gap/>ſque ad pun-<lb/>ctum contactus, indicare horam ab ortu, reliquam verò portionem monſtrare h<gap/>ndem numero ab <lb/>occaſu Solis.</s>
  <s xml:id="echoid-s13388" xml:space="preserve"/>
</p>
<div xml:id="echoid-div690" type="float" level="2" n="2">
<note position="left" xlink:label="note-0218-06" xlink:href="note-0218-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0218-07" xlink:href="note-0218-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s13389" xml:space="preserve">EX dictis facile intelligi poteſt, vſum horologĳ Italici eſſe, vt ex eo cognoſcamus, quot horæ à pro-<lb/>
<anchor type="note" xlink:label="note-0218-08a" xlink:href="note-0218-08"/>
ximo Solis occaſu elapſæ ſint, &amp; </s>
  <s xml:id="echoid-s13390" xml:space="preserve">quot ſuperſint ad ſequentem occaſum; </s>
  <s xml:id="echoid-s13391" xml:space="preserve">adeo vt vmbra gnomonis caden-<lb/>te in aliquam lineam horariam ab occaſu, nempe in lineam horæ 19. </s>
  <s xml:id="echoid-s13392" xml:space="preserve">certi ſimus, tranſactas eſſe horas 19. <lb/></s>
  <s xml:id="echoid-s13393" xml:space="preserve">à proximo occaſu Solis, ac proinde, quoniam ab vno occaſu ad alterum intercedunt horæ 24. </s>
  <s xml:id="echoid-s13394" xml:space="preserve">ſupereſſe <lb/>vſque ad ſequentem occaſum horas quinque, quæ nimirum deſunt horis 19. </s>
  <s xml:id="echoid-s13395" xml:space="preserve">ad complendum numerum ho<unsure/> <lb/>rarum 24. </s>
  <s xml:id="echoid-s13396" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13397" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s13398" xml:space="preserve"/>
</p>
<div xml:id="echoid-div691" type="float" level="2" n="3">
<note position="left" xlink:label="note-0218-08" xlink:href="note-0218-08a" xml:space="preserve">Vſus horologii <lb/>Italici eſt, vt <lb/>intelligamus, <lb/>quot horæ ſint <lb/>elapſæ à proxi-<lb/>mo occaſu So-<lb/>lis, quotque ad <lb/>alterum ſuper-<lb/>ſint.</note>
</div>
<pb o="199" file="0219" n="219" rhead="LIBER SECVNDVS."/>
</div>
<div xml:id="echoid-div693" type="section" level="1" n="173">
<head xml:id="echoid-head176" xml:space="preserve">PROBLEMA. 11. PROPOSITIO 11.</head>
<p>
  <s xml:id="echoid-s13399" xml:space="preserve">HOROLOGIVM Babylonicum horizontale conſtituere. <lb/></s>
  <s xml:id="echoid-s13400" xml:space="preserve">Hoc eſt, lineas horarum ab ortu Solis in plano Horizonti æquidiſtan-<lb/>te deſcribere.</s>
  <s xml:id="echoid-s13401" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s13402" xml:space="preserve">EADEM arte, qua in deſcribendis lineis horarum ab occaſu vſi ſumus, deſcribemus lineas <lb/>horarum ab ortu. </s>
  <s xml:id="echoid-s13403" xml:space="preserve">Hæ enim ab illis non differunt, niſi ſitu, &amp; </s>
  <s xml:id="echoid-s13404" xml:space="preserve">ordine; </s>
  <s xml:id="echoid-s13405" xml:space="preserve">ita vt hora 23. </s>
  <s xml:id="echoid-s13406" xml:space="preserve">ab occaſu <lb/>translata ad horas ante meridiem ſit hora prima ab ortu, &amp; </s>
  <s xml:id="echoid-s13407" xml:space="preserve">hora 22. </s>
  <s xml:id="echoid-s13408" xml:space="preserve">eodem modo translata ſit ho <lb/>
<anchor type="note" xlink:label="note-0219-01a" xlink:href="note-0219-01"/>
ra ſecunda, &amp;</s>
  <s xml:id="echoid-s13409" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13410" xml:space="preserve">vt perſpicuum eſt, ſi rectè contemplemur naturam, &amp; </s>
  <s xml:id="echoid-s13411" xml:space="preserve">ſitum iſtorum circulorum <lb/>horariorum, &amp; </s>
  <s xml:id="echoid-s13412" xml:space="preserve">figuram antecedentis propoſ. </s>
  <s xml:id="echoid-s13413" xml:space="preserve">Quemadmodum ergo pro horologio Italico deſcri <lb/>
<anchor type="note" xlink:label="note-0219-02a" xlink:href="note-0219-02"/>
bendo ſecundum priorem modum diuiſie<unsure/>nem circuli M a N b, incepimus à punctis b, &amp; </s>
  <s xml:id="echoid-s13414" xml:space="preserve">e, occi-<lb/>
<anchor type="figure" xlink:label="fig-0219-01a" xlink:href="fig-0219-01"/>
<anchor type="note" xlink:label="note-0219-03a" xlink:href="note-0219-03"/>
<anchor type="note" xlink:label="note-0219-04a" xlink:href="note-0219-04"/>
dentalibus, ita eandem pro horologio Babylonico inchoabimus à punctis a, &amp; </s>
  <s xml:id="echoid-s13415" xml:space="preserve">d, orientalibus; <lb/></s>
  <s xml:id="echoid-s13416" xml:space="preserve">ita vt puncta a, d, pertineant ad horam 24. </s>
  <s xml:id="echoid-s13417" xml:space="preserve">ab ortu in vtroque tropico, proxima verò verſus N, ad <lb/>
<anchor type="note" xlink:label="note-0219-05a" xlink:href="note-0219-05"/>
horam primam, &amp; </s>
  <s xml:id="echoid-s13418" xml:space="preserve">ſequentia ad ſecundam, &amp;</s>
  <s xml:id="echoid-s13419" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13420" xml:space="preserve">Per hæc enim diuiſionum puncta reperiemus in <lb/>vtroque tropico puncta horarum ab ortu Solis, vt ſupra de punctis horarum ab occaſu diximus.</s>
  <s xml:id="echoid-s13421" xml:space="preserve"/>
</p>
<div xml:id="echoid-div693" type="float" level="2" n="1">
<note position="left" xlink:label="note-0219-01" xlink:href="note-0219-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0219-02" xlink:href="note-0219-02a" xml:space="preserve">Deſcriptio@ ho-<lb/>rologii Babylo <lb/>nici horizo@ta-<lb/>lis.</note>
  <figure xlink:label="fig-0219-01" xlink:href="fig-0219-01a">
    <image file="0219-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0219-01"/>
  </figure>
<note position="left" xlink:label="note-0219-03" xlink:href="note-0219-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0219-04" xlink:href="note-0219-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0219-05" xlink:href="note-0219-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s13422" xml:space="preserve">POTEST etiam diuiſio circuli M a N b, initium habere à puncto cuiuſuis horæ ab ortu in <lb/>cius circunferentia inuentę, vt in pręcedenti propoſ. </s>
  <s xml:id="echoid-s13423" xml:space="preserve">declaratum eſt.</s>
  <s xml:id="echoid-s13424" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s13425" xml:space="preserve">IN alijs modis nulla etiam difficultas eſt, ſi pręcepta pręcedentis propoſ. </s>
  <s xml:id="echoid-s13426" xml:space="preserve">rectè intelligantur, &amp; </s>
  <s xml:id="echoid-s13427" xml:space="preserve"><lb/>tabulæ propoſ. </s>
  <s xml:id="echoid-s13428" xml:space="preserve">19. </s>
  <s xml:id="echoid-s13429" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13430" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13431" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13432" xml:space="preserve">ſuperioris libri diligenter expendantur, vt puncta inueniantur, in <lb/>quibus ſe mutuo interſecant lineæ horarum à meridie vel media nocte, &amp; </s>
  <s xml:id="echoid-s13433" xml:space="preserve">ab ortu vel occaſu.</s>
  <s xml:id="echoid-s13434" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s13435" xml:space="preserve">SIT enim exempli gratia deſcribendum horologium Babylonicum iuxta ſecundum modum <lb/>
<anchor type="note" xlink:label="note-0219-06a" xlink:href="note-0219-06"/>
per arcus diurnos. </s>
  <s xml:id="echoid-s13436" xml:space="preserve">Hora prima ab ortu tranſit, vt ex tabulis propoſ. </s>
  <s xml:id="echoid-s13437" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13438" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s13439" xml:space="preserve">pater, per <lb/>horam ſextam à media nocte in arcu diurno horaru m 14. </s>
  <s xml:id="echoid-s13440" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13441" xml:space="preserve">per horam ſeptimam à media nocte <lb/>
<anchor type="note" xlink:label="note-0219-07a" xlink:href="note-0219-07"/>
in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s13442" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13443" xml:space="preserve">per horam octauam à media nocte in arcu diurno horarum 10. <lb/></s>
  <s xml:id="echoid-s13444" xml:space="preserve">Igitur recta linea per haſce horas à med. </s>
  <s xml:id="echoid-s13445" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s13446" xml:space="preserve">ducta dabit horam 1. </s>
  <s xml:id="echoid-s13447" xml:space="preserve">ab ortu Solis; </s>
  <s xml:id="echoid-s13448" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13449" xml:space="preserve">ita de reliquis. </s>
  <s xml:id="echoid-s13450" xml:space="preserve"><lb/>Horæ autem, quæ in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s13451" xml:space="preserve">nulla habent puncta, vt ſunt omnes horæ poſt ho@ã <lb/>nonam ab ortu in noſtro exemplo, ducendæ erunt per puncta in arcubus diurnis horatum 14. </s>
  <s xml:id="echoid-s13452" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13453" xml:space="preserve"><lb/>12. </s>
  <s xml:id="echoid-s13454" xml:space="preserve">At hora duodecima ab ortu ducenda eſt parallela lineę ęquinoctiali (quia linea horę duodeci <lb/>mę ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s13455" xml:space="preserve">linea ęquinoctialis, parallelę ſunt in horologio horizontali, vt ex ſcholio <lb/>propoſ. </s>
  <s xml:id="echoid-s13456" xml:space="preserve">22. </s>
  <s xml:id="echoid-s13457" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s13458" xml:space="preserve">manifeſtum eſt) per horam quintam à meridie in arcu diurno hora-<lb/>rum 14. </s>
  <s xml:id="echoid-s13459" xml:space="preserve">Pro hora deinde 13. </s>
  <s xml:id="echoid-s13460" xml:space="preserve">ab ortu, quoniam ſolum punctum habet horæ ſextę à meridie in a@-<lb/>cu diurno horarum 14. </s>
  <s xml:id="echoid-s13461" xml:space="preserve">ducemus 13. </s>
  <s xml:id="echoid-s13462" xml:space="preserve">ab occaſu per horam octauam à media nocte in arcu diur-<lb/>no horarum 14. </s>
  <s xml:id="echoid-s13463" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13464" xml:space="preserve">per horam ſeptimam à media nocte in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s13465" xml:space="preserve">Hæc enim vl-<lb/>tra arcum maximi parallelorum ſemper apparentium producta dabit, vt in ſcholio pręcedentis
<pb o="200" file="0220" n="220" rhead="GNOMONICES"/>
propoſ. </s>
  <s xml:id="echoid-s13466" xml:space="preserve">oſtendimus, horam 13. </s>
  <s xml:id="echoid-s13467" xml:space="preserve">ab ortu per horam ſextam à meridie in arcu diurno horarum 14. <lb/></s>
  <s xml:id="echoid-s13468" xml:space="preserve">incedentem. </s>
  <s xml:id="echoid-s13469" xml:space="preserve">Pari ratione pro hora 14. </s>
  <s xml:id="echoid-s13470" xml:space="preserve">ab ortu, cum nullum habeat punctum in arcubus prædi-<lb/>ctis, ducemus 14. </s>
  <s xml:id="echoid-s13471" xml:space="preserve">ab occaſu per horã nonam à media nocte in arcu diurno horarũ 14. </s>
  <s xml:id="echoid-s13472" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13473" xml:space="preserve">per horã <lb/>octauam à media nocte in arcu diurno horarũ 12. </s>
  <s xml:id="echoid-s13474" xml:space="preserve">Nam hæc producta indicabit etiã horam 14. </s>
  <s xml:id="echoid-s13475" xml:space="preserve"><lb/>ab ortu. </s>
  <s xml:id="echoid-s13476" xml:space="preserve">Atque in hunc modum procedemus in aliis horis poſt 14. </s>
  <s xml:id="echoid-s13477" xml:space="preserve">ab ortu, ſi ducendæ fuerint.</s>
  <s xml:id="echoid-s13478" xml:space="preserve"/>
</p>
<div xml:id="echoid-div694" type="float" level="2" n="2">
<note position="right" xlink:label="note-0219-06" xlink:href="note-0219-06a" xml:space="preserve">Alia deſcriptio <lb/>horologii Baby <lb/>lonici horizon-<lb/>talis, ex arcu-<lb/>bus diurnis.</note>
<note position="left" xlink:label="note-0219-07" xlink:href="note-0219-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s13479" xml:space="preserve">HAC igitur artè expeditè ex prędictis tabulis propoſ. </s>
  <s xml:id="echoid-s13480" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13481" xml:space="preserve">ſuperioris libri vtrumque horolo-<lb/>
<anchor type="note" xlink:label="note-0220-01a" xlink:href="note-0220-01"/>
gium tam Italicum, quàm Babylonicum deſcribetur, ſi pro illis horis ab occaſu, quę vnum tantũ <lb/>punctum, vel etiam nullum habent in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s13482" xml:space="preserve">ducamus horas eaſdem ab ortu, <lb/>&amp; </s>
  <s xml:id="echoid-s13483" xml:space="preserve">è contrario, vt factũ à nobis eſt in horis 11. </s>
  <s xml:id="echoid-s13484" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13485" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13486" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s13487" xml:space="preserve">13. </s>
  <s xml:id="echoid-s13488" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13489" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13490" xml:space="preserve">ab ortu, &amp;</s>
  <s xml:id="echoid-s13491" xml:space="preserve">c.</s>
  <s xml:id="echoid-s13492" xml:space="preserve"/>
</p>
<div xml:id="echoid-div695" type="float" level="2" n="3">
<note position="left" xlink:label="note-0220-01" xlink:href="note-0220-01a" xml:space="preserve">Doctrina notã <lb/>da i<unsure/> deſcriptio <lb/>ne horologii tã <lb/>Italiei quàm <lb/>Babylonici, per <lb/>arcus diurnos, <lb/>ac nocturnos, <lb/>ſiue tabulas <lb/>propoſ 33. præ. <lb/>cedentis lib.</note>
</div>
<p>
  <s xml:id="echoid-s13493" xml:space="preserve">EODEM artificio conficiemus horologium Babylonicum ex arcu diurno horarum 24. </s>
  <s xml:id="echoid-s13494" xml:space="preserve">Item <lb/>
<anchor type="note" xlink:label="note-0220-02a" xlink:href="note-0220-02"/>
beneficio lineę horę 12. </s>
  <s xml:id="echoid-s13495" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s13496" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s13497" xml:space="preserve">atque etiam ſecundum alios modos in pręcedenti propoſ. <lb/></s>
  <s xml:id="echoid-s13498" xml:space="preserve">pręſcriptos. </s>
  <s xml:id="echoid-s13499" xml:space="preserve">Id quod perſpicue apparet ex figura præcedentis propoſ. </s>
  <s xml:id="echoid-s13500" xml:space="preserve">Itaque horologium Baby-<lb/>lonicum horizontale conſtituimus, &amp;</s>
  <s xml:id="echoid-s13501" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13502" xml:space="preserve">Quod faciendum erat. </s>
  <s xml:id="echoid-s13503" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0220-03a" xlink:href="note-0220-03"/>
</s>
</p>
<div xml:id="echoid-div696" type="float" level="2" n="4">
<note position="left" xlink:label="note-0220-02" xlink:href="note-0220-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0220-03" xlink:href="note-0220-03a" xml:space="preserve">Vſus horologii <lb/>Babylonici eſt, <lb/>vt ex vmbra <lb/>gnomonis in <lb/>eius lineas ho <lb/>rarias cadente <lb/>cognoſcamus, <lb/>quotnam horæ <lb/>à proximo ortu <lb/>Solis ſiat cla-<lb/>pſæ, &amp; quot ad <lb/>alterum ortum <lb/>ſint reliquę.</note>
</div>
</div>
<div xml:id="echoid-div698" type="section" level="1" n="174">
<head xml:id="echoid-head177" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s13504" xml:space="preserve">QVEMADMODVM ex horologio Italico didicimus, quot horæ tranſactæ ſint à proximo oc-<lb/>caſu Solis, &amp; </s>
  <s xml:id="echoid-s13505" xml:space="preserve">quot ſuperſint ad ſequentem occaſum, ita<unsure/> ex Babylonico horologio cognoſcemus, quot horæ <lb/>à proximo ortu Solis ſint elapſæ, &amp; </s>
  <s xml:id="echoid-s13506" xml:space="preserve">quot ad ſequentem ortum adhuc requirantur. </s>
  <s xml:id="echoid-s13507" xml:space="preserve">Cadente namque gno-<lb/>monis vmbra in lineam aliquam horariam ab ortu, puta in lineam horæ decimæ, dubitandum nullo mo-<lb/>do erit, quin horæ 10. </s>
  <s xml:id="echoid-s13508" xml:space="preserve">tranſactæ ſint à proximo ortu Solis, atque adeo vſque ad ſequentem ortum ſuper-<lb/>
<anchor type="note" xlink:label="note-0220-04a" xlink:href="note-0220-04"/>
eſſe horas 14. </s>
  <s xml:id="echoid-s13509" xml:space="preserve">quæ nimirum horis 10. </s>
  <s xml:id="echoid-s13510" xml:space="preserve">deſunt ad complendum numerum horarum 24. </s>
  <s xml:id="echoid-s13511" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13512" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s13513" xml:space="preserve"/>
</p>
<div xml:id="echoid-div698" type="float" level="2" n="1">
<note position="left" xlink:label="note-0220-04" xlink:href="note-0220-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s13514" xml:space="preserve">QVOD ſi in eodem plano deſcriptum ſit &amp; </s>
  <s xml:id="echoid-s13515" xml:space="preserve">horologium Italicum, &amp; </s>
  <s xml:id="echoid-s13516" xml:space="preserve">Babylonicum, ſiue ſecundum <lb/>eundem ſtylum, vt nos in propoſito horologio fecimus, ſiue ſecundum diuerſos, cognoſcemus quouis momẽ-<lb/>
<anchor type="note" xlink:label="note-0220-05a" xlink:href="note-0220-05"/>
to temporis ex vmbra ſtyli magnitudinem diei, ac noctis, tempus meridiei ac mediæ noctis tam ſecundum <lb/>horas ab occaſu, quàm ab ortu, tempus ortus Solis ſecundum horas ab occaſu, &amp; </s>
  <s xml:id="echoid-s13517" xml:space="preserve">tempus occaſus Solis <lb/>ſecundum horas ab ortu. </s>
  <s xml:id="echoid-s13518" xml:space="preserve">Nam ſi horæ ab ortu per gnomonis vmbram deprehenſæ deducantur ex horis ab <lb/>occaſu eodem tempore inuentis, relinquetur hora ortus Solis ſecundum horas ab occaſu. </s>
  <s xml:id="echoid-s13519" xml:space="preserve">Vnde facile re-<lb/>liqua eliciemus hac arte. </s>
  <s xml:id="echoid-s13520" xml:space="preserve">Ponamus vmbram ſtyli cadere in horam tertiam ab ortu, &amp; </s>
  <s xml:id="echoid-s13521" xml:space="preserve">in horam 14. </s>
  <s xml:id="echoid-s13522" xml:space="preserve">ab <lb/>occaſu. </s>
  <s xml:id="echoid-s13523" xml:space="preserve">Quoniam igitur tres horæ præterierunt, poſtquam ortus eſt Sol illa die, detrahemus 3. </s>
  <s xml:id="echoid-s13524" xml:space="preserve">ex 14. </s>
  <s xml:id="echoid-s13525" xml:space="preserve">re-<lb/>manebit{q́ue} hora vndecima ab occaſu, qua Sol ortus eſt. </s>
  <s xml:id="echoid-s13526" xml:space="preserve">Quare nox comprehendet tunc horas 11. </s>
  <s xml:id="echoid-s13527" xml:space="preserve">atque <lb/>
<anchor type="note" xlink:label="note-0220-06a" xlink:href="note-0220-06"/>
adeò dies horas 13. </s>
  <s xml:id="echoid-s13528" xml:space="preserve">quia dies, &amp; </s>
  <s xml:id="echoid-s13529" xml:space="preserve">nox conficiunt ſimul horas 24. </s>
  <s xml:id="echoid-s13530" xml:space="preserve">Quòd ſi diuidamus bifariam tempus no-<lb/>cturnum horarum 11. </s>
  <s xml:id="echoid-s13531" xml:space="preserve">inueniemus horas 5 {1/2}. </s>
  <s xml:id="echoid-s13532" xml:space="preserve">pro tempore medię noctis, quoad horas ab occaſu. </s>
  <s xml:id="echoid-s13533" xml:space="preserve">Et quia <lb/>à media nocte vſque ad meridiem exiſtunt horæ 12. </s>
  <s xml:id="echoid-s13534" xml:space="preserve">ſi horas 12. </s>
  <s xml:id="echoid-s13535" xml:space="preserve">ad horas 5 {1/2}. </s>
  <s xml:id="echoid-s13536" xml:space="preserve">adĳciamus, conficiemus ho <lb/>ras 17 {1/2}. </s>
  <s xml:id="echoid-s13537" xml:space="preserve">pro tempore meridiei ſecundum eaſdem horas ab occaſu. </s>
  <s xml:id="echoid-s13538" xml:space="preserve">Idem etiam tempus meridiei reperie-<lb/>mus, ſi arcum ſemidiurnum, qui in hoc exemplo complectitur hor. </s>
  <s xml:id="echoid-s13539" xml:space="preserve">6 {1/2}. </s>
  <s xml:id="echoid-s13540" xml:space="preserve">ex horis 24. </s>
  <s xml:id="echoid-s13541" xml:space="preserve">auferamus: </s>
  <s xml:id="echoid-s13542" xml:space="preserve">quia ar-<lb/>cus ſemidiurnus additus tempori meridiei conficit neceſſario horas 24. </s>
  <s xml:id="echoid-s13543" xml:space="preserve">nempe totum diem natur alem ho <lb/>rarum 24. </s>
  <s xml:id="echoid-s13544" xml:space="preserve">ab vno occaſu ad alterum, vt patet. </s>
  <s xml:id="echoid-s13545" xml:space="preserve">Ita vides, ſihor. </s>
  <s xml:id="echoid-s13546" xml:space="preserve">6 {1/2}. </s>
  <s xml:id="echoid-s13547" xml:space="preserve">demantur ex 24. </s>
  <s xml:id="echoid-s13548" xml:space="preserve">relinqui hor. </s>
  <s xml:id="echoid-s13549" xml:space="preserve">17 {1/2}. <lb/></s>
  <s xml:id="echoid-s13550" xml:space="preserve">pro tempore meridiei. </s>
  <s xml:id="echoid-s13551" xml:space="preserve">Deinde ſi diuidamus tempus diurnum horarum 13. </s>
  <s xml:id="echoid-s13552" xml:space="preserve">bifariam, reperiemus horas <lb/>6 {1/2}. </s>
  <s xml:id="echoid-s13553" xml:space="preserve">pro tempore meridiei ſecundum horas ab ortu. </s>
  <s xml:id="echoid-s13554" xml:space="preserve">Et quoniam à meridie ad mediam noctem fluunt ho-<lb/>ræ 12. </s>
  <s xml:id="echoid-s13555" xml:space="preserve">ſi addamus 12. </s>
  <s xml:id="echoid-s13556" xml:space="preserve">ad 6 {1/2}. </s>
  <s xml:id="echoid-s13557" xml:space="preserve">habebimus horas 18 {1/2}. </s>
  <s xml:id="echoid-s13558" xml:space="preserve">pro tempore mediæ noctis ſecundum eaſdem ho-<lb/>
<anchor type="note" xlink:label="note-0220-07a" xlink:href="note-0220-07"/>
ras ab ortu. </s>
  <s xml:id="echoid-s13559" xml:space="preserve">Quod etiam tempus mediæ noctis inueniemus, ſi arcum ſeminocturnum, qui in nostro <lb/>exemplo comprehendit hor. </s>
  <s xml:id="echoid-s13560" xml:space="preserve">5 {1/2}. </s>
  <s xml:id="echoid-s13561" xml:space="preserve">detrahamus ex horis 24. </s>
  <s xml:id="echoid-s13562" xml:space="preserve">quia arcus ſeminocturnus additus tempori <lb/>mediæ noctis conficit neceſſario horas 24. </s>
  <s xml:id="echoid-s13563" xml:space="preserve">nimirum totum diem naturalem horarum 24. </s>
  <s xml:id="echoid-s13564" xml:space="preserve">ab vno ortu ad <lb/>alterum. </s>
  <s xml:id="echoid-s13565" xml:space="preserve">Ita vides, ſi hor. </s>
  <s xml:id="echoid-s13566" xml:space="preserve">5 {1/2}. </s>
  <s xml:id="echoid-s13567" xml:space="preserve">demantur ex 24. </s>
  <s xml:id="echoid-s13568" xml:space="preserve">relinqui hor. </s>
  <s xml:id="echoid-s13569" xml:space="preserve">18 {1/2}. </s>
  <s xml:id="echoid-s13570" xml:space="preserve">pro tempore mediæ noctis. </s>
  <s xml:id="echoid-s13571" xml:space="preserve">Sol autem <lb/>occidet hora 13. </s>
  <s xml:id="echoid-s13572" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s13573" xml:space="preserve">Ponamus rurſum vmbrã ſtyli indicare horam 6 {1/4}. </s>
  <s xml:id="echoid-s13574" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s13575" xml:space="preserve">horã 17 {1/2}. </s>
  <s xml:id="echoid-s13576" xml:space="preserve">ab oc-<lb/>caſu. </s>
  <s xml:id="echoid-s13577" xml:space="preserve">Si detrahamus 6 {1/4}. </s>
  <s xml:id="echoid-s13578" xml:space="preserve">ex 17 {1/2}. </s>
  <s xml:id="echoid-s13579" xml:space="preserve">inueniemus horam 11 {1/4} ab occaſu, qua Sol illa die ortus eſt; </s>
  <s xml:id="echoid-s13580" xml:space="preserve">atq; </s>
  <s xml:id="echoid-s13581" xml:space="preserve">adeo <lb/>nox tunc complectetur horas 11 {1/4}. </s>
  <s xml:id="echoid-s13582" xml:space="preserve">dies autem erit horarũ 12 {3/4}. </s>
  <s xml:id="echoid-s13583" xml:space="preserve">media autem nox fiet hora 5 {1/2}. </s>
  <s xml:id="echoid-s13584" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13585" xml:space="preserve">{1/8}. <lb/></s>
  <s xml:id="echoid-s13586" xml:space="preserve">hoc eſt, hora 5 {5/8}. </s>
  <s xml:id="echoid-s13587" xml:space="preserve">quoad horas ab occaſu, meridies verò hora 17 {1/2}. </s>
  <s xml:id="echoid-s13588" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13589" xml:space="preserve">{1/8}. </s>
  <s xml:id="echoid-s13590" xml:space="preserve">hoc eſt, hora 17 {5/8}. </s>
  <s xml:id="echoid-s13591" xml:space="preserve">ſecundũ eaſ-<lb/>dem horas ab occaſu. </s>
  <s xml:id="echoid-s13592" xml:space="preserve">Item ſecundum horas ab ortu meridies fiet hora 6 {1/4}. </s>
  <s xml:id="echoid-s13593" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13594" xml:space="preserve">{1/8}. </s>
  <s xml:id="echoid-s13595" xml:space="preserve">hoc eſt, hora 6 {3/8}. </s>
  <s xml:id="echoid-s13596" xml:space="preserve">media <lb/>nox autem hora 18 {1/4}. </s>
  <s xml:id="echoid-s13597" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13598" xml:space="preserve">{1/8}. </s>
  <s xml:id="echoid-s13599" xml:space="preserve">id eſt, hora 18 {3/8}. </s>
  <s xml:id="echoid-s13600" xml:space="preserve">Sol denique occidet hora 12 {3/4}. </s>
  <s xml:id="echoid-s13601" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s13602" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s13603" xml:space="preserve"/>
</p>
<div xml:id="echoid-div699" type="float" level="2" n="2">
<note position="left" xlink:label="note-0220-05" xlink:href="note-0220-05a" xml:space="preserve">Quomodo ex <lb/>horologio Itali <lb/>co &amp; Babyloni <lb/>co ſimul inue-<lb/>niatur quolibet <lb/>tempore ex vm <lb/>bra ſtyli magni <lb/>tudo diei ac no <lb/>ctis, tempus me <lb/>ridiei ac medię <lb/>noctis tam ſe-<lb/>cundum horas <lb/>ab occ. quàm <lb/>ab or. tempus <lb/>ortus Solis quo <lb/>ad horas ab oc. <lb/>caſu &amp; tempus <lb/>occaſus Solis <lb/>quoad horas ab <lb/>ortu.</note>
<note position="left" xlink:label="note-0220-06" xlink:href="note-0220-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0220-07" xlink:href="note-0220-07a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s13604" xml:space="preserve">IDEM quoque deprehendi poteſt beneficio horologĳ Aſtronomici, quod propoſ. </s>
  <s xml:id="echoid-s13605" xml:space="preserve">1. </s>
  <s xml:id="echoid-s13606" xml:space="preserve">huius libri con-<lb/>
<anchor type="note" xlink:label="note-0220-09a" xlink:href="note-0220-09"/>
ſtruximus. </s>
  <s xml:id="echoid-s13607" xml:space="preserve">Nam ſtatim ex eo veniemus in cognitionem temporis meridiei ſecundum horas Italicas, vel <lb/>Babylonicas. </s>
  <s xml:id="echoid-s13608" xml:space="preserve">Vnde &amp; </s>
  <s xml:id="echoid-s13609" xml:space="preserve">reliqua cognoſcemus hoc modo. </s>
  <s xml:id="echoid-s13610" xml:space="preserve">Ponamus vmbram cadere in horam 9 {1/2}. </s>
  <s xml:id="echoid-s13611" xml:space="preserve">à media <lb/>nocte, &amp; </s>
  <s xml:id="echoid-s13612" xml:space="preserve">in horam quartam ab ortu, &amp; </s>
  <s xml:id="echoid-s13613" xml:space="preserve">in horam 15. </s>
  <s xml:id="echoid-s13614" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s13615" xml:space="preserve">Quoniam igitur ad meridiem vſque de-<lb/>ſunt horæ 2 {1/2}. </s>
  <s xml:id="echoid-s13616" xml:space="preserve">ſi addamus 2 {1/2}. </s>
  <s xml:id="echoid-s13617" xml:space="preserve">ad 4. </s>
  <s xml:id="echoid-s13618" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13619" xml:space="preserve">ad 15. </s>
  <s xml:id="echoid-s13620" xml:space="preserve">inucniemus meridiem ſecundum horas ab ortu contingere <lb/>hora 6 {1/2}. </s>
  <s xml:id="echoid-s13621" xml:space="preserve">at que idcirco mediam noctem hora 18 {1/2}. </s>
  <s xml:id="echoid-s13622" xml:space="preserve">At ſecundum horas Italicas meridiem hora 17 {1/2}. <lb/></s>
  <s xml:id="echoid-s13623" xml:space="preserve">mediam noctem verò hora 5 {1/2}. </s>
  <s xml:id="echoid-s13624" xml:space="preserve">cum ſemper meridies, &amp; </s>
  <s xml:id="echoid-s13625" xml:space="preserve">media nox inter ſe diſtent horis 12. </s>
  <s xml:id="echoid-s13626" xml:space="preserve">vel ſemicir-<lb/>culo. </s>
  <s xml:id="echoid-s13627" xml:space="preserve">Hinc quantitas diei manifeſta erit. </s>
  <s xml:id="echoid-s13628" xml:space="preserve">Nam cum meridies fiat hora 6 {1/2}. </s>
  <s xml:id="echoid-s13629" xml:space="preserve">ab ortu, ſupererunt totidẽ ho-<lb/>ræ vſq; </s>
  <s xml:id="echoid-s13630" xml:space="preserve">ad occaſum; </s>
  <s xml:id="echoid-s13631" xml:space="preserve">ac proinde cõtinebit dies horas 13. </s>
  <s xml:id="echoid-s13632" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13633" xml:space="preserve">nox 11. </s>
  <s xml:id="echoid-s13634" xml:space="preserve">Hora ergo 11. </s>
  <s xml:id="echoid-s13635" xml:space="preserve">ab occaſu orietur tũc <lb/>Sol, &amp; </s>
  <s xml:id="echoid-s13636" xml:space="preserve">occidet hora 13. </s>
  <s xml:id="echoid-s13637" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s13638" xml:space="preserve">Similiter quia media nox efficitur hora 5 {1/2}. </s>
  <s xml:id="echoid-s13639" xml:space="preserve">ab occaſu, ſupererunt toti-<lb/>dem horæ vſq; </s>
  <s xml:id="echoid-s13640" xml:space="preserve">ad Solis ortum; </s>
  <s xml:id="echoid-s13641" xml:space="preserve">ac proinde nox comprehendet horas 11. </s>
  <s xml:id="echoid-s13642" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13643" xml:space="preserve">dies 13. </s>
  <s xml:id="echoid-s13644" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13645" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13646" xml:space="preserve">Rurſus ponamus
<pb o="201" file="0221" n="221" rhead="LIBER SECVNDVS."/>
inuentam eſſe horam 3 {1/2}. </s>
  <s xml:id="echoid-s13647" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s13648" xml:space="preserve">horam 8 {1/4}. </s>
  <s xml:id="echoid-s13649" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s13650" xml:space="preserve">horam 22 {3/4}. </s>
  <s xml:id="echoid-s13651" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s13652" xml:space="preserve">Quoniam igitur <lb/>elapſæ ſunt poſt meridiem horæ 3 {1/2}. </s>
  <s xml:id="echoid-s13653" xml:space="preserve">ſi detrahamus 3 {1/2}. </s>
  <s xml:id="echoid-s13654" xml:space="preserve">ex 8 {1/4}. </s>
  <s xml:id="echoid-s13655" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13656" xml:space="preserve">ex 22 {3/4}. </s>
  <s xml:id="echoid-s13657" xml:space="preserve">reperiemus meridiem ſecun-<lb/>dum horas ab ortu fieri hora 4 {3/4}. </s>
  <s xml:id="echoid-s13658" xml:space="preserve">mediam noctem autem hora 16 {3/4}. </s>
  <s xml:id="echoid-s13659" xml:space="preserve">At vero ſecundum horas ab occaſu, <lb/>meridiem effici hora 19 {1/4}. </s>
  <s xml:id="echoid-s13660" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13661" xml:space="preserve">mediam noctem hora 7 {1/4}. </s>
  <s xml:id="echoid-s13662" xml:space="preserve">Itaque cum meridies fiat hora 4 {3/4}.</s>
  <s xml:id="echoid-s13663" xml:space="preserve"><unsure/> ab ortu, ſu-<lb/>pererunt totidem horæ vſque ad Solis occaſum. </s>
  <s xml:id="echoid-s13664" xml:space="preserve">Quamobrem complectetur dies horas 9 {1/2}. </s>
  <s xml:id="echoid-s13665" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13666" xml:space="preserve">nox horas <lb/>14 {1/2}. </s>
  <s xml:id="echoid-s13667" xml:space="preserve">Vnde Sol tunc orietur hora 14 {1/2}. </s>
  <s xml:id="echoid-s13668" xml:space="preserve">ab occaſu, occidet{q́ue} hora 9 {1/2}. </s>
  <s xml:id="echoid-s13669" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s13670" xml:space="preserve">Pari ratione, quia media <lb/>nox, more Italorum, fit hora 7 {1/4}. </s>
  <s xml:id="echoid-s13671" xml:space="preserve">ſupererunt totidem horæ vſque ad ortum Solis. </s>
  <s xml:id="echoid-s13672" xml:space="preserve">Quocirca continebit <lb/>nox horas 14 {1/2}. </s>
  <s xml:id="echoid-s13673" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13674" xml:space="preserve">dies horas 9 {1/2}. </s>
  <s xml:id="echoid-s13675" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13676" xml:space="preserve">c.</s>
  <s xml:id="echoid-s13677" xml:space="preserve"/>
</p>
<div xml:id="echoid-div700" type="float" level="2" n="3">
<note position="left" xlink:label="note-0220-09" xlink:href="note-0220-09a" xml:space="preserve">Quomodo ea-<lb/>dem, de quibus <lb/>proxime dictũ <lb/>eſt, beneficio <lb/>horologii Aſtro <lb/>nomici inue-<lb/>niantur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s13678" xml:space="preserve">EX deſcriptione porrò horologĳ Italici, &amp; </s>
  <s xml:id="echoid-s13679" xml:space="preserve">Babylonici in hac, &amp; </s>
  <s xml:id="echoid-s13680" xml:space="preserve">præcedenti propoſ. </s>
  <s xml:id="echoid-s13681" xml:space="preserve">tradita perſpi-<lb/>
<anchor type="note" xlink:label="note-0221-01a" xlink:href="note-0221-01"/>
cuum eſt, duo hæc horologia non differre inter ſe, niſi ſitu, &amp; </s>
  <s xml:id="echoid-s13682" xml:space="preserve">ordine horarum; </s>
  <s xml:id="echoid-s13683" xml:space="preserve">ita vt pars ſiniſtra vnius re <lb/>
<anchor type="note" xlink:label="note-0221-02a" xlink:href="note-0221-02"/>
ſpondeat dextræ alterius &amp; </s>
  <s xml:id="echoid-s13684" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s13685" xml:space="preserve">Quapropter ſi horologium Italicum deſcribatur, inſeruiet idem pro <lb/>Babylonico, ſi modo inuertatur, vt pars ſiniſtra fiat dextra, &amp; </s>
  <s xml:id="echoid-s13686" xml:space="preserve">contra, &amp; </s>
  <s xml:id="echoid-s13687" xml:space="preserve">ex linea horæ 23. </s>
  <s xml:id="echoid-s13688" xml:space="preserve">ab oc-<lb/>caſu fiat hora prima ab ortu, &amp; </s>
  <s xml:id="echoid-s13689" xml:space="preserve">ſecunda ab ortu fiat ex 22. </s>
  <s xml:id="echoid-s13690" xml:space="preserve">ab occaſu, &amp;</s>
  <s xml:id="echoid-s13691" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13692" xml:space="preserve">Id quod ſacile patet: </s>
  <s xml:id="echoid-s13693" xml:space="preserve">ſi horo-<lb/>logium Babylonicum hac propoſ. </s>
  <s xml:id="echoid-s13694" xml:space="preserve">delineatũ cũ horologio Italico propos. </s>
  <s xml:id="echoid-s13695" xml:space="preserve">præcedenti deſcripto confer atur.</s>
  <s xml:id="echoid-s13696" xml:space="preserve"/>
</p>
<div xml:id="echoid-div701" type="float" level="2" n="4">
<note position="right" xlink:label="note-0221-01" xlink:href="note-0221-01a" xml:space="preserve">Quomodo dif-<lb/>ferant inter ſe <lb/>horologium Ita <lb/>licum, &amp; Baby-<lb/>lonicum; &amp; qua <lb/>ratione ex It<unsure/>all <lb/>co componatur <lb/>Babylonicum, <lb/>&amp; ex Babyloni-<lb/>co Italic<unsure/>um.</note>
<note position="left" xlink:label="note-0221-02" xlink:href="note-0221-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s13697" xml:space="preserve">IT AQVE ſi horologium Italicum in charta aliqua deſcribatur, &amp; </s>
  <s xml:id="echoid-s13698" xml:space="preserve">in parte oppoſita ducantur li <lb/>neæ reſpondentes ad vnguem lineis horologĳ Italici, deſcriptum erit in parte oppoſita horologium Baby-<lb/>lonicum, dummodo numeri horarum in Italico mutentur in Babylonico in earum complementa vſque ad <lb/>24. </s>
  <s xml:id="echoid-s13699" xml:space="preserve">vt hora 23. </s>
  <s xml:id="echoid-s13700" xml:space="preserve">Italica in primam Babylonicam, &amp; </s>
  <s xml:id="echoid-s13701" xml:space="preserve">22. </s>
  <s xml:id="echoid-s13702" xml:space="preserve">in ſecundam, &amp; </s>
  <s xml:id="echoid-s13703" xml:space="preserve">21. </s>
  <s xml:id="echoid-s13704" xml:space="preserve">in tertiam, &amp;</s>
  <s xml:id="echoid-s13705" xml:space="preserve">c.</s>
  <s xml:id="echoid-s13706" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s13707" xml:space="preserve">EODEM modo ſi prius deſcribatur horologium Babylonicum deſcribetur in parte oppoſita horo-<lb/>logium Italicum, ita vt ſingulæ lineæ ſingulis lineis reſpondeant ad vnguem, mutatis quoque numeris <lb/>
<anchor type="note" xlink:label="note-0221-03a" xlink:href="note-0221-03"/>
horarum in Babylonico in earum complementa vſque ad 24. </s>
  <s xml:id="echoid-s13708" xml:space="preserve">in Italico. </s>
  <s xml:id="echoid-s13709" xml:space="preserve">Vt hora prima Babylonica in 23. <lb/></s>
  <s xml:id="echoid-s13710" xml:space="preserve">Italicam, &amp; </s>
  <s xml:id="echoid-s13711" xml:space="preserve">ſecunda in 22. </s>
  <s xml:id="echoid-s13712" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13713" xml:space="preserve">tertia in 21. </s>
  <s xml:id="echoid-s13714" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13715" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13716" xml:space="preserve">Quod item intelligendum eſt in alĳs horologĳs Italicis, <lb/>&amp; </s>
  <s xml:id="echoid-s13717" xml:space="preserve">Babylonicis, quæ in aliis planis, quæ nimirum non Horizonti, ſed alĳs circulis maximis in ſphæra pa-<lb/>rallela ſunt, deſcribuntur.</s>
  <s xml:id="echoid-s13718" xml:space="preserve"/>
</p>
<div xml:id="echoid-div702" type="float" level="2" n="5">
<note position="left" xlink:label="note-0221-03" xlink:href="note-0221-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div704" type="section" level="1" n="175">
<head xml:id="echoid-head178" xml:space="preserve">PROBLEMA 12. PROPOSITIO 12.</head>
<p>
  <s xml:id="echoid-s13719" xml:space="preserve">HOROLOGIVM Antiquum horizontale conſtituere. </s>
  <s xml:id="echoid-s13720" xml:space="preserve">Hoc eſt, <lb/>lineas horarũ inęqualium in plano Horizonti ęquidiſtante deſcribere.</s>
  <s xml:id="echoid-s13721" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s13722" xml:space="preserve">DIVISO circulo ex E, deſcripto in arcum diurnum tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s13723" xml:space="preserve">tropici ♑, d N e, vt <lb/>
<anchor type="note" xlink:label="note-0221-05a" xlink:href="note-0221-05"/>
in propoſ. </s>
  <s xml:id="echoid-s13724" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13725" xml:space="preserve">huius libri factum eſt, ſecetur vterque arcus diurnus in partes 12. </s>
  <s xml:id="echoid-s13726" xml:space="preserve">æquales, initio fa-<lb/>
<anchor type="figure" xlink:label="fig-0221-01a" xlink:href="fig-0221-01"/>
<anchor type="note" xlink:label="note-0221-06a" xlink:href="note-0221-06"/>
<anchor type="note" xlink:label="note-0221-07a" xlink:href="note-0221-07"/>
cto à punctis a, &amp; </s>
  <s xml:id="echoid-s13727" xml:space="preserve">d, orientalibus, ita vt proxima puncta poſt a, &amp; </s>
  <s xml:id="echoid-s13728" xml:space="preserve">d, verſus N, pertineant ad horã<unsure/> <lb/>primam inęqualem in vtroque tropico, &amp; </s>
  <s xml:id="echoid-s13729" xml:space="preserve">ſequentia ad ſecundam, &amp;</s>
  <s xml:id="echoid-s13730" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13731" xml:space="preserve">tranſibunt per hæc puncto<unsure/> <lb/>diuiſionum, ſi horologium, &amp; </s>
  <s xml:id="echoid-s13732" xml:space="preserve">circulus M a N b, proprium ſitum habeant, circuli maximi per po-<lb/>los mundi, &amp; </s>
  <s xml:id="echoid-s13733" xml:space="preserve">horas inæquales tropicorum ♋, &amp; </s>
  <s xml:id="echoid-s13734" xml:space="preserve">♑, ducti, vt ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s13735" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13736" xml:space="preserve">huius li-
<pb o="202" file="0222" n="222" rhead="GNOMONICES"/>
bri manifeſtum eſt. </s>
  <s xml:id="echoid-s13737" xml:space="preserve">Eadem enim demõſtratio huc afferri poteſt; </s>
  <s xml:id="echoid-s13738" xml:space="preserve">quia eodem modo oſtendemus, <lb/>circulum per polos mundi, &amp; </s>
  <s xml:id="echoid-s13739" xml:space="preserve">horam 12. </s>
  <s xml:id="echoid-s13740" xml:space="preserve">inæqualem in tropico ♋. </s>
  <s xml:id="echoid-s13741" xml:space="preserve">ductum tranſire per punctum <lb/>b, cùm idem punctum in tropico ♋, ſit horæ 12. </s>
  <s xml:id="echoid-s13742" xml:space="preserve">inæqualis, &amp; </s>
  <s xml:id="echoid-s13743" xml:space="preserve">horæ 24. </s>
  <s xml:id="echoid-s13744" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s13745" xml:space="preserve">Hinc rurſus oſten <lb/>demus (cum arcus inter b, &amp; </s>
  <s xml:id="echoid-s13746" xml:space="preserve">proximum punctum diuiſionis verſus N, ſimilis ſit arcui tropici ♋, <lb/>
<anchor type="figure" xlink:label="fig-0222-01a" xlink:href="fig-0222-01"/>
<anchor type="note" xlink:label="note-0222-01a" xlink:href="note-0222-01"/>
<anchor type="note" xlink:label="note-0222-02a" xlink:href="note-0222-02"/>
inter duos maximos circulos per polos mundi ductos interiecto, quorum vnus per horam 12. </s>
  <s xml:id="echoid-s13747" xml:space="preserve">in-<lb/>
<anchor type="note" xlink:label="note-0222-03a" xlink:href="note-0222-03"/>
æqualem, alter vero per horam 11. </s>
  <s xml:id="echoid-s13748" xml:space="preserve">inæqualem in tropico ♋, ducitur; </s>
  <s xml:id="echoid-s13749" xml:space="preserve">quòd vterque arcus duode-<lb/>cima pars ſit arcus ſemidiurni tropici ♋, in ſuo circulo) circulum maximum per polos mundi, &amp; </s>
  <s xml:id="echoid-s13750" xml:space="preserve"><lb/>horam 11. </s>
  <s xml:id="echoid-s13751" xml:space="preserve">inæqualem in tropico ♋, ductum tranſire per proximum punctum diuiſionis à b, ver-<lb/>ſus N, &amp; </s>
  <s xml:id="echoid-s13752" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s13753" xml:space="preserve">Si igitur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s13754" xml:space="preserve">centrum E, rectæ ducantur ſecantes <lb/>æquinoctialem lineam in punctis, per quæ rurſus ex H, centro horologii emittantur rectæ, repe-<lb/>rientur in tropicis ♋, &amp; </s>
  <s xml:id="echoid-s13755" xml:space="preserve">♑, puncta horarum inæqualium, non ſecus ac propoſ. </s>
  <s xml:id="echoid-s13756" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13757" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13758" xml:space="preserve">11. </s>
  <s xml:id="echoid-s13759" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s13760" xml:space="preserve">in eiſdem puncta inuenimus horarum ab occaſu, &amp; </s>
  <s xml:id="echoid-s13761" xml:space="preserve">ortu. </s>
  <s xml:id="echoid-s13762" xml:space="preserve">Vnde ſi reſpondentia puncta lineis re-<lb/>ctis iungantur, deſcriptum erit horologium Antiquum. </s>
  <s xml:id="echoid-s13763" xml:space="preserve">Tranſibunt autem omnes lineæ horarum <lb/>inæqualium per horas à meridie, vel media nocte in linea æquinoctiali, vt conſtat ex tabula 13. </s>
  <s xml:id="echoid-s13764" xml:space="preserve"><lb/>ſcholii propoſ. </s>
  <s xml:id="echoid-s13765" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13766" xml:space="preserve">præcedentis libri. </s>
  <s xml:id="echoid-s13767" xml:space="preserve">Sed accipe huiuſce deſcriptionis vnum, aut alterum exem-<lb/>
<anchor type="note" xlink:label="note-0222-04a" xlink:href="note-0222-04"/>
plum. </s>
  <s xml:id="echoid-s13768" xml:space="preserve">Ex f, puncto horæ 3. </s>
  <s xml:id="echoid-s13769" xml:space="preserve">inæqualis in tropico ♑, per E, ducta recta ſecat æquinoctialem lineã <lb/>in g; </s>
  <s xml:id="echoid-s13770" xml:space="preserve">recta autem ex H, per g, emiſſa ſecat tropicum ♑, in h, puncto horæ tertiæ inæqualis. </s>
  <s xml:id="echoid-s13771" xml:space="preserve">Rurſus <lb/>ex puncto m, quod opponitur horæ vndecimæ inæquali in tropico ♋, recta emiſſa per E, ſecat li-<lb/>neam æquinoctialem in n, at recta H n, ſecat tropicum ♋, in puncto p, quod ſemicirculo maximi <lb/>circuli per punctum m, ducto debetur: </s>
  <s xml:id="echoid-s13772" xml:space="preserve">producta autem n H, vltra centrum ſecat eundem tropi-<lb/>cum ♋, in q, puncto horæ vndecimæ inæqualis, &amp; </s>
  <s xml:id="echoid-s13773" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13774" xml:space="preserve">Quæ omnia ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s13775" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13776" xml:space="preserve">huius <lb/>libri perſpicua ſunt.</s>
  <s xml:id="echoid-s13777" xml:space="preserve"/>
</p>
<div xml:id="echoid-div704" type="float" level="2" n="1">
<note position="right" xlink:label="note-0221-05" xlink:href="note-0221-05a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Antiqui <lb/>horizontalis.</note>
  <figure xlink:label="fig-0221-01" xlink:href="fig-0221-01a">
    <image file="0221-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0221-01"/>
  </figure>
<note position="left" xlink:label="note-0221-06" xlink:href="note-0221-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0221-07" xlink:href="note-0221-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0222-01" xlink:href="fig-0222-01a">
    <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-01"/>
  </figure>
<note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0222-02" xlink:href="note-0222-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0222-03" xlink:href="note-0222-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0222-04" xlink:href="note-0222-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s13778" xml:space="preserve">HIC quoque, vt in propoſ. </s>
  <s xml:id="echoid-s13779" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13780" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s13781" xml:space="preserve">reperiemus in circulo M a N b, arcum diurnum no-<lb/>cturnumq́; </s>
  <s xml:id="echoid-s13782" xml:space="preserve">tropici ♋, vel ♑, aliter, quàm per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s13783" xml:space="preserve">1. </s>
  <s xml:id="echoid-s13784" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s13785" xml:space="preserve">ſcripſi-<lb/>mus; </s>
  <s xml:id="echoid-s13786" xml:space="preserve">ſi nimirum à puncto N, vtrinque ſupputemus arcum ſemidiurnum tropici ♋, vſque ad a, <lb/>
<anchor type="note" xlink:label="note-0222-05a" xlink:href="note-0222-05"/>
&amp; </s>
  <s xml:id="echoid-s13787" xml:space="preserve">b, vel tropici ♑, vſque ad d, &amp; </s>
  <s xml:id="echoid-s13788" xml:space="preserve">e.</s>
  <s xml:id="echoid-s13789" xml:space="preserve"/>
</p>
<div xml:id="echoid-div705" type="float" level="2" n="2">
<note position="left" xlink:label="note-0222-05" xlink:href="note-0222-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s13790" xml:space="preserve">IMMO etiamſi dictum circulum non diuidamus in dictos arcus, reperiemus in eo punctum <lb/>cuiuſuis horæ inæqualis, Sole in quocunque parallelo exiſtente, hac ratione. </s>
  <s xml:id="echoid-s13791" xml:space="preserve">Diuidatur ar-<lb/>cus diurnus dati paralleli per 12. </s>
  <s xml:id="echoid-s13792" xml:space="preserve">vt in numero quotiente habeamus quantitatem vnius ho-<lb/>ræ inæqualis in dato parallelo; </s>
  <s xml:id="echoid-s13793" xml:space="preserve">atque adeo in eodem numero duplicato magnitudinem dua-<lb/>rum horarum, &amp; </s>
  <s xml:id="echoid-s13794" xml:space="preserve">in triplicato trium, &amp;</s>
  <s xml:id="echoid-s13795" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13796" xml:space="preserve">Deinde conſideretur, quantum diſter hora inæqua-<lb/>lis propoſita à Meridiano circulo ante meridiem, ſiue poſt. </s>
  <s xml:id="echoid-s13797" xml:space="preserve">Si enim hæc diſtantia in circulo <lb/>M a N b, numeretur à puncto N, verſus a, ſi hora data fuerit antemeridiana, aut verſus b, <lb/>ſi pomeridiana, offendemus punctum datæ horæ inæqualis. </s>
  <s xml:id="echoid-s13798" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s13799" xml:space="preserve">Arcus diurnus tro-<lb/>pici ♋, continet horas 15. </s>
  <s xml:id="echoid-s13800" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13801" xml:space="preserve">4. </s>
  <s xml:id="echoid-s13802" xml:space="preserve">hoc eſt, Gradus 226. </s>
  <s xml:id="echoid-s13803" xml:space="preserve">quibus gradibus diuiſis per 12. </s>
  <s xml:id="echoid-s13804" xml:space="preserve">pro-<lb/>dibunt grad. </s>
  <s xml:id="echoid-s13805" xml:space="preserve">18. </s>
  <s xml:id="echoid-s13806" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13807" xml:space="preserve">50. </s>
  <s xml:id="echoid-s13808" xml:space="preserve">pro magnitudine vnius horæ inæqualis in tropico ♋. </s>
  <s xml:id="echoid-s13809" xml:space="preserve">Vnde duæ
<pb o="203" file="0223" n="223" rhead="LIBER SECVNDVS."/>
horæ efficient grad. </s>
  <s xml:id="echoid-s13810" xml:space="preserve">37. </s>
  <s xml:id="echoid-s13811" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13812" xml:space="preserve">40. </s>
  <s xml:id="echoid-s13813" xml:space="preserve">Tres autem horæ grad. </s>
  <s xml:id="echoid-s13814" xml:space="preserve">56. </s>
  <s xml:id="echoid-s13815" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13816" xml:space="preserve">30. </s>
  <s xml:id="echoid-s13817" xml:space="preserve">Quatuor vero horæ <lb/>grad. </s>
  <s xml:id="echoid-s13818" xml:space="preserve">75. </s>
  <s xml:id="echoid-s13819" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13820" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13821" xml:space="preserve">Quinque autem horæ grad. </s>
  <s xml:id="echoid-s13822" xml:space="preserve">94. </s>
  <s xml:id="echoid-s13823" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13824" xml:space="preserve">10. </s>
  <s xml:id="echoid-s13825" xml:space="preserve">Sex denique horæ grad. </s>
  <s xml:id="echoid-s13826" xml:space="preserve">113. <lb/></s>
  <s xml:id="echoid-s13827" xml:space="preserve">Itaque ſi quæratur in circulo M a N b, punctum horæ nonæ inæqualis tropici ♋, quoniam hæc <lb/>hora pomeridiana eſt, ſi numeretur eius diſtantia à meridie ex puncto N, verſus b, nempe grad. </s>
  <s xml:id="echoid-s13828" xml:space="preserve"><lb/>56. </s>
  <s xml:id="echoid-s13829" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13830" xml:space="preserve">30. </s>
  <s xml:id="echoid-s13831" xml:space="preserve">inuenietur punctum horæ nonę inęqualis tropici ♋. </s>
  <s xml:id="echoid-s13832" xml:space="preserve">Eademq́ue ratio de cęte-<lb/>r<unsure/>is habenda eſt.</s>
  <s xml:id="echoid-s13833" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s13834" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s13835" xml:space="preserve">Deſcribantur ex propoſ. </s>
  <s xml:id="echoid-s13836" xml:space="preserve">3. </s>
  <s xml:id="echoid-s13837" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s13838" xml:space="preserve">duo paralleli, Borealis vnus, qui arcum diur-<lb/>
<anchor type="note" xlink:label="note-0223-01a" xlink:href="note-0223-01"/>
num habeat horarum 18. </s>
  <s xml:id="echoid-s13839" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13840" xml:space="preserve">Auſtralis alter, cuius arcus diurnus horas ſex comprehendat. </s>
  <s xml:id="echoid-s13841" xml:space="preserve">Nam <lb/>ex tabulis arcuum diurnorum horarũ 18. </s>
  <s xml:id="echoid-s13842" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13843" xml:space="preserve">6. </s>
  <s xml:id="echoid-s13844" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13845" xml:space="preserve">12. </s>
  <s xml:id="echoid-s13846" xml:space="preserve">quas pro horis inæqualibus in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s13847" xml:space="preserve">33. </s>
  <s xml:id="echoid-s13848" xml:space="preserve">præcedentis libri deſcripſimus, mox cognoſcemus, per quaſnam horas à meridie, vel me-<lb/>
<anchor type="note" xlink:label="note-0223-02a" xlink:href="note-0223-02"/>
dia nocte in dictis arcubus ſingulæ horæ inæquales ducendæ ſint. </s>
  <s xml:id="echoid-s13849" xml:space="preserve">Ita vides horam primã inæqua-<lb/>lem ducendam eſſe per horam 4 {1/2}. </s>
  <s xml:id="echoid-s13850" xml:space="preserve">à media nocte in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s13851" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13852" xml:space="preserve">per ſeptimam à <lb/>media nocte in arcu horarum 12. </s>
  <s xml:id="echoid-s13853" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13854" xml:space="preserve">per 9 {1/2}. </s>
  <s xml:id="echoid-s13855" xml:space="preserve">à media nocte in arcu diurno horarum 6. </s>
  <s xml:id="echoid-s13856" xml:space="preserve">Horam au <lb/>tem ſecundam inæqualem per horam 6. </s>
  <s xml:id="echoid-s13857" xml:space="preserve">à media nocte in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s13858" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13859" xml:space="preserve">per octa-<lb/>uam à media nocte in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s13860" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s13861" xml:space="preserve">per horam decimam à media nocte in arcu <lb/>diurno horarum 6. </s>
  <s xml:id="echoid-s13862" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13863" xml:space="preserve">c.</s>
  <s xml:id="echoid-s13864" xml:space="preserve"/>
</p>
<div xml:id="echoid-div706" type="float" level="2" n="3">
<note position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">Alia dcſcriptio <lb/>horologii Anti@ <lb/>qui horizonta-<lb/>lis, per arcus di-<lb/>urnos horarum <lb/>18. &amp; 6.</note>
<note position="left" xlink:label="note-0223-02" xlink:href="note-0223-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s13865" xml:space="preserve">SATIS tamen erit, ſi parallelum Borealem horarum 18. </s>
  <s xml:id="echoid-s13866" xml:space="preserve">duntaxat deſcribamus in horologio <lb/>horizontali, cum Auſtralis horarum 6. </s>
  <s xml:id="echoid-s13867" xml:space="preserve">nimium excurrat extra tropicos. </s>
  <s xml:id="echoid-s13868" xml:space="preserve">Horologium itaque An-<lb/>tiquum horizontale conſtituimus, &amp;</s>
  <s xml:id="echoid-s13869" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13870" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s13871" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div708" type="section" level="1" n="176">
<head xml:id="echoid-head179" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s13872" xml:space="preserve">DOCET vmbra gnomonis cadens in lineas horarum inæqualium, quanta pars diei tranſancta ſit, <lb/>
<anchor type="note" xlink:label="note-0223-04a" xlink:href="note-0223-04"/>
&amp; </s>
  <s xml:id="echoid-s13873" xml:space="preserve">quanta adhuc ſuperſit. </s>
  <s xml:id="echoid-s13874" xml:space="preserve">Quoniam enim quilibet dies in 12. </s>
  <s xml:id="echoid-s13875" xml:space="preserve">partes æquales diuiditur, quæ horæ inæqua-<lb/>les dicuntur; </s>
  <s xml:id="echoid-s13876" xml:space="preserve">fit vt vmbra ſtyli cadente v.</s>
  <s xml:id="echoid-s13877" xml:space="preserve">g. </s>
  <s xml:id="echoid-s13878" xml:space="preserve">in horam tertiam inæqualem, tranſacta ſit quarta pars diei, <lb/>&amp; </s>
  <s xml:id="echoid-s13879" xml:space="preserve">ſuperſint tres quartæ. </s>
  <s xml:id="echoid-s13880" xml:space="preserve">Cadente autem eadem vmbra in horam octauam inæqualem, elapſæ ſint duæ ter <lb/>tiæ partes illius diei, &amp; </s>
  <s xml:id="echoid-s13881" xml:space="preserve">ſuperſit ad huc vna tertia pars, &amp;</s>
  <s xml:id="echoid-s13882" xml:space="preserve">c.</s>
  <s xml:id="echoid-s13883" xml:space="preserve"/>
</p>
<div xml:id="echoid-div708" type="float" level="2" n="1">
<note position="right" xlink:label="note-0223-04" xlink:href="note-0223-04a" xml:space="preserve">Vſus horologii <lb/>Antiqui eſt, ut<unsure/> <lb/>intelligamus, <lb/>quãta pars diei <lb/>ſit tranſacta, &amp; <lb/>quanta adhuc <lb/>ſuperſit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s13884" xml:space="preserve">IAM vero omnia, quæ proximis 12. </s>
  <s xml:id="echoid-s13885" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s13886" xml:space="preserve">ſcripta ſunt de vſu vario earum rerum, quas in horolo <lb/>gio Horizontali depinximus, intelligenda quoque ſunt in alĳs horologĳs omnibus, de quibus in ĳs, quæ ſe-<lb/>quuntur, agemus.</s>
  <s xml:id="echoid-s13887" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s13888" xml:space="preserve">SED non deerunt fortaſſis, qui ſcire etiam deſiderent, quonam pacto horæ illæ inæquales deprehendi <lb/>
<anchor type="note" xlink:label="note-0223-06a" xlink:href="note-0223-06"/>
poſſint, quæ temporales, naturales, ac planetariæ dicuntur, vt in cõmentarĳs in ſphæram expoſuimus, &amp; </s>
  <s xml:id="echoid-s13889" xml:space="preserve"><lb/>quarum ſingulæ ſpatium illud temporis cõprehendunt, quo medietas ſigni Zodiaci, hoc eſt, quindecim gra <lb/>dus Eclipticæ ſupra Horizontẽ aſcendunt. </s>
  <s xml:id="echoid-s13890" xml:space="preserve">Hæ enim diuidũt diem artificialem in 12. </s>
  <s xml:id="echoid-s13891" xml:space="preserve">partes inæquales, cũ <lb/>aſcenſio priorum graduum 15. </s>
  <s xml:id="echoid-s13892" xml:space="preserve">Ecliptic æinæqualis ſit aſcenſioni ſequentium grad. </s>
  <s xml:id="echoid-s13893" xml:space="preserve">15. </s>
  <s xml:id="echoid-s13894" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s13895" xml:space="preserve">c. </s>
  <s xml:id="echoid-s13896" xml:space="preserve">His ita ſa-<lb/>tisfaciemus. </s>
  <s xml:id="echoid-s13897" xml:space="preserve">Sit exempli gratia explorandum tempus horæ ſeptimæ inæqualis, cum Sol in gradu 20. </s>
  <s xml:id="echoid-s13898" xml:space="preserve">♉, <lb/>exiſtit. </s>
  <s xml:id="echoid-s13899" xml:space="preserve">Quoniam igitur quælibet hora inæqualis cõplectitur grad. </s>
  <s xml:id="echoid-s13900" xml:space="preserve">15. </s>
  <s xml:id="echoid-s13901" xml:space="preserve">Eclipticæ, neceſſe eſt, vt hora ſepti-<lb/>ma inæquali aſcẽderint grad. </s>
  <s xml:id="echoid-s13902" xml:space="preserve">105. </s>
  <s xml:id="echoid-s13903" xml:space="preserve">Eclipticæ, quos ſi numeremus à grad. </s>
  <s xml:id="echoid-s13904" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13905" xml:space="preserve">♉, ſecundum ſucceſſionem ſi-<lb/>gnorum, incidemus in gradum 5. </s>
  <s xml:id="echoid-s13906" xml:space="preserve">♍, qui aſcendit ſupra Horizontem hora ſeptima inæquali eo die. </s>
  <s xml:id="echoid-s13907" xml:space="preserve">Quare <lb/>ſi ex aſcenſionibus obliquis inquir amus aſcenſionem arcus Eclipticæ inter grad. </s>
  <s xml:id="echoid-s13908" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13909" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s13910" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s13911" xml:space="preserve">5. </s>
  <s xml:id="echoid-s13912" xml:space="preserve">♍, re-<lb/>
<anchor type="note" xlink:label="note-0223-07a" xlink:href="note-0223-07"/>
periemus eam, ad latitudinem grad. </s>
  <s xml:id="echoid-s13913" xml:space="preserve">42. </s>
  <s xml:id="echoid-s13914" xml:space="preserve">continere grad. </s>
  <s xml:id="echoid-s13915" xml:space="preserve">117. </s>
  <s xml:id="echoid-s13916" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13917" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13918" xml:space="preserve">hoc eſt, horas ęquinoctiales 7. </s>
  <s xml:id="echoid-s13919" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s13920" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13921" xml:space="preserve">Dicemus ergo horam 7. </s>
  <s xml:id="echoid-s13922" xml:space="preserve">inęqualẽ tunc eſſe, cum inſtat hora 7. </s>
  <s xml:id="echoid-s13923" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13924" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13925" xml:space="preserve">ab ortu Solis: </s>
  <s xml:id="echoid-s13926" xml:space="preserve">ac proinde cum <lb/>in horologio Babylonico ex vmbra gnomonis deprehenſa fuerit hora 7. </s>
  <s xml:id="echoid-s13927" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13928" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13929" xml:space="preserve">pronunciabimus tunc in-<lb/>ſtare horam 7. </s>
  <s xml:id="echoid-s13930" xml:space="preserve">temporalem, ſiue planetariam illa die, qua Sol in grad. </s>
  <s xml:id="echoid-s13931" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13932" xml:space="preserve">♉, exiſtit. </s>
  <s xml:id="echoid-s13933" xml:space="preserve">Quod ſi horam 7. </s>
  <s xml:id="echoid-s13934" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s13935" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13936" xml:space="preserve">ab ortureducere velimus ad horas Aſtronomicas, et Italicas, efficiemus id hunc in modum. </s>
  <s xml:id="echoid-s13937" xml:space="preserve">Quo <lb/>niam tunc arcus diurnus continet horas 14. </s>
  <s xml:id="echoid-s13938" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13939" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13940" xml:space="preserve">ſemidiurnus vero arcus horas 7. </s>
  <s xml:id="echoid-s13941" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13942" xml:space="preserve">7. </s>
  <s xml:id="echoid-s13943" xml:space="preserve">ſi detraha-<lb/>mus hor. </s>
  <s xml:id="echoid-s13944" xml:space="preserve">7. </s>
  <s xml:id="echoid-s13945" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13946" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13947" xml:space="preserve">ab arcu diurno horarũ 14. </s>
  <s xml:id="echoid-s13948" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13949" xml:space="preserve">14. </s>
  <s xml:id="echoid-s13950" xml:space="preserve">ſupererunt vſq; </s>
  <s xml:id="echoid-s13951" xml:space="preserve">ad occaſum Solis horæ. </s>
  <s xml:id="echoid-s13952" xml:space="preserve">6. </s>
  <s xml:id="echoid-s13953" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13954" xml:space="preserve"><lb/>25. </s>
  <s xml:id="echoid-s13955" xml:space="preserve">Igitur à proximo occaſu ſolis elapſæ tunc ſunt horæ 17. </s>
  <s xml:id="echoid-s13956" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13957" xml:space="preserve">35. </s>
  <s xml:id="echoid-s13958" xml:space="preserve">At vero ſi arcũ ſemidiurnũ horarũ <lb/>7. </s>
  <s xml:id="echoid-s13959" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13960" xml:space="preserve">7. </s>
  <s xml:id="echoid-s13961" xml:space="preserve">ſubducamus ex hor. </s>
  <s xml:id="echoid-s13962" xml:space="preserve">7. </s>
  <s xml:id="echoid-s13963" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13964" xml:space="preserve">49. </s>
  <s xml:id="echoid-s13965" xml:space="preserve">ab ortu (quia ille numerus minor hoc eſt.) </s>
  <s xml:id="echoid-s13966" xml:space="preserve">remanebunt hor. </s>
  <s xml:id="echoid-s13967" xml:space="preserve">0. </s>
  <s xml:id="echoid-s13968" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s13969" xml:space="preserve">42. </s>
  <s xml:id="echoid-s13970" xml:space="preserve">à meridie proxime elapſo. </s>
  <s xml:id="echoid-s13971" xml:space="preserve">Igitur ſi eodẽ die in horologio Italico obſeruata fuerit hora 17. </s>
  <s xml:id="echoid-s13972" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13973" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0223-08a" xlink:href="note-0223-08"/>
35. </s>
  <s xml:id="echoid-s13974" xml:space="preserve">vel in Aſtronomico hora 0. </s>
  <s xml:id="echoid-s13975" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s13976" xml:space="preserve">42. </s>
  <s xml:id="echoid-s13977" xml:space="preserve">post meridiem, dicemus rurſum, inſtare tunc horam 7. </s>
  <s xml:id="echoid-s13978" xml:space="preserve">tempora-<lb/>lem, inæqualemue.</s>
  <s xml:id="echoid-s13979" xml:space="preserve"/>
</p>
<div xml:id="echoid-div709" type="float" level="2" n="2">
<note position="right" xlink:label="note-0223-06" xlink:href="note-0223-06a" xml:space="preserve">Qua ratione de<unsure/> <lb/>prehendãtur ho <lb/>rę inæquales, <lb/>quæ planetariæ <lb/>dicuntur, reſpõ <lb/>dentq́ f<unsure/>ingulæ <lb/>quindenis gra-<lb/>dibus Eclipticę.</note>
<note position="left" xlink:label="note-0223-07" xlink:href="note-0223-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0223-08" xlink:href="note-0223-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s13980" xml:space="preserve">RVRSVS operæpretium ſit, eodem die explorare tempus horę 3. </s>
  <s xml:id="echoid-s13981" xml:space="preserve">temporalis, inæqualisve. </s>
  <s xml:id="echoid-s13982" xml:space="preserve">Quoniã <lb/>igitur horæ ſingulæ temporales comprehendũt gr. </s>
  <s xml:id="echoid-s13983" xml:space="preserve">15. </s>
  <s xml:id="echoid-s13984" xml:space="preserve">Eclipticæ, neceſſe eſt, vt hora tertia inæquali aſcẽ-<lb/>derint grad. </s>
  <s xml:id="echoid-s13985" xml:space="preserve">45. </s>
  <s xml:id="echoid-s13986" xml:space="preserve">Eclipticæ, quos ſi numeremus à grad. </s>
  <s xml:id="echoid-s13987" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13988" xml:space="preserve">♉, ſecundum ſucceſſionem ſignorum, peruenie-<lb/>mus ad grad. </s>
  <s xml:id="echoid-s13989" xml:space="preserve">5. </s>
  <s xml:id="echoid-s13990" xml:space="preserve">♋. </s>
  <s xml:id="echoid-s13991" xml:space="preserve">Aſcẽſio obliqua arcus Eclipticę inter gr. </s>
  <s xml:id="echoid-s13992" xml:space="preserve">20. </s>
  <s xml:id="echoid-s13993" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s13994" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s13995" xml:space="preserve">5. </s>
  <s xml:id="echoid-s13996" xml:space="preserve">♋. </s>
  <s xml:id="echoid-s13997" xml:space="preserve">ad latitudinẽ grad. </s>
  <s xml:id="echoid-s13998" xml:space="preserve">42. <lb/></s>
  <s xml:id="echoid-s13999" xml:space="preserve">complectitur gr. </s>
  <s xml:id="echoid-s14000" xml:space="preserve">41. </s>
  <s xml:id="echoid-s14001" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14002" xml:space="preserve">45. </s>
  <s xml:id="echoid-s14003" xml:space="preserve">hoc eſt, horas ęquales 2. </s>
  <s xml:id="echoid-s14004" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14005" xml:space="preserve">47. </s>
  <s xml:id="echoid-s14006" xml:space="preserve">Igitur cum in horologio Babylonico de-<lb/>prehenderimus horam 2. </s>
  <s xml:id="echoid-s14007" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14008" xml:space="preserve">47. </s>
  <s xml:id="echoid-s14009" xml:space="preserve">inſtabit præciſe hora 3. </s>
  <s xml:id="echoid-s14010" xml:space="preserve">temporalis Iam vero ſi hor. </s>
  <s xml:id="echoid-s14011" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14012" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14013" xml:space="preserve">47. </s>
  <s xml:id="echoid-s14014" xml:space="preserve">ab ortu <lb/>deducantur ab arcu diurno horarum 14. </s>
  <s xml:id="echoid-s14015" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14016" xml:space="preserve">14. </s>
  <s xml:id="echoid-s14017" xml:space="preserve">remanebunt horæ 11. </s>
  <s xml:id="echoid-s14018" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14019" xml:space="preserve">27. </s>
  <s xml:id="echoid-s14020" xml:space="preserve">vſque ad occaſum Solis; </s>
  <s xml:id="echoid-s14021" xml:space="preserve"><lb/>atque adeo incidet hora 3. </s>
  <s xml:id="echoid-s14022" xml:space="preserve">inæqualis in horam 13. </s>
  <s xml:id="echoid-s14023" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14024" xml:space="preserve">33. </s>
  <s xml:id="echoid-s14025" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s14026" xml:space="preserve">Si vero hor. </s>
  <s xml:id="echoid-s14027" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14028" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14029" xml:space="preserve">47. </s>
  <s xml:id="echoid-s14030" xml:space="preserve">ab ortu ab <lb/>a<unsure/>rcu ſemidiurno horarũ 7. </s>
  <s xml:id="echoid-s14031" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14032" xml:space="preserve">7. </s>
  <s xml:id="echoid-s14033" xml:space="preserve">ſubtrahamus, (quia ille minor boc eſt.) </s>
  <s xml:id="echoid-s14034" xml:space="preserve">ſupererunt horæ 4. </s>
  <s xml:id="echoid-s14035" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14036" xml:space="preserve">20. </s>
  <s xml:id="echoid-s14037" xml:space="preserve">vſ-
<pb o="204" file="0224" n="224" rhead="GNOMONICES"/>
que ad meridiem. </s>
  <s xml:id="echoid-s14038" xml:space="preserve">Igitur eadem hora. </s>
  <s xml:id="echoid-s14039" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14040" xml:space="preserve">inæqualis incidet in horam 7. </s>
  <s xml:id="echoid-s14041" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s14042" xml:space="preserve">40. </s>
  <s xml:id="echoid-s14043" xml:space="preserve">à proxima media nocte. <lb/></s>
  <s xml:id="echoid-s14044" xml:space="preserve">Hoc artificio horam temporalem, ſiue inæqualẽ deprehendemus quocunque tempore propoſito, ad quam-<lb/>cunque latitudinem.</s>
  <s xml:id="echoid-s14045" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div711" type="section" level="1" n="177">
<head xml:id="echoid-head180" xml:space="preserve">DE HOROLOGIIS VERTICALIBVS. <lb/>PROBLEMA 13. PROPOSITIO 13.</head>
<p>
  <s xml:id="echoid-s14046" xml:space="preserve">HOROLOGIVM Aſtronomicum Verticale conſtituere. <lb/></s>
  <s xml:id="echoid-s14047" xml:space="preserve">
<anchor type="note" xlink:label="note-0224-01a" xlink:href="note-0224-01"/>
Hoc eſt, lineas horarum à meridie, vel media nocte in plano, quod <lb/>Verticali circulo ęquidiſtat, deſcribere.</s>
  <s xml:id="echoid-s14048" xml:space="preserve"/>
</p>
<div xml:id="echoid-div711" type="float" level="2" n="1">
<note position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s14049" xml:space="preserve">SIT rurſus, vt in propoſ. </s>
  <s xml:id="echoid-s14050" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14051" xml:space="preserve">huius libri, portio Analemmatis A B C, hoc eſt, Meridiani ſemi-<lb/>
<anchor type="note" xlink:label="note-0224-02a" xlink:href="note-0224-02"/>
circulus ſit A B C, cuius centrum D; </s>
  <s xml:id="echoid-s14052" xml:space="preserve">communis ſectio ipſius &amp; </s>
  <s xml:id="echoid-s14053" xml:space="preserve">Horizontis, B C; </s>
  <s xml:id="echoid-s14054" xml:space="preserve">communis ſe-<lb/>
<anchor type="figure" xlink:label="fig-0224-01a" xlink:href="fig-0224-01"/>
ctio eiuſdem &amp; </s>
  <s xml:id="echoid-s14055" xml:space="preserve">Verticalis, A D; </s>
  <s xml:id="echoid-s14056" xml:space="preserve">com-<lb/>munis ſectio eiuſdem &amp; </s>
  <s xml:id="echoid-s14057" xml:space="preserve">Aequatoris, <lb/>F D; </s>
  <s xml:id="echoid-s14058" xml:space="preserve">axis mundi E D. </s>
  <s xml:id="echoid-s14059" xml:space="preserve">Productis autẽ <lb/>rectis F D, E D, ad partes D, ſumatur <lb/>
<anchor type="note" xlink:label="note-0224-03a" xlink:href="note-0224-03"/>
in recta B C, ſtylo horologij futuri, <lb/>cuiuſcunque magnitudinis datus fue-<lb/>rit, æqualis recta D G, ex vtraque par-<lb/>te. </s>
  <s xml:id="echoid-s14060" xml:space="preserve">Et per G, agatur ipſi A D, parallela <lb/>H I, ſecans E D, &amp; </s>
  <s xml:id="echoid-s14061" xml:space="preserve">F D, in H, I. </s>
  <s xml:id="echoid-s14062" xml:space="preserve">Si igi-<lb/>tur per A D, duci intelligatur Vertica <lb/>lis circulus propriè dictus, &amp; </s>
  <s xml:id="echoid-s14063" xml:space="preserve">per H I, <lb/>planũ horologii illi Verticali æquidi-<lb/>ſtans; </s>
  <s xml:id="echoid-s14064" xml:space="preserve">cum &amp; </s>
  <s xml:id="echoid-s14065" xml:space="preserve">Meridianus, &amp; </s>
  <s xml:id="echoid-s14066" xml:space="preserve">Horizon <lb/>ad dictum Verticalẽ rectus ſit, erit ad <lb/>
<anchor type="note" xlink:label="note-0224-04a" xlink:href="note-0224-04"/>
eundem communis illorẽ ſectio BC, <lb/>
<anchor type="note" xlink:label="note-0224-05a" xlink:href="note-0224-05"/>
perpendicularis, atque adeo &amp; </s>
  <s xml:id="echoid-s14067" xml:space="preserve">ad pla-<lb/>num horologii per H I, ductum Ver-<lb/>ticali parallelum, ex demonſtratis à <lb/>nobis ad propoſ. </s>
  <s xml:id="echoid-s14068" xml:space="preserve">14. </s>
  <s xml:id="echoid-s14069" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14070" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14071" xml:space="preserve">Euclidis, <lb/>perpendicularis erit. </s>
  <s xml:id="echoid-s14072" xml:space="preserve">Erit ergo H I, in <lb/>plano horologii linea meridiana, vel <lb/>horæ 12. </s>
  <s xml:id="echoid-s14073" xml:space="preserve">nempe cõmunis ſectio Me-<lb/>ridiani, &amp; </s>
  <s xml:id="echoid-s14074" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s14075" xml:space="preserve">Eſt enim <lb/>recta H I, in plano rectarum H D, I D, hoc eſt, in plano Meridiani. </s>
  <s xml:id="echoid-s14076" xml:space="preserve">D G, gnomon erit ad horologii <lb/>
<anchor type="note" xlink:label="note-0224-06a" xlink:href="note-0224-06"/>
<anchor type="note" xlink:label="note-0224-07a" xlink:href="note-0224-07"/>
planum rectus, ac proinde &amp; </s>
  <s xml:id="echoid-s14077" xml:space="preserve">ad H I, lineam Meridianam, per definitionem 3. </s>
  <s xml:id="echoid-s14078" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14079" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14080" xml:space="preserve">Euclidis, per-<lb/>pendicularis, cuius vertex D, idem eſt, quod centrum mundi, ex propoſ. </s>
  <s xml:id="echoid-s14081" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14082" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14083" xml:space="preserve">Locus <lb/>gnomonis punctum G, in linea meridiana diſtans à puncto H, in quo axis mundi plano horolo-<lb/>gii occurrit, &amp; </s>
  <s xml:id="echoid-s14084" xml:space="preserve">quod centrum horologii dicitur, interuallo G H, vel à puncto I, in quo planum <lb/>Aequatoris lineam meridianam ſecat, interuallo G I. </s>
  <s xml:id="echoid-s14085" xml:space="preserve">Quæ omnia perſpicua ſunt, ſi Meridianus <lb/>proprium ſitum habere concipiatur, vt videlicet punctum E, in boream vergat, &amp; </s>
  <s xml:id="echoid-s14086" xml:space="preserve">F, in auſtrum. <lb/></s>
  <s xml:id="echoid-s14087" xml:space="preserve">Figuram autem ita cõſtructam appellabimus, doctrinæ cauſa, portionem Analemmatis, quemad-<lb/>modum &amp; </s>
  <s xml:id="echoid-s14088" xml:space="preserve">illam, quam ad initium propoſ. </s>
  <s xml:id="echoid-s14089" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14090" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14091" xml:space="preserve">deſcripſimus, portionem Analemma-<lb/>tis vocauimus.</s>
  <s xml:id="echoid-s14092" xml:space="preserve"/>
</p>
<div xml:id="echoid-div712" type="float" level="2" n="2">
<note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Aſtrono <lb/>mi@i Verticalis.</note>
  <figure xlink:label="fig-0224-01" xlink:href="fig-0224-01a">
    <image file="0224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-01"/>
  </figure>
<note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0224-04" xlink:href="note-0224-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0224-05" xlink:href="note-0224-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0224-06" xlink:href="note-0224-06a" xml:space="preserve">2. v<unsure/>ndec<unsure/>.</note>
<note position="left" xlink:label="note-0224-07" xlink:href="note-0224-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s14093" xml:space="preserve">IAM verò beneficio trianguli D H I, conficiemus horologium Verticale Aſtronomicum hoc <lb/>
<anchor type="note" xlink:label="note-0224-08a" xlink:href="note-0224-08"/>
modo. </s>
  <s xml:id="echoid-s14094" xml:space="preserve">In lineam rectam H E, ductam vtcunque in plano, in quo horologium deſcribendum eſt, <lb/>transferatur recta H I, linea meridiana portionis Analemmatis, deorſum quidem à puncto H, ſi <lb/>horologium ad meridiem ſpectans ſit deſcribendum, ſurſum autem, ſi ſeptentrionale delinean-<lb/>dum ſit, vt ex portione Analemmatis patet. </s>
  <s xml:id="echoid-s14095" xml:space="preserve">Nam planum horologii ad meridiem ſpectans, rece <lb/>dens nimirum à D, centro mundi ad partes poli Borealis E, ſecat Aequatorem F D, infra punctũ <lb/>H, in puncto I; </s>
  <s xml:id="echoid-s14096" xml:space="preserve">planum verò horologii reſpiciens Septentrionem, recedens videlicet à D, centro <lb/>mundi ad partes auſtrales, ſecat eundem Aequatorem ſupra punctum H, in puncto I, &amp;</s>
  <s xml:id="echoid-s14097" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14098" xml:space="preserve">Deinde <lb/>ex recta H E, abſcindatur I E, rectæ D I, portionis Analemmatis æqualis: </s>
  <s xml:id="echoid-s14099" xml:space="preserve">Et per I, educatur ad <lb/>H E, in plano horologii perpendicularis F K. </s>
  <s xml:id="echoid-s14100" xml:space="preserve">Ex E, verò deſcribatur circulus cuiuſuis magnitu-<lb/>dinis, quo diuiſo in partes 24. </s>
  <s xml:id="echoid-s14101" xml:space="preserve">æquales, initio facto à linea meridiana H E, producta, ducantur per <lb/>puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s14102" xml:space="preserve">centrum E, rectæ lineæ occultæ ſecantes rectam F K, in punctis, per quæ,
<pb o="205" file="0225" n="225" rhead="LIBER SECVNDVS."/>
&amp; </s>
  <s xml:id="echoid-s14103" xml:space="preserve">punctum H, emiſſæ lineæ rectæ dabunt lineas horarias à meridie, vel media nocte in plano, <lb/>quod Verticali æquidiſtat, quarum ordinem paulo infra explicabimus in vtroque horologio. </s>
  <s xml:id="echoid-s14104" xml:space="preserve">Pro <lb/>hora verò ſexta ducenda eſt per H, linea C L, ad H E, perpendicularis, vel ipſi F K, æquidiſtans. <lb/></s>
  <s xml:id="echoid-s14105" xml:space="preserve">Quæ quidem omnia ita demonſtrabuntur.</s>
  <s xml:id="echoid-s14106" xml:space="preserve"/>
</p>
<div xml:id="echoid-div713" type="float" level="2" n="3">
<note position="left" xlink:label="note-0224-08" xlink:href="note-0224-08a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0225-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0225-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s14107" xml:space="preserve">INTELLIGATVR portio Analemmatis horologio ſuperpoſita, ita vt punctum H, <lb/>
<anchor type="note" xlink:label="note-0225-05a" xlink:href="note-0225-05"/>
puncto H, &amp; </s>
  <s xml:id="echoid-s14108" xml:space="preserve">punctum I, puncto I, atque recta H I, rectæ H I, congruat, (congruet autem ei, pro-<lb/>pter æqualitatem rectarum H I, H I,) ipſaq́ue portio Analemmatis concipiatur animo recta ad <lb/>
<anchor type="note" xlink:label="note-0225-06a" xlink:href="note-0225-06"/>
planum horologij, &amp; </s>
  <s xml:id="echoid-s14109" xml:space="preserve">meridiana linea H E, habeat proprium ſitum, ita vt ſit communis ſectio <lb/>Meridiani &amp; </s>
  <s xml:id="echoid-s14110" xml:space="preserve">plani horologii, punctumq́; </s>
  <s xml:id="echoid-s14111" xml:space="preserve">H, in Auſtrali horologio verſus Zenith, &amp; </s>
  <s xml:id="echoid-s14112" xml:space="preserve">E, verſus Na-<lb/>dir; </s>
  <s xml:id="echoid-s14113" xml:space="preserve">In Boreali vero punctum H, verſus Nadir, &amp; </s>
  <s xml:id="echoid-s14114" xml:space="preserve">E, verſus Zenith vergat; </s>
  <s xml:id="echoid-s14115" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14116" xml:space="preserve">denique recta B C, <lb/>ad planum horologij ſit perpendicularis, ita vt ſit communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s14117" xml:space="preserve">Horizontis, cum <lb/>D, vertex ſtyli ſit centrum mundi, vt propoſ. </s>
  <s xml:id="echoid-s14118" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14119" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14120" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s14121" xml:space="preserve">Vel ſi mauis, loco por-<lb/>tionis Analemmatis intelligatur duntaxat triangulum D H I, ea ratione, vt diximus, ſuperpoſitũ <lb/>eſſe horologio, ita vt D H, referat axem mundi, &amp; </s>
  <s xml:id="echoid-s14122" xml:space="preserve">D I, communem ſectionem Meridiani &amp; </s>
  <s xml:id="echoid-s14123" xml:space="preserve">Aequa-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s14124" xml:space="preserve">tandem D G, ſtylus communem ſectionem Meridiani atque Horizontis per D, centrum <lb/>mundi ducti. </s>
  <s xml:id="echoid-s14125" xml:space="preserve">Quod quidem triangulum D H I, vna cum gnomone D G, deſcriptum eſt in vtroq; <lb/></s>
  <s xml:id="echoid-s14126" xml:space="preserve">horologio. </s>
  <s xml:id="echoid-s14127" xml:space="preserve">His ita poſitis, occurret axis H D, plano horologij in H, &amp; </s>
  <s xml:id="echoid-s14128" xml:space="preserve">Aequatoris diameter D I, <lb/>in I; </s>
  <s xml:id="echoid-s14129" xml:space="preserve">Horizontis autem diameter D G, in G. </s>
  <s xml:id="echoid-s14130" xml:space="preserve">Quoniam igitur tam planum Aequatoris, quàm pla-
<pb o="206" file="0226" n="226" rhead="GNOMONICES"/>
num horologij Verticali æquidiſtans rectum eſt ad Meridiani planum; </s>
  <s xml:id="echoid-s14131" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s14132" xml:space="preserve">communis ſectio <lb/>Aequatoris, ac plani horologii ad idem planum Meridiani, ideoq́; </s>
  <s xml:id="echoid-s14133" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14134" xml:space="preserve">per defin. </s>
  <s xml:id="echoid-s14135" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14136" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14137" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14138" xml:space="preserve">Euclidis, <lb/>
<anchor type="note" xlink:label="note-0226-01a" xlink:href="note-0226-01"/>
ad lineam meridianam H I, in plano Meridiani exiſtentem, perpendicularis in puncto I, in quo <lb/>Aequator lineæ meridianæ in horologio occcurrit, vt dictum eſt. </s>
  <s xml:id="echoid-s14139" xml:space="preserve">Recta igitur F K, quæ in horo-<lb/>
<anchor type="figure" xlink:label="fig-0226-01a" xlink:href="fig-0226-01"/>
<anchor type="note" xlink:label="note-0226-02a" xlink:href="note-0226-02"/>
<anchor type="note" xlink:label="note-0226-03a" xlink:href="note-0226-03"/>
<anchor type="note" xlink:label="note-0226-04a" xlink:href="note-0226-04"/>
<anchor type="note" xlink:label="note-0226-05a" xlink:href="note-0226-05"/>
logio per I, ad meridianam lineam H I, perpendicularis eſt ducta, communis ſectio eſt Aequato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s14140" xml:space="preserve">plani horologii, nempe linea æquinoctialis: </s>
  <s xml:id="echoid-s14141" xml:space="preserve">Circa quam ſi moueri intelligatur planum cir-<lb/>culi ex centro E, deſcripti, donec cum mundi centro D, in triangulo D H I, (quod rectum eſſe di-<lb/>
<anchor type="note" xlink:label="note-0226-06a" xlink:href="note-0226-06"/>
ximus ad planum horologii, &amp; </s>
  <s xml:id="echoid-s14142" xml:space="preserve">in plano Meridiani exiſtere, vnà cum tota portione Analemmatis, <lb/>quamuis ſolum triangulum in horologio deſcriptum ſit) coniungatur E, centrum circuli, propte-<lb/>rea quòd rectę D I, I E, æquales ſunt, ex conſtructione, &amp; </s>
  <s xml:id="echoid-s14143" xml:space="preserve">in illo motu circuli ex E, deſcripti recta <lb/>I E, ſem per maneat in plano Meridiani, in quo exiſtit D I, erit ipſe circulus circa D, centrum mun-<lb/>di, ſeu Aequatoris deſcriptus, &amp; </s>
  <s xml:id="echoid-s14144" xml:space="preserve">in plano eiuſdem Aequatoris exiſtens, cùm Aequatoris planum <lb/>per rectas D I, I K, ducatur, quemadmodum &amp; </s>
  <s xml:id="echoid-s14145" xml:space="preserve">circulus dictus in tali poſitione per eaſdem eſt du-<lb/>ctus; </s>
  <s xml:id="echoid-s14146" xml:space="preserve">ita vt circulus hic, &amp; </s>
  <s xml:id="echoid-s14147" xml:space="preserve">Aequator in eodem exiſtant plano, idemq́; </s>
  <s xml:id="echoid-s14148" xml:space="preserve">habeant centrum, nimirum <lb/>D, centrum mundi. </s>
  <s xml:id="echoid-s14149" xml:space="preserve">Intelligatur quoque I E, protracta in vtramque partem in eadem poſitione, <lb/>quippe quę ſimul cum circuli plano moueatur tanquam communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s14150" xml:space="preserve">Aequato <lb/>ris, cum tam Meridianus, quàm Aequator in huiuſmodi poſitione per rectam D I, vel I E, trãſeat. <lb/></s>
  <s xml:id="echoid-s14151" xml:space="preserve">Quocirca per ca, quæ propoſ. </s>
  <s xml:id="echoid-s14152" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14153" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14154" xml:space="preserve">de horologio horizontali demonſtrata ſunt, erunt rectæ
<pb o="207" file="0227" n="227" rhead="LIBER SECVNDVS."/>
ex centro E, egredientes, communes ſectiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s14155" xml:space="preserve">circulorum horariorum à meridie, <lb/>vel media nocte, nempe N M, communis ſectio Aequatoris, et circuli horæ 12. </s>
  <s xml:id="echoid-s14156" xml:space="preserve">O P, communis ſe-<lb/>ctio Aequatoris, et circuli horæ primæ à meridie, vel media nocte; </s>
  <s xml:id="echoid-s14157" xml:space="preserve">Q R, ſectio communis Aequa-<lb/>toris, et circuli horæ ſecundæ à meridie, vel media nocte, etc. </s>
  <s xml:id="echoid-s14158" xml:space="preserve">Quare vt ibidem demonſtrauimus, <lb/>crunt rectæ ex H, per puncta rectæ F K, ductæ, lineæ horarum à meridie, vel media nocte. </s>
  <s xml:id="echoid-s14159" xml:space="preserve">Eadem <lb/>enim demonſtratio huc afferri poteſt. </s>
  <s xml:id="echoid-s14160" xml:space="preserve">Sola linea horæ ſextæ ducenda eſt per H, perpendicularis, <lb/>ad H I, vel æquidiſtans ipſi F K, qualis eſt C L. </s>
  <s xml:id="echoid-s14161" xml:space="preserve">Cum enim ex ſcholio propoſ. </s>
  <s xml:id="echoid-s14162" xml:space="preserve">22. </s>
  <s xml:id="echoid-s14163" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14164" xml:space="preserve">in <lb/>horologio Verticali parallelæ ſint linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s14165" xml:space="preserve">linea horæ ſextæ à meridie, vel media no-<lb/>cte, perſpicuum eſt, rectam C L, eſſe lineam horæ ſextæ, quandoquidem parallela eſt æquinoctiali <lb/>lineæ F K, tranſitq́ue per punctum H, vbi omnes horariæ lineæ à meridie, vel media nocte ſe <lb/>
<anchor type="note" xlink:label="note-0227-01a" xlink:href="note-0227-01"/>
interſecant.</s>
  <s xml:id="echoid-s14166" xml:space="preserve"/>
</p>
<div xml:id="echoid-div714" type="float" level="2" n="4">
<note position="right" xlink:label="note-0225-05" xlink:href="note-0225-05a" xml:space="preserve">Demonſtratio <lb/>conſtructionis <lb/>horologii Ver-<lb/>ticalis.</note>
<note position="left" xlink:label="note-0225-06" xlink:href="note-0225-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0226-01" xlink:href="note-0226-01a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0226-01" xlink:href="fig-0226-01a">
    <image file="0226-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0226-01"/>
  </figure>
<note position="left" xlink:label="note-0226-02" xlink:href="note-0226-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0226-03" xlink:href="note-0226-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0226-04" xlink:href="note-0226-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0226-05" xlink:href="note-0226-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0226-06" xlink:href="note-0226-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s14167" xml:space="preserve">IN auſtrali porrò horologio meridiana linea H I, à centro verſus lineam æquinoctialem indi-<lb/>
<anchor type="note" xlink:label="note-0227-02a" xlink:href="note-0227-02"/>
cat horam 12. </s>
  <s xml:id="echoid-s14168" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s14169" xml:space="preserve">reliqua portio ſurſum verſus horam 12. </s>
  <s xml:id="echoid-s14170" xml:space="preserve">mediæ noctis: </s>
  <s xml:id="echoid-s14171" xml:space="preserve">Lineæ verò ad ſi-<lb/>niſtram meridianæ lineæ oſtendunt horas à media nocte, &amp; </s>
  <s xml:id="echoid-s14172" xml:space="preserve">earum portiones ad dexteram eiuſdẽ <lb/>lineæ meridianæ horas à meridie monſtrant. </s>
  <s xml:id="echoid-s14173" xml:space="preserve">Contrariũ intelligatur in horologio boreali. </s>
  <s xml:id="echoid-s14174" xml:space="preserve">Quæ <lb/>omnia perſpicua ſunt, ſi circulorum horariorum poſitio rectè intelligatur, &amp; </s>
  <s xml:id="echoid-s14175" xml:space="preserve">ea atttente conſideren <lb/>tur, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s14176" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14177" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14178" xml:space="preserve">ſcripſimus obſeruanda eſſe in lineis, quæ in horologio de-<lb/>ſcribuntur: </s>
  <s xml:id="echoid-s14179" xml:space="preserve">nempe quem ſemicirculum cœleſtem ſingulæ referant, &amp; </s>
  <s xml:id="echoid-s14180" xml:space="preserve">qua ratione quælibet hora <lb/>à mer. </s>
  <s xml:id="echoid-s14181" xml:space="preserve">producta vltra centrum horologii monſtret eandem horam numero à med. </s>
  <s xml:id="echoid-s14182" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s14183" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14184" xml:space="preserve">contra. <lb/></s>
  <s xml:id="echoid-s14185" xml:space="preserve">Horologium igitur Aſtronomicum Verticale conſtituimus, &amp; </s>
  <s xml:id="echoid-s14186" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14187" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s14188" xml:space="preserve"/>
</p>
<div xml:id="echoid-div715" type="float" level="2" n="5">
<note position="right" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">Ordo horarum <lb/>in vtroque ho-<lb/>rologio Verti-<lb/>cali.</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div717" type="section" level="1" n="178">
<head xml:id="echoid-head181" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Alia deſcriptio <lb/>horologii Ver-<lb/>ticalis Aſtrono <lb/>mici cõmodiſ-<lb/>ſima pro illis <lb/>horis delinean-<lb/>dis, quæ propin <lb/>quæ ſunt lineæ <lb/>horæ 6. à mer. <lb/>vel med. noc.</note>
<p style="it">
  <s xml:id="echoid-s14189" xml:space="preserve">TRADIT Andreas Schonerus aliam viam, qua horariæ lineæ deſcribi poſſint, ſimilem illi, quam <lb/>ex eodem in ſcholio propoſ. </s>
  <s xml:id="echoid-s14190" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14191" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14192" xml:space="preserve">explicauimus pro horologio horizontali deſcribendo. </s>
  <s xml:id="echoid-s14193" xml:space="preserve">Eſt autem <lb/>ferèhæc. </s>
  <s xml:id="echoid-s14194" xml:space="preserve">In æquinoctiali linea F K, accipiatur recta I a, æqualis rectæ I E, vel I D, &amp; </s>
  <s xml:id="echoid-s14195" xml:space="preserve">per a, ducatur re-<lb/>cta a b, ad lineam æquinoctialem perpendicularis, vel meridianæ lineæ parallela, ſecans lineam horæ ſex-<lb/>tæ, quæ videlicet ex H, ducitur perpendicularis ad H I, in b, puncto. </s>
  <s xml:id="echoid-s14196" xml:space="preserve">Sumpta autem recta b d, æquali ipſi <lb/>a b, ducatur per d, ad b d, perpendicularis e f, vel parallela meridianæ lineæ. </s>
  <s xml:id="echoid-s14197" xml:space="preserve">Ex centro denique d, circu-<lb/>lo deſcripto, eo diuiſo in partes 24. </s>
  <s xml:id="echoid-s14198" xml:space="preserve">æquales, initio facto à recta b d, ducantur ex centro d, per puncta di-<lb/>
<anchor type="note" xlink:label="note-0227-05a" xlink:href="note-0227-05"/>
uiſionum rectæ lineæ occultæ. </s>
  <s xml:id="echoid-s14199" xml:space="preserve">Hę namque rectam a b, ſecabunt in punctis, per quæ ex centro horologĳ H, <lb/>
<anchor type="note" xlink:label="note-0227-06a" xlink:href="note-0227-06"/>
lineæ horariæ ſunt educendæ. </s>
  <s xml:id="echoid-s14200" xml:space="preserve">Exemplum huius deſcriptionis poſuimus in horologio Auſtrali.</s>
  <s xml:id="echoid-s14201" xml:space="preserve"/>
</p>
<div xml:id="echoid-div717" type="float" level="2" n="1">
<note position="left" xlink:label="note-0227-05" xlink:href="note-0227-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0227-06" xlink:href="note-0227-06a" xml:space="preserve">Segmẽta lineæ <lb/>ęquinoctialis in <lb/>horologio Ver-<lb/>ticali inter li-<lb/>neam meridia-<lb/>nam, &amp; binas <lb/>horas vtrinque <lb/>à meridiana li-<lb/>nea æquali tem <lb/>poris ſpatio re-<lb/>motas, ſunt æ-<lb/>qualia.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14202" xml:space="preserve">IN horologio autem quolibet Verticali lineæ binæ quæcunque horariæ hinc inde à meridiana linea <lb/>æquali temporis interuallo remotæ, auferũt ex linea æquinoctiali F K, lineas ęquales, illas videlicet, quę <lb/>inter ipſas, &amp; </s>
  <s xml:id="echoid-s14203" xml:space="preserve">lineam meridianã interĳciuntur, ita vt in linea æquinoctiali ſpatia hor aria ante meridiem <lb/>æqualia ſint horarĳs ſpatĳs post meridiem, ſingula ſingulis. </s>
  <s xml:id="echoid-s14204" xml:space="preserve">Ex quo ſequitur, arcus circuli cuiuſuis ex <lb/>H, deſcripti in horologio Verticali interceptos inter lineam meridianam, &amp; </s>
  <s xml:id="echoid-s14205" xml:space="preserve">binas quaſcunque lineas <lb/>horarias æquali temporis ſpatio hinc inde à meridiana linea diſtantes, æquales eſſe. </s>
  <s xml:id="echoid-s14206" xml:space="preserve">Item interualla inter <lb/>E, centrũ Aequatoris, &amp; </s>
  <s xml:id="echoid-s14207" xml:space="preserve">binas horas quaſcunque in æquinoctiali linea ęquali temporis interuallo hinc <lb/>
<anchor type="note" xlink:label="note-0227-07a" xlink:href="note-0227-07"/>
inde à meridiana linea remotas, eſſe æqualia. </s>
  <s xml:id="echoid-s14208" xml:space="preserve">Quæ omnia demonſtrabũtur eo modo, quo in ſcholio propoſ. <lb/></s>
  <s xml:id="echoid-s14209" xml:space="preserve">
<anchor type="note" xlink:label="note-0227-08a" xlink:href="note-0227-08"/>
1. </s>
  <s xml:id="echoid-s14210" xml:space="preserve">huius libri vſi ſumus ad eadem hæc demonstranda in horologio horizontali.</s>
  <s xml:id="echoid-s14211" xml:space="preserve"/>
</p>
<div xml:id="echoid-div718" type="float" level="2" n="2">
<note position="right" xlink:label="note-0227-07" xlink:href="note-0227-07a" xml:space="preserve">Satis eſt ad de-<lb/>ſcriptionẽ Ver-<lb/>ticalis horolo-<lb/>gii A ſtronomi-<lb/>ci, ſi vnus tan <lb/>tum quadrans <lb/>circuli ex E, de-<lb/>ſcripti in 6. par-<lb/>tes æqu ales di-<lb/>ſtribuatur.</note>
<note position="left" xlink:label="note-0227-08" xlink:href="note-0227-08a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s14212" xml:space="preserve">EX quo fit, vt ſatis ſit ad deſcriptionẽ horologĳ Verticalis, ſi vnus tantum quadrans circuli ex E, de-<lb/>ſcripti diuidatur in ſex partes ęquales, cuiuſmodi eſt v.</s>
  <s xml:id="echoid-s14213" xml:space="preserve">g. </s>
  <s xml:id="echoid-s14214" xml:space="preserve">quadrans Mg. </s>
  <s xml:id="echoid-s14215" xml:space="preserve">Qua de re vide ea, quæ in hunc fi-<lb/>nem de horologio horizontali ſcripſimus in ſcholio propopoſ. </s>
  <s xml:id="echoid-s14216" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14217" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s14218" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s14219" xml:space="preserve">HIC etiam ſi in triangulo D H I, ad planum horologĳ recto intelligatur axis H D, filum exten-<lb/>
<anchor type="note" xlink:label="note-0227-09a" xlink:href="note-0227-09"/>
tum, vel etiam ferrum aliquod tenue faciens in H, cum linea meridiana angulum æqualem angulo <lb/>D H I, &amp; </s>
  <s xml:id="echoid-s14220" xml:space="preserve">cum recta C L, angulos rectos; </s>
  <s xml:id="echoid-s14221" xml:space="preserve">vel certè ipſum triangulum D H I, in ſuperiori horologio <lb/>contentum conſtruatur ex materia aliqua ſolida, statuatur{q́ue} ad planum horologĳ rectum, indicabit vm-<lb/>hra axis D I, ſingulas horas à meridie, vel media nocte, ſi horologium in plano, quod V erticali circulo <lb/>propriè dicto æquidiſtet, ita collocetur, vt recta H I, nempe linea meridiana, perpendicularis ſit ad Ho-<lb/>
<anchor type="note" xlink:label="note-0227-10a" xlink:href="note-0227-10"/>
rizontẽ, rectaque F K, eidem Horizonti æquidiſtet; </s>
  <s xml:id="echoid-s14222" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14223" xml:space="preserve">in eo quidem horologio, quod ad auſtrum vergit, <lb/>
<anchor type="note" xlink:label="note-0227-11a" xlink:href="note-0227-11"/>
linea æquinoctialis F K, ſit infra punctum H, quod centrũ est horologĳ, in eo vero, quod ad Boreã, ſupra. <lb/></s>
  <s xml:id="echoid-s14224" xml:space="preserve">Ex quo fit, vt &amp; </s>
  <s xml:id="echoid-s14225" xml:space="preserve">vmbram verticis D, ſtyli D G, recti ad planum horologĳ in puncto G, qui quidem ver-<lb/>tex idem eſt, quod centrum mundi, ex propoſ. </s>
  <s xml:id="echoid-s14226" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14227" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14228" xml:space="preserve">indicet eaſdem horas, hoc eſt, in lineas ho-<lb/>rarias proĳciatur: </s>
  <s xml:id="echoid-s14229" xml:space="preserve">quemadmodum de horologio horizontali dictum eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s14230" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14231" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14232" xml:space="preserve">Ea-<lb/>dem enim hic est demonstratio.</s>
  <s xml:id="echoid-s14233" xml:space="preserve"/>
</p>
<div xml:id="echoid-div719" type="float" level="2" n="3">
<note position="right" xlink:label="note-0227-09" xlink:href="note-0227-09a" xml:space="preserve">Quomodo vtrũ<unsure/> <lb/>que horologiũ <lb/>Verticale vnà <lb/>cum axe mũdi <lb/>collocandũ ſit, <lb/>vt monſtret ho <lb/>ras à mer. vel <lb/>med. noc.</note>
<note position="left" xlink:label="note-0227-10" xlink:href="note-0227-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0227-11" xlink:href="note-0227-11a" xml:space="preserve">Si ſtylus D G, <lb/>in G, rectus ſit <lb/>ad horologii <lb/>planum, mon-<lb/>ſtrabi<unsure/>t vmbra <lb/>ſolius verticis <lb/>D, horas à mer. <lb/>vel med. noc.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14234" xml:space="preserve">QVOD ſi &amp; </s>
  <s xml:id="echoid-s14235" xml:space="preserve">dimidiatas horas, &amp; </s>
  <s xml:id="echoid-s14236" xml:space="preserve">earum quartas partes, vel octauas, vel quaſuis alias, in horolo-<lb/>
<anchor type="note" xlink:label="note-0227-12a" xlink:href="note-0227-12"/>
gio deſcribere velimus, diuidendi erunt ſinguli arcus circuli ex E, deſcripti in duas partes, quatuor, vel <lb/>octo vel alias quaſcunque, reliqua autem omnia peragenda, vt prius.</s>
  <s xml:id="echoid-s14237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div720" type="float" level="2" n="4">
<note position="right" xlink:label="note-0227-12" xlink:href="note-0227-12a" xml:space="preserve">Qua ratione di <lb/>midiatæ horæ, <lb/>&amp; eatũ quartæ <lb/>partes, vel quę-<lb/>cunque aliæ, in <lb/>horologio de-<lb/>ſcribant<unsure/>ur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14238" xml:space="preserve">IAM vero, quando altitudo poli ſupra Horizontẽ tanta eſt, vt axis E D, in portione Analemmatis <lb/>à V erticalis Circuli diametro A D, parum differat, &amp; </s>
  <s xml:id="echoid-s14239" xml:space="preserve">idcirco recta H I, ſi ſtylus D G, non ſit valde
<pb o="208" file="0228" n="228" rhead="GNOMONICES"/>
<anchor type="note" xlink:label="note-0228-01a" xlink:href="note-0228-01"/>
exiguus, in remotiſſimo puncto cum eo conueniat in H, acutiſſimum{q́ue} angulum efficiat; </s>
  <s xml:id="echoid-s14240" xml:space="preserve">deſcribemus <lb/>nihilominus horologium, etiamſi centrum H, non habeamus, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s14241" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14242" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14243" xml:space="preserve">horizontale <lb/>horologium conſtruximus, licet in eo centrum H, non haberemus, (quod quidem contingit, cum perexi-<lb/>gua eſt altitudo poli ſupra Horizontem.) </s>
  <s xml:id="echoid-s14244" xml:space="preserve">hoc excepto, quòd loco anguli altitudinis poli D E F, conſtituen <lb/>dus eſt in V erticali horologio angulus complementi altitudinis poli: </s>
  <s xml:id="echoid-s14245" xml:space="preserve">Reliqua omnia abſoluenda ſunt, vt <lb/>in dicto ſcholio.</s>
  <s xml:id="echoid-s14246" xml:space="preserve"/>
</p>
<div xml:id="echoid-div721" type="float" level="2" n="5">
<note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">Quando altitu <lb/>do poli ſupra <lb/>Horizõtem tan <lb/>ta eſt, vt parum <lb/>à vert@ce capitis <lb/>polus recedat, <lb/>quid agendum <lb/>in horologii de <lb/>ſcri ptione.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14247" xml:space="preserve">RVRSVS quando altitudo politam exigua eſt, vt Aequatoris diameter F D, acutiſſimum angu <lb/>
<anchor type="note" xlink:label="note-0228-02a" xlink:href="note-0228-02"/>
lum cum H I, &amp; </s>
  <s xml:id="echoid-s14248" xml:space="preserve">in remotiſſimo puncto I, conſtituat; </s>
  <s xml:id="echoid-s14249" xml:space="preserve">ac proinde difficile ſit punctum illud, in quo dictus <lb/>angulus conſtituitur, dignoſcere, vtemur eodem remedio, quod in dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s14250" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14251" xml:space="preserve">huius lihri tradi <lb/>dimus pro horologio horizontali, cum altitudo poli tanta ponebatur, vt polus parum à vertice capitis <lb/>
<anchor type="note" xlink:label="note-0228-03a" xlink:href="note-0228-03"/>
abeſſet; </s>
  <s xml:id="echoid-s14252" xml:space="preserve">dummodo ad Verticale horologium conſtruendum pro angulo altitudinis poli B A N, conſtitua-<lb/>mus angulum complementi altitudinis poli.</s>
  <s xml:id="echoid-s14253" xml:space="preserve"/>
</p>
<div xml:id="echoid-div722" type="float" level="2" n="6">
<note position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">Quando altitu-<lb/>do poli ſupra <lb/>Horizontẽ per <lb/>exigua el<unsure/>t, quid <lb/>in deſcriptione <lb/>horologii agen-<lb/>dum.</note>
<note position="left" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s14254" xml:space="preserve">CAETERVM horologium verticale auſtrale hactenus deſcriptum indicabit quoque horas in op-<lb/>
<anchor type="note" xlink:label="note-0228-04a" xlink:href="note-0228-04"/>
poſita parte plani horologĳ, quæ ad boream ſpectat, ſi omnes illius partes ita inuertantur, vt ex ſuperio-<lb/>re fiat inferior, &amp; </s>
  <s xml:id="echoid-s14255" xml:space="preserve">quæ poſt hanc inuerſionem nobis ad horologium conuerſis dextra eſt, in ſiniſtram mute-<lb/>tur, &amp; </s>
  <s xml:id="echoid-s14256" xml:space="preserve">contra, manentibus tamen ĳſdem proſus horarum numeris. </s>
  <s xml:id="echoid-s14257" xml:space="preserve">Sed tunc portio lineæ meridianæ à <lb/>centro horologĳ H, inchoata, et verſus lineam æquinoctialem procedens, quæ in horologio auſtrali indica-<lb/>bat horam 12. </s>
  <s xml:id="echoid-s14258" xml:space="preserve">meridiei, in hoc boreali horologio horam 12. </s>
  <s xml:id="echoid-s14259" xml:space="preserve">mediæ noctis ſignificabit; </s>
  <s xml:id="echoid-s14260" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14261" xml:space="preserve">quæ in illo horã <lb/>12. </s>
  <s xml:id="echoid-s14262" xml:space="preserve">mediæ noctis, in hoc horam 12. </s>
  <s xml:id="echoid-s14263" xml:space="preserve">meridiei monſtrabit: </s>
  <s xml:id="echoid-s14264" xml:space="preserve">at que adeo horæ, quæ ibi à meridie computaban-<lb/>tur, hic à media nocte, &amp; </s>
  <s xml:id="echoid-s14265" xml:space="preserve">quæ ibi à media nocte, hic à meridie numer andæ erunt. </s>
  <s xml:id="echoid-s14266" xml:space="preserve">Quod ex ĳs, quæiam de <lb/>
<anchor type="note" xlink:label="note-0228-05a" xlink:href="note-0228-05"/>
<anchor type="figure" xlink:label="fig-0228-01a" xlink:href="fig-0228-01"/>
monſtrabimus, perſpicuum fiet. </s>
  <s xml:id="echoid-s14267" xml:space="preserve">Sit <lb/>in Auſtrali horologio linea meri-<lb/>diana H I, centrum horologĳ H, li-<lb/>nea æquinoctialis F K; </s>
  <s xml:id="echoid-s14268" xml:space="preserve">ſtylus G D, <lb/>eius{q́ue} locus punctum G; </s>
  <s xml:id="echoid-s14269" xml:space="preserve">linea, v. </s>
  <s xml:id="echoid-s14270" xml:space="preserve">g. <lb/></s>
  <s xml:id="echoid-s14271" xml:space="preserve">horæ 5. </s>
  <s xml:id="echoid-s14272" xml:space="preserve">à meridie H K; </s>
  <s xml:id="echoid-s14273" xml:space="preserve">linea horæ <lb/>octauæ à media nocte H R, et axis <lb/>mundi H D. </s>
  <s xml:id="echoid-s14274" xml:space="preserve">Quoniam igitur axis <lb/>D H, plano horologĳ auſtralis oc-<lb/>currit in H, &amp; </s>
  <s xml:id="echoid-s14275" xml:space="preserve">productus planum <lb/>
<anchor type="note" xlink:label="note-0228-06a" xlink:href="note-0228-06"/>
ſecat, faciens angulum A H B, in <lb/>facie oppoſita &amp; </s>
  <s xml:id="echoid-s14276" xml:space="preserve">boreali cũ linea <lb/>meridiana, quæ eadem est in vtra-<lb/>que facie plani, (cum ſit communis <lb/>ſectio Meridiani circuli, &amp; </s>
  <s xml:id="echoid-s14277" xml:space="preserve">pla-<lb/>ni horologĳ.) </s>
  <s xml:id="echoid-s14278" xml:space="preserve">æqualem angulo D H I, in facie auſtrali cõprehenſo ſub eadem linea meridiana, &amp; </s>
  <s xml:id="echoid-s14279" xml:space="preserve">axe; </s>
  <s xml:id="echoid-s14280" xml:space="preserve">fit, <lb/>
<anchor type="note" xlink:label="note-0228-07a" xlink:href="note-0228-07"/>
vt ſi accipiatur recta H C, in parte plani oppoſita, æqualis rectæ H G, in facie auſtrali, &amp; </s>
  <s xml:id="echoid-s14281" xml:space="preserve">ex C, eriga-<lb/>tur ſtylus ad planum horologĳ borealis, atque adeò &amp; </s>
  <s xml:id="echoid-s14282" xml:space="preserve">ad rectam H C, perpendicularis, ſecans axem in <lb/>A; </s>
  <s xml:id="echoid-s14283" xml:space="preserve">ſtylus C A, ſtylo G D, &amp; </s>
  <s xml:id="echoid-s14284" xml:space="preserve">axis H A, axi H D, ſit æqualis. </s>
  <s xml:id="echoid-s14285" xml:space="preserve">Quoniã enim intriangulo A H C, duo <lb/>anguli H, C, duobus angulis H, G, trianguli D H G, æquales ſunt; </s>
  <s xml:id="echoid-s14286" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14287" xml:space="preserve">latus H C, lateri H G, ſumptum <lb/>
<anchor type="note" xlink:label="note-0228-08a" xlink:href="note-0228-08"/>
æqualc; </s>
  <s xml:id="echoid-s14288" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s14289" xml:space="preserve">latus C A, lateri G D, æquale, &amp; </s>
  <s xml:id="echoid-s14290" xml:space="preserve">latus A H, lateri D H. </s>
  <s xml:id="echoid-s14291" xml:space="preserve">Quòd ſi ex A, ducatur ad axẽ <lb/>
<anchor type="note" xlink:label="note-0228-09a" xlink:href="note-0228-09"/>
H A, perpendicularis A B, occurrens lineæ meridianæ in B, erit A B, exiſtens in plano Meridiani per <lb/>rectas A H, H B, ducto, communis ſectio Aequatoris ac Meridiani. </s>
  <s xml:id="echoid-s14292" xml:space="preserve">Nam quoniam axis H A, per pro-<lb/>
<anchor type="note" xlink:label="note-0228-10a" xlink:href="note-0228-10"/>
poſ. </s>
  <s xml:id="echoid-s14293" xml:space="preserve">10. </s>
  <s xml:id="echoid-s14294" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14295" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14296" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s14297" xml:space="preserve">ad planum Aequatoris est perpendicularis, tranſit{q́ue} per centrum eius; </s>
  <s xml:id="echoid-s14298" xml:space="preserve">erit quoque <lb/>idem axis, per def. </s>
  <s xml:id="echoid-s14299" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14300" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14301" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14302" xml:space="preserve">Euclidis, ad communem ſectionem Aequatoris, &amp; </s>
  <s xml:id="echoid-s14303" xml:space="preserve">Meridiani per idem cen-<lb/>trum ductam perpendicularis. </s>
  <s xml:id="echoid-s14304" xml:space="preserve">Quare poſito A, centro Aequatoris, ſeu mundi, erit A B, in plano Meri <lb/>diani exiſtens, &amp; </s>
  <s xml:id="echoid-s14305" xml:space="preserve">ad axem H A, perpendicularis, communis ſectio Aequatoris, ac Meridiani. </s>
  <s xml:id="echoid-s14306" xml:space="preserve">Erit autẽ <lb/>recta A B, ipſi D I, &amp; </s>
  <s xml:id="echoid-s14307" xml:space="preserve">H B, ipſi H I, æqualis; </s>
  <s xml:id="echoid-s14308" xml:space="preserve">propterea quòd in triangulo A H B, duo anguli A, H, <lb/>
<anchor type="note" xlink:label="note-0228-11a" xlink:href="note-0228-11"/>
duobus angulis D, I, trianguli D H I, ſunt æquales, &amp; </s>
  <s xml:id="echoid-s14309" xml:space="preserve">latus A H, lateri D H, oſtenſum æquale, &amp; </s>
  <s xml:id="echoid-s14310" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s14311" xml:space="preserve">Igitur ſi per B, ducatur in horologio boreali linea æquinoctialis B L, ad lineam meridianam perpendicu-<lb/>
<anchor type="note" xlink:label="note-0228-12a" xlink:href="note-0228-12"/>
laris, diſtabit ea tantum à centro H, ſurſum verſus, quantum æquinoctialis linea F K, ab eodem centro <lb/>H, abeſt deorſum verſus in horologio auſtrali. </s>
  <s xml:id="echoid-s14312" xml:space="preserve">Quamobrem ſi in linea meridiana H B, producta ſumatur <lb/>recta B M, rectæ B A, æqualis, &amp; </s>
  <s xml:id="echoid-s14313" xml:space="preserve">ex M, circulus deſcribatur, &amp; </s>
  <s xml:id="echoid-s14314" xml:space="preserve">in partes 24. </s>
  <s xml:id="echoid-s14315" xml:space="preserve">ſecetur, &amp; </s>
  <s xml:id="echoid-s14316" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14317" xml:space="preserve">deſcribetur <lb/>in facie plani oppoſita, &amp; </s>
  <s xml:id="echoid-s14318" xml:space="preserve">boreali horologium boreale, quemadmodum in facie auſtr ali deſcriptum eſt au-<lb/>ſtrale, cum ſumpſimus rectam I E, æqualem rectæ I D, &amp; </s>
  <s xml:id="echoid-s14319" xml:space="preserve">ex E, circulum deſcripſimus, &amp; </s>
  <s xml:id="echoid-s14320" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14321" xml:space="preserve">vt ſupra <lb/>demonſtratum eſt. </s>
  <s xml:id="echoid-s14322" xml:space="preserve">Eadem enim prorſus hic demonſtratio erit.</s>
  <s xml:id="echoid-s14323" xml:space="preserve"/>
</p>
<div xml:id="echoid-div723" type="float" level="2" n="7">
<note position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve">Si horologium <lb/>auſtrale inuer-<lb/>tatur, vt ex ſupe <lb/>riore parte fiat <lb/>inferior, &amp; quæ <lb/>poſt hanc inuer <lb/>ſionem dextra <lb/>eſt, fiat ſiniſtra, <lb/>&amp; contra, ma-<lb/>nentibus @iſdẽ <lb/>numeris hora-<lb/>rum, conſtructũ <lb/>erit horologiũ <lb/>boreale Sed ho <lb/>ræ, quæ prius à <lb/>meridie nume-<lb/>rabantur, nunc <lb/>à med. noc. nu <lb/>merandæ erũ@ <lb/>&amp; contra.</note>
<note position="left" xlink:label="note-0228-05" xlink:href="note-0228-05a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0228-01" xlink:href="fig-0228-01a">
    <image file="0228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0228-01"/>
  </figure>
<note position="left" xlink:label="note-0228-06" xlink:href="note-0228-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0228-07" xlink:href="note-0228-07a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0228-08" xlink:href="note-0228-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0228-09" xlink:href="note-0228-09a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0228-10" xlink:href="note-0228-10a" xml:space="preserve">2. vndec.</note>
<note position="left" xlink:label="note-0228-11" xlink:href="note-0228-11a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0228-12" xlink:href="note-0228-12a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s14324" xml:space="preserve">HOC autem horologium boreale habetur quoque, ſi omnes lineæ auſtralis horologĳ per centrum H, <lb/>producantur. </s>
  <s xml:id="echoid-s14325" xml:space="preserve">Cum enim omnes circuli horarĳ à meridie, vel media nocte incedant per axem D H A, <lb/>ita vt ſecent planum horologĳ in H, erunt communes ſectiones ipſorum, &amp; </s>
  <s xml:id="echoid-s14326" xml:space="preserve">plani horologĳ tam in facie <lb/>auſtrali, quàm in boreali, eædem rectæ lineę per H, trãſeuntes; </s>
  <s xml:id="echoid-s14327" xml:space="preserve">ita tamen, vt hę ſectiones, hoc eſt, lineę ho-<lb/>rarię, in boreali horologio intelligantur in parte plani oppoſita, quandoquidem &amp; </s>
  <s xml:id="echoid-s14328" xml:space="preserve">axis mundi D H, pro-
<pb o="209" file="0229" n="229" rhead="LIBER SECVNDVS."/>
ductus cadit in oppoſitam partem; </s>
  <s xml:id="echoid-s14329" xml:space="preserve">hoc eſt, ea lege &amp; </s>
  <s xml:id="echoid-s14330" xml:space="preserve">conditione, vt conuerſo ad nos horologio auſtrali, <lb/>exiſtenteq́, puncto F, ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s14331" xml:space="preserve">K, ad dexteram, lineę horar ie in facie oppoſita, &amp; </s>
  <s xml:id="echoid-s14332" xml:space="preserve">boreali ducan-<lb/>tur omnino reſpondentes horarĳs lineis auſtralis horologĳ per centrum H, eductis; </s>
  <s xml:id="echoid-s14333" xml:space="preserve">adeò vt nobis faciem <lb/>plani borealem aſpicientibus punctum F, poſitum ſit ad dexterarn, &amp; </s>
  <s xml:id="echoid-s14334" xml:space="preserve">K, ad ſiniſtram; </s>
  <s xml:id="echoid-s14335" xml:space="preserve">contra ſcilicet, <lb/>quàm in auſtr ali contingit; </s>
  <s xml:id="echoid-s14336" xml:space="preserve">vel quod idem eſt, F, vergat in occaſum, &amp; </s>
  <s xml:id="echoid-s14337" xml:space="preserve">K, in ortum, vt in auſtrali.</s>
  <s xml:id="echoid-s14338" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s14339" xml:space="preserve">ERIT autem horologium boreale arte proxime tradita delineatum omnino ęquale, &amp; </s>
  <s xml:id="echoid-s14340" xml:space="preserve">ſimile au-<lb/>ſtrali ob ęqualitatem axium H A, H D; </s>
  <s xml:id="echoid-s14341" xml:space="preserve">gnomonum C A, G D; </s>
  <s xml:id="echoid-s14342" xml:space="preserve">communium ſectionum Aequatoris, &amp; </s>
  <s xml:id="echoid-s14343" xml:space="preserve"><lb/>Meridiani A B, D I; </s>
  <s xml:id="echoid-s14344" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14345" xml:space="preserve">portionum meridianę lineę H B, H I, inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s14346" xml:space="preserve">lineas ęquino <lb/>ctiales poſitarum. </s>
  <s xml:id="echoid-s14347" xml:space="preserve">Hinc enim efficitur, triangulum H B L, in boreali horologio, cuius later a ſunt linea me <lb/>ridiana H B, ęquinoctialis B L, &amp; </s>
  <s xml:id="echoid-s14348" xml:space="preserve">linea horę quintę H L, ęquale eſſe, &amp; </s>
  <s xml:id="echoid-s14349" xml:space="preserve">ſimile prorſus triangulo H I K, <lb/>
<anchor type="note" xlink:label="note-0229-01a" xlink:href="note-0229-01"/>
<anchor type="note" xlink:label="note-0229-02a" xlink:href="note-0229-02"/>
in horologio auſtrali, cuius etiam latera ſunt meridiana linea H I, ęquinoctialis I K, &amp; </s>
  <s xml:id="echoid-s14350" xml:space="preserve">linea horę 5. <lb/></s>
  <s xml:id="echoid-s14351" xml:space="preserve">H K; </s>
  <s xml:id="echoid-s14352" xml:space="preserve">propterea quod duo anguli illius B H L, H B L, duobus angulis huius I H K, H I K, ęquales ſunt, <lb/>(Nam anguli ad H, æquales ſunt, cum ſint ad verticem, &amp; </s>
  <s xml:id="echoid-s14353" xml:space="preserve">anguli ad B, I, recti.) </s>
  <s xml:id="echoid-s14354" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14355" xml:space="preserve">latus H B, lateri <lb/>
<anchor type="note" xlink:label="note-0229-03a" xlink:href="note-0229-03"/>
H I, ęquale, vt oſtenſum eſt, &amp; </s>
  <s xml:id="echoid-s14356" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14357" xml:space="preserve">Eadem ratio eſt de cęteris triangulis, quorum baſes ſunt lineę horarię <lb/>inter centrum H, &amp; </s>
  <s xml:id="echoid-s14358" xml:space="preserve">lineas ęquinoctales poſitę, ſubtenſęque angulis rectis ad B, I, comprehenſis ſub me-<lb/>ridiana linea, &amp; </s>
  <s xml:id="echoid-s14359" xml:space="preserve">lineis ęquinoctialibus. </s>
  <s xml:id="echoid-s14360" xml:space="preserve">Totum ergo horologium boreale toti auſtrali ęquale erit, &amp; </s>
  <s xml:id="echoid-s14361" xml:space="preserve">ſimi <lb/>le, cum ſingulę partes ſingulis partibus ęquales ſint &amp; </s>
  <s xml:id="echoid-s14362" xml:space="preserve">ſimiles.</s>
  <s xml:id="echoid-s14363" xml:space="preserve"/>
</p>
<div xml:id="echoid-div724" type="float" level="2" n="8">
<note position="left" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0229-03" xlink:href="note-0229-03a" xml:space="preserve">15. primi.</note>
</div>
<note position="right" xml:space="preserve">Si lineamenta <lb/>auſtialis horo-<lb/>logu deicriban <lb/>tur in facie pla <lb/>ni oppoſita, ita <lb/>vt ad vnguem-<lb/>reſpondeant li-<lb/>neamentis ho-<lb/>rologii auſtra-<lb/>lis, &amp; poſt hanc <lb/>deſcriptionem <lb/>pars ſuperior <lb/>mutetur in in-<lb/>feriorem, deſcri <lb/>ptum crit horo <lb/>gium boreale.</note>
<p style="it">
  <s xml:id="echoid-s14364" xml:space="preserve">VNDE ſi in parte oppoſita plani horologii deſcribantur lineę reſpondentes ad vnguem lineis in ho-<lb/>rologio auſtrali, &amp; </s>
  <s xml:id="echoid-s14365" xml:space="preserve">deinde pars ſuperior mutetur in inferiorem, ac proinde &amp; </s>
  <s xml:id="echoid-s14366" xml:space="preserve">illa, quę poſt deſcriptionẽ <lb/>illam dextra eſt, fiat ſiniſtra, et contra, deſcriptum erit horologium boreale in facie plani horologii borea-<lb/>
<anchor type="note" xlink:label="note-0229-05a" xlink:href="note-0229-05"/>
li. </s>
  <s xml:id="echoid-s14367" xml:space="preserve">Quia hac ratione punctum K, quod in auſtrali horologio nobis eſt ad dexteram, &amp; </s>
  <s xml:id="echoid-s14368" xml:space="preserve">in boreali poſt illam <lb/>deſcriptionem ad ſiniſtram, fit nobis iterum ad dexteram, ſi ſuperior pars in inſeriorem mutetur, vt con-<lb/>ſtat. </s>
  <s xml:id="echoid-s14369" xml:space="preserve">Sed hac de re plura in propoſ. </s>
  <s xml:id="echoid-s14370" xml:space="preserve">ſequenti ſcribemus.</s>
  <s xml:id="echoid-s14371" xml:space="preserve"/>
</p>
<div xml:id="echoid-div725" type="float" level="2" n="9">
<note position="left" xlink:label="note-0229-05" xlink:href="note-0229-05a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s14372" xml:space="preserve">EX his omnibus (vt ad id, quod propoſitum eſt, veniamus) perſpicuum eſſe arbitror, horologium au <lb/>ſtrale indicare horas in facie plani V erticalis boreali, ſi omnia immut entur, vt dictum eſt, hoc eſt, ſi ſu-<lb/>perior pars mutetur in inferiorem, &amp; </s>
  <s xml:id="echoid-s14373" xml:space="preserve">quæ poſt hanc mutationem nobis ad horologium conuerſis dextra <lb/>eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s14374" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s14375" xml:space="preserve">Nam auſtrale horologium H R K, ſi inuertatur, vt punctum I, ſurſum ver-<lb/>ſus, &amp; </s>
  <s xml:id="echoid-s14376" xml:space="preserve">H, deorſum verſus ponatur, punctum{q́ue} R, quod in eo ſitu nobis ad horologium conuerſis eſt ad <lb/>dextram, in ſiniſtram partem, &amp; </s>
  <s xml:id="echoid-s14377" xml:space="preserve">K, in dextram cadat, acquiret omnino eundem ſitum, quem habet bo-<lb/>reale horologium L H B, in facie oppoſita delineatum, vbi punctum L, nobis ad horologium conuerſis <lb/>
<anchor type="note" xlink:label="note-0229-06a" xlink:href="note-0229-06"/>
poſitum eſt ad dextram, &amp; </s>
  <s xml:id="echoid-s14378" xml:space="preserve">B, ad ſinistram, vt manifestum eſt. </s>
  <s xml:id="echoid-s14379" xml:space="preserve">Similiter ex ĳs, quæ in ſcbolio propoſ. </s>
  <s xml:id="echoid-s14380" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s14381" xml:space="preserve">huius libri tradidimus, manifeſtum eſt, portionem illam lineę meridianæ, quæ in horologio Auſtrali indi-<lb/>cabat horam 12. </s>
  <s xml:id="echoid-s14382" xml:space="preserve">meridiei, in boreali monstrare horam 12. </s>
  <s xml:id="echoid-s14383" xml:space="preserve">mediæ noctis; </s>
  <s xml:id="echoid-s14384" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14385" xml:space="preserve">horas, quæ ibi à meridie nu-<lb/>merabantur, hic à media nocte, et quæibi à media nocte, hic à meridie computandas eſſe: </s>
  <s xml:id="echoid-s14386" xml:space="preserve">quoniam vide-<lb/>licet, vt proxime demonstratum eſt, horæ Auſtralis horologĳ vltra centrum horologĳ dant in facie bo-<lb/>reali eaſdem numero horas; </s>
  <s xml:id="echoid-s14387" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14388" xml:space="preserve">vt ex dicto ſcholio conſtat, horę antemeridianæ vltra centrum horolo-<lb/>gĳ productæ faciunt pomeridianas, &amp; </s>
  <s xml:id="echoid-s14389" xml:space="preserve">pomeridianæ antemeridianas. </s>
  <s xml:id="echoid-s14390" xml:space="preserve">Quod etiam facile intelligetur, ſi <lb/>in facie boreali concipiantur per axem H A, ducti circuli horarĳ. </s>
  <s xml:id="echoid-s14391" xml:space="preserve">Nam vmbra axis, vel ſtyli, dummodo <lb/>Sol faciem borealem illuſtret, proĳcietur in meridianam lineam H B, Sole exiſtente in ſemicirculo Meri-<lb/>diani ſub terra, in lineas verò horarias verſus punctum L, quod nobis in boreali horologio eſt ad dexte-<lb/>
<anchor type="note" xlink:label="note-0229-07a" xlink:href="note-0229-07"/>
ram, Sole exiſtente in ſemicirculis horarĳs poſt mediã noctem, hoc eſt, in ſemicir culis, qui opponuntur il-<lb/>lis, in quibus Sol exiſtit, cum vmbra axis, vel ſtyli in Auſtrali horologio proĳcitur in horarias lineas ver <lb/>ſus K, &amp; </s>
  <s xml:id="echoid-s14392" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14393" xml:space="preserve">vt perſpicuum eſt, ſi &amp; </s>
  <s xml:id="echoid-s14394" xml:space="preserve">horologium boreale L H B, &amp; </s>
  <s xml:id="echoid-s14395" xml:space="preserve">axis H A, &amp; </s>
  <s xml:id="echoid-s14396" xml:space="preserve">circuli horarĳ in propria <lb/>poſitione concipiantur. </s>
  <s xml:id="echoid-s14397" xml:space="preserve">Hæc omnia planiora fient, ſi horologium boreale L H B, in facie oppoſita, vt di-<lb/>ctum eſt, delineatum confer atur cum boreali horologio, quod ante deſcripſimus. </s>
  <s xml:id="echoid-s14398" xml:space="preserve">Deprehendemus enim <lb/>hoc illi omnino ſimile eſſe, &amp; </s>
  <s xml:id="echoid-s14399" xml:space="preserve">æquale.</s>
  <s xml:id="echoid-s14400" xml:space="preserve"/>
</p>
<div xml:id="echoid-div726" type="float" level="2" n="10">
<note position="left" xlink:label="note-0229-06" xlink:href="note-0229-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0229-07" xlink:href="note-0229-07a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s14401" xml:space="preserve">EADEM hæc demonſtratio in horologia tam à V erticali circulo, quàm ab Horizonte declinan-<lb/>
<anchor type="note" xlink:label="note-0229-08a" xlink:href="note-0229-08"/>
tia: </s>
  <s xml:id="echoid-s14402" xml:space="preserve">Item in inclinata ad Horizontem, &amp; </s>
  <s xml:id="echoid-s14403" xml:space="preserve">in ea, quæ &amp; </s>
  <s xml:id="echoid-s14404" xml:space="preserve">à Verticali circulo declinant, &amp; </s>
  <s xml:id="echoid-s14405" xml:space="preserve">ad Horizontem <lb/>ſunt inclinata, de quibus libro inſequenti dicemus, quadrat omni ex parte; </s>
  <s xml:id="echoid-s14406" xml:space="preserve">ſi modo in illis rectam B I, nõ <lb/>intelligamus eſſe meridianam, ſed lineam ſtyli, ſiue indicis, &amp; </s>
  <s xml:id="echoid-s14407" xml:space="preserve">pro Meridiano circulo per axem A D, &amp; </s>
  <s xml:id="echoid-s14408" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0229-09a" xlink:href="note-0229-09"/>
meridianam lineam B I, ducto ſumamus circulum alium maximum, qui per axem A D, &amp; </s>
  <s xml:id="echoid-s14409" xml:space="preserve">lineam ſtyli <lb/>B I, ducitur, inſtar noui cuiuſdam Meridiani in illorum horologiorum planis, vt ſuis locis monebimus. <lb/></s>
  <s xml:id="echoid-s14410" xml:space="preserve">Quodcunque enim horologium eiuſmodi in vna facie plani deſcriptum, vt v. </s>
  <s xml:id="echoid-s14411" xml:space="preserve">g. </s>
  <s xml:id="echoid-s14412" xml:space="preserve">in ea, quæ à meridie decli-<lb/>nat, ſi planum ad Horizontem fuerit rectum, vel in ſuperiori facie, ſi planum ad Horizontem fuerit incli-<lb/>natum, erit quoque horologium in facie plani eiuſdem oppoſita deſcribendum, vt in ea, quę à Septentrio-<lb/>ne declinat, vel in facie inferiori; </s>
  <s xml:id="echoid-s14413" xml:space="preserve">ſi tamen omnes partes inuertantur, vt diximus, hoc eſt, ſuperior primũ <lb/>mutetur in inferiorem, &amp; </s>
  <s xml:id="echoid-s14414" xml:space="preserve">quæ poſt hanc mutationem primam dextra eſt, euadat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s14415" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s14416" xml:space="preserve">Quæ <lb/>omnia ſuo loco perſpicua erunt.</s>
  <s xml:id="echoid-s14417" xml:space="preserve"/>
</p>
<div xml:id="echoid-div727" type="float" level="2" n="11">
<note position="right" xlink:label="note-0229-08" xlink:href="note-0229-08a" xml:space="preserve">Ea, quæ proxi-<lb/>me dicta ſunt <lb/>de inuerſione <lb/>omnium parti@ <lb/>horologii, intel <lb/>ligenda quoque <lb/>ſunt in horolo-<lb/>giis declinanti-<lb/>bus, &amp; inclina-<lb/>tis.</note>
<note position="left" xlink:label="note-0229-09" xlink:href="note-0229-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s14418" xml:space="preserve">HACTENVS conſtruximus V erticale horologium in plana ſuperficie quacunque, vt illud po-<lb/>ſtea in murum, vel planum, quod ad Horizontem rectum eſt, &amp; </s>
  <s xml:id="echoid-s14419" xml:space="preserve">directò ad meridiem, Septentrionemve <lb/>ſpectat, transferri poſſit, ita vt H E, meridiana linea ad Horizontem ſit perpendicularis, ęquinoctialis
<pb o="210" file="0230" n="230" rhead="GNOMONICES"/>
autem linea F K, eidem Horizonti æquidiſtet; </s>
  <s xml:id="echoid-s14420" xml:space="preserve">hac tamen addita conditione, vt in Auſtrali horologio <lb/>æquinoctialis F K, exiſtat infra centrum horologĳ H, in boreali verò ſupra idem, vt ante in hoc eodem <lb/>ſcholio præcepimus. </s>
  <s xml:id="echoid-s14421" xml:space="preserve">Quòd ſi in ipſo muro, vel plano quopiam ad Horizontem recto, &amp; </s>
  <s xml:id="echoid-s14422" xml:space="preserve">directò ad meri-<lb/>
<anchor type="note" xlink:label="note-0230-01a" xlink:href="note-0230-01"/>
diem, Septentrionemve ſpectante ſit delineandum, efficiemus id hoc modo. </s>
  <s xml:id="echoid-s14423" xml:space="preserve">Beneficio perpendiculi duce-<lb/>mus in plano dato rectam H E, perpendicularem ad Horizontem, quæ linea meridiana erit in horologio. <lb/></s>
  <s xml:id="echoid-s14424" xml:space="preserve">Hanc ad angulos rectos ſecabimus in I, per rectam F K, quæ linea erit æquinoctialis. </s>
  <s xml:id="echoid-s14425" xml:space="preserve">Deinde ex I, @ur-<lb/>ſum verſus in Auſtrali horologio, deorſum autem verſus in boreali, transferemus vſque ad H, rectam <lb/>I H, ex portione Analemmatis, &amp; </s>
  <s xml:id="echoid-s14426" xml:space="preserve">rectam I E, accipiemus ęqualem rectæ I E, ex eadem portione Ana-<lb/>lemmatis, ſiue ſurſum verſus, ſiue deorſum. </s>
  <s xml:id="echoid-s14427" xml:space="preserve">Poſtremò deſcripto circulo ex E, eo{q́ue} in 24. </s>
  <s xml:id="echoid-s14428" xml:space="preserve">partes æquales <lb/>ſecto, reliqua perficiemus, vt antea.</s>
  <s xml:id="echoid-s14429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div728" type="float" level="2" n="12">
<note position="left" xlink:label="note-0230-01" xlink:href="note-0230-01a" xml:space="preserve">Qua ratione in <lb/>plano ſtabili, <lb/>quod Verticali <lb/>proprie dicto <lb/>æquidiſtet, ho-<lb/>rologium ſit de <lb/>ſcribendum.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s14430" xml:space="preserve">POSSVMVS quoque eandem conſtructionem inchoare hac ratione. </s>
  <s xml:id="echoid-s14431" xml:space="preserve">Ducta recta F K, Hori-<lb/>zonti par allela in muro, planove propoſito, (quod quidem facile fiet beneficio perpendiculi, &amp; </s>
  <s xml:id="echoid-s14432" xml:space="preserve">libellæ) <lb/>pro linea æquinoctiali, ſecabimus eam ad angulos rectos in I, per rectam H E, quæ meridiana linea erit. <lb/></s>
  <s xml:id="echoid-s14433" xml:space="preserve">Reliqua deinde, vt proximè ſcripſimus, abſoluemus.</s>
  <s xml:id="echoid-s14434" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s14435" xml:space="preserve">SI autem idem horologiũ deſcribendum ſit in dato plano, ſine portione Analemmatis ſeorſum conſtru <lb/>
<anchor type="note" xlink:label="note-0230-03a" xlink:href="note-0230-03"/>
cta, ad quamcunque styli longitudinem, cuius etiam locus datus ſit, vtendum erit hac arte. </s>
  <s xml:id="echoid-s14436" xml:space="preserve">Sit longitu-<lb/>do ſtyli data D G, eius{q́ue} locus in plano horologĳ ſit punctum G. </s>
  <s xml:id="echoid-s14437" xml:space="preserve">Si igitur planum horologĳ fuerit quod-<lb/>cunque, vt borologium in eo deſcriptum in proprio deinde ſitu collocetur, vel in planum ſtabile, quod <lb/>
<anchor type="figure" xlink:label="fig-0230-01a" xlink:href="fig-0230-01"/>
<anchor type="note" xlink:label="note-0230-04a" xlink:href="note-0230-04"/>
<anchor type="note" xlink:label="note-0230-05a" xlink:href="note-0230-05"/>
<anchor type="note" xlink:label="note-0230-06a" xlink:href="note-0230-06"/>
Verticali proprie dicto ſit parallelum, transferatur, vt paulo ante diximus, ducenda eſt per G, locum <lb/>ſtyli linea recta M N, vtcunque pro linea meridiana: </s>
  <s xml:id="echoid-s14438" xml:space="preserve">Si autem planum horologĳ ſtabile proponatur, <lb/>verticali proprie dicto parallelum, cuiuſmodi eſt planum cuiuſuis muri ad Horizontem recti, qui dire-<lb/>cto ad meridiem ſpectet, vel ad Septentrionem, ducenda eſt per G, locum ſtyli, beneficio perpendiculi, <lb/>recta M N, ad Horizontem perpendicularis pro linea meridiana; </s>
  <s xml:id="echoid-s14439" xml:space="preserve">Vel certe beneficio perpendiculi ac <lb/>libellæ per G, ducenda linea Horizonti parallela, tanquam communis ſectio plani horologĳ, &amp; </s>
  <s xml:id="echoid-s14440" xml:space="preserve">Horizon-<lb/>
<anchor type="note" xlink:label="note-0230-07a" xlink:href="note-0230-07"/>
tis, quam ſi in G, ſecet recta M N, ad angulos rectos, erit rurſus M N, ad Horizontem perpendicula-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s14441" xml:space="preserve">linea meridiana, communis nimirum ſectio plani horologĳ ac Meridiani. </s>
  <s xml:id="echoid-s14442" xml:space="preserve">Quoniam enim tam pla-<lb/>num horologĳ, quàm planum Meridiani ad Horizontem rectum eſt, erit quoque eorum ſectio communis <lb/>ad eundem perpendicularis, at que adeo, per defin. </s>
  <s xml:id="echoid-s14443" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14444" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14445" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14446" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s14447" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14448" xml:space="preserve">ad rectam, quæ per G, ducta eſt æqui <lb/>
<anchor type="note" xlink:label="note-0230-08a" xlink:href="note-0230-08"/>
diſtans Horizonti, tanquam communis ſectio Horizontis ac plani horologii, cum hæc recta in Horizonte <lb/>exiſtat. </s>
  <s xml:id="echoid-s14449" xml:space="preserve">Quare cum Meridianus tranſeat per G; </s>
  <s xml:id="echoid-s14450" xml:space="preserve">(Eſt enim ſtylus D G, communis ſectio Horizontis ac <lb/>Meridiani) erit M N, quæ per G, ducta eſt perpendicularis ad illam rectam, communis ſectio Meridiani <lb/>&amp; </s>
  <s xml:id="echoid-s14451" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s14452" xml:space="preserve">Ad hanc deinde lineam meridianam M N, excitanda eſt in G, per pendicularis <lb/>B G D, ſumenda{q́ue} G D, dato ſtylo æqualis. </s>
  <s xml:id="echoid-s14453" xml:space="preserve">Facto autem D, centro, deſcribendus eſt arcus circuli A B C, <lb/>in quo à recta D B, verſus A, hoc eſt, ſurſum verſus, ſi horologium ad meridiem ſpectet, numeretur alti-<lb/>tudo poli B A, &amp; </s>
  <s xml:id="echoid-s14454" xml:space="preserve">deorſum verſus complementum altitudinis poli B C. </s>
  <s xml:id="echoid-s14455" xml:space="preserve">Quòd ſi horologium ſpectet ad
<pb o="211" file="0231" n="231" rhead="LIBER SECVNDVS."/>
Septentrionem, ſumendus erit arcus altitudinis poli B A, deorſum verſus, &amp; </s>
  <s xml:id="echoid-s14456" xml:space="preserve">arcus complementi B C, <lb/>ſurſum verſus. </s>
  <s xml:id="echoid-s14457" xml:space="preserve">Ductis vero rectis D A, D C, ſecabitur meridiana linea in punctis H, &amp; </s>
  <s xml:id="echoid-s14458" xml:space="preserve">I. </s>
  <s xml:id="echoid-s14459" xml:space="preserve">Poſt hæc in <lb/>I, excitabimus ad meridianam lineam perpendicularem F K, pro linea æquinoctiali. </s>
  <s xml:id="echoid-s14460" xml:space="preserve">Poſtremo ſumpta <lb/>recta I E, æquali ipſi I D, deſcribemus ex E, circulum cuiuſcunque magnitudinis, quo diuiſo in partes <lb/>24. </s>
  <s xml:id="echoid-s14461" xml:space="preserve">æquales, initio facto à linea meridiana, reliqua abſoluemus, vt ante docuimus ad initium hu-<lb/>ius propoſ.</s>
  <s xml:id="echoid-s14462" xml:space="preserve"/>
</p>
<div xml:id="echoid-div729" type="float" level="2" n="13">
<note position="left" xlink:label="note-0230-03" xlink:href="note-0230-03a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Vertica <lb/>lis ad datam ſty <lb/>li longitudinẽ, <lb/>cuius etiam lo-<lb/>cus datus ſit, ſi-<lb/>ne portione A-<lb/>nalẽmatis ſeor-<lb/>ſum conſtructa.</note>
  <figure xlink:label="fig-0230-01" xlink:href="fig-0230-01a">
    <image file="0230-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0230-01"/>
  </figure>
<note position="left" xlink:label="note-0230-04" xlink:href="note-0230-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0230-05" xlink:href="note-0230-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0230-06" xlink:href="note-0230-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0230-07" xlink:href="note-0230-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0230-08" xlink:href="note-0230-08a" xml:space="preserve">19. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14463" xml:space="preserve">DEMONSTRATIO huius deſcriptionis hæc eſt. </s>
  <s xml:id="echoid-s14464" xml:space="preserve">Si linea meridiana M N, proprium ſitum <lb/>
<anchor type="note" xlink:label="note-0231-01a" xlink:href="note-0231-01"/>
habeat in plano, quod rectum eſt ad Horizontem, &amp; </s>
  <s xml:id="echoid-s14465" xml:space="preserve">directo ad meridiem, vel boream ſpectat, ita vt M, <lb/>ſurſum verſus, &amp; </s>
  <s xml:id="echoid-s14466" xml:space="preserve">N, deorſum verſus vergat, triangulum{q́ue} H D I, rectum ſtatuatur ad planum horo-<lb/>logii, ita vt in plano Meridiani ſitum ſit; </s>
  <s xml:id="echoid-s14467" xml:space="preserve">quoniam angulus H D G, per conſtructionem, æqualis eſt alti-<lb/>
<anchor type="note" xlink:label="note-0231-02a" xlink:href="note-0231-02"/>
tudini poli, erit reliquus D H G, complemento altitudinis poli ęqualis. </s>
  <s xml:id="echoid-s14468" xml:space="preserve">Rurſus quia per conſtructionem <lb/>I D G, complemento altitudinis poli eſt æqualis, erit reliquus D I G, altitudini poli æqualis. </s>
  <s xml:id="echoid-s14469" xml:space="preserve">Sumpto igi-<lb/>tur D, vertice ſtyli pro centro mundi, erit D H, faciens cum linea meridiana in H, angulum complemen-<lb/>to altitudinis poli ęqualem axis mundi occurrens plano horologii in H, centro horologii. </s>
  <s xml:id="echoid-s14470" xml:space="preserve">Recta autem D I, <lb/>conſtituens cum eadem linea meridiana in I, angulum altitudinis poli, erit communis ſectio Meridiani at-<lb/>que Aequatoris, cum eiuſmodi ſectio inſphæra cum meridiana linca in Verticali efficiat ſemper angulum <lb/>altitudinis poli, cum axe vero angulum rectum, cuiuſmodi est angulus H D I, compoſitus ex angulo alti-<lb/>tudinis poli, &amp; </s>
  <s xml:id="echoid-s14471" xml:space="preserve">angulo complementi eiuſdem altitudinis poli. </s>
  <s xml:id="echoid-s14472" xml:space="preserve">Occurrit igitur Aequator plano horolo-<lb/>gii in I, ac proinde, vt ſupra oſtenſum eſt, erit recta F K, linea æquinoctialis. </s>
  <s xml:id="echoid-s14473" xml:space="preserve">Recta autem D G, communis <lb/>ſectio erit Meridiani atque Horizontis. </s>
  <s xml:id="echoid-s14474" xml:space="preserve">Reliqua omnia demonſtr abuntur, vt prius.</s>
  <s xml:id="echoid-s14475" xml:space="preserve"/>
</p>
<div xml:id="echoid-div730" type="float" level="2" n="14">
<note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">Demonſtratio <lb/>huius deſcri-<lb/>ptionis.</note>
<note position="left" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s14476" xml:space="preserve">IDEM horologium deſcribemus ſine punctis in æquinoctiali linea inuentis, beneficio Ellipſis, vt &amp; </s>
  <s xml:id="echoid-s14477" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0231-04a" xlink:href="note-0231-04"/>
borizontale deſcripſimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s14478" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14479" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14480" xml:space="preserve">hoc modo. </s>
  <s xml:id="echoid-s14481" xml:space="preserve">Ex H, centro horologii deſcribantur <lb/>duo circuli, vnus ad interuallum H I, alter vero ad interuallum I D: </s>
  <s xml:id="echoid-s14482" xml:space="preserve">Vel ſi hę ſemidiametri nimis bre-<lb/>ues videantur, ſumatur punctum in axe remotius à puncto H, quàm D, (vt &amp; </s>
  <s xml:id="echoid-s14483" xml:space="preserve">in horizontali horologio <lb/>factum eſt) à quo ad axem perpendicularis ducatur ſecans meridianam lineam in puncto, quod maioris <lb/>circuli ſemidiametrum terminabit: </s>
  <s xml:id="echoid-s14484" xml:space="preserve">pro minoris autem circuli ſemidiametro accipiatur ſegmentũ illius <lb/>perpendicularis inter idem punctum, &amp; </s>
  <s xml:id="echoid-s14485" xml:space="preserve">axem interpoſitum. </s>
  <s xml:id="echoid-s14486" xml:space="preserve">Diuiſo deinde vtroque circulo in 24. </s>
  <s xml:id="echoid-s14487" xml:space="preserve">par-<lb/>tes ęquales, initio facto à linea meridiana, inueniemus beneficio punctorum diuiſionum in plano horologii <lb/>puncta Ellipſis, per quæ ducendę ſunt lineę horariæ ex puncto H, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s14488" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14489" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14490" xml:space="preserve">tradi-<lb/>dimus. </s>
  <s xml:id="echoid-s14491" xml:space="preserve">Eadem enim demonſtratio huc afferri poterit. </s>
  <s xml:id="echoid-s14492" xml:space="preserve">Exemplum huius deſcriptionis non ponimus, quia <lb/>
<anchor type="note" xlink:label="note-0231-05a" xlink:href="note-0231-05"/>
luce clarius res ipſa intelligi potest ex figura, quam in dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s14493" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14494" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14495" xml:space="preserve">depinximus. </s>
  <s xml:id="echoid-s14496" xml:space="preserve">Ea <lb/>enim figura refert Verticale horologium ad latitudinem loci gr. </s>
  <s xml:id="echoid-s14497" xml:space="preserve">48. </s>
  <s xml:id="echoid-s14498" xml:space="preserve">quæ nimirum cum ea latitudine, pro <lb/>qua illud horologium horizontale conſtructum eſt, grad. </s>
  <s xml:id="echoid-s14499" xml:space="preserve">90. </s>
  <s xml:id="echoid-s14500" xml:space="preserve">conficit; </s>
  <s xml:id="echoid-s14501" xml:space="preserve">dummodo numeri horarum mutentur <lb/>in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s14502" xml:space="preserve">Eſt enim Verticalis proprie dictus cuiusuis Horizontis inſtar cuiuſ-<lb/>
<anchor type="note" xlink:label="note-0231-06a" xlink:href="note-0231-06"/>
dam Horizontis, ſupra quem polus attollitur tot gradibus, quot deſunt latitudini loci, ad quam horizon-<lb/>tale horologium conſtructum eſt, ad explendum numerum grad. </s>
  <s xml:id="echoid-s14503" xml:space="preserve">90. </s>
  <s xml:id="echoid-s14504" xml:space="preserve">vt perſpicuum eſt ex portione Ana-<lb/>lemmatis in principio huius propoſ. </s>
  <s xml:id="echoid-s14505" xml:space="preserve">deſcripta, in qua angulus D H G, complementum anguli H D G, alti-<lb/>tudinis poli ſupra Horizontem B C, constituit altitudinem poli ſupra Verticalem H I, tanquam ſupra Ho <lb/>rizontem quempiam: </s>
  <s xml:id="echoid-s14506" xml:space="preserve">Ita vt quodcunque horologium horizontale ad quamcunque latitudinem loci fabri <lb/>catum, ſit Verticale in regione eius latitudinis, quæ illius complementum eſt: </s>
  <s xml:id="echoid-s14507" xml:space="preserve">Et quodlibet horologium <lb/>
<anchor type="note" xlink:label="note-0231-07a" xlink:href="note-0231-07"/>
Verticale in priore latitudine ſit viciſſim horizontale in poſteriore; </s>
  <s xml:id="echoid-s14508" xml:space="preserve">ſi numeri horarum mutentur in ea-<lb/>rum complementa vſque ad 12. </s>
  <s xml:id="echoid-s14509" xml:space="preserve">vt diximus.</s>
  <s xml:id="echoid-s14510" xml:space="preserve"/>
</p>
<div xml:id="echoid-div731" type="float" level="2" n="15">
<note position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>benefie<unsure/>io Elli-<lb/>pſis.</note>
<note position="left" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0231-06" xlink:href="note-0231-06a" xml:space="preserve">Horologiũ ho-<lb/>rizontale ad <lb/>quamcunque la <lb/>titudinem con-<lb/>ſtructũ<unsure/>, eſt Ver-<lb/>ticale in regio-<lb/>ne, cuius latitu-<lb/>do complemen <lb/>tum eſt illius <lb/>latitudinis, &amp; <lb/>contra Vertica <lb/>le illius eſt hori <lb/>@ontale huius.</note>
<note position="left" xlink:label="note-0231-07" xlink:href="note-0231-07a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div733" type="section" level="1" n="179">
<head xml:id="echoid-head182" xml:space="preserve">PROBLEMA 14. PROPOSITIO 14.</head>
<p>
  <s xml:id="echoid-s14511" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in Verticali ho-<lb/>rologio prædicto deſcribere.</s>
  <s xml:id="echoid-s14512" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s14513" xml:space="preserve">REPETATVR portio Analemmatis præcedentis propoſ. </s>
  <s xml:id="echoid-s14514" xml:space="preserve">cõpleaturq́; </s>
  <s xml:id="echoid-s14515" xml:space="preserve">Meridianus A B C, <lb/>
<anchor type="note" xlink:label="note-0231-09a" xlink:href="note-0231-09"/>
in quo, iuxta Analemma propoſ. </s>
  <s xml:id="echoid-s14516" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14517" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14518" xml:space="preserve">conſtructum, ducantur parallelorum diametri, <lb/>vnà cum diametris oppoſita ſigna coniungentibus, facientibusq́; </s>
  <s xml:id="echoid-s14519" xml:space="preserve">in conis, quorum baſes ſunt pa-<lb/>ralleli, vertex autem communis centrum D, triangula per axem. </s>
  <s xml:id="echoid-s14520" xml:space="preserve">Erit igitur ex demonſtratis in <lb/>propoſ. </s>
  <s xml:id="echoid-s14521" xml:space="preserve">4. </s>
  <s xml:id="echoid-s14522" xml:space="preserve">5. </s>
  <s xml:id="echoid-s14523" xml:space="preserve">6. </s>
  <s xml:id="echoid-s14524" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14525" xml:space="preserve">7. </s>
  <s xml:id="echoid-s14526" xml:space="preserve">præcedentis libri K R, diameter conicæ ſectionis, quam Sol in principio ♋, <lb/>exiſtens deſcribit: </s>
  <s xml:id="echoid-s14527" xml:space="preserve">L R, diameter ſectionis, quam Sol in principio ♊, &amp; </s>
  <s xml:id="echoid-s14528" xml:space="preserve">♌, percurrit: </s>
  <s xml:id="echoid-s14529" xml:space="preserve">M R, dia-<lb/>meter ſectionis deſcriptæ à radio Solis in primo puncto ♉, &amp; </s>
  <s xml:id="echoid-s14530" xml:space="preserve">♍, exiſtentis. </s>
  <s xml:id="echoid-s14531" xml:space="preserve">At verò N Q, O Q, <lb/>P Q, erunt diametri ſectionum conicarum, quas radii Solis in oppoſitis parallelis exiſtentis <lb/>deſcribunt.</s>
  <s xml:id="echoid-s14532" xml:space="preserve"/>
</p>
<div xml:id="echoid-div733" type="float" level="2" n="1">
<note position="right" xlink:label="note-0231-09" xlink:href="note-0231-09a" xml:space="preserve">Deſcriptio a@-<lb/>cuum ſignorũ <lb/>Zodiaci in ho-<lb/>rologio Vertica <lb/>li, ex Anal@-<lb/>mate.</note>
</div>
<p>
  <s xml:id="echoid-s14533" xml:space="preserve">HAE autem diametri conicarum ſectionum reperientur etiam in quocunque alio Analem-<lb/>mate, quod vel maius ſit, vel minus hoc propoſito, etiamſi horologium ſine portione Analemma-
<pb o="212" file="0232" n="232" rhead="GNOMONICES"/>
tis conſtructum ſit, vt in antecedenti ſcholio docuimus; </s>
  <s xml:id="echoid-s14534" xml:space="preserve">ſi tamen in alio illo Analemmate ex dia-<lb/>
<anchor type="note" xlink:label="note-0232-01a" xlink:href="note-0232-01"/>
metro Horizontis abſcindatur vtrinque à centro recta æqualis gnomoni D G, producta ipſa dia-<lb/>metro Horizontis, ſi longitudo gno-<lb/>
<anchor type="figure" xlink:label="fig-0232-01a" xlink:href="fig-0232-01"/>
monis id poſtulet, &amp; </s>
  <s xml:id="echoid-s14535" xml:space="preserve">ex vtraque par-<lb/>te per extremum punctum recta duca <lb/>tur parallela diametro Verticalis, per <lb/>quam planum horologii ducitur. </s>
  <s xml:id="echoid-s14536" xml:space="preserve">Hęc <lb/>enim recta in maiori, vel minori Ana <lb/>lemmate à diametris ſignorum oppo <lb/>ſitorum diuidetur in partes æquales <lb/>
<anchor type="note" xlink:label="note-0232-02a" xlink:href="note-0232-02"/>
partibus rectæ Q R, in noſtro hoc A-<lb/>nalemmate. </s>
  <s xml:id="echoid-s14537" xml:space="preserve">Quod ita demonſtrari <lb/>poteſt. </s>
  <s xml:id="echoid-s14538" xml:space="preserve">Quoniam tam illa recta, quàm <lb/>hæc Q R, æqualiter à centro ſui Ana-<lb/>lemmatis diſtat, &amp; </s>
  <s xml:id="echoid-s14539" xml:space="preserve">anguli, quos dia-<lb/>metri oppoſitorum ſignorum faciunt <lb/>cum diametro Aequatoris, in quoli-<lb/>bet Analemmate eiuſdem magnitudi <lb/>nis ſunt, cum ſemper eiſdem declina-<lb/>tionibus eorundem ſignorum inſiſtãt <lb/>
<anchor type="note" xlink:label="note-0232-03a" xlink:href="note-0232-03"/>
ad centra; </s>
  <s xml:id="echoid-s14540" xml:space="preserve">efficitur, vt &amp; </s>
  <s xml:id="echoid-s14541" xml:space="preserve">anguli, quos <lb/>eædem diametri cum diametro Hori <lb/>zontis faciunt, (qui quidem vel com-<lb/>ponuntur ex illis, &amp; </s>
  <s xml:id="echoid-s14542" xml:space="preserve">ex angulo cõple-<lb/>menti altitudinis poli contento ſub diametro Æquatoris, &amp; </s>
  <s xml:id="echoid-s14543" xml:space="preserve">diametro Horizontis, vel relinquun <lb/>tur poſt detractionem illorum ex eodem angulo complementi altitudinis poli) æquales inter ſe <lb/>
<anchor type="note" xlink:label="note-0232-04a" xlink:href="note-0232-04"/>
ſint, cum &amp; </s>
  <s xml:id="echoid-s14544" xml:space="preserve">anguli contenti ſub diametro Horizontis, &amp; </s>
  <s xml:id="echoid-s14545" xml:space="preserve">diametro Æquatoris æquales ſint. </s>
  <s xml:id="echoid-s14546" xml:space="preserve">Qua-<lb/>re cum anguli, quos rectæ per extremitatem gnomonis (nempe per punctum G, in noſtro Analem <lb/>mate, &amp; </s>
  <s xml:id="echoid-s14547" xml:space="preserve">per punctum huic reſpondens in alio Analemmate) ductæ diametro Verticalis æquidi-<lb/>ſtantes cum diametro Horizontis faciunt, recti ſint, &amp; </s>
  <s xml:id="echoid-s14548" xml:space="preserve">anguli, quos in vtroque Analemmate ra-<lb/>
<anchor type="note" xlink:label="note-0232-05a" xlink:href="note-0232-05"/>
dius cuiusuis ſigni cum eadem diametro Horizontis conſtituit, æquales quoque, vt diximus; </s>
  <s xml:id="echoid-s14549" xml:space="preserve">re-<lb/>perientur ſemper bina triangula in vtroque Analemmate, nempe vnum in vno, &amp; </s>
  <s xml:id="echoid-s14550" xml:space="preserve">alterum in al-<lb/>tero, habentia binos angulos æquales, vtrumque vtrique. </s>
  <s xml:id="echoid-s14551" xml:space="preserve">Cum igitur &amp; </s>
  <s xml:id="echoid-s14552" xml:space="preserve">latus habeant æquale, <lb/>quod dictis angulis adiacet, nempe magnitudinem ſtyli; </s>
  <s xml:id="echoid-s14553" xml:space="preserve">habebunt quoque reliqua latera æqua-<lb/>lia, nimirum illa, quæ inter extremitatem ſtyli, &amp; </s>
  <s xml:id="echoid-s14554" xml:space="preserve">radium cuiuſque ſigni in vtroque Analemma-<lb/>
<anchor type="note" xlink:label="note-0232-06a" xlink:href="note-0232-06"/>
te interijciuntur, &amp;</s>
  <s xml:id="echoid-s14555" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14556" xml:space="preserve">Quod etiam inde patere poteſt; </s>
  <s xml:id="echoid-s14557" xml:space="preserve">quòd ſi Analemma illud maius aut minus <lb/>ſuperponi intelligatur huic noſtro, ita vt centra, &amp; </s>
  <s xml:id="echoid-s14558" xml:space="preserve">diametri Horizontis, Verticalis, atque Æqua-<lb/>toris inter ſe congruant, recta per extremitatem ſtyli in illo ducta congruat rectæ Q R, in noſtro <lb/>Analemmate, propter æqualitatem gnomonum, &amp; </s>
  <s xml:id="echoid-s14559" xml:space="preserve">angulorum rectorum, quos gnomones cum <lb/>dictis rectis conſtituunt. </s>
  <s xml:id="echoid-s14560" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s14561" xml:space="preserve">diametri Eclipticæ oppoſita ſigna connectentes inter ſe <lb/>
<anchor type="note" xlink:label="note-0232-07a" xlink:href="note-0232-07"/>
congruant, (quod eoſdem angulos in vtroque Analemmate cum diametro Æquatoris efficiant, <lb/>propter eaſdem declinationes in vtroque, vt ex conſtructione Analemmatis conſtat) liquido con-<lb/>ſtat, rectas inter extremitatem ſtyli G, &amp; </s>
  <s xml:id="echoid-s14562" xml:space="preserve">radios ſignorum in noſtro Analemmate æquales eſſe eiſ-<lb/>dem rectis in alio Analemmate; </s>
  <s xml:id="echoid-s14563" xml:space="preserve">propterea quòd illę his congruant.</s>
  <s xml:id="echoid-s14564" xml:space="preserve"/>
</p>
<div xml:id="echoid-div734" type="float" level="2" n="2">
<note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">Quo pacto dia-<lb/>metri conicorũ <lb/>ſectionũ in quo <lb/>uis Analemma <lb/>te reperiantur.</note>
  <figure xlink:label="fig-0232-01" xlink:href="fig-0232-01a">
    <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0232-01"/>
  </figure>
<note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">@7. tertĳ.</note>
<note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0232-07" xlink:href="note-0232-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s14565" xml:space="preserve">ITAQVE ſi in lineam meridianam horologii deſcripti, ſiue ex centro H, ſiue ex puncto I, <lb/>vbi Æquatoris planum plano horologii occurrit, transferantur puncta G, K, L, M, I, P, O, N, eo <lb/>ordine, quo in figura poſita ſunt, accepta beneficio circini ex puncto, vbi in Analemmate axis mun <lb/>di, vel diameter Aequatoris rectam, quæ per extremitatem gnomonis ducta eſt diametro Vertica-<lb/>lis æquidiſtans, interſecat; </s>
  <s xml:id="echoid-s14566" xml:space="preserve">erit G, locus ſtyli D G; </s>
  <s xml:id="echoid-s14567" xml:space="preserve">reliqua verò puncta erunt illa, in quæ vmbra ſty-<lb/>li proiicitur, Sole exiſtente in Meridiano circulo, &amp; </s>
  <s xml:id="echoid-s14568" xml:space="preserve">initiis ſignorum, &amp; </s>
  <s xml:id="echoid-s14569" xml:space="preserve">per quæ duci debent coni-<lb/>
<anchor type="note" xlink:label="note-0232-08a" xlink:href="note-0232-08"/>
cæ ſectiones ſignorum, quæ ſunt vel circuli, vel parabolæ, vel hyperbolæ, vel Ellipſes, vt in præce-<lb/>denti lib. </s>
  <s xml:id="echoid-s14570" xml:space="preserve">demonſtratum eſt. </s>
  <s xml:id="echoid-s14571" xml:space="preserve">Si igitur per I, ad meridianam lineam linea perpendicularis duca-<lb/>tur, erit hæc æquinoctialis linea: </s>
  <s xml:id="echoid-s14572" xml:space="preserve">Si vero circa diametros K R, L R, M R, N Q, O Q, P Q, de-<lb/>ſcribantur ex propoſ. </s>
  <s xml:id="echoid-s14573" xml:space="preserve">8. </s>
  <s xml:id="echoid-s14574" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14575" xml:space="preserve">conicæ ſectiones in aliqua materia dura, vt in charta craſſio <lb/>re, vel etiam in tabella quadam exili &amp; </s>
  <s xml:id="echoid-s14576" xml:space="preserve">plana, vel certè in chartis conglutinatis, excindanturq́ue <lb/>vt fiant quædam quaſi regulæ curuæ, per quas eædem ſectiones in horologio deſcribantur, ita vt <lb/>per puncta K, L, M, N, O, P, tranſeant, &amp; </s>
  <s xml:id="echoid-s14577" xml:space="preserve">axes earum lineæ meridianæ cõgruant, deſcripti erunt <lb/>paralleli ſignorum Zodiaci. </s>
  <s xml:id="echoid-s14578" xml:space="preserve">Satis eſt autem, ſi deſcribantur ſectiones conicæ ſignorum Borealiũ, <lb/>vel Auſtralium, quando Verticalis omnes parallelos ſecat; </s>
  <s xml:id="echoid-s14579" xml:space="preserve">quia hæ æquales ſunt ſectionibus ſigno-<lb/>rum oppoſitorum. </s>
  <s xml:id="echoid-s14580" xml:space="preserve">Vnde eiſdem regulis, quas hunc in finem excindi iuſſimus, facile in oppoſita <lb/>parte horologii (Appello nunc partes horologii oppoſitas illas, quas linea æquinoctialis diri-
<pb o="213" file="0233" n="233" rhead="LIBER SECVNDVS."/>
mit, quarum vna borealis eſt, &amp; </s>
  <s xml:id="echoid-s14581" xml:space="preserve">auſtralis altera) deſcribentur.</s>
  <s xml:id="echoid-s14582" xml:space="preserve"/>
</p>
<div xml:id="echoid-div735" type="float" level="2" n="3">
<note position="left" xlink:label="note-0232-08" xlink:href="note-0232-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s14583" xml:space="preserve">CÆTERVM in vtroque horologio ducenda eſt per G, locum gnomonis ad lineam meri-<lb/>
<anchor type="note" xlink:label="note-0233-01a" xlink:href="note-0233-01"/>
dianam perpendicularis A B, quæ quidem communis ſectio erit Horizontis, &amp; </s>
  <s xml:id="echoid-s14584" xml:space="preserve">plani horologij, <lb/>diceturq́ue linea horizontalis. <lb/></s>
  <s xml:id="echoid-s14585" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0233-01a" xlink:href="fig-0233-01"/>
Cum enim &amp; </s>
  <s xml:id="echoid-s14586" xml:space="preserve">plan um horologij <lb/>Verticali propriè dicto æquidi-<lb/>ſtans, &amp; </s>
  <s xml:id="echoid-s14587" xml:space="preserve">planũ Horizontis rectũ <lb/>ſit ad Meridiani planũ, erit quo-<lb/>
<anchor type="note" xlink:label="note-0233-02a" xlink:href="note-0233-02"/>
que communis illorum ſectio <lb/>ad idem planum Meridiani, ac <lb/>
<anchor type="note" xlink:label="note-0233-03a" xlink:href="note-0233-03"/>
proinde, per defi. </s>
  <s xml:id="echoid-s14588" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14589" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14590" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14591" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s14592" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14593" xml:space="preserve">ad meridianam lineam HI, <lb/>in Meridiani plano exiſtentem <lb/>perpendicularis in puncto G, cũ <lb/>in hoc puncto occurrat plano <lb/>Meridiani: </s>
  <s xml:id="echoid-s14594" xml:space="preserve">quod ita oſtendi po-<lb/>teſt. </s>
  <s xml:id="echoid-s14595" xml:space="preserve">Quoniam Horizon per gno <lb/>monem, qui in puncto G, per-<lb/>pendicularis eſt ad planum ho-<lb/>rologij, ductus horologio occur <lb/>
<anchor type="note" xlink:label="note-0233-04a" xlink:href="note-0233-04"/>
rit in G, tranſibit quoque com-<lb/>munis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s14596" xml:space="preserve">ho-<lb/>rologij per idem punctum G. <lb/></s>
  <s xml:id="echoid-s14597" xml:space="preserve">Quare recta A B, quæ in plano <lb/>horologij per G, ad meridianam <lb/>lineam H I, perpendicularis du-<lb/>cta eſt, communis ſectio eſt Hori <lb/>zontis, ac plani horologij, eſtq́; </s>
  <s xml:id="echoid-s14598" xml:space="preserve"><lb/>æquinoctiali lineæ parallela, vt <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s14599" xml:space="preserve">22. </s>
  <s xml:id="echoid-s14600" xml:space="preserve">ſuperioris <lb/>
<anchor type="note" xlink:label="note-0233-05a" xlink:href="note-0233-05"/>
lib. </s>
  <s xml:id="echoid-s14601" xml:space="preserve">tradidimus.</s>
  <s xml:id="echoid-s14602" xml:space="preserve"/>
</p>
<div xml:id="echoid-div736" type="float" level="2" n="4">
<note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" xml:space="preserve">Horizontalis <lb/>linea quid, &amp; <lb/>quomodo in <lb/>horologio Ver-<lb/>ticali ducenda.</note>
  <figure xlink:label="fig-0233-01" xlink:href="fig-0233-01a">
    <image file="0233-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0233-01"/>
  </figure>
<note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0233-03" xlink:href="note-0233-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0233-04" xlink:href="note-0233-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0233-05" xlink:href="note-0233-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s14603" xml:space="preserve">QVONIAM vero Sole exi-<lb/>
<anchor type="note" xlink:label="note-0233-06a" xlink:href="note-0233-06"/>
ſtente in Horizonte, cum videli-<lb/>cet oritur, vel occidit, vmbra ſty-<lb/>li proijcitur in communem ſectionem Horizontis ac plani horologij, hoc eſt, in rectam A B, vt cõ <lb/>ſtar ex propoſ. </s>
  <s xml:id="echoid-s14604" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14605" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s14606" xml:space="preserve">fit, vt toto reliquo tempore cuiuſque diei, cum Sol ſupta Horizon <lb/>tem eleuatus eſt, eadem vmbra cadat in planum horologij infra lineam horizontalem. </s>
  <s xml:id="echoid-s14607" xml:space="preserve">Quare <lb/>in omni horologio reſecanda eſt pars illa, quæ ſupra lineam horizontalem extat, tanquam ſuper-<lb/>uacanea, ita vt in horologio Verticali, quod ad boream ſpectat, ſolum ea particula relinquatur, <lb/>quæ inter horizontalem lineam, &amp; </s>
  <s xml:id="echoid-s14608" xml:space="preserve">arcum, ſeu parallelum ♋, comprehenditur.</s>
  <s xml:id="echoid-s14609" xml:space="preserve"/>
</p>
<div xml:id="echoid-div737" type="float" level="2" n="5">
<note position="right" xlink:label="note-0233-06" xlink:href="note-0233-06a" xml:space="preserve">In omni horo-<lb/>logio portio il-<lb/>la, quæ ſupra li <lb/>neam horizon-<lb/>talem dcſcripta <lb/>eſt, ſuperuaca <lb/>nea eſt, ac pro-<lb/>inde reſecãda.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve">Portio hotolo-<lb/>gii borea lis in-<lb/>fra lineam hori <lb/>zontalem æqua <lb/>lis eſt portioni <lb/>horologii au-<lb/>ſtralis ſupra ho <lb/>rizontalem li-<lb/>neam.</note>
<p>
  <s xml:id="echoid-s14610" xml:space="preserve">HÆC autem pars Verticalis horologij borealis inter lineam horizontalem, &amp; </s>
  <s xml:id="echoid-s14611" xml:space="preserve">arcum ♋, <lb/>cõprehenſa, æqualis omnino eſt illi parti, quam linea horizõtalis ex Auſtrali horologio, tanquam <lb/>ſuperfluã, abſcindit. </s>
  <s xml:id="echoid-s14612" xml:space="preserve">Tantũ enim diſtat in horologio boreali parallelus ♋, ab H, centro horologii, <lb/>quantum ab eodem in Auſtrali parallelus ♑, abeſt, vt conſtat ex Analemmate huius propoſ. </s>
  <s xml:id="echoid-s14613" xml:space="preserve">Quod <lb/>ita probari poteſt. </s>
  <s xml:id="echoid-s14614" xml:space="preserve">Quoniam in triangulo D G K, ad ſiniſtram, duo anguli D, G, æquales ſunt duo <lb/>bus angulis D, G, in triangulo D G N, ad dexteram; </s>
  <s xml:id="echoid-s14615" xml:space="preserve">quòd anguli G, recti ſint, &amp; </s>
  <s xml:id="echoid-s14616" xml:space="preserve">anguli D, ad Ver <lb/>ticem conſtituti, æquales: </s>
  <s xml:id="echoid-s14617" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s14618" xml:space="preserve">latera D G, D G, æqualia, propterea quòd vtrumque gno <lb/>
<anchor type="note" xlink:label="note-0233-09a" xlink:href="note-0233-09"/>
moni eſt æquale; </s>
  <s xml:id="echoid-s14619" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s14620" xml:space="preserve">latera D K, D N, æqualia, &amp; </s>
  <s xml:id="echoid-s14621" xml:space="preserve">anguli reliqui K, N, æquales. </s>
  <s xml:id="echoid-s14622" xml:space="preserve">Quamobrẽ, <lb/>
<anchor type="note" xlink:label="note-0233-10a" xlink:href="note-0233-10"/>
cum in triangulis D H K, D H N, &amp; </s>
  <s xml:id="echoid-s14623" xml:space="preserve">anguli K D H, N D H, ad verticem D, æquales ſint, erun@ <lb/>
<anchor type="note" xlink:label="note-0233-11a" xlink:href="note-0233-11"/>
quoque latera H K, H N, æqualia; </s>
  <s xml:id="echoid-s14624" xml:space="preserve">ac proinde cum per K, tranſeat ſectio conica ♋, in boreali ho-<lb/>
<anchor type="note" xlink:label="note-0233-12a" xlink:href="note-0233-12"/>
<anchor type="note" xlink:label="note-0233-13a" xlink:href="note-0233-13"/>
rologio, &amp; </s>
  <s xml:id="echoid-s14625" xml:space="preserve">per N, ſectio conica ♑, in auſtrali, tantum diſtabit in horologio boreali arcus ♋, ab <lb/>H, quantum diſtat ab eodem puncto H, arcus ♑, in horologio Auſtrali. </s>
  <s xml:id="echoid-s14626" xml:space="preserve">Igitur cum in conis ♋, <lb/>&amp; </s>
  <s xml:id="echoid-s14627" xml:space="preserve">♑, triangula per axem ſint æqualia, Item &amp; </s>
  <s xml:id="echoid-s14628" xml:space="preserve">rectæ D K, D N, &amp; </s>
  <s xml:id="echoid-s14629" xml:space="preserve">anguli D K H, D N H, æquales, <lb/>vt demonſtratum eſt; </s>
  <s xml:id="echoid-s14630" xml:space="preserve">erit ſectio conica ♋, cuins diameter K Q, in horologio boreali, æqualis ſe-<lb/>ctioni conicæ ♑, cuius diameter N Q, in horologio Auſtrali: </s>
  <s xml:id="echoid-s14631" xml:space="preserve">propterea quòd planum illius ho-<lb/>rologij ita ſecat triangulum per axem in cono vmbræ ♋, vt à plano huius horologij ſecatur trian <lb/>gulum per axem in cono vmbræ ♑, ob æqualitatem rectarum D K, D N, &amp; </s>
  <s xml:id="echoid-s14632" xml:space="preserve">angulorum D K H, <lb/>D N H, vt oſtẽſum eſt. </s>
  <s xml:id="echoid-s14633" xml:space="preserve">Si igitur pars illa horologij Auſtralis abſciſſa à linea horizontali ſuperpona <lb/>tur horologio boreali, (ita vt pars illa, quæ nunc eſt ſuperior, fiat inferior, &amp; </s>
  <s xml:id="echoid-s14634" xml:space="preserve">quæ inferior, euadat <lb/>ſuperior; </s>
  <s xml:id="echoid-s14635" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14636" xml:space="preserve">pars quæ dextra eſt, inuerſo hoc modo, vt dictum eſt, horologio, quæ nimirum eſt ver-<lb/>ſus A, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s14637" xml:space="preserve">ſiniſtra ſiat dextra, quemadmodum ſupra demonſtrauimus fieri debere, ſi vo
<pb o="214" file="0234" n="234" rhead="GNOMONICES"/>
lumus, vt Auſtrale horologium indicet etiam horas in facie plani boreali.) </s>
  <s xml:id="echoid-s14638" xml:space="preserve">omnia lineamenta cũ <lb/>
<anchor type="note" xlink:label="note-0234-01a" xlink:href="note-0234-01"/>
numeris inter ſe reſpondebunt, ob æqualitatem rectarum H N, H K, &amp; </s>
  <s xml:id="echoid-s14639" xml:space="preserve">H G, H G, &amp; </s>
  <s xml:id="echoid-s14640" xml:space="preserve">ſectionum <lb/>conicarum, &amp;</s>
  <s xml:id="echoid-s14641" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14642" xml:space="preserve">Quocirca ſatis erit, ſi horologiũ Verticale, quod ad meridiem ſpectat, delineetur, <lb/>vna cum ſignorũ parallelis. </s>
  <s xml:id="echoid-s14643" xml:space="preserve">Nam linea horizõtalis A B, abſc indet portionẽ ex parte ſuperiore, quę <lb/>horologiũ boreale referet, ſi modo talẽ ſortiatur ſitũ in facie plani boreali, vt horizontalis linea in <lb/>ſuperiori loco collocetur, &amp; </s>
  <s xml:id="echoid-s14644" xml:space="preserve">pars dextra, quæ tunc eſt verſus A, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s14645" xml:space="preserve">ſiniſtra fiat dextra. <lb/></s>
  <s xml:id="echoid-s14646" xml:space="preserve">Hæc autẽ inuerſio ita facile fiet. </s>
  <s xml:id="echoid-s14647" xml:space="preserve">Cõuerſo ad nos horologio auſtrali (quod inuerti debet) ita vt pro-<lb/>prium ſuũ ſitum habeat, ac poſitionẽ; </s>
  <s xml:id="echoid-s14648" xml:space="preserve">ſi in facie plani oppoſita, nempe boreali, eadem lineamenta <lb/>
<anchor type="note" xlink:label="note-0234-02a" xlink:href="note-0234-02"/>
deſcribãtur, ita vt nulla in re à lineamentis Auſtralis horologij diſcrepent, ſed eis reſpondeant ad <lb/>vnguem; </s>
  <s xml:id="echoid-s14649" xml:space="preserve">deinde horologium hoc modo in facie oppoſita deſcriptum circumuoluatur circa ſtylũ, <lb/>
<anchor type="note" xlink:label="note-0234-03a" xlink:href="note-0234-03"/>
tanquam axem, in eadem facie oppoſita, donec pars ſuperior euadat inferior, &amp; </s>
  <s xml:id="echoid-s14650" xml:space="preserve">contra, lineaq́; </s>
  <s xml:id="echoid-s14651" xml:space="preserve">ho <lb/>rizontalis Horizonti æquidiſtet, habebimus in oppoſita facie horologium boreale in proprio ſitu, <lb/>ac ſi Auſtrale horologiũ inuerſum fuiſſet, vt diximus; </s>
  <s xml:id="echoid-s14652" xml:space="preserve">hoc eſt, ac ſi ſuperior pars Auſtralis horolo-<lb/>gii in inferiorem, &amp; </s>
  <s xml:id="echoid-s14653" xml:space="preserve">dextra in ſiniſtram fuiſſet commutata: </s>
  <s xml:id="echoid-s14654" xml:space="preserve">vt patet rem attente conſideranti.</s>
  <s xml:id="echoid-s14655" xml:space="preserve"/>
</p>
<div xml:id="echoid-div738" type="float" level="2" n="6">
<note position="right" xlink:label="note-0233-09" xlink:href="note-0233-09a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0233-10" xlink:href="note-0233-10a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0233-11" xlink:href="note-0233-11a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0233-12" xlink:href="note-0233-12a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0233-13" xlink:href="note-0233-13a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">@atis eſt, vt de-<lb/>ſ@ribatur horo-<lb/>logium auſtra-<lb/>le; quia portio <lb/>ſuperior abſciſ-<lb/>ſa à linea hori-<lb/>zõtali d abit ho <lb/>rologium bo-<lb/>reale, ſi omnes <lb/>eius partes in-<lb/>uertantur.</note>
<note position="left" xlink:label="note-0234-02" xlink:href="note-0234-02a" xml:space="preserve">Qu@ pacto in-<lb/>@e@ti debeant <lb/>partes illius por <lb/>tionis horologii <lb/>auſtralis, quam <lb/>horizontalis li-<lb/>nea abſcindit, <lb/>vt exhibeat ho-<lb/>rologiũ borea-<lb/>le.</note>
<note position="left" xlink:label="note-0234-03" xlink:href="note-0234-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s14656" xml:space="preserve">QVOD autem portio illa <lb/>
<anchor type="figure" xlink:label="fig-0234-01a" xlink:href="fig-0234-01"/>
horologii Auſtralis, quam ab-<lb/>ſcindit linea horizontalis ex par <lb/>te ſuperiore, exhibeat nobis ho-<lb/>rologium Boreale, ſi inuertatur, <lb/>vt diximus, hinc etiam perſpi-<lb/>
<anchor type="note" xlink:label="note-0234-04a" xlink:href="note-0234-04"/>
cuum fiet. </s>
  <s xml:id="echoid-s14657" xml:space="preserve">Quoniam, vt in ſcho <lb/>lio præcedentis propoſ. </s>
  <s xml:id="echoid-s14658" xml:space="preserve">demon-<lb/>ſtrauimus, horologium Auſtra-<lb/>le conuerſum, vt ſuperiora fiant <lb/>inferiora, &amp; </s>
  <s xml:id="echoid-s14659" xml:space="preserve">dextra euadant ſini <lb/>ſtra, &amp; </s>
  <s xml:id="echoid-s14660" xml:space="preserve">contra, mutatur in Bo-<lb/>reale; </s>
  <s xml:id="echoid-s14661" xml:space="preserve">eſtq́ue recta A B, commu-<lb/>nis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s14662" xml:space="preserve">horolo-<lb/>gii, vt hic oſtẽſum eſt; </s>
  <s xml:id="echoid-s14663" xml:space="preserve">fit vt pars <lb/>illa, quam horizontalis linea ab-<lb/>
<anchor type="note" xlink:label="note-0234-05a" xlink:href="note-0234-05"/>
ſcindit verſus lineam æquino-<lb/>ctialem, hoc eſt, verſus partem <lb/>ſuperiorem in horologio Borea <lb/>li, (quod factum eſt ex illa inuer <lb/>ſione horologii Auſtralis) ſit ſu <lb/>peruacanea, cum in illam vm-<lb/>bra ſtyli cadere non poſſit. </s>
  <s xml:id="echoid-s14664" xml:space="preserve">Qua-<lb/>re portio reliqua abſciſſa erit ho <lb/>rologium Boreale; </s>
  <s xml:id="echoid-s14665" xml:space="preserve">quod ad li-<lb/>neas horarum attinet. </s>
  <s xml:id="echoid-s14666" xml:space="preserve">Quod ve-<lb/>
<anchor type="note" xlink:label="note-0234-06a" xlink:href="note-0234-06"/>
rò ſpectat ad arcus, parallelosve <lb/>ſignorũ, mutantur arcus ſigno-<lb/>rum horologii Auſtralis in ho-<lb/>rologio boreali in arcus ſigno-<lb/>rum oppoſitorum, vt arcus ♑, <lb/>in arcum ♋, &amp;</s>
  <s xml:id="echoid-s14667" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14668" xml:space="preserve">vt perſpicuum eſt ex Analemmate huius propoſ. </s>
  <s xml:id="echoid-s14669" xml:space="preserve">ſi rectè conſiderentur coni vm-<lb/>
<anchor type="note" xlink:label="note-0234-07a" xlink:href="note-0234-07"/>
bre, quibus planum horologij Auſtralis occurrit, &amp; </s>
  <s xml:id="echoid-s14670" xml:space="preserve">coni vmbræ, quibus occurrit planum Borealis <lb/>horologii. </s>
  <s xml:id="echoid-s14671" xml:space="preserve">Sunt enim huiuſmodi coni vmbræ in vtroque horologio ſignorum oppoſitorum. <lb/></s>
  <s xml:id="echoid-s14672" xml:space="preserve">Vt quemadmodum conus vmbræ, Sole exiſtente in principio ♑, abrumpitur in Auſtrali horolo-<lb/>gio in puncto N, &amp; </s>
  <s xml:id="echoid-s14673" xml:space="preserve">prope locum ſtyli G, ita in horologio Boreali conus vmbræ, Sole exiſtente in <lb/>
<anchor type="note" xlink:label="note-0234-08a" xlink:href="note-0234-08"/>
principio ♋, abrumpitur in puncto K, prope locum etiã ſtyli G, &amp;</s>
  <s xml:id="echoid-s14674" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14675" xml:space="preserve">Idem intelligendũ eſt de arcu <lb/>
<anchor type="note" xlink:label="note-0234-09a" xlink:href="note-0234-09"/>
bus diurnis, de quibus in ſequenti propoſ. </s>
  <s xml:id="echoid-s14676" xml:space="preserve">agemus. </s>
  <s xml:id="echoid-s14677" xml:space="preserve">Mutantur enim &amp; </s>
  <s xml:id="echoid-s14678" xml:space="preserve">hi in arcus diurnos oppoſi-<lb/>tos in horologio boreali. </s>
  <s xml:id="echoid-s14679" xml:space="preserve">Vt arcus diurnus horarũ 10. </s>
  <s xml:id="echoid-s14680" xml:space="preserve">Auſtralis horologii mutatur in horologio <lb/>boreali in arcũ diurnũ horarum 14. </s>
  <s xml:id="echoid-s14681" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s14682" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14683" xml:space="preserve">Sed huius rei aliã cauſam afferemus propoſ. </s>
  <s xml:id="echoid-s14684" xml:space="preserve">21. </s>
  <s xml:id="echoid-s14685" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s14686" xml:space="preserve"/>
</p>
<div xml:id="echoid-div739" type="float" level="2" n="7">
  <figure xlink:label="fig-0234-01" xlink:href="fig-0234-01a">
    <image file="0234-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0234-01"/>
  </figure>
<note position="left" xlink:label="note-0234-04" xlink:href="note-0234-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0234-05" xlink:href="note-0234-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0234-06" xlink:href="note-0234-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0234-07" xlink:href="note-0234-07a" xml:space="preserve">Arcus ſignorũ <lb/>horologii au-<lb/>ſtralis mutan-<lb/>tur in horolo <lb/>gio boreali in <lb/>arcus ſignorum <lb/>oppoſitorum.</note>
<note position="left" xlink:label="note-0234-08" xlink:href="note-0234-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0234-09" xlink:href="note-0234-09a" xml:space="preserve">Arcus quoque <lb/>diurni horolo-<lb/>gii auſtralis mu <lb/>tantur in borea <lb/>li horologio in <lb/>arcus diurnos <lb/>oppoſitos.</note>
</div>
<p>
  <s xml:id="echoid-s14687" xml:space="preserve">PORRO horizontalis linea pulchrè demonſtrat, quanam hora Sol in quolibet parallelo exi-<lb/>ſtens oriatur, aut occidat. </s>
  <s xml:id="echoid-s14688" xml:space="preserve">Nam vbi ſectiones conicæ ſecant lineam horizontalem, ibi Sol oritur <lb/>
<anchor type="note" xlink:label="note-0234-10a" xlink:href="note-0234-10"/>
vel occidit exiſtens in illis parallelis, quos dictæ ſectiones referunt. </s>
  <s xml:id="echoid-s14689" xml:space="preserve">Si igitur per illa puncta, vbi <lb/>ſe mutuo ſecant linea horizontalis, &amp; </s>
  <s xml:id="echoid-s14690" xml:space="preserve">ſectiones conicę, lineæ horariæ ducantur indicabunt hæ tem <lb/>pus ortus &amp; </s>
  <s xml:id="echoid-s14691" xml:space="preserve">occaſus Solis, &amp;</s>
  <s xml:id="echoid-s14692" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14693" xml:space="preserve">Ita vides in horologio Auſtrali, Solem exiſtentẽ in principio ♑, ori-<lb/>ri circa horam 7 {1/2}. </s>
  <s xml:id="echoid-s14694" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s14695" xml:space="preserve">occidere circ a horam 4 {1/2}. </s>
  <s xml:id="echoid-s14696" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s14697" xml:space="preserve">In ♒, verò &amp; </s>
  <s xml:id="echoid-s14698" xml:space="preserve">♐, eun-<lb/>dem oriri paulo ante horam 7 {1/2}. </s>
  <s xml:id="echoid-s14699" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s14700" xml:space="preserve">occidere paulo poſt horam 4 {1/2}. </s>
  <s xml:id="echoid-s14701" xml:space="preserve">à meridie.</s>
  <s xml:id="echoid-s14702" xml:space="preserve">
<pb o="215" file="0235" n="235" rhead="LIBER SECVNDVS."/>
In ♓, denique &amp; </s>
  <s xml:id="echoid-s14703" xml:space="preserve">♏, eundẽ oriri paulò ante ſeptimam horá à media nocte, &amp; </s>
  <s xml:id="echoid-s14704" xml:space="preserve">occidere paulo poſt <lb/>horam 5. </s>
  <s xml:id="echoid-s14705" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s14706" xml:space="preserve">Sic quoque vides in boreali horologio, Solem in principio ♋, exiſtentem <lb/>oriri circam horam 4 {1/2}. </s>
  <s xml:id="echoid-s14707" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s14708" xml:space="preserve">occidere circa horam 7 {1/2}. </s>
  <s xml:id="echoid-s14709" xml:space="preserve">à meridie, &amp;</s>
  <s xml:id="echoid-s14710" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14711" xml:space="preserve">Idem officiũ <lb/>habet linea horizontalis in omnibus alijs horologijs, excepto horizontali, in quo linea horizonta-<lb/>lis duci non poteſt, vt conſtat ex ſcholio propoſ. </s>
  <s xml:id="echoid-s14712" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14713" xml:space="preserve">ſuperioris lib.</s>
  <s xml:id="echoid-s14714" xml:space="preserve"/>
</p>
<div xml:id="echoid-div740" type="float" level="2" n="8">
<note position="left" xlink:label="note-0234-10" xlink:href="note-0234-10a" xml:space="preserve">Horizontalis li <lb/>nea indicat, qua <lb/>hora Sol otia-<lb/>@ur, vel occidat.</note>
</div>
<p>
  <s xml:id="echoid-s14715" xml:space="preserve">HIC autem, &amp; </s>
  <s xml:id="echoid-s14716" xml:space="preserve">in omnibus alijs ſequentibus horologijs, in quibus horizontalis linea ducitur, <lb/>
<anchor type="note" xlink:label="note-0235-01a" xlink:href="note-0235-01"/>
animaduertendum eſt, lineam horizontalem diſtribuere etiam totum horologium in duas par-<lb/>tes, quarum ea, quæ infra ipſam eſt, interdiu horas commonſtrat, quamdiu à Sole illuſtratur; </s>
  <s xml:id="echoid-s14717" xml:space="preserve">illa <lb/>verò, quæ ſupra horizontalem lineã eſt poſita, noctu, hoc eſt, mane ante aſcenſum Solis ſupra Ho-<lb/>rizontem, vel veſperi poſt deſcenſum Solis ſub Horizontem horas indicaret, ſi, ablato impedimen <lb/>
<anchor type="note" xlink:label="note-0235-02a" xlink:href="note-0235-02"/>
<anchor type="note" xlink:label="note-0235-03a" xlink:href="note-0235-03"/>
to terræ, Sol eam poſſet illuminare. </s>
  <s xml:id="echoid-s14718" xml:space="preserve">Quemadmodum enim, Sole ſupra Horizontem exiſtente, in-<lb/>terdiu vmbra ſtyli proiicitur infra horizontalem lineam, in ipſam verò lineam horizontalem, cũ <lb/>in ipſo Horizonte fuerit conſtitutus ſiue mane, ſiue veſperi; </s>
  <s xml:id="echoid-s14719" xml:space="preserve">ita eodem exiſtente ſub Horizonte, <lb/>vmbra gnomonis ſupra lineam horizontalem caderet tam mane, quàm veſperi, ſi planum horolo <lb/>gii tunc temporis à Sole illuminaretur. </s>
  <s xml:id="echoid-s14720" xml:space="preserve">Itaque nõ ineptè priorem partem horologii auſtralis, quæ <lb/>nimirũ infra horizontalẽ lineam exiſtit, horologiũ diurnũ appellabimus, omnesq́, arcus ſignorũ, <lb/>&amp; </s>
  <s xml:id="echoid-s14721" xml:space="preserve">dierũ in c<unsure/>o contentos dicemus arcus diurnos; </s>
  <s xml:id="echoid-s14722" xml:space="preserve">poſteriorem autem partem ſupra lineam hori-<lb/>zontalẽ contentam, horologiũ nocturnũ, omnesq́; </s>
  <s xml:id="echoid-s14723" xml:space="preserve">arcus, quos horizontalis linea abſcindit, no-<lb/>cturnos dicere licebit: </s>
  <s xml:id="echoid-s14724" xml:space="preserve">ita vt arcus nocturni ſint cõplementa arcuum diurnorum vſque ad 24. </s>
  <s xml:id="echoid-s14725" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14726" xml:space="preserve"><lb/>contra, hoc eſt, ſi v. </s>
  <s xml:id="echoid-s14727" xml:space="preserve">g. </s>
  <s xml:id="echoid-s14728" xml:space="preserve">arcus diurnus comprehendit horas 10. </s>
  <s xml:id="echoid-s14729" xml:space="preserve">nocturnus complectatur 14. </s>
  <s xml:id="echoid-s14730" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14731" xml:space="preserve">c.</s>
  <s xml:id="echoid-s14732" xml:space="preserve"/>
</p>
<div xml:id="echoid-div741" type="float" level="2" n="9">
<note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">Horizontalis li <lb/>nea diſtribuit <lb/>totum horolo-<lb/>gium in portio <lb/>nem diurnam, <lb/>&amp; nocturnam.</note>
<note position="left" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0235-03" xlink:href="note-0235-03a" xml:space="preserve">Portio horolo-<lb/>gii infra lineã <lb/>horizontalem <lb/>dicitur horolo-<lb/>gium diurnũ, <lb/>&amp; arcus ſigno-<lb/>rum, ac dierum <lb/>appellantur ar-<lb/>cus diurni. Por <lb/>tio vero eiuſdẽ <lb/>ſupra lineã ho-<lb/>rizontalem di-<lb/>citur horologiũ <lb/>nocturnum, &amp; <lb/>arcus ſignorũ <lb/>ac dierũ uocan <lb/>tur arcus no-<lb/>cturni.</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s14733" xml:space="preserve">EADEM ratione in horologio boreali, quod diximus eſſe illam portionem, quæ à linea ho-<lb/>rizontali abſcinditur, ſi tamen inuertatur, vt ſupra diximus, arcus, qui ſunt in eo, diurni; </s>
  <s xml:id="echoid-s14734" xml:space="preserve">qui ve-<lb/>
<anchor type="note" xlink:label="note-0235-05a" xlink:href="note-0235-05"/>
rò ſupra lineam horizontalem, quales ſunt omnes illi, qui in auſtrali horologio includuntur, no-<lb/>cturni dicendi erunt: </s>
  <s xml:id="echoid-s14735" xml:space="preserve">ita vt linea æquinoctialis, quæ in horologio boreali ſupra lineam horizon-<lb/>talem exiſtit, ſit arcus nocturnus horarum 12. </s>
  <s xml:id="echoid-s14736" xml:space="preserve">cum in auſtrali horologio eadem ſit arcus diurnus <lb/>horarum 12. </s>
  <s xml:id="echoid-s14737" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14738" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s14739" xml:space="preserve">Quæ res mirificum vſum habebit in deſcriptione horarum ab or-<lb/>tu, vel occaſu, vt ſuo loco docebimus.</s>
  <s xml:id="echoid-s14740" xml:space="preserve"/>
</p>
<div xml:id="echoid-div742" type="float" level="2" n="10">
<note position="right" xlink:label="note-0235-05" xlink:href="note-0235-05a" xml:space="preserve">Arcus nocturni <lb/>ſunt complemẽ <lb/>ta arcuum diur <lb/>norũ vſque ad <lb/>24. &amp; contra.</note>
</div>
<note position="right" xml:space="preserve">Qua ratione ex <lb/>Anal ẽmate hu <lb/>ius ꝓpoſ. in ho-<lb/>rologio deſcri-<lb/>bantur arcus ſi <lb/>gnorum ad ma <lb/>@orẽ, minorẽve <lb/>longitudinem <lb/>gnomonis.</note>
<p>
  <s xml:id="echoid-s14741" xml:space="preserve">QVOD ſi maius, vel minus horologium deſcribendum fuerit, ſumendus erit longior, aut <lb/>breuior ſtylus D M, in Analemmate huius propoſ. </s>
  <s xml:id="echoid-s14742" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s14743" xml:space="preserve">per M, parallela ducenda ipſi A D. </s>
  <s xml:id="echoid-s14744" xml:space="preserve">Ita enim <lb/>inuenientur maiores, minoresve diametri conicarum ſectionũ, circa quas eodem modo ſectiones <lb/>
<anchor type="note" xlink:label="note-0235-07a" xlink:href="note-0235-07"/>
ipſæ conicæ deſcribi poſſunt. </s>
  <s xml:id="echoid-s14745" xml:space="preserve">Sed ęquinoctialis linea in meridiana linea tãto interuallo debet diſta <lb/>re à cẽtro H, quãta eſt portio parallelæ per M, ductæ inter puncta, vbi ab axe DE, &amp; </s>
  <s xml:id="echoid-s14746" xml:space="preserve">radio Æ quato-<lb/>ris F D, ſecatur. </s>
  <s xml:id="echoid-s14747" xml:space="preserve">Lineæ autem horariæ non mutantur, ſed eædẽ permanent, in eadẽ altitudine poli.</s>
  <s xml:id="echoid-s14748" xml:space="preserve"/>
</p>
<div xml:id="echoid-div743" type="float" level="2" n="11">
<note position="left" xlink:label="note-0235-07" xlink:href="note-0235-07a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s14749" xml:space="preserve">DESCRIBI quoque <lb/>
<anchor type="figure" xlink:label="fig-0235-01a" xlink:href="fig-0235-01"/>
<anchor type="note" xlink:label="note-0235-08a" xlink:href="note-0235-08"/>
poſſunt arcus ſignorũ hac ra-<lb/>tione. </s>
  <s xml:id="echoid-s14750" xml:space="preserve">Circa rectam D H, vt-<lb/>cunque ductam, quæ mundi <lb/>axem referat, ex quolibet pun <lb/>cto D, vt centro ſemicirculus <lb/>deſcribatur cuiuſcunque ma-<lb/>
<anchor type="note" xlink:label="note-0235-09a" xlink:href="note-0235-09"/>
gnitudinis, ſitq́ue D H, ex par-<lb/>te dextra ipſius D, æqualis aſ-<lb/>ſumpto axi D H, in portione <lb/>Analẽmatis præcedentis pro-<lb/>poſ. </s>
  <s xml:id="echoid-s14751" xml:space="preserve">vel in triangulo H D I, ex <lb/>quo ad ſinem ſcholij eiuſdem <lb/>propoſ. </s>
  <s xml:id="echoid-s14752" xml:space="preserve">horologium ſine por-<lb/>tione Analemmatis deſcripſi-<lb/>mus; </s>
  <s xml:id="echoid-s14753" xml:space="preserve">ductaq́; </s>
  <s xml:id="echoid-s14754" xml:space="preserve">D C, pro radio <lb/>Æquatoris perpendiculari ad <lb/>
<anchor type="note" xlink:label="note-0235-10a" xlink:href="note-0235-10"/>
axem D H, ſumatur D I, æqui <lb/>noctiali lineæ D I, eiuſdẽ por-<lb/>tionis Analemmatis, vel dicti <lb/>trianguli H D I, æqualis, duca <lb/>turq́ue recta H I, ad partes I, <lb/>quantumlibet, vel certè (ne <lb/>error committatur in ducen-<lb/>da recta H I, ob propinquita-<lb/>tem punctorum H, &amp; </s>
  <s xml:id="echoid-s14755" xml:space="preserve">I,) ex <lb/>puncto H, deſcribatur arcus <lb/>ad partes D, in quo ſumatur-
<pb o="216" file="0236" n="236" rhead="GNOMONICES"/>
A B, verſus rectam D C, æqualis complemento altitudinis poli ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s14756" xml:space="preserve">per B, duca-<lb/>tur recta H B, ſecans æquinoctialem lineam D C, in I. </s>
  <s xml:id="echoid-s14757" xml:space="preserve">Erit triangulum D H I, omnino æquàle triã <lb/>gulo D H I, præfatæ portionis Analemmatis, vel triangulo horologij ſine portione Analemmatis <lb/>deſcripti, &amp; </s>
  <s xml:id="echoid-s14758" xml:space="preserve">H I, æqualis lineæ meridianæ H I, eiuſdem portionis Analemmatis, vel dicti triangu-<lb/>
<anchor type="figure" xlink:label="fig-0236-01a" xlink:href="fig-0236-01"/>
li, vt ex vtraque conſtructio-<lb/>ne huius trianguli in hac ſigu <lb/>ra conſtat. </s>
  <s xml:id="echoid-s14759" xml:space="preserve">Ex priori enim cõ <lb/>ſtructione, ſunt duo latera <lb/>D H, D I, huius triãguli duo-<lb/>bus lateribus D H, D I, illius <lb/>
<anchor type="note" xlink:label="note-0236-01a" xlink:href="note-0236-01"/>
æqualia, angulosq́ continent <lb/>æquales, vtpote rectos. </s>
  <s xml:id="echoid-s14760" xml:space="preserve">Igitur <lb/>tota triangula æqualia ſunt. <lb/></s>
  <s xml:id="echoid-s14761" xml:space="preserve">Ex conſtructione vero poſte-<lb/>
<anchor type="note" xlink:label="note-0236-02a" xlink:href="note-0236-02"/>
riori, ſunt duo anguli H D I, <lb/>D H I, vnius trianguli duo-<lb/>bus angulis H D I, D H I, alte-<lb/>rius trianguli æquales, (quòd <lb/>in vtroque triangulo prior an <lb/>gulus rectus ſit, &amp; </s>
  <s xml:id="echoid-s14762" xml:space="preserve">poſterior <lb/>
<anchor type="note" xlink:label="note-0236-03a" xlink:href="note-0236-03"/>
complemento altitudinis po-<lb/>li æqualis) eſtq́ue latus D H, <lb/>vnius lateri DH, alterius equa <lb/>le. </s>
  <s xml:id="echoid-s14763" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s14764" xml:space="preserve">latera D I, H I, <lb/>vnius æqualia ſunt lateribus <lb/>
<anchor type="note" xlink:label="note-0236-04a" xlink:href="note-0236-04"/>
D I, H I, alterius, &amp;</s>
  <s xml:id="echoid-s14765" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14766" xml:space="preserve">Ex cẽtro <lb/>deinde E, Aequatoris in ho-<lb/>rologio, ex quo videlicet cir-<lb/>culus fuit deſcriptus, diui-<lb/>ſusq́; </s>
  <s xml:id="echoid-s14767" xml:space="preserve">in partes 24. </s>
  <s xml:id="echoid-s14768" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s14769" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14770" xml:space="preserve">tranſ-<lb/>
<anchor type="note" xlink:label="note-0236-05a" xlink:href="note-0236-05"/>
ferantur omnia interualla in-<lb/>ter centrum E, &amp; </s>
  <s xml:id="echoid-s14771" xml:space="preserve">lineas hora <lb/>rias in linea æquinoctiali F K, poſita in lineam D C, huius figuræ, quam nunc conſtruimus, à pun <lb/>cto D; </s>
  <s xml:id="echoid-s14772" xml:space="preserve">Nempe interuallo E F, vel E K, in horologio præcedẽti propoſ. </s>
  <s xml:id="echoid-s14773" xml:space="preserve">deſcripto (quę æqualia ſunt, <lb/>quemadmodum &amp; </s>
  <s xml:id="echoid-s14774" xml:space="preserve">quęcunque interualla inter E, &amp; </s>
  <s xml:id="echoid-s14775" xml:space="preserve">binas horas æquali temporis ſpatio à meridia <lb/>na linea diſtantes, vt conſtat ex ſcholio præcedentis propoſ.) </s>
  <s xml:id="echoid-s14776" xml:space="preserve">æqualis ſit recta D C, &amp; </s>
  <s xml:id="echoid-s14777" xml:space="preserve">interuallo <lb/>E R, vel E S, æqualis ſit recta D T, &amp;</s>
  <s xml:id="echoid-s14778" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14779" xml:space="preserve">Per puncta autem C, T, &amp; </s>
  <s xml:id="echoid-s14780" xml:space="preserve">reliqua in linea D C, inuenta, ex <lb/>H, emittantur rectæ, quibus aſcribantur numeri horarum reſpondentes aſſumptis interuallis, ita <lb/>vt recta H C, ſit linea ſeptimæ horæ poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s14781" xml:space="preserve">quintæ poſt meridiem; </s>
  <s xml:id="echoid-s14782" xml:space="preserve">H T, horæ <lb/>octauæ poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s14783" xml:space="preserve">quartæ poſt meridiem, &amp;</s>
  <s xml:id="echoid-s14784" xml:space="preserve">c.</s>
  <s xml:id="echoid-s14785" xml:space="preserve"/>
</p>
<div xml:id="echoid-div744" type="float" level="2" n="12">
  <figure xlink:label="fig-0235-01" xlink:href="fig-0235-01a">
    <image file="0235-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0235-01"/>
  </figure>
<note position="right" xlink:label="note-0235-08" xlink:href="note-0235-08a" xml:space="preserve">Alia deſcriptio <lb/>arcuũ ſignorũ <lb/>Zodiaci in ho-<lb/>sologi@ Ver@@-<lb/><gap/>.</note>
<note position="left" xlink:label="note-0235-09" xlink:href="note-0235-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0235-10" xlink:href="note-0235-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0236-01" xlink:href="fig-0236-01a">
    <image file="0236-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0236-01"/>
  </figure>
<note position="left" xlink:label="note-0236-01" xlink:href="note-0236-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0236-02" xlink:href="note-0236-02a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0236-04" xlink:href="note-0236-04a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0236-05" xlink:href="note-0236-05a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s14786" xml:space="preserve">HAS autem eaſdem lineas horarias ex H, emiſſas ducemus quoque, ſi interualla horarum in <lb/>horologio inter centrum H, &amp; </s>
  <s xml:id="echoid-s14787" xml:space="preserve">æquinoctialem lineam transferamus in radium Æquatoris huius <lb/>figuræ ex H. </s>
  <s xml:id="echoid-s14788" xml:space="preserve">Inueniemus enim hac ratione in radio Æquatoris eadem puncta, quæ prius, per <lb/>quæ horariæ lineæ ex H, emiſſæ ſunt, vt propoſ. </s>
  <s xml:id="echoid-s14789" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14790" xml:space="preserve">huius libri de horologio horizontali de-<lb/>monſtrauimus.</s>
  <s xml:id="echoid-s14791" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s14792" xml:space="preserve">PRO hora autem ſexta à mer, vel med. </s>
  <s xml:id="echoid-s14793" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s14794" xml:space="preserve">ducatur ex H, ipſi D C, parallela H V. </s>
  <s xml:id="echoid-s14795" xml:space="preserve">Et pro ho-<lb/>ra quinta poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s14796" xml:space="preserve">ſeptimam poſt meridiem, ducatur H X, angulum V H X, æqua-<lb/>lem faciens angulo V H C. </s>
  <s xml:id="echoid-s14797" xml:space="preserve">Simili modo pro hora quarta poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s14798" xml:space="preserve">octaua poſt <lb/>meridiem, ducatur H Y, faciens angulum V H Y, angulo V H T, æqualem, &amp; </s>
  <s xml:id="echoid-s14799" xml:space="preserve">ſic de cęteris. <lb/></s>
  <s xml:id="echoid-s14800" xml:space="preserve">Quod facile fiet, ſi ex H, arcus circuli deſcribatur. </s>
  <s xml:id="echoid-s14801" xml:space="preserve">Nam ſi circunſerentiæ huius arcus inter-<lb/>
<anchor type="note" xlink:label="note-0236-07a" xlink:href="note-0236-07"/>
ceptæ inter H V, &amp; </s>
  <s xml:id="echoid-s14802" xml:space="preserve">rectas ex H, ad ſiniſtram ipſius H V, eductas, (quæ nimirum rectam D C, ſe-<lb/>cant) transferantur ad dexteram eiuſdem H V, in dictum arcum, &amp;</s>
  <s xml:id="echoid-s14803" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14804" xml:space="preserve">vt in horologio horizon-<lb/>tali diximus.</s>
  <s xml:id="echoid-s14805" xml:space="preserve"/>
</p>
<div xml:id="echoid-div745" type="float" level="2" n="13">
<note position="left" xlink:label="note-0236-07" xlink:href="note-0236-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s14806" xml:space="preserve">POST hæc ex puncto D, ducantur radij ſignorum, vt in horologio horizontali dictum eft, <lb/>propoſ. </s>
  <s xml:id="echoid-s14807" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14808" xml:space="preserve">huius libri.</s>
  <s xml:id="echoid-s14809" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s14810" xml:space="preserve">EX hac ergo figura non ſecus ac in horologio horizontali arcus ſignorum deſcribemus; </s>
  <s xml:id="echoid-s14811" xml:space="preserve">tranſ-<lb/>ferendo ſcilicet interualla horaria huius figuræ intercepta inter H, &amp; </s>
  <s xml:id="echoid-s14812" xml:space="preserve">radios ſignorum, in horas <lb/>horologij ex centro H, &amp;</s>
  <s xml:id="echoid-s14813" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14814" xml:space="preserve">Qua de re vide ea, quæ propoſ. </s>
  <s xml:id="echoid-s14815" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14816" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14817" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s14818" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s14819" xml:space="preserve">IN deſcriptione arcuum ſignorum in boreali horologio mutantur radii ſignorum auſtralium <lb/>in radios borealium, &amp; </s>
  <s xml:id="echoid-s14820" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s14821" xml:space="preserve">Vt ex radio ♑, fit radius ♋, ex ♐, fit ♊, &amp;</s>
  <s xml:id="echoid-s14822" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14823" xml:space="preserve">Quod etiam de radijs <lb/>arcuum diurnorum, de quibus in propoſ. </s>
  <s xml:id="echoid-s14824" xml:space="preserve">ſequenti dicemus, intelligendum eſt. </s>
  <s xml:id="echoid-s14825" xml:space="preserve">Quoniam videli-
<pb o="217" file="0237" n="237" rhead="LIBER SECVNDVS."/>
cet &amp; </s>
  <s xml:id="echoid-s14826" xml:space="preserve">arcus auſtrales horologii auſtralis mutantur in boreali horologio in arcus boreales, &amp; </s>
  <s xml:id="echoid-s14827" xml:space="preserve">con-<lb/>tra, vt ſupra dictum eſt.</s>
  <s xml:id="echoid-s14828" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s14829" xml:space="preserve">DEMONSTRATIO autem huius rei non differt ab ea, quam in horologio horizontali <lb/>adduximus propoſ. </s>
  <s xml:id="echoid-s14830" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14831" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s14832" xml:space="preserve">Eſtenim &amp; </s>
  <s xml:id="echoid-s14833" xml:space="preserve">Verticalis circulus Horizon quidam, &amp; </s>
  <s xml:id="echoid-s14834" xml:space="preserve">angulus <lb/>D H I, æqualis altitudini poli ſupra ipſum, vt conſtat. </s>
  <s xml:id="echoid-s14835" xml:space="preserve">Quare eadem erit demonſtratio in vtro-<lb/>que horologio.</s>
  <s xml:id="echoid-s14836" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s14837" xml:space="preserve">CÆTERVM in horologio Auſtrali arcus ſignorum auſtralium continentur inter centrũ <lb/>
<anchor type="note" xlink:label="note-0237-01a" xlink:href="note-0237-01"/>
horologii, &amp; </s>
  <s xml:id="echoid-s14838" xml:space="preserve">lineam æquinoctialem, borealium vero vltra lineam æquinoctialem: </s>
  <s xml:id="echoid-s14839" xml:space="preserve">In boreali au-<lb/>tem horologio contrario modo ſe res habet; </s>
  <s xml:id="echoid-s14840" xml:space="preserve">vt ex Analemmate huius propoſ. </s>
  <s xml:id="echoid-s14841" xml:space="preserve">colligitur. </s>
  <s xml:id="echoid-s14842" xml:space="preserve">Idem <lb/>etiam hinc apparere poteſt, quòd Sol in auſtralibus ſignis exiſtens breuiores vmbras facit in horo-<lb/>
<anchor type="note" xlink:label="note-0237-02a" xlink:href="note-0237-02"/>
gio auſtrali circa meridiem, quàm cum in borealibus ſignis moratur: </s>
  <s xml:id="echoid-s14843" xml:space="preserve">quia in his maiores meridia <lb/>nas altitudines habet, quàm in illis. </s>
  <s xml:id="echoid-s14844" xml:space="preserve">Vnde cum breuiores vmbræ meridianæ fiant inter centrum <lb/>horologii auſtralis, &amp; </s>
  <s xml:id="echoid-s14845" xml:space="preserve">lineam æquinoctialem, longiores autem vltra eandem lineam æquinoctia-<lb/>lem; </s>
  <s xml:id="echoid-s14846" xml:space="preserve">perſpicuum eſt, ſigna auſtralia eſſe inter centrum &amp; </s>
  <s xml:id="echoid-s14847" xml:space="preserve">æquinoctialem lineam, borealia vero <lb/>vltra lineam æquinoctialem, &amp;</s>
  <s xml:id="echoid-s14848" xml:space="preserve">c.</s>
  <s xml:id="echoid-s14849" xml:space="preserve"/>
</p>
<div xml:id="echoid-div746" type="float" level="2" n="14">
<note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">Qni arcus ad <lb/>ſigna auſtralia, <lb/>&amp; qui ad borea <lb/>lia pertineant.</note>
<note position="left" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s14850" xml:space="preserve">QVORVM autem ſignorum arcus ſint hyperbolæ, vel parabolæ, aut Ellipſes, percipiemus <lb/>exiis, quæ propoſ. </s>
  <s xml:id="echoid-s14851" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14852" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14853" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s14854" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Quomodo ex <lb/>uno arcu oppo-<lb/>ſicus arcus de-<lb/>ſcribatur, &amp;c.</note>
<p>
  <s xml:id="echoid-s14855" xml:space="preserve">HIC etiam commodius, &amp; </s>
  <s xml:id="echoid-s14856" xml:space="preserve">accuratius deſcribemus hyperbolas ſignorum borealium infra li-<lb/>neam æquinoctialem, beneficio hyperbolarum ſignorum auſtralium ſupra lineam æquinoctialem <lb/>deſcriptarum; </s>
  <s xml:id="echoid-s14857" xml:space="preserve">ſi per doctrinam, quam propoſ. </s>
  <s xml:id="echoid-s14858" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14859" xml:space="preserve">huius libri tradidimus, prius inueniantur dia-<lb/>
<anchor type="note" xlink:label="note-0237-04a" xlink:href="note-0237-04"/>
metri tranſuerſæ ſectionum oppoſitarum, earumq́; </s>
  <s xml:id="echoid-s14860" xml:space="preserve">centra, &amp;</s>
  <s xml:id="echoid-s14861" xml:space="preserve">c.</s>
  <s xml:id="echoid-s14862" xml:space="preserve"/>
</p>
<div xml:id="echoid-div747" type="float" level="2" n="15">
<note position="left" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s14863" xml:space="preserve">POSSVMVS quoque vti duobus illis modis, quos ad finem eiuſdem propoſ. </s>
  <s xml:id="echoid-s14864" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14865" xml:space="preserve">huius libri <lb/>ſcripſimus. </s>
  <s xml:id="echoid-s14866" xml:space="preserve">Qua de re conſule ea, quæ ibi tradidimus. </s>
  <s xml:id="echoid-s14867" xml:space="preserve">Parallelos igitur, ſiue arcus ſignorum Zo-<lb/>diaci in Verticali horologio prædicto deſcripſimus. </s>
  <s xml:id="echoid-s14868" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s14869" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div749" type="section" level="1" n="180">
<head xml:id="echoid-head183" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s14870" xml:space="preserve">HOC modo eaſdem lineas horarias præcedentis figuræ ex H, egredientes deſcribit Andreas Schone <lb/>
<anchor type="note" xlink:label="note-0237-05a" xlink:href="note-0237-05"/>
rus. </s>
  <s xml:id="echoid-s14871" xml:space="preserve">Ducta recta H I B, quæ conſtituat angulum A H B, æqualem complemẽto altitudinis poli ſupra Ho <lb/>rizontem, vel ipſi altitudini poli ſupra Verticalem circulũ, vt &amp; </s>
  <s xml:id="echoid-s14872" xml:space="preserve">nos fecimus, ſumit in ea punctũ quod-<lb/>
<anchor type="note" xlink:label="note-0237-06a" xlink:href="note-0237-06"/>
cunque φ, per quod ipſi D H, parallelam agit φ V, quæ rectã ductam ex H, ipſi D C, parallelã ſecet in <lb/>V, puncto, è quo, vt centro, interuallo {q́ue} V φ, circulum deſcribit. </s>
  <s xml:id="echoid-s14873" xml:space="preserve">Hoc diuiſo in partes 24. </s>
  <s xml:id="echoid-s14874" xml:space="preserve">æquales, eadẽ <lb/>facit, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s14875" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14876" xml:space="preserve">huius libri de borizontali horologio docuimus.</s>
  <s xml:id="echoid-s14877" xml:space="preserve"/>
</p>
<div xml:id="echoid-div749" type="float" level="2" n="1">
<note position="right" xlink:label="note-0237-05" xlink:href="note-0237-05a" xml:space="preserve">Praxis pulcher-<lb/>rima pro lineis <lb/>horariis in figu <lb/>ra radioiũ Zo-<lb/>diaei ducendis, <lb/>ſine interuallis <lb/>horariis horo-<lb/>logii.</note>
<note position="left" xlink:label="note-0237-06" xlink:href="note-0237-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s14878" xml:space="preserve">EX figura autem radiorum conſtructa, vt docet Andreas Schonerus, deſcribi poterit horologiũ Ver <lb/>
<anchor type="note" xlink:label="note-0237-07a" xlink:href="note-0237-07"/>
ticale ad datam ſtyli magnitudinem, vt de horizontali diximus in ſcholio propoſ. </s>
  <s xml:id="echoid-s14879" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14880" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s14881" xml:space="preserve">dummodo <lb/>angulus ρ D H, æqualis fiat altitudini poli, non autem eius complemento, vt in horizont ali horologio.</s>
  <s xml:id="echoid-s14882" xml:space="preserve"/>
</p>
<div xml:id="echoid-div750" type="float" level="2" n="2">
<note position="right" xlink:label="note-0237-07" xlink:href="note-0237-07a" xml:space="preserve">Deſcriptio ho-<lb/>rologii<unsure/> Vertica <lb/>lis ex figura ra-<lb/>diorũ Andreæ <lb/>Schoneri.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14883" xml:space="preserve">STYLVS iuxta poſteriorem modum deſcribendi parallelos ſignorum, qui per figur am radiorum Zo <lb/>
<anchor type="note" xlink:label="note-0237-08a" xlink:href="note-0237-08"/>
diaci abſoluitur, habetur, ſi ex D, ad H I, perpendicularis ducatur D ρ, vel certe recta D ρ, faciens angu <lb/>lum ρ D I, æqualem angulo complemento altitudinis poli ſupra Horizontem. </s>
  <s xml:id="echoid-s14884" xml:space="preserve">Longitudo enim ſtyli eſt ip-<lb/>ſa recta D ρ: </s>
  <s xml:id="echoid-s14885" xml:space="preserve">Locus vero eius eſt punctum ρ, diſtans ab H, centro horologĳ interuallo H ρ, in linea me <lb/>
<anchor type="note" xlink:label="note-0237-09a" xlink:href="note-0237-09"/>
ridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana, verſus centrum H.</s>
  <s xml:id="echoid-s14886" xml:space="preserve"/>
</p>
<div xml:id="echoid-div751" type="float" level="2" n="3">
<note position="right" xlink:label="note-0237-08" xlink:href="note-0237-08a" xml:space="preserve">Qua ratione ex <lb/>figura radiorũ <lb/>longitudo ſtyli, <lb/>eiusq́; locus in <lb/>horologio inue <lb/>niatur.</note>
<note position="left" xlink:label="note-0237-09" xlink:href="note-0237-09a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s14887" xml:space="preserve">DESCRIPTIS autem lineis horarĳs in proxime antecedenti figura ex puncto H, ſi ſecundum <lb/>
<anchor type="note" xlink:label="note-0237-10a" xlink:href="note-0237-10"/>
poſteriorem hunc modum ex dicta figura radiorum zodiaci deſumptum, maius, aut minus horologium cõ <lb/>ſtruendum ſit, deſcribenda erit figura radiorum Zodiaci magis, vel minus diſtans à puncto H, &amp;</s>
  <s xml:id="echoid-s14888" xml:space="preserve">c. </s>
  <s xml:id="echoid-s14889" xml:space="preserve">vt de <lb/>horologio Horizontali dictum eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s14890" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14891" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s14892" xml:space="preserve"/>
</p>
<div xml:id="echoid-div752" type="float" level="2" n="4">
<note position="right" xlink:label="note-0237-10" xlink:href="note-0237-10a" xml:space="preserve">Quomodo per <lb/>figuram radio-<lb/>rum Zodiaci <lb/>maius aut mi-<lb/>nus horologiũ <lb/>deſcubendum <lb/>ſit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14893" xml:space="preserve">QVOD ſimagnitudo ſiyli data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodiaci à <lb/>
<anchor type="note" xlink:label="note-0237-11a" xlink:href="note-0237-11"/>
puncto H, in axe H D. </s>
  <s xml:id="echoid-s14894" xml:space="preserve">In portione Analemmatis propoſ. </s>
  <s xml:id="echoid-s14895" xml:space="preserve">præcedentis abſcindatur ex B D C, protracta <lb/>recta D M, æqualis gnomoni dato, &amp; </s>
  <s xml:id="echoid-s14896" xml:space="preserve">per M, ipſi A D, diametro Verticalis parallela agatur N O, ſecans <lb/>axem D E, in N, &amp; </s>
  <s xml:id="echoid-s14897" xml:space="preserve">Aequatoris diametrum F D, in O. </s>
  <s xml:id="echoid-s14898" xml:space="preserve">Punctum enim D, figurę radiorum huius pro-<lb/>poſ. </s>
  <s xml:id="echoid-s14899" xml:space="preserve">in quo conueniunt omnes radĳ zodiaci, diſtare debet ab H, interuallo D N, vt de horologio horizõ-<lb/>
<anchor type="note" xlink:label="note-0237-12a" xlink:href="note-0237-12"/>
tali diximus in ſcholio propoſ. </s>
  <s xml:id="echoid-s14900" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14901" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s14902" xml:space="preserve"/>
</p>
<div xml:id="echoid-div753" type="float" level="2" n="5">
<note position="right" xlink:label="note-0237-11" xlink:href="note-0237-11a" xml:space="preserve">Quomodo ex <lb/>data ſtyli longi <lb/>tudine inuenia <lb/>tur diſtantia ra <lb/>diorum Zodia-<lb/>ci à puncto H, <lb/>in figura radio-<lb/>rum.</note>
<note position="left" xlink:label="note-0237-12" xlink:href="note-0237-12a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s14903" xml:space="preserve">HIC etiam in horologio illo, quod in ſcholio præcedentis propoſ. </s>
  <s xml:id="echoid-s14904" xml:space="preserve">docuimus conficere, etiam ſi centrũ <lb/>
<anchor type="note" xlink:label="note-0237-13a" xlink:href="note-0237-13"/>
eius non habeatur, deſcribemus arcus ſignorum, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s14905" xml:space="preserve">2. </s>
  <s xml:id="echoid-s14906" xml:space="preserve">huius libri tradidimus.</s>
  <s xml:id="echoid-s14907" xml:space="preserve"/>
</p>
<div xml:id="echoid-div754" type="float" level="2" n="6">
<note position="right" xlink:label="note-0237-13" xlink:href="note-0237-13a" xml:space="preserve">Qua ratione at <lb/>cus ſignorũ in <lb/>horologio Ver-<lb/>ticali, vbi cen-<lb/>trum non habe <lb/>tur, deſcriban-<lb/>tur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s14908" xml:space="preserve">QV AMVIS autem rectè demonſtratum ſit hac propoſ. </s>
  <s xml:id="echoid-s14909" xml:space="preserve">portionem ſuperiorẽ horologĳ auſtralis, <lb/>quam horizontalis linea abſcindit, exhibere nobis horologium boreale, ſi omnes eius partes ita permuten-<lb/>tur, vt ſuperior vertatur in inferiorem, hoc eſt, horizontalis linea occupet ſuperiorem locum, &amp; </s>
  <s xml:id="echoid-s14910" xml:space="preserve">pars, <lb/>quæ in eo ſitu nobis ad horologiũ conuerſis dextra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s14911" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s14912" xml:space="preserve">operætamen pretium me fa <lb/>cturum exiſtimaui, idem vniuerſe hoc loco oſtendere, nimirum non ſolum in Verticali horologia auſtrali, <lb/>ſed in alĳs etiam omnibus (vt in meridiano, polari, in eo quod à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s14913" xml:space="preserve">in eo quod ab Hori <lb/>zonte, in inclinato ad Horizontem, &amp; </s>
  <s xml:id="echoid-s14914" xml:space="preserve">in eo quod à Verticali declinat, ſimulq́, ad Horizontem inclinatũ <lb/>eſt) lineam horizontalem ad partes ſuperiores portionem auferre, quæ in facie plani horologii oppoſita,
<pb o="218" file="0238" n="238" rhead="GNOMONICES"/>
ſi ita collocetur, vt omnes eius partes inuertantur, vt diximus, eaſdem omnino res nobis indicet per vm-<lb/>
<anchor type="note" xlink:label="note-0238-01a" xlink:href="note-0238-01"/>
bram ſtyli, quas in altera facie, in qua horologium deſcriptum fuit à principio, nobis monſtrat altera ho-<lb/>rologĳ portio infra horizontalem lineam comprehenſa; </s>
  <s xml:id="echoid-s14915" xml:space="preserve">adeo vt ſegmenta linearum ſupra lineam hori-<lb/>zontalem exiſtentia ſint eorundem maximorum circulorum ſectiones communes cum plano horologii in <lb/>facie oppoſita collocandi, ſi illa partium inuerſio fiat, de qua loquuti ſumus, quorum communes ſectiones <lb/>cum plano horologii, quod ab initio in altera facie deſcriptum est, ſunt ſegmenta earundem linearum in-<lb/>fra horizontalem lineam poſita, ſiue illi circuli ſint horarii à meridie, vel media nocte, ſiue Verticales, ſi-<lb/>ue Meridiani, ſiue domorum cœleſtium, ſiue Zodiacum repreſentãtes, quatenus varias obtinet poſitiones, <lb/>dum ſigna cœlestia oriuntur, ſiue horarum ab ortu, vel occaſu, ſiue denique inæqualium horarum indices. <lb/></s>
  <s xml:id="echoid-s14916" xml:space="preserve">Hoc autem ita demonſtrabimus.</s>
  <s xml:id="echoid-s14917" xml:space="preserve"/>
</p>
<div xml:id="echoid-div755" type="float" level="2" n="7">
<note position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">Horizontalis li <lb/>nea in omni ho <lb/>rologio aufert <lb/>portionem ſupe <lb/>tiorem, quæ ex <lb/>hibet horolo-<lb/>giũ in facie ho-<lb/>rologli oppoſi-<lb/>ta collocandũ, <lb/>ſi prius ſupe-<lb/>r<unsure/>ior pars fiat in <lb/>ferior, &amp; quæ <lb/>poſt hanc inuer <lb/>ſionẽ nobis ad <lb/>horologium cõ <lb/>uerſis dextra <lb/>eſt, fiat ſiniſtra, <lb/>&amp; contra.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s14918" xml:space="preserve">SINT duo horologia, vnum australe, &amp; </s>
  <s xml:id="echoid-s14919" xml:space="preserve">boreale alterum, ſi plana ipſorum ad Horizontem recta <lb/>ſunt; </s>
  <s xml:id="echoid-s14920" xml:space="preserve">vel vnum ſuperius, &amp; </s>
  <s xml:id="echoid-s14921" xml:space="preserve">alterum inferius, ſi plana eorum ad Horizontem non ſunt recta; </s>
  <s xml:id="echoid-s14922" xml:space="preserve">in quibus <lb/>ſtyli A B, C D, æquales, &amp; </s>
  <s xml:id="echoid-s14923" xml:space="preserve">ad plana horologiorum recti. </s>
  <s xml:id="echoid-s14924" xml:space="preserve">Intelligantur autem ambo horologia in propria <lb/>poſitione, ita vt Auſtrale ad auſtrum, &amp; </s>
  <s xml:id="echoid-s14925" xml:space="preserve">boreale ad Boream vergat, vel ſuperius ſpectet ad Zenith, &amp; </s>
  <s xml:id="echoid-s14926" xml:space="preserve">in-<lb/>
<anchor type="figure" xlink:label="fig-0238-01a" xlink:href="fig-0238-01"/>
<anchor type="note" xlink:label="note-0238-03a" xlink:href="note-0238-03"/>
ferius ad Nadir; </s>
  <s xml:id="echoid-s14927" xml:space="preserve">ipſa{q́ue} inter ſe ſint parallela, ac vertices ſtylorum B, D, coniungantur in centro mundi, <lb/>
<anchor type="note" xlink:label="note-0238-04a" xlink:href="note-0238-04"/>
ipſismet ſtylis lineam vnam rectam constituentibus, nempe axem illius circuli maximi, cui vtrumque ho-<lb/>rologium æquidiſt at, ita vt horologia ſe mutuo aſpiciant. </s>
  <s xml:id="echoid-s14928" xml:space="preserve">Præterea intelligatur circulus maximus duci <lb/>per polos plani vtriuſque horologii, &amp; </s>
  <s xml:id="echoid-s14929" xml:space="preserve">per polos Horizontis. </s>
  <s xml:id="echoid-s14930" xml:space="preserve">Erit hic circulus ad planum vtriuſque ho <lb/>rologii, &amp; </s>
  <s xml:id="echoid-s14931" xml:space="preserve">ad Horizontem, per propoſ. </s>
  <s xml:id="echoid-s14932" xml:space="preserve">15. </s>
  <s xml:id="echoid-s14933" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14934" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14935" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s14936" xml:space="preserve">rectus, tranſibit{q́ue}, per ſtylos A B, C D, hoc eſt, <lb/>per axem plani vtriuſque horologii, cum per eiuſdem polos ducatur, vt diximus. </s>
  <s xml:id="echoid-s14937" xml:space="preserve">Faciat autem dictus cir-<lb/>culus maximus cum horologiorum planis communes ſectiones rectas A E, C F, quæ parallelæ inter ſe <lb/>
<anchor type="note" xlink:label="note-0238-05a" xlink:href="note-0238-05"/>
erunt. </s>
  <s xml:id="echoid-s14938" xml:space="preserve">Huiuſmodi circulus in horologio Verticali, polari, æquinoctiali, &amp; </s>
  <s xml:id="echoid-s14939" xml:space="preserve">ad Horizontem inclinato erit <lb/>Meridianus ipſe; </s>
  <s xml:id="echoid-s14940" xml:space="preserve">propterea quòd cùm in Meridiano exiſtant &amp; </s>
  <s xml:id="echoid-s14941" xml:space="preserve">poli plani vtriuſque horologii Vertica-<lb/>lis, polaris, æquinoctialis, atque ad Horizontem inclinati, &amp; </s>
  <s xml:id="echoid-s14942" xml:space="preserve">poli Horizontis, (vt conſtat, ſi attentius <lb/>poſitio maximorum circulorum, cui eiuſmodi horologia æquidiſtant, perpendatur) Meridianus per dictos <lb/>
<anchor type="note" xlink:label="note-0238-06a" xlink:href="note-0238-06"/>
polos neceſſariò tranſeat, atque adeo ad plana illorum horologiorum, &amp; </s>
  <s xml:id="echoid-s14943" xml:space="preserve">ad Horizontem rectus ſit, per <lb/>propoſ. </s>
  <s xml:id="echoid-s14944" xml:space="preserve">15. </s>
  <s xml:id="echoid-s14945" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14946" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14947" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s14948" xml:space="preserve">Ex quo efficitur, rectas A E, C F, eſſe in nominatis horologiis lineas meridia-<lb/>nas, In aliis autem horologiis maximus ille circulus non poteſt eſſe Meridianus; </s>
  <s xml:id="echoid-s14949" xml:space="preserve">quia Meridianus ad eo-<lb/>rum plana rectus non eſt, cum per eorum polos minimè tranſeat, vt patet: </s>
  <s xml:id="echoid-s14950" xml:space="preserve">Sed in Meridiano quidem ho-<lb/>rologio, &amp; </s>
  <s xml:id="echoid-s14951" xml:space="preserve">declinante ab Horizonte, is circulus erit proprie dictus Verticalis, cum tranſeat &amp; </s>
  <s xml:id="echoid-s14952" xml:space="preserve">per polos <lb/>Meridiani horologii, declinantis{q́ue} ab Horizonte, &amp; </s>
  <s xml:id="echoid-s14953" xml:space="preserve">per polos Horizontis: </s>
  <s xml:id="echoid-s14954" xml:space="preserve">In declinantibus autem à Ver <lb/>ticali erit idem circulus vnus ex Verticalibus tantum à Meridiano declinans, quantum planum horolo-<lb/>gĳ declinantis abeſt à Verticali circulo; </s>
  <s xml:id="echoid-s14955" xml:space="preserve">atque adeo in horologĳs inclinatis metietur inclinationem pla-<lb/>ni horologĳ ad Horizontem, cùm per polos horologii, &amp; </s>
  <s xml:id="echoid-s14956" xml:space="preserve">per polos Horizontis ducatur.</s>
  <s xml:id="echoid-s14957" xml:space="preserve"/>
</p>
<div xml:id="echoid-div756" type="float" level="2" n="8">
  <figure xlink:label="fig-0238-01" xlink:href="fig-0238-01a">
    <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-01"/>
  </figure>
<note position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0238-05" xlink:href="note-0238-05a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0238-06" xlink:href="note-0238-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s14958" xml:space="preserve">RVRSVS concipiatur duci alius circulus maximus per polos plani vtriuſque horologii, &amp; </s>
  <s xml:id="echoid-s14959" xml:space="preserve">per po <lb/>
<anchor type="note" xlink:label="note-0238-07a" xlink:href="note-0238-07"/>
los prioris circuli maximi per rectas A E, C F, ducti. </s>
  <s xml:id="echoid-s14960" xml:space="preserve">Erit hic circulus ad planum quoque vtriuſque ho <lb/>rologii, &amp; </s>
  <s xml:id="echoid-s14961" xml:space="preserve">ad priorem illum circulum maximum, per propoſ. </s>
  <s xml:id="echoid-s14962" xml:space="preserve">15. </s>
  <s xml:id="echoid-s14963" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14964" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14965" xml:space="preserve">Theodoſii, rectus, tranſibit{q́ue} per <lb/>ſtylos A B, C D, nempe per axem plani vtriuſque horologii, cum per eiuſdem polos ducatur, vt dictum <lb/>eſt. </s>
  <s xml:id="echoid-s14966" xml:space="preserve">Faciat autem dictus circulus maximus cum planis horologiorum communes ſectiones rectas A G, <lb/>C H, quæ etiam inter ſe parallelæ erunt. </s>
  <s xml:id="echoid-s14967" xml:space="preserve">Eædem quoque ad rec<unsure/>tas A E, C F, erunt perpendiculares. </s>
  <s xml:id="echoid-s14968" xml:space="preserve">Cũ <lb/>
<anchor type="note" xlink:label="note-0238-08a" xlink:href="note-0238-08"/>
enim &amp; </s>
  <s xml:id="echoid-s14969" xml:space="preserve">planum horologii, cuius ſtylus A B, &amp; </s>
  <s xml:id="echoid-s14970" xml:space="preserve">planum circuli huius poſterioris per rectam A G, ducti <lb/>rectum ſit ad planum prioris illius circuli per rectam A E, ducti, ex conſtructione; </s>
  <s xml:id="echoid-s14971" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s14972" xml:space="preserve">communis <lb/>illorum ſectio A G, ad planum eiuſdem circuli per A E, ducti, atque adeò per defin. </s>
  <s xml:id="echoid-s14973" xml:space="preserve">3. </s>
  <s xml:id="echoid-s14974" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14975" xml:space="preserve">11. </s>
  <s xml:id="echoid-s14976" xml:space="preserve">Euclidis, <lb/>
<anchor type="note" xlink:label="note-0238-09a" xlink:href="note-0238-09"/>
ad rectam quoque A E, in dicto circulo exiſtentem perpendicularis: </s>
  <s xml:id="echoid-s14977" xml:space="preserve">Eadem ratione erit C H, ad C F, <lb/>perpendicularis. </s>
  <s xml:id="echoid-s14978" xml:space="preserve">Poſterior autem hic circulus in Verticali horologio, Meridiano, &amp; </s>
  <s xml:id="echoid-s14979" xml:space="preserve">declinante à Ver-<lb/>ticali eſt ipſemet Horizon. </s>
  <s xml:id="echoid-s14980" xml:space="preserve">Cum enim horum horologiorum plana ad Horizontem recta ſint, erit viciſ-
<pb o="219" file="0239" n="239" rhead="LIBER SECVNDVS."/>
ſim &amp; </s>
  <s xml:id="echoid-s14981" xml:space="preserve">Horizon ad eadem rectus, ac proinde &amp; </s>
  <s xml:id="echoid-s14982" xml:space="preserve">per polos eorundem horologiorum tranſibit, ex propoſ. <lb/></s>
  <s xml:id="echoid-s14983" xml:space="preserve">13. </s>
  <s xml:id="echoid-s14984" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s14985" xml:space="preserve">1. </s>
  <s xml:id="echoid-s14986" xml:space="preserve">Theodoſii, &amp; </s>
  <s xml:id="echoid-s14987" xml:space="preserve">ob id etiam per stylos eorundem, nempe per axem illorum. </s>
  <s xml:id="echoid-s14988" xml:space="preserve">Eundem autem Ho-<lb/>rizontem ad circulum quoque maximum per A E, ductum eſſe rectum, perſpicuum eſt; </s>
  <s xml:id="echoid-s14989" xml:space="preserve">propterea quòd <lb/>in illis horologiis dictus circulus vnus est ex Verticalibus, qui omnes recti ſunt ad Horizontem, &amp; </s>
  <s xml:id="echoid-s14990" xml:space="preserve">viciſ-<lb/>ſim Horizon ad eoſdem rectus. </s>
  <s xml:id="echoid-s14991" xml:space="preserve">Hinc fit, rectas A G, C H, eſſe lineas horizontales in dictis horologiis. </s>
  <s xml:id="echoid-s14992" xml:space="preserve"><lb/>In reliquis antem horologĳs ille circulus nullo modo eſſe poteſt Horizon; </s>
  <s xml:id="echoid-s14993" xml:space="preserve">quia Horizon ad eorum plana <lb/>rectus non est, cum huiuſmodi plana ad Horizontem ponantur eſſe inclinata: </s>
  <s xml:id="echoid-s14994" xml:space="preserve">quare neque rectę A G, <lb/>C H, horizontales erunt lineæ. </s>
  <s xml:id="echoid-s14995" xml:space="preserve">Sed in polari quidẽ horologio circulus ille erit Aequator, &amp; </s>
  <s xml:id="echoid-s14996" xml:space="preserve">lineæ A G, <lb/>C H, æquinoctiales erunt: </s>
  <s xml:id="echoid-s14997" xml:space="preserve">In æquinoctiali vero horologio idem circulus erit horæ 6. </s>
  <s xml:id="echoid-s14998" xml:space="preserve">à meridie vel me-<lb/>
<anchor type="note" xlink:label="note-0239-01a" xlink:href="note-0239-01"/>
dia nocte, &amp; </s>
  <s xml:id="echoid-s14999" xml:space="preserve">lineæ A G, C H, horam 6. </s>
  <s xml:id="echoid-s15000" xml:space="preserve">à meridie, vel media nocte monstrabunt, vt patet poſitionem <lb/>horum circulorum diligenter contemplanti, &amp; </s>
  <s xml:id="echoid-s15001" xml:space="preserve">ex ſequentibus planum fiet, ac manifeſtum. </s>
  <s xml:id="echoid-s15002" xml:space="preserve">In cæteris de-<lb/>nique horologiis dictus circulus erit alius, atque alius; </s>
  <s xml:id="echoid-s15003" xml:space="preserve">ſemper tamen rectæ A G, C H, parallelæ erunt <lb/>horizontali lineæ vtriuſque horologii. </s>
  <s xml:id="echoid-s15004" xml:space="preserve">Cum enim circulus hic maximus, de quo poſteriori loco diximus, re <lb/>ctus ſit ad priorem circulum maximum per rectas A E, C F, &amp; </s>
  <s xml:id="echoid-s15005" xml:space="preserve">ſtylos A B, C D, ductum, hic autem ad <lb/>Horizontem rectus ſit poſitus, atque adeo &amp; </s>
  <s xml:id="echoid-s15006" xml:space="preserve">Horizon viciſſim ad eundem rectus ſit, tranſibit tam Hori-<lb/>zon, quàm maximus ille circulus per rectas A G, C H, ductus, per polos huius circuli maximi per re-<lb/>ctas A E, C F, ducti, ex propoſ. </s>
  <s xml:id="echoid-s15007" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15008" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15009" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15010" xml:space="preserve">Theodoſii; </s>
  <s xml:id="echoid-s15011" xml:space="preserve">ac proinde axis eiuſdem huius circuli per rectas <lb/>A E, C F, ducti erit communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s15012" xml:space="preserve">alterius illius circuli maximi, qui per rectas A G, <lb/>C H, ducitur. </s>
  <s xml:id="echoid-s15013" xml:space="preserve">Sed &amp; </s>
  <s xml:id="echoid-s15014" xml:space="preserve">circulus maximus, cui horologium æquidiſtat, per eoſdem polos circuli maximi per <lb/>rectas A E, C F, ducti tranſit. </s>
  <s xml:id="echoid-s15015" xml:space="preserve">(Quia enim circulus maximus per rectas A E, C F, &amp; </s>
  <s xml:id="echoid-s15016" xml:space="preserve">ſtylos A B, C D, <lb/>
<anchor type="note" xlink:label="note-0239-02a" xlink:href="note-0239-02"/>
ductus rectus eſt, per conſtructionem, ad planum horologĳ, hoc eſt, ad circulum, quem in ſphæra facit horo <lb/>logĳ planum, tranſibit idem per polos huius circuli in ſphęra procreati, per propoſ. </s>
  <s xml:id="echoid-s15017" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15018" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15019" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15020" xml:space="preserve">Theodoſii. <lb/></s>
  <s xml:id="echoid-s15021" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s15022" xml:space="preserve">per polos circuli maximi, cui horologium ęquidiſtat, quòd circuli paralleli eoſdem habeant <lb/>polos, ex propoſ. </s>
  <s xml:id="echoid-s15023" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15024" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15025" xml:space="preserve">2. </s>
  <s xml:id="echoid-s15026" xml:space="preserve">Thcodoſii. </s>
  <s xml:id="echoid-s15027" xml:space="preserve">Quare viciſſim circulus hic maximus, cui horologium æquidistat, per <lb/>polos illius, qui per rectas A E, C F, ducitur, tranſibit, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s15028" xml:space="preserve">15 lib. </s>
  <s xml:id="echoid-s15029" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15030" xml:space="preserve">Theodoſii.) </s>
  <s xml:id="echoid-s15031" xml:space="preserve">Habent <lb/>ergo Horizon, circulus maximus per rectas A G, C H, &amp; </s>
  <s xml:id="echoid-s15032" xml:space="preserve">ſtylos A B, C D, ductus, &amp; </s>
  <s xml:id="echoid-s15033" xml:space="preserve">circulus maxi-<lb/>mus, cui horologium æquidiſtat, eandem communem ſectionem, nempe axem circuli maximi per rectas <lb/>A E, C G, &amp; </s>
  <s xml:id="echoid-s15034" xml:space="preserve">ſtylos A B, C D, ducti. </s>
  <s xml:id="echoid-s15035" xml:space="preserve">Quamobrem cum planum horologii huic poſtremo circulo æquidiſtet, <lb/>erunt per propoſ. </s>
  <s xml:id="echoid-s15036" xml:space="preserve">18. </s>
  <s xml:id="echoid-s15037" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15038" xml:space="preserve">communes ſectiones aliorum, (nempe Horizontis, &amp; </s>
  <s xml:id="echoid-s15039" xml:space="preserve">eius, qui per <lb/>
<anchor type="note" xlink:label="note-0239-03a" xlink:href="note-0239-03"/>
rectas A G, C H, &amp; </s>
  <s xml:id="echoid-s15040" xml:space="preserve">per ſtylos A B, C D, ducitur, &amp; </s>
  <s xml:id="echoid-s15041" xml:space="preserve">plani horologii illos ſecantis) parallelę; </s>
  <s xml:id="echoid-s15042" xml:space="preserve">Ac pro-<lb/>inde cum ſectio, quam facit Horizon, ſit linea horizõtalis in horologio, ſectio autem alterius circuli maxi <lb/>mi ſit recta A G, in vno horologio, &amp; </s>
  <s xml:id="echoid-s15043" xml:space="preserve">recta C H, in altero, parallelæ erunt rectæ A G, C H, horizontali <lb/>lineæ vtriuſque horologĳ.</s>
  <s xml:id="echoid-s15044" xml:space="preserve"/>
</p>
<div xml:id="echoid-div757" type="float" level="2" n="9">
<note position="left" xlink:label="note-0238-07" xlink:href="note-0238-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0238-08" xlink:href="note-0238-08a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0238-09" xlink:href="note-0238-09a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0239-03" xlink:href="note-0239-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s15045" xml:space="preserve">IAM verò circulus aliquis maximus, ſiue horarius is ſit, ſiue alius quiſpiam, in horologio Auſtrali, <lb/>vel ſuperiori per centrum mundi, id eſt, per B, vel D, (duo enim hæc puncta vnum punctum conficiunt) <lb/>verticem ſtyli tranſiens faciat ſectionem E G, quę ſecet rectam A E, infra ſtylum in E, &amp; </s>
  <s xml:id="echoid-s15046" xml:space="preserve">rectam A G, <lb/>ad dextram in G. </s>
  <s xml:id="echoid-s15047" xml:space="preserve">Secabit idem hic circulus in horologio boreali, vel inferiori, cum per ſtyli verticem <lb/>tranſeat, rectas C F, C H, in partibus oppoſitis, vt perſpicuum eſt, ſi planum horologĳ vtriuſque, &amp; </s>
  <s xml:id="echoid-s15048" xml:space="preserve">pla-<lb/>num circuli ſectionem E G, facientis in proprĳs poſitionibus conſiderentur; </s>
  <s xml:id="echoid-s15049" xml:space="preserve">ſecabit, inquam, rectam C F, <lb/>ſupra ſtylum, &amp; </s>
  <s xml:id="echoid-s15050" xml:space="preserve">rectam C H, ad partem dextram. </s>
  <s xml:id="echoid-s15051" xml:space="preserve">Superior enim pars borealis horologĳ, vel inferioris, <lb/>
<anchor type="note" xlink:label="note-0239-04a" xlink:href="note-0239-04"/>
parti inferiori Auſtralis, vel ſuperioris horologĳ opponitur, atque inferior ſuperiori, &amp; </s>
  <s xml:id="echoid-s15052" xml:space="preserve">dextra dextræ, <lb/>ſiniſtra{q́ue} ſiniſtrę. </s>
  <s xml:id="echoid-s15053" xml:space="preserve">Appellamus autem partem dextram, ſiniſtramve, quæ nobis ad horologium conuerſis <lb/>ad dexteram eſt, vel ad ſiniſtram. </s>
  <s xml:id="echoid-s15054" xml:space="preserve">Vnde cum duo illa horologia ſe mutuo reſpiciant, reſpondebit dextra <lb/>pars vnius parti ſiniſtr æ alterius, &amp; </s>
  <s xml:id="echoid-s15055" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s15056" xml:space="preserve">dextra autem dextræ, &amp; </s>
  <s xml:id="echoid-s15057" xml:space="preserve">ſiniſtra ſiniſtræ opponetur, cum <lb/>inter has partes medio loco ponatur ſtylus. </s>
  <s xml:id="echoid-s15058" xml:space="preserve">Sit ergo communis ſectio dicti circuli, &amp; </s>
  <s xml:id="echoid-s15059" xml:space="preserve">plani horologĳ in <lb/>boreali horologio, ſeu inferiori, recta F H, ſecans C F, in F, ſupra ſtylum, &amp; </s>
  <s xml:id="echoid-s15060" xml:space="preserve">C H, in H, ad partem eius <lb/>dextram. </s>
  <s xml:id="echoid-s15061" xml:space="preserve">Erunt autem ambæ ſectiones E G, F H, parallelæ, cum eas idem circulus in planis parallelis <lb/>
<anchor type="note" xlink:label="note-0239-05a" xlink:href="note-0239-05"/>
horologiorum efficiat. </s>
  <s xml:id="echoid-s15062" xml:space="preserve">Itaque quoniam rectæ A E, C F, parallelæ ſunt, vt demonſtratum eſt, erunt æqua-<lb/>les inter ſe anguli alterni in punctis E, &amp; </s>
  <s xml:id="echoid-s15063" xml:space="preserve">F, rectarum E A, F C, facti à communi ſectione maximorum <lb/>
<anchor type="note" xlink:label="note-0239-06a" xlink:href="note-0239-06"/>
circulorum ſectiones A E, C F, &amp; </s>
  <s xml:id="echoid-s15064" xml:space="preserve">E G, C H, facientium, quæ quidem communis ſectio per puncta E, B, <lb/>
<anchor type="note" xlink:label="note-0239-07a" xlink:href="note-0239-07"/>
D, F, tranſit, cum per hæc eadem ipſi circuli maximi tranſeant. </s>
  <s xml:id="echoid-s15065" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s15066" xml:space="preserve">anguli recti A, C, quos <lb/>ſtyli cum rectis A E, C F, per defin. </s>
  <s xml:id="echoid-s15067" xml:space="preserve">3. </s>
  <s xml:id="echoid-s15068" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15069" xml:space="preserve">11. </s>
  <s xml:id="echoid-s15070" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s15071" xml:space="preserve">conſtituunt, æquales; </s>
  <s xml:id="echoid-s15072" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s15073" xml:space="preserve">ſtyli A B, C D, æquales, <lb/>qui æqualibus angulis E, F, ſubtenduntur in triangulis A B E, C D F, quorum baſes ſunt partes commu <lb/>nis ſectionis maximorum circulorum ſectiones A E, C F, &amp; </s>
  <s xml:id="echoid-s15074" xml:space="preserve">E G, C H, in horologio vtroque facientium. <lb/></s>
  <s xml:id="echoid-s15075" xml:space="preserve">Erunt igitur latera quoque A E, C F, æqualia. </s>
  <s xml:id="echoid-s15076" xml:space="preserve">Tantum ergo abest ſectio E G, in recta A E, à ſtylo <lb/>
<anchor type="note" xlink:label="note-0239-08a" xlink:href="note-0239-08"/>
deorſum verſus, quantum ſectio F H, in recta C F, à ſtylo ſurſum verſus diſtat. </s>
  <s xml:id="echoid-s15077" xml:space="preserve">Rurſus quia rectæ E K, <lb/>E I, rectis F C, F H, parallelæ ſunt, vt ostendimus, erit angulus K E I, angulo C F H, æqualis. </s>
  <s xml:id="echoid-s15078" xml:space="preserve">Cum er-<lb/>
<anchor type="note" xlink:label="note-0239-09a" xlink:href="note-0239-09"/>
go angulo K E I, æqualis ſit angulus A E G, ad verticem, eruntin triangulis A E G, C F H, anguli ad <lb/>
<anchor type="note" xlink:label="note-0239-10a" xlink:href="note-0239-10"/>
E, F, æquales. </s>
  <s xml:id="echoid-s15079" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s15080" xml:space="preserve">anguli E A G, F C H, æquales, vtpotè recti; </s>
  <s xml:id="echoid-s15081" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15082" xml:space="preserve">latera A E, C F, dictis <lb/>angulis adiacentia, oſtenſa ſunt æqualia. </s>
  <s xml:id="echoid-s15083" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s15084" xml:space="preserve">latera A G, C H, æqualia erunt. </s>
  <s xml:id="echoid-s15085" xml:space="preserve">Aequalibus ergo <lb/>
<anchor type="note" xlink:label="note-0239-11a" xlink:href="note-0239-11"/>
ſpatĳs abſunt rectæ E G, F H, in rectis A G, C H, à ſtylis dextram verſus. </s>
  <s xml:id="echoid-s15086" xml:space="preserve">Quòd ſi recta E G, ſecet re-
<pb o="220" file="0240" n="240" rhead="GNOMONICES"/>
ctam A E, ſupra ſtylum, vel rectam A G, ad ſiniſtram, oſtendemus eadem ratione, rectam F H, ſecare <lb/>rectam C F, infra ſtylum, &amp; </s>
  <s xml:id="echoid-s15087" xml:space="preserve">rectam C H, ad ſiniſtram quoque, nempe in oppoſitis ſemper partibus; </s>
  <s xml:id="echoid-s15088" xml:space="preserve">re-<lb/>ctas{q́ue}, quas F H, ex rectis C F, C H, aufert, æquales eſſerectis, quas E G, abſcindit ex rectis <lb/>A E, A G.</s>
  <s xml:id="echoid-s15089" xml:space="preserve"/>
</p>
<div xml:id="echoid-div758" type="float" level="2" n="10">
<note position="left" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">10. vndec.</note>
<note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0239-11" xlink:href="note-0239-11a" xml:space="preserve">26. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s15090" xml:space="preserve">DEINDE alius quiſpiam circulus maximus in Auſtrali horologio, inferiorive, per verticem ſty-<lb/>li B, vel D, ductus, faciat ſectionem L M, quæ non ſecet vtramque A E, A G, ſed alteram tantum, nem-<lb/>
<anchor type="figure" xlink:label="fig-0240-01a" xlink:href="fig-0240-01"/>
<anchor type="note" xlink:label="note-0240-01a" xlink:href="note-0240-01"/>
<anchor type="note" xlink:label="note-0240-02a" xlink:href="note-0240-02"/>
pe A E, in L, ſupra ſtylum, parallela autem ſit alteri, nimirum ipſi A G, Secabit idem hic circulus, cum <lb/>per ſtyli verticem incedat, boreale horologium, inferiusve, infra ſtylum, hoc eſt, in oppoſita parte, per re-<lb/>ctam N O, quę rectam C F, ſecet in N: </s>
  <s xml:id="echoid-s15091" xml:space="preserve">eritq́, N O, ipſi C H, parallela. </s>
  <s xml:id="echoid-s15092" xml:space="preserve">Cum enim L M, ponatur paralle-<lb/>
<anchor type="note" xlink:label="note-0240-03a" xlink:href="note-0240-03"/>
la ipſi A G, eidem verò A G, parallela quoque ſit C H, vt ante diximus; </s>
  <s xml:id="echoid-s15093" xml:space="preserve">erunt etiam inter ſe parallelæ <lb/>
<anchor type="note" xlink:label="note-0240-04a" xlink:href="note-0240-04"/>
L M, C H. </s>
  <s xml:id="echoid-s15094" xml:space="preserve">Rurſus quoniam N O, ipſi L M, parallela eſt, (quod L M, N O, ſectiones ſint factæ ab vno, <lb/>
<anchor type="note" xlink:label="note-0240-05a" xlink:href="note-0240-05"/>
eodem{q́ue} plano in planis parallelis) &amp; </s>
  <s xml:id="echoid-s15095" xml:space="preserve">eidem L M, oſtenſa proximè eſt parallela C H; </s>
  <s xml:id="echoid-s15096" xml:space="preserve">erunt quoque N O, <lb/>C H, inter ſe parallelæ. </s>
  <s xml:id="echoid-s15097" xml:space="preserve">Igitur cum L M, ipſi A G, &amp; </s>
  <s xml:id="echoid-s15098" xml:space="preserve">N O, ipſi C H, parallela ſit; </s>
  <s xml:id="echoid-s15099" xml:space="preserve">erunt anguli L, N, <lb/>
<anchor type="note" xlink:label="note-0240-06a" xlink:href="note-0240-06"/>
angulis A, C, æquales, ac propterea recti. </s>
  <s xml:id="echoid-s15100" xml:space="preserve">Quoniam verò A E, C F, parallelæ ſunt, vt ſuperius oſtenſum <lb/>
<anchor type="note" xlink:label="note-0240-07a" xlink:href="note-0240-07"/>
<anchor type="note" xlink:label="note-0240-08a" xlink:href="note-0240-08"/>
eſt, erunt inter ſe æquales anguli alterni in punctis L, &amp; </s>
  <s xml:id="echoid-s15101" xml:space="preserve">N, rectarum A E, C F, facti à communi ſectione <lb/>circulorum maximorum ſectiones A E, C F, &amp; </s>
  <s xml:id="echoid-s15102" xml:space="preserve">L M, N O, facientium, quæ quidem communis ſectio per <lb/>puncta L, B, D, N, tranſit, cum per hæc eadem circuli ipſi maximi tranſeant. </s>
  <s xml:id="echoid-s15103" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s15104" xml:space="preserve">anguli re-<lb/>cti A, C, quos ſtyli cum rectis A L, C N, constituunt, æquales: </s>
  <s xml:id="echoid-s15105" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s15106" xml:space="preserve">ſtyli A B, C D, æquales, qui <lb/>æqualibus angulis L, N, ſubtenduntur in triangulis A B L, C D N, quorum baſes ſunt partes communis <lb/>ſectionis maximorum circulorum ſectiones A E, C F, &amp; </s>
  <s xml:id="echoid-s15107" xml:space="preserve">L M, N O, in vtroque horologio facientium. <lb/></s>
  <s xml:id="echoid-s15108" xml:space="preserve">
<anchor type="note" xlink:label="note-0240-09a" xlink:href="note-0240-09"/>
Igitur latera quoque A L, C N, æqualia erunt. </s>
  <s xml:id="echoid-s15109" xml:space="preserve">Tanto ergo interuallo in recta A E, remouetur ſectio <lb/>L M, à ſtylo ſurſum verſus, quanto in recta C F, ſectio N O, à ſtylo deorſum verſus abeſt. </s>
  <s xml:id="echoid-s15110" xml:space="preserve">Quòd ſi recta <lb/>L M, ſecet rectam A E, infra ſtylum, ostendemus eadem ratione, rectam N O, ſecare rectam C F, ſupra <lb/>ſtylum, parallelam{q́ue} eſſe N O, ipſi L M, &amp; </s>
  <s xml:id="echoid-s15111" xml:space="preserve">rectam, quam N O, ex C F, abſcindit, ęqualem eſſe rectæ, quam <lb/>L M, ex A E, aufert.</s>
  <s xml:id="echoid-s15112" xml:space="preserve"/>
</p>
<div xml:id="echoid-div759" type="float" level="2" n="11">
  <figure xlink:label="fig-0240-01" xlink:href="fig-0240-01a">
    <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0240-01"/>
  </figure>
<note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0240-05" xlink:href="note-0240-05a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0240-06" xlink:href="note-0240-06a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0240-07" xlink:href="note-0240-07a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0240-08" xlink:href="note-0240-08a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0240-09" xlink:href="note-0240-09a" xml:space="preserve">26. primi.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s15113" xml:space="preserve">POSTREMO alius quiſpiam maximus circulus in horologio Auſtrali, ſiue ſuperiori, faciat ſe-<lb/>ctionem M P, quæ rurſus non ſecet vtramque A E, C F, ſed ipſam A G, duntaxat in P, ad ſiniſtram, pa-<lb/>rallela autem ſit ipſi A E. </s>
  <s xml:id="echoid-s15114" xml:space="preserve">Secabit hic idem circulus, cum per verticem ſtyli ducatur, horologium borea-<lb/>le, ſeu inferius in oppoſita parte, hoc eſt, ad ſiniſtram quoque, per rectam O Q, quæ rectam C H, ſecet <lb/>in Q: </s>
  <s xml:id="echoid-s15115" xml:space="preserve">erit{q́ue} O Q, ipſi C F, parallela. </s>
  <s xml:id="echoid-s15116" xml:space="preserve">Cum enim M P, parallela ponatur ipſi A E, eidem verò A E, <lb/>
<anchor type="note" xlink:label="note-0240-11a" xlink:href="note-0240-11"/>
parallela quoque oſtenſa ſit antea C F; </s>
  <s xml:id="echoid-s15117" xml:space="preserve">erunt inter ſe quoque parallelæ M P, C F. </s>
  <s xml:id="echoid-s15118" xml:space="preserve">Rurſus quoniam O Q, <lb/>
<anchor type="note" xlink:label="note-0240-12a" xlink:href="note-0240-12"/>
ipſi M P, parallela eſt, (quod M P, O Q, ſectiones ſint factæ ab vno, eodem{q́ue} plano in planis paralle-<lb/>
<anchor type="note" xlink:label="note-0240-13a" xlink:href="note-0240-13"/>
lis) &amp; </s>
  <s xml:id="echoid-s15119" xml:space="preserve">eidem M P, oſtenſa eſt proximè parallela C F; </s>
  <s xml:id="echoid-s15120" xml:space="preserve">erunt etiam inter ſe parallelæ O Q, C F. </s>
  <s xml:id="echoid-s15121" xml:space="preserve">Igitur <lb/>
<anchor type="note" xlink:label="note-0240-14a" xlink:href="note-0240-14"/>
cum M P, ipſi A E, parallela ſit, &amp; </s>
  <s xml:id="echoid-s15122" xml:space="preserve">O Q, ipſi C F; </s>
  <s xml:id="echoid-s15123" xml:space="preserve">erunt anguli P, Q, angulis A, C, æquales, ac pro-<lb/>
<anchor type="note" xlink:label="note-0240-15a" xlink:href="note-0240-15"/>
<anchor type="note" xlink:label="note-0240-16a" xlink:href="note-0240-16"/>
inderecti. </s>
  <s xml:id="echoid-s15124" xml:space="preserve">Quia verò, vt ſuperius oſtendimus, A G, C H, parallelæ ſunt, erunt inter ſe æquales anguli <lb/>alterni in punctis P, Q, rectarum A G, C H, facti à communi ſectione circulorum maximorum ſectio-<lb/>ctiones A G, C H, &amp; </s>
  <s xml:id="echoid-s15125" xml:space="preserve">M P, O Q, facientium, quæ quidem ſectio communis per puncta P, B, D, Q, <lb/>tranſit, quòd per hæc eadem circuli ipſi maximi tranſeant quoque. </s>
  <s xml:id="echoid-s15126" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s15127" xml:space="preserve">anguli recti A, C, <lb/>quos ſtyli cum rectis A P, C Q, faciunt, æquales: </s>
  <s xml:id="echoid-s15128" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s15129" xml:space="preserve">ſtyli A B, C D, æquales, qui æqualibus an-<lb/>gulis P, Q, ſubtenduntur in triangulis A B P, C D Q, quorum baſes ſunt ſegmenta communis ſectio-<lb/>nis maximorum circulorum ſectiones A G, C H, &amp; </s>
  <s xml:id="echoid-s15130" xml:space="preserve">M P, O Q, in vtroque horologio facientium. </s>
  <s xml:id="echoid-s15131" xml:space="preserve">Igi-<lb/>
<anchor type="note" xlink:label="note-0240-17a" xlink:href="note-0240-17"/>
tur latera quoque A P, C Q, æqualia erunt. </s>
  <s xml:id="echoid-s15132" xml:space="preserve">Spatĳs ergo æqualibus rectæ M P, O Q, in rectis A G, <lb/>C H, abſunt à ſtylis ſiniſtram verſus. </s>
  <s xml:id="echoid-s15133" xml:space="preserve">Quòd ſi recta M P, ſecet rectam A G, ad dextram, demonſtra-<lb/>bimus eadem argumentatione, rectam O Q, ſecare rectam C H, ad dextram quoque, &amp; </s>
  <s xml:id="echoid-s15134" xml:space="preserve">parallelam <lb/>eſſe O Q, ipſi M P, rectas, quas M P, O Q, ex A G, C H, amputant, eſſe æquales.</s>
  <s xml:id="echoid-s15135" xml:space="preserve"/>
</p>
<div xml:id="echoid-div760" type="float" level="2" n="12">
<note position="left" xlink:label="note-0240-11" xlink:href="note-0240-11a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0240-12" xlink:href="note-0240-12a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0240-13" xlink:href="note-0240-13a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0240-14" xlink:href="note-0240-14a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0240-15" xlink:href="note-0240-15a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0240-16" xlink:href="note-0240-16a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0240-17" xlink:href="note-0240-17a" xml:space="preserve">26. primi.</note>
</div>
<pb o="221" file="0241" n="241" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s15136" xml:space="preserve">HIS ita demonstratis, facile oſtendemus, rectas E G, L M, M P, &amp; </s>
  <s xml:id="echoid-s15137" xml:space="preserve">quaſcunque alias, in horolo-<lb/>gio boreali, vel inferiori, eſſe eorundem circulorum maximorum, &amp; </s>
  <s xml:id="echoid-s15138" xml:space="preserve">plani horologĳ ſectiones communes, <lb/>quorum ſunt ſectiones in auſtrali, ſuperiorive horologio; </s>
  <s xml:id="echoid-s15139" xml:space="preserve">ſi auſt rale, vel ſuperius horologium in facie bo-<lb/>reali, vel inferiori plani horologĳ ita collocetur, vt pars eius ſuperior mutetur in inferiorẽ, &amp; </s>
  <s xml:id="echoid-s15140" xml:space="preserve">pars, quæ <lb/>in eo ſitu poſt hanc permutationem nobis ad horologium conuerſis dextra eſt, fiat ſinistra, &amp; </s>
  <s xml:id="echoid-s15141" xml:space="preserve">contra. <lb/></s>
  <s xml:id="echoid-s15142" xml:space="preserve">Nam ſi horologium auſtrale, ſiue ſuperius intelligatur poni ſupra boreale, ſeu inferius, vt stylus ſtylo <lb/>congruat, &amp; </s>
  <s xml:id="echoid-s15143" xml:space="preserve">dextra pars ad G, dextræ parti ad H, punctum{q́ue}, A, puncto C, et linea A G, lineæ C H; </s>
  <s xml:id="echoid-s15144" xml:space="preserve">ca-<lb/>dent puncta G, P, in puncta H, Q, propterea quòd rectæ A G, A P, rectis C H, C Q, oſtenſæ ſunt <lb/>æquales. </s>
  <s xml:id="echoid-s15145" xml:space="preserve">Quòd ſi in hoc ſitu auſtrale horologium, ſiue ſuperius, circa rectam G P, vel (quod idem eſt) <lb/>circa H Q, quia hę duæ lineæ in hoc ſitu vnam &amp; </s>
  <s xml:id="echoid-s15146" xml:space="preserve">eandem conſtituunt, conuerti animo concipiamus, vt <lb/>
<anchor type="note" xlink:label="note-0241-01a" xlink:href="note-0241-01"/>
pars ſuperior fiat inferior, &amp; </s>
  <s xml:id="echoid-s15147" xml:space="preserve">contra, cadent puncta E, L, in puncta F, N, eo quòd rectæ A E, A L, <lb/>rectis C F, C N, demonſtratæ ſint æquales. </s>
  <s xml:id="echoid-s15148" xml:space="preserve">Quare linea E G, lineæ F H, congruet, quòd puncta E, G, <lb/>punctis F, H, congruere oſtenderimus; </s>
  <s xml:id="echoid-s15149" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15150" xml:space="preserve">linea L M, lineæ N O, &amp; </s>
  <s xml:id="echoid-s15151" xml:space="preserve">linea M P, lineæ O Q, congruet, <lb/>propterea quòd puncta L, P, in punctis N, Q, existunt, &amp; </s>
  <s xml:id="echoid-s15152" xml:space="preserve">anguli ad L, P, N, Q, oſtenſi ſunt recti. <lb/></s>
  <s xml:id="echoid-s15153" xml:space="preserve">Eadem ratione concludemus, quamlibet aliam lineam in horologio australi, vel ſuperiori, ſiue ea ſecet <lb/>vtramque A E, A G, ſiue alter am tantum, &amp; </s>
  <s xml:id="echoid-s15154" xml:space="preserve">alteri ſit parallela, congruere lineæ ſibi reſpondenti in ho-<lb/>rologio boreali, ſeu inferiori, ſi illa ſuperpoſitio, &amp; </s>
  <s xml:id="echoid-s15155" xml:space="preserve">permutatio, vt proximè diximus, fiat. </s>
  <s xml:id="echoid-s15156" xml:space="preserve">Quocirca to-<lb/>tum horologium auſtrale, ſuperiusve toti boreali horologio, ſiue inferiori, ea ratione congruet. </s>
  <s xml:id="echoid-s15157" xml:space="preserve">Cum ergo <lb/>per illam ſuperpoſitionem, conuerſionem{q́ue}, ſuperior pars auſtralis horologĳ, ſuperiorisve, fiat inferior, <lb/>&amp; </s>
  <s xml:id="echoid-s15158" xml:space="preserve">dextra ſiniſtra, vt patet: </s>
  <s xml:id="echoid-s15159" xml:space="preserve">(Nam ſi auſtrale horologium ſeorſum intelligatur conuerti, vt pars ſupe-<lb/>
<anchor type="note" xlink:label="note-0241-02a" xlink:href="note-0241-02"/>
rior in inferiorem mutetur, remanebit nobis ad horologium conuerſis punctum G, ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s15160" xml:space="preserve">P, ad <lb/>dextram. </s>
  <s xml:id="echoid-s15161" xml:space="preserve">Vnde vt recta E G, rectæ F H, congruat, &amp; </s>
  <s xml:id="echoid-s15162" xml:space="preserve">reliquæ lineæ reliquis lineis, neceſſe eſt, partem <lb/>ſiniſtram G, mutari in dextram, &amp; </s>
  <s xml:id="echoid-s15163" xml:space="preserve">dextram P, in ſiniſtram. </s>
  <s xml:id="echoid-s15164" xml:space="preserve">Ita enim fiet, vt ſingulæ lineæ congruant <lb/>ſingulis. </s>
  <s xml:id="echoid-s15165" xml:space="preserve">Quod etiam hac ratione fiet perſpicuum. </s>
  <s xml:id="echoid-s15166" xml:space="preserve">Poſtquam recta G P, rectæ H Q, ſuperpoſita eſt, <lb/>manet quidem punctum G, nobis ad horologium conuerſis ad dexteram, quemadmodum &amp; </s>
  <s xml:id="echoid-s15167" xml:space="preserve">punctum H, <lb/>borealis, vel inferioris horologĳ: </s>
  <s xml:id="echoid-s15168" xml:space="preserve">Sed poſt conuerſionem horologĳ auſtralis, ſuperiorisve, circa rectam <lb/>G P, vel H Q, vt ſuperiora fiant inferiora, poſitum erit nobis punctum G, ad ſiniſtram, vt dictum eſt, <lb/>ſi conuertamus faciem ad horologium ipſum: </s>
  <s xml:id="echoid-s15169" xml:space="preserve">quia verò tunc horologium conuerſum est ad meridiem, <lb/>fit vt eius lineamenta deſcribenda ſint in facie oppoſita, quæ boream reſpicit, atque ita exiſtet n@bis co@ <lb/>uerſis ad faciem borealem horologĳ idem punctum G, ad dextram) liquido conſtat, ex horologio auſtra-<lb/>
<anchor type="note" xlink:label="note-0241-03a" xlink:href="note-0241-03"/>
li, vel ſuperiori, ſi fiat omnium partium permutatio, vt ſuperior in inferiorem mutetur, &amp; </s>
  <s xml:id="echoid-s15170" xml:space="preserve">quæ poſt <lb/>hanc mutationem nobis ad horologium conuerſis dextra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s15171" xml:space="preserve">contra, fieri horologium bo-<lb/>reale, ſiue inferius.</s>
  <s xml:id="echoid-s15172" xml:space="preserve"/>
</p>
<div xml:id="echoid-div761" type="float" level="2" n="13">
<note position="left" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s15173" xml:space="preserve">QVONIAM verò in prædicta ſuperpoſitione, conuerſione{q́ue} horologĳ auſtralis, ſuperiorisve, li-<lb/>nea eius horizontalis horizontali lineæ horologĳ borealis, ſeu inferioris, cõgruit, (quia inhorologiĳs, quo-<lb/>rum plana ad Horizontem recta ſunt, cuiuſmodi ſunt Verticale, Declinans à<unsure/> Verticali, &amp; </s>
  <s xml:id="echoid-s15174" xml:space="preserve">Meridia-<lb/>num, linea horizontalis ducitur per locum ſtyli, at que ita horizontales lineæ erunt A G, C H, quæ ex <lb/>ipſa ſuperpoſitione ſibi mutuo congruunt: </s>
  <s xml:id="echoid-s15175" xml:space="preserve">In alĳs verò horologĳs, quorum plana ad Horizontem non <lb/>ſunt recta, qualia ſunt Polare, Aequinoctiale, Declinans ab Horizonte, Inclinatum ad Horizontem, &amp; </s>
  <s xml:id="echoid-s15176" xml:space="preserve"><lb/>Declinans à Verticali, quod ſimul ad Horizontem inclinatum eſt, quoniam linea horizontalis cadit in ſu-<lb/>
<anchor type="note" xlink:label="note-0241-04a" xlink:href="note-0241-04"/>
perioribus quidem ſupra ſtylum, in inferioribus autem infra eundem, eſt{q́ue} ſemper parallela rectæ A G, <lb/>vt paulo ante demonſtrauimus, fit vt hac ratione horizontalis linea ſuperioris horologĳ lineæ horizonta-<lb/>li inferioris etiam congruat; </s>
  <s xml:id="echoid-s15177" xml:space="preserve">quod demonſtrabitur, vt demonſtratum est, rectam L M, congruere rectæ <lb/>N O,) est portio horologĳ ſupra lineam horizontalem existens ſuperuacanea in quouis horologio, cum <lb/>in illam vmbra styli nunquam cadere poſſit interdiu; </s>
  <s xml:id="echoid-s15178" xml:space="preserve">efficitur vniuersè verum eſſe, lineam horizonta-<lb/>lem in quocunque horologio ad partes ſuperiores portionem auferre, quæ in facie plani horologĳ oppoſita <lb/>idem horologium nobis exhibeat, ſi it a collocetur, vt linea horizontalis ſuperiorem locum occupet in fa-<lb/>cie oppoſita, &amp; </s>
  <s xml:id="echoid-s15179" xml:space="preserve">pars, quę in eo ſitu nobis ad horologium conuerſis dextra est, fiat ſinistra, &amp; </s>
  <s xml:id="echoid-s15180" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s15181" xml:space="preserve">quia <lb/>facta illa partium permutatione, pars ſupra lineam horizontalem australis horologii collocatur in borea <lb/>li horologio infra eandem lineam horizontalem, vt manifestum est. </s>
  <s xml:id="echoid-s15182" xml:space="preserve">Quod erat demonstrandum.</s>
  <s xml:id="echoid-s15183" xml:space="preserve"/>
</p>
<div xml:id="echoid-div762" type="float" level="2" n="14">
<note position="left" xlink:label="note-0241-04" xlink:href="note-0241-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s15184" xml:space="preserve">QVOD ſi quando contingat, lineas in horologio, quæ communes ſectiones ſunt plani horologĳ, &amp; </s>
  <s xml:id="echoid-s15185" xml:space="preserve"><lb/>circulorum maximorum, per A, locum styli in australi, vel ſuperiori horologio, &amp; </s>
  <s xml:id="echoid-s15186" xml:space="preserve">per C, locum styli <lb/>in boreali, inferiorive horologio tranſire, (vt accidit in domibus cœlestibus horologii Verticalis, &amp; </s>
  <s xml:id="echoid-s15187" xml:space="preserve">ho-<lb/>ris à meridie, vel media nocte, atque Meridianis circulis horologii æquinoctialis, vt perſpicuum fiet ex <lb/>ſequentibus) nihilominus ſequetur, australe horologium, vel ſuperius congruere boreali, inferiorive, ſi il-<lb/>li@s partes omnes inuertantur, vt docuimus. </s>
  <s xml:id="echoid-s15188" xml:space="preserve">Circulus enim aliquis maximus in australi horologio, vel <lb/>ſuperiori, per stylum A B, ductus ſaciat ſectionem R S, per locum ſtyli A, tranſeuntem. </s>
  <s xml:id="echoid-s15189" xml:space="preserve">Secabit idem <lb/>ci@culus, cum per stylum tranſeat, boreale horologium, ſeu inferius, per rectam T V, per C, locum ſty-<lb/>li quoque tranſeuntem, in partihus tamen non oppoſitis, ſed correſpondentibus, hoc eſt, ſi ſectio R S, ſu-<lb/>pra ſiylum vergit ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s15190" xml:space="preserve">infra ſtylum ad dextram, deflectet ſectio T V, ſupra ſtylum in par-<lb/>tem dextram, &amp; </s>
  <s xml:id="echoid-s15191" xml:space="preserve">in ſiniſtram infra ſ@ylum, &amp; </s>
  <s xml:id="echoid-s15192" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s15193" xml:space="preserve">Hæ enim partes illis partibus reſpondent, vt patet
<pb o="222" file="0242" n="242" rhead="GNOMONICES"/>
poſitionem vtriuſque horologii diligenter conſideranti. </s>
  <s xml:id="echoid-s15194" xml:space="preserve">Erunt autem ſectiones R S, T V, inter ſe paral-<lb/>
<anchor type="note" xlink:label="note-0242-01a" xlink:href="note-0242-01"/>
lelæ, cum factæ ſint in planis horologiorum parallelis ab eodem circuli maximi plano. </s>
  <s xml:id="echoid-s15195" xml:space="preserve">Quoniam verò &amp; </s>
  <s xml:id="echoid-s15196" xml:space="preserve"><lb/>rectæ A E, C N, parallelæ ſunt, vt dudum oſtendimus; </s>
  <s xml:id="echoid-s15197" xml:space="preserve">erunt anguli E A S, N C V, inter ſe æquales, <lb/>
<anchor type="note" xlink:label="note-0242-02a" xlink:href="note-0242-02"/>
Cum ergo anguli ad verticem E A S, L A R, ſint etiam ęquales, erunt quoque anguli L A R, N C V, <lb/>ęquales. </s>
  <s xml:id="echoid-s15198" xml:space="preserve">Superpoſita ergo rurſus recta A G, rectæ C H, vt punctum A, in punctum C, cadat, &amp; </s>
  <s xml:id="echoid-s15199" xml:space="preserve">in hoc <lb/>ſitu auſtrale ſiue ſuperius horologium conuerti intelligatur circa rectam A G, vel C H, (quę eadem in <lb/>eo ſitu eſt) vt pars ſuperior in inferiorem mutetur, &amp; </s>
  <s xml:id="echoid-s15200" xml:space="preserve">contra, cadet recta A R, in rectam C V, pro-<lb/>pter ęqualitatem angulorum L A R, N C V. </s>
  <s xml:id="echoid-s15201" xml:space="preserve">Eadem{q́ue} ratio eſt de quibuſcunque aliis lineis per A, <lb/>&amp; </s>
  <s xml:id="echoid-s15202" xml:space="preserve">C, loca ſtylorum ductis. </s>
  <s xml:id="echoid-s15203" xml:space="preserve">Quare, vt prius, portio à linea horizontali abſciſſa, ſi inuertatur, vt ante <lb/>dictum eſt, dabit horologium in facie plani horologii oppoſita delineandum.</s>
  <s xml:id="echoid-s15204" xml:space="preserve"/>
</p>
<div xml:id="echoid-div763" type="float" level="2" n="15">
<note position="left" xlink:label="note-0242-01" xlink:href="note-0242-01a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0242-02" xlink:href="note-0242-02a" xml:space="preserve">10. vndec. <lb/>15. primi.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s15205" xml:space="preserve">LIBVIT hæc vberius hoc loco demonſtrare, ne eandem demonſtrationem in ſequentibus cogere-<lb/>mur ſæpius inculcare. </s>
  <s xml:id="echoid-s15206" xml:space="preserve">Magnam enim vtilitatem ſequentibus afferent, vt ſuis locis manifeſtum erit.</s>
  <s xml:id="echoid-s15207" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div765" type="section" level="1" n="181">
<head xml:id="echoid-head184" xml:space="preserve">PROBLEMA 15. PROPOSITIO 15.</head>
<p>
  <s xml:id="echoid-s15208" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio Ver-<lb/>ticali deſcribere.</s>
  <s xml:id="echoid-s15209" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15210" xml:space="preserve">SI loco radiorum Zodiaci ex puncto D, figuræ radiorum Zodiaci antecedentis propoſ. </s>
  <s xml:id="echoid-s15211" xml:space="preserve">edu-<lb/>
<anchor type="note" xlink:label="note-0242-04a" xlink:href="note-0242-04"/>
<anchor type="note" xlink:label="note-0242-05a" xlink:href="note-0242-05"/>
cantur radii longitudinum dierum inuenti propoſ. </s>
  <s xml:id="echoid-s15212" xml:space="preserve">33. </s>
  <s xml:id="echoid-s15213" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15214" xml:space="preserve">vel in Analemmate eiuſdem <lb/>
<anchor type="figure" xlink:label="fig-0242-01a" xlink:href="fig-0242-01"/>
<anchor type="note" xlink:label="note-0242-06a" xlink:href="note-0242-06"/>
<anchor type="note" xlink:label="note-0242-07a" xlink:href="note-0242-07"/>
præcedentis propoſ. </s>
  <s xml:id="echoid-s15215" xml:space="preserve">loco parallelorum per initia ſignorum tranſeuntium aſſumantur paralleli ar-<lb/>cuum diurnorum; </s>
  <s xml:id="echoid-s15216" xml:space="preserve">deſcribemus parallelos horum arcuum eo modo, quo ſignorum parallelos de-<lb/>ſcripſimus. </s>
  <s xml:id="echoid-s15217" xml:space="preserve">Eadem enim eſt in his, &amp; </s>
  <s xml:id="echoid-s15218" xml:space="preserve">in illis ratio, cum omnes Aequatori ſint æquidiſtantes. </s>
  <s xml:id="echoid-s15219" xml:space="preserve">Pa-<lb/>rallelos igitur arcuum diurnorum, &amp;</s>
  <s xml:id="echoid-s15220" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15221" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s15222" xml:space="preserve"/>
</p>
<div xml:id="echoid-div765" type="float" level="2" n="1">
<note position="left" xlink:label="note-0242-04" xlink:href="note-0242-04a" xml:space="preserve">Deſcriptio ar-<lb/>cuum diurnorũ <lb/>in prædicto ho-<lb/>rologio Verti-<lb/>cali.</note>
<note position="left" xlink:label="note-0242-05" xlink:href="note-0242-05a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0242-01" xlink:href="fig-0242-01a">
    <image file="0242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0242-01"/>
  </figure>
<note position="left" xlink:label="note-0242-06" xlink:href="note-0242-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0242-07" xlink:href="note-0242-07a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div767" type="section" level="1" n="182">
<head xml:id="echoid-head185" xml:space="preserve">PROBLEMA. 16. PROPOSITIO 16.</head>
<p>
  <s xml:id="echoid-s15223" xml:space="preserve">CIRCVLOS Verticales in eodem horologio Verticali de-<lb/>ſcribere.</s>
  <s xml:id="echoid-s15224" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15225" xml:space="preserve">IN lineam meridianam horologii ex G, loco ſtyli transferatur magnitudo ſtyli vſque ad A, <lb/>
<anchor type="note" xlink:label="note-0242-09a" xlink:href="note-0242-09"/>
punctum, quod vel infra G, vel ſupra ſumi poteſt. </s>
  <s xml:id="echoid-s15226" xml:space="preserve">Ex A, autem circulus cuiuſque magnitudinis <lb/>deſcribatur, quo diuiſo in 360. </s>
  <s xml:id="echoid-s15227" xml:space="preserve">partes æquales, initio facto à linea meridiana, ſi omnes Verticales <lb/>deſiderentur, vel in pauciores, pro numero Verticalium deſcribendorum, (Nos eum diuiſimus in <lb/>24. </s>
  <s xml:id="echoid-s15228" xml:space="preserve">vt ſingula ſpatia contineant 15. </s>
  <s xml:id="echoid-s15229" xml:space="preserve">grad.) </s>
  <s xml:id="echoid-s15230" xml:space="preserve">ducantur per diuiſionum puncta, &amp; </s>
  <s xml:id="echoid-s15231" xml:space="preserve">centrum A, rectæ <lb/>occultæ ſecantes lineam horizontalem in punctis, per quæ ſi ducantur rectę æquidiſtantes lineæ
<pb o="223" file="0243" n="243" rhead="LIBER SECVNDVS."/>
meridianæ H I, deſcripti erunt circuli Verticales. </s>
  <s xml:id="echoid-s15232" xml:space="preserve">Facile autem ducentur hæ lineæ æquidiſtantes, <lb/>ſi per quodcunque punctum lineæ meridianæ, vt per B, horizontali lineæ parallela agatur, &amp; </s>
  <s xml:id="echoid-s15233" xml:space="preserve">om-<lb/>nia puncta lineæ horizontalis beneficio circini ex G, ſumpta transferantur in dictam parallelam <lb/>ex puncto B. </s>
  <s xml:id="echoid-s15234" xml:space="preserve">Nam rectæ connectentes bina puncta æqualiter à G, &amp; </s>
  <s xml:id="echoid-s15235" xml:space="preserve">B, remota ipſi G B, pa-<lb/>
<anchor type="note" xlink:label="note-0243-01a" xlink:href="note-0243-01"/>
rallelæ erunt.</s>
  <s xml:id="echoid-s15236" xml:space="preserve"/>
</p>
<div xml:id="echoid-div767" type="float" level="2" n="1">
<note position="left" xlink:label="note-0242-09" xlink:href="note-0242-09a" xml:space="preserve">Deſcriptio eir-<lb/>culorum Verti-<lb/>calium in eode <lb/>Verticali horo-<lb/>logio.</note>
<note position="right" xlink:label="note-0243-01" xlink:href="note-0243-01a" xml:space="preserve">33. primi.</note>
</div>
<p>
  <s xml:id="echoid-s15237" xml:space="preserve">QVOD autem <lb/>
<anchor type="figure" xlink:label="fig-0243-01a" xlink:href="fig-0243-01"/>
<anchor type="note" xlink:label="note-0243-02a" xlink:href="note-0243-02"/>
huiuſmodi parallelæ <lb/>ſint in plano Vertica <lb/>lis horologii circuli <lb/>Verticales, ſeu potius <lb/>
<anchor type="note" xlink:label="note-0243-03a" xlink:href="note-0243-03"/>
communes ſectiones <lb/>Verticalium circulo-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s15238" xml:space="preserve">pìani horo-<lb/>logii Verticalis, hac <lb/>ratione demonſtrabi <lb/>mus. </s>
  <s xml:id="echoid-s15239" xml:space="preserve">Intelligatur pla <lb/>num circuli ex A, de-<lb/>ſcripti circa horizon <lb/>talem lineam circum <lb/>uerti, donec centrum <lb/>
<anchor type="note" xlink:label="note-0243-04a" xlink:href="note-0243-04"/>
A, coniungatur cum <lb/>D, vertice ſtyli, ita vt <lb/>idem ſit, quod pla-<lb/>num Horizontis per <lb/>lineam horizontalẽ, <lb/>&amp; </s>
  <s xml:id="echoid-s15240" xml:space="preserve">gnomonem G D, <lb/>tranſeuntis. </s>
  <s xml:id="echoid-s15241" xml:space="preserve">Quoniã <lb/>igitur communes ſe-<lb/>ctiones Horizontis ac circulorum Verticaliũ per polos Horizontis incedentium diuidunt Hori-<lb/>zontem, atque adeo &amp; </s>
  <s xml:id="echoid-s15242" xml:space="preserve">circulum ex A, deſcriptum, (cum in tali poſitione idem centrum habeant <lb/>
<anchor type="note" xlink:label="note-0243-05a" xlink:href="note-0243-05"/>
Horizon, &amp; </s>
  <s xml:id="echoid-s15243" xml:space="preserve">circulus dictus) in partes æquales; </s>
  <s xml:id="echoid-s15244" xml:space="preserve">erunt rectæ ex A, per puncta diuiſionum tranſeun <lb/>tes, communes ſectiones Verticalium, &amp; </s>
  <s xml:id="echoid-s15245" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s15246" xml:space="preserve">Quare Verticales circuli ſecabunt planum <lb/>horologii in punctis, in quibus dictæ ſectiones communes lineæ horizontali occurrunt. </s>
  <s xml:id="echoid-s15247" xml:space="preserve">Quoniã <lb/>verò, ex propoſ. </s>
  <s xml:id="echoid-s15248" xml:space="preserve">18. </s>
  <s xml:id="echoid-s15249" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15250" xml:space="preserve">communes ſectiones Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s15251" xml:space="preserve">plani horolo-<lb/>gii Verticalis parallelæ ſunt, quòd planum horologij Verticalis æquidiſtet communi illorum ſe-<lb/>ctioni, nempe axi Horizontis per verticem, eiusq́ue oppoſitum ducto; </s>
  <s xml:id="echoid-s15252" xml:space="preserve">manifeſtum eſt, rectas il-<lb/>las, quæ meridianæ lineæ (quę vna eſt ex Verticalibus lineis) parallelæ ſunt, eſſe communes ſectio-<lb/>nes circulorum Verticalium, &amp; </s>
  <s xml:id="echoid-s15253" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s15254" xml:space="preserve">Verticalis autem propriè dictus proiici non po-<lb/>teſt in planum horologii, cum ei æquidiſtet, atque adeò nullam in eo ſectionem faciat. </s>
  <s xml:id="echoid-s15255" xml:space="preserve">Circulos<unsure/> <lb/>ergo Verticales in eodem Verticali horologio deſcripſimus. </s>
  <s xml:id="echoid-s15256" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s15257" xml:space="preserve"/>
</p>
<div xml:id="echoid-div768" type="float" level="2" n="2">
  <figure xlink:label="fig-0243-01" xlink:href="fig-0243-01a">
    <image file="0243-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243-01"/>
  </figure>
<note position="right" xlink:label="note-0243-02" xlink:href="note-0243-02a" xml:space="preserve">Demonſtratio <lb/>deſcription is <lb/>Verticalium c<unsure/>it <lb/>culorum.</note>
<note position="left" xlink:label="note-0243-03" xlink:href="note-0243-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0243-04" xlink:href="note-0243-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0243-05" xlink:href="note-0243-05a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div770" type="section" level="1" n="183">
<head xml:id="echoid-head186" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s15258" xml:space="preserve">PERSPICVVM autem eſt, hos circulos Verticales, auſtrales eſſe in horologio, quod ad meri-<lb/>
<anchor type="note" xlink:label="note-0243-07a" xlink:href="note-0243-07"/>
diem ſpectat; </s>
  <s xml:id="echoid-s15259" xml:space="preserve">In eo verò, quod ad Bore@m, Septentrionales. </s>
  <s xml:id="echoid-s15260" xml:space="preserve">In vtroque porrò numerus graduum ter-<lb/>minatur in linea meridiana; </s>
  <s xml:id="echoid-s15261" xml:space="preserve">eadem{q́ue} vtrobique eſt deſcriptio. </s>
  <s xml:id="echoid-s15262" xml:space="preserve">Vnde &amp; </s>
  <s xml:id="echoid-s15263" xml:space="preserve">hic linea horizontalis abſcindet <lb/>portionem, quæ ponenda erit in facie boreali, ita tamen vt horizont alis linea in ſuperiori loco collocetur, <lb/>vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15264" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15265" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15266" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s15267" xml:space="preserve">Non eſt autem hic opus mutare dextram partem <lb/>in ſiniſtram, &amp; </s>
  <s xml:id="echoid-s15268" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s15269" xml:space="preserve">quia ĳ dem numeri ſunt in vtraque parte, &amp; </s>
  <s xml:id="echoid-s15270" xml:space="preserve">eundem ſitum habent lineę Verti-<lb/>cales ad vtraſque partes meridianæ lineæ, vt conſtat.</s>
  <s xml:id="echoid-s15271" xml:space="preserve"/>
</p>
<div xml:id="echoid-div770" type="float" level="2" n="1">
<note position="right" xlink:label="note-0243-07" xlink:href="note-0243-07a" xml:space="preserve">Verticales @ir-<lb/>culi in auſtrali <lb/>horologio om-<lb/>nes ſunt auſtra <lb/>les, &amp; boreal@s <lb/>in boreali.</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div772" type="section" level="1" n="184">
<head xml:id="echoid-head187" xml:space="preserve">PROBLEMA 17. PROPOSITIO 17.</head>
<p>
  <s xml:id="echoid-s15272" xml:space="preserve">PARALLELOS Horizontis in codem horologio Verticali <lb/>deſcribere.</s>
  <s xml:id="echoid-s15273" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15274" xml:space="preserve">DESCRIBATVR Analemmatis Meridianus A B C D, in quo Horizontis diameter B D; <lb/></s>
  <s xml:id="echoid-s15275" xml:space="preserve">
<anchor type="note" xlink:label="note-0243-09a" xlink:href="note-0243-09"/>
diameter Verticalis A C. </s>
  <s xml:id="echoid-s15276" xml:space="preserve">Diuiſo autem vtroque quadrante A B, A D, in 90 partes æquales, vt ſin <lb/>gulæ partes ſingulos complectantur gradus, vel in pauciores; </s>
  <s xml:id="echoid-s15277" xml:space="preserve">pro magnitudine horologii, (Nos <lb/>vtrumque partiti ſumus in fex, vt ſingulæ partes reſpondeant 15. </s>
  <s xml:id="echoid-s15278" xml:space="preserve">gradibus) iungantur bina puncta <lb/>æqualiter à recta B D, diſtantia lineis rectis, quæ communes ſectiones erunt Meridiani, &amp; </s>
  <s xml:id="echoid-s15279" xml:space="preserve">paralle-
<pb o="224" file="0244" n="244" rhead="GNOMONICES"/>
lorum Horizontis, quos Almucantarath dicunt, Deinde ex punctis diuiſionum vtriuſque qua-<lb/>drantis per centrum E, ducantur rectæ lineæ, vt fiant triangula per axem in conis, quorum baſes <lb/>ſunt paralleli Horizontis tam infra Horizontem, quàm ſupra, vertex autem communis centrum <lb/>
<anchor type="figure" xlink:label="fig-0244-01a" xlink:href="fig-0244-01"/>
mũdi E. </s>
  <s xml:id="echoid-s15280" xml:space="preserve">Meridianus enim A B C D, <lb/>dictos conos ſecans per eorum axem <lb/>A C, facit, per propoſ. </s>
  <s xml:id="echoid-s15281" xml:space="preserve">3. </s>
  <s xml:id="echoid-s15282" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15283" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15284" xml:space="preserve">Apol-<lb/>lonii, triangula per axem. </s>
  <s xml:id="echoid-s15285" xml:space="preserve">Abſcin-<lb/>datur quoque ex B D, vtrinque à pun <lb/>cto E, recta E G, gnomoni æqualis, <lb/>&amp; </s>
  <s xml:id="echoid-s15286" xml:space="preserve">per G, ipſi A C, parallela agatur <lb/>
<anchor type="note" xlink:label="note-0244-01a" xlink:href="note-0244-01"/>
G O, cõmunis videlicet ſectio plani <lb/>horologii, &amp; </s>
  <s xml:id="echoid-s15287" xml:space="preserve">Meridiani, ſecans latera <lb/>triangulorum per axem in K, L, M, <lb/>N, punctis, vt ſint diametri conica-<lb/>rum ſectionum K O, L, M O, N O. <lb/></s>
  <s xml:id="echoid-s15288" xml:space="preserve">Si igitur puncta K, L, M, N, ſumpta <lb/>in hoc Analemmate ex puncto G, in <lb/>lineam meridianam vtriuſque horo-<lb/>logii transferantur infra horizonta-<lb/>lem lineam ex loco ſtyli G, &amp; </s>
  <s xml:id="echoid-s15289" xml:space="preserve">circa <lb/>
<anchor type="note" xlink:label="note-0244-02a" xlink:href="note-0244-02"/>
lineam meridianam dictæ conicæ ſe-<lb/>ctiones deſcribantur, per propoſ. </s>
  <s xml:id="echoid-s15290" xml:space="preserve">8. <lb/></s>
  <s xml:id="echoid-s15291" xml:space="preserve">ſuperioris lib tranſeuntes per pun-<lb/>cta K, L, M, N, (quæ quidem coni-<lb/>cæ ſectiones ſunt hyperbolæ, per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s15292" xml:space="preserve">6, antecedentis lib. </s>
  <s xml:id="echoid-s15293" xml:space="preserve">cum Verticalis per polos parallelorum Horizontis incedens ipſos ſecet) <lb/>ita vt earum cornua à linea horizontali ſemper magis ac magis auertantur, deſcripti erunt pa-<lb/>ralleli Horizontis, vt in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s15294" xml:space="preserve">cernitur.</s>
  <s xml:id="echoid-s15295" xml:space="preserve"/>
</p>
<div xml:id="echoid-div772" type="float" level="2" n="1">
<note position="right" xlink:label="note-0243-09" xlink:href="note-0243-09a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis, ſiue Al <lb/>mucatarath, in <lb/>eodem Verti@@ <lb/>li horologio.</note>
  <figure xlink:label="fig-0244-01" xlink:href="fig-0244-01a">
    <image file="0244-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-01"/>
  </figure>
<note position="left" xlink:label="note-0244-01" xlink:href="note-0244-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0244-02" xlink:href="note-0244-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s15296" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s15297" xml:space="preserve">Deſcripto quadrante A B C, cuiuslibet magnitudinis, diuiſoq́; </s>
  <s xml:id="echoid-s15298" xml:space="preserve">in 90. </s>
  <s xml:id="echoid-s15299" xml:space="preserve">gradus, vel <lb/>
<anchor type="note" xlink:label="note-0244-03a" xlink:href="note-0244-03"/>
in pauciores partes, pro numero parallelorum de-<lb/>
<anchor type="note" xlink:label="note-0244-04a" xlink:href="note-0244-04"/>
<anchor type="figure" xlink:label="fig-0244-02a" xlink:href="fig-0244-02"/>
ſcribendorum, emittantur ex centro A, per puncta <lb/>diuiſionum lineæ rectæ, quæ reſpondebunt radiis <lb/>parallelorũ Horizontis in quadrante E B C, præce-<lb/>dentis figuræ contentis, initio facto à recta A B, ita <lb/>vt radius proximus rectæ A B, ſit paralleli Horizon <lb/>tis grad. </s>
  <s xml:id="echoid-s15300" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15301" xml:space="preserve">ſequens 30 &amp;</s>
  <s xml:id="echoid-s15302" xml:space="preserve">c vt numeri declarant.</s>
  <s xml:id="echoid-s15303" xml:space="preserve"/>
</p>
<div xml:id="echoid-div773" type="float" level="2" n="2">
<note position="left" xlink:label="note-0244-03" xlink:href="note-0244-03a" xml:space="preserve">Alia deſcriptio <lb/>parallelor@ Ho <lb/>rizontis in Ver <lb/>ticali horolo-<lb/>gio.</note>
<note position="left" xlink:label="note-0244-04" xlink:href="note-0244-04a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0244-02" xlink:href="fig-0244-02a">
    <image file="0244-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0244-02"/>
  </figure>
</div>
<p>
  <s xml:id="echoid-s15304" xml:space="preserve">POST hæc ex horologio præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s15305" xml:space="preserve">ſumantur interualla inter centrum A, &amp; </s>
  <s xml:id="echoid-s15306" xml:space="preserve">puncta, <lb/>quibus Verticales lineæ horizontalem lineam inter-<lb/>ſecant, eaq́; </s>
  <s xml:id="echoid-s15307" xml:space="preserve">ex A, in@rectam A B, huius figuræ trans-<lb/>
<anchor type="note" xlink:label="note-0244-05a" xlink:href="note-0244-05"/>
ferantur, aſcriptis iuxta A B, numeris Verticalium <lb/>linearum, ſignatisq́; </s>
  <s xml:id="echoid-s15308" xml:space="preserve">punctis, quæ dicta interualla <lb/>terminant. </s>
  <s xml:id="echoid-s15309" xml:space="preserve">Poſtremo per puncta in recta A B, nota-<lb/>ta agantur ipſi A C, parallelæ, vel perpendiculares <lb/>ad A B, ducantur. </s>
  <s xml:id="echoid-s15310" xml:space="preserve">Quod facile fiet, ſi ipſi A B, pa-<lb/>rallela aliqua ducatur, &amp; </s>
  <s xml:id="echoid-s15311" xml:space="preserve">in hanc puncta lineæ <lb/>A B, transferantur, initio facto à recta A C, &amp;</s>
  <s xml:id="echoid-s15312" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15313" xml:space="preserve">Exem <lb/>pli gratia, ex figura præcedentis propoſ. </s>
  <s xml:id="echoid-s15314" xml:space="preserve">interual-<lb/>lum A K, transferatur in rectam A B, huius figuræ, <lb/>vſque ad punctum E, apponendo numerum 30, &amp; </s>
  <s xml:id="echoid-s15315" xml:space="preserve">per E, ipſi A C, parallela agatur E F, &amp;</s>
  <s xml:id="echoid-s15316" xml:space="preserve">c.</s>
  <s xml:id="echoid-s15317" xml:space="preserve"/>
</p>
<div xml:id="echoid-div774" type="float" level="2" n="3">
<note position="left" xlink:label="note-0244-05" xlink:href="note-0244-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s15318" xml:space="preserve">HAC figura in hunc modum parata, deſcribentur hac ratione paralleli Horizontis, id eſt, ar-<lb/>cus altitudinum Solis. </s>
  <s xml:id="echoid-s15319" xml:space="preserve">Interualla linearum ipſi A C, æquidiſtantium inter rectam A B, &amp; </s>
  <s xml:id="echoid-s15320" xml:space="preserve">radiũ <lb/>v. </s>
  <s xml:id="echoid-s15321" xml:space="preserve">g. </s>
  <s xml:id="echoid-s15322" xml:space="preserve">paralleli Horizontis grad. </s>
  <s xml:id="echoid-s15323" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15324" xml:space="preserve">comprehenſa transferantur vtrinque ex punctis, in quibus ho-<lb/>rizontalis linea in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s15325" xml:space="preserve">à lineis Verticalibus ſecatur, in lineas Vertica@es cor <lb/>reſpondentes numeris in recta A B, huius figuræ notatis, ſignando puncta in Verticalibus lineis. <lb/></s>
  <s xml:id="echoid-s15326" xml:space="preserve">Verbi gratia, rectæ E F, capiatur æqualis K L, in vtraque Verticali linea grad. </s>
  <s xml:id="echoid-s15327" xml:space="preserve">30. </s>
  <s xml:id="echoid-s15328" xml:space="preserve">tam infra horizon <lb/>talem lineam, quàm ſupra, &amp; </s>
  <s xml:id="echoid-s15329" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s15330" xml:space="preserve">Nam ſi hæc puncta appoſitè coniungantur linea qua-<lb/>dam curua, deſcriptus erit arcus, vel parallelus Horizontis gr. </s>
  <s xml:id="echoid-s15331" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15332" xml:space="preserve">tam in auſtrali horologio, quàm <lb/>in boreali, quod quidem abſcinditur à linea horizontali, vt oſtendimus. </s>
  <s xml:id="echoid-s15333" xml:space="preserve">Eodem modo paralleli <lb/>reliqui Horizontis deſcribentur, ſi rectæ inter lineam A B, &amp; </s>
  <s xml:id="echoid-s15334" xml:space="preserve">radios parallelorum Horizontis in-<lb/>terceptæ in lineas Verticales horologii correſpondentes ex linea horizontali vtrinque transferan-
<pb o="225" file="0245" n="245" rhead="LIBER SECVNDVS."/>
tur. </s>
  <s xml:id="echoid-s15335" xml:space="preserve">Non eſt tamen neceſſarium, vt dictas rectas omnes transferamus in Verticales lineas vtrin-<lb/>que, hoc eſt, ſupra, &amp; </s>
  <s xml:id="echoid-s15336" xml:space="preserve">infra horizontalem lineam; </s>
  <s xml:id="echoid-s15337" xml:space="preserve">quia non eſt opus tot parallelos Horizontis de-<lb/>ſcribere in horologio boreali, quot in Verticali. </s>
  <s xml:id="echoid-s15338" xml:space="preserve">Ita vides nos in Boreali deſcripſiſ@e duntaxat pa-<lb/>rall<unsure/>elum grad. </s>
  <s xml:id="echoid-s15339" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15340" xml:space="preserve">quia alii caderent extra tropicum omnino, ac proinde in illos vmbra cade-<lb/>re non poſſet.</s>
  <s xml:id="echoid-s15341" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15342" xml:space="preserve">RECTE autem hac arte deſcribi parallelos Horizontis, ita demonſtrabitur. </s>
  <s xml:id="echoid-s15343" xml:space="preserve">Intelligatur in <lb/>
<anchor type="note" xlink:label="note-0245-01a" xlink:href="note-0245-01"/>
figura præcedentis propoſ. </s>
  <s xml:id="echoid-s15344" xml:space="preserve">recta A G, quæ gnomoni ſumpta eſt æqualis, ad rectos angulos plano <lb/>horologii inſiſtere in puncto G, &amp; </s>
  <s xml:id="echoid-s15345" xml:space="preserve">figura nuper conſtructa circa punctum A. </s>
  <s xml:id="echoid-s15346" xml:space="preserve">cum centro mundi <lb/>coniunctum circumduci, ita vt punctum A, huius figuræ à puncto A, figuræ præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s15347" xml:space="preserve">hoc eſt, à centro mundi nunquam recedat, &amp; </s>
  <s xml:id="echoid-s15348" xml:space="preserve">recta A C, perpetuo lineæ meridianæ H I, æquidiſtet, <lb/>
<anchor type="note" xlink:label="note-0245-02a" xlink:href="note-0245-02"/>
hoc eſt, coniuncta ſit axi Horizontis, eiusq́ue parallelorum, ac punctum B, verſus horologium por <lb/>rigatur, &amp; </s>
  <s xml:id="echoid-s15349" xml:space="preserve">propterea recta A B, à plano Horizontis non recedens occurrat ſemper illo motu hori-<lb/>zontali lineæ: </s>
  <s xml:id="echoid-s15350" xml:space="preserve">Cadet in hac circumductione punctum E, v. </s>
  <s xml:id="echoid-s15351" xml:space="preserve">g. </s>
  <s xml:id="echoid-s15352" xml:space="preserve">in punctum K, propterea quòd re <lb/>ctæ A K, in præcedẽti propoſ. </s>
  <s xml:id="echoid-s15353" xml:space="preserve">ſumpta eſt hic æqualis A E Eſt enim recta A K, cadens ex puncto A, <lb/>in ſublimi, nempe à vertice ſtyli, rectæ A K, in plano horologii æqualis; </s>
  <s xml:id="echoid-s15354" xml:space="preserve">Vt facile probabitur, ſi <lb/>triangulum A K G, in plano conferatur cum triangulo A K G, in ſublimi. </s>
  <s xml:id="echoid-s15355" xml:space="preserve">Cum enim latera A G, <lb/>G K, illius æqualia ſint lateribus A G, G K, huius, angulosq́; </s>
  <s xml:id="echoid-s15356" xml:space="preserve">contineant æquales, vtpote rectos; </s>
  <s xml:id="echoid-s15357" xml:space="preserve">erit <lb/>baſis A K, illius baſi A K, huius æqualis. </s>
  <s xml:id="echoid-s15358" xml:space="preserve">Cum igitur tam recta K L, quàm E F, axi Horizontis <lb/>
<anchor type="note" xlink:label="note-0245-03a" xlink:href="note-0245-03"/>
æquidiſtet, erunt quoque K L, E F, inter ſe parallelæ; </s>
  <s xml:id="echoid-s15359" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15360" xml:space="preserve">idcirco congruente puncto E, ipſi K, pun-<lb/>
<anchor type="note" xlink:label="note-0245-04a" xlink:href="note-0245-04"/>
cto, vt oſtendimus, congruet etiam recta E F, rectæ K L; </s>
  <s xml:id="echoid-s15361" xml:space="preserve">alias non eſſer illa huic parallela, quando-<lb/>
<anchor type="note" xlink:label="note-0245-05a" xlink:href="note-0245-05"/>
quidem ambæ in illa circumductione conueniunt in puncto K. </s>
  <s xml:id="echoid-s15362" xml:space="preserve">Igitur cum K L, ſumpta ſit æqua-<lb/>lis rectæ E F, cadet punctum F, in punctum L, atque adeò radius paralleli Horizontis grad. </s>
  <s xml:id="echoid-s15363" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15364" xml:space="preserve">pla-<lb/>no horologii occurret in L. </s>
  <s xml:id="echoid-s15365" xml:space="preserve">Per punctum ergo L, tranſibit arcus paralleli prædicti grad. </s>
  <s xml:id="echoid-s15366" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15367" xml:space="preserve">cum <lb/>in illud radius dicti paralleli incidat in illa circumuolutione, vt oſtenſum eſt. </s>
  <s xml:id="echoid-s15368" xml:space="preserve">Non aliter demon-<lb/>ſtrabimus punctum M, eiuſdem radii cadere in punctum N, &amp; </s>
  <s xml:id="echoid-s15369" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s15370" xml:space="preserve">Parallelos igitur <lb/>Horizontis in eodem horologio Verticali deſcripſimns. </s>
  <s xml:id="echoid-s15371" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s15372" xml:space="preserve"/>
</p>
<div xml:id="echoid-div775" type="float" level="2" n="4">
<note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">Demonſtratio <lb/>poſterioris de-<lb/>ſcriptionis pa-<lb/>rallelorum Ho <lb/>rizontis.</note>
<note position="left" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0245-05" xlink:href="note-0245-05a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div777" type="section" level="1" n="185">
<head xml:id="echoid-head188" xml:space="preserve">PROBLEMA 18. PROPOSITIO 18.</head>
<p>
  <s xml:id="echoid-s15373" xml:space="preserve">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in eo-<lb/>
<anchor type="note" xlink:label="note-0245-06a" xlink:href="note-0245-06"/>
dem Verticali horologio deſcribere.</s>
  <s xml:id="echoid-s15374" xml:space="preserve"/>
</p>
<div xml:id="echoid-div777" type="float" level="2" n="1">
<note position="left" xlink:label="note-0245-06" xlink:href="note-0245-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s15375" xml:space="preserve">HI deſcribuntur, vt lineæ horarię à meridie, vel media nocte, quemadmodum propoſ. </s>
  <s xml:id="echoid-s15376" xml:space="preserve">6. </s>
  <s xml:id="echoid-s15377" xml:space="preserve">hu-<lb/>
<anchor type="note" xlink:label="note-0245-07a" xlink:href="note-0245-07"/>
ius libri diximus, dummodo circulus ex E, deſcriptus initium diuiſionis habeat à Meridiano inſu <lb/>larum Fortunatarum, qui habetur, ſi longitudo loci numeretur ab N, in horologio quidem auſtra-<lb/>li propoſ. </s>
  <s xml:id="echoid-s15378" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15379" xml:space="preserve">huius libri deſcripto verſus ſiniſtram, in boreali verò verſus dextram, nempe ad par <lb/>tes ſemper occidentales, vt ratio poſtulat. </s>
  <s xml:id="echoid-s15380" xml:space="preserve">Quod quidem facile intelligetur, ſi in vtroque horolo-<lb/>gio circulus ex E, deſcriptus circumuertatur circa lineam æquinoctialem, donec propriam adipi-<lb/>ſcatur poſitionem, nempe in plano Aequatoris ſit conſtitutus, &amp;</s>
  <s xml:id="echoid-s15381" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15382" xml:space="preserve">Itaque Meridianos, ſeu circu-<lb/>
<anchor type="note" xlink:label="note-0245-08a" xlink:href="note-0245-08"/>
los longitudinum ciuitatum in eodem Verticali horologio deſcripſimus. </s>
  <s xml:id="echoid-s15383" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s15384" xml:space="preserve"/>
</p>
<div xml:id="echoid-div778" type="float" level="2" n="2">
<note position="right" xlink:label="note-0245-07" xlink:href="note-0245-07a" xml:space="preserve">Deſcriptio Me-<lb/>ridianorum in <lb/>eodem horolo-<lb/>gio Verticali.</note>
<note position="left" xlink:label="note-0245-08" xlink:href="note-0245-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div780" type="section" level="1" n="186">
<head xml:id="echoid-head189" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s15385" xml:space="preserve">SI circuli Meridiani, vel potius communes eorum, &amp; </s>
  <s xml:id="echoid-s15386" xml:space="preserve">plani horologii ſectiones in auſtrali horologio <lb/>
<anchor type="note" xlink:label="note-0245-09a" xlink:href="note-0245-09"/>
producantur vltra lineam horizontalem, &amp; </s>
  <s xml:id="echoid-s15387" xml:space="preserve">centrum H, habebuntur quoque iidem Meridiani circuli in <lb/>horologio boreali, quod quidem linea horizontalis abſcindit, dummodo memor ſis, totum horologium de-<lb/>bere inuerti, ita vt ſuperiora fiant inferiora, &amp; </s>
  <s xml:id="echoid-s15388" xml:space="preserve">dextra euadant ſiniſtra, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15389" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15390" xml:space="preserve">huius <lb/>libri oſtenſum eſt: </s>
  <s xml:id="echoid-s15391" xml:space="preserve">Item has ſectiones Meridianorum, &amp; </s>
  <s xml:id="echoid-s15392" xml:space="preserve">plani horologii auſtralis referre in borcali ho-<lb/>rologio ſectiones ſemicir culorum Meridianorum oppoſitorum, ita vt habeant numeros, qui conficiuntur <lb/>
<anchor type="note" xlink:label="note-0245-10a" xlink:href="note-0245-10"/>
ex additione graduum 180. </s>
  <s xml:id="echoid-s15393" xml:space="preserve">ad numeros, quos habent in horologio auſtrali, (abiectis tamen grad. </s>
  <s xml:id="echoid-s15394" xml:space="preserve">360. <lb/></s>
  <s xml:id="echoid-s15395" xml:space="preserve">ſi ex illa additione fiat maior numerus, quàm grad. </s>
  <s xml:id="echoid-s15396" xml:space="preserve">360.) </s>
  <s xml:id="echoid-s15397" xml:space="preserve">vel certè qui in circulo ex E, deſcripto per <lb/>diametrum opponuntur numeris illis, quos dictæ ſectiones habent in horologio auſtrali. </s>
  <s xml:id="echoid-s15398" xml:space="preserve">Veruntamen li-<lb/>neæ auſtralis horologii vltra centrum H, protractæ habebunt in boreali iterum eoſdem omnino numeros, <lb/>quos in auſtrali horologio, propterea quòd illæ in horologio boreali ſint iterum ſectiones ſemicir culorum <lb/>oppoſitorum, quemadmodum de lineis horariis à meridie, vel media nocte dictum est. </s>
  <s xml:id="echoid-s15399" xml:space="preserve">I<unsure/>bi enim linea <lb/>v. </s>
  <s xml:id="echoid-s15400" xml:space="preserve">g. </s>
  <s xml:id="echoid-s15401" xml:space="preserve">horę 7. </s>
  <s xml:id="echoid-s15402" xml:space="preserve">à media nocte in auſtrali horologio producta vltra lineam horizontalem, antequam ad cen-<lb/>trum H, perueniat, indicat in horeali horologio (ſi fiat inuerſio ſupradicta horologii) horam 7. </s>
  <s xml:id="echoid-s15403" xml:space="preserve">à meri-<lb/>di@, hoc eſt, communis ſectio eſt plani horologii, &amp; </s>
  <s xml:id="echoid-s15404" xml:space="preserve">ſemicirculi horæ 7. </s>
  <s xml:id="echoid-s15405" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s15406" xml:space="preserve">non à media nocte, <lb/>vt in auſtrali horologio: </s>
  <s xml:id="echoid-s15407" xml:space="preserve">producta verò vltra centrum H, oſtendet iterum horam 7. </s>
  <s xml:id="echoid-s15408" xml:space="preserve">à media nocte, vt <lb/>in horologio auſtrali. </s>
  <s xml:id="echoid-s15409" xml:space="preserve">Eadem{q́ue}<unsure/> ratio de cæteris habenda eſt, vt perſpicuum eſt ex horologio propoſ. </s>
  <s xml:id="echoid-s15410" xml:space="preserve">14.</s>
  <s xml:id="echoid-s15411" xml:space="preserve">
<pb o="226" file="0246" n="246" rhead="GNOMONICES"/>
<anchor type="figure" xlink:label="fig-0246-01a" xlink:href="fig-0246-01"/>
<anchor type="note" xlink:label="note-0246-01a" xlink:href="note-0246-01"/>
<anchor type="note" xlink:label="note-0246-02a" xlink:href="note-0246-02"/>
<anchor type="note" xlink:label="note-0246-03a" xlink:href="note-0246-03"/>
huius libri. </s>
  <s xml:id="echoid-s15412" xml:space="preserve">Ita igitur hic fit. </s>
  <s xml:id="echoid-s15413" xml:space="preserve">Nam Meridianus 120. </s>
  <s xml:id="echoid-s15414" xml:space="preserve">in auſtrali horologio productus vltra lineam ho-<lb/>rizontalem dat in Boreali horologio Meridianum 300. </s>
  <s xml:id="echoid-s15415" xml:space="preserve">ſed vlterius product<unsure/>us per centrum H, præbet in <lb/>eodem horologio bor eali Meridianum iterum 120. </s>
  <s xml:id="echoid-s15416" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s15417" xml:space="preserve">c.</s>
  <s xml:id="echoid-s15418" xml:space="preserve"/>
</p>
<div xml:id="echoid-div780" type="float" level="2" n="1">
<note position="right" xlink:label="note-0245-09" xlink:href="note-0245-09a" xml:space="preserve">Quomodo Me-<lb/>ridiani auſtra-<lb/>lis horologii vl-<lb/>tra lineam hori <lb/>zontalem pro-<lb/>ducti præbeant <lb/>eoſdem Meri-<lb/>dianos in horo <lb/>logio boreali.</note>
<note position="left" xlink:label="note-0245-10" xlink:href="note-0245-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0246-01" xlink:href="fig-0246-01a">
    <image file="0246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0246-01"/>
  </figure>
<note position="left" xlink:label="note-0246-01" xlink:href="note-0246-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0246-02" xlink:href="note-0246-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0246-03" xlink:href="note-0246-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div782" type="section" level="1" n="187">
<head xml:id="echoid-head190" xml:space="preserve">PROBLEMA 19. PROPOSITIO 19.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s15419" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in eo-<lb/>dem horologio Verticali deſcribere.</s>
  <s xml:id="echoid-s15420" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15421" xml:space="preserve">HI deſcribuntur, vt paralleli ſignorum Zodiaci, de quibus egimus propoſ. </s>
  <s xml:id="echoid-s15422" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15423" xml:space="preserve">huius libri; </s>
  <s xml:id="echoid-s15424" xml:space="preserve">ſi <lb/>
<anchor type="note" xlink:label="note-0246-05a" xlink:href="note-0246-05"/>
tamen loco parallelorum per ſigna Zodiaci tranſeuntium, accipiantur paralleli per vertices ciui-<lb/>tatum incedentes, &amp;</s>
  <s xml:id="echoid-s15425" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15426" xml:space="preserve">Parallelos ergo ciuitatum, &amp;</s>
  <s xml:id="echoid-s15427" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15428" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s15429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div782" type="float" level="2" n="1">
<note position="left" xlink:label="note-0246-05" xlink:href="note-0246-05a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ciui <lb/>ratum, latitudi <lb/>numve in eodẽ <lb/>horologio Ver-<lb/>ticali.</note>
</div>
</div>
<div xml:id="echoid-div784" type="section" level="1" n="188">
<head xml:id="echoid-head191" xml:space="preserve">PROBLEMA 20. PROPOSITIO 20.</head>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s15430" xml:space="preserve">DOMOS cœleſtes in eodem horologio Verticali deſcribere.</s>
  <s xml:id="echoid-s15431" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15432" xml:space="preserve">IVXTA ſententiam Ioan. </s>
  <s xml:id="echoid-s15433" xml:space="preserve">Regiom .</s>
  <s xml:id="echoid-s15434" xml:space="preserve">qui vult circulos domorum cœleſtium tranſire per com-<lb/>
<anchor type="note" xlink:label="note-0246-07a" xlink:href="note-0246-07"/>
munes ſectiones Horizontis, ac Meridiani, partiriq́; </s>
  <s xml:id="echoid-s15435" xml:space="preserve">Æquatorem in 12. </s>
  <s xml:id="echoid-s15436" xml:space="preserve">partes æquales, ita domus <lb/>cœleſtes deſcribentur. </s>
  <s xml:id="echoid-s15437" xml:space="preserve">Circulus ex E, deſcriptus ſecetur in 12. </s>
  <s xml:id="echoid-s15438" xml:space="preserve">partes æquales, initio facto à linea <lb/>meridiana; </s>
  <s xml:id="echoid-s15439" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15440" xml:space="preserve">per puncta diniſionum, atque centrum E, rectæ occultæ ductæ ſecent lineam æqui-<lb/>noctialem in punctis, per quæ ex G, vbi linea horizontalis lineam meridianam interſecat, lineæ re-<lb/>ctæ emiſſæ dabunt circulos domorum cœleſtium ſecundum Ioan. </s>
  <s xml:id="echoid-s15441" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s15442" xml:space="preserve">Nam circumducto <lb/>circulo ex E, deſcripto circa lineam æquinoctialem, donec E, coniungatur cum centro mundi, ip-<lb/>
<anchor type="note" xlink:label="note-0246-08a" xlink:href="note-0246-08"/>
feq́; </s>
  <s xml:id="echoid-s15443" xml:space="preserve">circulus in plano Æquatoris iaceat, erunt rectæ per centrum ´E, tranſeuntes, communes ſe-<lb/>ctiones circulorum domorum cœleſtium, (in quorum numero eſt etiam Meridianus) &amp; </s>
  <s xml:id="echoid-s15444" xml:space="preserve">Aequa-
<pb o="227" file="0247" n="247" rhead="LIBER SECVNDVS."/>
toris; </s>
  <s xml:id="echoid-s15445" xml:space="preserve">cum horum circulorum &amp; </s>
  <s xml:id="echoid-s15446" xml:space="preserve">Aequatoris communes ſectiones, ſecundum Ioan. </s>
  <s xml:id="echoid-s15447" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s15448" xml:space="preserve">Ae-<lb/>q uatorem, ac proinde &amp; </s>
  <s xml:id="echoid-s15449" xml:space="preserve">circulum ſibi concentricũ ex E, deſcriptum partiantur in 12. </s>
  <s xml:id="echoid-s15450" xml:space="preserve">partes æqua-<lb/>les, tranſeantq́ue per centrum mundi, in quo nunc punctum E, ponitur. </s>
  <s xml:id="echoid-s15451" xml:space="preserve">Occurrent igitur eiuſmo <lb/>
<anchor type="figure" xlink:label="fig-0247-01a" xlink:href="fig-0247-01"/>
<anchor type="note" xlink:label="note-0247-01a" xlink:href="note-0247-01"/>
<anchor type="note" xlink:label="note-0247-02a" xlink:href="note-0247-02"/>
di eirculi plano horologii in punctis, in quibus lineam æquinoctialem ſecant rectæ per E, trãſmiſ-<lb/>ſæ; </s>
  <s xml:id="echoid-s15452" xml:space="preserve">atque adeo per eadem illa puncta æquinoctialis lineæ tranſibunt communes ſectiones plani <lb/>
<anchor type="note" xlink:label="note-0247-03a" xlink:href="note-0247-03"/>
horologii, &amp; </s>
  <s xml:id="echoid-s15453" xml:space="preserve">circulorum cœleſtium domorum: </s>
  <s xml:id="echoid-s15454" xml:space="preserve">Sed hæ communes ſectiones ſecant quoque ſe <lb/>mutuo in G, ex propoſ. </s>
  <s xml:id="echoid-s15455" xml:space="preserve">18. </s>
  <s xml:id="echoid-s15456" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15457" xml:space="preserve">quòd horum circulorum communis ſectio, nempe axis <lb/>Verticalis circuli, vel ſectio communis Horizontis, ac Meridiani, plano horologii occurrat in G, <lb/>vbi linea meridiana lineam horizontalem ſecat, vt perſpicuum eſt ex portione Analemmatis pro-<lb/>poſ. </s>
  <s xml:id="echoid-s15458" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15459" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s15460" xml:space="preserve">Igitur rectæ ex G, per puncta æquinoctialis lineæ eductæ, communes ſectio-<lb/>nes erunt plani horologii, &amp; </s>
  <s xml:id="echoid-s15461" xml:space="preserve">circulorum domorum cœleſtium. </s>
  <s xml:id="echoid-s15462" xml:space="preserve">Quod eſt propoſitum.</s>
  <s xml:id="echoid-s15463" xml:space="preserve"/>
</p>
<div xml:id="echoid-div784" type="float" level="2" n="1">
<note position="left" xlink:label="note-0246-07" xlink:href="note-0246-07a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium ſecundũ <lb/>Ioan. Regiom. <lb/>in eodem Vet-<lb/>tieali horolo-<lb/>gio.</note>
<note position="left" xlink:label="note-0246-08" xlink:href="note-0246-08a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domorum cœle <lb/>ſtium.</note>
  <figure xlink:label="fig-0247-01" xlink:href="fig-0247-01a">
    <image file="0247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0247-01"/>
  </figure>
<note position="left" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0247-02" xlink:href="note-0247-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0247-03" xlink:href="note-0247-03a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio cœ-<lb/>leſtium domo-<lb/>rum ſecundum <lb/>Campanum in <lb/>eodem Vertica <lb/>li horologio.</note>
<p>
  <s xml:id="echoid-s15464" xml:space="preserve">AT verò ſecundum Campani opinionem, qui circulos domorum cœleſtium ducit per ſectio <lb/>nes communes Meridiani, &amp; </s>
  <s xml:id="echoid-s15465" xml:space="preserve">Horizontis diuidentes Verticalem circulum propriè dictum in 12. <lb/></s>
  <s xml:id="echoid-s15466" xml:space="preserve">partes æquales, ita propoſitum exequemur. </s>
  <s xml:id="echoid-s15467" xml:space="preserve">Ex G, loco ſtyli circulum cuiuſuis magnitudinis de-<lb/>ſcriptum in 12. </s>
  <s xml:id="echoid-s15468" xml:space="preserve">partes æquales diſtribuemus, initio facto à linea horizontali, vel meridiana. </s>
  <s xml:id="echoid-s15469" xml:space="preserve">Nam <lb/>rectæ ex G, per diuiſionum puncta emiſſæ dabunt domos cœleſtes, ſecundum Campanum Quod <lb/>
<anchor type="note" xlink:label="note-0247-05a" xlink:href="note-0247-05"/>
ita oſtendemus.</s>
  <s xml:id="echoid-s15470" xml:space="preserve"/>
</p>
<div xml:id="echoid-div785" type="float" level="2" n="2">
<note position="left" xlink:label="note-0247-05" xlink:href="note-0247-05a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Demonſtratio <lb/>poſterioris de-<lb/>ſcriptionis do-<lb/>morum cœle-<lb/>ſtium.</note>
<p>
  <s xml:id="echoid-s15471" xml:space="preserve">QVONIAM circuli domorum cœleſtium ſecant Verticalem circulum, ſecundum Campa-<lb/>num, in partes æquales, initio facto à communi ſectione Verticalis, &amp; </s>
  <s xml:id="echoid-s15472" xml:space="preserve">Horizontis, atque adeò, &amp; </s>
  <s xml:id="echoid-s15473" xml:space="preserve"><lb/>circulum, quem planum horologii Verticali circulo æquidiſtans in ſphæra, per propoſ. </s>
  <s xml:id="echoid-s15474" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15475" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15476" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s15477" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s15478" xml:space="preserve">facit, in totidem partes æquales diuidunt, initio facto à linea horizontali, nempe à com-<lb/>muni ſectione plani horologii, &amp; </s>
  <s xml:id="echoid-s15479" xml:space="preserve">Horizontis, propterea quòd per polos Verticalis circuli tran-<lb/>ſeuntes diuidant per propoſ. </s>
  <s xml:id="echoid-s15480" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15481" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15482" xml:space="preserve">2. </s>
  <s xml:id="echoid-s15483" xml:space="preserve">Theodoſii, Verticalem, eiusq́; </s>
  <s xml:id="echoid-s15484" xml:space="preserve">parallelos in ſegmenta ſi-<lb/>milia; </s>
  <s xml:id="echoid-s15485" xml:space="preserve">efficitur, vt circuli domorum cœleſtium, atque adeò &amp; </s>
  <s xml:id="echoid-s15486" xml:space="preserve">eorum, ac plani horologii commu <lb/>nes ſectiones, tranſeant per puncta diuiſionum circuli ex G, deſcripti; </s>
  <s xml:id="echoid-s15487" xml:space="preserve">(Nam punctum G, in quod <lb/>cadit axis Verticalis circuli, centrum eſt circuli ab horologii plano in ſphera procreati, per propoſ. </s>
  <s xml:id="echoid-s15488" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0247-07a" xlink:href="note-0247-07"/>
10. </s>
  <s xml:id="echoid-s15489" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15490" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15491" xml:space="preserve">Theodoſii, ac proinde circulus ille, &amp; </s>
  <s xml:id="echoid-s15492" xml:space="preserve">quem ex G, deſcripſimus, in arcus ſimiles diui-<lb/>duntur à rectis lineis è centro G, egredientibus) ac propterea &amp; </s>
  <s xml:id="echoid-s15493" xml:space="preserve">per punctum G, ex ´propoſ. </s>
  <s xml:id="echoid-s15494" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s15495" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15496" xml:space="preserve">in quo nimirum communis ſectio circulorum domorum cœleſtium plano horolo-<lb/>gii occurrit, &amp; </s>
  <s xml:id="echoid-s15497" xml:space="preserve">in quo r<unsure/>idem circuli ſe mutuo ſecant. </s>
  <s xml:id="echoid-s15498" xml:space="preserve">Rectæ ergo illæ ex G, emiſſæ per puncta di-<lb/>uiſionum circuli ex G, deſcripti, communes ſectiones erunt plani horologii, ac circulorum domo <lb/>rum cœleſtium, ſecundum Campanum. </s>
  <s xml:id="echoid-s15499" xml:space="preserve">Quare domos cœleſtes in eodem horologio Verticali de-<lb/>ſcripſimus. </s>
  <s xml:id="echoid-s15500" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s15501" xml:space="preserve"/>
</p>
<div xml:id="echoid-div786" type="float" level="2" n="3">
<note position="left" xlink:label="note-0247-07" xlink:href="note-0247-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Qua ratione <lb/>parté<unsure/>s domorũ <lb/>cœleſtium in <lb/>eodem horolo-<lb/>gio Verticali de <lb/>ſcribantur.</note>
</div>
<div xml:id="echoid-div788" type="section" level="1" n="189">
<head xml:id="echoid-head192" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s15502" xml:space="preserve">QVIA verò quęlibet domus cœleſtis cõtinet 30. </s>
  <s xml:id="echoid-s15503" xml:space="preserve">gradus, ſi quælibet pars duodecima circuli ex E, vel <lb/>G, deſeriptiin 30. </s>
  <s xml:id="echoid-s15504" xml:space="preserve">partes, vel pauciores æquales, pro magnitudine horologii, diuidatur, et reliquafiãt, quæ
<pb o="228" file="0248" n="248" rhead="GNOMONICES"/>
prius, deſcripti erunt alii circuli poſitionum per partes domorum cœleſtium tranſeuntes. </s>
  <s xml:id="echoid-s15505" xml:space="preserve">Id quod &amp; </s>
  <s xml:id="echoid-s15506" xml:space="preserve">in <lb/>domibus cœleſtibus aliorum horologiorum obſeruandum erit.</s>
  <s xml:id="echoid-s15507" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s15508" xml:space="preserve">QVOD ſi lineæ domorum cœleſtium in auſtrali horologio vltra horizontalem lineam excurrant, <lb/>exhibebit nobis portio abſciſſa à linea horizontali, ſi inuertatnr, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15509" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15510" xml:space="preserve">huius libri do-<lb/>cuimus, eaſdem lineas in horologio horeali, vt in eodem ſcholio demonſtratum eſt.</s>
  <s xml:id="echoid-s15511" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div789" type="section" level="1" n="190">
<head xml:id="echoid-head193" xml:space="preserve">PROBLEMA 21. PROPOSITIO 21.</head>
<p>
  <s xml:id="echoid-s15512" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem Verticali horologio <lb/>
<anchor type="note" xlink:label="note-0248-01a" xlink:href="note-0248-01"/>
deſcribere.</s>
  <s xml:id="echoid-s15513" xml:space="preserve"/>
</p>
<div xml:id="echoid-div789" type="float" level="2" n="1">
<note position="left" xlink:label="note-0248-01" xlink:href="note-0248-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s15514" xml:space="preserve">EX prioribus duabus tabellis propoſ. </s>
  <s xml:id="echoid-s15515" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15516" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15517" xml:space="preserve">Sole exiſtente Sole exiſtente in principio ♈, <lb/>
<anchor type="note" xlink:label="note-0248-02a" xlink:href="note-0248-02"/>
&amp; </s>
  <s xml:id="echoid-s15518" xml:space="preserve">♎, ſumantur horæ, quibus 12. </s>
  <s xml:id="echoid-s15519" xml:space="preserve">ſigna Zodiaci oriuntur, quæ in circulo ex E, deſcripto ſupputen-<lb/>tur à linea meridiana vel verſus ortum, vel verſus occaſum, prout tabellæ indicant. </s>
  <s xml:id="echoid-s15520" xml:space="preserve">Per fines dein <lb/>
<anchor type="figure" xlink:label="fig-0248-01a" xlink:href="fig-0248-01"/>
<anchor type="note" xlink:label="note-0248-03a" xlink:href="note-0248-03"/>
<anchor type="note" xlink:label="note-0248-04a" xlink:href="note-0248-04"/>
<anchor type="note" xlink:label="note-0248-05a" xlink:href="note-0248-05"/>
de ſupputationum, &amp; </s>
  <s xml:id="echoid-s15521" xml:space="preserve">centrum E, rectæ occultæ educantur ſecantes lineam æquinoctialem in pun-<lb/>ctis, per quæ lineæ aſcen dentium ſignorum, hoc eſt, communes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s15522" xml:space="preserve">Zo-<lb/>diaci in ortu ſignorum duci debent. </s>
  <s xml:id="echoid-s15523" xml:space="preserve">Verbi gratia, quoniam Sole exiſtente in æquinoctiali circulo, <lb/>nempe in principio ♈, principium ♉, oritur hora 4. </s>
  <s xml:id="echoid-s15524" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s15525" xml:space="preserve">51. </s>
  <s xml:id="echoid-s15526" xml:space="preserve">ante meridiem, ſupputandę erunt <lb/>in horologio auſtrali horæ 4. </s>
  <s xml:id="echoid-s15527" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s15528" xml:space="preserve">51. </s>
  <s xml:id="echoid-s15529" xml:space="preserve">à puncto N, dextram verſus vſq; </s>
  <s xml:id="echoid-s15530" xml:space="preserve">ad punctum A; </s>
  <s xml:id="echoid-s15531" xml:space="preserve">atque per <lb/>A, &amp; </s>
  <s xml:id="echoid-s15532" xml:space="preserve">centrum E, recta occulta protrahenda ſecans æquinoctialem lineam in B, puncto, per quod <lb/>traiicienda eſt linea aſcendentis ſigni ♉. </s>
  <s xml:id="echoid-s15533" xml:space="preserve">Nam Sole exiſtente in principio ♈, &amp; </s>
  <s xml:id="echoid-s15534" xml:space="preserve">oriente ♉, hoc eſt, <lb/>hora 4. </s>
  <s xml:id="echoid-s15535" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s15536" xml:space="preserve">51 ante meridiem, vmbra gnomonis proiicitur in punctum B, vt conſtat ex iis, quæ <lb/>propoſ. </s>
  <s xml:id="echoid-s15537" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15538" xml:space="preserve">huius libri demonſtrata ſunt. </s>
  <s xml:id="echoid-s15539" xml:space="preserve">Non ſecus inquirenda erunt puncta aliorum ſignorum <lb/>aſcendentium in linea æquinoctiali.</s>
  <s xml:id="echoid-s15540" xml:space="preserve"/>
</p>
<div xml:id="echoid-div790" type="float" level="2" n="2">
<note position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">Deſcriptio aſcẽ <lb/>dentium ſigno-<lb/>rum in eodem <lb/>horologio Ver <lb/>ticali.</note>
  <figure xlink:label="fig-0248-01" xlink:href="fig-0248-01a">
    <image file="0248-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0248-01"/>
  </figure>
<note position="left" xlink:label="note-0248-03" xlink:href="note-0248-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0248-04" xlink:href="note-0248-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0248-05" xlink:href="note-0248-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s15541" xml:space="preserve">POST hęc in linea horizontali notentur ex propoſ. </s>
  <s xml:id="echoid-s15542" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15543" xml:space="preserve">huius libri puncta, in quibus ab ar-<lb/>cubus ſignorum ſecatur. </s>
  <s xml:id="echoid-s15544" xml:space="preserve">In hæc enim proiicientur vmbræ ſtyli, illis ſignis orientibus, occidenti-<lb/>busve cuiuſmodi ſunt puncta C, D, F, K, L, M. </s>
  <s xml:id="echoid-s15545" xml:space="preserve">Nam in C, in horologio auſtrali occidunt ♏, &amp; </s>
  <s xml:id="echoid-s15546" xml:space="preserve"><lb/>♓; </s>
  <s xml:id="echoid-s15547" xml:space="preserve">in D, ♐, &amp; </s>
  <s xml:id="echoid-s15548" xml:space="preserve">♒; </s>
  <s xml:id="echoid-s15549" xml:space="preserve">in F, ♑; </s>
  <s xml:id="echoid-s15550" xml:space="preserve">At in punctis K, L, M, eadem ſigna oriuntur. </s>
  <s xml:id="echoid-s15551" xml:space="preserve">In horologio autem bo <lb/>reali in C, occidunt ♉, &amp; </s>
  <s xml:id="echoid-s15552" xml:space="preserve">♍; </s>
  <s xml:id="echoid-s15553" xml:space="preserve">in D, ♊, &amp; </s>
  <s xml:id="echoid-s15554" xml:space="preserve">♌; </s>
  <s xml:id="echoid-s15555" xml:space="preserve">in F, ♋; </s>
  <s xml:id="echoid-s15556" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15557" xml:space="preserve">in punctis K, L, M, eadem ſigna oriun-<lb/>tur, vt perſpicuum eſt, ſi horologium boreale in proprio ſitu collocetur in facie Septentrionali, <lb/>ita vt centrum horologii H, ſit infra lineam horizontalem, &amp; </s>
  <s xml:id="echoid-s15558" xml:space="preserve">puncta K, L, M, ad dextram partem, <lb/>&amp; </s>
  <s xml:id="echoid-s15559" xml:space="preserve">C, D, E, ad ſiniſtram. </s>
  <s xml:id="echoid-s15560" xml:space="preserve">Sumimus enim nunc pro horologio boreali totum auſtrale, ſi ſuperior <lb/>pars mutetur in inferiorem, ita vt centrum H, infra lineam horizontalem poſitum ſit.</s>
  <s xml:id="echoid-s15561" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15562" xml:space="preserve">HÆC autem puncta inueniemus etiam hac ratione in linea horizontali vtriuſque horolo-<lb/>gii, etiamſi arcus ſignorum in eo non ſint deſcripti. </s>
  <s xml:id="echoid-s15563" xml:space="preserve">Ex quinta tabella propoſ. </s>
  <s xml:id="echoid-s15564" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15565" xml:space="preserve">huius libri ſu-
<pb o="229" file="0249" n="249" rhead="LIBER SECVNDVS."/>
memus arcus ſemidiurnos ſignorum auſtralium pro horologio auſtrali, eosq́ue numerabimus ab <lb/>
<anchor type="note" xlink:label="note-0249-01a" xlink:href="note-0249-01"/>
N, in vtramque partem, &amp; </s>
  <s xml:id="echoid-s15566" xml:space="preserve">à terminis numerationum per E, rectas ducemus ſecantes lineam æqui <lb/>noctialem in punctis, per quæ rectæ ex H, emiſſæ ſecabunt horizontalem lineam in punctis C, D, <lb/>F, K, L, M, per quæ ſignorum arcus tranſeunt. </s>
  <s xml:id="echoid-s15567" xml:space="preserve">In illis enim punctis oritur, &amp; </s>
  <s xml:id="echoid-s15568" xml:space="preserve">occidit Sol in prin <lb/>cipiis ſignorum exiſtens, propterea quòd dictæ rectæ ex H, egredientes indicant horas, quando <lb/>Sol oritur, &amp; </s>
  <s xml:id="echoid-s15569" xml:space="preserve">occidit, &amp;</s>
  <s xml:id="echoid-s15570" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15571" xml:space="preserve">Pro horologio vero boreali ſumemus arcus ſemidiurnos ſignorum bo-<lb/>realium, eoſq́ue numerabimus ab M, in vtramque partem, &amp;</s>
  <s xml:id="echoid-s15572" xml:space="preserve">c.</s>
  <s xml:id="echoid-s15573" xml:space="preserve"/>
</p>
<div xml:id="echoid-div791" type="float" level="2" n="3">
<note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">Qua ratione in <lb/>linea horizonta <lb/>li horologii Ver <lb/>ticalis puncta <lb/>inueniantur, in <lb/>quibus Sol ori-<lb/>tur, aut occidit <lb/>in principiis @ſi-<lb/>gnorũ exiſtens.</note>
</div>
<p>
  <s xml:id="echoid-s15574" xml:space="preserve">GEOMETRICE quoque, &amp; </s>
  <s xml:id="echoid-s15575" xml:space="preserve">certius per latitudines ortiuas, &amp; </s>
  <s xml:id="echoid-s15576" xml:space="preserve">occiduas eadem puncta, in <lb/>
<anchor type="note" xlink:label="note-0249-02a" xlink:href="note-0249-02"/>
quibus Sol oritur in principiis ſignorum exiſtens, inueniemus hoc modo. </s>
  <s xml:id="echoid-s15577" xml:space="preserve">Sit Horizon A B C D, <lb/>
<anchor type="note" xlink:label="note-0249-03a" xlink:href="note-0249-03"/>
cuius cẽtrum E; </s>
  <s xml:id="echoid-s15578" xml:space="preserve">communis ſectio <lb/>
<anchor type="figure" xlink:label="fig-0249-01a" xlink:href="fig-0249-01"/>
illius cum Meridiano B D; </s>
  <s xml:id="echoid-s15579" xml:space="preserve">eiuſdẽ <lb/>communis ſectio cum Verticali, <lb/>atque adeò cum Aequatore, A C. <lb/></s>
  <s xml:id="echoid-s15580" xml:space="preserve">In recta B D, quærantur puncta, <lb/>vbi à ſignorum parallelis ſecatur, <lb/>quod ita fiet. </s>
  <s xml:id="echoid-s15581" xml:space="preserve">Ex B, verſus A, com <lb/>puretur altitudo Æquatoris B e, vel <lb/>ex A, verſus B, altitudo poli A e; </s>
  <s xml:id="echoid-s15582" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15583" xml:space="preserve"><lb/>à puncto e, vtrinque ducantur, vt <lb/>
<anchor type="note" xlink:label="note-0249-04a" xlink:href="note-0249-04"/>
in Analemmate, diametri paralle-<lb/>lorum ſignorum diametro Aequa-<lb/>toris ef, æquidiſtantes. </s>
  <s xml:id="echoid-s15584" xml:space="preserve">Hæ enim <lb/>ſecabunt rectam B D, in punctis F, <lb/>G, H, I, K, L, quæ quæruntur. </s>
  <s xml:id="echoid-s15585" xml:space="preserve">I<unsure/>d <lb/>quod facile demonſtrabitur, ſi ſe-<lb/>
<anchor type="note" xlink:label="note-0249-05a" xlink:href="note-0249-05"/>
micirculus B A D, intelligatur cir <lb/>ca B D, circumuerti, vſque dum ad <lb/>Horizontem rectus ſit, &amp; </s>
  <s xml:id="echoid-s15586" xml:space="preserve">cum Me-<lb/>ridiano coniunctus. </s>
  <s xml:id="echoid-s15587" xml:space="preserve">Erunt enim <lb/>
<anchor type="note" xlink:label="note-0249-06a" xlink:href="note-0249-06"/>
tunc dictæ parallelę communes ſe<unsure/>-<lb/>ctiones Meridiani, &amp; </s>
  <s xml:id="echoid-s15588" xml:space="preserve">parallelorum <lb/>ſignorum Zodiaci, atque adeò ipſi <lb/>paralleli rectam B D, in punctis F, G, H, I, K, L, ſecabunt, cum per dictas lineas parallelas du-<lb/>cantur. </s>
  <s xml:id="echoid-s15589" xml:space="preserve">Deinde per puncta F, G, H, I, K, L, ad B D, ducantur perpendiculares M N, O P, Q R, <lb/>S T, V X, Y Z. </s>
  <s xml:id="echoid-s15590" xml:space="preserve">Erunt hæ communes ſectiones parallelorum ſignorum Zodiaci, &amp; </s>
  <s xml:id="echoid-s15591" xml:space="preserve">Horizontis. <lb/></s>
  <s xml:id="echoid-s15592" xml:space="preserve">Cum enim tam Horizon, quàm paralleli ſignorum Zodiaci ad Meridianum recti ſint, erunt quo-<lb/>que communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s15593" xml:space="preserve">parallelorum ad Meridianum, atque adeò per defin. </s>
  <s xml:id="echoid-s15594" xml:space="preserve">3. </s>
  <s xml:id="echoid-s15595" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15596" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0249-07a" xlink:href="note-0249-07"/>
11. </s>
  <s xml:id="echoid-s15597" xml:space="preserve">Euclidis, &amp; </s>
  <s xml:id="echoid-s15598" xml:space="preserve">ad rectam B D, in Meridiano exiſtentem, perpendiculares. </s>
  <s xml:id="echoid-s15599" xml:space="preserve">Quamobrem dictæ <lb/>
<anchor type="note" xlink:label="note-0249-08a" xlink:href="note-0249-08"/>
perpendiculares communes ſectiones ſunt parallelorum, &amp; </s>
  <s xml:id="echoid-s15600" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s15601" xml:space="preserve">Ex quo fit, cum Vertica-<lb/>lis proprie dictus ducatur per rectam A C, arcus C M, C O, C Q, C S, C V, C Y, eſſe amplitu-<lb/>
<anchor type="note" xlink:label="note-0249-09a" xlink:href="note-0249-09"/>
dines ortiuas; </s>
  <s xml:id="echoid-s15602" xml:space="preserve">arcus verò A N, A P, A R, A T, A X, A Z, latitudines occiduas.</s>
  <s xml:id="echoid-s15603" xml:space="preserve"/>
</p>
<div xml:id="echoid-div792" type="float" level="2" n="4">
<note position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">Qua ratione <lb/>inueniãtur ea-<lb/>dem puncta per <lb/>Analemma.</note>
<note position="left" xlink:label="note-0249-03" xlink:href="note-0249-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0249-01" xlink:href="fig-0249-01a">
    <image file="0249-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0249-01"/>
  </figure>
<note position="left" xlink:label="note-0249-04" xlink:href="note-0249-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0249-05" xlink:href="note-0249-05a" xml:space="preserve">Demonſtratio <lb/>poſterioris inué <lb/>rionis dictorum <lb/>punctorum.</note>
<note position="left" xlink:label="note-0249-06" xlink:href="note-0249-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0249-07" xlink:href="note-0249-07a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0249-08" xlink:href="note-0249-08a" xml:space="preserve">Amplitudines <lb/>ortiuæ, occi-<lb/>duæq́uc per A-<lb/>nalemma in-<lb/>uentæ.</note>
<note position="left" xlink:label="note-0249-09" xlink:href="note-0249-09a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s15604" xml:space="preserve">ITAQVE ſi ex E D, abſcindatur recta E a, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s15605" xml:space="preserve">per a, ducatur b d, ad E D, per-<lb/>pendicularis, erit b d, linea horizontalis in auſtrali horologio Verticali; </s>
  <s xml:id="echoid-s15606" xml:space="preserve">radii verò ex punctis S, <lb/>V, Y, &amp; </s>
  <s xml:id="echoid-s15607" xml:space="preserve">T, X, Z, per centrum E, traiecti ſecabunt horizontalem lineam in punctis, in quæ vmbra <lb/>ſtyli proiicitur, Sole oriente, &amp; </s>
  <s xml:id="echoid-s15608" xml:space="preserve">occidente, cum eſt in initiis ſignorum. </s>
  <s xml:id="echoid-s15609" xml:space="preserve">Quare hæc puncta ex pun <lb/>cto a, accepta, &amp; </s>
  <s xml:id="echoid-s15610" xml:space="preserve">in lineam horizontalem horologii translata ex loco gnomonis G, dabunt eadem <lb/>puncta in horologio. </s>
  <s xml:id="echoid-s15611" xml:space="preserve">Id quod liquido conſtare cuilibet poteſt, ſi Horizon A B C D, ponatur in <lb/>horologio auſtrali in propria poſitione, ita vt punctum a, ſit in loco ſtyli G, &amp; </s>
  <s xml:id="echoid-s15612" xml:space="preserve">recta b d, eadem, quę <lb/>horizontalis linea, atque adeò E, in centro mundi, tanquam vertex ſtyli. </s>
  <s xml:id="echoid-s15613" xml:space="preserve">Hoc enim poſito, oriente <lb/>Sole in punctis Horizontis S, V, Y, &amp; </s>
  <s xml:id="echoid-s15614" xml:space="preserve">occidente in T, X, Z, proiicietur vmbra ſtyli in dicta pun <lb/>
<anchor type="note" xlink:label="note-0249-10a" xlink:href="note-0249-10"/>
cta linęæ horizontalis: </s>
  <s xml:id="echoid-s15615" xml:space="preserve">quæ quidem puncta ſunt ſignorum auſtralium. </s>
  <s xml:id="echoid-s15616" xml:space="preserve">Eodem modo in boreali <lb/>horologio reperientur puncta ſignorum borealium, ſi ex E B, auferatur recta E a, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s15617" xml:space="preserve"><lb/>per a, ducatur ad E B, perpendicularis b d, quæ rurſus erit linea horizontalis in horologio borea-<lb/>li, &amp;</s>
  <s xml:id="echoid-s15618" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15619" xml:space="preserve">Ex hac porrò figura inueniemus eadem puncta in linea horizontali cuiuſcunque horolo-<lb/>
<anchor type="note" xlink:label="note-0249-11a" xlink:href="note-0249-11"/>
gii, vt ex ſequentibus manifeſtum fiet. </s>
  <s xml:id="echoid-s15620" xml:space="preserve">Poterunt autem diametri huius figuræ Y N, V P, &amp;</s>
  <s xml:id="echoid-s15621" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15622" xml:space="preserve">non <lb/>ineptè vocari radii latitudinum ortiuarum, vel occiduarum.</s>
  <s xml:id="echoid-s15623" xml:space="preserve"/>
</p>
<div xml:id="echoid-div793" type="float" level="2" n="5">
<note position="left" xlink:label="note-0249-10" xlink:href="note-0249-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0249-11" xlink:href="note-0249-11a" xml:space="preserve">Radii latitudi-<lb/>num ortiuarũ, <lb/>&amp; occiduarum <lb/>qui.</note>
</div>
<p>
  <s xml:id="echoid-s15624" xml:space="preserve">PERSPICVE quoque hic apparet ratio, cur auſtralia ſigna mutentur in horologio boreali <lb/>
<anchor type="note" xlink:label="note-0249-12a" xlink:href="note-0249-12"/>
in borealia; </s>
  <s xml:id="echoid-s15625" xml:space="preserve">quia videlicet radii latitudinum ſignorum auſtralium per centrum E, ducti ſecant re-<lb/>ctam b d, ductã ex parte Septentrionis per punctũ a, quæ refert horizontalem lineam in auſtrali <lb/>horologio; </s>
  <s xml:id="echoid-s15626" xml:space="preserve">at verò rectã b d, ductã per a, ex parte meridiei, quæ refert lineam horizontalẽ in horo <lb/>logio boreali, ſecant radii latitudinum ſignorũ borealiũ per centrũ E, ed ucti, vt ex figura conſtat.</s>
  <s xml:id="echoid-s15627" xml:space="preserve"/>
</p>
<div xml:id="echoid-div794" type="float" level="2" n="6">
<note position="right" xlink:label="note-0249-12" xlink:href="note-0249-12a" xml:space="preserve">Ratio, cur in bo <lb/>reali horologio <lb/>arcus ſignorum <lb/>auſtralium mu <lb/>tentur in arcus <lb/>borealium ſi-<lb/>gnorum.</note>
</div>
<pb o="230" file="0250" n="250" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s15628" xml:space="preserve">QVONIAM vero ♉, oritur, cum ♏, ſignum oppoſitum occidit, hoc eſt, quando vmbra ſty-<lb/>li in horologio proiicitur in punctum C; </s>
  <s xml:id="echoid-s15629" xml:space="preserve">ſi coniungamus B, punctum ♉, in æquinoctiali linea in-<lb/>uentum cum puncto C, inuento in linea horizontali, habebimus ſignum ♉, aſcendens. </s>
  <s xml:id="echoid-s15630" xml:space="preserve">Eodem <lb/>
<anchor type="figure" xlink:label="fig-0250-01a" xlink:href="fig-0250-01"/>
modo ſi punctum ♊, in æquino-<lb/>ctiali inuentum cõnectamus cum <lb/>puncto D, in quo ♐, occidit, habe-<lb/>bimus ſignum ♊, aſcendens, &amp; </s>
  <s xml:id="echoid-s15631" xml:space="preserve">ita <lb/>de cæteris ſignis Borealibus. </s>
  <s xml:id="echoid-s15632" xml:space="preserve">Rur-<lb/>ſus quia Sole exiſtente in principio <lb/>♐, orienteq́; </s>
  <s xml:id="echoid-s15633" xml:space="preserve">eodem ſigno, vmbra <lb/>
<anchor type="note" xlink:label="note-0250-01a" xlink:href="note-0250-01"/>
ſtyli proiicitur in L, coniungemus <lb/>punctum L, cũ puncto ♐, in æqui-<lb/>noctiali linea inuento, vt habea-<lb/>mus ſignum ♐, aſcendens. </s>
  <s xml:id="echoid-s15634" xml:space="preserve">Ita <lb/>quoque punctum ♑, in linea æqui <lb/>noctiali inuentum iungemus cum <lb/>puncto M, vbi ♑, oritur, vt habea <lb/>mus ſignum ♑, aſcendens, &amp; </s>
  <s xml:id="echoid-s15635" xml:space="preserve">ſic <lb/>de reliquis ſignis auſtralibus.</s>
  <s xml:id="echoid-s15636" xml:space="preserve"/>
</p>
<div xml:id="echoid-div795" type="float" level="2" n="7">
  <figure xlink:label="fig-0250-01" xlink:href="fig-0250-01a">
    <image file="0250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0250-01"/>
  </figure>
<note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s15637" xml:space="preserve">OBSERVANDVM autem <lb/>
<anchor type="note" xlink:label="note-0250-02a" xlink:href="note-0250-02"/>
eſt, ne in deſcriptione ſignorum in <lb/>auſtrali horologio accipiantur ex <lb/>prioribus duabus tabellis propoſ. <lb/></s>
  <s xml:id="echoid-s15638" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15639" xml:space="preserve">huius libri illorum ſignorũ ho-<lb/>ræ, quæ ſex horis, aut pluribus an-<lb/>te meridiem, vel poſt oriuntur. </s>
  <s xml:id="echoid-s15640" xml:space="preserve"><lb/>Hæ etenim æquinoctialem lineam non ſecant. </s>
  <s xml:id="echoid-s15641" xml:space="preserve">In horologio verò boreali pro deſcriptione eorun-<lb/>dem ſignorum ſumendæ ſunt huiuſmodi horæ, non autem illorum ſignorum, quæ ſex horis, aut <lb/>paucioribus ante, vel poſt meridiem oriuntur, eandem ob cauſam: </s>
  <s xml:id="echoid-s15642" xml:space="preserve">quia in horologio boreali li-<lb/>neam æquinoctialem ſecant illarum duntaxat horarum lineę, quæ pluribus horis, quàm ſex, à me-<lb/>
<anchor type="note" xlink:label="note-0250-03a" xlink:href="note-0250-03"/>
ridie abſunt, vt ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s15643" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15644" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15645" xml:space="preserve">ſcripſimus, conſtat.</s>
  <s xml:id="echoid-s15646" xml:space="preserve"/>
</p>
<div xml:id="echoid-div796" type="float" level="2" n="8">
<note position="left" xlink:label="note-0250-02" xlink:href="note-0250-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0250-03" xlink:href="note-0250-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Quomodo in <lb/>tropicis inueniã <lb/>t<unsure/>ur puncta aſcẽ <lb/>dentium ſigno-<lb/>r<unsure/>um.</note>
<p>
  <s xml:id="echoid-s15647" xml:space="preserve">POSSVMVS quoque, ſi placet, in duobus tropicis inuenire puncta, per quæ ſigna aſcenden <lb/>tia duci debeant; </s>
  <s xml:id="echoid-s15648" xml:space="preserve">ducendo nimirum occultè lineam illius horæ, qua ſignum datum oritur, vt in <lb/>tertia, &amp; </s>
  <s xml:id="echoid-s15649" xml:space="preserve">quarta tabella propoſ. </s>
  <s xml:id="echoid-s15650" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15651" xml:space="preserve">huius libri apparet, quemadmodum in horologio horizontali <lb/>factum eſt: </s>
  <s xml:id="echoid-s15652" xml:space="preserve">dummodo illorum ſignorum horæ accipiantur, quæ tropicos ſecant; </s>
  <s xml:id="echoid-s15653" xml:space="preserve">nempe ex ter-<lb/>tia tabella illorum, quæ tropicum ♋, ex quarta autem, quæ tropicum ♑, ſecant. </s>
  <s xml:id="echoid-s15654" xml:space="preserve">Quod in vtro-<lb/>que horologio intelligendum eſt. </s>
  <s xml:id="echoid-s15655" xml:space="preserve">Vt v.</s>
  <s xml:id="echoid-s15656" xml:space="preserve">g. </s>
  <s xml:id="echoid-s15657" xml:space="preserve">quoniam ſignum ♍, oritur hora 2. </s>
  <s xml:id="echoid-s15658" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s15659" xml:space="preserve">34. </s>
  <s xml:id="echoid-s15660" xml:space="preserve">ante meri-<lb/>diem, Sole exiſtente in principio ♋, fit vt linea illius horæ ſecet arcum ♋, in puncto, per quod ſi-<lb/>gnum ♍, duci debet, &amp;</s>
  <s xml:id="echoid-s15661" xml:space="preserve">c.</s>
  <s xml:id="echoid-s15662" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Quo pacto ſi-<lb/>gua aſcenden-<lb/>tia per doctrinã <lb/>conicorũ Apoll. <lb/>in horologio <lb/>deſcribantur.</note>
<p>
  <s xml:id="echoid-s15663" xml:space="preserve">IMMO lineæ in his punctis tangentes tropicos (quæ ducentur, vt in coroll. </s>
  <s xml:id="echoid-s15664" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s15665" xml:space="preserve">37. </s>
  <s xml:id="echoid-s15666" xml:space="preserve">libri <lb/>
<anchor type="note" xlink:label="note-0250-06a" xlink:href="note-0250-06"/>
primi Apoll. </s>
  <s xml:id="echoid-s15667" xml:space="preserve">docuimus) erunt ſigna aſcendentia, vt conſtat ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s15668" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15669" xml:space="preserve">huius libri de-<lb/>monſtrauimus.</s>
  <s xml:id="echoid-s15670" xml:space="preserve"/>
</p>
<div xml:id="echoid-div797" type="float" level="2" n="9">
<note position="left" xlink:label="note-0250-06" xlink:href="note-0250-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s15671" xml:space="preserve">LINEAS verò ♈, &amp; </s>
  <s xml:id="echoid-s15672" xml:space="preserve">♎, hoc modo deſcribemus. </s>
  <s xml:id="echoid-s15673" xml:space="preserve">Quoniam aſcendente principio ♈, &amp; </s>
  <s xml:id="echoid-s15674" xml:space="preserve">So-<lb/>le exiſtente in principio ♑, meridies eſt, vt conſtat ex quarta tabella propoſ. </s>
  <s xml:id="echoid-s15675" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15676" xml:space="preserve">huius libri; </s>
  <s xml:id="echoid-s15677" xml:space="preserve">perſpi-<lb/>cuum eſt, communem tunc ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s15678" xml:space="preserve">Eclipticæ tranſire per illud punctum tro <lb/>pici ♑, per quod linea meridiana ducitur. </s>
  <s xml:id="echoid-s15679" xml:space="preserve">Quia verò eo tempore Æquator, circulus horæ 6. </s>
  <s xml:id="echoid-s15680" xml:space="preserve">à me <lb/>ridie vel media nocte, Verticalis proprie dictus, Ecliptica, &amp; </s>
  <s xml:id="echoid-s15681" xml:space="preserve">Horizon, eandem habent ſectionem <lb/>communem, cui planum horologii æquidiſtat, cum parallelum ſit ipſi Verticali; </s>
  <s xml:id="echoid-s15682" xml:space="preserve">erunt per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s15683" xml:space="preserve">18. </s>
  <s xml:id="echoid-s15684" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15685" xml:space="preserve">linea æquinoctialis, linea horę ſextæ, communis ſectio Eclipticæ ac plani <lb/>horologii, &amp; </s>
  <s xml:id="echoid-s15686" xml:space="preserve">linea horizontalis, parallelæ inter ſe. </s>
  <s xml:id="echoid-s15687" xml:space="preserve">Recta ergo linea æquinoctiali lineæ, vel lineæ <lb/>
<anchor type="note" xlink:label="note-0250-07a" xlink:href="note-0250-07"/>
horæ ſextæ, vel lineæ horizontali parallela per punctum, in quo linea meridiana tropicum ♑, ſe-<lb/>cat, educta dabit ſignum ♈, aſcendens. </s>
  <s xml:id="echoid-s15688" xml:space="preserve">Non aliter recta, quæ per punctum, in quo linea meridia-<lb/>na tropicum ♋, ſecat, lineæ æquinoctiali parallela ducitur, ſignum ♎, aſcendens dabit.</s>
  <s xml:id="echoid-s15689" xml:space="preserve"/>
</p>
<div xml:id="echoid-div798" type="float" level="2" n="10">
<note position="left" xlink:label="note-0250-07" xlink:href="note-0250-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s15690" xml:space="preserve">ALITER ſigna aſcendentia delineabimus hoc modo. </s>
  <s xml:id="echoid-s15691" xml:space="preserve">Extabella 6. </s>
  <s xml:id="echoid-s15692" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s15693" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15694" xml:space="preserve">huius libri <lb/>
<anchor type="note" xlink:label="note-0250-08a" xlink:href="note-0250-08"/>
ſumantur declinationes mediationum cœli, &amp; </s>
  <s xml:id="echoid-s15695" xml:space="preserve">ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s15696" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15697" xml:space="preserve">eiuſdem huius <lb/>lib. </s>
  <s xml:id="echoid-s15698" xml:space="preserve">in linea meridiana horologii auſtralis quærantur puncta, per quæ paralleli illarum declina-<lb/>tionum duci debent. </s>
  <s xml:id="echoid-s15699" xml:space="preserve">Similiter ex tabella ſeptima eiuſdem propoſ. </s>
  <s xml:id="echoid-s15700" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15701" xml:space="preserve">huius libri accipiantur de-<lb/>clinationes punctorum auſtralium in circulo horæ ſextæ exiſtentium tam ante meridiem, quàm <lb/>poſt, vt tabella indicat; </s>
  <s xml:id="echoid-s15702" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15703" xml:space="preserve">ſecundum doctrinam dictæ propoſ. </s>
  <s xml:id="echoid-s15704" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15705" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15706" xml:space="preserve">in linea horæ 6. </s>
  <s xml:id="echoid-s15707" xml:space="preserve">eiuſ-<lb/>dem horologii auſtralis inueniantur puncta, per quæ illarum declinationum paralleli ducuntur <lb/>tam ante meridiem, quàm poſt, vt in tabella apparet. </s>
  <s xml:id="echoid-s15708" xml:space="preserve">Si enim hæc puncta cum reſpondentibus
<pb o="231" file="0251" n="251" rhead="LIBER SECVNDVS."/>
punctis in linea meridiana inuentis iungantur rectis lineis, deſcripta erunt aſcendentia ſigna, vt <lb/>prius, quemadmodum in horologio horizontali propoſ. </s>
  <s xml:id="echoid-s15709" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15710" xml:space="preserve">huius libri diximus, quæ neceſſario <lb/>tranſibunt per puncta inuenta in linea horizontali.</s>
  <s xml:id="echoid-s15711" xml:space="preserve"/>
</p>
<div xml:id="echoid-div799" type="float" level="2" n="11">
<note position="left" xlink:label="note-0250-08" xlink:href="note-0250-08a" xml:space="preserve">Deſcriptio ſi-<lb/>gnorum aſcen-<lb/>dentium in ho <lb/>rologio per cœli <lb/>mediationes, &amp; <lb/>puncta Eclipti-<lb/>cæ in circulo <lb/>horæ 6. à mer. <lb/>vel med. noc. cõ <lb/>ſtituta, dum ini <lb/>tia ſignorum <lb/>aſcendunt.</note>
</div>
<p>
  <s xml:id="echoid-s15712" xml:space="preserve">EODEM modo eadẽ ſigna aſcendentia deſcribentur in horologio boreali, ſi pro punctis in li <lb/>nea meridiana, ſeu in linea horæ 12. </s>
  <s xml:id="echoid-s15713" xml:space="preserve">meridiei inueniẽdis, ſumantur in linea horę 12. </s>
  <s xml:id="echoid-s15714" xml:space="preserve">mediæ noctis <lb/>ex tabella ſexta propoſ. </s>
  <s xml:id="echoid-s15715" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15716" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15717" xml:space="preserve">declinationes angulorum terræ. </s>
  <s xml:id="echoid-s15718" xml:space="preserve">Pro punctis verò in linea ho-<lb/>ræ 6. </s>
  <s xml:id="echoid-s15719" xml:space="preserve">reperiendis capiantur ex tabella ſeptima eiuſdem propoſ. </s>
  <s xml:id="echoid-s15720" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15721" xml:space="preserve">huius libri declinationes pun-<lb/>ctorum borealium in circulo horæ 6. </s>
  <s xml:id="echoid-s15722" xml:space="preserve">exiſtentium, &amp;</s>
  <s xml:id="echoid-s15723" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15724" xml:space="preserve">Sed ſatius eſt, ſi puncta in horologio auſtra-<lb/>li reperta transferantur in boreale, mutatis nominibus auſtralium in nomina borealium, &amp; </s>
  <s xml:id="echoid-s15725" xml:space="preserve">con-<lb/>tra. </s>
  <s xml:id="echoid-s15726" xml:space="preserve">Cum enim habeant eaſdem declinationes, habebunt in vtroque horologio eundem ſitum, <lb/>
<anchor type="note" xlink:label="note-0251-01a" xlink:href="note-0251-01"/>
&amp; </s>
  <s xml:id="echoid-s15727" xml:space="preserve">diſtantiam.</s>
  <s xml:id="echoid-s15728" xml:space="preserve"/>
</p>
<div xml:id="echoid-div800" type="float" level="2" n="12">
<note position="left" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s15729" xml:space="preserve">IMMO lineæ rectæ ductæ ex punctis in linea meridiana inuentis tangentes tropicos erunt <lb/>
<anchor type="note" xlink:label="note-0251-02a" xlink:href="note-0251-02"/>
ſigna aſcendentia, vt demonſtratum eſt propoſ. </s>
  <s xml:id="echoid-s15730" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15731" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s15732" xml:space="preserve">Ducentur autem huiuſmodi lineæ <lb/>contingentes, vt docuimus in coroll. </s>
  <s xml:id="echoid-s15733" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s15734" xml:space="preserve">37. </s>
  <s xml:id="echoid-s15735" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s15736" xml:space="preserve">1. </s>
  <s xml:id="echoid-s15737" xml:space="preserve">Apollonii. </s>
  <s xml:id="echoid-s15738" xml:space="preserve">Itaque ſigna Zodiaci aſcenden-<lb/>tia in eodem Verticali horologio deſcripſimus. </s>
  <s xml:id="echoid-s15739" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s15740" xml:space="preserve"/>
</p>
<div xml:id="echoid-div801" type="float" level="2" n="13">
<note position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">Quo pacto rur-<lb/>ſum aſcenden-<lb/>tia ſigna per el@ <lb/>men@a conica <lb/>deſcribantur.</note>
</div>
</div>
<div xml:id="echoid-div803" type="section" level="1" n="191">
<head xml:id="echoid-head194" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s15741" xml:space="preserve">EX Andrea Schonero eadem ſigna aſcendentia hoc pacto delineabimus. </s>
  <s xml:id="echoid-s15742" xml:space="preserve">In prima figura ſcholĳ <lb/>
<anchor type="note" xlink:label="note-0251-03a" xlink:href="note-0251-03"/>
propoſ. </s>
  <s xml:id="echoid-s15743" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15744" xml:space="preserve">huius libri abſcindatur ex E B, recta E a, æqualis meridianæ lineæ E I, horologĳ interceptæ <lb/>
<anchor type="note" xlink:label="note-0251-04a" xlink:href="note-0251-04"/>
inter E, centrum Aequatoris, &amp; </s>
  <s xml:id="echoid-s15745" xml:space="preserve">lineam æquinoctialem; </s>
  <s xml:id="echoid-s15746" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15747" xml:space="preserve">per a, ipſi A C, parallela agatur; </s>
  <s xml:id="echoid-s15748" xml:space="preserve">adeo <lb/>vt poſito centro E, in centro Aequatoris, &amp; </s>
  <s xml:id="echoid-s15749" xml:space="preserve">puncto a, in puncto I, parallela per a, ducta congruat li-<lb/>neæ æquinoctiali. </s>
  <s xml:id="echoid-s15750" xml:space="preserve">Secabit parallela per a, ducta lineas ſignorum ex E, emiſſas in punctis, quæ ex a, ac-<lb/>cepta beneficio circini, &amp; </s>
  <s xml:id="echoid-s15751" xml:space="preserve">in æquinoctialem lineam ex I, in vtramque partem translata dabunt puncta in <lb/>æquinoctiali linea, per quæ ſi ex puncto G, vbi meridiana linea horizontalem lineã interſecat, rectæ emit-<lb/>tantur, ſecabuntur duo tropici in punctis, per quæ lineæ ſignorum aſcendentium ducendæ erunt, eo tamen <lb/>ordine, quem in horizontali horologio præſcripſimus.</s>
  <s xml:id="echoid-s15752" xml:space="preserve"/>
</p>
<div xml:id="echoid-div803" type="float" level="2" n="1">
<note position="right" xlink:label="note-0251-03" xlink:href="note-0251-03a" xml:space="preserve">Quomodo eadé<unsure/> <lb/>ſigna aſcenden-<lb/>tia deſcribãtur <lb/>ſecundum pra-<lb/>xim Andreæ <lb/>Schoneri.</note>
<note position="left" xlink:label="note-0251-04" xlink:href="note-0251-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s15753" xml:space="preserve">QVOD ſi quando recta ex puncto G, educta non ſecet tropicum ♋, vt in exemplo contingit in ſi-<lb/>gno ♌, &amp; </s>
  <s xml:id="echoid-s15754" xml:space="preserve">♐, argumento id eſt, huiuſmodi ſigna non oriri, Sole exiſtente in principio ♋, illuminante{q́ue} fa-<lb/>ciem circuli Verticalis auſtralem, ſed dum partem borealem illuſtrat; </s>
  <s xml:id="echoid-s15755" xml:space="preserve">atque ita lineæ illæ ex G, emiſſæ <lb/>
<anchor type="note" xlink:label="note-0251-05a" xlink:href="note-0251-05"/>
ſecabunt tropicum ♋, in horologio boreali, quod à linea horizontali abſcinditur.</s>
  <s xml:id="echoid-s15756" xml:space="preserve"/>
</p>
<div xml:id="echoid-div804" type="float" level="2" n="2">
<note position="left" xlink:label="note-0251-05" xlink:href="note-0251-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s15757" xml:space="preserve">RVRSVS inſecunda figura eiuſdem ſcholĳ propoſ. </s>
  <s xml:id="echoid-s15758" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15759" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15760" xml:space="preserve">ſumatur in E B, recta E a, eidem <lb/>lineæ meridianæ E I, æqualis ex horologio, agatur{q́ue} per a, ipſi A C, parallela, ita vt poſito centro E, in <lb/>E, centro Aequatoris, &amp; </s>
  <s xml:id="echoid-s15761" xml:space="preserve">puncto a, in puncto I, parallela per a, ducta lineæ æquinoctiali congruat. </s>
  <s xml:id="echoid-s15762" xml:space="preserve">Se-<lb/>cabit parallela per a, ducta ſignorum lineas ex E, emiſſas in punctis, quæ ex α, accepta, &amp; </s>
  <s xml:id="echoid-s15763" xml:space="preserve">in lineam ęqui <lb/>noctialem ab I, translata dabunt in æquinoctiali linea puncta, per quæ lineæ aſcendentium ſignor um in-<lb/>cedere debent, ordine in horologio horizontali tradito. </s>
  <s xml:id="echoid-s15764" xml:space="preserve">Si igitur hæc puncta æquinoctialis lineæ cum <lb/>punctis tropicorum reſpondentibus iungantur, habebuntur lineæ ſignorum aſcendentium, vt prius. </s>
  <s xml:id="echoid-s15765" xml:space="preserve">Hu-<lb/>ius deſcriptionis exemplum non poſuimus, quia, vt confuſio linearum vitaretur, tropicos in horologio <lb/>non deſcripſimus.</s>
  <s xml:id="echoid-s15766" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s15767" xml:space="preserve">IAM vcrò ſi lineæ ſignorum aſcendentium vltra horizontalem lineam extendantur, habebuntur <lb/>
<anchor type="note" xlink:label="note-0251-07a" xlink:href="note-0251-07"/>
eadem ſigna aſcendentia in horologio boreali, quod ab horizontali linea abſcinditur; </s>
  <s xml:id="echoid-s15768" xml:space="preserve">dummodo ita collo-<lb/>cetur, vt horizontalis linea in ſuperiori loco ſtatuatur, &amp; </s>
  <s xml:id="echoid-s15769" xml:space="preserve">pars, quæ tunc in eo ſitu nobis ad horologium <lb/>conuerſis dextra eſt, fiat ſinistra, &amp; </s>
  <s xml:id="echoid-s15770" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15771" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15772" xml:space="preserve">huius libri demonſtrauimus.</s>
  <s xml:id="echoid-s15773" xml:space="preserve"/>
</p>
<div xml:id="echoid-div805" type="float" level="2" n="3">
<note position="right" xlink:label="note-0251-07" xlink:href="note-0251-07a" xml:space="preserve">Lineæ ſignor@ <lb/>aſcendentiũ vl-<lb/>tra horizontalé <lb/>lineam produ-<lb/>ctæ efficiunt ho <lb/>rologium bore@ <lb/>le.</note>
</div>
<p style="it">
  <s xml:id="echoid-s15774" xml:space="preserve">POTERVNT tamen, ſi libet, ſigna aſcendentia in horologio Boreali deſcribi non ſecus, acin <lb/>auſtrali deſcripta ſunt: </s>
  <s xml:id="echoid-s15775" xml:space="preserve">ſed facilius multo, &amp; </s>
  <s xml:id="echoid-s15776" xml:space="preserve">expeditius ea ex auſtrali horologio deducemus, productis <lb/>lineis aſcendentium ſignorum vltra lineam horizontalem, &amp; </s>
  <s xml:id="echoid-s15777" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15778" xml:space="preserve">vt diximus.</s>
  <s xml:id="echoid-s15779" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div807" type="section" level="1" n="192">
<head xml:id="echoid-head195" xml:space="preserve">PROBLEMA 22. PROPOSITIO 22.</head>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s15780" xml:space="preserve">HOROLOGIVM Italicum Verticale conſtituere.</s>
  <s xml:id="echoid-s15781" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s15782" xml:space="preserve">HOC non aliter deſcribetur, quàm horizontale; </s>
  <s xml:id="echoid-s15783" xml:space="preserve">ſi tamen in primo modo pro auſtrali horo-<lb/>
<anchor type="note" xlink:label="note-0251-09a" xlink:href="note-0251-09"/>
logio arcus diurni tropicorum ♋, &amp; </s>
  <s xml:id="echoid-s15784" xml:space="preserve">♑, in circulo M a N b, ſint a N b, d N e: </s>
  <s xml:id="echoid-s15785" xml:space="preserve">quia punctum N, <lb/>ad meridiem pertinet, cum vergat ad Meridianum circulum in hemiſphærio ſuperiori; </s>
  <s xml:id="echoid-s15786" xml:space="preserve">diuiſio <lb/>quoque circuli initium ſumat à punctis b, &amp; </s>
  <s xml:id="echoid-s15787" xml:space="preserve">e, quæ occidentalia ſunt, ſi horologium, &amp; </s>
  <s xml:id="echoid-s15788" xml:space="preserve">circulus <lb/>M a N b, in proprio ſitu collocentur. </s>
  <s xml:id="echoid-s15789" xml:space="preserve">Sumendus etiam erit nocturnus arcus ♑, ſupra lineam <lb/>horizontalem, vt in eo reperiantur puncta horarum 15. </s>
  <s xml:id="echoid-s15790" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15791" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15792" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15793" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15794" xml:space="preserve">quæ in circulo continentur <lb/>in arcu nocturno ♑. </s>
  <s xml:id="echoid-s15795" xml:space="preserve">Pro horologio verò boreali, arcus diurni tropicorum ♋, &amp; </s>
  <s xml:id="echoid-s15796" xml:space="preserve">♑, erunt d M e, <lb/>@ M b; </s>
  <s xml:id="echoid-s15797" xml:space="preserve">quoniam horologio, &amp; </s>
  <s xml:id="echoid-s15798" xml:space="preserve">circulo M a N b, in proprio ſitu collocatis, punctum M, pertinet
<pb o="232" file="0252" n="252" rhead="GNOMONICES"/>
ad meridiem, cum ad Meridianum circulum vergat in hemiſphærio ſuperno; </s>
  <s xml:id="echoid-s15799" xml:space="preserve">diuiſioq́; </s>
  <s xml:id="echoid-s15800" xml:space="preserve">circuli in-<lb/>choanda erit à punctis e, &amp; </s>
  <s xml:id="echoid-s15801" xml:space="preserve">b, quæ occidentalia ſunt, &amp; </s>
  <s xml:id="echoid-s15802" xml:space="preserve">ad horam 24. </s>
  <s xml:id="echoid-s15803" xml:space="preserve">ſpectant. </s>
  <s xml:id="echoid-s15804" xml:space="preserve">Sumimus enim <lb/>nunc pro horologio boreali totum auſtrale, ſi ex ſuperiori parte fiat inferior, ita vt centrum H, in-<lb/>fra horizontalem lineam contineatur. </s>
  <s xml:id="echoid-s15805" xml:space="preserve">Vnde proxima puncta verſus M, ad horam 23. </s>
  <s xml:id="echoid-s15806" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15807" xml:space="preserve">ſequen-<lb/>tia ad 22. </s>
  <s xml:id="echoid-s15808" xml:space="preserve">pertinebunt, &amp;</s>
  <s xml:id="echoid-s15809" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15810" xml:space="preserve">Memor autem eſto, in horeali horologio tropicum ♋, eſſe inter centrũ <lb/>
<anchor type="figure" xlink:label="fig-0252-01a" xlink:href="fig-0252-01"/>
<anchor type="note" xlink:label="note-0252-01a" xlink:href="note-0252-01"/>
<anchor type="note" xlink:label="note-0252-02a" xlink:href="note-0252-02"/>
<anchor type="note" xlink:label="note-0252-03a" xlink:href="note-0252-03"/>
H, &amp; </s>
  <s xml:id="echoid-s15811" xml:space="preserve">æquinoctialem lineam. </s>
  <s xml:id="echoid-s15812" xml:space="preserve">Exemplum huius deſcriptionis in horologio auſtrali habes in hora <lb/>14. </s>
  <s xml:id="echoid-s15813" xml:space="preserve">tropici ♋, &amp; </s>
  <s xml:id="echoid-s15814" xml:space="preserve">hora 13. </s>
  <s xml:id="echoid-s15815" xml:space="preserve">tropici ♑. </s>
  <s xml:id="echoid-s15816" xml:space="preserve">Nam ex f, puncto horæ 14. </s>
  <s xml:id="echoid-s15817" xml:space="preserve">tropici ♋, ducta recta per E, cen <lb/>trum ſecat lineam æquinoctialem in puncto quodam, per quod ducta ex centro H, recta oſtendet <lb/>in tropico ♋, punctum h, pro hora 14. </s>
  <s xml:id="echoid-s15818" xml:space="preserve">Rurſus recta ex m, puncto horæ primæ nocturnæ tropici <lb/>♑, quæ horæ 13. </s>
  <s xml:id="echoid-s15819" xml:space="preserve">opponitur, ducta per E, occurrit æquinoctiali lineæ in n. </s>
  <s xml:id="echoid-s15820" xml:space="preserve">Et quia linea m E, du-<lb/>cta ab hora prima nocturna ♑, tranſit per centrum E, antequam æquinoctialem lineam ſecet, id-<lb/>circo recta H n, in tropico ♑, exhibet punctum q, pro hora prima nocturna ♑, producta verò vl-<lb/>tra centrum H, offert in eodem tropico punctum p, pro hora 13. </s>
  <s xml:id="echoid-s15821" xml:space="preserve">vt demonſtrauimus propoſ 10. <lb/></s>
  <s xml:id="echoid-s15822" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s15823" xml:space="preserve">In horologio boreali nullum exemplum poſuimus, ne multitudo linearum confuſio-<lb/>nem pareret: </s>
  <s xml:id="echoid-s15824" xml:space="preserve">præſertim quia facile ex auſtrali deducirur, vt in ſcholio ſequentis propoſ. </s>
  <s xml:id="echoid-s15825" xml:space="preserve">dicemus. </s>
  <s xml:id="echoid-s15826" xml:space="preserve"><lb/>Tranſibunt autem hic quoque lineæ horarum ab occ. </s>
  <s xml:id="echoid-s15827" xml:space="preserve">per horas à mer. </s>
  <s xml:id="echoid-s15828" xml:space="preserve">vel med noc. </s>
  <s xml:id="echoid-s15829" xml:space="preserve">æquinoctialis <lb/>
<anchor type="note" xlink:label="note-0252-04a" xlink:href="note-0252-04"/>
lineæ, vt propoſ. </s>
  <s xml:id="echoid-s15830" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15831" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15832" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s15833" xml:space="preserve">Cæterum in hac figura non aſcripſimus numeros hora-<lb/>rum à mer. </s>
  <s xml:id="echoid-s15834" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s15835" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s15836" xml:space="preserve">quia ex figura propoſ. </s>
  <s xml:id="echoid-s15837" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15838" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15839" xml:space="preserve">facile intelligitur ordo huiuſmo-<lb/>di horarum.</s>
  <s xml:id="echoid-s15840" xml:space="preserve"/>
</p>
<div xml:id="echoid-div807" type="float" level="2" n="1">
<note position="right" xlink:label="note-0251-09" xlink:href="note-0251-09a" xml:space="preserve">Italici horolo-<lb/>gii Verticalis <lb/>conſtructio.</note>
  <figure xlink:label="fig-0252-01" xlink:href="fig-0252-01a">
    <image file="0252-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0252-01"/>
  </figure>
<note position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0252-02" xlink:href="note-0252-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0252-03" xlink:href="note-0252-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0252-04" xlink:href="note-0252-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s15841" xml:space="preserve">IN Secundo modo, qui ſit per arcus diurnos nocturnosq́ue, nulla eſt difficultas, ſi rectè con-<lb/>
<anchor type="note" xlink:label="note-0252-05a" xlink:href="note-0252-05"/>
ſiderentur tabulæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s15842" xml:space="preserve">33. </s>
  <s xml:id="echoid-s15843" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15844" xml:space="preserve">poſitæ: </s>
  <s xml:id="echoid-s15845" xml:space="preserve">ſed deſcribendus etiam erit in ho-<lb/>rologio auſtrali arcus nocturnus horarum 24. </s>
  <s xml:id="echoid-s15846" xml:space="preserve">cum eius ope &amp; </s>
  <s xml:id="echoid-s15847" xml:space="preserve">auxilio facilis reddatur deſcriptio <lb/>horologii Italici. </s>
  <s xml:id="echoid-s15848" xml:space="preserve">Ducitur enim hora 24. </s>
  <s xml:id="echoid-s15849" xml:space="preserve">ab occaſu per horam quintam à meridie in arcu diur-<lb/>no horarum 10. </s>
  <s xml:id="echoid-s15850" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15851" xml:space="preserve">per horam 12. </s>
  <s xml:id="echoid-s15852" xml:space="preserve">à media nocte in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s15853" xml:space="preserve">qui eſt parallelus <lb/>ſemper latentium maximus, ſecatq́ue horam 12. </s>
  <s xml:id="echoid-s15854" xml:space="preserve">à media nocte, quæ eſt hora 12. </s>
  <s xml:id="echoid-s15855" xml:space="preserve">meridiei, in loco <lb/>ſtyli. </s>
  <s xml:id="echoid-s15856" xml:space="preserve">Eſt autem hora 24. </s>
  <s xml:id="echoid-s15857" xml:space="preserve">ab occaſu parallela lineæ æquinoctiali, cum eadem ſit, quæ horizontalis <lb/>
<anchor type="note" xlink:label="note-0252-06a" xlink:href="note-0252-06"/>
linea, quam in ſcholio propoſ. </s>
  <s xml:id="echoid-s15858" xml:space="preserve">22. </s>
  <s xml:id="echoid-s15859" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s15860" xml:space="preserve">parallelam eſſe æquinoctiali lineæ oſtendimus. <lb/></s>
  <s xml:id="echoid-s15861" xml:space="preserve">At hora 23. </s>
  <s xml:id="echoid-s15862" xml:space="preserve">tranſit per horam 4. </s>
  <s xml:id="echoid-s15863" xml:space="preserve">à meridie in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s15864" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15865" xml:space="preserve">per horam quintam à <lb/>meridie in arcu horarum 12. </s>
  <s xml:id="echoid-s15866" xml:space="preserve">quem in auſtrali horologio tota æquinoctialis linea præbet. </s>
  <s xml:id="echoid-s15867" xml:space="preserve">Immo <lb/>quia hora 23. </s>
  <s xml:id="echoid-s15868" xml:space="preserve">ab occaſu producta vltra parallelum ſemper latentium maximum, ſeu arcum no-<lb/>cturnum horarum 24. </s>
  <s xml:id="echoid-s15869" xml:space="preserve">fungitur munere horæ 23. </s>
  <s xml:id="echoid-s15870" xml:space="preserve">ab ortu, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15871" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15872" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s15873" xml:space="preserve">oſten <lb/>dimus, idcirco vides lineam horæ 23. </s>
  <s xml:id="echoid-s15874" xml:space="preserve">ab ortu ita productam tranſire per horam 6. </s>
  <s xml:id="echoid-s15875" xml:space="preserve">à media nocte <lb/>in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s15876" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15877" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s15878" xml:space="preserve">Hora autem 13. </s>
  <s xml:id="echoid-s15879" xml:space="preserve">ab occaſu, quia non habet pun-<lb/>ctum reſpondens in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s15880" xml:space="preserve">ducta eſt per horam ſextam à media nocte in <lb/>arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s15881" xml:space="preserve">Hora denique 12. </s>
  <s xml:id="echoid-s15882" xml:space="preserve">ab occaſu ducenda eſt per horam 12. </s>
  <s xml:id="echoid-s15883" xml:space="preserve">à meridie, <lb/>hoc eſt, per horam 12. </s>
  <s xml:id="echoid-s15884" xml:space="preserve">mediæ noctis, in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s15885" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15886" xml:space="preserve">æquidiſtans lineæ æqui-
<pb o="235" file="0253" n="253" rhead="LIBER SECVNDVS."/>
horam primam ab occaſu) per horam 6. </s>
  <s xml:id="echoid-s15887" xml:space="preserve">à meridie in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s15888" xml:space="preserve">vt ex tabula hu-<lb/>ius arcus nocturni conſtat; </s>
  <s xml:id="echoid-s15889" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15890" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s15891" xml:space="preserve">Hora autem 11. </s>
  <s xml:id="echoid-s15892" xml:space="preserve">ab ortu, quia non habet punctum in <lb/>arcu diurno horarum 10. </s>
  <s xml:id="echoid-s15893" xml:space="preserve">ducta eſt per horam 6. </s>
  <s xml:id="echoid-s15894" xml:space="preserve">à meridie in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s15895" xml:space="preserve">Poſtre-<lb/>mo hora 12. </s>
  <s xml:id="echoid-s15896" xml:space="preserve">ab ortu ducenda eſt per horam 12. </s>
  <s xml:id="echoid-s15897" xml:space="preserve">à meridie in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s15898" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15899" xml:space="preserve">vt ſu-<lb/>pra oſtendimus, lineæ æquinoctiali æquidiſtans.</s>
  <s xml:id="echoid-s15900" xml:space="preserve"/>
</p>
<div xml:id="echoid-div808" type="float" level="2" n="2">
<note position="left" xlink:label="note-0252-05" xlink:href="note-0252-05a" xml:space="preserve">Alia de@criptio <lb/>horologii Itali <lb/>ci Verticalis per <lb/>@tcus diurnos, <lb/>@octurnosq́;.</note>
<note position="left" xlink:label="note-0252-06" xlink:href="note-0252-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s15901" xml:space="preserve">HOC igitur modo in omnibus aliis horologiis deſcribemus h<unsure/>oras ab ortu, &amp; </s>
  <s xml:id="echoid-s15902" xml:space="preserve">occaſu, benefi-<lb/>
<anchor type="note" xlink:label="note-0253-01a" xlink:href="note-0253-01"/>
cio tabularum arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s15903" xml:space="preserve">nocturnorum, aſſumendo puncta in arcubus nocturnis, quã <lb/>do eis deſtituimur in diurnis arcubus; </s>
  <s xml:id="echoid-s15904" xml:space="preserve">obſeruando præterea, vt cum aliqua hora ab occaſu non <lb/>habet puncta in dictis arcubus, ducamus eiuſdem numeri horam ab ortu. </s>
  <s xml:id="echoid-s15905" xml:space="preserve">Nam hæc producta vl-<lb/>tra maximum parallelorum ſemper apparentium, vel occultorum dabit eandem horam numero <lb/>
<anchor type="note" xlink:label="note-0253-02a" xlink:href="note-0253-02"/>
ab occaſu, vt ſupra oſtendimus. </s>
  <s xml:id="echoid-s15906" xml:space="preserve">Idem faciendum eſt, cum hora aliqua ab ortu puncta non habet <lb/>in memoratis arcubus. </s>
  <s xml:id="echoid-s15907" xml:space="preserve">Nam ſi ducamus horam eandem ab occaſu, dabit hæc producta vltra no-<lb/>minatum parallelum maximum horam eiuſdem numeri ab ortu.</s>
  <s xml:id="echoid-s15908" xml:space="preserve"/>
</p>
<div xml:id="echoid-div809" type="float" level="2" n="3">
<note position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve">Quando vſur-<lb/>pãdus ſit atcus <lb/>n@cturnus pro <lb/>durno, &amp; quan <lb/>do ducenda ſit <lb/>hora ab or. pro <lb/>ho@a ab occ. &amp; <lb/>contra, in de-<lb/>ſcriptione horo <lb/>logii Italici, vel <lb/>Babylonici cu-<lb/>iuſcunque.</note>
<note position="left" xlink:label="note-0253-02" xlink:href="note-0253-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s15909" xml:space="preserve">DE deſcriptione horologii borealis Babylonici non neceſle eſt ponere exemplum, cum eodem <lb/>modo delineetur exarcubus prædictis, præſertim cum &amp; </s>
  <s xml:id="echoid-s15910" xml:space="preserve">Babylonicum, &amp; </s>
  <s xml:id="echoid-s15911" xml:space="preserve">Italicum Boreale habe-<lb/>re poſſimus ex auſtrali, ſi eius lineæ producantur vltra horizontalem lineam, vt in ſequenti ſcho-<lb/>lio docebimus. </s>
  <s xml:id="echoid-s15912" xml:space="preserve">Horologium igitur Babylonicum Verticale conſtituimus. </s>
  <s xml:id="echoid-s15913" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s15914" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div811" type="section" level="1" n="193">
<head xml:id="echoid-head196" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s15915" xml:space="preserve">SI lineæ horarum ab ortu, &amp; </s>
  <s xml:id="echoid-s15916" xml:space="preserve">occaſu vltra lineam horizontalem producantur, habebuntur eædem <lb/>horæ ab ortu, &amp; </s>
  <s xml:id="echoid-s15917" xml:space="preserve">occaſu in boreali horologio, quod à linea horizontali abſcinditur, dummodo ita colloce-<lb/>tur in facie plani horologĳ, qisæ ad boream ſpectat, vt ſupremum locum occupet horizontalis linea, &amp; </s>
  <s xml:id="echoid-s15918" xml:space="preserve"><lb/>pars, quæ in eo ſitu e<unsure/>ſt nobis ad dexteram, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s15919" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15920" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15921" xml:space="preserve">huius libri <lb/>oſt<unsure/>enſum eſt.</s>
  <s xml:id="echoid-s15922" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s15923" xml:space="preserve">QVAE autem horæ ab ortu, &amp; </s>
  <s xml:id="echoid-s15924" xml:space="preserve">occaſu productæ vltra lineam horizontalem numerandę ſint ab or-<lb/>
<anchor type="note" xlink:label="note-0253-04a" xlink:href="note-0253-04"/>
tu, &amp; </s>
  <s xml:id="echoid-s15925" xml:space="preserve">quæ ab occaſu, in horologio boreali, non difficile erit iudicare, ſi in proprĳs poſitionibus conſide-<lb/>rentur circuli horarii, &amp; </s>
  <s xml:id="echoid-s15926" xml:space="preserve">vtrumque horologium, auſtrale &amp; </s>
  <s xml:id="echoid-s15927" xml:space="preserve">boreale, ita vt vertices gnomonum in centro <lb/>mundi coeant, efficiantq́, vnam lineam rectam, quemadmodum in ſcholio propoſ. </s>
  <s xml:id="echoid-s15928" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15929" xml:space="preserve">huius libri ſcripſi-<lb/>mus. </s>
  <s xml:id="echoid-s15930" xml:space="preserve">Quoniam enim in ſectionem circuli horæ 23. </s>
  <s xml:id="echoid-s15931" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15932" xml:space="preserve">plani horologii borealis in proprio ſitu poſiti proĳ-<lb/>
<anchor type="note" xlink:label="note-0253-05a" xlink:href="note-0253-05"/>
citur vmbra ſtyli, Sole exiſtente in ſemicirculo dicti circuli occidentali, perſ@icuum eſt, lineam illam 23. <lb/></s>
  <s xml:id="echoid-s15933" xml:space="preserve">horæ, pertinere ad horam 23. </s>
  <s xml:id="echoid-s15934" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s15935" xml:space="preserve">Idem{q́ue} dicendum eſt de linea horæ 22. </s>
  <s xml:id="echoid-s15936" xml:space="preserve">21. </s>
  <s xml:id="echoid-s15937" xml:space="preserve">20. </s>
  <s xml:id="echoid-s15938" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s15939" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15940" xml:space="preserve">Quare re-<lb/>liquę horę ex eadem parte horologĳ, nempe 13. </s>
  <s xml:id="echoid-s15941" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15942" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15943" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s15944" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15945" xml:space="preserve">ab ortu Solis erunt numerandæ. </s>
  <s xml:id="echoid-s15946" xml:space="preserve">Rurſus <lb/>quia in ſectionem circuli horę 1. </s>
  <s xml:id="echoid-s15947" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15948" xml:space="preserve">plani eiuſdem horologii borealis cadit vmbra ſtyli, Sole exiſtente in <lb/>ſemicirculo dicti circuli orientali, pertinebit linea illa horæ 1. </s>
  <s xml:id="echoid-s15949" xml:space="preserve">ad horam primam ab ortu Solis. </s>
  <s xml:id="echoid-s15950" xml:space="preserve">Idem{q́ue} <lb/>de hora 2. </s>
  <s xml:id="echoid-s15951" xml:space="preserve">3. </s>
  <s xml:id="echoid-s15952" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15953" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15954" xml:space="preserve">dicendum est. </s>
  <s xml:id="echoid-s15955" xml:space="preserve">Vnde reliquę horę eadem ex parte horologii, cuiuſmodi ſunt 11. </s>
  <s xml:id="echoid-s15956" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15957" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15958" xml:space="preserve"><lb/>8. </s>
  <s xml:id="echoid-s15959" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s15960" xml:space="preserve">c. </s>
  <s xml:id="echoid-s15961" xml:space="preserve">computandę erunt à Solis occaſu.</s>
  <s xml:id="echoid-s15962" xml:space="preserve"/>
</p>
<div xml:id="echoid-div811" type="float" level="2" n="1">
<note position="right" xlink:label="note-0253-04" xlink:href="note-0253-04a" xml:space="preserve">Quæ lineæ ho-<lb/>rarũ ab or. uel <lb/>occ. productæ vl <lb/>tra lineam hori <lb/>zontalem indi-<lb/>cent horas ab <lb/>o@. &amp; quę horas <lb/>ab occ. in horo <lb/>logio boreali.</note>
<note position="left" xlink:label="note-0253-05" xlink:href="note-0253-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s15963" xml:space="preserve">CLARIVS autcm percipietur fortaſſis, quænam lineę productæ ad horas ab ortu pertineant, &amp; </s>
  <s xml:id="echoid-s15964" xml:space="preserve"><lb/>quę ad horas ab occaſu, hoc modo. </s>
  <s xml:id="echoid-s15965" xml:space="preserve">Conſiderentur in portione horologii auſtralis nocturna, qùam nimirum <lb/>amputat horizontalis linea, vt propoſ. </s>
  <s xml:id="echoid-s15966" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15967" xml:space="preserve">huius libri monuimus, horę ab ortu, &amp; </s>
  <s xml:id="echoid-s15968" xml:space="preserve">occaſu; </s>
  <s xml:id="echoid-s15969" xml:space="preserve">quę res obſcu <lb/>
<anchor type="note" xlink:label="note-0253-06a" xlink:href="note-0253-06"/>
ra non eſt. </s>
  <s xml:id="echoid-s15970" xml:space="preserve">Omnes enim horę ab occaſu productæ vltra horizontalem lineam, antequam contingant pa-<lb/>rallelum maximum, qui horizontalem lineam tangit in Verticali hoc noſtro horologio in hora 12. </s>
  <s xml:id="echoid-s15971" xml:space="preserve">aſtro-<lb/>nomica, numer antur etiam ab occaſu in portione horologii nocturna, poſt puncta verò contactuum compu <lb/>tandæ ſunt ab ortu. </s>
  <s xml:id="echoid-s15972" xml:space="preserve">Pari ratione horę ab ortu productæ vltra eandem horizontalem lineam dant in ca-<lb/>dem portione nocturna horas ab ortu ante contactuum puncta, poſt hæc vero puncta horas ab occaſu, <lb/>vt perſpicuum eſt ex ſcholio propoſ. </s>
  <s xml:id="echoid-s15973" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15974" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s15975" xml:space="preserve">Ita vt in nocturna portione noſtri horologii hæ <lb/>quidem horæ 23. </s>
  <s xml:id="echoid-s15976" xml:space="preserve">22. </s>
  <s xml:id="echoid-s15977" xml:space="preserve">9. </s>
  <s xml:id="echoid-s15978" xml:space="preserve">10. </s>
  <s xml:id="echoid-s15979" xml:space="preserve">11. </s>
  <s xml:id="echoid-s15980" xml:space="preserve">numerandę ſint ab ortu, hæ vero 1. </s>
  <s xml:id="echoid-s15981" xml:space="preserve">2. </s>
  <s xml:id="echoid-s15982" xml:space="preserve">13. </s>
  <s xml:id="echoid-s15983" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15984" xml:space="preserve">15. </s>
  <s xml:id="echoid-s15985" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s15986" xml:space="preserve">His <lb/>rectè conſideratis, luce clarius intelligemus horas ab ortu, vel occaſu in horologio boreali. </s>
  <s xml:id="echoid-s15987" xml:space="preserve">Nam <lb/>horæ omnes, quæ in portione nocturna ſupputantur ab occaſu, in boreali horologio ab ortu ſunt nume-<lb/>randę, &amp; </s>
  <s xml:id="echoid-s15988" xml:space="preserve">quę ibi ſumuntur ab ortu, hic ab occaſu horas indicant. </s>
  <s xml:id="echoid-s15989" xml:space="preserve">Ratio huiuſce rei aperta eſt, &amp; </s>
  <s xml:id="echoid-s15990" xml:space="preserve">per-<lb/>
<anchor type="note" xlink:label="note-0253-07a" xlink:href="note-0253-07"/>
ſpicua. </s>
  <s xml:id="echoid-s15991" xml:space="preserve">Quoniam enim portio illa à linea horizontali abſciſſa, vt monſtret horas in facie plani, quę ad <lb/>Boream ſpectat, ita inuertenda eſt, vt pars dextra mutetur in ſiniſtram, &amp; </s>
  <s xml:id="echoid-s15992" xml:space="preserve">poſt hanc immutationem ſu-<lb/>perior in inferiorem, vt propoſ. </s>
  <s xml:id="echoid-s15993" xml:space="preserve">14. </s>
  <s xml:id="echoid-s15994" xml:space="preserve">huius libri docuimus, fit vt Sol in diuerſis eiuſdem circuli borarii ſe-<lb/>micirculis exiſtat, vt vmbra ſtyli in eius lineam horariam proiic<unsure/>i poſſit tam in horologio nocturno, quàm <lb/>in Boreali, poſito vtroque in proprio ſitu: </s>
  <s xml:id="echoid-s15995" xml:space="preserve">quandoquidem eadem illa linea horaria diuerſos ſitus habet in <lb/>vtroque horologio, ita vt ſi in nocturno vergit in occidentem, in Boreali in orientem ſpectet, &amp; </s>
  <s xml:id="echoid-s15996" xml:space="preserve">contra. <lb/></s>
  <s xml:id="echoid-s15997" xml:space="preserve">Quare cum vnus ſemicirculus horam ab ortu, &amp; </s>
  <s xml:id="echoid-s15998" xml:space="preserve">alter eandem ab occaſu ſignificet, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s15999" xml:space="preserve"><lb/>10. </s>
  <s xml:id="echoid-s16000" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16001" xml:space="preserve">docuimus, neceſſe est horam illam, quæ in nocturno horologio computatur ab ortu, in <lb/>Boreali ab occaſu numerari, &amp; </s>
  <s xml:id="echoid-s16002" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s16003" xml:space="preserve">Exempli gratia, in lineam horæ 23. </s>
  <s xml:id="echoid-s16004" xml:space="preserve">in nocturno horologio cadit <lb/>vmbra ſi<unsure/>yli, Sole existente in ſemicir culo illius horæ orientali ſub Horizonte, cum illa linea recedat à sty-<lb/>lo occaſum verſus; </s>
  <s xml:id="echoid-s16005" xml:space="preserve">quare hora illa ſupput anda erit ab ortu Solis. </s>
  <s xml:id="echoid-s16006" xml:space="preserve">In eandem autem lineam in horolo-
<pb o="236" file="0254" n="254" rhead="GNOMONICES"/>
gio Boreali, quia à ſtylo remouetur verſus ortum, vmbra ſtyli proĳcitur, dum Sol eſt in ſemicirculo oc-<lb/>cidentali ſupra Horizontem, quocirca eadem illa hora ab occaſu Solis erit numeranda. </s>
  <s xml:id="echoid-s16007" xml:space="preserve">Eadem{q́ue} eſt ratio <lb/>de cæteris lineis horarĳs. </s>
  <s xml:id="echoid-s16008" xml:space="preserve">Itaque horę iſte<unsure/> 23. </s>
  <s xml:id="echoid-s16009" xml:space="preserve">22. </s>
  <s xml:id="echoid-s16010" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16011" xml:space="preserve">10. </s>
  <s xml:id="echoid-s16012" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16013" xml:space="preserve">ab ortu, hę verò 1. </s>
  <s xml:id="echoid-s16014" xml:space="preserve">2. </s>
  <s xml:id="echoid-s16015" xml:space="preserve">13. </s>
  <s xml:id="echoid-s16016" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16017" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16018" xml:space="preserve">ab oc-<lb/>caſu numerandæ ſunt, vt dictum eſt. </s>
  <s xml:id="echoid-s16019" xml:space="preserve">Quod in aliis quoque horologiis intelligi volumus, etiam inclinatis <lb/>ad Horizontem, ſumendo inferiora horologia pro Borealibus, vt ſuis locis monebimus.</s>
  <s xml:id="echoid-s16020" xml:space="preserve"/>
</p>
<div xml:id="echoid-div812" type="float" level="2" n="2">
<note position="left" xlink:label="note-0253-06" xlink:href="note-0253-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0253-07" xlink:href="note-0253-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s16021" xml:space="preserve">EX horologio Verticali à nobis deſcripto perſpicuum eſt, Federicum Commandinum in ſuo libro de <lb/>
<anchor type="note" xlink:label="note-0254-01a" xlink:href="note-0254-01"/>
horologiorum deſcriptione hallucinatum fuiſſe in lineis horarum 10. </s>
  <s xml:id="echoid-s16022" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16023" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16024" xml:space="preserve">horologĳ Verticalis Itali-<lb/>ci Septentrionalis. </s>
  <s xml:id="echoid-s16025" xml:space="preserve">Tribuit enim illis eundem prorſus ſitum, quem habent lineæ horarũ 23. </s>
  <s xml:id="echoid-s16026" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16027" xml:space="preserve">22. </s>
  <s xml:id="echoid-s16028" xml:space="preserve">quod <lb/>fieri non poteſt, vt ex noſtra conſtructione conſtat.</s>
  <s xml:id="echoid-s16029" xml:space="preserve"/>
</p>
<div xml:id="echoid-div813" type="float" level="2" n="3">
<note position="left" xlink:label="note-0254-01" xlink:href="note-0254-01a" xml:space="preserve">Federic<unsure/>us Com <lb/>mandinus non <lb/>rectè ducit hor. <lb/>10. &amp; 11. ab occ. <lb/>in horologio <lb/>Boreali Italico.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div815" type="section" level="1" n="194">
<head xml:id="echoid-head197" xml:space="preserve">PROBLEMA 24. PROPOSITIO 24.</head>
<p>
  <s xml:id="echoid-s16030" xml:space="preserve">HOROLOGIVM Antiquum Verticale conſtituere.</s>
  <s xml:id="echoid-s16031" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16032" xml:space="preserve">CIRCVLO M a N b, diuiſo, vt in propoſ. </s>
  <s xml:id="echoid-s16033" xml:space="preserve">10. </s>
  <s xml:id="echoid-s16034" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16035" xml:space="preserve">22. </s>
  <s xml:id="echoid-s16036" xml:space="preserve">huius libri factum eſt, in arcum diur-<lb/>
<anchor type="note" xlink:label="note-0254-03a" xlink:href="note-0254-03"/>
num, &amp; </s>
  <s xml:id="echoid-s16037" xml:space="preserve">nocturnum tropicorum ♋, &amp; </s>
  <s xml:id="echoid-s16038" xml:space="preserve">♑; </s>
  <s xml:id="echoid-s16039" xml:space="preserve">arcus diurnus tam tropici ♋, a N b, quàm tropici ♑, <lb/>
<anchor type="figure" xlink:label="fig-0254-01a" xlink:href="fig-0254-01"/>
<anchor type="note" xlink:label="note-0254-04a" xlink:href="note-0254-04"/>
<anchor type="note" xlink:label="note-0254-05a" xlink:href="note-0254-05"/>
<anchor type="note" xlink:label="note-0254-06a" xlink:href="note-0254-06"/>
d N e, ſecetur in partes 12. </s>
  <s xml:id="echoid-s16040" xml:space="preserve">æquales, initio facto à punctis a, &amp; </s>
  <s xml:id="echoid-s16041" xml:space="preserve">d, quæ orientalia ſunt, vt patet, ſi <lb/>horologium, &amp; </s>
  <s xml:id="echoid-s16042" xml:space="preserve">circulus dictus propriam poſitionem habeant. </s>
  <s xml:id="echoid-s16043" xml:space="preserve">Ex punctis enim diuiſionum inue-<lb/>niemus puncta horarum inæqualium in vtroque tropico, horologiumq́; </s>
  <s xml:id="echoid-s16044" xml:space="preserve">Antiquum abſoluemus, <lb/>vt propoſ. </s>
  <s xml:id="echoid-s16045" xml:space="preserve">12. </s>
  <s xml:id="echoid-s16046" xml:space="preserve">huius libri tradidimus. </s>
  <s xml:id="echoid-s16047" xml:space="preserve">Vt exempli gratia, in auſtrali horologio linea recta ex f, pun-<lb/>cto horæ 4. </s>
  <s xml:id="echoid-s16048" xml:space="preserve">inæqualis tropici ♋, per E, ducta ſecat lineam æquinoctialem in g; </s>
  <s xml:id="echoid-s16049" xml:space="preserve">Recta verò ex H, <lb/>per g, ducta ſecat tropicum ♋, in h, puncto horæ 4. </s>
  <s xml:id="echoid-s16050" xml:space="preserve">inæqualis. </s>
  <s xml:id="echoid-s16051" xml:space="preserve">Sic etiam recta ex m, puncto ho-<lb/>ræ 4. </s>
  <s xml:id="echoid-s16052" xml:space="preserve">inæqualis tropici ♑, per E, ducta ſecat æquinoctialem lineam in n; </s>
  <s xml:id="echoid-s16053" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16054" xml:space="preserve">recta H n, tropicum <lb/>♑, ſecat in p, puncto horæ 4. </s>
  <s xml:id="echoid-s16055" xml:space="preserve">inæqualis, &amp;</s>
  <s xml:id="echoid-s16056" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16057" xml:space="preserve">vt ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s16058" xml:space="preserve">12. </s>
  <s xml:id="echoid-s16059" xml:space="preserve">huius libri liquet. </s>
  <s xml:id="echoid-s16060" xml:space="preserve">Ea-<lb/>demq́ue ratio de cæteris habenda eſt. </s>
  <s xml:id="echoid-s16061" xml:space="preserve">Pro horologio boreali exemplum non ponimus, tum quia <lb/>ex dictis in propoſ. </s>
  <s xml:id="echoid-s16062" xml:space="preserve">22. </s>
  <s xml:id="echoid-s16063" xml:space="preserve">huius libri facile deſcribetur, tum etiam, quia ſatius eſt, illud ex auftrali de-<lb/>
<anchor type="note" xlink:label="note-0254-07a" xlink:href="note-0254-07"/>
riuare, vt in ſequenti ſcholio mox docebimus.</s>
  <s xml:id="echoid-s16064" xml:space="preserve"/>
</p>
<div xml:id="echoid-div815" type="float" level="2" n="1">
<note position="left" xlink:label="note-0254-03" xlink:href="note-0254-03a" xml:space="preserve">Deſctiptio ho-<lb/>rologii Antiqui <lb/>@etticalis.</note>
  <figure xlink:label="fig-0254-01" xlink:href="fig-0254-01a">
    <image file="0254-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0254-01"/>
  </figure>
<note position="left" xlink:label="note-0254-04" xlink:href="note-0254-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0254-05" xlink:href="note-0254-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0254-06" xlink:href="note-0254-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0254-07" xlink:href="note-0254-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s16065" xml:space="preserve">QVOD ſi deſcribatur arcus diurnus horarum 6. </s>
  <s xml:id="echoid-s16066" xml:space="preserve">qui in horologio boreali erit horarum 18. <lb/></s>
  <s xml:id="echoid-s16067" xml:space="preserve">
<anchor type="note" xlink:label="note-0254-08a" xlink:href="note-0254-08"/>
conficiemus idem horologium, vt de horizontali dictum eſt propoſ. </s>
  <s xml:id="echoid-s16068" xml:space="preserve">12. </s>
  <s xml:id="echoid-s16069" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s16070" xml:space="preserve">Nam hora <lb/>1. </s>
  <s xml:id="echoid-s16071" xml:space="preserve">inæqualis in auſtrali horologio ducitur per horam 9 {1/2}. </s>
  <s xml:id="echoid-s16072" xml:space="preserve">à media nocte in arcu diurno horarum <lb/>6. </s>
  <s xml:id="echoid-s16073" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16074" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s16075" xml:space="preserve">à media nocte in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s16076" xml:space="preserve">Item per horam 4 {1/2}. </s>
  <s xml:id="echoid-s16077" xml:space="preserve">à meridie in <lb/>arcu nocturno horarum 18. </s>
  <s xml:id="echoid-s16078" xml:space="preserve">vt tabulæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s16079" xml:space="preserve">33. </s>
  <s xml:id="echoid-s16080" xml:space="preserve">præcedentis libri poſitæ indicant; </s>
  <s xml:id="echoid-s16081" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16082" xml:space="preserve"><lb/>ſic de cæteris. </s>
  <s xml:id="echoid-s16083" xml:space="preserve">In boreali verò horologio tranſit eadem hora 1. </s>
  <s xml:id="echoid-s16084" xml:space="preserve">inæqualis per horam 4 {1/2}. </s>
  <s xml:id="echoid-s16085" xml:space="preserve">à media <lb/>nocte in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s16086" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16087" xml:space="preserve">per horam 9 {1/2}. </s>
  <s xml:id="echoid-s16088" xml:space="preserve">à meridie in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s16089" xml:space="preserve">Item <lb/>per horam 7. </s>
  <s xml:id="echoid-s16090" xml:space="preserve">à meridie in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s16091" xml:space="preserve">vt eædem tabulæ docent, &amp;</s>
  <s xml:id="echoid-s16092" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16093" xml:space="preserve">Horologium <lb/>igitur Antiquum Verticale conſtuimus. </s>
  <s xml:id="echoid-s16094" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s16095" xml:space="preserve"/>
</p>
<div xml:id="echoid-div816" type="float" level="2" n="2">
<note position="left" xlink:label="note-0254-08" xlink:href="note-0254-08a" xml:space="preserve">Alia deſcriptio <lb/>horologii Anti <lb/>qui Verticalis, <lb/>ex arcubus diur <lb/>nis, nocturnis-<lb/>que.</note>
</div>
<pb o="237" file="0255" n="255" rhead="LIBER SECVNDVS."/>
</div>
<div xml:id="echoid-div818" type="section" level="1" n="195">
<head xml:id="echoid-head198" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s16096" xml:space="preserve">HIC etiam, vt demonſir auimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s16097" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16098" xml:space="preserve">huius libri, horæ inæquales horologĳ auſtralis <lb/>vltra horizontalem lineam productæ exhibebunt eaſdem numero horas inæquales in Boreali horologio, <lb/>ſi fiat illa inuerſio horologĳ, de qua in ſcholio propoſ. </s>
  <s xml:id="echoid-s16099" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16100" xml:space="preserve">huius libri dictum eſt.</s>
  <s xml:id="echoid-s16101" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div819" type="section" level="1" n="196">
<head xml:id="echoid-head199" xml:space="preserve">DE HOROLOGIIS MERIDIANIS.</head>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div820" type="section" level="1" n="197">
<head xml:id="echoid-head200" xml:space="preserve">PROBLEMA 25. PROPOSITIO 25.</head>
<p>
  <s xml:id="echoid-s16102" xml:space="preserve">HOROLOGIVM Aſtronomicum Meridianum conſtituere. <lb/></s>
  <s xml:id="echoid-s16103" xml:space="preserve">Hoc eſt, Lineas horarum à meridie, vel media nocte in plano, quod Me-<lb/>ridiano circulo æquidiſtat, deſcribere.</s>
  <s xml:id="echoid-s16104" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16105" xml:space="preserve">DVCTA linea recta A B, vtcunque, deſcribatur ex A, centro arcus circuli B C, quouis in-<lb/>
<anchor type="note" xlink:label="note-0255-02a" xlink:href="note-0255-02"/>
teruallo, in quo numerata altitudine Æquatoris, ſiue complemento altitudinis poli B C, (ad ſini-<lb/>ſtram quidem par-<lb/>
<anchor type="note" xlink:label="note-0255-03a" xlink:href="note-0255-03"/>
<anchor type="figure" xlink:label="fig-0255-01a" xlink:href="fig-0255-01"/>
tem puncti A, ſi ho-<lb/>rologium ad ortum <lb/>ſpectans deſcriben-<lb/>dum ſit; </s>
  <s xml:id="echoid-s16106" xml:space="preserve">ad dextram <lb/>verò, ſi ad occaſum <lb/>vergẽs horologium <lb/>ſit conſtruendum) <lb/>ducatur per A, &amp; </s>
  <s xml:id="echoid-s16107" xml:space="preserve">C, <lb/>recta A C, quam in <lb/>A, ſecet ad angulos <lb/>
<anchor type="note" xlink:label="note-0255-04a" xlink:href="note-0255-04"/>
rectos recta D E. <lb/></s>
  <s xml:id="echoid-s16108" xml:space="preserve">Sũpta deinde recta <lb/>A E, quæ longitudi-<lb/>ni gnomonis cuiuſ-<lb/>libet magnitudinis <lb/>ſit ęqualis, deſcriba-<lb/>tur ex E, centro, ad <lb/>quodcunque inter-<lb/>uallũ circulus F G-<lb/>H I, qui in 24. </s>
  <s xml:id="echoid-s16109" xml:space="preserve">horas <lb/>
<anchor type="note" xlink:label="note-0255-05a" xlink:href="note-0255-05"/>
æquales ſecetur, ini-<lb/>tio ſumpto à recta <lb/>F H, vel à recta G I, <lb/>rectam F H, in cen-<lb/>tro E, ad angulos rectos ſecante. </s>
  <s xml:id="echoid-s16110" xml:space="preserve">Poſt hæc per centrum E, &amp; </s>
  <s xml:id="echoid-s16111" xml:space="preserve">puncta diuiſionum rectæ occultæ <lb/>emittantur ſecantes rectam A C, in punctis, per quæ ipſi D E, parallelæ ductæ dabunt lineas hora-<lb/>rum à meridie, vel media nocte in plano, quod Meridiano circulo æquidiſtat. </s>
  <s xml:id="echoid-s16112" xml:space="preserve">Hæ autem paral-<lb/>lelæ facile ducentur, ſi per quodcunque punctum lineæ D E, vt per D, ipſi A C, parallela agatur, <lb/>&amp; </s>
  <s xml:id="echoid-s16113" xml:space="preserve">in hanc à puncto D, omnia puncta lineæ A C, transferantur, ſumendo eorum interualla à pun <lb/>cto A. </s>
  <s xml:id="echoid-s16114" xml:space="preserve">Nam rectæ connectentes bina puncta æqualiter à recta D E, remota parallelæ erunt. </s>
  <s xml:id="echoid-s16115" xml:space="preserve">Cuius <lb/>
<anchor type="note" xlink:label="note-0255-06a" xlink:href="note-0255-06"/>
<anchor type="note" xlink:label="note-0255-07a" xlink:href="note-0255-07"/>
deſcriptionis hæc eſt demonſtratio.</s>
  <s xml:id="echoid-s16116" xml:space="preserve"/>
</p>
<div xml:id="echoid-div820" type="float" level="2" n="1">
<note position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Aſtrono <lb/>mici Meridla-<lb/>ni.</note>
<note position="left" xlink:label="note-0255-03" xlink:href="note-0255-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0255-01" xlink:href="fig-0255-01a">
    <image file="0255-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-01"/>
  </figure>
<note position="left" xlink:label="note-0255-04" xlink:href="note-0255-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0255-05" xlink:href="note-0255-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0255-06" xlink:href="note-0255-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0255-07" xlink:href="note-0255-07a" xml:space="preserve">33. primi. <lb/>Demonſtratio <lb/>conſt@uction is <lb/>horologii Me-<lb/>tidiani.</note>
</div>
<p>
  <s xml:id="echoid-s16117" xml:space="preserve">QVONIAM communes ſectiones ab Æquatore factæ in planis parallelis, nempe in Meri-<lb/>diano circulo, &amp; </s>
  <s xml:id="echoid-s16118" xml:space="preserve">plano horologii, parallelæ ſunt: </s>
  <s xml:id="echoid-s16119" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s16120" xml:space="preserve">communes ſectiones ab Horizonte factę <lb/>
<anchor type="note" xlink:label="note-0255-08a" xlink:href="note-0255-08"/>
in eiſdem planis; </s>
  <s xml:id="echoid-s16121" xml:space="preserve">erit angulus ſub illis ſectionibus comprehenſus in plano Meridiani circuli æqua <lb/>
<anchor type="note" xlink:label="note-0255-09a" xlink:href="note-0255-09"/>
lis angulo ſub eiſdem ſectionibus in plano horologii cõtento. </s>
  <s xml:id="echoid-s16122" xml:space="preserve">Poſita igitur A B, communi ſectio-<lb/>ne horizontis &amp; </s>
  <s xml:id="echoid-s16123" xml:space="preserve">plani horologii, erit A C, communis ſectio Aequatoris &amp; </s>
  <s xml:id="echoid-s16124" xml:space="preserve">plani horologii, quan-<lb/>doquidem angulus B A C, ſumptus eſt æqualis angulo altitudinis Æquatoris, ei nimirum, quem <lb/>in Meridiano circulo ſectio Æquatoris cum ſectione Horizontis conſtituit. </s>
  <s xml:id="echoid-s16125" xml:space="preserve">Quòd ſi intelligatur <lb/>circa A C, rectam quieſcentem moueri planum circuli F G H I, donec cum plano Æquatoris, &amp; </s>
  <s xml:id="echoid-s16126" xml:space="preserve"><lb/>E, vertex aſſumpti ſtyli A E, cum centro mundi coniungatur; </s>
  <s xml:id="echoid-s16127" xml:space="preserve">(Eſt enim vertex ſtyli in centro mun <lb/>di concipiendus, ex propoſ. </s>
  <s xml:id="echoid-s16128" xml:space="preserve">@ ſuperioris lib.) </s>
  <s xml:id="echoid-s16129" xml:space="preserve">erit circulus ipſe Æquatori concentricus, &amp; </s>
  <s xml:id="echoid-s16130" xml:space="preserve">rectæ
<pb o="238" file="0256" n="256" rhead="GNOMONICES"/>
per E, &amp; </s>
  <s xml:id="echoid-s16131" xml:space="preserve">puncta diuiſionum ductæ communes ſectiones circulorum horariorum à meridie, vel <lb/>media nocte, ac Æquatoris; </s>
  <s xml:id="echoid-s16132" xml:space="preserve">cum Æquator, &amp; </s>
  <s xml:id="echoid-s16133" xml:space="preserve">circulus F G H I, circa idem centrum E, deſcripti <lb/>in arcus ſimiles ſecentur à dictis rectis, vt conſtat ex iis, quæ ad finem cap. </s>
  <s xml:id="echoid-s16134" xml:space="preserve">1. </s>
  <s xml:id="echoid-s16135" xml:space="preserve">in ſphæram ſcripſi-<lb/>
<anchor type="figure" xlink:label="fig-0256-01a" xlink:href="fig-0256-01"/>
mus: </s>
  <s xml:id="echoid-s16136" xml:space="preserve">Nempe G I, <lb/>pſi A C, parallela, <lb/>cõmunis ſectio Æ-<lb/>quatoris, &amp; </s>
  <s xml:id="echoid-s16137" xml:space="preserve">circuli <lb/>horæ 12. </s>
  <s xml:id="echoid-s16138" xml:space="preserve">ſeu Meri-<lb/>diani. </s>
  <s xml:id="echoid-s16139" xml:space="preserve">Nam com-<lb/>munes ſectiones Me <lb/>
<anchor type="note" xlink:label="note-0256-01a" xlink:href="note-0256-01"/>
ridiani, hoc eſt cir-<lb/>culi horæ 12. </s>
  <s xml:id="echoid-s16140" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16141" xml:space="preserve">pla-<lb/>ni horologii factæ <lb/>ab Aequatore paral-<lb/>lelę ſunt, atque adeo <lb/>cum A C, ſit cõmu-<lb/>nis ſectio Æquato-<lb/>ris, ac plani horolo-<lb/>gii, vt oſtendimus, <lb/>erit G I, communis <lb/>
<anchor type="note" xlink:label="note-0256-02a" xlink:href="note-0256-02"/>
ſectio Æquatoris, &amp; </s>
  <s xml:id="echoid-s16142" xml:space="preserve"><lb/>Meridiani, ſeu circu <lb/>li horæ 12. </s>
  <s xml:id="echoid-s16143" xml:space="preserve">K L, cõ-<lb/>munis ſectio Æqua-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s16144" xml:space="preserve">circuli horę <lb/>11. </s>
  <s xml:id="echoid-s16145" xml:space="preserve">in horologio ad <lb/>ortum ſpectante; </s>
  <s xml:id="echoid-s16146" xml:space="preserve">at <lb/>in eo quod in occa-<lb/>ſum vergit, commu-<lb/>nis ſectio Æquatoris, &amp; </s>
  <s xml:id="echoid-s16147" xml:space="preserve">circuli horæ primæ, &amp; </s>
  <s xml:id="echoid-s16148" xml:space="preserve">ſic deinceps; </s>
  <s xml:id="echoid-s16149" xml:space="preserve">vt cõſtat, ſi diligenter circuli F G H I, <lb/>
<anchor type="note" xlink:label="note-0256-03a" xlink:href="note-0256-03"/>
vel Æquatoris propria poſitio conſideretur in vtriuſque horologii Meridiani plano. </s>
  <s xml:id="echoid-s16150" xml:space="preserve">Quamobrem <lb/>circuli horarii à meridie, vel media nocte ſecabunt æquinoctialem lineam A C, in plano horolo-<lb/>gii in punctis, in quæ cadunt rectæ per centrum E, &amp; </s>
  <s xml:id="echoid-s16151" xml:space="preserve">puncta diuiſionum circuli F G H I, eductæ; <lb/></s>
  <s xml:id="echoid-s16152" xml:space="preserve">ac proinde per hæc puncta ducentur communes ſectiones eorundem circulorum horariorum, &amp; </s>
  <s xml:id="echoid-s16153" xml:space="preserve"><lb/>plani horologii, quæ quidem ſunt horariæ lineæ à meridie, vel media nocte. </s>
  <s xml:id="echoid-s16154" xml:space="preserve">Cum ergo ex coroll. </s>
  <s xml:id="echoid-s16155" xml:space="preserve"><lb/>propoſ. </s>
  <s xml:id="echoid-s16156" xml:space="preserve">22. </s>
  <s xml:id="echoid-s16157" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16158" xml:space="preserve">hæ lineæ horariæ parallelæ ſint in Meridiano horologio, perſpicuum eſt <lb/>rectas, quæ per puncta lineæ A C, ipſi D E, parallelæ aguntur, lineas horarias eſſe à meridie, vel me <lb/>dia nocte. </s>
  <s xml:id="echoid-s16159" xml:space="preserve">Sed dubitabit fortaſſe quiſpiam, an lineæ horarum à mer. </s>
  <s xml:id="echoid-s16160" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16161" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16162" xml:space="preserve">ſint perpendi-<lb/>culares ad lineam æquinoctialem A C; </s>
  <s xml:id="echoid-s16163" xml:space="preserve">atqueadeo parallelæ ipſi D E, quæ perpendicularis du-<lb/>cta eſt ad A C, quemadmodum eas nos duximus: </s>
  <s xml:id="echoid-s16164" xml:space="preserve">demonſtrabimus &amp; </s>
  <s xml:id="echoid-s16165" xml:space="preserve">hoc hac ratione. </s>
  <s xml:id="echoid-s16166" xml:space="preserve">Quo-<lb/>
<anchor type="note" xlink:label="note-0256-04a" xlink:href="note-0256-04"/>
niam tam planum horologii, quàm planum cuiuſuis circuli horarii à mer. </s>
  <s xml:id="echoid-s16167" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16168" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16169" xml:space="preserve">rectum <lb/>eſtad Æquatorem, erit quoque communis illorum ſectio ad eundem Æquatorem perpendicula-<lb/>
<anchor type="note" xlink:label="note-0256-05a" xlink:href="note-0256-05"/>
ris, atque adeo, per defin. </s>
  <s xml:id="echoid-s16170" xml:space="preserve">3. </s>
  <s xml:id="echoid-s16171" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s16172" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16173" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s16174" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16175" xml:space="preserve">ad rectam A C, in Æquatore exiſtentem. </s>
  <s xml:id="echoid-s16176" xml:space="preserve">Igitur omnes <lb/>lineæ horariæ à mer. </s>
  <s xml:id="echoid-s16177" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16178" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16179" xml:space="preserve">nempe communes ſectiones circulorum horariorum &amp; </s>
  <s xml:id="echoid-s16180" xml:space="preserve">plani <lb/>horologii ad rectam A C, perpendiculares ſunt: </s>
  <s xml:id="echoid-s16181" xml:space="preserve">Ac proinde cum per puncta inuenta in recta A C, <lb/>
<anchor type="note" xlink:label="note-0256-06a" xlink:href="note-0256-06"/>
ducendæ ſint, recte eas per illa puncta parallelas ipſi D E, quæ ad A C, perpẽdicularis eſt, duximus: <lb/></s>
  <s xml:id="echoid-s16182" xml:space="preserve">quia hac ratione omnes ad A C, perpendiculares erunt. </s>
  <s xml:id="echoid-s16183" xml:space="preserve">Quod idem hac ratione demonſtrabitur. </s>
  <s xml:id="echoid-s16184" xml:space="preserve"><lb/>Quoniam ſectiones factæ in Meridiano &amp; </s>
  <s xml:id="echoid-s16185" xml:space="preserve">plano horologii ab Horizonte parallelæ ſunt; </s>
  <s xml:id="echoid-s16186" xml:space="preserve">Item ſe-<lb/>
<anchor type="note" xlink:label="note-0256-07a" xlink:href="note-0256-07"/>
ctiones factæ in eiſdẽ planis à circulo horæ 6. </s>
  <s xml:id="echoid-s16187" xml:space="preserve">erit angulus ſub illis contentus in Meridiano æqua <lb/>
<anchor type="note" xlink:label="note-0256-08a" xlink:href="note-0256-08"/>
lis angulo comprehenſo ſub his in plano horologii. </s>
  <s xml:id="echoid-s16188" xml:space="preserve">Cum ergo ille ſit angulus altitudinis poli, <lb/>
<anchor type="note" xlink:label="note-0256-09a" xlink:href="note-0256-09"/>
vt conſtat, erit quoque hic angulus altitudinis poli. </s>
  <s xml:id="echoid-s16189" xml:space="preserve">Quocirca cum angulus B A D, ſit angulus al-<lb/>titudinis poli, propterea quòd, per conſtructionem, reliquus ex recto B A C, æqualis eſt comple-<lb/>mento altitudinis poli; </s>
  <s xml:id="echoid-s16190" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16191" xml:space="preserve">A B, ſit communis ſectio plani horologii &amp; </s>
  <s xml:id="echoid-s16192" xml:space="preserve">Horizontis, erit A D, com-<lb/>munis ſectio eiuſdem plani horologii, &amp; </s>
  <s xml:id="echoid-s16193" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s16194" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s16195" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16196" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16197" xml:space="preserve">Ac proinde cum om <lb/>nes lineæ horariæ ſint inter ſe parallelæ, ac idcirco &amp; </s>
  <s xml:id="echoid-s16198" xml:space="preserve">ipſi A D, æquidiſtent, vt oſtendimus; </s>
  <s xml:id="echoid-s16199" xml:space="preserve">erunt <lb/>omnes ad A C, perpendiculares, quemadmodum &amp; </s>
  <s xml:id="echoid-s16200" xml:space="preserve">ipſa A D, ad A C, perpendicularis eſt. </s>
  <s xml:id="echoid-s16201" xml:space="preserve">Sola li-<lb/>
<anchor type="note" xlink:label="note-0256-10a" xlink:href="note-0256-10"/>
nea meridiana, vel horæ 12. </s>
  <s xml:id="echoid-s16202" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s16203" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16204" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16205" xml:space="preserve">deſcribi in hoc horologio n<unsure/>on poteſt, ſed euane-<lb/>
<anchor type="note" xlink:label="note-0256-11a" xlink:href="note-0256-11"/>
ſcit, vt liquido conſtat ex ſcholio propoſ. </s>
  <s xml:id="echoid-s16206" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16207" xml:space="preserve">primi libri, cum Meridianus circulus planum ho-<lb/>rologii non ſecet, ſed ei æquidiſtet. </s>
  <s xml:id="echoid-s16208" xml:space="preserve">Itaque horologium Aſtronomicum Meridianum conſtitui-<lb/>mus, &amp;</s>
  <s xml:id="echoid-s16209" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16210" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s16211" xml:space="preserve"/>
</p>
<div xml:id="echoid-div821" type="float" level="2" n="2">
<note position="right" xlink:label="note-0255-08" xlink:href="note-0255-08a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0255-09" xlink:href="note-0255-09a" xml:space="preserve">10. vndec.</note>
  <figure xlink:label="fig-0256-01" xlink:href="fig-0256-01a">
    <image file="0256-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0256-01"/>
  </figure>
<note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0256-05" xlink:href="note-0256-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0256-06" xlink:href="note-0256-06a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0256-07" xlink:href="note-0256-07a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0256-08" xlink:href="note-0256-08a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0256-09" xlink:href="note-0256-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0256-10" xlink:href="note-0256-10a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0256-11" xlink:href="note-0256-11a" xml:space="preserve">Linea meridia-<lb/>na, ſeu horæ 12. <lb/>deſcribi nequit <lb/>in Meridiano <lb/>horologio.</note>
</div>
<pb o="239" file="0257" n="257" rhead="LIBER SECVNDVS."/>
</div>
<div xml:id="echoid-div823" type="section" level="1" n="198">
<head xml:id="echoid-head201" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Segmenta lineę <lb/>ęqu<unsure/>i<unsure/>noctialis in <lb/>utrouis horolo-<lb/>gi<unsure/>o Meridi<unsure/>ano <lb/>inter lineã ho-<lb/>ræ 6. &amp; b@nas ho <lb/>ras u@rinque à <lb/>linea ho@æ 6. <lb/>æquali @empo-<lb/>ris @patio re<unsure/>m<unsure/>o <lb/>tas, ſ<unsure/>untæqua-<lb/>lia.</note>
<p style="it">
  <s xml:id="echoid-s16212" xml:space="preserve">IN quocunq; </s>
  <s xml:id="echoid-s16213" xml:space="preserve">horologio Meridiano binæ lineæ quæunq; </s>
  <s xml:id="echoid-s16214" xml:space="preserve">horariæ hinc inde à linea horæ ſextæ D E, <lb/>æquali ſpatio temporis remotæ auferunt ex linea æquinoctiali A C, lineas inter ipſas, &amp; </s>
  <s xml:id="echoid-s16215" xml:space="preserve">lineã horæ ſex-<lb/>tæ interiectas æquales, ita vt in linea æquinoctiali ſpatia horaria ante ſextam horam æqualia ſint hora-<lb/>rĳs ſpatĳs poſt ſextam horam, ſingula ſingulis. </s>
  <s xml:id="echoid-s16216" xml:space="preserve">Vt lineæ A M, A N, in occident ali horologio, quarum <lb/>quælibet quatuor horas complectitur, æquales ſunt. </s>
  <s xml:id="echoid-s16217" xml:space="preserve">Cũ enim anguli M E A, N E A, in centro E, æqua-<lb/>libus arcubus ſubtenſi æquales ſint, &amp; </s>
  <s xml:id="echoid-s16218" xml:space="preserve">anguli ad A, recti, latus{q́ue} A E, commune; </s>
  <s xml:id="echoid-s16219" xml:space="preserve">erunt quoque rectæ <lb/>A M, A N, æquales, ſimiliter &amp; </s>
  <s xml:id="echoid-s16220" xml:space="preserve">E M, E N. </s>
  <s xml:id="echoid-s16221" xml:space="preserve">Eademq́, de cæteris ratio eſt habenda. </s>
  <s xml:id="echoid-s16222" xml:space="preserve">Ex quo fit, ſatis eſſe <lb/>
<anchor type="note" xlink:label="note-0257-02a" xlink:href="note-0257-02"/>
<anchor type="note" xlink:label="note-0257-03a" xlink:href="note-0257-03"/>
ad deſcriptionem horologĳ Meridiani, ſi per centrum E, &amp; </s>
  <s xml:id="echoid-s16223" xml:space="preserve">puncta diuiſionum vnius quadrantis, nem-<lb/>
<anchor type="note" xlink:label="note-0257-04a" xlink:href="note-0257-04"/>
<anchor type="note" xlink:label="note-0257-05a" xlink:href="note-0257-05"/>
pe H I, rectæ ducantur ſecantes æquinoctialem lineam in punctis S, N, Q, &amp; </s>
  <s xml:id="echoid-s16224" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16225" xml:space="preserve">Nam ſi hæc puncta ex <lb/>A, in alteram partem eiuſdem lineæ æquinoctialis beneficio circini trans ferantur, habebuntur omnia pũ <lb/>cta, per quæ ducendæ ſunt lineæ horariæ.</s>
  <s xml:id="echoid-s16226" xml:space="preserve"/>
</p>
<div xml:id="echoid-div823" type="float" level="2" n="1">
<note position="right" xlink:label="note-0257-02" xlink:href="note-0257-02a" xml:space="preserve">27. tertĳ.</note>
<note position="right" xlink:label="note-0257-03" xlink:href="note-0257-03a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0257-04" xlink:href="note-0257-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0257-05" xlink:href="note-0257-05a" xml:space="preserve">Saus e@tad de-<lb/>ſcriptionẽ horo <lb/>logii Meridia-<lb/>ni, ſi vnus dun-<lb/>taxat quadrans <lb/>circuli ex E, de-<lb/>ſcripu in 6. par <lb/>tes æquales di<unsure/>-<lb/>ſtribuatur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s16227" xml:space="preserve">IAM vero ſi horologium in plano, quod Meridiano æquidiſtet, collocetur, it a vt A B, recta Hori-<lb/>zonti ſit æquidiſtans, &amp; </s>
  <s xml:id="echoid-s16228" xml:space="preserve">punctum A, Boream, punctum vero B, Auſtrum reſpiciat, adeo vt angulus com-<lb/>plementi altitudinis poli B A C, qui ſupra a lineam horizontalem A B, exiſtit, in auſtrum vergat in vtro-<lb/>
<anchor type="note" xlink:label="note-0257-06a" xlink:href="note-0257-06"/>
que horologio, qui vero infra eandem lineam horizontalem huic oppoſitus eſt, in Boream, indicabuntur ho <lb/>ræ à gnomone A E, ad angulos rectos inſiſtente plano horologĳ in puncto A, ita vt ſtylus ipſe communis <lb/>ſectio ſit Horizontis, &amp; </s>
  <s xml:id="echoid-s16229" xml:space="preserve">Aequatoris, ſeu circuli horæſextæ, Verticaliſue. </s>
  <s xml:id="echoid-s16230" xml:space="preserve">Hæc enim cõmunis ſectio per-<lb/>
<anchor type="note" xlink:label="note-0257-07a" xlink:href="note-0257-07"/>
pendicularis eſt ad planum horologĳ in puncto A, per quod dictorum circulorum plana ad planum ho-<lb/>rologii recta exiſtentia tranſeunt. </s>
  <s xml:id="echoid-s16231" xml:space="preserve">Quòd ſi ex duobus punctis quibuslibet rectæ D E, vt ex D, &amp; </s>
  <s xml:id="echoid-s16232" xml:space="preserve">E, eri-<lb/>
<anchor type="note" xlink:label="note-0257-08a" xlink:href="note-0257-08"/>
gantur ad planum horologĳ duæ perpendiculares E O, <lb/>
<anchor type="figure" xlink:label="fig-0257-01a" xlink:href="fig-0257-01"/>
D P, gnomoni aſſumpto A E, æquales, ipſis{q́ue} ſuperpo-<lb/>natur recta O P, fungetur hæc munere axis, cum per cen <lb/>trum mundi tranſeat; </s>
  <s xml:id="echoid-s16233" xml:space="preserve">per punctum nimirum, quod eſt <lb/>vertex styli ex A, erecti, æquidiſtet{q́ue} lineæ horæ 6. </s>
  <s xml:id="echoid-s16234" xml:space="preserve">vt <lb/>ratio poſtulat. </s>
  <s xml:id="echoid-s16235" xml:space="preserve">Nam linea horæ ſextæ, &amp; </s>
  <s xml:id="echoid-s16236" xml:space="preserve">axis mundi <lb/>
<anchor type="note" xlink:label="note-0257-09a" xlink:href="note-0257-09"/>
ſunt æquidiſtantes, communes videlicet ſectiones Meri-<lb/>diani circuli, &amp; </s>
  <s xml:id="echoid-s16237" xml:space="preserve">plani horology factæ à circulo horæ 6. <lb/></s>
  <s xml:id="echoid-s16238" xml:space="preserve">Huius igitur axis O P, vmbra proiecta in lineas hora-<lb/>
<anchor type="note" xlink:label="note-0257-10a" xlink:href="note-0257-10"/>
rias à meridie, vel media nocte, indicabit quoque horas à meridie, vel media nocte, quemadmodum de ho <lb/>rologio horizontali, Verticali{q́ue} diximus.</s>
  <s xml:id="echoid-s16239" xml:space="preserve"/>
</p>
<div xml:id="echoid-div824" type="float" level="2" n="2">
<note position="right" xlink:label="note-0257-06" xlink:href="note-0257-06a" xml:space="preserve">Quon odovtrũ <lb/>que horologiũ <lb/>Meridianu<unsure/> @@ <lb/>collecandum, <lb/>vnà cum ſtylo, <lb/>vt horas demon <lb/>ſtret.</note>
<note position="left" xlink:label="note-0257-07" xlink:href="note-0257-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0257-08" xlink:href="note-0257-08a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0257-01" xlink:href="fig-0257-01a">
    <image file="0257-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01"/>
  </figure>
<note position="right" xlink:label="note-0257-09" xlink:href="note-0257-09a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0257-10" xlink:href="note-0257-10a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Cui ſegmento <lb/>æquinoctialis li <lb/>neæ in vtroque <lb/>horologio Me-<lb/>ridiano ſtylus <lb/>æqualis ſit.</note>
<p style="it">
  <s xml:id="echoid-s16240" xml:space="preserve">GNOMON autem aſſumptus A E, perpetuo æqualis est parti æquinoctialis lineæ, quæ inter A, <lb/>&amp; </s>
  <s xml:id="echoid-s16241" xml:space="preserve">horam tertiam vel nonam interĳcitur, id eſt, rectæ A Q, vel A R, in occidentali horologio. </s>
  <s xml:id="echoid-s16242" xml:space="preserve">Quo-<lb/>niam enim totus quadrans G H, diuiſus eſt in 6. </s>
  <s xml:id="echoid-s16243" xml:space="preserve">æquales horas, diuidet circulus horæ nonæ tribus horis <lb/>diſtans à recta E H, horæſextæ, vel à recta E G, horæ 12. </s>
  <s xml:id="echoid-s16244" xml:space="preserve">eundem quadrantem bifariam; </s>
  <s xml:id="echoid-s16245" xml:space="preserve">ac proinde an-<lb/>gulus A E R, angulo G E R, æqualis erit. </s>
  <s xml:id="echoid-s16246" xml:space="preserve">Cum ergo totus A E G, rectus ſit, erit vterq; </s>
  <s xml:id="echoid-s16247" xml:space="preserve">angulorũ G E R, <lb/>
<anchor type="note" xlink:label="note-0257-12a" xlink:href="note-0257-12"/>
A E R, ſemirectus. </s>
  <s xml:id="echoid-s16248" xml:space="preserve">Quare cum angulus E A R, rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s16249" xml:space="preserve">reliquus angulus E R A, ſemirectus; <lb/></s>
  <s xml:id="echoid-s16250" xml:space="preserve">
<anchor type="note" xlink:label="note-0257-13a" xlink:href="note-0257-13"/>
<anchor type="note" xlink:label="note-0257-14a" xlink:href="note-0257-14"/>
ac propterea exiſtentibus angulis E R A, A E R, æqualibus, æquales quoque erunt rectæ A E, A R; </s>
  <s xml:id="echoid-s16251" xml:space="preserve">Ea-<lb/>dem{q́ue} ratio eſt de A E, A Q, &amp; </s>
  <s xml:id="echoid-s16252" xml:space="preserve">c.</s>
  <s xml:id="echoid-s16253" xml:space="preserve"/>
</p>
<div xml:id="echoid-div825" type="float" level="2" n="3">
<note position="right" xlink:label="note-0257-12" xlink:href="note-0257-12a" xml:space="preserve">27. tertĳ.</note>
<note position="right" xlink:label="note-0257-13" xlink:href="note-0257-13a" xml:space="preserve">32. primi.</note>
<note position="right" xlink:label="note-0257-14" xlink:href="note-0257-14a" xml:space="preserve">O@entale horo <lb/>logium, ſi ita <lb/>inuertatur, vt <lb/>ſuperiota in in <lb/>feriora, &amp; quæ <lb/>in hoc ſi@u dex-<lb/>rra ſunt, fiant ſi <lb/>niſtra, &amp; cõtra, <lb/>exhibet horolo <lb/>gium occiden-<lb/>tale. Eodemq́; <lb/>modo occiden-<lb/>tale dabi<unsure/>orien <lb/>tale.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s16254" xml:space="preserve">SATIS autem eſt, ſi ſolum horologiũ ad ortum ſpectans deſcribatur. </s>
  <s xml:id="echoid-s16255" xml:space="preserve">Hoc enim ſi ita inuertatur, <lb/>vt ſuperiora in inferiora, &amp; </s>
  <s xml:id="echoid-s16256" xml:space="preserve">dextra in ſiniſtra mutentur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s16257" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16258" xml:space="preserve">huius libri docuimus, <lb/>præbebit nobis alterum horologium, quod ad occaſum ſpectat. </s>
  <s xml:id="echoid-s16259" xml:space="preserve">Quod hac etiam ratione faciemus perſpi-<lb/>cuum. </s>
  <s xml:id="echoid-s16260" xml:space="preserve">Quoniam in triangulo A E C, in orientali horologio, &amp; </s>
  <s xml:id="echoid-s16261" xml:space="preserve">in triangulo A E S, in occidentali, anguli <lb/>ad A, æquales ſunt, nempe recti, &amp; </s>
  <s xml:id="echoid-s16262" xml:space="preserve">anguli quoque ad E, æquales, ob æquales arcus inter H, &amp; </s>
  <s xml:id="echoid-s16263" xml:space="preserve">rectas <lb/>E C, E S, poſitos, quibus inſistunt, necnon &amp; </s>
  <s xml:id="echoid-s16264" xml:space="preserve">latera A E, A E, dictis angulis adiacentia ſunt æqualia, <lb/>cum vtrumq; </s>
  <s xml:id="echoid-s16265" xml:space="preserve">ſit longitudo ſtyli; </s>
  <s xml:id="echoid-s16266" xml:space="preserve">erunt quoque latera A C, A S, æqualia. </s>
  <s xml:id="echoid-s16267" xml:space="preserve">Quoniam vero, ſi horologium <lb/>orientale occidentali ſuperponatur, ita vt punctum A, puncto A, &amp; </s>
  <s xml:id="echoid-s16268" xml:space="preserve">linea horizontalis A B, lineæ hori <lb/>
<anchor type="note" xlink:label="note-0257-16a" xlink:href="note-0257-16"/>
zontali A B, congruat, &amp; </s>
  <s xml:id="echoid-s16269" xml:space="preserve">pars ſuperior Orientalis horologĳ cadat infra horizontalem lineam, &amp; </s>
  <s xml:id="echoid-s16270" xml:space="preserve">infe <lb/>
<anchor type="note" xlink:label="note-0257-17a" xlink:href="note-0257-17"/>
rior ſupra: </s>
  <s xml:id="echoid-s16271" xml:space="preserve">Item in co ſitu pars dextra mutetur in ſiniſtram, &amp; </s>
  <s xml:id="echoid-s16272" xml:space="preserve">contra, æquinoctialis linea A C, Orien <lb/>
<anchor type="note" xlink:label="note-0257-18a" xlink:href="note-0257-18"/>
talis horologĳ lineæ æquinoctiali A S, horologĳ occidentalis congruit, propter æqualitatem angulorum, <lb/>quos vtraq; </s>
  <s xml:id="echoid-s16273" xml:space="preserve">linea æquinoctialis cum horizontali facit verſus eaſdem partes in hoc ſitu, quem orienta-<lb/>le horologium habet eo modo inuerſum, vt diximus; </s>
  <s xml:id="echoid-s16274" xml:space="preserve">cadet quoque punctum C, in punctum S, propter <lb/>æquales lineas A C, A S. </s>
  <s xml:id="echoid-s16275" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s16276" xml:space="preserve">linea primæ horæ orientalis horologii per punctum C, ducta lineæ <lb/>primæ horæ occidentalis horologii per punctum S, ductæ congruet, cum vtraq; </s>
  <s xml:id="echoid-s16277" xml:space="preserve">cum æquinoctiali linea an <lb/>gulum rectum conſtituat, vt ſupra ostendimus. </s>
  <s xml:id="echoid-s16278" xml:space="preserve">Eodem modo reliquas lineas horarias horologii orienta-<lb/>lis reliquis lineis horariis occidentalis horologii demonſtrabimus congruere. </s>
  <s xml:id="echoid-s16279" xml:space="preserve">Quocirca orientale horolo-<lb/>gium inuerſum, vt dictum eſt, exhibebit horologium occidentale, cum illud hac ratione eundem ſitum, <lb/>quem hoc, ſortiatur, ei{q́ue} æquale ſit omni ex parte, vt oſtendimus.</s>
  <s xml:id="echoid-s16280" xml:space="preserve"/>
</p>
<div xml:id="echoid-div826" type="float" level="2" n="4">
<note position="right" xlink:label="note-0257-16" xlink:href="note-0257-16a" xml:space="preserve">27. tertĳ.</note>
<note position="right" xlink:label="note-0257-17" xlink:href="note-0257-17a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0257-18" xlink:href="note-0257-18a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s16281" xml:space="preserve">SED horæ, quæ in orientali horologio numer antur à media nocte, ſunt poſt illam inuerſionem compu <lb/>tandæ à meridie, cum iam factum ſit occidentale.</s>
  <s xml:id="echoid-s16282" xml:space="preserve"/>
</p>
<pb o="240" file="0258" n="258" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s16283" xml:space="preserve">EADEM ratione ſatis eſſet, ſi ſolum deſcriberetur horologium occidentale. </s>
  <s xml:id="echoid-s16284" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s16285" xml:space="preserve">hoc, ſi inuer-<lb/>teretur, vt diximns, exhiberet nobis horologium orientale; </s>
  <s xml:id="echoid-s16286" xml:space="preserve">quod eodem modo demonſtrari poteſt. </s>
  <s xml:id="echoid-s16287" xml:space="preserve">Sed ho <lb/>ræ, quæ in occidentali horolo gio deſcripto indicant horas à meridie, numerandæ eſſent poſt illam inuer-<lb/>ſionem à media nocte, propterea quod iam factum eſſet orientale ex occidentali.</s>
  <s xml:id="echoid-s16288" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Lineamenta ho <lb/>rologii otienta <lb/>lis in facie pla-<lb/>ni oppoſita de-<lb/>ſcripta exhibẽt <lb/>horologium oc <lb/>ci<unsure/>dentale, &amp; cõ <lb/>tra, ſi numeti <lb/>horarum mutẽ <lb/>tut in earũ cõ-<lb/>plementa uſque <lb/>ad 12.</note>
<p style="it">
  <s xml:id="echoid-s16289" xml:space="preserve">IMMO deſcripto horologio orientali in plano quopiam, ſi in parte oppoſita plani deſcribantur li-<lb/>neæ reſpondentes ad vnguem lineis illius, deſcriptum quoque erit occidentale horologium in facie plani, <lb/>quę ad occaſum ſpectat, collocandum; </s>
  <s xml:id="echoid-s16290" xml:space="preserve">quia hac ratione angulus complementi altitudinis poli, quem ęqui-<lb/>noctialis linea cum horizontali facit ſupra lineam horizõtalem, in auſtrum vergit, quemadmodũ in orien <lb/>tali horologio: </s>
  <s xml:id="echoid-s16291" xml:space="preserve">Sed numeri horarum commutandi ſunt in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s16292" xml:space="preserve">vt hora 11. </s>
  <s xml:id="echoid-s16293" xml:space="preserve">in <lb/>1. </s>
  <s xml:id="echoid-s16294" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16295" xml:space="preserve">10. </s>
  <s xml:id="echoid-s16296" xml:space="preserve">in 2. </s>
  <s xml:id="echoid-s16297" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16298" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16299" xml:space="preserve">Pari ratione deſcripto occidentali borologio, ſi in altera parte plani lineę ducãtur re-<lb/>ſpondentes lineis illius, deſcriptum erit horologium orientale.</s>
  <s xml:id="echoid-s16300" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s16301" xml:space="preserve">CAETERVM ſi dimidiatas quoque horas, &amp; </s>
  <s xml:id="echoid-s16302" xml:space="preserve">earum partes quartas, octauas, &amp; </s>
  <s xml:id="echoid-s16303" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16304" xml:space="preserve">deſcribere pla <lb/>
<anchor type="note" xlink:label="note-0258-03a" xlink:href="note-0258-03"/>
cuerit, diuidendę erunt ſingulæ horę circuli F G H I, in duas partes, quatuor, octo, &amp; </s>
  <s xml:id="echoid-s16305" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16306" xml:space="preserve">reliqua autem <lb/>perficienda, vt prius.</s>
  <s xml:id="echoid-s16307" xml:space="preserve"/>
</p>
<div xml:id="echoid-div827" type="float" level="2" n="5">
<note position="left" xlink:label="note-0258-03" xlink:href="note-0258-03a" xml:space="preserve">Qua ratione <lb/>partes horarum <lb/>in Meridiano <lb/>horologio de-<lb/>ſcribendz.</note>
</div>
<p style="it">
  <s xml:id="echoid-s16308" xml:space="preserve">QVOD ſi in plano aliquo ſtabili, vt in muro ad ortum, occaſumve directo ſpectante horologium de-<lb/>
<anchor type="note" xlink:label="note-0258-04a" xlink:href="note-0258-04"/>
ſcribendũ ſit, (Hactenus enim illud in quolibet plano delineauimus, vt poſtea in proprio ſitu collocetur) <lb/>ducenda erit beneficio perpendiculi, &amp; </s>
  <s xml:id="echoid-s16309" xml:space="preserve">libellę, in plano propoſito recta A B, Horizonti ęquidiſtans, &amp; </s>
  <s xml:id="echoid-s16310" xml:space="preserve"><lb/>ex quolibet puncto A, arcus circuli deſcribendus B C, verſus partes auſtrales, vt in eo numeretur com-<lb/>plementum altitudinis poli B C. </s>
  <s xml:id="echoid-s16311" xml:space="preserve">Reliqua abſoluenda erunt, vt prius.</s>
  <s xml:id="echoid-s16312" xml:space="preserve"/>
</p>
<div xml:id="echoid-div828" type="float" level="2" n="6">
<note position="left" xlink:label="note-0258-04" xlink:href="note-0258-04a" xml:space="preserve">Quomodo ho-<lb/>rol<unsure/>ogium Meri <lb/>dianum in pla-<lb/>no ſtabili, quod <lb/>directo in ortũ, <lb/>occaſumve ver-<lb/>git, deſcriben-<lb/>dum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s16313" xml:space="preserve">EODEM modo, ſi detur locus ſtyli in puncto A, eius{q́ue} longitudo A E, ducenda erit dicta recta <lb/>
<anchor type="note" xlink:label="note-0258-05a" xlink:href="note-0258-05"/>
A B, Horizõti ęquidiſtans per punctũ A, &amp; </s>
  <s xml:id="echoid-s16314" xml:space="preserve">ex A, arcus circuli deſcribẽdus, vt proxime diximus, etc.</s>
  <s xml:id="echoid-s16315" xml:space="preserve"/>
</p>
<div xml:id="echoid-div829" type="float" level="2" n="7">
<note position="left" xlink:label="note-0258-05" xlink:href="note-0258-05a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">Si detur locus <lb/>ſtyli datæ lon-<lb/>gitudinis qua <lb/>ratione horolo-<lb/>gium Meridia-<lb/>g<unsure/>ũ deſcribarur.</note>
</div>
<div xml:id="echoid-div831" type="section" level="1" n="199">
<head xml:id="echoid-head202" xml:space="preserve">PROBLEMA 26. PROPOSITIO 26.</head>
<p>
  <s xml:id="echoid-s16316" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in prædicto ho-<lb/>rologio Meridiano deſcribere.</s>
  <s xml:id="echoid-s16317" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16318" xml:space="preserve">SIT Analemma A B C D, cum diametris circulorum, vt in propoſ. </s>
  <s xml:id="echoid-s16319" xml:space="preserve">1. </s>
  <s xml:id="echoid-s16320" xml:space="preserve">ſuperioris libris. <lb/></s>
  <s xml:id="echoid-s16321" xml:space="preserve">Quoniam verò Meridianus A B C D, Analemmatis planum horologij non ſecat, intelligatur <lb/>
<anchor type="note" xlink:label="note-0258-07a" xlink:href="note-0258-07"/>
circulus A B C D, eſſe circulus horæ ſextæ à meridie, vel media nocte, tanquam proprius Meri-<lb/>
<anchor type="note" xlink:label="note-0258-08a" xlink:href="note-0258-08"/>
dianus Meridiani circuli, qui nunc Horizontis recti vice fungitur. </s>
  <s xml:id="echoid-s16322" xml:space="preserve">Manifeſtum autem eſt, com-<lb/>munes ſectiones circuli horæ ſextæ, &amp; </s>
  <s xml:id="echoid-s16323" xml:space="preserve">Æquatoris, parallelorumq́; </s>
  <s xml:id="echoid-s16324" xml:space="preserve">ipſius, diuerſas non eſſe ab ijs, <lb/>quæ in Meridiano circulo fiunt, propterea quòd Meridianus, &amp; </s>
  <s xml:id="echoid-s16325" xml:space="preserve">circulus horæ ſextæ per polos pa-<lb/>
<anchor type="figure" xlink:label="fig-0258-01a" xlink:href="fig-0258-01"/>
rallelorum deſcripti eodem modo <lb/>omnes parallelos ſecãt, quemadmo <lb/>dum &amp; </s>
  <s xml:id="echoid-s16326" xml:space="preserve">omnes alij Horizontes re-<lb/>cti. </s>
  <s xml:id="echoid-s16327" xml:space="preserve">Et quia Meridianus per polos <lb/>mundi tranſit, ſicut &amp; </s>
  <s xml:id="echoid-s16328" xml:space="preserve">circulus ho-<lb/>ræ ſextæ à mer. </s>
  <s xml:id="echoid-s16329" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s16330" xml:space="preserve">nocte, erit <lb/>axis F G, communis ſectio circuli <lb/>
<anchor type="note" xlink:label="note-0258-09a" xlink:href="note-0258-09"/>
horæ ſextæ A B C D, &amp; </s>
  <s xml:id="echoid-s16331" xml:space="preserve">Meridiani <lb/>tanquam diameter Horizõtis cuiuſ-<lb/>dam recti, atque adeo Æquatoris ſe-<lb/>ctio H I, tanquam diameter proprij <lb/>Verticalis ipſius Meridiani circuli, <lb/>vt &amp; </s>
  <s xml:id="echoid-s16332" xml:space="preserve">in ſphæra recta contingit. </s>
  <s xml:id="echoid-s16333" xml:space="preserve">In <lb/>omni enim Horizonte recto Æqua-<lb/>tor fungitur officio proprie dicti <lb/>Verticalis circuli. </s>
  <s xml:id="echoid-s16334" xml:space="preserve">Sumpta iam in <lb/>H I, vtrinq; </s>
  <s xml:id="echoid-s16335" xml:space="preserve">à puncto E, recta E K, <lb/>
<anchor type="note" xlink:label="note-0258-10a" xlink:href="note-0258-10"/>
aſſumpto gnomoni A E, in præce-<lb/>denti horologio æquali, ducatur per <lb/>vtrumq; </s>
  <s xml:id="echoid-s16336" xml:space="preserve">punctum K, ipſi F G, pa-<lb/>rallela L M. </s>
  <s xml:id="echoid-s16337" xml:space="preserve">Erit utraque parallela <lb/>communis ſectio circuli horæ ſextæ <lb/>A B C D, &amp; </s>
  <s xml:id="echoid-s16338" xml:space="preserve">plani horologij, cum <lb/>hac ratione æquidiſter planum ho-<lb/>rologij per rectam L M, ductum <lb/>ipſius Meridiani plano per F G, ducto, ſecundum magnitudinem ſtyli E K. </s>
  <s xml:id="echoid-s16339" xml:space="preserve">Ducantur quoquo <lb/>diametri Zodiaci ſigna oppoſira connectentes, vt fiant triangula per axem conorum, quorum ba-<lb/>ſes ſunt para Heli, vertex autem communis centrum E. </s>
  <s xml:id="echoid-s16340" xml:space="preserve">Igitur ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s16341" xml:space="preserve">6. </s>
  <s xml:id="echoid-s16342" xml:space="preserve">ſuperio-
<pb o="241" file="0259" n="259" rhead="LIBER SECVNDVS."/>
ris lib. </s>
  <s xml:id="echoid-s16343" xml:space="preserve">erunt N L, O L, P L, Q M, R M, S M, diametri conicarum ſectionum. </s>
  <s xml:id="echoid-s16344" xml:space="preserve">Et ſi puncta <lb/>N, O, P, Q, R, S, ex puncto K, accepta transferantur hinc inde in lineam horæ ſextæ horolo-<lb/>gij ex puncto A, vbi ſtylus collocandus eſt, proijcietur vmbra ſtyli in hæc puncta, cum Sol in ini <lb/>tijs ſignorum, &amp; </s>
  <s xml:id="echoid-s16345" xml:space="preserve">circulo A B C D, horæ ſextæ Aſtronomicæ extiterit. </s>
  <s xml:id="echoid-s16346" xml:space="preserve">Si igitur circa diametros <lb/>N L, O L, P L, &amp;</s>
  <s xml:id="echoid-s16347" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16348" xml:space="preserve">ex propoſ. </s>
  <s xml:id="echoid-s16349" xml:space="preserve">8. </s>
  <s xml:id="echoid-s16350" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16351" xml:space="preserve">deſcribantur in aliqua materia dura conicæ ſe-<lb/>ctiones, excindanturq́ue, ut fiant quædam quaſi regulæ inflexæ, per quas eædem ſectiones in ho-<lb/>rologio deſcribantur, ita vt per puncta N, O, P, Q, R, S, tranſeant, earumq́ue axes cum linea <lb/>
<anchor type="note" xlink:label="note-0259-01a" xlink:href="note-0259-01"/>
D E, horæ ſextæ coniungantur, deſcripti erunt paralleli ſignorum zodiaci. </s>
  <s xml:id="echoid-s16352" xml:space="preserve">Satis eſt autem, ſi ſectio <lb/>nes conicæ Signorum Borealium, vel Auſtralium deſcribantur; </s>
  <s xml:id="echoid-s16353" xml:space="preserve">quia hæ æquales ſunt ſectionibus <lb/>oppoſitorum ſignorum, cum omnes hyperbolæ ſint, vt ex propoſ. </s>
  <s xml:id="echoid-s16354" xml:space="preserve">6. </s>
  <s xml:id="echoid-s16355" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16356" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s16357" xml:space="preserve">Vnde <lb/>
<anchor type="note" xlink:label="note-0259-02a" xlink:href="note-0259-02"/>
beneficio earundem regularũ facile in oppoſita parte horologij deſcribentur per illa puncta, quæ <lb/>in linea horæ ſextę ſunt notata.</s>
  <s xml:id="echoid-s16358" xml:space="preserve"/>
</p>
<div xml:id="echoid-div831" type="float" level="2" n="1">
<note position="left" xlink:label="note-0258-07" xlink:href="note-0258-07a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum, ſiue <lb/>arcuum ſigno-<lb/>rum in eodem <lb/>horologio Me-<lb/>ridiano, ex A-<lb/>@alemmate.</note>
<note position="left" xlink:label="note-0258-08" xlink:href="note-0258-08a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a">
    <image file="0258-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0258-01"/>
  </figure>
<note position="left" xlink:label="note-0258-09" xlink:href="note-0258-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0258-10" xlink:href="note-0258-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">Satis eſt, deſcri-<lb/>bantur arcus ſi-<lb/>gnorum borea-<lb/>lium duntaxat, <lb/>vel auſtralium.</note>
<note position="left" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s16359" xml:space="preserve">IN vtroque autem horologio ſigna Borealia ſunt ea, quæ infra lineam æquinoctialem ſunt de-<lb/>
<anchor type="note" xlink:label="note-0259-03a" xlink:href="note-0259-03"/>
ſcripta, Auſtralia vero, quæ ſupra eandem continentur, ita vt in vtroque horologio proprium ſitũ <lb/>obtinente Borealia recedant à linea æquinoctiali in Auſtrum, &amp; </s>
  <s xml:id="echoid-s16360" xml:space="preserve">Auſtralia in Boream. </s>
  <s xml:id="echoid-s16361" xml:space="preserve">Ratio hu-<lb/>ius eſt, quòd cum ſol oritur, vel occidit in ſignis Borealibus exiſtens, vmbra ſtyli cadat in partes au <lb/>ſtrales horizontalis lineæ; </s>
  <s xml:id="echoid-s16362" xml:space="preserve">in boreales vero, cum exiſtens in ſignis auſtralibus oritur, vel occidit, vt <lb/>manifeſtum eſt.</s>
  <s xml:id="echoid-s16363" xml:space="preserve"/>
</p>
<div xml:id="echoid-div832" type="float" level="2" n="2">
<note position="right" xlink:label="note-0259-03" xlink:href="note-0259-03a" xml:space="preserve">In horologiis <lb/>Meridianis ſi-<lb/>gna borealia <lb/>ſ<unsure/>unt infra lineã <lb/>æquinoctialem, <lb/>&amp; auſtralia ſu-<lb/>pra.</note>
</div>
  <figure>
    <image file="0259-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0259-01"/>
  </figure>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s16364" xml:space="preserve">QVONIAM autem Sole oriente, vmbra gnomonis iu horizontalem lineam A B, proijcitur <lb/>
<anchor type="note" xlink:label="note-0259-07a" xlink:href="note-0259-07"/>
in horologio orientali; </s>
  <s xml:id="echoid-s16365" xml:space="preserve">occidente vero eodem, in eandem horizontalem lineam proijcitur in oc-<lb/>cidentali horologio, vt ex propoſ. </s>
  <s xml:id="echoid-s16366" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16367" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16368" xml:space="preserve">patet, fit vt toto reliquo tẽpore cuiuslibet diei, <lb/>Sole ſupra Horizontem eleuato, eadem vmbra in planum horologij infra lineam horizõtalem ca <lb/>
<anchor type="note" xlink:label="note-0259-08a" xlink:href="note-0259-08"/>
dat. </s>
  <s xml:id="echoid-s16369" xml:space="preserve">Quocirca reſecanda eſt pars illa horologij, quæ ſupra horizontalem lineam continetur, tan-<lb/>quam ſuperuacanea, cum in illam vmbra ſtyli nunquam cadat.</s>
  <s xml:id="echoid-s16370" xml:space="preserve"/>
</p>
<div xml:id="echoid-div833" type="float" level="2" n="3">
<note position="right" xlink:label="note-0259-07" xlink:href="note-0259-07a" xml:space="preserve">Portio horolo-<lb/>gii Meridiani <lb/>ſupra lineã ho-<lb/>rizontalem reſe <lb/>canda eſt, tan-<lb/>quam ſuperua-<lb/>canea.</note>
<note position="left" xlink:label="note-0259-08" xlink:href="note-0259-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s16371" xml:space="preserve">PARS tamen illa ſuperior vtriuſuis horologii abſciſſa à linea horizontali dabit horologium <lb/>
<anchor type="note" xlink:label="note-0259-09a" xlink:href="note-0259-09"/>
in facie plani horologij oppoſita collocandum, dummodo inuertatur, vt pars, quæ nunc ſuperior <lb/>eſt, fiat inferior, &amp; </s>
  <s xml:id="echoid-s16372" xml:space="preserve">contra, &amp; </s>
  <s xml:id="echoid-s16373" xml:space="preserve">quæ poſt hanc inuerſionem dextra eſt, fiat ſiniſtra, vt in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s16374" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16375" xml:space="preserve">huius libri præcepimus; </s>
  <s xml:id="echoid-s16376" xml:space="preserve">horæq́ue, quæ à media nocte computabantur, numerentur à meri <lb/>die, &amp; </s>
  <s xml:id="echoid-s16377" xml:space="preserve">è contrario; </s>
  <s xml:id="echoid-s16378" xml:space="preserve">ſigna denique borealia mutentur in auſtralia, &amp; </s>
  <s xml:id="echoid-s16379" xml:space="preserve">auſtralia in borealia. </s>
  <s xml:id="echoid-s16380" xml:space="preserve">Cũ enim, <lb/>vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s16381" xml:space="preserve">antecedentis oſtendimus, hac facta inuerſione, lineæ horariæ ſuperiotis par-<lb/>tis abſciſſæ in vtrouis horologio congruant horariis lineis horologii in facie plani oppoſita deſcri <lb/>pti, congruet etiam axis hyperbolarum ♋, &amp; </s>
  <s xml:id="echoid-s16382" xml:space="preserve">♑, axi hyperbolarum ♋, &amp; </s>
  <s xml:id="echoid-s16383" xml:space="preserve">♑, cum vtrobique axis <lb/>hic ſit linea horæ 6. </s>
  <s xml:id="echoid-s16384" xml:space="preserve">à meridie, vel media nocte. </s>
  <s xml:id="echoid-s16385" xml:space="preserve">Cum ergo axis tranſuerſus hyperbolarum dictarũ <lb/>in horologio orientali æqualis ſit axi tranſuerſo earundem in occidentali, propterea quòd &amp; </s>
  <s xml:id="echoid-s16386" xml:space="preserve">hy-
<pb o="242" file="0260" n="260" rhead="GNOMONICES"/>
perbolæ illius hyperbolis huius ſint æquales, cum ab æqualibus ſty lis proiiciantur vmbræ eas de-<lb/>ſcribentes in planis Meridiano circulo æquidiſtantibus, congruent quoque hyperbolæ hyperbo-<lb/>lis, nempe hyperbola ♋, congruet hyperbolæ ♑, &amp; </s>
  <s xml:id="echoid-s16387" xml:space="preserve">hyperbola ♑, hyperbolæ ♋. </s>
  <s xml:id="echoid-s16388" xml:space="preserve">Eademq́ue ratio <lb/>elt de cæteris hyperbolis aliorum ſignorum. </s>
  <s xml:id="echoid-s16389" xml:space="preserve">Quæ cum ita ſint, liquido conſtat, partem ſuperio-<lb/>rem abſciſſam in vtrolibet horologio exhibere horologium in facie oppoſita plani, ſi inuertatur, <lb/>vt diximus.</s>
  <s xml:id="echoid-s16390" xml:space="preserve"/>
</p>
<div xml:id="echoid-div834" type="float" level="2" n="4">
<note position="right" xlink:label="note-0259-09" xlink:href="note-0259-09a" xml:space="preserve">Portio vtriuſ-<lb/>uis horologii <lb/>Meridiani ab-<lb/>ſciſſa à<unsure/> linea ho <lb/>rizontali efficic<unsure/> <lb/>horologium in <lb/>parte oppoſita <lb/>plani, ſi partes <lb/>immutentur, ut <lb/>ſupra dictũ eſt.</note>
</div>
<p>
  <s xml:id="echoid-s16391" xml:space="preserve">RVRSVS linea horizontalis A B, vtrumque horologium diuidit in diurnum, &amp; </s>
  <s xml:id="echoid-s16392" xml:space="preserve">nocturnũ, <lb/>
<anchor type="note" xlink:label="note-0260-01a" xlink:href="note-0260-01"/>
ſicut de Verticali horologio dictum eſt propoſ. </s>
  <s xml:id="echoid-s16393" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16394" xml:space="preserve">huius libri, quorum illud infra lineam horizon <lb/>talem, hoc verò ſupra eandem exiſtit. </s>
  <s xml:id="echoid-s16395" xml:space="preserve">Nam in partem quidem ſuperiorem orientalis horologii <lb/>proiiceretur vmbra ſtyli poſt mediam noctem vſque ad ortum Soli, niſi denſitas terræ obſtaret: </s>
  <s xml:id="echoid-s16396" xml:space="preserve">in <lb/>
<anchor type="note" xlink:label="note-0260-02a" xlink:href="note-0260-02"/>
partem verò ſuperiorem horologii occidentalis vmbra ſtyli caderet poſt occaſum Solis vſque ad <lb/>mediam noctem, ſi eam Sol poſſet illuminare.</s>
  <s xml:id="echoid-s16397" xml:space="preserve"/>
</p>
<div xml:id="echoid-div835" type="float" level="2" n="5">
<note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">Linea horizon-<lb/>talis diuidit ho <lb/>rologium Me-<lb/>ridianũ in diur <lb/>num, noctur-<lb/>numq́ue.</note>
<note position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s16398" xml:space="preserve">EOSDEM arcus ſignorum deſcribemus hac ratione. </s>
  <s xml:id="echoid-s16399" xml:space="preserve">Ducta recta D C, vtcunque pro radio <lb/>
<anchor type="note" xlink:label="note-0260-03a" xlink:href="note-0260-03"/>
Æquatoris, &amp; </s>
  <s xml:id="echoid-s16400" xml:space="preserve">hinc inde radiis aliorum ſignorum deſcriptis, vt propoſ. </s>
  <s xml:id="echoid-s16401" xml:space="preserve">2. </s>
  <s xml:id="echoid-s16402" xml:space="preserve">huius libri in horologio <lb/>
<anchor type="figure" xlink:label="fig-0260-01a" xlink:href="fig-0260-01"/>
horizontali dictum <lb/>eſt, transferantur in <lb/>Aequatoris radium <lb/>D C, ex D, omnia ho <lb/>raria interualla inter <lb/>cepta inter E, centrũ <lb/>
<anchor type="note" xlink:label="note-0260-04a" xlink:href="note-0260-04"/>
circuli F G H I, præ-<lb/>cedentis propoſitio-<lb/>nis, &amp; </s>
  <s xml:id="echoid-s16403" xml:space="preserve">lineam Æqui-<lb/>noctialem A C, ita vt <lb/>recta D C, æqualis <lb/>ſit ſpatio E S, vel EC; <lb/></s>
  <s xml:id="echoid-s16404" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16405" xml:space="preserve">recta D T, ſpatio <lb/>E N, vel E M, &amp;</s>
  <s xml:id="echoid-s16406" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16407" xml:space="preserve"><lb/>imprimendo puncta <lb/>in recta D C, per quę <lb/>
<anchor type="note" xlink:label="note-0260-05a" xlink:href="note-0260-05"/>
axi mundi D G, re-<lb/>ctã D C, ad rectos an <lb/>gulos ſecanti paralle <lb/>læ agantur, (quod <lb/>quidem facile fiet, ſi <lb/>omnia puncta rectæ <lb/>D C, traducantur in <lb/>rectã G F, ipſi D C, <lb/>parallelam, &amp;</s>
  <s xml:id="echoid-s16408" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s16409" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16410" xml:space="preserve"><lb/>his parallelis numeri horarum ſpatijs horarijs translatis reſpondentes apponantur. </s>
  <s xml:id="echoid-s16411" xml:space="preserve">Nam ſi par-<lb/>
<anchor type="note" xlink:label="note-0260-06a" xlink:href="note-0260-06"/>
tes harum parallelarum interceptæ inter radium Æquatoris D C, &amp; </s>
  <s xml:id="echoid-s16412" xml:space="preserve">radios aliorum ſignorum <lb/>transferantur in reſpõdentes horarias lineas horologij à linea æquinoctiali A C, imprimendo pũ <lb/>cta, &amp; </s>
  <s xml:id="echoid-s16413" xml:space="preserve">per hęc puncta lineæ curuæ ducantur, vt in ſuperioribus horologiis diximus, deſcripti erũt <lb/>rurſus paralleli Zodiaci. </s>
  <s xml:id="echoid-s16414" xml:space="preserve">Æqualiter autem diſtant quilibet paralleli oppoſiti ab æquinoctiali linea. <lb/></s>
  <s xml:id="echoid-s16415" xml:space="preserve">Nam cum anguli, quos Æquatoris radius D T, facit cum radiis oppoſitorum ſignorum, æquales <lb/>
<anchor type="note" xlink:label="note-0260-07a" xlink:href="note-0260-07"/>
ſint, quòd inſiſtant huiuſmodi anguli ad centrum æqualibus arcubus æqualium declinationum; <lb/></s>
  <s xml:id="echoid-s16416" xml:space="preserve">ſint quoque duo anguli ad α, æquales, nempe recti, &amp; </s>
  <s xml:id="echoid-s16417" xml:space="preserve">latus D α, commune; </s>
  <s xml:id="echoid-s16418" xml:space="preserve">erunt quoque rectæ <lb/>inter α, &amp; </s>
  <s xml:id="echoid-s16419" xml:space="preserve">radios quorumlibet oppoſitorum ſignorum ęquales. </s>
  <s xml:id="echoid-s16420" xml:space="preserve">quod eſt propoſitum. </s>
  <s xml:id="echoid-s16421" xml:space="preserve">Idem etiam <lb/>
<anchor type="note" xlink:label="note-0260-08a" xlink:href="note-0260-08"/>
liquido conſtat ex Analemmate huius propoſ. </s>
  <s xml:id="echoid-s16422" xml:space="preserve">ſi recte conſiderentur triangula E K N, E K Q; <lb/></s>
  <s xml:id="echoid-s16423" xml:space="preserve">
<anchor type="note" xlink:label="note-0260-09a" xlink:href="note-0260-09"/>
E K O, E K R; </s>
  <s xml:id="echoid-s16424" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16425" xml:space="preserve">E K P, E K S. </s>
  <s xml:id="echoid-s16426" xml:space="preserve">Vnde vna eademq́ue opera quosuis parallelos oppoſitos in horo <lb/>
<anchor type="note" xlink:label="note-0260-10a" xlink:href="note-0260-10"/>
logio deſcribemus, ſi hinc inde à linea æquinoctiali in lineis horariis puncta imprimamus æquali <lb/>ter à linea æquinoctiali diſtantia. </s>
  <s xml:id="echoid-s16427" xml:space="preserve">Hanc autem poſteriorem parallelorum Zodiaci deſcriptionem <lb/>hoc modo demonſtrabimus.</s>
  <s xml:id="echoid-s16428" xml:space="preserve"/>
</p>
<div xml:id="echoid-div836" type="float" level="2" n="6">
<note position="left" xlink:label="note-0260-03" xlink:href="note-0260-03a" xml:space="preserve">Alia deſcriptio <lb/>arcuum ſigno-<lb/>rum in horolo-<lb/>gio Meridiano.</note>
  <figure xlink:label="fig-0260-01" xlink:href="fig-0260-01a">
    <image file="0260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0260-01"/>
  </figure>
<note position="left" xlink:label="note-0260-04" xlink:href="note-0260-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0260-05" xlink:href="note-0260-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0260-06" xlink:href="note-0260-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0260-07" xlink:href="note-0260-07a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0260-08" xlink:href="note-0260-08a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0260-09" xlink:href="note-0260-09a" xml:space="preserve">Quo pacto ar-<lb/>cus ſignorũ op-<lb/>poſitorum una <lb/>cademq́ue ope-<lb/>ra deſcribantur <lb/>in horologio <lb/>Meridiano.</note>
<note position="left" xlink:label="note-0260-10" xlink:href="note-0260-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s16429" xml:space="preserve">INTELLIGATVR in horologio ſtylus A E, ad rectos angulos inſiſtere plano horologii, <lb/>
<anchor type="note" xlink:label="note-0260-11a" xlink:href="note-0260-11"/>
&amp; </s>
  <s xml:id="echoid-s16430" xml:space="preserve">figura radiorum Zodiaci proxime conftructa circa verticem ſtyli E, circumuerti verſus planum <lb/>horologii, ita vt punctum D, coniungatur cum puncto E, ſeu cum centro mundi, &amp; </s>
  <s xml:id="echoid-s16431" xml:space="preserve">recta D G, <lb/>perpetuo æquidiſtet lineæ horæ 6. </s>
  <s xml:id="echoid-s16432" xml:space="preserve">hoc eſt, cum axe mundi ſit coniuncta, ac propterea recta D C, à <lb/>plano Aequatoris non recedens illo motu occurrat ſemper lineæ æquinoctiali. </s>
  <s xml:id="echoid-s16433" xml:space="preserve">Quo poſito, cadet <lb/>in hac circumuolutione punctum T, v. </s>
  <s xml:id="echoid-s16434" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16435" xml:space="preserve">in punctum N, propterea quòd in conſtructione recta <lb/>D T, ſumpta fuit æqualis rectæ E N. </s>
  <s xml:id="echoid-s16436" xml:space="preserve">Eſt enim recta E N, cadens ex puncto E, in ſublimi poſito, <lb/>nempe à vertice ſtyli, in punctum N, æqualis rectæ E N, in plano horologii; </s>
  <s xml:id="echoid-s16437" xml:space="preserve">vt facile probabitur,
<pb o="245" file="0261" n="261" rhead="LIBER SECVNDVS."/>
parallela agatur F K, communis videlicet ſectio Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s16438" xml:space="preserve">plani horologij, ſecans latera <lb/>triangulorum per axẽ in G, H, I, K, &amp;</s>
  <s xml:id="echoid-s16439" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16440" xml:space="preserve">vt ſint diametri conicarũ ſectionum G K, H K, I K, &amp;</s>
  <s xml:id="echoid-s16441" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s16442" xml:space="preserve">Si igitur puncta G, H, I, K, in lineam Verticalem A D, horologij transferantur ex A, infra hori-<lb/>zontalem lineam, &amp; </s>
  <s xml:id="echoid-s16443" xml:space="preserve">circa Verticalem lineam deſcribantur, per propoſ. </s>
  <s xml:id="echoid-s16444" xml:space="preserve">8. </s>
  <s xml:id="echoid-s16445" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16446" xml:space="preserve">dictæ ſe-<lb/>ctiones conicæ tranſeuntes per puncta G, H, I, K, (quæ quidem conicæ ſectiones hyperbolæ ſunt, <lb/>ex propoſ. </s>
  <s xml:id="echoid-s16447" xml:space="preserve">6. </s>
  <s xml:id="echoid-s16448" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s16449" xml:space="preserve">cum Meridianus, cui planum horologij æquidiſtat, per polos paral-<lb/>lelorum Horizontis deſcriptus ipſos omnes ſecet.) </s>
  <s xml:id="echoid-s16450" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16451" xml:space="preserve">ſemper à linea horizontali eo magis recedẽ <lb/>tes, quo longius productæ fuerint ex vtraque parte Verticalis lineæ A D, deſcripti erunt paralleli <lb/>Horizontis. </s>
  <s xml:id="echoid-s16452" xml:space="preserve">quod eſt propoſitum.</s>
  <s xml:id="echoid-s16453" xml:space="preserve"/>
</p>
<div xml:id="echoid-div837" type="float" level="2" n="7">
<note position="left" xlink:label="note-0260-11" xlink:href="note-0260-11a" xml:space="preserve">Demonitratio <lb/>poſterioris de-<lb/>ſcriptionis pa-<lb/>ralleloru<unsure/>m So <lb/>lis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s16454" xml:space="preserve">ALITER Deſcripto quadrante A B C, cuiuſcunque magnitudinis, diuiſoq́ue in 90. </s>
  <s xml:id="echoid-s16455" xml:space="preserve">grad. <lb/></s>
  <s xml:id="echoid-s16456" xml:space="preserve">
<anchor type="note" xlink:label="note-0261-02a" xlink:href="note-0261-02"/>
vel in pauciores partes pro numero parallelorum deſcribendorum, emittantur ex centro A, per <lb/>puncta diuiſionum rectæ lineæ, quæ reſpon-<lb/>
<anchor type="figure" xlink:label="fig-0261-01a" xlink:href="fig-0261-01"/>
debunt radiis parallelorũ Horizontis in qua <lb/>drante E C D, præcedentis figuræ contentis; <lb/></s>
  <s xml:id="echoid-s16457" xml:space="preserve">initio ſumpto à recta A B, ita vt radius proxi <lb/>mus rectæ A B, ſit paralleli Horizontis grad. </s>
  <s xml:id="echoid-s16458" xml:space="preserve"><lb/>15. </s>
  <s xml:id="echoid-s16459" xml:space="preserve">ſequens, 30, &amp;</s>
  <s xml:id="echoid-s16460" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16461" xml:space="preserve">vt numeri appoſiti indi-<lb/>cant. </s>
  <s xml:id="echoid-s16462" xml:space="preserve">Deinde ex figura præcedentis propoſi-<lb/>ſitionis ſumantur interualla inter centrum <lb/>
<anchor type="note" xlink:label="note-0261-03a" xlink:href="note-0261-03"/>
F, &amp; </s>
  <s xml:id="echoid-s16463" xml:space="preserve">puncta, quibus Verticales lineæ horizon <lb/>talem lineam interſecant, eaque ex A, hu-<lb/>ius figuræ in rectam A B, tranferantur, aſcri-<lb/>ptis numeris Verticalium linearum prope <lb/>puncta, quæ translata interualla in recta A B, <lb/>terminant, atq; </s>
  <s xml:id="echoid-s16464" xml:space="preserve">per hæc puncta agantur ipſi <lb/>A C, parallelæ.</s>
  <s xml:id="echoid-s16465" xml:space="preserve"><unsure/> Quod facile fiet, ſi ipſi A B, pa <lb/>rallela ducatur G H, &amp; </s>
  <s xml:id="echoid-s16466" xml:space="preserve">in hanc puncta lineæ <lb/>A B, transferantur, &amp;</s>
  <s xml:id="echoid-s16467" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16468" xml:space="preserve">Exempli gratia, ex fi-<lb/>gura pręcedentis propoſ. </s>
  <s xml:id="echoid-s16469" xml:space="preserve">interuallum E L, <lb/>transferatur in rectam A B, huius figuræ <lb/>
<anchor type="note" xlink:label="note-0261-04a" xlink:href="note-0261-04"/>
vſquead punctũ D, apponendo numerũ 60. <lb/></s>
  <s xml:id="echoid-s16470" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16471" xml:space="preserve">per D, ipſi A C, parallella agatur D E, &amp;</s>
  <s xml:id="echoid-s16472" xml:space="preserve">c.</s>
  <s xml:id="echoid-s16473" xml:space="preserve"/>
</p>
<div xml:id="echoid-div838" type="float" level="2" n="8">
<note position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">A@ia deſcriptio <lb/>pa@allelorũ Ho <lb/>rizontis i<unsure/>n eo-<lb/>dem horologi<unsure/>o <lb/>Meridi<unsure/>ano.</note>
  <figure xlink:label="fig-0261-01" xlink:href="fig-0261-01a">
    <image file="0261-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0261-01"/>
  </figure>
<note position="left" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0261-04" xlink:href="note-0261-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s16474" xml:space="preserve">HAC antem figura ita conſtructa, deſcri <lb/>bentur paralleli Horizontis hoc modo. </s>
  <s xml:id="echoid-s16475" xml:space="preserve">Interualla rectarum ipſi A C, æquidiſtantium comprehẽ-<lb/>ſa inter rectam A B, radium v. </s>
  <s xml:id="echoid-s16476" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16477" xml:space="preserve">paralleli Horizontis grad. </s>
  <s xml:id="echoid-s16478" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16479" xml:space="preserve">transferantur ex punctis, quibus li-<lb/>nea horizontalis in figura præcedẽtis propoſ. </s>
  <s xml:id="echoid-s16480" xml:space="preserve">ſecatur à lineis Verticalibus, in lineas Verticales cor <lb/>reſpondentes numeris in recta A B, notatis, ſignando puncta in Verticalibus lineis: </s>
  <s xml:id="echoid-s16481" xml:space="preserve">vt v. </s>
  <s xml:id="echoid-s16482" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16483" xml:space="preserve">rectæ <lb/>D E, accipiatur æqualis L M, in Verticali linea grad. </s>
  <s xml:id="echoid-s16484" xml:space="preserve">60 &amp; </s>
  <s xml:id="echoid-s16485" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s16486" xml:space="preserve">Si enim hæc puncta ap-<lb/>poſite iungantur linea quadã inflexa, deſcriptus erit parallelus Horizontis gr. </s>
  <s xml:id="echoid-s16487" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16488" xml:space="preserve">Eodem modo <lb/>reliqui paralleli Horizontis deſcribentur, ſi rectæ inter lineam A B, &amp; </s>
  <s xml:id="echoid-s16489" xml:space="preserve">radios parallelorũ Horizon-<lb/>
<anchor type="note" xlink:label="note-0261-05a" xlink:href="note-0261-05"/>
tis interiectæ transferantur in lineas Verticales correſpondentes, ex linea horizontali, &amp;</s>
  <s xml:id="echoid-s16490" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16491" xml:space="preserve">Quod <lb/>hac ratione demonſtrabimus.</s>
  <s xml:id="echoid-s16492" xml:space="preserve"/>
</p>
<div xml:id="echoid-div839" type="float" level="2" n="9">
<note position="left" xlink:label="note-0261-05" xlink:href="note-0261-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s16493" xml:space="preserve">IN figura antecedentis propoſ. </s>
  <s xml:id="echoid-s16494" xml:space="preserve">intelligatur recta A F, quæ ſtylo ſumpta eſt æqualis, ad rectos <lb/>
<anchor type="note" xlink:label="note-0261-06a" xlink:href="note-0261-06"/>
angulos inſiſtere plano horologij in puncto A, &amp; </s>
  <s xml:id="echoid-s16495" xml:space="preserve">figura proxime cõſtructa circa punctũ F, quod <lb/>eſt in centro mundi, circumduci verſus horologiũ, ita vt punctum A, coniungatur cũ centro mũ-<lb/>di, ſeu puncto E, &amp; </s>
  <s xml:id="echoid-s16496" xml:space="preserve">recta A C, perpetuo lineæ Verticali A D, æquidiſter, hoc eſt, coniuncta ſit cũ <lb/>axe Horizontis, eiuſque parallelorum, &amp; </s>
  <s xml:id="echoid-s16497" xml:space="preserve">idcirco recta A B, à plano Horizontis non recedens oc-<lb/>currat ſemper illo motu horizontali lineæ. </s>
  <s xml:id="echoid-s16498" xml:space="preserve">Nam in hac circumductione cadet punctum D, v. </s>
  <s xml:id="echoid-s16499" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16500" xml:space="preserve">in <lb/>punctum L, horizontalis lineæ, propterea quòd rectæ F L, in præcedenti propoſ. </s>
  <s xml:id="echoid-s16501" xml:space="preserve">ſumpta eſt hic <lb/>
<anchor type="note" xlink:label="note-0261-07a" xlink:href="note-0261-07"/>
æqualis, A D. </s>
  <s xml:id="echoid-s16502" xml:space="preserve">Eſt enim recta F L, cadens ex puncto F, in ſublimi, nempe à Vertice ſtyli, rectæ <lb/>F L, in plano horologii æqualis; </s>
  <s xml:id="echoid-s16503" xml:space="preserve">vt conſtat, ſi triangulum F A L, in ſublimi conferatur cum trian-<lb/>
<anchor type="note" xlink:label="note-0261-08a" xlink:href="note-0261-08"/>
gulo F A L, in plano horologij, quemadmodũ propoſ. </s>
  <s xml:id="echoid-s16504" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16505" xml:space="preserve">huius libri de trangulis E A N, E A N, <lb/>dictum eſt. </s>
  <s xml:id="echoid-s16506" xml:space="preserve">Cum igitur tam recta L M, quàm D E, axi Horizontis æquidiſtet, erunt etiam L M, <lb/>
<anchor type="note" xlink:label="note-0261-09a" xlink:href="note-0261-09"/>
D E, inter ſe parallelæ, &amp; </s>
  <s xml:id="echoid-s16507" xml:space="preserve">ob id congruet recta D E, rectæ L M, aliàs nõ eſſent parallelæ L M, D E, <lb/>cum in illa circumductione in L, conueniant; </s>
  <s xml:id="echoid-s16508" xml:space="preserve">ac proinde cum L M, ſumpta ſit æqualis rectæ D E, <lb/>cadet punctum E, in punctum M, atque adeo radius paralleli Horizontis grad. </s>
  <s xml:id="echoid-s16509" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16510" xml:space="preserve">occurret plano <lb/>horologii in puncto M. </s>
  <s xml:id="echoid-s16511" xml:space="preserve">Per punctum ergo M, tranſibit arcus paralleli Horizontis grad. </s>
  <s xml:id="echoid-s16512" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16513" xml:space="preserve">cum <lb/>in illud radius dicti paralleli in illa circumuolutione incidat, vt demonſtratum eſt. </s>
  <s xml:id="echoid-s16514" xml:space="preserve">Non aliter oſtẽ <lb/>demus punctum F, eiuſdem radii cadere in punctum N, &amp; </s>
  <s xml:id="echoid-s16515" xml:space="preserve">ſic de cætetis. </s>
  <s xml:id="echoid-s16516" xml:space="preserve">Parallelos igitur Hori-<lb/>zontis in eodem horologio Meridiano deſcripſimus. </s>
  <s xml:id="echoid-s16517" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s16518" xml:space="preserve"/>
</p>
<div xml:id="echoid-div840" type="float" level="2" n="10">
<note position="right" xlink:label="note-0261-06" xlink:href="note-0261-06a" xml:space="preserve">Demonſtratio <lb/>poſterioris de-<lb/>ſcriptionis pa-<lb/>rallelorum Ho<unsure/> <lb/>rizontis.</note>
<note position="left" xlink:label="note-0261-07" xlink:href="note-0261-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0261-08" xlink:href="note-0261-08a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0261-09" xlink:href="note-0261-09a" xml:space="preserve">9. vndec.</note>
</div>
<pb o="246" file="0262" n="262" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div842" type="section" level="1" n="200">
<head xml:id="echoid-head203" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s16519" xml:space="preserve">QVONIAM lineæ uerticales, &amp; </s>
  <s xml:id="echoid-s16520" xml:space="preserve">hyperbolæ parallelorum Horizontis eundem ſitum, eoſdem-<lb/>
<anchor type="note" xlink:label="note-0262-01a" xlink:href="note-0262-01"/>
que numeros in vtroque horologio habent, vt ex ipſa deſcriptione, &amp; </s>
  <s xml:id="echoid-s16521" xml:space="preserve">ex figura propoſ. </s>
  <s xml:id="echoid-s16522" xml:space="preserve">præcedẽtis liquet, <lb/>perſpicuum eſt, ſi in facie oppoſita vtriuſuis horologĳ deſcribantur lineę uerticales, &amp; </s>
  <s xml:id="echoid-s16523" xml:space="preserve">paralleli Hori-<lb/>zontis reſpondentes ad vnguem lineis Verticalibus, &amp; </s>
  <s xml:id="echoid-s16524" xml:space="preserve">parallelis Horizontisin horologio delineatis, de-<lb/>ſcriptum quoque eſſe horologium cum lineis uerticalibus, &amp; </s>
  <s xml:id="echoid-s16525" xml:space="preserve">parallelis Horizontis in oppoſita plani fa-<lb/>cie collocandum. </s>
  <s xml:id="echoid-s16526" xml:space="preserve">Quam ob rem ſatis erit, ſi vnum ſolum horologium deſcribatur, vel orientale, vel occi <lb/>dent ale. </s>
  <s xml:id="echoid-s16527" xml:space="preserve">Nam in facie oppoſita ex hoc facile alterum delineabimus, vt dictum eſt.</s>
  <s xml:id="echoid-s16528" xml:space="preserve"/>
</p>
<div xml:id="echoid-div842" type="float" level="2" n="1">
<note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Deſcriptis li-<lb/>neis Verticali-<lb/>bus, &amp; paralle-<lb/>lis Horizontis <lb/>in alterutro ho <lb/>rologio Mer<unsure/>i-<unsure/> <lb/>diano, ſi in op-<lb/>poſita facie pla-<lb/>ni depingantur <lb/>lineæ Vertica-<lb/>les<unsure/>, &amp; paralleli <lb/>Horizontis re-<lb/>ſpondentes ad <lb/>vnguem illis in <lb/>horologio deli-<lb/>neatis, deſcripti <lb/>erunt in facie <lb/>oppoſita iidem <lb/>circuli Vertica <lb/>les, &amp; paralleli <lb/>Horizontis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div844" type="section" level="1" n="201">
<head xml:id="echoid-head204" xml:space="preserve">PROBLEMA 30. PROPOSITIO 30.</head>
<p>
  <s xml:id="echoid-s16529" xml:space="preserve">MERIDIANOS, ſiue circulos longitudinum ciuitatum, in e<unsure/>o-<lb/>dem Meridiano horologio deſcribere.</s>
  <s xml:id="echoid-s16530" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16531" xml:space="preserve">HORVM deſcrip tio non differt à deſcriptione circulorum horariorum à meridie, vel me-<lb/>
<anchor type="note" xlink:label="note-0262-03a" xlink:href="note-0262-03"/>
dia nocte, vt propoſ. </s>
  <s xml:id="echoid-s16532" xml:space="preserve">6. </s>
  <s xml:id="echoid-s16533" xml:space="preserve">huius libri docuimus; </s>
  <s xml:id="echoid-s16534" xml:space="preserve">ſi modo circulus F G H I, ex E, deſcriptus principiũ <lb/>diuiſionis habeat à Meridiano inſularum Fortunatarum; </s>
  <s xml:id="echoid-s16535" xml:space="preserve">qui habetur, ſi longitudo loci numere-<lb/>tur à G, in horologio quidem orientali propoſ. </s>
  <s xml:id="echoid-s16536" xml:space="preserve">25. </s>
  <s xml:id="echoid-s16537" xml:space="preserve">huius libri deſcripto verſus H, in occidentali <lb/>
<anchor type="note" xlink:label="note-0262-04a" xlink:href="note-0262-04"/>
<anchor type="figure" xlink:label="fig-0262-01a" xlink:href="fig-0262-01"/>
<anchor type="note" xlink:label="note-0262-05a" xlink:href="note-0262-05"/>
<anchor type="note" xlink:label="note-0262-06a" xlink:href="note-0262-06"/>
<anchor type="note" xlink:label="note-0262-07a" xlink:href="note-0262-07"/>
<anchor type="note" xlink:label="note-0262-08a" xlink:href="note-0262-08"/>
vero verſus F, nimirum ad partes occidentales à Meridiano circulo, vt ratio poſtulat. </s>
  <s xml:id="echoid-s16538" xml:space="preserve">Quod qui-<lb/>dem facile intelligetur, ſi in vtroque horologio circulus F G H I, circumuetatur circa rectã A C, <lb/>donec cum plano Æquinoctialis circuli coniungatur, &amp;</s>
  <s xml:id="echoid-s16539" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16540" xml:space="preserve">Meridianos ergo, ſiue circulos longitu <lb/>dinum ciuitatum, in eodem Meridiano horologio deſcripſimus. </s>
  <s xml:id="echoid-s16541" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s16542" xml:space="preserve"/>
</p>
<div xml:id="echoid-div844" type="float" level="2" n="1">
<note position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">Deſcriptio Me <lb/>ridianorum in <lb/>eodem horolo-<lb/>gio Meridiano.</note>
<note position="left" xlink:label="note-0262-04" xlink:href="note-0262-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0262-01" xlink:href="fig-0262-01a">
    <image file="0262-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0262-01"/>
  </figure>
<note position="left" xlink:label="note-0262-05" xlink:href="note-0262-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0262-06" xlink:href="note-0262-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0262-07" xlink:href="note-0262-07a" xml:space="preserve">Deſcripto vtro-<lb/>uis horologi<unsure/>o <lb/>Meridiano cũ <lb/>Meridianis, ſi <lb/>portio ſupra li-<lb/>neam horizon-<lb/>talem inuerta-<lb/>tur, vt ſuperiota <lb/>fiant inferiota, <lb/>&amp; dextra ſini-<lb/>ſtra, confectum <lb/>erit aliud horo <lb/>logium conti-<lb/>ne@s Meridia-<lb/>nos circulos in <lb/>facie oppoſita <lb/>collocandum.</note>
<note position="left" xlink:label="note-0262-08" xlink:href="note-0262-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div846" type="section" level="1" n="202">
<head xml:id="echoid-head205" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s16543" xml:space="preserve">SI pars ſuperior horologĳ orientalis, quam linea horizontalis aufert, inuertatur, vt in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s16544" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16545" xml:space="preserve">huius libri diximus, nempe vt inferiora fiant ſuperiora, &amp; </s>
  <s xml:id="echoid-s16546" xml:space="preserve">dextra ſiniſtra, habebimus horologiũ <lb/>occidentale cum Meridianis, vt in eodem ſcholio oſtendimus; </s>
  <s xml:id="echoid-s16547" xml:space="preserve">dummodo numeri in orientali poſiti muten-
<pb o="247" file="0263" n="263" rhead="LIBER SECVNDVS."/>
tur in occident ali in numeros, qui e<unsure/>x additione<unsure/> grad. </s>
  <s xml:id="echoid-s16548" xml:space="preserve">180. </s>
  <s xml:id="echoid-s16549" xml:space="preserve">ad numeros orient alis horologii cõflantur, (ab-<lb/>iectis tamen grad. </s>
  <s xml:id="echoid-s16550" xml:space="preserve">360. </s>
  <s xml:id="echoid-s16551" xml:space="preserve">ſi ex illa additione maior numerus, quàm 360. </s>
  <s xml:id="echoid-s16552" xml:space="preserve">componatur.) </s>
  <s xml:id="echoid-s16553" xml:space="preserve">vel, quod id@m eſt, <lb/>in numeros, qui in circulo ex E, deſcripto opponuntur per di<unsure/>ametrum illis numeris, qui in orientali horo <lb/>logio ponuntur. </s>
  <s xml:id="echoid-s16554" xml:space="preserve">Quę omnia hac etiam ratione oſtendemus. </s>
  <s xml:id="echoid-s16555" xml:space="preserve">Quoniam in triangulo A E C, in orientali ho-<lb/>logio, &amp; </s>
  <s xml:id="echoid-s16556" xml:space="preserve">in triangulo A E S, in occidentali, anguli ad A, recti ſunt, idcoque æquales, &amp; </s>
  <s xml:id="echoid-s16557" xml:space="preserve">anguli ad E, <lb/>æquales quoque, ob ęquales arcus inter H, &amp; </s>
  <s xml:id="echoid-s16558" xml:space="preserve">rectas E C, E S, interiectos; </s>
  <s xml:id="echoid-s16559" xml:space="preserve">(quòd enim hi arcus ęquales <lb/>
<anchor type="note" xlink:label="note-0263-01a" xlink:href="note-0263-01"/>
ſint, ita confirmabimus. </s>
  <s xml:id="echoid-s16560" xml:space="preserve">Arcus G ***, in orientali horologio æqualis eſt arcui G ***, in occidentali, cum <lb/>vterque longitudinem loci numeret. </s>
  <s xml:id="echoid-s16561" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s16562" xml:space="preserve">arcus *** 15. </s>
  <s xml:id="echoid-s16563" xml:space="preserve">in illo æqualis arcui *** 15. </s>
  <s xml:id="echoid-s16564" xml:space="preserve">in hoc. </s>
  <s xml:id="echoid-s16565" xml:space="preserve">Igitur <lb/>&amp; </s>
  <s xml:id="echoid-s16566" xml:space="preserve">reliquus arcus G 15. </s>
  <s xml:id="echoid-s16567" xml:space="preserve">illius arcui reliquo G 15. </s>
  <s xml:id="echoid-s16568" xml:space="preserve">huius æqualis erit; </s>
  <s xml:id="echoid-s16569" xml:space="preserve">atque adeo &amp; </s>
  <s xml:id="echoid-s16570" xml:space="preserve">reliquus 15 H, ex <lb/>
<anchor type="note" xlink:label="note-0263-02a" xlink:href="note-0263-02"/>
quadrante G H, reliquo 15 F, ex quadrante G F, æqualis erit. </s>
  <s xml:id="echoid-s16571" xml:space="preserve">Cum ergo arcus 15 F, &amp; </s>
  <s xml:id="echoid-s16572" xml:space="preserve">ille, qui inter <lb/>H, &amp; </s>
  <s xml:id="echoid-s16573" xml:space="preserve">rectam E S, interĳcitur, in horologio occidentali æquales ſint, ob æquale<unsure/>s angulos ad Verticem E, <lb/>
<anchor type="note" xlink:label="note-0263-03a" xlink:href="note-0263-03"/>
æquales quoque erunt arcus 15 H, in orientali, &amp; </s>
  <s xml:id="echoid-s16574" xml:space="preserve">ille qui inter H, &amp; </s>
  <s xml:id="echoid-s16575" xml:space="preserve">rectam E S, in occidentali interĳ <lb/>citur, hoc eſt, arcus inter puncta H, &amp; </s>
  <s xml:id="echoid-s16576" xml:space="preserve">rectas E C, E S, interpoſiti.) </s>
  <s xml:id="echoid-s16577" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s16578" xml:space="preserve">latera A E, A E, æqua-<lb/>lia, quę dictis angulis adiacent; </s>
  <s xml:id="echoid-s16579" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s16580" xml:space="preserve">recta A C, rectæ A S, æqualis. </s>
  <s xml:id="echoid-s16581" xml:space="preserve">Vnde oſtendemus, vt in ſcholio <lb/>
<anchor type="note" xlink:label="note-0263-04a" xlink:href="note-0263-04"/>
propoſ. </s>
  <s xml:id="echoid-s16582" xml:space="preserve">25. </s>
  <s xml:id="echoid-s16583" xml:space="preserve">huius libri, ſi pars ſuperior orientalis horologii inferiori parti occident alis ſuperponatur, vt <lb/>in ſcholio dicto docuimus, lineam æquinoctialem lineæ æquinoctiali congruere, &amp; </s>
  <s xml:id="echoid-s16584" xml:space="preserve">Meridianum 195. </s>
  <s xml:id="echoid-s16585" xml:space="preserve">per <lb/>punctum C, in orientali horologio ductum, Meridiano 15. </s>
  <s xml:id="echoid-s16586" xml:space="preserve">per punctum S, in occidentali ducto, qui illi <lb/>per diametrum obiicitur. </s>
  <s xml:id="echoid-s16587" xml:space="preserve">Non aliter oſtendemus reliquos Meridianos in parte ſuperiori orientalis horo-<lb/>logĳ contentos reliquis Meridiani<unsure/>s in inferiori parte horologii occidentalis exiſtentibus, qui quidem illis <lb/>
<anchor type="note" xlink:label="note-0263-05a" xlink:href="note-0263-05"/>
in circulo ex E, deſcripto per diametrum oppoſiti ſunt, congruere. </s>
  <s xml:id="echoid-s16588" xml:space="preserve">Quapropter pars ſuperior horologĳ <lb/>orientalis auulſa à linea horizontali, ſi inuertatur, vt diximus, dabit Meridianos circulos in occidentali <lb/>horologio, ſi tamen numero cuilibet prius adiiciantur gradus 180. </s>
  <s xml:id="echoid-s16589" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16590" xml:space="preserve">abiiciantur ex ſumma grad. </s>
  <s xml:id="echoid-s16591" xml:space="preserve">360, ſi <lb/>ſumma hunc numerum exceſſerit, vt habeamus numerum in occidentali horologio illius ſemicir culi Me-<lb/>ridiani, qui ſemicir culo eiuſdẽ Meridiani obĳcitur, cuius ſectio in parte ſuperiori horologĳ orientalis exi <lb/>ſtit; </s>
  <s xml:id="echoid-s16592" xml:space="preserve">ſicut &amp; </s>
  <s xml:id="echoid-s16593" xml:space="preserve">in lineis horarum à meridie, vel med. </s>
  <s xml:id="echoid-s16594" xml:space="preserve">nocte factum eſt. </s>
  <s xml:id="echoid-s16595" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s16596" xml:space="preserve">ibi in occidentali horologio <lb/>continentur horæ à meridie, quarum ſemicir culi opponuntur ſemicirculis horarum earundem à media no <lb/>cte in ſuperiori parte horologii orientalis; </s>
  <s xml:id="echoid-s16597" xml:space="preserve">quia hora 1. </s>
  <s xml:id="echoid-s16598" xml:space="preserve">v. </s>
  <s xml:id="echoid-s16599" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16600" xml:space="preserve">in orientali horologio computatur à media no <lb/>cte, at eadem hora in occidentali horologio, facta illa inuerſione ſuperioris partis orientalis horologĳ, à <lb/>meridie numeranda eſt, &amp; </s>
  <s xml:id="echoid-s16601" xml:space="preserve">c.</s>
  <s xml:id="echoid-s16602" xml:space="preserve"/>
</p>
<div xml:id="echoid-div846" type="float" level="2" n="1">
<note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">27. t@rtĳ.</note>
<note position="left" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">26. tertĳ.</note>
<note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s16603" xml:space="preserve">EADEM ratione ſi pars ſuperior occidentalis horologĳ inuertatur, vt præcepimus, habebimus <lb/>
<anchor type="note" xlink:label="note-0263-06a" xlink:href="note-0263-06"/>
horologium orientale cum Meridianis, ſi prius numeri mutentur, vt nuper diximus.</s>
  <s xml:id="echoid-s16604" xml:space="preserve"/>
</p>
<div xml:id="echoid-div847" type="float" level="2" n="2">
<note position="left" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div849" type="section" level="1" n="203">
<head xml:id="echoid-head206" xml:space="preserve">PROBLEMA 31. PROPOSITIO 31.</head>
<p>
  <s xml:id="echoid-s16605" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in e<unsure/>o-<lb/>dem horologio Meridiano deſcribere.</s>
  <s xml:id="echoid-s16606" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16607" xml:space="preserve">LOCO parallelorum per Zodiaci ſigna tranſeuntium ſumantur paralleli per vertices ciuita <lb/>
<anchor type="note" xlink:label="note-0263-07a" xlink:href="note-0263-07"/>
tum intra tropicos conſtitutarum deſcripti, &amp; </s>
  <s xml:id="echoid-s16608" xml:space="preserve">reliqua omnia fiant, vt de parallelis ſignorum Zo-<lb/>
<anchor type="note" xlink:label="note-0263-08a" xlink:href="note-0263-08"/>
diaci diximus propoſ. </s>
  <s xml:id="echoid-s16609" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16610" xml:space="preserve">huius libri, deſcriptiq́ue erunt peralleli ciuitatum. </s>
  <s xml:id="echoid-s16611" xml:space="preserve">vt conſtat ex propoſ. <lb/></s>
  <s xml:id="echoid-s16612" xml:space="preserve">7. </s>
  <s xml:id="echoid-s16613" xml:space="preserve">huius libri Parallelos itaque ciuitatum, &amp;</s>
  <s xml:id="echoid-s16614" xml:space="preserve">c. </s>
  <s xml:id="echoid-s16615" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s16616" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s16617" xml:space="preserve"/>
</p>
<div xml:id="echoid-div849" type="float" level="2" n="1">
<note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ciui <lb/>ta@um, laiitudi <lb/>numve in eodẽ <lb/>horolog@o Me-<lb/>ridiano.</note>
<note position="left" xlink:label="note-0263-08" xlink:href="note-0263-08a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div851" type="section" level="1" n="204">
<head xml:id="echoid-head207" xml:space="preserve">PROBLEMA 32. PROPOSITIO 32.</head>
<p>
  <s xml:id="echoid-s16618" xml:space="preserve">DOMOS cęleſtes in eodem horologio Meridiano deſcribere.</s>
  <s xml:id="echoid-s16619" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16620" xml:space="preserve">EX Ioan. </s>
  <s xml:id="echoid-s16621" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s16622" xml:space="preserve">ſententia cæleſtes domus Æquatorem in 12. </s>
  <s xml:id="echoid-s16623" xml:space="preserve">partes æquales diuidentes, ita <lb/>
<anchor type="note" xlink:label="note-0263-09a" xlink:href="note-0263-09"/>
deſcribentur. </s>
  <s xml:id="echoid-s16624" xml:space="preserve">Circulus ex E, deſcriptus in 12. </s>
  <s xml:id="echoid-s16625" xml:space="preserve">partes æquales ſecetur, initio facto à recta GI, vel FH, <lb/>
<anchor type="note" xlink:label="note-0263-10a" xlink:href="note-0263-10"/>
&amp; </s>
  <s xml:id="echoid-s16626" xml:space="preserve">per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s16627" xml:space="preserve">centrum E, rectæ occultæ emiſſæ ſecent lineam equinoctialem AC, <lb/>in punctis, per quæ lineæ parallelæ ipſi horizontali lineæ A B, ductæ, erunt lineæ domorum cæle-<lb/>ſtium. </s>
  <s xml:id="echoid-s16628" xml:space="preserve">Nam circumducto circulo ex E, deſcripto circa æquinoctialem lineam, donec centrum E, <lb/>
<anchor type="note" xlink:label="note-0263-11a" xlink:href="note-0263-11"/>
cumcentro mundi coniungatur, ipſeq; </s>
  <s xml:id="echoid-s16629" xml:space="preserve">circulus in plano Æquatoris ſtatuatur, erunt rectæ per cen <lb/>trum E, tranſeuntes communes ſectiones circulorum domorum cæleſtium, (ex quorum numero <lb/>eſt etiam Meridianus per rectam G I, tranſiens, &amp; </s>
  <s xml:id="echoid-s16630" xml:space="preserve">Horizon incedẽs per F H.) </s>
  <s xml:id="echoid-s16631" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16632" xml:space="preserve">Æquatoris, quòd <lb/>communes ſectiones horum circu<unsure/>lorum &amp; </s>
  <s xml:id="echoid-s16633" xml:space="preserve">Æquatoris Æquatorem, ac proinde, ex demonſtratis <lb/>à nobis in ſphæram, &amp; </s>
  <s xml:id="echoid-s16634" xml:space="preserve">circulum ſibi concentricum ex E, deſcriptum partiãrur in partes 12. </s>
  <s xml:id="echoid-s16635" xml:space="preserve">æqua <lb/>les, tranſeantq́ue per mundi centrum. </s>
  <s xml:id="echoid-s16636" xml:space="preserve">Igitur circuli domorum cæleſtium occurrent plano horolo <lb/>gij in punctis, in quibus lineam æquinoctialem interſecant rectæ dictæ per E, tranſmiſſæ; </s>
  <s xml:id="echoid-s16637" xml:space="preserve">atque <lb/>adeo per eadem illa puncta lineæ æquinoctialis tranſibunt communes ſectiones eorundem circu-
<pb o="248" file="0264" n="264" rhead="GNOMONICES"/>
lorum, &amp; </s>
  <s xml:id="echoid-s16638" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s16639" xml:space="preserve">Cum igitur communes hę ſectiones parallelæ ſint, ex propoſ. </s>
  <s xml:id="echoid-s16640" xml:space="preserve">18. </s>
  <s xml:id="echoid-s16641" xml:space="preserve">ſupe-<lb/>rioris lib. </s>
  <s xml:id="echoid-s16642" xml:space="preserve">propterea quòd planum horologij æquidiſtat communi ſectioni illorum circulorum, <lb/>
<anchor type="figure" xlink:label="fig-0264-01a" xlink:href="fig-0264-01"/>
<anchor type="note" xlink:label="note-0264-01a" xlink:href="note-0264-01"/>
<anchor type="note" xlink:label="note-0264-02a" xlink:href="note-0264-02"/>
nempe axi Verticalis circuli, erunt rectæ ipſi horizontali lineæ parallelæ, ac per puncta lineæ æqui <lb/>noctialis educte, communes ſectiones eirculorum domorum cæleſtium, &amp; </s>
  <s xml:id="echoid-s16643" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s16644" xml:space="preserve">Quod <lb/>eſt propoſitum.</s>
  <s xml:id="echoid-s16645" xml:space="preserve"/>
</p>
<div xml:id="echoid-div851" type="float" level="2" n="1">
<note position="right" xlink:label="note-0263-09" xlink:href="note-0263-09a" xml:space="preserve">Deſcriptio do-<lb/>mo@um cœle-<lb/>ſtium ſecundũ <lb/>Ioan. Regiom. <lb/>in eodem horo <lb/>logio Meridia-<lb/>no.</note>
<note position="left" xlink:label="note-0263-10" xlink:href="note-0263-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0263-11" xlink:href="note-0263-11a" xml:space="preserve">D. monſtratio <lb/>deſcriptionis <lb/>demo@um cœle <lb/>ſtium @ecun<unsure/>dũ<unsure/> <lb/>loan. Regiom.</note>
  <figure xlink:label="fig-0264-01" xlink:href="fig-0264-01a">
    <image file="0264-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0264-01"/>
  </figure>
<note position="left" xlink:label="note-0264-01" xlink:href="note-0264-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0264-02" xlink:href="note-0264-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s16646" xml:space="preserve">SECVNDVM vero ſententiam Campani, Domus cæleſtes Verticalem circulum diuiden-<lb/>
<anchor type="note" xlink:label="note-0264-03a" xlink:href="note-0264-03"/>
<anchor type="note" xlink:label="note-0264-04a" xlink:href="note-0264-04"/>
tes in 12. </s>
  <s xml:id="echoid-s16647" xml:space="preserve">partes æquales delineabuntur hac ratione. </s>
  <s xml:id="echoid-s16648" xml:space="preserve">Per A, demittatur ad horizontalem lineam <lb/>A B, perdicularis A D, quæ erit communis ſectio Verticalis circuli &amp; </s>
  <s xml:id="echoid-s16649" xml:space="preserve">plani horologij, vt demon-<lb/>ſtrauimus propoſ. </s>
  <s xml:id="echoid-s16650" xml:space="preserve">28. </s>
  <s xml:id="echoid-s16651" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s16652" xml:space="preserve">Deinde in linea horizontali ſum pta recta A B, ſtylo A E, æqua-<lb/>li, deſcribatur ex B, ad quodcunque interuallum circulus, qui in 12. </s>
  <s xml:id="echoid-s16653" xml:space="preserve">partes æquales ſecetur, initio <lb/>facto à linea horizontali, ac per centrum B, &amp; </s>
  <s xml:id="echoid-s16654" xml:space="preserve">diuiſionum puncta rectæ occultæ tranſmittantur <lb/>ſecantes rectam A D, in punctis, per quæ lineæ horizontali parallelæ actæ erunt lineæ cæleſtiũ do-<lb/>morum. </s>
  <s xml:id="echoid-s16655" xml:space="preserve">Circumducto enim circulo ex B, deſcripto circa rectam A D, donec rectus ſit ad horolo-<lb/>
<anchor type="note" xlink:label="note-0264-05a" xlink:href="note-0264-05"/>
gij planum, centrumque B, cum centro mundi coniungatur, ita vt recta A B, eadem ſiat, quæ linea <lb/>ſtyli, &amp; </s>
  <s xml:id="echoid-s16656" xml:space="preserve">circulus ipſe in plano circuli Verticalis conſtituatur; </s>
  <s xml:id="echoid-s16657" xml:space="preserve">erunt rectæ per centrum B, tranſeun <lb/>tes, comunes ſectiones circulorum domorum cæleſtium, (ex quorum numero etiam eſt Horizon <lb/>
<anchor type="note" xlink:label="note-0264-06a" xlink:href="note-0264-06"/>
per rectam A B, incedens) &amp; </s>
  <s xml:id="echoid-s16658" xml:space="preserve">Verticalis circuli. </s>
  <s xml:id="echoid-s16659" xml:space="preserve">Nam horum circulorũ, &amp; </s>
  <s xml:id="echoid-s16660" xml:space="preserve">Verticalis ſectiones com <lb/>munes Verticalem, &amp; </s>
  <s xml:id="echoid-s16661" xml:space="preserve">proinde, ex demonſtratis à nobis in ſphærã, &amp; </s>
  <s xml:id="echoid-s16662" xml:space="preserve">circulũ ſibi concentricum ex <lb/>B, deſcriptum ſecant in partes 12. </s>
  <s xml:id="echoid-s16663" xml:space="preserve">æquales, ac per mundi centrum ducuntur. </s>
  <s xml:id="echoid-s16664" xml:space="preserve">Igitur dicti circuli <lb/>plano horologij occurrent in punctis, in quibus rectæ ex B, emiſſæ rectam A D, ſecant; </s>
  <s xml:id="echoid-s16665" xml:space="preserve">ac idcirco <lb/>per eadem illa puncta rectæ AD, tranſibunt communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s16666" xml:space="preserve">plani <lb/>horologij. </s>
  <s xml:id="echoid-s16667" xml:space="preserve">Cum igitur communes hæ ſectiones ſint parallelæ, per propoſ. </s>
  <s xml:id="echoid-s16668" xml:space="preserve">18. </s>
  <s xml:id="echoid-s16669" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s16670" xml:space="preserve">quod <lb/>planum horologij communi ſectioni illorum circulorum, nempe axi Verticalis circuli, æquidi-<lb/>ſtet, liquido conſtat, rectas ipſi horizontali lineæ pallalelas per puncta lineæ A D, eductas, com-<lb/>munes eſſe ſectiones circulorum domorum cæleſtium, &amp; </s>
  <s xml:id="echoid-s16671" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s16672" xml:space="preserve">Domos igitur cæleſtes <lb/>in eodem horologio Meridiano deſcripſimus. </s>
  <s xml:id="echoid-s16673" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s16674" xml:space="preserve"/>
</p>
<div xml:id="echoid-div852" type="float" level="2" n="2">
<note position="left" xlink:label="note-0264-03" xlink:href="note-0264-03a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium ſecun dũ <lb/>Campanũ, in <lb/>eodem Meri-<lb/>diano horolo <lb/>gio.</note>
<note position="left" xlink:label="note-0264-04" xlink:href="note-0264-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0264-05" xlink:href="note-0264-05a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domo@um cœle <lb/>ſtium ſeoundũ <lb/>Campanum.</note>
<note position="left" xlink:label="note-0264-06" xlink:href="note-0264-06a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div854" type="section" level="1" n="205">
<head xml:id="echoid-head208" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s16675" xml:space="preserve">MANIFESTVM eſt aute<unsure/>m, lineas domorum cæleſtium ſecundum priorem modum per ea pun <lb/>
<anchor type="note" xlink:label="note-0264-08a" xlink:href="note-0264-08"/>
cta lineæ æquinoctialis duci, per quæ lineę horariæ à linea horizontali duabus, &amp; </s>
  <s xml:id="echoid-s16676" xml:space="preserve">quatuor horis diſtantes <lb/>ducuntur, quales ſunt in orientali horologio horæ 8. </s>
  <s xml:id="echoid-s16677" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16678" xml:space="preserve">10. </s>
  <s xml:id="echoid-s16679" xml:space="preserve">poſt mediam noctem, in occidentali vero 2. </s>
  <s xml:id="echoid-s16680" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16681" xml:space="preserve"><lb/>4. </s>
  <s xml:id="echoid-s16682" xml:space="preserve">poſt meridiem. </s>
  <s xml:id="echoid-s16683" xml:space="preserve">Et quoni<unsure/>am quælibet domus complectitur grad. </s>
  <s xml:id="echoid-s16684" xml:space="preserve">30. </s>
  <s xml:id="echoid-s16685" xml:space="preserve">ſi quælibet pars duodecima circuli <lb/>ex E, vel B, deſcripti in 30. </s>
  <s xml:id="echoid-s16686" xml:space="preserve">partes, vel pauciores æquales diuidatur, pro magnitudine horologii, cęteraq́, <lb/>fiant, quę prius, deſcriptæ erunt lineę aliorum circulorum poſitionum per partes domorum cęleſtiũ tran-<lb/>ſeuntium. </s>
  <s xml:id="echoid-s16687" xml:space="preserve">In exemplo ſingulę domus diuiſę ſunt bifariam, ita vt inter quaſcunque binas lineas cadant <lb/>grad. </s>
  <s xml:id="echoid-s16688" xml:space="preserve">15. </s>
  <s xml:id="echoid-s16689" xml:space="preserve">vt figurę indicant.</s>
  <s xml:id="echoid-s16690" xml:space="preserve"/>
</p>
<div xml:id="echoid-div854" type="float" level="2" n="1">
<note position="left" xlink:label="note-0264-08" xlink:href="note-0264-08a" xml:space="preserve">Per quas horas <lb/>in æquinoctiali <lb/>linea ducantur <lb/>domus cœleſtes <lb/>ſecundum Ioa. <lb/>Regiom.</note>
</div>
<pb o="249" file="0265" n="265" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s16691" xml:space="preserve">CAETERVM quia eodem modo lineę domorum cęleſtium &amp; </s>
  <s xml:id="echoid-s16692" xml:space="preserve">in orie<unsure/>ntali, &amp; </s>
  <s xml:id="echoid-s16693" xml:space="preserve">in occidentali horo <lb/>
<anchor type="note" xlink:label="note-0265-01a" xlink:href="note-0265-01"/>
logio deſcribuntur, tam ſecundum Ioan. </s>
  <s xml:id="echoid-s16694" xml:space="preserve">Regi<unsure/>om. </s>
  <s xml:id="echoid-s16695" xml:space="preserve">quàm ex ſententia Campani, proptcrea in priori figura <lb/>@as delineauimus in horologio orientali. </s>
  <s xml:id="echoid-s16696" xml:space="preserve">Nam eædem deſcriptæ in facie occidentali illis correſpondentes <lb/>dabunt domos cęleſtes in horologio occidẽtali, vt numeri indicãt, quorũ illi, qui tropico ♋, appoſiti ſunt, <lb/>ad orientale horologium, alii vero tropico ♑, aſcripti ad occidentale pertinent. </s>
  <s xml:id="echoid-s16697" xml:space="preserve">In poſteriori autem fi-<lb/>gura duximus lineas domorum in occidentali horologio, propterea quòd eædem in facie orientali ipſis cor <lb/>reſpondentes dant domos cęleſtes in horologio orie<unsure/>ntali. </s>
  <s xml:id="echoid-s16698" xml:space="preserve">Numeri enim tropico ♋, aſcripti ad horologium <lb/>occidentale, alii vero tropico ♑, appoſiti ad orientale ſpectant.</s>
  <s xml:id="echoid-s16699" xml:space="preserve"/>
</p>
<div xml:id="echoid-div855" type="float" level="2" n="2">
<note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">Lineæ domor@ <lb/>cœleſtium eun-<lb/>dem ſ@@um in <lb/>vtroque horolo <lb/>gio Meridiano <lb/>habent. Vnde <lb/>ſatis eſt, vi de-<lb/>ſcribatur he<unsure/>ro-<lb/>logium dunta-<lb/>xat orientale@, <lb/>vel occidentale.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div857" type="section" level="1" n="206">
<head xml:id="echoid-head209" xml:space="preserve">PROBLEMA 33. PROPOSITIO 33.</head>
<p>
  <s xml:id="echoid-s16700" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem Meridiano horologio <lb/>deſcribere.</s>
  <s xml:id="echoid-s16701" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s16702" xml:space="preserve">ACCIPIANTVR ex prioribus duabus tabellis propoſ. </s>
  <s xml:id="echoid-s16703" xml:space="preserve">42. </s>
  <s xml:id="echoid-s16704" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16705" xml:space="preserve">Sole exiſtente in <lb/>
<anchor type="note" xlink:label="note-0265-03a" xlink:href="note-0265-03"/>
principio ♈, &amp; </s>
  <s xml:id="echoid-s16706" xml:space="preserve">♎, horæ, quibus 12. </s>
  <s xml:id="echoid-s16707" xml:space="preserve">ſigna Zodiaci oriuntur, in horologio quidem orientali, ante <lb/>meridiẽ, in occidentali vero poſt meridiem; </s>
  <s xml:id="echoid-s16708" xml:space="preserve">que in circulo ex E, deſcripto numerentur à linea GI, <lb/>vel verſus ortũ, vel verſus occaſum, hoc eſt, vel verſus partẽ antemeridianã, aut pomeridianã, prout <lb/>
<anchor type="note" xlink:label="note-0265-04a" xlink:href="note-0265-04"/>
tabellæ indicant. </s>
  <s xml:id="echoid-s16709" xml:space="preserve">In orientali horologio ſemper facienda eſt numeratio verſus dexterã, in occiden-<lb/>tali autem verſus ſiniſtram, hoc eſt, ſemper verſus F, vt patet, ſi circulus ex E, deſcriptus conſidere-<lb/>tur in propria poſitione in vtroque horologio. </s>
  <s xml:id="echoid-s16710" xml:space="preserve">Deinde per fines numerationum, &amp; </s>
  <s xml:id="echoid-s16711" xml:space="preserve">centrum E, du <lb/>cantur occultæ rectæ ſecantes æquinoctialem lineam ſiue infra horizontalem lineam, ſiue ſupra, <lb/>in punctis, per quæ aſcendentium ſignorum lineæ duci debent. </s>
  <s xml:id="echoid-s16712" xml:space="preserve">Poſtea notentur ex propoſ. </s>
  <s xml:id="echoid-s16713" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16714" xml:space="preserve">hu-<lb/>ius lib. </s>
  <s xml:id="echoid-s16715" xml:space="preserve">in linea horizontali puncta, quibus eam arcus ſignorum ſecant. </s>
  <s xml:id="echoid-s16716" xml:space="preserve">In hæc enim proiicientur <lb/>vmbrę gnomonis in orientali horologio, cum ſigna oriuntur, at in horologio occidentali, cum oc <lb/>cidunt. </s>
  <s xml:id="echoid-s16717" xml:space="preserve">Quæ quidem puncta hac etiam arte inueniemus, etiamſi in horologio arcus omnium ſi-<lb/>
<anchor type="note" xlink:label="note-0265-05a" xlink:href="note-0265-05"/>
gnorum non ſint deſcripti. </s>
  <s xml:id="echoid-s16718" xml:space="preserve">Ex quinta tabella propoſ. </s>
  <s xml:id="echoid-s16719" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16720" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16721" xml:space="preserve">accipiemus arcus ſemidiurnos <lb/>ſignorum, eosq́ue in vtroque horologio à G, verſus F, ſupputabimus, &amp; </s>
  <s xml:id="echoid-s16722" xml:space="preserve">à terminis ſupputationũ <lb/>
<anchor type="note" xlink:label="note-0265-06a" xlink:href="note-0265-06"/>
per E, centrum ducemus rectas ſecantes æquinoctialem lineam in punctis, per quæ rectæ ęquino-<lb/>ctialem lineam ſecantes ad angulos rectos ſecabunt lineam horizontalem in punctis, in quibus ar-<lb/>cus ſignorum eandem diuidunt; </s>
  <s xml:id="echoid-s16723" xml:space="preserve">cum, Sole exiſtente in initiis ſignorũ, vmbra ſtyli in ea pũcta pro-<lb/>ijciatur, cum oritur, vel occidit, propterea quòd dictæ lineæ perpendiculares indicent horas or-<lb/>tus, &amp; </s>
  <s xml:id="echoid-s16724" xml:space="preserve">occaſus ſolis in initiis ſignorum exiſtentis, vt ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s16725" xml:space="preserve">25. </s>
  <s xml:id="echoid-s16726" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16727" xml:space="preserve">demonſtraui-<lb/>mus, conſtat. </s>
  <s xml:id="echoid-s16728" xml:space="preserve">Cum ergo in ortu, &amp; </s>
  <s xml:id="echoid-s16729" xml:space="preserve">occaſu Solis vmbra ſtyli proiiciatur in lineam horizontalẽ, ma-<lb/>nifeſtum eſt, in illis punctis Solem oriri, &amp; </s>
  <s xml:id="echoid-s16730" xml:space="preserve">occidere, in quibus lineam horizontalem ſecant dictæ <lb/>lineæ perpendiculares.</s>
  <s xml:id="echoid-s16731" xml:space="preserve"/>
</p>
<div xml:id="echoid-div857" type="float" level="2" n="1">
<note position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">Deſcriptio ſi-<lb/>gnorum aſcen-<lb/>dentium in eo-<lb/>dem horologio <lb/>Meridiano.</note>
<note position="left" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">Inuentio<unsure/> pun-<lb/>ctorum in linea<unsure/> <lb/>horizontali u-<lb/>triuſque horolo <lb/>gii Met<unsure/>idiani, <lb/>in quæ vmbra<unsure/> <lb/>ſtyli ea dit, cum <lb/>ſigna oriuntur, <lb/>aut occidunt.</note>
<note position="left" xlink:label="note-0265-06" xlink:href="note-0265-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s16732" xml:space="preserve">EADEM puncta hoc modo reperiemus. </s>
  <s xml:id="echoid-s16733" xml:space="preserve">Ex recta E A, figuræ vltimæ propoſ. </s>
  <s xml:id="echoid-s16734" xml:space="preserve">21. </s>
  <s xml:id="echoid-s16735" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s16736" xml:space="preserve">
<anchor type="note" xlink:label="note-0265-07a" xlink:href="note-0265-07"/>
detrahatur recta æqualis ſtylo horologii Meridiani, &amp; </s>
  <s xml:id="echoid-s16737" xml:space="preserve">per punctum extremum@huius ducatur ad <lb/>
<anchor type="note" xlink:label="note-0265-08a" xlink:href="note-0265-08"/>
E A, perpendicularis, quæ erit linea horizontalis in orientali horologio. </s>
  <s xml:id="echoid-s16738" xml:space="preserve">Si igitur à puncto extre-<lb/>mo lineæ, quæ ſtylo ex E A, æqualis abſciſſa eſt, ſumantur interualla omnium punctorum, quibus <lb/>dicta perpendicularis à radijs ex M, O, Q, S, V, Y, per centrum E, ductis ſecatur, &amp; </s>
  <s xml:id="echoid-s16739" xml:space="preserve">in lineã ho-<lb/>rizontalem horologii orientalis ex A, loco ſtyli transferantur, habebuntur puncta, quæ inquirun-<lb/>tur; </s>
  <s xml:id="echoid-s16740" xml:space="preserve">vt perſpicuum eſt, ſi Horizon A B C D, in horologio orientali conc<unsure/>ipiatur in propria poſi-<lb/>tione, ita vt punctum extremum rectæ aſſumptæ in E A, ſit in A, loco ſtyli, &amp; </s>
  <s xml:id="echoid-s16741" xml:space="preserve">perpendicularis per <lb/>illud punctum ducta fiat eadem, quæ horizontalis linea in horologio, ac proinde E, in centro mun <lb/>di, tanquam vertex gnomonis, ſtatuatur. </s>
  <s xml:id="echoid-s16742" xml:space="preserve">Ita enim fiet, vt Sole exoriente in pũctis M, O, Q, S, V, Y, <lb/>vmbra ſtyli proiiciatur in dicta puncta lineę horizontalis in orientali horologio, vt patet. </s>
  <s xml:id="echoid-s16743" xml:space="preserve">Eodem <lb/>pacto in occidentali horologio eadem puncta deprehendentur, ſi ex E C, eiuſdem figurę propoſ. <lb/></s>
  <s xml:id="echoid-s16744" xml:space="preserve">
<anchor type="note" xlink:label="note-0265-09a" xlink:href="note-0265-09"/>
21. </s>
  <s xml:id="echoid-s16745" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16746" xml:space="preserve">abſcindatur recta æqualis ſtylo, &amp; </s>
  <s xml:id="echoid-s16747" xml:space="preserve">per extremum punctum ad E C, perpendicula-<lb/>ris ducatur pro horizontali linea horologij occidentalis, &amp;</s>
  <s xml:id="echoid-s16748" xml:space="preserve">c.</s>
  <s xml:id="echoid-s16749" xml:space="preserve"/>
</p>
<div xml:id="echoid-div858" type="float" level="2" n="2">
<note position="right" xlink:label="note-0265-07" xlink:href="note-0265-07a" xml:space="preserve">Qua ratione all <lb/>ter inueniantur <lb/>puncta in linea <lb/>horizõtali, quæ <lb/>prius.</note>
<note position="left" xlink:label="note-0265-08" xlink:href="note-0265-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0265-09" xlink:href="note-0265-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s16750" xml:space="preserve">ITAQVE ſi puncta inuẽta in æquinoctiali linea cum punctis reſpondentiũ ſignorũ in orien <lb/>tali horolog@o, oppoſitorũ vero in occidẽtali, inuentis in linea horizõtali iungantur rectis lineis, <lb/>deſcripta erunt ſigna aſcendentia. </s>
  <s xml:id="echoid-s16751" xml:space="preserve">Nam cum in horologio orientali vmbra proiicitur in aliquod <lb/>punctum horizontalis lineæ, oritur ſignum illud, in quo Sol exiſtit; </s>
  <s xml:id="echoid-s16752" xml:space="preserve">cum autem vmbra in occiden <lb/>tali horologio cadit in aliquod punctum lineæ horizontalis, oritur ſignum oppoſitum, cum illud <lb/>tunc, in quo Sol eſt, occidat,</s>
</p>
<p>
  <s xml:id="echoid-s16753" xml:space="preserve">POSSVMVS quoque in duobus tropicis pũcta reperire ex tertia, &amp; </s>
  <s xml:id="echoid-s16754" xml:space="preserve">quarta tabella propoſ. <lb/></s>
  <s xml:id="echoid-s16755" xml:space="preserve">
<anchor type="note" xlink:label="note-0265-10a" xlink:href="note-0265-10"/>
9. </s>
  <s xml:id="echoid-s16756" xml:space="preserve">hu@us lib. </s>
  <s xml:id="echoid-s16757" xml:space="preserve">per quæ ſigna aſcendentia duci debent; </s>
  <s xml:id="echoid-s16758" xml:space="preserve">deſcribendo videlicet occulte lineam illius <lb/>horæ, qua ſignorum quodlibet oritur. </s>
  <s xml:id="echoid-s16759" xml:space="preserve">Vbi enim hæc tropicum ſecuerit, per illud punctum ducen <lb/>da eſt linea illius ſigni aſcedentis, vt in horologio horizontali factum eſt. </s>
  <s xml:id="echoid-s16760" xml:space="preserve">Perutile autẽ eſt, immo
<pb o="250" file="0266" n="266" rhead="GNOMONICES"/>
neceſſarium fere inuenire in tropicis puncta illorum ſignorum, quorum puncta in linea æquino <lb/>ctiali inuenta adeo propinqua ſunt lineæ horizontali, vt vix ſine errore aliquo linca ſigni aſcenden <lb/>tis per duo illa puncta vicina duci poſſit, niſi accedat tertium in tropico repertum. </s>
  <s xml:id="echoid-s16761" xml:space="preserve">Quod ſi pun <lb/>ctum inueniendum ſit in tropico ſupra lineam horizontalem, inueniemus illud, etiamſi tropicus <lb/>
<anchor type="figure" xlink:label="fig-0266-01a" xlink:href="fig-0266-01"/>
<anchor type="note" xlink:label="note-0266-01a" xlink:href="note-0266-01"/>
<anchor type="note" xlink:label="note-0266-02a" xlink:href="note-0266-02"/>
<anchor type="note" xlink:label="note-0266-03a" xlink:href="note-0266-03"/>
<anchor type="note" xlink:label="note-0266-04a" xlink:href="note-0266-04"/>
non ſit deſcriptus ſupra horizontalem lineam hac arte. </s>
  <s xml:id="echoid-s16762" xml:space="preserve">Sit inueniendum v. </s>
  <s xml:id="echoid-s16763" xml:space="preserve">g. </s>
  <s xml:id="echoid-s16764" xml:space="preserve">punctum pro ſigno <lb/>♍. </s>
  <s xml:id="echoid-s16765" xml:space="preserve">Quoniam Sole exiſtente in principio ♑, ſignum ♍, oritur hora 9. </s>
  <s xml:id="echoid-s16766" xml:space="preserve">min. </s>
  <s xml:id="echoid-s16767" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16768" xml:space="preserve">poſt meridiem, vt <lb/>ex 4. </s>
  <s xml:id="echoid-s16769" xml:space="preserve">tabella propoſ. </s>
  <s xml:id="echoid-s16770" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16771" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16772" xml:space="preserve">patet, numerabimus in occidentali horologio à G, verſus F, horas <lb/>9. </s>
  <s xml:id="echoid-s16773" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16774" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16775" xml:space="preserve">vel (quod idem eſt) à puncto I, (quoniam circulus in occidentali horologio non eſt in-<lb/>teger deſcriptus.) </s>
  <s xml:id="echoid-s16776" xml:space="preserve">verſus F, complementum illarum horaru m vſque ad 12. </s>
  <s xml:id="echoid-s16777" xml:space="preserve">hoc eſt, hor. </s>
  <s xml:id="echoid-s16778" xml:space="preserve">2. </s>
  <s xml:id="echoid-s16779" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16780" xml:space="preserve">34. <lb/></s>
  <s xml:id="echoid-s16781" xml:space="preserve">vſque ad punctum O, per quod ducemus rectam occulte tranſeuntem per E, centrum, quæ æqui-<lb/>noctialem lineam ſecet in L, puncto, per quod verſus arcum ♑, ducemus perpendicularem ad li-<lb/>neam æquinoctialem L K, quæ tropicum ♑, ſi deſcriptus eſſet, ſecaret in puncto, per quod ſignũ <lb/>aſcendens ♉, ducendum eſſet. </s>
  <s xml:id="echoid-s16782" xml:space="preserve">Sed quia tropicus ♑, vltra horizontalem lineam non eſt deſcriptus <lb/>in occidentali horologio, abſcindemus ex linea æquinoctiali infra lineam horizontalem rectam <lb/>
<anchor type="note" xlink:label="note-0266-05a" xlink:href="note-0266-05"/>
A M, rectæ A L, æqualem, &amp; </s>
  <s xml:id="echoid-s16783" xml:space="preserve">ex M, ad æquinoctialem lineam ducemus perpendicularem M N, <lb/>quæ tropicum ♑, ſecet in N, &amp; </s>
  <s xml:id="echoid-s16784" xml:space="preserve">rectæ M N, abſcindemus æqualem L K. </s>
  <s xml:id="echoid-s16785" xml:space="preserve">Punctum igitur K, erit <lb/>illud, per quod &amp; </s>
  <s xml:id="echoid-s16786" xml:space="preserve">tropicus ♑, &amp; </s>
  <s xml:id="echoid-s16787" xml:space="preserve">ſignum aſcendens ♍, ducendum eſt, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s16788" xml:space="preserve">Eadem eſt <lb/>ratio in cæteris obſeruanda. </s>
  <s xml:id="echoid-s16789" xml:space="preserve">Neque vero mirum tibi videatur, quod acceperimus nonnulla puncta <lb/>tam in æquinoctiali linea, quàm in tropicis ſupra lineam horizontalem, cum tamen nunquam <lb/>à Sole illuminetur pars illa horologii, quæ ſupra lineam horizontalem extat: </s>
  <s xml:id="echoid-s16790" xml:space="preserve">quoniam niſi denſi-<lb/>tas terræ obſiſteret, planum horologii orientalis ſemper à media nocte vſque ad meridiem inte-<lb/>gris 12. </s>
  <s xml:id="echoid-s16791" xml:space="preserve">horis, quarum vna pars infra horizontalem lineam, altera ſupra eandem continetur, à ra-<lb/>
<anchor type="note" xlink:label="note-0266-06a" xlink:href="note-0266-06"/>
diis ſolaribus illuſtraretur. </s>
  <s xml:id="echoid-s16792" xml:space="preserve">quod idem dices de plano occidentalis horologij à meridie in mediã <lb/>noctem. </s>
  <s xml:id="echoid-s16793" xml:space="preserve">Vnde tunc illæ horæ indicarent, quænam ſigna Zodiaci Horizontem attingant. </s>
  <s xml:id="echoid-s16794" xml:space="preserve">Quòd ſi <lb/>lineæ tangentes tropicos ducantur per puncta in tropicis inuenta, (quæ ducentur, vt in coroll.</s>
  <s xml:id="echoid-s16795" xml:space="preserve">
<pb o="251" file="0267" n="267" rhead="LIBER SECVNDVS."/>
propoſ. </s>
  <s xml:id="echoid-s16796" xml:space="preserve">37. </s>
  <s xml:id="echoid-s16797" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s16798" xml:space="preserve">1. </s>
  <s xml:id="echoid-s16799" xml:space="preserve">Apollonii docuimus.) </s>
  <s xml:id="echoid-s16800" xml:space="preserve">deſcripta rurſus erunt aſcendentia ſigna, vt conſtat ex de-<lb/>monſtratis propoſ. </s>
  <s xml:id="echoid-s16801" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16802" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s16803" xml:space="preserve"/>
</p>
<div xml:id="echoid-div859" type="float" level="2" n="3">
<note position="right" xlink:label="note-0265-10" xlink:href="note-0265-10a" xml:space="preserve">Quomodo in <lb/>tropicis inueſti-<lb/>gentur puncta <lb/>aſcendentium <lb/>ſignorum.</note>
  <figure xlink:label="fig-0266-01" xlink:href="fig-0266-01a">
    <image file="0266-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0266-01"/>
  </figure>
<note position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0266-02" xlink:href="note-0266-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0266-03" xlink:href="note-0266-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0266-04" xlink:href="note-0266-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0266-05" xlink:href="note-0266-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0266-06" xlink:href="note-0266-06a" xml:space="preserve">Qua rationę <lb/>aſcendentia ſi-<lb/>gna per doctri-<lb/>nam conicorũ <lb/>A poll. deſcribã <lb/>tur.</note>
</div>
<p>
  <s xml:id="echoid-s16804" xml:space="preserve">PORRO lineas ♈, &amp; </s>
  <s xml:id="echoid-s16805" xml:space="preserve">♎, quæ per punctum A, neceſſario tranſeunt, vbi horizontalis linea, <lb/>
<anchor type="note" xlink:label="note-0267-01a" xlink:href="note-0267-01"/>
&amp; </s>
  <s xml:id="echoid-s16806" xml:space="preserve">æquinoctialis, &amp; </s>
  <s xml:id="echoid-s16807" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s16808" xml:space="preserve">à meridie, vel media nocte ſe mutuo interſecãt, (propterea quòd <lb/>Sole exiſtente in principio ♈, principium ♈, aſcendat ſupra Horizontem hora 6. </s>
  <s xml:id="echoid-s16809" xml:space="preserve">ante meridiem, <lb/>&amp; </s>
  <s xml:id="echoid-s16810" xml:space="preserve">principium ♎, hora 6. </s>
  <s xml:id="echoid-s16811" xml:space="preserve">poſt meridiem: </s>
  <s xml:id="echoid-s16812" xml:space="preserve">Sole vero exiſtente in principio ♎, principium ♈, aſcẽ-<lb/>dat hora 6. </s>
  <s xml:id="echoid-s16813" xml:space="preserve">poſt meridiem, principium autem ♎, hora 6. </s>
  <s xml:id="echoid-s16814" xml:space="preserve">ante meridiem, vt patet) hoc modo de-<lb/>ſcribemus. </s>
  <s xml:id="echoid-s16815" xml:space="preserve">Quoniam Ecliptica ſecat Æquatorem in principio ♈, &amp; </s>
  <s xml:id="echoid-s16816" xml:space="preserve">♎, fa citq́ue cum eo duos an-<lb/>gulos grad. </s>
  <s xml:id="echoid-s16817" xml:space="preserve">23. </s>
  <s xml:id="echoid-s16818" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16819" xml:space="preserve">30. </s>
  <s xml:id="echoid-s16820" xml:space="preserve">quanta nimirum eſt maxima declinatio Solis, ſi ad vtraſque partes æquino-<lb/>ctialis lineæ ad punctum A, conſtituamus duos angulos grad. </s>
  <s xml:id="echoid-s16821" xml:space="preserve">23. </s>
  <s xml:id="echoid-s16822" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16823" xml:space="preserve">30. </s>
  <s xml:id="echoid-s16824" xml:space="preserve">(quod fiet, ſi ex A, de-<lb/>
<anchor type="note" xlink:label="note-0267-02a" xlink:href="note-0267-02"/>
ſcribatur circunferentia circuli, ex qua accipiãtur duo arcus hinc inde ab æquinoctiali linea grad. <lb/></s>
  <s xml:id="echoid-s16825" xml:space="preserve">23. </s>
  <s xml:id="echoid-s16826" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16827" xml:space="preserve">30. </s>
  <s xml:id="echoid-s16828" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16829" xml:space="preserve">ex A, per fines arcuum lineæ rectæ ducantur.) </s>
  <s xml:id="echoid-s16830" xml:space="preserve">deſcriptæ erunt lineæ ♈, &amp; </s>
  <s xml:id="echoid-s16831" xml:space="preserve">♎, quarũ <lb/>ea, quæ vergit ad tropicum ♋, dabit initium ♎, altera vero initium ♈; </s>
  <s xml:id="echoid-s16832" xml:space="preserve">quia in ſphæra cæleſti, poſi <lb/>to principio ♎, in oriente, Ecliptica ab Æquatore deflectit in Boream, verſus parallelum ♋; </s>
  <s xml:id="echoid-s16833" xml:space="preserve">in <lb/>auſtrum verò, verſus tropicũ ♑, conſtituto principio ♈, in ortu, vt ex ſphæra materiali cõſtat. </s>
  <s xml:id="echoid-s16834" xml:space="preserve">Hinc <lb/>enim fit, vt principio ♎, in oriente conſtituto, omnia puncta ſemicirculi Eclipticæ borealis ſupra <lb/>Horizontem exiſtentia, in quorum aliquo neceſſe eſt Sol exiſtat, cum principiũ ♎, interdiu oritur, <lb/>proiiciant vmbras in partes oppoſitas, nempe auſtrales, ad quas tropicus ♋, quoque vergit; </s>
  <s xml:id="echoid-s16835" xml:space="preserve">Princi <lb/>pio vero ♈, poſito in oriente, puncta omnia ſemicirculi Eclipticæ auſtralis exiſtentia ſupra Hori-<lb/>zontem, in quorum aliquo neceſſario Sol exiſtit, cum principium ♈, interdiu oritur, proijciant vm <lb/>
<anchor type="note" xlink:label="note-0267-03a" xlink:href="note-0267-03"/>
bras in oppoſitas partes, vt in boreales, ad quas tropicus ♑, declinat. </s>
  <s xml:id="echoid-s16836" xml:space="preserve">Quòd autem hoc modo re-<lb/>cte ſint deſcriptæ lineæ ♈, &amp; </s>
  <s xml:id="echoid-s16837" xml:space="preserve">♎, ita perſpicuum fiet. </s>
  <s xml:id="echoid-s16838" xml:space="preserve">Quia poſito principio ♈, vel ♎, in ortu, ſty-<lb/>lus horologij communis ſectio eſt plani Eclipticæ, &amp; </s>
  <s xml:id="echoid-s16839" xml:space="preserve">Æquatoris, occurret vterque circulus plano <lb/>horologii in A, puncto Quia vero communes ſectiones, quas Ecliptica &amp; </s>
  <s xml:id="echoid-s16840" xml:space="preserve">Æquator in plano ho-<lb/>rologii faciunt, parallelæ ſunt communibus ſectionibus, quas faciunt in Meridiano circulo, æqua-<lb/>
<anchor type="note" xlink:label="note-0267-04a" xlink:href="note-0267-04"/>
lis erit angulus linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s16841" xml:space="preserve">linea ♈, vel ♎, contentus in plano horologij, angulo eiſdem <lb/>
<anchor type="note" xlink:label="note-0267-05a" xlink:href="note-0267-05"/>
lineis comprehenſo in plano Meridiani circuli. </s>
  <s xml:id="echoid-s16842" xml:space="preserve">Cum ergo in plano Meridiani circuli dictus angu <lb/>lus complectatur grad. </s>
  <s xml:id="echoid-s16843" xml:space="preserve">23. </s>
  <s xml:id="echoid-s16844" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s16845" xml:space="preserve">30. </s>
  <s xml:id="echoid-s16846" xml:space="preserve">conſtat propoſitum.</s>
  <s xml:id="echoid-s16847" xml:space="preserve"/>
</p>
<div xml:id="echoid-div860" type="float" level="2" n="4">
<note position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">Quomodo de-<lb/>ſcribantur ſi-<lb/>gna aſcẽdentia <lb/>Ar<unsure/>ietis, &amp; Li-<lb/>br<unsure/>ę.</note>
<note position="left" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0267-03" xlink:href="note-0267-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0267-04" xlink:href="note-0267-04a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0267-05" xlink:href="note-0267-05a" xml:space="preserve">10. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s16848" xml:space="preserve">ALITER delineabuntur ſigna aſcendentia hunc in modum. </s>
  <s xml:id="echoid-s16849" xml:space="preserve">Ex tabella 8. </s>
  <s xml:id="echoid-s16850" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s16851" xml:space="preserve">9 huius <lb/>
<anchor type="note" xlink:label="note-0267-06a" xlink:href="note-0267-06"/>
lib. </s>
  <s xml:id="echoid-s16852" xml:space="preserve">accipiantur declinationes omnium punctorum in circulo horæ 11. </s>
  <s xml:id="echoid-s16853" xml:space="preserve">ante meridiem exiſtentiũ, <lb/>
<anchor type="note" xlink:label="note-0267-07a" xlink:href="note-0267-07"/>
quæ quidem hora eſt vndecima poſt med. </s>
  <s xml:id="echoid-s16854" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16855" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16856" xml:space="preserve">ſecundũ doctrinã propoſ. </s>
  <s xml:id="echoid-s16857" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16858" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16859" xml:space="preserve">in linea <lb/>horę 11. </s>
  <s xml:id="echoid-s16860" xml:space="preserve">in horologio orientali reperiantur puncta, per quæ duci debent paralleli illarũ declinatio-<lb/>num. </s>
  <s xml:id="echoid-s16861" xml:space="preserve">Hæc enim puncta cum reſpondentibus punctis in horizontali linea repertis iuncta dabunt <lb/>aſcendẽtia ſigna. </s>
  <s xml:id="echoid-s16862" xml:space="preserve">Vel certe ex tabella 9. </s>
  <s xml:id="echoid-s16863" xml:space="preserve">eiuſdem propoſ. </s>
  <s xml:id="echoid-s16864" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16865" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16866" xml:space="preserve">ſumantur declinationes pun-<lb/>ctorum in circulo horæ primæ antemeridianæ exiſtentium, quæ eſt hora prima poſt med. </s>
  <s xml:id="echoid-s16867" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16868" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16869" xml:space="preserve"><lb/>ſecundũ doctrinã propoſ. </s>
  <s xml:id="echoid-s16870" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16871" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16872" xml:space="preserve">reperiantur puncta in linea horæ 1. </s>
  <s xml:id="echoid-s16873" xml:space="preserve">à media nocte, hoc eſt, <lb/>primę antemeridianę, (quę quidem ſupra lineã horizõtalem deſcribitur tantũ ab ea diſtans, quã-<lb/>tum linea horę 11. </s>
  <s xml:id="echoid-s16874" xml:space="preserve">infra eandem ab ea diſtat.) </s>
  <s xml:id="echoid-s16875" xml:space="preserve">per quę paralleli illarum declinationum duci debẽt. <lb/></s>
  <s xml:id="echoid-s16876" xml:space="preserve">Hęc enim iuncta cum reſpondentibus punctis in hora 11. </s>
  <s xml:id="echoid-s16877" xml:space="preserve">inuentis dabunt ſigna aſcendentia, vt <lb/>prius, quę neceſſario tranſibunt per puncta horizontalis lineę.</s>
  <s xml:id="echoid-s16878" xml:space="preserve"/>
</p>
<div xml:id="echoid-div861" type="float" level="2" n="5">
<note position="right" xlink:label="note-0267-06" xlink:href="note-0267-06a" xml:space="preserve">Alia deſcriptio <lb/>ſigno<unsure/>rum aſcen <lb/>denti<unsure/>um in ho <lb/>rologio Meri-<lb/>diano, per pun-<lb/>cta Eclipti<unsure/>cæ in <lb/>circulis horæ 1. <lb/>à mer. &amp; 11. à <lb/>med. noc. exiſtẽ-<lb/>tia, cum princi-<lb/>pia ſignoru@ <lb/>aſcendunt.</note>
<note position="left" xlink:label="note-0267-07" xlink:href="note-0267-07a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s16879" xml:space="preserve">RVRSVS ex tabella 9. </s>
  <s xml:id="echoid-s16880" xml:space="preserve">eiuſdem propoſ. </s>
  <s xml:id="echoid-s16881" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16882" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16883" xml:space="preserve">accipiantur declinationes punctorum in <lb/>circulo horę 1. </s>
  <s xml:id="echoid-s16884" xml:space="preserve">poſt meridiem exiſtentium, &amp; </s>
  <s xml:id="echoid-s16885" xml:space="preserve">ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s16886" xml:space="preserve">26. </s>
  <s xml:id="echoid-s16887" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16888" xml:space="preserve">in linea <lb/>horę 1. </s>
  <s xml:id="echoid-s16889" xml:space="preserve">in occidentali horologio puncta inueſtigentur, per quæ paralleli illarum declinationum <lb/>ducendi ſunt. </s>
  <s xml:id="echoid-s16890" xml:space="preserve">Hęc enim puncta lineis rectis cum reſpondentibus punctis lineæ horizontalis con-<lb/>nexa dabunt aſcendentia ſigna. </s>
  <s xml:id="echoid-s16891" xml:space="preserve">Vel certe ex tabella 8. </s>
  <s xml:id="echoid-s16892" xml:space="preserve">eiuſdem propoſ. </s>
  <s xml:id="echoid-s16893" xml:space="preserve">9 huius lib. </s>
  <s xml:id="echoid-s16894" xml:space="preserve">capiantur decli-<lb/>nationes punctorum in circulo horę 11. </s>
  <s xml:id="echoid-s16895" xml:space="preserve">poſt meridiem exiſtentium, &amp; </s>
  <s xml:id="echoid-s16896" xml:space="preserve">per doctrinam propoſ. </s>
  <s xml:id="echoid-s16897" xml:space="preserve">26. <lb/></s>
  <s xml:id="echoid-s16898" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16899" xml:space="preserve">inueniantur puncta in linea horę 11. </s>
  <s xml:id="echoid-s16900" xml:space="preserve">poſt meridiem, (quę quidem ſupra lineam horizõ-<lb/>talem deſcribitur tantum ab ea diſtans, quantum ab eadem diſtat linea horę 1. </s>
  <s xml:id="echoid-s16901" xml:space="preserve">à meridie.) </s>
  <s xml:id="echoid-s16902" xml:space="preserve">per quę <lb/>illarum declinationum paralleli duci debent. </s>
  <s xml:id="echoid-s16903" xml:space="preserve">Hęc enim puncta lineis rectis cum punctis reſpon-<lb/>dentibus in hora 1. </s>
  <s xml:id="echoid-s16904" xml:space="preserve">à mer inuentis coniuncta dabunt ſigna aſcendentia, vt prius; </s>
  <s xml:id="echoid-s16905" xml:space="preserve">quę neceſſario <lb/>
<anchor type="note" xlink:label="note-0267-09a" xlink:href="note-0267-09"/>
per inuenta puncta in linea horizontali tranſibunt.</s>
  <s xml:id="echoid-s16906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div862" type="float" level="2" n="6">
<note position="left" xlink:label="note-0267-09" xlink:href="note-0267-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s16907" xml:space="preserve">QVOD ſi ex tabella 7. </s>
  <s xml:id="echoid-s16908" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s16909" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16910" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16911" xml:space="preserve">inueniantur in linea horę 6. </s>
  <s xml:id="echoid-s16912" xml:space="preserve">puncta, per quę tran-<lb/>
<anchor type="note" xlink:label="note-0267-10a" xlink:href="note-0267-10"/>
ſeunt paralleli declinationum punctorum Eclipticę in hora 6. </s>
  <s xml:id="echoid-s16913" xml:space="preserve">exiſtentium, &amp; </s>
  <s xml:id="echoid-s16914" xml:space="preserve">per illa ducatur, ſe-<lb/>cundum doctrinam coroll. </s>
  <s xml:id="echoid-s16915" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s16916" xml:space="preserve">37. </s>
  <s xml:id="echoid-s16917" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s16918" xml:space="preserve">1. </s>
  <s xml:id="echoid-s16919" xml:space="preserve">Apollonij, lineę rectę tangentes tropicos, habebuntur <lb/>ſigna, vt prius, vt liquet ex iis, quę propoſ. </s>
  <s xml:id="echoid-s16920" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16921" xml:space="preserve">huius lib demonſtrauimus. </s>
  <s xml:id="echoid-s16922" xml:space="preserve">Igitur ſigna Zodiaci aſcẽ-<lb/>dentia in eodem Meridiano horologio deſcripſimus. </s>
  <s xml:id="echoid-s16923" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s16924" xml:space="preserve"/>
</p>
<div xml:id="echoid-div863" type="float" level="2" n="7">
<note position="right" xlink:label="note-0267-10" xlink:href="note-0267-10a" xml:space="preserve">Alia deſcriptio <lb/>ſignorum aſcen <lb/>dentium, ex do <lb/>ctrina conicorũ <lb/>Apoll.</note>
</div>
</div>
<div xml:id="echoid-div865" type="section" level="1" n="207">
<head xml:id="echoid-head210" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Alia adhuc de-<lb/>ſcriptio ſignorũ <lb/>aſcendentium, <lb/>ſecundum pra-<lb/>xim Andreæ <lb/>Schoneri.</note>
<p style="it">
  <s xml:id="echoid-s16925" xml:space="preserve">SECVNDVM doctrinam Andreæ Schoneri ita deſcribi poterunt ſigna aſcendentia. </s>
  <s xml:id="echoid-s16926" xml:space="preserve">In prima <lb/>figura ſcholĳ propoſ. </s>
  <s xml:id="echoid-s16927" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16928" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16929" xml:space="preserve">abſcindatur recta E a, ex recta E C, gnomoni borologii æqualis, et per a,
<pb o="252" file="0268" n="268" rhead="GNOMONICES"/>
ipſi B D, parallela agatur; </s>
  <s xml:id="echoid-s16930" xml:space="preserve">adeo vt cẽtro E, poſito in cẽtro E, in horologio, et pũcto a, in pũcto A, parallela <lb/>per a, ducta congruat lineæ æquinoctiali. </s>
  <s xml:id="echoid-s16931" xml:space="preserve">Secabit autem parallela per a, ducta rectas ſignorum ex E, pro <lb/>deuntes in punctis, quorum diſtantiæ circino acceptæ ex a, transferantur in lineã æquinoctialem horologii <lb/>f acto initio ab A, tam ſupra lineam horizontalẽ, quàm infra, &amp; </s>
  <s xml:id="echoid-s16932" xml:space="preserve">per puncta notata in linea æquinoctiali <lb/>ducantur rectę occultę ipſi horizontali lineæ parallelæ ſecantes vtrumque tropicum, etiam ſupra lineam <lb/>horizontalem deſcriptum, in punctis, per quæ ſigna aſcendentia ſunt educenda: </s>
  <s xml:id="echoid-s16933" xml:space="preserve">hoc tamen ordine ſerua-<lb/>to. </s>
  <s xml:id="echoid-s16934" xml:space="preserve">In horologio orientali punctum tropici ♋, vbi ſecat lineam horizontalem, pertinet ad ♋; </s>
  <s xml:id="echoid-s16935" xml:space="preserve">proximũ <lb/>
<anchor type="note" xlink:label="note-0268-01a" xlink:href="note-0268-01"/>
infra, ad ♌; </s>
  <s xml:id="echoid-s16936" xml:space="preserve">ſequens ad ♍: </s>
  <s xml:id="echoid-s16937" xml:space="preserve">proximum verò punctum ſupra horizontalẽlineam ſpectat ad ♊; </s>
  <s xml:id="echoid-s16938" xml:space="preserve">ſequens ad <lb/>♉. </s>
  <s xml:id="echoid-s16939" xml:space="preserve">Item punctum tropici ♑, vbi lineam horizontalem ſecat, ſpectat ad ♑; </s>
  <s xml:id="echoid-s16940" xml:space="preserve">proximum infra, ad ♒; </s>
  <s xml:id="echoid-s16941" xml:space="preserve">ſe-<lb/>quens ad ♓; </s>
  <s xml:id="echoid-s16942" xml:space="preserve">proximum autem punctum ſupra lineam horizontalem pertinet ad ♐; </s>
  <s xml:id="echoid-s16943" xml:space="preserve">ſequens ad ♏. </s>
  <s xml:id="echoid-s16944" xml:space="preserve">At <lb/>
<anchor type="note" xlink:label="note-0268-02a" xlink:href="note-0268-02"/>
in horologio occidentali punctum tropici ♋, vbi interſecat lineam horizontalem, pertinet ad ♑, proxi-<lb/>mum infra, ad ♐; </s>
  <s xml:id="echoid-s16945" xml:space="preserve">ſequens ad ♏: </s>
  <s xml:id="echoid-s16946" xml:space="preserve">proximum verò punctum ſupra lineam horizontalem ſpectat ad ♒; </s>
  <s xml:id="echoid-s16947" xml:space="preserve">ſe-<lb/>quens ad ♓. </s>
  <s xml:id="echoid-s16948" xml:space="preserve">Item punctum tropici ♑, ubi lineam horizontalem interſecat, ſpectat ad ♋; </s>
  <s xml:id="echoid-s16949" xml:space="preserve">proximum ve-<lb/>rò infra, ad ♊; </s>
  <s xml:id="echoid-s16950" xml:space="preserve">ſequens ad ♉: </s>
  <s xml:id="echoid-s16951" xml:space="preserve">proximum autem ſupra horizontalem lineam pertinet ad ♌; </s>
  <s xml:id="echoid-s16952" xml:space="preserve">ſe-<lb/>quens ad ♍.</s>
  <s xml:id="echoid-s16953" xml:space="preserve"/>
</p>
<div xml:id="echoid-div865" type="float" level="2" n="1">
<note position="left" xlink:label="note-0268-01" xlink:href="note-0268-01a" xml:space="preserve">Ordo ſignorũ <lb/>a ſcendentium, <lb/>in tropicis.</note>
<note position="left" xlink:label="note-0268-02" xlink:href="note-0268-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s16954" xml:space="preserve">RVRSVS in ſecunda figura ſcholĳ propoſ. </s>
  <s xml:id="echoid-s16955" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16956" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16957" xml:space="preserve">ex recta E C, aufer atur E a, æqualis gnomo <lb/>ni, &amp; </s>
  <s xml:id="echoid-s16958" xml:space="preserve">per a, ipſi B D, parallela agatur; </s>
  <s xml:id="echoid-s16959" xml:space="preserve">ita vt rurſus centro E, poſito in E, centro horologii, &amp; </s>
  <s xml:id="echoid-s16960" xml:space="preserve">puncto a, <lb/>in puncto A, parallela per a, ducta lineæ æquinoctiali congruat. </s>
  <s xml:id="echoid-s16961" xml:space="preserve">Secabit autem hęc parallela per a, ducta <lb/>rectas ſignorum ex E, prodeuntes, etiam illorum ſignorum, quæ ſunt ſupra rectam B D, ſi tamen eorum li <lb/>neæ infra centrum E, producantur, in punctis, quorum distantiæ circino acceptæ ex a, ſi trans fer antur in <lb/>
<anchor type="note" xlink:label="note-0268-03a" xlink:href="note-0268-03"/>
lineam æquinoctialem horologĳ, initio facto ab A, tam ſupra lineam horizontalem, quàm infra, habebun-<lb/>tur<unsure/> puncta in æquinoctiali linea, per quæ tranſibunt lineæ aſcendentium ſignorum, hoc ordine. </s>
  <s xml:id="echoid-s16962" xml:space="preserve">In horologio <lb/>
<anchor type="note" xlink:label="note-0268-04a" xlink:href="note-0268-04"/>
orientali puncta lineæ æquinoctialis ſignata infra horizontalem lineam debentur ſignis, quæ ſunt ad ſini-<lb/>ſtram rectæ E C, computando etiam ſigna ſupra rectam BD, quæ infra centrum E, ſunt, &amp; </s>
  <s xml:id="echoid-s16963" xml:space="preserve">vltra centrũ <lb/>E, producta, qualia ſunt ♉, ♊, ♋, ♐, ♏: </s>
  <s xml:id="echoid-s16964" xml:space="preserve">puncta verò lineæ æquinoctialis ſupra horizontalẽ lineã illis <lb/>ſignis tribuenda ſunt, quæ ad dexteram rectæ E C, reperiuntur, cuiuſmodi ſunt ♓, ♒, ♑, ♌, ♍. </s>
  <s xml:id="echoid-s16965" xml:space="preserve">At in <lb/>horologio occidentali contrarium omnino intelligatur. </s>
  <s xml:id="echoid-s16966" xml:space="preserve">Nam ſignis, quæ ſunt ad ſiniſtram rectæ E C, re-<lb/>ſpondent puncta æquinoctialis lineæ ſupra horizontalem lineã; </s>
  <s xml:id="echoid-s16967" xml:space="preserve">ſignis verò, quæ ſunt ad dexteram eiuſdem <lb/>rectæ E C, conueniunt puncta æquinoctialis lineæ infra horizontalem lineam. </s>
  <s xml:id="echoid-s16968" xml:space="preserve">His ritè peractis, ſi puncta <lb/>reſpondentium ſignorum in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s16969" xml:space="preserve">tropicis inuenta rectis lineis iungantur, deſcripta erunt <lb/>
<anchor type="note" xlink:label="note-0268-05a" xlink:href="note-0268-05"/>
ſigna aſcendentia. </s>
  <s xml:id="echoid-s16970" xml:space="preserve">Lineas tamen ♈, &amp; </s>
  <s xml:id="echoid-s16971" xml:space="preserve">♎, deſcribemus, vt prius.</s>
  <s xml:id="echoid-s16972" xml:space="preserve"/>
</p>
<div xml:id="echoid-div866" type="float" level="2" n="2">
<note position="left" xlink:label="note-0268-03" xlink:href="note-0268-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0268-04" xlink:href="note-0268-04a" xml:space="preserve">Ordo ſignorũ <lb/>aſcendentium <lb/>in linea æqui-<lb/>noctiali.</note>
<note position="left" xlink:label="note-0268-05" xlink:href="note-0268-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s16973" xml:space="preserve">IAM verò lineæ aſcendentium ſignorum vtriuslibet horologĳ vltra horizõtalem lineam productæ, <lb/>exhibent eorundem ſignorum lineas in oppoſita facie plani horologĳ, dummodo pars illa ſuperior ablata <lb/>à linea horizontali inuertatur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s16974" xml:space="preserve">14. </s>
  <s xml:id="echoid-s16975" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16976" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s16977" xml:space="preserve">Itaque ſatis erit, ſi ſi-<lb/>gna aſcendentia deſcribantur in orientali horologio, vel occidentali. </s>
  <s xml:id="echoid-s16978" xml:space="preserve">Nam omnia eius lineamenta vltra <lb/>horizontalem lineã producta dabunt eadẽ ſigna aſcendentia in oppoſito horologio, ſi illa inuerſio fiat, &amp; </s>
  <s xml:id="echoid-s16979" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s16980" xml:space="preserve">Nos maxime in figur a deſcripſimus hoc loco ſigna aſcendentia ex tabula 8. </s>
  <s xml:id="echoid-s16981" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16982" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16983" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s16984" xml:space="preserve">9. </s>
  <s xml:id="echoid-s16985" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s16986" xml:space="preserve">nimi-<lb/>rum per puncta in lineis horarum 11. </s>
  <s xml:id="echoid-s16987" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s16988" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16989" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16990" xml:space="preserve">1. </s>
  <s xml:id="echoid-s16991" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s16992" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s16993" xml:space="preserve">Item 1. </s>
  <s xml:id="echoid-s16994" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s16995" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s16996" xml:space="preserve">11. </s>
  <s xml:id="echoid-s16997" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s16998" xml:space="preserve">inuenta.</s>
  <s xml:id="echoid-s16999" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div868" type="section" level="1" n="208">
<head xml:id="echoid-head211" xml:space="preserve">PROBLEMA 34, PROPOSITIO 34.</head>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div869" type="section" level="1" n="209">
<head xml:id="echoid-head212" xml:space="preserve">HOROLOGIVM Italicum Meridianum conſtituere.</head>
<p>
  <s xml:id="echoid-s17000" xml:space="preserve">SECETVR circulus F G H I, in arcum diurnum &amp; </s>
  <s xml:id="echoid-s17001" xml:space="preserve">nocturnum tropici ♋, vt in ſcholio pro-<lb/>
<anchor type="note" xlink:label="note-0268-07a" xlink:href="note-0268-07"/>
poſ. </s>
  <s xml:id="echoid-s17002" xml:space="preserve">1. </s>
  <s xml:id="echoid-s17003" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17004" xml:space="preserve">docuimus, ſitq́ue arcus diurnus B G C, nocturnus C I B; </s>
  <s xml:id="echoid-s17005" xml:space="preserve">qui arcus inuenien <lb/>tur etiam, vt propoſ. </s>
  <s xml:id="echoid-s17006" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17007" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s17008" xml:space="preserve">ſcripſimus, ſi à puncto G, meridiei vtrinque ſupputetur arcus <lb/>ſemidiurnus tropici ♋, vſque ad B, &amp; </s>
  <s xml:id="echoid-s17009" xml:space="preserve">C, nempe horæ 7. </s>
  <s xml:id="echoid-s17010" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s17011" xml:space="preserve">32. </s>
  <s xml:id="echoid-s17012" xml:space="preserve">vbi polus habet altitudinem <lb/>grad. </s>
  <s xml:id="echoid-s17013" xml:space="preserve">42. </s>
  <s xml:id="echoid-s17014" xml:space="preserve">vt fit Romæ. </s>
  <s xml:id="echoid-s17015" xml:space="preserve">Deinde circulus F G H I, in horas 24. </s>
  <s xml:id="echoid-s17016" xml:space="preserve">æquales diuidatur, ſumpto @initio <lb/>à termino arcus diurni occidentali, cuiuſmodi in orientali horologio eſt punctum C, in occiden-<lb/>
<anchor type="note" xlink:label="note-0268-08a" xlink:href="note-0268-08"/>
tali verò B, vt conſtat, ſi circulus F G H I, ad propriam poſitionem moueri intelligatur circa ęqui-<lb/>noctialem lineam, donec videlicet ſtatuatur in plano Aequatoris. </s>
  <s xml:id="echoid-s17017" xml:space="preserve">Deinde in orientali horologio <lb/>ex horis inter puncta B, &amp; </s>
  <s xml:id="echoid-s17018" xml:space="preserve">G, ortus Solis, &amp; </s>
  <s xml:id="echoid-s17019" xml:space="preserve">meridiei, in occidentali autem inter puncta B, &amp; </s>
  <s xml:id="echoid-s17020" xml:space="preserve">G, oc-<lb/>caſus Solis, &amp; </s>
  <s xml:id="echoid-s17021" xml:space="preserve">meridiei, per centrum circuli F G H I, ducantur rectę lineæ, quæ, vt propoſ. </s>
  <s xml:id="echoid-s17022" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17023" xml:space="preserve">huius <lb/>lib. </s>
  <s xml:id="echoid-s17024" xml:space="preserve">oſtendimus, communes ſectiones ſunt Aequatoris, &amp; </s>
  <s xml:id="echoid-s17025" xml:space="preserve">circulorum maximorum, qui per polos <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s17026" xml:space="preserve">horas Italicas paralleli ♋, ducuntur, inſtar circulorum horariorum à meridie, vel me-<lb/>dianocte. </s>
  <s xml:id="echoid-s17027" xml:space="preserve">Secabunt hæ lineæ æquinoctialem lineam in punctis, per quæ ad lineam æquinoctialõ<unsure/> <lb/>perpendiculares lineæ occultæ eductæ ſecabunt tropicum ♋, in horis Italicis, vel ab occaſu Solis, <lb/>cum hæ perpendiculares ſint lineæ horariæ ab occaſu Solis, inſtar linearum horariarum à mer. </s>
  <s xml:id="echoid-s17028" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s17029" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17030" xml:space="preserve">Sole exiſtente in principio ♋, vt ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s17031" xml:space="preserve">25. </s>
  <s xml:id="echoid-s17032" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s17033" xml:space="preserve">demonſtrauimus, per-<lb/>ſpicuum eſt. </s>
  <s xml:id="echoid-s17034" xml:space="preserve">Eodem modo, ſi arcubus I B, I C, ſumantur æqualesarcus G D, G E, vt D G E, ſit
<pb o="253" file="0269" n="269" rhead="LIBER SECVNDVS."/>
arcus diurnus tropici ♑, rurſumq́; </s>
  <s xml:id="echoid-s17035" xml:space="preserve">circulus F G H I, in partes 24. </s>
  <s xml:id="echoid-s17036" xml:space="preserve">ęquales ſecetur, initio factoà ter <lb/>mino occidẽtali arcus diurni tropici ♑, vt à puncto E, in orientali horologio, &amp; </s>
  <s xml:id="echoid-s17037" xml:space="preserve">à D, in occidẽrali, <lb/>inueniemus in tropico ♑, horas Italicas. </s>
  <s xml:id="echoid-s17038" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s17039" xml:space="preserve">ſi horæ inter ſe reſpõdentes in tropicis iungantur li-<lb/>neis rectis, deſcriptum erit horologiũ Italicũ. </s>
  <s xml:id="echoid-s17040" xml:space="preserve">Tranſibunt autem neceſſario hæ lineæ horariæ per <lb/>
<anchor type="figure" xlink:label="fig-0269-01a" xlink:href="fig-0269-01"/>
<anchor type="note" xlink:label="note-0269-01a" xlink:href="note-0269-01"/>
<anchor type="note" xlink:label="note-0269-02a" xlink:href="note-0269-02"/>
<anchor type="note" xlink:label="note-0269-03a" xlink:href="note-0269-03"/>
puncta horarum à meridie, vel media nocte in linea æquinoctiali, vt hora 9. </s>
  <s xml:id="echoid-s17041" xml:space="preserve">Italica per 3. </s>
  <s xml:id="echoid-s17042" xml:space="preserve">à me-<lb/>
<anchor type="note" xlink:label="note-0269-04a" xlink:href="note-0269-04"/>
dia nocte; </s>
  <s xml:id="echoid-s17043" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17044" xml:space="preserve">per 4. </s>
  <s xml:id="echoid-s17045" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s17046" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17047" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17048" xml:space="preserve">20. </s>
  <s xml:id="echoid-s17049" xml:space="preserve">per 2. </s>
  <s xml:id="echoid-s17050" xml:space="preserve">à meridie, &amp;</s>
  <s xml:id="echoid-s17051" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17052" xml:space="preserve">vt perſpicuum eſt ex tabula propoſ. <lb/></s>
  <s xml:id="echoid-s17053" xml:space="preserve">19. </s>
  <s xml:id="echoid-s17054" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17055" xml:space="preserve">cui titulus eſt, ÆQVINOCTIALIS LINEA. </s>
  <s xml:id="echoid-s17056" xml:space="preserve">quòd ſi aliquæ horæ <lb/>ab occaſu in alterutro tropicorum non habeant in altero tropico puncta reſpondentia, ducendæ <lb/>erunt illæ per horas reſpondentes in æquinoctiali linea, prout ex tabula dicta propoſ. </s>
  <s xml:id="echoid-s17057" xml:space="preserve">19. </s>
  <s xml:id="echoid-s17058" xml:space="preserve">ſuperio-<lb/>ris lib. </s>
  <s xml:id="echoid-s17059" xml:space="preserve">colligitur. </s>
  <s xml:id="echoid-s17060" xml:space="preserve">Vt in horologio orientali hora 16. </s>
  <s xml:id="echoid-s17061" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17062" xml:space="preserve">hora 17. </s>
  <s xml:id="echoid-s17063" xml:space="preserve">ductæ ſunt per puncta in tropico <lb/>♑, inuenta, &amp; </s>
  <s xml:id="echoid-s17064" xml:space="preserve">per horam 10. </s>
  <s xml:id="echoid-s17065" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17066" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17067" xml:space="preserve">à media nocte in linea æquinoctiali, quia in tropico ♋, non ha <lb/>bent puncta reſpondentia. </s>
  <s xml:id="echoid-s17068" xml:space="preserve">Linea autem horæ 18. </s>
  <s xml:id="echoid-s17069" xml:space="preserve">ducenda eſt per punctum in tropico ♑, inuen <lb/>tum parellela lineæ æquinoctiali, vt conſtat. </s>
  <s xml:id="echoid-s17070" xml:space="preserve">Cum enim circuli horæ 6. </s>
  <s xml:id="echoid-s17071" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17072" xml:space="preserve">18. </s>
  <s xml:id="echoid-s17073" xml:space="preserve">ab ortu, vel occaſu <lb/>cum Aequatore eandem habeant ſectionem communem, per propoſ. </s>
  <s xml:id="echoid-s17074" xml:space="preserve">16. </s>
  <s xml:id="echoid-s17075" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17076" xml:space="preserve">Item ean-<lb/>dem cum Meridiano, per propoſ. </s>
  <s xml:id="echoid-s17077" xml:space="preserve">17. </s>
  <s xml:id="echoid-s17078" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s17079" xml:space="preserve">ſuperioris, habeant autem duo illi circuli vnam <lb/>
<anchor type="note" xlink:label="note-0269-05a" xlink:href="note-0269-05"/>
duntaxat communem ſectionem; </s>
  <s xml:id="echoid-s17080" xml:space="preserve">fit, vt duo illi circuli, &amp; </s>
  <s xml:id="echoid-s17081" xml:space="preserve">Aequator, Meridianusq́; </s>
  <s xml:id="echoid-s17082" xml:space="preserve">habeant vnã <lb/>&amp; </s>
  <s xml:id="echoid-s17083" xml:space="preserve">eandem communem ſectionem, nempe eam, quæ communis ſectio eſt quoque Meridiani, &amp; </s>
  <s xml:id="echoid-s17084" xml:space="preserve"><lb/>A equatoris. </s>
  <s xml:id="echoid-s17085" xml:space="preserve">Cum ergo planum horologii Meridiani huic ſectioni communi æquidiſtet, nempe <lb/>ipſi Meridiano circulo; </s>
  <s xml:id="echoid-s17086" xml:space="preserve">erunt per propoſ. </s>
  <s xml:id="echoid-s17087" xml:space="preserve">18. </s>
  <s xml:id="echoid-s17088" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17089" xml:space="preserve">reliquorum circulorum ſectiones <lb/>cum plano horologii, cuiuſmodi ſunt linea horæ 6. </s>
  <s xml:id="echoid-s17090" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17091" xml:space="preserve">linea horæ 18. </s>
  <s xml:id="echoid-s17092" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s17093" xml:space="preserve">linea <lb/>æquinoctialis, inter ſe parallelæ.</s>
  <s xml:id="echoid-s17094" xml:space="preserve"/>
</p>
<div xml:id="echoid-div869" type="float" level="2" n="1">
<note position="left" xlink:label="note-0268-07" xlink:href="note-0268-07a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Italici <lb/>Meridiani.</note>
<note position="left" xlink:label="note-0268-08" xlink:href="note-0268-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0269-01" xlink:href="fig-0269-01a">
    <image file="0269-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0269-01"/>
  </figure>
<note position="left" xlink:label="note-0269-01" xlink:href="note-0269-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0269-02" xlink:href="note-0269-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0269-03" xlink:href="note-0269-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0269-04" xlink:href="note-0269-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0269-05" xlink:href="note-0269-05a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Alia deſcriptio <lb/>eiuſdem horo-<lb/>logii Italici Me <lb/>ridiani per ar-<lb/>cus diurnos, no <lb/>cturnosq̃<unsure/>ue ho-<lb/>rarũ 14. &amp; 10. <lb/>Item 24.</note>
<p>
  <s xml:id="echoid-s17095" xml:space="preserve">PER binos arcus diurnos, nocturnosq́ue horarum 14. </s>
  <s xml:id="echoid-s17096" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17097" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17098" xml:space="preserve">deſcribetur idem horologium <lb/>Italicum, vt in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s17099" xml:space="preserve">Verticali declarauimus. </s>
  <s xml:id="echoid-s17100" xml:space="preserve">Idem fiet beneficio parallelo-<lb/>rum duorum, quorum vnus eſt ſemper apparentium maximus, vel arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s17101" xml:space="preserve">al-<lb/>ter verò maximus perpetuo deliteſcentium, ſeu arcus nocturnus horarum 24. </s>
  <s xml:id="echoid-s17102" xml:space="preserve">ſi eorum hyperbolæ <lb/>deſcribantur in horologio. </s>
  <s xml:id="echoid-s17103" xml:space="preserve">Nam lineæ horarum ab occaſu Solis, vel ortu tangunt dictas hyperbo
<pb o="254" file="0270" n="270" rhead="GNOMONICES"/>
las in punctis illis, in quibus eaſdem ſecant lineæ horarum à meridie, vel media nocte, ex propoſ. <lb/></s>
  <s xml:id="echoid-s17104" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17105" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17106" xml:space="preserve">exceptis lineis hor. </s>
  <s xml:id="echoid-s17107" xml:space="preserve">12. </s>
  <s xml:id="echoid-s17108" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17109" xml:space="preserve">24. </s>
  <s xml:id="echoid-s17110" xml:space="preserve">hæ enim non conueniunt cum dictis hyperbolis, <lb/>vt conſtat ex coroll. </s>
  <s xml:id="echoid-s17111" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s17112" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17113" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s17114" xml:space="preserve">ſuperioris.</s>
  <s xml:id="echoid-s17115" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17116" xml:space="preserve">PORRO pro horologio Iralico orientali accipiendæ ſunt ex arcubus diurnis, nocturnisq́ue <lb/>illæ horæ ab occaſu duntaxat, quæ habent reſpondentes horas à media nocte, quoniam horæ à me <lb/>ridie in illo non continentur. </s>
  <s xml:id="echoid-s17117" xml:space="preserve">Pro occidentali verò ſumendę ſunt horæ illæ, quibus reſpondent <lb/>horæ à meridie, quòd hæ ſolæ in eo reperiantur deſcriptæ. </s>
  <s xml:id="echoid-s17118" xml:space="preserve">Idemq́ue obſeruetur in arcu diurno, <lb/>&amp; </s>
  <s xml:id="echoid-s17119" xml:space="preserve">nocturno horarum 24. </s>
  <s xml:id="echoid-s17120" xml:space="preserve">Itaque has horas 9. </s>
  <s xml:id="echoid-s17121" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17122" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17123" xml:space="preserve">12. </s>
  <s xml:id="echoid-s17124" xml:space="preserve">13. </s>
  <s xml:id="echoid-s17125" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17126" xml:space="preserve">ab occaſu deſcribemus in horo-<lb/>logio orientali per horas 2. </s>
  <s xml:id="echoid-s17127" xml:space="preserve">3. </s>
  <s xml:id="echoid-s17128" xml:space="preserve">4. </s>
  <s xml:id="echoid-s17129" xml:space="preserve">5. </s>
  <s xml:id="echoid-s17130" xml:space="preserve">6. </s>
  <s xml:id="echoid-s17131" xml:space="preserve">7. </s>
  <s xml:id="echoid-s17132" xml:space="preserve">à media nocte in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s17133" xml:space="preserve">Item ho-<lb/>ras has 9. </s>
  <s xml:id="echoid-s17134" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17135" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17136" xml:space="preserve">12. </s>
  <s xml:id="echoid-s17137" xml:space="preserve">ab occaſu per horas 3. </s>
  <s xml:id="echoid-s17138" xml:space="preserve">4. </s>
  <s xml:id="echoid-s17139" xml:space="preserve">5. </s>
  <s xml:id="echoid-s17140" xml:space="preserve">6. </s>
  <s xml:id="echoid-s17141" xml:space="preserve">à media nocte in arcu nocturno horarum <lb/>
<anchor type="note" xlink:label="note-0270-01a" xlink:href="note-0270-01"/>
12. </s>
  <s xml:id="echoid-s17142" xml:space="preserve">Has autem 13. </s>
  <s xml:id="echoid-s17143" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17144" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17145" xml:space="preserve">16. </s>
  <s xml:id="echoid-s17146" xml:space="preserve">17. </s>
  <s xml:id="echoid-s17147" xml:space="preserve">ab occaſu per 7. </s>
  <s xml:id="echoid-s17148" xml:space="preserve">8. </s>
  <s xml:id="echoid-s17149" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17150" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17151" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17152" xml:space="preserve">à media nocte in arcu diurno ho-<lb/>rarum 12. </s>
  <s xml:id="echoid-s17153" xml:space="preserve">Præterea hor. </s>
  <s xml:id="echoid-s17154" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17155" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17156" xml:space="preserve">ab occaſu per horas 4. </s>
  <s xml:id="echoid-s17157" xml:space="preserve">5. </s>
  <s xml:id="echoid-s17158" xml:space="preserve">à media nocte in arcu nocturno hora-<lb/>rum 10. </s>
  <s xml:id="echoid-s17159" xml:space="preserve">Has verò 10. </s>
  <s xml:id="echoid-s17160" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17161" xml:space="preserve">12. </s>
  <s xml:id="echoid-s17162" xml:space="preserve">13. </s>
  <s xml:id="echoid-s17163" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17164" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17165" xml:space="preserve">16. </s>
  <s xml:id="echoid-s17166" xml:space="preserve">ab occaſu per 5. </s>
  <s xml:id="echoid-s17167" xml:space="preserve">6. </s>
  <s xml:id="echoid-s17168" xml:space="preserve">7. </s>
  <s xml:id="echoid-s17169" xml:space="preserve">8. </s>
  <s xml:id="echoid-s17170" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17171" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17172" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17173" xml:space="preserve">à media no-<lb/>cte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s17174" xml:space="preserve">Et has 14. </s>
  <s xml:id="echoid-s17175" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17176" xml:space="preserve">16. </s>
  <s xml:id="echoid-s17177" xml:space="preserve">17. </s>
  <s xml:id="echoid-s17178" xml:space="preserve">18. </s>
  <s xml:id="echoid-s17179" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s17180" xml:space="preserve">per horas 7. </s>
  <s xml:id="echoid-s17181" xml:space="preserve">8. </s>
  <s xml:id="echoid-s17182" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17183" xml:space="preserve">10. </s>
  <s xml:id="echoid-s17184" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17185" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s17186" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17187" xml:space="preserve">in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s17188" xml:space="preserve">Eadem ratione in occidentali horologio ex tabulis dictis repe-<lb/>riemus horas à mer. </s>
  <s xml:id="echoid-s17189" xml:space="preserve">per quas horæ ab occ. </s>
  <s xml:id="echoid-s17190" xml:space="preserve">ducendæ ſunt. </s>
  <s xml:id="echoid-s17191" xml:space="preserve">Quoniam verò hora 18. </s>
  <s xml:id="echoid-s17192" xml:space="preserve">ab occaſu <lb/>vnicum punctum habet in vtroque horologio, nempe in orientali horam 11. </s>
  <s xml:id="echoid-s17193" xml:space="preserve">a media nocte in ar-<lb/>cu diurno horarum 10. </s>
  <s xml:id="echoid-s17194" xml:space="preserve">in occidentali autem horam primam à meridie in arcu diurno horarum <lb/>14. </s>
  <s xml:id="echoid-s17195" xml:space="preserve">ducemus eam in horologio orientali per horam 11. </s>
  <s xml:id="echoid-s17196" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s17197" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17198" xml:space="preserve">in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s17199" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s17200" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s17201" xml:space="preserve">à media nocte in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s17202" xml:space="preserve">In occidentali vero horologio per <lb/>
<anchor type="note" xlink:label="note-0270-02a" xlink:href="note-0270-02"/>
horam 1. </s>
  <s xml:id="echoid-s17203" xml:space="preserve">à mer in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s17204" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17205" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s17206" xml:space="preserve">à meridie in arcu diurno horarum <lb/>24. </s>
  <s xml:id="echoid-s17207" xml:space="preserve">In vtroq; </s>
  <s xml:id="echoid-s17208" xml:space="preserve">autem horologio linea horæ 18. </s>
  <s xml:id="echoid-s17209" xml:space="preserve">ab occaſu parallela eſt æquinoctiali lineæ, vt ex ſcho-<lb/>lio propoſ. </s>
  <s xml:id="echoid-s17210" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17211" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17212" xml:space="preserve">perſpicuum eſt.</s>
  <s xml:id="echoid-s17213" xml:space="preserve"/>
</p>
<div xml:id="echoid-div870" type="float" level="2" n="2">
<note position="left" xlink:label="note-0270-01" xlink:href="note-0270-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0270-02" xlink:href="note-0270-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s17214" xml:space="preserve">POSTREMO idem horologium Italicum abſoluetur beneficio lineæ horæ 12. </s>
  <s xml:id="echoid-s17215" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s17216" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0270-03a" xlink:href="note-0270-03"/>
occaſu, vt conſtat ex tabula ſecunda propoſ. </s>
  <s xml:id="echoid-s17217" xml:space="preserve">20. </s>
  <s xml:id="echoid-s17218" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17219" xml:space="preserve">cui titulus eſt, LINEA HOR Æ, <lb/>XII. </s>
  <s xml:id="echoid-s17220" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
  <s xml:id="echoid-s17221" xml:space="preserve">Item beneficio lineæ horæ 24. </s>
  <s xml:id="echoid-s17222" xml:space="preserve">ab ortu, vel occaſu, <lb/>(quæ eadem eſt, quæ linea horizontalis) vt colligitur ex prima tabula eiuſdem propoſitionis, cui <lb/>titulus eſt, LINEA HOR Æ XXIIII. </s>
  <s xml:id="echoid-s17223" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
  <s xml:id="echoid-s17224" xml:space="preserve">Immo accu-<lb/>ratius deſcribetur beneficio lineæ horæ 12. </s>
  <s xml:id="echoid-s17225" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17226" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s17227" xml:space="preserve">ac lineæ horæ 24. </s>
  <s xml:id="echoid-s17228" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17229" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s17230" xml:space="preserve">vnà cum <lb/>linea æquinoctiali, propterea quòd in orientali horologio lineæ horarum ab occaſu, quæ parum <lb/>
<anchor type="note" xlink:label="note-0270-04a" xlink:href="note-0270-04"/>
diſtant à linea horæ 12. </s>
  <s xml:id="echoid-s17231" xml:space="preserve">ab ortu, vel occaſu, vix ipſam lineam horæ 12. </s>
  <s xml:id="echoid-s17232" xml:space="preserve">interſecant, quod idem <lb/>cernitur in linels horarum ab occaſu, quæ parum à linea horizontali diſtant in horologio occi-<lb/>dentali, ſi cum linea horizontali conferantur, Hæc enim vix ab illis ſecatur. </s>
  <s xml:id="echoid-s17233" xml:space="preserve">Vnde in prioribus <lb/>deſcribendis vtemur linea horizontali, &amp; </s>
  <s xml:id="echoid-s17234" xml:space="preserve">linea æquinoctiali: </s>
  <s xml:id="echoid-s17235" xml:space="preserve">In p@ſterioribus vero linea horæ 12. <lb/></s>
  <s xml:id="echoid-s17236" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17237" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s17238" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17239" xml:space="preserve">linea æquinoctiali.</s>
  <s xml:id="echoid-s17240" xml:space="preserve"/>
</p>
<div xml:id="echoid-div871" type="float" level="2" n="3">
<note position="left" xlink:label="note-0270-03" xlink:href="note-0270-03a" xml:space="preserve">Alia deſcriptio <lb/>horologii Itali-<lb/>ci Meridiani p<unsure/> <lb/>lincam horæ <lb/>12. ab or. &amp; occ. <lb/>&amp; per lineam <lb/>horæ 24. ab or. <lb/>uel occ.</note>
<note position="left" xlink:label="note-0270-04" xlink:href="note-0270-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s17241" xml:space="preserve">PORRO lineam horæ 12. </s>
  <s xml:id="echoid-s17242" xml:space="preserve">ab ortu, vel occaſu hac ratione delineabimus. </s>
  <s xml:id="echoid-s17243" xml:space="preserve">Ex puncto A, deſcri <lb/>
<anchor type="note" xlink:label="note-0270-05a" xlink:href="note-0270-05"/>
bemus circulum cuiuſcunque magnitudinis @ L, qui ſecet lineam horæ 6. </s>
  <s xml:id="echoid-s17244" xml:space="preserve">à meridie, vel media <lb/>nocte, productam in M; </s>
  <s xml:id="echoid-s17245" xml:space="preserve">eritq́ue arcus K M, (ſi in deſcriptione lineæ horæ 6. </s>
  <s xml:id="echoid-s17246" xml:space="preserve">erratum non eſt, alti-<lb/>tudo poli ſupra Horizontem, propter angulum K A M, propterea quòd angulus contentus linea <lb/>horæ 6. </s>
  <s xml:id="echoid-s17247" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17248" xml:space="preserve">linea æquinoctiali rectus eſt, ex conſtructione, &amp; </s>
  <s xml:id="echoid-s17249" xml:space="preserve">reliquus angulus ex hoc recto, quem <lb/>
<anchor type="note" xlink:label="note-0270-06a" xlink:href="note-0270-06"/>
linea æquinoctialis infra horizontalem cum linea horizontali facit in A, ſit angulus altitudinis <lb/>Æquatoris ſupra Horizontem, ex conſtructione, vt propoſ. </s>
  <s xml:id="echoid-s17250" xml:space="preserve">25 huius lib, dictum eſt. </s>
  <s xml:id="echoid-s17251" xml:space="preserve">Deinde arcui <lb/>K M, ſumemus æqualem arcum M L, &amp; </s>
  <s xml:id="echoid-s17252" xml:space="preserve">per L, &amp; </s>
  <s xml:id="echoid-s17253" xml:space="preserve">A, rectam producemus L A. </s>
  <s xml:id="echoid-s17254" xml:space="preserve">Quam dico eſſe li-<lb/>neam horæ 12 ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s17255" xml:space="preserve">Quoniam enim communes ſectiones circuli horæ 12. </s>
  <s xml:id="echoid-s17256" xml:space="preserve">ab or-<lb/>tu, vel occaſu factæ in planis parallelis, puta in Meridiani plano, &amp; </s>
  <s xml:id="echoid-s17257" xml:space="preserve">plano horologii, parallelæ ſunt; <lb/></s>
  <s xml:id="echoid-s17258" xml:space="preserve">
<anchor type="note" xlink:label="note-0270-07a" xlink:href="note-0270-07"/>
Item &amp; </s>
  <s xml:id="echoid-s17259" xml:space="preserve">communes ſectiones Horizontis factæ in eiſdem planis; </s>
  <s xml:id="echoid-s17260" xml:space="preserve">erit angulus ſub illis ſectionibus <lb/>in plano Meridiani comprehenſus æqualis angulo ſub eiſdem ſectionibus contento in plano ho-<lb/>
<anchor type="note" xlink:label="note-0270-08a" xlink:href="note-0270-08"/>
rologii. </s>
  <s xml:id="echoid-s17261" xml:space="preserve">Cum ergo A K, ſit communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s17262" xml:space="preserve">plani horologii, &amp; </s>
  <s xml:id="echoid-s17263" xml:space="preserve">angulus K A L, <lb/>æqualis ei, quem in plano Meridiani conſtituunt communes ſectiones factæ à circulo horæ 12. </s>
  <s xml:id="echoid-s17264" xml:space="preserve">ab <lb/>ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s17265" xml:space="preserve">Horizonte, propterea quòd arcus K L, ſimilis eſt arcui Meridiani inter Hori-<lb/>
<anchor type="note" xlink:label="note-0270-09a" xlink:href="note-0270-09"/>
zontem, &amp; </s>
  <s xml:id="echoid-s17266" xml:space="preserve">circulum horæ 12. </s>
  <s xml:id="echoid-s17267" xml:space="preserve">interiecto, vt conſtat ex figura propoſ. </s>
  <s xml:id="echoid-s17268" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17269" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17270" xml:space="preserve">cùm diame-<lb/>ter paralleli omnium ſemper apparentium maximi punctis K, L, claudatur; </s>
  <s xml:id="echoid-s17271" xml:space="preserve">erit recta L A, com-<lb/>munis ſectio circuli horæ 12. </s>
  <s xml:id="echoid-s17272" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s17273" xml:space="preserve">plani horologii; </s>
  <s xml:id="echoid-s17274" xml:space="preserve">quod eſt propoſitum. </s>
  <s xml:id="echoid-s17275" xml:space="preserve">Diui-<lb/>det autem ſemper linea æquinoctialis angulum contentum ſub linea horæ 12. </s>
  <s xml:id="echoid-s17276" xml:space="preserve">ab ortu, vel occaſu, <lb/>&amp; </s>
  <s xml:id="echoid-s17277" xml:space="preserve">horizontali linea in vtroque horologio bifariam. </s>
  <s xml:id="echoid-s17278" xml:space="preserve">Cum enim angulus M A L, ſit ęqualis alti-<lb/>tudini poli ſupra Horizontem, erit reliquus ex recto contentus ſub linea L A, &amp; </s>
  <s xml:id="echoid-s17279" xml:space="preserve">linea æquinoctia-<lb/>li æqualis altitudini Æquatoris ſupra Horizontem. </s>
  <s xml:id="echoid-s17280" xml:space="preserve">Quare cum &amp; </s>
  <s xml:id="echoid-s17281" xml:space="preserve">angulus acutus contentus ſub <lb/>linea horizontali, &amp; </s>
  <s xml:id="echoid-s17282" xml:space="preserve">linea æquinoctiali æqualis ſit, per conſtructionem, eidem altitudini Æquato-<lb/>ris; </s>
  <s xml:id="echoid-s17283" xml:space="preserve">ęquales inter ſe erunt anguli, quos linea æquinoctialis cum linea horæ 12. </s>
  <s xml:id="echoid-s17284" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17285" xml:space="preserve">horizontali linea <lb/>facit. </s>
  <s xml:id="echoid-s17286" xml:space="preserve">Vnde facile quoque ducetur linea horæ 12. </s>
  <s xml:id="echoid-s17287" xml:space="preserve">ſi ad lineã æquinoctialẽ cõſtituatur angulus altitu <lb/>
<anchor type="note" xlink:label="note-0270-10a" xlink:href="note-0270-10"/>
dinis Æquatoris verſus angulum obtuſum, quem linea æquinoctialis cum horizontali conſtituit.</s>
  <s xml:id="echoid-s17288" xml:space="preserve"/>
</p>
<div xml:id="echoid-div872" type="float" level="2" n="4">
<note position="left" xlink:label="note-0270-05" xlink:href="note-0270-05a" xml:space="preserve">Deſcriptio li-<lb/>neæ horę 12. ab <lb/>or. uel occ. in <lb/>horologio Me-<lb/>ridiano.</note>
<note position="left" xlink:label="note-0270-06" xlink:href="note-0270-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0270-07" xlink:href="note-0270-07a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0270-08" xlink:href="note-0270-08a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0270-09" xlink:href="note-0270-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0270-10" xlink:href="note-0270-10a" xml:space="preserve">Alia deſcriptio <lb/>lineæ horæ 12. <lb/>ab or. uel occ.</note>
</div>
<pb o="255" file="0271" n="271" rhead="LIBER SECVNDVS."/>
<p>
  <s xml:id="echoid-s17289" xml:space="preserve">MANIFESTVM autem eſt, lineam horæ 12, ab or. </s>
  <s xml:id="echoid-s17290" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s17291" xml:space="preserve">cum linea horizontali conſti-<lb/>
<anchor type="note" xlink:label="note-0271-01a" xlink:href="note-0271-01"/>
tuere angulum rectum K A L, quando altitudo poli K M, continer gr. </s>
  <s xml:id="echoid-s17292" xml:space="preserve">45. </s>
  <s xml:id="echoid-s17293" xml:space="preserve">quia tunc totus arcus <lb/>K L, quadrans eſt: </s>
  <s xml:id="echoid-s17294" xml:space="preserve">acutum vero, quando poli altitudo minor eſt, quàm grad. </s>
  <s xml:id="echoid-s17295" xml:space="preserve">45. </s>
  <s xml:id="echoid-s17296" xml:space="preserve">vt in noſtro exem <lb/>plo; </s>
  <s xml:id="echoid-s17297" xml:space="preserve">quoniam totus tunc arous K L, quadrante minor eſt: </s>
  <s xml:id="echoid-s17298" xml:space="preserve">obtuſum denique, quando altitudo po-<lb/>li ſuperat gr. </s>
  <s xml:id="echoid-s17299" xml:space="preserve">45. </s>
  <s xml:id="echoid-s17300" xml:space="preserve">quia arcus totus K L, maior tunc eſt quadrante. </s>
  <s xml:id="echoid-s17301" xml:space="preserve">Id quod perſpicue colligitur ex <lb/>deſcriptione lineæ horæ 12. </s>
  <s xml:id="echoid-s17302" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17303" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s17304" xml:space="preserve">hoc loco tradita.</s>
  <s xml:id="echoid-s17305" xml:space="preserve"/>
</p>
<div xml:id="echoid-div873" type="float" level="2" n="5">
<note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Quando linea <lb/>horæ 12. ab or. <lb/>ucl occ. cum li-<lb/>nea horizontali <lb/>efticiat angulũ <lb/>rectũ, &amp; quádo <lb/>acutũ aut obtu <lb/>ſum.</note>
</div>
<p>
  <s xml:id="echoid-s17306" xml:space="preserve">CÆTERVM hic neque linea horizontalis, neque linea horæ 12. </s>
  <s xml:id="echoid-s17307" xml:space="preserve">ab ortu, vel occaſu deſcri-<lb/>bi poterit eo modo, quem in Verticali horologio præſcripſimus propoſ. </s>
  <s xml:id="echoid-s17308" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17309" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s17310" xml:space="preserve">nempe per <lb/>arcus parallelorum ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s17311" xml:space="preserve">ſemper latentium maximorum lineam meridianam <lb/>ſecantes, quia in hoc horologio &amp; </s>
  <s xml:id="echoid-s17312" xml:space="preserve">linea meridiana duci non poteſt, vt propoſ. </s>
  <s xml:id="echoid-s17313" xml:space="preserve">25. </s>
  <s xml:id="echoid-s17314" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s17315" xml:space="preserve">oſten-<lb/>
<anchor type="note" xlink:label="note-0271-02a" xlink:href="note-0271-02"/>
dimus, &amp; </s>
  <s xml:id="echoid-s17316" xml:space="preserve">prædictæ lineæ, nempe horizontalis, &amp; </s>
  <s xml:id="echoid-s17317" xml:space="preserve">horæ 12. </s>
  <s xml:id="echoid-s17318" xml:space="preserve">ab ortu, vel occaſu, arcus dictorum pa-<lb/>rallelorum neque ſecant, neque tangunt, ſed nunquam cum eis conueniunt, vt à nobis demonſtra-<lb/>tum eſt propoſ. </s>
  <s xml:id="echoid-s17319" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17320" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17321" xml:space="preserve">Itaque horologium Italicum Meridianum conſtituimus. </s>
  <s xml:id="echoid-s17322" xml:space="preserve">Quod <lb/>faciendum erat.</s>
  <s xml:id="echoid-s17323" xml:space="preserve"/>
</p>
<div xml:id="echoid-div874" type="float" level="2" n="6">
<note position="left" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div876" type="section" level="1" n="210">
<head xml:id="echoid-head213" xml:space="preserve">PROBLEMA. 35. PROPOSITIO 35.</head>
<head xml:id="echoid-head214" xml:space="preserve">HOROLOGIVM Babylonicum Meridianum deſcribere.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s17324" xml:space="preserve">EISDEM ferè modis deſcribemus Babylonicum horologium, quibus Italicum conſtruxi-<lb/>
<anchor type="note" xlink:label="note-0271-04a" xlink:href="note-0271-04"/>
mus; </s>
  <s xml:id="echoid-s17325" xml:space="preserve">dummodo in primo modo diuiſio circuli F G H I, in 24. </s>
  <s xml:id="echoid-s17326" xml:space="preserve">horas æquales initium habeat à <lb/>termino orientali arcus diurni tam tropici ♋, quàm tropici ♑, puta tam à puncto B, quàm à D, <lb/>in horologio orientali, &amp; </s>
  <s xml:id="echoid-s17327" xml:space="preserve">in occidentali tam à puncto C, quàm ab E. </s>
  <s xml:id="echoid-s17328" xml:space="preserve">Linea autem horæ 6. </s>
  <s xml:id="echoid-s17329" xml:space="preserve">ab ortu <lb/>ducenda eſt parallela æquinoctiali lineę, vt in pręcedenti propoſ. </s>
  <s xml:id="echoid-s17330" xml:space="preserve">oſtendimus; </s>
  <s xml:id="echoid-s17331" xml:space="preserve">in orientali quidem <lb/>horologio per punctum dictæ horę in tropico ♋, repertum, in occidentali autem per idem pun-<lb/>ctum inuentum in tropico ♑.</s>
  <s xml:id="echoid-s17332" xml:space="preserve"/>
</p>
<div xml:id="echoid-div876" type="float" level="2" n="1">
<note position="right" xlink:label="note-0271-04" xlink:href="note-0271-04a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Babylo <lb/>nici Meridiani.</note>
</div>
<p>
  <s xml:id="echoid-s17333" xml:space="preserve">IN ſecundo modo, qui per arcus diurnos, nocturnosq́ue perficitur, obſeruandum idem erit <lb/>
<anchor type="note" xlink:label="note-0271-05a" xlink:href="note-0271-05"/>
hic, quod in horologio Italico obſeruauimus: </s>
  <s xml:id="echoid-s17334" xml:space="preserve">hoc eſt, pro horologio Babylonico orientali ſumen <lb/>dę ſunt ex arcubus diurnis, nocturnisq́; </s>
  <s xml:id="echoid-s17335" xml:space="preserve">illę horę ab ortu, quibus reſpondent horę à media nocte: <lb/></s>
  <s xml:id="echoid-s17336" xml:space="preserve">
<anchor type="note" xlink:label="note-0271-06a" xlink:href="note-0271-06"/>
Pro occidentali verò illę, quibus reſpondent horę à meridie. </s>
  <s xml:id="echoid-s17337" xml:space="preserve">Linea autem horę 6. </s>
  <s xml:id="echoid-s17338" xml:space="preserve">ab ortu, quę pa <lb/>rallela etiam eſt lineę ęquinoctiali in vtroque horologio, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17339" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17340" xml:space="preserve">ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s17341" xml:space="preserve">oſtenſum eſt, ducenda etiam erit in orientali horologio per horam 6. </s>
  <s xml:id="echoid-s17342" xml:space="preserve">à media nocte in arcu diur-<lb/>no horarum 24. </s>
  <s xml:id="echoid-s17343" xml:space="preserve">In occidentali verò per horam 6. </s>
  <s xml:id="echoid-s17344" xml:space="preserve">à meridie in arcu nocturno horarum 24.</s>
  <s xml:id="echoid-s17345" xml:space="preserve"/>
</p>
<div xml:id="echoid-div877" type="float" level="2" n="2">
<note position="right" xlink:label="note-0271-05" xlink:href="note-0271-05a" xml:space="preserve">Alia @deſcriptio <lb/>horologii Baby <lb/>lonici Meridia <lb/>ni per arcus <lb/>diurnos noctu@ <lb/>nosq́ue.</note>
<note position="left" xlink:label="note-0271-06" xlink:href="note-0271-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s17346" xml:space="preserve">TERTIVS modus ex tabula L I N E A E H O R AE X I I. </s>
  <s xml:id="echoid-s17347" xml:space="preserve">A B O R T V, V E L O C-<lb/>
<anchor type="note" xlink:label="note-0271-07a" xlink:href="note-0271-07"/>
C A S V, &amp; </s>
  <s xml:id="echoid-s17348" xml:space="preserve">ex tabula L I N E Æ H O R Æ X X I I I I. </s>
  <s xml:id="echoid-s17349" xml:space="preserve">A B O R T V, V E L O C C A S V, <lb/>depromptus nullam habet difficultatem, hoc ſolum notato, horas ab ortu in horologio occiden-<lb/>tali facilius deſcribi per lineam horizontalem, ſeu horæ 24. </s>
  <s xml:id="echoid-s17350" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17351" xml:space="preserve">per lineam æquinoctialem, quàm <lb/>per lineam horę 12. </s>
  <s xml:id="echoid-s17352" xml:space="preserve">ab ortu, vel occaſu; </s>
  <s xml:id="echoid-s17353" xml:space="preserve">quia vix, aut ęgre ſecant lineam horę 12. </s>
  <s xml:id="echoid-s17354" xml:space="preserve">ab ortu, vel occaſu <lb/>in occidentali horologio: </s>
  <s xml:id="echoid-s17355" xml:space="preserve">At verò in horologio orientali eaſdem facilius deſcribi per lineam ho-<lb/>
<anchor type="note" xlink:label="note-0271-08a" xlink:href="note-0271-08"/>
rę 12. </s>
  <s xml:id="echoid-s17356" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s17357" xml:space="preserve">lineam ęquinoctialem: </s>
  <s xml:id="echoid-s17358" xml:space="preserve">quia vix, aut ęgre lineam horizontalem inter-<lb/>ſecant, vt ex figura patet.</s>
  <s xml:id="echoid-s17359" xml:space="preserve"/>
</p>
<div xml:id="echoid-div878" type="float" level="2" n="3">
<note position="right" xlink:label="note-0271-07" xlink:href="note-0271-07a" xml:space="preserve">Alia adhuc de-<lb/>ſctiptio horolo <lb/>gii Babylonici <lb/>Meridiani per <lb/>lineas horarum <lb/>12 &amp; 24. ab or. <lb/>vel occ.</note>
<note position="left" xlink:label="note-0271-08" xlink:href="note-0271-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s17360" xml:space="preserve">EXEMPLVM horologii Babylonici in figura pręcedentis propoſ. </s>
  <s xml:id="echoid-s17361" xml:space="preserve">poſitum eſt. </s>
  <s xml:id="echoid-s17362" xml:space="preserve">In ea enim <lb/>
<anchor type="note" xlink:label="note-0271-09a" xlink:href="note-0271-09"/>
continentur &amp; </s>
  <s xml:id="echoid-s17363" xml:space="preserve">horæ à meridie, &amp; </s>
  <s xml:id="echoid-s17364" xml:space="preserve">media nocte, atque ab ortu, &amp; </s>
  <s xml:id="echoid-s17365" xml:space="preserve">occaſu. </s>
  <s xml:id="echoid-s17366" xml:space="preserve">Nam lineæ parallelę inter <lb/>ſe, &amp; </s>
  <s xml:id="echoid-s17367" xml:space="preserve">ad lineam ęquinoctialem perpendiculares, quibus iuxta lineam ęquinoctialem appoſiti ſunt <lb/>numeri horarum, pertinent ad horas à meridie, &amp; </s>
  <s xml:id="echoid-s17368" xml:space="preserve">media nocte. </s>
  <s xml:id="echoid-s17369" xml:space="preserve">Lineę autem alię, quę in orien-<lb/>tali horologio lineam horizontalem interſecant, &amp; </s>
  <s xml:id="echoid-s17370" xml:space="preserve">in occidentali lineam horę 12. </s>
  <s xml:id="echoid-s17371" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17372" xml:space="preserve">vel occ. <lb/></s>
  <s xml:id="echoid-s17373" xml:space="preserve">monſtrant horas ab occaſu. </s>
  <s xml:id="echoid-s17374" xml:space="preserve">Lineę denique, quę in orientali horologio lineam horę 12. </s>
  <s xml:id="echoid-s17375" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s17376" xml:space="preserve">vel <lb/>occ. </s>
  <s xml:id="echoid-s17377" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17378" xml:space="preserve">in occidentali lineam horizontalem interſecant, horas ab ortu Solis ſignificant. </s>
  <s xml:id="echoid-s17379" xml:space="preserve">Itaque ho <lb/>rologium Babylonicum Meridianum deſcripſimus. </s>
  <s xml:id="echoid-s17380" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s17381" xml:space="preserve"/>
</p>
<div xml:id="echoid-div879" type="float" level="2" n="4">
<note position="right" xlink:label="note-0271-09" xlink:href="note-0271-09a" xml:space="preserve">Quæ lineæ in <lb/>figura indicent <lb/>horas à mer. <lb/>vel med. noc. &amp; <lb/>quæ horas ab <lb/>occ. aut ab or.</note>
</div>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Horologium <lb/>Italicum otien-<lb/>tale in facie op-<lb/>poſita deſcriptũ <lb/>dat Babylcni-<lb/>cum occidenta <lb/>le: Et Italicum <lb/>occidentale in <lb/>facie oppoſita <lb/>delineatum ex-<lb/>hibet Babylo-<lb/>nicum orienta-<lb/>le, &amp; contra; dũ <lb/>modo numeri <lb/>horatum mu@é <lb/>tur in earum <lb/>complementa <lb/>vſque ad 24.</note>
</div>
<div xml:id="echoid-div881" type="section" level="1" n="211">
<head xml:id="echoid-head215" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s17382" xml:space="preserve">EX figura a antecedentis propoſ. </s>
  <s xml:id="echoid-s17383" xml:space="preserve">perſpicuum eſt, lineas horarum ab occaſu in horologio orientali eun-<lb/>dem prorſus ſitum habere, quem lineę horarum ab ortu in occidentali horologio ſeruant. </s>
  <s xml:id="echoid-s17384" xml:space="preserve">Quod idem ve-<lb/>rum eſt de horis ab ortu in orientali horologio, &amp; </s>
  <s xml:id="echoid-s17385" xml:space="preserve">de horis ab occaſu, in occidentali. </s>
  <s xml:id="echoid-s17386" xml:space="preserve">Vnde horologium <lb/>Italicum orientale in facie oppoſita plani horologĳ deſcriptum, ita vt lineę lineis reſpondeant, erit Baby-<lb/>lonicum occidentale. </s>
  <s xml:id="echoid-s17387" xml:space="preserve">Sic etiam Italicum occidentale erit Babylonicum orientale, &amp; </s>
  <s xml:id="echoid-s17388" xml:space="preserve">è contrario: </s>
  <s xml:id="echoid-s17389" xml:space="preserve">dum-<lb/>modo ſinguli numeri horarnm mutentur in earundem complementa vſque ad 24. </s>
  <s xml:id="echoid-s17390" xml:space="preserve">vt 9. </s>
  <s xml:id="echoid-s17391" xml:space="preserve">in 15. </s>
  <s xml:id="echoid-s17392" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17393" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s17394" xml:space="preserve">in 21. </s>
  <s xml:id="echoid-s17395" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s17396" xml:space="preserve">c.</s>
  <s xml:id="echoid-s17397" xml:space="preserve"/>
</p>
<pb o="256" file="0272" n="272" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div882" type="section" level="1" n="212">
<head xml:id="echoid-head216" xml:space="preserve">PROBLEMA 36. PROPOSITIO 36.</head>
<head xml:id="echoid-head217" xml:space="preserve">HOROLOGIVM Antiquum Meridianum conſtituere.</head>
<p>
  <s xml:id="echoid-s17398" xml:space="preserve">ARCVS diurnus tam tropici ♋, B G C, quàm tropici ♑, D G E, in circulo F G H I, diuida <lb/>
<anchor type="note" xlink:label="note-0272-01a" xlink:href="note-0272-01"/>
tur in 12. </s>
  <s xml:id="echoid-s17399" xml:space="preserve">partes æquales. </s>
  <s xml:id="echoid-s17400" xml:space="preserve">Harum enim beneficio inueniemus in vtroque tropico puncta, per quę <lb/>
<anchor type="figure" xlink:label="fig-0272-01a" xlink:href="fig-0272-01"/>
<anchor type="note" xlink:label="note-0272-02a" xlink:href="note-0272-02"/>
<anchor type="note" xlink:label="note-0272-03a" xlink:href="note-0272-03"/>
<anchor type="note" xlink:label="note-0272-04a" xlink:href="note-0272-04"/>
ducendæ erunt horæ inæquales, eodem modo, quo in duabus præcedentibus propoſitionibus pun <lb/>cta horarum ab ortu, &amp; </s>
  <s xml:id="echoid-s17401" xml:space="preserve">occaſu in eiſdem tropicis inueſtigauimus. </s>
  <s xml:id="echoid-s17402" xml:space="preserve">Tranſibunt autẽ horę inæqua-<lb/>les per horas à meridie, vel media nocte in æquinoctiali linea, vt in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s17403" xml:space="preserve">Ver-<lb/>ticali docuimus, &amp; </s>
  <s xml:id="echoid-s17404" xml:space="preserve">perſpicuum eſt ex tabulis propoſ. </s>
  <s xml:id="echoid-s17405" xml:space="preserve">33. </s>
  <s xml:id="echoid-s17406" xml:space="preserve">ſuperioris lib.</s>
  <s xml:id="echoid-s17407" xml:space="preserve"/>
</p>
<div xml:id="echoid-div882" type="float" level="2" n="1">
<note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Antiqui <lb/>Meridiani.</note>
  <figure xlink:label="fig-0272-01" xlink:href="fig-0272-01a">
    <image file="0272-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0272-01"/>
  </figure>
<note position="left" xlink:label="note-0272-02" xlink:href="note-0272-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0272-03" xlink:href="note-0272-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0272-04" xlink:href="note-0272-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s17408" xml:space="preserve">SI rurſus duo arcus diurni delineentur, quorum vnus horas 18. </s>
  <s xml:id="echoid-s17409" xml:space="preserve">alter 6. </s>
  <s xml:id="echoid-s17410" xml:space="preserve">comprehendat, de-<lb/>
<anchor type="note" xlink:label="note-0272-05a" xlink:href="note-0272-05"/>
<anchor type="note" xlink:label="note-0272-06a" xlink:href="note-0272-06"/>
ſcribemus idem horologium, quemadmodum &amp; </s>
  <s xml:id="echoid-s17411" xml:space="preserve">in horizontali, &amp; </s>
  <s xml:id="echoid-s17412" xml:space="preserve">Verticali factum eſt, ex tabulis <lb/>ſcholii propoſ. </s>
  <s xml:id="echoid-s17413" xml:space="preserve">33. </s>
  <s xml:id="echoid-s17414" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17415" xml:space="preserve">quæ horis inęqualibus dicatæ ſunt. </s>
  <s xml:id="echoid-s17416" xml:space="preserve">Vtriuſque deſcriptionis <lb/>exemplum in propoſita figura apparet. </s>
  <s xml:id="echoid-s17417" xml:space="preserve">Horologium ergo Antiquum Meridianum conſtruxi-<lb/>mus. </s>
  <s xml:id="echoid-s17418" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17419" xml:space="preserve"/>
</p>
<div xml:id="echoid-div883" type="float" level="2" n="2">
<note position="left" xlink:label="note-0272-05" xlink:href="note-0272-05a" xml:space="preserve">Alia deſcriptio <lb/>horologii Anti <lb/>qui Meridiani <lb/>per arcus diur <lb/>nos horarum 6. <lb/>&amp; 18.</note>
<note position="left" xlink:label="note-0272-06" xlink:href="note-0272-06a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div885" type="section" level="1" n="213">
<head xml:id="echoid-head218" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s17420" xml:space="preserve">EX figura, &amp; </s>
  <s xml:id="echoid-s17421" xml:space="preserve">deſcriptione vtriuſque horologĳ apparet, lineas horarum inæqualium eandem poſi-<lb/>
<anchor type="note" xlink:label="note-0272-07a" xlink:href="note-0272-07"/>
tionem habere, &amp; </s>
  <s xml:id="echoid-s17422" xml:space="preserve">ſitum in vtroque horologio. </s>
  <s xml:id="echoid-s17423" xml:space="preserve">Quocirca vno deſcripto, ſi in oppoſita facie eædem lineæ <lb/>depingantur lineis prioribus omnino reſpondentes, habebitur etiam alterum horologium. </s>
  <s xml:id="echoid-s17424" xml:space="preserve">Numeri tamen <lb/>
<anchor type="note" xlink:label="note-0272-08a" xlink:href="note-0272-08"/>
horarum commutandi ſunt in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s17425" xml:space="preserve">Vt 1. </s>
  <s xml:id="echoid-s17426" xml:space="preserve">in 11. </s>
  <s xml:id="echoid-s17427" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17428" xml:space="preserve">2. </s>
  <s xml:id="echoid-s17429" xml:space="preserve">in 10. </s>
  <s xml:id="echoid-s17430" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s17431" xml:space="preserve">c.</s>
  <s xml:id="echoid-s17432" xml:space="preserve"/>
</p>
<div xml:id="echoid-div885" type="float" level="2" n="1">
<note position="left" xlink:label="note-0272-07" xlink:href="note-0272-07a" xml:space="preserve">Horologium <lb/>Antiquum ori ẽ <lb/>tale in facie pla <lb/>ni oppoſita de-<lb/>pictum dat An <lb/>tiquum occidẽ-<lb/>tale, &amp; e contra <lb/>@io.</note>
<note position="left" xlink:label="note-0272-08" xlink:href="note-0272-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div887" type="section" level="1" n="214">
<head xml:id="echoid-head219" xml:space="preserve">DE HOROLOGIIS POLARIBVS.</head>
<head xml:id="echoid-head220" xml:space="preserve">PROBLEMA 37. PROPOSITIO 37.</head>
<p>
  <s xml:id="echoid-s17433" xml:space="preserve">HOROLOGIVM Aſtronomicum polare delineare. </s>
  <s xml:id="echoid-s17434" xml:space="preserve">Id eſt, <lb/>Lineas horarum à meridie, vel media nocte in plano, quod ęquidiſtat
<pb o="257" file="0273" n="273" rhead="LIBER SECVNDVS."/>
circulo ſextæ horæ à meridie, vel media nocte, qui per polos mundi <lb/>ducitur, rectusq́; </s>
  <s xml:id="echoid-s17435" xml:space="preserve">eſt ad Meridianum, deſcribere.</s>
  <s xml:id="echoid-s17436" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17437" xml:space="preserve">NON differt hoc horologium à Meridiano horologio, excepto numero horarum, &amp; </s>
  <s xml:id="echoid-s17438" xml:space="preserve">ordine. <lb/></s>
  <s xml:id="echoid-s17439" xml:space="preserve">
<anchor type="note" xlink:label="note-0273-01a" xlink:href="note-0273-01"/>
In hoc enim ex vtraque parte rectæ D E, ſumendæ ſunt omnes horę, quę in planum horologii ca-<lb/>dere poſſunt, &amp; </s>
  <s xml:id="echoid-s17440" xml:space="preserve">recta D E, non monſtrat amplius horam 6. </s>
  <s xml:id="echoid-s17441" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s17442" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s17443" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17444" xml:space="preserve">vt ibi, ſed 12. </s>
  <s xml:id="echoid-s17445" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17446" xml:space="preserve"><lb/>linee, quę ab ea <lb/>
<anchor type="figure" xlink:label="fig-0273-01a" xlink:href="fig-0273-01"/>
recedũt verſus or <lb/>tum, horas indi-<lb/>
<anchor type="note" xlink:label="note-0273-02a" xlink:href="note-0273-02"/>
cant à mer. </s>
  <s xml:id="echoid-s17447" xml:space="preserve">quæ <lb/>verò verſus occa-<lb/>ſum ſunt poſitę, <lb/>horas à med. </s>
  <s xml:id="echoid-s17448" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s17449" xml:space="preserve">monſtrant, vt in <lb/>appoſito horolo-<lb/>
<anchor type="note" xlink:label="note-0273-03a" xlink:href="note-0273-03"/>
gio apparet. </s>
  <s xml:id="echoid-s17450" xml:space="preserve">Nam <lb/>ſi horologiũ hoc <lb/>ita collocetur, vt <lb/>recta C S, Hori-<lb/>
<anchor type="note" xlink:label="note-0273-04a" xlink:href="note-0273-04"/>
zonti ęquidiſtet, <lb/>rectaq́ue D E, in <lb/>plano Meridiani <lb/>circuli ſita ſit, pun <lb/>ctumq́ue E ad au-<lb/>ſtrum, &amp; </s>
  <s xml:id="echoid-s17451" xml:space="preserve">D, ad boream vergat, punctum denique D, ex parte Septentrionis eleuetur ſecundum al-<lb/>titudinem poli, hoc eſt, recta D E, cum meridiana linea in plano, quod parallelum ſit Horizonti, <lb/>conſtituat ad partes puncti D, angulum altitudinis poli, indicabit ſtylus A E, in A, ad angulos re-<lb/>ctos inſiſtens plano horologii, ita vt ſit communis ſectio Æ quatoris, ac Meridiani, vel certe recta <lb/>O P, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17452" xml:space="preserve">25. </s>
  <s xml:id="echoid-s17453" xml:space="preserve">huius libri docuimus, horas à mer. </s>
  <s xml:id="echoid-s17454" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17455" xml:space="preserve">med. </s>
  <s xml:id="echoid-s17456" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17457" xml:space="preserve">ita vt lineæ, quę orien <lb/>
<anchor type="note" xlink:label="note-0273-05a" xlink:href="note-0273-05"/>
taliores ſunt, quàm D E, cuiuſmodi ſunt lineę verſus punctum S, dent horas à mer. </s>
  <s xml:id="echoid-s17458" xml:space="preserve">quę verò ſunt <lb/>occidentaliores, quales ſunt lineę verſus punctum C, pertineant ad horas à med. </s>
  <s xml:id="echoid-s17459" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s17460" xml:space="preserve">vt in fi-<lb/>gura apparet.</s>
  <s xml:id="echoid-s17461" xml:space="preserve"/>
</p>
<div xml:id="echoid-div887" type="float" level="2" n="1">
<note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">Quomodo dif<unsure/>-<lb/>ferat polare ho <lb/>rologium Aſtro <lb/>nomicum a Me <lb/>ridiano.</note>
  <figure xlink:label="fig-0273-01" xlink:href="fig-0273-01a">
    <image file="0273-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0273-01"/>
  </figure>
<note position="left" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">Quomodo pol<unsure/>a <lb/>re horologium <lb/>in proprio ſitu <lb/>collocandũ ſit.</note>
<note position="left" xlink:label="note-0273-04" xlink:href="note-0273-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0273-05" xlink:href="note-0273-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s17462" xml:space="preserve">ITAQVE ſi deſcribendum ſit horologium polare Aſtronomicum, ducendę erunt in plano <lb/>
<anchor type="note" xlink:label="note-0273-06a" xlink:href="note-0273-06"/>
aliquo duæ rectę lineę C S, D E, ſeſe ad angulos rectos ſecantes in A, &amp; </s>
  <s xml:id="echoid-s17463" xml:space="preserve">in recta D E, ſumenda re-<lb/>cta A E, ſtylo propoſito æqualis. </s>
  <s xml:id="echoid-s17464" xml:space="preserve">Deinde ex E, deſcripto circulo cuiuſcunque magnitudinis, eoq́ <lb/>diuiſo in partes 24. </s>
  <s xml:id="echoid-s17465" xml:space="preserve">æquales, reliqua perficienda, vt in Meridiano horologio, &amp;</s>
  <s xml:id="echoid-s17466" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17467" xml:space="preserve">Quòd autem <lb/>horologium Meridianum ſit polare, ſi fiat illa permutatio numerorum horarum, vt diximus, fa-<lb/>cile hoc modo intelligi poterit. </s>
  <s xml:id="echoid-s17468" xml:space="preserve">Quoniam tam circulus horæ 6. </s>
  <s xml:id="echoid-s17469" xml:space="preserve">à meridie, vel media nocte, cui <lb/>planum horologii polaris æquidiſtat, quàm Meridianus, cui æquidiſtat horologium Meridianũ, <lb/>
<anchor type="note" xlink:label="note-0273-07a" xlink:href="note-0273-07"/>
per polos mundi ducitur, fit, vt circuli horarum à meridie, vel media nocte eodem modo vtriuſ-<lb/>que horologii planum ſecent, cum eodem modo ſe ſe habeant reſpectu vtriuſque, mutato ſolum <lb/>ordine, &amp; </s>
  <s xml:id="echoid-s17470" xml:space="preserve">numero horarum. </s>
  <s xml:id="echoid-s17471" xml:space="preserve">Nam vt ſe habet circulus horæ 6. </s>
  <s xml:id="echoid-s17472" xml:space="preserve">reſpectu Meridiani, ſecans nimi-<lb/>rum ipſum ad rectos angalos, ita quoque viciſſim ſe habet Meridianus reſpectu circuli horæ 6. <lb/></s>
  <s xml:id="echoid-s17473" xml:space="preserve">
<anchor type="note" xlink:label="note-0273-08a" xlink:href="note-0273-08"/>
ac proinde linea, quæ in Meridiano horologio dat horam 6. </s>
  <s xml:id="echoid-s17474" xml:space="preserve">dabit horam 12. </s>
  <s xml:id="echoid-s17475" xml:space="preserve">in horologio pola-<lb/>ri, &amp;</s>
  <s xml:id="echoid-s17476" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17477" xml:space="preserve">Verum geometricè quoque conſtructionem horologii polaris, quam proxime expoſuimus, <lb/>ita demonſtrabimus. </s>
  <s xml:id="echoid-s17478" xml:space="preserve">Quia plana Meridiani, &amp; </s>
  <s xml:id="echoid-s17479" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s17480" xml:space="preserve">ad planum Æ quatoris recta ſunt, <lb/>per propoſ. </s>
  <s xml:id="echoid-s17481" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17482" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s17483" xml:space="preserve">1. </s>
  <s xml:id="echoid-s17484" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s17485" xml:space="preserve">cum per eius polos tranſeant; </s>
  <s xml:id="echoid-s17486" xml:space="preserve">erit communis eorum ſectio ad idem <lb/>
<anchor type="note" xlink:label="note-0273-09a" xlink:href="note-0273-09"/>
planum Æ quatoris recta. </s>
  <s xml:id="echoid-s17487" xml:space="preserve">Cum ergo huic ſectioni parallela ſit ſectio, quam Meridianus in plano <lb/>
<anchor type="note" xlink:label="note-0273-10a" xlink:href="note-0273-10"/>
horologii polaris efficit, nempe linea meridiana; </s>
  <s xml:id="echoid-s17488" xml:space="preserve">erit quoque linea meridiana horologii ad planũ <lb/>
<anchor type="note" xlink:label="note-0273-11a" xlink:href="note-0273-11"/>
<anchor type="note" xlink:label="note-0273-12a" xlink:href="note-0273-12"/>
Æquatoris recta; </s>
  <s xml:id="echoid-s17489" xml:space="preserve">atque adeo per defin. </s>
  <s xml:id="echoid-s17490" xml:space="preserve">3. </s>
  <s xml:id="echoid-s17491" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s17492" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17493" xml:space="preserve">Euclid &amp; </s>
  <s xml:id="echoid-s17494" xml:space="preserve">ad communem ſectionem plani horo-<lb/>logii, &amp; </s>
  <s xml:id="echoid-s17495" xml:space="preserve">Æ quatoris, nempe ad lineam æquinoctialem horologii in plano Æ quatoris exiſtentem, <lb/>perpendicularis erit. </s>
  <s xml:id="echoid-s17496" xml:space="preserve">Quocirca ſi recta C S, ponatur linea æquinoctialis, erit recta D E, linea meri <lb/>diana in horologio polari, quandoquidem recta D E, ad C S, per conſtructionem, perpendicula-<lb/>ris eſt. </s>
  <s xml:id="echoid-s17497" xml:space="preserve">Igitur ſi circa rectam C S, quieſcentem intelligatur moueri planum circuli ex E, deſcripti, <lb/>donec cum plano Æ quatoris, &amp; </s>
  <s xml:id="echoid-s17498" xml:space="preserve">E, vertex ſtyli aſſumpti A E, cum centro mundi coniungatur, erit <lb/>circulus ipſe Æ quatori concentricus, &amp; </s>
  <s xml:id="echoid-s17499" xml:space="preserve">rectæ per E, &amp; </s>
  <s xml:id="echoid-s17500" xml:space="preserve">puncta diuiſionum circuli emiſſæ, commu-<lb/>nes ſectiones circulorum horariorum à meridie vel media nocte, &amp; </s>
  <s xml:id="echoid-s17501" xml:space="preserve">Æ quatoris; </s>
  <s xml:id="echoid-s17502" xml:space="preserve">cum Æ quator &amp; </s>
  <s xml:id="echoid-s17503" xml:space="preserve"><lb/>circulus ex E, deſcriptus circa idem centrum E, deſcripti in arcus ſimiles à dictis rectis ſecentur, <lb/>vt ad finem cap. </s>
  <s xml:id="echoid-s17504" xml:space="preserve">1. </s>
  <s xml:id="echoid-s17505" xml:space="preserve">in ſphæram dem onſtrauimus; </s>
  <s xml:id="echoid-s17506" xml:space="preserve">nempe diameter circuli ex E, deſcripti ad C S, <lb/>perpendicularis, communis ſectio Æ quatoris, &amp; </s>
  <s xml:id="echoid-s17507" xml:space="preserve">circuli horæ 12. </s>
  <s xml:id="echoid-s17508" xml:space="preserve">ſeu Meridiani, &amp;</s>
  <s xml:id="echoid-s17509" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17510" xml:space="preserve">vt perſpi-
<pb o="258" file="0274" n="274" rhead="GNOMONICES"/>
cuum eſt, ſi rectè conſideretur propria poſitio circuli ex E, deſcripti, vel Æ quatoris in plano ho-<lb/>rologii polaris, ita vt ad planum horologii rectus ſit. </s>
  <s xml:id="echoid-s17511" xml:space="preserve">Quapropter circuli horarii à meridie, vel <lb/>media nocte ſecant ęquinoctialem lineam C S, in plano horologii in punctis, in quibus rectæ per <lb/>centrum E, &amp; </s>
  <s xml:id="echoid-s17512" xml:space="preserve">puncta diuiſionum circuli ex E, deſcripti ductæ eidem occurrunt, ac propterea per <lb/>hęc puncta ducẽdæ ſunt communes ſectiones circulorum eorundem, ac plani horologii, quæ qui-<lb/>dem ſunt horarię lineæ à meridie, vel media nocte. </s>
  <s xml:id="echoid-s17513" xml:space="preserve">Quamobrẽ cũ ex coroll propoſ. </s>
  <s xml:id="echoid-s17514" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17515" xml:space="preserve">ſuperioris <lb/>lib. </s>
  <s xml:id="echoid-s17516" xml:space="preserve">hæ lineæ horariæ ſint parallelæ in polari horologio, liquido cõſtat, rectas, quę per puncta lineæ <lb/>C S, ipſi D E, meridianæ lineæ, ſeu lineæ horæ 12. </s>
  <s xml:id="echoid-s17517" xml:space="preserve">parallelæ ducũtur, eſſe lineas horarias à meridie, <lb/>
<anchor type="note" xlink:label="note-0274-01a" xlink:href="note-0274-01"/>
vel media nocte, eo ordine, vt ſupra dictũ eſt. </s>
  <s xml:id="echoid-s17518" xml:space="preserve">Sola linea horæ 6. </s>
  <s xml:id="echoid-s17519" xml:space="preserve">deſcribi non poteſt, ſed euaneſcit, <lb/>vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17520" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17521" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17522" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s17523" xml:space="preserve">Atque hactenus Polare horologium Su-<lb/>
<anchor type="note" xlink:label="note-0274-02a" xlink:href="note-0274-02"/>
perius, quod Zenith reſpicit, conſtruximus.</s>
  <s xml:id="echoid-s17524" xml:space="preserve"/>
</p>
<div xml:id="echoid-div888" type="float" level="2" n="2">
<note position="right" xlink:label="note-0273-06" xlink:href="note-0273-06a" xml:space="preserve">Deſcriptio ho-<lb/>rologii polaris <lb/>Aſtronomici <lb/>Superioris.</note>
<note position="left" xlink:label="note-0273-07" xlink:href="note-0273-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0273-08" xlink:href="note-0273-08a" xml:space="preserve">Demonſtratio <lb/>conſtru ctionis <lb/>horologii pola-<lb/>ris Aſtronomi-<lb/>ci.</note>
<note position="right" xlink:label="note-0273-09" xlink:href="note-0273-09a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0273-10" xlink:href="note-0273-10a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0273-11" xlink:href="note-0273-11a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0273-12" xlink:href="note-0273-12a" xml:space="preserve">8. vndec.</note>
<note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">Linea horæ 6. à <lb/>mer. vel med. <lb/>noc. deſcribi ne <lb/>quit in polari <lb/>horologio.</note>
<note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s17525" xml:space="preserve">IAM verò eædem lineæ horariæ in facie oppoſita plani horologii (quam quidem Sol illuſtrat <lb/>
<anchor type="note" xlink:label="note-0274-03a" xlink:href="note-0274-03"/>
ante horam 6. </s>
  <s xml:id="echoid-s17526" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s17527" xml:space="preserve">poſt 6. </s>
  <s xml:id="echoid-s17528" xml:space="preserve">à meridie, vt patet) deſcriptæ, ita vt ſingulæ lineæ ſingulis <lb/>lineis omni ex parte reſpondeant, dabunt quoque horas in horologio polari inferiori, mutato ta-<lb/>men numero cuiuslibet horæ in complementum eius vſque ad 12. </s>
  <s xml:id="echoid-s17529" xml:space="preserve">adeo vt linea horæ 7. </s>
  <s xml:id="echoid-s17530" xml:space="preserve">à media <lb/>nocte in ſuperiori horologio ſit linea horæ 5. </s>
  <s xml:id="echoid-s17531" xml:space="preserve">à media nocte in inferiori, &amp;</s>
  <s xml:id="echoid-s17532" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17533" xml:space="preserve">Appellamus horolo <lb/>gium Superius, quod Zenith reſpicit, Inferius autem, quod Nadir. </s>
  <s xml:id="echoid-s17534" xml:space="preserve">Demonſtratio eadem omnino <lb/>eſt, quæ prius, ſi circulus ex E, deſcriptus intelligatur circa C S, moueri deorſum verſus, donec E, <lb/>cum centro mundi coniungatur, &amp;</s>
  <s xml:id="echoid-s17535" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17536" xml:space="preserve">Nam diameter illius ſecans C S, ad angulos rectos erit com <lb/>munis ſectio Æ quatoris, &amp; </s>
  <s xml:id="echoid-s17537" xml:space="preserve">circuli horæ 12. </s>
  <s xml:id="echoid-s17538" xml:space="preserve">mediæ noctis, &amp;</s>
  <s xml:id="echoid-s17539" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17540" xml:space="preserve">vt facile intelligi poteſt, ſi circulus <lb/>
<anchor type="note" xlink:label="note-0274-04a" xlink:href="note-0274-04"/>
dictus in propria poſitione concipiatur in plano horologii Inferioris. </s>
  <s xml:id="echoid-s17541" xml:space="preserve">Horologium igitur Aſtro-<lb/>nomicum polare delineauimus. </s>
  <s xml:id="echoid-s17542" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17543" xml:space="preserve"/>
</p>
<div xml:id="echoid-div889" type="float" level="2" n="3">
<note position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">Horologiũ po-<lb/>lare Superius in <lb/>facie oppoſita <lb/>deſcriptum, ita <lb/>vt lineæ ſingu-<lb/>lę ſingulis lineis <lb/>reſpodeant, dat <lb/>horologium po <lb/>lare Interius, <lb/>dummodo nu <lb/>meri horarum <lb/>mutentur in ea <lb/>rum complemẽ <lb/>ta vſque ad 12.</note>
<note position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div891" type="section" level="1" n="215">
<head xml:id="echoid-head221" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s17544" xml:space="preserve">SI in plano ſtabili, quod circulo horæ 6. </s>
  <s xml:id="echoid-s17545" xml:space="preserve">æquidistet, deſcribendum ſit horologium, non autem in quo-<lb/>
<anchor type="note" xlink:label="note-0274-05a" xlink:href="note-0274-05"/>
cunque plano, vt postea in proprio ſitu collocetur, quemadmodum hactenus factum est à nobis; </s>
  <s xml:id="echoid-s17546" xml:space="preserve">ducenda <lb/>erit beneficio libellæ, ac perpendiculi in plano dato recta C S, Horizonti æquidiſtans pro linea æquino-<lb/>ctiali, &amp; </s>
  <s xml:id="echoid-s17547" xml:space="preserve">ad hanc perpendicularis excitanda D E, pro linea meridiana; </s>
  <s xml:id="echoid-s17548" xml:space="preserve">ſumpta deinde in recta D E, lon-<lb/>gitudine styli A E, at que ex E, deſcripto circulo cuiuslibet magnitudinis, reliqua abſoluenda erunt, vt <lb/>
<anchor type="note" xlink:label="note-0274-06a" xlink:href="note-0274-06"/>
in Meridiano horologio, vt &amp; </s>
  <s xml:id="echoid-s17549" xml:space="preserve">ante docuimus.</s>
  <s xml:id="echoid-s17550" xml:space="preserve"/>
</p>
<div xml:id="echoid-div891" type="float" level="2" n="1">
<note position="left" xlink:label="note-0274-05" xlink:href="note-0274-05a" xml:space="preserve">Quomodo in <lb/>plano ſtabili po <lb/>lare horologiũ <lb/>Aſtronomicum <lb/>conſtruatur.</note>
<note position="left" xlink:label="note-0274-06" xlink:href="note-0274-06a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Quando datur <lb/>l@@@@ ſtyli, ei<unsure/>uſ-<lb/>que longitudo, <lb/>qua ratione de-<lb/>ſcribatur horo-<lb/>logium Aſtro-<lb/>nomicum Pola <lb/>re.</note>
<p style="it">
  <s xml:id="echoid-s17551" xml:space="preserve">QVOD ſi detur locus ſtyli, vt in A, vna cum eius longitudine, ducenda erit C S, Horizonti æquidi <lb/>ſtans per A, locum styli, &amp; </s>
  <s xml:id="echoid-s17552" xml:space="preserve">ad C S, ex eodem loco ſtyli A, per pendicularis excitanda D E, &amp;</s>
  <s xml:id="echoid-s17553" xml:space="preserve">c.</s>
  <s xml:id="echoid-s17554" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div893" type="section" level="1" n="216">
<head xml:id="echoid-head222" xml:space="preserve">PROBLEMA 38. PROPOSITIO 38.</head>
<p>
  <s xml:id="echoid-s17555" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in prædicto ho-<lb/>rologio polari deſcribere.</s>
  <s xml:id="echoid-s17556" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s17557" xml:space="preserve">DESCRIBENTVR arcus ſignorum Zodiaci in horologio polari, quemadmodũ in Mc-<lb/>
<anchor type="note" xlink:label="note-0274-09a" xlink:href="note-0274-09"/>
<anchor type="figure" xlink:label="fig-0274-01a" xlink:href="fig-0274-01"/>
ridiano horolo-<lb/>gio deſcripti sũt. <lb/></s>
  <s xml:id="echoid-s17558" xml:space="preserve">Eædem enim de-<lb/>mõſtrationes huc <lb/>trãsferri poſſunt, <lb/>hoc ſolum obſer <lb/>uato, in prima fi-<lb/>gura propoſ. </s>
  <s xml:id="echoid-s17559" xml:space="preserve">26. </s>
  <s xml:id="echoid-s17560" xml:space="preserve"><lb/>huius libri circu-<lb/>
<anchor type="note" xlink:label="note-0274-10a" xlink:href="note-0274-10"/>
lum Analemma-<lb/>tis A B C D, non <lb/>ſumendum eſſe, <lb/>vtibi, pro circu-<lb/>lo horæ 6. </s>
  <s xml:id="echoid-s17561" xml:space="preserve">à me-<lb/>ridie, vel media <lb/>nocte, ſed pro <lb/>ipſo Meridiano, <lb/>atque adeò axem <lb/>F G, eſſe communem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s17562" xml:space="preserve">circuli 6. </s>
  <s xml:id="echoid-s17563" xml:space="preserve">horæ; </s>
  <s xml:id="echoid-s17564" xml:space="preserve">rectam autem L M, ſectio-<lb/>nem communem eiuſdem Meridiani, &amp; </s>
  <s xml:id="echoid-s17565" xml:space="preserve">plani horologii polaris, hoc eſt, lineam meridianam
<pb o="259" file="0275" n="275" rhead="LIBER SECVNDVS."/>
horologii, vel horæ 12. </s>
  <s xml:id="echoid-s17566" xml:space="preserve">non autem horæ 6. </s>
  <s xml:id="echoid-s17567" xml:space="preserve">vt ibi. </s>
  <s xml:id="echoid-s17568" xml:space="preserve">Pari ratione in figura tertia eiuſdem propoſ. </s>
  <s xml:id="echoid-s17569" xml:space="preserve">26. <lb/></s>
  <s xml:id="echoid-s17570" xml:space="preserve">lineam α β, quæ in horologio Meridiano pertinebat ad horam 6. </s>
  <s xml:id="echoid-s17571" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s17572" xml:space="preserve">eſſe lineam meridianam, <lb/>ſeu horæ 12 in horologio polari; </s>
  <s xml:id="echoid-s17573" xml:space="preserve">proximam verò illi parallelam pertinere ad horam 1. </s>
  <s xml:id="echoid-s17574" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17575" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17576" xml:space="preserve">à me <lb/>ridie, &amp; </s>
  <s xml:id="echoid-s17577" xml:space="preserve">media nocte, &amp;</s>
  <s xml:id="echoid-s17578" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17579" xml:space="preserve">In vtroque porrò horologio polari ſigna Borealia infra lineam æquino-<lb/>
<anchor type="note" xlink:label="note-0275-01a" xlink:href="note-0275-01"/>
ctialem verſus auſtrum, &amp; </s>
  <s xml:id="echoid-s17580" xml:space="preserve">ſupra eandem verſus boream auſtralia continentur, vt ex Analemmate, <lb/>ſeu figura prima propoſ. </s>
  <s xml:id="echoid-s17581" xml:space="preserve">26. </s>
  <s xml:id="echoid-s17582" xml:space="preserve">huius libri colligi poteſt. </s>
  <s xml:id="echoid-s17583" xml:space="preserve">Nam Sole exiſtente in ♋, vmbra ſtyli proii-<lb/>citur in partes inferiores lineæ meridianæ in vtroque horologio, nempe in punctum N, verſus au-<lb/>ſtrum tempore meridiei; </s>
  <s xml:id="echoid-s17584" xml:space="preserve">exiſtente verò eodem in ♑, in ſuperiores partes, vt in punctum Q, ver-<lb/>ſus boream.</s>
  <s xml:id="echoid-s17585" xml:space="preserve"/>
</p>
<div xml:id="echoid-div893" type="float" level="2" n="1">
<note position="left" xlink:label="note-0274-09" xlink:href="note-0274-09a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſig norũ <lb/>Zodi<unsure/>ac@ in ho-<lb/>rologio polari.</note>
  <figure xlink:label="fig-0274-01" xlink:href="fig-0274-01a">
    <image file="0274-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0274-01"/>
  </figure>
<note position="left" xlink:label="note-0274-10" xlink:href="note-0274-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">In horologio <lb/>polati tam Su-<lb/>periori, quàm <lb/>Inferioti ſigna <lb/>borealia ſunt <lb/>inſra lineã ęqui <lb/>noctialem, &amp; au <lb/>ſiralia ſupra.</note>
</div>
<note position="right" xml:space="preserve">Linea hor@zon-<lb/>talis in horolo-<lb/>g@o Polari quo <lb/>modo deſcriba-<lb/>@ur.</note>
<p>
  <s xml:id="echoid-s17586" xml:space="preserve">QVONIAM verò planum horologii polaris ab Horizonte ſecatur, cum ei non ſit parallelũ, <lb/>
<anchor type="note" xlink:label="note-0275-03a" xlink:href="note-0275-03"/>
quemadmodum &amp; </s>
  <s xml:id="echoid-s17587" xml:space="preserve">circulus horæ 6. </s>
  <s xml:id="echoid-s17588" xml:space="preserve">à meridie, vel media nocte, cui horologium æquidiſtat, ab eo-<lb/>dem Horizonte ſecatur, deſcribemus communem ſectionem Horizontis, ac plani horologii, nem <lb/>pe lineam horizontalem, in quam vmbra ſtyli proiicitur, cum Soloritur, vel occidit, vt ex propoſ. <lb/></s>
  <s xml:id="echoid-s17589" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17590" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17591" xml:space="preserve">conſtat, hac ratione. </s>
  <s xml:id="echoid-s17592" xml:space="preserve">Ad punctum B, vbi hora 3. </s>
  <s xml:id="echoid-s17593" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s17594" xml:space="preserve">lineam æquinoctialem ſe-<lb/>cat, fiat angulus A B D, complemento altitudinis poli æqualis, ſecetq́ue recta B D, lineam meri-<lb/>dianam in D, ſupra quidem locum ſtyli in horologio ſuperiori, infra verò eundẽ in inferiori; </s>
  <s xml:id="echoid-s17595" xml:space="preserve">quod <lb/>facile fiet, ſi ex B, deſcribatur arcus circuli vltra lineam meridianam, in quo à recta C S, comple-<lb/>mentum altitudinis poli ſupputetur, &amp; </s>
  <s xml:id="echoid-s17596" xml:space="preserve">ex ſine ſupputationis ad B, recta ducatur, &amp;</s>
  <s xml:id="echoid-s17597" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17598" xml:space="preserve">Si enim per <lb/>D, lineæ æquinoctiali C S, parallela ducatur, erit hæc, linea horizontalis. </s>
  <s xml:id="echoid-s17599" xml:space="preserve">Nam quia recta A B, <lb/>longitudini ſtyli A E, eſt æqualis, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17600" xml:space="preserve">25. </s>
  <s xml:id="echoid-s17601" xml:space="preserve">huius libri oſtendimus, ſi triangulum <lb/>
<anchor type="note" xlink:label="note-0275-04a" xlink:href="note-0275-04"/>
D B A, circa rectam A D, intelligatur conuerti, donec ad planum horologii rectum ſit, &amp; </s>
  <s xml:id="echoid-s17602" xml:space="preserve">in plano <lb/>Meridiani circuli exiſtat, tranſibit Horizon per punctum B, nempe per verticem ſtyli, ſeu centrum <lb/>mundi; </s>
  <s xml:id="echoid-s17603" xml:space="preserve">Nam recta A B, in illo ſitu, quem in illa conuerſione trianguli acquiſiuit, perpendicularis <lb/>eſt ad planum horologii, &amp; </s>
  <s xml:id="echoid-s17604" xml:space="preserve">in plano Æ quatoris exiſtit, atque adeo B, erit vertex ſtyli, ſeu centrum <lb/>mundi. </s>
  <s xml:id="echoid-s17605" xml:space="preserve">Cum ergo angulus D B A, conſtitutus ſit æqualis complemento altitudinis poli, qualem <lb/>nimirum Horizon facit cum plano Æ quatoris, atque adeo reliquus B D A, altitudini poli æqualis <lb/>ſit, nempe inclinationi plani horologii ad Horizontem, tranſibit Horizon per rectam B D, occur-<lb/>retq́ue plano horologii in D; </s>
  <s xml:id="echoid-s17606" xml:space="preserve">quandoquidem hac ratione in plano Meridiani circuli cum A B, cõ-<lb/>muni ſectione Aequatoris, &amp; </s>
  <s xml:id="echoid-s17607" xml:space="preserve">Meridiani conſtituit angulum complemento altitudinis poli æqua-<lb/>lem, cum recta verò A E, communi ſectione plani horologii, ac Meridiani angulum æqualem alti-<lb/>
<anchor type="note" xlink:label="note-0275-05a" xlink:href="note-0275-05"/>
tudini poli, vt res exigit. </s>
  <s xml:id="echoid-s17608" xml:space="preserve">Quare per D, ducenda erit linea horizontalis. </s>
  <s xml:id="echoid-s17609" xml:space="preserve">Quia verò Aequator, Ho-<lb/>rizon, &amp; </s>
  <s xml:id="echoid-s17610" xml:space="preserve">circulus horæ ſextæ habent vnam communem ſectionem, æquidiſtatq́ue plannm horolo <lb/>gij vni illorum, nempe circulo horæ 6. </s>
  <s xml:id="echoid-s17611" xml:space="preserve">erunt communes ſectiones factæ à plano horologii in aliis <lb/>duobus circulis, nempe linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s17612" xml:space="preserve">horizontalis, parallelæ inter ſe, vt in ſcholio propoſ. <lb/></s>
  <s xml:id="echoid-s17613" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17614" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17615" xml:space="preserve">demonſtratum eſt. </s>
  <s xml:id="echoid-s17616" xml:space="preserve">Recta igitur per D, lineæ æquinoctiali parallela ducta, ho-<lb/>rizon talis linea eſt, quod eſt propoſitum.</s>
  <s xml:id="echoid-s17617" xml:space="preserve"/>
</p>
<div xml:id="echoid-div894" type="float" level="2" n="2">
<note position="left" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0275-04" xlink:href="note-0275-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0275-05" xlink:href="note-0275-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s17618" xml:space="preserve">INVENIEMVS quoque punctum D, per quod horizontalis linea ducenda eſt, hoc mo-<lb/>
<anchor type="note" xlink:label="note-0275-06a" xlink:href="note-0275-06"/>
do. </s>
  <s xml:id="echoid-s17619" xml:space="preserve">In Analemmate, ex quo arcus ſignorũ deſcripti ſunt, notentur puncta l, m, vbi diameter Hori-<lb/>zontis B D, parallelas L M, L M, per quas ducũtur horologiorum plana, interſecat, &amp; </s>
  <s xml:id="echoid-s17620" xml:space="preserve">recta K l, vel <lb/>K m, trãsferatur in lineã meridianã ex loco ſtyli A, ſurſum verſus vſq; </s>
  <s xml:id="echoid-s17621" xml:space="preserve">ad D, in horologio ſuperio-<lb/>
<anchor type="note" xlink:label="note-0275-07a" xlink:href="note-0275-07"/>
ri, deorſum autẽ verſus in inferiori. </s>
  <s xml:id="echoid-s17622" xml:space="preserve">Nam per D, ducenda eſt linea horizontalis, vt prius. </s>
  <s xml:id="echoid-s17623" xml:space="preserve">quoniã in <lb/>punctis l, &amp; </s>
  <s xml:id="echoid-s17624" xml:space="preserve">m, planum Horizontis per B D, ductum occurrit planis horologiorum per L M, L M, <lb/>rectas ductis, ſupra K, quidem locũ ſtyli in horologio ſuperiori, infra verò in inferiori, &amp;</s>
  <s xml:id="echoid-s17625" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17626" xml:space="preserve">Et quo-<lb/>niam recta K l, rectæ K m, æqualis eſt; </s>
  <s xml:id="echoid-s17627" xml:space="preserve">(Nam in triangulis E K l, E K m, anguli ad K, recti ſunt, <lb/>
<anchor type="note" xlink:label="note-0275-08a" xlink:href="note-0275-08"/>
&amp; </s>
  <s xml:id="echoid-s17628" xml:space="preserve">anguli ad verticem E, æquales; </s>
  <s xml:id="echoid-s17629" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s17630" xml:space="preserve">latera E K, E K, ęqualia. </s>
  <s xml:id="echoid-s17631" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s17632" xml:space="preserve">latera K l, K m, æqualia <lb/>
<anchor type="note" xlink:label="note-0275-09a" xlink:href="note-0275-09"/>
erunt) propterea diximus eandẽ K l, vel K m, transferendã in lineam meridianam ſupra vel infra <lb/>locum ſtyli in vtroque horologio, vt punctum reperiatur, per quod horizontalis linea ducatur.</s>
  <s xml:id="echoid-s17633" xml:space="preserve"/>
</p>
<div xml:id="echoid-div895" type="float" level="2" n="3">
<note position="right" xlink:label="note-0275-06" xlink:href="note-0275-06a" xml:space="preserve">Alia deſcriptio<unsure/> <lb/>lineæ horizon-<lb/>talis in eodem <lb/>horologio Po. <lb/>lari.</note>
<note position="left" xlink:label="note-0275-07" xlink:href="note-0275-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0275-08" xlink:href="note-0275-08a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0275-09" xlink:href="note-0275-09a" xml:space="preserve">26. primi.</note>
</div>
<p>
  <s xml:id="echoid-s17634" xml:space="preserve">PORRO ſi horologium polare ſuperius inuertatur, ita vt ſuperiora fiant inferiora, &amp; </s>
  <s xml:id="echoid-s17635" xml:space="preserve">quæ <lb/>
<anchor type="note" xlink:label="note-0275-10a" xlink:href="note-0275-10"/>
dextra ſunt poſt eam inuerſionem, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s17636" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17637" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17638" xml:space="preserve">huius libri ſcri-<lb/>pſimus, indicabit idem horas in facie oppoſita plani, hoc eſt, in inferiori, quæ ad Nadir ſpectat, vt <lb/>
<anchor type="note" xlink:label="note-0275-11a" xlink:href="note-0275-11"/>
in dicto ſcholio demonſtrauimus. </s>
  <s xml:id="echoid-s17639" xml:space="preserve">Sed linea meridiana monſtrabit tunc horam 12. </s>
  <s xml:id="echoid-s17640" xml:space="preserve">mediæ noctis, <lb/>cum in ſuperiori hologio horam 12. </s>
  <s xml:id="echoid-s17641" xml:space="preserve">meridiei indicet: </s>
  <s xml:id="echoid-s17642" xml:space="preserve">reliquæ verò horæ, quæ in eodem ſuperio-<lb/>ri horologio à meridie numerantur, à media nocte ſupputandæ erunt in inferiori, &amp; </s>
  <s xml:id="echoid-s17643" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s17644" xml:space="preserve">Quo-<lb/>niam enim Sol in alio ſemicirculo eiuſdem circuli horarij exiſtat neceſſe eſt, cum vmbra ſtyli in <lb/>ſuperius horologium cadit, &amp; </s>
  <s xml:id="echoid-s17645" xml:space="preserve">in alio, cum in inferius, vt patet; </s>
  <s xml:id="echoid-s17646" xml:space="preserve">efficitur, vt linea, quæ in ſuperiori <lb/>horologio indicat horam à meridie, monſtret in inferiori eandem horam à media nocte, &amp; </s>
  <s xml:id="echoid-s17647" xml:space="preserve">con-<lb/>tra; </s>
  <s xml:id="echoid-s17648" xml:space="preserve">quandoquidem vnus ſemicirculus ad horas à meridie, &amp; </s>
  <s xml:id="echoid-s17649" xml:space="preserve">alter ad horas à media nocte perti-<lb/>net, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17650" xml:space="preserve">9. </s>
  <s xml:id="echoid-s17651" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17652" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s17653" xml:space="preserve">Arcus quoque vel paralleli ſignorum au-<lb/>ſtralium ſuperioris horologii mutantur in arcus borealium ſignorum in inferiori, &amp; </s>
  <s xml:id="echoid-s17654" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s17655" xml:space="preserve">vt <lb/>parallelus ♑, in parallelum ♋, parallelus ♐, &amp; </s>
  <s xml:id="echoid-s17656" xml:space="preserve">♒, in parallelum ♊, &amp; </s>
  <s xml:id="echoid-s17657" xml:space="preserve">♌, &amp;</s>
  <s xml:id="echoid-s17658" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17659" xml:space="preserve">Quod oſtendemus, <lb/>vt in propoſ, 26. </s>
  <s xml:id="echoid-s17660" xml:space="preserve">huius libri idem demonſtrauimus in Meridiano horologio, hoc ſolum mutato,
<pb o="260" file="0276" n="276" rhead="GNOMONICES"/>
axem hyperbolarum hic eſſe lineam horæ 12. </s>
  <s xml:id="echoid-s17661" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17662" xml:space="preserve">non 6. </s>
  <s xml:id="echoid-s17663" xml:space="preserve">vt ibi. </s>
  <s xml:id="echoid-s17664" xml:space="preserve">Idem conſtat ex Analemmate, <lb/>ex quo arcus ſignorum ſunt deſcripti. </s>
  <s xml:id="echoid-s17665" xml:space="preserve">In eo enim radius ♑, per centrum E, ductus ſecat meridia-<lb/>nam lineam M L, in ſuperiori horologio prope Horizontem B D. </s>
  <s xml:id="echoid-s17666" xml:space="preserve">In inferiori verò radius ♋, per <lb/>idem centrum E, tranſiens ſecat lineam meridianam prope Horizontem, vt conſtat. </s>
  <s xml:id="echoid-s17667" xml:space="preserve">Idem dicen-<lb/>
<anchor type="note" xlink:label="note-0276-01a" xlink:href="note-0276-01"/>
dum eſt de alijs ſignis auſtralibus, &amp; </s>
  <s xml:id="echoid-s17668" xml:space="preserve">borealibus.</s>
  <s xml:id="echoid-s17669" xml:space="preserve"/>
</p>
<div xml:id="echoid-div896" type="float" level="2" n="4">
<note position="right" xlink:label="note-0275-10" xlink:href="note-0275-10a" xml:space="preserve">Si omnes par-<lb/>tes Superioris <lb/>horologii Pola-<lb/>ris inuertantur, <lb/>vt ſuperior fiat <lb/>inferior, &amp; dex-<lb/>t@a ſiniſtra, fa-<lb/>ctum erit horo-<lb/>logiũ Inferius; <lb/>ſed horæ, quæ <lb/>prius numera-<lb/>bantur à n@er@ <lb/>numerande sũt <lb/>à med. noc. &amp; <lb/>contra.</note>
<note position="left" xlink:label="note-0275-11" xlink:href="note-0275-11a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">Linea horizon-<lb/>talis aufert ex <lb/>pa@te ſuperiore <lb/>hot<unsure/>ologu ſupe <lb/>rioris horolo-<lb/>gium inf<unsure/>erius, <lb/>ſ<unsure/>i omnes ei<unsure/>us <lb/>partes i@uertan <lb/>tur, vt ſupra di-<lb/>ctum eſt.</note>
</div>
<p>
  <s xml:id="echoid-s17670" xml:space="preserve">ITAQVE portio horologii ſuperioris, quam linea horizontalis amputat, collocata in facie <lb/>inferiori horologii, ita vt horizontalis linea ſuperiorem locum occupet, infra tamẽ ſtylum, &amp; </s>
  <s xml:id="echoid-s17671" xml:space="preserve">quæ <lb/>dextra pars tunc eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s17672" xml:space="preserve">è contrario, dabit horologium polare inferius, vna cum ar-<lb/>cubus ſignorum.</s>
  <s xml:id="echoid-s17673" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17674" xml:space="preserve">EADEM quoque portio abſciſſa in ſuperiori horologio erit horologium nocturnum, vt in <lb/>
<anchor type="note" xlink:label="note-0276-02a" xlink:href="note-0276-02"/>
<anchor type="note" xlink:label="note-0276-03a" xlink:href="note-0276-03"/>
ſuperioribus dictum eſt. </s>
  <s xml:id="echoid-s17675" xml:space="preserve">In illud enim caderet vmbra ſtyli mane ante ortum Solis, &amp; </s>
  <s xml:id="echoid-s17676" xml:space="preserve">veſperi ante <lb/>occaſum, Sole in auſtralibus ſignis exiſtente, niſi terræ denſitas obſiſteret.</s>
  <s xml:id="echoid-s17677" xml:space="preserve"/>
</p>
<div xml:id="echoid-div897" type="float" level="2" n="5">
<note position="left" xlink:label="note-0276-02" xlink:href="note-0276-02a" xml:space="preserve">Portio Supetio <lb/>ris horologii <lb/>abſciſſa à linea <lb/>horizontali eſt <lb/>horologium no <lb/>cturnum.</note>
<note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s17678" xml:space="preserve">MANIFESTVM autem eſt, quo maior fuerit altitudo poli, eo plures horas recipi in horo <lb/>logio inferiori, ſeu portione abſciſſa à linea horizontali, eò pauciores verò, quò minor fuerit poli <lb/>
<anchor type="note" xlink:label="note-0276-04a" xlink:href="note-0276-04"/>
altitudo. </s>
  <s xml:id="echoid-s17679" xml:space="preserve">Nam quò maior eſt altitudo poli, eò minor fiet angulus complementi altitudinis poli <lb/>D B A, atque adeo punctum D, vicinius erit æquinoctiali lineæ. </s>
  <s xml:id="echoid-s17680" xml:space="preserve">quare plures horas linea hori-<lb/>zontalis interſecabit, &amp;</s>
  <s xml:id="echoid-s17681" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17682" xml:space="preserve">Quod idem ex eo patere poteſt, quòd quanto maior eſt altitudo poli, <lb/>tanto propius ad Verticalem circulum accedit circulus horæ 6. </s>
  <s xml:id="echoid-s17683" xml:space="preserve">cui horologiũ polare æquidiſtat, <lb/>ac proinde pluribus horis Sol Borealem faciem illuminabit, &amp;</s>
  <s xml:id="echoid-s17684" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17685" xml:space="preserve">Igitur parallelos, ſiue arcus ſigno <lb/>ruin Zodiaci in prædicto horologio polari deſcripſimus. </s>
  <s xml:id="echoid-s17686" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s17687" xml:space="preserve"/>
</p>
<div xml:id="echoid-div898" type="float" level="2" n="6">
<note position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">Quo maior eſt <lb/>poli altitudo, eò <lb/>plures horæ in <lb/>horologio pola-<lb/>r<unsure/>i Inferioti, ſeu <lb/>noctutno com-<lb/>prehenduntur, <lb/>quò aũt minor, <lb/>eò<unsure/> pauciores.</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div900" type="section" level="1" n="217">
<head xml:id="echoid-head223" xml:space="preserve">PROBLEMA 39. PROPOSITIO 39.</head>
<p>
  <s xml:id="echoid-s17688" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem polari horolo-<lb/>gio deſcribere.</s>
  <s xml:id="echoid-s17689" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17690" xml:space="preserve">QVEMADMODVM paralleli ſignorum, ita &amp; </s>
  <s xml:id="echoid-s17691" xml:space="preserve">paralleli arcuum diurnorum deſcribun-<lb/>
<anchor type="note" xlink:label="note-0276-06a" xlink:href="note-0276-06"/>
tur in horologio, cum tam hi, quàm illi Æquatori ſint æquidiſtantes; </s>
  <s xml:id="echoid-s17692" xml:space="preserve">dummodo loco parallelo-<lb/>rum per ſignorum principia deſcriptorum accipiantur paralleli arcuum diurnorum, &amp;</s>
  <s xml:id="echoid-s17693" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17694" xml:space="preserve">Paralle-<lb/>
<anchor type="note" xlink:label="note-0276-07a" xlink:href="note-0276-07"/>
los igitur arcuum diurnorum in eodem polari horologio deſcripſimus. </s>
  <s xml:id="echoid-s17695" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17696" xml:space="preserve"/>
</p>
<div xml:id="echoid-div900" type="float" level="2" n="1">
<note position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">De ſcriptio ar-<lb/>arcuum diur-<lb/>no@um in eo-<lb/>dem horologio <lb/>polaii.</note>
<note position="left" xlink:label="note-0276-07" xlink:href="note-0276-07a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div902" type="section" level="1" n="218">
<head xml:id="echoid-head224" xml:space="preserve">PROBLEMA 40. PROPOSITIO 40.</head>
<p>
  <s xml:id="echoid-s17697" xml:space="preserve">CIRCVLOS Verticales in eodem horologio polari deſcribere.</s>
  <s xml:id="echoid-s17698" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17699" xml:space="preserve">IN horologio auferatur ex linea æquinoctiali recta A B, æqualis ſtylo, cuiuſmodi eſt recta in-<lb/>ter lineam horæ 12. </s>
  <s xml:id="echoid-s17700" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17701" xml:space="preserve">lineam horæ 3. </s>
  <s xml:id="echoid-s17702" xml:space="preserve">vel 9 interiecta, vt demonſtrauimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s17703" xml:space="preserve">25. <lb/></s>
  <s xml:id="echoid-s17704" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s17705" xml:space="preserve">ad punctum B, conſtituatur angulus A B C, altitudini poli æqualis, ſecetq́ue recta <lb/>
<anchor type="note" xlink:label="note-0276-08a" xlink:href="note-0276-08"/>
B C, lineam meridianam infra lineam æquinoctialem in C, in ſuperiori horologio, in inferiori <lb/>autem ſupra lineam æquinoctialem. </s>
  <s xml:id="echoid-s17706" xml:space="preserve">Ducta deinde recta B D, quæ faciat angulum A B D, com-<lb/>plemento altitudinis poli æqualem, aut (quod idem eſt) angulum rectum cum recta B C, ita vt ſe-<lb/>cet meridianam lineam in puncto D, per quod linea horizontalis ducitur, vt propoſ. </s>
  <s xml:id="echoid-s17707" xml:space="preserve">38. </s>
  <s xml:id="echoid-s17708" xml:space="preserve">huius <lb/>libri oſtenſum eſt, ſumatur in linea meridiana ipſi B D, æqualis D E, ſiue ſupra horizontalem li-<lb/>neam, ſiue inſra. </s>
  <s xml:id="echoid-s17709" xml:space="preserve">Ex centro autem E, deſcripto circulo cuiuſcunque magnitudinis, eoq́ue diuiſo <lb/>in partes 360. </s>
  <s xml:id="echoid-s17710" xml:space="preserve">vel in pauciores, ſi horologium omnium Verticalium non eſt capax, (Nos eum ſe-<lb/>cuimus in partes 24. </s>
  <s xml:id="echoid-s17711" xml:space="preserve">vt ſingulæ grad. </s>
  <s xml:id="echoid-s17712" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17713" xml:space="preserve">complectantur) ducantur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s17714" xml:space="preserve">cen-<lb/>trum E, rectæ occultæ ſecantes lineam horizontalem in punctis, per quæ, &amp; </s>
  <s xml:id="echoid-s17715" xml:space="preserve">per punctum C, re-<lb/>ctæ emiſſæ dabunt circulos Verticales, hoc eſt, communes Verticalium, &amp; </s>
  <s xml:id="echoid-s17716" xml:space="preserve">plani horologii ſectio-<lb/>
<anchor type="note" xlink:label="note-0276-09a" xlink:href="note-0276-09"/>
nes, quarum initium ſumitur à Verticali linea, quæ per C, ipſi A B, vel lineæ horizontali paralle-<lb/>la ducitur, ita vt linea meridiana det nonageſimum Verticalem. </s>
  <s xml:id="echoid-s17717" xml:space="preserve">Quæ omnia hoc modo de-<lb/>monſtrabimus.</s>
  <s xml:id="echoid-s17718" xml:space="preserve"/>
</p>
<div xml:id="echoid-div902" type="float" level="2" n="1">
<note position="left" xlink:label="note-0276-08" xlink:href="note-0276-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0276-09" xlink:href="note-0276-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s17719" xml:space="preserve">INTELLIGATVR triangulum C B D, vnà cum recta A B, circa C D, circumduci, do-<lb/>
<anchor type="note" xlink:label="note-0276-10a" xlink:href="note-0276-10"/>
nec rectum ſit ad planum horologii, atque cum Meridiano coniungatur, punctumq́ue B, idem <lb/>fiat, quod centrum mundi. </s>
  <s xml:id="echoid-s17720" xml:space="preserve">Quoniam igitur, vt propoſitione 38. </s>
  <s xml:id="echoid-s17721" xml:space="preserve">huius libri demonſtrauimus, <lb/>Horizon per rectam B D, tranſit, ita vt B D, communis ſectio ſit Horizontis ac Meridiani; </s>
  <s xml:id="echoid-s17722" xml:space="preserve">eſtq́ue <lb/>angulus D B C, rectus, quippe qui ex altitudine poli, &amp; </s>
  <s xml:id="echoid-s17723" xml:space="preserve">complemento eiuſdem componatur, erit <lb/>recta B C, communis ſectio Verticalis proprie dicti, &amp; </s>
  <s xml:id="echoid-s17724" xml:space="preserve">Meridiani, ita vt C, ſit Zenith, ſeu vertex <lb/>capitis. </s>
  <s xml:id="echoid-s17725" xml:space="preserve">Cum enim tam Meridianus, quàm Verticalis ad Horizontem rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s17726" xml:space="preserve">eorum ſe-<lb/>ctio communis, axis nimirum Horizontis, ad eundem Horizontem perpendicularis, atque adeo
<pb o="261" file="0277" n="277" rhead="LIBER SECVNDVS."/>
&amp; </s>
  <s xml:id="echoid-s17727" xml:space="preserve">ad rectam B D, in Horizonte exiſtentem, per defin. </s>
  <s xml:id="echoid-s17728" xml:space="preserve">3. </s>
  <s xml:id="echoid-s17729" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s17730" xml:space="preserve">11. </s>
  <s xml:id="echoid-s17731" xml:space="preserve">Euclid. </s>
  <s xml:id="echoid-s17732" xml:space="preserve">perpendicularis erit in cen <lb/>tro mundi B. </s>
  <s xml:id="echoid-s17733" xml:space="preserve">Quare B C, axis erit Horizontis, hoc eſt, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s17734" xml:space="preserve">Verticalis <lb/>propriè dicti, ac proinde, &amp; </s>
  <s xml:id="echoid-s17735" xml:space="preserve">omnium aliorum Verticalium. </s>
  <s xml:id="echoid-s17736" xml:space="preserve">Quod etiam inde patere poteſt, quòd <lb/>
<anchor type="figure" xlink:label="fig-0277-01a" xlink:href="fig-0277-01"/>
<anchor type="note" xlink:label="note-0277-01a" xlink:href="note-0277-01"/>
<anchor type="note" xlink:label="note-0277-02a" xlink:href="note-0277-02"/>
angulus A B C, æqualis ſit altitudini poli, qualis nimirum eſt angulus inclinationis Æquatoris <lb/>
<anchor type="note" xlink:label="note-0277-03a" xlink:href="note-0277-03"/>
per A B, rectam tranſeuntis ad Vetticalem propriè dictum. </s>
  <s xml:id="echoid-s17737" xml:space="preserve">Iam circulus ex E, deſcriptus moueri <lb/>concipiatur circa lineam horizontalem, donec cum Horizonte, ac proinde eius centrum E, cum <lb/>centro mundi B, propter æqual@@atem rectarum D B, D E, coniungatur. </s>
  <s xml:id="echoid-s17738" xml:space="preserve">Hoc poſito, erunt rectæ <lb/>ex centro E, per puncta diuiſionum procedentes, communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s17739" xml:space="preserve">Verticaliũ <lb/>circulorum, eò quòd Horizon, &amp; </s>
  <s xml:id="echoid-s17740" xml:space="preserve">circulus ex E, deſcriptus in partes ſimiles diuidantur, per ea, quę <lb/>ad finem cap. </s>
  <s xml:id="echoid-s17741" xml:space="preserve">1 in ſphæram demonſtrauimus. </s>
  <s xml:id="echoid-s17742" xml:space="preserve">Occurruntigitur Verticales circuli plano horolo-<lb/>gii in punctis illis horizontalis lineæ, in quæ cadunt rectæ ex E, ductæ. </s>
  <s xml:id="echoid-s17743" xml:space="preserve">Quocirca cum communes <lb/>ſectiones circulorum Verticalium, &amp; </s>
  <s xml:id="echoid-s17744" xml:space="preserve">plani horologii, per propoſ. </s>
  <s xml:id="echoid-s17745" xml:space="preserve">18. </s>
  <s xml:id="echoid-s17746" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17747" xml:space="preserve">coeant in pun-<lb/>cto C, in quo nimirum communis illorum omnium ſectio, hoc eſt, axis Horizontis planum horo <lb/>logii ſecat; </s>
  <s xml:id="echoid-s17748" xml:space="preserve">erunt rectæ ex C, per puncta inuenta in linea horizontali emiſſæ, communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0277-04a" xlink:href="note-0277-04"/>
nes plani horologii, &amp; </s>
  <s xml:id="echoid-s17749" xml:space="preserve">Verticalium circulorum. </s>
  <s xml:id="echoid-s17750" xml:space="preserve">Communis autem ſectio Verticalis propriè di-<lb/>cti, ac plani horologii ducenda eſt pe@ C, parallela lineę æquinoctiali, &amp; </s>
  <s xml:id="echoid-s17751" xml:space="preserve">horizontali. </s>
  <s xml:id="echoid-s17752" xml:space="preserve">Cum enim <lb/>Verticalis propriè dictus, Horizon, Æquator, &amp; </s>
  <s xml:id="echoid-s17753" xml:space="preserve">circulus horæ 6. </s>
  <s xml:id="echoid-s17754" xml:space="preserve">cui planum horologii æquidi-<lb/>ſtat, habeant vnam communem ſectionem, erunt per ſcholium propoſ. </s>
  <s xml:id="echoid-s17755" xml:space="preserve">22. </s>
  <s xml:id="echoid-s17756" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s17757" xml:space="preserve">com <lb/>munes ſectiones priorum trium circulorum factæ à plano horologii, nempe linea Verticalis, hori <lb/>zontalis, &amp; </s>
  <s xml:id="echoid-s17758" xml:space="preserve">æquinoctialis, inter ſeſe parallelæ.</s>
  <s xml:id="echoid-s17759" xml:space="preserve"/>
</p>
<div xml:id="echoid-div903" type="float" level="2" n="2">
<note position="left" xlink:label="note-0276-10" xlink:href="note-0276-10a" xml:space="preserve">Demonſtratio <lb/>deſcriprionis <lb/>citculorũ Ver-<lb/>ticalium in ho-<lb/>rologio polati.</note>
  <figure xlink:label="fig-0277-01" xlink:href="fig-0277-01a">
    <image file="0277-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0277-01"/>
  </figure>
<note position="left" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s17760" xml:space="preserve">CAETERVM punctum C, inuenietur etiam hoc modo. </s>
  <s xml:id="echoid-s17761" xml:space="preserve">In prima figura propoſ. </s>
  <s xml:id="echoid-s17762" xml:space="preserve">26. </s>
  <s xml:id="echoid-s17763" xml:space="preserve">huius <lb/>lib. </s>
  <s xml:id="echoid-s17764" xml:space="preserve">notentur puncta n, &amp; </s>
  <s xml:id="echoid-s17765" xml:space="preserve">o, in quibus diameter Verticalis A C, parallelas L M, L M, ſecat, &amp; </s>
  <s xml:id="echoid-s17766" xml:space="preserve"><lb/>recta k n, vel K o, transferatur in meridianam lineam, in horologio quidem ſuperiori infra locum <lb/>ſtyli vſque ad C, in inferiori verò ſupra locum ſtyli, initio ſem per facto à loco ſtyli A. </s>
  <s xml:id="echoid-s17767" xml:space="preserve">Nam per C, <lb/>
<anchor type="note" xlink:label="note-0277-05a" xlink:href="note-0277-05"/>
ducenda eſt Verticalis linea proprie dicta parallela lineæ æquinoctiali, vt prius, quia in punctis n, <lb/>
<anchor type="note" xlink:label="note-0277-06a" xlink:href="note-0277-06"/>
&amp; </s>
  <s xml:id="echoid-s17768" xml:space="preserve">o, Verticalis cireulus propriè dictus, qui ducitur per A C, occurrit plano vtriuſque horologii <lb/>
<anchor type="note" xlink:label="note-0277-07a" xlink:href="note-0277-07"/>
per L M, ducto in punctis n, &amp; </s>
  <s xml:id="echoid-s17769" xml:space="preserve">o, infra quidem locum ſtyli in ſuperiori horologio, ſupra verò in <lb/>
<anchor type="note" xlink:label="note-0277-08a" xlink:href="note-0277-08"/>
inferiori, &amp;</s>
  <s xml:id="echoid-s17770" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17771" xml:space="preserve">Et quoniam recta K n, rectæ K o, æqualis eſt, (cum enim in triangulis E K n, E K o, <lb/>anguli ad K, recti ſint, &amp; </s>
  <s xml:id="echoid-s17772" xml:space="preserve">anguli ad verticem E, æquales; </s>
  <s xml:id="echoid-s17773" xml:space="preserve">Item &amp; </s>
  <s xml:id="echoid-s17774" xml:space="preserve">latera E K, E K, æqualia, erunt &amp; </s>
  <s xml:id="echoid-s17775" xml:space="preserve"><lb/>latera K n, K o, æqualia) propterea diximus eandem K n, vel k o, in vtroque horologio transfe-<lb/>rendam eſſe in lineam meridianam infra, vel ſupra locum ſtyli.</s>
  <s xml:id="echoid-s17776" xml:space="preserve"/>
</p>
<div xml:id="echoid-div904" type="float" level="2" n="3">
<note position="left" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0277-06" xlink:href="note-0277-06a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0277-07" xlink:href="note-0277-07a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0277-08" xlink:href="note-0277-08a" xml:space="preserve">Por@o ſuperio <lb/>ris horologii ab <lb/>ſciſ@a à linea ho <lb/>rizontali, ſi in-<lb/>uertanrur eius <lb/>par@es in facie <lb/>horologii cppo <lb/>fita, @a vt ho@i-<lb/>zo@talis linea <lb/>occupet ſupre-<lb/>mum locũ, da-<lb/>bit Verticales <lb/>circulos in infe <lb/>riori hor<unsure/>c<unsure/>logio.</note>
</div>
<p>
  <s xml:id="echoid-s17777" xml:space="preserve">QVOD ſi portio abſciſſa à linea horizontali ponatur in facie inferiori plani, ita vt horizon-<lb/>talis linea ſuperiorem occuper locum, &amp; </s>
  <s xml:id="echoid-s17778" xml:space="preserve">quæ dextra pars tune eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s17779" xml:space="preserve">contra, habebi-<lb/>mus eoſdem circulos Verticales in horologio inferiori, vt demonſtrauimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s17780" xml:space="preserve">14. <lb/></s>
  <s xml:id="echoid-s17781" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s17782" xml:space="preserve">Immo verò hic non eſt neceſſarium, vt pars dextra fiat ſiniſtra, quia ad vtramque par-
<pb o="262" file="0278" n="278" rhead="GNOMONICES"/>
tem ipſius lineæ meridianæ eundem ſitum habent, eoſdemq́ue numeros lineæ Verticales, vt pa-<lb/>tet. </s>
  <s xml:id="echoid-s17783" xml:space="preserve">Circulos igitur Verticales in eodem horologio polari deſcripſimus. </s>
  <s xml:id="echoid-s17784" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17785" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div906" type="section" level="1" n="219">
<head xml:id="echoid-head225" xml:space="preserve">PROBLEMA 41. PROPOSITIO 41.</head>
<p>
  <s xml:id="echoid-s17786" xml:space="preserve">PARALLELOS Horizontis in eodem polari horologio <lb/>deſcribere.</s>
  <s xml:id="echoid-s17787" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17788" xml:space="preserve">SIT Analemma A B C, in quo Horizon B C; </s>
  <s xml:id="echoid-s17789" xml:space="preserve">Verticalis A D; </s>
  <s xml:id="echoid-s17790" xml:space="preserve">axis mundi, vel communis ſe-<lb/>
<anchor type="note" xlink:label="note-0278-01a" xlink:href="note-0278-01"/>
<anchor type="note" xlink:label="note-0278-02a" xlink:href="note-0278-02"/>
ctio circuli horæ 6. </s>
  <s xml:id="echoid-s17791" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17792" xml:space="preserve">Meridiani E F; </s>
  <s xml:id="echoid-s17793" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17794" xml:space="preserve">Aequator G H, Diuiſo autem ſemicirculo B A C, in 180. <lb/></s>
  <s xml:id="echoid-s17795" xml:space="preserve">partes æquales, vt ſingulæ ſingulos contineant gradus, vel in pauciores, habita ratione magnitu-<lb/>dinis horologii, (Nos eum partiti <lb/>ſumus in partes 12. </s>
  <s xml:id="echoid-s17796" xml:space="preserve">vt quælibet <lb/>
<anchor type="figure" xlink:label="fig-0278-01a" xlink:href="fig-0278-01"/>
grad. </s>
  <s xml:id="echoid-s17797" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17798" xml:space="preserve">comprehendat) iungantur <lb/>bina puncta à recta B C, vel à pun-<lb/>cto A, æqualiter remota, lineis re-<lb/>ctis, quæ communes erunt ſectio-<lb/>nes Meridiani, &amp; </s>
  <s xml:id="echoid-s17799" xml:space="preserve">parallelorum Ho <lb/>rizontis, quos vocant Almucanta-<lb/>
<anchor type="note" xlink:label="note-0278-03a" xlink:href="note-0278-03"/>
rath. </s>
  <s xml:id="echoid-s17800" xml:space="preserve">Deinde ex punctis diuiſionũ <lb/>per centrum D, rectæ ducantur li-<lb/>neæ, vt conſtituantur triangula per <lb/>axem in conis, quorum baſes ſunt <lb/>paralleli Horizontis tam infra Ho-<lb/>rizontem, quàm ſupra, vertex autẽ <lb/>communis centrum mundi D. </s>
  <s xml:id="echoid-s17801" xml:space="preserve">Me-<lb/>ridianus enim A B C, per A D, axẽ <lb/>dictorũ conorũ ductus facit trian-<lb/>gúla per axem, ex propoſ. </s>
  <s xml:id="echoid-s17802" xml:space="preserve">3. </s>
  <s xml:id="echoid-s17803" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s17804" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s17805" xml:space="preserve">
<anchor type="note" xlink:label="note-0278-04a" xlink:href="note-0278-04"/>
Apóllonij. </s>
  <s xml:id="echoid-s17806" xml:space="preserve">In Aequatore quoque <lb/>G H, qui inſtar Verticalis eſt reſpe-<lb/>ctu circuli horæ 6. </s>
  <s xml:id="echoid-s17807" xml:space="preserve">E F, tanquam <lb/>Horizontis cuiuſdam, cui horolo-<lb/>gium æquidiſtat, ſumatur ex vtra-<lb/>que parte recta D I, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s17808" xml:space="preserve">per I, ipſi E F, parallela agatur R Q. </s>
  <s xml:id="echoid-s17809" xml:space="preserve">Erit hæc infra quidem <lb/>centrum D, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s17810" xml:space="preserve">plani horologii ſuperioris ad Zenith A, ſpectantis, il-<lb/>la verò ſupra centrum D, communis ſectio eiuſdem Meridiani, &amp; </s>
  <s xml:id="echoid-s17811" xml:space="preserve">plani horologii inferioris ad Na <lb/>dir pertinentis. </s>
  <s xml:id="echoid-s17812" xml:space="preserve">Secabit autem recta R Q, latera triangulorum per axem in punctis K, L, M, <lb/>N, O, &amp;</s>
  <s xml:id="echoid-s17813" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17814" xml:space="preserve">eruntq́ue diametri conicarum ſectionum K Q, L Q, M Q, N Q, O Q. </s>
  <s xml:id="echoid-s17815" xml:space="preserve">Itaque ſi pun <lb/>
<anchor type="note" xlink:label="note-0278-05a" xlink:href="note-0278-05"/>
cta K, L, M, N, (omittimus enim hic punctum O, cum translatum cadat extra tropicos) transfe-<lb/>rantur in lineam meridianam ſuperioris horologii infra ho@izontalem lineam, initio facto in hac <lb/>figura à puncto T, Horizontis, in horologio autem à puncto D, lineæ horizontalis; </s>
  <s xml:id="echoid-s17816" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17817" xml:space="preserve">per propoſ. <lb/></s>
  <s xml:id="echoid-s17818" xml:space="preserve">S. </s>
  <s xml:id="echoid-s17819" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s17820" xml:space="preserve">circa lineam meridianam dictæ conicæ ſectiones deſcribantur tranſeuntes per <lb/>puncta K, L, M, N, (erunt autem hæ conicæ ſectiones partim hyperbolæ, partim Ellipſes, vt con-<lb/>ſtat ex propoſ. </s>
  <s xml:id="echoid-s17821" xml:space="preserve">6. </s>
  <s xml:id="echoid-s17822" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17823" xml:space="preserve">7. </s>
  <s xml:id="echoid-s17824" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s17825" xml:space="preserve">Parallelus autem Horizontis 42. </s>
  <s xml:id="echoid-s17826" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s17827" xml:space="preserve">erit parabola, ex <lb/>propoſ. </s>
  <s xml:id="echoid-s17828" xml:space="preserve">5. </s>
  <s xml:id="echoid-s17829" xml:space="preserve">eiuſdem ſuperioris lib. </s>
  <s xml:id="echoid-s17830" xml:space="preserve">cum illum circulus horæ 6. </s>
  <s xml:id="echoid-s17831" xml:space="preserve">contingat in polo E,) &amp; </s>
  <s xml:id="echoid-s17832" xml:space="preserve">à linea hori-<lb/>zontali eò magis ſemper recedentes, quò longius fuerint ex vtraque parte lineæ meridianæ pro-<lb/>ductæ, deſcripti erunt paralleli Horizontis. </s>
  <s xml:id="echoid-s17833" xml:space="preserve">In horologio inferiori transferenda eſt recta T S, in <lb/>lineam meridianam à puncto D, infra horizontalem lineam, &amp;</s>
  <s xml:id="echoid-s17834" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17835" xml:space="preserve">Nam S Q, diameter eſt conicæ <lb/>
<anchor type="note" xlink:label="note-0278-06a" xlink:href="note-0278-06"/>
ſectionis paralleli Horizontis grad. </s>
  <s xml:id="echoid-s17836" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17837" xml:space="preserve">ſupra Horizontem in horologio inferiori. </s>
  <s xml:id="echoid-s17838" xml:space="preserve">Eodemq́ue mo-<lb/>do reliqua puncta infra S, verſus Q, transferenda eſſent, ſi latera triangulorum per axem rectam <lb/>T Q, ſecarent. </s>
  <s xml:id="echoid-s17839" xml:space="preserve">In figura præcedentis propoſ. </s>
  <s xml:id="echoid-s17840" xml:space="preserve">deſcripſimus parallelum Horizontis grad. </s>
  <s xml:id="echoid-s17841" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17842" xml:space="preserve">in <lb/>portione, quam linea horizontalis amputat, quia illa locum inferioris horologii ſupplet, vt in ea-<lb/>dem propoſ. </s>
  <s xml:id="echoid-s17843" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s17844" xml:space="preserve">Eſt igitur, vt pater, recta E F, veluti Horizon, &amp; </s>
  <s xml:id="echoid-s17845" xml:space="preserve">G H, tanquam Verticalis; <lb/></s>
  <s xml:id="echoid-s17846" xml:space="preserve">B C, quaſi Aequator quidam, paralleli verò Horizontis inſtar parallelorum Aequatoris noui B C. </s>
  <s xml:id="echoid-s17847" xml:space="preserve"><lb/>Quo poſito, erunt Verticales circuli inſtar horariorum circulorum, qui omnes meridianam lineã <lb/>horologii ſecant in puncto V, vbi eandem interſecat A D, axis Horizontis, quem nunc munere <lb/>Æquatoris cuiuſdam noui fungi diximus: </s>
  <s xml:id="echoid-s17848" xml:space="preserve">Ita vt ſi hæc permutatio circulorum bene cõſideretur, <lb/>deſcriptio hæc parallelorum Horizontis à deſcriptione parallelorum Aequatoris in horizontali <lb/>horologio non deſcrepet.</s>
  <s xml:id="echoid-s17849" xml:space="preserve"/>
</p>
<div xml:id="echoid-div906" type="float" level="2" n="1">
<note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis in eodẽ <lb/>polari horolo <lb/>gio.</note>
<note position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a">
    <image file="0278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0278-01"/>
  </figure>
<note position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0278-06" xlink:href="note-0278-06a" xml:space="preserve">50</note>
</div>
<pb o="263" file="0279" n="279" rhead="LIBER SECVNDVS."/>
<p>
  <s xml:id="echoid-s17850" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s17851" xml:space="preserve">Deſcripto quadrante A B C, cuiuſuis magnitudinis, eoq́ue diuiſo in grad. </s>
  <s xml:id="echoid-s17852" xml:space="preserve">90. <lb/></s>
  <s xml:id="echoid-s17853" xml:space="preserve">
<anchor type="note" xlink:label="note-0279-01a" xlink:href="note-0279-01"/>
vel in pauciores partes pro numero parallelorum Horizontis delineandorum, ducantu<unsure/>r ex A, cen-<lb/>tro per puncta diuiſionum lineæ rectæ, quæ reſpondebunt radiis parallelorum Horizontis in qua-<lb/>drante D C 90. </s>
  <s xml:id="echoid-s17854" xml:space="preserve">figuræ præcedentis contenti, initio ſumpto à recta A B, vt figura indicat. </s>
  <s xml:id="echoid-s17855" xml:space="preserve">Deinde <lb/>ex figura antecedentis propoſ. </s>
  <s xml:id="echoid-s17856" xml:space="preserve">rectæ B C, ſumatur æqualis A D, in linea A C, huius figuræ; </s>
  <s xml:id="echoid-s17857" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17858" xml:space="preserve">re-<lb/>ctæ D B, vel D E, in recta A B, acci-<lb/>piatur æqualis A E, ducaturq́ue recta <lb/>
<anchor type="figure" xlink:label="fig-0279-01a" xlink:href="fig-0279-01"/>
D E. </s>
  <s xml:id="echoid-s17859" xml:space="preserve">Erit triangulum hoc A D E, <lb/>æquale omnino triangulo C B D, fi-<lb/>
<anchor type="note" xlink:label="note-0279-02a" xlink:href="note-0279-02"/>
guræ præcedentis propoſ. </s>
  <s xml:id="echoid-s17860" xml:space="preserve">cum angu <lb/>
<anchor type="note" xlink:label="note-0279-03a" xlink:href="note-0279-03"/>
li ad A, &amp; </s>
  <s xml:id="echoid-s17861" xml:space="preserve">B, recti ſint, continean-<lb/>turq́; </s>
  <s xml:id="echoid-s17862" xml:space="preserve">lateribus æqualibus, ex conſtru <lb/>ctione; </s>
  <s xml:id="echoid-s17863" xml:space="preserve">ita vt D E, meridianæ lineæ <lb/>C D, ſit æqualis. </s>
  <s xml:id="echoid-s17864" xml:space="preserve">Idẽ quoque triangu-<lb/>lum A D E, æquale erit triangulo <lb/>D V T, proximè antecedentis figu-<lb/>ræ, cum hoc æquale ſit prædicto triã <lb/>gulo C B D. </s>
  <s xml:id="echoid-s17865" xml:space="preserve">Cum enim angulus <lb/>I D V, angulo A B C, ſit æqualis, cũ <lb/>vterque ſit altitudinis poli, &amp; </s>
  <s xml:id="echoid-s17866" xml:space="preserve">angu-<lb/>
<anchor type="note" xlink:label="note-0279-04a" xlink:href="note-0279-04"/>
lus rectus D I V, recto angulo B A C, <lb/>ſintq́ue latera D I, A B, inter ſe æqua <lb/>lia, quòd vtrumque ſumptũ ſit æqua-<lb/>le ſtylo; </s>
  <s xml:id="echoid-s17867" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s17868" xml:space="preserve">latera D V, V I, late-<lb/>
<anchor type="note" xlink:label="note-0279-05a" xlink:href="note-0279-05"/>
ribus B A, C A, æqualia. </s>
  <s xml:id="echoid-s17869" xml:space="preserve">Eademq́ue <lb/>ratione latera D T, T I, lateribus <lb/>B D, D A, æqualia erũt, &amp;</s>
  <s xml:id="echoid-s17870" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17871" xml:space="preserve">Poſt hęc <lb/>ex figura præcedentis propoſ. </s>
  <s xml:id="echoid-s17872" xml:space="preserve">inter-<lb/>ualla omnia inter centrum E, &amp; </s>
  <s xml:id="echoid-s17873" xml:space="preserve">pun-<lb/>cta, in quibus Verticales lineæ horizontalem lineam interſecant, in hanc figuram transferantur ex <lb/>
<anchor type="note" xlink:label="note-0279-06a" xlink:href="note-0279-06"/>
A, in rectam A B, notatis punctis in recta A B, aſcriptisq́ue numeris linearum Verticalium, vt 90. <lb/></s>
  <s xml:id="echoid-s17874" xml:space="preserve">iuxta punctum E, &amp; </s>
  <s xml:id="echoid-s17875" xml:space="preserve">75. </s>
  <s xml:id="echoid-s17876" xml:space="preserve">prope proximum, &amp;</s>
  <s xml:id="echoid-s17877" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17878" xml:space="preserve">Poſtremo ex D, per puncta in A B, ſignata educan-<lb/>tur rectæ lineæ. </s>
  <s xml:id="echoid-s17879" xml:space="preserve">Pro Verticali autem linea proprie dicta, à qua principium aliarum ſumitur, du-<lb/>cenda eſt per D, ipſi A B, parallela D F, &amp; </s>
  <s xml:id="echoid-s17880" xml:space="preserve">in alteram partem transferendæ ſunt quoque lineæ iam <lb/>ductæ ex puncto D, per puncta rectæ A B, vt habeantur lineæ Verticales trans, &amp; </s>
  <s xml:id="echoid-s17881" xml:space="preserve">citra lineam Ver <lb/>ticalem propriè dictam, quemadmodum in horologio horizontali factum eſt de lineis ante 6. </s>
  <s xml:id="echoid-s17882" xml:space="preserve">ho-<lb/>ram, &amp; </s>
  <s xml:id="echoid-s17883" xml:space="preserve">poſt, in propoſ. </s>
  <s xml:id="echoid-s17884" xml:space="preserve">2. </s>
  <s xml:id="echoid-s17885" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s17886" xml:space="preserve">Nam lineæ ex D, per puncta rectæ A B, ductæ, ſunt Vertica-<lb/>les lineæ vltra Verticalem lineam propriè dictam, in quas videlicet vmbra ſtyli proiicitur, Sole <lb/>exiſtente in Verticalibus auſtralibus; </s>
  <s xml:id="echoid-s17887" xml:space="preserve">aliæ verò, Verticales lineæ citra Verticalem lineam pro-<lb/>prie dictam, &amp;</s>
  <s xml:id="echoid-s17888" xml:space="preserve">c.</s>
  <s xml:id="echoid-s17889" xml:space="preserve"/>
</p>
<div xml:id="echoid-div907" type="float" level="2" n="2">
<note position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">Alia deſctiptio <lb/>parallelorum <lb/>Horizon@is in <lb/>c<unsure/>odem horolo-<lb/>gio polati.</note>
  <figure xlink:label="fig-0279-01" xlink:href="fig-0279-01a">
    <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0279-01"/>
  </figure>
<note position="right" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0279-03" xlink:href="note-0279-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0279-04" xlink:href="note-0279-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0279-05" xlink:href="note-0279-05a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0279-06" xlink:href="note-0279-06a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s17890" xml:space="preserve">IAM verò ſi interualla ſingula rectarum ex D, prodeuntium inter D, &amp; </s>
  <s xml:id="echoid-s17891" xml:space="preserve">radium v. </s>
  <s xml:id="echoid-s17892" xml:space="preserve">g. </s>
  <s xml:id="echoid-s17893" xml:space="preserve">paralleli <lb/>Horizontis grad. </s>
  <s xml:id="echoid-s17894" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17895" xml:space="preserve">comprehenſa transferantur ex puncto C, figuræ præcedentis propoſ. </s>
  <s xml:id="echoid-s17896" xml:space="preserve">in lineas <lb/>binas Verticales æqualiter à meridiana linea diſtantes, reſpondentesq́ue numeris in recta A B, hu-<lb/>ius figuræ ſignatis, notando puncta in ipſis lineis Verticalibus, (ita tamen, vt interualla rectarum <lb/>ex D, in A B, cadentium tranſportentur ex Zenith C, in lineas Verticales horologii ſupra lineam <lb/>Verticalem propriè dictã, interualla vero rectarum ex D, cadentium ad dextram rectæ D F, tranſ-<lb/>ferantur in Verticales lineas infra lineam propriè dictam Verticalem) &amp; </s>
  <s xml:id="echoid-s17897" xml:space="preserve">hæc puncta appoſitè<unsure/>, &amp; </s>
  <s xml:id="echoid-s17898" xml:space="preserve"><lb/>concinne coniungantur linea quadam flexa, deſcriptus erit parallelus Horizontis grad. </s>
  <s xml:id="echoid-s17899" xml:space="preserve">15. </s>
  <s xml:id="echoid-s17900" xml:space="preserve">Eo-<lb/>demq́ue modo reliqui paralleli Horizontis deſcribentur. </s>
  <s xml:id="echoid-s17901" xml:space="preserve">Demonſtratio huius rei non differt ab <lb/>
<anchor type="note" xlink:label="note-0279-08a" xlink:href="note-0279-08"/>
ea, quam in horologio horizontali tradidimus in ſecundo modo deſcribendorum arcuum ſigno-<lb/>
<anchor type="note" xlink:label="note-0279-09a" xlink:href="note-0279-09"/>
rum. </s>
  <s xml:id="echoid-s17902" xml:space="preserve">Nam hic linea horizontalis eſt veluti Aequatoris linea, &amp; </s>
  <s xml:id="echoid-s17903" xml:space="preserve">lineæ Verticales tanquam lineæ <lb/>horariæ, quarum centrum eſt Zenith, nempe punctum C, &amp;</s>
  <s xml:id="echoid-s17904" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17905" xml:space="preserve">vt in præcedenti Analemmate di-<lb/>ximus. </s>
  <s xml:id="echoid-s17906" xml:space="preserve">Itaque linea A B, huius figuræ reſpondebit radio Aequatoris D C, poſtremæ figuræ pro-<lb/>poſ. </s>
  <s xml:id="echoid-s17907" xml:space="preserve">2. </s>
  <s xml:id="echoid-s17908" xml:space="preserve">huius libri, in qua radii ſignorum deſcripti ſunt, &amp; </s>
  <s xml:id="echoid-s17909" xml:space="preserve">rectæ ex A, ductæ radiis aliorum ſigno-<lb/>rum ex D, emiſſis in dicta illa figura; </s>
  <s xml:id="echoid-s17910" xml:space="preserve">recta autem A D, axi D H, &amp; </s>
  <s xml:id="echoid-s17911" xml:space="preserve">punctum D, puncto H; </s>
  <s xml:id="echoid-s17912" xml:space="preserve">lineæ <lb/>denique Verticales ex D, cadentes lineis horariis ex H, productis. </s>
  <s xml:id="echoid-s17913" xml:space="preserve">Idem fiet, ſi int<unsure/>erualla rectarũ <lb/>ex D, progredientium inter rectam A B, quæ eſt, (vt diximus) inſtar Æquatoris, &amp; </s>
  <s xml:id="echoid-s17914" xml:space="preserve">rectas ex A, <lb/>emiſſas transferantur in reſpondentes lineas Verticales à linea horizontali horologii, &amp;</s>
  <s xml:id="echoid-s17915" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17916" xml:space="preserve">quemad <lb/>modum in horizontali horologio interualla inter radium Aequatoris, &amp; </s>
  <s xml:id="echoid-s17917" xml:space="preserve">radios ſignorum transla <lb/>ta ſunt, vt arcus ſignorum deſcriberentur. </s>
  <s xml:id="echoid-s17918" xml:space="preserve">Pro horologio polari inferiori transferendi ſunt in hac <lb/>figura radii parallelorum Horizontis ex A, educti ad ſiniſtrã partem rectæ A B, ita vt quemadmo-
<pb o="264" file="0280" n="280" rhead="GNOMONICES"/>
dum in figura radiorum Zodiaci propoſ. </s>
  <s xml:id="echoid-s17919" xml:space="preserve">2. </s>
  <s xml:id="echoid-s17920" xml:space="preserve">huius libri radii ſignorum ad dextram radii<unsure/> Æqua-<lb/>toris pertinent ad ſigna auſtralia infra æquinoctialem lineam deſcribenda, &amp; </s>
  <s xml:id="echoid-s17921" xml:space="preserve">radii ad ſiniſtram ad <lb/>ſigna borealia ſupra lineam æquinoctialem deſcribenda, ita etiam hic radii parallelorum Hori-<lb/>zontis ex A, emiſſi ad dextram rectæ A B, quæ eſt inſtar noui cuiuſdam radii Æquatoris, vt dictum <lb/>eſt, pertineant ad parallelos Horizontis infra lineam horizontalem, quæ eſt velut noua quædam <lb/>linea æquinoctialis, deſcribendos, tanquam ſigna auſtralia: </s>
  <s xml:id="echoid-s17922" xml:space="preserve">radii verò educti ad ſiniſtram rectæ <lb/>A B, pertineant ad parallelos Horizontis ſupra lineam horizontalem horologii deſcribendos, tan-<lb/>quam ſigna borealia. </s>
  <s xml:id="echoid-s17923" xml:space="preserve">Vnde cum portio horologii ſupra lineam horizonralem æqualis ſit inferio-<lb/>ri horolog@o, rectè transferuntur in eam radii parallelorum Horizontis ex A, educti ad ſiniſtram <lb/>partem rectæ A B, &amp;</s>
  <s xml:id="echoid-s17924" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17925" xml:space="preserve">quæ omnia in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s17926" xml:space="preserve">apparent.</s>
  <s xml:id="echoid-s17927" xml:space="preserve"/>
</p>
<div xml:id="echoid-div908" type="float" level="2" n="3">
<note position="right" xlink:label="note-0279-08" xlink:href="note-0279-08a" xml:space="preserve">Demonſtratio <lb/>poſterioris hu-<lb/>iuſce deſcriptio <lb/>nis parallelorũ <lb/>Horizontis.</note>
<note position="left" xlink:label="note-0279-09" xlink:href="note-0279-09a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s17928" xml:space="preserve">SED facilius deſcribentur in inferiori horologio ſupra lineam horizontalem paralleli Ho<unsure/>ri-<lb/>
<anchor type="note" xlink:label="note-0280-02a" xlink:href="note-0280-02"/>
zontis ex eorum oppoſitis in ſuperiori horologio deſcriptis, ſi ſecundum doctrinam, quam prope <lb/>finem propoſ. </s>
  <s xml:id="echoid-s17929" xml:space="preserve">2. </s>
  <s xml:id="echoid-s17930" xml:space="preserve">huius lib tradidimus, reperiamus prius diametros tranſuerſas oppoſitarũ ſectio-<lb/>num, earumq́ue centra, &amp;</s>
  <s xml:id="echoid-s17931" xml:space="preserve">c. </s>
  <s xml:id="echoid-s17932" xml:space="preserve">In poſteriori figura diametri tranſuerſæ ſunt portiones rectæ D E, in-<lb/>terceptę inter radios parallelorum Horizontis oppoſitorum ex A, eductos, æqualiterq́ue à recta <lb/>A B, diſtantes. </s>
  <s xml:id="echoid-s17933" xml:space="preserve">Parallelos igitur Horizontis in eodem polari horologio deſignauimus. </s>
  <s xml:id="echoid-s17934" xml:space="preserve">Quod <lb/>erat faciendum.</s>
  <s xml:id="echoid-s17935" xml:space="preserve"/>
</p>
<div xml:id="echoid-div909" type="float" level="2" n="4">
<note position="left" xlink:label="note-0280-02" xlink:href="note-0280-02a" xml:space="preserve">Parælleli Hori-<lb/>zoncis ſupra li-<lb/>neam horizon-<lb/>@alem deſcribũ <lb/>t<unsure/>ur ex eorũ op-<lb/>po<unsure/>ſitis inſca ho <lb/>@iz@ntalem li-<lb/>neã @eſcr@p@is.</note>
</div>
</div>
<div xml:id="echoid-div911" type="section" level="1" n="220">
<head xml:id="echoid-head226" xml:space="preserve">PROBLEMA 42. PROPOSITIO 42.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s17936" xml:space="preserve">MERIDIANOS, hoc eſt, circulos longitudinum ciuitatum in <lb/>eodem polari horologio deſcribere.</s>
  <s xml:id="echoid-s17937" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17938" xml:space="preserve">DESCRIBENTVR circuli Meridiani in horologio polari, non ſecus ac horæ à meri-<lb/>die, vel media nocte, quemadmodum &amp; </s>
  <s xml:id="echoid-s17939" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s17940" xml:space="preserve">6. </s>
  <s xml:id="echoid-s17941" xml:space="preserve">huius libri tradidimus, dummodo circulus <lb/>F G H I, cuius beneficio lineas horarias duximus, diuiſionis principium habeat à Meridiano in-<lb/>
<anchor type="figure" xlink:label="fig-0280-01a" xlink:href="fig-0280-01"/>
<anchor type="note" xlink:label="note-0280-04a" xlink:href="note-0280-04"/>
<anchor type="note" xlink:label="note-0280-05a" xlink:href="note-0280-05"/>
ſularum Fortunatarum, qui habetur, ſi loci longitudo numeretur à Meridiano loci, nempe à pun <lb/>cto F, verſus G, partes occidentales, vt res ipſa exigit. </s>
  <s xml:id="echoid-s17942" xml:space="preserve">Id quod facile intelligi poteſt, ſi circulus <lb/>F G H I, concipiatur circumuolui circa lineam æquinoctialem, vſque dum cum Aequatore con-<lb/>iunctus ſit, &amp;</s>
  <s xml:id="echoid-s17943" xml:space="preserve">c.</s>
  <s xml:id="echoid-s17944" xml:space="preserve"/>
</p>
<div xml:id="echoid-div911" type="float" level="2" n="1">
  <figure xlink:label="fig-0280-01" xlink:href="fig-0280-01a">
    <image file="0280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0280-01"/>
  </figure>
<note position="left" xlink:label="note-0280-04" xlink:href="note-0280-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0280-05" xlink:href="note-0280-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s17945" xml:space="preserve">PRO Meridianis autem inferioris horologii, numeranda eſt longitudo loci à puncto H, ver-<lb/>ſus G, vt Meridianus inſularum Fortunatarum reperiatur. </s>
  <s xml:id="echoid-s17946" xml:space="preserve">Nam ſi horologium inferius poſitum <lb/>intelligatur in proprio ſitu, ita vt linea horizontalis ſupremum teneat locum, &amp; </s>
  <s xml:id="echoid-s17947" xml:space="preserve">circulus F G H I, <lb/>circa æquinoctialem lineam moueatur, donec cum Aequatore ſit coniunctus, &amp; </s>
  <s xml:id="echoid-s17948" xml:space="preserve">centrum E, cum <lb/>centro mundi; </s>
  <s xml:id="echoid-s17949" xml:space="preserve">ſecabit Meridianus loci circulum dictum ſupra Horizontem in puncto H, infra <lb/>verò in F. </s>
  <s xml:id="echoid-s17950" xml:space="preserve">Itaque ab H, verſus G, ſunt partes occidentales, orientales verò verſus I. </s>
  <s xml:id="echoid-s17951" xml:space="preserve">Reliqua fiant <lb/>vt prius. </s>
  <s xml:id="echoid-s17952" xml:space="preserve">In exemplo vides Meridianos grad. </s>
  <s xml:id="echoid-s17953" xml:space="preserve">140. </s>
  <s xml:id="echoid-s17954" xml:space="preserve">150. </s>
  <s xml:id="echoid-s17955" xml:space="preserve">ex vna parte, &amp; </s>
  <s xml:id="echoid-s17956" xml:space="preserve">285. </s>
  <s xml:id="echoid-s17957" xml:space="preserve">295. </s>
  <s xml:id="echoid-s17958" xml:space="preserve">ex altera in ho-<lb/>
<anchor type="note" xlink:label="note-0280-07a" xlink:href="note-0280-07"/>
rologio inferiori, quod nobis præbet portio à linea horizontali abſciſla.</s>
  <s xml:id="echoid-s17959" xml:space="preserve"/>
</p>
<div xml:id="echoid-div912" type="float" level="2" n="2">
<note position="left" xlink:label="note-0280-07" xlink:href="note-0280-07a" xml:space="preserve">Meridiani vi-<lb/>@ra lineã hori-<lb/>z@alẽ productę <lb/>efficiunt hot<unsure/>o-<lb/>logiũ inferius <lb/>cum Merid@a-<lb/>nis.</note>
</div>
<p>
  <s xml:id="echoid-s17960" xml:space="preserve">EOSDEM tamen Meridianos inferioris horologii facilius obtinebimus, ſi horologii ſupe-<lb/>rioris Meridianos vltra lineam horizontalem producamus, eiſdemq́ue aſcribamus numeros, qui <lb/>componuntur ex additione grad. </s>
  <s xml:id="echoid-s17961" xml:space="preserve">180. </s>
  <s xml:id="echoid-s17962" xml:space="preserve">ad numeros Meridianorum ſuperioris horologii, abiectis
<pb o="265" file="0281" n="281" rhead="LIBER SECVNDVS."/>
tamen grad. </s>
  <s xml:id="echoid-s17963" xml:space="preserve">360. </s>
  <s xml:id="echoid-s17964" xml:space="preserve">ſi íumma maior fuerit, quàm grad. </s>
  <s xml:id="echoid-s17965" xml:space="preserve">360. </s>
  <s xml:id="echoid-s17966" xml:space="preserve">id eſt, numeros, qui in circulo ex E, de-<lb/>ſcripto per diametrum opponuntur numeris in ſuperiori horologio ſcriptis. </s>
  <s xml:id="echoid-s17967" xml:space="preserve">Nam portio ablata <lb/>ab horizontali linea dabit in facie oppoſita, nempe inferiori, Meridiatios circulos, ſi omnes eius <lb/>partes inuertantur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s17968" xml:space="preserve">14. </s>
  <s xml:id="echoid-s17969" xml:space="preserve">huius libri demonſtratum eſt. </s>
  <s xml:id="echoid-s17970" xml:space="preserve">Mutantur autem nu-<lb/>meri inferioris horologii in numeros ſemicirculorum, qui ſemicirculis ſuperioris horologii op-<lb/>ponuntur, quia Sol in alio ſemicirculo exiſtit, cum vmbra in inferius horologium cadit, &amp; </s>
  <s xml:id="echoid-s17971" xml:space="preserve">in alio, <lb/>cum in ſuperius, vt propoſ. </s>
  <s xml:id="echoid-s17972" xml:space="preserve">38. </s>
  <s xml:id="echoid-s17973" xml:space="preserve">huius libri docuimus. </s>
  <s xml:id="echoid-s17974" xml:space="preserve">Itaque Meridianos, hoc eſt, circulos longi-<lb/>tudinum ciuitatum, in eodem polari horologio deſcripſimus. </s>
  <s xml:id="echoid-s17975" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17976" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div914" type="section" level="1" n="221">
<head xml:id="echoid-head227" xml:space="preserve">PROBLEMA 43. PROPOSITIO 43.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s17977" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in eo-<lb/>dem horologio polari delineare.</s>
  <s xml:id="echoid-s17978" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17979" xml:space="preserve">ACCIPIANTVR paralleli per vertices ciuitatum intra tropicos conſtitutarum (Nam ad <lb/>
<anchor type="note" xlink:label="note-0281-02a" xlink:href="note-0281-02"/>
aliarum parallelos Sol nunquam peruenit) deſcripti, loco parallelorum per ſigna Zodiaci tran-<lb/>ſeuntium, &amp; </s>
  <s xml:id="echoid-s17980" xml:space="preserve">cætera omnia fiant, vt de parallelis ſignorum Zodiaci deſcribendis propoſ. </s>
  <s xml:id="echoid-s17981" xml:space="preserve">38. </s>
  <s xml:id="echoid-s17982" xml:space="preserve">huius <lb/>libri præcepimus, factumq́; </s>
  <s xml:id="echoid-s17983" xml:space="preserve">erit quod proponitur. </s>
  <s xml:id="echoid-s17984" xml:space="preserve">Parallelos ergo ciuitatum, hoc eſt, circulos lati <lb/>tudinum, in eodem horologio polari delineauimus. </s>
  <s xml:id="echoid-s17985" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s17986" xml:space="preserve"/>
</p>
<div xml:id="echoid-div914" type="float" level="2" n="1">
<note position="right" xlink:label="note-0281-02" xlink:href="note-0281-02a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ci-<lb/>uitatum, ſeu la-<lb/>titudinum in <lb/>eodem horolo-<lb/>gio polari.</note>
</div>
</div>
<div xml:id="echoid-div916" type="section" level="1" n="222">
<head xml:id="echoid-head228" xml:space="preserve">PROBLEMA 44. PROPOSITIO 44.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s17987" xml:space="preserve">DOMOS cęleſtes in eodem horologio polari deſcribere.</s>
  <s xml:id="echoid-s17988" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s17989" xml:space="preserve">SI circulus ex E, deſcriptus, quo vſi ſumus in deſcriptione horarum, ſecetur in 12. </s>
  <s xml:id="echoid-s17990" xml:space="preserve">partes æqua <lb/>
<anchor type="note" xlink:label="note-0281-04a" xlink:href="note-0281-04"/>
les, initio facto à linea meridiana, per puncta autem diuiſionum, &amp; </s>
  <s xml:id="echoid-s17991" xml:space="preserve">centrum E, rectæ ducantur ſe-<lb/>cantes lin eam æquinoctialem in punctis, dabunt rectæ coniungentes hæc puncta cum puncto D, <lb/>
<anchor type="figure" xlink:label="fig-0281-01a" xlink:href="fig-0281-01"/>
<anchor type="note" xlink:label="note-0281-05a" xlink:href="note-0281-05"/>
<anchor type="note" xlink:label="note-0281-06a" xlink:href="note-0281-06"/>
<anchor type="note" xlink:label="note-0281-07a" xlink:href="note-0281-07"/>
<anchor type="note" xlink:label="note-0281-08a" xlink:href="note-0281-08"/>
in quo linea horizontalis meridianam lineam interſecat, initia domorum cęleſtium ſecundum do <lb/>ctrinam Ioan. </s>
  <s xml:id="echoid-s17992" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s17993" xml:space="preserve">vt propoſ. </s>
  <s xml:id="echoid-s17994" xml:space="preserve">20. </s>
  <s xml:id="echoid-s17995" xml:space="preserve">huius libri de Verticali horologio demonſtrauimus; </s>
  <s xml:id="echoid-s17996" xml:space="preserve">quia
<pb o="266" file="0282" n="282" rhead="GNOMONICES"/>
&amp; </s>
  <s xml:id="echoid-s17997" xml:space="preserve">hic communis ſectio omnium circulorum cœleſtium domorum, hoc eſt, axis Verticalis circu-<lb/>li, ſeu communis ſectio Meridiani circuli, &amp; </s>
  <s xml:id="echoid-s17998" xml:space="preserve">Horizontis, plano horologij in puncto D, occurrit, vt <lb/>patet ex figura propoſ. </s>
  <s xml:id="echoid-s17999" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18000" xml:space="preserve">huius libri, in qua hæc communis ſectio eſt recta B D, ſi triangulum <lb/>A B D, intelligatur rectum ad planum horologii.</s>
  <s xml:id="echoid-s18001" xml:space="preserve"/>
</p>
<div xml:id="echoid-div916" type="float" level="2" n="1">
<note position="right" xlink:label="note-0281-04" xlink:href="note-0281-04a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle <lb/>ſtium in code<unsure/> <lb/>polari horolo <lb/>gio, ſecundum <lb/>Ioan. Regiom.</note>
  <figure xlink:label="fig-0281-01" xlink:href="fig-0281-01a">
    <image file="0281-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0281-01"/>
  </figure>
<note position="left" xlink:label="note-0281-05" xlink:href="note-0281-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0281-06" xlink:href="note-0281-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0281-07" xlink:href="note-0281-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0281-08" xlink:href="note-0281-08a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domorum cœle <lb/>ſtium ſecundũ <lb/>loan Region.</note>
</div>
<p>
  <s xml:id="echoid-s18002" xml:space="preserve">SED ex Campani ſententia ita eaſdem domos cęleſtes delineabimus. </s>
  <s xml:id="echoid-s18003" xml:space="preserve">Ex figura propoſ. </s>
  <s xml:id="echoid-s18004" xml:space="preserve">40. <lb/></s>
  <s xml:id="echoid-s18005" xml:space="preserve">
<anchor type="note" xlink:label="note-0282-01a" xlink:href="note-0282-01"/>
huius libri accipiemus rectam B C, per quam Zenith C, inueſtigauimus, eamq́ue in lineam meri <lb/>dianam à puncto C, ſiue ſurſum, ſiue deorſum verſus transferemus vſque ad F. </s>
  <s xml:id="echoid-s18006" xml:space="preserve">Deinde deſcripto <lb/>circulo ex F, eoq́ue in 12. </s>
  <s xml:id="echoid-s18007" xml:space="preserve">partes æquales diſtributo, facto initio à linea meridiana, ducemus per <lb/>puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s18008" xml:space="preserve">per centrum F, rectas occultas ſecantes lineam Verticalem in punctis, quæ <lb/>lineis rectis iuncta cum D, exhibebunt domos cęleſtes, vt vult Campanus. </s>
  <s xml:id="echoid-s18009" xml:space="preserve">Nam ſi hic circulus cir <lb/>
<anchor type="note" xlink:label="note-0282-02a" xlink:href="note-0282-02"/>
ca linea in Verticalem vertatur, donec cum Verticali propriè dicto, eiusq́; </s>
  <s xml:id="echoid-s18010" xml:space="preserve">centrum F, cum centro <lb/>mundi B, coniungatur; </s>
  <s xml:id="echoid-s18011" xml:space="preserve">erunt occultæ illæ rectæ per F, ductæ, communes ſectiones circulorum <lb/>cœleſtium domorum, &amp; </s>
  <s xml:id="echoid-s18012" xml:space="preserve">Verticali, ac proin de circuli domorum cęleſtium plano horologii occur-<lb/>rent in prædictis punctis lineæ Verticalis. </s>
  <s xml:id="echoid-s18013" xml:space="preserve">Quare lineæ domorum cœleſtium per eadem puncta <lb/>tranſibunt, atque idcirco, cum tranſeant quoque per punctum D, vt dictum eſt, erunt prędictæ re-<lb/>ctæ puncta Verticalis lineæ cum D, connectentes, lineæ domorum cœleſtium. </s>
  <s xml:id="echoid-s18014" xml:space="preserve">Quam obrem do-<lb/>mos cœleſtes in eodem horologio polari deſcripſimus. </s>
  <s xml:id="echoid-s18015" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s18016" xml:space="preserve"/>
</p>
<div xml:id="echoid-div917" type="float" level="2" n="2">
<note position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium in eodẽ <lb/>horologio pola <lb/>ri, ſecundum <lb/>Campanum.</note>
<note position="left" xlink:label="note-0282-02" xlink:href="note-0282-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div919" type="section" level="1" n="223">
<head xml:id="echoid-head229" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s18017" xml:space="preserve">LINEAE domorum cęleſtium vltra horizontalem lineã productæ dabunt eaſdem domos cœleſtes <lb/>
<anchor type="note" xlink:label="note-0282-04a" xlink:href="note-0282-04"/>
in horologio inferiori, ſi inuertatur horologium, vt ſæpe dictum eſt, at que in ſcholio propoſ. </s>
  <s xml:id="echoid-s18018" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18019" xml:space="preserve">huius li-<lb/>bri demonſtratum. </s>
  <s xml:id="echoid-s18020" xml:space="preserve">Verum domus cœleſtes in inferiori horologio nullum vſum habent, præter illas, quæ <lb/>ultra horizontalem lineam tropicum ♋, ſecant, quod eò commodius fit, quò polus maiorem eleuationem <lb/>habet ſupra Horizontem, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s18021" xml:space="preserve">In noſtro exemplo, quod ad latitudinem grad. </s>
  <s xml:id="echoid-s18022" xml:space="preserve">42. </s>
  <s xml:id="echoid-s18023" xml:space="preserve">fabrica-<lb/>tum eſt, nulla domus cœleſtis in inferiori horologio integra deſcribi poteſt, cum nulla tropicum ultra li-<lb/>neam horizontalem ſecet. </s>
  <s xml:id="echoid-s18024" xml:space="preserve">Solum partes domus 12. </s>
  <s xml:id="echoid-s18025" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18026" xml:space="preserve">7. </s>
  <s xml:id="echoid-s18027" xml:space="preserve">hoc eſt, lineæ ductæ per gradus intermedios <lb/>dictarum domorum in horologio inferiori deſcribi poſſunt, pręſcrtim per illos, qui ab Horizonte non <lb/>longè abſunt.</s>
  <s xml:id="echoid-s18028" xml:space="preserve"/>
</p>
<div xml:id="echoid-div919" type="float" level="2" n="1">
<note position="left" xlink:label="note-0282-04" xlink:href="note-0282-04a" xml:space="preserve">Domus cęleſtes <lb/>vltra lineam ho <lb/>rizontalem pro <lb/>ductę dant eaſ-<lb/>dem domos in <lb/>Inferiori horo-<lb/>logio, ſi portio <lb/>illa horologii à <lb/>linea horizon-<lb/>tali abſciſta in-<lb/>uertatur ſecun -<lb/>dum omnes ſui <lb/>partes.</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div921" type="section" level="1" n="224">
<head xml:id="echoid-head230" xml:space="preserve">PROBLEMA. 45. PROPOSITIO 45.</head>
<p>
  <s xml:id="echoid-s18029" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem horologio polari de-<lb/>ſcribere.</s>
  <s xml:id="echoid-s18030" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18031" xml:space="preserve">EX primis duabus tabellis propoſ. </s>
  <s xml:id="echoid-s18032" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18033" xml:space="preserve">huius libri ſumantur horæ, quibus 12. </s>
  <s xml:id="echoid-s18034" xml:space="preserve">ſigna Zodiaci <lb/>
<anchor type="note" xlink:label="note-0282-06a" xlink:href="note-0282-06"/>
oriuntur, Sole exiſtente in principio ♈, &amp; </s>
  <s xml:id="echoid-s18035" xml:space="preserve">♎, quæ in circulo F G H I, ex E, deſcripto, per quem vi-<lb/>delicet horæ ſunt deſignatæ, numerentur à puncto F, vel verſus ortum, vel verſus occaſum, prout <lb/>tabulæ offerunt horas ante, vel poſt meridiem. </s>
  <s xml:id="echoid-s18036" xml:space="preserve">Semper autem horæ ante meridiem numerandæ <lb/>
<anchor type="note" xlink:label="note-0282-07a" xlink:href="note-0282-07"/>
ſunt ab F, verſus I, horæ verò poſt meridiem ab F, verſus G, in horologio ſuperiori: </s>
  <s xml:id="echoid-s18037" xml:space="preserve">in inferiori au <lb/>tem horæ antemeridianæ ab H, verſus I, pomeridianæ ab H, verſus G, vt liquido conſtat, ſi in vtro-<lb/>que horologio circulus F G H I, in propria poſitione intelligatur conſtitutus. </s>
  <s xml:id="echoid-s18038" xml:space="preserve">Nam ſi circulus <lb/>F G H I, in plano Aequatoris intelligatur, &amp; </s>
  <s xml:id="echoid-s18039" xml:space="preserve">centrum E, in centro mundi, &amp; </s>
  <s xml:id="echoid-s18040" xml:space="preserve">in vertice ſtyli, erit in <lb/>ſuperiori quidem horologio F, in meridie, &amp; </s>
  <s xml:id="echoid-s18041" xml:space="preserve">H, in media nocte; </s>
  <s xml:id="echoid-s18042" xml:space="preserve">in inferiori verò H, exiſtet in me-<lb/>ridie, &amp; </s>
  <s xml:id="echoid-s18043" xml:space="preserve">F, in media nocte. </s>
  <s xml:id="echoid-s18044" xml:space="preserve">Deinde per fines num erationum, &amp; </s>
  <s xml:id="echoid-s18045" xml:space="preserve">centrum E, ducantur occultæ li-<lb/>neæ rectæ ſecantes æquinoctialem lineam in punctis illarum horarum, per quæ lineæ ſignorum <lb/>aſcendentium ſunt ducendæ. </s>
  <s xml:id="echoid-s18046" xml:space="preserve">Cauendum eſt autem, ne ex dictis tabellis ſumantur horæ illorum <lb/>ſignorum, quæ ſex horis, vel pluribus ante, vel poſt meridiem oriuntur. </s>
  <s xml:id="echoid-s18047" xml:space="preserve">Hæ enim in horologium <lb/>ſuperius polare non cadunt. </s>
  <s xml:id="echoid-s18048" xml:space="preserve">Quòd ſi ſigna aſcendentia deſcribenda ſint in inferiori horologio, <lb/>
<anchor type="note" xlink:label="note-0282-08a" xlink:href="note-0282-08"/>
accipiendæ ſunt hæ horæ, non autem illorum ſignorum, quę ſex horis, ante aut poſt meridiem, vel <lb/>paucioribus oriuntur. </s>
  <s xml:id="echoid-s18049" xml:space="preserve">Poſt hæc in linea horizontali notentur puncta, per quæ arcus ſignorum du <lb/>cuntur. </s>
  <s xml:id="echoid-s18050" xml:space="preserve">In illa enim, quæ in parte antemeridiana continentur, (nempe in ſiniſtra ſuperioris horo-<lb/>logii, vel in dextra inferioris) proiiciuntur vmbræ, cum illa ſigna oriuntur, nempe ♑, in ſuperiori <lb/>horologio &amp; </s>
  <s xml:id="echoid-s18051" xml:space="preserve">♐, ♒, &amp; </s>
  <s xml:id="echoid-s18052" xml:space="preserve">♏, ♓. </s>
  <s xml:id="echoid-s18053" xml:space="preserve">in inferiori verò ♋, &amp; </s>
  <s xml:id="echoid-s18054" xml:space="preserve">♊, ♌, &amp; </s>
  <s xml:id="echoid-s18055" xml:space="preserve">♉, ♍. </s>
  <s xml:id="echoid-s18056" xml:space="preserve">In ea autem puncta, quæ <lb/>in pomeridiana parte ſunt ſignata, (hoc eſt, in dextra horologii ſuperioris, vel in ſiniſtra inferio-<lb/>ris) proiiciuntur vmbræ illorum ſignorum occidentium, quorum oppoſita tunc oriuntur, qua-<lb/>lia ſunt in ſuperiori horologio ♑, &amp; </s>
  <s xml:id="echoid-s18057" xml:space="preserve">♐, ♒, &amp; </s>
  <s xml:id="echoid-s18058" xml:space="preserve">♏, ♓. </s>
  <s xml:id="echoid-s18059" xml:space="preserve">horum enim vmbræ in illa puncta cadunt, cũ <lb/>occidunt. </s>
  <s xml:id="echoid-s18060" xml:space="preserve">oppoſita verò ſigna vt ♋, &amp; </s>
  <s xml:id="echoid-s18061" xml:space="preserve">♊, ♌, &amp; </s>
  <s xml:id="echoid-s18062" xml:space="preserve">♉, ♍, tunc oriuntur. </s>
  <s xml:id="echoid-s18063" xml:space="preserve">In inferiori autem horolo-<lb/>gio vmbræ horum ſignorum ♋, &amp; </s>
  <s xml:id="echoid-s18064" xml:space="preserve">♊, ♌, &amp; </s>
  <s xml:id="echoid-s18065" xml:space="preserve">♉, ♍, in illa puncta cadunt, cum occidunt: </s>
  <s xml:id="echoid-s18066" xml:space="preserve">oppoſi-<lb/>ta verò ſigna, nempe ♑, &amp; </s>
  <s xml:id="echoid-s18067" xml:space="preserve">♐, ♒, &amp; </s>
  <s xml:id="echoid-s18068" xml:space="preserve">♏, ♓, tunc ſupra Horizontem aſcendunt. </s>
  <s xml:id="echoid-s18069" xml:space="preserve">Itaque ſi puncta ſi-
<pb o="267" file="0283" n="283" rhead="LIBER SECVNDVS."/>
gnorum aſcendentium in linea horizontali cum punctis reſpondentibus in linea æquinoctiali re-<lb/>pertis iungantur rectis lineis, deſcripta erunt ſigna aſcendentia, vt ex demonſtrationibus in horo-<lb/>logio horizontali, Verticali, &amp; </s>
  <s xml:id="echoid-s18070" xml:space="preserve">Meridiano allatis perſpicuum eſt.</s>
  <s xml:id="echoid-s18071" xml:space="preserve"/>
</p>
<div xml:id="echoid-div921" type="float" level="2" n="1">
<note position="left" xlink:label="note-0282-06" xlink:href="note-0282-06a" xml:space="preserve">Aſcendentium <lb/>ſignorum in eo <lb/>dem polari ho-<lb/>rologio deſcri-<lb/>ptio.</note>
<note position="left" xlink:label="note-0282-07" xlink:href="note-0282-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0282-08" xlink:href="note-0282-08a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0283-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s18072" xml:space="preserve">PORRO lineas ♈, &amp; </s>
  <s xml:id="echoid-s18073" xml:space="preserve">♎, ita deſcribemus. </s>
  <s xml:id="echoid-s18074" xml:space="preserve">Quia principio ♈, aſcendente ſupra Horizonteẽ, <lb/>
<anchor type="note" xlink:label="note-0283-03a" xlink:href="note-0283-03"/>
&amp; </s>
  <s xml:id="echoid-s18075" xml:space="preserve">Sole exiſtente in principio ♑, meridies eſt, vt ex tabella 4. </s>
  <s xml:id="echoid-s18076" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s18077" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18078" xml:space="preserve">huius libri conſtat, ducen <lb/>
<anchor type="note" xlink:label="note-0283-04a" xlink:href="note-0283-04"/>
dum erit ſignum ♈, aſcendens per punctum illud tropici ♑, per quod linea meridiana tranſit. <lb/></s>
  <s xml:id="echoid-s18079" xml:space="preserve">Quoniam vero eo tempore Aequator, circulus horæ 6. </s>
  <s xml:id="echoid-s18080" xml:space="preserve">à meridie, vel media nocte, Ecliptica, Ho-<lb/>rizon, &amp; </s>
  <s xml:id="echoid-s18081" xml:space="preserve">Verticalis circulus propriè dictus habent vnam, &amp; </s>
  <s xml:id="echoid-s18082" xml:space="preserve">eandem ſectionem communem, cui <lb/>quidem planum horologii æquidiſtat, cum parallelum ſit circulo horæ 6. </s>
  <s xml:id="echoid-s18083" xml:space="preserve">erunt per propoſ. </s>
  <s xml:id="echoid-s18084" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18085" xml:space="preserve"><lb/>antecedentis lib. </s>
  <s xml:id="echoid-s18086" xml:space="preserve">parallelæ in plano horologii linea æquinoctialis, communis ſectio Eclipticæ &amp; </s>
  <s xml:id="echoid-s18087" xml:space="preserve"><lb/>plani horologii, linea horizontalis, lineaq́; </s>
  <s xml:id="echoid-s18088" xml:space="preserve">Verticalis. </s>
  <s xml:id="echoid-s18089" xml:space="preserve">Quare recta linea æquinoctiali lineæ æqui-<lb/>diſtans ducta per punctum, in quo linea meridiana tropicum ♑, ſecat, dabit ſignum ♈, aſcendẽs. </s>
  <s xml:id="echoid-s18090" xml:space="preserve"><lb/>Eodem modo recta æquinoctiali lineæ ęquidiſtans &amp; </s>
  <s xml:id="echoid-s18091" xml:space="preserve">per punctum illud tranſiens, in quo meri-<lb/>diana linea tropicum ♋, ſecat, dabit ſignum ♎, aſcendens.</s>
  <s xml:id="echoid-s18092" xml:space="preserve"/>
</p>
<div xml:id="echoid-div922" type="float" level="2" n="2">
<note position="right" xlink:label="note-0283-03" xlink:href="note-0283-03a" xml:space="preserve">Quomodo de-<lb/>ſcribantur ſi-<lb/>gna alcenden-<lb/>tia Arietis &amp; Li <lb/>bræ.</note>
<note position="left" xlink:label="note-0283-04" xlink:href="note-0283-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s18093" xml:space="preserve">QVOD ſi placet, illa eadem puncta in linea horizontali, in quibus Sol principia ſignorum <lb/>
<anchor type="note" xlink:label="note-0283-05a" xlink:href="note-0283-05"/>
<anchor type="note" xlink:label="note-0283-06a" xlink:href="note-0283-06"/>
poſſidens oritur, &amp; </s>
  <s xml:id="echoid-s18094" xml:space="preserve">occidit, inueniemus hac quoque ratione, etiamſi arcus ſignorum non ſint de-<lb/>ſcripti in horologio. </s>
  <s xml:id="echoid-s18095" xml:space="preserve">Ex tabella quinta propoſ. </s>
  <s xml:id="echoid-s18096" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18097" xml:space="preserve">huius libri accipiemus arcus ſemidiurnos ſigno-<lb/>rum auſtralium pro ſuperiori horologio, eosq́ue ab F, in vtramque partem numerabimus: </s>
  <s xml:id="echoid-s18098" xml:space="preserve">pro <lb/>inferiori verò horologio ſumemus arcus ſemidiurnos ſignorum Borealium, eosq́; </s>
  <s xml:id="echoid-s18099" xml:space="preserve">ab H, in vtram-<lb/>que partem ſupputabimus. </s>
  <s xml:id="echoid-s18100" xml:space="preserve">Deinde ex terminis ſupputationũ per centrum E, rectas occultas traii-<lb/>ciemus ſecantes lineã æquinoctialẽ in punctis, per quæ rectæ ad lineam æquinoctialem perpendicu <lb/>lares ductæ ſecabunt horizõtalem lineã in punctis, quæ quærimus. </s>
  <s xml:id="echoid-s18101" xml:space="preserve">Cum enim in illis horis oriatur <lb/>Sol, &amp; </s>
  <s xml:id="echoid-s18102" xml:space="preserve">occidat in linea horizontali, ac dictæ perpendiculares ſint lineæ illarum horarum, vt conſtat <lb/>ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s18103" xml:space="preserve">37. </s>
  <s xml:id="echoid-s18104" xml:space="preserve">huius libri, perſpicuum eſt, rectè inuenta eſſe propoſita puncta.</s>
  <s xml:id="echoid-s18105" xml:space="preserve"/>
</p>
<div xml:id="echoid-div923" type="float" level="2" n="3">
<note position="left" xlink:label="note-0283-05" xlink:href="note-0283-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0283-06" xlink:href="note-0283-06a" xml:space="preserve">Inuentio pun-<lb/>ctorum in linea<unsure/> <lb/>horizontali, in <lb/>quæ cadit vm-<lb/>bra ſtyli, cum <lb/>principia ſigno <lb/>rum oriuntur, <lb/>aut occidunt.</note>
</div>
<p>
  <s xml:id="echoid-s18106" xml:space="preserve">SED eadem reperiri poſſunt hoc modo. </s>
  <s xml:id="echoid-s18107" xml:space="preserve">Ex figura vltima propoſ. </s>
  <s xml:id="echoid-s18108" xml:space="preserve">21. </s>
  <s xml:id="echoid-s18109" xml:space="preserve">huius libri ſumatur in <lb/>
<anchor type="note" xlink:label="note-0283-07a" xlink:href="note-0283-07"/>
<anchor type="note" xlink:label="note-0283-08a" xlink:href="note-0283-08"/>
E D, recta E g, æqualis rectæ B D, in figura propoſ. </s>
  <s xml:id="echoid-s18110" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18111" xml:space="preserve">huius libri, per quam ſcilicet lineam hori-<lb/>zontalem deſcripſimus, &amp; </s>
  <s xml:id="echoid-s18112" xml:space="preserve">per g, ad E D, ducatur perpendicularis, quæ erit linea horizontalis in <lb/>ſuperiori horologio, vt conſtat, ſi Horizon A B C D, illius figuræ in horologio ſuperiori intelliga-<lb/>tur in propria poſitione, id eſt, vt punctum g, ſit in D, &amp; </s>
  <s xml:id="echoid-s18113" xml:space="preserve">perpẽdicularis per g, ducta eadem fiat, quę <lb/>horizontalis linea, ac proinde centrum E, cum centro mundi, &amp; </s>
  <s xml:id="echoid-s18114" xml:space="preserve">vertice ſtyli coniungatur. </s>
  <s xml:id="echoid-s18115" xml:space="preserve">Radii <lb/>ergo ex S, V, Y, per E, ducti ſecabunt in illa poſitione rectam, quæ per g, perpendicularis ducta eſt, <lb/>hoc eſt, horizontalem lineam, in punctis, in quibus Sol oritur exiſtens in principiis ſignorum au-<lb/>ſtralium. </s>
  <s xml:id="echoid-s18116" xml:space="preserve">Radii verò ex T, X, Z, per E, tranſeuntes eandẽlineam horizontalem ſecabunt in punctis, <lb/>in quibus Sol, cum eſt in initiis auſtralium ſignorum, occidit. </s>
  <s xml:id="echoid-s18117" xml:space="preserve">Quare ſi interualla lineę perpendi-<lb/>cularis per g, ductæ inter g, &amp; </s>
  <s xml:id="echoid-s18118" xml:space="preserve">dictos radios poſita transferantur in lineam horizontalem horolo-<lb/>gii ſuperioris ex puncto D, in vtramque partem, inuenta erunt puncta propoſita. </s>
  <s xml:id="echoid-s18119" xml:space="preserve">Similiter in ho-
<pb o="268" file="0284" n="284" rhead="GNOMONICES"/>
rologio inferiori eadem puncta inquiremus, ſi ex E B, eiuſdem vltimæ figuræ propoſ. </s>
  <s xml:id="echoid-s18120" xml:space="preserve">21. </s>
  <s xml:id="echoid-s18121" xml:space="preserve">huius li-<lb/>bri abſcindatur recta æqualis rectæ B D, in figura propoſ. </s>
  <s xml:id="echoid-s18122" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18123" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s18124" xml:space="preserve">per extremum punctũ <lb/>ducatur ad E B, perpendicularis, &amp; </s>
  <s xml:id="echoid-s18125" xml:space="preserve">c.</s>
  <s xml:id="echoid-s18126" xml:space="preserve"/>
</p>
<div xml:id="echoid-div924" type="float" level="2" n="4">
<note position="left" xlink:label="note-0283-07" xlink:href="note-0283-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0283-08" xlink:href="note-0283-08a" xml:space="preserve">Alia inuentio <lb/>eorundem pun <lb/>ctorum in ho-<lb/>rizontali linea, <lb/>in quibus ſigno <lb/>ium inicia ori-<lb/>untur, aut occi-<lb/>dunt.</note>
</div>
<p>
  <s xml:id="echoid-s18127" xml:space="preserve">VERVM inuentis punctis in linea æquinoctiali ex prioribus duabus tabel is propoſ. </s>
  <s xml:id="echoid-s18128" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18129" xml:space="preserve">huius <lb/>
<anchor type="note" xlink:label="note-0284-01a" xlink:href="note-0284-01"/>
libri, per quæ duci debeant ſigna aſcendentia, inueniri poterunt eadem arte ex tertia, &amp; </s>
  <s xml:id="echoid-s18130" xml:space="preserve">quarta ta-<lb/>bella puncta in tropicis, per quæ eadem ſigna aſcendentia ſint educenda: </s>
  <s xml:id="echoid-s18131" xml:space="preserve">ſi nimirum ducantur <lb/>occultæ lineæ illarũ horarũ, quibus ſigna oriuntur, quas quidẽ horas tabellæ prædictæ offerunt. <lb/></s>
  <s xml:id="echoid-s18132" xml:space="preserve">Cauendũ tamen eſt in ſuperiori horologio, ne ſumãtur horæ illorũ ſignorũ, quę ſex horis, aut pluri <lb/>bus ante vel poſt meridiẽ oriuntur. </s>
  <s xml:id="echoid-s18133" xml:space="preserve">Nã huiuſmodi horæ in ſuperius horologium non cadunt. </s>
  <s xml:id="echoid-s18134" xml:space="preserve">In <lb/>horologio verò inferiori accipiendæ ſunt illorũ ſignorũ horæ duntaxat, quæ pluribus horis, quàm <lb/>
<anchor type="note" xlink:label="note-0284-02a" xlink:href="note-0284-02"/>
ſex, ante vel poſt meridiẽ oriuntur, cum hæ in horologio cõtineantur, vt pater. </s>
  <s xml:id="echoid-s18135" xml:space="preserve">Immo lineæ rectæ <lb/>
<anchor type="note" xlink:label="note-0284-03a" xlink:href="note-0284-03"/>
tangentes tropicos, (quæ ducẽtur, vt in coroll. </s>
  <s xml:id="echoid-s18136" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s18137" xml:space="preserve">37. </s>
  <s xml:id="echoid-s18138" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18139" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18140" xml:space="preserve">Apollonii docuimus) in punctis in <lb/>tropicis inuentis, dant ſigna aſcendentia, vt ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s18141" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18142" xml:space="preserve">huius libri manifeſtũ eſt.</s>
  <s xml:id="echoid-s18143" xml:space="preserve"/>
</p>
<div xml:id="echoid-div925" type="float" level="2" n="5">
<note position="left" xlink:label="note-0284-01" xlink:href="note-0284-01a" xml:space="preserve">Qua ratione pũ <lb/>@a a ſcendentiũ <lb/>ſignorũ in tro-<lb/>picis inuenian-<lb/>tur.</note>
<note position="left" xlink:label="note-0284-02" xlink:href="note-0284-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0284-03" xlink:href="note-0284-03a" xml:space="preserve">Quomodo aſcẽ <lb/>dena ſigna per <lb/>doctrinam coni <lb/>corum Apoll. <lb/>deſcribantur. <lb/>Deſcrio@io ſi. <lb/>gnorum aſcen-<lb/>dentiũ per me-<lb/>diationes cęli, &amp; <lb/>angulos terræ</note>
</div>
<p>
  <s xml:id="echoid-s18144" xml:space="preserve">ALITER aſcendentia ſigna deſcribemus hac arte. </s>
  <s xml:id="echoid-s18145" xml:space="preserve">Ex tabella ſexta propoſ. </s>
  <s xml:id="echoid-s18146" xml:space="preserve">9 huius libri ac-<lb/>cipiemus declinationes mediationum cœli pro ſuperiori horologio; </s>
  <s xml:id="echoid-s18147" xml:space="preserve">pro inferiori verò angulorũ <lb/>terræ, &amp; </s>
  <s xml:id="echoid-s18148" xml:space="preserve">ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s18149" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18150" xml:space="preserve">huius libri, in linea meridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s18151" xml:space="preserve">quæ quidẽ <lb/>in inferiori horologio eſt linea mediæ noctis, inueſtigabimus puncta, per quæ illarum declinatio-<lb/>num paralleli ſunt ducendi. </s>
  <s xml:id="echoid-s18152" xml:space="preserve">Si enim hæc puncta cum reſpõdentibus punctis in linea horizontali <lb/>iamdudum inuentis connectamus lineis rectis, deſcripta erunt ſigna aſcendentia, vt patet ex dictis.</s>
  <s xml:id="echoid-s18153" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18154" xml:space="preserve">ALITER adhuc deſcribi poſſunt, &amp; </s>
  <s xml:id="echoid-s18155" xml:space="preserve">quidem commodiſſimè hoc modo. </s>
  <s xml:id="echoid-s18156" xml:space="preserve">Ex tabella decima <lb/>
<anchor type="note" xlink:label="note-0284-04a" xlink:href="note-0284-04"/>
<anchor type="note" xlink:label="note-0284-05a" xlink:href="note-0284-05"/>
propoſ. </s>
  <s xml:id="echoid-s18157" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18158" xml:space="preserve">huius libri accipiantur declinationes omnium punctorum Eclipticæ tam auſtralium, <lb/>quàm borealium in circulo horæ 7. </s>
  <s xml:id="echoid-s18159" xml:space="preserve">antemeridianæ exiſtentium, &amp; </s>
  <s xml:id="echoid-s18160" xml:space="preserve">ſecundum doctrinam propoſ. <lb/></s>
  <s xml:id="echoid-s18161" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18162" xml:space="preserve">huius libri in linea horæ 7. </s>
  <s xml:id="echoid-s18163" xml:space="preserve">antemeridianæ inquirantur puncta, per quæ paralleli illarum decli <lb/>nationum ſunt ducendi. </s>
  <s xml:id="echoid-s18164" xml:space="preserve">Rurſus ex tabella vndecima eiuſdem propoſ. </s>
  <s xml:id="echoid-s18165" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18166" xml:space="preserve">huius libri ſamantur de-<lb/>clinationes omnium punctorum Eclipticæ in circulo horæ quintæ pomeridianæ exiſtentium, &amp; </s>
  <s xml:id="echoid-s18167" xml:space="preserve"><lb/>ſimiliter per doctrinam propoſ. </s>
  <s xml:id="echoid-s18168" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18169" xml:space="preserve">huius libri quærantur puncta in linea horæ quintæ pomeri-<lb/>dianæ, per quæ illarum declinationum paralleli tranſeunt. </s>
  <s xml:id="echoid-s18170" xml:space="preserve">Si namque hæc puncta cum punctis <lb/>reſpondentibus in linea horæ 7. </s>
  <s xml:id="echoid-s18171" xml:space="preserve">inuentis iungantur, habebuntur in horologio ſuperiori ſigna <lb/>aſcend entia, per ca, quæ in horologio horizontali demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s18172" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18173" xml:space="preserve">hurus libri, quæ ne-<lb/>ceſſariò per puncta iamdudũ in linea horizõtali in uẽta, immo &amp; </s>
  <s xml:id="echoid-s18174" xml:space="preserve">per puncta in linea meridiana per <lb/>
<anchor type="note" xlink:label="note-0284-06a" xlink:href="note-0284-06"/>
cœli mediationes reperta tranſibunt. </s>
  <s xml:id="echoid-s18175" xml:space="preserve">Non aliter ſigna aſcendentia in horologio inſeriori delinea-<lb/>buntur, ſi ex prædictis tabellis ſumãtur declinationes punctorũ Eclipticæ in circulis horæ 7. </s>
  <s xml:id="echoid-s18176" xml:space="preserve">pome <lb/>ridianæ, &amp; </s>
  <s xml:id="echoid-s18177" xml:space="preserve">horæ quintæ antemeridianæ, &amp; </s>
  <s xml:id="echoid-s18178" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18179" xml:space="preserve">Sed hæc puncta eadem prorſus ſunt in horologio in-<lb/>feriori, quæ in ſuperiori. </s>
  <s xml:id="echoid-s18180" xml:space="preserve">Declinariones enim eædẽ ſunt in vtroq; </s>
  <s xml:id="echoid-s18181" xml:space="preserve">horologio, vt ex tabellis conſtat.</s>
  <s xml:id="echoid-s18182" xml:space="preserve"/>
</p>
<div xml:id="echoid-div926" type="float" level="2" n="6">
<note position="left" xlink:label="note-0284-04" xlink:href="note-0284-04a" xml:space="preserve">Alia deſcriptio <lb/>ſignorum aſeen <lb/>dentiũ per pun <lb/>cta Eclipticæ in <lb/>circulis horæ 7. <lb/>à med noc. &amp; 1. <lb/>à mer. exiſten-<lb/>ti<unsure/>a, cum ſigno-<lb/>rum principia <lb/>aſcendũt ſupra <lb/>Honi<unsure/>ontem.</note>
<note position="left" xlink:label="note-0284-05" xlink:href="note-0284-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0284-06" xlink:href="note-0284-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s18183" xml:space="preserve">QVOD ſi ex punctis in linea meridiana, quæ diameter eſt hyperbolarum, inuentis ducantur <lb/>
<anchor type="note" xlink:label="note-0284-07a" xlink:href="note-0284-07"/>
rectæ tangentes tropicos, ſecundum doctrinam in coroll, propoſ. </s>
  <s xml:id="echoid-s18184" xml:space="preserve">37. </s>
  <s xml:id="echoid-s18185" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18186" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18187" xml:space="preserve">Apollonij traditam, ha-<lb/>bebuntur eadem ſigna aſcendentia, vt in propoſ. </s>
  <s xml:id="echoid-s18188" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18189" xml:space="preserve">huius libri oſtendimus. </s>
  <s xml:id="echoid-s18190" xml:space="preserve">Signa ergo Zodiaci <lb/>aſcendentia in eodem horologio polari deſcripſimus. </s>
  <s xml:id="echoid-s18191" xml:space="preserve">Quod ſaciendum erat.</s>
  <s xml:id="echoid-s18192" xml:space="preserve"/>
</p>
<div xml:id="echoid-div927" type="float" level="2" n="7">
<note position="left" xlink:label="note-0284-07" xlink:href="note-0284-07a" xml:space="preserve">Alia deſcriptio <lb/>ſignorum aſcen <lb/>dentium ex do-<lb/>ct@na conicorũ <lb/>Apoll.</note>
</div>
</div>
<div xml:id="echoid-div929" type="section" level="1" n="225">
<head xml:id="echoid-head231" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s18193" xml:space="preserve">CVM Andrea Schonero aſcendentia ſigna it a deſignabimus. </s>
  <s xml:id="echoid-s18194" xml:space="preserve">In figura prima ſcholii propoſ. </s>
  <s xml:id="echoid-s18195" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18196" xml:space="preserve">hu-<lb/>
<anchor type="note" xlink:label="note-0284-09a" xlink:href="note-0284-09"/>
ius libri in recta E D, ſurnatur recta E b, ſtylo horologii æqualis, &amp; </s>
  <s xml:id="echoid-s18197" xml:space="preserve">per b, ipſi A C, parallela agatur, it a <lb/>vt centro E, illius figuræ poſito in E, centro circuli F G H I, in horologio, &amp; </s>
  <s xml:id="echoid-s18198" xml:space="preserve">puncto b, in puncto A, pa-<lb/>rallela per b, ducta congruat lineæ æquinoctiali. </s>
  <s xml:id="echoid-s18199" xml:space="preserve">Secabit autem hæc par allela per b, ductarectas ſigno-<lb/>rum ex E, procedentes in punctis, quorum interualla ex b, accepta, &amp; </s>
  <s xml:id="echoid-s18200" xml:space="preserve">in lineam æquinoctialem horologii <lb/>translata ex puncto A, vbi ineridiana linea æquino ctialem lineam interſecat, dabunt in linea æquinoctia <lb/>li puncta, per quę ſi ad punctum D, in quo horizont alis linea meridianam lineam ſecat, lineæ rectæ ducan <lb/>tur, ſecabuntur tropici in punctis, per quæ ſigna aſcendentia ſunt ducenda, hoc tamen ordine. </s>
  <s xml:id="echoid-s18201" xml:space="preserve">In horolo-<lb/>gio ſuperiori, &amp; </s>
  <s xml:id="echoid-s18202" xml:space="preserve">in parte antemeridiana, quæ eſt ad ſiniſtram, punctum in tropico ♋, remotius à linea me <lb/>
<anchor type="note" xlink:label="note-0284-10a" xlink:href="note-0284-10"/>
ridiana debetur ſigno ♌, vicinius autem ſigno ♍, &amp; </s>
  <s xml:id="echoid-s18203" xml:space="preserve">punctum in ipſa linea meridiana ſigno ♎. </s>
  <s xml:id="echoid-s18204" xml:space="preserve">In parte <lb/>
<anchor type="note" xlink:label="note-0284-11a" xlink:href="note-0284-11"/>
poſtea pomeridiana punctum vicinius lineę meridianæ in eodem tropico ♋, debetur ſigno ♏, remotius ve-<lb/>ro ſigno ♐. </s>
  <s xml:id="echoid-s18205" xml:space="preserve">Deinde in parte borologii antemeridiana punctum tropici ♑, vhi à linea horizontali ſecatur, <lb/>tribuendum eſt ſigno ♑, ſequens autem ſigno ♒, &amp; </s>
  <s xml:id="echoid-s18206" xml:space="preserve">vicinius meridianæ lineæ ſigno ♓, &amp; </s>
  <s xml:id="echoid-s18207" xml:space="preserve">punctum in <lb/>ipſa linea meridiana ſigno ♈, proximum verò in parte pomeridiana ſigno ♉, ſequens vero ſigno ♊, &amp; </s>
  <s xml:id="echoid-s18208" xml:space="preserve"><lb/>punctum in linea horizontali ſigno ♋. </s>
  <s xml:id="echoid-s18209" xml:space="preserve">In horologio verò inferiori, cum ex tropico ♋, fiat tropicus ♑, <lb/>&amp; </s>
  <s xml:id="echoid-s18210" xml:space="preserve">ex tropico ♑, tropicus ♋, erit in parte pomeridiana punctum tropici ♋, in quo lineam horizontalem <lb/>ſecat, aſſignandum ſigno ♑, ſequens autem ſigno ♒, &amp; </s>
  <s xml:id="echoid-s18211" xml:space="preserve">ſequens aliud ſigno ♓, &amp; </s>
  <s xml:id="echoid-s18212" xml:space="preserve">punctum in ipſa linea me <lb/>ridiana ſigno ♈. </s>
  <s xml:id="echoid-s18213" xml:space="preserve">Sequens deinde in parte antemeridiana ſigno ♉, ſequens vero ſigno ♊, &amp; </s>
  <s xml:id="echoid-s18214" xml:space="preserve">punctum in <lb/>horizontali linea ſigno ♋. </s>
  <s xml:id="echoid-s18215" xml:space="preserve">Punctum autem in tropico ♑, in parte pomeridiana, &amp; </s>
  <s xml:id="echoid-s18216" xml:space="preserve">remotius à linea me <lb/>ridiana, pertinebit ad ♌, vicinius ad ♍, punctum verò in ipſa meridiana linea ad ♎, proximum deinde <lb/>in parte antemeridiana ad ♏, &amp; </s>
  <s xml:id="echoid-s18217" xml:space="preserve">ſequens ad ♐, vt in figura apparet.</s>
  <s xml:id="echoid-s18218" xml:space="preserve"/>
</p>
<div xml:id="echoid-div929" type="float" level="2" n="1">
<note position="left" xlink:label="note-0284-09" xlink:href="note-0284-09a" xml:space="preserve">Deſcriptio eo-<lb/>rundem ſigno-<lb/>rum aſcenden-<lb/>tium ex praxi <lb/>Andreæ Scho-<lb/>neri.</note>
<note position="left" xlink:label="note-0284-10" xlink:href="note-0284-10a" xml:space="preserve">Ordo fignotũ <lb/>aſcendentiũ in <lb/>tropicis.</note>
<note position="left" xlink:label="note-0284-11" xlink:href="note-0284-11a" xml:space="preserve">50</note>
</div>
<pb o="269" file="0285" n="285" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s18219" xml:space="preserve">RVRSVS in ſecunda figura ſcholii eiuſdem propoſ. </s>
  <s xml:id="echoid-s18220" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18221" xml:space="preserve">huius libri ex recta E D, abſcindatur recta <lb/>E b, gnomoni æqualis, &amp; </s>
  <s xml:id="echoid-s18222" xml:space="preserve">per b, ipſi A C, parallela agatur, adeò vt rurſum centro E, dictæ figuræ colloca-<lb/>to in centro E, circuli F G H I, in horologio, &amp; </s>
  <s xml:id="echoid-s18223" xml:space="preserve">puncto b, in puncto A, parallela per b, ducta congruat <lb/>æquinoctiali lineæ. </s>
  <s xml:id="echoid-s18224" xml:space="preserve">Secabit porrò parallela ducta per b, rectas ſignorum ex E, emiſſas, etiam illorum, quæ <lb/>ſunt ſupra rectam A C, productas tamen infra centrum E, in punctis, quorum interualla beneficio cir cini <lb/>ex puncto b, ſumpta, &amp; </s>
  <s xml:id="echoid-s18225" xml:space="preserve">in æquinoctialem lineam horologii translata ex puncto A, dabunt in linea æqui-<lb/>noctiali puncta, per quæ ſigna aſcendentia ſunt ducenda, hoc tamen ordine. </s>
  <s xml:id="echoid-s18226" xml:space="preserve">In horologio vtroque in partem <lb/>
<anchor type="note" xlink:label="note-0285-01a" xlink:href="note-0285-01"/>
antemcridianam, hoc eſt, in ſiniſtr am ſuperioris horologii, &amp; </s>
  <s xml:id="echoid-s18227" xml:space="preserve">in dextram inferioris, transferenda ſunt pun <lb/>cta ſupra punctum b; </s>
  <s xml:id="echoid-s18228" xml:space="preserve">in partem verò pomeridianam puncta infra punctum b, computando etiam ſigna, <lb/>quæ infra centrum E, ſunt, &amp; </s>
  <s xml:id="echoid-s18229" xml:space="preserve">vltra centrum E, producta, ita vt in illa parte ſint ♉, ♊, ♏, ♋, &amp; </s>
  <s xml:id="echoid-s18230" xml:space="preserve">♐; </s>
  <s xml:id="echoid-s18231" xml:space="preserve">in <lb/>
<anchor type="note" xlink:label="note-0285-02a" xlink:href="note-0285-02"/>
hac verò ♌, ♑, ♍, ♒, &amp; </s>
  <s xml:id="echoid-s18232" xml:space="preserve">♓. </s>
  <s xml:id="echoid-s18233" xml:space="preserve">His ita peractis, ſi puncta in tropicis inuenta cum punctis reſpondentibus <lb/>in linea æquinoctiali coniungantur, delineata erunt ſigna aſcendentia, vt prius. </s>
  <s xml:id="echoid-s18234" xml:space="preserve">Quæ omnia in ſuperiori fi-<lb/>gura manifeſta ſunt. </s>
  <s xml:id="echoid-s18235" xml:space="preserve">Lineæ ♈, &amp; </s>
  <s xml:id="echoid-s18236" xml:space="preserve">♎, ducendæ ſunt parallelæ lineæ æquinoctiali per puncta tropicorum, <lb/>in quibus à linea meridiana diuiduntur, vt ſupra dictum eſt.</s>
  <s xml:id="echoid-s18237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div930" type="float" level="2" n="2">
<note position="right" xlink:label="note-0285-01" xlink:href="note-0285-01a" xml:space="preserve">Ordo ſignorũ <lb/>aſcen dentiũ in <lb/>linca ęquino-<lb/>ctiali.</note>
<note position="left" xlink:label="note-0285-02" xlink:href="note-0285-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s18238" xml:space="preserve">LINEAE porrò aſcendentium ſignorum in ſuperiori horologio vltra lineam horizont alem produ-<lb/>
<anchor type="note" xlink:label="note-0285-03a" xlink:href="note-0285-03"/>
ctæ dabunt quoque eadem ſigna aſcendentia in horologio inferiori, ſi tamen ſuperior pars in inferiorem, et <lb/>quæ dextratunc eſt, in ſiniſtram mutetur; </s>
  <s xml:id="echoid-s18239" xml:space="preserve">vt conſtat ex demonſtratis in ſcholio propoſ. </s>
  <s xml:id="echoid-s18240" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18241" xml:space="preserve">huius libri.</s>
  <s xml:id="echoid-s18242" xml:space="preserve"/>
</p>
<div xml:id="echoid-div931" type="float" level="2" n="3">
<note position="right" xlink:label="note-0285-03" xlink:href="note-0285-03a" xml:space="preserve">Signa aſcenden <lb/>tia vltra lineã <lb/>horizontalem <lb/>producta dant <lb/>eadem ſigna in <lb/>horologio infe-<lb/>riori, ſi paries <lb/>permutentur, <lb/>vt ſæpe dictum <lb/>eſt.</note>
</div>
</div>
<div xml:id="echoid-div933" type="section" level="1" n="226">
<head xml:id="echoid-head232" xml:space="preserve">PROBLEMA 46. PROPOSITIO 46.</head>
<p>
  <s xml:id="echoid-s18243" xml:space="preserve">HOROLOGIVM Italicum polare deſcribere.</s>
  <s xml:id="echoid-s18244" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s18245" xml:space="preserve">CIRCVLVS ſæpe nominatus F G H I, ſecetur, ut in ſcholio propoſ. </s>
  <s xml:id="echoid-s18246" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18247" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18248" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18249" xml:space="preserve">docuimus, in <lb/>
<anchor type="note" xlink:label="note-0285-05a" xlink:href="note-0285-05"/>
arcum diurnum, &amp; </s>
  <s xml:id="echoid-s18250" xml:space="preserve">nocturnum tropici ♋, ſitq́ue arcus diurnus a F b, ita vt recta a b, communis ſe-<lb/>
<anchor type="figure" xlink:label="fig-0285-01a" xlink:href="fig-0285-01"/>
<anchor type="note" xlink:label="note-0285-06a" xlink:href="note-0285-06"/>
<anchor type="note" xlink:label="note-0285-07a" xlink:href="note-0285-07"/>
<anchor type="note" xlink:label="note-0285-08a" xlink:href="note-0285-08"/>
ctio paralleli, &amp; </s>
  <s xml:id="echoid-s18251" xml:space="preserve">Horizontis lineæ æquinoctiali ſit parallela. </s>
  <s xml:id="echoid-s18252" xml:space="preserve">Deinde circulus F G H I, diuidatur <lb/>in horas 24. </s>
  <s xml:id="echoid-s18253" xml:space="preserve">æquales, initio facto à termino arcus diurni occidentali, nempe à puncto a. </s>
  <s xml:id="echoid-s18254" xml:space="preserve">Si enim ex <lb/>punctis diuiſionum per centrum rectæ lineæ occultæ ducantur, quæ ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s18255" xml:space="preserve">10.</s>
  <s xml:id="echoid-s18256" xml:space="preserve">
<pb o="270" file="0286" n="286" rhead="GNOMONICES"/>
huius libri cõmunes ſectiones ſunt Aequatoris, &amp; </s>
  <s xml:id="echoid-s18257" xml:space="preserve">maximorũ circulorũ per polos mundi, &amp; </s>
  <s xml:id="echoid-s18258" xml:space="preserve">horas <lb/>Italicas paralleli ♋, tranſeuntium, inſtar circulorũ horariorũ à meridie, vel media nocte, ſecabitur <lb/>linea æquinoctialis in punctis, per quæ ad ipſam perpendiculares lineæ eductæ ſecabunt tropicum <lb/>♋, in horis Italicis, ſiue ab occaſu Solis, cum hæ perpendiculares ſint lineæ horariæ ab occaſu So-<lb/>lis, Sole exiſtente in principio ♋, ac ſi eſſent communes ſectiones plan@ horologii, &amp; </s>
  <s xml:id="echoid-s18259" xml:space="preserve">circulorum <lb/>maximorum per polos mundi, &amp; </s>
  <s xml:id="echoid-s18260" xml:space="preserve">horas Italicas in tropico ♋, tranſeuntium, vt ex ſupra demonſtra <lb/>tis liquet. </s>
  <s xml:id="echoid-s18261" xml:space="preserve">Quòd ſi per centrum circuli F G H I, ducatur recta G I, æquinoctiali lineæ parallela, nõ <lb/>
<anchor type="figure" xlink:label="fig-0286-01a" xlink:href="fig-0286-01"/>
<anchor type="note" xlink:label="note-0286-01a" xlink:href="note-0286-01"/>
<anchor type="note" xlink:label="note-0286-02a" xlink:href="note-0286-02"/>
<anchor type="note" xlink:label="note-0286-03a" xlink:href="note-0286-03"/>
<anchor type="note" xlink:label="note-0286-04a" xlink:href="note-0286-04"/>
cadent horæ in arcubus a G, b I, (quales ſunt in noſtro exemplo 23. </s>
  <s xml:id="echoid-s18262" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18263" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18264" xml:space="preserve">9.) </s>
  <s xml:id="echoid-s18265" xml:space="preserve">in planum horologii <lb/>ſuperioris, cum circulus horæ 6. </s>
  <s xml:id="echoid-s18266" xml:space="preserve">à meridie, vel media nocte, cui planum horologii æquidiſtat, per <lb/>rectam G I, ducatur; </s>
  <s xml:id="echoid-s18267" xml:space="preserve">vt conſtat, ſi circulus F G H I, in propria poſitione intelligatur eſſe conſtitu-<lb/>tus, ita vt centrum illius idem ſit, quod centrum mundi, &amp; </s>
  <s xml:id="echoid-s18268" xml:space="preserve">vertex ſtyli. </s>
  <s xml:id="echoid-s18269" xml:space="preserve">Eodem modo ſi recta a b, <lb/>transferatur vltra centrum circuli in d e, ita vt d F e, ſit arcus diurnus ♑, &amp; </s>
  <s xml:id="echoid-s18270" xml:space="preserve">rurſus circulus in ho-<lb/>ras 24 ſecetur, initio facto à puncto d, hoc eſt, à termino occidẽtali, reperiemus in tropico ♑, pun-<lb/>cta horarum Italicarum. </s>
  <s xml:id="echoid-s18271" xml:space="preserve">Si igitur puncta horarum Italicarum in tropicis inter ſe reſpondentium <lb/>rectis lineis iungantur, deſcriptum erit horologium Italicum polare. </s>
  <s xml:id="echoid-s18272" xml:space="preserve">Tranſibunt autem horæ Ita-<lb/>
<anchor type="note" xlink:label="note-0286-05a" xlink:href="note-0286-05"/>
cæ per puncta horarum à meridie, vel media nocte in linea æquinoctiali. </s>
  <s xml:id="echoid-s18273" xml:space="preserve">Vt hora 23. </s>
  <s xml:id="echoid-s18274" xml:space="preserve">Italica per <lb/>quintam à meridie, 22. </s>
  <s xml:id="echoid-s18275" xml:space="preserve">per 4. </s>
  <s xml:id="echoid-s18276" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18277" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18278" xml:space="preserve">vt perſpicuum eſt ex tabula propoſ. </s>
  <s xml:id="echoid-s18279" xml:space="preserve">19. </s>
  <s xml:id="echoid-s18280" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18281" xml:space="preserve">Vnde ſi ali <lb/>quæ horæ Italicæ in alterutro tropicorum in altero tropico non habeant puncta reſpondentia, du-<lb/>cendæ ſunt illæ per horas à meridie, vel media nocte reſpondentes in linea æquinoctiali, vt ex di-<lb/>cta tabella propoſ. </s>
  <s xml:id="echoid-s18282" xml:space="preserve">19. </s>
  <s xml:id="echoid-s18283" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18284" xml:space="preserve">colligitur. </s>
  <s xml:id="echoid-s18285" xml:space="preserve">Ita vides horas Italicas 13. </s>
  <s xml:id="echoid-s18286" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18287" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18288" xml:space="preserve">ductas eſſe per <lb/>puncta in tropico ♋, inuenta, &amp; </s>
  <s xml:id="echoid-s18289" xml:space="preserve">per horas 7. </s>
  <s xml:id="echoid-s18290" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18291" xml:space="preserve">8. </s>
  <s xml:id="echoid-s18292" xml:space="preserve">à media nocte in linea æquinoctiali, quia in tro <lb/>pico ♑, non habent puncta reſpondentia illis, quæ in tropico ♋, inuenta ſunt. </s>
  <s xml:id="echoid-s18293" xml:space="preserve">Eodem modo ho-<lb/>ra 23. </s>
  <s xml:id="echoid-s18294" xml:space="preserve">ducta eſt per punctum in tropico ♑, inuentum, &amp; </s>
  <s xml:id="echoid-s18295" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s18296" xml:space="preserve">à meridie in æquinoctiali <lb/>linea, &amp; </s>
  <s xml:id="echoid-s18297" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s18298" xml:space="preserve">Linea autem horæ 12. </s>
  <s xml:id="echoid-s18299" xml:space="preserve">ab occaſu ducenda eſt parallela æquinoctiali lineæ <lb/>per punctum in tropico ♋, inuentum. </s>
  <s xml:id="echoid-s18300" xml:space="preserve">Quoniam enim circuli horæ 12. </s>
  <s xml:id="echoid-s18301" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18302" xml:space="preserve">24. </s>
  <s xml:id="echoid-s18303" xml:space="preserve">ab ortu, vel occa-<lb/>ſu, cum Aequatore eandem communem ſectionem habent, per propoſ. </s>
  <s xml:id="echoid-s18304" xml:space="preserve">16. </s>
  <s xml:id="echoid-s18305" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18306" xml:space="preserve">Item
<pb o="271" file="0287" n="287" rhead="LIBER SECVNDVS."/>
eandem quoque cum circulo horæ 6. </s>
  <s xml:id="echoid-s18307" xml:space="preserve">à meridie, vel media nocte, per propoſ. </s>
  <s xml:id="echoid-s18308" xml:space="preserve">17. </s>
  <s xml:id="echoid-s18309" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s18310" xml:space="preserve">ſu-<lb/>perioris; </s>
  <s xml:id="echoid-s18311" xml:space="preserve">efficitur, vt duo illi circuli, &amp; </s>
  <s xml:id="echoid-s18312" xml:space="preserve">Aequator, &amp; </s>
  <s xml:id="echoid-s18313" xml:space="preserve">circulus horæ 6. </s>
  <s xml:id="echoid-s18314" xml:space="preserve">à meridie, vel media nocte, <lb/>habeant vnam &amp; </s>
  <s xml:id="echoid-s18315" xml:space="preserve">eandem ſectionem communem, nempe eam, per quam circulus dictæ horæ 6. <lb/></s>
  <s xml:id="echoid-s18316" xml:space="preserve">Aequatorem ſecat. </s>
  <s xml:id="echoid-s18317" xml:space="preserve">Cum ergo huic circulo, atque adeo dictæ communi ſectioni omnium illorũ, <lb/>æquidiſtet planum horologij polaris, erunt per propoſ. </s>
  <s xml:id="echoid-s18318" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18319" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18320" xml:space="preserve">reliquorum circulorum <lb/>ſectiones cum plano horologij, quales ſunt lineæ horæ 12. </s>
  <s xml:id="echoid-s18321" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18322" xml:space="preserve">24. </s>
  <s xml:id="echoid-s18323" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s18324" xml:space="preserve">linea æqui-<lb/>noctialis, inter ſe ſe parallelæ. </s>
  <s xml:id="echoid-s18325" xml:space="preserve">Atque hæc de horologio ſuperiori intelligenda ſunt. </s>
  <s xml:id="echoid-s18326" xml:space="preserve">Pro inferiori <lb/>autem ſatis erit, illud ex ſuperiori elicere, vt in ſequenti propoſ. </s>
  <s xml:id="echoid-s18327" xml:space="preserve">docebimus.</s>
  <s xml:id="echoid-s18328" xml:space="preserve"/>
</p>
<div xml:id="echoid-div933" type="float" level="2" n="1">
<note position="right" xlink:label="note-0285-05" xlink:href="note-0285-05a" xml:space="preserve">Horologii Ita-<lb/>lici polaris de-<lb/>ſcriptio.</note>
  <figure xlink:label="fig-0285-01" xlink:href="fig-0285-01a">
    <image file="0285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0285-01"/>
  </figure>
<note position="left" xlink:label="note-0285-06" xlink:href="note-0285-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0285-07" xlink:href="note-0285-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0285-08" xlink:href="note-0285-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0286-01" xlink:href="fig-0286-01a">
    <image file="0286-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0286-01"/>
  </figure>
<note position="left" xlink:label="note-0286-01" xlink:href="note-0286-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0286-02" xlink:href="note-0286-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0286-03" xlink:href="note-0286-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0286-04" xlink:href="note-0286-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0286-05" xlink:href="note-0286-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s18329" xml:space="preserve">SIGNATIS quoque in lineis horarum à meridie, vel media nocte punctis, ſecundum do-<lb/>
<anchor type="note" xlink:label="note-0287-01a" xlink:href="note-0287-01"/>
ctrinam propoſ. </s>
  <s xml:id="echoid-s18330" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18331" xml:space="preserve">huius libri, per quæ paralleli, quorum vnus ſit horarum 14. </s>
  <s xml:id="echoid-s18332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18333" xml:space="preserve">alter 10. </s>
  <s xml:id="echoid-s18334" xml:space="preserve">du-<lb/>
<anchor type="note" xlink:label="note-0287-02a" xlink:href="note-0287-02"/>
cuntur, deſcribemus beneficio illorum, &amp; </s>
  <s xml:id="echoid-s18335" xml:space="preserve">tabularum, quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s18336" xml:space="preserve">33. </s>
  <s xml:id="echoid-s18337" xml:space="preserve">ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s18338" xml:space="preserve">compoſuimus, horologium Italicum, vt in ſuperioribus horologijs tradidimus.</s>
  <s xml:id="echoid-s18339" xml:space="preserve"/>
</p>
<div xml:id="echoid-div934" type="float" level="2" n="2">
<note position="right" xlink:label="note-0287-01" xlink:href="note-0287-01a" xml:space="preserve">Alia deſcriptio <lb/>horologii Itali-<lb/>ci polaris per ar <lb/>cus diurnos ho <lb/>rarũ 10. &amp; 14.</note>
<note position="left" xlink:label="note-0287-02" xlink:href="note-0287-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s18340" xml:space="preserve">RVRSVS commodiſſime idem conſtruemus per duos parallelos, quorum vnus eſt ſemper <lb/>
<anchor type="note" xlink:label="note-0287-03a" xlink:href="note-0287-03"/>
apparentium maximus, hoc eſt, arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s18341" xml:space="preserve">alter verò maximus perpetuo delite-<lb/>ſcentium, ſeu arcus nocturnus horarum 24. </s>
  <s xml:id="echoid-s18342" xml:space="preserve">ſi in horis à meridie, &amp; </s>
  <s xml:id="echoid-s18343" xml:space="preserve">media nocte notentur puncta, <lb/>per quę tranſeunt. </s>
  <s xml:id="echoid-s18344" xml:space="preserve">Nam horæ ab ortu, vel occaſu tangunt dictos parallelos in plano horologij de-<lb/>ſcriptos in punctis, per quæ ducuntur horæ à meridie, vel media nocte, exceptis horis 6. </s>
  <s xml:id="echoid-s18345" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18346" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18347" xml:space="preserve">quę <lb/>cum dictis hyperbolis non conueniunt, vt ex coroll. </s>
  <s xml:id="echoid-s18348" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s18349" xml:space="preserve">15. </s>
  <s xml:id="echoid-s18350" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18351" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s18352" xml:space="preserve">Quænam <lb/>autem horæ ab occaſu tangant arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s18353" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18354" xml:space="preserve">quæ arcum nocturnum horarum <lb/>24. </s>
  <s xml:id="echoid-s18355" xml:space="preserve">item &amp; </s>
  <s xml:id="echoid-s18356" xml:space="preserve">in quibus horis à meridie, vel media nocte, pulchrè indicant tabulæ arcus diurni, &amp; </s>
  <s xml:id="echoid-s18357" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0287-04a" xlink:href="note-0287-04"/>
arcus nocturni horarum 24. </s>
  <s xml:id="echoid-s18358" xml:space="preserve">ſcholij propoſ. </s>
  <s xml:id="echoid-s18359" xml:space="preserve">33. </s>
  <s xml:id="echoid-s18360" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18361" xml:space="preserve">Quoniam enim in horologio ſupe <lb/>riori polari continentur ſolum horæ 7. </s>
  <s xml:id="echoid-s18362" xml:space="preserve">8. </s>
  <s xml:id="echoid-s18363" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18364" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18365" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18366" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18367" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18368" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s18369" xml:space="preserve">Item 1. </s>
  <s xml:id="echoid-s18370" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18371" xml:space="preserve">3. </s>
  <s xml:id="echoid-s18372" xml:space="preserve">4. </s>
  <s xml:id="echoid-s18373" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18374" xml:space="preserve">5. </s>
  <s xml:id="echoid-s18375" xml:space="preserve">à <lb/>meridie, accipiendæ erunt ex vtraque tabula horæ ab occaſu dictis horis reſpondentes, &amp; </s>
  <s xml:id="echoid-s18376" xml:space="preserve">non alię. <lb/></s>
  <s xml:id="echoid-s18377" xml:space="preserve">Vt ex tabula arcus diurni horarum 24. </s>
  <s xml:id="echoid-s18378" xml:space="preserve">ſumendæ ſunt hæ horæ ab occaſu 7. </s>
  <s xml:id="echoid-s18379" xml:space="preserve">8. </s>
  <s xml:id="echoid-s18380" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18381" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18382" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18383" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18384" xml:space="preserve">13. </s>
  <s xml:id="echoid-s18385" xml:space="preserve"><lb/>14. </s>
  <s xml:id="echoid-s18386" xml:space="preserve">15. </s>
  <s xml:id="echoid-s18387" xml:space="preserve">16. </s>
  <s xml:id="echoid-s18388" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18389" xml:space="preserve">17. </s>
  <s xml:id="echoid-s18390" xml:space="preserve">hæ enim dictum arcum tangunt in horis 7. </s>
  <s xml:id="echoid-s18391" xml:space="preserve">8. </s>
  <s xml:id="echoid-s18392" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18393" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18394" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18395" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18396" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18397" xml:space="preserve">à media nocte, <lb/>&amp; </s>
  <s xml:id="echoid-s18398" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18399" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18400" xml:space="preserve">3. </s>
  <s xml:id="echoid-s18401" xml:space="preserve">4. </s>
  <s xml:id="echoid-s18402" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18403" xml:space="preserve">5. </s>
  <s xml:id="echoid-s18404" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s18405" xml:space="preserve">Ex tabula autem arcus no cturni horarum 24. </s>
  <s xml:id="echoid-s18406" xml:space="preserve">ſumendæ ſunt hæ ho <lb/>ræ ab occaſu 1. </s>
  <s xml:id="echoid-s18407" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18408" xml:space="preserve">3. </s>
  <s xml:id="echoid-s18409" xml:space="preserve">4. </s>
  <s xml:id="echoid-s18410" xml:space="preserve">5. </s>
  <s xml:id="echoid-s18411" xml:space="preserve">19. </s>
  <s xml:id="echoid-s18412" xml:space="preserve">20. </s>
  <s xml:id="echoid-s18413" xml:space="preserve">21. </s>
  <s xml:id="echoid-s18414" xml:space="preserve">22. </s>
  <s xml:id="echoid-s18415" xml:space="preserve">23. </s>
  <s xml:id="echoid-s18416" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18417" xml:space="preserve">24. </s>
  <s xml:id="echoid-s18418" xml:space="preserve">Nam hæ contingunt arcum dictum in horis <lb/>1. </s>
  <s xml:id="echoid-s18419" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18420" xml:space="preserve">3. </s>
  <s xml:id="echoid-s18421" xml:space="preserve">4. </s>
  <s xml:id="echoid-s18422" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18423" xml:space="preserve">5. </s>
  <s xml:id="echoid-s18424" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s18425" xml:space="preserve">in 7. </s>
  <s xml:id="echoid-s18426" xml:space="preserve">8. </s>
  <s xml:id="echoid-s18427" xml:space="preserve">9. </s>
  <s xml:id="echoid-s18428" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18429" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18430" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18431" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18432" xml:space="preserve">à media nocte, vt ex prædictis tabu-<lb/>lis conſtat.</s>
  <s xml:id="echoid-s18433" xml:space="preserve"/>
</p>
<div xml:id="echoid-div935" type="float" level="2" n="3">
<note position="right" xlink:label="note-0287-03" xlink:href="note-0287-03a" xml:space="preserve">Alia a dhuc de-<lb/>ſcriptio eiuſdẽ <lb/>horologii Itali-<lb/>ci polatis per <lb/>arcum diurnũ, <lb/>nocturnum que <lb/>horarum 24.</note>
<note position="left" xlink:label="note-0287-04" xlink:href="note-0287-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s18434" xml:space="preserve">POSTREMO idem horologium Italicum conficiemus per lineam horæ 12. </s>
  <s xml:id="echoid-s18435" xml:space="preserve">ab ortu, vel oc <lb/>
<anchor type="note" xlink:label="note-0287-05a" xlink:href="note-0287-05"/>
<anchor type="note" xlink:label="note-0287-06a" xlink:href="note-0287-06"/>
caſu, vt ex tabula ſecunda propoſ. </s>
  <s xml:id="echoid-s18436" xml:space="preserve">20. </s>
  <s xml:id="echoid-s18437" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18438" xml:space="preserve">conſtat, cui titulus eſt, LINEA HORÆ <lb/>XII. </s>
  <s xml:id="echoid-s18439" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
  <s xml:id="echoid-s18440" xml:space="preserve">Item per lineam horæ 24. </s>
  <s xml:id="echoid-s18441" xml:space="preserve">ab ortu, vel occaſu, vt ex <lb/>prima tabula propoſ. </s>
  <s xml:id="echoid-s18442" xml:space="preserve">20. </s>
  <s xml:id="echoid-s18443" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s18444" xml:space="preserve">ſuperioris colligitur, cui titulus eſt. </s>
  <s xml:id="echoid-s18445" xml:space="preserve">LINEA HORAE <lb/>XXIIII. </s>
  <s xml:id="echoid-s18446" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s18447" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18448" xml:space="preserve">quæ quidem eadem omnino eſt, quæ horizontalis linea, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s18449" xml:space="preserve">Vel <lb/>etiam beneficio vtriuſque lineæ, ſi diligenter in prędictis tabulis notentur puncta horarum à me-<lb/>ridie, vel media nocte, per quæ ducendæ ſint horæ Italicæ, &amp;</s>
  <s xml:id="echoid-s18450" xml:space="preserve">c.</s>
  <s xml:id="echoid-s18451" xml:space="preserve"/>
</p>
<div xml:id="echoid-div936" type="float" level="2" n="4">
<note position="left" xlink:label="note-0287-05" xlink:href="note-0287-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0287-06" xlink:href="note-0287-06a" xml:space="preserve">Alia adhuc de-<lb/>ſcriptio horolo <lb/>gii Italici pola-<lb/>ris per lineam <lb/>horæ 12. &amp; li-<lb/>neam horæ 24. <lb/>ab or. vel occ.</note>
</div>
<p>
  <s xml:id="echoid-s18452" xml:space="preserve">CAETERVM lineam horæ 12. </s>
  <s xml:id="echoid-s18453" xml:space="preserve">ab ortu, vel occaſu hac ratione deſcribemus. </s>
  <s xml:id="echoid-s18454" xml:space="preserve">In linea æqui-<lb/>
<anchor type="note" xlink:label="note-0287-07a" xlink:href="note-0287-07"/>
noctiali ex puncto A, vbi lineam meridianam interſecat, accipiemus rectam A B, æqualem ſtylo, <lb/>nempe rectam inter lineam meridianam, &amp; </s>
  <s xml:id="echoid-s18455" xml:space="preserve">lineam horę 3. </s>
  <s xml:id="echoid-s18456" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s18457" xml:space="preserve">à meridie, vel media nocte. </s>
  <s xml:id="echoid-s18458" xml:space="preserve">hæc <lb/>enim ſtylo æqualis eſt, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s18459" xml:space="preserve">25. </s>
  <s xml:id="echoid-s18460" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s18461" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s18462" xml:space="preserve">Deinde ex B, termino il-<lb/>
<anchor type="note" xlink:label="note-0287-08a" xlink:href="note-0287-08"/>
lius ad æquinoctialem lineam ducentes perpendicularem B f, qualis eſt ipſamet linea horæ 9. </s>
  <s xml:id="echoid-s18463" xml:space="preserve">vel <lb/>3. </s>
  <s xml:id="echoid-s18464" xml:space="preserve">producta, deſcribemus ex eodem puncto B, vt centro, circulum, in quo ſumemus arcum f g, al-<lb/>titudini poli æqualem, &amp; </s>
  <s xml:id="echoid-s18465" xml:space="preserve">ex g, per centrum B, rectam ducemus, quæ ſecabit lineam meridianam <lb/>in puncto k, per quod ipſi ęquinoctiali lineę parallela acta, erit linea horæ 12. </s>
  <s xml:id="echoid-s18466" xml:space="preserve">ab ortu, vel occaſu. <lb/></s>
  <s xml:id="echoid-s18467" xml:space="preserve">Intelligatur enim circulus f g, circa meridianam lineam F H, conuerti, donec cum Meridiano cir-<lb/>culo, &amp; </s>
  <s xml:id="echoid-s18468" xml:space="preserve">eius centrum B, cum centro mundi, ſeu vertice ſtyli coniungatur. </s>
  <s xml:id="echoid-s18469" xml:space="preserve">Quo poſito, erit f, polus <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s18470" xml:space="preserve">g, punctum, in quo circulus horę 12. </s>
  <s xml:id="echoid-s18471" xml:space="preserve">ab ortu, vel occaſu parallelum omniũ ſemper ap-<lb/>parentium maximum tangit, ipſumq́ue Meridianum ſecat, cum hic parallelus à polo diſtet tot <lb/>gradibus, quot continentur in altitudine poli. </s>
  <s xml:id="echoid-s18472" xml:space="preserve">Quare recta ex g, per centrum circuli f g, emiſſa, <lb/>communis erit ſectio dicti circuli horæ 12. </s>
  <s xml:id="echoid-s18473" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18474" xml:space="preserve">Meridiani, ideoq́ue circulus horę 12. </s>
  <s xml:id="echoid-s18475" xml:space="preserve">ſecabit planũ <lb/>
<anchor type="note" xlink:label="note-0287-09a" xlink:href="note-0287-09"/>
horologij in puncto K, in quo dicta recta meridianã lineam abrumpit. </s>
  <s xml:id="echoid-s18476" xml:space="preserve">Cum ergo ex ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s18477" xml:space="preserve">22. </s>
  <s xml:id="echoid-s18478" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18479" xml:space="preserve">linea horę dictę 12. </s>
  <s xml:id="echoid-s18480" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18481" xml:space="preserve">ęquinoctialis parallelę ſint, liquido conſtat, paralle-<lb/>lam ipſi lineę ęquinoctiali per punctum K, meridianę lineę actam, eſſe lineam horę 12. </s>
  <s xml:id="echoid-s18482" xml:space="preserve">ab ortu, <lb/>vel occaſu, quod eſt propoſitum.</s>
  <s xml:id="echoid-s18483" xml:space="preserve"/>
</p>
<div xml:id="echoid-div937" type="float" level="2" n="5">
<note position="right" xlink:label="note-0287-07" xlink:href="note-0287-07a" xml:space="preserve">Quo pacto li-<lb/>nea horæ 12. ab <lb/>or. vel occ. du-<lb/>cenda ſit in po-<lb/>lari horologio.</note>
<note position="left" xlink:label="note-0287-08" xlink:href="note-0287-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0287-09" xlink:href="note-0287-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s18484" xml:space="preserve">QVONIAM verò angulus altitudinis poli f B g, æqualis eſt angulo ad verticem K B L, ſit, <lb/>
<anchor type="note" xlink:label="note-0287-10a" xlink:href="note-0287-10"/>
vr ſi in linea ęquinoctiali accipiamus rectam gnomoni ęqualem, &amp; </s>
  <s xml:id="echoid-s18485" xml:space="preserve">in extremo ad lineam ęquino-<lb/>
<anchor type="note" xlink:label="note-0287-11a" xlink:href="note-0287-11"/>
ctialem conſtituamus angulum complementi altitudinis poli, qualis eſt reliquus ex recto A B K, <lb/>inueniamus in linea meridiana idem punctum K, per quod linea horę 12. </s>
  <s xml:id="echoid-s18486" xml:space="preserve">ab ortu, vel occaſu eſt <lb/>
<anchor type="note" xlink:label="note-0287-12a" xlink:href="note-0287-12"/>
ducenda. </s>
  <s xml:id="echoid-s18487" xml:space="preserve">Immò ſi rectę A D, abſcindamus ęqualem A K, habebimus idem punctum K. </s>
  <s xml:id="echoid-s18488" xml:space="preserve">Quoniã <lb/>enim angulus A B D, æqualis eſt conſtitutus complemento altitudinis poli, vt ex propoſ. </s>
  <s xml:id="echoid-s18489" xml:space="preserve">38. </s>
  <s xml:id="echoid-s18490" xml:space="preserve">huius <lb/>libri conſtat, &amp; </s>
  <s xml:id="echoid-s18491" xml:space="preserve">angulus A B K, eidem cõplemento altitudinis poli æqualis, vt oſtendimus; </s>
  <s xml:id="echoid-s18492" xml:space="preserve">erunt
<pb o="272" file="0288" n="288" rhead="GNOMONICES"/>
duo anguli A B D, A B K, ęquales in triangulis A B D, A B K; </s>
  <s xml:id="echoid-s18493" xml:space="preserve">ſed &amp; </s>
  <s xml:id="echoid-s18494" xml:space="preserve">anguli ad A, ęquales ſunt, <lb/>vtpote recti, eſtq́ue latus A B, dictis angulis adiacens commune. </s>
  <s xml:id="echoid-s18495" xml:space="preserve">Igitur latera A D, A k, æqualia <lb/>
<anchor type="note" xlink:label="note-0288-01a" xlink:href="note-0288-01"/>
erunt; </s>
  <s xml:id="echoid-s18496" xml:space="preserve">atque adeo cum per K, tranſeat linea horę 12. </s>
  <s xml:id="echoid-s18497" xml:space="preserve">ab ortu, vel occaſu, vt demonſtrauimus, per-<lb/>ſpicuum eſt, ſi ipſi A D, ſumatur æqualis A K, per K, ducendam eſſe dictam lineam horæ 12. </s>
  <s xml:id="echoid-s18498" xml:space="preserve">quę <lb/>quidem in K, tangit parallelum ſem per apparentium maximum. </s>
  <s xml:id="echoid-s18499" xml:space="preserve">Quamobrem horologium Ita <lb/>licum polare deſcripſimus. </s>
  <s xml:id="echoid-s18500" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s18501" xml:space="preserve"/>
</p>
<div xml:id="echoid-div938" type="float" level="2" n="6">
<note position="right" xlink:label="note-0287-10" xlink:href="note-0287-10a" xml:space="preserve">Alia daſeriptio <lb/>lineæ horæ 12. <lb/>ab or. vel occ.</note>
<note position="right" xlink:label="note-0287-11" xlink:href="note-0287-11a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0287-12" xlink:href="note-0287-12a" xml:space="preserve">Alia adhuc de-<lb/>icriptio lineæ <lb/>horæ 12 ab o@. <lb/>vel occ.</note>
<note position="left" xlink:label="note-0288-01" xlink:href="note-0288-01a" xml:space="preserve">26. primi.</note>
</div>
</div>
<div xml:id="echoid-div940" type="section" level="1" n="227">
<head xml:id="echoid-head233" xml:space="preserve">PROBLEMA 47. PROPOSITIO 47.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s18502" xml:space="preserve">HOROLOGIVM Babylonicum polare delineare.</s>
  <s xml:id="echoid-s18503" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18504" xml:space="preserve">DESCRIBEMVS hoc horologium eiſdem rationibus fermè, quibus Italicum delineaui-<lb/>
<anchor type="note" xlink:label="note-0288-03a" xlink:href="note-0288-03"/>
mus: </s>
  <s xml:id="echoid-s18505" xml:space="preserve">ſi tamen in primo modo diuiſio circuli F G H I, in partes 24. </s>
  <s xml:id="echoid-s18506" xml:space="preserve">æquales initium habeat à ter <lb/>mino orientali arcus diurni tam tropici ♋, quàm tropici ♑, tum in puncto b, tum in e. </s>
  <s xml:id="echoid-s18507" xml:space="preserve">Linea <lb/>autem horę 12. </s>
  <s xml:id="echoid-s18508" xml:space="preserve">ducenda eſt parallela lineę ęquinoctiali per punctum in tropico ♋, inuentum, <lb/>vt prius.</s>
  <s xml:id="echoid-s18509" xml:space="preserve"/>
</p>
<div xml:id="echoid-div940" type="float" level="2" n="1">
<note position="left" xlink:label="note-0288-03" xlink:href="note-0288-03a" xml:space="preserve">Horologii Ba-<lb/>bylonici polaris <lb/>deſcriptio.</note>
</div>
<p>
  <s xml:id="echoid-s18510" xml:space="preserve">IN ſecundo modo nullum prorſus diſcrimen eſt, ſi modo pro horis ab occ. </s>
  <s xml:id="echoid-s18511" xml:space="preserve">quarum mentio <lb/>facta eſt in antecedenti propoſ. </s>
  <s xml:id="echoid-s18512" xml:space="preserve">ſumantur eędem ab ortu, &amp;</s>
  <s xml:id="echoid-s18513" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18514" xml:space="preserve">Exemplum horologij Babylonici <lb/>habes in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s18515" xml:space="preserve">vbi lineę parallelę inter ſe, &amp; </s>
  <s xml:id="echoid-s18516" xml:space="preserve">ad lineam ęquinoctialem per-<lb/>
<anchor type="note" xlink:label="note-0288-04a" xlink:href="note-0288-04"/>
pendiculares indicant horas à meridie, vel media nocte, quarum numeri aſcripti ſunt arcui diur-<lb/>no horarum 24. </s>
  <s xml:id="echoid-s18517" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18518" xml:space="preserve">nocturno arcui totidem horarum. </s>
  <s xml:id="echoid-s18519" xml:space="preserve">Deinde lineę, quibus appoſiti ſunt numeri <lb/>infra lineam ęquinoctialem, indicant horas Italicas. </s>
  <s xml:id="echoid-s18520" xml:space="preserve">Lineę denique, quibus numeri ſupra lineã <lb/>ęquinoctialem aſcripti ſunt, horis Babylonicis, ſeu ab ortu, tribuendę ſunt. </s>
  <s xml:id="echoid-s18521" xml:space="preserve">Horologium igitur <lb/>Babylonicum polare delineauimus. </s>
  <s xml:id="echoid-s18522" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s18523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div941" type="float" level="2" n="2">
<note position="left" xlink:label="note-0288-04" xlink:href="note-0288-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div943" type="section" level="1" n="228">
<head xml:id="echoid-head234" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">Quomodo ho-<lb/>rologium Itali <lb/>cum polare dif-<lb/>ferat a Eabylo-<lb/>nico polari.</note>
<p style="it">
  <s xml:id="echoid-s18524" xml:space="preserve">EX figura præcedentis horologii manifeſtum eſt, horologium Babylonicum non differre ab Italico, <lb/>niſi ſitu, &amp; </s>
  <s xml:id="echoid-s18525" xml:space="preserve">ordine horarum, quemadmodum in horizontali horologio expoſuimus.</s>
  <s xml:id="echoid-s18526" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s18527" xml:space="preserve">HABET autem inferius horologium polare à ſuperiori ortum, ſi omnium horarum lineæ vltra ho-<lb/>
<anchor type="note" xlink:label="note-0288-07a" xlink:href="note-0288-07"/>
rizontalem lineam producantur, &amp; </s>
  <s xml:id="echoid-s18528" xml:space="preserve">ſuperior pars mutetur in inferiorem, &amp; </s>
  <s xml:id="echoid-s18529" xml:space="preserve">quæ dextra eſt poſt hanc mu <lb/>tationem, vertatur in ſiniſtram, vt oſtendimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s18530" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18531" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s18532" xml:space="preserve">Quæ autem horæ in infe-<lb/>riori horologio numerandę ſint ab occaſu, &amp; </s>
  <s xml:id="echoid-s18533" xml:space="preserve">quæ ab ortu, cognoſcemus ex iis, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s18534" xml:space="preserve">23. <lb/></s>
  <s xml:id="echoid-s18535" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s18536" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s18537" xml:space="preserve"/>
</p>
<div xml:id="echoid-div943" type="float" level="2" n="1">
<note position="left" xlink:label="note-0288-07" xlink:href="note-0288-07a" xml:space="preserve">Qua ratione <lb/>Infcrius horo-<lb/>logium polare <lb/>iam Italicum, <lb/>quàm Babylo-<lb/>nicum à Supe-<lb/>riore ortum ha <lb/>beat.</note>
</div>
<p style="it">
  <s xml:id="echoid-s18538" xml:space="preserve">NON eſt etiam prætereundum hoc loco, in ea regione, vbi altitudo poli æqualis eſt complemento <lb/>
<anchor type="note" xlink:label="note-0288-08a" xlink:href="note-0288-08"/>
maximæ declinationis Solis, hoc eſt, grad. </s>
  <s xml:id="echoid-s18539" xml:space="preserve">66. </s>
  <s xml:id="echoid-s18540" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s18541" xml:space="preserve">30. </s>
  <s xml:id="echoid-s18542" xml:space="preserve">duos tropicos fungi munere duorum parallelorum, <lb/>quorum vnus ſemper apparentium, alter verò ſemper latentium maximus eſt. </s>
  <s xml:id="echoid-s18543" xml:space="preserve">Vnde lineę horarum ab <lb/>ortu, vel occaſu tangent duos tropicos in horis à meridie, vel media nocte tam in utroque horologio Me-<lb/>ridiano, quàm in Polari. </s>
  <s xml:id="echoid-s18544" xml:space="preserve">In ea autem regione, ubi altitudo poli maior eſt, quàm grad. </s>
  <s xml:id="echoid-s18545" xml:space="preserve">66. </s>
  <s xml:id="echoid-s18546" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s18547" xml:space="preserve">30. </s>
  <s xml:id="echoid-s18548" xml:space="preserve">duos <lb/>
<anchor type="note" xlink:label="note-0288-09a" xlink:href="note-0288-09"/>
prędictos parallelos cadere intra duos tropicos, ita vt lineæ horarum ab ortu, vel occaſu illos parallelos <lb/>tangentes ad ipſos tropicos nullo modo perueniant. </s>
  <s xml:id="echoid-s18549" xml:space="preserve">Vmbra enim ſtyli monſtrare tunc non poteſt horas <lb/>ab ortu, uel occaſu Solis elapſas, cum Sol exiſtens in tropicis neque oriatur, neque occidat, ſed perpetuo <lb/>ſupra Horizontem exiſtat, uel infra.</s>
  <s xml:id="echoid-s18550" xml:space="preserve"/>
</p>
<div xml:id="echoid-div944" type="float" level="2" n="2">
<note position="left" xlink:label="note-0288-08" xlink:href="note-0288-08a" xml:space="preserve">In latitudine <lb/>loci gr. 66. Min. <lb/>30. horæ ab or. <lb/>&amp; occ. tangunt <lb/>duos tropicos. <lb/>In maiori vero <lb/>latitudine horę <lb/>ab or. &amp; occ. nõ <lb/>perueniunt ad <lb/>tropicos, ſed tan <lb/>gunt alios pa-<lb/>rallelos propin-<lb/>quiores lineæ <lb/>æquinoctiali, tã <lb/>in horologio <lb/>Meridiano, q̃ <lb/>in polari.</note>
<note position="left" xlink:label="note-0288-09" xlink:href="note-0288-09a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div946" type="section" level="1" n="229">
<head xml:id="echoid-head235" xml:space="preserve">PROBLEMA 48. PROPOSITIO 48.</head>
<p>
  <s xml:id="echoid-s18551" xml:space="preserve">HOROLOGIVM Antiquum polare conſtituere.</s>
  <s xml:id="echoid-s18552" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18553" xml:space="preserve">SECETVR arcus diurnus tam tropici ♋, a F b, quàm tropici ♑, d F e, in circulo F G H I, <lb/>
<anchor type="note" xlink:label="note-0288-10a" xlink:href="note-0288-10"/>
<anchor type="note" xlink:label="note-0288-11a" xlink:href="note-0288-11"/>
in 12. </s>
  <s xml:id="echoid-s18554" xml:space="preserve">partes ęquales. </s>
  <s xml:id="echoid-s18555" xml:space="preserve">Ex his enim inueniemus in vtroque tropico puncta, per quæ ducendę erunt <lb/>horę inęquales, non aliter, ac in præcedentibus duabus propoſitionibus puncta horarum ab ortu, <lb/>&amp; </s>
  <s xml:id="echoid-s18556" xml:space="preserve">occaſu Solis in eiſdem tropicis inueſtigauimus. </s>
  <s xml:id="echoid-s18557" xml:space="preserve">Tranſibunt autem neceſſario horæ inæqua-<lb/>les per puncta horarum à meridie, vel media nocte in linea ęquinoctiali, vt ſupra docuimus in ho-<lb/>rizontali horologio propoſ. </s>
  <s xml:id="echoid-s18558" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18559" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s18560" xml:space="preserve">Certum autem eſt, vt ex figura appoſita apparet, ho-<lb/>ram 1. </s>
  <s xml:id="echoid-s18561" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18562" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18563" xml:space="preserve">non cadere in horologium ſuperius, cum Sol in principio ♋, exiſtit.</s>
  <s xml:id="echoid-s18564" xml:space="preserve"/>
</p>
<div xml:id="echoid-div946" type="float" level="2" n="1">
<note position="left" xlink:label="note-0288-10" xlink:href="note-0288-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0288-11" xlink:href="note-0288-11a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Antiqui <lb/>polaris.</note>
</div>
<p>
  <s xml:id="echoid-s18565" xml:space="preserve">PER arcus quoque duos diurnos in horologio deſcriptos, quorum vnus horas 18. </s>
  <s xml:id="echoid-s18566" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18567" xml:space="preserve">al-<lb/>
<anchor type="note" xlink:label="note-0288-12a" xlink:href="note-0288-12"/>
ter ſex comprehendat, conſtruemus idem horologium Antiquum, vt in ſuperioribus factum <lb/>eſt, propoſ. </s>
  <s xml:id="echoid-s18568" xml:space="preserve">12. </s>
  <s xml:id="echoid-s18569" xml:space="preserve">24. </s>
  <s xml:id="echoid-s18570" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18571" xml:space="preserve">36. </s>
  <s xml:id="echoid-s18572" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s18573" xml:space="preserve">Id quod figura appoſita perſpicuè docet. </s>
  <s xml:id="echoid-s18574" xml:space="preserve">Horologiũ igitur <lb/>Antiquum polare conſtituimus. </s>
  <s xml:id="echoid-s18575" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s18576" xml:space="preserve"/>
</p>
<div xml:id="echoid-div947" type="float" level="2" n="2">
<note position="left" xlink:label="note-0288-12" xlink:href="note-0288-12a" xml:space="preserve">Deſcriptio An-<lb/>tiqui horologii <lb/>polaris per ar-<lb/>cus diurnos ho <lb/>rarum 6. &amp; 18.</note>
</div>
<pb o="273" file="0289" n="289" rhead="LIBER SECVNDVS."/>
  <figure>
    <image file="0289-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0289-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div949" type="section" level="1" n="230">
<head xml:id="echoid-head236" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s18577" xml:space="preserve">CAETERVM &amp; </s>
  <s xml:id="echoid-s18578" xml:space="preserve">hic lineæ horarum inæqualium vltra horizontalem lineam productæ exhibent <lb/>
<anchor type="note" xlink:label="note-0289-03a" xlink:href="note-0289-03"/>
earundem horarum lineas in inferiori horologio, dummodo portio horologii abſciſſa à linea horizontali <lb/>inuertatur ſecundum omnes ſui partes, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s18579" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18580" xml:space="preserve">huius libri dictũ eſt, atque demonſtr at ũ. <lb/></s>
</p>
</div>
<div xml:id="echoid-div950" type="section" level="1" n="231">
<head xml:id="echoid-head237" xml:space="preserve">DE HOROLOGIIS ÆQVINOCTIALIBVS.</head>
<head xml:id="echoid-head238" xml:space="preserve">PROBLEMA 49. PROPOSITIO 49.</head>
<p>
  <s xml:id="echoid-s18581" xml:space="preserve">HOROLOGIVM Aſtronomicum æquinoctiale deſcribere. <lb/></s>
  <s xml:id="echoid-s18582" xml:space="preserve">
<anchor type="note" xlink:label="note-0289-05a" xlink:href="note-0289-05"/>
hoc eſt, Lineas horarum à meridie, vel media nocte in plano, quod <lb/>æquinoctiali circulo æquidiſtat, deſignare.</s>
  <s xml:id="echoid-s18583" xml:space="preserve"/>
</p>
<div xml:id="echoid-div950" type="float" level="2" n="1">
<note position="right" xlink:label="note-0289-03" xlink:href="note-0289-03a" xml:space="preserve">Quomodo In-<lb/>ferius horolo-<lb/>gium Antiquũ <lb/>polare à ſuperio <lb/>re oriatur.</note>
<note position="left" xlink:label="note-0289-05" xlink:href="note-0289-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s18584" xml:space="preserve">IN plano aliquo ducatur vtcunque recta A B, pro linea meridiana, vel horæ 12. </s>
  <s xml:id="echoid-s18585" xml:space="preserve">quam ad re-<lb/>
<anchor type="note" xlink:label="note-0289-06a" xlink:href="note-0289-06"/>
ctos angulos ſecet alia recta C D, in E. </s>
  <s xml:id="echoid-s18586" xml:space="preserve">Ex E, autem circulus cuiuslibet magnitudinis deſcriptus <lb/>diuidatur in 24. </s>
  <s xml:id="echoid-s18587" xml:space="preserve">partes æquales, initio facto vel à C D, vel à recta A B; </s>
  <s xml:id="echoid-s18588" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18589" xml:space="preserve">per diuiſionum puncta, <lb/>ac per centrum E, rectæ educantur. </s>
  <s xml:id="echoid-s18590" xml:space="preserve">Dico has rectas eſſe lineas horarum à meridie, vel media no-<lb/>cte in plano, quod Aequatori æquidiſtet: </s>
  <s xml:id="echoid-s18591" xml:space="preserve">adeò vt ſi in E, ponatur ſtylus E F, cuiusuis longitudinis <lb/>
<anchor type="note" xlink:label="note-0289-07a" xlink:href="note-0289-07"/>
rectus ad planum horologij, ipſumq́ue horologium ita collocetur, vt C D, Horizonti æquidiſtet, <lb/>
<anchor type="note" xlink:label="note-0289-08a" xlink:href="note-0289-08"/>
&amp; </s>
  <s xml:id="echoid-s18592" xml:space="preserve">A B, in plano Meridiani circuli ſtatuatur, tanquam communis ſectio plani horologij &amp; </s>
  <s xml:id="echoid-s18593" xml:space="preserve">Meri-<lb/>diani, punctum denique A, ex parte auſtrali (puncto B, ad boream vergente, C, ad ortum, &amp; </s>
  <s xml:id="echoid-s18594" xml:space="preserve">D, <lb/>ad occaſum) eleuetur ſecundum altitudinem Aequatoris, hoc eſt, ſecundum complementum al-<lb/>titudinis poli, ita vt angulus, quem recta A B, cum meridiana linea in plano Horizontis inuenta <lb/>conſtituit ad partes ſeptentrionis, hoc eſt, ad partes B, æqualis ſit complemento altitudinis poli, <lb/>vmbra ſtyli horas à meridie, vel media nocte indicet in horologio ſuperiori, quod nimirum ad <lb/>Zenith ſpectat, &amp; </s>
  <s xml:id="echoid-s18595" xml:space="preserve">illuſtratur à Sole in borealibus ſignis exiſtente, Aequatorique eſt parallelum. <lb/></s>
  <s xml:id="echoid-s18596" xml:space="preserve">Quòd ſi in facie oppoſita horologij ſic eleuati eædem lineæ intelligantur deſcriptæ reſpondentes <lb/>ad vnguem hiſce lineis ſuperioris horologij, ſtylusq́ue E F, in eadem ad rectos angulos infigatur, <lb/>indicabit vmbra ſtyli eaſdem horas in horologio inferiori, quod videlicet à Sole ſigna auſtralia <lb/>percurrente illuminatur. </s>
  <s xml:id="echoid-s18597" xml:space="preserve">Quod hac ratione demonſtrabitur.</s>
  <s xml:id="echoid-s18598" xml:space="preserve"/>
</p>
<div xml:id="echoid-div951" type="float" level="2" n="2">
<note position="right" xlink:label="note-0289-06" xlink:href="note-0289-06a" xml:space="preserve">Aequinoctialis <lb/>horologij Aſtro <lb/>nomici deſcri-<lb/>ptio.</note>
<note position="right" xlink:label="note-0289-07" xlink:href="note-0289-07a" xml:space="preserve">Quomodo ho-<lb/>rologium æqui <lb/>noctiale collo-<lb/>candum ſit, ve <lb/>horas mõſtret.</note>
<note position="left" xlink:label="note-0289-08" xlink:href="note-0289-08a" xml:space="preserve">50</note>
</div>
<pb o="274" file="0290" n="290" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s18599" xml:space="preserve">QVONIAM punctum F, extremum ſtyli idem eſt, quod centrum mundi, ex propoſ. </s>
  <s xml:id="echoid-s18600" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18601" xml:space="preserve">ſupe-<lb/>
<anchor type="note" xlink:label="note-0290-01a" xlink:href="note-0290-01"/>
rioris lib. </s>
  <s xml:id="echoid-s18602" xml:space="preserve">fit vt, ſi circa centrum mundi F, intelligatur æquinoctialis circulus, cui planum horolo-<lb/>gii æquidiſtat, in propria poſi-<lb/>
<anchor type="figure" xlink:label="fig-0290-01a" xlink:href="fig-0290-01"/>
tione, ſtylus E F, ſit axis mundi. <lb/></s>
  <s xml:id="echoid-s18603" xml:space="preserve">Cum enim axis mundi rectus <lb/>ſitad planũ Aequatoris in mun <lb/>di centro, ſitq́ue ſtylus E F, qui <lb/>rectus eſt ad planum horologij, <lb/>ad planum Aequatoris rectus, <lb/>vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s18604" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18605" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18606" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18607" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0290-02a" xlink:href="note-0290-02"/>
Euclidis demõſtrauimus, quòd <lb/>duo hæc plana parallela ponan-<lb/>tur; </s>
  <s xml:id="echoid-s18608" xml:space="preserve">erit omnino ſtylus E F, pars <lb/>axis mundani. </s>
  <s xml:id="echoid-s18609" xml:space="preserve">Quia vero circu-<lb/>li horarum à meridie, vel me-<lb/>dia nocte ſecant maximum pa-<lb/>rallelorum ſemper apparentiũ, <lb/>atque adeò, ex propoſ. </s>
  <s xml:id="echoid-s18610" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18611" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18612" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s18613" xml:space="preserve">Theodoſii, &amp; </s>
  <s xml:id="echoid-s18614" xml:space="preserve">Aequatorem, qui <lb/>eſt omnium parallelorum maxi <lb/>
<anchor type="note" xlink:label="note-0290-03a" xlink:href="note-0290-03"/>
mus, &amp; </s>
  <s xml:id="echoid-s18615" xml:space="preserve">parallelum illum ſphæ-<lb/>ræ, in quo planum horologii <lb/>exiſtit, &amp; </s>
  <s xml:id="echoid-s18616" xml:space="preserve">cuius centrum eſt E, <lb/>(quòd per propoſ. </s>
  <s xml:id="echoid-s18617" xml:space="preserve">10. </s>
  <s xml:id="echoid-s18618" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18619" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s18620" xml:space="preserve">Theodoſii, axis E F, per centrũ <lb/>ipſius neceſſario tranſit) in 24. </s>
  <s xml:id="echoid-s18621" xml:space="preserve"><lb/>partes æquales, tranſeuntq́ue <lb/>omnes per axem mundi, atque <lb/>adeo per punctum E, in quo, per propoſ. </s>
  <s xml:id="echoid-s18622" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18623" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18624" xml:space="preserve">communes eorum, &amp; </s>
  <s xml:id="echoid-s18625" xml:space="preserve">dicti paralleli ſe-<lb/>ctiones ſe interſecant; </s>
  <s xml:id="echoid-s18626" xml:space="preserve">erunt rectæ ex E, ad puncta diuiſionum illius paralleli, in quo horologium <lb/>
<anchor type="note" xlink:label="note-0290-04a" xlink:href="note-0290-04"/>
exiſtit, eductæ, ſectiones communes circulorum horariorum à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s18627" xml:space="preserve">dicti <lb/>paralleli. </s>
  <s xml:id="echoid-s18628" xml:space="preserve">Cum ergo hæ rectæ diuidant quoque, ex jis, quæ prope finem cap. </s>
  <s xml:id="echoid-s18629" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18630" xml:space="preserve">ſphæræ demon-<lb/>ſtrauimus, circulum A C B D, illi parallelo ſphæræ concentricum, in 24. </s>
  <s xml:id="echoid-s18631" xml:space="preserve">partes æquales, erunt <lb/>eædem rectæ per centrum E, &amp; </s>
  <s xml:id="echoid-s18632" xml:space="preserve">puncta diuiſionum circuli A C B D, emiſſæ, communes ſectiones <lb/>circulorum horarum à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s18633" xml:space="preserve">plani horologij, hoc eſt, lineæ horarum à me-<lb/>ridie, vel media nocte; </s>
  <s xml:id="echoid-s18634" xml:space="preserve">ita vt A B, ſit ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s18635" xml:space="preserve">plani horologij, recta deinde per ſequens <lb/>punctum ab A, verſus D, &amp; </s>
  <s xml:id="echoid-s18636" xml:space="preserve">per centrum E, ducta communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s18637" xml:space="preserve">circuli ho-<lb/>ræ 1. </s>
  <s xml:id="echoid-s18638" xml:space="preserve">à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s18639" xml:space="preserve">ſic deinceps. </s>
  <s xml:id="echoid-s18640" xml:space="preserve">Horologium igitur Aſtronomicum æquinoctia-<lb/>le deſcripſimus, &amp;</s>
  <s xml:id="echoid-s18641" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18642" xml:space="preserve">Quod erat faciendum. <lb/></s>
</p>
</div>
<div xml:id="echoid-div953" type="section" level="1" n="232">
<head xml:id="echoid-head239" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s18643" xml:space="preserve">SI in plano aliquo ſtabili, quod Aequatori æquidiſtet, horologium ſit deſcribendum, datus ſit lo-<lb/>
<anchor type="note" xlink:label="note-0290-06a" xlink:href="note-0290-06"/>
cus ſtyli cuiusuis in puncto E, ducenda erit beneficio libellæ, &amp; </s>
  <s xml:id="echoid-s18644" xml:space="preserve">perpendiculi per E, recta C D, Horizonti <lb/>æquidiſtans, quam in E, ad angulos rectos ſecet recta A B. </s>
  <s xml:id="echoid-s18645" xml:space="preserve">Hæc enim erit linea meridiana. </s>
  <s xml:id="echoid-s18646" xml:space="preserve">Reliqua om-<lb/>nia perficienda erunt, vt prius.</s>
  <s xml:id="echoid-s18647" xml:space="preserve"/>
</p>
<div xml:id="echoid-div953" type="float" level="2" n="1">
<note position="left" xlink:label="note-0290-01" xlink:href="note-0290-01a" xml:space="preserve">Demonſtratio <lb/>conſtructionis <lb/>horologii æqui-<lb/>noctialis Aſtro <lb/>nomici.</note>
  <figure xlink:label="fig-0290-01" xlink:href="fig-0290-01a">
    <image file="0290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0290-01"/>
  </figure>
<note position="left" xlink:label="note-0290-02" xlink:href="note-0290-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0290-03" xlink:href="note-0290-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0290-04" xlink:href="note-0290-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0290-06" xlink:href="note-0290-06a" xml:space="preserve">Quo pacto idẽ <lb/>horologiã ęqui <lb/>noctiale con-<lb/>ſtruendũ ſit in <lb/>plano ſtabili, in <lb/>quo locus ſtyli <lb/>datus ſit.</note>
</div>
</div>
<div xml:id="echoid-div955" type="section" level="1" n="233">
<head xml:id="echoid-head240" xml:space="preserve">PROBLEMA 50. PROPOSITIO 50.</head>
<p>
  <s xml:id="echoid-s18648" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in prædicto ho-<lb/>
<anchor type="note" xlink:label="note-0290-07a" xlink:href="note-0290-07"/>
rologio æquinoctiali deſignare.</s>
  <s xml:id="echoid-s18649" xml:space="preserve"/>
</p>
<div xml:id="echoid-div955" type="float" level="2" n="1">
<note position="left" xlink:label="note-0290-07" xlink:href="note-0290-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s18650" xml:space="preserve">REPETATVR prima figura propoſ. </s>
  <s xml:id="echoid-s18651" xml:space="preserve">26. </s>
  <s xml:id="echoid-s18652" xml:space="preserve">huius libri, in qua ex axe E G, abſcindatur recta <lb/>
<anchor type="note" xlink:label="note-0290-08a" xlink:href="note-0290-08"/>
E a, ſtylo cuiuſuis magnitudinis aſſumpto æqualis, &amp; </s>
  <s xml:id="echoid-s18653" xml:space="preserve">per a, Æquatoris diametro HI, parallela <lb/>agatur, quæ erit communis ſectio plani horologii, ac Meridiani, cum planum horologii per illam <lb/>parallelam ductum plano Aequatoris per rectam HI, ducto æquidiſtet ſecundum magnitudinem <lb/>ſtyli E a. </s>
  <s xml:id="echoid-s18654" xml:space="preserve">Productis autem diametris Zodiaci ſigna oppoſita connectentibus, vt fiant triangula per <lb/>axem in conis, quorum baſes ſunt paralleli Aequatoris, &amp; </s>
  <s xml:id="echoid-s18655" xml:space="preserve">vertex communis centrum E, erunt por <lb/>tiones parallelæ per a, ductæ, interceptæ inter latera triangulorum per axem, diametri conicarum <lb/>ſectionum, quæ quidem ex coroll. </s>
  <s xml:id="echoid-s18656" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s18657" xml:space="preserve">4. </s>
  <s xml:id="echoid-s18658" xml:space="preserve">ſuperioris lib circuli ſunt habentes centra in puncto
<pb o="275" file="0291" n="291" rhead="LIBER SECVNDVS."/>
E, in horologio, hoc eſt, in axe mundi, per eandem propoſitionem 4. </s>
  <s xml:id="echoid-s18659" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s18660" xml:space="preserve">Quare ſi ex <lb/>a, ſumantur ſemidiametri vſque ad triangulorum per axem latera, &amp; </s>
  <s xml:id="echoid-s18661" xml:space="preserve">ad earum interualla ex E, cen <lb/>tro horologii circuli deſcribantur, deſcripti erunt paralleli borealium ſignorum Zodiaci in horo-<lb/>logio ſuperiori, cum radij ſignorum borealium in prædictam parallelam cadant per centrum E, <lb/>
<anchor type="figure" xlink:label="fig-0291-01a" xlink:href="fig-0291-01"/>
<anchor type="note" xlink:label="note-0291-01a" xlink:href="note-0291-01"/>
<anchor type="note" xlink:label="note-0291-02a" xlink:href="note-0291-02"/>
<anchor type="note" xlink:label="note-0291-03a" xlink:href="note-0291-03"/>
producti. </s>
  <s xml:id="echoid-s18662" xml:space="preserve">Quòd ſi ex axe E F, accipiatur rurſum recta E e, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s18663" xml:space="preserve">eadem fiant, deſcriben-<lb/>tur eodem modo in inferiori horologio paralleli ſignorum auſtralium Zodiaci, quòd radii ſigno <lb/>rum auſtralium in parallelam per e, ductam cadant, ſi per centrum E, extendantur. </s>
  <s xml:id="echoid-s18664" xml:space="preserve">Sed ſatis eſt, <lb/>ſi eiſdem ſemidiametris ex a, ſumptis circuli deſcribantur in horologio inferiori. </s>
  <s xml:id="echoid-s18665" xml:space="preserve">Nam ſemidia-<lb/>metri in parallela per a, ducta contentæ, æquales ſunt reſpondentibus ſemidiametris in parallela <lb/>
<anchor type="note" xlink:label="note-0291-04a" xlink:href="note-0291-04"/>
per e, ducta contentis. </s>
  <s xml:id="echoid-s18666" xml:space="preserve">Quoniam enim, verbi gratia, in triangulis E a b, E e g, anguli ad puncta a, &amp; </s>
  <s xml:id="echoid-s18667" xml:space="preserve"><lb/>e, recti ſunt, &amp; </s>
  <s xml:id="echoid-s18668" xml:space="preserve">anguli alterni b, &amp; </s>
  <s xml:id="echoid-s18669" xml:space="preserve">g, æquales, propter parallelas lineas per a, &amp; </s>
  <s xml:id="echoid-s18670" xml:space="preserve">e, ductas, ſuntq́ue la-<lb/>
<anchor type="note" xlink:label="note-0291-05a" xlink:href="note-0291-05"/>
tera E a, E e, æqualia; </s>
  <s xml:id="echoid-s18671" xml:space="preserve">erunt quoque latera a b, e g, æqualia, nempe ſemidiametri conicarum ſectio-<lb/>
<anchor type="note" xlink:label="note-0291-06a" xlink:href="note-0291-06"/>
num: </s>
  <s xml:id="echoid-s18672" xml:space="preserve">eademq̀ue in cæteris eſt demonſtratio.</s>
  <s xml:id="echoid-s18673" xml:space="preserve"/>
</p>
<div xml:id="echoid-div956" type="float" level="2" n="2">
<note position="left" xlink:label="note-0290-08" xlink:href="note-0290-08a" xml:space="preserve">Arcus ſignorũ <lb/>in horologio ę <lb/>quinoctiali quo <lb/>modo deſcribã <lb/>tur ex Analem-<lb/>mate.</note>
  <figure xlink:label="fig-0291-01" xlink:href="fig-0291-01a">
    <image file="0291-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0291-01"/>
  </figure>
<note position="left" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0291-02" xlink:href="note-0291-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0291-03" xlink:href="note-0291-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0291-04" xlink:href="note-0291-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0291-05" xlink:href="note-0291-05a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0291-06" xlink:href="note-0291-06a" xml:space="preserve">26. primi.</note>
</div>
<note position="right" xml:space="preserve">Alia deſcriptio <lb/>arcuum ſigno-<lb/>rnm in eodem <lb/>horologio æqui <lb/>noctiali.</note>
<p>
  <s xml:id="echoid-s18674" xml:space="preserve">EOSDEM parallelos deſcribemus ex poſtrema figura propoſ. </s>
  <s xml:id="echoid-s18675" xml:space="preserve">26. </s>
  <s xml:id="echoid-s18676" xml:space="preserve">huius libri, hoc modo. <lb/></s>
  <s xml:id="echoid-s18677" xml:space="preserve">Ex axe D G, vtrinque abſcindantur rectæ D h, D q, ſtylo æquales, &amp; </s>
  <s xml:id="echoid-s18678" xml:space="preserve">per h, q, agantur h l, q n, pa-<lb/>rallelæ radio Æquatoris D C. </s>
  <s xml:id="echoid-s18679" xml:space="preserve">Nam rectæ inter puncta h, q, &amp; </s>
  <s xml:id="echoid-s18680" xml:space="preserve">radios ſignorum comprehenſæ ſunt <lb/>æquales ſemidiametris conicarum ſectionum prius inuentis. </s>
  <s xml:id="echoid-s18681" xml:space="preserve">Quoniam enim v. </s>
  <s xml:id="echoid-s18682" xml:space="preserve">g. </s>
  <s xml:id="echoid-s18683" xml:space="preserve">in triangulis <lb/>
<anchor type="note" xlink:label="note-0291-08a" xlink:href="note-0291-08"/>
E a b, D h m, D q o, quorum illud in priori figura, hæc autem in poſteriori cõtinentur, anguli ad <lb/>puncta a, h, q, recti ſunt, &amp; </s>
  <s xml:id="echoid-s18684" xml:space="preserve">anguli a E b, h D m, q D o, ęquales, quòd quilibet eorũ ſit cõplemento <lb/>
<anchor type="note" xlink:label="note-0291-09a" xlink:href="note-0291-09"/>
declinationis accepti paralleli æqualis, vt conſtat; </s>
  <s xml:id="echoid-s18685" xml:space="preserve">ſuntq́ue latera E a, D h, D q, æqualia, ex con-<lb/>
<anchor type="note" xlink:label="note-0291-10a" xlink:href="note-0291-10"/>
ſtructione; </s>
  <s xml:id="echoid-s18686" xml:space="preserve">erunt quoque latera a b, h m, q o, æqualia. </s>
  <s xml:id="echoid-s18687" xml:space="preserve">Ex quo patet, ſatis etiam eſſe, ſi vna tantũ <lb/>
<anchor type="note" xlink:label="note-0291-11a" xlink:href="note-0291-11"/>
parallela ducatur, nempe vel h l, vel q n, vt inueniantur ſemidia metri circulorum, vel ſectionum <lb/>conicarum in vtroque horologio. </s>
  <s xml:id="echoid-s18688" xml:space="preserve">Cum enim oſtenſum ſit, ſemidiametros vtriuſque parallelæ <lb/>æquales eſſe ſemidiametris parallelę per a, ductę in priori figura; </s>
  <s xml:id="echoid-s18689" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s18690" xml:space="preserve">ipſæ inter ſe æquales. <lb/></s>
  <s xml:id="echoid-s18691" xml:space="preserve">
<anchor type="note" xlink:label="note-0291-12a" xlink:href="note-0291-12"/>
Manifeſtum autem eſt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s18692" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18693" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18694" xml:space="preserve">lineam æquinoctialem in horologio <lb/>æquinoctiali deſcribi non poſſe, ſed totam euaneſcere; </s>
  <s xml:id="echoid-s18695" xml:space="preserve">propterea quòd Aequator plano vtriuſq; <lb/></s>
  <s xml:id="echoid-s18696" xml:space="preserve">horologii ęquinoctialis æquidiſtat. </s>
  <s xml:id="echoid-s18697" xml:space="preserve">Quòd ſi horas obſeruare libuerit prope tempus ęquinoctio-<lb/>
<anchor type="note" xlink:label="note-0291-13a" xlink:href="note-0291-13"/>
rum, nempe ante, vel poſt ęquinoctia, producendæ erunt lineę horarię vltra extremum circulum, <lb/>qui in ſuperiori horologio ſignis ♉, &amp; </s>
  <s xml:id="echoid-s18698" xml:space="preserve">♍, in inferiori verò ſignis ♏, &amp; </s>
  <s xml:id="echoid-s18699" xml:space="preserve">♓, deputatur; </s>
  <s xml:id="echoid-s18700" xml:space="preserve">producen-<lb/>dę, inquam, erunt, quantum magnitudo plani, in quo deſcribitur horologium, patietur: </s>
  <s xml:id="echoid-s18701" xml:space="preserve">vel certè
<pb o="276" file="0292" n="292" rhead="GNOMONICES"/>
deſcribendus erit circulus alicuius gradus Eclipticæ prope equinoctialẽ circulum, vt in horologio <lb/>ſuperiori v. </s>
  <s xml:id="echoid-s18702" xml:space="preserve">g. </s>
  <s xml:id="echoid-s18703" xml:space="preserve">gradus 25. </s>
  <s xml:id="echoid-s18704" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s18705" xml:space="preserve">gradus 5. </s>
  <s xml:id="echoid-s18706" xml:space="preserve">♈; </s>
  <s xml:id="echoid-s18707" xml:space="preserve">in inferiori autẽ gradus 25. </s>
  <s xml:id="echoid-s18708" xml:space="preserve">♓, &amp; </s>
  <s xml:id="echoid-s18709" xml:space="preserve">gradus 5. </s>
  <s xml:id="echoid-s18710" xml:space="preserve">♎, &amp;</s>
  <s xml:id="echoid-s18711" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s18712" xml:space="preserve">quoniam circa æquinoctiorum tempora longiſſima efficitur vmbra ſtyli, in ipſis verò æquinoctiis <lb/>infinita, &amp; </s>
  <s xml:id="echoid-s18713" xml:space="preserve">plano horologij æquidiſtans, vt ex dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s18714" xml:space="preserve">11. </s>
  <s xml:id="echoid-s18715" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18716" xml:space="preserve">perſpicuum <lb/>eſt. </s>
  <s xml:id="echoid-s18717" xml:space="preserve">Idem de horis ab ortu, &amp; </s>
  <s xml:id="echoid-s18718" xml:space="preserve">occaſu intelligendum eſt, de quibus propoſ. </s>
  <s xml:id="echoid-s18719" xml:space="preserve">58. </s>
  <s xml:id="echoid-s18720" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18721" xml:space="preserve">59. </s>
  <s xml:id="echoid-s18722" xml:space="preserve">huius li-<lb/>bri agemus.</s>
  <s xml:id="echoid-s18723" xml:space="preserve"/>
</p>
<div xml:id="echoid-div957" type="float" level="2" n="3">
<note position="right" xlink:label="note-0291-08" xlink:href="note-0291-08a" xml:space="preserve">Demonſtratio <lb/>poſterioris hu-<lb/>r<unsure/>uſce deſcriptio <lb/>nis parallelor@ <lb/>solis.</note>
<note position="left" xlink:label="note-0291-09" xlink:href="note-0291-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0291-10" xlink:href="note-0291-10a" xml:space="preserve">26. primi.</note>
<note position="right" xlink:label="note-0291-11" xlink:href="note-0291-11a" xml:space="preserve">Satis eſt, ſ<unsure/>i<unsure/> <lb/>in poſteriori <lb/>modo ducatur <lb/>vel ſola paralle <lb/>la h l, vel q n.</note>
<note position="right" xlink:label="note-0291-12" xlink:href="note-0291-12a" xml:space="preserve">Linea ęquino-<lb/>ctialis deſcribi <lb/>nõ poteſt in ho <lb/>rologio æquino <lb/>cti<unsure/>ali.</note>
<note position="right" xlink:label="note-0291-13" xlink:href="note-0291-13a" xml:space="preserve">Quid agend@, <lb/>vt vmbra horas <lb/>indicet prope<unsure/> <lb/>tempus æquino <lb/>ctiorum.</note>
</div>
<p>
  <s xml:id="echoid-s18724" xml:space="preserve">LINEA horizontalis, in quam, Sole oriente, vel occidente, vmbra ſtyli proiicitur, ita deſcri-<lb/>
<anchor type="note" xlink:label="note-0292-01a" xlink:href="note-0292-01"/>
bitur. </s>
  <s xml:id="echoid-s18725" xml:space="preserve">In prima figura propoſ. </s>
  <s xml:id="echoid-s18726" xml:space="preserve">26. </s>
  <s xml:id="echoid-s18727" xml:space="preserve">huius libri notentur puncta h, i, in quibus Horizontis diame-<lb/>ter B D, parallelas per a, &amp; </s>
  <s xml:id="echoid-s18728" xml:space="preserve">e, ductas ſecat, &amp; </s>
  <s xml:id="echoid-s18729" xml:space="preserve">recta a h, vel e i, transferatur in lineam meridianã ho-<lb/>rologii ſuperioris ſupra locum ſtyli ex E, vſque ad m, infra verò locum ſtyli in horologio inferiori, <lb/>
<anchor type="note" xlink:label="note-0292-02a" xlink:href="note-0292-02"/>
atque per m, ducatur lineæ horæ ſextæ parallela. </s>
  <s xml:id="echoid-s18730" xml:space="preserve">Hæc enim erit horizontalis linea. </s>
  <s xml:id="echoid-s18731" xml:space="preserve">Cum enim <lb/>Horizon per B D, ductus plano horologij ſuperioris per a h, lineam meridianam ducto in puncto <lb/>h, plano verò horologij inferioris per lineam meridianam e i, ducto in puncto i, occurrat; </s>
  <s xml:id="echoid-s18732" xml:space="preserve">mani-<lb/>feſtum eſt, ſi rectam a h, ex loco ſtyli in ſuperiori horologio transferamus in lineam meridianam <lb/>ſupra locum ſtyli, vſque ad punctum m, lineam horizontalem per m, tranſire; </s>
  <s xml:id="echoid-s18733" xml:space="preserve">propterea quòd in <lb/>horologio ſuperiori in puncto h, coeant communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s18734" xml:space="preserve">Meridiani factæ à <lb/>plano horologij illos ſecante, ex propoſ. </s>
  <s xml:id="echoid-s18735" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18736" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18737" xml:space="preserve">quandoquidem communis ſectio Hori <lb/>zontis, &amp; </s>
  <s xml:id="echoid-s18738" xml:space="preserve">Meridiani, hoc eſt, recta B D, plano horologij ſuperioris occurrit in h; </s>
  <s xml:id="echoid-s18739" xml:space="preserve">cuiuſmodi ſectio-<lb/>nes ſunt linea horizontalis, &amp; </s>
  <s xml:id="echoid-s18740" xml:space="preserve">linea meridiana. </s>
  <s xml:id="echoid-s18741" xml:space="preserve">Quia verò Horizon, circulus horæ 6. </s>
  <s xml:id="echoid-s18742" xml:space="preserve">à meridie, <lb/>vel media nocte, &amp; </s>
  <s xml:id="echoid-s18743" xml:space="preserve">Aequator vnam habent, &amp; </s>
  <s xml:id="echoid-s18744" xml:space="preserve">eandem communem ſectionem, cui æquidiſtat pla-<lb/>
<anchor type="note" xlink:label="note-0292-03a" xlink:href="note-0292-03"/>
num horologij, quòd Aequatori, in quo illa communis ſectio eſt, æquidiſtet; </s>
  <s xml:id="echoid-s18745" xml:space="preserve">erunt reliquorum <lb/>circulorum communes ſectiones cum plano horologii parallelæ, nempe linea horizontalis, &amp; </s>
  <s xml:id="echoid-s18746" xml:space="preserve">li-<lb/>nea horæ 6. </s>
  <s xml:id="echoid-s18747" xml:space="preserve">ex propoſ. </s>
  <s xml:id="echoid-s18748" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18749" xml:space="preserve">vel ex ſcholio propoſ. </s>
  <s xml:id="echoid-s18750" xml:space="preserve">22. </s>
  <s xml:id="echoid-s18751" xml:space="preserve">præcedentis lib. </s>
  <s xml:id="echoid-s18752" xml:space="preserve">Quamobrem recta per m, du-<lb/>cta lineæ horæ 6. </s>
  <s xml:id="echoid-s18753" xml:space="preserve">parallela, horizontalis linea eſt, hoc eſt, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s18754" xml:space="preserve">plani <lb/>horologii. </s>
  <s xml:id="echoid-s18755" xml:space="preserve">Eodem modo, ſi rectam e<unsure/> i, in lineam meridianam horologii inferioris infra locũ gno-<lb/>monis transferamus, habebimus punctum, per quod linea horizontalis eſt ducenda. </s>
  <s xml:id="echoid-s18756" xml:space="preserve">Sed quia re-<lb/>cta e i, rectæ a h, eſt æqualis, (quoniam enim in triangulis E a h, E e i, anguli ad a, e, recti ſunt, &amp; </s>
  <s xml:id="echoid-s18757" xml:space="preserve"><lb/>anguli ad verticem E, æquales, lateraq́ue E a, E e, æqualia; </s>
  <s xml:id="echoid-s18758" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s18759" xml:space="preserve">latera a h, e i, æqualia) idcirco <lb/>
<anchor type="note" xlink:label="note-0292-04a" xlink:href="note-0292-04"/>
præcepimus, eandem a h, vel e i, in vtroque horologio transferendam eſſe in lineam meridianam <lb/>
<anchor type="note" xlink:label="note-0292-05a" xlink:href="note-0292-05"/>
ſupra vel infra locum ſtyli.</s>
  <s xml:id="echoid-s18760" xml:space="preserve"/>
</p>
<div xml:id="echoid-div958" type="float" level="2" n="4">
<note position="left" xlink:label="note-0292-01" xlink:href="note-0292-01a" xml:space="preserve">Horizontalis li <lb/>nea quo pacto <lb/>in æquinoctia-<lb/>li horologio de <lb/>ſcribatur.</note>
<note position="left" xlink:label="note-0292-02" xlink:href="note-0292-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0292-03" xlink:href="note-0292-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0292-04" xlink:href="note-0292-04a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0292-05" xlink:href="note-0292-05a" xml:space="preserve">26. primi.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s18761" xml:space="preserve">IDEM punctum m, per quod ducenda eſt linea horizontalis lineæ horæ 6. </s>
  <s xml:id="echoid-s18762" xml:space="preserve">parallela, hac arte <lb/>
<anchor type="note" xlink:label="note-0292-07a" xlink:href="note-0292-07"/>
inuenietur. </s>
  <s xml:id="echoid-s18763" xml:space="preserve">In linea horæ 6. </s>
  <s xml:id="echoid-s18764" xml:space="preserve">horologii accipiatur E l, æqualis ſtylo, &amp; </s>
  <s xml:id="echoid-s18765" xml:space="preserve">ſiat angulus E l m, altitudi-<lb/>ni poli æqualis, ita vt recta l m, ſecans lineam meridianam in m, cadat ſurſum verſus in ſuperiori <lb/>horologio, deorſum autem verſus in inferiori. </s>
  <s xml:id="echoid-s18766" xml:space="preserve">Quod facile fiet, ſi ex l, arcus circuli deſcribatur <lb/>ſiue ſupra rectam C D, ſiue infra, verſus meridianam lineam, &amp; </s>
  <s xml:id="echoid-s18767" xml:space="preserve">in eo numeretur à recta C D, ar-<lb/>cus altitudinis poli, à cuius extremo puncto ad l, recta ducatur ſecans meridianam lineam in pun-<lb/>cto m. </s>
  <s xml:id="echoid-s18768" xml:space="preserve">Per punctum enim m, ducenda eſt linea horizontalis, vt prius. </s>
  <s xml:id="echoid-s18769" xml:space="preserve">Intelligatur enim trian-<lb/>gulum E l m, circa lineam meridianam conuerti, donec rectum ſit ad planum horologij, &amp; </s>
  <s xml:id="echoid-s18770" xml:space="preserve">in pla-<lb/>no Meridiani exiſtat, atque adeò punctum l, cum vertice ſtvli, ſeu centro mundi coniungatur, &amp; </s>
  <s xml:id="echoid-s18771" xml:space="preserve"><lb/>recta E l, cum ſtylo, ſeu axe mundi. </s>
  <s xml:id="echoid-s18772" xml:space="preserve">tranſibit Horizon per l, verticem ſtyli, ac proinde per rectam <lb/>
<anchor type="note" xlink:label="note-0292-08a" xlink:href="note-0292-08"/>
l m; </s>
  <s xml:id="echoid-s18773" xml:space="preserve">propterea quòd angulus E l m, altitudini poli æqualis eſt, qualem nimitum cum axe in cen-<lb/>tro mundi l, facit communis ſectio Horizontis, ac Meridiani. </s>
  <s xml:id="echoid-s18774" xml:space="preserve">Immo &amp; </s>
  <s xml:id="echoid-s18775" xml:space="preserve">reliquus E m l, comple-<lb/>mento altitudinis poli æqualis eſt, qualem nimirum facit Horizon cum Aequatore in plano Meri <lb/>diani circuli; </s>
  <s xml:id="echoid-s18776" xml:space="preserve">qui quidem angulus æqual@s eſt angulo, quem Horizon cum plano horologii, quod <lb/>Aequatori parallelum eſt, in eodem Meridiani plano conſtituit. </s>
  <s xml:id="echoid-s18777" xml:space="preserve">Quoniam enim ſectiones Meri-<lb/>diani, quas cum Aequatore, &amp; </s>
  <s xml:id="echoid-s18778" xml:space="preserve">plano horologij illi parallelo facit, ſunt parallelæ, faciet communis <lb/>
<anchor type="note" xlink:label="note-0292-09a" xlink:href="note-0292-09"/>
ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s18779" xml:space="preserve">Meridiani angulos æquales cum dictis ſectionibus, quarum vna eſt linea me-<lb/>
<anchor type="note" xlink:label="note-0292-10a" xlink:href="note-0292-10"/>
ridiana in Aequatore, &amp; </s>
  <s xml:id="echoid-s18780" xml:space="preserve">altera in horologii plano, externũ ſcilicet, &amp; </s>
  <s xml:id="echoid-s18781" xml:space="preserve">internũ. </s>
  <s xml:id="echoid-s18782" xml:space="preserve">Quare Horizon pla <lb/>num horologij ſecabit in m; </s>
  <s xml:id="echoid-s18783" xml:space="preserve">ac idcirco pet m, linea horizontalis ducẽda eſt. </s>
  <s xml:id="echoid-s18784" xml:space="preserve">Parallelos igitur, ſiue <lb/>arcus ſignorum Zodiaci in prædicto horologio ęquinoctiali deſignauimus. </s>
  <s xml:id="echoid-s18785" xml:space="preserve">Quod faciendũ erat.</s>
  <s xml:id="echoid-s18786" xml:space="preserve"/>
</p>
<div xml:id="echoid-div959" type="float" level="2" n="5">
<note position="left" xlink:label="note-0292-07" xlink:href="note-0292-07a" xml:space="preserve">Alia deſcriptio <lb/>horizontalis li-<lb/>neæ in horolo-<lb/>gio æquino-<lb/>ctiali.</note>
<note position="left" xlink:label="note-0292-08" xlink:href="note-0292-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0292-09" xlink:href="note-0292-09a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0292-10" xlink:href="note-0292-10a" xml:space="preserve">29. primi.</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div961" type="section" level="1" n="234">
<head xml:id="echoid-head241" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">Pottio horolo-<lb/>gii æquinoctia-<lb/>lis abſciſſa à li-<lb/>nea horizonra <lb/>li, quo pacto ho <lb/>rologium Infe-<lb/>rius efficiatur.</note>
<p style="it">
  <s xml:id="echoid-s18787" xml:space="preserve">PARS ea horologĳ, quam linea horizont alis abſcindit, erit ipſum horologium inferius, ſi omnia in-<lb/>uertantur, vt in præcedentibus factum eſt, hoc eſt, ſi linea horizontalis in infcriori facie plani ſuperiorẽ <lb/>teneat locum, &amp; </s>
  <s xml:id="echoid-s18788" xml:space="preserve">pars, quæ in eo ſitu dextra eſt, mutetur in ſiniſtram, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s18789" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18790" xml:space="preserve">huius <lb/>libri ostendimus. </s>
  <s xml:id="echoid-s18791" xml:space="preserve">Verum arcus ſignorum borealium mutantur in arcus oppoſitorum ſignorum au-<lb/>ſtralium; </s>
  <s xml:id="echoid-s18792" xml:space="preserve">propterea quòd vmbra ſtyli cadit in inferius horologium, Sole exiſtente in ſignis auſtralibus, <lb/>
<anchor type="note" xlink:label="note-0292-13a" xlink:href="note-0292-13"/>
vt conſtat.</s>
  <s xml:id="echoid-s18793" xml:space="preserve"/>
</p>
<div xml:id="echoid-div961" type="float" level="2" n="1">
<note position="left" xlink:label="note-0292-13" xlink:href="note-0292-13a" xml:space="preserve">Eadem pottio <lb/>abſciſſa in ſupe <lb/>riori horologio <lb/>eſt hotologium <lb/>@octuinum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s18794" xml:space="preserve">PORTIO quoque abſciſſa à linea horizontali exhibet nobis horologium nocturnum, vt in præce-<lb/>dentibus dictum eſt.</s>
  <s xml:id="echoid-s18795" xml:space="preserve"/>
</p>
<pb o="277" file="0293" n="293" rhead="LIBER SECVNDVS."/>
<p style="it">
  <s xml:id="echoid-s18796" xml:space="preserve">QVONIAM verò, vt in præcedenti propoſ. </s>
  <s xml:id="echoid-s18797" xml:space="preserve">oſtendimus, circuli horarum à meridie, vel media <lb/>
<anchor type="note" xlink:label="note-0293-01a" xlink:href="note-0293-01"/>
nocte diuidunt circulum quemcunque ex centro E, deſcriptum (eadem enim demonſtratio in omnem cir-<lb/>culum, quæ in circulum A C B D, ibi deſcriptum, conuenit) in partes æquales, fit vt in æquinoctiali ho-<lb/>rologio lineæ earundem horarum ſecent parallelos ſignorum in partes æquales, quippe qui circuli ſint ex <lb/>eodem centro E, deſcripti, vt in hac propoſ. </s>
  <s xml:id="echoid-s18798" xml:space="preserve">probatum eſt. </s>
  <s xml:id="echoid-s18799" xml:space="preserve">Id quod in nullo alio horologio contingit. <lb/></s>
  <s xml:id="echoid-s18800" xml:space="preserve">Inęqualia enim ſpatia intercipiunt lineæ horarum à meridie, vel media nocte in parallelis ſignorum in <lb/>alĳs horologĳs deſcriptis.</s>
  <s xml:id="echoid-s18801" xml:space="preserve"/>
</p>
<div xml:id="echoid-div962" type="float" level="2" n="2">
<note position="right" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">Arcus ſignorũ <lb/>in horologio ę-<lb/>quinoctiali di-<lb/>uiduntur à li-<lb/>neis horarum à <lb/>mer. vel med. <lb/>noc. in partes <lb/>equales.</note>
</div>
</div>
<div xml:id="echoid-div964" type="section" level="1" n="235">
<head xml:id="echoid-head242" xml:space="preserve">PROBLEMA 51. PROPOSITIO 51.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s18802" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem æquinoctiali <lb/>horologio deſcribere.</s>
  <s xml:id="echoid-s18803" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18804" xml:space="preserve">SI loco parallelorum per ſignorum principia ductorum accipiantur paralleli arcuum diurno <lb/>
<anchor type="note" xlink:label="note-0293-03a" xlink:href="note-0293-03"/>
rum, &amp; </s>
  <s xml:id="echoid-s18805" xml:space="preserve">pro radijs ſignorum radij arcuum diurnorum, deſcribentur in horologio æquinoctiali <lb/>paralleli arcuum diurnorum, quemadmodum parallelos ſignorum in præcedenti propoſ. </s>
  <s xml:id="echoid-s18806" xml:space="preserve">deſcri-<lb/>pſimus. </s>
  <s xml:id="echoid-s18807" xml:space="preserve">Quamobrem parallelos arcuum diurnorum in eodem æquinoctiali horologio deſcri-<lb/>pſimus. </s>
  <s xml:id="echoid-s18808" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s18809" xml:space="preserve"/>
</p>
<div xml:id="echoid-div964" type="float" level="2" n="1">
<note position="right" xlink:label="note-0293-03" xlink:href="note-0293-03a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſignorũ <lb/>in eodem horo <lb/>logio æquino-<lb/>ctiali.</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div966" type="section" level="1" n="236">
<head xml:id="echoid-head243" xml:space="preserve">PROBLEMA 52. PROPOSITIO 52.</head>
<p>
  <s xml:id="echoid-s18810" xml:space="preserve">CIRCVLOS Verticales in horologio codem æquinoctiali <lb/>delineare.</s>
  <s xml:id="echoid-s18811" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18812" xml:space="preserve">IN figura prima propoſ. </s>
  <s xml:id="echoid-s18813" xml:space="preserve">26. </s>
  <s xml:id="echoid-s18814" xml:space="preserve">huius libri notentur puncta n, &amp; </s>
  <s xml:id="echoid-s18815" xml:space="preserve">o, vbi diameter Verticalis A C, <lb/>
<anchor type="note" xlink:label="note-0293-05a" xlink:href="note-0293-05"/>
parallelas per a, &amp; </s>
  <s xml:id="echoid-s18816" xml:space="preserve">e, ductas ſecat; </s>
  <s xml:id="echoid-s18817" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18818" xml:space="preserve">recta a n, vel e o, transferatur in lineam meridianam ex loco <lb/>ſtyli, deorſum quidem in ſuperiori horologio, ſurſum autem in inferiori, vſque ad p. </s>
  <s xml:id="echoid-s18819" xml:space="preserve">Erit punctũ <lb/>p, Verticale, in quod nimirum cadit axis Horizontis, cum A C, axis Horizontis, ſeu diameter Ver-<lb/>
<anchor type="note" xlink:label="note-0293-06a" xlink:href="note-0293-06"/>
ticalis, ſecet planum horologij vtriuſque per parallelas a n, e o, ductum in punctis n, &amp; </s>
  <s xml:id="echoid-s18820" xml:space="preserve">o, infra <lb/>quidem locum ſtyli E, in ſuperiori horologio, ſupra verò in inferiori. </s>
  <s xml:id="echoid-s18821" xml:space="preserve">Quia verò recta a n, rectæ <lb/>e o, æqualis eſt, (Nam quia in triangulis E a n, E e o, anguli ad a, &amp; </s>
  <s xml:id="echoid-s18822" xml:space="preserve">e, recti ſunt, &amp; </s>
  <s xml:id="echoid-s18823" xml:space="preserve">anguli ad E, ver <lb/>
<anchor type="note" xlink:label="note-0293-07a" xlink:href="note-0293-07"/>
ticem æquales, atque latera E a, E e, æqualia; </s>
  <s xml:id="echoid-s18824" xml:space="preserve">erunt etiam latera a n, e o, æqualia) idcircò iuſſimus <lb/>
<anchor type="note" xlink:label="note-0293-08a" xlink:href="note-0293-08"/>
candem a n, vel e o, transferri in vtroque horologio in lineam meridianam infra vel ſupra lo-<lb/>cum ſtyli.</s>
  <s xml:id="echoid-s18825" xml:space="preserve"/>
</p>
<div xml:id="echoid-div966" type="float" level="2" n="1">
<note position="right" xlink:label="note-0293-05" xlink:href="note-0293-05a" xml:space="preserve">Verticales circu <lb/>li in codem ho <lb/>rologio quomo <lb/>do deſcribãtur.</note>
<note position="left" xlink:label="note-0293-06" xlink:href="note-0293-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0293-07" xlink:href="note-0293-07a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0293-08" xlink:href="note-0293-08a" xml:space="preserve">16. primi.</note>
</div>
<p>
  <s xml:id="echoid-s18826" xml:space="preserve">HOC autem punctum Verticale p, comperiemus hac etiam induſtria. </s>
  <s xml:id="echoid-s18827" xml:space="preserve">Ex E, loco ſtyli duca-<lb/>tur ad meridianam lineam perpendicularis E F, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s18828" xml:space="preserve">ad punctum F, couſtituatur angu <lb/>lus E F p, complemento altitudinis poli æqualis, ita vt recta F p, ſecet lineam meridianam in pun <lb/>cto p; </s>
  <s xml:id="echoid-s18829" xml:space="preserve">infra quidem locum ſtyli in horologio ſuperiori, ſupra vero in inferiori. </s>
  <s xml:id="echoid-s18830" xml:space="preserve">Dico p, eſſe pun-<lb/>
<anchor type="note" xlink:label="note-0293-09a" xlink:href="note-0293-09"/>
ctum Verticale. </s>
  <s xml:id="echoid-s18831" xml:space="preserve">Intelligatur enim triangulum E F p, conuerti circa rectam E p, donec rectum ſit <lb/>ad planum horologij, ac proinde in plano Meridiani exiſtat, punctumq́ue F, cum vertice ſtyli, <lb/>centrove mundi coniungatur, &amp; </s>
  <s xml:id="echoid-s18832" xml:space="preserve">recta ipía E F, cum ſtylo, ſeu axe mundano. </s>
  <s xml:id="echoid-s18833" xml:space="preserve">Tranſibit Verticalis <lb/>circulus propriè dictus per verticem ſtyli, mundive centrum F, ac proinde per rectam F p, propte-<lb/>rea quòd Verticalis circulus cum axe mundi in Meridiani plano facit angulum complemento al-<lb/>titudinis poli æqualem, qualis eſt E F p, &amp; </s>
  <s xml:id="echoid-s18834" xml:space="preserve">cum linea meridiana in Æquatore angulum altitudi-<lb/>ni poli ęqualem, vt conſtat; </s>
  <s xml:id="echoid-s18835" xml:space="preserve">qui quidem æqualis eſt illi angulo, quem idem Verticalis cum linea <lb/>meridiana plani horologij Aequatori æquidiſtantis conficit, qualis eſt angulus E p F. </s>
  <s xml:id="echoid-s18836" xml:space="preserve">Cum enim <lb/>ſectiones Meridiani, quas cum Aequatore, &amp; </s>
  <s xml:id="echoid-s18837" xml:space="preserve">plano horologij illi parallelo facit, ſint parallelæ, fa-<lb/>
<anchor type="note" xlink:label="note-0293-10a" xlink:href="note-0293-10"/>
ciet communis ſectio Verticalis, &amp; </s>
  <s xml:id="echoid-s18838" xml:space="preserve">Meridiani angulos æquales cum dictis lineis Meridianis, ex-<lb/>
<anchor type="note" xlink:label="note-0293-11a" xlink:href="note-0293-11"/>
<anchor type="note" xlink:label="note-0293-12a" xlink:href="note-0293-12"/>
ternum videlicet, &amp; </s>
  <s xml:id="echoid-s18839" xml:space="preserve">internum. </s>
  <s xml:id="echoid-s18840" xml:space="preserve">Quamobrem Verticalis propriè dictus planum horologii ſe-<lb/>cabit in p.</s>
  <s xml:id="echoid-s18841" xml:space="preserve"/>
</p>
<div xml:id="echoid-div967" type="float" level="2" n="2">
<note position="left" xlink:label="note-0293-09" xlink:href="note-0293-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0293-10" xlink:href="note-0293-10a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0293-11" xlink:href="note-0293-11a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0293-12" xlink:href="note-0293-12a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s18842" xml:space="preserve">POST hæc ducta recta F m, quæ faciat angulum E F m, altitudini poli æqualem, ita vt ſe-<lb/>cet meridianam lineam in m, puncto, per quod oſtendimus prope finem propoſ. </s>
  <s xml:id="echoid-s18843" xml:space="preserve">50. </s>
  <s xml:id="echoid-s18844" xml:space="preserve">huius libri <lb/>lineam horizontalem eſſe ducendam, ſumatur in linea meridiana ipſi F m, æqualis m e, ſiue infra <lb/>lineam horizontalem, ſiue ſupra. </s>
  <s xml:id="echoid-s18845" xml:space="preserve">Ex e, autem centro deſcripto circulo cuiuſcunque magnitudi-<lb/>nis, eoq́ue in gradus 360. </s>
  <s xml:id="echoid-s18846" xml:space="preserve">diſtributo, vel in partes pauciores, habita ratione magnitudinis horolo-<lb/>gij, (Nos eum diſtribuimus in 24. </s>
  <s xml:id="echoid-s18847" xml:space="preserve">vt ſingulæ grad. </s>
  <s xml:id="echoid-s18848" xml:space="preserve">15. </s>
  <s xml:id="echoid-s18849" xml:space="preserve">contineant) ducantur per puncta diuiſio-<lb/>num, &amp; </s>
  <s xml:id="echoid-s18850" xml:space="preserve">per centrum e, rectæ occultæ ſecantes lineam horizontalem in punctis, per quæ, &amp; </s>
  <s xml:id="echoid-s18851" xml:space="preserve">punctũ <lb/>Verticale p, rectæ emiſſæ dabunt circulos Verticales, id eſt, communes ſectiones plani horologij, <lb/>&amp; </s>
  <s xml:id="echoid-s18852" xml:space="preserve">circulorum Verticalium, quarum initium in vtroque horologio ſumitur à Verticali linea, quæ
<pb o="278" file="0294" n="294" rhead="GNOMONICES"/>
per p, horizontali lineæ, &amp; </s>
  <s xml:id="echoid-s18853" xml:space="preserve">horæ 6. </s>
  <s xml:id="echoid-s18854" xml:space="preserve">parallela ducitur; </s>
  <s xml:id="echoid-s18855" xml:space="preserve">ita vt linea meridiana det nonageſimum <lb/>Verticalem.</s>
  <s xml:id="echoid-s18856" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18857" xml:space="preserve">HVIVS rei hanc accipe demonſtrationem. </s>
  <s xml:id="echoid-s18858" xml:space="preserve">Intelligatur circulus ex e, deſcriptus circa ho-<lb/>
<anchor type="note" xlink:label="note-0294-01a" xlink:href="note-0294-01"/>
rizontalem lineam conuerti, donec cum Horizonte coniungatur, ac propterea eius centrum e, <lb/>
<anchor type="figure" xlink:label="fig-0294-01a" xlink:href="fig-0294-01"/>
<anchor type="note" xlink:label="note-0294-02a" xlink:href="note-0294-02"/>
<anchor type="note" xlink:label="note-0294-03a" xlink:href="note-0294-03"/>
<anchor type="note" xlink:label="note-0294-04a" xlink:href="note-0294-04"/>
cum centro mundi F, propter æqualitatem rectarum m F, m e. </s>
  <s xml:id="echoid-s18859" xml:space="preserve">Erunt rectæ ex centro e, egredien-<lb/>tes per puncta diuiſionum circuli, communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s18860" xml:space="preserve">circulorum Verticalium, <lb/>eò quòd Horizon, &amp; </s>
  <s xml:id="echoid-s18861" xml:space="preserve">circulus ex e, centro mundi, ſeu Horizontis deſcriptus in partes ſimiles diui-<lb/>dantur à rectis ex centro egredientibus, vt ad finem cap 1. </s>
  <s xml:id="echoid-s18862" xml:space="preserve">in ſphæram demonſtrauimus: </s>
  <s xml:id="echoid-s18863" xml:space="preserve">certum <lb/>autem eſt, Horizontem, cuius centrum tunc eſt punctum F, vel e, à circulis Verticalibus in partes <lb/>
<anchor type="note" xlink:label="note-0294-05a" xlink:href="note-0294-05"/>
æquales diuidi per rectas è centro emiſſas. </s>
  <s xml:id="echoid-s18864" xml:space="preserve">Occurrent igitur Verticales circuli plano horologij <lb/>in illis punctis lineæ horizontalis, in quæ cadunt rectæ illæ occultæ ex e, emiſſæ. </s>
  <s xml:id="echoid-s18865" xml:space="preserve">Quapropter cũ, <lb/>per propoſ. </s>
  <s xml:id="echoid-s18866" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18867" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18868" xml:space="preserve">communes ſectiones circulorum Verticalium, &amp; </s>
  <s xml:id="echoid-s18869" xml:space="preserve">plani horologij <lb/>coeant in puncto p, in quo communis illorum omnium ſectio, nempe axis Horizontis, plano ho-<lb/>rologij occurrit, erunt rectæ per p, &amp; </s>
  <s xml:id="echoid-s18870" xml:space="preserve">puncta reperta in linea horizontali eductæ, communes ſe-<lb/>ctiones plani horologij, &amp; </s>
  <s xml:id="echoid-s18871" xml:space="preserve">Verticalium circulorum. </s>
  <s xml:id="echoid-s18872" xml:space="preserve">Sola ſectio communis plani horologij, &amp; </s>
  <s xml:id="echoid-s18873" xml:space="preserve"><lb/>Verticalis propriè dicti ducenda eſt lineæ horizontali, &amp; </s>
  <s xml:id="echoid-s18874" xml:space="preserve">horæ 6. </s>
  <s xml:id="echoid-s18875" xml:space="preserve">parallela per p. </s>
  <s xml:id="echoid-s18876" xml:space="preserve">Cum enim Ver-<lb/>ticalis propriè dictus, Horizon, circulus horæ 6. </s>
  <s xml:id="echoid-s18877" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18878" xml:space="preserve">Aequator, cui planum horologij æquidiſtat, <lb/>habeant vnam eandemq́ue communem ſectionem, erunt per propoſ. </s>
  <s xml:id="echoid-s18879" xml:space="preserve">18. </s>
  <s xml:id="echoid-s18880" xml:space="preserve">vel per ſcholium pro-<lb/>poſ. </s>
  <s xml:id="echoid-s18881" xml:space="preserve">22. </s>
  <s xml:id="echoid-s18882" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18883" xml:space="preserve">communes ſectiones priorum trium circulorum, &amp; </s>
  <s xml:id="echoid-s18884" xml:space="preserve">plani horologij, qua-<lb/>
<anchor type="note" xlink:label="note-0294-06a" xlink:href="note-0294-06"/>
les ſi<unsure/>i<unsure/>nt linea Verticalis, horizontalis, &amp; </s>
  <s xml:id="echoid-s18885" xml:space="preserve">horæ 6. </s>
  <s xml:id="echoid-s18886" xml:space="preserve">inter ſe parallelæ. </s>
  <s xml:id="echoid-s18887" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s18888" xml:space="preserve">circulos Verticales in ho-<lb/>rologio eodem æquinoctiali delineauimus. </s>
  <s xml:id="echoid-s18889" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s18890" xml:space="preserve"/>
</p>
<div xml:id="echoid-div968" type="float" level="2" n="3">
<note position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>circulorũ Ver-<lb/>ticalium.</note>
  <figure xlink:label="fig-0294-01" xlink:href="fig-0294-01a">
    <image file="0294-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0294-01"/>
  </figure>
<note position="left" xlink:label="note-0294-02" xlink:href="note-0294-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0294-03" xlink:href="note-0294-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0294-04" xlink:href="note-0294-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0294-05" xlink:href="note-0294-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0294-06" xlink:href="note-0294-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div970" type="section" level="1" n="237">
<head xml:id="echoid-head244" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s18891" xml:space="preserve">SI portio horologĳ abſciſſa à linea horizontali collocetur in facie inferiori plani, ita vt linea hori-<lb/>
<anchor type="note" xlink:label="note-0294-07a" xlink:href="note-0294-07"/>
zontalis ſuperiorem locum teneat, &amp; </s>
  <s xml:id="echoid-s18892" xml:space="preserve">pars, quæ in eo ſitu dextra est, mutetur in ſiniſtram, habebimus <lb/>coſdem Verticales circulos in horologio inferiori, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s18893" xml:space="preserve">14. </s>
  <s xml:id="echoid-s18894" xml:space="preserve">huius libri demonſtrauimus. <lb/></s>
  <s xml:id="echoid-s18895" xml:space="preserve">Sed quoniam lineæ Verticales ad vtraſque partes meridianæ eundem ſitum, &amp; </s>
  <s xml:id="echoid-s18896" xml:space="preserve">diſtantiam obtinent, non <lb/>erit neceſſarium, partem dextram in ſiniſtram mutari, &amp; </s>
  <s xml:id="echoid-s18897" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s18898" xml:space="preserve"/>
</p>
<div xml:id="echoid-div970" type="float" level="2" n="1">
<note position="left" xlink:label="note-0294-07" xlink:href="note-0294-07a" xml:space="preserve">Quiomodo or-<lb/>tum habeat in-<lb/>ferius horolo-<lb/>gium cum Ver <lb/>ticalibus à ſu-<lb/>periori æquino <lb/>ctiali.</note>
</div>
<pb o="279" file="0295" n="295" rhead="LIBER SECVNDVS."/>
</div>
<div xml:id="echoid-div972" type="section" level="1" n="238">
<head xml:id="echoid-head245" xml:space="preserve">PROBLEMA 53. PROPOSITIO 53.</head>
<p>
  <s xml:id="echoid-s18899" xml:space="preserve">PARALLELOS Horizontis in eodem æquinoctiali horolo-<lb/>gio ducere.</s>
  <s xml:id="echoid-s18900" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s18901" xml:space="preserve">SIT Analemma A B C, in quo Horizon B C; </s>
  <s xml:id="echoid-s18902" xml:space="preserve">Verticalis A D; </s>
  <s xml:id="echoid-s18903" xml:space="preserve">axis mundi E F; </s>
  <s xml:id="echoid-s18904" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18905" xml:space="preserve">Aequator <lb/>
<anchor type="note" xlink:label="note-0295-01a" xlink:href="note-0295-01"/>
G H. </s>
  <s xml:id="echoid-s18906" xml:space="preserve">Diuiſo autem ſemicirculo B A C, in grad. </s>
  <s xml:id="echoid-s18907" xml:space="preserve">180. </s>
  <s xml:id="echoid-s18908" xml:space="preserve">vel in pauciores partes æquales, prout ho-<lb/>rologium capax fuerit, (Nos illum diuiſimus in 12. </s>
  <s xml:id="echoid-s18909" xml:space="preserve">vt quælibet complectatur grad. </s>
  <s xml:id="echoid-s18910" xml:space="preserve">15.) </s>
  <s xml:id="echoid-s18911" xml:space="preserve">iungan-<lb/>tur bina puncta à recta B C, vel à puncto A, æqualiter remota, lineis rectis, quæ communes ſe-<lb/>ctiones erunt Meridiani, &amp; </s>
  <s xml:id="echoid-s18912" xml:space="preserve">pa-<lb/>
<anchor type="note" xlink:label="note-0295-02a" xlink:href="note-0295-02"/>
<anchor type="figure" xlink:label="fig-0295-01a" xlink:href="fig-0295-01"/>
rallelorum Horizontis, quos Al-<lb/>mucantarath dicunt. </s>
  <s xml:id="echoid-s18913" xml:space="preserve">Deinde ex <lb/>diuiſionum punctis per cẽtrum <lb/>D, ducantur rectæ lineæ, vt con-<lb/>ſtituantur triangula per axem in <lb/>conis, quorum baſes ſunt paral-<lb/>leli Horizontis tam infra Hori-<lb/>zontem, quàm ſupra, vertex au-<lb/>tem communis centrum mundi <lb/>D. </s>
  <s xml:id="echoid-s18914" xml:space="preserve">Meridianus enim A B C, <lb/>
<anchor type="note" xlink:label="note-0295-03a" xlink:href="note-0295-03"/>
per axem A D, dictorũ conorũ <lb/>incedens facit triangula per axẽ, <lb/>ex propoſ. </s>
  <s xml:id="echoid-s18915" xml:space="preserve">3. </s>
  <s xml:id="echoid-s18916" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s18917" xml:space="preserve">1. </s>
  <s xml:id="echoid-s18918" xml:space="preserve">Apollonij. </s>
  <s xml:id="echoid-s18919" xml:space="preserve">In <lb/>axe quoque E F, accipiatur vtrin <lb/>que recta D I, gnomoni æqualis, <lb/>&amp; </s>
  <s xml:id="echoid-s18920" xml:space="preserve">per I, Aequatori G H, vtrinq; <lb/></s>
  <s xml:id="echoid-s18921" xml:space="preserve">parallela agatur K L. </s>
  <s xml:id="echoid-s18922" xml:space="preserve">Erit hæc <lb/>infra quidem G H, communis <lb/>ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s18923" xml:space="preserve">plani ho-<lb/>rologij ſuperioris, illa verò ſupra <lb/>
<anchor type="note" xlink:label="note-0295-04a" xlink:href="note-0295-04"/>
G H, communis ſectio Meridia-<lb/>ni &amp; </s>
  <s xml:id="echoid-s18924" xml:space="preserve">plani horologii inferioris. <lb/></s>
  <s xml:id="echoid-s18925" xml:space="preserve">Secabit autem vtraque recta KL, <lb/>latera triangulorum per axem in <lb/>punctis M, N, O, P, Q, R, eruntq́ue diametri ſectionum conicarum M L, N L, O L, P L, Q R. </s>
  <s xml:id="echoid-s18926" xml:space="preserve"><lb/>Si igitur puncta M, N, O, P, (omittimus hic punctum Q, quoniam conica ſectio per ipſum du-<lb/>cta extra tropicos cadit) transferantur in lineam meridianam infra horizontalem lineam in horo <lb/>logio ſuperiori, incipiendo in hac figura ab S, puncto Horizontis, in horologio verò ab m, puncto <lb/>horizontalis lineæ &amp; </s>
  <s xml:id="echoid-s18927" xml:space="preserve">per propoſitionem 8. </s>
  <s xml:id="echoid-s18928" xml:space="preserve">ſupetioris lib. </s>
  <s xml:id="echoid-s18929" xml:space="preserve">circa lineam meridianam dictæ coni-<lb/>cæ ſectiones deſcribantur tranſeuntes per puncta M, N, O, P, (quæ ſectiones conicę partim erunt <lb/>
<anchor type="note" xlink:label="note-0295-05a" xlink:href="note-0295-05"/>
hyperbolæ, partim ellipſes, vt ex propoſ. </s>
  <s xml:id="echoid-s18930" xml:space="preserve">6. </s>
  <s xml:id="echoid-s18931" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18932" xml:space="preserve">7. </s>
  <s xml:id="echoid-s18933" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s18934" xml:space="preserve">conſtat: </s>
  <s xml:id="echoid-s18935" xml:space="preserve">Parallelus autem Horizon <lb/>tis grad. </s>
  <s xml:id="echoid-s18936" xml:space="preserve">48. </s>
  <s xml:id="echoid-s18937" xml:space="preserve">erit parabola, ex propoſ. </s>
  <s xml:id="echoid-s18938" xml:space="preserve">5. </s>
  <s xml:id="echoid-s18939" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s18940" xml:space="preserve">ſuperioris, quòd illum Aequator in puncto <lb/>G, contingat) &amp; </s>
  <s xml:id="echoid-s18941" xml:space="preserve">à linea horizontali eò magis ſemper recedentes, quò longius ex vtraque parte li-<lb/>neæ meridianę fuerint productæ, deſcripti erunt paralleli Horizontis. </s>
  <s xml:id="echoid-s18942" xml:space="preserve">In horologio inferiori <lb/>transferendæ ſunt rectæ S T, S V, in lineam meridianam à puncto m, infra lineam horizon-<lb/>talem, &amp;</s>
  <s xml:id="echoid-s18943" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18944" xml:space="preserve">Nam T L, eſt diameter conicæ ſectionis paralleli Horizontis grad. </s>
  <s xml:id="echoid-s18945" xml:space="preserve">15. </s>
  <s xml:id="echoid-s18946" xml:space="preserve">ſupra Hori-<lb/>zontem, &amp; </s>
  <s xml:id="echoid-s18947" xml:space="preserve">V L, diameter conicæ ſectionis paralleli Horizontis grad. </s>
  <s xml:id="echoid-s18948" xml:space="preserve">30. </s>
  <s xml:id="echoid-s18949" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s18950" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18951" xml:space="preserve">Eſt igitur G H, <lb/>tanquam Horizon, &amp; </s>
  <s xml:id="echoid-s18952" xml:space="preserve">E F, veluti Verticalis; </s>
  <s xml:id="echoid-s18953" xml:space="preserve">B C, quaſi Aequator quidam, &amp; </s>
  <s xml:id="echoid-s18954" xml:space="preserve">paralleli Horizontis <lb/>inſtar parallelorum noui Aequatoris B C. </s>
  <s xml:id="echoid-s18955" xml:space="preserve">Quibus poſitis, erunt Verticales circuli inſtar horario-<lb/>rum circulorum, qui omnes meridianam lineam horologij ſecant in puncto X, vbi eandem ſecat <lb/>
<anchor type="note" xlink:label="note-0295-06a" xlink:href="note-0295-06"/>
A D, axis Horizontis, quem nunc munere Æquatoris cuiuſdam noui fungi diximus: </s>
  <s xml:id="echoid-s18956" xml:space="preserve">Ita vt ſi per-<lb/>mutatio hæc circulorum benè conſideretur, deſcriptio hæc parallelorum Horizontis à deſcriptio-<lb/>ne parallelorum Aequatoris in horizontali horologio non differat.</s>
  <s xml:id="echoid-s18957" xml:space="preserve"/>
</p>
<div xml:id="echoid-div972" type="float" level="2" n="1">
<note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">Paralleli Hori-<lb/>zontis qua ra-<lb/>tione in eodem <lb/>horologio æqui <lb/>noctiali deſcri-<lb/>bantur.</note>
<note position="left" xlink:label="note-0295-02" xlink:href="note-0295-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0295-01" xlink:href="fig-0295-01a">
    <image file="0295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0295-01"/>
  </figure>
<note position="left" xlink:label="note-0295-03" xlink:href="note-0295-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0295-04" xlink:href="note-0295-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0295-05" xlink:href="note-0295-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0295-06" xlink:href="note-0295-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s18958" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s18959" xml:space="preserve">Deſcripto quadrante A B C, cuiuslibet magnitudinis, eoq́ue diuiſo in grad. </s>
  <s xml:id="echoid-s18960" xml:space="preserve">90. <lb/></s>
  <s xml:id="echoid-s18961" xml:space="preserve">
<anchor type="note" xlink:label="note-0295-07a" xlink:href="note-0295-07"/>
vel in partes pauciores, pro capacitate horologii, ducantur ex A, centro per puncta diuiſionum li-<lb/>neæ rectæ, quæ reſpondebunt radijs parallelorum Horizontis in quadrante D C 90. </s>
  <s xml:id="echoid-s18962" xml:space="preserve">figuræ ante-<lb/>cedentis comprehenſis, initio facto à recta A B, vt figura indicat. </s>
  <s xml:id="echoid-s18963" xml:space="preserve">Deinde ex figura præcedentis <lb/>propoſ. </s>
  <s xml:id="echoid-s18964" xml:space="preserve">rectæ F p, in linea A C, huius figuræ ſumatur æqualis A D; </s>
  <s xml:id="echoid-s18965" xml:space="preserve">Et rectæ m F, vel m e, acci-<lb/>piatur in linea A B, æqualis AE, ducaturq́; </s>
  <s xml:id="echoid-s18966" xml:space="preserve">recta D E. </s>
  <s xml:id="echoid-s18967" xml:space="preserve">Erit triangulũ hoc A D E, omnino æquale triã <lb/>
<anchor type="note" xlink:label="note-0295-08a" xlink:href="note-0295-08"/>
gulo F p m, figuræ præcedentis propoſ. </s>
  <s xml:id="echoid-s18968" xml:space="preserve">cum anguli ad puncta A, &amp; </s>
  <s xml:id="echoid-s18969" xml:space="preserve">F, recti ſint, contineanturq́ue <lb/>æqualibus lateribus, ex conſtructione. </s>
  <s xml:id="echoid-s18970" xml:space="preserve">Itaque linea D E, meridianæ lineæ p m, æqualis erit. </s>
  <s xml:id="echoid-s18971" xml:space="preserve">Idem
<pb o="280" file="0296" n="296" rhead="GNOMONICES"/>
quoque triangulum A D E, æquale erit triangulo D X S, proximè antecedentis figuræ, cum trian-<lb/>gulum D X S, æquale ſit prædicto triangulo F p m. </s>
  <s xml:id="echoid-s18972" xml:space="preserve">Quoniam enim angulus I D X, in Analemma-<lb/>te huius figuræ angulo E F p, in figura antecedentis propoſ. </s>
  <s xml:id="echoid-s18973" xml:space="preserve">eſt æqualis, quòd vterque ſit angulus <lb/>complementi altitudinis poli; </s>
  <s xml:id="echoid-s18974" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18975" xml:space="preserve">angulus rectus D I X, angulo recto F E p; </s>
  <s xml:id="echoid-s18976" xml:space="preserve">ſuntq́ue latera D I, <lb/>F E, æqualia, quòd vtrumque ſtylo ſit ſumptum æquale; </s>
  <s xml:id="echoid-s18977" xml:space="preserve">erunt quoque latera D X, X I, lateribus <lb/>
<anchor type="note" xlink:label="note-0296-01a" xlink:href="note-0296-01"/>
F p, p E, æqualia. </s>
  <s xml:id="echoid-s18978" xml:space="preserve">Eademq́ue ratione D S, S I, lateribus F m, m E, æqualia erunt, &amp;</s>
  <s xml:id="echoid-s18979" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18980" xml:space="preserve">Poſt hæc <lb/>ex figura præcedentis propoſ. </s>
  <s xml:id="echoid-s18981" xml:space="preserve">omnia interualla inter centrum e, &amp; </s>
  <s xml:id="echoid-s18982" xml:space="preserve">puncta, quibus lineæ Verticales <lb/>lineam horizontalem ſecant, transferantur in hanc figuram ex A, in rectam A B, notatis punctis <lb/>in recta A B, appoſitisq́ue numeris linearum Verticalium, vt 90. </s>
  <s xml:id="echoid-s18983" xml:space="preserve">iuxta punctum E, &amp; </s>
  <s xml:id="echoid-s18984" xml:space="preserve">75. </s>
  <s xml:id="echoid-s18985" xml:space="preserve">ad ſequẽs <lb/>punctum, &amp;</s>
  <s xml:id="echoid-s18986" xml:space="preserve">c. </s>
  <s xml:id="echoid-s18987" xml:space="preserve">Poſtremo ex D, per puncta in A B, ſignata educantur rectæ lineæ: </s>
  <s xml:id="echoid-s18988" xml:space="preserve">Pro Verticali au-<lb/>
<anchor type="note" xlink:label="note-0296-02a" xlink:href="note-0296-02"/>
tem linea proprie dicta, à qua aliarum principium ſumitur, ducenda eſt per D, ipſi A B, parallela <lb/>D F, &amp; </s>
  <s xml:id="echoid-s18989" xml:space="preserve">ad dextram partem ipſius trãsferendæ quoque ſunt lineæ iam ductæ ex D, per puncta rectę <lb/>A B, vt habeantur lineæ Verticales vltra, &amp; </s>
  <s xml:id="echoid-s18990" xml:space="preserve">citra lineam Verticalem proprie dictam, quemadmodũ <lb/>in horologio horizontali factum eſt propoſ. </s>
  <s xml:id="echoid-s18991" xml:space="preserve">2. </s>
  <s xml:id="echoid-s18992" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s18993" xml:space="preserve">de lineis ante horam 6. </s>
  <s xml:id="echoid-s18994" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s18995" xml:space="preserve">poſt. </s>
  <s xml:id="echoid-s18996" xml:space="preserve">Nam li-<lb/>neę ex D, per puncta rectæ A B, emiſſæ ſpectant ad lineas Verticales ante Verticalem propriè dictã, <lb/>in quas ſcilicet vmbra ſtyli proiicitur, Sole exiſtente in Verticalibus borealibus; </s>
  <s xml:id="echoid-s18997" xml:space="preserve">aliæ verò perti-<lb/>nent ad Verticales lineas vltra Verticalem circulum propriè dictum, &amp;</s>
  <s xml:id="echoid-s18998" xml:space="preserve">c.</s>
  <s xml:id="echoid-s18999" xml:space="preserve"/>
</p>
<div xml:id="echoid-div973" type="float" level="2" n="2">
<note position="right" xlink:label="note-0295-07" xlink:href="note-0295-07a" xml:space="preserve">Alia deſcriptio <lb/>parallelorũ Ho <lb/>rizontis in eo-<lb/>dem æquino-<lb/>ctiali horolo<unsure/>-<lb/>gio.</note>
<note position="right" xlink:label="note-0295-08" xlink:href="note-0295-08a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0296-01" xlink:href="note-0296-01a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0296-02" xlink:href="note-0296-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s19000" xml:space="preserve">ITAQVE ſi interualla rectarum ex D, egredientium inter D, &amp; </s>
  <s xml:id="echoid-s19001" xml:space="preserve">radium v.</s>
  <s xml:id="echoid-s19002" xml:space="preserve">g. </s>
  <s xml:id="echoid-s19003" xml:space="preserve">paralleli Hori-<lb/>zontis grad. </s>
  <s xml:id="echoid-s19004" xml:space="preserve">15. </s>
  <s xml:id="echoid-s19005" xml:space="preserve">poſita transferantur ex puncto p, figuræ pręcedentis propoſ. </s>
  <s xml:id="echoid-s19006" xml:space="preserve">in lineas Verticales re-<lb/>ſpondentes numeris in recta A B, huius figuræ aſſignatis, notando puncta in ipſis lineis Verticali-<lb/>
<anchor type="note" xlink:label="note-0296-03a" xlink:href="note-0296-03"/>
bus, (ita tamen vt interualla rectarum ex D, emiſſarum, &amp; </s>
  <s xml:id="echoid-s19007" xml:space="preserve">verſus A B, cadentium trans ferantur ex <lb/>Zenith p, in lineas Ver-<lb/>ticales horologii ſupra <lb/>lineam Verticalem pro-<lb/>
<anchor type="figure" xlink:label="fig-0296-01a" xlink:href="fig-0296-01"/>
priè dictam, interualla <lb/>verò rectarum ex D, ca-<lb/>dentium ad dextram re <lb/>ctæ D F, transferantur <lb/>in Verticales lineas in-<lb/>fra Verticalem lineam <lb/>
<anchor type="note" xlink:label="note-0296-04a" xlink:href="note-0296-04"/>
propriè dictam) &amp; </s>
  <s xml:id="echoid-s19008" xml:space="preserve">hæc <lb/>puncta appoſitè, con-<lb/>gruenterq́ue linea qua-<lb/>dam inflexa coniungan <lb/>tur, deſcriptus erit pa-<lb/>rallelus Horizontis gr. <lb/></s>
  <s xml:id="echoid-s19009" xml:space="preserve">15. </s>
  <s xml:id="echoid-s19010" xml:space="preserve">Eademque ratione <lb/>reliqui paralleli Hori-<lb/>zontis deſcribentur. </s>
  <s xml:id="echoid-s19011" xml:space="preserve"><lb/>Demonſtratio huius rei <lb/>
<anchor type="note" xlink:label="note-0296-05a" xlink:href="note-0296-05"/>
<anchor type="note" xlink:label="note-0296-06a" xlink:href="note-0296-06"/>
non differt ab illa, quã <lb/>tradidimus in ſecundo <lb/>modo deſcribendi pa-<lb/>rallelos ſignorum Zo-<lb/>diaci in horologio ho-<lb/>rizontali. </s>
  <s xml:id="echoid-s19012" xml:space="preserve">Nam hic li-<lb/>nea horizontalis eſt veluti Æquatoris linea, &amp; </s>
  <s xml:id="echoid-s19013" xml:space="preserve">lineæ Verticales tanquam lineæ horariæ, quarum <lb/>centrum eſt Zenith p, &amp;</s>
  <s xml:id="echoid-s19014" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19015" xml:space="preserve">vt in præcedenti Analemmate diximus. </s>
  <s xml:id="echoid-s19016" xml:space="preserve">Itaque recta A B, huius <lb/>figuræ reſpondet radio Æquatoris in poſtrema figura propoſ. </s>
  <s xml:id="echoid-s19017" xml:space="preserve">2. </s>
  <s xml:id="echoid-s19018" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19019" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19020" xml:space="preserve">rectæ ex A, emiſ-<lb/>ſæ radijs ſignorum ex D, emiſſis: </s>
  <s xml:id="echoid-s19021" xml:space="preserve">recta autem A D, axi D H, &amp; </s>
  <s xml:id="echoid-s19022" xml:space="preserve">punctum D, puncto H, li-<lb/>
<anchor type="note" xlink:label="note-0296-07a" xlink:href="note-0296-07"/>
neæ denique Verticales ex D, cadentes lineis horarijs ex H, ductis. </s>
  <s xml:id="echoid-s19023" xml:space="preserve">Idem fiet, ſi interualla re-<lb/>ctarum ex D, exeuntium inter rectam A B, quæ (vt diximus) eſt inſtar radij Æquatoris, &amp; </s>
  <s xml:id="echoid-s19024" xml:space="preserve"><lb/>rectas ex A, emiſſas, quæ ſunt veluti radij ſignorum, transferantur in reſpondentes lineas Verti-<lb/>cales à linea horizontali horologij, &amp;</s>
  <s xml:id="echoid-s19025" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19026" xml:space="preserve">quemadmodum in horizontali horologio interualla <lb/>inter radium Æquatoris, &amp; </s>
  <s xml:id="echoid-s19027" xml:space="preserve">radios ſignorum translata ſunt, vt arcus ſignorum deſcriberentur. <lb/></s>
  <s xml:id="echoid-s19028" xml:space="preserve">Pro horologio æquinoctiali inferiori transferendi ſunt radij parallelorum Horizontis ex A, per <lb/>puncta quadrantis B C, egredientes ad ſiniſtram rectæ A B, ita, vt quemadmodum in figura vlti-<lb/>ma propoſ. </s>
  <s xml:id="echoid-s19029" xml:space="preserve">2. </s>
  <s xml:id="echoid-s19030" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19031" xml:space="preserve">radij ſignorum ad partem dextram radij Æquatoris pertinent ad ſigna <lb/>auſtralia infra lineam æquinoctialem horologij deſcribenda, &amp; </s>
  <s xml:id="echoid-s19032" xml:space="preserve">radij ad ſiniſtram, ad ſigna borea-<lb/>lia ſupra æquinoctialem lineam deſcribenda: </s>
  <s xml:id="echoid-s19033" xml:space="preserve">ita etiam hic radij parallelorum Horizontis ex A, <lb/>educti ad dexteram rectæ A B, quæ eſt inſtar noui cuiuſdam radij Æquatoris, vt dictum eſt, per-
<pb o="281" file="0297" n="297" rhead="LIBER SECVNDVS."/>
tineant ad parallelos Horizontis infra lineam horizontalem, quæ eſt tanquam noua quædã æqui-<lb/>noctialis linea, deſcribendos, tanquam ſigna auſtralia; </s>
  <s xml:id="echoid-s19034" xml:space="preserve">radij verò emiſſi ad ſiniſtram rectæ A B, <lb/>referantur ad parallelos Horizontis ſupra lineam horizontalem horologij, nempe in horologio <lb/>inferiori, deſcribendos, tanquam ſigna borealia. </s>
  <s xml:id="echoid-s19035" xml:space="preserve">Vnde cum portio horologij ſupra lineam hori-<lb/>zontalem æqualis ſit inferiori horologio, rectè transferuntur in eam radij parallelorum Hori-<lb/>zontis ex A, educti ad partem ſiniſtram rectæ A B, &amp;</s>
  <s xml:id="echoid-s19036" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19037" xml:space="preserve">quę omnia in figura præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s19038" xml:space="preserve">apparent. </s>
  <s xml:id="echoid-s19039" xml:space="preserve">Parallelos ergo Horizontis in eodem æquinoctiali horologio duximus. </s>
  <s xml:id="echoid-s19040" xml:space="preserve">quod erat <lb/>faciendum.</s>
  <s xml:id="echoid-s19041" xml:space="preserve"/>
</p>
<div xml:id="echoid-div974" type="float" level="2" n="3">
<note position="left" xlink:label="note-0296-03" xlink:href="note-0296-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0296-01" xlink:href="fig-0296-01a">
    <image file="0296-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0296-01"/>
  </figure>
<note position="left" xlink:label="note-0296-04" xlink:href="note-0296-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0296-05" xlink:href="note-0296-05a" xml:space="preserve">Demonſtratio <lb/>poſterioris hu-<lb/>iuſce deſcriptio <lb/>nis parallelorũ <lb/>Horizontis.</note>
<note position="left" xlink:label="note-0296-06" xlink:href="note-0296-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0296-07" xlink:href="note-0296-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div976" type="section" level="1" n="239">
<head xml:id="echoid-head246" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s19042" xml:space="preserve">QVONIAM verò Ellipſes, cum integræ ſunt deſcribendæ, cuiuſmodi eſt Ellipſis paralleli Hori-<lb/>
<anchor type="note" xlink:label="note-0297-01a" xlink:href="note-0297-01"/>
<anchor type="note" xlink:label="note-0297-02a" xlink:href="note-0297-02"/>
zontis grad. </s>
  <s xml:id="echoid-s19043" xml:space="preserve">60. </s>
  <s xml:id="echoid-s19044" xml:space="preserve">in noſtro exemplo difficulter, incommode{q́ue} deſcribuntur per omnia puncta in lineis Ver-<lb/>ticalibus inuenta; </s>
  <s xml:id="echoid-s19045" xml:space="preserve">vt hic per ea, quæ existunt prope alterum extremum q, diametri Ellipſis P q; </s>
  <s xml:id="echoid-s19046" xml:space="preserve">vte-<lb/>mur hac induſtria, vt vniformiter eas deſcribamus. </s>
  <s xml:id="echoid-s19047" xml:space="preserve">Inuento in linea meridiana altero extremo diame-<lb/>tri, vt hic puncto q, (quod quidem reperietur, ſi recta D 90. </s>
  <s xml:id="echoid-s19048" xml:space="preserve">ad dexteram ipſius D F, in proxima figura in-<lb/>tercepta inter D, &amp; </s>
  <s xml:id="echoid-s19049" xml:space="preserve">radium paralleli grad. </s>
  <s xml:id="echoid-s19050" xml:space="preserve">60. </s>
  <s xml:id="echoid-s19051" xml:space="preserve">transferatur in lineam meridianam horologĳ ex p, vſque <lb/>ad q; </s>
  <s xml:id="echoid-s19052" xml:space="preserve">vel certein Analemmate huius propoſ. </s>
  <s xml:id="echoid-s19053" xml:space="preserve">ſumatur diameter Ellipſis par alleli gr. </s>
  <s xml:id="echoid-s19054" xml:space="preserve">60. </s>
  <s xml:id="echoid-s19055" xml:space="preserve">inter P, &amp; </s>
  <s xml:id="echoid-s19056" xml:space="preserve">aliud <lb/>latus trianguli per axem in cono, cuius baſes ſunt paralleli gr. </s>
  <s xml:id="echoid-s19057" xml:space="preserve">60. </s>
  <s xml:id="echoid-s19058" xml:space="preserve">intercepta, transferatur q; </s>
  <s xml:id="echoid-s19059" xml:space="preserve">ex P, uſque <lb/>ad q.) </s>
  <s xml:id="echoid-s19060" xml:space="preserve">ſecabimus totam diametrum P q, bifariam in r, vt r, ſit centrum Ellipſis, vt conſtat ex definitio-<lb/>nibus ſecundis Apollonĳ, ducemus{q́ue} per r, perpendicularem ad P q, nempe diametrum ſecundam El-<lb/>lipſis. </s>
  <s xml:id="echoid-s19061" xml:space="preserve">Deinde quia per propoſ. </s>
  <s xml:id="echoid-s19062" xml:space="preserve">30. </s>
  <s xml:id="echoid-s19063" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s19064" xml:space="preserve">1. </s>
  <s xml:id="echoid-s19065" xml:space="preserve">Apollonĳ, recta linea quæcunq; </s>
  <s xml:id="echoid-s19066" xml:space="preserve">per centrum Ellipſis ducta in <lb/>
<anchor type="note" xlink:label="note-0297-03a" xlink:href="note-0297-03"/>
centro bifariam diuiditur, ducemus ex punctis verticalium linearum, per quæ medietas ſuperior Ellipſis <lb/>tranſit, (quæ quidem medietas commodius deſcribi poteſt, quam inferior, vt patet) per centrum r, lineas <lb/>occultas, &amp; </s>
  <s xml:id="echoid-s19067" xml:space="preserve">earum partibus inter dicta puncta, &amp; </s>
  <s xml:id="echoid-s19068" xml:space="preserve">centrum r, abſcind cmus infra centrum æquales rectas <lb/>lineas, imprimendo puncta in lineis illis occultis. </s>
  <s xml:id="echoid-s19069" xml:space="preserve">Per hæc enim puncta ducenda erit inferior medietas <lb/>Ellipſis. </s>
  <s xml:id="echoid-s19070" xml:space="preserve">Facile autem ex propoſitione 75. </s>
  <s xml:id="echoid-s19071" xml:space="preserve">ſuperioris libri, &amp; </s>
  <s xml:id="echoid-s19072" xml:space="preserve">priori figura huius propoſ. </s>
  <s xml:id="echoid-s19073" xml:space="preserve">cognoſcemus, <lb/>quinã parallelus Horizontis Ellipſim faciat in horologio. </s>
  <s xml:id="echoid-s19074" xml:space="preserve">Hac arte vtemur quoque in Ellipſibus aliorum <lb/>horologiorum, vbi hæ deſcribendæ erunt.</s>
  <s xml:id="echoid-s19075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div976" type="float" level="2" n="1">
<note position="left" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0297-02" xlink:href="note-0297-02a" xml:space="preserve">Quo pacto ex <lb/>vna medietate <lb/>Ellipſis reliqua <lb/>medietas deſc<unsure/>ri <lb/>benda ſit.</note>
<note position="left" xlink:label="note-0297-03" xlink:href="note-0297-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s19076" xml:space="preserve">EODEM modo in horologio inferiori deſcribemus parallelos Horizontis ſupra lineam horizonta-<lb/>
<anchor type="note" xlink:label="note-0297-04a" xlink:href="note-0297-04"/>
lem, ex eorum oppoſitis in horologio ſuperiori deſcriptis, &amp; </s>
  <s xml:id="echoid-s19077" xml:space="preserve">accur atius multo, ſi ſecundum doctrinam in <lb/>fine propoſ. </s>
  <s xml:id="echoid-s19078" xml:space="preserve">2. </s>
  <s xml:id="echoid-s19079" xml:space="preserve">huius libri traditam inueniamus prius diametros tranſuerſas oppoſitarum ſectionum, ea-<lb/>
<anchor type="note" xlink:label="note-0297-05a" xlink:href="note-0297-05"/>
rumq; </s>
  <s xml:id="echoid-s19080" xml:space="preserve">centra, &amp;</s>
  <s xml:id="echoid-s19081" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19082" xml:space="preserve">In poſteriori quidem figura huius propoſ. </s>
  <s xml:id="echoid-s19083" xml:space="preserve">diametri tranſuerſæ ſunt portiones rectæ <lb/>D E, poſitæ inter radios parallelorum horizontis oppoſitorum ex A, egredientes, æqualiter q; </s>
  <s xml:id="echoid-s19084" xml:space="preserve">diſtantes <lb/>à recta A B.</s>
  <s xml:id="echoid-s19085" xml:space="preserve"/>
</p>
<div xml:id="echoid-div977" type="float" level="2" n="2">
<note position="right" xlink:label="note-0297-04" xlink:href="note-0297-04a" xml:space="preserve">Qua tatione pa <lb/>ralleli ſupra li-<lb/>neam horizon-<lb/>talem ex eorũ<unsure/> <lb/>oppoſitis infra <lb/>horizontalem <lb/>lineam deſcri-<lb/>ptis deſcriban-<lb/>tur.</note>
<note position="left" xlink:label="note-0297-05" xlink:href="note-0297-05a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div979" type="section" level="1" n="240">
<head xml:id="echoid-head247" xml:space="preserve">PROBLEMA 54. PROPOSITIO 54.</head>
<p>
  <s xml:id="echoid-s19086" xml:space="preserve">MERIDIANOS, id eſt, circulos longitudinum ciuitatum, in eo-<lb/>dem horologio æquinoctiali deſcribere.</s>
  <s xml:id="echoid-s19087" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s19088" xml:space="preserve">CIRCVLI Meri-<lb/>
<anchor type="figure" xlink:label="fig-0297-01a" xlink:href="fig-0297-01"/>
<anchor type="note" xlink:label="note-0297-06a" xlink:href="note-0297-06"/>
diani deſcribentur, vt <lb/>
<anchor type="note" xlink:label="note-0297-07a" xlink:href="note-0297-07"/>
horæ à meridie, vel me-<lb/>dia nocte, quemadmo-<lb/>dum docuimus propoſ. <lb/></s>
  <s xml:id="echoid-s19089" xml:space="preserve">6. </s>
  <s xml:id="echoid-s19090" xml:space="preserve">huius libri, ſi tamen <lb/>circulus A C B D, be-<lb/>neficio cuiuspropoſ. </s>
  <s xml:id="echoid-s19091" xml:space="preserve">49. </s>
  <s xml:id="echoid-s19092" xml:space="preserve"><lb/>huius libri lineas hora-<lb/>rias duximus, principiũ <lb/>diuiſionis in 360. </s>
  <s xml:id="echoid-s19093" xml:space="preserve">gra-<lb/>dus ſumat à Meridiano <lb/>
<anchor type="note" xlink:label="note-0297-08a" xlink:href="note-0297-08"/>
circulo inſularum For-<lb/>tunatarum, qui habetur <lb/>in horologio ſuperiori, <lb/>ſi loci longitudo nume-<lb/>retur à Meridiano loci, <lb/>nempe à puncto A, uer-<lb/>ſus D, partes occidenta-<lb/>les, vſq; </s>
  <s xml:id="echoid-s19094" xml:space="preserve">ad punctum G; <lb/></s>
  <s xml:id="echoid-s19095" xml:space="preserve">vt perſpicuum eſt, ſi ho-<lb/>rologium in proprio ſi-<lb/>tu intelligatur eſſe poſi-
<pb o="282" file="0298" n="298" rhead="GNOMONICES"/>
tum. </s>
  <s xml:id="echoid-s19096" xml:space="preserve">In inferiori verò habetur idem Meridianus inſularum fortunatarum, ſi longitudo loci ſup-<lb/>putetur à puncto B, verſus D, vſque ad H. </s>
  <s xml:id="echoid-s19097" xml:space="preserve">Nam ſi horologium inferius propriam habeat poſi-<lb/>tionem, ita vt linea horizontalis ſuperiorem occupet locum, &amp; </s>
  <s xml:id="echoid-s19098" xml:space="preserve">punctum A, in feriorem, atq; </s>
  <s xml:id="echoid-s19099" xml:space="preserve">pun <lb/>ctum C, ortum reſpiciat, &amp; </s>
  <s xml:id="echoid-s19100" xml:space="preserve">D, occaſum, ſecabit Meridianus loci planum horologij ſupra Hori-<lb/>zontem in puncto B, infra verò Horizontem in puncto A, Quare à B, verſus D, ſunt partes oc-<lb/>cidentales, &amp; </s>
  <s xml:id="echoid-s19101" xml:space="preserve">orientales verſus C, &amp;</s>
  <s xml:id="echoid-s19102" xml:space="preserve">c.</s>
  <s xml:id="echoid-s19103" xml:space="preserve"/>
</p>
<div xml:id="echoid-div979" type="float" level="2" n="1">
  <figure xlink:label="fig-0297-01" xlink:href="fig-0297-01a">
    <image file="0297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0297-01"/>
  </figure>
<note position="right" xlink:label="note-0297-06" xlink:href="note-0297-06a" xml:space="preserve">Meridianorum <lb/>deſcriptio in eo <lb/>dem horologio <lb/>@quinoctiali.</note>
<note position="left" xlink:label="note-0297-07" xlink:href="note-0297-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0297-08" xlink:href="note-0297-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s19104" xml:space="preserve">SED præſtat Meridianos circulos in horologio inferiori deſcribere ex circulis Meridianis ſu-<lb/>
<anchor type="note" xlink:label="note-0298-01a" xlink:href="note-0298-01"/>
perioris horologij, vt oſtenſum eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s19105" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19106" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s19107" xml:space="preserve">in verticali horologio fa-<lb/>ctum eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s19108" xml:space="preserve">28. </s>
  <s xml:id="echoid-s19109" xml:space="preserve">huius libri, omnia enim, quæ ibi dicta ſunt, huc transferri poſ-<lb/>ſunt, intelligendo tamen ſemper pro auſtrali horologio ſuperius æquinoctiale, &amp; </s>
  <s xml:id="echoid-s19110" xml:space="preserve">pro boreali in-<lb/>
<anchor type="note" xlink:label="note-0298-02a" xlink:href="note-0298-02"/>
ferius. </s>
  <s xml:id="echoid-s19111" xml:space="preserve">Exemplum habes in figura propoſita. </s>
  <s xml:id="echoid-s19112" xml:space="preserve">Vbi vides Meridianum 105. </s>
  <s xml:id="echoid-s19113" xml:space="preserve">vltra centrum E, pro-<lb/>ductum in ſuperiori horologio habere grad. </s>
  <s xml:id="echoid-s19114" xml:space="preserve">285. </s>
  <s xml:id="echoid-s19115" xml:space="preserve">qui illi opponitur, at vltra lineam horizontalem <lb/>productum, iterum aſſumere grad 105. </s>
  <s xml:id="echoid-s19116" xml:space="preserve">in inferiori horologio, &amp; </s>
  <s xml:id="echoid-s19117" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s19118" xml:space="preserve">Meridianos ergo, <lb/>id eſt, circulos longitudinũ, in eodem horologio æquinoctiali deſcripſimus. </s>
  <s xml:id="echoid-s19119" xml:space="preserve">Quod faciendũ erat.</s>
  <s xml:id="echoid-s19120" xml:space="preserve"/>
</p>
<div xml:id="echoid-div980" type="float" level="2" n="2">
<note position="left" xlink:label="note-0298-01" xlink:href="note-0298-01a" xml:space="preserve">Quo modo In <lb/>ferius horolo <lb/>gium Meridia-<lb/>norum ex Supe <lb/>riori ori<unsure/>um ha <lb/>beat.</note>
<note position="left" xlink:label="note-0298-02" xlink:href="note-0298-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div982" type="section" level="1" n="241">
<head xml:id="echoid-head248" xml:space="preserve">PROBLEMA 55. PROPOSITIO 55.</head>
<p>
  <s xml:id="echoid-s19121" xml:space="preserve">PARALLELOS ciuitatum, ſiue circulos latitudinum, in eodem <lb/>æquinoctiali horologio depingere.</s>
  <s xml:id="echoid-s19122" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s19123" xml:space="preserve">PRO parallelis per initia ſignorum Zodiaci ductis accipiantur paralleli per vertices ciuitatũ <lb/>
<anchor type="note" xlink:label="note-0298-04a" xlink:href="note-0298-04"/>
intra tropicos exiſtentium tranſeuntes, &amp; </s>
  <s xml:id="echoid-s19124" xml:space="preserve">alia omnia fiant, quæ de parallelis ſignorum Zodiaci de-<lb/>ſcribendis propoſ. </s>
  <s xml:id="echoid-s19125" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19126" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19127" xml:space="preserve">præcepimus; </s>
  <s xml:id="echoid-s19128" xml:space="preserve">factumq́ue erit, quod proponitur. </s>
  <s xml:id="echoid-s19129" xml:space="preserve">Igitur parallelos <lb/>cíuitatum, ſiue circulos latitudinum, &amp;</s>
  <s xml:id="echoid-s19130" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19131" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s19132" xml:space="preserve"/>
</p>
<div xml:id="echoid-div982" type="float" level="2" n="1">
<note position="left" xlink:label="note-0298-04" xlink:href="note-0298-04a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ciui <lb/>tatum, latitudi-<lb/>numve, in eodẽ <lb/>horologio æqui <lb/>noctiali.</note>
</div>
</div>
<div xml:id="echoid-div984" type="section" level="1" n="242">
<head xml:id="echoid-head249" xml:space="preserve">PROBLEMA 56. PROPOSITIO 56.</head>
<p>
  <s xml:id="echoid-s19133" xml:space="preserve">DOMOS cœleſtes in codem horologio æquinoctiali de-<lb/>
<anchor type="note" xlink:label="note-0298-05a" xlink:href="note-0298-05"/>
ſcribere.</s>
  <s xml:id="echoid-s19134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div984" type="float" level="2" n="1">
<note position="left" xlink:label="note-0298-05" xlink:href="note-0298-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s19135" xml:space="preserve">SECETVR circulus A C B D, principio facto à linea meridiana, in 12. </s>
  <s xml:id="echoid-s19136" xml:space="preserve">partes æquales, vel <lb/>
<anchor type="note" xlink:label="note-0298-06a" xlink:href="note-0298-06"/>
in plures, ſi ſingularum domorum partes etiam defideremus. </s>
  <s xml:id="echoid-s19137" xml:space="preserve">Nos illum diuiſimus in 12. </s>
  <s xml:id="echoid-s19138" xml:space="preserve">vt inte-<lb/>græ domus duntaxat deſcribantur. </s>
  <s xml:id="echoid-s19139" xml:space="preserve">Per puncta autem diuiſionum, &amp; </s>
  <s xml:id="echoid-s19140" xml:space="preserve">centrum E, ducantnr rectæ <lb/>lineæ occultæ. </s>
  <s xml:id="echoid-s19141" xml:space="preserve">Deinde per punctum m, vbi meridiana linea horizontalem interſecat, dictis lineis <lb/>agantur lineæ parallelæ, deſcriptæq́ue erunt domus cœleſtes in vtroque horologio ſecundum do-<lb/>ctrinam Ioan, Regiom. </s>
  <s xml:id="echoid-s19142" xml:space="preserve">Quoniam enim circuli domorum cœleſtium ſecundum Ioan. </s>
  <s xml:id="echoid-s19143" xml:space="preserve">Regiom. <lb/></s>
  <s xml:id="echoid-s19144" xml:space="preserve">
<anchor type="note" xlink:label="note-0298-07a" xlink:href="note-0298-07"/>
diuidunt Aequatorem in partes æquales, initio facto à Meridiano, qui vnus eſt ex dictis circulis, <lb/>tranſeuntq́ue per centrum mundi, ſiue Æquatoris, tranſibunt neceſſario per communes ſectiones <lb/>
<anchor type="note" xlink:label="note-0298-08a" xlink:href="note-0298-08"/>
Aequatoris, &amp; </s>
  <s xml:id="echoid-s19145" xml:space="preserve">circulorum horariorum à meridie, vel media nocte, cum hi quoque per centrum <lb/>mundi incedentes ſecent Aequatorem in partes æquales, principio facto à Meridiano; </s>
  <s xml:id="echoid-s19146" xml:space="preserve">ita vt com-<lb/>munes ſectiones circulorum domorum cœleſtium &amp; </s>
  <s xml:id="echoid-s19147" xml:space="preserve">Aequatoris à communibus ſectionibus cir-<lb/>culorum horariorum &amp; </s>
  <s xml:id="echoid-s19148" xml:space="preserve">Aequatoris non diſcrepent. </s>
  <s xml:id="echoid-s19149" xml:space="preserve">Sed communes ſectiones plani horologij, <lb/>&amp; </s>
  <s xml:id="echoid-s19150" xml:space="preserve">circulorum domorum cœleſtium parallelæ ſunt communibus ſectionibus Aequatoris, &amp; </s>
  <s xml:id="echoid-s19151" xml:space="preserve">eo-<lb/>
<anchor type="note" xlink:label="note-0298-09a" xlink:href="note-0298-09"/>
rundem circulorum; </s>
  <s xml:id="echoid-s19152" xml:space="preserve">his autem parallelæ quoque ſunt (cum ſint oſtenſæ eædem, quæ ſectiones <lb/>
<anchor type="note" xlink:label="note-0298-10a" xlink:href="note-0298-10"/>
communes Aequatoris, &amp; </s>
  <s xml:id="echoid-s19153" xml:space="preserve">horariorum circulorum) communes ſectiones plani horologij, &amp; </s>
  <s xml:id="echoid-s19154" xml:space="preserve">cir-<lb/>culorum horarum à meridie, vel media nocte. </s>
  <s xml:id="echoid-s19155" xml:space="preserve">Igitur communes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s19156" xml:space="preserve"><lb/>circulorum domorum cœleſtium parallelæ quoque erunt communibus ſectionibus eiuſdem pla-<lb/>
<anchor type="note" xlink:label="note-0298-11a" xlink:href="note-0298-11"/>
ni horologii, &amp; </s>
  <s xml:id="echoid-s19157" xml:space="preserve">horariorum circulorum. </s>
  <s xml:id="echoid-s19158" xml:space="preserve">Cum ergo rectæ per centrum E, ductæ, diuidentesq́ue <lb/>
<anchor type="note" xlink:label="note-0298-12a" xlink:href="note-0298-12"/>
circulum A C B D, in 12. </s>
  <s xml:id="echoid-s19159" xml:space="preserve">partes æquales, vel etiam in plures, vel pauciores, ſint communes ſectio-<lb/>nes plani horologii, &amp; </s>
  <s xml:id="echoid-s19160" xml:space="preserve">circulorum horariorum, vt propoſ. </s>
  <s xml:id="echoid-s19161" xml:space="preserve">49. </s>
  <s xml:id="echoid-s19162" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19163" xml:space="preserve">demonſtrauimus; </s>
  <s xml:id="echoid-s19164" xml:space="preserve">erunt <lb/>his rectis parallelæ, communes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s19165" xml:space="preserve">circulorum domorum cœleſtium. <lb/></s>
  <s xml:id="echoid-s19166" xml:space="preserve">Quocirca cum communes ſectiones hæ tranſeant omnes per punctum m, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s19167" xml:space="preserve"><lb/>18. </s>
  <s xml:id="echoid-s19168" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s19169" xml:space="preserve">propterea quòd cõmunis ſectio omnium circulorum cœleſtium domorum, hoc <lb/>eſt, axis Verticalis circuli, ſeu cõmunis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s19170" xml:space="preserve">Horizontis, plano horologii occurrit <lb/>in eodem puncto m, vt patet ex figura propoſ. </s>
  <s xml:id="echoid-s19171" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19172" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19173" xml:space="preserve">in qua communis iſta ſectio eſt recta <lb/>l m, ſi triangulum E l m, intelligatur rectum ad planum horologii, hoc eſt, in plano Meridiani; </s>
  <s xml:id="echoid-s19174" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0298-13a" xlink:href="note-0298-13"/>
erunt rectæ per m, ductæ rectis per E, emiſſis parallelæ, communes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s19175" xml:space="preserve"><lb/>circulorum cœleſtium domorum. </s>
  <s xml:id="echoid-s19176" xml:space="preserve">Quod eſt propoſitum. </s>
  <s xml:id="echoid-s19177" xml:space="preserve">Manifeſtum autem eſt, initia domo-<lb/>rum cœleſtium parallela eſſe lineis horarum à meridiana linea diſtantibus duabus, quatuor, &amp; </s>
  <s xml:id="echoid-s19178" xml:space="preserve">ſex
<pb o="283" file="0299" n="299" rhead="LIBER SECVNDVS."/>
horis; </s>
  <s xml:id="echoid-s19179" xml:space="preserve">eò quòd circuli domorum cœleſtium in illis horis Aequatorem diuidant.</s>
  <s xml:id="echoid-s19180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div985" type="float" level="2" n="2">
<note position="left" xlink:label="note-0298-06" xlink:href="note-0298-06a" xml:space="preserve">Cœleſtium do-<lb/>morum in eo-<lb/>dẽ æquinoctiali <lb/>horologio de-<lb/>ſcriptio ſecun-<lb/>dum<unsure/> loan. Re-<lb/>giom.</note>
<note position="left" xlink:label="note-0298-07" xlink:href="note-0298-07a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domorum cœle <lb/>ſtium ſecundũ <lb/>10. Regiom.</note>
<note position="left" xlink:label="note-0298-08" xlink:href="note-0298-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0298-09" xlink:href="note-0298-09a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0298-10" xlink:href="note-0298-10a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0298-11" xlink:href="note-0298-11a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0298-12" xlink:href="note-0298-12a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0298-13" xlink:href="note-0298-13a" xml:space="preserve">Quibus horis à <lb/>mer vel med. <lb/>noc initia do-<lb/>morum cœle-<lb/>ſtium parallela <lb/>ſint.</note>
</div>
<p>
  <s xml:id="echoid-s19181" xml:space="preserve">CÆTERVM vt facile per m, ducamus rectis per E, ductis parallelas lineas, hoc eſt, lineas <lb/>domorum cœleſtium, vtemur hac arte. </s>
  <s xml:id="echoid-s19182" xml:space="preserve">Lineæ meridianæ ducemus vtcunque parallelam F G, in <lb/>
<anchor type="figure" xlink:label="fig-0299-01a" xlink:href="fig-0299-01"/>
<anchor type="note" xlink:label="note-0299-01a" xlink:href="note-0299-01"/>
<anchor type="note" xlink:label="note-0299-02a" xlink:href="note-0299-02"/>
<anchor type="note" xlink:label="note-0299-03a" xlink:href="note-0299-03"/>
<anchor type="note" xlink:label="note-0299-04a" xlink:href="note-0299-04"/>
qua ex punctis, vbi à rectis per E, ductis ſecatur, ſurſum verſus abſcindemus rectæ E m, æquales <lb/>lineas rectas F H, I K, L M, N P, &amp;</s>
  <s xml:id="echoid-s19183" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19184" xml:space="preserve">Nam rectæ ex m, per puncta H, K, M, P, &amp;</s>
  <s xml:id="echoid-s19185" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19186" xml:space="preserve">ductæ pa-<lb/>rallelæ ſunt rectis ex E, prodeuntibus. </s>
  <s xml:id="echoid-s19187" xml:space="preserve">Cũ enim rectæ E m, F H, æquales ſint, &amp; </s>
  <s xml:id="echoid-s19188" xml:space="preserve">parallelæ, ex con <lb/>ſtructione, erunt quoq; </s>
  <s xml:id="echoid-s19189" xml:space="preserve">rectæ cõiungentes puncta E, F, &amp; </s>
  <s xml:id="echoid-s19190" xml:space="preserve">m, H, parallelæ inter ſe, &amp; </s>
  <s xml:id="echoid-s19191" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s19192" xml:space="preserve"/>
</p>
<div xml:id="echoid-div986" type="float" level="2" n="3">
  <figure xlink:label="fig-0299-01" xlink:href="fig-0299-01a">
    <image file="0299-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0299-01"/>
  </figure>
<note position="left" xlink:label="note-0299-01" xlink:href="note-0299-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0299-02" xlink:href="note-0299-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0299-03" xlink:href="note-0299-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0299-04" xlink:href="note-0299-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">33. primi.</note>
<note position="right" xml:space="preserve">Domorum cœ-<lb/>leſtium in eodẽ <lb/>horologio æqui <lb/>noctiali deſeri-<lb/>ptio ſecundum <lb/>Campanum.</note>
<p>
  <s xml:id="echoid-s19193" xml:space="preserve">SECVNDVM Campanum domos cæleſtes ita figurabimus. </s>
  <s xml:id="echoid-s19194" xml:space="preserve">Ex figura propoſ. </s>
  <s xml:id="echoid-s19195" xml:space="preserve">52. </s>
  <s xml:id="echoid-s19196" xml:space="preserve">huius <lb/>libri ſumemus rectam F p, per quam punctum p, nempe zenith, inueſtigauimus in linea meri-<lb/>diana, eamq; </s>
  <s xml:id="echoid-s19197" xml:space="preserve">in lineam meridianam à puncto p, ſiue ſurſum, ſiue deorſum verſus transferemus <lb/>vſque ad G. </s>
  <s xml:id="echoid-s19198" xml:space="preserve">Deinde ex G, deſcripto cuiuſcunque magnitudinis circulo, eoq́; </s>
  <s xml:id="echoid-s19199" xml:space="preserve">in 12. </s>
  <s xml:id="echoid-s19200" xml:space="preserve">partes æqua-<lb/>les diuiſo, vel in plures, ſi partes etiam domorum cœleſtium deſideremus habere, ducemus ex cen <lb/>tro G, per diuiſionũ puncta rectas occultas, quæ lineam verticalem ſecent in punctis, quæ lineis <lb/>
<anchor type="note" xlink:label="note-0299-08a" xlink:href="note-0299-08"/>
rectis cum puncto m, coniuncta dabunt cæleſtes domos ex ſententia Campani. </s>
  <s xml:id="echoid-s19201" xml:space="preserve">Nam ſi hic cir-<lb/>culus conuertatur circa lineam verticalem, quouſque cum Verticali propriè dicto coniungatur, <lb/>centrumq́ G, cum centro mundi F, erunt rectæ per G, ductæ, communes ſectiones verticalis <lb/>circuli, &amp; </s>
  <s xml:id="echoid-s19202" xml:space="preserve">circulorum domorum cœleſtium. </s>
  <s xml:id="echoid-s19203" xml:space="preserve">Quare circuli domorum cœleſtium occurrent pla-<lb/>no horologij in prædictis punctis lineæ Verticalis; </s>
  <s xml:id="echoid-s19204" xml:space="preserve">ac propterea lineæ domorum cœleſtium, hoc
<pb o="284" file="0300" n="300" rhead="GNOMONICES"/>
eſt, communes ſectiones plani horologij, &amp; </s>
  <s xml:id="echoid-s19205" xml:space="preserve">circulorum domorum cœleſtium, per eadem puncta <lb/>incedent. </s>
  <s xml:id="echoid-s19206" xml:space="preserve">Cum ergo tranſeant etiam per punctum m, vt oſtendimus, erunt rectæ connectentes <lb/>dicta puncta ve@ticalis lineæ cum puncto m, lineæ domorum cœleſtium. </s>
  <s xml:id="echoid-s19207" xml:space="preserve">Quapropter domos <lb/>cœleſtes in eodem horologio æquinoctiali deſcripſimus. </s>
  <s xml:id="echoid-s19208" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s19209" xml:space="preserve"/>
</p>
<div xml:id="echoid-div987" type="float" level="2" n="4">
<note position="right" xlink:label="note-0299-08" xlink:href="note-0299-08a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>domorũ cœle-<lb/>ſtium ſecundũ<unsure/> <lb/>Campanum.</note>
</div>
</div>
<div xml:id="echoid-div989" type="section" level="1" n="243">
<head xml:id="echoid-head250" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s19210" xml:space="preserve">SI lineæ domorum cœleſtium ſuperioris horologĳ vltra lineam horizontalem producantur, deſcri-<lb/>
<anchor type="note" xlink:label="note-0300-01a" xlink:href="note-0300-01"/>
ptæ erunt quoque earundem domorum lineæ in horologio inferiori; </s>
  <s xml:id="echoid-s19211" xml:space="preserve">ſi tamen omnes partes portionis ho-<lb/>rologĳ, quam horizontalis linea aufert, inuertantur, vt in præcedentibus dictum est, at que in fcholio <lb/>
<anchor type="note" xlink:label="note-0300-02a" xlink:href="note-0300-02"/>
propoſ. </s>
  <s xml:id="echoid-s19212" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19213" xml:space="preserve">huius libris demonſtr atum.</s>
  <s xml:id="echoid-s19214" xml:space="preserve"/>
</p>
<div xml:id="echoid-div989" type="float" level="2" n="1">
<note position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">Quomodo do-<lb/>mus cœleſtes vl <lb/>tra lineam ho-<lb/>rizontalẽ pro-<lb/>ductæ exhibeãt <lb/>eaſdem domos <lb/>in horologio in <lb/>feriori.</note>
<note position="left" xlink:label="note-0300-02" xlink:href="note-0300-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div991" type="section" level="1" n="244">
<head xml:id="echoid-head251" xml:space="preserve">PROBLEMA 57. PROPOSITIO 57.</head>
<p>
  <s xml:id="echoid-s19215" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem æquinoctiali horologio <lb/>figurare.</s>
  <s xml:id="echoid-s19216" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s19217" xml:space="preserve">DVCANTVR ex horologij centro E, lineæ occultæ illarum horarum quibus, Sole exiſten-<lb/>
<anchor type="note" xlink:label="note-0300-03a" xlink:href="note-0300-03"/>
te in principio ♋, ſi de horologio ſuperiori agatur, vel in principio ♑, ſi ſermo ſit de inferiori, <lb/>
<anchor type="note" xlink:label="note-0300-04a" xlink:href="note-0300-04"/>
principia ſignorum aſcendunt ſupra Horizontem, prout in tertia vel in quarta tabella propoſ. </s>
  <s xml:id="echoid-s19218" xml:space="preserve">9. <lb/></s>
  <s xml:id="echoid-s19219" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0300-01a" xlink:href="fig-0300-01"/>
<anchor type="note" xlink:label="note-0300-05a" xlink:href="note-0300-05"/>
<anchor type="note" xlink:label="note-0300-06a" xlink:href="note-0300-06"/>
<anchor type="note" xlink:label="note-0300-07a" xlink:href="note-0300-07"/>
huius libris apparet, ſumendo etiam horas illorum ſignorum, quæ pluribus horis poſt, &amp; </s>
  <s xml:id="echoid-s19220" xml:space="preserve">ante me <lb/>ridiem oriuntur, quam in arcu ſemidiurno ♋, vel ♑, contineantur. </s>
  <s xml:id="echoid-s19221" xml:space="preserve">Deinde quoniam in illis <lb/>punctis tropici ♋, vel ♑, vbi à dictis lineis horarijs ſecatur, ſigna aſcendentia tropicum tangunt, <lb/>vt oſtendimus propoſ. </s>
  <s xml:id="echoid-s19222" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19223" xml:space="preserve">huius libri, ſi per illa puucta ducantur lineæ tangentes tropicum, hoc <lb/>eſt, lineæ perpendiculares ad dictas lineas horarias, (hæ enim ex coroll. </s>
  <s xml:id="echoid-s19224" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s19225" xml:space="preserve">16. </s>
  <s xml:id="echoid-s19226" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s19227" xml:space="preserve">3. </s>
  <s xml:id="echoid-s19228" xml:space="preserve">Euclidis,
<pb o="285" file="0301" n="301" rhead="LIBER SECVNDVS."/>
circulum A C B D, qui tropicum refert, contingunt) deſcripta erunt ſigna aſcendentia, hoc or-<lb/>dine. </s>
  <s xml:id="echoid-s19229" xml:space="preserve">In vtroque horologio ſignum ♈, tranſit per A; </s>
  <s xml:id="echoid-s19230" xml:space="preserve">ſignum ♉, per punctum ſequens verſus D; <lb/></s>
  <s xml:id="echoid-s19231" xml:space="preserve">
<anchor type="note" xlink:label="note-0301-01a" xlink:href="note-0301-01"/>
ſignum ♊, per ſequens, &amp; </s>
  <s xml:id="echoid-s19232" xml:space="preserve">ſic deinceps, accipiendo tantum illas portiones linearum in ſuperiori <lb/>horologio, quæ infra lineam horizontalem in horologium ſuperius cadunt; </s>
  <s xml:id="echoid-s19233" xml:space="preserve">in inferiori autem <lb/>illas duntaxat earundem linearum portiones, quæ infra horizontalem lineam in horologium <lb/>inferius cadunt. </s>
  <s xml:id="echoid-s19234" xml:space="preserve">Atque hic ordo facile ex dictis tabellis, tertia &amp; </s>
  <s xml:id="echoid-s19235" xml:space="preserve">quarta, colligitur, ſi diligenter in <lb/>vtroq; </s>
  <s xml:id="echoid-s19236" xml:space="preserve">horologio conſideretur pars antemeridiana, pomeridianaque. </s>
  <s xml:id="echoid-s19237" xml:space="preserve">Sumimus hic, vt in præce-<lb/>dentibus, pro inferiori horologio portionem illam, quam horizontalis linea abſcindit, inuerſis ta-<lb/>men omnibus partibus, vt ſæpe diximus. </s>
  <s xml:id="echoid-s19238" xml:space="preserve">Vnde in inferiori horologio horæ ante meridiem nu-<lb/>merandæ erunt à puncto A, verſus C, poſt meridiem verò verſus D. </s>
  <s xml:id="echoid-s19239" xml:space="preserve">Tranſibunt autem ſigna a-<lb/>
<anchor type="note" xlink:label="note-0301-02a" xlink:href="note-0301-02"/>
ſcendentia, ſi in deſcriptione error non fuerit commiſſus, per ea puncta lineæ horizontalis, in <lb/>quibus paralleli per initia ſignorum ducti eam interſecant, cuiuſmodi ſunt puncta F, G, H, I, K, L, <lb/>vt perſpicuum eſt ex ijs, quæ in verticali horologio tradidimus propoſ. </s>
  <s xml:id="echoid-s19240" xml:space="preserve">21. </s>
  <s xml:id="echoid-s19241" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s19242" xml:space="preserve">Quæ qui-<lb/>dem puncta inuenientur quoqne hac ratione, etiam ſi paralleli ſignorum non deſcribantur. </s>
  <s xml:id="echoid-s19243" xml:space="preserve">Ex <lb/>
<anchor type="note" xlink:label="note-0301-03a" xlink:href="note-0301-03"/>
centro E, ducantur lineæ occultæ terminantes in vtroque tropico arcus ſemidiurnos, ſignorum <lb/>quidem borealium in ſuperiori horologio, auſtralium verò in inferiori, prout in tabella 5. </s>
  <s xml:id="echoid-s19244" xml:space="preserve">propoſ. <lb/></s>
  <s xml:id="echoid-s19245" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19246" xml:space="preserve">huius libri continentur; </s>
  <s xml:id="echoid-s19247" xml:space="preserve">ita tamen, vt arcus ſemidiurni ſignorum borealium ſupputentur à B, <lb/>vtrinque in tropico ♋, auſtralium verò ab A, vtrinque in tropico ♑. </s>
  <s xml:id="echoid-s19248" xml:space="preserve">Hæ etenim lineæ ſecabunt <lb/>lineam horizontalem in dictis punctis.</s>
  <s xml:id="echoid-s19249" xml:space="preserve"/>
</p>
<div xml:id="echoid-div991" type="float" level="2" n="1">
<note position="left" xlink:label="note-0300-03" xlink:href="note-0300-03a" xml:space="preserve">A ſcendentium <lb/>ſignorum in eo <lb/>dem horologio <lb/>æquinoctiali de <lb/>lineatio.</note>
<note position="left" xlink:label="note-0300-04" xlink:href="note-0300-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0300-01" xlink:href="fig-0300-01a">
    <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0300-01"/>
  </figure>
<note position="left" xlink:label="note-0300-05" xlink:href="note-0300-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0300-06" xlink:href="note-0300-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0300-07" xlink:href="note-0300-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">Ordo ſignorú <lb/>aſcendentium <lb/>in æquinoctia-<lb/>li horologio.</note>
<note position="left" xlink:label="note-0301-02" xlink:href="note-0301-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0301-03" xlink:href="note-0301-03a" xml:space="preserve">Inuentio pun-<lb/>ctorum in li-<lb/>nea horizonta-<lb/>li, per quę ſigna <lb/>aſcendentia du <lb/>cenda ſunt.</note>
</div>
<p>
  <s xml:id="echoid-s19250" xml:space="preserve">EADEM puncta reperiemus ex vltima figura propoſ. </s>
  <s xml:id="echoid-s19251" xml:space="preserve">21. </s>
  <s xml:id="echoid-s19252" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s19253" xml:space="preserve">Si enim in recta E B, <lb/>
<anchor type="note" xlink:label="note-0301-04a" xlink:href="note-0301-04"/>
<anchor type="note" xlink:label="note-0301-05a" xlink:href="note-0301-05"/>
vel E D, illius figuræ accipiatur recta E h, æqualis rectæ l m, in horologio propoſ. </s>
  <s xml:id="echoid-s19254" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19255" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s19256" xml:space="preserve">per quam in horologio lineam horizontalem deſcripſimus; </s>
  <s xml:id="echoid-s19257" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19258" xml:space="preserve">per h, ad B D, perpendicularis ex-<lb/>citetur, erit hæc linea horizontalis in horologio, vt perſpicuum eſt, ſi Horizon A B C D, in horo-<lb/>logio concipiatur in proprio ſitu, vt nimirum punctum h, ſit in m, &amp; </s>
  <s xml:id="echoid-s19259" xml:space="preserve">perpendicularis per h, du-<lb/>cta fiat eadem quæ horizontalis per m, ducta; </s>
  <s xml:id="echoid-s19260" xml:space="preserve">ac proinde centrum E, figuræ propoſ. </s>
  <s xml:id="echoid-s19261" xml:space="preserve">21. </s>
  <s xml:id="echoid-s19262" xml:space="preserve">huius li-<lb/>bri cum centro mundi, &amp; </s>
  <s xml:id="echoid-s19263" xml:space="preserve">vertice ſtyli coniungatur, propter æqualitatẽ rectarum E h, l m. </s>
  <s xml:id="echoid-s19264" xml:space="preserve">Itaque ſi <lb/>interualla perpendicularis lineæ per h, ductæ, inter h, &amp; </s>
  <s xml:id="echoid-s19265" xml:space="preserve">puncta, in quibus à radiis ex E, proceden <lb/>tibus ſecatur, in horizontalem lineam ex m, transferantur, habebuntur eadem puncta, vt prius.</s>
  <s xml:id="echoid-s19266" xml:space="preserve"/>
</p>
<div xml:id="echoid-div992" type="float" level="2" n="2">
<note position="left" xlink:label="note-0301-04" xlink:href="note-0301-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0301-05" xlink:href="note-0301-05a" xml:space="preserve">Alia inuentio <lb/>corundem pun<unsure/> <lb/>ctorum.</note>
</div>
<p>
  <s xml:id="echoid-s19267" xml:space="preserve">RVRSVM, ſi ex tabella 6. </s>
  <s xml:id="echoid-s19268" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s19269" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19270" xml:space="preserve">huius libri ſumantur declinationes mediationum cæ-<lb/>
<anchor type="note" xlink:label="note-0301-06a" xlink:href="note-0301-06"/>
li, &amp; </s>
  <s xml:id="echoid-s19271" xml:space="preserve">angulorum terræ, earumq́; </s>
  <s xml:id="echoid-s19272" xml:space="preserve">puncta inueniantur in linea meridiana, per quæ ſcilicet paralleli <lb/>
<anchor type="note" xlink:label="note-0301-07a" xlink:href="note-0301-07"/>
illarum declinationum tranſeunt, ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s19273" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19274" xml:space="preserve">huius libri, tranſibunt quoque <lb/>ſigna aſcendentia per ea puncta, ſi erratum non fuerit in eorum deſcriptione. </s>
  <s xml:id="echoid-s19275" xml:space="preserve">In ſuperiori quidem <lb/>horologio mediationes cæli ſignorum borealiũ continentur in portione lineæ meridianæ ex pun <lb/>cto E, per B, extenſa, cum hæc horam 12. </s>
  <s xml:id="echoid-s19276" xml:space="preserve">meridiei indicet; </s>
  <s xml:id="echoid-s19277" xml:space="preserve">angulorũ vero terræ in portione reli-<lb/>qua lineæ meridianæ ex eodem puncto E, per A, educta, quæ nimirum horam 12. </s>
  <s xml:id="echoid-s19278" xml:space="preserve">mediæ noctis <lb/>monſtrat; </s>
  <s xml:id="echoid-s19279" xml:space="preserve">adeo vt hæc ſigna ♌, ♐; </s>
  <s xml:id="echoid-s19280" xml:space="preserve">♍, ♏, &amp; </s>
  <s xml:id="echoid-s19281" xml:space="preserve">♎, tranſeant per puncta inuenta in linea E B, protracta; <lb/></s>
  <s xml:id="echoid-s19282" xml:space="preserve">quia his ſignis aſcendentibus, mediant cælum puncta Eclipticæ borealia: </s>
  <s xml:id="echoid-s19283" xml:space="preserve">hæc vero ſigna ♋, ♑, ♊, <lb/>♒, ♉, ♓, &amp; </s>
  <s xml:id="echoid-s19284" xml:space="preserve">♈, ducantur per puncta inuenta in recta E A, producta, quòd, his ſignis orientibus, <lb/>cõſtituantur in angulo terræ puncta eclipticæ borealia, vt ex dicta tabella 6. </s>
  <s xml:id="echoid-s19285" xml:space="preserve">apparet. </s>
  <s xml:id="echoid-s19286" xml:space="preserve">In horologio <lb/>vero inferiori mediationes cæli ſignorum auſtralium continentur in linea meridiana E A, produ-<lb/>
<anchor type="note" xlink:label="note-0301-08a" xlink:href="note-0301-08"/>
cta, angulorum autem terræ in linea mediæ noctis E B, protracta; </s>
  <s xml:id="echoid-s19287" xml:space="preserve">ita vt hæc ſigna ♋, ♑, ♊, ♒, <lb/>♉, ♓, &amp; </s>
  <s xml:id="echoid-s19288" xml:space="preserve">♈, incedant per puncta reperta incta E A, proptetea quòd, hiſce ſignis aſcendentibus, <lb/>in medio cæli reperiantur puncta eclipticæ auſtralia; </s>
  <s xml:id="echoid-s19289" xml:space="preserve">hæc autem ſigna ♌, ♐, ♍, ♏, &amp; </s>
  <s xml:id="echoid-s19290" xml:space="preserve">♎, tranſeant <lb/>per puncta inuenta in recta E B, protracta; </s>
  <s xml:id="echoid-s19291" xml:space="preserve">Nam illis orientibus, puncta Eclipticæ auſtralia in an-<lb/>gulo terræ exiſtunt. </s>
  <s xml:id="echoid-s19292" xml:space="preserve">Perſpicuum autem eſt, in ſuperiori horologio deſcribi tantum poſſe declina-<lb/>tiones boreales, &amp; </s>
  <s xml:id="echoid-s19293" xml:space="preserve">auſtrales in inferiori.</s>
  <s xml:id="echoid-s19294" xml:space="preserve"/>
</p>
<div xml:id="echoid-div993" type="float" level="2" n="3">
<note position="right" xlink:label="note-0301-06" xlink:href="note-0301-06a" xml:space="preserve">Alia deſcriptio <lb/>ſignorum aſcẽ-<lb/>dentium in eo <lb/>dem horologio <lb/>æquinoctiali P<unsure/> <lb/>mediationes cę <lb/>li, &amp; angulos <lb/>tetræ.</note>
<note position="left" xlink:label="note-0301-07" xlink:href="note-0301-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0301-08" xlink:href="note-0301-08a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Alia defcriptio <lb/>ſignorũ aſcen-<lb/>dentium in ho <lb/>rologio æquino <lb/>ctiali, per pun-<lb/>cta Eclipticæ in <lb/>linea horæ 6. à <lb/>mer. uel med. <lb/>noc. exiſtentia, <lb/>cũ ſignorũ prin <lb/>cipia oriuntur.</note>
<p>
  <s xml:id="echoid-s19295" xml:space="preserve">POSTREMO, ſi ex tabella 7. </s>
  <s xml:id="echoid-s19296" xml:space="preserve">ciuſdem propoſ. </s>
  <s xml:id="echoid-s19297" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19298" xml:space="preserve">huius lib accipiantur declinationes pun-<lb/>ctorum Eclipticæ borealium in linea horæ 6. </s>
  <s xml:id="echoid-s19299" xml:space="preserve">ante meridiem, &amp; </s>
  <s xml:id="echoid-s19300" xml:space="preserve">poſt exiſtentium, cum principia <lb/>ſignorum oriuntut<unsure/>, eorumq́; </s>
  <s xml:id="echoid-s19301" xml:space="preserve">puncta in linea horę 6. </s>
  <s xml:id="echoid-s19302" xml:space="preserve">ante, vel poſt meridiem inueniantur in horo <lb/>logio ſuperiori; </s>
  <s xml:id="echoid-s19303" xml:space="preserve">Itemq́; </s>
  <s xml:id="echoid-s19304" xml:space="preserve">fiat de declinationibus punctorum Eclipticæ auſtralium in eadem linea <lb/>
<anchor type="note" xlink:label="note-0301-10a" xlink:href="note-0301-10"/>
exiſtentium in inferiori horologio; </s>
  <s xml:id="echoid-s19305" xml:space="preserve">tranſibunt eadem ſigna aſcedentia per hæc puncta inuenta in <lb/>linea horæ 6. </s>
  <s xml:id="echoid-s19306" xml:space="preserve">Quocirca ſigna zodiaci aſcendentia in eodem æquinoctiali horologio figurauimus. <lb/></s>
  <s xml:id="echoid-s19307" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s19308" xml:space="preserve"/>
</p>
<div xml:id="echoid-div994" type="float" level="2" n="4">
<note position="left" xlink:label="note-0301-10" xlink:href="note-0301-10a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div996" type="section" level="1" n="245">
<head xml:id="echoid-head252" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s19309" xml:space="preserve">SIGNA Zodiaci aſcendentia cum Andrea Schonero ita depingemus. </s>
  <s xml:id="echoid-s19310" xml:space="preserve">In prima figura ſcholĳ <lb/>
<anchor type="note" xlink:label="note-0301-11a" xlink:href="note-0301-11"/>
propoſ. </s>
  <s xml:id="echoid-s19311" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19312" xml:space="preserve">huius libri in recta E B, accipiatur recta E β, æqualis portioni meridianæ lineæ E M, inter <lb/>centrum horologĳ, &amp; </s>
  <s xml:id="echoid-s19313" xml:space="preserve">lineam horizontalem interiectæ in ſigura propoſ. </s>
  <s xml:id="echoid-s19314" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19315" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s19316" xml:space="preserve">per β, ipſi <lb/>A C, parallela agatur, ita vt centro E, illius figuræ in puncto m, collocato in horologio, &amp; </s>
  <s xml:id="echoid-s19317" xml:space="preserve">puncto β, in <lb/>centro E, parallela per β, ducta congruat lineæ horæ 6. </s>
  <s xml:id="echoid-s19318" xml:space="preserve">ſecabit hæc par allela per β, ducta rectas ſignorum
<pb o="286" file="0302" n="302" rhead="GNOMONICES"/>
ex E, centro prodeuntes in punctis, quorum interualla ex β, ſumpta, &amp; </s>
  <s xml:id="echoid-s19319" xml:space="preserve">in lineam horę 6. </s>
  <s xml:id="echoid-s19320" xml:space="preserve">horologĳ æqui-<lb/>noctialis ex centro E, translata ad vtraſque partes dabunt in linea horæ 6. </s>
  <s xml:id="echoid-s19321" xml:space="preserve">puncta, per quæ ſi ex puncto <lb/>m, vbi horizontalis linea, &amp; </s>
  <s xml:id="echoid-s19322" xml:space="preserve">meridiana ſe interſecant, lineæ occultæ ducantur ſecantes tropicum ♋, in <lb/>ſuperiori horologio, vel tropicum ♑, in inferiori in punctis, per quæ ſi rurſus ad centrum E, ducantur re-<lb/>ctæ, &amp; </s>
  <s xml:id="echoid-s19323" xml:space="preserve">ad has ex dictis punctis tropici ducantur lineæ perpendiculares, ſiue tropicum tangentes, deſcri-<lb/>pta erunt aſcendentia ſigna, vt prius, ordine ſeruato, quem figura commonſtrat.</s>
  <s xml:id="echoid-s19324" xml:space="preserve"/>
</p>
<div xml:id="echoid-div996" type="float" level="2" n="1">
<note position="right" xlink:label="note-0301-11" xlink:href="note-0301-11a" xml:space="preserve">Qua ratione ſe <lb/>c<unsure/>ũdum praxim<unsure/> <lb/>Andreæ Scho-<lb/>neri eadem ſi-<lb/>gna aſcenden-<lb/>tia in horolo-<lb/>gio æquinoctia <lb/>li delincentu@.</note>
</div>
<p style="it">
  <s xml:id="echoid-s19325" xml:space="preserve">SATIS autem eſi, ſi ſigna aſcendentia in horologio ſuperiori deſcribantur. </s>
  <s xml:id="echoid-s19326" xml:space="preserve">Hæc enim producta vl-<lb/>
<anchor type="note" xlink:label="note-0302-01a" xlink:href="note-0302-01"/>
tra lineam horizontalem offerent eadem in inferiori horologio, ſi portio horologii abſciſſa à linea hori-<lb/>zontali inuertatur, vt in præcedentibus dictum eſt, atq; </s>
  <s xml:id="echoid-s19327" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s19328" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19329" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19330" xml:space="preserve">demonſtratum.</s>
  <s xml:id="echoid-s19331" xml:space="preserve"/>
</p>
<div xml:id="echoid-div997" type="float" level="2" n="2">
<note position="left" xlink:label="note-0302-01" xlink:href="note-0302-01a" xml:space="preserve">Signa aſcendẽ-<lb/>tia ſuperioris <lb/>hor<unsure/>olog@@ vltra <lb/>horizontalem <lb/>lineam produ-<lb/>ctę dant eadem <lb/>lig@a in horolo <lb/>g@o interiori.</note>
</div>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div999" type="section" level="1" n="246">
<head xml:id="echoid-head253" xml:space="preserve">PROBLEMA 58. PROPOSITIO 58. <lb/>HOROLOGIVM Italicum æquinoctiale conſtruere.</head>
<note position="left" xml:space="preserve">Horologii Ita-<lb/>lic@ æquinoctia <lb/>lis<unsure/> conſtructio.</note>
<p>
  <s xml:id="echoid-s19332" xml:space="preserve">PAR ALLELI, ſiue arcus ſignorum (quos deſcripſimus vnà cum linea horizontali, pro-<lb/>poſ. </s>
  <s xml:id="echoid-s19333" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19334" xml:space="preserve">huius libri) diuidantur ſinguli, vel duo ſaltem, (quod ſatis eſt) interior, &amp; </s>
  <s xml:id="echoid-s19335" xml:space="preserve">exterior, in 24. <lb/></s>
  <s xml:id="echoid-s19336" xml:space="preserve">partes æquales, initio facto à linea horizontali ex ea parte, in quam vmbra ſtyli cadit ſub occaſum <lb/>Solis, vt in horologio ſuperiori ex parte ſiniſtra, quæ ad ortum vergit. </s>
  <s xml:id="echoid-s19337" xml:space="preserve">Deinde per proxima puncta <lb/>horum arcuum ſupra, vel infra horizontalem lineam ex ſiniſtra parte, vbi diuiſic inchoata eſt, li-<lb/>
<anchor type="note" xlink:label="note-0302-04a" xlink:href="note-0302-04"/>
nea recta ducatur, itemq́ue per proximè ſequentia puncta, &amp; </s>
  <s xml:id="echoid-s19338" xml:space="preserve">ita deinceps, donec omnia abſoluan-<lb/>tur. </s>
  <s xml:id="echoid-s19339" xml:space="preserve">Hæ enim rectæ horas ab occaſu indicabunt in horologio ſuperiori, ac proinde horologium <lb/>
<anchor type="note" xlink:label="note-0302-05a" xlink:href="note-0302-05"/>
æquinoctiale Italicum ſuperius deſcriptum erit, in quo horarum numerus, &amp; </s>
  <s xml:id="echoid-s19340" xml:space="preserve">ordo hic eſt. </s>
  <s xml:id="echoid-s19341" xml:space="preserve">Prima, <lb/>ſeu proxima linea ſupra horizontalem lineam, quæ horam 24. </s>
  <s xml:id="echoid-s19342" xml:space="preserve">indicat, hoc eſt, in horologio no-<lb/>cturno, (quod exhibet portio abſciſſa à linea horizontali) à parte ſiniſtra monſtrat horam primã <lb/>ab occaſu, ſequens ſecundam, &amp; </s>
  <s xml:id="echoid-s19343" xml:space="preserve">ſic deinceps, ita vt proxima linea infra eandem lineam horizon-<lb/>talem ad partem ſiniſtram oſtendat horam 23. </s>
  <s xml:id="echoid-s19344" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s19345" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19346" xml:space="preserve">Quod hac ratione demonſtrabimus.</s>
  <s xml:id="echoid-s19347" xml:space="preserve"/>
</p>
<div xml:id="echoid-div999" type="float" level="2" n="1">
<note position="left" xlink:label="note-0302-04" xlink:href="note-0302-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0302-05" xlink:href="note-0302-05a" xml:space="preserve">Ordo horarum <lb/>ab occ. in horo <lb/>logio æquino-<lb/>ct@ali.</note>
</div>
<p>
  <s xml:id="echoid-s19348" xml:space="preserve">INTELLIGANTVR circuli maximi duci per polos mundi, &amp; </s>
  <s xml:id="echoid-s19349" xml:space="preserve">per horas ab occaſu in <lb/>
<anchor type="note" xlink:label="note-0302-06a" xlink:href="note-0302-06"/>
parallelo v. </s>
  <s xml:id="echoid-s19350" xml:space="preserve">g. </s>
  <s xml:id="echoid-s19351" xml:space="preserve">♋, inſtar horariorum circulorum à meridie, vel media nocte, hoc eſt, tranſire per <lb/>
<anchor type="note" xlink:label="note-0302-07a" xlink:href="note-0302-07"/>
<anchor type="figure" xlink:label="fig-0302-01a" xlink:href="fig-0302-01"/>
<anchor type="note" xlink:label="note-0302-08a" xlink:href="note-0302-08"/>
<anchor type="note" xlink:label="note-0302-09a" xlink:href="note-0302-09"/>
ea puncta, in quibus per propoſ. </s>
  <s xml:id="echoid-s19352" xml:space="preserve">10. </s>
  <s xml:id="echoid-s19353" xml:space="preserve">ſuperioris libri Horizon, &amp; </s>
  <s xml:id="echoid-s19354" xml:space="preserve">cæteri circuli horarum ab occaſu <lb/>parallelum ♋, in partes ęquales ſecan. </s>
  <s xml:id="echoid-s19355" xml:space="preserve">Secabunt hi circuli parallelum quoque ♋, in horologio
<pb o="287" file="0303" n="303" rhead="LIBER SECVNDVS."/>
æquinoctiali in partes æquales, vt ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s19356" xml:space="preserve">49. </s>
  <s xml:id="echoid-s19357" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19358" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s19359" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19360" xml:space="preserve">huius libri ſcri-<lb/>pſimus, conſtat. </s>
  <s xml:id="echoid-s19361" xml:space="preserve">Quare cum circulus maximus per polos, &amp; </s>
  <s xml:id="echoid-s19362" xml:space="preserve">per horam 24. </s>
  <s xml:id="echoid-s19363" xml:space="preserve">ductus ſecet paralle-<lb/>lum ♋, horologii in eo puncto, vbi eundem Horizon ſecat, quòd in illud punctum vmbra gno-<lb/>monis cadat, Sole exiſtente in communi ſectione Horizontis, ſeu paralleli ♋, &amp; </s>
  <s xml:id="echoid-s19364" xml:space="preserve">dicti circuli, vt <lb/>ex demonſtratis in ſuperiori lib perſpicuum eſt; </s>
  <s xml:id="echoid-s19365" xml:space="preserve">incedent alij circuli maximi per alia puncta pa-<lb/>ralleli ♋, in horologio, quæ ipſum in partes æquales partiuntur, cum in ea cadat quoque vmbra <lb/>ſtyli, Sole exiſtente in communi ſectione paralleli ♋, &amp; </s>
  <s xml:id="echoid-s19366" xml:space="preserve">illorum circulorum; </s>
  <s xml:id="echoid-s19367" xml:space="preserve">atque adeo per ea-<lb/>dem puncta circuli horarum ab occaſu tranſibunt, eadem de cauſa; </s>
  <s xml:id="echoid-s19368" xml:space="preserve">quia nimirum vmbra ſtyli in <lb/>ea puncta cadit, cum Sol in communibus ſectionibus paralleli ♋, &amp; </s>
  <s xml:id="echoid-s19369" xml:space="preserve">circulorum horarum ab oc-<lb/>caſu, nec non circulorum maximorum per polos mundi, &amp; </s>
  <s xml:id="echoid-s19370" xml:space="preserve">per horas ab occaſu in parallelo ♋, <lb/>
<anchor type="note" xlink:label="note-0303-01a" xlink:href="note-0303-01"/>
tranſeuntium exiſtit. </s>
  <s xml:id="echoid-s19371" xml:space="preserve">Radius enim Solis à communibus ſectionibus illorum circulorum maxi-<lb/>morum tunc non differet, cum hæ ſectiones per centrum mundi, hoc eſt, per verticem ſtyli, ſicut <lb/>&amp; </s>
  <s xml:id="echoid-s19372" xml:space="preserve">radius Solis, ducantur. </s>
  <s xml:id="echoid-s19373" xml:space="preserve">Cum ergo tunc radius Solis cadat in prædicta puncta paralleli ♋, in <lb/>horologio, cadent quoque in eadem communes illę ſectiones; </s>
  <s xml:id="echoid-s19374" xml:space="preserve">ac proinde in illis punctis plana <lb/>circulorum horarum ab occaſu plano horologii occurrent. </s>
  <s xml:id="echoid-s19375" xml:space="preserve">Eodem modo oſtendemus, circulos <lb/>horarum ab occaſu trãſire per puncta aliorum parallelorum in horologio, quæ ipſos in partes di-<lb/>ſtribuunt æquales, ſi videlicet concipiantur duci alii circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s19376" xml:space="preserve">per ho-<lb/>ras ab occaí<unsure/>u in ipſis parallellis. </s>
  <s xml:id="echoid-s19377" xml:space="preserve">Quare rectæ lineæ puncta dicta arcuum ſignorum connectentes, <lb/>ſunt communes ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s19378" xml:space="preserve">circulorum horas ab occaſu Solis monſtrantium.</s>
  <s xml:id="echoid-s19379" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1000" type="float" level="2" n="2">
<note position="left" xlink:label="note-0302-06" xlink:href="note-0302-06a" xml:space="preserve">Demonſtratio <lb/>con@tru@tionis <lb/>horologu<unsure/> Itali-<lb/>ci ęquinoctialis.</note>
<note position="left" xlink:label="note-0302-07" xlink:href="note-0302-07a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0302-01" xlink:href="fig-0302-01a">
    <image file="0302-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0302-01"/>
  </figure>
<note position="left" xlink:label="note-0302-08" xlink:href="note-0302-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0302-09" xlink:href="note-0302-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0303-01" xlink:href="note-0303-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s19380" xml:space="preserve">EADEM ratione inferius horologium Italicum conſtruemus, ſi diuiſionem parallelorum <lb/>
<anchor type="note" xlink:label="note-0303-02a" xlink:href="note-0303-02"/>
in inferiori horologio, quod nobis repreſentat portio abſciſſa à linea horizontali, inchoemus ex <lb/>ea parte, in quam vmbra ſtyli proiicitur ſub ſolis occaſum, qualis eſt pars dextra ad ortum vergẽs. <lb/></s>
  <s xml:id="echoid-s19381" xml:space="preserve">Voco partem dextram, quę nobis ad horologium inferius, hoc eſt, ad portionem à linea horizon-<lb/>tali abciſſam conuerſis, &amp; </s>
  <s xml:id="echoid-s19382" xml:space="preserve">horizontali linea ſuperiorem occupante locum, ad dexteram poſita eſt: </s>
  <s xml:id="echoid-s19383" xml:space="preserve"><lb/>non enim ad hanc rem vtimur illa inuerſione partium, de qua in ſuperioribus locuti ſumus. </s>
  <s xml:id="echoid-s19384" xml:space="preserve">Nam <lb/>proxima linea ſupra lineam horizontalem dabit horam 1. </s>
  <s xml:id="echoid-s19385" xml:space="preserve">ab occaſu, quæ nimirum in ſ@periori <lb/>horologio indicabat horam 23. </s>
  <s xml:id="echoid-s19386" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19387" xml:space="preserve">ſequens, quæ erat linea horæ 22. </s>
  <s xml:id="echoid-s19388" xml:space="preserve">dabit 2. </s>
  <s xml:id="echoid-s19389" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19390" xml:space="preserve">ſic deinceps, aſſumẽ <lb/>do ſemper complementa horarum ſuperioris horologij vſque ad 24. </s>
  <s xml:id="echoid-s19391" xml:space="preserve">ita vt linea horæ 1. </s>
  <s xml:id="echoid-s19392" xml:space="preserve">ab occa-<lb/>ſu in horologio ſuperiori; </s>
  <s xml:id="echoid-s19393" xml:space="preserve">quæ nimirum eſt prima ſub linea horizontali in inferiori horologio, in <lb/>dicet horam 23. </s>
  <s xml:id="echoid-s19394" xml:space="preserve">ab occaſu, &amp;</s>
  <s xml:id="echoid-s19395" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19396" xml:space="preserve">Hæc autem complementa horarum non ſcripſimus in figura, ſed <lb/>
<anchor type="note" xlink:label="note-0303-03a" xlink:href="note-0303-03"/>
cogitatione tantum intelligenda ſunt.</s>
  <s xml:id="echoid-s19397" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1001" type="float" level="2" n="3">
<note position="left" xlink:label="note-0303-02" xlink:href="note-0303-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0303-03" xlink:href="note-0303-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s19398" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s19399" xml:space="preserve">Per doctrinam propoſ. </s>
  <s xml:id="echoid-s19400" xml:space="preserve">51. </s>
  <s xml:id="echoid-s19401" xml:space="preserve">huius libri deſcribatur arcus diurnus horarum 14. </s>
  <s xml:id="echoid-s19402" xml:space="preserve">cu <lb/>
<anchor type="note" xlink:label="note-0303-04a" xlink:href="note-0303-04"/>
ius portio à linea horizontali abſciſſa erit arcus diurnus horarum 10. </s>
  <s xml:id="echoid-s19403" xml:space="preserve">in inferiori horologio, vel <lb/>arcus nocturnus horarum 10. </s>
  <s xml:id="echoid-s19404" xml:space="preserve">in horologio nocturno, quod idem eſt, quod horologium Inſerius, <lb/>cum portio illa horologij, quam horizontalis linea abſcindit, vtrumque horologiũ exhibeat &amp; </s>
  <s xml:id="echoid-s19405" xml:space="preserve"><lb/>inferius, &amp; </s>
  <s xml:id="echoid-s19406" xml:space="preserve">nocturnum, vt ex ſuperioribus perſpicuum eſt. </s>
  <s xml:id="echoid-s19407" xml:space="preserve">Si enim per horas à meridie, vel media <lb/>nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19408" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19409" xml:space="preserve">nocturno horarum 10. </s>
  <s xml:id="echoid-s19410" xml:space="preserve">reſpondentes horis ab occaſu, vt in ta <lb/>bula 3. </s>
  <s xml:id="echoid-s19411" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19412" xml:space="preserve">4. </s>
  <s xml:id="echoid-s19413" xml:space="preserve">ſcholii propoſ. </s>
  <s xml:id="echoid-s19414" xml:space="preserve">33 ſuperioris lib. </s>
  <s xml:id="echoid-s19415" xml:space="preserve">videre licet, lineas rectas duxerimus, deſcriptũ erit ho-<lb/>rologium Italicum ſuperius, vt prius. </s>
  <s xml:id="echoid-s19416" xml:space="preserve">Aduertendum tamen eſt, horas ſingulas ab occaſu, ſingulas <lb/>tantum horas à meridie, vel media nocte reſpondentes habere in dictis tabulis. </s>
  <s xml:id="echoid-s19417" xml:space="preserve">Vnde vt recte duci <lb/>
<anchor type="note" xlink:label="note-0303-05a" xlink:href="note-0303-05"/>
poſſint, ſumendæ erunt quoque horæ à meridie, vel media nocte reſpondentes eiſdem numero <lb/>horis ab ortu ex eiſdem tabulis. </s>
  <s xml:id="echoid-s19418" xml:space="preserve">Exempli gratia Hora 23. </s>
  <s xml:id="echoid-s19419" xml:space="preserve">ab occaſu ducitur per horam 6. </s>
  <s xml:id="echoid-s19420" xml:space="preserve">à meridie <lb/>in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19421" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19422" xml:space="preserve">quia eadem vltra. </s>
  <s xml:id="echoid-s19423" xml:space="preserve">arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s19424" xml:space="preserve">qui horizontalem <lb/>lineam in puncto m, tangit, producta indicat horam 23. </s>
  <s xml:id="echoid-s19425" xml:space="preserve">ab ortu, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s19426" xml:space="preserve">10. </s>
  <s xml:id="echoid-s19427" xml:space="preserve">huius <lb/>libri docuimus; </s>
  <s xml:id="echoid-s19428" xml:space="preserve">tranſit autem hora 23. </s>
  <s xml:id="echoid-s19429" xml:space="preserve">ab ortu per horam 4. </s>
  <s xml:id="echoid-s19430" xml:space="preserve">à media nocte in arcu nocturno ho-<lb/>rarum 10. </s>
  <s xml:id="echoid-s19431" xml:space="preserve">idcirco, vt recte hora 23. </s>
  <s xml:id="echoid-s19432" xml:space="preserve">ab occaſu ducatur per horam 6. </s>
  <s xml:id="echoid-s19433" xml:space="preserve">à meridie in arcu diurno ho-<lb/>rarum 14. </s>
  <s xml:id="echoid-s19434" xml:space="preserve">accipienda etiam erit hora 4. </s>
  <s xml:id="echoid-s19435" xml:space="preserve">à media nocte reſpondens horæ 23. </s>
  <s xml:id="echoid-s19436" xml:space="preserve">ab ortu in arcu noctur <lb/>no horarum 10. </s>
  <s xml:id="echoid-s19437" xml:space="preserve">Eodem pacto hora 22. </s>
  <s xml:id="echoid-s19438" xml:space="preserve">ab occaſu ducitur per horam 5. </s>
  <s xml:id="echoid-s19439" xml:space="preserve">à meridie in arcu diurno <lb/>horarum 14. </s>
  <s xml:id="echoid-s19440" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19441" xml:space="preserve">per horam 3. </s>
  <s xml:id="echoid-s19442" xml:space="preserve">à media nocte in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s19443" xml:space="preserve">quæ horæ 22. </s>
  <s xml:id="echoid-s19444" xml:space="preserve">ab ortu <lb/>correſpondet. </s>
  <s xml:id="echoid-s19445" xml:space="preserve">Sic quoque (vt rem totam paucis complectar) hora 11. </s>
  <s xml:id="echoid-s19446" xml:space="preserve">ab occaſu incedit per horam <lb/>
<anchor type="note" xlink:label="note-0303-06a" xlink:href="note-0303-06"/>
6. </s>
  <s xml:id="echoid-s19447" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19448" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19449" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s19450" xml:space="preserve">à meridie in eodem arcu, quæ horæ <lb/>11. </s>
  <s xml:id="echoid-s19451" xml:space="preserve">ab ortu reſpondet. </s>
  <s xml:id="echoid-s19452" xml:space="preserve">Item hora 1. </s>
  <s xml:id="echoid-s19453" xml:space="preserve">ab occaſu ducta eſt per horam 8. </s>
  <s xml:id="echoid-s19454" xml:space="preserve">à meridie in arcu nocturno <lb/>horarum 10. </s>
  <s xml:id="echoid-s19455" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19456" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s19457" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19458" xml:space="preserve">horæ 1. </s>
  <s xml:id="echoid-s19459" xml:space="preserve">ab ortu re-<lb/>ſpondentem, &amp;</s>
  <s xml:id="echoid-s19460" xml:space="preserve">c.</s>
  <s xml:id="echoid-s19461" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1002" type="float" level="2" n="4">
<note position="right" xlink:label="note-0303-04" xlink:href="note-0303-04a" xml:space="preserve">Alia deſcriptio <lb/>horologii Itali-<lb/>ci ęquinoctialis <lb/>per arcus diur-<lb/>nos nocturnos-<lb/>que horarum <lb/>14. &amp; 10.</note>
<note position="left" xlink:label="note-0303-05" xlink:href="note-0303-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0303-06" xlink:href="note-0303-06a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Quomodo In-<lb/>ferius horolo-<lb/>gium Italicum <lb/>ex ſuperiori col <lb/>ligatur.</note>
<p>
  <s xml:id="echoid-s19462" xml:space="preserve">NON aliter horologium Italicum inferius conficiemus. </s>
  <s xml:id="echoid-s19463" xml:space="preserve">Sed ſatius erit illud ex ſuperiori col-<lb/>ligere. </s>
  <s xml:id="echoid-s19464" xml:space="preserve">Nam horæ ab occaſu ſuperioris horologij productæ vltra lineam horizõtalem dabunt eaſ-<lb/>dem numero horas ab occaſu in inferiori horologio, ſi tamen omnes eius partes inuertantur, vt <lb/>in ſuperioribus dictum eſt, &amp; </s>
  <s xml:id="echoid-s19465" xml:space="preserve">demonſtratum in ſcholio propoſ. </s>
  <s xml:id="echoid-s19466" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19467" xml:space="preserve">huius libri.</s>
  <s xml:id="echoid-s19468" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Eiuſdem horo-<lb/>logii@ Italici æ-<lb/>quinoctialis de <lb/>ſcriptio, per ar-<lb/>cum diurnum <lb/>horarum 24.</note>
<p>
  <s xml:id="echoid-s19469" xml:space="preserve">FACILI quoque negotio idem Italicum horologium abſoluemus per arcum diurnum ho-<lb/>rarum 24. </s>
  <s xml:id="echoid-s19470" xml:space="preserve">ſeu parallelum omnium ſemper apparentium maximum, qui horizontalem lineam <lb/>tangit in m, eſtq; </s>
  <s xml:id="echoid-s19471" xml:space="preserve">in inferiori horologio arcus nocturnus horarum 24. </s>
  <s xml:id="echoid-s19472" xml:space="preserve">ſiue parallelus ſemper la-
<pb o="288" file="0304" n="304" rhead="GNOMONICES"/>
tentium maximus. </s>
  <s xml:id="echoid-s19473" xml:space="preserve">Cum enim hic arcus circulus ſit, ex coroll. </s>
  <s xml:id="echoid-s19474" xml:space="preserve">propoſ, 4. </s>
  <s xml:id="echoid-s19475" xml:space="preserve">ſuperioris libri, &amp; </s>
  <s xml:id="echoid-s19476" xml:space="preserve">eum <lb/>per propoſ. </s>
  <s xml:id="echoid-s19477" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19478" xml:space="preserve">eiuſdem libri tangant horæ ab ortu, vel occaſu in punctis, in quibus eundem horę <lb/>à meridie, vel media nocte ſecant, manifeſtum eſt, lineas dictum circulum tangentes in punctis <lb/>
<anchor type="figure" xlink:label="fig-0304-01a" xlink:href="fig-0304-01"/>
<anchor type="note" xlink:label="note-0304-01a" xlink:href="note-0304-01"/>
<anchor type="note" xlink:label="note-0304-02a" xlink:href="note-0304-02"/>
<anchor type="note" xlink:label="note-0304-03a" xlink:href="note-0304-03"/>
horarum à meridie, vel media nocte, hoc eſt, perpendiculares ad lineas horarum à meridie, vel <lb/>media nocte in punctis, vbi prædictum circulum ſecant, monſtrare horas ab occaſu. </s>
  <s xml:id="echoid-s19479" xml:space="preserve">Quæ autem <lb/>horæ ab occaſu quibus horis à meridie, vel media nocte reſpondeant in dicto arcu horarum 24. <lb/></s>
  <s xml:id="echoid-s19480" xml:space="preserve">docebit tabula ſeptima ſcholii propoſ. </s>
  <s xml:id="echoid-s19481" xml:space="preserve">33. </s>
  <s xml:id="echoid-s19482" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s19483" xml:space="preserve">pro horologio ſuperiori; </s>
  <s xml:id="echoid-s19484" xml:space="preserve">pro inferiori <lb/>autem idem præſtabit tabula octaua eiuſdem ſcholii. </s>
  <s xml:id="echoid-s19485" xml:space="preserve">Tranſibunt autem neceſſario hæ lineæ tan-<lb/>gentes per horas à meridie, vel media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19486" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19487" xml:space="preserve">nocturno horarum 10. </s>
  <s xml:id="echoid-s19488" xml:space="preserve"><lb/>Ita cernis horam 23. </s>
  <s xml:id="echoid-s19489" xml:space="preserve">ab occaſu tangere arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s19490" xml:space="preserve">in hora 11. </s>
  <s xml:id="echoid-s19491" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s19492" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0304-04a" xlink:href="note-0304-04"/>
<anchor type="note" xlink:label="note-0304-05a" xlink:href="note-0304-05"/>
tranſire per horam 6. </s>
  <s xml:id="echoid-s19493" xml:space="preserve">à meridie in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19494" xml:space="preserve">Item horam primam ab occaſu tan-<lb/>gere priorem arcum in hora 1. </s>
  <s xml:id="echoid-s19495" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s19496" xml:space="preserve">incedere per horam 8. </s>
  <s xml:id="echoid-s19497" xml:space="preserve">à meridie, in arcu noctur-<lb/>no horarum 10. </s>
  <s xml:id="echoid-s19498" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s19499" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19500" xml:space="preserve">Itaque commodiſſime hora quæcunque ab occaſu deſcribetur in ſuperiori <lb/>quidem horologio ex duobus arcubus, quorum vnus ſit diurnus horarum 24. </s>
  <s xml:id="echoid-s19501" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19502" xml:space="preserve">alter diurnus ho <lb/>rarum 14. </s>
  <s xml:id="echoid-s19503" xml:space="preserve">vel nocturnus horarum 10. </s>
  <s xml:id="echoid-s19504" xml:space="preserve">In inferiori autem ex duobus, quorum vnus nocturnus ſit <lb/>horarum 24. </s>
  <s xml:id="echoid-s19505" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19506" xml:space="preserve">alter diurnus horarum 10. </s>
  <s xml:id="echoid-s19507" xml:space="preserve">vel nocturnus horarum 14.</s>
  <s xml:id="echoid-s19508" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1003" type="float" level="2" n="5">
  <figure xlink:label="fig-0304-01" xlink:href="fig-0304-01a">
    <image file="0304-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0304-01"/>
  </figure>
<note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0304-02" xlink:href="note-0304-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0304-03" xlink:href="note-0304-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0304-04" xlink:href="note-0304-04a" xml:space="preserve">Cõmodiſſima <lb/>deſcriptio eiuſ <lb/>dem horologii <lb/>Italici per arcũ <lb/>diurnũ horatũ <lb/>24. vna cũ diur <lb/>no horarũ 14. <lb/>&amp; nocturno ho <lb/>rarum 10.</note>
<note position="left" xlink:label="note-0304-05" xlink:href="note-0304-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s19509" xml:space="preserve">IDEM horologium Italicum conſtruemus per lineam horæ 12. </s>
  <s xml:id="echoid-s19510" xml:space="preserve">ab ortu, vel occaſu, vt ex ta-<lb/>
<anchor type="note" xlink:label="note-0304-06a" xlink:href="note-0304-06"/>
bula ſecunda propoſ. </s>
  <s xml:id="echoid-s19511" xml:space="preserve">20. </s>
  <s xml:id="echoid-s19512" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s19513" xml:space="preserve">comſtat. </s>
  <s xml:id="echoid-s19514" xml:space="preserve">Item per lineam horizontalem, ſeu horæ 24. </s>
  <s xml:id="echoid-s19515" xml:space="preserve">ab <lb/>ortu, vel occaſu, vt ex tabula prima eiuſdem propoſ. </s>
  <s xml:id="echoid-s19516" xml:space="preserve">20. </s>
  <s xml:id="echoid-s19517" xml:space="preserve">colligitur, vt in ſuperioribus dictum eſt. <lb/></s>
  <s xml:id="echoid-s19518" xml:space="preserve">Immo<unsure/> &amp; </s>
  <s xml:id="echoid-s19519" xml:space="preserve">ex tabula tertia eiuſdem propoſ. </s>
  <s xml:id="echoid-s19520" xml:space="preserve">perſpicuum erit, quænam horæ ab occaſu ſe mutuo ſe-<lb/>
<anchor type="note" xlink:label="note-0304-07a" xlink:href="note-0304-07"/>
cent in linea horæ 6. </s>
  <s xml:id="echoid-s19521" xml:space="preserve">à meridie, vel media nocte, &amp;</s>
  <s xml:id="echoid-s19522" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19523" xml:space="preserve">Linea autem horæ 12. </s>
  <s xml:id="echoid-s19524" xml:space="preserve">ab ortu, vel occaſu hac <lb/>ratione duci poterit. </s>
  <s xml:id="echoid-s19525" xml:space="preserve">In linea horæ 6. </s>
  <s xml:id="echoid-s19526" xml:space="preserve">à meridie, vel media nocte ex centro E, abſcindatur recta <lb/>E A, gnomoni æqualis, &amp; </s>
  <s xml:id="echoid-s19527" xml:space="preserve">centro A, ad quodcunque interuallum circulo deſcripto, ſumatur in eo <lb/>
<anchor type="note" xlink:label="note-0304-08a" xlink:href="note-0304-08"/>
arcus B C, altitudini poli æqualis, initio facto à linea E B, &amp; </s>
  <s xml:id="echoid-s19528" xml:space="preserve">verſus lineam horizontalem progre-<lb/>diendo. </s>
  <s xml:id="echoid-s19529" xml:space="preserve">Deinde ex C, per centrum A, linea recta ducatur, ſecans meridianam lineam in D. </s>
  <s xml:id="echoid-s19530" xml:space="preserve">Nam <lb/>recta lineæ horæ 6. </s>
  <s xml:id="echoid-s19531" xml:space="preserve">à meridie, vel media nocte parallela ducta per D, monſtrabit horam 12. </s>
  <s xml:id="echoid-s19532" xml:space="preserve">ab or <lb/>tu, vel occaſu. </s>
  <s xml:id="echoid-s19533" xml:space="preserve">Intelligatur enim circulus B C, circa meridianam lineam conuerti, vſque dum cũ <lb/>Meridiano circulo,<unsure/> &amp; </s>
  <s xml:id="echoid-s19534" xml:space="preserve">eius centrum A, cum mundi centro, ſeu ſtyli vertice coniungatur. </s>
  <s xml:id="echoid-s19535" xml:space="preserve">Quo po <lb/>ſito, erit B, polus mundi, &amp; </s>
  <s xml:id="echoid-s19536" xml:space="preserve">C, punctum, vbi circulus horæ 12. </s>
  <s xml:id="echoid-s19537" xml:space="preserve">ab ortu, vel occaſu parallelũ om-<lb/>nium ſemper apparentium maximum tangit, Meridianumq́ue ſecat, quòd hic parallelus Meridia <lb/>num ſecet in C. </s>
  <s xml:id="echoid-s19538" xml:space="preserve">Quare recta C A, communis erit ſectio circuli horæ 12. </s>
  <s xml:id="echoid-s19539" xml:space="preserve">ab ortu, vel occaſu, &amp;</s>
  <s xml:id="echoid-s19540" xml:space="preserve">
<pb o="289" file="0305" n="305" rhead="LIBER SECVNDVS."/>
Meridiani, proptereaq́ue circulus horæ 12. </s>
  <s xml:id="echoid-s19541" xml:space="preserve">ab ortu, vel occaſu plano horologii occurret in pun-<lb/>cto D. </s>
  <s xml:id="echoid-s19542" xml:space="preserve">Quia verò linea horæ 12. </s>
  <s xml:id="echoid-s19543" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s19544" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s19545" xml:space="preserve">à meridie, vel media nocte <lb/>parallelæ ſunt, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s19546" xml:space="preserve">22. </s>
  <s xml:id="echoid-s19547" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s19548" xml:space="preserve">ſcripſimus, ſequitur rectam, quæ <lb/>per D, ducitur parallela lineæ horæ 6. </s>
  <s xml:id="echoid-s19549" xml:space="preserve">à meridie, vel media nocte, lineam eſſe horæ 12. </s>
  <s xml:id="echoid-s19550" xml:space="preserve">ab ortu, <lb/>vel occaſu. </s>
  <s xml:id="echoid-s19551" xml:space="preserve">Quoniam autem angulus altitudinis poli B A C, æqualis eſt angulo E A D, ad verti-<lb/>
<anchor type="note" xlink:label="note-0305-01a" xlink:href="note-0305-01"/>
<anchor type="note" xlink:label="note-0305-02a" xlink:href="note-0305-02"/>
cem, efficitur, vt ſi in linea horæ 6. </s>
  <s xml:id="echoid-s19552" xml:space="preserve">à meridie, vel media nocte accipiamus rectam E A, ſtylo æqua <lb/>lem, &amp; </s>
  <s xml:id="echoid-s19553" xml:space="preserve">in A, conſtituamus angulum E A D, altitudini poli æqualem, reperiamus in meridiana li-<lb/>nea idem punctum D, per quod linea horæ 12. </s>
  <s xml:id="echoid-s19554" xml:space="preserve">ab ortu, vel occaſu ducenda eſt, etiam ſi circulus <lb/>B C, non deſcribatur. </s>
  <s xml:id="echoid-s19555" xml:space="preserve">Quinetiam ſi rectę E m, æqualem abſcindamus E D, habebimus idem pun-<lb/>ctum D. </s>
  <s xml:id="echoid-s19556" xml:space="preserve">Cum enim &amp; </s>
  <s xml:id="echoid-s19557" xml:space="preserve">angulus E A m, æqualis ſit conſtitutus altitudini poli, vt ex propoſ. </s>
  <s xml:id="echoid-s19558" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19559" xml:space="preserve">hu-<lb/>
<anchor type="note" xlink:label="note-0305-03a" xlink:href="note-0305-03"/>
ius libri conſtat, æquales erunt anguli E A m, E A D, in triangulis E A m, E A D, in triangulis <lb/>E A m, E A D: </s>
  <s xml:id="echoid-s19560" xml:space="preserve">ſed &amp; </s>
  <s xml:id="echoid-s19561" xml:space="preserve">anguli ad E, æquales ſunt, nemper recti, eſtq́ue latus E A, dictis angulis adia-<lb/>cens commune. </s>
  <s xml:id="echoid-s19562" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s19563" xml:space="preserve">latera E m, E D, æqualia erunt; </s>
  <s xml:id="echoid-s19564" xml:space="preserve">ac proinde cum per D, tranſeat linea ho <lb/>
<anchor type="note" xlink:label="note-0305-04a" xlink:href="note-0305-04"/>
rę 12. </s>
  <s xml:id="echoid-s19565" xml:space="preserve">ab ortu, vel occaſu, vt oſtendimus, liquido conſtat, ſi ipſi E m, æqualis abſcindatur E D, per <lb/>D, ducendam eſſe lineam horæ 12. </s>
  <s xml:id="echoid-s19566" xml:space="preserve">ab ortu, vel occaſu, quę quidem in D, tangit parallelum ſem-<lb/>per apparentium maximum, quemadmodum &amp; </s>
  <s xml:id="echoid-s19567" xml:space="preserve">eundem in m, tangit linea horizontalis.</s>
  <s xml:id="echoid-s19568" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1004" type="float" level="2" n="6">
<note position="left" xlink:label="note-0304-06" xlink:href="note-0304-06a" xml:space="preserve">Gõſtructio eiuſ <lb/>dem horologii <lb/>Italici per lineã <lb/>horæ 12. ab or. <lb/>vel occ. &amp; per <lb/>lineam horizõ-<lb/>talem, ſeu hor<unsure/> <lb/>24. ab or<unsure/>. vel <lb/>occ.</note>
<note position="left" xlink:label="note-0304-07" xlink:href="note-0304-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0304-08" xlink:href="note-0304-08a" xml:space="preserve">Linea horæ 12. <lb/>ab or. vel occ. <lb/>quomodo in <lb/>equinoctiali ho <lb/>rologio ducen-<lb/>da ſit.</note>
<note position="right" xlink:label="note-0305-01" xlink:href="note-0305-01a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0305-02" xlink:href="note-0305-02a" xml:space="preserve">Aliæ deſcriptio <lb/>ne@ lineæ horę <lb/>12. ab or. vel <lb/>occ. in æquino-<lb/>ctiali horologio</note>
<note position="left" xlink:label="note-0305-03" xlink:href="note-0305-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0305-04" xlink:href="note-0305-04a" xml:space="preserve">26. primi.</note>
</div>
<p>
  <s xml:id="echoid-s19569" xml:space="preserve">SVNT autem ſem per binæ lineę horarum ab occaſu alicui horæ à meridie, vel media nocte <lb/>
<anchor type="note" xlink:label="note-0305-05a" xlink:href="note-0305-05"/>
parallelæ, vt ex tabula propoſ. </s>
  <s xml:id="echoid-s19570" xml:space="preserve">19. </s>
  <s xml:id="echoid-s19571" xml:space="preserve">libri ſuperioris liquet, &amp; </s>
  <s xml:id="echoid-s19572" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s19573" xml:space="preserve">22. </s>
  <s xml:id="echoid-s19574" xml:space="preserve">eiuſdem libri <lb/>probatum eſt. </s>
  <s xml:id="echoid-s19575" xml:space="preserve">Vt hora 23. </s>
  <s xml:id="echoid-s19576" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19577" xml:space="preserve">11. </s>
  <s xml:id="echoid-s19578" xml:space="preserve">ab occaſu parallelæ ſunt horæ quintæ à meridie, vel media no-<lb/>cte, &amp;</s>
  <s xml:id="echoid-s19579" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19580" xml:space="preserve">Vnde ſi in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19581" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19582" xml:space="preserve">nocturno horarum 10. </s>
  <s xml:id="echoid-s19583" xml:space="preserve">veì etiam in diurno ho-<lb/>
<anchor type="note" xlink:label="note-0305-06a" xlink:href="note-0305-06"/>
rarum 24. </s>
  <s xml:id="echoid-s19584" xml:space="preserve">notentur horæ à meridie, vel media nocte reſpondentes horis ab occaſu, prout tabulæ <lb/>ſcholii propoſ. </s>
  <s xml:id="echoid-s19585" xml:space="preserve">33. </s>
  <s xml:id="echoid-s19586" xml:space="preserve">ſuperioris libri indicant, percommodè eaſdem horas ab occaſu deſcribemus, <lb/>
<anchor type="note" xlink:label="note-0305-07a" xlink:href="note-0305-07"/>
ſi per illas horas à meridie, vel media nocte in dictis arcubus notatas ducamus lineas patallelas il-<lb/>lis horis à meridie, vel media nocte, quas tabula prædicta ſcholii propoſ. </s>
  <s xml:id="echoid-s19587" xml:space="preserve">19. </s>
  <s xml:id="echoid-s19588" xml:space="preserve">eiuſdem libri de-<lb/>monſtrat. </s>
  <s xml:id="echoid-s19589" xml:space="preserve">Vt quoniam hora 16. </s>
  <s xml:id="echoid-s19590" xml:space="preserve">ab occaſu reſpondet ſecundum tabulam tertiam propoſ. </s>
  <s xml:id="echoid-s19591" xml:space="preserve">33. </s>
  <s xml:id="echoid-s19592" xml:space="preserve">di-<lb/>cti libri horæ 11. </s>
  <s xml:id="echoid-s19593" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19594" xml:space="preserve">eſtq́ue parallela horæ 10. </s>
  <s xml:id="echoid-s19595" xml:space="preserve">à meridie <lb/>vel media nocte, vt vult tabula propoſ. </s>
  <s xml:id="echoid-s19596" xml:space="preserve">19. </s>
  <s xml:id="echoid-s19597" xml:space="preserve">eiuſdem libri, propterea recta ducta per horam 11. </s>
  <s xml:id="echoid-s19598" xml:space="preserve">à <lb/>media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s19599" xml:space="preserve">parallela horæ 10. </s>
  <s xml:id="echoid-s19600" xml:space="preserve">à meridie, vel media nocte, erit linea <lb/>horæ 16. </s>
  <s xml:id="echoid-s19601" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s19602" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s19603" xml:space="preserve">Horologium igitur Italicum e<unsure/>quinoctiale conſtruximus. <lb/></s>
  <s xml:id="echoid-s19604" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s19605" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1005" type="float" level="2" n="7">
<note position="right" xlink:label="note-0305-05" xlink:href="note-0305-05a" xml:space="preserve">Singulis horis <lb/>à mer. vel med. <lb/>noc. parallelæ <lb/>ſunt binę horæ <lb/>ab or. vel occ.</note>
<note position="left" xlink:label="note-0305-06" xlink:href="note-0305-06a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0305-07" xlink:href="note-0305-07a" xml:space="preserve">Alia deſcriptio <lb/>horarũ ab occ. <lb/>in borologio ę-<lb/>quinoctiali.</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1007" type="section" level="1" n="247">
<head xml:id="echoid-head254" xml:space="preserve">PROBLEMA 59. PROPOSITIO 59.</head>
<head xml:id="echoid-head255" xml:space="preserve">HOROLOGIVM Babylonicum ęquinoctiale componere.</head>
<note position="right" xml:space="preserve">Horologii Ba-<lb/>bylonici æqui-<lb/>noctialis com-<lb/>poſitio.</note>
<p>
  <s xml:id="echoid-s19606" xml:space="preserve">EISDEM vijs, ac rationibus, quibus Italicũ conſtruximus, horologiũ Babylonicum conficie-<lb/>mus, ſi tamen in primo modo diuiſio circulorum ex E, deſcriptorum initium ſumat à parte dextra <lb/>ſuperioris horologii, quæ nimirum vmbram ſtyli ſub ortum Solis excipere ſolet; </s>
  <s xml:id="echoid-s19607" xml:space="preserve">in inferiori verò <lb/>à parte ſiniſtra, accipiendo horologium inferius, vt in primo modo antecedentis propoſ. </s>
  <s xml:id="echoid-s19608" xml:space="preserve">diximus. <lb/></s>
  <s xml:id="echoid-s19609" xml:space="preserve">Item horariæ lineæ ita ducantur, vt primum per proxima puncta diuiſionum ſupra, vel infra ho-<lb/>rizontalem lineam, à qua diuiſio initium habuit, vna ducatur; </s>
  <s xml:id="echoid-s19610" xml:space="preserve">Deinde per ſequentia puncta ince-<lb/>
<anchor type="note" xlink:label="note-0305-10a" xlink:href="note-0305-10"/>
dat alia, &amp; </s>
  <s xml:id="echoid-s19611" xml:space="preserve">ita deinceps. </s>
  <s xml:id="echoid-s19612" xml:space="preserve">Ordo horarum hic eſt. </s>
  <s xml:id="echoid-s19613" xml:space="preserve">Prima linea infra horizontalem lineam ex parte <lb/>
<anchor type="note" xlink:label="note-0305-11a" xlink:href="note-0305-11"/>
dextra dat in ſuperiori horologio horam 1. </s>
  <s xml:id="echoid-s19614" xml:space="preserve">ab ortu, ſequens 2. </s>
  <s xml:id="echoid-s19615" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s19616" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19617" xml:space="preserve">In horologio autem inferiori <lb/>proxima linea infra horizontalem lineam ad ſiniſtram monſtrabit horam 1. </s>
  <s xml:id="echoid-s19618" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s19619" xml:space="preserve">inſequens <lb/>ſecundam, &amp;</s>
  <s xml:id="echoid-s19620" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19621" xml:space="preserve">ita vt ſint horarum ab ortu in ſuperiori horologio complementa vſque ad 24. <lb/></s>
  <s xml:id="echoid-s19622" xml:space="preserve">Quæ enim in ſuperiori dabat horam 23. </s>
  <s xml:id="echoid-s19623" xml:space="preserve">in inferiori exhibet primam, &amp;</s>
  <s xml:id="echoid-s19624" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19625" xml:space="preserve">vt de Italico diximus <lb/>in præcedenti propoſ. </s>
  <s xml:id="echoid-s19626" xml:space="preserve">quamuis nullum exemplum inferioris horologii ſecundum hanc viam po-<lb/>ſuerimus. </s>
  <s xml:id="echoid-s19627" xml:space="preserve">Demonſtratio eadem hic erit, quæ in præcedenti propoſ. </s>
  <s xml:id="echoid-s19628" xml:space="preserve">ſumendo pro horis ab occa. </s>
  <s xml:id="echoid-s19629" xml:space="preserve"><lb/>ſu horas ab ortu in parallelis Solis.</s>
  <s xml:id="echoid-s19630" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1007" type="float" level="2" n="1">
<note position="left" xlink:label="note-0305-10" xlink:href="note-0305-10a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0305-11" xlink:href="note-0305-11a" xml:space="preserve">Ordo horarum <lb/>ab or. in horo-<lb/>gio æquinoctia <lb/>li.</note>
</div>
<p>
  <s xml:id="echoid-s19631" xml:space="preserve">IN reliquis modis nulla eſt difficultas, ſi ea, quæ ſupra dicta ſunt de horis ab occaſu, hic de ho <lb/>
<anchor type="note" xlink:label="note-0305-12a" xlink:href="note-0305-12"/>
ris ab ortu, &amp; </s>
  <s xml:id="echoid-s19632" xml:space="preserve">contra, quæ ibi de horis ab or. </s>
  <s xml:id="echoid-s19633" xml:space="preserve">hic de horis ab occ. </s>
  <s xml:id="echoid-s19634" xml:space="preserve">intelligantur. </s>
  <s xml:id="echoid-s19635" xml:space="preserve">Exemplum horolo-<lb/>
<anchor type="note" xlink:label="note-0305-13a" xlink:href="note-0305-13"/>
gii Babylonici extat in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s19636" xml:space="preserve">vbi etiam continentur horæ à meridie, vel me-<lb/>dia nocte, &amp; </s>
  <s xml:id="echoid-s19637" xml:space="preserve">ab occaſu, quæ ita inter ſe diſtinguuntur. </s>
  <s xml:id="echoid-s19638" xml:space="preserve">Horis à meridie, vel media nocte aſcripſi-<lb/>mus numeros prope arcum diurnum horarum 14. </s>
  <s xml:id="echoid-s19639" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19640" xml:space="preserve">nocturnum horarum 10. </s>
  <s xml:id="echoid-s19641" xml:space="preserve">earumq́ue lineæ <lb/>punctis duntaxat notatæ vſque ad arcum horarum 24. </s>
  <s xml:id="echoid-s19642" xml:space="preserve">excurrunt. </s>
  <s xml:id="echoid-s19643" xml:space="preserve">Horæ ab occaſu habent chara <lb/>cteres numerorum communes hoc modo 24. </s>
  <s xml:id="echoid-s19644" xml:space="preserve">23. </s>
  <s xml:id="echoid-s19645" xml:space="preserve">22. </s>
  <s xml:id="echoid-s19646" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s19647" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19648" xml:space="preserve">Horæ denique ab ortu notis numerorũ <lb/>antiquis ab alijs ſecernuntur hoc modo I. </s>
  <s xml:id="echoid-s19649" xml:space="preserve">II. </s>
  <s xml:id="echoid-s19650" xml:space="preserve">III. </s>
  <s xml:id="echoid-s19651" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s19652" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19653" xml:space="preserve">Itaque horologium Babylonicum æquino <lb/>ctiale compoſuimus. </s>
  <s xml:id="echoid-s19654" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s19655" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1008" type="float" level="2" n="2">
<note position="right" xlink:label="note-0305-12" xlink:href="note-0305-12a" xml:space="preserve">Aliæ deſcriptio <lb/>nes horologii <lb/>Babylonici æ-<lb/>ꝗnoctialis quo-<lb/>modo fiant.</note>
<note position="left" xlink:label="note-0305-13" xlink:href="note-0305-13a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1010" type="section" level="1" n="248">
<head xml:id="echoid-head256" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Quomodo In-<lb/>ferius horolo-<lb/>gium Babyloni <lb/>cum ex ſupetio <lb/>ri colligatur.</note>
<p style="it">
  <s xml:id="echoid-s19656" xml:space="preserve">LINEAE horarum ab ortu in ſuperiori horologio vltra lineam horizontalem protractæ in-
<pb o="290" file="0306" n="306" rhead="GNOMONICES"/>
dicant eaſdem horas in inferiori, ſi eius partes inuertantur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s19657" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19658" xml:space="preserve">huius libri de-<lb/>monſtrauimus.</s>
  <s xml:id="echoid-s19659" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s19660" xml:space="preserve">PORRO horologium Italicum, ac Babylonicum deſcribemus etiam hoc modo, nulla habita ratio-<lb/>
<anchor type="note" xlink:label="note-0306-01a" xlink:href="note-0306-01"/>
ne parallclorum Solis. </s>
  <s xml:id="echoid-s19661" xml:space="preserve">Ex A, centro cir culus B G F, ad quod cunque interuallum de ſcriptus in partes <lb/>24. </s>
  <s xml:id="echoid-s19662" xml:space="preserve">æquales ſecetur, ductis diametris per centrum A, &amp; </s>
  <s xml:id="echoid-s19663" xml:space="preserve">quælibet duo puncta oppoſita, excitentur ad <lb/>
<anchor type="figure" xlink:label="fig-0306-01a" xlink:href="fig-0306-01"/>
<anchor type="note" xlink:label="note-0306-02a" xlink:href="note-0306-02"/>
<anchor type="note" xlink:label="note-0306-03a" xlink:href="note-0306-03"/>
<anchor type="note" xlink:label="note-0306-04a" xlink:href="note-0306-04"/>
<anchor type="note" xlink:label="note-0306-05a" xlink:href="note-0306-05"/>
ipſas in extremis punctis lineæ perpendiculares, vel (quod idem eſt) circulum tangentes: </s>
  <s xml:id="echoid-s19664" xml:space="preserve">quas dico <lb/>horas indicare ab ortu, &amp; </s>
  <s xml:id="echoid-s19665" xml:space="preserve">occaſu in horologio æquinoctiali; </s>
  <s xml:id="echoid-s19666" xml:space="preserve">ita vt ſi quamlibet harum linearum tangen-<lb/>tium pro<unsure/> linea horizontali, ſeu horæ 24. </s>
  <s xml:id="echoid-s19667" xml:space="preserve">elegeris, nempe ipſam C D, proxima linea infra hanc <lb/>ad ſiniſtram monſtret horam 23. </s>
  <s xml:id="echoid-s19668" xml:space="preserve">ab occaſu, inſequens 22. </s>
  <s xml:id="echoid-s19669" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19670" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19671" xml:space="preserve">in horologio ſuperiori. </s>
  <s xml:id="echoid-s19672" xml:space="preserve">Proxima <lb/>verò linea infra eandem horizontalem C D, ad dextram exhibeat horam primam ab ortu, &amp; </s>
  <s xml:id="echoid-s19673" xml:space="preserve">quæ ſe-<lb/>quitur, ſecundam, &amp; </s>
  <s xml:id="echoid-s19674" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19675" xml:space="preserve">in eodem ſuperiori horologio. </s>
  <s xml:id="echoid-s19676" xml:space="preserve">Quoniam enim vt in præcedenti propoſ. </s>
  <s xml:id="echoid-s19677" xml:space="preserve">docui-<lb/>mus, demonſtratum{q́ue} eſt propoſ. </s>
  <s xml:id="echoid-s19678" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19679" xml:space="preserve">libri ſuperioris, horæ ab ortu, vel occaſu tangunt paralle-<lb/>lum omnium ſemper apparentium maximum cuiuſcunque horologii (qui in æquinoctiali horologio cir cu-<lb/>lus eſt) in punctis, vbi eundem horæ à meridie, vel media nocte ſecant; </s>
  <s xml:id="echoid-s19680" xml:space="preserve">ſi cir culus B G F, intelligatur <lb/>in horologio æquinoctiali dictus maximus parallelus, erunt puncta diuiſionum ipſius, horæ à meridie, <lb/>
<anchor type="note" xlink:label="note-0306-06a" xlink:href="note-0306-06"/>
vel media nocte, cũ ipſum in partes æquales 24. </s>
  <s xml:id="echoid-s19681" xml:space="preserve">diſtribuant; </s>
  <s xml:id="echoid-s19682" xml:space="preserve">ac idcirco lineæ tangentes eundem in eiſdem <lb/>punctis, horas ab ortu, vel occaſu monſtr abunt. </s>
  <s xml:id="echoid-s19683" xml:space="preserve">In horologio inferiori, quod nobis ſubminiſtrat portio <lb/>abſciſſa à linea horizontali C D, ſi omnes eius partes inuertantur, eadem ratio eſt, ut figura indicat, &amp; </s>
  <s xml:id="echoid-s19684" xml:space="preserve"><lb/>ex dictis manifeſtum eſſe poteſt.</s>
  <s xml:id="echoid-s19685" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1010" type="float" level="2" n="1">
<note position="left" xlink:label="note-0306-01" xlink:href="note-0306-01a" xml:space="preserve">Horologiũ Ita <lb/>licum ac Baby <lb/>lonicũ quomo-<lb/>do conſtruatur, <lb/>nulla habita ra <lb/>tione parallelo <lb/>rum Solis.</note>
  <figure xlink:label="fig-0306-01" xlink:href="fig-0306-01a">
    <image file="0306-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0306-01"/>
  </figure>
<note position="left" xlink:label="note-0306-02" xlink:href="note-0306-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0306-03" xlink:href="note-0306-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0306-04" xlink:href="note-0306-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0306-05" xlink:href="note-0306-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0306-06" xlink:href="note-0306-06a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s19686" xml:space="preserve">DVCEMVS autem dictas perpendiculares, ſeu tangentes circulum ſine magno labore, hac ra-<lb/>
<anchor type="note" xlink:label="note-0306-07a" xlink:href="note-0306-07"/>
tione. </s>
  <s xml:id="echoid-s19687" xml:space="preserve">Ducta vna perpendiculari, ſeu tangente linea C D, deſcribatur ex A, circulus quantæcunque ma <lb/>gnitudinis occultus per puncta C, D, tranſiens, qui maior tamen ſit circulo B G F. </s>
  <s xml:id="echoid-s19688" xml:space="preserve">Diuidatur in 24. </s>
  <s xml:id="echoid-s19689" xml:space="preserve">par <lb/>tes ęquales, principio facto à puncto C, &amp; </s>
  <s xml:id="echoid-s19690" xml:space="preserve">iterum in alias partes 24. </s>
  <s xml:id="echoid-s19691" xml:space="preserve">initio facto à puncto D, cuiusmodi <lb/>eſt extremus circulus proximè antecedentis figurę punctis notatus. </s>
  <s xml:id="echoid-s19692" xml:space="preserve">Nam quemadmodum recta C D, <lb/>perpendicularis eſt ad B A, &amp; </s>
  <s xml:id="echoid-s19693" xml:space="preserve">tangit circulum B G F, in B, ducitur{q́ue} per prima puncta diuiſionum, ita
<pb o="291" file="0307" n="307" rhead="LIBER SECVNDVS."/>
quoque recta ducta per ſecunda puncta diuiſionum, quorum vnum ſit primæ diuiſionis, &amp; </s>
  <s xml:id="echoid-s19694" xml:space="preserve">infra rectam <lb/>C D, &amp; </s>
  <s xml:id="echoid-s19695" xml:space="preserve">alterum ſecundæ diuiſionis, &amp; </s>
  <s xml:id="echoid-s19696" xml:space="preserve">ſupra rectam C D, perpendicularis erit ad lineam ipſi B A, proxi-<lb/>mam, tanget{q́ue} circulum B G F, in puncto proximo ipſi B. </s>
  <s xml:id="echoid-s19697" xml:space="preserve">Ita quoque cum tertĳs punctis diuiſionum, <lb/>quartis, &amp; </s>
  <s xml:id="echoid-s19698" xml:space="preserve">cæteris agatur. </s>
  <s xml:id="echoid-s19699" xml:space="preserve">Ratio huius rei hæc eſt: </s>
  <s xml:id="echoid-s19700" xml:space="preserve">quia dictæ lineæ horarum ab or. </s>
  <s xml:id="echoid-s19701" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19702" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s19703" xml:space="preserve">diuidunt ſin-<lb/>gulos circulos ex A, deſcriptos in 24. </s>
  <s xml:id="echoid-s19704" xml:space="preserve">partes æquales, vt ex demonstratis in propoſ. </s>
  <s xml:id="echoid-s19705" xml:space="preserve">præcedenti liquet, <lb/>initio facto tam à puncto C, quàm à puncto D; </s>
  <s xml:id="echoid-s19706" xml:space="preserve">ita vt ſi proximum punctum infra C, fuerit hora 23. </s>
  <s xml:id="echoid-s19707" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s19708" xml:space="preserve">proximum punctum ſupra punctum D, ſit hora 23. </s>
  <s xml:id="echoid-s19709" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s19710" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19711" xml:space="preserve">c.</s>
  <s xml:id="echoid-s19712" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1011" type="float" level="2" n="2">
<note position="left" xlink:label="note-0306-07" xlink:href="note-0306-07a" xml:space="preserve">Quomodo li-<lb/>neę horarię pro <lb/>xime antecedẽ-<lb/>tis figurę facile <lb/>ducantur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s19713" xml:space="preserve">LONGITVDINEM ſtyli, qui in centro collocatus horas indicet in horologio hac arte deli-<lb/>
<anchor type="note" xlink:label="note-0307-01a" xlink:href="note-0307-01"/>
neato, ita inueniemus. </s>
  <s xml:id="echoid-s19714" xml:space="preserve">Fiat angulus A B E, complemento altitudinis poli æqualis, quod quidem facile <lb/>efficietur, ſi ex B, arcus circuli deſcribatur, in eo{q́ue} complementum altitudinis poli à recta B A, verſus <lb/>
<anchor type="note" xlink:label="note-0307-02a" xlink:href="note-0307-02"/>
C, ſupputetur. </s>
  <s xml:id="echoid-s19715" xml:space="preserve">Nam recta B E, ducta ex B, per finem ſupputationis conſtituet angulum A B F, com-<lb/>plemento altitudinis poli æqualem, abſcindet{q́ue} ex recta A E, longitudinem ſtyli A E, in centro A, affi-<lb/>gendi ad angulos rectos. </s>
  <s xml:id="echoid-s19716" xml:space="preserve">Si enim horologio in propria poſitione conſtituto, ita vt æquinoctiali circulo <lb/>æquidiſtet, &amp; </s>
  <s xml:id="echoid-s19717" xml:space="preserve">recta C D, Horizonti ſit parallela, triangulum A B E, circa rectam A E, quæ commu-<lb/>nis ſectio eſt plani horologii, &amp; </s>
  <s xml:id="echoid-s19718" xml:space="preserve">Meridiani circuli, moueri intelligatur, donec in plano Meridiani ſtatua-<lb/>tur rectum ad horologĳ planum, erit A E, axis mundi, &amp; </s>
  <s xml:id="echoid-s19719" xml:space="preserve">B E, communis@ ſectio Horizontis per C D, <lb/>ducti, &amp; </s>
  <s xml:id="echoid-s19720" xml:space="preserve">Meridiani, cum eſficiat cum meridiana linea A B, angulum complemento altitudinis poli æqua-<lb/>lem, vt res poſtulat, vt ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s19721" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19722" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19723" xml:space="preserve">colligitur. </s>
  <s xml:id="echoid-s19724" xml:space="preserve">Quare A E, longitudo ſtyli <lb/>erit, cum Sole in Horizonte, qui per C D, &amp; </s>
  <s xml:id="echoid-s19725" xml:space="preserve">E B, ducitur, exiſtente extremitas vmbræ ipſius in lineam <lb/>horizontalem C D, proĳciatur, vt conſtat. </s>
  <s xml:id="echoid-s19726" xml:space="preserve">Quòd ſi non placeat deſcribere arcum circuli ex B, ad conſti-<lb/>
<anchor type="note" xlink:label="note-0307-03a" xlink:href="note-0307-03"/>
tuendum angulum complemento altitudinis poli æqualem, ſupputetur in circulo B G F, duplum comple-<lb/>menti altitudinis poli ab F, vſque ad G. </s>
  <s xml:id="echoid-s19727" xml:space="preserve">Recta enim ducta B G, conſtituet angulum A B G, comple-<lb/>mento altitudinis poli æqualem. </s>
  <s xml:id="echoid-s19728" xml:space="preserve">Cum enim (ſi ducta eſſet recta G A) angulus G A F, in centro duplus <lb/>
<anchor type="note" xlink:label="note-0307-04a" xlink:href="note-0307-04"/>
ſit anguli complementi altitudinis poli in eodem centro conſtituti, quòd &amp; </s>
  <s xml:id="echoid-s19729" xml:space="preserve">arcus F G, eiuſdem comple-<lb/>menti ſii duplus: </s>
  <s xml:id="echoid-s19730" xml:space="preserve">Duplus autem ſit angulus G A F, in centro anguli G B F, in circumferentia; </s>
  <s xml:id="echoid-s19731" xml:space="preserve">erit an-<lb/>
<anchor type="note" xlink:label="note-0307-05a" xlink:href="note-0307-05"/>
gulus G B F, complemento altitudinis poli æqualis.</s>
  <s xml:id="echoid-s19732" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1012" type="float" level="2" n="3">
<note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">Longitudo ſty-<lb/>li quomodo in <lb/>ueſtigetur in po <lb/>ſteriori hac d<unsure/>e-<lb/>ſcriptione horo <lb/>logii Italici &amp; <lb/>Babylonici.</note>
<note position="left" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">33. ſext@.</note>
<note position="right" xlink:label="note-0307-05" xlink:href="note-0307-05a" xml:space="preserve">20. tertĳ</note>
</div>
<p style="it">
  <s xml:id="echoid-s19733" xml:space="preserve">INVENTO autem ſtylo A E, poterunt pro eius magnitudine deſcribi arcus, ſeu paralleli ſigno-<lb/>
<anchor type="note" xlink:label="note-0307-06a" xlink:href="note-0307-06"/>
rum, veluti propoſ. </s>
  <s xml:id="echoid-s19734" xml:space="preserve">50. </s>
  <s xml:id="echoid-s19735" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s19736" xml:space="preserve">docuimus; </s>
  <s xml:id="echoid-s19737" xml:space="preserve">vt videlicet in remotiſſimo eorum, &amp; </s>
  <s xml:id="echoid-s19738" xml:space="preserve">in arcu ♋, vel ♑, ho-<lb/>rariæ lineæ terminentur, vt in præcedentis propoſ. </s>
  <s xml:id="echoid-s19739" xml:space="preserve">horologio factum eſt.</s>
  <s xml:id="echoid-s19740" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1013" type="float" level="2" n="4">
<note position="right" xlink:label="note-0307-06" xlink:href="note-0307-06a" xml:space="preserve">Quomodo in <lb/>poſteriori hoc <lb/>horologio arcus <lb/>ſignornm de-<lb/>ſeribantur.</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1015" type="section" level="1" n="249">
<head xml:id="echoid-head257" xml:space="preserve">PROBLEMA 60. PROPOSITIO 60.</head>
<head xml:id="echoid-head258" xml:space="preserve">HOROLOGIVM Antiquum æquinoctiale conſtituere.</head>
<p>
  <s xml:id="echoid-s19741" xml:space="preserve">DIVIDANTVR ſingulæ portiones arcuum ſignorum, quas horizontalis linea amputat, in <lb/>
<anchor type="note" xlink:label="note-0307-08a" xlink:href="note-0307-08"/>
vtroque horologio tam ſuperiori, quàm inferiori, in 12. </s>
  <s xml:id="echoid-s19742" xml:space="preserve">partes æquales. </s>
  <s xml:id="echoid-s19743" xml:space="preserve">Deinde per proxima pun <lb/>cta infra, &amp; </s>
  <s xml:id="echoid-s19744" xml:space="preserve">ſupra lineam horizontalem ad vtraſque partes quatuor lineæ rectæ ducantur, idemq́; <lb/></s>
  <s xml:id="echoid-s19745" xml:space="preserve">fiat in ſequentibus punctis ſibi reſpondentibus, deſcriptumq́ue erit horologium Antiquum. </s>
  <s xml:id="echoid-s19746" xml:space="preserve">Nã <lb/>proxima linea infra lineam horizontalem ad dextram dabit in ſuperiori horologio horam 1. </s>
  <s xml:id="echoid-s19747" xml:space="preserve">in-<lb/>
<anchor type="note" xlink:label="note-0307-09a" xlink:href="note-0307-09"/>
æqualem, ſubſequens ſecundam, &amp; </s>
  <s xml:id="echoid-s19748" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19749" xml:space="preserve">In inferiori idem cernitur ad ſiniſtrã horizontalis lineæ, hoc <lb/>eſt, in portione abſciſſa à linea horizontali, ſi tamen omnes eius partes inuertantur. </s>
  <s xml:id="echoid-s19750" xml:space="preserve">Demonſtrabi-<lb/>mus autem, rectè hac ratione deſcriptas eſſe horas inæquales, non aliter, ac oſtendimus propoſ. <lb/></s>
  <s xml:id="echoid-s19751" xml:space="preserve">58. </s>
  <s xml:id="echoid-s19752" xml:space="preserve">huius libri, rectè ductas eſſe lineas horarum ab occaſu ſecundum primum modum; </s>
  <s xml:id="echoid-s19753" xml:space="preserve">ſi intelli-<lb/>gantur circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s19754" xml:space="preserve">per horas inæquales parallelorum Solis tranſire. </s>
  <s xml:id="echoid-s19755" xml:space="preserve">Hi <lb/>enim ſecabunt quoque arcus ſignorum in horologio æquinoctiali in partes æquales, per ea, quæ <lb/>propoſ. </s>
  <s xml:id="echoid-s19756" xml:space="preserve">49. </s>
  <s xml:id="echoid-s19757" xml:space="preserve">huius libri demonſtrauimus: </s>
  <s xml:id="echoid-s19758" xml:space="preserve">ac proinde per puncta diuiſionum arcuum ſignorum <lb/>circuli horarum inæqualium ducentur, vt de circulis horarum ab occaſu dictum eſt propoſ. </s>
  <s xml:id="echoid-s19759" xml:space="preserve">58. </s>
  <s xml:id="echoid-s19760" xml:space="preserve"><lb/>huius libri.</s>
  <s xml:id="echoid-s19761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1015" type="float" level="2" n="1">
<note position="right" xlink:label="note-0307-08" xlink:href="note-0307-08a" xml:space="preserve">Conſtructio ho <lb/>rologii Antiqui <lb/>æquinoctialis.</note>
<note position="left" xlink:label="note-0307-09" xlink:href="note-0307-09a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s19762" xml:space="preserve">IDEM horologium Antiquum, horarumve inæqualium delineabimus beneficio arcus diur <lb/>
<anchor type="note" xlink:label="note-0307-10a" xlink:href="note-0307-10"/>
<anchor type="note" xlink:label="note-0307-11a" xlink:href="note-0307-11"/>
ni horarum 18. </s>
  <s xml:id="echoid-s19763" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19764" xml:space="preserve">nocturni horarum 6. </s>
  <s xml:id="echoid-s19765" xml:space="preserve">Nam hora 1. </s>
  <s xml:id="echoid-s19766" xml:space="preserve">inæqualis ducenda eſt in arcu diurno hora-<lb/>rum 18. </s>
  <s xml:id="echoid-s19767" xml:space="preserve">per horam 4 {1/2}. </s>
  <s xml:id="echoid-s19768" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s19769" xml:space="preserve">in nocturno horarum 6. </s>
  <s xml:id="echoid-s19770" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19771" xml:space="preserve">9 {1/2}. </s>
  <s xml:id="echoid-s19772" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s19773" xml:space="preserve">Ho-<lb/>ra autem ſecunda per hor. </s>
  <s xml:id="echoid-s19774" xml:space="preserve">6. </s>
  <s xml:id="echoid-s19775" xml:space="preserve">à media nocte in priori arcu, &amp; </s>
  <s xml:id="echoid-s19776" xml:space="preserve">per horam 10. </s>
  <s xml:id="echoid-s19777" xml:space="preserve">à meridie in poſte-<lb/>riori. </s>
  <s xml:id="echoid-s19778" xml:space="preserve">Hora deinde tertia inæqualis ducenda eſt in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s19779" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19780" xml:space="preserve">7 {1/2}. </s>
  <s xml:id="echoid-s19781" xml:space="preserve">à media <lb/>nocte, &amp; </s>
  <s xml:id="echoid-s19782" xml:space="preserve">in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s19783" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19784" xml:space="preserve">10 {1/2} à meridie. </s>
  <s xml:id="echoid-s19785" xml:space="preserve">Hora vero quarta inæqualis tranſi-<lb/>re debet in priori arcu per hor. </s>
  <s xml:id="echoid-s19786" xml:space="preserve">9. </s>
  <s xml:id="echoid-s19787" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s19788" xml:space="preserve">in arcu poſteriori per hor. </s>
  <s xml:id="echoid-s19789" xml:space="preserve">11. </s>
  <s xml:id="echoid-s19790" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s19791" xml:space="preserve">Quin <lb/>ta autem hora inæqualis ducenda eſt per hor. </s>
  <s xml:id="echoid-s19792" xml:space="preserve">10 {1/2}. </s>
  <s xml:id="echoid-s19793" xml:space="preserve">à media nocte in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s19794" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19795" xml:space="preserve"><lb/>in arcu nocturno horarum 6.</s>
  <s xml:id="echoid-s19796" xml:space="preserve"><unsure/> per hor. </s>
  <s xml:id="echoid-s19797" xml:space="preserve">11 {1/2}. </s>
  <s xml:id="echoid-s19798" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s19799" xml:space="preserve">Hora vero ſexta inæqualis à linea meridia-<lb/>na, ſine horæ 12. </s>
  <s xml:id="echoid-s19800" xml:space="preserve">aſtronomicæ non differt. </s>
  <s xml:id="echoid-s19801" xml:space="preserve">Poſt hæc hora ſeptima inæqualis ducenda eſt in arcu <lb/>diurno horarum 18. </s>
  <s xml:id="echoid-s19802" xml:space="preserve">per hor 1 {1/2}. </s>
  <s xml:id="echoid-s19803" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s19804" xml:space="preserve">in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s19805" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19806" xml:space="preserve">{1/2}. </s>
  <s xml:id="echoid-s19807" xml:space="preserve">à media <lb/>nocte. </s>
  <s xml:id="echoid-s19808" xml:space="preserve">Octaua autem hora inæqualis ducenda eſt in priori arcu per hor. </s>
  <s xml:id="echoid-s19809" xml:space="preserve">3. </s>
  <s xml:id="echoid-s19810" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s19811" xml:space="preserve">in arcu
<pb o="292" file="0308" n="308" rhead="GNOMONICES"/>
poſteriori per hor. </s>
  <s xml:id="echoid-s19812" xml:space="preserve">1. </s>
  <s xml:id="echoid-s19813" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s19814" xml:space="preserve">Hora vero nona inæqualis in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s19815" xml:space="preserve">du-<lb/>cenda eſt per hor. </s>
  <s xml:id="echoid-s19816" xml:space="preserve">4 {1/2}. </s>
  <s xml:id="echoid-s19817" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s19818" xml:space="preserve">in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s19819" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19820" xml:space="preserve">1 {1/2}. </s>
  <s xml:id="echoid-s19821" xml:space="preserve">à media nocte. <lb/></s>
  <s xml:id="echoid-s19822" xml:space="preserve">Hora item decima inæqualis per hor. </s>
  <s xml:id="echoid-s19823" xml:space="preserve">6. </s>
  <s xml:id="echoid-s19824" xml:space="preserve">à meridie ducenda eſt in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s19825" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19826" xml:space="preserve">per <lb/>
<anchor type="figure" xlink:label="fig-0308-01a" xlink:href="fig-0308-01"/>
<anchor type="note" xlink:label="note-0308-01a" xlink:href="note-0308-01"/>
<anchor type="note" xlink:label="note-0308-02a" xlink:href="note-0308-02"/>
<anchor type="note" xlink:label="note-0308-03a" xlink:href="note-0308-03"/>
hor. </s>
  <s xml:id="echoid-s19827" xml:space="preserve">2. </s>
  <s xml:id="echoid-s19828" xml:space="preserve">à media nocte in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s19829" xml:space="preserve">Vndecima autẽ hora inæqualis per hor. </s>
  <s xml:id="echoid-s19830" xml:space="preserve">7 {1/2}. <lb/></s>
  <s xml:id="echoid-s19831" xml:space="preserve">à meridie in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s19832" xml:space="preserve">ducenda eſt, &amp; </s>
  <s xml:id="echoid-s19833" xml:space="preserve">in arcu nocturno horarum 6. </s>
  <s xml:id="echoid-s19834" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s19835" xml:space="preserve">2 {1/2}. </s>
  <s xml:id="echoid-s19836" xml:space="preserve"><lb/>à media nocte. </s>
  <s xml:id="echoid-s19837" xml:space="preserve">Hora denique duodecima inæqualis eadem eſt, quæ linea horizontalis. </s>
  <s xml:id="echoid-s19838" xml:space="preserve">Quæ om-<lb/>nia ex tabulis 11. </s>
  <s xml:id="echoid-s19839" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19840" xml:space="preserve">12. </s>
  <s xml:id="echoid-s19841" xml:space="preserve">ſcholii propoſ. </s>
  <s xml:id="echoid-s19842" xml:space="preserve">33. </s>
  <s xml:id="echoid-s19843" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s19844" xml:space="preserve">patent, &amp; </s>
  <s xml:id="echoid-s19845" xml:space="preserve">in appoſita figura videre licet. </s>
  <s xml:id="echoid-s19846" xml:space="preserve"><lb/>Horologium ergo Antiquum æquinoctiale conſtituimus. </s>
  <s xml:id="echoid-s19847" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s19848" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1016" type="float" level="2" n="2">
<note position="left" xlink:label="note-0307-10" xlink:href="note-0307-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0307-11" xlink:href="note-0307-11a" xml:space="preserve">Eiuſdẽ<unsure/> horolo-<lb/>gii Antiqui æ-<lb/>quinoctialis de <lb/>ſcriptio per ar-<lb/>cum diurnum <lb/>horarum 18. &amp; <lb/>nocturnum ho <lb/>rarum 6.</note>
  <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a">
    <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0308-01"/>
  </figure>
<note position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0308-02" xlink:href="note-0308-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0308-03" xlink:href="note-0308-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1018" type="section" level="1" n="250">
<head xml:id="echoid-head259" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s19849" xml:space="preserve">CAETERVM productæhoræ inæquales ſuperioris horologii vltra lineam horizontalem indicant <lb/>
<anchor type="note" xlink:label="note-0308-05a" xlink:href="note-0308-05"/>
in inferiori, ſi eius partes omnes inuertantur, vt in præcedentibus, eaſdem horas, vt ex ĳ<unsure/>s, quæ in ſcholio <lb/>propoſ. </s>
  <s xml:id="echoid-s19850" xml:space="preserve">14. </s>
  <s xml:id="echoid-s19851" xml:space="preserve">huius libri demonſtr auimus, manifeſtum eſt. </s>
  <s xml:id="echoid-s19852" xml:space="preserve">Ex quo efficitur, ſingulas lineas horarum inæqua <lb/>lium per octona puncta diuiſionum arcuum ſignorum, vna cum arcu diurno horam 18. </s>
  <s xml:id="echoid-s19853" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19854" xml:space="preserve">nocturno hora-<lb/>
<anchor type="note" xlink:label="note-0308-06a" xlink:href="note-0308-06"/>
rum 6. </s>
  <s xml:id="echoid-s19855" xml:space="preserve">duci, quorum quaterna in horologio ſuperiori, &amp; </s>
  <s xml:id="echoid-s19856" xml:space="preserve">quaterna in inferiori continentur. </s>
  <s xml:id="echoid-s19857" xml:space="preserve">Quin <lb/>etiam &amp; </s>
  <s xml:id="echoid-s19858" xml:space="preserve">illud ſequitur, ſatis eſſe ad deſcriptionem horarum inæqualium, ſi duæ portiones <lb/>vnius duntaxat paralleli, nimirum maioris &amp; </s>
  <s xml:id="echoid-s19859" xml:space="preserve">extimi, cuiuſmodi eſt parallelus <lb/>
<anchor type="note" xlink:label="note-0308-07a" xlink:href="note-0308-07"/>
♉, &amp; </s>
  <s xml:id="echoid-s19860" xml:space="preserve">♍, in partes 12. </s>
  <s xml:id="echoid-s19861" xml:space="preserve">æquales diſtribuantur duntaxat. </s>
  <s xml:id="echoid-s19862" xml:space="preserve">Nam recta <lb/>ducta per primum punctum infra horizontalem lineam <lb/>ad dextram, et per primum ſupra eandem ad <lb/>
<anchor type="note" xlink:label="note-0308-08a" xlink:href="note-0308-08"/>
ſiniſtram, dabit horam 1. </s>
  <s xml:id="echoid-s19863" xml:space="preserve">inæqualem, &amp; </s>
  <s xml:id="echoid-s19864" xml:space="preserve"><lb/>recta per ſequentia duo puncta <lb/>protracta, ſecun-<lb/>dam, &amp; </s>
  <s xml:id="echoid-s19865" xml:space="preserve">c.</s>
  <s xml:id="echoid-s19866" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1018" type="float" level="2" n="1">
<note position="left" xlink:label="note-0308-05" xlink:href="note-0308-05a" xml:space="preserve">Quomodo ex <lb/>ſuperiori horo-<lb/>logio Antiquo <lb/>oriatur Infe-<lb/>rius.</note>
<note position="left" xlink:label="note-0308-06" xlink:href="note-0308-06a" xml:space="preserve">Singulę horę <lb/>inęquales per <lb/>octe<unsure/>na puncta <lb/>ducuntur.</note>
<note position="left" xlink:label="note-0308-07" xlink:href="note-0308-07a" xml:space="preserve">Satis eſt ad de-<lb/>ſc<unsure/>ript ionem ho <lb/>rologii Anti-<lb/>qui, ſi duæ por-<lb/>tione. vnius pa <lb/>ralleli ſecentur <lb/>in partes 12. <lb/>æquales.</note>
<note position="left" xlink:label="note-0308-08" xlink:href="note-0308-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1020" type="section" level="1" n="251">
<head xml:id="echoid-head260" style="it" xml:space="preserve">FINIS SECVNDI LIBRI.</head>
<pb o="293" file="0309" n="309"/>
</div>
<div xml:id="echoid-div1021" type="section" level="1" n="252">
<head xml:id="echoid-head261" xml:space="preserve">GNOMONICES LIBER TERTIVS.</head>
  <figure>
    <image file="0309-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0309-01"/>
  </figure>
</div>
<div xml:id="echoid-div1022" type="section" level="1" n="253">
<head xml:id="echoid-head262" xml:space="preserve">AVCTORE <lb/>
CHRISTOPHORO CLAVIO BAMBER GENSI
SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s19867" xml:space="preserve">QVINQVE genera horologiorum, dequibus ſuperiore libro <lb/>
<anchor type="note" xlink:label="note-0309-02a" xlink:href="note-0309-02"/>
egimus, hoc eſt, Horizontale, Verticale, Meridianum, Pola-<lb/>re, &amp; </s>
  <s xml:id="echoid-s19868" xml:space="preserve">Aequinoctiale, dici poſſunt regularia, propterea quòd <lb/>plana, in quibus deſcribuntur, determinato ſem per puncto cę-<lb/>li vbiuis terrarum opponuntur; </s>
  <s xml:id="echoid-s19869" xml:space="preserve">vtpote primum vertici capi-<lb/>
<anchor type="note" xlink:label="note-0309-03a" xlink:href="note-0309-03"/>
tis, ſeu polo Horizontis; </s>
  <s xml:id="echoid-s19870" xml:space="preserve">ſecundum polo Verticalis circuli pro-<lb/>
<anchor type="note" xlink:label="note-0309-04a" xlink:href="note-0309-04"/>
priè dicti, in quo videlicet ſe mutuo interſecant Horizon, at-<lb/>que Meridianus; </s>
  <s xml:id="echoid-s19871" xml:space="preserve">tertium polo Meridiani, ſiue puncto veri or-<lb/>tus, occaſusve, vbi Aequator Horizontem diuidit; </s>
  <s xml:id="echoid-s19872" xml:space="preserve">quartum <lb/>puncto Meridiani circuli, in quo ab Aequatore ſecatur; </s>
  <s xml:id="echoid-s19873" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19874" xml:space="preserve">quintum denique polo <lb/>mundi, ſeu Aequatoris. </s>
  <s xml:id="echoid-s19875" xml:space="preserve">Reliqua autem quatuor genera, quæ hoc libro deſcriben-<lb/>
<anchor type="note" xlink:label="note-0309-05a" xlink:href="note-0309-05"/>
da proponimus, irregularia poſſunt appellari, qualia ſunt, Declinans à Verticali cir-<lb/>culo proprie dicto; </s>
  <s xml:id="echoid-s19876" xml:space="preserve">Declinans ab Horizonte; </s>
  <s xml:id="echoid-s19877" xml:space="preserve">Inclinatum ad Horizontem; </s>
  <s xml:id="echoid-s19878" xml:space="preserve">Decli-<lb/>nans à Verticali, &amp; </s>
  <s xml:id="echoid-s19879" xml:space="preserve">ſimul ad Horizontem inclinatum. </s>
  <s xml:id="echoid-s19880" xml:space="preserve">Nam puncta cæli, quibus eo-<lb/>rum plana obiiciuntur, ſexcentis modis variari poſſunt, cum magis, &amp; </s>
  <s xml:id="echoid-s19881" xml:space="preserve">minus à Ver-<lb/>
<anchor type="note" xlink:label="note-0309-06a" xlink:href="note-0309-06"/>
ticali, ſeu Horizonte poſſint deflectere, &amp; </s>
  <s xml:id="echoid-s19882" xml:space="preserve">ad Horizontem inclinare, vt perſpicuum <lb/>eſt. </s>
  <s xml:id="echoid-s19883" xml:space="preserve">Id quod de prioribus planis nulla ratione dici poteſt. </s>
  <s xml:id="echoid-s19884" xml:space="preserve">In omni enim climate, ſiue <lb/>regione eodem modo ſe habent, &amp; </s>
  <s xml:id="echoid-s19885" xml:space="preserve">ſeſe interſecant Horizon, Verticalis primarius, <lb/>
<anchor type="note" xlink:label="note-0309-07a" xlink:href="note-0309-07"/>
Meridianus, circulus horæ ſextæ à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s19886" xml:space="preserve">Aequator, quibus <lb/>priora quinque horologia æquidiſtant; </s>
  <s xml:id="echoid-s19887" xml:space="preserve">cum perpetuò tam priores tres, quàm tres <lb/>poſteriores, (cõputato ſemper Meridiano tam in prioribus, quàm in poſterioribus) <lb/>ſe mutuo ad angulos rectos diuidant. </s>
  <s xml:id="echoid-s19888" xml:space="preserve">Quod facile ex ſphæricis elementis Theodoſij <lb/>demonſtrari poteſt. </s>
  <s xml:id="echoid-s19889" xml:space="preserve">Quoniam enim tam priorum trium quilibet, quàm trium po-<lb/>ſteriorum, per reliquorum duorum polos ducitur, vt manifeſtum eſt, ſi dictorum cir <lb/>culorum poſitiones in ſphæra attente conſiderentur, ſecabit neceſſario, per propoſ. <lb/></s>
  <s xml:id="echoid-s19890" xml:space="preserve">
<anchor type="note" xlink:label="note-0309-08a" xlink:href="note-0309-08"/>
15. </s>
  <s xml:id="echoid-s19891" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s19892" xml:space="preserve">1. </s>
  <s xml:id="echoid-s19893" xml:space="preserve">Theodoſii, illos ad angulos rectos. </s>
  <s xml:id="echoid-s19894" xml:space="preserve">At verò longè alia ratio eſt de circulis <lb/>maximis, quibus plana horologiorum irregularium æquidiſtant, cum in eodem cli <lb/>mate non habeant ſemper eundem ſitum. </s>
  <s xml:id="echoid-s19895" xml:space="preserve">Nam circulus maximus, cui horologiü <lb/>
<anchor type="note" xlink:label="note-0309-09a" xlink:href="note-0309-09"/>
à Verticali declinans ęquidiſtat, rectus quidem eſt ad Horizontem, cum per eius po-<lb/>los ducatur, ſed Meridianum oblique ſecat infinitis modis, cum infinita propemo-<lb/>dum genera horologiorum a Verticali declinantium reperiantur:</s>
  <s xml:id="echoid-s19896" xml:space="preserve">, quorum quædã <lb/>magis à<unsure/> Verticali declinant, &amp; </s>
  <s xml:id="echoid-s19897" xml:space="preserve">quædam minus. </s>
  <s xml:id="echoid-s19898" xml:space="preserve">Sic etiam circulus maximus, cui <lb/>horologium ab Horizonte declinans parallelum eſt, rectus quidem eſt ad Vertica-<lb/>lem circulum proprie dictum, cum per polos ipſius incedat, at Meridianum innu-<lb/>meris quoque modis oblique diuidit, prout magis, aut minus ab Horizonte <lb/>
<anchor type="note" xlink:label="note-0309-10a" xlink:href="note-0309-10"/>
declinat. </s>
  <s xml:id="echoid-s19899" xml:space="preserve">Rurſus circulus maximus, cui æquidiſtat horologium ad Hori-<lb/>zontem inclinatum, rectus quidem eſt ad Meridianum, per cuius po-<lb/>los ducitur, ſed Horizontem ſexcentis quoque modis obli-<lb/>que interſecat. </s>
  <s xml:id="echoid-s19900" xml:space="preserve">Poſtremo circulus maximus, cui <lb/>poſtremum horologium æquidiſtat, ne-<lb/>que ad Horizontem, neque ad <lb/>Verticalem, neque ad <lb/>Meridianum <lb/>rectus exiſtit, ſed omnes hos <lb/>circulos obliquè <lb/>diuidit.</s>
  <s xml:id="echoid-s19901" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1022" type="float" level="2" n="1">
<note position="right" xlink:label="note-0309-02" xlink:href="note-0309-02a" xml:space="preserve">Cur quinque<unsure/> <lb/>genera horolo-<lb/>giorum, de qui <lb/>bus ſuperiore <lb/>lib. egimus, Re-<lb/>gularia dican-<lb/>tur.</note>
<note position="left" xlink:label="note-0309-03" xlink:href="note-0309-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0309-04" xlink:href="note-0309-04a" xml:space="preserve">Cuinam pũcto <lb/>cœli opponai<unsure/>ur <lb/>horologium ho <lb/>rizon tale, Verti <lb/>eale, Meridia-<lb/>num, Polare, &amp; <lb/>æquine<unsure/>ctiale.</note>
<note position="right" xlink:label="note-0309-05" xlink:href="note-0309-05a" xml:space="preserve">Cur quatuor <lb/>horologiorum <lb/>genera, de qui-<lb/>bus hoc lib. agi <lb/>tur, Irregulatia <lb/>dicantur.</note>
<note position="left" xlink:label="note-0309-06" xlink:href="note-0309-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0309-07" xlink:href="note-0309-07a" xml:space="preserve">Hotizon, Verti <lb/>calis, ac Meri-<lb/>dianus, It<unsure/>em <lb/>Meridianus, cir <lb/>culus horæ 6. à <lb/>mer. vel med. <lb/>noc. atque Ae-<lb/>quator, in om-<lb/>ni climate ſe <lb/>mutuo ſecãt<unsure/> ad <lb/>rectos angulos<unsure/>.</note>
<note position="left" xlink:label="note-0309-08" xlink:href="note-0309-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0309-09" xlink:href="note-0309-09a" xml:space="preserve">Circuli maxi-<lb/>mi, quibus qua <lb/>tuor genera ho <lb/>rologiorũ huius <lb/>lib. æquidiſtãt, <lb/>quomodo ſe ha <lb/>beant reſpectu <lb/>Horizõtis, Ver-<lb/>ticalis, ac Meri <lb/>diani.</note>
<note position="left" xlink:label="note-0309-10" xlink:href="note-0309-10a" xml:space="preserve">50</note>
</div>
<pb o="294" file="0310" n="310" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1024" type="section" level="1" n="254">
<head xml:id="echoid-head263" xml:space="preserve">DE HOROLOGIIS, QVAE A VER-<lb/>ticali circulo declinant. <lb/>PROBLEMA 1. PROPOSITIO 1.</head>
<p>
  <s xml:id="echoid-s19902" xml:space="preserve">HOROLOGIVM Aſtronomicum à Verticali circulo decli-<lb/>nans, hoc eſt, Lineas horarum à meridie, vel media nocte in plano, <lb/>
<anchor type="note" xlink:label="note-0310-01a" xlink:href="note-0310-01"/>
quod circulo cuipiam maximo ęquidiſtat, qui à Verticali circulo pro-<lb/>prie dicto declinat, &amp; </s>
  <s xml:id="echoid-s19903" xml:space="preserve">ad Horizontem rectus eſt, deſcribere.</s>
  <s xml:id="echoid-s19904" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1024" type="float" level="2" n="1">
<note position="left" xlink:label="note-0310-01" xlink:href="note-0310-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s19905" xml:space="preserve">IN plano aliquo ducantur duæ rectæ A B, C D, ſeſe ad angulos rectos ſecantes in <lb/>
<anchor type="note" xlink:label="note-0310-02a" xlink:href="note-0310-02"/>
E. </s>
  <s xml:id="echoid-s19906" xml:space="preserve">Deinde ad rectam C D, in puncto E, conſtituatur angulus declinationis plani, <lb/>in quo horologium ponendum eſt, quæ qua ratione inquiratur, demonſtrauimus <lb/>propoſ. </s>
  <s xml:id="echoid-s19907" xml:space="preserve">23. </s>
  <s xml:id="echoid-s19908" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s19909" xml:space="preserve">Hoc autem ordine conſtituendus erit hic angulus. </s>
  <s xml:id="echoid-s19910" xml:space="preserve">Si pla-<lb/>num declinat à meridie, conſtituendus erit angulus declinationis infra rectam <lb/>A B, verſus quidem punctum A, ſi in ortum vergit, ſi verò in occaſum, verſus B. <lb/></s>
  <s xml:id="echoid-s19911" xml:space="preserve">Si autem planum à ſeptentrione declinat, erit angulus conſtituendus ſupra rectam A B, verſus <lb/>
<anchor type="note" xlink:label="note-0310-03a" xlink:href="note-0310-03"/>
<anchor type="note" xlink:label="note-0310-04a" xlink:href="note-0310-04"/>
quidem B, ſi in ortum vergit, ſi verò in occaſum, verſus A. </s>
  <s xml:id="echoid-s19912" xml:space="preserve">In propoſito exemplo ponimus planũ <lb/>
<anchor type="figure" xlink:label="fig-0310-01a" xlink:href="fig-0310-01"/>
<anchor type="note" xlink:label="note-0310-05a" xlink:href="note-0310-05"/>
<anchor type="note" xlink:label="note-0310-06a" xlink:href="note-0310-06"/>
<anchor type="note" xlink:label="note-0310-07a" xlink:href="note-0310-07"/>
declinare à meridie in ortum grad. </s>
  <s xml:id="echoid-s19913" xml:space="preserve">30. </s>
  <s xml:id="echoid-s19914" xml:space="preserve">idcirco angulus declinationis D E F, conſtitutus eſt infra <lb/>rectam A B, verſus A; </s>
  <s xml:id="echoid-s19915" xml:space="preserve">qui quidem angulus facile conſtituetur, ſi ex E, arcus circuli deſcribatur, <lb/>in eoq́ue declinatio ſupputetur à recta C D. </s>
  <s xml:id="echoid-s19916" xml:space="preserve">Nam E F, recta ex E, per finem ſupputationis educta <lb/>
<anchor type="note" xlink:label="note-0310-08a" xlink:href="note-0310-08"/>
conſtituet angulum declinationis in puncto E. </s>
  <s xml:id="echoid-s19917" xml:space="preserve">Atque recta E F, dici poteſt linea declinationis.</s>
  <s xml:id="echoid-s19918" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1025" type="float" level="2" n="2">
<note position="left" xlink:label="note-0310-02" xlink:href="note-0310-02a" xml:space="preserve">Conſtructio ho <lb/>rologii Aſtrono <lb/>mici à Vertica-<lb/>li declinantis.</note>
<note position="left" xlink:label="note-0310-03" xlink:href="note-0310-03a" xml:space="preserve">Horologiam, <lb/>quod deſcribi-<lb/>t<unsure/>ur, declinat à <lb/>meridie in or-<lb/>c<unsure/>um grad. 30.</note>
<note position="left" xlink:label="note-0310-04" xlink:href="note-0310-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0310-01" xlink:href="fig-0310-01a">
    <image file="0310-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0310-01"/>
  </figure>
<note position="left" xlink:label="note-0310-05" xlink:href="note-0310-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0310-06" xlink:href="note-0310-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0310-07" xlink:href="note-0310-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0310-08" xlink:href="note-0310-08a" xml:space="preserve">Linea declina-<lb/>tionis quæ ſit <lb/>in horologio de <lb/>cli nante.</note>
</div>
<p>
  <s xml:id="echoid-s19919" xml:space="preserve">POST hæc in recta A B, ſumpto puncto quocunque β, ſiue ad dextram ipſius E, ſiue ad ſi-
<pb o="295" file="0311" n="311" rhead="LIBER TERTIVS."/>
niſ<unsure/>tram, (commodius tamen fuerit, ſi ſumatur ad partes oppoſitas lineæ declinationis E F; </s>
  <s xml:id="echoid-s19920" xml:space="preserve">vt ſi <lb/>E F, fuerit ad ſiniſtram rectæ C D, punctum β, accipiatur ad dextram eiuſdem rectæ C D, &amp;</s>
  <s xml:id="echoid-s19921" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s19922" xml:space="preserve">quoniam in ea parte, quæ rectæ E F, opponitur, pauciores lineæ horariæ,<unsure/> ducentur, vt mox planũ <lb/>fiet. </s>
  <s xml:id="echoid-s19923" xml:space="preserve">Quò etiam remotius fuerit punctum β, à puncto E, eò maius efficietur horologium) con-<lb/>ſtituatur ad rectam E β, in puncto β, angulus altitudinis poli E β C, ſupra quidem rectam A B, <lb/>ſi planum à meridie declinat,<unsure/> infra verò eandem rectam A B, ſi planum declinat à Borea, &amp; </s>
  <s xml:id="echoid-s19924" xml:space="preserve">ſem-<lb/>
<anchor type="note" xlink:label="note-0311-01a" xlink:href="note-0311-01"/>
per verſus rectam C D, ita vt recta β C, ſecet rectam C D, in C, puncto, quod erit centrum horo-<lb/>gii, per quod omnes horariæ lineæ ducendæ ſunt, vt demonſtrabimus.</s>
  <s xml:id="echoid-s19925" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1026" type="float" level="2" n="3">
<note position="right" xlink:label="note-0311-01" xlink:href="note-0311-01a" xml:space="preserve">Centrum ho-<lb/>rologu.</note>
</div>
<p>
  <s xml:id="echoid-s19926" xml:space="preserve">RVRSVS in linea declinationis E F, ſumpta recta E F, ipſi E β, æquali, ducatur ex F, ad A B, <lb/>perpendicularis F G, &amp; </s>
  <s xml:id="echoid-s19927" xml:space="preserve">ex centro horologii C, per G, recta ducatur C G, quæ linea ſtyli, vel indi-<lb/>
<anchor type="note" xlink:label="note-0311-02a" xlink:href="note-0311-02"/>
<anchor type="note" xlink:label="note-0311-03a" xlink:href="note-0311-03"/>
cis vocetur; </s>
  <s xml:id="echoid-s19928" xml:space="preserve">quoniam in ea figendus erit ſtylus angulos rectos faciens cum plano horologij. </s>
  <s xml:id="echoid-s19929" xml:space="preserve">Ad <lb/>hanc autem lineam Indicis C G, ex G, educatur in vtramque partem perpendicularis G H; </s>
  <s xml:id="echoid-s19930" xml:space="preserve">erit <lb/>hæc, linea æquinoctialis; </s>
  <s xml:id="echoid-s19931" xml:space="preserve">in qua accepta recta G H, ſiue ad dextram puncti G, ſiue ad ſiniſtram, ipſi <lb/>
<anchor type="note" xlink:label="note-0311-04a" xlink:href="note-0311-04"/>
F G, æquali, ductaq́ue recta C H, ducatur ad eam perpendicularis G I; </s>
  <s xml:id="echoid-s19932" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19933" xml:space="preserve">ex I, ad lineam indicis <lb/>C G, perpendicularis I K. </s>
  <s xml:id="echoid-s19934" xml:space="preserve">Erit C H, axis mundi, &amp; </s>
  <s xml:id="echoid-s19935" xml:space="preserve">I K, longitudo ſtyli, eiusq́ue locus K, in linea <lb/>
<anchor type="note" xlink:label="note-0311-05a" xlink:href="note-0311-05"/>
ſtyli, ſiue indicis: </s>
  <s xml:id="echoid-s19936" xml:space="preserve">Angulus autem G C H, erit angulus altitudinis poli ſupra planum declinans, <lb/>vt demonſtrabimus.</s>
  <s xml:id="echoid-s19937" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1027" type="float" level="2" n="4">
<note position="left" xlink:label="note-0311-02" xlink:href="note-0311-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0311-03" xlink:href="note-0311-03a" xml:space="preserve">Linea ſty li.</note>
<note position="right" xlink:label="note-0311-04" xlink:href="note-0311-04a" xml:space="preserve">Linea ęquino-<lb/>ctialis.</note>
<note position="right" xlink:label="note-0311-05" xlink:href="note-0311-05a" xml:space="preserve">Axis mundi. <lb/>Longitudo ſty-<lb/>li, e iu@q; locus.</note>
</div>
<note position="right" xml:space="preserve">Altitudo poli <lb/>ſupra planum <lb/>declinans.</note>
<p>
  <s xml:id="echoid-s19938" xml:space="preserve">POSTREMO in linea indicis C G, ſumpta recta G L, ſiue ſupra G, ſiue infra, ipſi G I, æqua-<lb/>li, deſcribatur ex L, circulus cuiuſuis magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s19939" xml:space="preserve">æquales diſtribuatur, initio <lb/>facto à recta L M, quæ ex L, centro circuli per punctum M, vbi æquinoctialis linea rectam D, in-<lb/>
<anchor type="note" xlink:label="note-0311-07a" xlink:href="note-0311-07"/>
terſecat. </s>
  <s xml:id="echoid-s19940" xml:space="preserve">Si enim per hæc puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s19941" xml:space="preserve">centrum L, rectæ occultæ egrediantur, ſecabitur <lb/>linea æquinoctialis G H, in punctis, per quæ rectæ emiſſæ ex C, centro horologii dabunt horas à <lb/>meridie, vel media nocte, eundem ordinem ſeruantes, quem in Verticali horologio habent. </s>
  <s xml:id="echoid-s19942" xml:space="preserve">In <lb/>horologio enim, quod à meridie declinat ſiue in ortum, ſiue in occaſum, portio rectæ C D, inci-<lb/>
<anchor type="note" xlink:label="note-0311-08a" xlink:href="note-0311-08"/>
piens à C, verſusq́ue æquinoctialem lineam extenſa, monſtrat horam 12. </s>
  <s xml:id="echoid-s19943" xml:space="preserve">meridiei: </s>
  <s xml:id="echoid-s19944" xml:space="preserve">lineæ verò <lb/>æquinoctialem lineam ſecantes ad partem ſiniſtram ipſius C D, hoc eſt, ad partes A, occidenta-<lb/>lesve, indicant horas à media nocte; </s>
  <s xml:id="echoid-s19945" xml:space="preserve">lineę denique ſecantes æquinoctialem lineam ad partem dex-<lb/>tram, id eſt, ad partes B, ſeu orientales, pertinent ad horas à meridie; </s>
  <s xml:id="echoid-s19946" xml:space="preserve">ita vt proxima linea ad ſini-<lb/>ſtram ipſius C D, ſignificet horam 11. </s>
  <s xml:id="echoid-s19947" xml:space="preserve">à media nocte, proxima verò ad dexteram eiuſdem oſten-<lb/>dat horam 1. </s>
  <s xml:id="echoid-s19948" xml:space="preserve">à meridie, &amp;</s>
  <s xml:id="echoid-s19949" xml:space="preserve">c. </s>
  <s xml:id="echoid-s19950" xml:space="preserve">In horologio verò, quod à ſeptentrione in ortũ, occaſumve deflectit, <lb/>
<anchor type="note" xlink:label="note-0311-09a" xlink:href="note-0311-09"/>
contrarium intelligatur. </s>
  <s xml:id="echoid-s19951" xml:space="preserve">Nam portio rectæ C D, à C, verſus ęquinoctialem lineam protenſa da-<lb/>bit horam 12. </s>
  <s xml:id="echoid-s19952" xml:space="preserve">mediæ noctis, quæ verò ei ſunt ad ſiniſtram in æquinoctiali linea, horas à meridie, <lb/>quæ autem ad dextram, horas à media nocte, vt in vtroque Verticali horologio.</s>
  <s xml:id="echoid-s19953" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1028" type="float" level="2" n="5">
<note position="left" xlink:label="note-0311-07" xlink:href="note-0311-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0311-08" xlink:href="note-0311-08a" xml:space="preserve">Ordo horarum <lb/>in horologio <lb/>declinante à <lb/>Verticali.</note>
<note position="left" xlink:label="note-0311-09" xlink:href="note-0311-09a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Quando linea <lb/>horatia per cen <lb/>trnm horologii <lb/>C, ducenda ſit <lb/>æquinoctiali li-<lb/>neæ pa rallela.</note>
<p>
  <s xml:id="echoid-s19954" xml:space="preserve">QVOD ſi quando recta per aliquod punctum diuiſionis circuli ex L, deſcripti, &amp; </s>
  <s xml:id="echoid-s19955" xml:space="preserve">per cen-<lb/>trum L, ducta parallela ſit æquinoctiali lineæ, tum ducta per C, linea recta æquinoctiali lineæ pa-<lb/>rallela dabit illam horam, quæcunque fuerit, non aliter, qnàm in horologio horizontali contin-<lb/>git, vbi hora 6. </s>
  <s xml:id="echoid-s19956" xml:space="preserve">ducitur per centrum horologii lineæ æquinoctiali æquidiſtans, quia recta in cir-<lb/>culo ex E, ibi deſcripto ducta per punctum horæ 6. </s>
  <s xml:id="echoid-s19957" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19958" xml:space="preserve">centrum E, æquinoctiali lineæ æquidiſtat.</s>
  <s xml:id="echoid-s19959" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s19960" xml:space="preserve">HANC autem conſtructionem hoc modo demonſtrabimus. </s>
  <s xml:id="echoid-s19961" xml:space="preserve">Intelligatur in plano horologij <lb/>
<anchor type="note" xlink:label="note-0311-11a" xlink:href="note-0311-11"/>
recta A B, æquidiſtare Horizonti, ita vt ſit communis ſectio plani horologii horizontalis, &amp; </s>
  <s xml:id="echoid-s19962" xml:space="preserve">pla-<lb/>
<anchor type="note" xlink:label="note-0311-12a" xlink:href="note-0311-12"/>
ni horologii declinantis; </s>
  <s xml:id="echoid-s19963" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s19964" xml:space="preserve">planum per rectas A B, E F, E D, ductum concipiatur animo moueri <lb/>circa rectam A B, donec Horizonti æquidiſtet, atque adeò cum plano horologii horizontalis con-<lb/>iungatur. </s>
  <s xml:id="echoid-s19965" xml:space="preserve">His poſitis, cum D E F, ſit angulus declinationis plani horologii à Verticali, erit A E F, <lb/>angulus complementi dictæ declinationis, qualem nimirum Meridianus cum plano declinante <lb/>comprehendit. </s>
  <s xml:id="echoid-s19966" xml:space="preserve">Quare recta E F, communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s19967" xml:space="preserve">plani horologii horizonta-<lb/>lis, proptereaq́ue Meridianus planum horologii declinantis in puncto E, ſecabit. </s>
  <s xml:id="echoid-s19968" xml:space="preserve">Quoniam verò <lb/>tam planum Meridiani, quàm planum horologii declinantis ad planum horologii horizontalis <lb/>
<anchor type="note" xlink:label="note-0311-13a" xlink:href="note-0311-13"/>
rectum eſt, erit quoque communis eorum ſectio ad idem perpendicularis, ac proinde &amp; </s>
  <s xml:id="echoid-s19969" xml:space="preserve">ad rectã <lb/>A B, in dicto plano perpendicularis erit, ex defin. </s>
  <s xml:id="echoid-s19970" xml:space="preserve">3. </s>
  <s xml:id="echoid-s19971" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s19972" xml:space="preserve">11. </s>
  <s xml:id="echoid-s19973" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s19974" xml:space="preserve">Cum ergo communis hæc <lb/>ſectio per E, tranſeat, &amp; </s>
  <s xml:id="echoid-s19975" xml:space="preserve">recta C D, perpendicularis ſit, per conſtructionem, ad A B; </s>
  <s xml:id="echoid-s19976" xml:space="preserve">erit C D, ſectio <lb/>
<anchor type="note" xlink:label="note-0311-14a" xlink:href="note-0311-14"/>
communis Meridiani, &amp; </s>
  <s xml:id="echoid-s19977" xml:space="preserve">plani horologii declinantis, hoc eſt, linea meridiana horologii declinan <lb/>tis. </s>
  <s xml:id="echoid-s19978" xml:space="preserve">Rurſus quia tam planum Meridiani, quàm planum horologii declinantis rectum eſt ad pla-<lb/>num horologii horizontalis, erit eorum communis ſectio C E, ad idem perpendicularis, atque <lb/>
<anchor type="note" xlink:label="note-0311-15a" xlink:href="note-0311-15"/>
adeò, per defin. </s>
  <s xml:id="echoid-s19979" xml:space="preserve">3. </s>
  <s xml:id="echoid-s19980" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s19981" xml:space="preserve">11. </s>
  <s xml:id="echoid-s19982" xml:space="preserve">Euclidis, &amp; </s>
  <s xml:id="echoid-s19983" xml:space="preserve">ad rectam E F, in plano horologii horizontalis exiſtentem. <lb/></s>
  <s xml:id="echoid-s19984" xml:space="preserve">Si igitur triangulum β E C, intelligatur moueri circa C E, donec cum plano Meridiani per re-<lb/>ctas C E, E F, ducti coniungatur, congruet angulus rectus β E C, recto angulo C E F, &amp; </s>
  <s xml:id="echoid-s19985" xml:space="preserve">punctum <lb/>β, puncto F, propter æqualitatem rectarum E β, E F. </s>
  <s xml:id="echoid-s19986" xml:space="preserve">Quare recta β C, conſtituens in eo ſitu cum <lb/>meridiana linea E F, horologii horizontalis angulum altitudinis poli E β C, porrectaq́ue verſus <lb/>partes ſeptentrionales ex parte ſuperiori rectæ E F, erit axis mundi occurrens plano horologii de-<lb/>clinantis in C, puncto; </s>
  <s xml:id="echoid-s19987" xml:space="preserve">ac proinde ex coroll. </s>
  <s xml:id="echoid-s19988" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s19989" xml:space="preserve">21. </s>
  <s xml:id="echoid-s19990" xml:space="preserve">primi lib. </s>
  <s xml:id="echoid-s19991" xml:space="preserve">punctum C, centrum erit ho-<lb/>rologii declinantis. </s>
  <s xml:id="echoid-s19992" xml:space="preserve">Axis enim cum meridiana linea horologii horizontalis conſtituit angulum
<pb o="296" file="0312" n="312" rhead="GNOMONICES"/>
altitudinis poli ſupra Horizontem verſus partes poli manifeſti, vt patet ex portione Analemma-<lb/>tis propoſ. </s>
  <s xml:id="echoid-s19993" xml:space="preserve">1. </s>
  <s xml:id="echoid-s19994" xml:space="preserve">ſuperioris lib.</s>
  <s xml:id="echoid-s19995" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1029" type="float" level="2" n="6">
<note position="right" xlink:label="note-0311-11" xlink:href="note-0311-11a" xml:space="preserve">Demonſtratio <lb/>conſtructionis <lb/>horolo gii de cli <lb/>nantis à<unsure/> Verti-<lb/>cali.</note>
<note position="left" xlink:label="note-0311-12" xlink:href="note-0311-12a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0311-13" xlink:href="note-0311-13a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0311-14" xlink:href="note-0311-14a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0311-15" xlink:href="note-0311-15a" xml:space="preserve">19. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s19996" xml:space="preserve">DEINDE quia linea indicis, in qua videlicet ſtylus, vel index affigendus eſt, talis eſſe debet, <lb/>vt ſtylus, vel alia linea ex quocunque eius puncto ad planum horologii perpendicularis educta, in <lb/>axem mundi cadat, ita vt planum per illam perpendicularem, &amp; </s>
  <s xml:id="echoid-s19997" xml:space="preserve">axem mundi ductum, rectum ſit <lb/>
<anchor type="note" xlink:label="note-0312-01a" xlink:href="note-0312-01"/>
<anchor type="figure" xlink:label="fig-0312-01a" xlink:href="fig-0312-01"/>
<anchor type="note" xlink:label="note-0312-02a" xlink:href="note-0312-02"/>
<anchor type="note" xlink:label="note-0312-03a" xlink:href="note-0312-03"/>
<anchor type="note" xlink:label="note-0312-04a" xlink:href="note-0312-04"/>
<anchor type="note" xlink:label="note-0312-05a" xlink:href="note-0312-05"/>
ad planum horologii, inſtar proprii cuiuſdam Meridiani ipſius plani horologii; </s>
  <s xml:id="echoid-s19998" xml:space="preserve">propterea quòd <lb/>vertex ſtyli, per propoſ. </s>
  <s xml:id="echoid-s19999" xml:space="preserve">2. </s>
  <s xml:id="echoid-s20000" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20001" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20002" xml:space="preserve">idem eſt, quod centrum mundi, per quod axis mundi tranſit; </s>
  <s xml:id="echoid-s20003" xml:space="preserve">de-<lb/>monſtrabimus talem eſſe lineam C G, quam diximus eſſe lineam indicis in conſtructione, hoc mo <lb/>do. </s>
  <s xml:id="echoid-s20004" xml:space="preserve">Intelligatur triangulum E F G, moueri circa rectam E G, donec coniungatur cum plano ho-<lb/>rologii horizontalis, ipſiq́ue Horizonti æquidiſtet, atque adeò ad planum horologii declinantis <lb/>rectum ſit. </s>
  <s xml:id="echoid-s20005" xml:space="preserve">Quo poſito, erit recta F G, per defin. </s>
  <s xml:id="echoid-s20006" xml:space="preserve">4. </s>
  <s xml:id="echoid-s20007" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20008" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20009" xml:space="preserve">Euclidis, ad planum horologii decli-<lb/>
<anchor type="note" xlink:label="note-0312-06a" xlink:href="note-0312-06"/>
nantis perpendicularis, ac proinde cum axis mundi in punctum F, cadat in illo ſitu, vt proximè <lb/>oſtendimus, quia à puncto β, tunc non differt, erit planum per rectam F G, &amp; </s>
  <s xml:id="echoid-s20010" xml:space="preserve">per axem mundi du <lb/>ctum, rectum ad planum horologii declinantis, inſtar proprii cuiuſdam Meridiani. </s>
  <s xml:id="echoid-s20011" xml:space="preserve">Quare cum <lb/>omnes rectæ, quæ in illo plano per axem, &amp; </s>
  <s xml:id="echoid-s20012" xml:space="preserve">rectam F G, ducto ad rectam C G, perpendiculares <lb/>
<anchor type="note" xlink:label="note-0312-07a" xlink:href="note-0312-07"/>
ducuntur, rectæ ſint ad planum horologii declinantis, ex defin. </s>
  <s xml:id="echoid-s20013" xml:space="preserve">4. </s>
  <s xml:id="echoid-s20014" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20015" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20016" xml:space="preserve">Euclidis, ſequitur om-<lb/>nes perpendiculares ad planum horologii ductas ex punctis rectæ C G, in axem mundi cadere, ac <lb/>proinde rectam C G, lineam ſtyli eſſe, nempe communem ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s20017" xml:space="preserve">proprii <lb/>Meridiani dicti, tanquam lineam meridianam, ſi circulus, cui horologium æquidiſtat, eſſet Hori-<lb/>zon. </s>
  <s xml:id="echoid-s20018" xml:space="preserve">Quoniam verò recta G H, ſumpta eſt ęqualis rectæ F G, ſi triangulum C G H, intelligatur <lb/>moueri circa C G, donec rectum ſit ad planum horologii declinantis, atque adeo recta H G, (quæ <lb/>perpendicularis ducta eſt ad rectam C G) ad idem ſit perpendicularis, cadet punctum H, in pun-<lb/>ctum F, quòd &amp; </s>
  <s xml:id="echoid-s20019" xml:space="preserve">F G, oſtenſa ſit ad idem planum perpendicularis; </s>
  <s xml:id="echoid-s20020" xml:space="preserve">ac propterea recta C H, axis <lb/>mundi erit. </s>
  <s xml:id="echoid-s20021" xml:space="preserve">Ex quo efficitur, angulum G C H, eſſe angulum altitudinis poli ſupra planum decli-<lb/>nans, quia æqualis eſt ei, quem axis mundi, &amp; </s>
  <s xml:id="echoid-s20022" xml:space="preserve">communis ſectio Meridiani ipſius plani declinan-<lb/>tis, &amp; </s>
  <s xml:id="echoid-s20023" xml:space="preserve">circuli maximi, cui planum horologii æquidiſtat, in centro mundi conſtituunt; </s>
  <s xml:id="echoid-s20024" xml:space="preserve">propterea <lb/>
<anchor type="note" xlink:label="note-0312-08a" xlink:href="note-0312-08"/>
<pb o="297" file="0313" n="313" rhead="LIBER TERTIVS."/>
quòd hæc communis ſectio parallela eſt rectæ C G, in plano horologii. </s>
  <s xml:id="echoid-s20025" xml:space="preserve">Manifeſtum eſt autem <lb/>
<anchor type="note" xlink:label="note-0313-01a" xlink:href="note-0313-01"/>
hunc angulum in Meridiano proprio plani declinantis conſ<unsure/>titutum in centro mundi inſiſtere ar-<lb/>cui altitudinis poli ſupra illum circulum maximum, cui horologium æquidiſtat.</s>
  <s xml:id="echoid-s20026" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1030" type="float" level="2" n="7">
<note position="left" xlink:label="note-0312-01" xlink:href="note-0312-01a" xml:space="preserve">18. vndec.</note>
  <figure xlink:label="fig-0312-01" xlink:href="fig-0312-01a">
    <image file="0312-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0312-01"/>
  </figure>
<note position="left" xlink:label="note-0312-02" xlink:href="note-0312-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0312-03" xlink:href="note-0312-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0312-04" xlink:href="note-0312-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0312-05" xlink:href="note-0312-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0312-06" xlink:href="note-0312-06a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0312-07" xlink:href="note-0312-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0312-08" xlink:href="note-0312-08a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">16. vndec.</note>
</div>
<p>
  <s xml:id="echoid-s20027" xml:space="preserve">RECTAM autem G H, ad lineam ſtyli C G, perpendicularem, communem eſſe ſectionem <lb/>Aequatoris, &amp; </s>
  <s xml:id="echoid-s20028" xml:space="preserve">plani horologii declinantis, vt in conſtructione aſſumpſimus, ita faciemus perſpi-<lb/>cuum. </s>
  <s xml:id="echoid-s20029" xml:space="preserve">Quoniam axis mundi C H, rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s20030" xml:space="preserve">10. </s>
  <s xml:id="echoid-s20031" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20032" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20033" xml:space="preserve">Theodoſii, ad Aequatoris pla-<lb/>num, tranſitq́ue per eius centrum, atque adeo, per defin. </s>
  <s xml:id="echoid-s20034" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20035" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20036" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20037" xml:space="preserve">Euclidis, perpendicularis eſt <lb/>ad communem ſectionem Aequatoris, &amp; </s>
  <s xml:id="echoid-s20038" xml:space="preserve">plani per axem mundi C H, &amp; </s>
  <s xml:id="echoid-s20039" xml:space="preserve">rectam G H, ducti, quod <lb/>quidem ad planum horologii declinantis rectum eſt, tanquam nouus quidam, &amp; </s>
  <s xml:id="echoid-s20040" xml:space="preserve">proprius Meri-<lb/>
<anchor type="note" xlink:label="note-0313-02a" xlink:href="note-0313-02"/>
dianus ipſius, quòd &amp; </s>
  <s xml:id="echoid-s20041" xml:space="preserve">linea G H, per quam ducitur, ad idem recta ſit facta, propter motum trian-<lb/>
<anchor type="note" xlink:label="note-0313-03a" xlink:href="note-0313-03"/>
guli C G H, circa rectam C G, vt proxime dictum eſt; </s>
  <s xml:id="echoid-s20042" xml:space="preserve">efficitur rectam I G, ſi punctum I, pro cen-<lb/>tro mundi, Aequatorisve accipiatur, (poteſt autem quodlibet punctum axis pro centro ſumi, cum <lb/>inſenſibilis ſit, ac planè imperceptibilis eius diſtantia in plano horologii declinãtis à centro mun <lb/>di, ſi cum diſtantia ipſius à Sole conferatur, vt in ſphæra docuimus) communem ſectionem eſſe <lb/>Aequatoris, &amp; </s>
  <s xml:id="echoid-s20043" xml:space="preserve">plani per axem C I, &amp; </s>
  <s xml:id="echoid-s20044" xml:space="preserve">rectam I G, ducti; </s>
  <s xml:id="echoid-s20045" xml:space="preserve">quandoquidem recta I G, in plano hoc <lb/>exiſtens perpendicularis eſt ad axem. </s>
  <s xml:id="echoid-s20046" xml:space="preserve">Si enim Aequator non tranſiret per rectam I G, ſed per aliã <lb/>quampiam ex puncto I, quod accepimus pro centro, per quod neceſſario Aequator incedit, du-<lb/>ctam, eſſet axis C I, ad hanc<unsure/> etiam perpendicularis, per defin. </s>
  <s xml:id="echoid-s20047" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20048" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20049" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20050" xml:space="preserve">Euclidis, quòd rectus ſit ad <lb/>Aequatoris planum, in quo hæc recta exiſteret. </s>
  <s xml:id="echoid-s20051" xml:space="preserve">Quare in plano per axem C I, &amp; </s>
  <s xml:id="echoid-s20052" xml:space="preserve">rectam I G, ducto <lb/>duæ perpendiculares ad axem in puncto I, ducerentur, quod eſt abſurdum. </s>
  <s xml:id="echoid-s20053" xml:space="preserve">Occurret igitur Ae-<lb/>
<anchor type="note" xlink:label="note-0313-04a" xlink:href="note-0313-04"/>
quatoris planum per rectam I G, ductum plano horologii declinantis in G, puncto lineæ indicis; <lb/></s>
  <s xml:id="echoid-s20054" xml:space="preserve">ac proinde per punctum G, ducenda erit linea æquinoctialis, communis nimirum ſectio Aequa-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s20055" xml:space="preserve">plani horologii declinantis. </s>
  <s xml:id="echoid-s20056" xml:space="preserve">Quoniam verò planum trianguli C G I, rectum eſt ad Aequa-<lb/>
<anchor type="note" xlink:label="note-0313-05a" xlink:href="note-0313-05"/>
torem, propterea quòd recta C I, per quam ducitur dictum triangulum, perpendicularis eſt ad <lb/>eundem, vt dictum eſt; </s>
  <s xml:id="echoid-s20057" xml:space="preserve">vel certe per propoſ. </s>
  <s xml:id="echoid-s20058" xml:space="preserve">15. </s>
  <s xml:id="echoid-s20059" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20060" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20061" xml:space="preserve">Theodoſii, propterea quòd planum trian-<lb/>guli C G I, per axem C I, atque adeò per polos mundi ſeu Aequatoris ductum ſit; </s>
  <s xml:id="echoid-s20062" xml:space="preserve">erit viciſſim &amp; </s>
  <s xml:id="echoid-s20063" xml:space="preserve"><lb/>Aequator ad planum trianguli C G I, rectus: </s>
  <s xml:id="echoid-s20064" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s20065" xml:space="preserve">planum horologii declinantis rectum <lb/>ad idem planum@trianguli C G I, quòd hoc ad illud nuper oſtenſum ſit rectum. </s>
  <s xml:id="echoid-s20066" xml:space="preserve">Igitur communis <lb/>ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s20067" xml:space="preserve">plani horologii declinantis ad idem planum trianguli C G I, recta erit, atque <lb/>
<anchor type="note" xlink:label="note-0313-06a" xlink:href="note-0313-06"/>
adeò &amp; </s>
  <s xml:id="echoid-s20068" xml:space="preserve">perpendicularis erit, per defin. </s>
  <s xml:id="echoid-s20069" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20070" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20071" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20072" xml:space="preserve">Euclidis, ad lineam indicis C G, in eo plano exi-<lb/>
<anchor type="note" xlink:label="note-0313-07a" xlink:href="note-0313-07"/>
ſtentem. </s>
  <s xml:id="echoid-s20073" xml:space="preserve">Quare cum dicta communis ſectio ducenda ſit per punctum G, vt proximè oſtendimus, <lb/>erit G H, perpendicularis ducta ad C G, communis ſectio Aquatoris, &amp; </s>
  <s xml:id="echoid-s20074" xml:space="preserve">plani horologii declinan-<lb/>tis, id eſt, linea æquinoctialis.</s>
  <s xml:id="echoid-s20075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1031" type="float" level="2" n="8">
<note position="right" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0313-03" xlink:href="note-0313-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0313-06" xlink:href="note-0313-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0313-07" xlink:href="note-0313-07a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s20076" xml:space="preserve">ET quia punctum I, pro centro mundi acceptum eſt, ex quo cadit recta I K, ad planum horo <lb/>logii declinantis, per defin. </s>
  <s xml:id="echoid-s20077" xml:space="preserve">4. </s>
  <s xml:id="echoid-s20078" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20079" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20080" xml:space="preserve">Euclidis, perpendicularis, quòd perpendicularis ducta ſit ad <lb/>C G, communem ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s20081" xml:space="preserve">trianguli C G I, quod ad illud rectum eſt; </s>
  <s xml:id="echoid-s20082" xml:space="preserve">erit re-<lb/>cta I K, ſtylus, eiusq́ue locus in K, puncto lineæ indicis; </s>
  <s xml:id="echoid-s20083" xml:space="preserve">quia nulla alia linea ad planum horolo-<lb/>gii recta, præter K I, in centrum mundi I, cadere poteſt, vt patet.</s>
  <s xml:id="echoid-s20084" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s20085" xml:space="preserve">IAM verò ſi circulus ex centro L, deſcriptus circumduci intelligatur circa æquinoctialem li-<lb/>neam G H, donec centrum eius L, cum centro mundi I, coniungatur, (coniungetur autem neceſſa <lb/>
<anchor type="note" xlink:label="note-0313-08a" xlink:href="note-0313-08"/>
rio cum eo; </s>
  <s xml:id="echoid-s20086" xml:space="preserve">quia rectæ G I, G L, æquales ſunr, &amp; </s>
  <s xml:id="echoid-s20087" xml:space="preserve">vtraque ad lineam æquinoctialem perpendicula-<lb/>ris eſt, ſi triangulum C G I, intelligatur eſſe rectum ad planum horologii) erunt rectæ per centrũ <lb/>L, quod tunc idem eſt, quod centrum Aequatoris, &amp; </s>
  <s xml:id="echoid-s20088" xml:space="preserve">per diuiſiones circuli emiſſæ, communes ſe-<lb/>ctiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s20089" xml:space="preserve">horariorum circulorum à meridie, vel media nocte, quemadmodum in ho <lb/>rologio horizontali demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s20090" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20091" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s20092" xml:space="preserve">Nam in illa poſitione circulus hic <lb/>idem centrum cum Aequatore habens exiſtit in plano Aequatoris. </s>
  <s xml:id="echoid-s20093" xml:space="preserve">Principium autem diuiſionis <lb/>circuli ſumitur à recta L M, quæ per centrum L, &amp; </s>
  <s xml:id="echoid-s20094" xml:space="preserve">punctum M, vbi linea horæ 12. </s>
  <s xml:id="echoid-s20095" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20096" xml:space="preserve">linea æqui-<lb/>noctialis ſe mutuo interſecant, duo<unsure/>itur; </s>
  <s xml:id="echoid-s20097" xml:space="preserve">quia ea linea communis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s20098" xml:space="preserve">Meridia-<lb/>ni, ſeu circuli horæ 12. </s>
  <s xml:id="echoid-s20099" xml:space="preserve">cum plano horologii occurrat in puncto M, per quod linea meridiana, &amp; </s>
  <s xml:id="echoid-s20100" xml:space="preserve"><lb/>linea æquinoctialis tranſeunt: </s>
  <s xml:id="echoid-s20101" xml:space="preserve">hinc enim fit, vmbram ſtyli in punctum M, cadere, cum Sol in com <lb/>
<anchor type="note" xlink:label="note-0313-09a" xlink:href="note-0313-09"/>
muni ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s20102" xml:space="preserve">Aequatoris exiſtit, vt colligi vel facile poteſt ex propoſ. </s>
  <s xml:id="echoid-s20103" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20104" xml:space="preserve">primi lib. <lb/></s>
  <s xml:id="echoid-s20105" xml:space="preserve">Quoniam enim, Sole exiſtente in vtrolibet illorum circulorum, vmbra ſtyli cadit, per dictam pro-<lb/>poſ. </s>
  <s xml:id="echoid-s20106" xml:space="preserve">in communem ſectionem ipſius, &amp; </s>
  <s xml:id="echoid-s20107" xml:space="preserve">plani horologii, fit vt, Sole exiſtente in puncto, vbi ſe mu <lb/>tuo dicti circuli ſecant, vmbra ſtyli cadat in punctum, vbi communes ſectiones ipſorum, &amp; </s>
  <s xml:id="echoid-s20108" xml:space="preserve">plani <lb/>horologii ſe interſecant, cuiuſmodi eſt punctum M; </s>
  <s xml:id="echoid-s20109" xml:space="preserve">alias non caderet in vtramque lineam, vt pa-<lb/>tet. </s>
  <s xml:id="echoid-s20110" xml:space="preserve">Quæ<unsure/> cum ita ſint, ſecabunt circuli horarij planum horologii declinantis in ijſdem punctis, in <lb/>quibus rectæ per centrum L, &amp; </s>
  <s xml:id="echoid-s20111" xml:space="preserve">per diuiſiones circuli eductæ, tanquam communes ſectiones di-<lb/>ctorum circulorum &amp; </s>
  <s xml:id="echoid-s20112" xml:space="preserve">Aequatoris, lineæ æquinoctiali G H, occurrunt; </s>
  <s xml:id="echoid-s20113" xml:space="preserve">atque adeo communes ſe-<lb/>ctiones eorundem circulorum, ac plani horologii declinantis, hoc eſt, lineæ horariæ, per eadem <lb/>puncta ducendæ erunt. </s>
  <s xml:id="echoid-s20114" xml:space="preserve">Cum ergo eædem, ex coroll. </s>
  <s xml:id="echoid-s20115" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s20116" xml:space="preserve">21. </s>
  <s xml:id="echoid-s20117" xml:space="preserve">primi libri ſe mutuo ſecent in C, <lb/>centro horologij, erunt rectæ ex C, per puncta æquinoctialis lineæ ductæ, lineæ horarum à meri-
<pb o="298" file="0314" n="314" rhead="GNOMONICES"/>
die, vel media nocte. </s>
  <s xml:id="echoid-s20118" xml:space="preserve">Quæ autem ſint lineæ horarum à meridie, &amp; </s>
  <s xml:id="echoid-s20119" xml:space="preserve">quæ à media nocte, facile in-<lb/>telligi poteſt, ſi circulus ex L, deſcriptus cõcipiatur in propria poſitione, &amp; </s>
  <s xml:id="echoid-s20120" xml:space="preserve">ea diligenter cõſideren <lb/>tur, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s20121" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20122" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s20123" xml:space="preserve">ſcripſimus de ſectionibus rectarũ circuli ex L, deſcri-<lb/>pti (qui nimirũ in 24. </s>
  <s xml:id="echoid-s20124" xml:space="preserve">horas diuiditur) cũ linea ęquinoctiali, obſeruãdo nimirũ ſemper, ſi horolo-<lb/>giũ, &amp; </s>
  <s xml:id="echoid-s20125" xml:space="preserve">circulus ex L, deſcriptus, in propriis poſitionibus intelligantur, ea puncta diuiſionũ, quę ſe-<lb/>quuntur ex parte ſuperiori cõmunem ſectionẽ Meridiani &amp; </s>
  <s xml:id="echoid-s20126" xml:space="preserve">Aequatoris, nempe rectã L M, verſus <lb/>
<anchor type="figure" xlink:label="fig-0314-01a" xlink:href="fig-0314-01"/>
<anchor type="note" xlink:label="note-0314-01a" xlink:href="note-0314-01"/>
<anchor type="note" xlink:label="note-0314-02a" xlink:href="note-0314-02"/>
<anchor type="note" xlink:label="note-0314-03a" xlink:href="note-0314-03"/>
<anchor type="note" xlink:label="note-0314-04a" xlink:href="note-0314-04"/>
occidentẽ, pertinere ad horas à meridie, quæ verò eandẽ L M, ſequuntur ex parte inferiori verſus <lb/>orientẽ, horas à media nocte indicare. </s>
  <s xml:id="echoid-s20127" xml:space="preserve">Et quoniã, vt in eodẽ ſcholio docuimus, horæ illæ in horo-<lb/>logio ſcribendæ ſunt, quarũ lineæ in circulo ex L, deſcripto prius occurrũt centro L, quàm plano <lb/>horologij, facile poterit cognoſci, quænam puncta lineæ æquinoctialis indicent horas à meridie, <lb/>&amp; </s>
  <s xml:id="echoid-s20128" xml:space="preserve">quæ horas à media nocte. </s>
  <s xml:id="echoid-s20129" xml:space="preserve">Rectè ergo conſtructio horologij declinantis inſtituta eſt à nobis. <lb/></s>
  <s xml:id="echoid-s20130" xml:space="preserve">Quòd autem recta per C, ducta lineæ æquinoctiali æquidiſtans referat horam illam, à cuius pun <lb/>cto in circulo ex L, deſcripto recta ducta per L, eidem æquinoctiali æquidiſtat, (quod quidem <lb/>nonnunquam, licet rarò, contingere ſolet) facile demonſtrabimus hoc modo. </s>
  <s xml:id="echoid-s20131" xml:space="preserve">Quoniam paralle-<lb/>la illa per L, ducta, communis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s20132" xml:space="preserve">circuli horarii per illam ducti, cui quidem <lb/>
<anchor type="note" xlink:label="note-0314-05a" xlink:href="note-0314-05"/>
communi ſectioni, ſi circulus ex L, deſcriptus propriam intelligatur habere poſitionem, planum <lb/>horologii æquidiſtat, (alioquin parallela illa producta planũ horologii ſecaret, atqueadeo &amp; </s>
  <s xml:id="echoid-s20133" xml:space="preserve">li-<lb/>neam æquinoctialem, quæ in eodẽ Aequatoris plano, in quo illa parallela exiſtit, quod abſurdum <lb/>eſt; </s>
  <s xml:id="echoid-s20134" xml:space="preserve">cum æquinoctiali lineæ ſit parallela) erunt per propoſ. </s>
  <s xml:id="echoid-s20135" xml:space="preserve">18. </s>
  <s xml:id="echoid-s20136" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20137" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20138" xml:space="preserve">parallelæ inter ſeſe commu-<lb/>nes ſectiones factę à plano horologii in Aequatore, &amp; </s>
  <s xml:id="echoid-s20139" xml:space="preserve">dicto circulo horario, hoc eſt, linea æqui-<lb/>
<anchor type="note" xlink:label="note-0314-06a" xlink:href="note-0314-06"/>
noctialis, &amp; </s>
  <s xml:id="echoid-s20140" xml:space="preserve">horaria linea dicti circuli horarii. </s>
  <s xml:id="echoid-s20141" xml:space="preserve">Quare recta per C, ducta lineæ æquinoctiali æqui-<lb/>diſtans referet horam illam, à cuius puncto in circulo ex L, deſcripto, recta ducta per L, eidẽ æqui <lb/>noctiali lineæ æquidiſtat, vt in conſtructione diximus.</s>
  <s xml:id="echoid-s20142" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1032" type="float" level="2" n="9">
<note position="left" xlink:label="note-0313-08" xlink:href="note-0313-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0313-09" xlink:href="note-0313-09a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0314-01" xlink:href="fig-0314-01a">
    <image file="0314-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0314-01"/>
  </figure>
<note position="left" xlink:label="note-0314-01" xlink:href="note-0314-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0314-02" xlink:href="note-0314-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0314-03" xlink:href="note-0314-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0314-04" xlink:href="note-0314-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0314-05" xlink:href="note-0314-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0314-06" xlink:href="note-0314-06a" xml:space="preserve">Deſcriptio ho-<lb/>rologii declinã <lb/>tis à Verticali <lb/>proxime tradi-<lb/>ta non recte re-<lb/>prehenditur à <lb/>loan. Baptiſta <lb/>Benedicto in <lb/>ſua Gnomoni-<lb/>e<unsure/>a.</note>
</div>
<p>
  <s xml:id="echoid-s20143" xml:space="preserve">EX his liquido conſtat, non recte à Ioan. </s>
  <s xml:id="echoid-s20144" xml:space="preserve">Baptiſta Benedicto in ſua Gnomonica cap. </s>
  <s xml:id="echoid-s20145" xml:space="preserve">49. </s>
  <s xml:id="echoid-s20146" xml:space="preserve">repre-<lb/>hendi hanc rationem deſcribendi horologii declinantis, qua omnes ferealii ſcriptores vtuntur. <lb/></s>
  <s xml:id="echoid-s20147" xml:space="preserve">quoniam, vt ex demonſtratione à nobis allata conſtat, rectè per eam lineæ horariæ in plano, quod
<pb o="299" file="0315" n="315" rhead="LIBER TERTIVS."/>
à Verticali declinat, ducuntur. </s>
  <s xml:id="echoid-s20148" xml:space="preserve">Modus autem, quem eo loco pręſcribit differentem ab eo, quem <lb/>nos tradidimus, certus etiam eſt, ſed nulla ratione noſtro contrarius, quia nos conſtituimus D E F, <lb/>angulum declinationis plani à Verticali circulo proprie dicto, ipſe autem loco huius anguli aſſu-<lb/>mit angulum declinationis eiuſdem plani à Meridiano circulo. </s>
  <s xml:id="echoid-s20149" xml:space="preserve">Vnde mirum non eſt, modum ip-<lb/>ſius à noſtro diſcrepare. </s>
  <s xml:id="echoid-s20150" xml:space="preserve">Quòd ſi nos conſtitueremus D E F, angulum declinationis plani à Meri-<lb/>diano, vt ipſe, (quemadmodum forſitan ab alijs putauit fieri) &amp; </s>
  <s xml:id="echoid-s20151" xml:space="preserve">in reliqua deſcriptione progrede-<lb/>remur, vt tradidimus, proculdubio horologium declinans perperã deſcriberetur, vt recte docet.</s>
  <s xml:id="echoid-s20152" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s20153" xml:space="preserve">COMMODE etiam lineæ horariæ ex C, ducentur hac ratione. </s>
  <s xml:id="echoid-s20154" xml:space="preserve">Ex puncto F, egrediantur <lb/>
<anchor type="note" xlink:label="note-0315-01a" xlink:href="note-0315-01"/>
rectæ efficientes cum E F, eoſdem angulos, quos in horologio Horizontali propoſ. </s>
  <s xml:id="echoid-s20155" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20156" xml:space="preserve">ſuperioris <lb/>libri deſcripto lineæ horariæ cum linea meridiana conſtituunt, nempe linea horæ ſextæ, qualis in <lb/>
<anchor type="note" xlink:label="note-0315-02a" xlink:href="note-0315-02"/>
ſuperiori figura eſt F α, angulum rectum, &amp;</s>
  <s xml:id="echoid-s20157" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20158" xml:space="preserve">Quod facile fiet, ſi ex centro horologij horizonta-<lb/>lis deſcribatur arcus circuli occultus omnes horarias lineas ſecans, &amp; </s>
  <s xml:id="echoid-s20159" xml:space="preserve">ei æqualis, occultus etiam, <lb/>ex F, verſus rectam A B. </s>
  <s xml:id="echoid-s20160" xml:space="preserve">Si enim ex illo arcu omnia horaria interualla, initio facto à linea meri-<lb/>diana, transferantur in hunc ex F, deſcriptum, initio facto à recta E F, erunt rectæ ex F, per pun-<lb/>cta huius arcus emiſſę, lineæ horariæ reſpondentes lineis horarijs in horologio Horizontali. </s>
  <s xml:id="echoid-s20161" xml:space="preserve">Vbi <lb/>ergo hæ lineæ rectam A B, interſecant, per illa puncta eductæ rectæ ex C, cẽtro horologij dabunt <lb/>horarias lineas, vt prius. </s>
  <s xml:id="echoid-s20162" xml:space="preserve">Quoniam enim in plano horologij Horizontalis punctum F, centrum <lb/>eſt, in quo omnes horariæ lineæ à meridie, vel media nocte ſe diuidunt, cum in illud cadat axis <lb/>mundi, vt diximus; </s>
  <s xml:id="echoid-s20163" xml:space="preserve">fit vt per illa puncta rectæ A B, exiſtentis in plano horogij horizontalis du-<lb/>cendæ ſint horariæ lineæ in plano horologij declinantis, in quibus horariæ lineæ horologij hori-<lb/>
<anchor type="note" xlink:label="note-0315-03a" xlink:href="note-0315-03"/>
zontalis rectam A B, in eodem plano exiſtentem interſecant. </s>
  <s xml:id="echoid-s20164" xml:space="preserve">Nam in illis punctis circuli hora-<lb/>rij rectam A B, ſecant. </s>
  <s xml:id="echoid-s20165" xml:space="preserve">Cum ergo linea meridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s20166" xml:space="preserve">in horologio horizontali, hoc <lb/>eſt, recta F E, rectam A B, ſecet in E, puncto, per quod linea meridiana horologij declinantis <lb/>ducitur, atque adeo linea horæ ſextæ occurrat eidem rectæ A B, in puncto α, quandoquidem in-<lb/>horologio horizontali linea horæ ſextæ meridianã lineam ad angulos rectos ſecat; </s>
  <s xml:id="echoid-s20167" xml:space="preserve">fit vt per pun-<lb/>ctum α, ducenda ſit in horologio declinante linea horæ ſextæ. </s>
  <s xml:id="echoid-s20168" xml:space="preserve">Eadem ratione reliquæ ex F, egre <lb/>dientes pro ratione angulorum, quos horariæ lineæ cum meridiana linea F E, in horizontali ho-<lb/>rologio faciunt, dabunt in recta A B, puncta, per quæ in horologio declinante horariæ lineæ du-<lb/>ci debent. </s>
  <s xml:id="echoid-s20169" xml:space="preserve">Ex horologio porrò horizontali facile cognoſces, quænam puncta rectæ A B, ad horas <lb/>à meridie, &amp; </s>
  <s xml:id="echoid-s20170" xml:space="preserve">quæ ad horas à media nocte pertineant.</s>
  <s xml:id="echoid-s20171" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1033" type="float" level="2" n="10">
<note position="right" xlink:label="note-0315-01" xlink:href="note-0315-01a" xml:space="preserve">Alia delinea-<lb/>tio horarum à <lb/>mer. vel med. <lb/>noc.<unsure/> in horolo-<lb/>gio declinante <lb/>a Verticali, be-<lb/>neficio horolo-<lb/>gii horizõtalis.</note>
<note position="left" xlink:label="note-0315-02" xlink:href="note-0315-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0315-03" xlink:href="note-0315-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s20172" xml:space="preserve">HOC autem modo facile prior deſcriptio poterit examinari, &amp; </s>
  <s xml:id="echoid-s20173" xml:space="preserve">corrigi, ſi error fortaſſe ali-<lb/>
<anchor type="note" xlink:label="note-0315-05a" xlink:href="note-0315-05"/>
quis in ea commiſſus fuerit. </s>
  <s xml:id="echoid-s20174" xml:space="preserve">Nam ſi lineæ horariæ per puncta in recta A B, hoc modo inuenta du-<lb/>ctæ lineis horarijs ductis per puncta, quæ in linea æquinoctiali per priorem deſcriptionem inue-<lb/>nimus, reſpondeant, nullus error commiſſus erit in ducendis lineis horarijs. </s>
  <s xml:id="echoid-s20175" xml:space="preserve">Immo poſterior hæc <lb/>ratio horariarum linearum ducendarum perutilis eſt ad illas lineas ducendas, quæ vel nullo mo-<lb/>do, vel vix, niſi in punctis remotiſſimis, æquinoctialem lineam interſecant, quales ſunt in propoſi-<lb/>to exemplo lineæ horarum 3. </s>
  <s xml:id="echoid-s20176" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20177" xml:space="preserve">4. </s>
  <s xml:id="echoid-s20178" xml:space="preserve">à meridie, &amp;</s>
  <s xml:id="echoid-s20179" xml:space="preserve">c.</s>
  <s xml:id="echoid-s20180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1034" type="float" level="2" n="11">
<note position="right" xlink:label="note-0315-05" xlink:href="note-0315-05a" xml:space="preserve">Quomodo <lb/>prior deſcriptio <lb/>horatum cor<unsure/>ri-<lb/>genda ſit.</note>
</div>
<p>
  <s xml:id="echoid-s20181" xml:space="preserve">RVRSVS quoniam aliquando puncta L, &amp; </s>
  <s xml:id="echoid-s20182" xml:space="preserve">M, tam parum inter ſe diſtant, vt vix ſine er-<lb/>
<anchor type="note" xlink:label="note-0315-06a" xlink:href="note-0315-06"/>
rore per ipſa duci poſſit linea recta, à qua diuiſio circuli ex L, deſcripti inchoanda eſt; </s>
  <s xml:id="echoid-s20183" xml:space="preserve">facile enim <lb/>in hanc, vel illam partem deflectere poteſt; </s>
  <s xml:id="echoid-s20184" xml:space="preserve">vnde error in lineis horarijs ducendis continget inter <lb/>
<anchor type="note" xlink:label="note-0315-07a" xlink:href="note-0315-07"/>
dum non paruus; </s>
  <s xml:id="echoid-s20185" xml:space="preserve">rectè fecerimus, ſi prius ex F, ducamus ad E F, perpendicularem lineam F α, <lb/>quæ rectam A B, ſecet in α, vt recta C α, ducta det horam 6. </s>
  <s xml:id="echoid-s20186" xml:space="preserve">vt demonſtrauimus. </s>
  <s xml:id="echoid-s20187" xml:space="preserve">Vbi enim <lb/>recta C α, æquinoctialem ſecat, inde per centrum L, rectam ducemus, quam neceſſario in L, ad re-<lb/>ctos angulos ſecabit recta L M, ſi erratum non fuerit. </s>
  <s xml:id="echoid-s20188" xml:space="preserve">Hac ratione fiet, vt accuratiſſime lineæ ho. <lb/></s>
  <s xml:id="echoid-s20189" xml:space="preserve">rariæ ducantur, ſi dictæ duæ lineæ ſeſe ad angulos rectos ſecuerint. </s>
  <s xml:id="echoid-s20190" xml:space="preserve">Quare diligenter examinanda <lb/>erit operatio, antequam vlterius progrediamur in horologij deſcriptione.</s>
  <s xml:id="echoid-s20191" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1035" type="float" level="2" n="12">
<note position="right" xlink:label="note-0315-06" xlink:href="note-0315-06a" xml:space="preserve">Quando pnu-<lb/>cta L, M, ſupe-<lb/>rioris figurę pa <lb/>rum inter ſe di <lb/>ſtant, quid agen <lb/>dum.</note>
<note position="left" xlink:label="note-0315-07" xlink:href="note-0315-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s20192" xml:space="preserve">QVOD ſi fortaſſis recta F α, nimis procul à puncto E, rectam A B, ſecet, ducere poterimus lo-<lb/>
<anchor type="note" xlink:label="note-0315-08a" xlink:href="note-0315-08"/>
co horæ 6. </s>
  <s xml:id="echoid-s20193" xml:space="preserve">quam cunque aliam lineam horariam, quæ commode, &amp; </s>
  <s xml:id="echoid-s20194" xml:space="preserve">ſine errore rectam A B, ſecare <lb/>poſſit, ita tamen, vt cum recta F E, eum angulum faciat, quem illa hora in horologio horizontali <lb/>cum meridiana linea conſtituit. </s>
  <s xml:id="echoid-s20195" xml:space="preserve">Si enim per punctum, vbi hæc linea rectam A B, ſecat, duxerimus <lb/>
<anchor type="note" xlink:label="note-0315-09a" xlink:href="note-0315-09"/>
ad C, centrum horologii rectam lineam, &amp; </s>
  <s xml:id="echoid-s20196" xml:space="preserve">ex puncto, vbi hæc lineam æquinoctialem diuidit, aliã <lb/>rectam per centrum L, traiecerimus, habebimus in circulo ex L, deſcripto hanc rectam, à qua di-<lb/>uiſio ipſius inchoari poterit commodiſſime. </s>
  <s xml:id="echoid-s20197" xml:space="preserve">Vel certè ducemus lineam horæ 6. </s>
  <s xml:id="echoid-s20198" xml:space="preserve">alia ratione, quam <lb/>in ſequenti ſcholio ex Andrea Schonero trademus. </s>
  <s xml:id="echoid-s20199" xml:space="preserve">Si igitur tunc aliquod punctorum diuiſionis <lb/>ceciderit præcisè in rectam L M, recte inſtituta fuit operatio: </s>
  <s xml:id="echoid-s20200" xml:space="preserve">ſin minus, error aliquis omnino <lb/>commiſſus erit, quem corrigas, neceſſe eſt, antequam ad alia pergas.</s>
  <s xml:id="echoid-s20201" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1036" type="float" level="2" n="13">
<note position="right" xlink:label="note-0315-08" xlink:href="note-0315-08a" xml:space="preserve">Qua ratione <lb/>diuiſio circuli <lb/>ex L, deſcripti <lb/>aliunde poſſit <lb/>inchoari, quàm <lb/>à recta L M.</note>
<note position="left" xlink:label="note-0315-09" xlink:href="note-0315-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s20202" xml:space="preserve">HAS cautiones in ſequentibus etiam horologijs declinantibus, &amp; </s>
  <s xml:id="echoid-s20203" xml:space="preserve">inclinatis adhiberi vellem, <lb/>ſi deſcriptio linearum horariarum omnibus numeris abſoluta deſideretur: </s>
  <s xml:id="echoid-s20204" xml:space="preserve">dummodo in horolo-<lb/>gio, quod ab Horizonte declinat, de quo agemus propoſ. </s>
  <s xml:id="echoid-s20205" xml:space="preserve">13. </s>
  <s xml:id="echoid-s20206" xml:space="preserve">huius libri, rectæ ex F, emiſſæ, &amp; </s>
  <s xml:id="echoid-s20207" xml:space="preserve">re-<lb/>ctam A B, ſecantes, ſumantur ex horologio Verticali. </s>
  <s xml:id="echoid-s20208" xml:space="preserve">Nam recta E F, eſt linea meridiana Vertica-<lb/>lis horologii in eo horologio, vt ibi oſtendemus.</s>
  <s xml:id="echoid-s20209" xml:space="preserve"/>
</p>
<pb o="300" file="0316" n="316" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s20210" xml:space="preserve">ALITER idem horologium declinans conſtruemus, ad ſimilitudinem horologii horizon-<lb/>
<anchor type="note" xlink:label="note-0316-01a" xlink:href="note-0316-01"/>
talis, in hunc modum. </s>
  <s xml:id="echoid-s20211" xml:space="preserve">Per propoſ. </s>
  <s xml:id="echoid-s20212" xml:space="preserve">29. </s>
  <s xml:id="echoid-s20213" xml:space="preserve">primi libri inueniatur altitudo poli ſupra planum horolo-<lb/>gij declinantis, tanquam Horizontem aliquem; </s>
  <s xml:id="echoid-s20214" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20215" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s20216" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20217" xml:space="preserve">eiuſdem libri, inclinatio pro-<lb/>prii Meridiani plani horologii declinantis (Voco Meridianum huius plani, circulum maximum <lb/>per polos mundi, &amp; </s>
  <s xml:id="echoid-s20218" xml:space="preserve">polos plani declinantis ductum, qui nimirum ad planum declinans rectus eſt, <lb/>metiturq́; </s>
  <s xml:id="echoid-s20219" xml:space="preserve">altitudinem poli inuentam ſupra ipſum, inſtar Meridiani cuiuſdam reſpectu Horizon-<lb/>tis) ad Meridianum Horizontis, ſeu loci, in quo horologium conſtruitur. </s>
  <s xml:id="echoid-s20220" xml:space="preserve">Deinde ad altitudinẽ <lb/>poli inuentam, habita tamen ratione inclinationis dictorum Meridianorum inuentæ, conſtituatur <lb/>horologium horizontale, vt docuimus propoſ. </s>
  <s xml:id="echoid-s20221" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20222" xml:space="preserve">ſuperioris libri, exceptis paucis, quæ mutanda <lb/>hic ſunt, propter dictorum Meridianorum inclinationem, &amp; </s>
  <s xml:id="echoid-s20223" xml:space="preserve">ſitum plani declinantis, prout ſcili-<lb/>
<anchor type="note" xlink:label="note-0316-02a" xlink:href="note-0316-02"/>
<anchor type="figure" xlink:label="fig-0316-01a" xlink:href="fig-0316-01"/>
cet ad auſtrum, vel ad boream ſpectat. </s>
  <s xml:id="echoid-s20224" xml:space="preserve">Quod <lb/>qua ratione fieri debeat, ita planum faciemus. <lb/></s>
  <s xml:id="echoid-s20225" xml:space="preserve">Conſtituatur primum figura omnino ſimilis <lb/>priori figuræ propoſ. </s>
  <s xml:id="echoid-s20226" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20227" xml:space="preserve">ſuperioris libri, nempe <lb/>portio Analemmatis, in qua contineantur ſe-<lb/>ctiones communes Meridiani proprii ipſius <lb/>plani declinantis cum Horizonte, Verticali, &amp; </s>
  <s xml:id="echoid-s20228" xml:space="preserve"><lb/>Aequatore, &amp;</s>
  <s xml:id="echoid-s20229" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20230" xml:space="preserve">(circulus autem maximus, cui <lb/>planum horologij declinantis ęquidiſtat, vices <lb/>gerit Horizontis, &amp; </s>
  <s xml:id="echoid-s20231" xml:space="preserve">alius circulus maximus ad <lb/>
<anchor type="note" xlink:label="note-0316-03a" xlink:href="note-0316-03"/>
illum rectus, tranſiensq́ue per communes ſe-<lb/>ctiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s20232" xml:space="preserve">dicti Horizontis, mune-<lb/>re Verticalis circuli fungitur) ita vt arcus C E, <lb/>metiatur altitudinem poli ſupra planum decli <lb/>nans inuentã, &amp;</s>
  <s xml:id="echoid-s20233" xml:space="preserve">recta D G, æqualis ſit ſtylo ho-<lb/>rologii declinantis cuiuſuis magnitudinis, &amp;</s>
  <s xml:id="echoid-s20234" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s20235" xml:space="preserve">In noſtro exemplo arcus CE, complectitur gr. </s>
  <s xml:id="echoid-s20236" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0316-04a" xlink:href="note-0316-04"/>
40. </s>
  <s xml:id="echoid-s20237" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s20238" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20239" xml:space="preserve">Tanta enim ferè eſt altitudo poli inuenta ſupra planum propoſiti horologij declinan-<lb/>tis, (Eodem enim nunc plano vtimur, quo prius) &amp; </s>
  <s xml:id="echoid-s20240" xml:space="preserve">recta D G, ſumpta eſt æqualis ſtylo I K, eiuſ-<lb/>dem horologii, ne cogamur nouam figuram pro hac deſcriptione inſtituere. </s>
  <s xml:id="echoid-s20241" xml:space="preserve">Poſſemus tamen pro <lb/>
<anchor type="note" xlink:label="note-0316-05a" xlink:href="note-0316-05"/>
arbitrio noſtro ſtylum aſſumere cuiuſuis longitudinis.</s>
  <s xml:id="echoid-s20242" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1037" type="float" level="2" n="14">
<note position="left" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">Alia deſcriptio <lb/>horologii decli <lb/>nantis à Verti-<lb/>cali, ex altitudi-<lb/>ne poli ſupra <lb/>planum decli-<lb/>nans, &amp; inclina <lb/>tione Meridia-<lb/>ni propr@@ eiuſ-<lb/>dem plani<unsure/> decli <lb/>nan@@s ad Meri <lb/>dianum Hori-<lb/>zonus.</note>
<note position="left" xlink:label="note-0316-02" xlink:href="note-0316-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a">
    <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0316-01"/>
  </figure>
<note position="left" xlink:label="note-0316-03" xlink:href="note-0316-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0316-04" xlink:href="note-0316-04a" xml:space="preserve">Quanta ſit alti <lb/>tudo poli ſupra <lb/>planum propo-<lb/>ſiu horologii <lb/>@eclinanus à <lb/>Verticali.</note>
<note position="left" xlink:label="note-0316-05" xlink:href="note-0316-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s20243" xml:space="preserve">POST hęc in recta C N, ducta vtcunque in plano quopiam, qualis in ſuperiori deſcriptione <lb/>eſt linea indicis, abſcindatur rectę H I, quæ Horizonti æquidiſtat in portione Analemmatis, recta <lb/>C G, æqualis, &amp; </s>
  <s xml:id="echoid-s20244" xml:space="preserve">rurſus rectæ D I, ex eadem portione Analemmatis accipiatur æqualis G L; </s>
  <s xml:id="echoid-s20245" xml:space="preserve">atque <lb/>per G, ad C N, ducatur perpendicularis G H. </s>
  <s xml:id="echoid-s20246" xml:space="preserve">Erit C N, tanquam linea meridiana plani declinan-<lb/>tis, ſi pro Horizonte aliquo acciperetur, &amp; </s>
  <s xml:id="echoid-s20247" xml:space="preserve">G H, veluti linea æquinoctialis, vt in horizontali horo-<lb/>logio propoſ. </s>
  <s xml:id="echoid-s20248" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20249" xml:space="preserve">ſuperioris libri, rectæ HE, F K. </s>
  <s xml:id="echoid-s20250" xml:space="preserve">Deſcripto autem ex L, circulo cuiuſuis magnitu-<lb/>dinis, diuidemus eum in partes 24. </s>
  <s xml:id="echoid-s20251" xml:space="preserve">æquales, vt in eodem horizontali horologio, hac vna re exce-<lb/>pta, quòd diuiſio hæc circuli inchoanda hic non eſt à recta C N, vt ibi à recta H E; </s>
  <s xml:id="echoid-s20252" xml:space="preserve">(quia C N, nõ <lb/>eſt communis ſectio plani horologii declinantis, &amp; </s>
  <s xml:id="echoid-s20253" xml:space="preserve">Meridiani, ſeu circuli horæ 12. </s>
  <s xml:id="echoid-s20254" xml:space="preserve">ſed alterius cu <lb/>
<anchor type="note" xlink:label="note-0316-06a" xlink:href="note-0316-06"/>
iuſdam circuli maximi, qui altitudinem poli ſupra planum declinans metitur, tranſitq́; </s>
  <s xml:id="echoid-s20255" xml:space="preserve">per polos <lb/>mundi, &amp; </s>
  <s xml:id="echoid-s20256" xml:space="preserve">per polos plani declinantis, inſtar Meridiani reſpectu Horizontis. </s>
  <s xml:id="echoid-s20257" xml:space="preserve">In horologio verò <lb/>horizontali recta H E, eſt ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s20258" xml:space="preserve">Meridiani, ſiue circuli horæ 12.) </s>
  <s xml:id="echoid-s20259" xml:space="preserve">verum à pun-<lb/>cto N, numeranda eſt inclinatio circuli maximi altitudinem poli ſupra planum declinans me-<lb/>tientis, inſtar proprii eius Meridiani, ad Meridianum Horizontis, ſeuloci, in quo horologium <lb/>declinans deſcribitur; </s>
  <s xml:id="echoid-s20260" xml:space="preserve">quam quidem inclinationem in propoſito exemplo inuenimus eſſe grad. <lb/></s>
  <s xml:id="echoid-s20261" xml:space="preserve">40. </s>
  <s xml:id="echoid-s20262" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s20263" xml:space="preserve">48. </s>
  <s xml:id="echoid-s20264" xml:space="preserve">ferè. </s>
  <s xml:id="echoid-s20265" xml:space="preserve">A puncto enim, quod numerationẽ hanc claudit, diuiſio inchoanda eſt. </s>
  <s xml:id="echoid-s20266" xml:space="preserve">Vt au <lb/>
<anchor type="note" xlink:label="note-0316-07a" xlink:href="note-0316-07"/>
tem ſciamus, in quamnam partem numeratio iſta inſtituenda ſit, conſiderabimus prius, an planũ <lb/>horologii à meridie declinet, an à ſeptentrione. </s>
  <s xml:id="echoid-s20267" xml:space="preserve">Deinde vtrum in ortum vergat, an in occaſum. <lb/></s>
  <s xml:id="echoid-s20268" xml:space="preserve">Nam ſi deflectat à meridie in ortum, numerãda erit dicta inclinatio à puncto N, ſiniſtram verſus, <lb/>
<anchor type="note" xlink:label="note-0316-08a" xlink:href="note-0316-08"/>
hoc eſt, ad occidentales partes verſus A, vſque ad punctum O, in noſtro exemplo @ quoniam cum <lb/>
<anchor type="note" xlink:label="note-0316-09a" xlink:href="note-0316-09"/>
cum polus plani Verticalis propriè dicti ſit punctum Horizontis, vbi à Meridiano ſecatur, erit po <lb/>lus cuiuſcunque alterius Verticalis ab illo in ortum declinantis ex parte meridiei in quadrante <lb/>Horizontis auſtrali &amp; </s>
  <s xml:id="echoid-s20269" xml:space="preserve">orientali, vt ex ſphæra materiali apparere poteſt: </s>
  <s xml:id="echoid-s20270" xml:space="preserve">omnes enim Verticales <lb/>circuli polos habent in Horizonte; </s>
  <s xml:id="echoid-s20271" xml:space="preserve">nam cum ipſi per polos Horizontis ducantur, tranſibit viciſ-<lb/>ſim Horizon per illorum polos, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20272" xml:space="preserve">15. </s>
  <s xml:id="echoid-s20273" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20274" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20275" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s20276" xml:space="preserve">demonſtrauimus.) </s>
  <s xml:id="echoid-s20277" xml:space="preserve">Quare <lb/>circulus maximus per polos mundi, &amp; </s>
  <s xml:id="echoid-s20278" xml:space="preserve">per polos plani declinantis ductus, tanquam proprius eius <lb/>Meridianus ſecabit Aequatorem ſupra Horizontem in quadrante orientali, adeò vt Meridianus <lb/>Horizontis in Aequatoris ſemicirculo ſupra Horizontem ſit occidẽtalior, quàm Meridianus pro-<lb/>prius plani declinantis. </s>
  <s xml:id="echoid-s20279" xml:space="preserve">Vnde inclinatio hæc Meridianorum numeranda erit à puncto N, Me-<lb/>ridiani proprii ipſius plani declinantis, verſus occidentem, hoc eſt, ad ſiniſtram rectæ C N, verſus
<pb o="301" file="0317" n="317" rhead="LIBER TERTIVS."/>
A, vt habeatur punctum O, orientalius, in quo Meridianus Horizontis Aequatorem ſecat ſupra <lb/>Horizontem. </s>
  <s xml:id="echoid-s20280" xml:space="preserve">Si enim planũ horologii ponatur verſus meridiem, ita vt æquinoctialis linea G H, <lb/>ſit infra punctum C, &amp; </s>
  <s xml:id="echoid-s20281" xml:space="preserve">circulus ex L, deſcriptus circa rectam G H, circumuerti intelligatur, do-<lb/>nec cum plano Aequatoris coniungatur, erit punctum N, verſus ſuperius hemiſphærium, &amp; </s>
  <s xml:id="echoid-s20282" xml:space="preserve">par-<lb/>tes ad ſiniſtram ipſius C N, verſus A, tendent occidentem verſus, &amp; </s>
  <s xml:id="echoid-s20283" xml:space="preserve">partes ad dextram eiuſdem <lb/>rectæ C N, verſus B, in orientem vergent. </s>
  <s xml:id="echoid-s20284" xml:space="preserve">Si verò planum à meridie in occaſum declinet, ſuppu-<lb/>tanda erit inclinatio dicta Meridianorum à puncto N, ad dextram partem verſus B, nempe ad <lb/>partes orientales circuli ex L, deſcripti, ſi poſitionem illam, de qua proximè diximus, adeptus ſit: <lb/></s>
  <s xml:id="echoid-s20285" xml:space="preserve">quia tunc Meridianus plani declinantis eſt minus orientalis, quàm Meridianus Horizontis, vt <lb/>ex ſphæra materiali facile colligi poteſt, &amp; </s>
  <s xml:id="echoid-s20286" xml:space="preserve">ex ijs, quæ proximè ſcripſimus, quòd tunc polus eius ex <lb/>
<anchor type="note" xlink:label="note-0317-01a" xlink:href="note-0317-01"/>
parte meridie conſtitutus ſit in quadrante Horizontis auſtrali, atque occidentali.</s>
  <s xml:id="echoid-s20287" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1038" type="float" level="2" n="15">
<note position="left" xlink:label="note-0316-06" xlink:href="note-0316-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0316-07" xlink:href="note-0316-07a" xml:space="preserve">Quanta ſit in-<lb/>clinatio Meri-<lb/>diani plani de-<lb/>clinãtis ad Me-<lb/>ridianum Ho-<lb/>rizontis.</note>
<note position="left" xlink:label="note-0316-08" xlink:href="note-0316-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0316-09" xlink:href="note-0316-09a" xml:space="preserve">In quam partẽ <lb/>numerauda ſit <lb/>inclinatio Me-<lb/>ridiani plani@ <lb/>declinantis ad <lb/>Meridianũ Ho <lb/>rizontis, in cir-<lb/>culo ex L, de-<lb/>ſcripto.</note>
<note position="left" xlink:label="note-0317-01" xlink:href="note-0317-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s20288" xml:space="preserve">NON docemus autem, quamnam in partem numeranda ſit dicta Meridianorum inclinatio <lb/>in plano, quod à ſeptentrione in ortum, vel occaſum declinat, ne præceptorum multitudine in-<lb/>genium Lectoris confundatur, cum præſertim ex auſtrali horologio deſcripto boreale facilimo <lb/>negotio deduci poſſit, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20289" xml:space="preserve">13. </s>
  <s xml:id="echoid-s20290" xml:space="preserve">libri ſuperioris docuimus, &amp; </s>
  <s xml:id="echoid-s20291" xml:space="preserve">clarius ex ſequenti <lb/>ſcholio patebit. </s>
  <s xml:id="echoid-s20292" xml:space="preserve">Accedit etiam, quòd ex præceptis traditis pro plano, quod à meridie declinat, <lb/>quilibet proprio Marte inuenire ſine magno labore poterit, in quam partem numerare debeat di-<lb/>ctam inclinationem in circulo ex L, deſcripto, obferuando diligenter, an Meridianus loci, ſeu pro-<lb/>poſiti Horizontis in Aequatore infra Horizontem orientalior ſit, occidentaliorve Meridiano pro-<lb/>prio plani declinantis. </s>
  <s xml:id="echoid-s20293" xml:space="preserve">Dico infra Horizontem, quia in boreali horologio punctum N, ſpectat <lb/>
<anchor type="note" xlink:label="note-0317-02a" xlink:href="note-0317-02"/>
ad hemiſphærium inferius, adeò vt Meridianus proprius plani declinantis ipſum ſecet infra Ho-<lb/>rizontem in N, puncto, vt patet, ſi rectè poſitio borealis horologii conſideretur, vna cum circulo <lb/>deſcripto ex L. </s>
  <s xml:id="echoid-s20294" xml:space="preserve">Nam ſi orientalior fuerit, numeranda erit illa inclinatio ab N, verſus partes orien-<lb/>tales; </s>
  <s xml:id="echoid-s20295" xml:space="preserve">verſus occidentales verò, ſi occidentalior. </s>
  <s xml:id="echoid-s20296" xml:space="preserve">Non erit autem difficile iudicare, quænam par-<lb/>tes circuli ex L, deſcripti ab N, tendant verſus ortum, &amp; </s>
  <s xml:id="echoid-s20297" xml:space="preserve">quæ occaſum verſus; </s>
  <s xml:id="echoid-s20298" xml:space="preserve">ſi circulus ipſe vnà <lb/>cum horologio boreali in proprio ſitu cogitetur eſſe poſitus, ita vt punctum N, ad inferius hemi-<lb/>ſphærium ſpectet, &amp; </s>
  <s xml:id="echoid-s20299" xml:space="preserve">eius centrum cum centro mundi ſit coniunctum. </s>
  <s xml:id="echoid-s20300" xml:space="preserve">Partes enim ad ſiniſtram, <lb/>nobis ad horologium boreale conuerſis, erunt orientales, &amp; </s>
  <s xml:id="echoid-s20301" xml:space="preserve">ad dextram occidentales.</s>
  <s xml:id="echoid-s20302" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1039" type="float" level="2" n="16">
<note position="left" xlink:label="note-0317-02" xlink:href="note-0317-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s20303" xml:space="preserve">IAM verò ſi per puncta diuiſionũ, &amp; </s>
  <s xml:id="echoid-s20304" xml:space="preserve">per centrum L, ducantur rectæ occultæ ſecantes lineam <lb/>æquinoctialem G H, habebuntur puncta in linea æquinoctiali, per quæ lineæ emiſſæ ex centro C, <lb/>
<anchor type="note" xlink:label="note-0317-03a" xlink:href="note-0317-03"/>
dabunt horas à meridie, vel media nocte, vt in horizontali horologio demonſtrauimus, ita ta-<lb/>men, vt linea porrecta ex C, per punctum M, vbi recta O L, lineæ æquinoctiali occurrit, ſit linea <lb/>horæ 12. </s>
  <s xml:id="echoid-s20305" xml:space="preserve">meridiei in auſtrali horologio, mediæ noctis verò in boreali, non autem recta C G L, <lb/>vt in horizontali horologio; </s>
  <s xml:id="echoid-s20306" xml:space="preserve">quoniam in plano declinante, ſi circulus ex L, deſcriptus intelliga-<lb/>tur in propria poſitione, nimirum in plano Aequatoris circa eius centrum deſcriptus, Meridia-<lb/>nus Horizontis, ſeu circulus horæ 12. </s>
  <s xml:id="echoid-s20307" xml:space="preserve">tranſit per punctum O, ac proinde per rectam O L, occur-<lb/>rens plano horologij in M; </s>
  <s xml:id="echoid-s20308" xml:space="preserve">adeo, vt in auſtrali horologio punctum O, ſit in ſemicirculo Meridia-<lb/>ni ſupra Horizontem, ac propterea meridiem indicet, in boreali verò idem exiſtat in reliquo ſemi <lb/>circulo, atque adeo ad mediam noctem pertineat, vt manifeſtum eſt, ſi circulus ex L, deſcriptus <lb/>in inferiori quoque horologio intelligatur in propria poſitione. </s>
  <s xml:id="echoid-s20309" xml:space="preserve">Reliquæ horæ hunc ordinem ha <lb/>
<anchor type="note" xlink:label="note-0317-04a" xlink:href="note-0317-04"/>
bent. </s>
  <s xml:id="echoid-s20310" xml:space="preserve">In vtroque horologio lineæ, quæ 12. </s>
  <s xml:id="echoid-s20311" xml:space="preserve">horam ſequuntur verſus B, pertinent ad horas poſt <lb/>meridiem; </s>
  <s xml:id="echoid-s20312" xml:space="preserve">quæ verò verſus A, ad horas poſt mediam noctem. </s>
  <s xml:id="echoid-s20313" xml:space="preserve">Stylus, eiuſq́ue locus in recta <lb/>C N, reperietur, vt in horologio horizontali. </s>
  <s xml:id="echoid-s20314" xml:space="preserve">Nam ſi recta C K, ſumatur æqualis rectæ H G, por-<lb/>tionis Analemmatis, erit K, locus ſtyli. </s>
  <s xml:id="echoid-s20315" xml:space="preserve">Quòd ſi fiat in horologio triangulum C G I, æquale trian <lb/>gulo H I D, portionis Analemmatis ducaturq́; </s>
  <s xml:id="echoid-s20316" xml:space="preserve">recta K I, erit I K, longitudo ſtyli, &amp; </s>
  <s xml:id="echoid-s20317" xml:space="preserve">omnino æqua-<lb/>lis rectæ aſſumptæ D G, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s20318" xml:space="preserve">Cum enim latera C I, C K, trianguli C I K, æqualia <lb/>ſint lateribus D H, H G, trianguli D H G, &amp; </s>
  <s xml:id="echoid-s20319" xml:space="preserve">anguli C, H, æquales, ex conſtructione; </s>
  <s xml:id="echoid-s20320" xml:space="preserve">erunt &amp; </s>
  <s xml:id="echoid-s20321" xml:space="preserve">ba <lb/>
<anchor type="note" xlink:label="note-0317-05a" xlink:href="note-0317-05"/>
ſes I K, D G, æquales inter ſe.</s>
  <s xml:id="echoid-s20322" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1040" type="float" level="2" n="17">
<note position="left" xlink:label="note-0317-03" xlink:href="note-0317-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0317-04" xlink:href="note-0317-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0317-05" xlink:href="note-0317-05a" xml:space="preserve">4. primi.</note>
</div>
<p>
  <s xml:id="echoid-s20323" xml:space="preserve">POSSVMVS quoque eiuſdem horologii deſcriptionem inſtituere hoc modo. </s>
  <s xml:id="echoid-s20324" xml:space="preserve">Per propoſ. <lb/></s>
  <s xml:id="echoid-s20325" xml:space="preserve">
<anchor type="note" xlink:label="note-0317-06a" xlink:href="note-0317-06"/>
30. </s>
  <s xml:id="echoid-s20326" xml:space="preserve">primi libri reperiatur arcus plani declinantis interceptus inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s20327" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0317-07a" xlink:href="note-0317-07"/>
circulum maximum, qui per polos eiuſdem plani ducitur, altitudinemq́ue poli ſupra ipſum me-<lb/>titur, tanquam proprius eius Meridianus. </s>
  <s xml:id="echoid-s20328" xml:space="preserve">Hic arcus in noſtro exemplo comprehendit grad. </s>
  <s xml:id="echoid-s20329" xml:space="preserve">29. <lb/></s>
  <s xml:id="echoid-s20330" xml:space="preserve">
<anchor type="note" xlink:label="note-0317-08a" xlink:href="note-0317-08"/>
Min. </s>
  <s xml:id="echoid-s20331" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20332" xml:space="preserve">ferè. </s>
  <s xml:id="echoid-s20333" xml:space="preserve">Item per propoſ. </s>
  <s xml:id="echoid-s20334" xml:space="preserve">29. </s>
  <s xml:id="echoid-s20335" xml:space="preserve">eiuſdem primi libri inueniatur altitudo poli ſupra planum de-<lb/>clinans, quæ in eodem noſtro exemplo continet grad. </s>
  <s xml:id="echoid-s20336" xml:space="preserve">40. </s>
  <s xml:id="echoid-s20337" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s20338" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20339" xml:space="preserve">fere. </s>
  <s xml:id="echoid-s20340" xml:space="preserve">Deinde in plano aliquo <lb/>ducatur recta C D, vtcunque pro linea meridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s20341" xml:space="preserve">in qua ſumpto puncto quocun-<lb/>que C, deſcribatur ex eo arcus D P, in quo à recta C D, nempe à D, puncto numeretur arcus pla-<lb/>ni declinantis interceptus inter Meridianum ipſius, &amp; </s>
  <s xml:id="echoid-s20342" xml:space="preserve">Meridianum Horizontis, vſque ad P, <lb/>quem arcum diximus continere grad. </s>
  <s xml:id="echoid-s20343" xml:space="preserve">29. </s>
  <s xml:id="echoid-s20344" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s20345" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20346" xml:space="preserve">ferè, ducaturq́ue ex C, per P, recta C P, quæ <lb/>communis erit ſectio plani horologii declinantis, &amp; </s>
  <s xml:id="echoid-s20347" xml:space="preserve">Meridiani eiuſdem plani, vt infra mox de-<lb/>monſtrabimus. </s>
  <s xml:id="echoid-s20348" xml:space="preserve">Vtautem ſciamus, quam in partem numerandus ſit arcus D P, conſideranda <lb/>ſunt ea, quæ in præcedenti deſcriptione tradidimus. </s>
  <s xml:id="echoid-s20349" xml:space="preserve">Nam ſi planum à meridie declinet in ortum,
<pb o="302" file="0318" n="318" rhead="GNOMONICES"/>
ſupputandus erit dictus arcus ad ſiniſtram verſus A: </s>
  <s xml:id="echoid-s20350" xml:space="preserve">quia, vt diximus, Meridianus Horizontis <lb/>
<anchor type="note" xlink:label="note-0318-01a" xlink:href="note-0318-01"/>
tunc occidentalior eſt Meridiano ipſius plani declinantis. </s>
  <s xml:id="echoid-s20351" xml:space="preserve">Vnde horologio in propria poſitione <lb/>collocato, erit linea meridiana C D, orientalior, quàm recta C P, communis ſectio plani horolo-<lb/>gij, &amp; </s>
  <s xml:id="echoid-s20352" xml:space="preserve">Meridiani proprij ipſius plani declinantis, cum in plano horologij radius Solis in quocun-<lb/>que circulo exiſtentis proiiciatur ſemper in contrariam partem. </s>
  <s xml:id="echoid-s20353" xml:space="preserve">Perſpicuũ autem eſt, rectam C D, <lb/>eſſe orientaliorem recta C P, ſi horologium proprium ſitum habeat. </s>
  <s xml:id="echoid-s20354" xml:space="preserve">Si verò planum à meridie in <lb/>occaſum vergat, numerandus erit arcus D P, ad dextram verſus B: </s>
  <s xml:id="echoid-s20355" xml:space="preserve">quoniam tunc orientalior eſt <lb/>Meridianus Horizontis Meridiano plani declinantis, vt diximus, atque adeo in horologio occi-<lb/>dentalior eſſe debet meridiana linea C D, quàm recta C P.</s>
  <s xml:id="echoid-s20356" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1041" type="float" level="2" n="18">
<note position="right" xlink:label="note-0317-06" xlink:href="note-0317-06a" xml:space="preserve">Alia deſcriptio <lb/>eiuſdem horo-<lb/>logii declinan-<lb/>tis à Verticali.</note>
<note position="left" xlink:label="note-0317-07" xlink:href="note-0317-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0317-08" xlink:href="note-0317-08a" xml:space="preserve">Quantus ſit ar-<lb/>cus plani decli-<lb/>nãtis inter eius <lb/>Meridianum, <lb/>&amp; Meridianum <lb/>Horizontis in-<lb/>teriectus.</note>
<note position="left" xlink:label="note-0318-01" xlink:href="note-0318-01a" xml:space="preserve">Quam in partẽ <lb/>numerãdus ſit <lb/>arcus plani de-<lb/>clinantis inter <lb/>Meridianũ pro <lb/>prium, &amp; Meri <lb/>dianum Hori-<lb/>zontis interie-<lb/>ctus.</note>
</div>
<p>
  <s xml:id="echoid-s20357" xml:space="preserve">IN quam aut partem dictus arcus numerandus ſit in horologio boreali, non tradimus, pro-<lb/>
<anchor type="note" xlink:label="note-0318-02a" xlink:href="note-0318-02"/>
pter cauſas paulo ante explicatas, ne videlicet ingenium Lectoris obruatur multitudine præcepto-<lb/>rum, maximè cum ſatis ſit, ſi auſtrale horologiũ deſcribatur. </s>
  <s xml:id="echoid-s20358" xml:space="preserve">Ex hoc enim boreale deducetur ſine <lb/>vllo labore, vt ex ſcholio ſequenti manifeſtum erit. </s>
  <s xml:id="echoid-s20359" xml:space="preserve">Adde quòd res ipſa difficilis non eſt, ſi conſide <lb/>retur, an Meridianus proprius plani declinantis in hemiſphærio infero ſit orientalior Meridiano <lb/>Horizontis, occidentaliorve. </s>
  <s xml:id="echoid-s20360" xml:space="preserve">Nam arcus prædictus ſemper numerandus erit in horologio in con-<lb/>trariam partem, &amp;</s>
  <s xml:id="echoid-s20361" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20362" xml:space="preserve">hac tamen lege, vt in boreali horologio punctum C, ſit infra arcum D P.</s>
  <s xml:id="echoid-s20363" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1042" type="float" level="2" n="19">
<note position="left" xlink:label="note-0318-02" xlink:href="note-0318-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s20364" xml:space="preserve">POST hæc ex quocunque puncto rectæ C P, vt ex G, ducatur ad ipſam perpendicularis G H, <lb/>quæ erit linea æquinoctialis. </s>
  <s xml:id="echoid-s20365" xml:space="preserve">Nam recta C P, eſt linea indicis, vt mox oſtendemus, ad quam ne-<lb/>ceſſario linea æquinoctialis eſt perpendicularis, vt ſupra demonſtrauimus. </s>
  <s xml:id="echoid-s20366" xml:space="preserve">Inuenta autem, per <lb/>propoſ. </s>
  <s xml:id="echoid-s20367" xml:space="preserve">29. </s>
  <s xml:id="echoid-s20368" xml:space="preserve">primi libri, altitudine poli ſupra planum declinans, conſtituatur in C, ad rectam C P, <lb/>
<anchor type="note" xlink:label="note-0318-03a" xlink:href="note-0318-03"/>
angulus huius altitudinis poli inuentæ G C H. </s>
  <s xml:id="echoid-s20369" xml:space="preserve">Eritenim G H, axis mundi, ad quem ex G, per-<lb/>pendicularis excitetur G I, &amp; </s>
  <s xml:id="echoid-s20370" xml:space="preserve">reliqua fiant, vt in prima deſcriptione huius horologij declinantis; <lb/></s>
  <s xml:id="echoid-s20371" xml:space="preserve">hoc eſt, rectæ G I, ſumatur æqualis G L, &amp; </s>
  <s xml:id="echoid-s20372" xml:space="preserve">circulus ex L, deſcriptus ſecetur in partes 24. </s>
  <s xml:id="echoid-s20373" xml:space="preserve">ęquales, <lb/>principio ſumpto à recta L M, &amp;</s>
  <s xml:id="echoid-s20374" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20375" xml:space="preserve">Gnomon erit I K, perpendicularis ducta ex I, ad C P, vt prius.</s>
  <s xml:id="echoid-s20376" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1043" type="float" level="2" n="20">
<note position="left" xlink:label="note-0318-03" xlink:href="note-0318-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s20377" xml:space="preserve">QVOD autem recta C P, ſit ſectio communis plani horologij declinantis, &amp; </s>
  <s xml:id="echoid-s20378" xml:space="preserve">proprij Meri-<lb/>diani eiuſdem plani, hac ratione oſtendemus. </s>
  <s xml:id="echoid-s20379" xml:space="preserve">Quoniam Meridianus Horizontis, &amp; </s>
  <s xml:id="echoid-s20380" xml:space="preserve">Meridianus <lb/>plani declinantis, hoc eſt, circulus maximus per polos mundi, &amp; </s>
  <s xml:id="echoid-s20381" xml:space="preserve">per polos plani declinantis du-<lb/>ctus, per axem mundi ducuntur, occurruntq́ue circulo maximo, cui horologium æquidiſtat, in <lb/>centro mundi, nempe in I, vertice ſtyli; </s>
  <s xml:id="echoid-s20382" xml:space="preserve">fit vt cum hoc circulo maximo faciant communes ſectio-<lb/>nes, rectas lineas, quæ in mundi centro angulum conſtituant, cui ſubtenditur arcus eiuſdem circu <lb/>
<anchor type="note" xlink:label="note-0318-04a" xlink:href="note-0318-04"/>
li maximi, qui inter illos Meridianos interijcitur. </s>
  <s xml:id="echoid-s20383" xml:space="preserve">Quoniam verò ijdem Meridiani occurrunt <lb/>plano horologij in C, puncto, vbi axis eidem plano occurrere ponitur, faciuntq́ue cum eo ſectio-<lb/>nes communes lineas rectas, quæ illis in circulo maximo æquidiſtant, eò quod eidem circulo ma <lb/>
<anchor type="note" xlink:label="note-0318-05a" xlink:href="note-0318-05"/>
ximo planum horologij parallelum eſt, comprchendent huiuſmodi lineæ in plano horologij an-<lb/>gulum æqualem illi angulo, quem in circulo maximo priores illæ lineæ efficiunt. </s>
  <s xml:id="echoid-s20384" xml:space="preserve">Quare cum an-<lb/>
<anchor type="note" xlink:label="note-0318-06a" xlink:href="note-0318-06"/>
gulus D C P, ſit illi æqualis, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20385" xml:space="preserve">33. </s>
  <s xml:id="echoid-s20386" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20387" xml:space="preserve">6. </s>
  <s xml:id="echoid-s20388" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20389" xml:space="preserve">oſtendimus, quòd arcus D P, ſi-<lb/>milis ſit arcui illius circuli inter duos Meridianos interiecto, quia totidem gradus, ac Minuta con <lb/>tinet; </s>
  <s xml:id="echoid-s20390" xml:space="preserve">ponatur autem C D, linea meridiana, id eſt, communis ſectio Meridiani Horizontis, &amp; </s>
  <s xml:id="echoid-s20391" xml:space="preserve">pla-<lb/>ni horologij, erit C P, communis ſectio plani horologij declinantis, &amp; </s>
  <s xml:id="echoid-s20392" xml:space="preserve">Meridiani eiuſdem plani, <lb/>id eſt, circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s20393" xml:space="preserve">polos ipſius plani tranſeuntis: </s>
  <s xml:id="echoid-s20394" xml:space="preserve">ac proinde in ea ſtylus <lb/>
<anchor type="note" xlink:label="note-0318-07a" xlink:href="note-0318-07"/>
collocandus erit ad angulos rectos, cum hac ratione à plano huius Meridiani non recedat, ſed ad <lb/>ipſum axem mundi in eo exiſtentem pertingat. </s>
  <s xml:id="echoid-s20395" xml:space="preserve">Quare C P, linea erit Indicis, ſeu ſtyli. </s>
  <s xml:id="echoid-s20396" xml:space="preserve">Vnde reli-<lb/>qua conſtructio horologij demonſtrabitur, vt prima conſtructio ad initium huius propoſ. </s>
  <s xml:id="echoid-s20397" xml:space="preserve">Horo-<lb/>logium igitur Aſtronomicum à Verticali circulo declinans, hoc eſt, lineas horarum, &amp;</s>
  <s xml:id="echoid-s20398" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20399" xml:space="preserve">deſcri-<lb/>pſimus. </s>
  <s xml:id="echoid-s20400" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s20401" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1044" type="float" level="2" n="21">
<note position="left" xlink:label="note-0318-04" xlink:href="note-0318-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0318-05" xlink:href="note-0318-05a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0318-06" xlink:href="note-0318-06a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0318-07" xlink:href="note-0318-07a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1046" type="section" level="1" n="255">
<head xml:id="echoid-head264" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s20402" xml:space="preserve">SED videtur hoc loco ſcrupulus quidam ex animo Lectoris euellendus, qui illum fortaſſis non parũ <lb/>
<anchor type="note" xlink:label="note-0318-08a" xlink:href="note-0318-08"/>
angere ac torquere poſſet. </s>
  <s xml:id="echoid-s20403" xml:space="preserve">Qui enim fieri poteſt, dicet aliquis, vt angulus in plano horologii à ſectioni-<lb/>
<anchor type="note" xlink:label="note-0318-09a" xlink:href="note-0318-09"/>
bus illorum Meridianorum conſtitutus æqualis ſit angulo in circulo maximo, cui planum horologii æquidi <lb/>ſtat, ab eorundem Meridianorum ſectionibus conſtituto, cum illi Meridiani circulum à plano horologii <lb/>in ſphæra factum, &amp; </s>
  <s xml:id="echoid-s20404" xml:space="preserve">circulum muximum, cui horologium æquidiſtat, non ſecent in arcus ſimiles? </s>
  <s xml:id="echoid-s20405" xml:space="preserve">Si enini <lb/>in arcus ſimiles ipſos ſecarent, tranſirent per propoſ. </s>
  <s xml:id="echoid-s20406" xml:space="preserve">16. </s>
  <s xml:id="echoid-s20407" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20408" xml:space="preserve">2. </s>
  <s xml:id="echoid-s20409" xml:space="preserve">Theodoſii, vel per eorum polos, vel eun-<lb/>dem vnum parallelum tangerent, quorum neutrum hic fieri poteſt. </s>
  <s xml:id="echoid-s20410" xml:space="preserve">Nam cum per polos mundi ducantur <lb/>ambo, qui pol{us} ipſorum eſſe non poteſt, (ſiquidem polus ipſorum in Horizonte exiſtit) non poterunt <lb/>tranſire per illorum polos. </s>
  <s xml:id="echoid-s20411" xml:space="preserve">Præterea cum Meridianus plani declinantis per cius polos tranſeat, ſecabit <lb/>omnes ipſius parallelos bifarium, per propoſ. </s>
  <s xml:id="echoid-s20412" xml:space="preserve">15. </s>
  <s xml:id="echoid-s20413" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20414" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20415" xml:space="preserve">Theodoſii, ac proinde nullum tanget. </s>
  <s xml:id="echoid-s20416" xml:space="preserve">Quare am-<lb/>bo illi Meridiani eundem vnum parallelum tangere non poſſunt. </s>
  <s xml:id="echoid-s20417" xml:space="preserve">Non ergo ſimiles ſunt illi arcus, quos <lb/>prædicti anguli æquales auferunt. </s>
  <s xml:id="echoid-s20418" xml:space="preserve">Hoc idem ad ſenſum patet in ſphæra materiali, vbi manifeſtè cernitu<unsure/>r, <lb/>Meridianum, &amp; </s>
  <s xml:id="echoid-s20419" xml:space="preserve">vtrumuis Colurum non poſſe diuidere Horizontem, &amp; </s>
  <s xml:id="echoid-s20420" xml:space="preserve">circulum ſub Horizonte ei pa-
<pb o="303" file="0319" n="319" rhead="LIBER TERTIVS."/>
rallelum in arc{us} ſimiles, quòd illi circuli per horum polos non ducantur: </s>
  <s xml:id="echoid-s20421" xml:space="preserve">eadem{q́ue} ratio eſt de quocun-<lb/>que Verticali declinante, &amp; </s>
  <s xml:id="echoid-s20422" xml:space="preserve">circulo, qui ei ęquidiſtet. </s>
  <s xml:id="echoid-s20423" xml:space="preserve">Quę cum ita ſint, non videntur æquales poſſe eſſe <lb/>duo illi anguli à dictis ſectionib{us} conſtituti; </s>
  <s xml:id="echoid-s20424" xml:space="preserve">quandoquidem, vt oſtendim{us}, non auferunt arcus ſimiles <lb/>ex circulo maximo, cui horologium æquidistat, &amp; </s>
  <s xml:id="echoid-s20425" xml:space="preserve">ex ei{us} parallelo, quem in ſphæra planum horolo-<lb/>gii efficit.</s>
  <s xml:id="echoid-s20426" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1046" type="float" level="2" n="1">
<note position="left" xlink:label="note-0318-08" xlink:href="note-0318-08a" xml:space="preserve">Dubitatio ad-<lb/>uerſus ea, quæ <lb/>proxime dicta <lb/>ſunt.</note>
<note position="left" xlink:label="note-0318-09" xlink:href="note-0318-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s20427" xml:space="preserve">HAEC ſunt, quę anxium reddere poſſent Lectoris animum: </s>
  <s xml:id="echoid-s20428" xml:space="preserve">Vnde clarius rem iſtã explanare opor-<lb/>tebit. </s>
  <s xml:id="echoid-s20429" xml:space="preserve">Libet autem hoc loco dubitationem hanc diſſoluere, (et ſi ſcio illam apud exercitatos in elementis <lb/>ſphæricis locum non habere) quia ex ea multæ aliæ ſimiles dubitationes poterunt explicari, vt ex iis, quę <lb/>
<anchor type="note" xlink:label="note-0319-01a" xlink:href="note-0319-01"/>
ſequuntur, fiet perſpicuum. </s>
  <s xml:id="echoid-s20430" xml:space="preserve">Dico ergo rectè à nobis eſſe demonſtratum, angulos illos æquales eſſe: </s>
  <s xml:id="echoid-s20431" xml:space="preserve">neque <lb/>verò obſtat, quòd illi arcus ſimiles non ſint; </s>
  <s xml:id="echoid-s20432" xml:space="preserve">quoniam enim axis mundi non cadit in centrum circuli, quẽ <lb/>
<anchor type="note" xlink:label="note-0319-02a" xlink:href="note-0319-02"/>
planum horologii in ſphæra efficit, propterea quòd axis eius proprius, per propoſ. </s>
  <s xml:id="echoid-s20433" xml:space="preserve">10. </s>
  <s xml:id="echoid-s20434" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20435" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20436" xml:space="preserve">Theodoſii, in <lb/>ipſius centrum cadat, non erit punctum C, in quod cadit axis mundi, centrum illius circuli: </s>
  <s xml:id="echoid-s20437" xml:space="preserve">ac proinde fie-<lb/>ri non poteſt, vt lineæ rectæ angulum in plano horologii efficientes in C, auferant ex eo circulo arcum ſi-<lb/>milem ei, quem abſcindunt lineæ rectæ angulum æqualem comprehendentes ex circulo maximo, cui ille <lb/>æquidiſtat. </s>
  <s xml:id="echoid-s20438" xml:space="preserve">Soli enim anguli æquales ad centra circulorum, vel ad circumferentias conſtituti inſiſtunt <lb/>arcubus ſimilibus, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20439" xml:space="preserve">33. </s>
  <s xml:id="echoid-s20440" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20441" xml:space="preserve">6. </s>
  <s xml:id="echoid-s20442" xml:space="preserve">Euclidis, demonſtr auimus: </s>
  <s xml:id="echoid-s20443" xml:space="preserve">quales non ſunt duo prædi-<lb/>cti anguli. </s>
  <s xml:id="echoid-s20444" xml:space="preserve">Nam ille in circulo maximo, cui horologium æquidiſtat, conſtituitur in eius centro, put a in cen <lb/>tro mundi, alter verò in circulo, qui illi par allelus est, extra centrum, nempe in puncto C, quod oſtendi-<lb/>m{us} iam centrum illius non eſſe. </s>
  <s xml:id="echoid-s20445" xml:space="preserve">V erum tamen eſt, ſi ex C, in plano horologii circulus deſcribatur, arcum <lb/>quem dictus angul{us} D C P, abſcindit, qualis in noſtro exemplo eſt arcus D P, ſimilem fore arcui, quẽ <lb/>
<anchor type="note" xlink:label="note-0319-03a" xlink:href="note-0319-03"/>
æqualis angulus ex circulo maximo, cui horologium æquidiſtat, in centro eius conſtitutus aufert: </s>
  <s xml:id="echoid-s20446" xml:space="preserve">ſed ille <lb/>circulus parallelo, quem planum horologii facit in ſphæra, concentricus non eſt, vt oſtendimus. </s>
  <s xml:id="echoid-s20447" xml:space="preserve">Non ergo <lb/>locum habet dubitatio propoſita hoc loco.</s>
  <s xml:id="echoid-s20448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1047" type="float" level="2" n="2">
<note position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">Solutio dubi-<lb/>tationis ſupe-<lb/>rioris.</note>
<note position="left" xlink:label="note-0319-02" xlink:href="note-0319-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">20</note>
</div>
<note position="right" xml:space="preserve">Quomodo ho-<lb/>rologium decli <lb/>nans à Vertica <lb/>li collocandum <lb/>ſit, vt horas mõ <lb/>ſtret.</note>
<p style="it">
  <s xml:id="echoid-s20449" xml:space="preserve">IAM verò ſi horologium declinans hactenus delineatum ita collocetur in plano declinante, vt li-<lb/>nea meridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s20450" xml:space="preserve">C D, ad Horizontem perpendicularis ſit, &amp; </s>
  <s xml:id="echoid-s20451" xml:space="preserve">recta A B, illam ad angulos <lb/>rectos ſecans Horizonti æquidiſtet, &amp; </s>
  <s xml:id="echoid-s20452" xml:space="preserve">præterea punctum C, in iis, quæ à meridie declinant, ſurſum, &amp; </s>
  <s xml:id="echoid-s20453" xml:space="preserve"><lb/>punctum D, deorſum verſus statuatur; </s>
  <s xml:id="echoid-s20454" xml:space="preserve">in illis verò, quæ deflectunt à borea, punctum C, deorſum, &amp; </s>
  <s xml:id="echoid-s20455" xml:space="preserve">D, <lb/>ſurſum verſus ponatur; </s>
  <s xml:id="echoid-s20456" xml:space="preserve">nec non in puncto K, ad angulos rectos infigatur ſtylus I K, vel triangulũ C I G, <lb/>rectum ſtatuatur ad planum horologĳ, indicabit extremum vmbræ à vertice ſtyli proiectæ, veltota vm-<lb/>bra totius axis C I, horas à meridie, vel media nocte, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20457" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20458" xml:space="preserve">ſuperioris libri oſtendim{us}.</s>
  <s xml:id="echoid-s20459" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s20460" xml:space="preserve">QVOD ſi in ipſo muro declinante horologium deſcribendum ſit, non autem in quopiam alio plano, <lb/>
<anchor type="note" xlink:label="note-0319-06a" xlink:href="note-0319-06"/>
ex quo in murum transferatur, vt hactenus fecim{us}; </s>
  <s xml:id="echoid-s20461" xml:space="preserve">ducenda erit in muro recta C D, officio perpendicu-<lb/>li ad Horizontem perpendicularis, &amp; </s>
  <s xml:id="echoid-s20462" xml:space="preserve">ad hanc in eodem muro perpendicularis ducenda A B, quæ Hori-<lb/>zonti æquidiſtabit: </s>
  <s xml:id="echoid-s20463" xml:space="preserve">Vel ſi mauis, per libellam, &amp; </s>
  <s xml:id="echoid-s20464" xml:space="preserve">perpendiculum ducenda erit recta A B, Horizonti <lb/>æquidiſtans, &amp; </s>
  <s xml:id="echoid-s20465" xml:space="preserve">ad hanc excitanda perpendicularis C D, quæ ad Horizontem perpendicularis erit. </s>
  <s xml:id="echoid-s20466" xml:space="preserve">Cæte-<lb/>ra autem conſtruenda, vt in prima deſcriptione horologĳ declinantis; </s>
  <s xml:id="echoid-s20467" xml:space="preserve">Nimirum ducenda linea declina-<lb/>tionis E F, &amp; </s>
  <s xml:id="echoid-s20468" xml:space="preserve">ad A B, perpendicularis F G, &amp; </s>
  <s xml:id="echoid-s20469" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20470" xml:space="preserve">Si autem alĳs duob{us} modis vti malueris, ducenda <lb/>quoque erit ante omnia recta C D, ad Horizontem perpendicularis. </s>
  <s xml:id="echoid-s20471" xml:space="preserve">Deinde ducenda recta C P, ita vt <lb/>C D, C P, intercipiant arcum D P, vt in tertio modo dixim{us}, ea tamen lege, vt attentè conſideretur, <lb/>verſus quam partem arcas D P, per propoſ. </s>
  <s xml:id="echoid-s20472" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20473" xml:space="preserve">primi libri repert{us} numerari debeat, quemadmodum <lb/>
<anchor type="note" xlink:label="note-0319-07a" xlink:href="note-0319-07"/>
in tertio modo præſcripſimus. </s>
  <s xml:id="echoid-s20474" xml:space="preserve">Reliqua omnino conficienda, vt pri{us}: </s>
  <s xml:id="echoid-s20475" xml:space="preserve">hoc eſt, ducenda æquinoctialis linea <lb/>G H, perpendicularis ad C P, &amp; </s>
  <s xml:id="echoid-s20476" xml:space="preserve">c.</s>
  <s xml:id="echoid-s20477" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1048" type="float" level="2" n="3">
<note position="right" xlink:label="note-0319-06" xlink:href="note-0319-06a" xml:space="preserve">Quomodo in <lb/>plano ſtabili, <lb/>quod à Vertica <lb/>li declinet, ho-<lb/>rologium Aſtro <lb/>nomicum de-<lb/>ſcribendũ ſit.</note>
<note position="left" xlink:label="note-0319-07" xlink:href="note-0319-07a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Qua ratione li <lb/>neæ horarię du <lb/>ci poſſint ſecũ-<lb/>dum Andream <lb/>Schonerum, <lb/>etiamſi earum <lb/>puncta in æqui <lb/>noctiali inuen-<lb/>ta non ſint.</note>
<p style="it">
  <s xml:id="echoid-s20478" xml:space="preserve">QVONIAM verò aliquando contingit, vt aliquę lineæ horariæ aut nunquam, aut certè valde <lb/>procul æquinoctialem lineam ſecent, quod ideo cuenit, quòd interdum rectæ per centrum L, &amp; </s>
  <s xml:id="echoid-s20479" xml:space="preserve">puncta di-<lb/>uiſionum circuli ex L, deſcripti emiſſę vel ſunt parallelę ipſi ęquinoctiali lineę, vel in punctis remotiſſi-<lb/>mis eam interſecant; </s>
  <s xml:id="echoid-s20480" xml:space="preserve">excogitauit Andre{as} Schoner{us} rationem ſanè ingenioſam, qua eædem lineæ hora-<lb/>riæ ex C, centro horologii duci poſſint, nulla habita ratione lineę æquinoctialis. </s>
  <s xml:id="echoid-s20481" xml:space="preserve">Id quod in horologio ho-<lb/>rizontali etiam fecit, &amp; </s>
  <s xml:id="echoid-s20482" xml:space="preserve">in Verticali. </s>
  <s xml:id="echoid-s20483" xml:space="preserve">Hoc autem ſe modo ferè habet eius conſtructio. </s>
  <s xml:id="echoid-s20484" xml:space="preserve">Ex puncto E, <lb/>ad rect{as} β C, E F, perpendiculares ducantur E Y, E Q, ſit {q́ue} E Q, ipſi E Y, æqualis. </s>
  <s xml:id="echoid-s20485" xml:space="preserve">Ducta autem <lb/>recta Q F, quæ rectam A B, ſecet in R, ducatur per R, ad A B, perpendicularis R S, vel ipſi C D, pa-<lb/>
<anchor type="note" xlink:label="note-0319-09a" xlink:href="note-0319-09"/>
rallela, ſecans lineam C α, horæ 6. </s>
  <s xml:id="echoid-s20486" xml:space="preserve">in S. </s>
  <s xml:id="echoid-s20487" xml:space="preserve">Rurſus per S, ad R S, ducta perpendiculari S T, vel parallela <lb/>ipſi A B, ſumpta{q́ue} S T, ipſi R S, æquali, ducatur per T, ad S T, perpendicularis, vel ipſi R S, paralle-<lb/>la. </s>
  <s xml:id="echoid-s20488" xml:space="preserve">Postremo ſi ex T, centro ſemicirculus deſcriptus in partes 12. </s>
  <s xml:id="echoid-s20489" xml:space="preserve">æquales diſtribuatur, initio facto à re-<lb/>cta T S, ſecabunt rectæ ex T, per puncta diuiſionum emiſſæ rectam R S, in punctis, per quæ rectæ ex C, <lb/>centro horologii egredientes dabunt horari{as} line{as}, vt pri{us}. </s>
  <s xml:id="echoid-s20490" xml:space="preserve">Quòd ſi hæc ratio deſcriptionis cum prio-<lb/>rib{us} coniungatur, accuratè admodum, exquiſite{q́ue} omnes lineæ horariæ deſcribentur. </s>
  <s xml:id="echoid-s20491" xml:space="preserve">Nam quæ in pun-<lb/>ctis remotis rectam R S, ſecant, eæ non longè à puncto G, ęquinoctialem lineam diuident, vt in hora 11. <lb/></s>
  <s xml:id="echoid-s20492" xml:space="preserve">apparet: </s>
  <s xml:id="echoid-s20493" xml:space="preserve">Et quę ęgrè lineam ęquinoctialem ſecant, eę commodiſſimè rectam R S, interſecant, vt in ho-<lb/>ra 4. </s>
  <s xml:id="echoid-s20494" xml:space="preserve">perſpicuum eſt.</s>
  <s xml:id="echoid-s20495" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1049" type="float" level="2" n="4">
<note position="left" xlink:label="note-0319-09" xlink:href="note-0319-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s20496" xml:space="preserve">VERVM quia ad hanc deſcriptionem neceſſarium eſt, vt pri{us} ducatur linea horę 6.</s>
  <s xml:id="echoid-s20497" xml:space="preserve">1 ex C, centro <lb/>horologĳ per punctum α, rectæ A B. </s>
  <s xml:id="echoid-s20498" xml:space="preserve">in quod cadit recta F α, ad lineam declinationis E F, perpendicula
<pb o="304" file="0320" n="320" rhead="GNOMONICES"/>
ris; </s>
  <s xml:id="echoid-s20499" xml:space="preserve">ſine enim hac nullo modo haberi poteſt in recta R S, punctum S, vt patet: </s>
  <s xml:id="echoid-s20500" xml:space="preserve">accidit autem aliquando, <lb/>vt ęgrè hora hęc abſque errore duci poſſit, propterea quòd perpendicularis F α, nonnunquam in remotiſ-<lb/>ſimum punctum rectę A B, incidit; </s>
  <s xml:id="echoid-s20501" xml:space="preserve">quod quidem tum euenit, cum valdè exigua eſt declinatio plani horo-<lb/>logĳ à Verticali circulo, ac proinde linea declinationis E F, prope à recta C D, abeſt, vt manifeſtum eſt; <lb/></s>
  <s xml:id="echoid-s20502" xml:space="preserve">
<anchor type="note" xlink:label="note-0320-01a" xlink:href="note-0320-01"/>
docet idem Andreas, quo pacto hora 6. </s>
  <s xml:id="echoid-s20503" xml:space="preserve">tum, cum hoc accidit, poſſit deſcribi, etiam ſi recta F α, non ſit <lb/>ducta. </s>
  <s xml:id="echoid-s20504" xml:space="preserve">Ita autem rem cum illo exequemur: </s>
  <s xml:id="echoid-s20505" xml:space="preserve">Ex puncto β, ducatur ad A B, perpendicularis β Z, vel ipſi <lb/>C D, parallela, quam in Z, ſecet recta C Z, perpendicularis ad C D, parallelaveipſi A B. </s>
  <s xml:id="echoid-s20506" xml:space="preserve">Deinde in Z, <lb/>conſtituatur angulus declinationis C Z a, ſupra quidem rectam C Z, ſi planum à meridie declinet, infra <lb/>verò, ſi à Septentrione; </s>
  <s xml:id="echoid-s20507" xml:space="preserve">quod intelligendum eſt, ſi punctum β, extiterit in parte oppoſita lineæ declina-<lb/>tionis E F, vt in nostro exemplo: </s>
  <s xml:id="echoid-s20508" xml:space="preserve">Nam ſi punctum β, &amp; </s>
  <s xml:id="echoid-s20509" xml:space="preserve">recta E F, ad eaſdem partes rectę C D, exti-<lb/>
<anchor type="note" xlink:label="note-0320-02a" xlink:href="note-0320-02"/>
terint, conſtituend{us} erit angul{us} declinationis C Z a, infra C Z, in auſtralibus horologĳs, ſupra verò in <lb/>borealibus. </s>
  <s xml:id="echoid-s20510" xml:space="preserve">Sumpta quoque recta Z a, ęquali ipſi Z β, ducatur per punctum a, (quod inueniemus forſi-<lb/>tan facilius, ſi ex Z, ad interuallum Z β, arcum C a, deſcribamus ſupra rectam C Z, vel infra, vt de an-<lb/>gulo C Z a, dixim{us}, numerem{us}{q́ue} declinationem plani horologĳ à puncto C, vſque ad a) recta a b, paral <lb/>lela ipſi A B, vel perpendicularis ad β Z, ſecans β Z, in b. </s>
  <s xml:id="echoid-s20511" xml:space="preserve">Nam recta per b, &amp; </s>
  <s xml:id="echoid-s20512" xml:space="preserve">C, puncta educta da-<lb/>bit horam 6. </s>
  <s xml:id="echoid-s20513" xml:space="preserve">optatam.</s>
  <s xml:id="echoid-s20514" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1050" type="float" level="2" n="5">
<note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">Quo pacto li-<lb/>nea horæ 6. du-<lb/>ci queat in pla-<lb/>nis parũ à Ver-<lb/>ticali declinan-<lb/>tibus.</note>
<note position="left" xlink:label="note-0320-02" xlink:href="note-0320-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s20515" xml:space="preserve">QVOD ſi idem horologium declinans à Verticali circulo deſcribendum ſit in dato plano, ad quam-<lb/>
<anchor type="note" xlink:label="note-0320-03a" xlink:href="note-0320-03"/>
cunque ſtyli longitudinem, cuius etiam locus datus ſit, progrediemur hoc artificio. </s>
  <s xml:id="echoid-s20516" xml:space="preserve">Sit in plano horologĳ <lb/>datus loc{us} ſlyli in puncto K, eius{q́ue} longitudo K F. </s>
  <s xml:id="echoid-s20517" xml:space="preserve">Ducantur per K, locum ſtyli duærectę A B, F D, <lb/>ſe mutuo ſecantes in K, ad angulos rectos: </s>
  <s xml:id="echoid-s20518" xml:space="preserve">Vel, ſi planum ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s20519" xml:space="preserve">ad Horizontem rectum, duca-<lb/>
<anchor type="note" xlink:label="note-0320-04a" xlink:href="note-0320-04"/>
tur per K, recta A B, Horizonti ęquidiſtans beneficio libellæ &amp; </s>
  <s xml:id="echoid-s20520" xml:space="preserve">perpendiculi, quam in K, ad rectos an <lb/>gulos ſecet D F, quæ ad Horizontem perpendicularis erit, vt demonſtrabim{us}: </s>
  <s xml:id="echoid-s20521" xml:space="preserve">Vel primo loco ducatur <lb/>
<anchor type="figure" xlink:label="fig-0320-01a" xlink:href="fig-0320-01"/>
<anchor type="note" xlink:label="note-0320-05a" xlink:href="note-0320-05"/>
<anchor type="note" xlink:label="note-0320-06a" xlink:href="note-0320-06"/>
beneficio perpendiculi ad Horizontem perpendicularis F D, per locum ſtyli K, quam in K, ad rectos an-<lb/>gulos ſecet A B, quę Horizonti erit ęquidiſtans, immo communis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s20522" xml:space="preserve">plani horologii de-<lb/>
<anchor type="note" xlink:label="note-0320-07a" xlink:href="note-0320-07"/>
clinantis. </s>
  <s xml:id="echoid-s20523" xml:space="preserve">quod etiam demonſir abimus. </s>
  <s xml:id="echoid-s20524" xml:space="preserve">In F D, autem ſumpta longitudine dati ſtyli K F, ſiuc ſurſum, <lb/>ſiue deorſum verſus, deſcribatur ex F, vt centro, verſus A B, arcus circuli D H, verſus B, quidem, ſi <lb/>murus, planumve horologii à meridie in ortum, vel à Septentrione in occaſum declinet; </s>
  <s xml:id="echoid-s20525" xml:space="preserve">verſus A, vero, <lb/>ſi deflectat à meridie in occaſum, aut à borea in ertum. </s>
  <s xml:id="echoid-s20526" xml:space="preserve">In hoc vero arcu numer ata declinatione muri <lb/>D H, (Hanc ponimus continere gr. </s>
  <s xml:id="echoid-s20527" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20528" xml:space="preserve">à meridie in ortum, vt antea) ducta{q́ue} recta F H, ſecante ipſam <lb/>A B, in E, agatur per E, recta C E, ipſi F D, parallela, ſeu ad A B, perpendicularis. </s>
  <s xml:id="echoid-s20529" xml:space="preserve">Nam C E, erit <lb/>linea meridiana, ſiue horę 12. </s>
  <s xml:id="echoid-s20530" xml:space="preserve">Deinde in arcu H D, ex altera parte rectæ F D, producto ſupputetur cõ-<lb/>plementum declinationis D N, ducatur{q́ue} recta F N, vel certe ducatur recta F α, ad F E, perpendicu <lb/>laris ſecans A B, in α Per punctum enim α, ducenda eſt &amp; </s>
  <s xml:id="echoid-s20531" xml:space="preserve">linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s20532" xml:space="preserve">linea boræ 6. </s>
  <s xml:id="echoid-s20533" xml:space="preserve">Sumpta <lb/>quoque in A B, recta E β, ſiue ad dextram, ſiue ad ſiniſtram meridianæ lineę C E, quę ipſi E F, ęqualis <lb/>ſit, deſcribatur ex β, verſus C E, arcus circuli ſurſum quidem verſus in horologio declinante à meridie,
<pb o="305" file="0321" n="321" rhead="LIBER TERTIVS."/>
deorſum aut em in eo, quod à Septentrione deflectit, in quo numer ata altitudine poli, initio facto à re cta <lb/>A B, ducatur ex β, ad finem ſupputationis recta ſecans C E, in C, puncto, quod centrum erit horologii, <lb/>in quo omnes lineę horarię conuenient. </s>
  <s xml:id="echoid-s20534" xml:space="preserve">Ducta autem ex C, per K, locum ſtyli recta C K, pro linea styli, <lb/>quam recta ex α, ducta ſecet ad angulos rectos in G; </s>
  <s xml:id="echoid-s20535" xml:space="preserve">erit recta α G, linea æquinoctialis. </s>
  <s xml:id="echoid-s20536" xml:space="preserve">Post hæc excite <lb/>tur ex K, recta K I, ad C K, perpendicularis, &amp; </s>
  <s xml:id="echoid-s20537" xml:space="preserve">ſtylo K F, æqualis, iungantur rectę C I, G I, quæ in <lb/>I, angulum rectum continebunt, vt demonstrabimus. </s>
  <s xml:id="echoid-s20538" xml:space="preserve">Vnde ducta recta C I, ſi ad eam excitemus per-<lb/>pendicularem I G, inueniemus in linea ſtyli C K, punctum G, per quod ex α, ducenda eſt ęquinoctialis li-<lb/>nea α G, ad C K, perpendicularis. </s>
  <s xml:id="echoid-s20539" xml:space="preserve">Erit autem C I, axis mundi. </s>
  <s xml:id="echoid-s20540" xml:space="preserve">Iam vero in linea ſtyli C K, ſumpta <lb/>recta G L, ipſi G I, ęquali, deſcribatur ex L, circulus cuiuſuis magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s20541" xml:space="preserve">ęquales <lb/>diſtribuatur, initio facto à recta L M, quæ ex L, ducitur per punctum M, vbi ęquinoctialis linea meridia-<lb/>
<anchor type="note" xlink:label="note-0321-01a" xlink:href="note-0321-01"/>
nam interſecat, quæ quidem recta L M, neceſſario ductam rectam L α, ad angulos rectos ſecabit, ſi non <lb/>fuerit erratum. </s>
  <s xml:id="echoid-s20542" xml:space="preserve">Reliqua denique perficiantur, vt in principio huius propoſ. </s>
  <s xml:id="echoid-s20543" xml:space="preserve">traditum eſt.</s>
  <s xml:id="echoid-s20544" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1051" type="float" level="2" n="6">
<note position="left" xlink:label="note-0320-03" xlink:href="note-0320-03a" xml:space="preserve">Conſtructio ho <lb/>rologii declinã <lb/>tis ad datam <lb/>ſtyli longitudi-<lb/>nem, cuius etiã <lb/>locus datus ſit.</note>
<note position="left" xlink:label="note-0320-04" xlink:href="note-0320-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0320-01" xlink:href="fig-0320-01a">
    <image file="0320-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0320-01"/>
  </figure>
<note position="left" xlink:label="note-0320-05" xlink:href="note-0320-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0320-06" xlink:href="note-0320-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0320-07" xlink:href="note-0320-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0321-01" xlink:href="note-0321-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s20545" xml:space="preserve">HANC constructionem ita demonſtrabim{us}. </s>
  <s xml:id="echoid-s20546" xml:space="preserve">Intelligatur per rectam A B, &amp; </s>
  <s xml:id="echoid-s20547" xml:space="preserve">ſtylum K F, qui <lb/>
<anchor type="note" xlink:label="note-0321-02a" xlink:href="note-0321-02"/>
rectus ſit ad planum horologii in puncto K, duci Horizon, ita vt A B, communis ſectio ſit Horizontis <lb/>ac plani horologĳ declinantis, nempe linea horizontalis. </s>
  <s xml:id="echoid-s20548" xml:space="preserve">Per polum quoque plani declinantis, &amp; </s>
  <s xml:id="echoid-s20549" xml:space="preserve">polum <lb/>Horizontis concipiatur duci circulus maxim{us}, qui per propoſ. </s>
  <s xml:id="echoid-s20550" xml:space="preserve">15 lib. </s>
  <s xml:id="echoid-s20551" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20552" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s20553" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20554" xml:space="preserve">ad planum declinãs, <lb/>&amp; </s>
  <s xml:id="echoid-s20555" xml:space="preserve">ad Horizontem rectus erit, ac proinde cum per centrum mundi, id eſt, per verticem ſtyli F, tran-<lb/>ſeat, omnia autem plana ducta per ſtylum K F, qui rectus eſt ad planum declinans, recta ſint ad idem pla <lb/>
<anchor type="note" xlink:label="note-0321-03a" xlink:href="note-0321-03"/>
num declinans, tranſibit dictus circulus maximus per ſtylum F K, planum{q́ue} horologĳ declinantis ſecabit <lb/>in K. </s>
  <s xml:id="echoid-s20556" xml:space="preserve">Quoniam igitur tam planum horologĳ, quam planum huius circuli maximi rectum eſt ad Horizon-<lb/>
<anchor type="note" xlink:label="note-0321-04a" xlink:href="note-0321-04"/>
tem, erit quoque communis eorum ſectio ad eundem, at que adeo, per defin. </s>
  <s xml:id="echoid-s20557" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20558" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20559" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20560" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20561" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20562" xml:space="preserve">ad rect am <lb/>
<anchor type="note" xlink:label="note-0321-05a" xlink:href="note-0321-05"/>
A B, in Horizonte exiſtentem, perpendicularis erit. </s>
  <s xml:id="echoid-s20563" xml:space="preserve">Quare recta F D, quam per K, duximus ad A B, <lb/>perpendicularem, communis ſectio erit dicti maximi circuli, &amp; </s>
  <s xml:id="echoid-s20564" xml:space="preserve">plani horologĳ declinantis, ac proinde <lb/>ad Horizontem perpendicularis. </s>
  <s xml:id="echoid-s20565" xml:space="preserve">Quod ſi primo loco ducatur recta F D, ad Horizontem perpendicula-<lb/>ris, intelligatur per rectam F D, &amp; </s>
  <s xml:id="echoid-s20566" xml:space="preserve">per ſtylum F K, qui rectus ſit ad planum horologĳ declinantis, duci <lb/>planum, quod rectum erit &amp; </s>
  <s xml:id="echoid-s20567" xml:space="preserve">ad Horizontem, &amp; </s>
  <s xml:id="echoid-s20568" xml:space="preserve">ad planum horologĳ declinantis. </s>
  <s xml:id="echoid-s20569" xml:space="preserve">Quoniam igitur tam <lb/>
<anchor type="note" xlink:label="note-0321-06a" xlink:href="note-0321-06"/>
planum horologĳ, quam planum Horizontis rectum eſt ad planum per rectam F D, &amp; </s>
  <s xml:id="echoid-s20570" xml:space="preserve">ſtylum F K, du-<lb/>ctum, erit quoque ad idem planum recta communis illorum ſectio, atque adeo, per defin. </s>
  <s xml:id="echoid-s20571" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20572" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20573" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20574" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20575" xml:space="preserve">ad <lb/>
<anchor type="note" xlink:label="note-0321-07a" xlink:href="note-0321-07"/>
rectam F D, in dicto plano exiſtentem perpendicularis, in puncto K, per quod Horizon ducitur, cum per <lb/>ſtylum F K, ducatur. </s>
  <s xml:id="echoid-s20576" xml:space="preserve">Recta igitur A B, quam ad F D, duximus perpendicularem, communis ſectio e-<lb/>
<anchor type="note" xlink:label="note-0321-08a" xlink:href="note-0321-08"/>
rit plani horologĳ &amp; </s>
  <s xml:id="echoid-s20577" xml:space="preserve">Horizontis, hoc e st, linea horizontalis.</s>
  <s xml:id="echoid-s20578" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1052" type="float" level="2" n="7">
<note position="right" xlink:label="note-0321-02" xlink:href="note-0321-02a" xml:space="preserve">Demonſtratio <lb/>huius<unsure/> conſtru-<lb/>ctionis.</note>
<note position="right" xlink:label="note-0321-03" xlink:href="note-0321-03a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0321-04" xlink:href="note-0321-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0321-05" xlink:href="note-0321-05a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0321-06" xlink:href="note-0321-06a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0321-07" xlink:href="note-0321-07a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0321-08" xlink:href="note-0321-08a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s20579" xml:space="preserve">DEINDE quia E F k, angulus eſt declinationis plani horologĳ à Verticali, erit F E K, angu-<lb/>lus complementi eiuſdem declinationis, qualem nimirum Meridianus cum plano declinante conſtituit. <lb/></s>
  <s xml:id="echoid-s20580" xml:space="preserve">Quare ſi triangulum E F K, circa E K, moueatur, donec rectum ſit ad planum horologĳ in proprio ſitu <lb/>poſitum, erit F E, communis ſectio Horizontis ac Meridiani per F, verticem ſtyli ducti; </s>
  <s xml:id="echoid-s20581" xml:space="preserve">ac propte-<lb/>rea, vt in prima deſcriptione huius propoſ. </s>
  <s xml:id="echoid-s20582" xml:space="preserve">demonstrauimus, erit C M, linea meridiana, communis vi-<lb/>delicet ſectio Meridiani ac plani horologii. </s>
  <s xml:id="echoid-s20583" xml:space="preserve">Et quoniam arc{us} H N, quadrans eſt, erit angulus E F α, re-<lb/>ctus; </s>
  <s xml:id="echoid-s20584" xml:space="preserve">ac proinde recta F α, communis ſectio Verticalis at que Horizontis. </s>
  <s xml:id="echoid-s20585" xml:space="preserve">Cum enim tam Horizon, quàm <lb/>Verticalis ad Meridianum rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s20586" xml:space="preserve">eorum ſectio communis ad eundem recta, ac proinde, per <lb/>
<anchor type="note" xlink:label="note-0321-09a" xlink:href="note-0321-09"/>
defin. </s>
  <s xml:id="echoid-s20587" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20588" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20589" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20590" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20591" xml:space="preserve">ad rectam F E, in Meridiano exiſtentem perpendicularis in F, centro mundi. </s>
  <s xml:id="echoid-s20592" xml:space="preserve">Qua-<lb/>
<anchor type="note" xlink:label="note-0321-10a" xlink:href="note-0321-10"/>
re F α, quæ ad F E, perpendicularis eſt, communis ſectio est Verticalis atque Horizontis. </s>
  <s xml:id="echoid-s20593" xml:space="preserve">Habet autẽ <lb/>Aequator eandem communem ſectionem cum Horizonte ac Verticali, nempe axem Meridiani, cum om-<lb/>nes hi tres circuli per polos Meridiani tranſeant, per propoſ. </s>
  <s xml:id="echoid-s20594" xml:space="preserve">13. </s>
  <s xml:id="echoid-s20595" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20596" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20597" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s20598" xml:space="preserve">proptcrea quòd ad Meri-<lb/>dianum recti ſunt. </s>
  <s xml:id="echoid-s20599" xml:space="preserve">Igitur Aequator per rectam F α, ducitur, occurrit{q́ue} plano horologii declinantis in <lb/>puncto α; </s>
  <s xml:id="echoid-s20600" xml:space="preserve">at que adeo per α, ducenda erit linea æquinoctialis.</s>
  <s xml:id="echoid-s20601" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1053" type="float" level="2" n="8">
<note position="right" xlink:label="note-0321-09" xlink:href="note-0321-09a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0321-10" xlink:href="note-0321-10a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s20602" xml:space="preserve">MANENTE adhuc triangulo E F K, ad planum horologĳ recto, ita vt angulus C E F, rectus <lb/>ſit, (Quòd enim rect{us} ſit, it a ostendemus. </s>
  <s xml:id="echoid-s20603" xml:space="preserve">Quoniam tam planum horologĳ, quàm planum Meridiani re-<lb/>ctum est ad Horizontem, erit quoque communis eorum ſectio C E, ad eundem, atque adeo, per defin. </s>
  <s xml:id="echoid-s20604" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s20605" xml:space="preserve">
<anchor type="note" xlink:label="note-0321-11a" xlink:href="note-0321-11"/>
lib. </s>
  <s xml:id="echoid-s20606" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20607" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20608" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20609" xml:space="preserve">ad rectam F E, in Horizonte existentem in illo ſitu, perpendicularis) intelligatur trian-<lb/>gulum β E C, moueri circa rectam C E, donec recta β E, rectæ F E, &amp; </s>
  <s xml:id="echoid-s20610" xml:space="preserve">punctum β, puncto F, congruat <lb/>
<anchor type="note" xlink:label="note-0321-12a" xlink:href="note-0321-12"/>
propter angulos rectos β E C, F E C, &amp; </s>
  <s xml:id="echoid-s20611" xml:space="preserve">æqualitatem rectarum E β, E F. </s>
  <s xml:id="echoid-s20612" xml:space="preserve">Quo facto, erit β C, axis mun <lb/>di; </s>
  <s xml:id="echoid-s20613" xml:space="preserve">quandoquidem in plano Meridiani, qui per rectas F E, E C, ducitur, cum meridiana linea Horizon-<lb/>tis E F, in centro mundi F, angulum conſtituit E β C, altitudinis poli ſupra Horizontem. </s>
  <s xml:id="echoid-s20614" xml:space="preserve">Igitur per co <lb/>roll. </s>
  <s xml:id="echoid-s20615" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s20616" xml:space="preserve">21. </s>
  <s xml:id="echoid-s20617" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20618" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20619" xml:space="preserve">punctum C, in quod axis cadit, centrum erit horologĳ. </s>
  <s xml:id="echoid-s20620" xml:space="preserve">Hinc efficitur, rectam C K, <lb/>eſſe lineam styli, hoc eſt, communem ſectionem plani horologii declinantis, &amp; </s>
  <s xml:id="echoid-s20621" xml:space="preserve">Meridiani proprĳ ipſi{us} <lb/>plani declinantis, qui per axem &amp; </s>
  <s xml:id="echoid-s20622" xml:space="preserve">ſtylum ducitur, instar propriæ lineę meridianæ horologĳ declinantis: <lb/></s>
  <s xml:id="echoid-s20623" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s20624" xml:space="preserve">in prima deſcriptione hui{us} propoſ. </s>
  <s xml:id="echoid-s20625" xml:space="preserve">linea styli C G, ducta eſt ex centro horologii C, <lb/>per K, locum ſtyli. </s>
  <s xml:id="echoid-s20626" xml:space="preserve">Pari ratione efficitur, rectam α G, quæ ad lineam styli perpendicularis est, eſſe li-<lb/>neam ęquinoctialem, quandoquidem per punctum α, ducenda eſt, vt nuper oſtendim{us}, &amp; </s>
  <s xml:id="echoid-s20627" xml:space="preserve">angulos rectos <lb/>facit cum linea styli, vt in prima deſcriptione hui{us} propoſ. </s>
  <s xml:id="echoid-s20628" xml:space="preserve">demonstratum eſt.</s>
  <s xml:id="echoid-s20629" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1054" type="float" level="2" n="9">
<note position="right" xlink:label="note-0321-11" xlink:href="note-0321-11a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0321-12" xlink:href="note-0321-12a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s20630" xml:space="preserve">RECTAM autem C I, eſſe axem mundi, perſpicuum eſt. </s>
  <s xml:id="echoid-s20631" xml:space="preserve">Si enim triangulum C I K, circa C K,
<pb o="306" file="0322" n="322" rhead="GNOMONICES"/>
moueatur, donec rectum ſit ad planum horologĳ, &amp; </s>
  <s xml:id="echoid-s20632" xml:space="preserve">ſtyl{us} I K, ad idem rect{us}, congruet punctum I, <lb/>puncto F, atque adeo &amp; </s>
  <s xml:id="echoid-s20633" xml:space="preserve">puncto β. </s>
  <s xml:id="echoid-s20634" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s20635" xml:space="preserve">recta C I, axi C β, congruet. </s>
  <s xml:id="echoid-s20636" xml:space="preserve">Hinc fit, rectam G I, in eo <lb/>ſitu eſſe ſectionem communem Aequatoris, &amp; </s>
  <s xml:id="echoid-s20637" xml:space="preserve">Meridiani proprii ipſius plani declinantis, cum vterque <lb/>circulus per G, &amp; </s>
  <s xml:id="echoid-s20638" xml:space="preserve">per I, centrum mundi ducatur, Quare angul{us} C I G, rect{us} erit, cum dicta commu-<lb/>nis ſectio ſemper ſit ad axem perpendicularis, vt ex ſuperiorib{us} manifeſtum eſt. </s>
  <s xml:id="echoid-s20639" xml:space="preserve">Cætera ex demonſtra-<lb/>tis in prima conſtructione hui{us} propoſ. </s>
  <s xml:id="echoid-s20640" xml:space="preserve">perſpicua ſunt.</s>
  <s xml:id="echoid-s20641" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s20642" xml:space="preserve">BENEFICIO Ellipſis deſcribem{us} quoque idem horologium declinans à Verticali, quemadmo-<lb/>
<anchor type="note" xlink:label="note-0322-01a" xlink:href="note-0322-01"/>
dum &amp; </s>
  <s xml:id="echoid-s20643" xml:space="preserve">Horizontale, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20644" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20645" xml:space="preserve">ſuperioris lib, oſtendim{us}, pancis mutatis. </s>
  <s xml:id="echoid-s20646" xml:space="preserve">Sit enim rurſ{us} <lb/>longitudo styli data K F, eius{q́ue} loc{us} punctum K. </s>
  <s xml:id="echoid-s20647" xml:space="preserve">Inuenta igitur, vt in proxima deſcriptione præcepi-<lb/>m{us}, linea meridiana C E; </s>
  <s xml:id="echoid-s20648" xml:space="preserve">centro horologii C; </s>
  <s xml:id="echoid-s20649" xml:space="preserve">linea æquinoctiali α G; </s>
  <s xml:id="echoid-s20650" xml:space="preserve">axe mundi C I, &amp; </s>
  <s xml:id="echoid-s20651" xml:space="preserve">linea ſtyli C G: <lb/></s>
  <s xml:id="echoid-s20652" xml:space="preserve">
<anchor type="note" xlink:label="note-0322-02a" xlink:href="note-0322-02"/>
ſumatur in axe producto punctum H, remoti{us}, quàm I, vt accurati{us} horologium deſcribatur, à quo ad <lb/>
<anchor type="figure" xlink:label="fig-0322-01a" xlink:href="fig-0322-01"/>
<anchor type="note" xlink:label="note-0322-03a" xlink:href="note-0322-03"/>
<anchor type="note" xlink:label="note-0322-04a" xlink:href="note-0322-04"/>
<anchor type="note" xlink:label="note-0322-05a" xlink:href="note-0322-05"/>
axem perpendicularis ducatur H N, ſecans lineam ſtyli in N, vt H N, ſit noua quædam ſectio commu-<lb/>nis Acquatoris, &amp; </s>
  <s xml:id="echoid-s20653" xml:space="preserve">Meridiani proprii plani declinantis, punctum{q́ue} N, illud, per quod noua linea æquino-<lb/>ctialis ducenda eſſet ad lineam ſtyli perpendicularis. </s>
  <s xml:id="echoid-s20654" xml:space="preserve">Abſciſſa autem recta C O, ipſi H N, æquali, deſcri <lb/>bantur ex centro horologii C, ad interualla C N, C O, duo circuli, &amp; </s>
  <s xml:id="echoid-s20655" xml:space="preserve">in minori ducatur diameter S T, <lb/>ad N R, diametrũ maioris perpendicularis: </s>
  <s xml:id="echoid-s20656" xml:space="preserve">erit{q́ue}, N R, maior diameter Ellipſis, &amp; </s>
  <s xml:id="echoid-s20657" xml:space="preserve">S T, minor; </s>
  <s xml:id="echoid-s20658" xml:space="preserve">quemad-<lb/>modũ in horizontali horologio maior diameter eſt B V, &amp; </s>
  <s xml:id="echoid-s20659" xml:space="preserve">minor R X. </s>
  <s xml:id="echoid-s20660" xml:space="preserve">Iam verò puncta Ellipſis, per quæ <lb/>horæ ducendæ ſunt, inuenientur, vt in horologio horizontali dictum est, ſi dicti duo circuli in 24. </s>
  <s xml:id="echoid-s20661" xml:space="preserve">partes <lb/>æquales ſecentur, initio facto non à linea meridiana propria plani declinantis, hoc eſt, à linea styli R N, <lb/>
<anchor type="note" xlink:label="note-0322-06a" xlink:href="note-0322-06"/>
ſed ab alia quadam recta, quam ita reperiemus. </s>
  <s xml:id="echoid-s20662" xml:space="preserve">Ex L, centro circuli, beneficio cuius in pręcedenti de-<lb/>ſcriptione in linea æquinoctiali α G, puncta horaria inuestigauimus (quod quidem centrum diſtat à pun-<lb/>cto G, interuallo G I) ducatur per punctum M, vbi æquinoctialis linea &amp; </s>
  <s xml:id="echoid-s20663" xml:space="preserve">meridiana ſe mutuo ſecant, re-<lb/>cta L M, &amp; </s>
  <s xml:id="echoid-s20664" xml:space="preserve">angulo C L M, conſtituatur ad rectam C L, in centro C, ęqualis L C P, ex eadem parte, ex <lb/>qua punctum M, exiſtit. </s>
  <s xml:id="echoid-s20665" xml:space="preserve">Nam à recta P Q, inchoanda eſt diuiſio circulorum. </s>
  <s xml:id="echoid-s20666" xml:space="preserve">Idem punctum P, à quo <lb/>diniſio incipit, reperiemus, ſi ex N, verſus meridianam lineam C M, ſupputem{us} arcum Aequatoris in-<lb/>teriectum inter Meridianum proprium plani declinantis, &amp; </s>
  <s xml:id="echoid-s20667" xml:space="preserve">Meridianum Horizontis, vſque ad P: </s>
  <s xml:id="echoid-s20668" xml:space="preserve">qui <lb/>arcus in noſtro exemplo continet grad. </s>
  <s xml:id="echoid-s20669" xml:space="preserve">40. </s>
  <s xml:id="echoid-s20670" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s20671" xml:space="preserve">48. </s>
  <s xml:id="echoid-s20672" xml:space="preserve">fere. </s>
  <s xml:id="echoid-s20673" xml:space="preserve">Tanta enim eſt fere inclinatio dictorum Meri-<lb/>dianorum inuenta ex propoſ. </s>
  <s xml:id="echoid-s20674" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20675" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20676" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20677" xml:space="preserve">vt ſupra dixim{us}. </s>
  <s xml:id="echoid-s20678" xml:space="preserve">Itaque ſit inueniendum punctum Ellipſis, per <lb/>quod hora 12. </s>
  <s xml:id="echoid-s20679" xml:space="preserve">ducenda ſit. </s>
  <s xml:id="echoid-s20680" xml:space="preserve">Per P, punctum horę 12. </s>
  <s xml:id="echoid-s20681" xml:space="preserve">in maiori circulo ducatur minori Ellipſis diametro <lb/>S T, parallela P Z; </s>
  <s xml:id="echoid-s20682" xml:space="preserve">(quæ facile ducetur, ſi arcui P N, ſumatur æqualis N V. </s>
  <s xml:id="echoid-s20683" xml:space="preserve">Recta enim P V, paralle-
<pb o="307" file="0323" n="323" rhead="LIBER TERTIVS."/>
la erit ipſi S T, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s20684" xml:space="preserve">27. </s>
  <s xml:id="echoid-s20685" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20686" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20687" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20688" xml:space="preserve">ob æquales arcus inter puncta P, V, &amp; </s>
  <s xml:id="echoid-s20689" xml:space="preserve">diametrũ S T, <lb/>productam interceptos) &amp; </s>
  <s xml:id="echoid-s20690" xml:space="preserve">per punctum Y, horæ 12. </s>
  <s xml:id="echoid-s20691" xml:space="preserve">in minori circulo agatur maiori Ellipſis diametro <lb/>R N, par allela Y Z, (quæ eadem facilitate ducetur, ſi arcui S Y, æqualis accipiatur arcus S X. </s>
  <s xml:id="echoid-s20692" xml:space="preserve">Recta <lb/>euim X Y, ex epdem ſcholio propoſ. </s>
  <s xml:id="echoid-s20693" xml:space="preserve">27. </s>
  <s xml:id="echoid-s20694" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20695" xml:space="preserve">3. </s>
  <s xml:id="echoid-s20696" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s20697" xml:space="preserve">parallela erit ipſi R N, ob ęquales arcus inter puncta <lb/>Y, X, &amp; </s>
  <s xml:id="echoid-s20698" xml:space="preserve">diametrum R N, interiectos) ſecans P Z, in Z. </s>
  <s xml:id="echoid-s20699" xml:space="preserve">Erit ergo Z, punctum Ellipſis, cuius diametri <lb/>R N, S T, vt conſtat ex coroll. </s>
  <s xml:id="echoid-s20700" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s20701" xml:space="preserve">26. </s>
  <s xml:id="echoid-s20702" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20703" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20704" xml:space="preserve">Dico per idem ducendam eſſe lineam meridianam, ſeu <lb/>horę 12. </s>
  <s xml:id="echoid-s20705" xml:space="preserve">Intelligatur enim (poſito triangulo C H N, ad planum horologii recto, ita vt cum Meridiano <lb/>proprio plani declinantis ſit coniunctum) in plano Aequatoris ex H, centro mundi, Aequatorisve de-<lb/>ſcriptus ad interuallum H N, circulus N h ſ m, circulo O S T, æqualis, qui baſis ſit cylindri recti, cu-<lb/>ius axis idem qui axis mundi C H, &amp; </s>
  <s xml:id="echoid-s20706" xml:space="preserve">ſemicirculus N h ſ, vergat verſus punctum P, ſeu lineam meri-<lb/>
<anchor type="note" xlink:label="note-0323-01a" xlink:href="note-0323-01"/>
dianam, in quo ſumatur arcus N h, arcui O Y, æqualis, vel ipſi N P, ſimilis. </s>
  <s xml:id="echoid-s20707" xml:space="preserve">Ducetur per h, Meridia-<lb/>n{us} Horizontis, quandoquidem arcus N h, ſimilis eſt arcui Aequatoris inter Meridianum Horizontis, <lb/>&amp; </s>
  <s xml:id="echoid-s20708" xml:space="preserve">proprium Meridianum plani declinantis poſito. </s>
  <s xml:id="echoid-s20709" xml:space="preserve">Igitur latus cylindri ex puncto h, ductum, per quod <lb/>planum Meridiani Horizontis, vel circuli horę 12. </s>
  <s xml:id="echoid-s20710" xml:space="preserve">ducitur, cadet in punctum Ellipſis Z, ob ſimilitudi-<lb/>nem arcuum N h, N P, vt constat ex demonſtratis in ſcholio propoſ. </s>
  <s xml:id="echoid-s20711" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20712" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s20713" xml:space="preserve">Ibi enim, quia ar-<lb/>cus B P, B F, ſimiles erant, demonſtrauimus latus cylindri ex P, ductũ cadere in punctũ Ellipſis L, &amp; </s>
  <s xml:id="echoid-s20714" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s20715" xml:space="preserve">Eadem ratione ſi per puncta Q, u, oppoſita punctis P, Y, ducamus duas lineas duabus diametris Elli-<lb/>pſis parallelas, reperiemus aliud punctum δ, per quod eadem linea meridiana ducenda eſt. </s>
  <s xml:id="echoid-s20716" xml:space="preserve">Nam in illud <lb/>punctum cadet latus cylindri ductum ex puncto m, quod opponitur puncto h, per quod nimirum ducitur <lb/>Meridianus Horizontis, propter ſimi itudinem arcuum N m, N Q. </s>
  <s xml:id="echoid-s20717" xml:space="preserve">Sic etiam ex punctis a, b, horæ 6. </s>
  <s xml:id="echoid-s20718" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0323-02a" xlink:href="note-0323-02"/>
inuenietur punctum f, per quod hora 6. </s>
  <s xml:id="echoid-s20719" xml:space="preserve">ducenda eſt, &amp; </s>
  <s xml:id="echoid-s20720" xml:space="preserve">ex puncto t, oppoſito in maiore circulo, eius{q́ue} re-<lb/>ſpondente in minori circulo, aliud punctũ oppoſitum, per quod eadem hora 6. </s>
  <s xml:id="echoid-s20721" xml:space="preserve">ducẽda eſt. </s>
  <s xml:id="echoid-s20722" xml:space="preserve">Atque it a de cæ-<lb/>teris. </s>
  <s xml:id="echoid-s20723" xml:space="preserve">Vides igitur puncta Z, δ, cadere in lineam meridianam in initio ductam, &amp; </s>
  <s xml:id="echoid-s20724" xml:space="preserve">lineam horæ 6. </s>
  <s xml:id="echoid-s20725" xml:space="preserve">du-<lb/>ctam per f, eius{q́ue} punctum oppoſitum, tranſire per punctum α, per quod in præcedenti deſcriptione du-<lb/>cendam eſſe horam 6. </s>
  <s xml:id="echoid-s20726" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s20727" xml:space="preserve">Denique vides lineam horæ 3. </s>
  <s xml:id="echoid-s20728" xml:space="preserve">quæ vix ſine errore in precedenti deſcri-<lb/>ptione duci poterat, exquiſitiſſime duci poſſe beneficio huius ellipſis, &amp; </s>
  <s xml:id="echoid-s20729" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20730" xml:space="preserve">In noſtro exemplo, quoniam li-<lb/>nea ſtyli inęqualiter diſtat à binis horis hinc inde poſitis, inæqualiter etiam diſtabunt diametri Ellipſis à <lb/>binis punctis ex vtraque parte inuentis. </s>
  <s xml:id="echoid-s20731" xml:space="preserve">Vnde (quod ad demonſtrationem attinet) in circulo Aequatori <lb/>concentrico N h ſ m, à ſingulis horis ducendę erunt ad diametrũ ſ N, perpendiculares ſingulæ, per quas <lb/>ducenda ſunt plana axi parallela, vt fiant parallelogramma, quorum latera ex horis ducta cadunt in pun <lb/>
<anchor type="note" xlink:label="note-0323-03a" xlink:href="note-0323-03"/>
cta Ellipſis, vt in ſch olio dicto propoſ. </s>
  <s xml:id="echoid-s20732" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20733" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s20734" xml:space="preserve">demonstratum eſt. </s>
  <s xml:id="echoid-s20735" xml:space="preserve">In figura propoſita perpendi. <lb/></s>
  <s xml:id="echoid-s20736" xml:space="preserve">culares h g, m l, ducuntur ab hora 12. </s>
  <s xml:id="echoid-s20737" xml:space="preserve">tam meridiei, quàm mediæ noctis, perpendiculares autem p n<unsure/>, q r, <lb/>ab hora 6. </s>
  <s xml:id="echoid-s20738" xml:space="preserve">tam à mer. </s>
  <s xml:id="echoid-s20739" xml:space="preserve">quàm à med. </s>
  <s xml:id="echoid-s20740" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s20741" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1055" type="float" level="2" n="10">
<note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>beneficio Elli-<lb/>pſis.</note>
<note position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0322-01" xlink:href="fig-0322-01a">
    <image file="0322-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0322-01"/>
  </figure>
<note position="left" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0322-04" xlink:href="note-0322-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0322-05" xlink:href="note-0322-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0322-06" xlink:href="note-0322-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0323-01" xlink:href="note-0323-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0323-02" xlink:href="note-0323-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0323-03" xlink:href="note-0323-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s20742" xml:space="preserve">PORRO cum declinatio plani horologĳ à Verticali circulo tanta eſt, vt parum à grad. </s>
  <s xml:id="echoid-s20743" xml:space="preserve">90. </s>
  <s xml:id="echoid-s20744" xml:space="preserve">diffe-<lb/>
<anchor type="note" xlink:label="note-0323-04a" xlink:href="note-0323-04"/>
rat, ac proinde planum ipſum ferè cum Meridiano circulo coniungatur, vix per præcepta tradita con-<lb/>ſtruere quis poterit horologium, quin in difficultatem aliquam, eamq́, non leuem, incurrat. </s>
  <s xml:id="echoid-s20745" xml:space="preserve">Nam tunc li-<lb/>nea declinationis E F, valde prope accedit ad rectam A B, propterea{q́ue} nimis breuis efficitur recta F G, <lb/>&amp; </s>
  <s xml:id="echoid-s20746" xml:space="preserve">illi æqualis G H: </s>
  <s xml:id="echoid-s20747" xml:space="preserve">ex quo fit, axem C H, parum à linea ſtyli C H, diſtare, atque adeo ſtylum I K, fo-<lb/>re breuiſſimum, ita vt quaſi inutile horologium ipſum reddatur. </s>
  <s xml:id="echoid-s20748" xml:space="preserve">Quòd ſi velimus rectam F G, eſſe maio <lb/>ris cuiuſdam, &amp; </s>
  <s xml:id="echoid-s20749" xml:space="preserve">aptę, conuenientis{q́ue} magnitudinis, quis non videt, punctum F, futurum à puncto E, ni-<lb/>
<anchor type="note" xlink:label="note-0323-05a" xlink:href="note-0323-05"/>
mis remotum? </s>
  <s xml:id="echoid-s20750" xml:space="preserve">ideo{q́ue} &amp; </s>
  <s xml:id="echoid-s20751" xml:space="preserve">puncta G, β, C, ab eodem puncto E, ptuſquam deceat, excurſura? </s>
  <s xml:id="echoid-s20752" xml:space="preserve">Quæ ſanè res <lb/>non parum difficultatis, ac laboris in ſe continet, quòd tunc immenſum ferè planum ad horologii deſcri-<lb/>ptionem ſit neceſſarium. </s>
  <s xml:id="echoid-s20753" xml:space="preserve">Quod inde etiam constare poteſt, quòd lineæ horariæ (quę in horologio Meridia-<lb/>no parallelę ſunt, vt iamdudum propoſ. </s>
  <s xml:id="echoid-s20754" xml:space="preserve">25. </s>
  <s xml:id="echoid-s20755" xml:space="preserve">ſuperioris libri demonſtrauimus) in plano horologii, quod pa-<lb/>rum à Meridiano circulo diſtat, parallelæ inter ſe quaſi videantur; </s>
  <s xml:id="echoid-s20756" xml:space="preserve">præſertim quando declinatio fueri@ <lb/>grad. </s>
  <s xml:id="echoid-s20757" xml:space="preserve">89. </s>
  <s xml:id="echoid-s20758" xml:space="preserve">88. </s>
  <s xml:id="echoid-s20759" xml:space="preserve">vel 87. </s>
  <s xml:id="echoid-s20760" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20761" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20762" xml:space="preserve">Verum incommodo huic remedium afferemus ſimile ferè illi, quod in ſcholio <lb/>propoſ. </s>
  <s xml:id="echoid-s20763" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20764" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s20765" xml:space="preserve">pro horologio horizontali ſcripſimus, ita vt per præcepta ferè hactenus tradita horo-<lb/>logium declinans deſcribamus, quantumuis parum à circulo Meridiano diſtans, licet centrum horologii <lb/>(quod tunc plus æquo à puncto E, diſtet, neceſſe eſt, ſi cupimus habere ſtylum tantæ magnitudinis, vt <lb/>commodè horas indicare poſſit) nobis prorſus ſit ignotum, quippe quod in planum (niſi illud immenſam <lb/>
<anchor type="note" xlink:label="note-0323-06a" xlink:href="note-0323-06"/>
quodammodo habeat magnitudinem) cadere non poſſit, ſed extra ipſum exiſtat. </s>
  <s xml:id="echoid-s20766" xml:space="preserve">Hoc autem artifi-<lb/>cio vtemur.</s>
  <s xml:id="echoid-s20767" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1056" type="float" level="2" n="11">
<note position="right" xlink:label="note-0323-04" xlink:href="note-0323-04a" xml:space="preserve">Quando horo-<lb/>logii planum <lb/>parum à Meri-<lb/>diano c@culo <lb/>abeſt, difficul-<lb/>ter horologium <lb/>per tradita præ <lb/>cepta deſcribi <lb/>potcſt.</note>
<note position="left" xlink:label="note-0323-05" xlink:href="note-0323-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0323-06" xlink:href="note-0323-06a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s20768" xml:space="preserve">IN plano aliquo ductis duabus rectis A B, C D, ſe mutuo ad angulos rectos ſecantibus in E, puncto, <lb/>
<anchor type="note" xlink:label="note-0323-07a" xlink:href="note-0323-07"/>
constituatur in E, ad rectam C D, angulus declinationis infra, vel ſupra rectam A B, &amp; </s>
  <s xml:id="echoid-s20769" xml:space="preserve">ad dextram, <lb/>vel ſiniſtram rectę C D, prout planum à meridie, vel borea in ortum, occaſumve declinat, vt ad initium <lb/>huius propoſ. </s>
  <s xml:id="echoid-s20770" xml:space="preserve">ſcripſimus. </s>
  <s xml:id="echoid-s20771" xml:space="preserve">In hoc propoſito exemplo ponimus declinationem plani à circulo Verticali in <lb/>ortum grad. </s>
  <s xml:id="echoid-s20772" xml:space="preserve">60. </s>
  <s xml:id="echoid-s20773" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20774" xml:space="preserve">à Meridiano grad. </s>
  <s xml:id="echoid-s20775" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20776" xml:space="preserve">propterea angulus declinationis D E F, conſtitutus eſt infra <lb/>rectam A B, verſus A. </s>
  <s xml:id="echoid-s20777" xml:space="preserve">Non aſſumimus autem maiorem declinationem, vt magis perſpicua reddatur <lb/>deſcriptio hæc noſtra, eius demonſtratio planior fiat.</s>
  <s xml:id="echoid-s20778" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1057" type="float" level="2" n="12">
<note position="right" xlink:label="note-0323-07" xlink:href="note-0323-07a" xml:space="preserve">Quo pacto ho-<lb/>rologiũ deſcri-<lb/>ba@u@ in plano, <lb/>quod parum à <lb/>Meridiano cir-<lb/>culo abeſt, licet <lb/>centrum horo-<lb/>log@ non ha-<lb/>beatur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s20779" xml:space="preserve">POST hæc in recta A B, ſumpto quocunque puncto G, ſiue verſus eam partem, in quam linea de-<lb/>clinationis vergit à recta C D, ſiue in partem contrariam, quod magis placet, (quamuis in exemplo ex
<pb o="308" file="0324" n="324" rhead="GNOMONICES"/>
e<unsure/>adem parte illud acceptum ſit) constituatur ad rectam A B, in puncto G, angulus altitudinis poll <lb/>E G C, ſurſum, aut deorſum verſus, prout planum à meridie, vel à borea declinat; </s>
  <s xml:id="echoid-s20780" xml:space="preserve">ſecetq́, recta G C, <lb/>rectam C D, in C. </s>
  <s xml:id="echoid-s20781" xml:space="preserve">Abſciſſa quoque ex E F, recta E F, ipſi E G, æquali, ducatur ex F, ad A B, perpen-<lb/>dicularis F H. </s>
  <s xml:id="echoid-s20782" xml:space="preserve">Sed quoniam propter anguſtiam ſpatĳ inter rectas A B, E F, interiecti (vt euenire ſo-<lb/>
<anchor type="figure" xlink:label="fig-0324-01a" xlink:href="fig-0324-01"/>
<anchor type="note" xlink:label="note-0324-01a" xlink:href="note-0324-01"/>
<anchor type="note" xlink:label="note-0324-02a" xlink:href="note-0324-02"/>
<anchor type="note" xlink:label="note-0324-03a" xlink:href="note-0324-03"/>
<anchor type="note" xlink:label="note-0324-04a" xlink:href="note-0324-04"/>
let, cum valde magna eſt declinatio propoſita) non facile abſque errore ex puncto F, ad rectam A B, <lb/>duci poteſt perpendicularis, instituere poſſumus eandem hanc conſtructionem commodius in hanc formã. <lb/></s>
  <s xml:id="echoid-s20783" xml:space="preserve">Sumpto in recta A B, verſus eam partem, in quam ducta eſt recta E F, puncto quolibet H, ducatur ex <lb/>eo ad A B, perpendicularis H F, ſecans E F, in F. </s>
  <s xml:id="echoid-s20784" xml:space="preserve">Nam ſi ipſi E F, abſcindamus æqualem rectam E G, <lb/>&amp; </s>
  <s xml:id="echoid-s20785" xml:space="preserve">in G, ad rectam E G, angulum E G C, conſtituamus altitudinis poli, reperiemus punctum C, idem <lb/>quod prius, ſed certius aliquanto; </s>
  <s xml:id="echoid-s20786" xml:space="preserve">eo quòd facilius ſit ex accepto puncto H, in linea A B, ad eandem du-<lb/>cere perpendicularem ſine errore, quàm ex puncto F, ipſi rectę A B, viciniſſimo.</s>
  <s xml:id="echoid-s20787" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1058" type="float" level="2" n="13">
  <figure xlink:label="fig-0324-01" xlink:href="fig-0324-01a">
    <image file="0324-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0324-01"/>
  </figure>
<note position="left" xlink:label="note-0324-01" xlink:href="note-0324-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0324-02" xlink:href="note-0324-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0324-03" xlink:href="note-0324-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0324-04" xlink:href="note-0324-04a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s20788" xml:space="preserve">DEINDE ducta per C, &amp; </s>
  <s xml:id="echoid-s20789" xml:space="preserve">H, recta C H, ea{q́ue} quantumlibet producta, ducatur ad eam per H, <lb/>perpendicularis H I, in qua ſi abſcindatur H I, ipſi H F, ęqualis, recta{q́ue} C I, ducatur; </s>
  <s xml:id="echoid-s20790" xml:space="preserve">Item ducta <lb/>F N, ad E F, perpendiculari ſecante A B, rectam in N, puncto, quod cum C, recta linea C N, iunga-<lb/>
<anchor type="note" xlink:label="note-0324-05a" xlink:href="note-0324-05"/>
tur; </s>
  <s xml:id="echoid-s20791" xml:space="preserve">erit ex iis, quę prope initium huius propoſ. </s>
  <s xml:id="echoid-s20792" xml:space="preserve">demonſtrauimus, recta C D, linea horę 12. </s>
  <s xml:id="echoid-s20793" xml:space="preserve">in plano datæ <lb/>declinationis; </s>
  <s xml:id="echoid-s20794" xml:space="preserve">punctum C, centrum horologii declinantis; </s>
  <s xml:id="echoid-s20795" xml:space="preserve">C H, linea indicis, ſeu ſtyli; </s>
  <s xml:id="echoid-s20796" xml:space="preserve">C N, linea horæ <lb/>6. </s>
  <s xml:id="echoid-s20797" xml:space="preserve">C I, axis mundi; </s>
  <s xml:id="echoid-s20798" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20799" xml:space="preserve">H I, linea æquinoctialis. </s>
  <s xml:id="echoid-s20800" xml:space="preserve">Quòd ſi rurſus ducamus ex H, ad C I, perpendicularem <lb/>H K, erit hæc, ex demonſtratis quoque, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s20801" xml:space="preserve">plani, quod per rectam C H, <lb/>ductum ad planum horologii rectum eſt, inſtar Meridiani cuiuſdam proprii ipſius plani horologii. </s>
  <s xml:id="echoid-s20802" xml:space="preserve">Vnde <lb/>ſi in linea ſtyli C H, acciperetur recta H L, ipſi H K, ęqualis, &amp; </s>
  <s xml:id="echoid-s20803" xml:space="preserve">ex L, deſcriberetur circulus, conſtrue <lb/>retur horologium declinans, cuius omnes lineę horarię in C, coirent, proinde vt in priori deſcriptione <lb/>huius propoſ. </s>
  <s xml:id="echoid-s20804" xml:space="preserve">factum est. </s>
  <s xml:id="echoid-s20805" xml:space="preserve">Sed quia hoc modo conſtructi horologii ſtylus K M, ex K, in rectam C H, ca-<lb/>dens ad angulos rectos in punctum M, nimis breuis eſt, præſertim quando recta E F, parum à recta A B, <lb/>diſtat, (diſtabit autem eò min{us}, quò maior fuerit declinatio plani à Verticali, vt dictum eſt) idcirco <lb/>progrediendum nobis eſt, atque docendum, qua ratione maius horologium deſcribere poſſimus, quod aptũ,
<pb o="309" file="0325" n="325" rhead="LIBER TERTIVS."/>
&amp; </s>
  <s xml:id="echoid-s20806" xml:space="preserve">vſui accommodatum ſtylum recipiat, licet in propoſito nobis plano, in quo delineandum eſt horologiũ, <lb/>centrum horologii notari non poſſit, ac prcinde fortaſſis neque linea horę 12. </s>
  <s xml:id="echoid-s20807" xml:space="preserve">niſi planum in latitudinem <lb/>@@gis porrigatur, quàm in altitudinem, adeò vt hora 12. </s>
  <s xml:id="echoid-s20808" xml:space="preserve">quidem deſignaripoſſit, plano ob inſignem lati-<lb/>tudinem, quam habet, ipſam recipiente, centrum verò propter modicam altitudinem eiuſdem plani de-<lb/>ſcribi non poſſit. </s>
  <s xml:id="echoid-s20809" xml:space="preserve">Quamuis enim lineæ horariæ ex C, prodeuntes, quæ per puncta æquinoctialis lineę H I, <lb/>inuenta beneficio circuli ex L, deſcripti ducuntur, ſemper magis ac magis inter ſe diſtent, ſi producãtur, <lb/>atque adeo ex aliquo puncto lineæ indicis C L, infra punctum M, ſtylus maior duci poſſit perpendicularis <lb/>ad C L, vſque ad axem C I, productum, vt in ſcbolio propoſ. </s>
  <s xml:id="echoid-s20810" xml:space="preserve">ſequentis docebimus, cum maius aut minus <lb/>horologium deſcribemus ex iisdem lineamentis, pro data magnitudine ſtyli: </s>
  <s xml:id="echoid-s20811" xml:space="preserve">tamen, quia cum planum à <lb/>meridiano parum deflectit, lineæ borariæ ferè parallelæ ſunt, ita vt opus ſit in infinitum ferè illas produ-<lb/>
<anchor type="note" xlink:label="note-0325-01a" xlink:href="note-0325-01"/>
cere, antequam ſtylum propoſitæ magnitudinis ducere poſſimus, idcir co aliam rationem inire oportet. </s>
  <s xml:id="echoid-s20812" xml:space="preserve">Ita <lb/>igitur rem proſequemur.</s>
  <s xml:id="echoid-s20813" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1059" type="float" level="2" n="14">
<note position="left" xlink:label="note-0324-05" xlink:href="note-0324-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0325-01" xlink:href="note-0325-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s20814" xml:space="preserve">IN æquinoctiali linea H I, ſumatur punctum O, quodcunque, tantò remotius ab H, quantò amplius <lb/>borologium deſideratur, at que ſtylus longior; </s>
  <s xml:id="echoid-s20815" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20816" xml:space="preserve">per O, agatur axi I C, parallela O P, ad quam ex H, <lb/>perpendic@laris ducatur H Q, quæ cum etiam perpendicularis ſit ad I C, ipſi O P, parallelam, tranſi-<lb/>
<anchor type="note" xlink:label="note-0325-02a" xlink:href="note-0325-02"/>
bit omnino pork, quòd &amp; </s>
  <s xml:id="echoid-s20817" xml:space="preserve">H K, perpendicularis ſit ducta ad I C: </s>
  <s xml:id="echoid-s20818" xml:space="preserve">alioquin ex H, ad I C, duæ perpendi-<lb/>culares ducerentur. </s>
  <s xml:id="echoid-s20819" xml:space="preserve">quod abſurdum eſt. </s>
  <s xml:id="echoid-s20820" xml:space="preserve">Deinde ex H F, producta, quę ad A B, perpendicularis eſt, abſcin <lb/>datur ipſi H O, ęqualis H R; </s>
  <s xml:id="echoid-s20821" xml:space="preserve">ducta{q́ue} R S, ipſi F E, parallela, excitetur ex R, ad R S, perpendicularis R T, <lb/>vol ipſi F N, parallela, ſecans A B, in T, puncto, per quod ipſi C N, parallela agatur T V, ſecans æqui-<lb/>noctialem lineam H O, in X.</s>
  <s xml:id="echoid-s20822" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1060" type="float" level="2" n="15">
<note position="right" xlink:label="note-0325-02" xlink:href="note-0325-02a" xml:space="preserve">29. primi.</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s20823" xml:space="preserve">AD hęc, ſumpto in linea ſtyli H C, quocunque puncto Y, ducatur per illud rectę H Q, parallela <lb/>Y P, ſecans O P, in P, quæ ad O P, perpendicularis erit, quemadmodum &amp; </s>
  <s xml:id="echoid-s20824" xml:space="preserve">H Q: </s>
  <s xml:id="echoid-s20825" xml:space="preserve">Item per Y, ducatur <lb/>
<anchor type="note" xlink:label="note-0325-04a" xlink:href="note-0325-04"/>
ad H Y, perpendicularis Y V, vel ipſi H O, parallela, ſecans T V, in V.</s>
  <s xml:id="echoid-s20826" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1061" type="float" level="2" n="16">
<note position="right" xlink:label="note-0325-04" xlink:href="note-0325-04a" xml:space="preserve">29. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s20827" xml:space="preserve">POSTREMO ſumptis in recta H Y, rectis H Z, Y a, que rectis H Q, Y P, ęquales ſint, deſcri-<lb/>bantur ex Z, a, circuli, ĳ{q́ue} in partes 24. </s>
  <s xml:id="echoid-s20828" xml:space="preserve">ęquales ſecentur, initio facto à rectis, quę ex centris Z, a, <lb/>per puncta X, V, ducuntur. </s>
  <s xml:id="echoid-s20829" xml:space="preserve">Nam rectę occultæ per centra Z, a, &amp; </s>
  <s xml:id="echoid-s20830" xml:space="preserve">puncta diuiſionum ductæ ſecabunt <lb/>rectas H O, Y V, in punctis, per quæ eductæ lineæ rectæ (ſumendo bina ſemper puncta inter ſe reſpon-<lb/>dentia, hoc eſt, duo proxima punctis H, Y, deinde ſequentia duo, &amp; </s>
  <s xml:id="echoid-s20831" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s20832" xml:space="preserve">dabunt lineas horarias, quas <lb/>eatenus hincinde producemus, quoad plani magnitudo patietur. </s>
  <s xml:id="echoid-s20833" xml:space="preserve">Earum enim longitudines ab arcubus <lb/>ſignorum terminabuntur. </s>
  <s xml:id="echoid-s20834" xml:space="preserve">Styli longitudo erit Q b, perpendicularis ex Q, ad H Y, demiſſa, eius{q́ue} lo-<lb/>
<anchor type="note" xlink:label="note-0325-05a" xlink:href="note-0325-05"/>
cus in puncto b, in quod dicta perpendicularis cadit. </s>
  <s xml:id="echoid-s20835" xml:space="preserve">Quæ omnia hac ratione comprobabimus.</s>
  <s xml:id="echoid-s20836" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1062" type="float" level="2" n="17">
<note position="left" xlink:label="note-0325-05" xlink:href="note-0325-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s20837" xml:space="preserve">QVONIAM recta R S, rectę F E, parallela cum recta A B, tandem aliquando conueniat ne-<lb/>
<anchor type="note" xlink:label="note-0325-06a" xlink:href="note-0325-06"/>
ceſſe eſt; </s>
  <s xml:id="echoid-s20838" xml:space="preserve">conueniat in puncto S, (hoc autem punctum S, vt plurimum extra planum, niſi immenſum fue <lb/>rit, cadet, cum remotiſſimum ſit à puncto E, ſi declinatio plani horologii parum à grad. </s>
  <s xml:id="echoid-s20839" xml:space="preserve">90. </s>
  <s xml:id="echoid-s20840" xml:space="preserve">differt. </s>
  <s xml:id="echoid-s20841" xml:space="preserve">Vnde <lb/>tunc animo concipiendum erit duntaxat) per quod ad A B, duci intelligatur perpendicularis S π, vel ipſi <lb/>C D, parallela, conueniens cum H C, productain π. </s>
  <s xml:id="echoid-s20842" xml:space="preserve">Et quoniam angulus H S R, angulo H E F, comple-<lb/>
<anchor type="note" xlink:label="note-0325-07a" xlink:href="note-0325-07"/>
menti declinationis datæ æqualis est; </s>
  <s xml:id="echoid-s20843" xml:space="preserve">ſi recta π S, accipiatur pro linea meridiana in plano horologii, erit <lb/>S R, linea declinationis. </s>
  <s xml:id="echoid-s20844" xml:space="preserve">In qua cum ex puncto R, ad A B, ducta ſit perpendicularis R H, ducenda erit <lb/>linea indicis per punctum H, vt in priori deſcriptione huius propoſ. </s>
  <s xml:id="echoid-s20845" xml:space="preserve">oſtenſum eſt, faciens cum meridiana <lb/>linea S π, angulum ęqualem angulo E C H, quem linea ſtyli C H, in horologio, cuius centrum C, facit cum <lb/>
<anchor type="note" xlink:label="note-0325-08a" xlink:href="note-0325-08"/>
meridiana linea C E; </s>
  <s xml:id="echoid-s20846" xml:space="preserve">propterea quòd in eodem plano declinante eundem ſemper angulum faciat linea <lb/>ſtyli cum linea meridiana, atque adeo &amp; </s>
  <s xml:id="echoid-s20847" xml:space="preserve">cum recta A B, quæ Horizonti æquidiſtat, quæcunque ſtyli lon-<lb/>gitudo accipiatur; </s>
  <s xml:id="echoid-s20848" xml:space="preserve">alias linea æquinoctialis ducenda per punctum H, perpendicularis ad lineam indicis, <lb/>vt demonſtratum eſt, non ſemper eoſdem angulos cum recta A B, conſtitueret. </s>
  <s xml:id="echoid-s20849" xml:space="preserve">quod est abſurdum. <lb/></s>
  <s xml:id="echoid-s20850" xml:space="preserve">Quod hac etiam ratione confirmari poteſt. </s>
  <s xml:id="echoid-s20851" xml:space="preserve">Quoniam tam planum Meridiani proprii ipſius plani decli-<lb/>nantis faciens in ipſo plano lineam styli, quàm planum horologii horizont alis per rectam A B, ductum, <lb/>vt ex ſuperioribus patet, rectum est ad planum horologii declinantis, erit quoque communis corum ſectio <lb/>
<anchor type="note" xlink:label="note-0325-09a" xlink:href="note-0325-09"/>
ad idem planum perpendicularis, occurrens ei in puncto H, per quod linea ſtyli, ideoq́, &amp; </s>
  <s xml:id="echoid-s20852" xml:space="preserve">Meridianus <lb/>proprius plani declinantis illam efficiens ducitur, vt dictum eſt; </s>
  <s xml:id="echoid-s20853" xml:space="preserve">ac propterea eadem ſectio, per defin. </s>
  <s xml:id="echoid-s20854" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s20855" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20856" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20857" xml:space="preserve">Euclidis rectos angulos faciet &amp; </s>
  <s xml:id="echoid-s20858" xml:space="preserve">cum recta H E, &amp; </s>
  <s xml:id="echoid-s20859" xml:space="preserve">cum linea indicis per H, ductam in plano ho <lb/>
<anchor type="note" xlink:label="note-0325-10a" xlink:href="note-0325-10"/>
rologii. </s>
  <s xml:id="echoid-s20860" xml:space="preserve">Igitur ex defin. </s>
  <s xml:id="echoid-s20861" xml:space="preserve">6. </s>
  <s xml:id="echoid-s20862" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s20863" xml:space="preserve">11. </s>
  <s xml:id="echoid-s20864" xml:space="preserve">Euclidis, cum viciſſim vtraque cum illa ſectione communi rectos angu-<lb/>los efficiat, angulus à recta H E, &amp; </s>
  <s xml:id="echoid-s20865" xml:space="preserve">linea indicis comprehenſus, erit angulus inclinationis plani, in quo <lb/>exiſtit dictus Meridianus proprius plani declinantis, ad planum horologii horizontalis: </s>
  <s xml:id="echoid-s20866" xml:space="preserve">ac proinde cum <lb/>bæc inclinatio in eodem plano declinante non mutetur, efficiet linea indicis cum recta H E, eundem ſem-<lb/>per angulum. </s>
  <s xml:id="echoid-s20867" xml:space="preserve">Quamobrem cum H C, ſit linea indicis oſtenſa in horologio, cuius centrum C, demonſtra-<lb/>tum{q́ue} ſit, lineam indicis in horologio, in quo linea meridiana π S, tranſire per H, erit H C, producta, li-<lb/>nea indicis in eodem hoc horologio, quandoquidem in H, eundem angulum facit, &amp; </s>
  <s xml:id="echoid-s20868" xml:space="preserve">in π, cum linea me-<lb/>ridiana π S, angulum æqualem angulo H C E, quem linea indicis in priore horologio cum meridiana li-<lb/>nea C E, conſtituit. </s>
  <s xml:id="echoid-s20869" xml:space="preserve">Aequales autem eſſe angulos H C E, H π S, perſpicuum eſt, propterea quòd C E, <lb/>
<anchor type="note" xlink:label="note-0325-11a" xlink:href="note-0325-11"/>
π S, parallelæ ſunt. </s>
  <s xml:id="echoid-s20870" xml:space="preserve">Hinc efficitur, punctum π, eſſe centrum illius horologii, in quo linea meridiana eſt <lb/>π S; </s>
  <s xml:id="echoid-s20871" xml:space="preserve">ſiquidem in centro horologii conueniunt linea indicis, &amp; </s>
  <s xml:id="echoid-s20872" xml:space="preserve">linea meridiana. </s>
  <s xml:id="echoid-s20873" xml:space="preserve">Efficitur quoquere-
<pb o="310" file="0326" n="326" rhead="GNOMONICES"/>
ctam H O, quæ perpendicularis est ad lineam indicis, eſſe lineam æquinoctialem eiuſdem horologii, vt ex <lb/>ſuperioribus conſtat.</s>
  <s xml:id="echoid-s20874" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1063" type="float" level="2" n="18">
<note position="right" xlink:label="note-0325-06" xlink:href="note-0325-06a" xml:space="preserve">Demonſtratio <lb/>conſtruction is <lb/>horologii parũ <lb/>ã Meridiano <lb/>declinanus.</note>
<note position="right" xlink:label="note-0325-07" xlink:href="note-0325-07a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0325-08" xlink:href="note-0325-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0325-09" xlink:href="note-0325-09a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0325-10" xlink:href="note-0325-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0325-11" xlink:href="note-0325-11a" xml:space="preserve">29. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s20875" xml:space="preserve">QVIA verò in æquinoctiali linea H O, recta H O, ipſi H R, ſumpta eſt æqualis, erit per ea, quæ <lb/>demonstrata ſunt, recta ex centro π, ad O, ducta axis mundi, conſtituens in π, cum linea ſtyli π H, <lb/>angulum O π H, æqualem angulo I C H, quem prior axis I C, cum linea indicis facit. </s>
  <s xml:id="echoid-s20876" xml:space="preserve">Nam idem ſem-<lb/>per est angulus altitudinis poli ſupra idem planum declinans, quem quidem axis mundi cum linea indicis <lb/>conſtituit, vt ex ſuperiorib{us} conſtat. </s>
  <s xml:id="echoid-s20877" xml:space="preserve">Quare paralleli erunt axes O π, I C; </s>
  <s xml:id="echoid-s20878" xml:space="preserve">ac proinde recta O P, quæ <lb/>
<anchor type="note" xlink:label="note-0326-01a" xlink:href="note-0326-01"/>
ipſi I C, parallela ducta eſt, etiamſi illam non producamus vſque ad centrum π, quod aliquando nobis eſt <lb/>ignotum, erit axis mundi. </s>
  <s xml:id="echoid-s20879" xml:space="preserve">Ex quo fit rectam H Q, ad axem perpendicularem, communem ſectionem <lb/>eſſe Aequatoris, ac Meridiani proprii ipſius plani declinantis.</s>
  <s xml:id="echoid-s20880" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1064" type="float" level="2" n="19">
<note position="left" xlink:label="note-0326-01" xlink:href="note-0326-01a" xml:space="preserve">28. primi.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s20881" xml:space="preserve">RVRSVS cum ex R, ad lineam declinationis S R, ducta ſit perpendicularis R T, tranſibit neceſ-<lb/>ſario per T, vt ſupra oſtendimus, linea horæ 6. </s>
  <s xml:id="echoid-s20882" xml:space="preserve">ac propterea recta ex centro π, per punctum T, educta <lb/>dabit horam 6. </s>
  <s xml:id="echoid-s20883" xml:space="preserve">faciet{q́ue} in π, cum linea ſtyli angulum T π H, æqualem angulo N C H, quem minoris ho-<lb/>rologii linea horæ 6. </s>
  <s xml:id="echoid-s20884" xml:space="preserve">C N, cum indicis linea C H, constituit. </s>
  <s xml:id="echoid-s20885" xml:space="preserve">Nam circulus horæ 6. </s>
  <s xml:id="echoid-s20886" xml:space="preserve">eandem ſeruat perpe-<lb/>tuo inclinationem ad Meridianum proprium vnius eiuſdemq́, plani declinantis; </s>
  <s xml:id="echoid-s20887" xml:space="preserve">ac propterea communes <lb/>ſectiones horum circulorum, quas cum eodem plano declinante faciunt, (ſumpta quacunque longitudine <lb/>ſtyli, per cuius verticem ducuntur) eundem ſemper angulum conſtituent, qui videlicet æqualis ſit angulo, <lb/>quem eorundem circulorum ſectiones in circulo maximo, cui planum horologii ęquidiſtat, factæ conſti-<lb/>tuunt. </s>
  <s xml:id="echoid-s20888" xml:space="preserve">Nam dictæ ſectiones æquales angulos constituunt in plano horologii, &amp; </s>
  <s xml:id="echoid-s20889" xml:space="preserve">in circulo maximo, cui <lb/>horologium ęquidistans eſt, vt prope finem huius propoſ. </s>
  <s xml:id="echoid-s20890" xml:space="preserve">demonſtr auimus de angulis, quos conſtituunt ſe-<lb/>
<anchor type="note" xlink:label="note-0326-03a" xlink:href="note-0326-03"/>
ctiones, quas Meridianus proprius plani declinantis, &amp; </s>
  <s xml:id="echoid-s20891" xml:space="preserve">Meridianus Horizontis faciunt in eodem plano <lb/>horologii, &amp; </s>
  <s xml:id="echoid-s20892" xml:space="preserve">in maximo circulo, cui hoc planum æquidiſtat. </s>
  <s xml:id="echoid-s20893" xml:space="preserve">Quocirca parallelæ erunt lineæ T π, N C, <lb/>
<anchor type="note" xlink:label="note-0326-04a" xlink:href="note-0326-04"/>
ac propterea recta T V, quam ipſi N C, parallelam duximus, licet ea vſque ad centrum π, quod fortaſ-<lb/>ſis in plano horologii non exiſtit, non producatur, erit linea horæ 6.</s>
  <s xml:id="echoid-s20894" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1065" type="float" level="2" n="20">
<note position="left" xlink:label="note-0326-03" xlink:href="note-0326-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0326-04" xlink:href="note-0326-04a" xml:space="preserve">28. primi.</note>
</div>
<p style="it">
  <s xml:id="echoid-s20895" xml:space="preserve">HAEC cum ita ſint, perſpicuum eſt ex demonſtratis in priore deſcriptione huius propoſ. </s>
  <s xml:id="echoid-s20896" xml:space="preserve">lineas horæ <lb/>rias ducendas eſſe per puncta illa rectæ H O, vbi ab occultis lineis ex centro Z, prodeuntibus ſecatur, <lb/>quandoquidem diuiſio circuli ex Z, deſcripti initium habet à recta, quæ per horam vnam tranſit in æqui-<lb/>noctiali linea H O, nempe à recta Z X, quę per horam 6. </s>
  <s xml:id="echoid-s20897" xml:space="preserve">tranſit. </s>
  <s xml:id="echoid-s20898" xml:space="preserve">Eadem ratione, cum Y P, ſit communis <lb/>ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s20899" xml:space="preserve">proprii Meridiani ipſius plani declinantis, vt ex demonſtratis patet, quòd perpen-<lb/>dicularis ſit ad axem eundem O P, ducendę eruni horariæ lineæ per puncta æquinoctialis lineę Y V, in <lb/>
<anchor type="note" xlink:label="note-0326-05a" xlink:href="note-0326-05"/>
quibus eam ſecant occultæ lineæ ex a, emiſſæ; </s>
  <s xml:id="echoid-s20900" xml:space="preserve">propterea quòd diuiſio circuli ex a, deſcripti initium quoque <lb/>habet à recta a V, quæ per horam 6. </s>
  <s xml:id="echoid-s20901" xml:space="preserve">ducitur in æquinoctiali linea Y V. </s>
  <s xml:id="echoid-s20902" xml:space="preserve">Rectè ergo lineæ horariæ ducun-<lb/>tur per puncta illa in rectis H O, Y V, inuenta, etiamſi centrum π, vbi omnes coirent, ſi producerentur, <lb/>ignotum nobis ſit, nempe extra planum exiſtens, vel certè remotiſſimum à puncto H. </s>
  <s xml:id="echoid-s20903" xml:space="preserve">In exemplo propo-<lb/>ſito, quia lineæ horæ 12. </s>
  <s xml:id="echoid-s20904" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20905" xml:space="preserve">1. </s>
  <s xml:id="echoid-s20906" xml:space="preserve">à meridie ſunt etiam deſcriptæ, perſpicuè apparet, rectas per centra Z, a, <lb/>duct{as}, quæ ad rectos angulos ſecant rectas Z X, a V, tranſeuntes per horam 6. </s>
  <s xml:id="echoid-s20907" xml:space="preserve">in vtraque æquinoctiali <lb/>linea, cadere in illa puncta linearum æquinoctialium H O, Y V, per quæ linea horæ 12. </s>
  <s xml:id="echoid-s20908" xml:space="preserve">ducitur; </s>
  <s xml:id="echoid-s20909" xml:space="preserve">ac pro-<lb/>inde eſſe ill{as}, à quib{us} diuiſiones circulorum ex Z, a, deſcriptorum inchoandę eſſent, vt ſupra docuim{us}. <lb/></s>
  <s xml:id="echoid-s20910" xml:space="preserve">Sed quia, vt dixim{us}, in planis, quæ nimium à Verticali declinant, neque line a horæ 12. </s>
  <s xml:id="echoid-s20911" xml:space="preserve">neque centrum <lb/>commodè notari poteſt, iuſſimus eaſdem diuiſiones inchoandas eſſe à rectis Z X, a V, &amp;</s>
  <s xml:id="echoid-s20912" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20913" xml:space="preserve">Stylum autem <lb/>
<anchor type="note" xlink:label="note-0326-06a" xlink:href="note-0326-06"/>
eſſe Q b, eius{q́ue} locum in b, ex dictis conſtat, cum triangulum π Q H, perinde ſit conſtructum vt triangu <lb/>lum C I G, in ſuperiori figur a hui{us} propoſitionis.</s>
  <s xml:id="echoid-s20914" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1066" type="float" level="2" n="21">
<note position="left" xlink:label="note-0326-05" xlink:href="note-0326-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0326-06" xlink:href="note-0326-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s20915" xml:space="preserve">CAETERVM quodcunque horologium declinans à meridie, ſeptentrioneve in ortum, vel occa-<lb/>
<anchor type="note" xlink:label="note-0326-07a" xlink:href="note-0326-07"/>
ſum, ſi lineamenta ita inter ſe permutent ordinem, vt ſinistra in dextra, &amp; </s>
  <s xml:id="echoid-s20916" xml:space="preserve">dextra in ſinistra conuertan-<lb/>tur, adeo vt talem ſitum adipiſcantur, qualem haberent lineamenta horologii, ſi in facie oppoſita plani <lb/>deſcripta eſſent, ea lege, vt ſingulæ lineę ſingulis lineis reſponderent, exhibebit nobis aliud horologium à <lb/>meridie, vel ſeptentrione declinans totidem gradib{us}, quot antea, ſed in contrariam partem; </s>
  <s xml:id="echoid-s20917" xml:space="preserve">ita vt ſi il-<lb/>lud à meridie, vel ſeptentrione in ortum deflectat, hoc à meridie quoque, vel ſeptentrione vergat in oc-<lb/>caſum, &amp; </s>
  <s xml:id="echoid-s20918" xml:space="preserve">ſi illud declinet in occaſum, hoc in ortum ſpectet. </s>
  <s xml:id="echoid-s20919" xml:space="preserve">Commutandi autem ſunt numeri horarum <lb/>in earundem complementa vſque ad 12. </s>
  <s xml:id="echoid-s20920" xml:space="preserve">vt hora 1. </s>
  <s xml:id="echoid-s20921" xml:space="preserve">in 11. </s>
  <s xml:id="echoid-s20922" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20923" xml:space="preserve">2. </s>
  <s xml:id="echoid-s20924" xml:space="preserve">in 10. </s>
  <s xml:id="echoid-s20925" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s20926" xml:space="preserve">c. </s>
  <s xml:id="echoid-s20927" xml:space="preserve">Hac arte vides in ſequenti <lb/>
<anchor type="note" xlink:label="note-0326-08a" xlink:href="note-0326-08"/>
figura ex ſuperiore horologio declinante à meridie in ortum grad. </s>
  <s xml:id="echoid-s20928" xml:space="preserve">30. </s>
  <s xml:id="echoid-s20929" xml:space="preserve">fabricatum eſſe horologium decli-<lb/>nans à meridie in occaſum grad. </s>
  <s xml:id="echoid-s20930" xml:space="preserve">30.</s>
  <s xml:id="echoid-s20931" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1067" type="float" level="2" n="22">
<note position="left" xlink:label="note-0326-07" xlink:href="note-0326-07a" xml:space="preserve">Si lineamenta <lb/>cuiuſcũque ho-<lb/>rologii declinã <lb/>tis a meridi<unsure/>e, ſe <lb/>ptẽttioneve in <lb/>or@um ita im-<lb/>mutentur, vt <lb/>dextra fiant ſi-<lb/>niſtra, &amp; cõtra, <lb/>habebitur a <lb/>liud horologiũ <lb/>declinans à me <lb/>ridie ſeptentrio <lb/>neve in occasũ, <lb/>&amp; e contrario.</note>
<note position="left" xlink:label="note-0326-08" xlink:href="note-0326-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s20932" xml:space="preserve">RATIO huiuſce rei obſcura non eſt, ſi attentè, &amp; </s>
  <s xml:id="echoid-s20933" xml:space="preserve">diligenter præcepta hui{us} propoſ. </s>
  <s xml:id="echoid-s20934" xml:space="preserve">conſiderentur. <lb/></s>
  <s xml:id="echoid-s20935" xml:space="preserve">Quoniam enim duobus horologĳs à meridie, vel ſeptentrione in diuerſas partes declinantib{us}, nempe vno <lb/>in ortum, &amp; </s>
  <s xml:id="echoid-s20936" xml:space="preserve">in occaſum altero, linea declinationis E F, in oppoſit{as} partes ducitur ex puncto E, vt di-<lb/>ctum eſt, fit vt &amp; </s>
  <s xml:id="echoid-s20937" xml:space="preserve">linea ſtyliex centro C, in contrari{as} partes quoque protendatur, cum ea ducatur ex <lb/>C, per punctum G, in quod cadit F G, ducta ex F, puncto lineæ declinationis ad A B, perpendicularis, <lb/>&amp; </s>
  <s xml:id="echoid-s20938" xml:space="preserve">ob id linea quoque ęquinoctialis lineam ſtyli ad angulos rectos ſecans ſit{us} contrarios obtineat. </s>
  <s xml:id="echoid-s20939" xml:space="preserve">Eo-<lb/>dem pacto linea horæ 6. </s>
  <s xml:id="echoid-s20940" xml:space="preserve">quæ ex C, ducitur per illud punctum rectę A B, in quod cadit F α, ducta ex F, <lb/>ad lineam declinationis ad angulos rectos, non poterit habere eundem ſitum in vtroque horologio, idem{q́ue} <lb/>de alĳs lineis dicendum eſt. </s>
  <s xml:id="echoid-s20941" xml:space="preserve">Vnde cum lineę vni{us} horologĳ eaſdem inter ſe habeant diſtantias, qu{as}
<pb o="311" file="0327" n="327" rhead="LIBER TERTIVS."/>
in altero habent, propterea quòd &amp; </s>
  <s xml:id="echoid-s20942" xml:space="preserve">ſtyli ſumuntur æquales, &amp; </s>
  <s xml:id="echoid-s20943" xml:space="preserve">declinatio in vtroque eadem ponitur, li-<lb/>cet in contrari{as} ea partes vergat, fit vt lineamenta, quæ nobis ad vnum horologium conuerſis dextra <lb/>ſunt, in alio exiſtant ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s20944" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s20945" xml:space="preserve"/>
</p>
  <figure>
    <image file="0327-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0327-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s20946" xml:space="preserve">CAVSA quoque mutationis numerorum horarum in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s20947" xml:space="preserve">perſpicua <lb/>eſt. </s>
  <s xml:id="echoid-s20948" xml:space="preserve">Quoniam enim, vt ſupra dixim{us}, in auſtralib{us} horologiis horæ poſitæ ad dextram lineæ meridianę <lb/>
<anchor type="note" xlink:label="note-0327-03a" xlink:href="note-0327-03"/>
numerandæ ſunt à meridie, &amp; </s>
  <s xml:id="echoid-s20949" xml:space="preserve">quæ ad ſiniſtram ſunt, à media nocte; </s>
  <s xml:id="echoid-s20950" xml:space="preserve">in borealib{us} verò contra: </s>
  <s xml:id="echoid-s20951" xml:space="preserve">effici-<lb/>tur, vt horæ à meridie in vno horologio ſint horę à media nocte in altero, &amp; </s>
  <s xml:id="echoid-s20952" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s20953" xml:space="preserve">quandoquidem dex-<lb/>trę vni{us}, quæ numerabantur à meridie, fiunt ſiniſtræ in altero, ac propterea à media nocte ſupputantur, <lb/>&amp; </s>
  <s xml:id="echoid-s20954" xml:space="preserve">econtrario, vt docuimus. </s>
  <s xml:id="echoid-s20955" xml:space="preserve">Igitur linea proxima ad dextram lineæ horæ 12. </s>
  <s xml:id="echoid-s20956" xml:space="preserve">meridiei, quæ in auſtrali <lb/>horologio monſtr at horam 1. </s>
  <s xml:id="echoid-s20957" xml:space="preserve">à meridie, in altero auſtrali neceſſario oſtendet horam 11. </s>
  <s xml:id="echoid-s20958" xml:space="preserve">à media nocte, <lb/>cum iam in hoc translata ſiniſtram partem occupet, &amp; </s>
  <s xml:id="echoid-s20959" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s20960" xml:space="preserve">Linea verò proxima ad dextram lineæ <lb/>horæ 12. </s>
  <s xml:id="echoid-s20961" xml:space="preserve">mediæ noctis in vno boreali horologio indicans horam 1. </s>
  <s xml:id="echoid-s20962" xml:space="preserve">à media nocte, in altero boreali ad ſini-<lb/>ſtr am iam partem translata ſignificabit horam 11. </s>
  <s xml:id="echoid-s20963" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s20964" xml:space="preserve">è contrario.</s>
  <s xml:id="echoid-s20965" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1068" type="float" level="2" n="23">
<note position="left" xlink:label="note-0327-03" xlink:href="note-0327-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s20966" xml:space="preserve">IAM verò ſi horologium à meridie declinãs in ortum, vel occaſum inuertatur, it a vt ſuperior pars <lb/>
<anchor type="note" xlink:label="note-0327-04a" xlink:href="note-0327-04"/>
in inferiorem mutetur, &amp; </s>
  <s xml:id="echoid-s20967" xml:space="preserve">quæ poſt hane mutationem nobis ad horologium conuerſis dextra eſt, fiat ſini-<lb/>
<anchor type="note" xlink:label="note-0327-05a" xlink:href="note-0327-05"/>
ſtra, &amp; </s>
  <s xml:id="echoid-s20968" xml:space="preserve">contra, factum erit ex eo horologium à ſeptentrione totidem gradib{us}, quot illud à meridie rece-<lb/>dit, deflectens, in oppoſitam tamen partem, adeo vt illo vergente in ortum, hoc in occaſum ſpectet, &amp; </s>
  <s xml:id="echoid-s20969" xml:space="preserve"><lb/>contra: </s>
  <s xml:id="echoid-s20970" xml:space="preserve">quale eſt illud, quod in facie plani oppoſita depingi ſolet, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s20971" xml:space="preserve">13. </s>
  <s xml:id="echoid-s20972" xml:space="preserve">ſuperioris libri <lb/>demonſtr auimus. </s>
  <s xml:id="echoid-s20973" xml:space="preserve">Poteſt autem hæc inuerſio horologii ita quoque institui, vt prius dextra pars in ſiniſtrã, <lb/>&amp; </s>
  <s xml:id="echoid-s20974" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s20975" xml:space="preserve">deinde poſt hanc mutationem ſuperior in inferiorem mutetur, &amp; </s>
  <s xml:id="echoid-s20976" xml:space="preserve">è contrario. </s>
  <s xml:id="echoid-s20977" xml:space="preserve">Huiuſmodi ho-<lb/>rologium exprimunt lineamenta auſtr alis horologii in facie boreali deſcripta, ita vt ſingulæ lineæ ſingu-<lb/>lis lineis reſpondeant, dummodo pars ſuperior mutetur in inferiorem. </s>
  <s xml:id="echoid-s20978" xml:space="preserve">Nam ſi hæc mutatio fiat, appare-<lb/>bunt nobis ad faciem oppoſitam horologii conuerſis lineæ ad partem dextram, quæ pri{us} poſt illam muta<unsure/> <lb/>tionem ſuperioris partis in inferiorem in auſtrali facie ad ſiniſtram nobis collocatæ erant, &amp; </s>
  <s xml:id="echoid-s20979" xml:space="preserve">contra, vt <lb/>manifestum eſt.</s>
  <s xml:id="echoid-s20980" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1069" type="float" level="2" n="24">
<note position="right" xlink:label="note-0327-04" xlink:href="note-0327-04a" xml:space="preserve">Quomodo ex <lb/>horologio declí <lb/>nã te à meridie <lb/>fiat horologiú <lb/>declinans à bo <lb/>rea in oppoſita <lb/>facie plani ho-<lb/>rologii deline@<unsure/> <lb/>dum.</note>
<note position="left" xlink:label="note-0327-05" xlink:href="note-0327-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s20981" xml:space="preserve">QVIA verò ex horologio auſtrali, ſi pars ei{us} dextra fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s20982" xml:space="preserve">contra, fit aliud auſtrale, quod <lb/>in contrariam partem declinat, vt dictum eſt; </s>
  <s xml:id="echoid-s20983" xml:space="preserve">efficitur, vt ſi pars ſuperior hui{us} horologĳ, quod ex illo <lb/>factum eſt, in inferiorem mutetur, habeam{us} horologium boreale reſpondens priori illi horologio auſtrali, <lb/>
<anchor type="note" xlink:label="note-0327-07a" xlink:href="note-0327-07"/>
dummodo numeri reſtituantur, qui pri{us} in illo auſtrali horologio erant; </s>
  <s xml:id="echoid-s20984" xml:space="preserve">it a vt ſi illud à meridie in ortum <lb/>deflectit, hoc à borea in occaſum declinet, &amp; </s>
  <s xml:id="echoid-s20985" xml:space="preserve">ſi illud in occaſum, hoc in ortum vergat: </s>
  <s xml:id="echoid-s20986" xml:space="preserve">quia hac ratione <lb/>facta eſt mutatio partis ſiniſtræ in dextram, quando nimirum factum eſt horologium à meridie in contra-<lb/>riam partem declinans; </s>
  <s xml:id="echoid-s20987" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20988" xml:space="preserve">rurſus pars, quæ poſt hane mutationem ſuperior eſt, mutatur in inferiorem, &amp; </s>
  <s xml:id="echoid-s20989" xml:space="preserve"><lb/>contra, quæ quidem omnia requiruntur, vt ex auſtr ali fiat boreale in oppoſita facie deſcribendum, vt di-<lb/>ctum eſt. </s>
  <s xml:id="echoid-s20990" xml:space="preserve">Itaque hanc nobis regulam colligere licebit. </s>
  <s xml:id="echoid-s20991" xml:space="preserve">Horologium australe declinans in ortum, ſi ei{us} <lb/>pars ſuperior fiat inferior, dabit horologium boreale ęqualis declinationis in ortum quoque vergens: <lb/></s>
  <s xml:id="echoid-s20992" xml:space="preserve">Auſtrale verò in occaſum deflectens ſimiliter inuerſum, vt ſuperior pars in inferiorem mutetur, exhibe-
<pb o="312" file="0328" n="328" rhead="GNOMONICES"/>
bit boreale ſpectans quoque ad occaſum. </s>
  <s xml:id="echoid-s20993" xml:space="preserve">Vnde ſi quis deſideret horologium boreale declinans in or-<lb/>tum, deſcribendum crit auſtrale horologium ſpectans ad ortum. </s>
  <s xml:id="echoid-s20994" xml:space="preserve">Hocenim inuerſum, it a vt ſuperiora <lb/>cuadant inferiora, dabit opt at um horologium boreale in ortum v@rgens, ſi numeri horarum vertantur in <lb/>carum complementa vſq; </s>
  <s xml:id="echoid-s20995" xml:space="preserve">ad 12. </s>
  <s xml:id="echoid-s20996" xml:space="preserve">Similiter ſi quis optet horologium boreale, quod in occaſum deſlectat, <lb/>deſcribendum erit horologium auſtrale in occaſum declinans. </s>
  <s xml:id="echoid-s20997" xml:space="preserve">Nam ſi huius pars ſuperior fiat infe-<lb/>rior, habebitur boreale horologium ſpectans in occaſum, ſi numeri mutentur, vt dictum eſt. </s>
  <s xml:id="echoid-s20998" xml:space="preserve">Quę om-<lb/>nia ex ĳs, quę dicta ſunt, colliguntur, ac perſpicua ſunt, ſirecte conſiderentur plana horologiorum in <lb/>proprĳs poſitionib{us}.</s>
  <s xml:id="echoid-s20999" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1070" type="float" level="2" n="25">
<note position="right" xlink:label="note-0327-07" xlink:href="note-0327-07a" xml:space="preserve">Si pars ſupe-<lb/>rior horologii, <lb/>quod à meridie <lb/>in ortum defle <lb/>ctit, fiat infe-<lb/>rior, factũ erit <lb/>horologium à <lb/>borea in ott<unsure/>ũ <lb/>quoque decli-<lb/>nans; in occa-<lb/>ſum vero, ſi il-<lb/>lud ad occasũ <lb/>vergat.</note>
</div>
<p style="it">
  <s xml:id="echoid-s21000" xml:space="preserve">QVIN immo vna opera, &amp; </s>
  <s xml:id="echoid-s21001" xml:space="preserve">vno labore quatuor diuerſa horologia, ſeruata ſemper eadem quantita <lb/>
<anchor type="note" xlink:label="note-0328-01a" xlink:href="note-0328-01"/>
te declinationis, deſcribere commodiſſimè poterim{us}. </s>
  <s xml:id="echoid-s21002" xml:space="preserve">Nam ſi exempli gratia deſcribam{us} horologium <lb/>
<anchor type="note" xlink:label="note-0328-02a" xlink:href="note-0328-02"/>
declinans à meridie in ortum grad. </s>
  <s xml:id="echoid-s21003" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21004" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21005" xml:space="preserve">partem eius ſuperiorem mutem{us} in inferiorem, deſcriptum <lb/>quoque iam erit horologium declinans grad. </s>
  <s xml:id="echoid-s21006" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21007" xml:space="preserve">à Septentrione in ortum: </s>
  <s xml:id="echoid-s21008" xml:space="preserve">Si verò eiuſdem illi{us} dextrã <lb/>partem eſſiciam{us} ſiniſtram, non mutata parte ſuperiore in inferiorem, habebim{us} horologium declinans <lb/>à meridie in occaſum grad. </s>
  <s xml:id="echoid-s21009" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21010" xml:space="preserve">Si denique non ſolum dextram partem in ſinistram conuertam{us}, ſed <lb/>etiam partem, quę nobis poſt hanc mutationem ſuperior est, efficiam{us} inferiorem, conſtructum erit ho <lb/>rologium à borea deſlectens in occaſum grad. </s>
  <s xml:id="echoid-s21011" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21012" xml:space="preserve">Eadem ratione, ſi deſcribatur horologium declinans à <lb/>meridie in occaſum grad. </s>
  <s xml:id="echoid-s21013" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21014" xml:space="preserve">efficiemus ex eo horologium declinans à borea in occaſum declinans grad. <lb/></s>
  <s xml:id="echoid-s21015" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21016" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21017" xml:space="preserve">declinans à meridie in ortum totidem gradib{us}, nec non à borea in ortum grad. </s>
  <s xml:id="echoid-s21018" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21019" xml:space="preserve">deflectens, ſi <lb/>prædictę partium inuer ſiones fiant, vt ex dictis perſpicuum eſt. </s>
  <s xml:id="echoid-s21020" xml:space="preserve">Sed in omnibus numeri horarum lineis <lb/>aſcribendi ſunt, vt in priore deſcriptione horologĳ declinantis docuim{us} in hac pro poſitione.</s>
  <s xml:id="echoid-s21021" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1071" type="float" level="2" n="26">
<note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">Qua ratione ex <lb/>horologio, qd <lb/>a meridie decli <lb/>mat in ortum, <lb/>cõficiatur aliud <lb/>declinans à bo <lb/>rea in ortum, a <lb/>meridie in oc-<lb/>caſum, &amp; à bo-<lb/>rea in occasũ.</note>
<note position="left" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1073" type="section" level="1" n="256">
<head xml:id="echoid-head265" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
<p>
  <s xml:id="echoid-s21022" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in horologio, <lb/>quod à Verticali circulo declinat, deſcribere.</s>
  <s xml:id="echoid-s21023" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21024" xml:space="preserve">INVENTA altitudine poli ſupra planum declinans ex propoſ. </s>
  <s xml:id="echoid-s21025" xml:space="preserve">29. </s>
  <s xml:id="echoid-s21026" xml:space="preserve">primi libri, quam qui-<lb/>
<anchor type="note" xlink:label="note-0328-04a" xlink:href="note-0328-04"/>
dem, vt diximus, indicat etiam ſecundum priorem deſcriptionem horologii declinantis in præ-<lb/>cedenti propoſ. </s>
  <s xml:id="echoid-s21027" xml:space="preserve">vel etiam in deſcriptione, quam in ſcholio eiuſdem propoſ. </s>
  <s xml:id="echoid-s21028" xml:space="preserve">tradidimus ad datam <lb/>
<anchor type="note" xlink:label="note-0328-05a" xlink:href="note-0328-05"/>
ſtyli longitudinem, cuius quoque locus datus ſit, angulus G C I, comprehenſus â linea ſtyli, &amp; </s>
  <s xml:id="echoid-s21029" xml:space="preserve"><lb/>axe mundi; </s>
  <s xml:id="echoid-s21030" xml:space="preserve">conſtituatur ad eam Analemma, vt in propoſ. </s>
  <s xml:id="echoid-s21031" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21032" xml:space="preserve">præcedentis libri, ita vt arcus C E, in <lb/>Analemmate illius propoſ. </s>
  <s xml:id="echoid-s21033" xml:space="preserve">metiatur altitudinem poli ſupra planum declinans, hoc eſt, in propo-<lb/>ſito exemplo, contineat grad. </s>
  <s xml:id="echoid-s21034" xml:space="preserve">40. </s>
  <s xml:id="echoid-s21035" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s21036" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21037" xml:space="preserve">vel certè angulus C D E, illius Analemmatis æqualis ſit <lb/>angulo G C I, in horologio declinante præcedentis propoſ. </s>
  <s xml:id="echoid-s21038" xml:space="preserve">Si enim ſumatur in eodem Analem-<lb/>mate recta D G, æqualis ſtylo I K, quem horologium priori via deſcriptum offert, vel quem in <lb/>poſteriore deſcriptione aſſumpſimus in portione Analemmatis deſcripta in antecedenti propof. <lb/></s>
  <s xml:id="echoid-s21039" xml:space="preserve">quæ priori figuræ propoſ. </s>
  <s xml:id="echoid-s21040" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21041" xml:space="preserve">ſuperioris libri reſpondet, vel cerre quem aſſumpſimus in ea deſcri-<lb/>ptione, in qua longitudo ſtyli vnà cum eius loco data fuit; </s>
  <s xml:id="echoid-s21042" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21043" xml:space="preserve">per G, recta O R, parallela agatur ipſi <lb/>B C, habebimus in recta O R, diametros conicarum ſectionum, quemadmodum earundem dia-<lb/>
<anchor type="note" xlink:label="note-0328-06a" xlink:href="note-0328-06"/>
metros K R, L R, M R, N O, P O, Q O, habuimus in horizontali horologio propoſ. </s>
  <s xml:id="echoid-s21044" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21045" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21046" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s21047" xml:space="preserve">Quamobrem parallelos, ſiuearcus ſignorum hic deſcribemus, vt ibi docuimus, nempe conicas <lb/>ſectiones circa diametros inuentas, quarum illæ, quæ inter centrum C, &amp; </s>
  <s xml:id="echoid-s21048" xml:space="preserve">lineam æquinoctialẽ <lb/>continentur, cornua inflectent verſus centrum, reliquæ verò in oppoſitam partem, non ſecus at-<lb/>que in horizontali horologio. </s>
  <s xml:id="echoid-s21049" xml:space="preserve">Nam ſicut in horologio horizontali circulus Analemmatis A B C, <lb/>reſert Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s21050" xml:space="preserve">recta O R, communem ſectionem plani horologij horizonta-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s21051" xml:space="preserve">Meridiani, ſeu lineam meridianam; </s>
  <s xml:id="echoid-s21052" xml:space="preserve">ita in horologio declinante circulus idem ſumitur pro <lb/>Meridiano proprio plani declinantis, hoc eſt, pro circulo per polos mundi, &amp; </s>
  <s xml:id="echoid-s21053" xml:space="preserve">per polos plani de-<lb/>clinantis ducto, recta autem O R, pro communi ſectione dicti Meridiani, &amp; </s>
  <s xml:id="echoid-s21054" xml:space="preserve">plani horologii de-<lb/>clinantis, nempe pro linea ſtyli. </s>
  <s xml:id="echoid-s21055" xml:space="preserve">Non conſtituimus autem ad inuentam altitudinem poli ſupra <lb/>
<anchor type="note" xlink:label="note-0328-07a" xlink:href="note-0328-07"/>
planum declinans proprium Analemma, quia &amp; </s>
  <s xml:id="echoid-s21056" xml:space="preserve">tota hæc res facile intelligi poteſt ex Analemma <lb/>re propoſ. </s>
  <s xml:id="echoid-s21057" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21058" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21059" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21060" xml:space="preserve">nos in hac propoſ. </s>
  <s xml:id="echoid-s21061" xml:space="preserve">arcus ſignorum deſcribemus alia ratione, quam <lb/>
<anchor type="note" xlink:label="note-0328-08a" xlink:href="note-0328-08"/>
mox explicabimus.</s>
  <s xml:id="echoid-s21062" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1073" type="float" level="2" n="1">
<note position="left" xlink:label="note-0328-04" xlink:href="note-0328-04a" xml:space="preserve">Arcus ſignorũ <lb/>Zodiaci in ho-<lb/>rologio declinã <lb/>se à Verticali <lb/>quomodo de-<lb/>ſcribantur ex <lb/>Analem mate.</note>
<note position="left" xlink:label="note-0328-05" xlink:href="note-0328-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0328-06" xlink:href="note-0328-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0328-07" xlink:href="note-0328-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0328-08" xlink:href="note-0328-08a" xml:space="preserve">Qua ratione <lb/>maius aut mi-<lb/>nus horologiũ <lb/>ſecundum idẽ <lb/>Analemma de-<lb/>ſcribatur.</note>
</div>
<p>
  <s xml:id="echoid-s21063" xml:space="preserve">QVOD ſi maius horologium quis optet, aut minus, ſumendus erit in Analemmate longior, <lb/>aut breuior ſtylus D M, &amp; </s>
  <s xml:id="echoid-s21064" xml:space="preserve">per M, linea ducenda parallela ipſi B C, &amp;</s>
  <s xml:id="echoid-s21065" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21066" xml:space="preserve">vt de horizontali horolo-<lb/>gio diximus propoſ. </s>
  <s xml:id="echoid-s21067" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21068" xml:space="preserve">ſuperioris lib.</s>
  <s xml:id="echoid-s21069" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21070" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s21071" xml:space="preserve">Ducta recta C I, quæ axem mundi referat, excitetur in I, ad C I, perpendicularis <lb/>
<anchor type="note" xlink:label="note-0328-09a" xlink:href="note-0328-09"/>
I G, pro radio Aequatoris, ex cuius vtraque parte radij aliorum ſignorum educãtur, vt in ſuperio-<lb/>ribus non ſemel factum eſt: </s>
  <s xml:id="echoid-s21072" xml:space="preserve">ſumaturq́ue C I, æqualis rectæ C I, in axe horologij præcedentis pro-<lb/>poſ. </s>
  <s xml:id="echoid-s21073" xml:space="preserve">vel in horologio, quod in ſcholio eiuſdem propoſ. </s>
  <s xml:id="echoid-s21074" xml:space="preserve">conſtruximus ad datum ſtylum in dato lo-<lb/>co; </s>
  <s xml:id="echoid-s21075" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21076" xml:space="preserve">recta I G, æqualis rectæ I G, vel L G, in eodem horologio; </s>
  <s xml:id="echoid-s21077" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21078" xml:space="preserve">ex C, per G, recta emitta-
<pb o="313" file="0329" n="329" rhead="LIBER TERTIVS."/>
tur C G; </s>
  <s xml:id="echoid-s21079" xml:space="preserve">quam commodius fortaſſe ducemus, ſi ex C, ducamus rectam C G, facientem cum C I, <lb/>angulum G C I, æqualem angulo G C I, quem in horologio cõſtituunt axis C I, &amp; </s>
  <s xml:id="echoid-s21080" xml:space="preserve">linea ſtyli C G, <lb/>hoc eſt, angulo altitudinis poli ſupra planum declinans. </s>
  <s xml:id="echoid-s21081" xml:space="preserve">Erit triangulum hoc G C I, æquale om-<lb/>
<anchor type="figure" xlink:label="fig-0329-01a" xlink:href="fig-0329-01"/>
<anchor type="note" xlink:label="note-0329-01a" xlink:href="note-0329-01"/>
<anchor type="note" xlink:label="note-0329-02a" xlink:href="note-0329-02"/>
<anchor type="note" xlink:label="note-0329-03a" xlink:href="note-0329-03"/>
nino triangulo G C I, in horologio declinante præcedentis propoſ. </s>
  <s xml:id="echoid-s21082" xml:space="preserve">atque adeo recta C G, linea <lb/>indicis erit. </s>
  <s xml:id="echoid-s21083" xml:space="preserve">Nam ſecundum priorem conſtructionem, duo latera I C, I G, vnius trianguli æqualia <lb/>
<anchor type="note" xlink:label="note-0329-04a" xlink:href="note-0329-04"/>
ſunt duobus lateribus I C, I G, alterius trianguli, angulosq́ue continent æquales. </s>
  <s xml:id="echoid-s21084" xml:space="preserve">Igitur tota trian-<lb/>
<anchor type="note" xlink:label="note-0329-05a" xlink:href="note-0329-05"/>
gula æqualia ſunt, &amp;</s>
  <s xml:id="echoid-s21085" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21086" xml:space="preserve">Secundum poſteriorem autem conſtructionem, duo anguli I, C, vnius trian <lb/>guli æquales ſunt duobus angulis I, C, alterius trianguli. </s>
  <s xml:id="echoid-s21087" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s21088" xml:space="preserve">latus I C, vnius æquale ſit <lb/>lateri I C, alterius, erunt reliqua latera vnius reliquis lateribus alterius æqualia, &amp;</s>
  <s xml:id="echoid-s21089" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21090" xml:space="preserve">Deinde ex cen <lb/>
<anchor type="note" xlink:label="note-0329-06a" xlink:href="note-0329-06"/>
tro L, circuli illius, beneficio cuius puncta horarum in æquinoctiali linea inuenimus, accipiantur <lb/>omnia interualla vſque ad puncta horarum in linea æquinoctiali, eaq́ue ex I, in radium Aequato-<lb/>ris I G, transferantur. </s>
  <s xml:id="echoid-s21091" xml:space="preserve">Si enim ex C, per puncta, quæ in radio Aequatoris prædicta interualla ter-<lb/>minant, lineæ rectæ ducantur, erunt hæ omnium horarum lineæ citra, &amp; </s>
  <s xml:id="echoid-s21092" xml:space="preserve">vltra lineam ſtyli, <lb/>quæ lineam æquinoctialem interſecant, inſtar linearum horariarum horizontalis horologij, quæ <lb/>ex puncto H, in figura poſteriore propoſ. </s>
  <s xml:id="echoid-s21093" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21094" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21095" xml:space="preserve">per puncta in radio Aequatoris in-<lb/>
<anchor type="note" xlink:label="note-0329-07a" xlink:href="note-0329-07"/>
uenta ducuntur. </s>
  <s xml:id="echoid-s21096" xml:space="preserve">His igitur lineis apponantur numeri horarum reſpondentes horis, quarum in-<lb/>terualla inter centrum L, &amp; </s>
  <s xml:id="echoid-s21097" xml:space="preserve">lineam æquinoctialem poſita, translata ſunt in radium Aequatoris ex <lb/>puncto I, notando diligenter, quæ lineæ referãt horas ad ſiniſtram lineæ ſtyli poſitas, &amp; </s>
  <s xml:id="echoid-s21098" xml:space="preserve">quæ horas <lb/>ad dextram eiuſdem lineæ collocatas. </s>
  <s xml:id="echoid-s21099" xml:space="preserve">Id quod numeri lineis appoſiti vel facile indicant, reſpon-<lb/>dentes numeris linearum horariarum horologij, quæ æquinoctialem lineam interſecant. </s>
  <s xml:id="echoid-s21100" xml:space="preserve">Has <lb/>enim lineas duntaxat referunt lineæ hactenus ex puncto C, per radii Aequatoris puncta emiſſæ. <lb/></s>
  <s xml:id="echoid-s21101" xml:space="preserve">Eaſdem has lineas obtinebimus, ſi ex horologio ſumamus interualla horaria inter centrum C, &amp; </s>
  <s xml:id="echoid-s21102" xml:space="preserve"><lb/>lineam æquinoctialem poſita, eaq́ue ex C, transferamus in radium Aequatoris I G, &amp; </s>
  <s xml:id="echoid-s21103" xml:space="preserve">per puncta, <lb/>quæ terminant hæc interualla in radio Aequatoris, ex C, lineas ducamus, &amp;</s>
  <s xml:id="echoid-s21104" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21105" xml:space="preserve">vt &amp; </s>
  <s xml:id="echoid-s21106" xml:space="preserve">in horologio <lb/>horizontali fecimus, &amp; </s>
  <s xml:id="echoid-s21107" xml:space="preserve">in Verticali. </s>
  <s xml:id="echoid-s21108" xml:space="preserve">Quòd ſi contingat lineam quampiam horariam in horolo-<lb/>gio lineam ęquinoctialem non ſecare, etiamſi infinitè producatur, ſed ei æquidiſtare, ducenda erit
<pb o="314" file="0330" n="330" rhead="GNOMONICES"/>
ex C, linea C A, radio Aequatoris I G, parallela: </s>
  <s xml:id="echoid-s21109" xml:space="preserve">hæc enim illam horam referet; </s>
  <s xml:id="echoid-s21110" xml:space="preserve">quemadmodum <lb/>&amp; </s>
  <s xml:id="echoid-s21111" xml:space="preserve">in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s21112" xml:space="preserve">in Verticali, quia linea horæ 6. </s>
  <s xml:id="echoid-s21113" xml:space="preserve">æquinoctialem lineam non ſecat, ſed <lb/>ei parallela eſt, ducta eſt ex H, in poſteriori figura propoſ. </s>
  <s xml:id="echoid-s21114" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21115" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21116" xml:space="preserve">14. </s>
  <s xml:id="echoid-s21117" xml:space="preserve">ſuperioris libri, recta H V, radi@ <lb/>Aequatoris parallela pro hora 6.</s>
  <s xml:id="echoid-s21118" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1074" type="float" level="2" n="2">
<note position="left" xlink:label="note-0328-09" xlink:href="note-0328-09a" xml:space="preserve">Alia deſcriptio <lb/>atcuum ſigno-<lb/>rum in eodem <lb/>horologio de-<lb/>clinante à Ver <lb/>t<unsure/>icali.</note>
  <figure xlink:label="fig-0329-01" xlink:href="fig-0329-01a">
    <image file="0329-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0329-01"/>
  </figure>
<note position="left" xlink:label="note-0329-01" xlink:href="note-0329-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0329-02" xlink:href="note-0329-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0329-03" xlink:href="note-0329-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0329-04" xlink:href="note-0329-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0329-05" xlink:href="note-0329-05a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0329-06" xlink:href="note-0329-06a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0329-07" xlink:href="note-0329-07a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0330-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0330-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s21119" xml:space="preserve">VT autem lineas habeamus aliarum horarum, quæ æquinoctialem lineam neque ſecant, ne-<lb/>
<anchor type="note" xlink:label="note-0330-04a" xlink:href="note-0330-04"/>
<anchor type="note" xlink:label="note-0330-05a" xlink:href="note-0330-05"/>
que eidem parallelæ ſunt, vt ſunt illæ omnes, quæ poſtquam lineam æquinoctialem ſecuerũt, pro-<lb/>ductæ ſunt vltra centrum C, (quales in noſtro horologio declinante ſunt horæ 4. </s>
  <s xml:id="echoid-s21120" xml:space="preserve">5. </s>
  <s xml:id="echoid-s21121" xml:space="preserve">6. </s>
  <s xml:id="echoid-s21122" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21123" xml:space="preserve">cæteræ <lb/>poſt meridiem; </s>
  <s xml:id="echoid-s21124" xml:space="preserve">item 1. </s>
  <s xml:id="echoid-s21125" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21126" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21127" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21128" xml:space="preserve">poſt mediam noctem; </s>
  <s xml:id="echoid-s21129" xml:space="preserve">hæ etenim omnes vltra centrum C, produ-<lb/>ctæ ſunt, &amp; </s>
  <s xml:id="echoid-s21130" xml:space="preserve">earum reſpondentes citra centrum C, lineam æquinoctialem ſecant, quales ſunt 4. </s>
  <s xml:id="echoid-s21131" xml:space="preserve">5. <lb/></s>
  <s xml:id="echoid-s21132" xml:space="preserve">6. </s>
  <s xml:id="echoid-s21133" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21134" xml:space="preserve">cæteræ poſt mediam noctem. </s>
  <s xml:id="echoid-s21135" xml:space="preserve">Item 1. </s>
  <s xml:id="echoid-s21136" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21137" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21138" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21139" xml:space="preserve">poſt meridiem) hanc viam ſequemur. </s>
  <s xml:id="echoid-s21140" xml:space="preserve">Per C, <lb/>centrum horologii ducemus rectam C d, lineæ æquinoctiali parallelam, ſi nulla linea horaria ei <lb/>æquidiſtat, &amp; </s>
  <s xml:id="echoid-s21141" xml:space="preserve">per C, punctum figuræ proximè conſtructæ rectam C A, emittemus radio Aequa-<lb/>toris parallelam, quæ illi parallelæ C d, vel certè horæ illi, (ſi qua eſt) quæ lineæ æquinoctiali æqui <lb/>diſtat, reſpondebit, vt proximè docuimus. </s>
  <s xml:id="echoid-s21142" xml:space="preserve">Referet autem linea C d, in horologio circulum illũ <lb/>horarium, ſ<unsure/>eu circulum maximum per polos mundi ductum, cuius communis ſectio in circulo <lb/>
<anchor type="note" xlink:label="note-0330-06a" xlink:href="note-0330-06"/>
ex L, deſcripto per centrum L, tranſiens æquinoctiali lineæ æquidiſtat, lineamq́ue ſtyliad rectos <lb/>angulos ſecat, vt in præcedenti propoſ. </s>
  <s xml:id="echoid-s21143" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s21144" xml:space="preserve">Poſt hæc, quoniam quælibet linea horaria cũ <lb/>C d, ad verticem C, æquales angulos facit, transferemus lineas ex C, prodeuntes, radiumq́; </s>
  <s xml:id="echoid-s21145" xml:space="preserve">Aequa <lb/>
<anchor type="note" xlink:label="note-0330-07a" xlink:href="note-0330-07"/>
toris ſecantes, ad alteram partem rectæ C A, beneſicio arcus cuiuſdam circuli ex C, deſcripti, ita vt <lb/>lineæ hinc inde æqualiter à C A, diſtantes æquales arcus illius circuli ex C, deſcripti, &amp; </s>
  <s xml:id="echoid-s21146" xml:space="preserve">angulos <lb/>æquales ad C, comprehendant cum recta C A. </s>
  <s xml:id="echoid-s21147" xml:space="preserve">Nam hæ lineæ ita translatæ reſpondebunt illis ho <lb/>ris, quæ æquinoctialem lineam non ſecant, ſed vltra centrũ C, excurrunt, ita vt binæ lineæ æqua-<lb/>li interuallo à recta C A, remotæ pertineant ad binas horas eiuſdem numeri, quarum illa, quæ ra-<lb/>dium Aequatoris ſecat, vel à C, verſus radium Aequatoris ducitur, referat horam, quæ lineã ęqui-<lb/>noctialem interſecat in horologio, alia verò ad alteram partem rectæ C A, translata eidem horæ <lb/>reſpondeat vltra centrum C, productæ, quæ æquinoctialem lineam non ſecat: </s>
  <s xml:id="echoid-s21148" xml:space="preserve">Non ſecus ac in ho
<pb o="315" file="0331" n="331" rhead="LIBER TERTIVS."/>
rologio horizontali factum eſt, atque in Verticali propoſ. </s>
  <s xml:id="echoid-s21149" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21150" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21151" xml:space="preserve">14. </s>
  <s xml:id="echoid-s21152" xml:space="preserve">antecedentis lib. </s>
  <s xml:id="echoid-s21153" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s21154" xml:space="preserve">ibi li-<lb/>neæ vltram rectam H V, in figura radiorum translatæ referunt eaſdem horas numero, æquinoctia <lb/>lem tamen lineam non ſecantes, quibus reſpondent aliæ lineæ citra rectam H V; </s>
  <s xml:id="echoid-s21155" xml:space="preserve">quia nimirum <lb/>quæuis linea horaria in horologio horizontali &amp; </s>
  <s xml:id="echoid-s21156" xml:space="preserve">Verticali cum linea horæ 6. </s>
  <s xml:id="echoid-s21157" xml:space="preserve">quę lineæ æquino-<lb/>ctiali æquidiſtat, ad verticem, ſeu centrum H, æquales angulos conſtituit; </s>
  <s xml:id="echoid-s21158" xml:space="preserve">quemadmodum &amp; </s>
  <s xml:id="echoid-s21159" xml:space="preserve">hic <lb/>cum linea C d, ipſi æquinoctiali lineæ parallela, cui reſpondet recta C A, radio Aequatoris paralle <lb/>la in figura radiorum, inſtar rectæ H V, radio Aequatoris ibi in figura radiorum æquidiſtantis, &amp; </s>
  <s xml:id="echoid-s21160" xml:space="preserve"><lb/>horæ 6. </s>
  <s xml:id="echoid-s21161" xml:space="preserve">reſpondentis, quæ lineæ æquinoctiali parallela eſt. </s>
  <s xml:id="echoid-s21162" xml:space="preserve">Ita vides hic tran slatam eſſe vltra rectã <lb/>C A, lineam horæ 3. </s>
  <s xml:id="echoid-s21163" xml:space="preserve">à media nocte, quia hora 3. </s>
  <s xml:id="echoid-s21164" xml:space="preserve">à meridie æquinoctialem lineam ſecat, nec non <lb/>lineam horæ 4. </s>
  <s xml:id="echoid-s21165" xml:space="preserve">à meridie, quia hora 4. </s>
  <s xml:id="echoid-s21166" xml:space="preserve">à media nocte ſecat æquinoctialem, vt in horologio appa-<lb/>
<anchor type="note" xlink:label="note-0331-01a" xlink:href="note-0331-01"/>
ret. </s>
  <s xml:id="echoid-s21167" xml:space="preserve">Eademq́ue ratio habenda eſt de alijs.</s>
  <s xml:id="echoid-s21168" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1075" type="float" level="2" n="3">
<note position="left" xlink:label="note-0330-04" xlink:href="note-0330-04a" xml:space="preserve">Quomodo li-<lb/>neæ horariæ, <lb/>quæ lineã æqui <lb/>nectialem non <lb/>ſecant, ducãtut <lb/>in figura radio <lb/>rum proxime <lb/>conſtructa.</note>
<note position="left" xlink:label="note-0330-05" xlink:href="note-0330-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0330-06" xlink:href="note-0330-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0330-07" xlink:href="note-0330-07a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s21169" xml:space="preserve">QVOD ſi quando linea ſtyli vna ſit ex lineis horarijs, vel æqualiter à duabus horarijs lineis <lb/>
<anchor type="note" xlink:label="note-0331-02a" xlink:href="note-0331-02"/>
in medio earum poſita diſtet, (quod aliquando contingere poteſt) inſeruiet quælibet horaria li <lb/>nea in proximè conſtructa figura radiorum ex C, ducta duabus horis æqualiter à linea ſtyli hinc <lb/>inde remotis: </s>
  <s xml:id="echoid-s21170" xml:space="preserve">quia tunc interualla illarum horarum inter centrum L, &amp; </s>
  <s xml:id="echoid-s21171" xml:space="preserve">æquinoctialem lineam <lb/>æqualia ſunt, vt propoſ. </s>
  <s xml:id="echoid-s21172" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21173" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21174" xml:space="preserve">de horizontali horologio oſtendimus, atque adeò trans-<lb/>lata in radium Æ quatoris ex puncto I, vnum &amp; </s>
  <s xml:id="echoid-s21175" xml:space="preserve">idem punctum offerunt, &amp;</s>
  <s xml:id="echoid-s21176" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21177" xml:space="preserve">Vnde tunc ſingulis <lb/>lineis bini numeri aſcribendi erunt, reſpondentes binis illis horis hinc inde à linea ſtyli æquali <lb/>ſpatio remotis, quemadmodum &amp; </s>
  <s xml:id="echoid-s21178" xml:space="preserve">in horizontali horologio, ac in Verticali factum eſt. </s>
  <s xml:id="echoid-s21179" xml:space="preserve">Sed quan-<lb/>do linea ſtyli inæqualiter à lineis horarijs circumſtantibus remouetur, (quod frequentius ſolet ac-<lb/>
<anchor type="note" xlink:label="note-0331-03a" xlink:href="note-0331-03"/>
cidere) vt in dato exemplo euenit, reſpondebunt ſingulæ lineæ ſingulis tantum horis; </s>
  <s xml:id="echoid-s21180" xml:space="preserve">propterea <lb/>quòd tunc interualla horarũ inter centrũ L, &amp; </s>
  <s xml:id="echoid-s21181" xml:space="preserve">æquinoctialem lineã hinc inde à linea ſtyli diſtan-<lb/>tium inæqualia ſunt, atque adeò in radium Aequatoris ex I, translata diuerſa puncta offerunt, &amp;</s>
  <s xml:id="echoid-s21182" xml:space="preserve">c.</s>
  <s xml:id="echoid-s21183" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1076" type="float" level="2" n="4">
<note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Quando linea <lb/>ſiyli una eſt ex <lb/>li<unsure/>neis horariis. <lb/>vel æqualiter à <lb/>duabus hinc in <lb/>de diſtat, perti-<lb/>nebit quælibet <lb/>linea horaria <lb/>in figuta ra dio <lb/>rũ ad duas ho-<lb/>ras, vt in hori-<lb/>zontali horolo <lb/>gio.</note>
<note position="left" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s21184" xml:space="preserve">NON eſſet autem præter rem, quando linea ſtyli inæqualiter à proximis duabus horis diſtat, <lb/>
<anchor type="note" xlink:label="note-0331-04a" xlink:href="note-0331-04"/>
immo verò expediret, ſi conſtruerentur duæ figuræ radiorum Zodiaci, in quarum vna duceren-<lb/>tur horariæ lineæ ex C, reſpondentes illis lineis horariis in horologio, quæ ex vna parte, nempe ſi-<lb/>niſtra lineæ ſtyli continentur; </s>
  <s xml:id="echoid-s21185" xml:space="preserve">in alia verò horariæ lineæ reſpondentes lineis horarijs horologii ex <lb/>altera parte lineæ ſtyli. </s>
  <s xml:id="echoid-s21186" xml:space="preserve">Ita enim omnis linearum confuſio tolleretur, quæ, neceſſario ſequitur, <lb/>quando linea ſtyli ferè æqualiter à lineis hinc inde poſitis diſtat, quia tunc puncta in radio Aequa <lb/>toris inuenta vix inter ſe diſcernuntur, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s21187" xml:space="preserve">Hac ratione in noſtro exemplo in vna <lb/>
<anchor type="note" xlink:label="note-0331-05a" xlink:href="note-0331-05"/>
figurarum ducerentur lineæ ex C, reſpondentes hiſce horis 1. </s>
  <s xml:id="echoid-s21188" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21189" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21190" xml:space="preserve">4. </s>
  <s xml:id="echoid-s21191" xml:space="preserve">5. </s>
  <s xml:id="echoid-s21192" xml:space="preserve">6. </s>
  <s xml:id="echoid-s21193" xml:space="preserve">7. </s>
  <s xml:id="echoid-s21194" xml:space="preserve">8. </s>
  <s xml:id="echoid-s21195" xml:space="preserve">9. </s>
  <s xml:id="echoid-s21196" xml:space="preserve">à media no-<lb/>cte, quæ ſunt ad ſiniſtram lineæ ſtyli. </s>
  <s xml:id="echoid-s21197" xml:space="preserve">In altera verò continerentur lineæ reſpondentes horis ad <lb/>dexteram eiuſdem lineæ ſtyli, quales ſunt 10. </s>
  <s xml:id="echoid-s21198" xml:space="preserve">11. </s>
  <s xml:id="echoid-s21199" xml:space="preserve">12. </s>
  <s xml:id="echoid-s21200" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s21201" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21202" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21203" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21204" xml:space="preserve">4. </s>
  <s xml:id="echoid-s21205" xml:space="preserve">5. </s>
  <s xml:id="echoid-s21206" xml:space="preserve">6. </s>
  <s xml:id="echoid-s21207" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s21208" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21209" xml:space="preserve">à meridie. <lb/></s>
  <s xml:id="echoid-s21210" xml:space="preserve">In qualibet tamen figura ducenda eſſet C G, pro linea ſtyli. </s>
  <s xml:id="echoid-s21211" xml:space="preserve">Huius rei exemplum poſitum eſſe vi-<lb/>debis in propoſ. </s>
  <s xml:id="echoid-s21212" xml:space="preserve">38. </s>
  <s xml:id="echoid-s21213" xml:space="preserve">huius libri.</s>
  <s xml:id="echoid-s21214" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1077" type="float" level="2" n="5">
<note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">Quando linea <lb/>ſtyli inæquali-<lb/>ter diſtat à dua <lb/>bus proximis <lb/>horis, conſtruẽ-<lb/>dæ eſſent duæ <lb/>figuræ radiorũ, <lb/>vt omnis confu <lb/>ſio linearũ tol-<lb/>leretur.</note>
<note position="left" xlink:label="note-0331-05" xlink:href="note-0331-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s21215" xml:space="preserve">EX his hoc modo paratis deſcribentur arcus ſignorum, vt in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s21216" xml:space="preserve">Ver-<lb/>ticali, transferendo nimirum interualla horarum inter C, &amp; </s>
  <s xml:id="echoid-s21217" xml:space="preserve">radios ſignorum intercepta ex cen-<lb/>tro horologii C, in horas horologii reſpondentes, vel etiam transferendo horaria interualla in-<lb/>ter radium Aequatoris, &amp; </s>
  <s xml:id="echoid-s21218" xml:space="preserve">ſignorum radios poſita in lineas horarias horologij reſpondentes, ini-<lb/>tio facto à linea æquinoctiali, &amp;</s>
  <s xml:id="echoid-s21219" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21220" xml:space="preserve">Eadem enim demonſtratio hic erit, quæ in horologio horizon-<lb/>
<anchor type="note" xlink:label="note-0331-06a" xlink:href="note-0331-06"/>
tali, cum planum horologij declinantis ſit tanquam Horizon quidam, &amp; </s>
  <s xml:id="echoid-s21221" xml:space="preserve">angulus G C I, æqualis <lb/>altitudini poli ſupra ipſum, vt diximus, atque linea ſtyli inſtar lineæ meridianæ, licet non indicet <lb/>horam 12. </s>
  <s xml:id="echoid-s21222" xml:space="preserve">quia non computamus horas à Meridiano circulo plani declinantis, ſed à Meridiano <lb/>Horizontis illius loci, vbi declinans horologium deſcribitur. </s>
  <s xml:id="echoid-s21223" xml:space="preserve">Monſtraret autem proculdubio <lb/>dicta linea meridiana horam 12. </s>
  <s xml:id="echoid-s21224" xml:space="preserve">ſi horas computaremus à Meridiano plani declinantis; </s>
  <s xml:id="echoid-s21225" xml:space="preserve">quia tunc <lb/>circulus proprius Meridianus plani declinantis efficiens lineam ſtyli in horologio æqualiter diſta-<lb/>ret ab ortu, &amp; </s>
  <s xml:id="echoid-s21226" xml:space="preserve">occaſu Solis, atque adeo Sol in eo exiſtens meridiem efficeret, vel mediam noctem, <lb/>quemadmodum in Horizonte contingit.</s>
  <s xml:id="echoid-s21227" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1078" type="float" level="2" n="6">
<note position="left" xlink:label="note-0331-06" xlink:href="note-0331-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s21228" xml:space="preserve">PERSPICVVM autẽ eſt ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s21229" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21230" xml:space="preserve">ſuperioris libri, quando recta C G, <lb/>
<anchor type="note" xlink:label="note-0331-07a" xlink:href="note-0331-07"/>
in figura radiorum oppoſitos radios ſecat, arcus illorum ſignorum eſſe hyperbolas oppoſitas, &amp; </s>
  <s xml:id="echoid-s21231" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0331-08a" xlink:href="note-0331-08"/>
æquales: </s>
  <s xml:id="echoid-s21232" xml:space="preserve">quando verò æquidiſtat alteri radiorum oppoſitorum, &amp; </s>
  <s xml:id="echoid-s21233" xml:space="preserve">alterum ſecat, arcum ſigni il-<lb/>lius, cuius radius ſecatur, eſſe Parabolam, &amp; </s>
  <s xml:id="echoid-s21234" xml:space="preserve">alterius arcum deſcribi non poſſe: </s>
  <s xml:id="echoid-s21235" xml:space="preserve">quando denique <lb/>alterum oppoſitorum radiorum ſecat, alterum autem non, neque ei æquidiſtat, arcum illius ſigni, <lb/>cuius radius ſecatur, eſſe Ellipſim, &amp; </s>
  <s xml:id="echoid-s21236" xml:space="preserve">alterius arcum nullo modo poſſe deſcribi. </s>
  <s xml:id="echoid-s21237" xml:space="preserve">Eadem enim de-<lb/>monſtratio hic erit, quæ ibi: </s>
  <s xml:id="echoid-s21238" xml:space="preserve">quoniam ita hic ſe habet recta C G, in figura radiorum reſpondens <lb/>lineæ ſtyli in horologio, &amp; </s>
  <s xml:id="echoid-s21239" xml:space="preserve">diameter omnium ſectionum conicarum exiſtens, vt ibi recta H B, in <lb/>
<anchor type="note" xlink:label="note-0331-09a" xlink:href="note-0331-09"/>
figura radiorum referẽs lineam meridianam horologij, &amp; </s>
  <s xml:id="echoid-s21240" xml:space="preserve">diameter exiſtens omnium conicarum <lb/>ſectionum: </s>
  <s xml:id="echoid-s21241" xml:space="preserve">propterea quòd angulus C G I, æqualis eſt hic altitudini poli ſupra planum declinãs, <lb/>vt ibi angulus D H B, æqualis eſt poli altitudini ſupra Horizontem. </s>
  <s xml:id="echoid-s21242" xml:space="preserve">Ex his ſequitur, arcus paralle-<lb/>lorum, qui omnium ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s21243" xml:space="preserve">ſemper latentium maximi ſunt, eſſe in noſtro exem-<lb/>plo hyperbolas oppoſitas. </s>
  <s xml:id="echoid-s21244" xml:space="preserve">Quoniã enim angulus, quem radius arcus horarum 24. </s>
  <s xml:id="echoid-s21245" xml:space="preserve">cũ radio Æ qua-
<pb o="316" file="0332" n="332" rhead="GNOMONICES"/>
toris facit, cõtinet gr. </s>
  <s xml:id="echoid-s21246" xml:space="preserve">48. </s>
  <s xml:id="echoid-s21247" xml:space="preserve">cũ tanta ſit declinatio paralleli maximi ſemper apparentiũ, fit vt addito <lb/>angulorecto G I C, conficiatur angulus contentus radio eiuſdem paralleli, &amp; </s>
  <s xml:id="echoid-s21248" xml:space="preserve">axe I C, grad. </s>
  <s xml:id="echoid-s21249" xml:space="preserve">138. <lb/></s>
  <s xml:id="echoid-s21250" xml:space="preserve">Cum ergo angulus I C G, altitudinis poli ſupra planum declinans comprehendat grad. </s>
  <s xml:id="echoid-s21251" xml:space="preserve">40. </s>
  <s xml:id="echoid-s21252" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s21253" xml:space="preserve"><lb/>3. </s>
  <s xml:id="echoid-s21254" xml:space="preserve">fient anguli interni, quos dictus radius, &amp; </s>
  <s xml:id="echoid-s21255" xml:space="preserve">recta C G, cum axe faciunt, grad. </s>
  <s xml:id="echoid-s21256" xml:space="preserve">178. </s>
  <s xml:id="echoid-s21257" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s21258" xml:space="preserve">3. </s>
  <s xml:id="echoid-s21259" xml:space="preserve">hoc eſt, <lb/>minores duobus rectis. </s>
  <s xml:id="echoid-s21260" xml:space="preserve">Quare coibit linea C G, cum dicto radio; </s>
  <s xml:id="echoid-s21261" xml:space="preserve">ac proinde cum recta C G, ſe-<lb/>cet vtrumque radium, hoc eſt, eum, qui eſt paralleli maximi ſemper apparentium, &amp; </s>
  <s xml:id="echoid-s21262" xml:space="preserve">eum, qui eſt <lb/>
<anchor type="note" xlink:label="note-0332-01a" xlink:href="note-0332-01"/>
paralleli ſemper latentiũ maximus, fient duæ hyperbolæ oppoſitæ, &amp; </s>
  <s xml:id="echoid-s21263" xml:space="preserve">æquales, vt ex dictis conſtat.</s>
  <s xml:id="echoid-s21264" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1079" type="float" level="2" n="7">
<note position="right" xlink:label="note-0331-07" xlink:href="note-0331-07a" xml:space="preserve">Qui arens fi-<lb/>gnorũ ſint hy-<lb/>perbolæ, qui pa <lb/>rabolæ, &amp; qui <lb/>ellipſes in horo <lb/>logio declinan <lb/>te à Verticali.</note>
<note position="left" xlink:label="note-0331-08" xlink:href="note-0331-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0331-09" xlink:href="note-0331-09a" xml:space="preserve">Arcus paralle-<lb/>lorum ſemper <lb/>apparentium, <lb/>ſemperq; laten <lb/>titum maximo-<lb/>rum ſunt hy-<lb/>perbolæ in ſu-<lb/>periori horolo-<lb/>gio.</note>
<note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">Quando linea <lb/>ſtyli vna eſt ex <lb/>horariis lineis, <lb/>vel æqualiter à <lb/>duabus hinc in <lb/>de diſtat, facili 9 <lb/>arcus ſignorũ <lb/>deſcribuntur.</note>
</div>
<p>
  <s xml:id="echoid-s21265" xml:space="preserve">QVANDO linea ſtyli eſt vna ex lineis horarijs, vel æqualiter à duabus horis hinc inde po-<lb/>ſitis diſtat, transferenda erunt ſingula interualla prædicta in binas lineas horarias æqualiter à linea <lb/>ſtyli in horologio remotas, vt in horizontali etiam horologio, Verticaliq́; </s>
  <s xml:id="echoid-s21266" xml:space="preserve">factum eſt.</s>
  <s xml:id="echoid-s21267" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s21268" xml:space="preserve">VT autem accuratius ſignorum arcus delineari poſſint, quando linea ſtyli inæqualiter à dua-<lb/>
<anchor type="note" xlink:label="note-0332-03a" xlink:href="note-0332-03"/>
bus horarijs lineis hinc inde collocatis fuerit remota, transferri poterunt omnia puncta horaria <lb/>lineæ æquinoctialis ad ſiniſtram, vel dextram lineæ indicis poſita, in alteram partem æquinoctia-<lb/>lis lineæ, nempe dextram, vel ſiniſtram eiuſdẽ lineæ ſtyli, initio ſemper facto à linea ſtyli: </s>
  <s xml:id="echoid-s21269" xml:space="preserve">Vel certè <lb/>(quod ego magis probo, quoniã aliquæ lineæ horariæ vix, aut nunquã æquinoctialẽ lineam ſecãt) <lb/>deſcripto arcu circuli ex centro C, poterunt eius portiones inter lineã indicis, &amp; </s>
  <s xml:id="echoid-s21270" xml:space="preserve">horarias lineas ex <lb/>vna parte lineę indicis transferri in eundẽ arcũ ex altera parte eiuſdem lineæ indicis. </s>
  <s xml:id="echoid-s21271" xml:space="preserve">Si enim per <lb/>puncta ſiue in linea æquinoctiali, ſiue in illo arcu (quod magis probatur) notata, ex cẽtro C, lineas <lb/>occultas duxerimus, quales in proxima figura ſunt lineæ minutis illis lineis diſtinctæ ad dextram <lb/>ipſius lineæ indicis exiſtẽtes, habebimus ſemper binas lineas æqualiter à linea indicis hinc inde re <lb/>
<anchor type="note" xlink:label="note-0332-04a" xlink:href="note-0332-04"/>
motas, in quas vnum, &amp; </s>
  <s xml:id="echoid-s21272" xml:space="preserve">idem ſpatiũ horarium inter C, &amp; </s>
  <s xml:id="echoid-s21273" xml:space="preserve">radiũ cuiuslibet ſigni interceptũ tranſ-<lb/>ferri poteſt, vt in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s21274" xml:space="preserve">Verticali. </s>
  <s xml:id="echoid-s21275" xml:space="preserve">Quod quidem ſi fiat, ſatis erit, ſi in figura ra-<lb/>
<anchor type="note" xlink:label="note-0332-05a" xlink:href="note-0332-05"/>
diorum ex C, ducamus lineas horarias reſpondentes horis contentis in horologio ex vna dunta-<lb/>xat parte, dextra vel ſiniſtra, lineæ indicis. </s>
  <s xml:id="echoid-s21276" xml:space="preserve">Nam ſi puncta horarum illarum in æquinoctiali linea, <lb/>vel arcu ex centro C, deſcripto, transferantur in alteram partem lineæ æquinoctialis, vel dicti ar-<lb/>cus, principio ſemper facto à linea indicis, &amp; </s>
  <s xml:id="echoid-s21277" xml:space="preserve">reliqua perficiantur, vt proximè præcepimus, deſcri <lb/>bentur arcus ſignorum, vt in horizontali horologio. </s>
  <s xml:id="echoid-s21278" xml:space="preserve">Atque hac ratione vitaretur confuſio linea-<lb/>rum ex C, per radium Aequatoris ductarum in figura radiorum. </s>
  <s xml:id="echoid-s21279" xml:space="preserve">Id quod in deſcriptione arcuum <lb/>ſignorum in horologio declinante ab Horizonte propoſ. </s>
  <s xml:id="echoid-s21280" xml:space="preserve">14. </s>
  <s xml:id="echoid-s21281" xml:space="preserve">huius libri obſeruatum eſſe videbis. <lb/></s>
  <s xml:id="echoid-s21282" xml:space="preserve">Rurſus ſi portiones rectæ C A, inter C, &amp; </s>
  <s xml:id="echoid-s21283" xml:space="preserve">radios ſignorum transferantur in horologium ex C, in <lb/>
<anchor type="note" xlink:label="note-0332-06a" xlink:href="note-0332-06"/>
rectam C d, ex vtraque parte centri C, habebimus in recta C d, puncta, per quæ arcus ſignorum <lb/>ducendi ſunt, velut in linea horæ 6. </s>
  <s xml:id="echoid-s21284" xml:space="preserve">horizontalis horologij, &amp; </s>
  <s xml:id="echoid-s21285" xml:space="preserve">Verticalis factum eſt.</s>
  <s xml:id="echoid-s21286" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1080" type="float" level="2" n="8">
<note position="left" xlink:label="note-0332-03" xlink:href="note-0332-03a" xml:space="preserve">Quando linea <lb/>ſtyli inæquali-<lb/>ter à duabus <lb/>horis hinc inde <lb/>diſtat, quid fa-<lb/>ciendum, vt ac-<lb/>cura@us arcus <lb/>ſignorũ deſcri-<lb/>bantur.</note>
<note position="left" xlink:label="note-0332-04" xlink:href="note-0332-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0332-05" xlink:href="note-0332-05a" xml:space="preserve">Qua ratione ſa <lb/>tis ſit, ſi in figu <lb/>ra radiorũ du-<lb/>cãtur lineæ ho-<lb/>rariæ reſpondẽ <lb/>tes ho ris cõten <lb/>tis in horolo-<lb/>gio ex altera dũ <lb/>taxat parte li-<lb/>neę ſtyli.</note>
<note position="left" xlink:label="note-0332-06" xlink:href="note-0332-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s21287" xml:space="preserve">PERTINENT autem in horologijs declinantibus à meridie arcus ſupra lineam æquino-<lb/>
<anchor type="note" xlink:label="note-0332-07a" xlink:href="note-0332-07"/>
ctialem verſus centrum deſcripti ad ſigna auſtralia: </s>
  <s xml:id="echoid-s21288" xml:space="preserve">reliqui verò ad borealia, veluti in Verticalibus <lb/>horologijs. </s>
  <s xml:id="echoid-s21289" xml:space="preserve">In declinantibus autem à ſeptentrione contrarium intelligatur. </s>
  <s xml:id="echoid-s21290" xml:space="preserve">Vt facile quiuis per-<lb/>cipere poteſt, ſi rectè concipiat animo poſitionem vtriuſque horologij, &amp; </s>
  <s xml:id="echoid-s21291" xml:space="preserve">ſitum parallelorum per <lb/>ſignorum initia ductorum.</s>
  <s xml:id="echoid-s21292" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1081" type="float" level="2" n="9">
<note position="left" xlink:label="note-0332-07" xlink:href="note-0332-07a" xml:space="preserve">Qui arcus ſi-<lb/>gnorum in ho-<lb/>rologio declinã <lb/>re à Verticali <lb/>pertineant ad <lb/>ſigna auſtralia, <lb/>&amp; qui ad borea <lb/>lia.</note>
</div>
<p>
  <s xml:id="echoid-s21293" xml:space="preserve">CAETERVM quando arcus ſignorum hyperbolæ ſunt oppoſitæ, &amp; </s>
  <s xml:id="echoid-s21294" xml:space="preserve">æquales, (quod quan-<lb/>
<anchor type="note" xlink:label="note-0332-08a" xlink:href="note-0332-08"/>
do fiat, paulò ante docuimus) multò accuratius in horologijs à meridie declinantibus deſcribe-<lb/>mus arcus ſignorum borealium ex arcubus auſtralium ſignorum tribus illis modis, quos ad finem <lb/>
<anchor type="note" xlink:label="note-0332-09a" xlink:href="note-0332-09"/>
propoſ. </s>
  <s xml:id="echoid-s21295" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21296" xml:space="preserve">ſuperioris libri tradidimus poſt demonſtrationem ſecundi modi deſcribendorum ar-<lb/>cuum ſignorum Zodiaci in horologio horizontali, qui ex figura, in qua radij omnium ſignorum <lb/>Zodiaci continentur, abſoluitur. </s>
  <s xml:id="echoid-s21297" xml:space="preserve">Nam in primo illorum modorum nulla eſt difficultas, ſi in li-<lb/>nea ſtyli inueniatur diameter tranſuerſa oppoſitarum hyperbolarum, earumq́ue centrum, nempe<unsure/> <lb/>punctum medium tranſuerſæ diametri, &amp; </s>
  <s xml:id="echoid-s21298" xml:space="preserve">reliqua perficiantur, vt in dicta propoſ. </s>
  <s xml:id="echoid-s21299" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21300" xml:space="preserve">præcedentis <lb/>lib. </s>
  <s xml:id="echoid-s21301" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s21302" xml:space="preserve">Quod verò ad ſecundum illorum modorum ſpectat, axis hyperbolarum in his ho <lb/>rologijs declinantibus eſt ipſamet linea ſtyli. </s>
  <s xml:id="echoid-s21303" xml:space="preserve">Portiones autem arcuum ſignorum auſtralium vſq; <lb/></s>
  <s xml:id="echoid-s21304" xml:space="preserve">ad axem hyperbolarum oppoſitarum, ſeu lineam ſtyli, deſcribendæ ſunt ad partes horæ 6. </s>
  <s xml:id="echoid-s21305" xml:space="preserve">quia eæ <lb/>commodius deſcribi poſlunt, quàm aliæ verſus horam 12. </s>
  <s xml:id="echoid-s21306" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21307" xml:space="preserve">ex eis vno labore non ſolum reliquæ <lb/>portiones ex altera parte, verum etiam toti arcus ſignorum borealium, qui illis opponuntur, facili <lb/>
<anchor type="note" xlink:label="note-0332-10a" xlink:href="note-0332-10"/>
negotio delineabuntur, vt in prædicto modo oſtendimus ſuo loco. </s>
  <s xml:id="echoid-s21308" xml:space="preserve">Eſt porrò ſecundus hic modus <lb/>valde accommodatus ad arcus ſignorum borealium, &amp; </s>
  <s xml:id="echoid-s21309" xml:space="preserve">oppoſitorum rectè deſcribendos, hoc eſt, <lb/>qui à centro horologii remotiores ſunt. </s>
  <s xml:id="echoid-s21310" xml:space="preserve">Nam, vt vides, horariæ lineę ex C, in figura radiorum ca-<lb/>dentes, quò longius protenduntur, eò maiorem errandi prębent occaſionem in deſcribendis arcu-<lb/>bus per radios ſignorum ad ſiniſtram radij Aequatoris in illa figura collocatos, quales hic ſunt ra-<lb/>dij ſignorum borealium; </s>
  <s xml:id="echoid-s21311" xml:space="preserve">propterea quòd vix fieri poteſt, vt ſine errore accipiantur puncta, vbi di-<lb/>cti radij à lineis horarijs ſecantur, niſi ſumma diligentia dictæ omnes lineæ ductæ ſint. </s>
  <s xml:id="echoid-s21312" xml:space="preserve">At vero <lb/>puncta in radijs ſignorum, qui ad dextram radij Aequatoris ponuntur, vicinioresq́ue ſunt puncto <lb/>C, quales hic ſunt radij auſtralium ſignorum, facilius deprehendi poſſunt, propter breuitatem li-<lb/>nearum ex C, cadentium, quæ inter C, &amp; </s>
  <s xml:id="echoid-s21313" xml:space="preserve">dictos radios comprehenduntur, ſi conferantur cum eiſ-<lb/>dem rectis inter C, &amp; </s>
  <s xml:id="echoid-s21314" xml:space="preserve">radios ſignorum borealium comprehenſis. </s>
  <s xml:id="echoid-s21315" xml:space="preserve">Vnde certius arcus ſignorum
<pb o="317" file="0333" n="333" rhead="LIBER TERTIVS."/>
auſtralium, quorum radij puncto C, viciniores ſunt, deſcribemus, quàm borealium, quorum ra-<lb/>dij longius ab eodem puncto C, abſunt. </s>
  <s xml:id="echoid-s21316" xml:space="preserve">Nam in illis rectæ ex C, emiſſæ non poterunt nos indu-<lb/>cere in inſignem aliquem, &amp; </s>
  <s xml:id="echoid-s21317" xml:space="preserve">notabilem errorem, in his autem poſſunt, vt diximus, &amp; </s>
  <s xml:id="echoid-s21318" xml:space="preserve">ex ipſa figura <lb/>apparere poteſt. </s>
  <s xml:id="echoid-s21319" xml:space="preserve">Quod denique ad tertium modum attinet, commodius ducentur ex puncto Φ, <lb/>lineæ illæ rectæ occultæ, inſtar horariarum linearum ex centro C, egredientium; </s>
  <s xml:id="echoid-s21320" xml:space="preserve">beneficio arcuum <lb/>circulorum æqualiũ ex C, &amp; </s>
  <s xml:id="echoid-s21321" xml:space="preserve">Φ, deſcriptorũ, quàm miniſterio rectæ, quæ per χ, æquinoctiali lineæ <lb/>ducitur parallela; </s>
  <s xml:id="echoid-s21322" xml:space="preserve">quia vix, aut nunquam lineæ nonnullę horariæ dictam rectam ſecant, vt pater. <lb/></s>
  <s xml:id="echoid-s21323" xml:space="preserve">In exemplo duximus ex Φ, ad dextram lineæ ſtyli rectas occultas reſpondentes illis lineis, quæ ex <lb/>C, ductę ſunt etiam occultę per illa puncta æquinoctialis lineę, ſeu arcus circuli ex C, deſcripti, <lb/>quę translata ſunt ex altera parte lineę ęquinoctialis, vel dicti arcus; </s>
  <s xml:id="echoid-s21324" xml:space="preserve">quia hac ratione, vno labore <lb/>
<anchor type="note" xlink:label="note-0333-01a" xlink:href="note-0333-01"/>
hyperbolę deſcribi poſſunt ex vtraque parte lineæ ſtyli, vt in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s21325" xml:space="preserve">in Ver-<lb/>ticali, &amp;</s>
  <s xml:id="echoid-s21326" xml:space="preserve">c.</s>
  <s xml:id="echoid-s21327" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1082" type="float" level="2" n="10">
<note position="left" xlink:label="note-0332-08" xlink:href="note-0332-08a" xml:space="preserve">Quo pacto hy-<lb/>perbolæ borea-<lb/>lium ſignorum <lb/>ex hyperbolis <lb/>oppoſitis ſigno <lb/>rum auſtraliũ <lb/>deſcribantur.</note>
<note position="left" xlink:label="note-0332-09" xlink:href="note-0332-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0332-10" xlink:href="note-0332-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0333-01" xlink:href="note-0333-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s21328" xml:space="preserve">HORIZONTALIS linea, hoc eſt, communis ſectio plani horologij declinantis, &amp; </s>
  <s xml:id="echoid-s21329" xml:space="preserve">Ho-<lb/>
<anchor type="note" xlink:label="note-0333-02a" xlink:href="note-0333-02"/>
rizontis, ducitur per K, locum ſtyli ad lineam meridianam, ſeu horæ 12. </s>
  <s xml:id="echoid-s21330" xml:space="preserve">perpendicularis, tranſitq́; <lb/></s>
  <s xml:id="echoid-s21331" xml:space="preserve">neceſſario per punctum illud, vbi linea ęquinoctialis, &amp; </s>
  <s xml:id="echoid-s21332" xml:space="preserve">linea horę 6. </s>
  <s xml:id="echoid-s21333" xml:space="preserve">ſe mutuo interſecant, niſi er-<lb/>ratum ſit in ducenda linea horę 6. </s>
  <s xml:id="echoid-s21334" xml:space="preserve">vel ęquinoctiali. </s>
  <s xml:id="echoid-s21335" xml:space="preserve">Quoniam enim Horizon rectus eſt ad planũ <lb/>horologij declinantis, tranſitq́ue per verticem ſtyli, qui rectus eſt quoque ad idem planum, tranſi-<lb/>bit omnino per totum ſtylum, nempe per axem plani horologij: </s>
  <s xml:id="echoid-s21336" xml:space="preserve">Nam omnia plana per ſtylum <lb/>ducta ad planum horologij recta ſunt. </s>
  <s xml:id="echoid-s21337" xml:space="preserve">Quare Horizon plano horologij occurret in K, atque adeo <lb/>
<anchor type="note" xlink:label="note-0333-03a" xlink:href="note-0333-03"/>
per k, ducenda erit linea horizontalis. </s>
  <s xml:id="echoid-s21338" xml:space="preserve">Et quoniam tam planum horologij, quàm Meridiani ad <lb/>
<anchor type="note" xlink:label="note-0333-04a" xlink:href="note-0333-04"/>
Horizontem eſt rectum, erit &amp; </s>
  <s xml:id="echoid-s21339" xml:space="preserve">communis eorum ſectio, nempe linea meridiana, ad eundem per-<lb/>
<anchor type="note" xlink:label="note-0333-05a" xlink:href="note-0333-05"/>
pendicularis. </s>
  <s xml:id="echoid-s21340" xml:space="preserve">Igitur per definitionem tertiam lib. </s>
  <s xml:id="echoid-s21341" xml:space="preserve">11. </s>
  <s xml:id="echoid-s21342" xml:space="preserve">Euclidis, perpendicularis quoque erit ad <lb/>communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s21343" xml:space="preserve">plani horologii in ipſo Horizonte exiſtentem. </s>
  <s xml:id="echoid-s21344" xml:space="preserve">Quamobrẽ <lb/>recta per K, ducta perpendicularis ad meridianam lineam, communis ſectio erit Horizontis, &amp; </s>
  <s xml:id="echoid-s21345" xml:space="preserve"><lb/>plani horologij, hoc eſt, horizontalis linea; </s>
  <s xml:id="echoid-s21346" xml:space="preserve">quam neceſſario tranſire debere per horam 6. </s>
  <s xml:id="echoid-s21347" xml:space="preserve">in æqui <lb/>noctiali linea, ita perſpicuum faciemus. </s>
  <s xml:id="echoid-s21348" xml:space="preserve">Quoniam Sole exiſtente in communi ſectione Aequato-<lb/>ris, circuli horæ 6. </s>
  <s xml:id="echoid-s21349" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21350" xml:space="preserve">Horizontis, radius ipſius in centrum mundi cadens à planis horum circulo-<lb/>rum non recedit, ſed in communes eorum ſectiones, quas cum plano horologij faciunt, cadit, vt <lb/>ex propoſ. </s>
  <s xml:id="echoid-s21351" xml:space="preserve">11. </s>
  <s xml:id="echoid-s21352" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21353" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21354" xml:space="preserve">liquet; </s>
  <s xml:id="echoid-s21355" xml:space="preserve">cadet neceſſario vmbra ſtyli in punctum illud horologij, vbi ſe mutuo <lb/>ſecant dictorum circulorum ſectiones, hoc eſt, per horam 6. </s>
  <s xml:id="echoid-s21356" xml:space="preserve">in æquinoctiali linea; </s>
  <s xml:id="echoid-s21357" xml:space="preserve">alioquin vm-<lb/>
<anchor type="note" xlink:label="note-0333-06a" xlink:href="note-0333-06"/>
bra ſtyli non caderet in vtramque lineam, vt pater. </s>
  <s xml:id="echoid-s21358" xml:space="preserve">Tranſit igitur linea horizontalis per illud pun <lb/>ctum, vbi ſe mutuo interſecant linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s21359" xml:space="preserve">linea horæ 6.</s>
  <s xml:id="echoid-s21360" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1083" type="float" level="2" n="11">
<note position="right" xlink:label="note-0333-02" xlink:href="note-0333-02a" xml:space="preserve">Linea horizon-<lb/>talis in horolo <lb/>gio declinante <lb/>à Verticali quo <lb/>modo ducatur.</note>
<note position="right" xlink:label="note-0333-03" xlink:href="note-0333-03a" xml:space="preserve">13. vndec.</note>
<note position="left" xlink:label="note-0333-04" xlink:href="note-0333-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0333-05" xlink:href="note-0333-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0333-06" xlink:href="note-0333-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s21361" xml:space="preserve">HÆC autem linea horizontalis partitur totum horologium in duo, quorũ illud, in quo cen-<lb/>
<anchor type="note" xlink:label="note-0333-07a" xlink:href="note-0333-07"/>
trum non eſt, ad meridiem ſpectat, aliud verò ad Boream. </s>
  <s xml:id="echoid-s21362" xml:space="preserve">Vtrumque in muro, qui declinationẽ <lb/>habeat æqualem ei, ad quam horologium eſt conſtructum, ita collocandum eſt, vt linea horizon-<lb/>talis Horizonti ſit parallela, ſuperioremq́ue occupet locum, hac etiam conditione adiecta, vt in <lb/>
<anchor type="note" xlink:label="note-0333-08a" xlink:href="note-0333-08"/>
Boreali, in quo arcus ſignorum auſtralium in arcus borealium ſignorum mutantur, &amp; </s>
  <s xml:id="echoid-s21363" xml:space="preserve">contra, non <lb/>ſolum horizontalis linea in ſuperiori loco ponatur, verumetiam lineamenta, quæ nobis in eo ſitu <lb/>ad horologium conuerſis dextra ſunt, fiant ſiniſtra, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s21364" xml:space="preserve">14. </s>
  <s xml:id="echoid-s21365" xml:space="preserve">ſuperioris libri de-<lb/>monſtrauimus.</s>
  <s xml:id="echoid-s21366" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1084" type="float" level="2" n="12">
<note position="right" xlink:label="note-0333-07" xlink:href="note-0333-07a" xml:space="preserve">Horizontalis li <lb/>nea ſecat totũ <lb/>horologium in <lb/>auſtrale &amp; bo-<lb/>reale.</note>
<note position="right" xlink:label="note-0333-08" xlink:href="note-0333-08a" xml:space="preserve">Quomodo ho-<lb/>tologium tam <lb/>au@@ale, quàm <lb/>boreale in pro-<lb/>prio ſitu collo-<lb/>candum ſit.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s21367" xml:space="preserve">PLERVNQVE autem contingir, vt in boreali horologio ex altera tantum parte lineæ me-<lb/>
<anchor type="note" xlink:label="note-0333-10a" xlink:href="note-0333-10"/>
ridianæ contineantur horæ, in quam nimirum vmbra gnomonis cadit veſpertino tempore, ſi à <lb/>borea in occaſum declinet, vel matutino, ſi in ortum: </s>
  <s xml:id="echoid-s21368" xml:space="preserve">quoniam alteram partem matutino, aut ve-<lb/>ſpertino tempore Sol non illuſtrat, niſi quando planum parum à Verticali declinat, vt manifeſtum <lb/>eſt, ſi diligenter planum declinans in proprio ſitu conſideretur. </s>
  <s xml:id="echoid-s21369" xml:space="preserve">Id quod perpulchrè nobis linea <lb/>horizontalis demonſtrat. </s>
  <s xml:id="echoid-s21370" xml:space="preserve">Quando enim hęc duobus in locis parallelum ♑, in auſtrali horologio <lb/>interſecat, deſcribendæ erunt horæ in boreali horologio ad vtrainque partem lineæ meridianæ: <lb/></s>
  <s xml:id="echoid-s21371" xml:space="preserve">
<anchor type="note" xlink:label="note-0333-11a" xlink:href="note-0333-11"/>
quando vero in vno tantum loco, ad alteram partem duntaxat. </s>
  <s xml:id="echoid-s21372" xml:space="preserve">Siautem ſcire deſideres, quãta de-<lb/>beat eſſe declinatio, vt borealis facies plani declinantis tam mane, quàm veſperi à Sole illuminari <lb/>poſſit, voti compos fies hoc modo. </s>
  <s xml:id="echoid-s21373" xml:space="preserve">Quando declinatio plani minor fuerit latitudine ortiua, oc-<lb/>
<anchor type="note" xlink:label="note-0333-12a" xlink:href="note-0333-12"/>
ciduave primi puncti ♋, (quo pacto verò hæc latitudo ſit exploranda, demonſtrauimus propoſ. <lb/></s>
  <s xml:id="echoid-s21374" xml:space="preserve">34. </s>
  <s xml:id="echoid-s21375" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21376" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21377" xml:space="preserve">doceturq́ue à Ioan. </s>
  <s xml:id="echoid-s21378" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s21379" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21380" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21381" xml:space="preserve">Epitom. </s>
  <s xml:id="echoid-s21382" xml:space="preserve">propoſ 1. </s>
  <s xml:id="echoid-s21383" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21384" xml:space="preserve">2.) </s>
  <s xml:id="echoid-s21385" xml:space="preserve">plani facies borealis à So-<lb/>le in principio ♋, exiſtente illuminatur manè, &amp; </s>
  <s xml:id="echoid-s21386" xml:space="preserve">veſperi. </s>
  <s xml:id="echoid-s21387" xml:space="preserve">Quando verò maior fuerit declinatio pla <lb/>ni latitudine prædicta, eadem ſacies borealis plani veſperi duntaxat, aut mane radios Solis exci-<lb/>pit, prout in occaſum, vel ortum à borea deflectit. </s>
  <s xml:id="echoid-s21388" xml:space="preserve">Quę omnia vel facile ex ſphęra materiali co-<lb/>gnoſci poſſunt, &amp; </s>
  <s xml:id="echoid-s21389" xml:space="preserve">intelligi. </s>
  <s xml:id="echoid-s21390" xml:space="preserve">Etſi verò tam manè, quàm veſperi facies borealis illuſtratur à Sole, cũ <lb/>
<anchor type="note" xlink:label="note-0333-13a" xlink:href="note-0333-13"/>
declinatio plani minor eſt latitudine ortiua, &amp; </s>
  <s xml:id="echoid-s21391" xml:space="preserve">occidua principij ♋, longiori tamen temporis ſpa-<lb/>tio illuminabitur matutino tempore, quàm veſpertino, ſi planum à borea in ortum deflectat, bre-<lb/>uiori autem, ſi in occaſum vergat, vt perſpicuum eſt: </s>
  <s xml:id="echoid-s21392" xml:space="preserve">quemadmodum etiam facies auſtralis in or-<lb/>tum vergens longiore tempore illuſtratur mane, quàm veſperi, longiore autẽ veſperi, quàm ma-<lb/>ne, ſi facies auſtralis ad occaſum ſpectet.</s>
  <s xml:id="echoid-s21393" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1085" type="float" level="2" n="13">
<note position="right" xlink:label="note-0333-10" xlink:href="note-0333-10a" xml:space="preserve">Aliquando ho-<lb/>rologium bo-<lb/>reale habet ho-<lb/>ras ex vna tan-<lb/>tum parte lineę <lb/>meridianæ.</note>
<note position="right" xlink:label="note-0333-11" xlink:href="note-0333-11a" xml:space="preserve">Qua ratione co <lb/>gnoſci poſſit, <lb/>num borealis <lb/>facies plani de-<lb/>clinantis illu-<lb/>minati poſſit <lb/>mane&amp; ueſperi <lb/>à Sole, an ma-<lb/>ne tantum, aut <lb/>veſperi.</note>
<note position="left" xlink:label="note-0333-12" xlink:href="note-0333-12a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0333-13" xlink:href="note-0333-13a" xml:space="preserve">Quando planũ <lb/>tam ad boream <lb/>ſp@ctans, quàm <lb/>ad auſtrum, lon <lb/>giore tempore <lb/>illuminatur <lb/>mane à Sole, <lb/>quàm veſperi, <lb/>aut contia.</note>
</div>
<pb o="318" file="0334" n="334" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s21394" xml:space="preserve">EADEM linea horizontalis bipartitur horologium declinans in diurnum, quod infra ipſam <lb/>
<anchor type="note" xlink:label="note-0334-01a" xlink:href="note-0334-01"/>
lineam horizontalem continetur, &amp; </s>
  <s xml:id="echoid-s21395" xml:space="preserve">in nocturnum, quod ſupra eandem delineatum eſt, vt in ſu-<lb/>perioribus quoque diximus. </s>
  <s xml:id="echoid-s21396" xml:space="preserve">Itaque parallelos, ſiue arcus ſignorum Zodiaci in horologio, quod <lb/>à Verticali circulo declinat, deſcripſimus. </s>
  <s xml:id="echoid-s21397" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s21398" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1086" type="float" level="2" n="14">
<note position="left" xlink:label="note-0334-01" xlink:href="note-0334-01a" xml:space="preserve">Horizontalis li <lb/>nea totum ho-<lb/>rologium parti <lb/>tur in diurnũ <lb/>ac nocturnum.</note>
</div>
</div>
<div xml:id="echoid-div1088" type="section" level="1" n="257">
<head xml:id="echoid-head266" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s21399" xml:space="preserve">LINEAS horari{as} in figura radiorum ex puncto C, hac ratione educit Andreas Schonerus. </s>
  <s xml:id="echoid-s21400" xml:space="preserve">Du-<lb/>
<anchor type="note" xlink:label="note-0334-02a" xlink:href="note-0334-02"/>
cta recta C G, vt pri{us}, ſumit in ea producta punctum quodcunque B, per quod lineam B A, ipſi C I, pa <lb/>rallelam agit, quæ rectam C A, radio Aequatoris parallelam ſecet in A. </s>
  <s xml:id="echoid-s21401" xml:space="preserve">Deinde centro A, &amp; </s>
  <s xml:id="echoid-s21402" xml:space="preserve">interual-<lb/>lo A B, deſcriptum circulum ſecat in partes 24. </s>
  <s xml:id="echoid-s21403" xml:space="preserve">ęquales, initio facto à puncto quodam, quod hac ratio-<lb/>
<anchor type="note" xlink:label="note-0334-03a" xlink:href="note-0334-03"/>
ne inquirit. </s>
  <s xml:id="echoid-s21404" xml:space="preserve">Rectam L M, in horologio inter centrum L, &amp; </s>
  <s xml:id="echoid-s21405" xml:space="preserve">lineam meridianam interiectam transfert in <lb/>radium Aequatoris ex I, vſque ad E, &amp; </s>
  <s xml:id="echoid-s21406" xml:space="preserve">per E, ex C, rectam ducit C E, pro linea horę 12. </s>
  <s xml:id="echoid-s21407" xml:space="preserve">quæ rectam <lb/>B A, ſecet in D; </s>
  <s xml:id="echoid-s21408" xml:space="preserve">atque ex D, excitat ad B A, perpendicularem D E, quæ circunferentiam circuli ſecet <lb/>in F, puncto, quod initium diuiſionis circuli erit. </s>
  <s xml:id="echoid-s21409" xml:space="preserve">Sed quoniam, quando linea meridiana in horologio val-<lb/>
<anchor type="note" xlink:label="note-0334-04a" xlink:href="note-0334-04"/>
de vicina eſt lineæ ſtyli, at que adeo in figura radiorum recta C D, ipſi C B, linea D F, quę ad A B, per-<lb/>pendicularis ducta eſt, adeò obliquè circunferentiam ſecat in F, prope punctum B, vt vix ſine errore pun <lb/>ctum F, dignoſci queat, examinabimus punctum F, antequàm ad diuiſionem circuli accedam{us}, inueſti-<lb/>gando aliud punctum, à quo eadem diuiſio inchoari poſſit, hoc modo. </s>
  <s xml:id="echoid-s21410" xml:space="preserve">In horologio ſumem{us} interuallum <lb/>inter centrum L, &amp; </s>
  <s xml:id="echoid-s21411" xml:space="preserve">horam quamcumque in æquinoctiali linea, quę aliquanto remotior ſit à linea ſtyli, <lb/>quàm hora 12. </s>
  <s xml:id="echoid-s21412" xml:space="preserve">vt v.</s>
  <s xml:id="echoid-s21413" xml:space="preserve">g. </s>
  <s xml:id="echoid-s21414" xml:space="preserve">in exemplo propoſito, interuallum inter I, &amp; </s>
  <s xml:id="echoid-s21415" xml:space="preserve">horam 1. </s>
  <s xml:id="echoid-s21416" xml:space="preserve">illud{q́ue} in radium Aequa-<lb/>
<anchor type="note" xlink:label="note-0334-05a" xlink:href="note-0334-05"/>
toris ex I, transferem{us} vſque ad H, &amp; </s>
  <s xml:id="echoid-s21417" xml:space="preserve">ex C, per H, rectam ducemus C H, pro illa hora 1. </s>
  <s xml:id="echoid-s21418" xml:space="preserve">quæ rectam <lb/>B A, ſecet in L, atque ex L, erigem{us} ad B A, perpendicularem L M, quæ ſecet circunferentiam in M. <lb/></s>
  <s xml:id="echoid-s21419" xml:space="preserve">Ab hoc ergo puncto diuiſionem inchoare potcrim{us}. </s>
  <s xml:id="echoid-s21420" xml:space="preserve">Ducenda est autem perpendicularis L M, verſ{us} <lb/>eandem partem, in quam ducta eſt D F, ſi hora accepta fuerit ex eadem parte lineæ indicis, in qua hora <lb/>12. </s>
  <s xml:id="echoid-s21421" xml:space="preserve">exiſiit, in contrariam autem partem, ſi ex altera parte fuerit ſumpta, vt contingeret, ſi horam 5. </s>
  <s xml:id="echoid-s21422" xml:space="preserve">ſu-<lb/>merem{us}. </s>
  <s xml:id="echoid-s21423" xml:space="preserve">Hæc enim translata in radium Aequatoris ex I, vſque ad N, dabit quidem lineam C N, pro <lb/>hora 5. </s>
  <s xml:id="echoid-s21424" xml:space="preserve">quæ rectam B A, ſecat in O; </s>
  <s xml:id="echoid-s21425" xml:space="preserve">ſed quia hora 5. </s>
  <s xml:id="echoid-s21426" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21427" xml:space="preserve">hora 12. </s>
  <s xml:id="echoid-s21428" xml:space="preserve">ad diuerſas partes lineę styli exiſtunt, <lb/>propterea perpendiculares D F, O P, in diuerſ{as} quoque partes ductæ ſunt: </s>
  <s xml:id="echoid-s21429" xml:space="preserve">æquè tamen bene à puncto <lb/>P, diuiſio circuli principium ſumere poteſt, atque à puncto F, vel M. </s>
  <s xml:id="echoid-s21430" xml:space="preserve">Itaque ſiue à puncto M, ſiue à P, di-<lb/>uiſio initium habeat, ſi punctum aliquod diuiſionis cadat in F, quod per primam perpendicularem D F, <lb/>
<anchor type="note" xlink:label="note-0334-06a" xlink:href="note-0334-06"/>
inuentum fuerat, ex ſententia res ſuccedet, ſin minus, corrigend{us} erit error, qui fortaſſis alicubi commiſ-<lb/>ſus eſt. </s>
  <s xml:id="echoid-s21431" xml:space="preserve">Immo expedit omnino, ſi rem cupimus omnib{us} numeris abſolutam, vt duo puncta inueniamus, à <lb/>quibus diuiſio poſſit inchoari. </s>
  <s xml:id="echoid-s21432" xml:space="preserve">Nam ſi diuiſio ab vno inchoata in alterum cadat, certi erim{us}, diuiſionem <lb/>circuli eſſe ſatis exquiſitam. </s>
  <s xml:id="echoid-s21433" xml:space="preserve">Diuiſo igitur circulo, ducit idem auctor ex punctis diuiſionum ad rectam <lb/>B A, perpendiculares, vel ipſi C A, parallel{as} ſecantes rectam B A, in punctis, per quę rectæ ex C, emiſ-<lb/>ſę dant horari{as} line{as}, vt pri{us}. </s>
  <s xml:id="echoid-s21434" xml:space="preserve">Facile autem erit iudicare, quæ lineę quibus horis in horologio reſpon <lb/>deant. </s>
  <s xml:id="echoid-s21435" xml:space="preserve">Nam puncta diuiſionum circuli à puncto F, horæ 12. </s>
  <s xml:id="echoid-s21436" xml:space="preserve">procedendo verſ{us} B, in quod linea indicis <lb/>cadit, referunt hor{as}, quæ in linea æquinoctiali horologĳ boram 12. </s>
  <s xml:id="echoid-s21437" xml:space="preserve">ſequuntur verſ{us} indicis lineã, adeo <lb/>vt proximum punctum ab F, verſus B, in exemplo nostro pertineat ad horam 11. </s>
  <s xml:id="echoid-s21438" xml:space="preserve">ſequens ad 10. </s>
  <s xml:id="echoid-s21439" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21440" xml:space="preserve">ſic <lb/>deinceps, vt figura indicat. </s>
  <s xml:id="echoid-s21441" xml:space="preserve">Rectæ autẽ ex C, eductę per puncta perpendicularium in recta B A, illas ho-<lb/>
<anchor type="note" xlink:label="note-0334-07a" xlink:href="note-0334-07"/>
r{as} referunt, à quibus dictę perpendiculares in ipſam B A, cadunt.</s>
  <s xml:id="echoid-s21442" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1088" type="float" level="2" n="1">
<note position="left" xlink:label="note-0334-02" xlink:href="note-0334-02a" xml:space="preserve">Braxis pulcher-<lb/>rima pro lineis <lb/>horariis in figu <lb/>ra ra diorũ Zo-<lb/>diaci ducendis, <lb/>ſine interuallis <lb/>horariis horolo <lb/>g@@.</note>
<note position="left" xlink:label="note-0334-03" xlink:href="note-0334-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0334-04" xlink:href="note-0334-04a" xml:space="preserve">Quando linea <lb/>meridiana in <lb/>horologio pro-<lb/>pinqua eſt li-<lb/>neæ ſtyli, quo-<lb/>modo inueniẽ-<lb/>da ſint alia pun <lb/>cta, à quibus di <lb/>uiſio circuli ex <lb/>A, deſc ripti in-<lb/>choari poſſit.</note>
<note position="left" xlink:label="note-0334-05" xlink:href="note-0334-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0334-06" xlink:href="note-0334-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0334-07" xlink:href="note-0334-07a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s21443" xml:space="preserve">CAETERVM ſine magno negotio ex punctis diuiſionum circuli ex A, deſcripti, ad rectam B A, <lb/>perpendiculares, vel ipſi C A, parallelas ducem{us}, hac ratione. </s>
  <s xml:id="echoid-s21444" xml:space="preserve">Si contingat à puncto B, duo proxima <lb/>puncta æqualiter hinc inde diſtare (quod tum demum eueniet, cum ſtyli linea in horologio fuerit vel vna <lb/>ex lineis horarĳs, vel à duab{us} proximis horarĳs lineis hinc inde poſitis ęqualiter receſſerit) erunt re-<lb/>ctæ lineę bina puncta à puncto B, æqualiter distantia coniungentes ad rectam B A, perpendiculares. </s>
  <s xml:id="echoid-s21445" xml:space="preserve">Sin <lb/>minus, ſumptum cuiusuis puncti in ſemicirculo ſuperiori interuallum ex puncto B, transferatur in infe-<lb/>riorem ſemicirculum. </s>
  <s xml:id="echoid-s21446" xml:space="preserve">Recta enim ſuperi{us} punctum cum inferiori translato connectens perpendicularis <lb/>erit ad B A. </s>
  <s xml:id="echoid-s21447" xml:space="preserve">Nam hac ratione recta B A, per centrum A, ducta diuidet arcum inter duo illa puncta bi <lb/>fariam in D. </s>
  <s xml:id="echoid-s21448" xml:space="preserve">Quare ex priore coroll. </s>
  <s xml:id="echoid-s21449" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s21450" xml:space="preserve">10. </s>
  <s xml:id="echoid-s21451" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21452" xml:space="preserve">13. </s>
  <s xml:id="echoid-s21453" xml:space="preserve">Euclid. </s>
  <s xml:id="echoid-s21454" xml:space="preserve">recta B A, ad rectam illa puncta coniun-<lb/>
<anchor type="note" xlink:label="note-0334-08a" xlink:href="note-0334-08"/>
gentem perpendicularis erit. </s>
  <s xml:id="echoid-s21455" xml:space="preserve">Idem fiet, ſi interualla punctorum inferioris ſemicir culi ex B, in ſuperiorem <lb/>ſemicirculum transfer antur, vt factum eſſe vides in ſuperiori figur a radiorum.</s>
  <s xml:id="echoid-s21456" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1089" type="float" level="2" n="2">
<note position="left" xlink:label="note-0334-08" xlink:href="note-0334-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s21457" xml:space="preserve">QVOD ſi ex figura radiorum hactenus constructa mai{us}, aut min{us} horologium pro data ſtyli ma-<lb/>
<anchor type="note" xlink:label="note-0334-09a" xlink:href="note-0334-09"/>
gnitudine fabricandum ſit, efficiem{us} id hoc modo. </s>
  <s xml:id="echoid-s21458" xml:space="preserve">Deſcribatur ſeorſum, vt prope figuram radiorum fa-<lb/>ctum eſt, triangulum C I G, ex horologio antecedentis propoſ. </s>
  <s xml:id="echoid-s21459" xml:space="preserve">vel ex figura radiorum, vel certe ex horo <lb/>logio, quod in ſcholio propoſ. </s>
  <s xml:id="echoid-s21460" xml:space="preserve">antecedentis deſcripſim{us} ad datam ſtyli longitudinem, deſumptum, in quo <lb/>C I, axis mundi eſt; </s>
  <s xml:id="echoid-s21461" xml:space="preserve">I G, Aequator; </s>
  <s xml:id="echoid-s21462" xml:space="preserve">C G, linea ſtyli, in quam gnomon I K, cadit ad angulos rectos. </s>
  <s xml:id="echoid-s21463" xml:space="preserve">Pro-<lb/>ductis deinde rectis I C, I G, I k, ſi ſumatur in I K, recta I A, dato gnomoni æqualis, ſiue maior is fuerit <lb/>gnomone I K, ſiue minor, &amp; </s>
  <s xml:id="echoid-s21464" xml:space="preserve">per A, ipſi C G, parallela agatur B D, erit triangulũ B I D, triangulo C I G, <lb/>ſimile, ex coroll. </s>
  <s xml:id="echoid-s21465" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s21466" xml:space="preserve">4. </s>
  <s xml:id="echoid-s21467" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21468" xml:space="preserve">6. </s>
  <s xml:id="echoid-s21469" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s21470" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s21471" xml:space="preserve">ſi axis I B, trãsferatur in figurã radiorum ex C, vſque ad <lb/>B, verſus I, &amp; </s>
  <s xml:id="echoid-s21472" xml:space="preserve">ex B, radi{us} Aequatoris cũ aliorum ſignorũradĳs educatur, &amp; </s>
  <s xml:id="echoid-s21473" xml:space="preserve">reliqua omnia fiant, vt.</s>
  <s xml:id="echoid-s21474" xml:space="preserve">
<pb o="319" file="0335" n="335" rhead="LIBER TERTIVS."/>
pri{us}, deſcribentur arc{us} ſignorum pro magnitudine dati ſtyli I A, ſicut antea ad datum ſtylum I K, de-<lb/>ſcripti ſunt. </s>
  <s xml:id="echoid-s21475" xml:space="preserve">Nam lineæ horarię in horologio, &amp; </s>
  <s xml:id="echoid-s21476" xml:space="preserve">in figura radiorum eędem permanent in eadem altitudi-<lb/>ne poli, non variata declinatione plani. </s>
  <s xml:id="echoid-s21477" xml:space="preserve">Sed loc{us} styli I A, erit punctum in linea ſtyli, quod terminat <lb/>rectam à centro C, inchoatam ipſi B A, æqualem. </s>
  <s xml:id="echoid-s21478" xml:space="preserve">Aequinoctialis quoque linea ducenda eſt perpendicu-<lb/>laris ad lineam ſtyli per punctum, quod tanto ſpatio à centro C, abeſt, quanta eſt recta B D.</s>
  <s xml:id="echoid-s21479" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1090" type="float" level="2" n="3">
<note position="left" xlink:label="note-0334-09" xlink:href="note-0334-09a" xml:space="preserve">Qua ratione ex <lb/>figura radiorũ <lb/>maius, aut mi-<lb/>nus horologiũ <lb/>pro data ſtyli <lb/>longitudine fa <lb/>bricandum ſit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s21480" xml:space="preserve">IAM verò eoſdem parallelos, arcusve ſignorum in horologio declinante, quod in ſcholio pręceden-<lb/>
<anchor type="note" xlink:label="note-0335-01a" xlink:href="note-0335-01"/>
tis propoſ. </s>
  <s xml:id="echoid-s21481" xml:space="preserve">delineauim{us}, licet centrum illi{us} non inuenerim{us}, deſcribem{us} eiſdem ſerè rationib{us}, qu{as} <lb/>
<anchor type="figure" xlink:label="fig-0335-01a" xlink:href="fig-0335-01"/>
<anchor type="note" xlink:label="note-0335-02a" xlink:href="note-0335-02"/>
<anchor type="note" xlink:label="note-0335-03a" xlink:href="note-0335-03"/>
<anchor type="note" xlink:label="note-0335-04a" xlink:href="note-0335-04"/>
<anchor type="note" xlink:label="note-0335-05a" xlink:href="note-0335-05"/>
<anchor type="note" xlink:label="note-0335-06a" xlink:href="note-0335-06"/>
in hac propoſ. </s>
  <s xml:id="echoid-s21482" xml:space="preserve">tradidim{us}. </s>
  <s xml:id="echoid-s21483" xml:space="preserve">Nam quod ad priorem attinet, conficiendum erit Analemma pro altitudine <lb/>poli ſupra planum declinans, quam ex propoſ. </s>
  <s xml:id="echoid-s21484" xml:space="preserve">29. </s>
  <s xml:id="echoid-s21485" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21486" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21487" xml:space="preserve">reperiem{us}, vel certè eam ex angulo G C I, in di-
<pb o="320" file="0336" n="336" rhead="GNOMONICES"/>
cto horologio deſumem{us}, hic enim altitudinem poli ſupra planum declinans oſtendit, vt ex dictis con-<lb/>ſtat, cum contineatur linea ſtyli, &amp; </s>
  <s xml:id="echoid-s21488" xml:space="preserve">axe mundi. </s>
  <s xml:id="echoid-s21489" xml:space="preserve">In hoc autem Analemmate ducendi erunt radĳ ſigno-<lb/>rum, vt in conis habeam{us} triangula per axem, atque adeo diametros conicarum ſectionum, &amp; </s>
  <s xml:id="echoid-s21490" xml:space="preserve">reliqua <lb/>abſoluenda, vt ad finem ſcholĳ propoſ. </s>
  <s xml:id="echoid-s21491" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21492" xml:space="preserve">ſuperioris libri dixim{us}.</s>
  <s xml:id="echoid-s21493" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1091" type="float" level="2" n="4">
<note position="right" xlink:label="note-0335-01" xlink:href="note-0335-01a" xml:space="preserve">Qua ratio ne at <lb/>cus ſignotũ in <lb/>horologio decli <lb/>nante, quod cẽ <lb/>trum non ha-<lb/>ber, deſcriban <lb/>tur.</note>
  <figure xlink:label="fig-0335-01" xlink:href="fig-0335-01a">
    <image file="0335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0335-01"/>
  </figure>
<note position="left" xlink:label="note-0335-02" xlink:href="note-0335-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0335-03" xlink:href="note-0335-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0335-04" xlink:href="note-0335-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0335-05" xlink:href="note-0335-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0335-06" xlink:href="note-0335-06a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s21494" xml:space="preserve">QVOD verò ad poſteriorem rationem pertinet, ita negotium abſoluem{us}. </s>
  <s xml:id="echoid-s21495" xml:space="preserve">In radium Aequatoris <lb/>I G, transferantur ex I, omnia interualla inter centrum Z, &amp; </s>
  <s xml:id="echoid-s21496" xml:space="preserve">hor{as} in æquinoctiali linea H O, dicti ho-<lb/>rologii cõprehenſa, imprimendo puncta in ipſo radio Aequatoris. </s>
  <s xml:id="echoid-s21497" xml:space="preserve">Deinde in axe I A, abſcindatur recta <lb/>I A, æqu@@@ portioni axis Q P, in horologio eodem, &amp; </s>
  <s xml:id="echoid-s21498" xml:space="preserve">per A, radio Aequatoris I G, parallela agatur <lb/>A B, in quam eodem modo à puncto A, transferantur ſpatia inter aliud centrum a, &amp; </s>
  <s xml:id="echoid-s21499" xml:space="preserve">hor{as} in æqui-<lb/>noctiali linea Y V, incluſa, imprimendo quoque puncta in A B. </s>
  <s xml:id="echoid-s21500" xml:space="preserve">Postremo per bina ſemper puncta reſpon <lb/>
<anchor type="note" xlink:label="note-0336-01a" xlink:href="note-0336-01"/>
dentia in rectis I G, A B, rectæ lineę ductę dabunt horari{as} line{as}. </s>
  <s xml:id="echoid-s21501" xml:space="preserve">Nam vt in prędicto ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s21502" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21503" xml:space="preserve">ſuperioris libri oſtendim{us}, dictæ lineæ horarię tam per puncta inuent a in radio Aequatoris I G, <lb/>quàm in parallela A B, quę inſtar eſt alteri{us} cuiuſdam radii Aequatoris, ducendę ſunt. </s>
  <s xml:id="echoid-s21504" xml:space="preserve">Si igitur inter-<lb/>ualla harum linearum inter radium Aequatoris I G, &amp; </s>
  <s xml:id="echoid-s21505" xml:space="preserve">radios aliorum ſignorum poſita transfer antur <lb/>in reſpondentes line{as} hor ari{as} horologĳ ab ipſa ęquinoctiali linea H O, hac lege ſeruata, vt ducta recta <lb/>ex I, ad proximam lineam, quæ lineę ſtyli in horologio reſpondet, (Eſt enim interuallum quoque lineę ſty-<lb/>li inter centrum horologĳ &amp; </s>
  <s xml:id="echoid-s21506" xml:space="preserve">æquinoctialem lineam transferendum ex horologio in radium Aequatoris) <lb/>perpendiculari pro stylo, interualla illa linearum horariarum inter radios ſignorum ex illa parte, in quã <lb/>styl{us} ex I, cadit, transferantur à linea ęquinoctiali ſurſum verſ{us}, &amp;</s>
  <s xml:id="echoid-s21507" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21508" xml:space="preserve">Demonſtratio huius rei ex ſu-<lb/>perioribus colligitur, vt in dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s21509" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21510" xml:space="preserve">præcedentis libri monuim{us}.</s>
  <s xml:id="echoid-s21511" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1092" type="float" level="2" n="5">
<note position="left" xlink:label="note-0336-01" xlink:href="note-0336-01a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1094" type="section" level="1" n="258">
<head xml:id="echoid-head267" xml:space="preserve">PROBLEMA 3. PROPOSITIO 3.</head>
<p>
  <s xml:id="echoid-s21512" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio decli <lb/>nante deſignare.</s>
  <s xml:id="echoid-s21513" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21514" xml:space="preserve">NON differt horum deſcriptio à deſcriptione parallelorum, ſeu arcuum ſignorum. </s>
  <s xml:id="echoid-s21515" xml:space="preserve">Vnde <lb/>
<anchor type="note" xlink:label="note-0336-03a" xlink:href="note-0336-03"/>
hic vtemur præceptis in præcedenti propoſ. </s>
  <s xml:id="echoid-s21516" xml:space="preserve">traditis, dummodo pro parallelis ſignorum accipia-<lb/>mus parallelos arcuum diurnorum, vt in ſuperioribus horologiis, &amp;</s>
  <s xml:id="echoid-s21517" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21518" xml:space="preserve">Paralleios igitur arcuum <lb/>
<anchor type="note" xlink:label="note-0336-04a" xlink:href="note-0336-04"/>
diurnorum in eodem horologio declinante deſignauimus. </s>
  <s xml:id="echoid-s21519" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s21520" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1094" type="float" level="2" n="1">
<note position="left" xlink:label="note-0336-03" xlink:href="note-0336-03a" xml:space="preserve">Deſcripti@ ar-<lb/>cuum diurno-<lb/>rum in eodem <lb/>horologio de-<lb/>clinante à Ver <lb/>ticali.</note>
<note position="left" xlink:label="note-0336-04" xlink:href="note-0336-04a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1096" type="section" level="1" n="259">
<head xml:id="echoid-head268" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s21521" xml:space="preserve">PER hoſce arc{us} diurnos aperitur nobis via perfacilis, qua ducere poſſim{us} line{as} illas horari{as}, <lb/>
<anchor type="note" xlink:label="note-0336-05a" xlink:href="note-0336-05"/>
quæ vix æquinoctialem lineam ſecant, &amp; </s>
  <s xml:id="echoid-s21522" xml:space="preserve">ducendę ſunt ex illa parte, vbi æquinoctialis linea meridianam <lb/>lineam infra lineam horizontalem ſecat, cuiuſmodi ſunt horæ à meridie in horologio declinante à meridie <lb/>in ortum, quale nos conſtruxim{us}; </s>
  <s xml:id="echoid-s21523" xml:space="preserve">in horologio verò declinante à meridie in occaſum horæ à media no-<lb/>cte. </s>
  <s xml:id="echoid-s21524" xml:space="preserve">Hę enim vix ęquinoctialem lineam ſecant niſi in remotiſſimis punctis, ita vt difficilis admodum red-<lb/>datur earum delineatio. </s>
  <s xml:id="echoid-s21525" xml:space="preserve">Vtemur ergo hac arte. </s>
  <s xml:id="echoid-s21526" xml:space="preserve">Sit, exempli gratia, deſcribenda hora 3. </s>
  <s xml:id="echoid-s21527" xml:space="preserve">à meridie. <lb/></s>
  <s xml:id="echoid-s21528" xml:space="preserve">
<anchor type="note" xlink:label="note-0336-06a" xlink:href="note-0336-06"/>
Quoniam igitur in arcu diurno horarum 6. </s>
  <s xml:id="echoid-s21529" xml:space="preserve">Sol occidit hora 3. </s>
  <s xml:id="echoid-s21530" xml:space="preserve">à meridie, deſcribemus ex centro horolo-<lb/>gii C, ad interuallum lineę horę 3. </s>
  <s xml:id="echoid-s21531" xml:space="preserve">à meridie in figura radiorum præcedentis propoſ. </s>
  <s xml:id="echoid-s21532" xml:space="preserve">inter C, &amp; </s>
  <s xml:id="echoid-s21533" xml:space="preserve">radium <lb/>horarum 6. </s>
  <s xml:id="echoid-s21534" xml:space="preserve">comprehenſę, arcum circuli in parte horologii pomeridiana, notabim{us}{q́ue} punctum, vbi hori-<lb/>zontalem lineam ſecat. </s>
  <s xml:id="echoid-s21535" xml:space="preserve">Nam per illud ducenda eſt hora 3. </s>
  <s xml:id="echoid-s21536" xml:space="preserve">à meridie, cum per illud punctum arcus diur-<lb/>nus horarum 6. </s>
  <s xml:id="echoid-s21537" xml:space="preserve">tranſeat, &amp; </s>
  <s xml:id="echoid-s21538" xml:space="preserve">in eodem Sol occidat.</s>
  <s xml:id="echoid-s21539" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1096" type="float" level="2" n="1">
<note position="left" xlink:label="note-0336-05" xlink:href="note-0336-05a" xml:space="preserve">Qua ratione be <lb/>neficio arcuum <lb/>diurnorum illę <lb/>horæ deſcriban <lb/>tur, quę vix æ-<lb/>quinoctialem <lb/>lineam ſecant.</note>
<note position="left" xlink:label="note-0336-06" xlink:href="note-0336-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s21540" xml:space="preserve">EODEM modo, ſi deſcribam{us} in parte horologii antemeridiana arcum ad interuallum lineæ ho-<lb/>ræ 9. </s>
  <s xml:id="echoid-s21541" xml:space="preserve">qua Sol oritur, inter C, &amp; </s>
  <s xml:id="echoid-s21542" xml:space="preserve">radium horæ 6. </s>
  <s xml:id="echoid-s21543" xml:space="preserve">comprehenſæ, ducemus horam 9. </s>
  <s xml:id="echoid-s21544" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s21545" xml:space="preserve">Sic etiã <lb/>beneficio arcus diurni horarum 8. </s>
  <s xml:id="echoid-s21546" xml:space="preserve">deſignabim{us} horam 4. </s>
  <s xml:id="echoid-s21547" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s21548" xml:space="preserve">8. </s>
  <s xml:id="echoid-s21549" xml:space="preserve">à media nocte, &amp;</s>
  <s xml:id="echoid-s21550" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21551" xml:space="preserve">Non ali <lb/>ter ſemihoras ducem{us}, ſi accipiamus arcus diurnos horarum imparium. </s>
  <s xml:id="echoid-s21552" xml:space="preserve">Vt ſi ducenda eſſet linea horæ <lb/>3 {1/2}. </s>
  <s xml:id="echoid-s21553" xml:space="preserve">accipiend{us} foret radius horarum 7. </s>
  <s xml:id="echoid-s21554" xml:space="preserve">quia cum dies continet horas 7. </s>
  <s xml:id="echoid-s21555" xml:space="preserve">Sol oritur hora 8 {1/2}. </s>
  <s xml:id="echoid-s21556" xml:space="preserve">post me-<lb/>
<anchor type="note" xlink:label="note-0336-07a" xlink:href="note-0336-07"/>
diam noctem, &amp; </s>
  <s xml:id="echoid-s21557" xml:space="preserve">occidit hora 3 {1/2}. </s>
  <s xml:id="echoid-s21558" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s21559" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s21560" xml:space="preserve">Idem in ſequentibus horologiis obſer-<lb/>uandum erit.</s>
  <s xml:id="echoid-s21561" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1097" type="float" level="2" n="2">
<note position="left" xlink:label="note-0336-07" xlink:href="note-0336-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s21562" xml:space="preserve">SED quoniam in figuaradiorum illæ horæ, quæ æquinoctialem non ſecant, niſi in punctis remotiſſi-<lb/>mis, duci non poſſunt, niſi vti velimus praxi Andreæ Schoneri; </s>
  <s xml:id="echoid-s21563" xml:space="preserve">deſcribendi erunt illi arcus diurni, in qui-<lb/>bus Sol propoſitis horis occidit vel oritur, ex Analẽmate, vt in principio propoſ. </s>
  <s xml:id="echoid-s21564" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21565" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s21566" xml:space="preserve">docuimus.</s>
  <s xml:id="echoid-s21567" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1099" type="section" level="1" n="260">
<head xml:id="echoid-head269" xml:space="preserve">PROBLEMA 4. PROPOSITIO 4.</head>
<p>
  <s xml:id="echoid-s21568" xml:space="preserve">VERTICALES circulos in eodem declinante horologio <lb/>deſcribere.</s>
  <s xml:id="echoid-s21569" xml:space="preserve"/>
</p>
<pb o="321" file="0337" n="337" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s21570" xml:space="preserve">EX loco ſtyli K, erigatur ad horizontalem lineam linea perpendicularis K A, ſtylo I K, æqua-<lb/>
<anchor type="note" xlink:label="note-0337-01a" xlink:href="note-0337-01"/>
lis, &amp; </s>
  <s xml:id="echoid-s21571" xml:space="preserve">centro A, ad quodcunque interuallum circulus deſcriptus ſecetur in partes 360. </s>
  <s xml:id="echoid-s21572" xml:space="preserve">æquales, <lb/>aut in pauciores, pro numero Verticalium, quos horologii magnitudo capere poteſt, (Nos partiti <lb/>eum ſumus in partes 24. </s>
  <s xml:id="echoid-s21573" xml:space="preserve">vt ſingula ſpatia complectantur grad. </s>
  <s xml:id="echoid-s21574" xml:space="preserve">15.) </s>
  <s xml:id="echoid-s21575" xml:space="preserve">initio facto à recta, quæ ex cen <lb/>
<anchor type="figure" xlink:label="fig-0337-01a" xlink:href="fig-0337-01"/>
<anchor type="note" xlink:label="note-0337-02a" xlink:href="note-0337-02"/>
<anchor type="note" xlink:label="note-0337-03a" xlink:href="note-0337-03"/>
<anchor type="note" xlink:label="note-0337-04a" xlink:href="note-0337-04"/>
<anchor type="note" xlink:label="note-0337-05a" xlink:href="note-0337-05"/>
tro A, per punctum B, vbi linea meridiana, &amp; </s>
  <s xml:id="echoid-s21576" xml:space="preserve">horizontalis ſe mutuo interſecant, ducitur, vel etiam <lb/>à recta ex A, per punctum D, vbi lineam horizontalem æquinoctialis ſecat, ducta. </s>
  <s xml:id="echoid-s21577" xml:space="preserve">Deinde per cen <lb/>trum A, &amp; </s>
  <s xml:id="echoid-s21578" xml:space="preserve">puncta diuiſionum emittantur rectæ occultæ ſecantes horizontalem lineã in punctis, <lb/>
<anchor type="note" xlink:label="note-0337-06a" xlink:href="note-0337-06"/>
quæ diligenter notanda ſunt. </s>
  <s xml:id="echoid-s21579" xml:space="preserve">Nam rectæ per hęc puncta ad lineam horizontalem perpendicula-<lb/>res ductæ, vel ipſi meridianæ lineæ parallelæ, dabunt circulos Verticales, hoc eſt, communes ſe-<lb/>ctiones plani horologij, &amp; </s>
  <s xml:id="echoid-s21580" xml:space="preserve">circulorum Verticalium. </s>
  <s xml:id="echoid-s21581" xml:space="preserve">Ducentur autem parallelæ illæ ſine magno <lb/>negotio, ſi horizontali lineæ lineam parallelam ducamus, &amp; </s>
  <s xml:id="echoid-s21582" xml:space="preserve">in eam omnia puncta lineæ horizon-<lb/>talis beneſicio circini ex B, ſumpta transferantur, initio ſemper facto à linea meridiana: </s>
  <s xml:id="echoid-s21583" xml:space="preserve">qualis eſt <lb/>recta illa in inferiori parte horologij minutis illis lineis diſtincta. </s>
  <s xml:id="echoid-s21584" xml:space="preserve">Rectæ enim connectentes bi-<lb/>na puncta horizontalis lineæ, &amp; </s>
  <s xml:id="echoid-s21585" xml:space="preserve">prædictæ parallelæ, æqualiter à linea meridiana diſtantia, ipſi li-<lb/>neæ meridianæ parallelæ erunt.</s>
  <s xml:id="echoid-s21586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1099" type="float" level="2" n="1">
<note position="right" xlink:label="note-0337-01" xlink:href="note-0337-01a" xml:space="preserve">Verticaliũ cir-<lb/>culorum deſcri <lb/>ptio in eodem <lb/>horologio decli <lb/>nante à Verti-<lb/>cali.</note>
  <figure xlink:label="fig-0337-01" xlink:href="fig-0337-01a">
    <image file="0337-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0337-01"/>
  </figure>
<note position="left" xlink:label="note-0337-02" xlink:href="note-0337-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0337-03" xlink:href="note-0337-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0337-04" xlink:href="note-0337-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0337-05" xlink:href="note-0337-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0337-06" xlink:href="note-0337-06a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">33. primi.</note>
<p>
  <s xml:id="echoid-s21587" xml:space="preserve">HAS autem parallelas eſſe ſectiones communes circulorum Verticalium, &amp; </s>
  <s xml:id="echoid-s21588" xml:space="preserve">plani horolo-<lb/>gii, ita probabimus. </s>
  <s xml:id="echoid-s21589" xml:space="preserve">Intelligatur planum circuli ex A, deſcripti circa horizontalem lineam mo-<lb/>ueri, donec cum plano Horizontis coniungatur, atque adeò centrum A, cum vertice ſtyli, ſeu cen-
<pb o="322" file="0338" n="338" rhead="GNOMONICES"/>
tro mundi. </s>
  <s xml:id="echoid-s21590" xml:space="preserve">Et quia communes ſectiones Horizontis &amp; </s>
  <s xml:id="echoid-s21591" xml:space="preserve">circulorum Verticalium, inter quos eſt <lb/>eriam Meridianus, per polos Horizontis ductorum, diuidunt Horizõtem, ac proinde &amp; </s>
  <s xml:id="echoid-s21592" xml:space="preserve">circulum <lb/>ex A, centro Horizontis deſcriptum, in dicta poſitione, in partes æquales; </s>
  <s xml:id="echoid-s21593" xml:space="preserve">occurrit autem Meri-<lb/>dianus per A, centrum mundi ductus plano horologii in B, faciens cum eo communem ſectio-<lb/>nem, ipſam lineam meridianam B C, &amp; </s>
  <s xml:id="echoid-s21594" xml:space="preserve">Verticalis propriè dictus per centrum quoque mundi <lb/>incedens idem planum ſecat in D, quòd vmbra ſtyli, Sole exiſtente in communi ſectione Horizon <lb/>tis, Aequatoris, circuli horæ 6. </s>
  <s xml:id="echoid-s21595" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21596" xml:space="preserve">Verticalis propriè dicti, cadat in punctum D, nempe in com-<lb/>munem ſectionem plani horologii &amp; </s>
  <s xml:id="echoid-s21597" xml:space="preserve">Aequatoris, &amp; </s>
  <s xml:id="echoid-s21598" xml:space="preserve">communem ſectionem eiuſdem horologii <lb/>atque Horizontis, vt ex propoſ. </s>
  <s xml:id="echoid-s21599" xml:space="preserve">11. </s>
  <s xml:id="echoid-s21600" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21601" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21602" xml:space="preserve">conſtat; </s>
  <s xml:id="echoid-s21603" xml:space="preserve">erit A B, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s21604" xml:space="preserve">Meri-<lb/>diani; </s>
  <s xml:id="echoid-s21605" xml:space="preserve">A D, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s21606" xml:space="preserve">Verticalis proprie dicti; </s>
  <s xml:id="echoid-s21607" xml:space="preserve">ac proinde reliquæ occultæ <lb/>
<anchor type="note" xlink:label="note-0338-01a" xlink:href="note-0338-01"/>
lineæ per centrum A, &amp; </s>
  <s xml:id="echoid-s21608" xml:space="preserve">puncta diuiſionum circuli ex A, deſcripti ductæ, cõmunes ſectiones erunt <lb/>Horizontis &amp; </s>
  <s xml:id="echoid-s21609" xml:space="preserve">reliquorum circulorum Verticalium. </s>
  <s xml:id="echoid-s21610" xml:space="preserve">Quocirca Verticales circuli planum horolo-<lb/>gii ſecant in punctis lineæ horizontalis, in quæ cadunt dictæ ſectiones communes. </s>
  <s xml:id="echoid-s21611" xml:space="preserve">Cum ergo per <lb/>propoſ. </s>
  <s xml:id="echoid-s21612" xml:space="preserve">18. </s>
  <s xml:id="echoid-s21613" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21614" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21615" xml:space="preserve">ſectiones communes circulorum Verticalium, &amp; </s>
  <s xml:id="echoid-s21616" xml:space="preserve">plani horologii ſint parallelæ, <lb/>quòd planum horologij æquidiſtet communi illorum ſectioni, nempe axi Horizontis per verticẽ <lb/>loci, eiusq́ue oppoſitum ducto; </s>
  <s xml:id="echoid-s21617" xml:space="preserve">perſpicuum relinquitur, dictas illas lineas meridianę lineæ paral-<lb/>lelas, communes eſſe ſectiones plani horologii, &amp; </s>
  <s xml:id="echoid-s21618" xml:space="preserve">circulorum Verticalium. </s>
  <s xml:id="echoid-s21619" xml:space="preserve">Quamobrem Vertica <lb/>les circulos in eodem declinante horologio deſcripſimus. </s>
  <s xml:id="echoid-s21620" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s21621" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1100" type="float" level="2" n="2">
<note position="left" xlink:label="note-0338-01" xlink:href="note-0338-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1102" type="section" level="1" n="261">
<head xml:id="echoid-head270" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">20</note>
<p style="it">
  <s xml:id="echoid-s21622" xml:space="preserve">LINEA horizontalis aufert hic quoque portionem, quæ in facie eiuſdem plani collocanda eſt, ita <lb/>vt horizontalis linea in ſuperiori loco ſtatuatur, &amp; </s>
  <s xml:id="echoid-s21623" xml:space="preserve">pars, quę in eo ſitu nobis dextra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s21624" xml:space="preserve"><lb/>contra, vt conſtat ex demonſtratis in ſcholio propoſ. </s>
  <s xml:id="echoid-s21625" xml:space="preserve">14. </s>
  <s xml:id="echoid-s21626" xml:space="preserve">ſuperioris libri. </s>
  <s xml:id="echoid-s21627" xml:space="preserve">In vtroque porrò horologio <lb/>
<anchor type="note" xlink:label="note-0338-03a" xlink:href="note-0338-03"/>
tam australi, quàm boreali, numeri graduum incipiunt à parallela per punctum D, ducta, quæ communis <lb/>ſectio eſt Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s21628" xml:space="preserve">plani horologii, ita vt in exemplo noſtro proximæ lineæ hinc inde à <lb/>puncto D, habeant numeros grad. </s>
  <s xml:id="echoid-s21629" xml:space="preserve">15. </s>
  <s xml:id="echoid-s21630" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s21631" xml:space="preserve">c.</s>
  <s xml:id="echoid-s21632" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1102" type="float" level="2" n="1">
<note position="left" xlink:label="note-0338-03" xlink:href="note-0338-03a" xml:space="preserve">Ordo Vertica <lb/>lium circulorũ <lb/>in horologio.</note>
</div>
<p style="it">
  <s xml:id="echoid-s21633" xml:space="preserve">QVONIAM verò oſtenſum eſt, Verticalem propriè dictum tranſire per A D, &amp; </s>
  <s xml:id="echoid-s21634" xml:space="preserve">Meridianũ <lb/>per A B, ſi circulus ex A, deſcriptus propriam poſitionem habeat; </s>
  <s xml:id="echoid-s21635" xml:space="preserve">fit vt A D B, ſi erratum non eſt, <lb/>
<anchor type="note" xlink:label="note-0338-04a" xlink:href="note-0338-04"/>
ſit angul{us} declinationis, quẽ nimirum facit Verticalis propriè dictus cum plano declinante, &amp; </s>
  <s xml:id="echoid-s21636" xml:space="preserve">A B D, <lb/>eiuſdem complementum, quem videlicet Meridianus cum eodem plano conſtituit. </s>
  <s xml:id="echoid-s21637" xml:space="preserve">Vnde neceſſe eſt, angu-<lb/>lum reliquum B A D, in triangulo A B D, eſſe rectum. </s>
  <s xml:id="echoid-s21638" xml:space="preserve">Id quod luce clari{us} etiam conſtat ex horologio, <lb/>quod in ſcholio propoſ. </s>
  <s xml:id="echoid-s21639" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21640" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s21641" xml:space="preserve">ad datam ſtyli longitudinem conſtruximus. </s>
  <s xml:id="echoid-s21642" xml:space="preserve">Ibi enim linea F E, re-<lb/>ſpondet hic lineæ A B, &amp; </s>
  <s xml:id="echoid-s21643" xml:space="preserve">linea F α, ibi eadem eſt, quæ hic linea A D.</s>
  <s xml:id="echoid-s21644" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1103" type="float" level="2" n="2">
<note position="left" xlink:label="note-0338-04" xlink:href="note-0338-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s21645" xml:space="preserve">IN nostro quoque exemplo Verticalis grad. </s>
  <s xml:id="echoid-s21646" xml:space="preserve">60. </s>
  <s xml:id="echoid-s21647" xml:space="preserve">tranſit præcisè per K, locum ſtyli: </s>
  <s xml:id="echoid-s21648" xml:space="preserve">quia Verticalis <lb/>ille, qui per ſtylum ducitur, atque adeò rectus eſt ad planum declinans, recedit à Meridiano gradibus 30. <lb/></s>
  <s xml:id="echoid-s21649" xml:space="preserve">quot nimirum gradibus planum declinans à Verticali recedit. </s>
  <s xml:id="echoid-s21650" xml:space="preserve">Manifestum autem eſt, Verticalem grad. </s>
  <s xml:id="echoid-s21651" xml:space="preserve"><lb/>60. </s>
  <s xml:id="echoid-s21652" xml:space="preserve">declinare à Meridiano grad. </s>
  <s xml:id="echoid-s21653" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21654" xml:space="preserve">Eadem ratione in omni horologio declinante per locum ſtyli ille Ver <lb/>ticalis ducendus erit, qui tot gradibus à Meridiano abeſt, quot continet declinatio plani declinantis à <lb/>
<anchor type="note" xlink:label="note-0338-05a" xlink:href="note-0338-05"/>
Verticali circulo.</s>
  <s xml:id="echoid-s21655" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1104" type="float" level="2" n="3">
<note position="left" xlink:label="note-0338-05" xlink:href="note-0338-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1106" type="section" level="1" n="262">
<head xml:id="echoid-head271" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
<p>
  <s xml:id="echoid-s21656" xml:space="preserve">PARALLELOS Horizontis in eodem horologio declinante <lb/>figurare.</s>
  <s xml:id="echoid-s21657" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21658" xml:space="preserve">HOS parallelos in horologio declinante eiſdem rationibus deſcribemus, quibus in Verticali <lb/>
<anchor type="note" xlink:label="note-0338-06a" xlink:href="note-0338-06"/>
horologio deſcripti ſunt propoſ. </s>
  <s xml:id="echoid-s21659" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21660" xml:space="preserve">ſuperioris libri, his, quæ ſequuntur, mutatis. </s>
  <s xml:id="echoid-s21661" xml:space="preserve">In priore ratio-<lb/>
<anchor type="note" xlink:label="note-0338-07a" xlink:href="note-0338-07"/>
ne circulus Analemmatis referet hic non Meridianum, vt ibi, ſed Verticalem illum circulum, qui <lb/>ad planum declinans rectus eſt, qui nimirum tranſit per K, locum gnomonis, facitq́ue cum pla-<lb/>no horologij ſectionem cõmunem, quæ in puncto K, ad angulos rectos ſecat horizontalem lineã. <lb/></s>
  <s xml:id="echoid-s21662" xml:space="preserve">Talis eſt in noſtro exemplo Verticalis grad. </s>
  <s xml:id="echoid-s21663" xml:space="preserve">60. </s>
  <s xml:id="echoid-s21664" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21665" xml:space="preserve">diſtans à Meridiano ex parte auſtri verſus or-<lb/>tum grad. </s>
  <s xml:id="echoid-s21666" xml:space="preserve">30. </s>
  <s xml:id="echoid-s21667" xml:space="preserve">faciensq́ue in horologio ſectionem A K, vt in præcedenti ſcholio diximus. </s>
  <s xml:id="echoid-s21668" xml:space="preserve">Paral-<lb/>leli autem Horizontis non mutantur. </s>
  <s xml:id="echoid-s21669" xml:space="preserve">Rurſus recta G O, erit communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s21670" xml:space="preserve"><lb/>Verticalis illius per ſtylum ducti, ita tamen, vt diſtet à centro E, pro magnitudine ſtyli I k, vel A K. </s>
  <s xml:id="echoid-s21671" xml:space="preserve"><lb/>Puncta denique K, L, M, N, transferenda hic ſunt non in meridianam lineam horologii, vt ibi, <lb/>ſed in rectam, quæ per K, ad horizontalem lineam perpendicularis eſt ducta, hoc eſt, in commu-<lb/>nem ſectionem dicti Verticalis, &amp; </s>
  <s xml:id="echoid-s21672" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s21673" xml:space="preserve">Transſerenda ſunt autem hæc puncta ex loco <lb/>ſtyli tam infra lineam horizontalem, quàm ſupra, vt habeantur etiam paralleli Horizontis in por-
<pb o="323" file="0339" n="339" rhead="LIBER TERTIVS."/>
tione, quæ in facie plani boreali <lb/>
<anchor type="figure" xlink:label="fig-0339-01a" xlink:href="fig-0339-01"/>
collocanda eſt. </s>
  <s xml:id="echoid-s21674" xml:space="preserve">Nam conicæ ſe-<lb/>ctiones circa diametros KO, LO, <lb/>M O, NO, per propoſ. </s>
  <s xml:id="echoid-s21675" xml:space="preserve">8. </s>
  <s xml:id="echoid-s21676" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21677" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21678" xml:space="preserve">de-<lb/>ſcriptæ, &amp; </s>
  <s xml:id="echoid-s21679" xml:space="preserve">translatæ in horolo-<lb/>gium, ita vt diametri earum per-<lb/>pendiculari ex K, ductæ con-<lb/>gruant, tranſeantq́ue per puncta <lb/>K, L, M, N, earumq́ue cornua à <lb/>linea horizõtali magis, ac magis <lb/>
<anchor type="note" xlink:label="note-0339-01a" xlink:href="note-0339-01"/>
auertantur, dabunt parallelos Ho <lb/>rizontis.</s>
  <s xml:id="echoid-s21680" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1106" type="float" level="2" n="1">
<note position="left" xlink:label="note-0338-06" xlink:href="note-0338-06a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis in eo-<lb/>dem horologio <lb/>declinante à <lb/>Verticali.</note>
<note position="left" xlink:label="note-0338-07" xlink:href="note-0338-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0339-01" xlink:href="fig-0339-01a">
    <image file="0339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0339-01"/>
  </figure>
<note position="left" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s21681" xml:space="preserve">IN poſteriori autem ratione <lb/>lineæ ipſi A C, æquidiſtãtes in po <lb/>ſteriori figura propoſ. </s>
  <s xml:id="echoid-s21682" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21683" xml:space="preserve">præ-<lb/>cedentis libri, ducendæ ſunt hic, <lb/>vt ibi, per puncta rectæ A B, quæ <lb/>terminant interualla inter A, cen <lb/>trum circuli in figura præceden-<lb/>tis propoſ. </s>
  <s xml:id="echoid-s21684" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21685" xml:space="preserve">lineas Verticales in <lb/>
<anchor type="note" xlink:label="note-0339-02a" xlink:href="note-0339-02"/>
horizontali linea (intelligendo <lb/>etiam interuallum A K, ſi fortaſ-<lb/>ſis per K, nulla linea Verticalis <lb/>ducitur) translata ex A, in rectam <lb/>A B: </s>
  <s xml:id="echoid-s21686" xml:space="preserve">Sed numeri illarum hic nõ <lb/>reſpondebũt numeris earundem linearum in propoſ. </s>
  <s xml:id="echoid-s21687" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21688" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21689" xml:space="preserve">quoniam interuallum pri-<lb/>mum A K, in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s21690" xml:space="preserve">non eſt inter A, &amp; </s>
  <s xml:id="echoid-s21691" xml:space="preserve">Verticalem grad. </s>
  <s xml:id="echoid-s21692" xml:space="preserve">90. </s>
  <s xml:id="echoid-s21693" xml:space="preserve">ſed grad. </s>
  <s xml:id="echoid-s21694" xml:space="preserve">60. </s>
  <s xml:id="echoid-s21695" xml:space="preserve">in <lb/>dato noſtro exemplo. </s>
  <s xml:id="echoid-s21696" xml:space="preserve">Vnde linea parallela proxima ipſi A C, non habebit numerum 90. </s>
  <s xml:id="echoid-s21697" xml:space="preserve">ſed 60. <lb/></s>
  <s xml:id="echoid-s21698" xml:space="preserve">Deinde ſequens, hos duos numeros 45. </s>
  <s xml:id="echoid-s21699" xml:space="preserve">75. </s>
  <s xml:id="echoid-s21700" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s21701" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21702" xml:space="preserve">habita ratione numerorũ, quorum interualla trãs-<lb/>lata ſunt. </s>
  <s xml:id="echoid-s21703" xml:space="preserve">Immò continget aliquando, vt prima linea parallela nullum numerum habeat, vt quã <lb/>
<anchor type="note" xlink:label="note-0339-03a" xlink:href="note-0339-03"/>
do perpendicularis A K, non eſt vna ex lineis Verticalibus in horologio deſcriptis. </s>
  <s xml:id="echoid-s21704" xml:space="preserve">Præterea quã-<lb/>do punctum K, non eſt præcisè in medio duarum linearum Verticalium circumſtantium, ſed ab <lb/>illis inæqualiter diſtat, transferenda erunt interualla inter A, &amp; </s>
  <s xml:id="echoid-s21705" xml:space="preserve">lineas Verticales ex vtraque par-<lb/>te puncti K; </s>
  <s xml:id="echoid-s21706" xml:space="preserve">atque tunc plures erunt parallelæ in poſteriori figura propoſ. </s>
  <s xml:id="echoid-s21707" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21708" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21709" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21710" xml:space="preserve"><lb/>ſingulæ ſingulos numeros duntaxat habebunt, quemadmodum in lineis horarijs factum eſt pro-<lb/>poſ. </s>
  <s xml:id="echoid-s21711" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21712" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s21713" xml:space="preserve">non autem binos, vt in Verticali horologio, &amp; </s>
  <s xml:id="echoid-s21714" xml:space="preserve">in noſtro exemplo ſit. </s>
  <s xml:id="echoid-s21715" xml:space="preserve">Ad vltimũ, <lb/>interualla linearum ipſi A C, æquidiſtantium inter rectam A B, &amp; </s>
  <s xml:id="echoid-s21716" xml:space="preserve">radios parallelorum Horizon-<lb/>tis, ex A, egredientium comprehenſa, transferenda ſunt vtrinque à linea horizontali in lineas Vet <lb/>ticales reſpondentes numeris in recta A B, ſignatis, ita vt interualla parallelæ proximæ ipſi A C, <lb/>transferantur ex K, loco ſtyli in perpendicularem A K, ſurſum, &amp; </s>
  <s xml:id="echoid-s21717" xml:space="preserve">deorſum verſus, &amp;</s>
  <s xml:id="echoid-s21718" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21719" xml:space="preserve">Nam per <lb/>
<anchor type="note" xlink:label="note-0339-04a" xlink:href="note-0339-04"/>
puncta notata in Verticalibus lineis tranſibunt paralleli Horizontis, qui omnes ſunt hyperbolæ, vt <lb/>propoſ. </s>
  <s xml:id="echoid-s21720" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21721" xml:space="preserve">præcedentis libri diximus. </s>
  <s xml:id="echoid-s21722" xml:space="preserve">Quoniam verò accidit nonnunquam, vt in duabus paral-<lb/>lelis lineis idem numerus contineatur, transferenda erunt interualla parallelæ vicinioris ipſi A C, <lb/>in Verticalem lineam eiuſdem numeri viciniorem ipſi puncto K, &amp; </s>
  <s xml:id="echoid-s21723" xml:space="preserve">remotioris in remotiorem. <lb/></s>
  <s xml:id="echoid-s21724" xml:space="preserve">Quòd ſi perpendicularis A C, fuerit vna ex lineis Verticalibus, vel à circunſtantibus æqualiter fue <lb/>rit remota, transferenda erunt dicta interualla ſingula in binas lineas Verticales æqualiter à recta <lb/>A k, diſtantes, prout numeri indicabunt. </s>
  <s xml:id="echoid-s21725" xml:space="preserve">Id quod in noſtro exemplo contingit. </s>
  <s xml:id="echoid-s21726" xml:space="preserve">Appoſuimus po-<lb/>ſteriorem ſiguram propoſ. </s>
  <s xml:id="echoid-s21727" xml:space="preserve">17. </s>
  <s xml:id="echoid-s21728" xml:space="preserve">ſuperioris libri. </s>
  <s xml:id="echoid-s21729" xml:space="preserve">prope figuram præcedentis propoſ. </s>
  <s xml:id="echoid-s21730" xml:space="preserve">quatenus noſtro <lb/>exemplo reſpondet. </s>
  <s xml:id="echoid-s21731" xml:space="preserve">Itaque parallelos Horizontis in eodem horologio declinante ſigurauimus. </s>
  <s xml:id="echoid-s21732" xml:space="preserve"><lb/>Quod erat ſaciendum.</s>
  <s xml:id="echoid-s21733" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1107" type="float" level="2" n="2">
<note position="left" xlink:label="note-0339-02" xlink:href="note-0339-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0339-03" xlink:href="note-0339-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0339-04" xlink:href="note-0339-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1109" type="section" level="1" n="263">
<head xml:id="echoid-head272" xml:space="preserve">PROBLEMA 6. PROPOSITIO 6.</head>
<p>
  <s xml:id="echoid-s21734" xml:space="preserve">MERIDIANOS, ſiue circulos longitudinum ciuitatum, in eo-<lb/>dem horologio declinante delineare.</s>
  <s xml:id="echoid-s21735" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Meridianord <lb/>deſcriptio in <lb/>eodem horolo-<lb/>gio declinante <lb/>a Verticali.</note>
<p>
  <s xml:id="echoid-s21736" xml:space="preserve">HOS circulos in horologio declinante delineabimus, vt horas à meridie, vel media nocte in <lb/>eodem deſcripſimus propoſ. </s>
  <s xml:id="echoid-s21737" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21738" xml:space="preserve">huius libri, cum per polos mundi ducantur, inſtar horariorum cir <lb/>culorum. </s>
  <s xml:id="echoid-s21739" xml:space="preserve">Sed circulus in horologio propoſ. </s>
  <s xml:id="echoid-s21740" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21741" xml:space="preserve">huius libri ex L, deſcriptus diuiſionis initium hic <lb/>non habebit à diametro L M, ſed ab alia, quæ ab illa in occaſum diſtat tot gradibus, quot longitu
<pb o="324" file="0340" n="340" rhead="GNOMONICES"/>
do loci complectitur, vt in noſtro exemplo grad. </s>
  <s xml:id="echoid-s21742" xml:space="preserve">36. </s>
  <s xml:id="echoid-s21743" xml:space="preserve">Hæc enim diameter communis ſectio erit <lb/>Aequatoris, &amp; </s>
  <s xml:id="echoid-s21744" xml:space="preserve">Meridiani primi per inſulas Fortunatas ducti, vt patet. </s>
  <s xml:id="echoid-s21745" xml:space="preserve">Ex iis autem, quæ in ſecun <lb/>do modo deſcribendi horologii declinantis ſcripſimus, nullius negotij erit intelligere, quænam <lb/>
<anchor type="figure" xlink:label="fig-0340-01a" xlink:href="fig-0340-01"/>
<anchor type="note" xlink:label="note-0340-01a" xlink:href="note-0340-01"/>
<anchor type="note" xlink:label="note-0340-02a" xlink:href="note-0340-02"/>
<anchor type="note" xlink:label="note-0340-03a" xlink:href="note-0340-03"/>
pars circuli ex L, deſcripti occidentalior ſit, vel orientalior diametro L M, maximè ſi circulus il-<lb/>le in proprio ſitu intelligatur eſſe conſtitutus.</s>
  <s xml:id="echoid-s21746" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1109" type="float" level="2" n="1">
  <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a">
    <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0340-01"/>
  </figure>
<note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0340-03" xlink:href="note-0340-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s21747" xml:space="preserve">IN horologio porrò boreali in facie plani declinantis oppoſita deſcribendo, quod nobis exhi-<lb/>bet portio illa ablata à linea horizontali, ſi tamen omnes eius partes inuertantur, vt ſupra docui-<lb/>mus, apponendi ſunt Meridianis numeri, ſicut in Verticali horologio tradidimus propoſ. </s>
  <s xml:id="echoid-s21748" xml:space="preserve">18. </s>
  <s xml:id="echoid-s21749" xml:space="preserve">ſupe <lb/>rioris libri. </s>
  <s xml:id="echoid-s21750" xml:space="preserve">Id quod appoſita ſigura perſpicuè docet. </s>
  <s xml:id="echoid-s21751" xml:space="preserve">Meridianos igitur, ſiue circulos longitudinũ <lb/>ciuitatum, in eodem horologio declinante delineauimus. </s>
  <s xml:id="echoid-s21752" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s21753" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1111" type="section" level="1" n="264">
<head xml:id="echoid-head273" xml:space="preserve">PROBLEMA 7. PROPOSITIO 7.</head>
<p>
  <s xml:id="echoid-s21754" xml:space="preserve">PARALLELOS ciuitatum, id eſt, circulos latitudinum, in eo-<lb/>dem horologio declinante reponere.</s>
  <s xml:id="echoid-s21755" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21756" xml:space="preserve">NON differunt hi à parallelis ſignorum Zodiaci, niſi quòd per vertices locorum incedunt. <lb/></s>
  <s xml:id="echoid-s21757" xml:space="preserve">
<anchor type="note" xlink:label="note-0340-05a" xlink:href="note-0340-05"/>
Vnde eos deſcribemus in horologio, vt propoſ. </s>
  <s xml:id="echoid-s21758" xml:space="preserve">2. </s>
  <s xml:id="echoid-s21759" xml:space="preserve">huius libri docuimus, ſi pro parallelis ſignorũ <lb/>Zodiaci parallelos per vertices ciuitatum ductos accipiamus, &amp;</s>
  <s xml:id="echoid-s21760" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21761" xml:space="preserve">Igitur parallelos ciuitatum, id <lb/>eſt, circulos latitudinum, &amp;</s>
  <s xml:id="echoid-s21762" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21763" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s21764" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1111" type="float" level="2" n="1">
<note position="left" xlink:label="note-0340-05" xlink:href="note-0340-05a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum ciui <lb/>tatum, latitudi <lb/>numve, in eodẽ <lb/>horologio de-<lb/>clinante à Ver <lb/>ticali.</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1113" type="section" level="1" n="265">
<head xml:id="echoid-head274" xml:space="preserve">PROBLEMA 8. PROPOSITIO 8.</head>
<p>
  <s xml:id="echoid-s21765" xml:space="preserve">DOMOS cœleſtes in eodem horologio declinante depingere.</s>
  <s xml:id="echoid-s21766" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium ſecundũ <lb/>loan. Regiom. <lb/>in eodem horo <lb/>logio declinan <lb/>te à Verticali.</note>
<p>
  <s xml:id="echoid-s21767" xml:space="preserve">SECVNDVM ſententiam Ioan. </s>
  <s xml:id="echoid-s21768" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s21769" xml:space="preserve">ita rem propoſitam exequemur. </s>
  <s xml:id="echoid-s21770" xml:space="preserve">Secetur circu-<lb/>lus ex L, deſcriptus in partes 12. </s>
  <s xml:id="echoid-s21771" xml:space="preserve">æquales, vel etiam in plures, ſi partes domorum cœleſtium de-<lb/>ſcribendæ quoque ſint, initio facto à diametro L M, vt in deſcriptione linearum horariarum. <lb/></s>
  <s xml:id="echoid-s21772" xml:space="preserve">Deinde per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s21773" xml:space="preserve">centrum L, ductis rectis occultis, ſecabitur æquinoctialis linea <lb/>in punctis, per quæ ex puncto E, vbi linea meridiana horizontalem lineam interſecat, rectæ emiſ-<lb/>ſæ dabunt domos cœleſtes. </s>
  <s xml:id="echoid-s21774" xml:space="preserve">Circumducto enim circulo ex L, deſcripto circa lineam æquinoctia-
<pb o="325" file="0341" n="341" rhead="LIBER TERTIVS."/>
lem, donec eius centrum L, cum centro mundi coniungatur, &amp; </s>
  <s xml:id="echoid-s21775" xml:space="preserve">ipſe in Aequatoris plano ſtatua-<lb/>tur, erit recta L M, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s21776" xml:space="preserve">Meridiani, vt ſupra oſtendimus propoſ. </s>
  <s xml:id="echoid-s21777" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21778" xml:space="preserve">hu-<lb/>ius libri. </s>
  <s xml:id="echoid-s21779" xml:space="preserve">Cum ergo Meridianus, &amp; </s>
  <s xml:id="echoid-s21780" xml:space="preserve">reliqui circuli domorum cœleſtium Aequatorem partiantur <lb/>
<anchor type="figure" xlink:label="fig-0341-01a" xlink:href="fig-0341-01"/>
<anchor type="note" xlink:label="note-0341-01a" xlink:href="note-0341-01"/>
<anchor type="note" xlink:label="note-0341-02a" xlink:href="note-0341-02"/>
<anchor type="note" xlink:label="note-0341-03a" xlink:href="note-0341-03"/>
in partes 12. </s>
  <s xml:id="echoid-s21781" xml:space="preserve">æquales, erunt rectæ per centrum L, &amp; </s>
  <s xml:id="echoid-s21782" xml:space="preserve">puncta diuiſionum eductæ, communes ſe-<lb/>ctiones circulorum cœleſtium domorum, &amp; </s>
  <s xml:id="echoid-s21783" xml:space="preserve">Aequatoris. </s>
  <s xml:id="echoid-s21784" xml:space="preserve">Quare huiuſmodi circuli plano horolo <lb/>
<anchor type="note" xlink:label="note-0341-04a" xlink:href="note-0341-04"/>
gij occurrent in punctis, vbi æquinoctialis linea à prædictis lineis occultis ſecatur; </s>
  <s xml:id="echoid-s21785" xml:space="preserve">ac proinde per <lb/>eadem illa puncta lineæ æquinoctialis ducentur communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s21786" xml:space="preserve"><lb/>plani horologij. </s>
  <s xml:id="echoid-s21787" xml:space="preserve">Quia verò communes hæ ſectiones ſe mutuo ſecant, per propoſ. </s>
  <s xml:id="echoid-s21788" xml:space="preserve">18. </s>
  <s xml:id="echoid-s21789" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21790" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21791" xml:space="preserve">in pun <lb/>cto E, (quòd illorum circulorum communis ſectio, nempe ſectio communis Horizontis, &amp; </s>
  <s xml:id="echoid-s21792" xml:space="preserve">Me-<lb/>ridiani, plano horologij occurrat in E. </s>
  <s xml:id="echoid-s21793" xml:space="preserve">Sienim Sol exiſteret in communi ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s21794" xml:space="preserve"><lb/>Horizontis, atque adeo eius radius à communi ſectione circulorum cœleſtium domorũ non dif-<lb/>ferret, caderet vmbra ſtyli, ex propoſ. </s>
  <s xml:id="echoid-s21795" xml:space="preserve">11. </s>
  <s xml:id="echoid-s21796" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21797" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21798" xml:space="preserve">in communem ſectionem plani horologij, &amp; </s>
  <s xml:id="echoid-s21799" xml:space="preserve">tam <lb/>Horizontis, quàm Meridiani. </s>
  <s xml:id="echoid-s21800" xml:space="preserve">Quare in punctum E, cadat neceſſe eſt) perſpicuum eſt, rectas ex E, <lb/>per puncta dicta lineæ æquiaoctialis emiſſas, communes ſectiones eſſe circulorum cœleſtium do <lb/>morum, &amp; </s>
  <s xml:id="echoid-s21801" xml:space="preserve">plani horologij.</s>
  <s xml:id="echoid-s21802" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1113" type="float" level="2" n="1">
  <figure xlink:label="fig-0341-01" xlink:href="fig-0341-01a">
    <image file="0341-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0341-01"/>
  </figure>
<note position="left" xlink:label="note-0341-01" xlink:href="note-0341-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0341-02" xlink:href="note-0341-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0341-03" xlink:href="note-0341-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0341-04" xlink:href="note-0341-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s21803" xml:space="preserve">DOMOS verò cœleſtes ſecundum doctrinam Campani hac arte depingemus. </s>
  <s xml:id="echoid-s21804" xml:space="preserve">Ex K, loco <lb/>
<anchor type="note" xlink:label="note-0341-06a" xlink:href="note-0341-06"/>
ſtyli erigatur ad horizontalem lineam perpendicularis K A, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s21805" xml:space="preserve">ex A, ad punctum <lb/>B, vbi linea æquinoctialis horizontalẽ interſecat, recta ducatur A B, cui in horizontali linea æqua-<lb/>lis ſumatur B D. </s>
  <s xml:id="echoid-s21806" xml:space="preserve">Deinde ex D, centro circulus deſcriptus ſecetur in partes 12. </s>
  <s xml:id="echoid-s21807" xml:space="preserve">æquales, vel plures, <lb/>ſi partes domorum etiam deſiderentur, facto initio à linea horizontali. </s>
  <s xml:id="echoid-s21808" xml:space="preserve">Si enim ex centro D, per <lb/>puncta diuiſionum rectæ occultæ egrediantur, ſecabitur recta B F, quæ ex B, perpendicularis du-<lb/>citur ad lineam horizontalem, vel meridianæ lineæ parallela, in punctis, per quæ ſi rectæ emittan-<lb/>tur ex puncto E, deſcriptæ erunt domus cœleſtes, vt placet Campano. </s>
  <s xml:id="echoid-s21809" xml:space="preserve">Si enim triangulum A B K, <lb/>intelligatur moueri circa B K, donec rectum ſitad planum horologii, ac proinde &amp; </s>
  <s xml:id="echoid-s21810" xml:space="preserve">ſtylus A K, ad <lb/>idem rectus: </s>
  <s xml:id="echoid-s21811" xml:space="preserve">Item circulus ex D, deſcriptus circa rectam B F, conuerti concipiatur, donec eius <lb/>centrum cum vertice ſtyli A, hoc eſt, cum centro mundi coniungatur, (coniungetur autem, pro-
<pb o="326" file="0342" n="342" rhead="GNOMONICES"/>
pter æqualitatem<unsure/> rectatum B D, B A,) atque adeo ipſe in plano Verticalis circuli propriè dicti col <lb/>locetur, (Nam, vt propoſ. </s>
  <s xml:id="echoid-s21812" xml:space="preserve">4. </s>
  <s xml:id="echoid-s21813" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s21814" xml:space="preserve">demonſtrauimus, Verticalis propriè dictus ducitur per re-<lb/>ctas A B, B F, per quas etiam ducitur planum circuli ex D, deſcripti, ſi poſitionem habeat, quam <lb/>illa conuerſione acquiſiuit) erunt rectæ illæ per centrum D, &amp; </s>
  <s xml:id="echoid-s21815" xml:space="preserve">puncta diuiſionum eductæ, commu <lb/>nes ſectiones circuli Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s21816" xml:space="preserve">circulorum domorum cœleſtium; </s>
  <s xml:id="echoid-s21817" xml:space="preserve">quandoquidem <lb/>tunc recta, D B, eadem prorſus eſt, quæ A B, communis ſectio Verticalis dicti, &amp; </s>
  <s xml:id="echoid-s21818" xml:space="preserve">Horizontis, qui <lb/>quidem vnus eſt ex circulis domorum cœleſtium. </s>
  <s xml:id="echoid-s21819" xml:space="preserve">Igitur dicti circuli planum horologij ſecabunt <lb/>in punctis rectæ B F, in quæ dictæ ſectiones communes cadunt; </s>
  <s xml:id="echoid-s21820" xml:space="preserve">ac propterea per eadem puncta <lb/>tranſibunt communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s21821" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s21822" xml:space="preserve">Quamobrem, cum <lb/>etiam ducantur per punctum E, vt paulo ante oſten dimus, dabunt rectæ per E, &amp; </s>
  <s xml:id="echoid-s21823" xml:space="preserve">per puncta rectæ <lb/>
<anchor type="note" xlink:label="note-0342-01a" xlink:href="note-0342-01"/>
B F, emiſſæ domos cœleſtes ſecundum Campanum. </s>
  <s xml:id="echoid-s21824" xml:space="preserve">Has lineas referunt in figura illæ, quæ minu-<lb/>tiſſimis illis lineis ſunt diſtinctæ: </s>
  <s xml:id="echoid-s21825" xml:space="preserve">reliquæ verò lineæ pertinent ad domos cœleſtes prioris deſcri-<lb/>ptionis. </s>
  <s xml:id="echoid-s21826" xml:space="preserve">Domos igitur cœleſtes in eodẽ horologio declinante depinximus. </s>
  <s xml:id="echoid-s21827" xml:space="preserve">Quod erat faciendũ.</s>
  <s xml:id="echoid-s21828" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1114" type="float" level="2" n="2">
<note position="right" xlink:label="note-0341-06" xlink:href="note-0341-06a" xml:space="preserve">Deſcriptio do-<lb/>morum cœle <lb/>ſtium ſecundú<unsure/> <lb/>Campanum in <lb/>horologio eodé <lb/>declinante à <lb/>Verticali.</note>
<note position="left" xlink:label="note-0342-01" xlink:href="note-0342-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1116" type="section" level="1" n="266">
<head xml:id="echoid-head275" xml:space="preserve">PROBLEMA 9. PROPOSITIO 9.</head>
<p>
  <s xml:id="echoid-s21829" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem declinante horologio <lb/>deſcribere.</s>
  <s xml:id="echoid-s21830" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21831" xml:space="preserve">NON ſecus hic, ac in ſuperioribus ſigna Zodiaci aſcendentia deſeribemus. </s>
  <s xml:id="echoid-s21832" xml:space="preserve">Ex prioribus ta. <lb/></s>
  <s xml:id="echoid-s21833" xml:space="preserve">
<anchor type="note" xlink:label="note-0342-02a" xlink:href="note-0342-02"/>
<anchor type="note" xlink:label="note-0342-03a" xlink:href="note-0342-03"/>
men quatuor tabulis propoſ. </s>
  <s xml:id="echoid-s21834" xml:space="preserve">9. </s>
  <s xml:id="echoid-s21835" xml:space="preserve">ſuperioris libri, nõ poterunt omnia ſigna commodè deſcribi; </s>
  <s xml:id="echoid-s21836" xml:space="preserve">pro-<lb/>pterea quòd horæ à meridie, vel ante meridiem initium habentes à recta L M, diametro circuli <lb/>ex L, deſcripti, vix omnes cadunt in lineam æquinoctialem. </s>
  <s xml:id="echoid-s21837" xml:space="preserve">Vt in noſtro exemplo, ſigna illa, quæ <lb/>
<anchor type="figure" xlink:label="fig-0342-01a" xlink:href="fig-0342-01"/>
<anchor type="note" xlink:label="note-0342-04a" xlink:href="note-0342-04"/>
<anchor type="note" xlink:label="note-0342-05a" xlink:href="note-0342-05"/>
<anchor type="note" xlink:label="note-0342-06a" xlink:href="note-0342-06"/>
poſt horam 2. </s>
  <s xml:id="echoid-s21838" xml:space="preserve">à meridie oriuntur, ægrè admodum, vel nullo modo poterunt deſcribi, cum vix vl-<lb/>la linea horaria poſt horam 2. </s>
  <s xml:id="echoid-s21839" xml:space="preserve">à meridie lineam æquinoctialem ſecet. </s>
  <s xml:id="echoid-s21840" xml:space="preserve">At ex tabella 6. </s>
  <s xml:id="echoid-s21841" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21842" xml:space="preserve">7. </s>
  <s xml:id="echoid-s21843" xml:space="preserve">per me
<pb o="327" file="0343" n="343" rhead="LIBER TERTIVS."/>
diationes cœli, angulosq́ue terræ, ac puncta, quæ orientibus ſignis in circulo horæ 6 exiſtunt, com <lb/>modius omnia deſcribentur, vt patet. </s>
  <s xml:id="echoid-s21844" xml:space="preserve">Tranſibunt autem ſigna aſcendentia per ea puncta horizon <lb/>talis lineæ, vbi à parallelis ſignorum ſecatur, licet in noſtro exemplo vix ab arcubus ſignorum bo. <lb/></s>
  <s xml:id="echoid-s21845" xml:space="preserve">
<anchor type="note" xlink:label="note-0343-01a" xlink:href="note-0343-01"/>
realium ſecetur. </s>
  <s xml:id="echoid-s21846" xml:space="preserve">Quæ quidem puncta, quamuis arcus ſignorum non ſint delineati in horologio, <lb/>inueniemus vel ex tabella quinta propol. </s>
  <s xml:id="echoid-s21847" xml:space="preserve">9. </s>
  <s xml:id="echoid-s21848" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21849" xml:space="preserve">vt in præcedentibus dictum eſt; </s>
  <s xml:id="echoid-s21850" xml:space="preserve">(Nam <lb/>ſi lineas horarias ducamus, quæ indicent horas arcus ſemidiurnos terminantes, ſecabunt hæ lineã <lb/>horizontalem in dictis punctis) vel certè ex vltima figura propoſ. </s>
  <s xml:id="echoid-s21851" xml:space="preserve">21. </s>
  <s xml:id="echoid-s21852" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21853" xml:space="preserve">quam hic re-<lb/>petiuimus, quoad radios latitudinum ſignorum, hoc modo. </s>
  <s xml:id="echoid-s21854" xml:space="preserve">Sit vt ibi, Horizon A B C D, cuius <lb/>centrum E; </s>
  <s xml:id="echoid-s21855" xml:space="preserve">communis eius ſectio cum Meridiano B D; </s>
  <s xml:id="echoid-s21856" xml:space="preserve">eiuſdem cum Verticali primario ſectio <lb/>communis A C; </s>
  <s xml:id="echoid-s21857" xml:space="preserve">ſintq́ue radij latitudinum ortiuarum, &amp; </s>
  <s xml:id="echoid-s21858" xml:space="preserve">occiduarum, vt ibidem. </s>
  <s xml:id="echoid-s21859" xml:space="preserve">Pro horologio <lb/>
<anchor type="note" xlink:label="note-0343-02a" xlink:href="note-0343-02"/>
<anchor type="note" xlink:label="note-0343-03a" xlink:href="note-0343-03"/>
<anchor type="figure" xlink:label="fig-0343-01a" xlink:href="fig-0343-01"/>
<anchor type="note" xlink:label="note-0343-04a" xlink:href="note-0343-04"/>
<anchor type="note" xlink:label="note-0343-05a" xlink:href="note-0343-05"/>
ergo declinante à meridie in ortum conſtituatur in E, ad E D, angulus declinationis propoſiti plæ<unsure/> <lb/>ni D E K, ad partes ſeptentrionis verſus occaſum, id eſt, verſus punctum A: </s>
  <s xml:id="echoid-s21860" xml:space="preserve">In declinante verò <lb/>à meridie in occaſum, ex parte quoque ſeptẽtrionis verſus ortum, id eſt, verſus punctum C. </s>
  <s xml:id="echoid-s21861" xml:space="preserve">Quòd <lb/>ſi planum à borea declinet in ortum, conſticuendus erit dictus angulus declinationis in E, ad E B, <lb/>ad partes meridiei verſus occaſum, punctumve A: </s>
  <s xml:id="echoid-s21862" xml:space="preserve">at verò ex parte quoque meridiei verſus ortum, <lb/>
<anchor type="note" xlink:label="note-0343-06a" xlink:href="note-0343-06"/>
punctumve C, ſi à borea in occaſum deflectat. </s>
  <s xml:id="echoid-s21863" xml:space="preserve">Sumpta autem recta E K, ſtylo ęquali, in hac linea, <lb/>quæ dictum angulum declinationis cum B D, in E, conſtituit, ducatur per K, ad E K, perpendicu <lb/>laris ſecans B D, productam in M, &amp; </s>
  <s xml:id="echoid-s21864" xml:space="preserve">radios latitudinum ortiuarum, occiduarumve productos in <lb/>aliis punctis. </s>
  <s xml:id="echoid-s21865" xml:space="preserve">Dico hæc puncta circino accepta ex puncto M, &amp; </s>
  <s xml:id="echoid-s21866" xml:space="preserve">translata in horizontalem lineam <lb/>ex E, vbi à meridiana linea ſecatur, vel ſumpta ex puncto K, &amp; </s>
  <s xml:id="echoid-s21867" xml:space="preserve">translata in lineam horizontalem <lb/>ex k, loco ſtyli, dare puncta, per quæ arcus ſignorum, &amp; </s>
  <s xml:id="echoid-s21868" xml:space="preserve">ſigna aſcendentia duci debent. </s>
  <s xml:id="echoid-s21869" xml:space="preserve">Ducta <lb/>enim in horologio ex K, loco ſtyli ad horizontalem lineam perpendiculari K N, quæ ſtylo. </s>
  <s xml:id="echoid-s21870" xml:space="preserve">æqua-<lb/>lis ſit, coniunctaq́ue recta N E; </s>
  <s xml:id="echoid-s21871" xml:space="preserve">ſi intelligatur triangulum E K N, conuerti circa E K, donec re-<lb/>ctum ſit ad planum horologii, ac proinde in plano Horizontis ſit conſtitutum, &amp; </s>
  <s xml:id="echoid-s21872" xml:space="preserve">vertex ſtyli N, <lb/>idem, quod centrum mundi; </s>
  <s xml:id="echoid-s21873" xml:space="preserve">erit recta N E, communis ſectio Horizontis, ac Meridiani, propte <lb/>
<anchor type="note" xlink:label="note-0343-07a" xlink:href="note-0343-07"/>
rea quòd vterque circulus per centrum mundi, &amp; </s>
  <s xml:id="echoid-s21874" xml:space="preserve">per punctum E, in quo communes corum cum <lb/>plano horologii ſectiones conueniunt, ductus ſit: </s>
  <s xml:id="echoid-s21875" xml:space="preserve">ac propterea angulus N E K, quem Meridianus <lb/>cum plano horologij in Horizontis plano efficit, æqualis erit complem ento declinationis plani à <lb/>Verticali, &amp; </s>
  <s xml:id="echoid-s21876" xml:space="preserve">proinde E N K, angulus declinaticnis erit, &amp; </s>
  <s xml:id="echoid-s21877" xml:space="preserve">ipſi D E K, angulo declinationis in figu-<lb/>ra latitudinum ortiuarum æqualis. </s>
  <s xml:id="echoid-s21878" xml:space="preserve">Quoniam igitur anguli K, E, trianguli E K M, in figura lati-<lb/>tudinum, angulis K, N, trianguli E N K, in horologio æquales ſunt, &amp; </s>
  <s xml:id="echoid-s21879" xml:space="preserve">latera E K, N K, quibus <lb/>in vtroque triangulo adiacent, æqualia inter ſe; </s>
  <s xml:id="echoid-s21880" xml:space="preserve">erunt quoque latera M E, M K, prioris trianguli <lb/>
<anchor type="note" xlink:label="note-0343-08a" xlink:href="note-0343-08"/>
lateribus E N, E K, trianguli poſterioris æqualia, &amp; </s>
  <s xml:id="echoid-s21881" xml:space="preserve">angulus M, angulo E, æqualis. </s>
  <s xml:id="echoid-s21882" xml:space="preserve">Quare ſi re-<lb/>cta E M, rectæ N E, ſuperponatur, neutra alteram excedet, &amp; </s>
  <s xml:id="echoid-s21883" xml:space="preserve">ſtylus E K, ſtylo N K, &amp; </s>
  <s xml:id="echoid-s21884" xml:space="preserve">recta M K, <lb/>rectæ E K, congruet, ob æqualitatem angulorum; </s>
  <s xml:id="echoid-s21885" xml:space="preserve">ac proinde radij latitudinum ortiuarum, &amp; </s>
  <s xml:id="echoid-s21886" xml:space="preserve"><lb/>occiduarum horizontali lineæ occurrent in dictis punctis arcuum ſignorum, in quæ nimirum vm
<pb o="328" file="0344" n="344" rhead="GNOMONICES"/>
bra ſtyli cadit, cum Sol in ſignorum initijs exiſtens oritur. </s>
  <s xml:id="echoid-s21887" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s21888" xml:space="preserve">ſigna Zodiaci aſcendentia in eo-<lb/>dem declinante horologio deſcripſimus. </s>
  <s xml:id="echoid-s21889" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s21890" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1116" type="float" level="2" n="1">
<note position="left" xlink:label="note-0342-02" xlink:href="note-0342-02a" xml:space="preserve">A ſcenden@@m <lb/>figaorũ in e<unsure/>o-<lb/>dem horologio <lb/>declinante à <lb/>Verticali de-<lb/>ſcri ptie.</note>
<note position="left" xlink:label="note-0342-03" xlink:href="note-0342-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0342-01" xlink:href="fig-0342-01a">
    <image file="0342-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0342-01"/>
  </figure>
<note position="left" xlink:label="note-0342-04" xlink:href="note-0342-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0342-05" xlink:href="note-0342-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0342-06" xlink:href="note-0342-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">Inuentio pun-<lb/>cto@ũ in linea <lb/>horizon@@@, er <lb/>quæ a cus ſi <lb/>gnorum, &amp; aſ@é <lb/>dentia ſigna @u <lb/>@i debeant.</note>
<note position="left" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">Alia inuentio <lb/>eorundem pun <lb/>@@orum.</note>
  <figure xlink:label="fig-0343-01" xlink:href="fig-0343-01a">
    <image file="0343-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0343-01"/>
  </figure>
<note position="left" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0343-05" xlink:href="note-0343-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0343-06" xlink:href="note-0343-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0343-07" xlink:href="note-0343-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0343-08" xlink:href="note-0343-08a" xml:space="preserve">26. primi.</note>
</div>
</div>
<div xml:id="echoid-div1118" type="section" level="1" n="267">
<head xml:id="echoid-head276" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s21891" xml:space="preserve">HINC autem perſpicuè apparet ratio, cur in boreali horologio mutentur ſigna australia in borea-<lb/>
<anchor type="note" xlink:label="note-0344-01a" xlink:href="note-0344-01"/>
lia, &amp; </s>
  <s xml:id="echoid-s21892" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s21893" xml:space="preserve">quoniam videlicet, quemadmodum radii latitudinum ſignorum auſtralium per centrum <lb/>E, ducti ſecant rectam K M, prope locum ſtyli, &amp; </s>
  <s xml:id="echoid-s21894" xml:space="preserve">radii latitudinum ſignorum borealium eandem pro-<lb/>cul ab eodem, in horologio australi, it a in boreali radii latitudinum ſignorum borealium ſecant rectam <lb/>K M, prope ſtylum, &amp; </s>
  <s xml:id="echoid-s21895" xml:space="preserve">radii latitudinum auſtralium ſignorum eandem procul ab eodem, vt perſpicuum <lb/>
<anchor type="note" xlink:label="note-0344-02a" xlink:href="note-0344-02"/>
est ex figur a latitudinum ortiuarum.</s>
  <s xml:id="echoid-s21896" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1118" type="float" level="2" n="1">
<note position="left" xlink:label="note-0344-01" xlink:href="note-0344-01a" xml:space="preserve">G<unsure/>ut ſignorum <lb/>auſtralium ar <lb/>cus mutentur <lb/>in horologio <lb/>boreali in ar-<lb/>cus fignorum <lb/>borealium, &amp; <lb/>contra.</note>
<note position="left" xlink:label="note-0344-02" xlink:href="note-0344-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s21897" xml:space="preserve">IAM verò ſigna aſcendentia ex doctrina Andreę Schoneri ita depingemus. </s>
  <s xml:id="echoid-s21898" xml:space="preserve">In prima figura ſcho-<lb/>
<anchor type="note" xlink:label="note-0344-03a" xlink:href="note-0344-03"/>
lii propoſ. </s>
  <s xml:id="echoid-s21899" xml:space="preserve">9. </s>
  <s xml:id="echoid-s21900" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21901" xml:space="preserve">(Repetiuimus autem hic duas priores figuras illius ſcholii, quoad interualla <lb/>&amp; </s>
  <s xml:id="echoid-s21902" xml:space="preserve">angulos, quos ſignorum lineæ in centro E, faciunt, productis etiam illis lineis ſignorum vltra cen-<lb/>trum E, in ſecunda figura, quæ non habent ſibi reſpondentes lineas in directum coniunctas, quales ſunt <lb/>
<anchor type="note" xlink:label="note-0344-04a" xlink:href="note-0344-04"/>
<anchor type="figure" xlink:label="fig-0344-01a" xlink:href="fig-0344-01"/>
<anchor type="note" xlink:label="note-0344-05a" xlink:href="note-0344-05"/>
<anchor type="note" xlink:label="note-0344-06a" xlink:href="note-0344-06"/>
<anchor type="note" xlink:label="note-0344-07a" xlink:href="note-0344-07"/>
illę, quę punctis ſunt diſtinctę, vt in dicto ſcholio monuimus) ex recta E D, vel E B, abſcindatur re-<lb/>cta E F, æqualis rectæ L M, quæ in horologio intercipitur inter centrum L, &amp; </s>
  <s xml:id="echoid-s21903" xml:space="preserve">punctum M, vbi æqui-<lb/>noctialis linea, &amp; </s>
  <s xml:id="echoid-s21904" xml:space="preserve">meridiana ſe interſecant; </s>
  <s xml:id="echoid-s21905" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s21906" xml:space="preserve">in F, conſtituatur angulus E F G, æqualis angulo <lb/>L M D, quem in horologio a<unsure/>quinoctialis linea cum L M, recta efficit; </s>
  <s xml:id="echoid-s21907" xml:space="preserve">ea conditione tamen &amp; </s>
  <s xml:id="echoid-s21908" xml:space="preserve">lege, vt <lb/>centro E, poſito in centro L, &amp; </s>
  <s xml:id="echoid-s21909" xml:space="preserve">puncto F, in puncto M, recta F G, æquinoctiali lineæ congruat. </s>
  <s xml:id="echoid-s21910" xml:space="preserve">Dein-<lb/>de interualla rectæ F G, inter F, &amp; </s>
  <s xml:id="echoid-s21911" xml:space="preserve">lineas ſignorum intercepta transferantur in lineam ęquinoctia-<lb/>lem ex puncto M, eo ordine, quem haberent, ſi recta F G, lineæ æquinoctiali congrueret, imprimendo <lb/>puncta in ipſa linea æquinoctiali. </s>
  <s xml:id="echoid-s21912" xml:space="preserve">Nam ſiex E, puncto interſectionis meridianæ lineę, &amp; </s>
  <s xml:id="echoid-s21913" xml:space="preserve">horizonta-<lb/>lis per hæc puncta lineę æquinoctialis ducantur rectæ occultæ, ſecabuntur ambo tropici in punctis, per <lb/>quæ ducenda erunt aſcendentia ſigna. </s>
  <s xml:id="echoid-s21914" xml:space="preserve">Non erit autem difficile, quæ puncta quibus ſignis reſpondeant,
<pb o="329" file="0345" n="345" rhead="LIBER TERTIVS."/>
iudicare. </s>
  <s xml:id="echoid-s21915" xml:space="preserve">Namin horologio declinante in ortum, punctum vbi tropicus ♑, horizontalem lineam ſecat, <lb/>
<anchor type="note" xlink:label="note-0345-01a" xlink:href="note-0345-01"/>
verſus eam partem, in quam vmbra proĳcitur, cum Sol oritur, qualis eſt ea, quę in occaſum vergit, <lb/>pertinet ad ♑, proximum infra lineam horizontalem in eodem tropico ad ♒, ſequens ad ♓, &amp; </s>
  <s xml:id="echoid-s21916" xml:space="preserve">itade-<lb/>inceps, vtin priori figur a ſequuntur. </s>
  <s xml:id="echoid-s21917" xml:space="preserve">Puncta verò quæ in tropico ♋, vel in eodem tropico ♑, ab eiſdom <lb/>rectis occultis ex puncto E, per puncta ęquinoctialis lineæ inuenta eductis monſtrantur, ad ſigna oppoſi-<lb/>taſpectant. </s>
  <s xml:id="echoid-s21918" xml:space="preserve">Sic etiam punctum, vbi tropicus ♋, lineam horizontalem' diuidit, ad partes occidentales <lb/>horologii, in quas nimirum vmbra ſtyli proĳcitur antemeridiano tempore, ſpectat ad ♋, ſequens infra <lb/>lineam horizontalem ad ♌, ſequens ad ♍, &amp; </s>
  <s xml:id="echoid-s21919" xml:space="preserve">ſic deinceps, eo ordine, quem in dicta priori figura conti-<lb/>nent. </s>
  <s xml:id="echoid-s21920" xml:space="preserve">Inhorologio autem in occaſum declinante punctum, vbitropicus ♑, &amp; </s>
  <s xml:id="echoid-s21921" xml:space="preserve">linea horizontalis ſe mu-<lb/>tuo interſecant ad partes orientales horologii, in quas videlicet vmbra gnomonis tempore pomeridiano <lb/>
<anchor type="note" xlink:label="note-0345-02a" xlink:href="note-0345-02"/>
cadit, pertinet ad ♋, proximum verò in eo tropico infra lineam horizontalem ad ♊, &amp; </s>
  <s xml:id="echoid-s21922" xml:space="preserve">ſequens ad ♉, <lb/>&amp; </s>
  <s xml:id="echoid-s21923" xml:space="preserve">ſic ordine, prout in eadem figura priori continentur. </s>
  <s xml:id="echoid-s21924" xml:space="preserve">At vero punctum illud in quo tropicus idem ♋, <lb/>&amp; </s>
  <s xml:id="echoid-s21925" xml:space="preserve">horizontalis linea ſe interſecant, ad partes quoque orientales horologĳ, pertinet ad ♑, proximum de-<lb/>inde in eodem tropico infra horizontalem lineam, ad ♐, &amp; </s>
  <s xml:id="echoid-s21926" xml:space="preserve">ſequcns ad ♏, &amp; </s>
  <s xml:id="echoid-s21927" xml:space="preserve">ita deinceps, vt infigura <lb/>collocantur. </s>
  <s xml:id="echoid-s21928" xml:space="preserve">Semper tamen lineæ ſingulæ ex E, procedentes pertinent ad ſigna oppoſita in duob{us} tro-<lb/>picis, ita vt ſi vnum punctum vnius lineæ in vno tropico ſpectat ad ♏, alterum punctum eiuſdem lineæ <lb/>in altero tropico pertineat ad ♉, &amp; </s>
  <s xml:id="echoid-s21929" xml:space="preserve">contra, &amp;</s>
  <s xml:id="echoid-s21930" xml:space="preserve">c.</s>
  <s xml:id="echoid-s21931" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1119" type="float" level="2" n="2">
<note position="left" xlink:label="note-0344-03" xlink:href="note-0344-03a" xml:space="preserve">Aſcendentia ſi <lb/>gna quomodo <lb/>ſecundum pra-<lb/>kim Andreæ <lb/>Schoneri de-<lb/>ſcribantur in <lb/>eodem horolo-<lb/>gio declinante <lb/>a Verticali.</note>
<note position="left" xlink:label="note-0344-04" xlink:href="note-0344-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0344-01" xlink:href="fig-0344-01a">
    <image file="0344-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0344-01"/>
  </figure>
<note position="left" xlink:label="note-0344-05" xlink:href="note-0344-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0344-06" xlink:href="note-0344-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0344-07" xlink:href="note-0344-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">Orde fignorũ <lb/>aſcendentium <lb/>in tropicis.</note>
<note position="left" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s21932" xml:space="preserve">DEINDE in ſecunda figura dicti ſcholĳ interuallo L D, quod in horologio inter centrum L, &amp; </s>
  <s xml:id="echoid-s21933" xml:space="preserve">pun <lb/>ctum D, interĳcitur, vbi ſe mutuo interſecant linea æquinoctialis, horizontalis, &amp; </s>
  <s xml:id="echoid-s21934" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s21935" xml:space="preserve">ſuma-<lb/>tur æqualis E F, in recta E C, &amp; </s>
  <s xml:id="echoid-s21936" xml:space="preserve">in F, fiat angulo illi, quem recta L D, (ſi ducta eſſet) inter centrum L, <lb/>
<anchor type="note" xlink:label="note-0345-03a" xlink:href="note-0345-03"/>
&amp; </s>
  <s xml:id="echoid-s21937" xml:space="preserve">punctum D, interiecta cum linea æquinoctiali conſtituit, æqualis angul{us} E F G, ca conditione, vt <lb/>centro E, poſito in centro L, &amp; </s>
  <s xml:id="echoid-s21938" xml:space="preserve">puncto F, in puncto D, recta F G, lineæ æquinoctiali congruat. </s>
  <s xml:id="echoid-s21939" xml:space="preserve">Poſt <lb/>hæc, interualla rectæ F G, inter F, &amp; </s>
  <s xml:id="echoid-s21940" xml:space="preserve">ſignorum lineas interpoſita transfer antur in lineam æquinoctialem <lb/>ex puncto D, eo ordine, quem haberent, ſi recta F G, æquinoctiali lineæ congrueret, imprimendo puncta <lb/>in linea æquinoctiali. </s>
  <s xml:id="echoid-s21941" xml:space="preserve">Nam ſi puncta hæc æquinoctialis lineæ cum reſpondentibus punctis, quæ in tropi-<lb/>cis inuenta ſunt, coniungantur, deſcripta erunt aſcendentia ſigna, vt pri{us}. </s>
  <s xml:id="echoid-s21942" xml:space="preserve">Ordo autem ſignorum aſcen <lb/>
<anchor type="note" xlink:label="note-0345-04a" xlink:href="note-0345-04"/>
dentium in linea æquinoctiali hic eſt in horologio in ortum vergente. </s>
  <s xml:id="echoid-s21943" xml:space="preserve">Primum punctum infra horizonta-<lb/>lem lineam ratione proximè dicta inuentum tribuendum eſt ſigno ♉, ſequens ſignis ♊, &amp; </s>
  <s xml:id="echoid-s21944" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s21945" xml:space="preserve">ſequens <lb/>ſigno ♑, &amp; </s>
  <s xml:id="echoid-s21946" xml:space="preserve">ita deinceps, vt infigura poſteriori poſita ſunt: </s>
  <s xml:id="echoid-s21947" xml:space="preserve">proximum autem punctum ſupra lineam ho-<lb/>rizontalem pertinet ad ♓, ſequens verò ad ♒, &amp; </s>
  <s xml:id="echoid-s21948" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s21949" xml:space="preserve">ſic deinceps, prout eadem figura indicat. </s>
  <s xml:id="echoid-s21950" xml:space="preserve">In <lb/>
<anchor type="note" xlink:label="note-0345-05a" xlink:href="note-0345-05"/>
horologio autem in occaſum vergente, dandum erit primum punctum in linea æquinoctiali repertum in-<lb/>fra lineam horizontalem ſigno ♓, &amp; </s>
  <s xml:id="echoid-s21951" xml:space="preserve">ſequens ſignis ♒, &amp; </s>
  <s xml:id="echoid-s21952" xml:space="preserve">♍, atque ita ordine, prout in figur a dicta cer-<lb/>nuntur eſſe collocata: </s>
  <s xml:id="echoid-s21953" xml:space="preserve">Primum verò punctum ſupra horizontalem lineam pertinebit ad ♉, ſequens au-<lb/>tem ad ♊, &amp; </s>
  <s xml:id="echoid-s21954" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s21955" xml:space="preserve">ſic deinceps, veluti in eadem dicta figur a deſcribuntur.</s>
  <s xml:id="echoid-s21956" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1120" type="float" level="2" n="3">
<note position="left" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0345-04" xlink:href="note-0345-04a" xml:space="preserve">Ordo aſcenden <lb/>tium ſignorum <lb/>in linea æqui-<lb/>noctiali.</note>
<note position="left" xlink:label="note-0345-05" xlink:href="note-0345-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s21957" xml:space="preserve">PORRO ſigna aſceadentia vltra lineam horizontalem producta dant eadem ſigna in horologio <lb/>inferiori, ſi tamen portio illa abſciſſa à linea horizontali inuertatur, vt ſupra non ſemel iam dictum eſt.</s>
  <s xml:id="echoid-s21958" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1122" type="section" level="1" n="268">
<head xml:id="echoid-head277" xml:space="preserve">PROBLEMA 10. PROPOSITIO 10.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s21959" xml:space="preserve">HOROLOGIVM Italicum à Verticali circulo declinans <lb/>deſcribere.</s>
  <s xml:id="echoid-s21960" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s21961" xml:space="preserve">SECETVR circulus Ma Nb, ex L, deſcriptus, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s21962" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21963" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s21964" xml:space="preserve">1. </s>
  <s xml:id="echoid-s21965" xml:space="preserve">ſcri-<lb/>
<anchor type="note" xlink:label="note-0345-07a" xlink:href="note-0345-07"/>
pſimus, in arcum diurnum tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s21966" xml:space="preserve">arcum diurnum tropici ♑, d N e, ita vt rectæ a b, <lb/>d e, ſecent ad angulos rectos rectam M N, quæ communis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s21967" xml:space="preserve">Meridiani. <lb/></s>
  <s xml:id="echoid-s21968" xml:space="preserve">Diuiſo deinde bis eo circulo in partes 24. </s>
  <s xml:id="echoid-s21969" xml:space="preserve">æquales, primum facto initio à puncto a; </s>
  <s xml:id="echoid-s21970" xml:space="preserve">Deinde à pun <lb/>cto d, ita vt a, ſit hora 24. </s>
  <s xml:id="echoid-s21971" xml:space="preserve">tropici ♋, &amp; </s>
  <s xml:id="echoid-s21972" xml:space="preserve">proximum punctum verſus N, hora 23. </s>
  <s xml:id="echoid-s21973" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s21974" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21975" xml:space="preserve">at d, ſit hora <lb/>24. </s>
  <s xml:id="echoid-s21976" xml:space="preserve">tropici ♑, &amp; </s>
  <s xml:id="echoid-s21977" xml:space="preserve">proximum punctum verſus N, hora 23. </s>
  <s xml:id="echoid-s21978" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s21979" xml:space="preserve">c. </s>
  <s xml:id="echoid-s21980" xml:space="preserve">inueniemus per hæc puncta diui-<lb/>
<anchor type="note" xlink:label="note-0345-08a" xlink:href="note-0345-08"/>
ſionum in vtroque tropico puncta horarum ab occaſu, horologiumq́ue Italicum perficiemus nõ <lb/>aliter, atque horizontale Italicum conſtruximus propoſ. </s>
  <s xml:id="echoid-s21981" xml:space="preserve">10. </s>
  <s xml:id="echoid-s21982" xml:space="preserve">ſuperioris libri. </s>
  <s xml:id="echoid-s21983" xml:space="preserve">Eadem enim pror-<lb/>ſus demonſtratio huc accommodari poteſt. </s>
  <s xml:id="echoid-s21984" xml:space="preserve">Exempli cauſa. </s>
  <s xml:id="echoid-s21985" xml:space="preserve">Ex f, puncto horæ 16. </s>
  <s xml:id="echoid-s21986" xml:space="preserve">tropici ♋, <lb/>ducta recta per centrum L, ſecat æquinoctialem lineam in g, puncto, per quod ſi ex C, centro ho <lb/>rologii recta emittatur, ſecabitur tropicus ♋, in h, puncto horæ 16. </s>
  <s xml:id="echoid-s21987" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s21988" xml:space="preserve">Sic etiam recta <lb/>ex m, puncto horæ 21. </s>
  <s xml:id="echoid-s21989" xml:space="preserve">tropici ♑, per L, ciecta ſecat æquinoctialem lineam in puncto n, per quod <lb/>recta ducta ex C, ſecat tropicum ♑, in p, puncto horæ 21. </s>
  <s xml:id="echoid-s21990" xml:space="preserve">Pari ratione linea recta ex q, puncto ho-<lb/>ræ 14. </s>
  <s xml:id="echoid-s21991" xml:space="preserve">tropici ♑, quæ quidem in arcu nocturno d M e, continetur, ducta per L, ſecat lineam æqui <lb/>noctialem in r, puncto, per quod recta ducta ex C, ſecat tropicum ♑, in arcu nocturno in t, pun <lb/>cto horæ 14. </s>
  <s xml:id="echoid-s21992" xml:space="preserve">Hac ratione tamen inuenientur ſolum puncta illarum horarum, quæ in ſemicirculo <lb/>A N B, cuius diameter A B, æquinoctiali lineæ æquidiſtat, continentur, propterea quòd rectæ
<pb o="330" file="0346" n="346" rhead="GNOMONICES"/>
ex ipſis per L, ductæ tranſeunt prius per centrum L, antequam æquinoctialem lineam ſecent, <lb/>quod in alijs non contingit. </s>
  <s xml:id="echoid-s21993" xml:space="preserve">Vndealiarum horarum puncta inueniemus, vt de horizontali horo <lb/>logio diximus propoſ. </s>
  <s xml:id="echoid-s21994" xml:space="preserve">10. </s>
  <s xml:id="echoid-s21995" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s21996" xml:space="preserve">Vt ſi velimus reperire punctum horæ 23. </s>
  <s xml:id="echoid-s21997" xml:space="preserve">in tropico ♑, <lb/>
<anchor type="figure" xlink:label="fig-0346-01a" xlink:href="fig-0346-01"/>
<anchor type="note" xlink:label="note-0346-01a" xlink:href="note-0346-01"/>
<anchor type="note" xlink:label="note-0346-02a" xlink:href="note-0346-02"/>
<anchor type="note" xlink:label="note-0346-03a" xlink:href="note-0346-03"/>
cui in circulo Ma Nb, reſpondet punctum D, quod in ſemicirculo A N B, non continetur, duce-<lb/>
<anchor type="note" xlink:label="note-0346-04a" xlink:href="note-0346-04"/>
mus ex oppoſito puncto E, horæ 11 tropici ♑, in arcu nocturno ♑, comprehenſæ per L, &amp; </s>
  <s xml:id="echoid-s21998" xml:space="preserve">D, re-<lb/>ctam, quæ ſecabit æquinoctialem lineam in puncto R, valde remoto, (quod quidem in noſtro <lb/>exemplo non continetur) per quod ſi ducatur recta ex C, ſecabitur tropicus ♑, in arcu noctur-<lb/>no in puncto F, horæ 11. </s>
  <s xml:id="echoid-s21999" xml:space="preserve">producta verò recta R C, vltra centrum C, ſecabit eundem tropicum <lb/>♑, in puncto P, horæ 23. </s>
  <s xml:id="echoid-s22000" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22001" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s22002" xml:space="preserve">Pro horologio boreali, confuſionis vitandæ gratia, nul-<lb/>lum ponimusiexemplum, tum quia ipſum facile ex auſtrali deducitur, vt in alijs horologiis dixi-<lb/>mus, tum etiam, quia eodem pacto deſcribi poteſt, dummodo memor ſis, in boreali horologio ar-<lb/>cum diurnum tropici ♋, eſſe d Me, &amp; </s>
  <s xml:id="echoid-s22003" xml:space="preserve">tropici ♑, a Mb, vt de Verticali horologio diximus. </s>
  <s xml:id="echoid-s22004" xml:space="preserve">Vt <lb/>v. </s>
  <s xml:id="echoid-s22005" xml:space="preserve">g. </s>
  <s xml:id="echoid-s22006" xml:space="preserve">quoniam portio abſciſſa à linea horizontali, ſi ad nos conuertatur, vt centrum C, ſit infra li-<lb/>neam horizontalem, exhibet nobis horologium boreale declinans à ſeptentrione in ortum grad. <lb/></s>
  <s xml:id="echoid-s22007" xml:space="preserve">
<anchor type="note" xlink:label="note-0346-05a" xlink:href="note-0346-05"/>
30. </s>
  <s xml:id="echoid-s22008" xml:space="preserve">vt ſupra docuimus in ſcholio propoſ 1. </s>
  <s xml:id="echoid-s22009" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22010" xml:space="preserve">ſi ex E, puncto horæ 13. </s>
  <s xml:id="echoid-s22011" xml:space="preserve">tropici ♋, ducatur <lb/>recta per L, ſecabitur æquinoctialis linea in puncto R, per quod recta ex C, emiſſa ſecabit tropi-<lb/>cum ♋, in F, puncto horę 13. </s>
  <s xml:id="echoid-s22012" xml:space="preserve">in boreali horologio declinante à borea in ortum grad 30. </s>
  <s xml:id="echoid-s22013" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22014" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22015" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1122" type="float" level="2" n="1">
<note position="right" xlink:label="note-0345-07" xlink:href="note-0345-07a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Italici <lb/>à meridie in or <lb/>tum declinan-<lb/>tis.</note>
<note position="left" xlink:label="note-0345-08" xlink:href="note-0345-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0346-01" xlink:href="fig-0346-01a">
    <image file="0346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0346-01"/>
  </figure>
<note position="left" xlink:label="note-0346-01" xlink:href="note-0346-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0346-02" xlink:href="note-0346-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0346-03" xlink:href="note-0346-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0346-04" xlink:href="note-0346-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0346-05" xlink:href="note-0346-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s22016" xml:space="preserve">QVOD ſi quando punctum diuiſionis aliquod cadat præcisè in A, vel B, tunc recta ducta per <lb/>C, æquinoctiali lineæ parallela ſecabit tropicum ♑, in duobus punctis, quorũ illud, quod ad dez-<lb/>tram eſt ipſius C L, ad horam illam pertinebit, quæ in A, cadit, quod verò ad ſiniſtram eſt eiuſdẽ <lb/>C L, ſpectabit ad horam, quæ in B, cadit, vt conſtat ex ijs, quæ in propoſ. </s>
  <s xml:id="echoid-s22017" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22018" xml:space="preserve">huius libri oſtendimus <lb/>de recta C d, quæ per C, parallela ducta eſt lineæ æquinoctiali. </s>
  <s xml:id="echoid-s22019" xml:space="preserve">Ibi enim oſtendimus rectam C d, <lb/>
<anchor type="note" xlink:label="note-0346-06a" xlink:href="note-0346-06"/>
referre illam horam, à cuius puncto in circulo ex L, deſcripto recta per L, æquinoctiali lineæ <lb/>æquidiſtat.</s>
  <s xml:id="echoid-s22020" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1123" type="float" level="2" n="2">
<note position="left" xlink:label="note-0346-06" xlink:href="note-0346-06a" xml:space="preserve">Quo pacto aliis <lb/>modisidem ho <lb/>rologium Itali <lb/>cum deicriben <lb/>dum ſit.</note>
</div>
<p>
  <s xml:id="echoid-s22021" xml:space="preserve">IAM verò quod attinet ad alios modos, qui vel per arcus diurnos, nocturnosq́ue, vel perſe-
<pb o="331" file="0347" n="347" rhead="LIBER TERTIVS."/>
ctiones mutuas horarum à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s22022" xml:space="preserve">ab ortu, vel occaſu in linea horizontali, <lb/>vel linea horæ 12. </s>
  <s xml:id="echoid-s22023" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s22024" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22025" xml:space="preserve">abſoluuntur, nulla difficultas prorſus eſt, ſi attentè conſi <lb/>derentur tabulæ propoſ. </s>
  <s xml:id="echoid-s22026" xml:space="preserve">19. </s>
  <s xml:id="echoid-s22027" xml:space="preserve">20. </s>
  <s xml:id="echoid-s22028" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22029" xml:space="preserve">23. </s>
  <s xml:id="echoid-s22030" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22031" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22032" xml:space="preserve">ſæpius iam adductæ. </s>
  <s xml:id="echoid-s22033" xml:space="preserve">Nam (vt aliquod exemplum <lb/>habeas) hora 11. </s>
  <s xml:id="echoid-s22034" xml:space="preserve">ab occaſu ducitur per horam 6. </s>
  <s xml:id="echoid-s22035" xml:space="preserve">à media nocte in arcu, diurno horarum 14. </s>
  <s xml:id="echoid-s22036" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22037" xml:space="preserve"><lb/>per 5. </s>
  <s xml:id="echoid-s22038" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s22039" xml:space="preserve">nec non per horam 4. </s>
  <s xml:id="echoid-s22040" xml:space="preserve">à media nocte in arcu <lb/>nocturno herarum 14. </s>
  <s xml:id="echoid-s22041" xml:space="preserve">Ita quoque hora 20. </s>
  <s xml:id="echoid-s22042" xml:space="preserve">ab occaſu tranſit per horam 1. </s>
  <s xml:id="echoid-s22043" xml:space="preserve">à meridie in arcu diur-<lb/>no horarum 10. </s>
  <s xml:id="echoid-s22044" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22045" xml:space="preserve">per horam 2. </s>
  <s xml:id="echoid-s22046" xml:space="preserve">à meridie in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s22047" xml:space="preserve">Hora verò 21. </s>
  <s xml:id="echoid-s22048" xml:space="preserve">ab occaſu, <lb/>quæ vnum ſolum in noſtro exemplo punctum habet, qnod eſt in hora 2. </s>
  <s xml:id="echoid-s22049" xml:space="preserve">à meridie arcus diurni <lb/>horarum 10. </s>
  <s xml:id="echoid-s22050" xml:space="preserve">per quod tranſit, habebitur, ſi hora 21. </s>
  <s xml:id="echoid-s22051" xml:space="preserve">ab ortu ducatur per horam 4. </s>
  <s xml:id="echoid-s22052" xml:space="preserve">à media nocte <lb/>in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s22053" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22054" xml:space="preserve">per horam 2. </s>
  <s xml:id="echoid-s22055" xml:space="preserve">à meridie in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s22056" xml:space="preserve">extenda-<lb/>
<anchor type="note" xlink:label="note-0347-01a" xlink:href="note-0347-01"/>
tur. </s>
  <s xml:id="echoid-s22057" xml:space="preserve">Sic etiam pro hora 22. </s>
  <s xml:id="echoid-s22058" xml:space="preserve">ab occaſu ducenda erit hora 22. </s>
  <s xml:id="echoid-s22059" xml:space="preserve">ab ortu per horam 5. </s>
  <s xml:id="echoid-s22060" xml:space="preserve">à media nocte <lb/>in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s22061" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22062" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s22063" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s22064" xml:space="preserve">Hæc <lb/>enim producta vltra parallelum omnium ſemper latentium maximum, qui per punctum K, du-<lb/>citur, dabit 22. </s>
  <s xml:id="echoid-s22065" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s22066" xml:space="preserve">Eadem denique ratione pro hora 23. </s>
  <s xml:id="echoid-s22067" xml:space="preserve">ab occaſu ducenda erit hora 23. <lb/></s>
  <s xml:id="echoid-s22068" xml:space="preserve">ab ortu per horam 6. </s>
  <s xml:id="echoid-s22069" xml:space="preserve">à media nocte in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s22070" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22071" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s22072" xml:space="preserve">à media no-<lb/>cte in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s22073" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22074" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22075" xml:space="preserve">Linea autem horæ 12. </s>
  <s xml:id="echoid-s22076" xml:space="preserve">ab ortu, vel occaſu (ſi ſorte in de-<lb/>ſcriptione horologii Italici vti voles tabula ſecunda propoſ. </s>
  <s xml:id="echoid-s22077" xml:space="preserve">20. </s>
  <s xml:id="echoid-s22078" xml:space="preserve">primi libri, quæ ad horam 12. </s>
  <s xml:id="echoid-s22079" xml:space="preserve">@ab <lb/>ortu vel occaſu pertinet) ducenda eſt per punctum, vbi linea æquinoctialis, horizontalis, &amp; </s>
  <s xml:id="echoid-s22080" xml:space="preserve">horæ <lb/>6 à meridie, vel média nocte ſe mutuo interſecant, &amp; </s>
  <s xml:id="echoid-s22081" xml:space="preserve">per punctum lineæ horæ 12. </s>
  <s xml:id="echoid-s22082" xml:space="preserve">à meridie, per <lb/>
<anchor type="note" xlink:label="note-0347-02a" xlink:href="note-0347-02"/>
quod arcus diurnus horarum o, hoc eſt, parallelus omnium ſemper latentium maximus tranſit, <lb/>vt patet ex tabulis 5. </s>
  <s xml:id="echoid-s22083" xml:space="preserve">6. </s>
  <s xml:id="echoid-s22084" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22085" xml:space="preserve">8. </s>
  <s xml:id="echoid-s22086" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s22087" xml:space="preserve">33. </s>
  <s xml:id="echoid-s22088" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s22089" xml:space="preserve">Hoc porro punctum inueniemus, ſi ex figura <lb/>radiorum propoſ. </s>
  <s xml:id="echoid-s22090" xml:space="preserve">2. </s>
  <s xml:id="echoid-s22091" xml:space="preserve">huius libri lineam horæ 12. </s>
  <s xml:id="echoid-s22092" xml:space="preserve">mediæ noctis, vel poſt meridiem, quæ ex C, duci <lb/>tur ad dextram rectæ C A, interceptam inter C, &amp; </s>
  <s xml:id="echoid-s22093" xml:space="preserve">radium horarum o, transferamus ex C, centro <lb/>horologii in lineam meridianam ſupra centrum C. </s>
  <s xml:id="echoid-s22094" xml:space="preserve">Portio enim lineæ meridianæ ſupra centrum <lb/>C, ad mediam noctem pertinet, ita vt indicet horam 12. </s>
  <s xml:id="echoid-s22095" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s22096" xml:space="preserve">In noſtro exemplo ægrè <lb/>admodum huiuſinodi punctum reperiri poteſt, vt patet. </s>
  <s xml:id="echoid-s22097" xml:space="preserve">Horologium igitur Italicum à Vertica-<lb/>li circulo declinans deſcripſimus. </s>
  <s xml:id="echoid-s22098" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s22099" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1124" type="float" level="2" n="3">
<note position="left" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0347-02" xlink:href="note-0347-02a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1126" type="section" level="1" n="269">
<head xml:id="echoid-head278" xml:space="preserve">PROBLEMA 11. PROPOSITIO 11.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s22100" xml:space="preserve">HOROLOGIVM Babylonicum à Verticali circulo declinans <lb/>delineare.</s>
  <s xml:id="echoid-s22101" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s22102" xml:space="preserve">VT Italicum horologium, ita &amp; </s>
  <s xml:id="echoid-s22103" xml:space="preserve">Babylonicum deſcribitur, hoc excepto, quòd in priori modo <lb/>
<anchor type="note" xlink:label="note-0347-04a" xlink:href="note-0347-04"/>
diuiſio circuli in partes 24. </s>
  <s xml:id="echoid-s22104" xml:space="preserve">æquales principiũ habere debet à punctis b, e, quæ orientalia ſunt, vt <lb/>patet, ſi horologiom, &amp; </s>
  <s xml:id="echoid-s22105" xml:space="preserve">circulus in propria poſitione concipiantur eſſe collocata; </s>
  <s xml:id="echoid-s22106" xml:space="preserve">ita vt puncta b, e, <lb/>ſignificent horam 24. </s>
  <s xml:id="echoid-s22107" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22108" xml:space="preserve">proxima puncta verſus N, horam 1. </s>
  <s xml:id="echoid-s22109" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s22110" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22111" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1126" type="float" level="2" n="1">
<note position="right" xlink:label="note-0347-04" xlink:href="note-0347-04a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Babylo <lb/>nici à Vertica-<lb/>li deelinantie.</note>
</div>
<p>
  <s xml:id="echoid-s22112" xml:space="preserve">IN alijs modis res omnino facilis eſt, ex tabulis propoſ. </s>
  <s xml:id="echoid-s22113" xml:space="preserve">19. </s>
  <s xml:id="echoid-s22114" xml:space="preserve">20. </s>
  <s xml:id="echoid-s22115" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22116" xml:space="preserve">33. </s>
  <s xml:id="echoid-s22117" xml:space="preserve">primi libri, quarum fre-<lb/>quens mentio facta eſt hactenus. </s>
  <s xml:id="echoid-s22118" xml:space="preserve">Id quod figuta præcedentis propoſ. </s>
  <s xml:id="echoid-s22119" xml:space="preserve">apertè declarat, in qua horæ <lb/>
<anchor type="note" xlink:label="note-0347-05a" xlink:href="note-0347-05"/>
punctis ſolum diſtinctæ numerantur à meridie, vel media nocte, quæ verò characteres numero-<lb/>rum habent communes, ab occaſu; </s>
  <s xml:id="echoid-s22120" xml:space="preserve">quæ denique characteribus numerorum antiquis inſignitæ <lb/>ſunt, ab ortu Solis. </s>
  <s xml:id="echoid-s22121" xml:space="preserve">Igitur horologium Babylonicum à Verticali circulo declinans delineaui-<lb/>mus. </s>
  <s xml:id="echoid-s22122" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s22123" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1127" type="float" level="2" n="2">
<note position="left" xlink:label="note-0347-05" xlink:href="note-0347-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1129" type="section" level="1" n="270">
<head xml:id="echoid-head279" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s22124" xml:space="preserve">SI horæ ab ortu, &amp; </s>
  <s xml:id="echoid-s22125" xml:space="preserve">occaſu vltra lineam horizontalem producantur in horologio, quod à meridic de-<lb/>clinat, habebimus eaſdem horas in facie plani oppoſita, quæ à borea declinat, ſi partium cõmutatio fiat, <lb/>vt in ſuperioribus diximus.</s>
  <s xml:id="echoid-s22126" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s22127" xml:space="preserve">QVEMADMODVM autem ad finem ſcholii propoſ. </s>
  <s xml:id="echoid-s22128" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22129" xml:space="preserve">huius libri ſcripſimus, vna opera de-<lb/>ſcribi poſſe quatuor horologia aſtronomica diuerſa, quæ eandem tamen declinationis quantitatem ſeruẽt; <lb/></s>
  <s xml:id="echoid-s22130" xml:space="preserve">Ita etiam de horologio Italico, &amp; </s>
  <s xml:id="echoid-s22131" xml:space="preserve">Babylonico dicendum est. </s>
  <s xml:id="echoid-s22132" xml:space="preserve">Nam ſi v. </s>
  <s xml:id="echoid-s22133" xml:space="preserve">g. </s>
  <s xml:id="echoid-s22134" xml:space="preserve">deſcribamus horologium Ita-<lb/>
<anchor type="note" xlink:label="note-0347-07a" xlink:href="note-0347-07"/>
licum, vel Babylonicum declinans à meridie in ortum grad. </s>
  <s xml:id="echoid-s22135" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22136" xml:space="preserve">quale hactenus à nobis conſtructum eſt, <lb/>habebimus codem labore Italicum horologium, vel Babylonicum declinans 30. </s>
  <s xml:id="echoid-s22137" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s22138" xml:space="preserve">à borea in ortum, <lb/>quale eſt nocturnum illud, quod linea horizontalis abſcindit, ſi partem illius ſuperiorem commutemus in <lb/>inferiorem: </s>
  <s xml:id="echoid-s22139" xml:space="preserve">ſed numeri horarum mutandi ſunt in earum complementa vſque ad 24. </s>
  <s xml:id="echoid-s22140" xml:space="preserve">ita vt ex hora 11. <lb/></s>
  <s xml:id="echoid-s22141" xml:space="preserve">ab occaſu in portione nocturna fiat hora 13. </s>
  <s xml:id="echoid-s22142" xml:space="preserve">ab occaſu in horologio declinante à borea in ortum; </s>
  <s xml:id="echoid-s22143" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22144" xml:space="preserve">ex <lb/>23. </s>
  <s xml:id="echoid-s22145" xml:space="preserve">ab ortu ſiat 1. </s>
  <s xml:id="echoid-s22146" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s22147" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22148" xml:space="preserve">Si verò idem horologium à meridie declinans in ortum quotcunque gra-<lb/>dibus ita inuertamus, vt pars eius dextra ſiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s22149" xml:space="preserve">contra, non mutata parte eius ſuperiore in in-<lb/>feriorem, habebimus horologium declinans totidem gradibus à meridie in occaſum, ſed numeri horarum
<pb o="332" file="0348" n="348" rhead="GNOMONICES"/>
mutandi ſunt in earum complementa vſque ad 24. </s>
  <s xml:id="echoid-s22150" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22151" xml:space="preserve">quæ horæ prius ab ortu numer abantur, nunc ab oc-<lb/>caſu, &amp; </s>
  <s xml:id="echoid-s22152" xml:space="preserve">quæ ante ab occaſu, nunc ab ortu ſunt computandæ ita vt ex hora 1. </s>
  <s xml:id="echoid-s22153" xml:space="preserve">ab ortu fiat hora 23. </s>
  <s xml:id="echoid-s22154" xml:space="preserve">ab <lb/>occaſu, &amp; </s>
  <s xml:id="echoid-s22155" xml:space="preserve">ex hora 18. </s>
  <s xml:id="echoid-s22156" xml:space="preserve">ab occaſu fiat 6. </s>
  <s xml:id="echoid-s22157" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s22158" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22159" xml:space="preserve">Si denique portionem nocturnam horologii à meri-<lb/>die in ortum declinantis gr. </s>
  <s xml:id="echoid-s22160" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22161" xml:space="preserve">ita inuertamus, vt pars dextr a fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s22162" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s22163" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22164" xml:space="preserve">adhuc pars, <lb/>quæ post hanc mutationem ſuperior eſt, euadat inferior, &amp; </s>
  <s xml:id="echoid-s22165" xml:space="preserve">e contrario, deſcriptum erit horologium de-<lb/>clinans à borea in occaſum totidem gradibus: </s>
  <s xml:id="echoid-s22166" xml:space="preserve">ſed iidem numeri horarum hic retinentur; </s>
  <s xml:id="echoid-s22167" xml:space="preserve">conſider and ũ <lb/>tamen eſt, quænam ab ortu, &amp; </s>
  <s xml:id="echoid-s22168" xml:space="preserve">quæ ab occaſu numer andæ ſint, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s22169" xml:space="preserve">23. </s>
  <s xml:id="echoid-s22170" xml:space="preserve">ſuperioris libride <lb/>Verticali horologio diximus. </s>
  <s xml:id="echoid-s22171" xml:space="preserve">Simili modo, ſi horologium Italicum, vel Babylonicum deſcribatur decli-<lb/>nans à meridie in occaſum grad. </s>
  <s xml:id="echoid-s22172" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22173" xml:space="preserve">conſtruemus ex eohorologium declinans à borea in occaſum grad. <lb/></s>
  <s xml:id="echoid-s22174" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22175" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22176" xml:space="preserve">à meridie in ortum totidem gradibus, necnon à borea in ortum, ſi prædictæ partium inuerſiones <lb/>
<anchor type="note" xlink:label="note-0348-01a" xlink:href="note-0348-01"/>
fiant, &amp; </s>
  <s xml:id="echoid-s22177" xml:space="preserve">numeri horarum mutentur, vt proximè ſcripſimus.</s>
  <s xml:id="echoid-s22178" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1129" type="float" level="2" n="1">
<note position="right" xlink:label="note-0347-07" xlink:href="note-0347-07a" xml:space="preserve">Qua ratione ex <lb/>horologio Itali <lb/>co vel Babylo-<lb/>nico declipan-<lb/>te à merldie in <lb/>ortũ fiat aliud <lb/>declinans à bo <lb/>ica in ortum, <lb/>&amp; à meridiei in <lb/>occaſum, &amp; à <lb/>borea in occa-<lb/>ſum.</note>
<note position="left" xlink:label="note-0348-01" xlink:href="note-0348-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1131" type="section" level="1" n="271">
<head xml:id="echoid-head280" xml:space="preserve">PROBLEMA 12. PROPOSITIO 12.</head>
<p>
  <s xml:id="echoid-s22179" xml:space="preserve">HOROLOGIVM Antiquum declinans à Verticali con-<lb/>ſtruere.</s>
  <s xml:id="echoid-s22180" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s22181" xml:space="preserve">SECETVR tam arcus diurnus paralleli ♋, a Nb, quàm paralleli ♑, d N e, in partes 12. <lb/></s>
  <s xml:id="echoid-s22182" xml:space="preserve">
<anchor type="note" xlink:label="note-0348-02a" xlink:href="note-0348-02"/>
æquales in circulo Ma Nb, ita vt puncta proxima, quæ ſequuntur puncta b, e, verſus N, perti-<lb/>
<anchor type="note" xlink:label="note-0348-03a" xlink:href="note-0348-03"/>
neant ad horam 1, inæqualem, &amp; </s>
  <s xml:id="echoid-s22183" xml:space="preserve">ſequentia ad 2. </s>
  <s xml:id="echoid-s22184" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22185" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22186" xml:space="preserve">Ex punctis enim diuiſionum inueniemus in <lb/>
<anchor type="figure" xlink:label="fig-0348-01a" xlink:href="fig-0348-01"/>
<anchor type="note" xlink:label="note-0348-04a" xlink:href="note-0348-04"/>
<anchor type="note" xlink:label="note-0348-05a" xlink:href="note-0348-05"/>
<anchor type="note" xlink:label="note-0348-06a" xlink:href="note-0348-06"/>
vtroque tropico puncta horarum inæqualium, vt in Verticali horologio docuimus propoſ. </s>
  <s xml:id="echoid-s22187" xml:space="preserve">24. </s>
  <s xml:id="echoid-s22188" xml:space="preserve">ſu-<lb/>perioris libri. </s>
  <s xml:id="echoid-s22189" xml:space="preserve">Exempli gratia, recta ex f, puncto horæ 2. </s>
  <s xml:id="echoid-s22190" xml:space="preserve">inæqualis tropici ♋, per centrum L, edu <lb/>cta ſecat æquinoctialem lineam in g, puncto, per quod recta ex C, emiſſa ſecat tropicum ♋, in h, <lb/>puncto horæ 2. </s>
  <s xml:id="echoid-s22191" xml:space="preserve">inæqualis. </s>
  <s xml:id="echoid-s22192" xml:space="preserve">Sic etiam recta ex m, puncto horæ 9. </s>
  <s xml:id="echoid-s22193" xml:space="preserve">inæqualis tropici ♑, per L, ducta
<pb o="333" file="0349" n="349" rhead="LIBER TERTIVS."/>
ſecat lineam æquinoctialem in puncto n, &amp; </s>
  <s xml:id="echoid-s22194" xml:space="preserve">recta ex C, pern, ducta ſecat tropicum ♑, in p, pun-<lb/>cto horæ 9. </s>
  <s xml:id="echoid-s22195" xml:space="preserve">inæqualis, &amp; </s>
  <s xml:id="echoid-s22196" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s22197" xml:space="preserve">Pro hora 11. </s>
  <s xml:id="echoid-s22198" xml:space="preserve">inæquali tropici ♑, quoniam non contine-<lb/>tur in ſemicirculo A N B, cuius vnius puncta in tropicis inueniuntur, vt ſupra dictum eſt, acci-<lb/>piemus punctum ei oppoſitum D, quod cadit in horam 11. </s>
  <s xml:id="echoid-s22199" xml:space="preserve">inæqualem arcus nocturni tropici ♋, <lb/>vt mox demonſtrabimus, ex quo ſi per L, ducamus rectam, ſecabit hæc lineam æquinoctialem in <lb/>puncto quodam, nempe in R, (quod, quia remotiſſimum eſt, in noſtro horologio nõ continetur) <lb/>per quod recta ex C, emiſſa dabit in arcu nocturno tropici ♋, punctũ horæ 11. </s>
  <s xml:id="echoid-s22200" xml:space="preserve">inæqualis reſpon-<lb/>dens puncto D, eadem verò recta vltra cẽtrum C, eiecta offeret in arcu diurno ♑, punctum aliud <lb/>pro hora 11. </s>
  <s xml:id="echoid-s22201" xml:space="preserve">diurna inæquali tropici ♑, vt ex demonſtratis conſtat. </s>
  <s xml:id="echoid-s22202" xml:space="preserve">Eadem ratione pro horis 11. <lb/></s>
  <s xml:id="echoid-s22203" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22204" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22205" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22206" xml:space="preserve">inæqualibus tropici ♋, quoniam etiam extra dictum ſemicirculum A N D, cadunt, acci-<lb/>
<anchor type="note" xlink:label="note-0349-01a" xlink:href="note-0349-01"/>
piemus puncta ipſis oppoſita E, F, G, quæ cadunt in horas inæquales 11. </s>
  <s xml:id="echoid-s22207" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22208" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22209" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22210" xml:space="preserve">arcus nocturni <lb/>tropici ♑, vt mox oſtendemus, &amp; </s>
  <s xml:id="echoid-s22211" xml:space="preserve">ex ipſis rectas per L, ducemus, vt inueniamus in arcu nocturno <lb/>Capricorni puncta K, P, Q, reſpondẽtia punctis E, F, G, arcus nocturni tropici ♑. </s>
  <s xml:id="echoid-s22212" xml:space="preserve">Quòd ſi quãdo <lb/>hora aliqua cadat præcisè in punctum A, vel B, tum ducta recta per C, æquinoctiali lineæ æqui-<lb/>diſtãs, indicabit in tropico Capricorni duo puncta, quorũ illud, quod ad dextrã ipſius C L, exiſtet, <lb/>ad horam, quæ cadit in punctũ A, alterum verò, quod ad ſiniſtram ipſius CL, ſtatuetur, ad horam, <lb/>quæ in punctum B, cadit, pertinebit, vt conſtar ex ijs, quæ oſtendimus propoſ. </s>
  <s xml:id="echoid-s22213" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22214" xml:space="preserve">huius libri de <lb/>recta Cd, quæ per C, lineæ æquinoctiali ducta eſt parallela. </s>
  <s xml:id="echoid-s22215" xml:space="preserve">Ea enim refert illam horam, à cuius <lb/>puncto in circulo ex L, deſcripto, recta ducta per L, lineæ æquinoctiali æquidiſtat, vt ad finem de-<lb/>monſtrationis modi prioris conſtruendi horologii declinantis oſtendimus propoſ. </s>
  <s xml:id="echoid-s22216" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22217" xml:space="preserve">huius libri. <lb/></s>
  <s xml:id="echoid-s22218" xml:space="preserve">
<anchor type="note" xlink:label="note-0349-02a" xlink:href="note-0349-02"/>
Si igitur reſpondentia puncta in tropicis iungantur lineis rectis, deſcriptum erit horologium An-<lb/>tiquum; </s>
  <s xml:id="echoid-s22219" xml:space="preserve">tranſibuntq́ue omnes lineæ horarum inęqualium per horas à meridie, vel media nocte <lb/>in linea æquinoctiali, prout in tabulis 13. </s>
  <s xml:id="echoid-s22220" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22221" xml:space="preserve">14. </s>
  <s xml:id="echoid-s22222" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s22223" xml:space="preserve">33. </s>
  <s xml:id="echoid-s22224" xml:space="preserve">primi libri colligitur. </s>
  <s xml:id="echoid-s22225" xml:space="preserve">Quoniam verò <lb/>puncta horarum 11. </s>
  <s xml:id="echoid-s22226" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22227" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22228" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22229" xml:space="preserve">arcus ♑, non habent puncta reſpondentia in tropico ♋, iungemus <lb/>ea cum punctis arcus nocturni ♑, inuentis beneficio punctorum E, F, G, quæ eiſdem horis 11. <lb/></s>
  <s xml:id="echoid-s22230" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22231" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22232" xml:space="preserve">arcus diurni ♋, opponuntur, caduntq́ue in horas inæquales 11. </s>
  <s xml:id="echoid-s22233" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22234" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22235" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22236" xml:space="preserve">arcus no-<lb/>
<anchor type="note" xlink:label="note-0349-03a" xlink:href="note-0349-03"/>
cturni Capricorni.</s>
  <s xml:id="echoid-s22237" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1131" type="float" level="2" n="1">
<note position="left" xlink:label="note-0348-02" xlink:href="note-0348-02a" xml:space="preserve">Compoſitio ho <lb/>rologii Antiqui <lb/>à Verticali de <lb/>clinantis.</note>
<note position="left" xlink:label="note-0348-03" xlink:href="note-0348-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0348-01" xlink:href="fig-0348-01a">
    <image file="0348-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0348-01"/>
  </figure>
<note position="left" xlink:label="note-0348-04" xlink:href="note-0348-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0348-05" xlink:href="note-0348-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0348-06" xlink:href="note-0348-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0349-01" xlink:href="note-0349-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0349-02" xlink:href="note-0349-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0349-03" xlink:href="note-0349-03a" xml:space="preserve">Demonſtratio, <lb/>quòd horę di-<lb/>urnæ inæqua-<lb/>les in tropico <lb/>Caneri, oppo-<lb/>nuntur per dia <lb/>metrum eiſd@ <lb/>horis inęquali-<lb/>bu@ nocturnis <lb/>in tropico Ca-<lb/>pricorni; &amp; @ <lb/>in horologio <lb/>horæ diurnę <lb/>tropici Capri-<lb/>corni, ducendæ <lb/>ſint per eaſdem <lb/>horas noctur-<lb/>nas eiuſdẽ tro-<lb/>pici.</note>
</div>
<p>
  <s xml:id="echoid-s22238" xml:space="preserve">QVOD autem hoc ita ſit, &amp; </s>
  <s xml:id="echoid-s22239" xml:space="preserve">lineæ horarum diurnarum tropici ♑, ducendæ ſint per eaſdem <lb/>horas nocturnas eiuſdem tropici in horologio, ita demonſtrabimus. </s>
  <s xml:id="echoid-s22240" xml:space="preserve">Quoniam v. </s>
  <s xml:id="echoid-s22241" xml:space="preserve">g. </s>
  <s xml:id="echoid-s22242" xml:space="preserve">recta ex E, <lb/>puncto, quod opponitur horæ 11. </s>
  <s xml:id="echoid-s22243" xml:space="preserve">♋, contineturq́ue in arcu nocturno ♑, per L, ducta ſecat æqui <lb/>
<anchor type="note" xlink:label="note-0349-04a" xlink:href="note-0349-04"/>
noctialem lineam in H, &amp; </s>
  <s xml:id="echoid-s22244" xml:space="preserve">recta C H, arcum nocturnum ♑, ſecat in K, ſecabit circulus maximus <lb/>per polos mundi, &amp; </s>
  <s xml:id="echoid-s22245" xml:space="preserve">horam 11. </s>
  <s xml:id="echoid-s22246" xml:space="preserve">inæqualem tropici ♋, nec non per punctum E, ductus, planum ho <lb/>rologii per rectam C H, atque adeo tropicum ♑, in K, vt conſtat ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s22247" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22248" xml:space="preserve">ſupe-<lb/>rioris libri. </s>
  <s xml:id="echoid-s22249" xml:space="preserve">Quoniam verò circulus ille maximus in circulo Ma Nb, neceſſario aufert arcum e E, <lb/>horæ 11. </s>
  <s xml:id="echoid-s22250" xml:space="preserve">inæqualis arcus nocturni tropici ♑, d Me, (Nam quia arcus a M, e N, æquales ſunt, cum <lb/>dimidiatæ partes ſint arcuum æqualium a M b, e N d; </s>
  <s xml:id="echoid-s22251" xml:space="preserve">ſi addatur communis arcus e M, fiet arcus <lb/>a M e, ſemicirculo M e N, ęqualis. </s>
  <s xml:id="echoid-s22252" xml:space="preserve">Igitur recta ex a, ad e, @producta per centrum L, tranſibit, atq; <lb/></s>
  <s xml:id="echoid-s22253" xml:space="preserve">adeo in centro L, cum recta E L, ducta vſque ad horam 11. </s>
  <s xml:id="echoid-s22254" xml:space="preserve">tropici ♋, conſtituet angulos ad verti-<lb/>
<anchor type="note" xlink:label="note-0349-05a" xlink:href="note-0349-05"/>
cem æquales; </s>
  <s xml:id="echoid-s22255" xml:space="preserve">propteraq́ue arcus a 11, e E, æquales erunt. </s>
  <s xml:id="echoid-s22256" xml:space="preserve">Sicut igitur a 11, eſt pars duodecima ar <lb/>
<anchor type="note" xlink:label="note-0349-06a" xlink:href="note-0349-06"/>
cus diurni tropici ♋, a N b, ita e E, pars duodecima erit arcus nocturni tropici ♑, e M d; </s>
  <s xml:id="echoid-s22257" xml:space="preserve">quando-<lb/>
<anchor type="note" xlink:label="note-0349-07a" xlink:href="note-0349-07"/>
quidem arcus a N b, e M d, æquales ſunt; </s>
  <s xml:id="echoid-s22258" xml:space="preserve">ac proindee E, arcus erit horæ 11. </s>
  <s xml:id="echoid-s22259" xml:space="preserve">inæqualis in arcu no-<lb/>cturno ♑) ſit, vt tranſeat per horam 11. </s>
  <s xml:id="echoid-s22260" xml:space="preserve">nocturnam tropici ♑. </s>
  <s xml:id="echoid-s22261" xml:space="preserve">Cum enim dictus circulus maxi-<lb/>mus, &amp; </s>
  <s xml:id="echoid-s22262" xml:space="preserve">Meridianus auferant ex Aequatore, &amp; </s>
  <s xml:id="echoid-s22263" xml:space="preserve">tropico ♑, per propoſ. </s>
  <s xml:id="echoid-s22264" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22265" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22266" xml:space="preserve">2. </s>
  <s xml:id="echoid-s22267" xml:space="preserve">Theod arcus ſimi <lb/>les, contineat autem arcus M E, qui ſimilis eſt arcui Aequatoris inter dictum circulum maximũ, <lb/>&amp; </s>
  <s xml:id="echoid-s22268" xml:space="preserve">Meridianum interiecto, quinque ſextas partes arcus Me, qui ſimilis eſt arcui ſeminocturno tro <lb/>pici ♑, comprehendet quoque arcus tropici ♑, inter eundem circulum maximum, &amp; </s>
  <s xml:id="echoid-s22269" xml:space="preserve">Meridia-<lb/>num interpoſitus quinque ſextas partes ſui arcus ſeminocturni, atque adeo dictus maximus circu-<lb/>lus per horam 11. </s>
  <s xml:id="echoid-s22270" xml:space="preserve">inæqualem nocturnam tropici ♑, tranſibit. </s>
  <s xml:id="echoid-s22271" xml:space="preserve">Et quoniam hora 11. </s>
  <s xml:id="echoid-s22272" xml:space="preserve">inæqualis in <lb/>arcu diurno tropici ♋, &amp; </s>
  <s xml:id="echoid-s22273" xml:space="preserve">hora 11. </s>
  <s xml:id="echoid-s22274" xml:space="preserve">inæqualis in arcu nocturno tropici ♑, intercipiunt ex circulo <lb/>illo maximo per vtramque horam ducto ſemicirculum, (quoniam enim arcus ipſius inter paral-<lb/>
<anchor type="note" xlink:label="note-0349-08a" xlink:href="note-0349-08"/>
lelum ♋, &amp; </s>
  <s xml:id="echoid-s22275" xml:space="preserve">Aequatorem poſitus ſupra Horizontem) æqualis eſt arcui eiuſdem inter parallelum <lb/>♑, &amp; </s>
  <s xml:id="echoid-s22276" xml:space="preserve">Aequatorem collocato infra Horizontem, quòd vterque per propoſ. </s>
  <s xml:id="echoid-s22277" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22278" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22279" xml:space="preserve">2. </s>
  <s xml:id="echoid-s22280" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s22281" xml:space="preserve">æqua-<lb/>lis ſit arcui maximæ declinationis; </s>
  <s xml:id="echoid-s22282" xml:space="preserve">ſi addatur communis arcus eiuſdem inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s22283" xml:space="preserve">tro-<lb/>picum ♑, poſitus, tranſiensq́ue per polum antarcticum, fient arcus eiuſdem æquales, quorũ vnus <lb/>quidem inter tropicum ♋, &amp; </s>
  <s xml:id="echoid-s22284" xml:space="preserve">tropicum ♑, alter verò inter Aequatorem ponitur tranſiens per po <lb/>lum antarcticum. </s>
  <s xml:id="echoid-s22285" xml:space="preserve">Cum ergo Aequator ex illo auferat ſemicirculum ex propol. </s>
  <s xml:id="echoid-s22286" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22287" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22288" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22289" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s22290" xml:space="preserve">erit quoque alter arcus ſemicirculus) ſit, vt neceſſario circulus alius maximus qui vnus eſt ex cir-<lb/>culis horarum inæqualium, &amp; </s>
  <s xml:id="echoid-s22291" xml:space="preserve">per polos mundi non tranſit, &amp; </s>
  <s xml:id="echoid-s22292" xml:space="preserve">qui dictum circulum maximũ per <lb/>polos mundi, &amp; </s>
  <s xml:id="echoid-s22293" xml:space="preserve">horam 11. </s>
  <s xml:id="echoid-s22294" xml:space="preserve">tropici ♋, diurnam ductum ſecat in hora 11. </s>
  <s xml:id="echoid-s22295" xml:space="preserve">diurna tropici ♋, ſecet <lb/>eundem in puncto oppoſito, hoc eſt, in hora 11. </s>
  <s xml:id="echoid-s22296" xml:space="preserve">nocturna tropici ♑; </s>
  <s xml:id="echoid-s22297" xml:space="preserve">quandoquidem illum per <lb/>propoſ. </s>
  <s xml:id="echoid-s22298" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22299" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22300" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22301" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s22302" xml:space="preserve">ſecat biſariam, oſtenſumq́ue eſt, circulum dictum maximum in hora 11.</s>
  <s xml:id="echoid-s22303" xml:space="preserve">
<pb o="334" file="0350" n="350" rhead="GNOMONICES"/>
diurna tropici ♋, &amp; </s>
  <s xml:id="echoid-s22304" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22305" xml:space="preserve">nocturna tropici ♑, bifariam ſecari. </s>
  <s xml:id="echoid-s22306" xml:space="preserve">Quamobrem circulus maximus ho-<lb/>rarius horæ inæqualis 11. </s>
  <s xml:id="echoid-s22307" xml:space="preserve">diurnæ tropici ♋, tranſibit in plano horologii per punctum k, in quod <lb/>nimirum caderet vinbra ſtyli per propoſ. </s>
  <s xml:id="echoid-s22308" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22309" xml:space="preserve">primi libri, Sole exiſtente in hora 11. </s>
  <s xml:id="echoid-s22310" xml:space="preserve">nocturna tropi-<lb/>ci ♑, niſi terra radios Solis impediret; </s>
  <s xml:id="echoid-s22311" xml:space="preserve">quæ quidem hora inæqualis 11. </s>
  <s xml:id="echoid-s22312" xml:space="preserve">nocturna tropici ♑, in eo-<lb/>dem circulo maximo horario exiſtit, in quo hora 11. </s>
  <s xml:id="echoid-s22313" xml:space="preserve">inæqualis diurna tropici ♋, eſt, vt oſtendi-<lb/>mus. </s>
  <s xml:id="echoid-s22314" xml:space="preserve">Igitur communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s22315" xml:space="preserve">circuli horæ 11. </s>
  <s xml:id="echoid-s22316" xml:space="preserve">inæqualis per punctum K, tran-<lb/>ſibit, ac proinde recta coniungens punctum K, cum puncto horę 11. </s>
  <s xml:id="echoid-s22317" xml:space="preserve">arcus diurni ♑, dabit hotam <lb/>vndecimam inæqualem; </s>
  <s xml:id="echoid-s22318" xml:space="preserve">adeo vt recta illa communis ſectio ſit plani horologii, &amp; </s>
  <s xml:id="echoid-s22319" xml:space="preserve">circuli horæ <lb/>vndecimæ inæqualis: </s>
  <s xml:id="echoid-s22320" xml:space="preserve">quandoquidem hic circulus tranſit per horam vndecimam inæqualem tam <lb/>in tropico ♋, quàm in tropico ♑, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s22321" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22322" xml:space="preserve">primi libri oſtendimus, idemq́ue, vt <lb/>
<anchor type="note" xlink:label="note-0350-01a" xlink:href="note-0350-01"/>
proximè demonſtrauimus, per horam vndecimam inæqualem nocturnam in tropico ♑, ducitur. <lb/></s>
  <s xml:id="echoid-s22323" xml:space="preserve">Eadem ratione demonſtrabimus, rectain, quæ punctum P, cum puncto horæ decimæ arcus diur-<lb/>ni tropici ♑, iungit, dare horam decimam inæqualem, &amp; </s>
  <s xml:id="echoid-s22324" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s22325" xml:space="preserve">Hæc omnia, ſi adhibea-<lb/>tur ſphæra materialis, facilius percipientur.</s>
  <s xml:id="echoid-s22326" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1132" type="float" level="2" n="2">
<note position="left" xlink:label="note-0349-04" xlink:href="note-0349-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0349-05" xlink:href="note-0349-05a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0349-06" xlink:href="note-0349-06a" xml:space="preserve">26. tertĳ.</note>
<note position="left" xlink:label="note-0349-07" xlink:href="note-0349-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0349-08" xlink:href="note-0349-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0350-01" xlink:href="note-0350-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s22327" xml:space="preserve">EADEM hæc demonſtratio locum habet in omnibus horologiis Antiquis; </s>
  <s xml:id="echoid-s22328" xml:space="preserve">quia ſemper <lb/>
<anchor type="note" xlink:label="note-0350-02a" xlink:href="note-0350-02"/>
oſtendemus horam quamcunque inæqualem durnam in tropico ♋, per diametrum opponi horę <lb/>inæquali eidem nocturnæ in tropico ♑, &amp; </s>
  <s xml:id="echoid-s22329" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s22330" xml:space="preserve">ac proinde circulum horæ cuiuſcunque in-<lb/>æqualis tropici ♋, duci &amp; </s>
  <s xml:id="echoid-s22331" xml:space="preserve">per horam diurnam tropici ♑, &amp; </s>
  <s xml:id="echoid-s22332" xml:space="preserve">per eandem horam nocturnam eiuſ-<lb/>dem tropici. </s>
  <s xml:id="echoid-s22333" xml:space="preserve">In ſuperioribus autem horologiis nihil hac de re ſcripſimus, quoniam omnes horæ <lb/>inæquales commodiſſimè per horas à meridie, vel media nocte lineæ æquinoctialis duci poſſunt, <lb/>
<anchor type="note" xlink:label="note-0350-03a" xlink:href="note-0350-03"/>
quod in declinante horologio fieri non poteſt ſine magna difficultate; </s>
  <s xml:id="echoid-s22334" xml:space="preserve">propterea quòd horarum <lb/>aliquæ nimis procul cum linea æquinoctiali conueniunt.</s>
  <s xml:id="echoid-s22335" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1133" type="float" level="2" n="3">
<note position="left" xlink:label="note-0350-02" xlink:href="note-0350-02a" xml:space="preserve">Circulus hora-<lb/>rius cuiuſcun-<lb/>que horæ in <lb/>æqualis in tro-<lb/>pico Cãcri duci <lb/>tur &amp; p horam <lb/>diurnà in tropi <lb/>co Capricorni <lb/>&amp; per eandem <lb/>horam noctur-<lb/>nam in eodem <lb/>tropico.</note>
<note position="left" xlink:label="note-0350-03" xlink:href="note-0350-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s22336" xml:space="preserve">QVOD ſi arcus diurnus horarum 6. </s>
  <s xml:id="echoid-s22337" xml:space="preserve">qui ſupra lineam horizontalem eſt arcus nocturnus ho <lb/>
<anchor type="note" xlink:label="note-0350-04a" xlink:href="note-0350-04"/>
rarum 18. </s>
  <s xml:id="echoid-s22338" xml:space="preserve">deſcribatur, idem horologium Antiquum deſcriberur ex tabulis 9. </s>
  <s xml:id="echoid-s22339" xml:space="preserve">10. </s>
  <s xml:id="echoid-s22340" xml:space="preserve">13. </s>
  <s xml:id="echoid-s22341" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22342" xml:space="preserve">14. </s>
  <s xml:id="echoid-s22343" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s22344" xml:space="preserve">33. </s>
  <s xml:id="echoid-s22345" xml:space="preserve">libri primi, vt in figura apparet. </s>
  <s xml:id="echoid-s22346" xml:space="preserve">Horologium ergo Antiquum declinans à Verticali con <lb/>ſtruximus. </s>
  <s xml:id="echoid-s22347" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s22348" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1134" type="float" level="2" n="4">
<note position="left" xlink:label="note-0350-04" xlink:href="note-0350-04a" xml:space="preserve">Eiuſdem Anti <lb/>qui horologu <lb/>deſcriptio ex ta <lb/>bulis arcus di <lb/>urni horarũ 6. <lb/>&amp; nocturni ho <lb/>tarum 18.</note>
</div>
</div>
<div xml:id="echoid-div1136" type="section" level="1" n="272">
<head xml:id="echoid-head281" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s22349" xml:space="preserve">LINEAE horarum inæqualium auſtralis horologii productæ vltra horizontalem lineã conficient <lb/>
<anchor type="note" xlink:label="note-0350-05a" xlink:href="note-0350-05"/>
borologium Antiquum boreale, ſi fiat permutatio partium, vt in ſuperioribus dictum eſt.</s>
  <s xml:id="echoid-s22350" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1136" type="float" level="2" n="1">
<note position="left" xlink:label="note-0350-05" xlink:href="note-0350-05a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1138" type="section" level="1" n="273">
<head xml:id="echoid-head282" xml:space="preserve">DE HOROLOGIIS, QVAE <lb/>ab Horizonte declinant.</head>
<head xml:id="echoid-head283" xml:space="preserve">PROBLEMA 13. PROPOSITIO 13.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s22351" xml:space="preserve">HOROLOGIVM Aſtronomicum ab Horizonte declinans, <lb/>hoc eſt, lineas horarum à meridie, vel media nocte in plano, quod cir-<lb/>culo cuipiam maximo æquidiſtat, qui ab Horizonte declinat, ſed ad <lb/>Verticalem circulum rectus eſt, deſcribere.</s>
  <s xml:id="echoid-s22352" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s22353" xml:space="preserve">QVEMADMODVM ſe habent in ſphæra omnes circuli Verticales, quorum communis <lb/>
<anchor type="note" xlink:label="note-0350-07a" xlink:href="note-0350-07"/>
ſectio eſt axis Horizontis, ad Horizontem, ita ſe habent omnes circuli maximi, quorum commu-<lb/>nis ſectio eſt axis Verticalis circuli proprie dicti, quales ſunt omnes circuli poſitionum, &amp; </s>
  <s xml:id="echoid-s22354" xml:space="preserve">ex quo-<lb/>
<anchor type="note" xlink:label="note-0350-08a" xlink:href="note-0350-08"/>
rum numero eſt ipſe Horizon, ad Verticalem circulum propriè dictum; </s>
  <s xml:id="echoid-s22355" xml:space="preserve">adeo vt ſi Verticalis cir-<lb/>culus propriè dictus concipiatur eſſe Horizon aliquis, Horizon ipſe ſit tanquam Verticalis pro-<lb/>priè dictus, &amp; </s>
  <s xml:id="echoid-s22356" xml:space="preserve">alii circuli poſitionum ab Horizonte declinantes, inſtar Verticalium declinan-<lb/>tium, vt ex ſphæra materiali conſtat. </s>
  <s xml:id="echoid-s22357" xml:space="preserve">Ex quo fit, eandem eſſe deſcriptionem horologiorum <lb/>ab Horizonte declinantium, &amp; </s>
  <s xml:id="echoid-s22358" xml:space="preserve">declinãtium à Verticali, de quibus ſupra egimus, his exceptis, quæ <lb/>ſequuntur. </s>
  <s xml:id="echoid-s22359" xml:space="preserve">Loco declinationis à Verticali circulo ſumenda eſt in declinantibus ab Horizonte de-<lb/>clinatio ab Horizonte, hoc eſt, inclinatio ad Horizontem, ita vt angulus D E F, declinationis ab <lb/>
<anchor type="note" xlink:label="note-0350-09a" xlink:href="note-0350-09"/>
Horizonte, ſeu potius inclinationis ad Horizontem, (quæ qua induſtria inueſtigetur, oſtendimus <lb/>propoſ. </s>
  <s xml:id="echoid-s22360" xml:space="preserve">23. </s>
  <s xml:id="echoid-s22361" xml:space="preserve">primi libri) conſtituatur infra rectam AB, verſus punctum A, ſi horologium ſuperius <lb/>ſit, &amp; </s>
  <s xml:id="echoid-s22362" xml:space="preserve">ad occaſum ſpectet; </s>
  <s xml:id="echoid-s22363" xml:space="preserve">verſus B, autem, ſi ſit ſuperius, ſpectetq́ue ad ortum. </s>
  <s xml:id="echoid-s22364" xml:space="preserve">Quòd ſi horolo-<lb/>gium inferius ſit, occaſumq́ue reſpiciat, conſtituendus erit idem angulus ſupra rectam A B, ver-
<pb o="335" file="0351" n="351" rhead="LIBER TERTIVS."/>
ſus B; </s>
  <s xml:id="echoid-s22365" xml:space="preserve">ſi verò inferius ſit, &amp; </s>
  <s xml:id="echoid-s22366" xml:space="preserve">ad ortum ſpectet, verſus A. </s>
  <s xml:id="echoid-s22367" xml:space="preserve">Rurſus in puncto β, conſtituendus eſt an-<lb/>gulus E β C, non altitudinis poli ſupra Horizontem, ſed altitudinis poli ſupra Verticalem circu-<lb/>lum, qui nunc inſtar Horizontis cuiuſpiam ſumitur, hoc eſt, æqualis complemento latitudinis lo-<lb/>
<anchor type="note" xlink:label="note-0351-01a" xlink:href="note-0351-01"/>
ci, vel altitudinis poli ſupra Horizontem; </s>
  <s xml:id="echoid-s22368" xml:space="preserve">(Altitudo enim poli ſupra Horizontem, nempe in Ana <lb/>lemmate propoſ. </s>
  <s xml:id="echoid-s22369" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22370" xml:space="preserve">primi libri, arcus D F, cum altitudine poli ſupra Verticalem, id eſt, cum arcu <lb/>AF, quadrantem componit in quacunque regione; </s>
  <s xml:id="echoid-s22371" xml:space="preserve">ita vt complementum altitudinis poli ſupra <lb/>Horizontem cuiuſuis regionis ſit aìtitudo poli ſupra Verticalem proprie dictum eiuſdem regio-<lb/>nis) ſupra quidem rectam A B, ſi horologium fuerit ſuperius, ſi autem inferius, infra eandem A B. <lb/></s>
  <s xml:id="echoid-s22372" xml:space="preserve">Reliqua omnia abſoluantur, vt propoſ. </s>
  <s xml:id="echoid-s22373" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22374" xml:space="preserve">huius libri de horologiis declinantibus à Verticali dixi-<lb/>mus; </s>
  <s xml:id="echoid-s22375" xml:space="preserve">ita vt deſcribere horologium ab Horizonte declinans nil aliud ſit, quàm pro latitudine lo-<lb/>
<anchor type="note" xlink:label="note-0351-02a" xlink:href="note-0351-02"/>
<anchor type="note" xlink:label="note-0351-03a" xlink:href="note-0351-03"/>
ci, quæ cum eius loci latitudine, pro qua horologium conſtruitur, conficit grad. </s>
  <s xml:id="echoid-s22376" xml:space="preserve">90. </s>
  <s xml:id="echoid-s22377" xml:space="preserve">delineare ho-<lb/>rologium à Verticali declinans tot gradibus, quot continet inclinatio plani propoſiti ad Horizon <lb/>tem. </s>
  <s xml:id="echoid-s22378" xml:space="preserve">In ea enim regione Verticalis circulus proprie dictus fungitur munere Horizontis, &amp; </s>
  <s xml:id="echoid-s22379" xml:space="preserve">Hori-<lb/>zon vicem Verticalis circuli ſubit: </s>
  <s xml:id="echoid-s22380" xml:space="preserve">ita tamen, vt quod in ea regione declinat à meridie in occa-<lb/>ſum, in hac, pro qua conficitur horologium, ſit ſuperius ſpectans ad occaſum; </s>
  <s xml:id="echoid-s22381" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22382" xml:space="preserve">quod ibi à me-<lb/>ridie in ortum vergit, hic ſuperius ſit ortum Solis reſpiciens, vt patet, ſi res diligentius conſidere-<lb/>tur. </s>
  <s xml:id="echoid-s22383" xml:space="preserve">Sed in ea regione intelligendus eſt polus antarcticus eleuatus ſupra Verticalem noſtræ re-<lb/>gionis, tanquàm Horizontem, nimirum ſupra eius faciem auſtralẽ in qua horologium Verticale <lb/>potiſſimum deſcribitur in qualibet regione, atque adeo &amp; </s>
  <s xml:id="echoid-s22384" xml:space="preserve">Horizontale in regione illa, in qua poli <lb/>altitudo cum altitudine poli prioris regionis quadrantem conſtituit. </s>
  <s xml:id="echoid-s22385" xml:space="preserve">Vnde ſi ibi cõſtruendum ſit <lb/>
<anchor type="note" xlink:label="note-0351-04a" xlink:href="note-0351-04"/>
horologium declinans à Verticali à meridie in occaſum, ducenda erit linea declinationis E F, con <lb/>trario modo, quàm docuimus propoſ. </s>
  <s xml:id="echoid-s22386" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22387" xml:space="preserve">huius libri, nem pe verſus A, quia ibi meridies efficitur, <lb/>cum Sol borealior eſt, quàm Verticalis proprie dictus, atque adeo in meridie vmbra in auſtrum <lb/>proiicitur, vt ex ſphæra materiali patet, de qua re plura ſcribemus lib. </s>
  <s xml:id="echoid-s22388" xml:space="preserve">4. </s>
  <s xml:id="echoid-s22389" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s22390" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22391" xml:space="preserve">Deſcriptionẽ <lb/>huius horologij ab Horizonte declinantis ſequens figura declarat. </s>
  <s xml:id="echoid-s22392" xml:space="preserve">Eadem enim hic demonſtra-<lb/>tio erit, quæ in propoſ. </s>
  <s xml:id="echoid-s22393" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22394" xml:space="preserve">huius libri, paucis mutatis. </s>
  <s xml:id="echoid-s22395" xml:space="preserve">Ponimus autem planum horologij ab Hori-<lb/>zonte declinare in occaſum gr. </s>
  <s xml:id="echoid-s22396" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22397" xml:space="preserve">adeo vt hoc horologium ad latitudinem grad. </s>
  <s xml:id="echoid-s22398" xml:space="preserve">42. </s>
  <s xml:id="echoid-s22399" xml:space="preserve">fabricatum <lb/>idem ſit, quod Verticale déclinans à meridie in occaſum ad latitudinem gr. </s>
  <s xml:id="echoid-s22400" xml:space="preserve">48,</s>
</p>
<div xml:id="echoid-div1138" type="float" level="2" n="1">
<note position="left" xlink:label="note-0350-07" xlink:href="note-0350-07a" xml:space="preserve">Ita ſe habẽt cir <lb/>culi poſitionũ <lb/>ab Horizonte <lb/>declinanies ad <lb/>Verticalẽ pro-<lb/>prie dictũ, quẽ-<lb/>admodum Ver <lb/>ticales circuli à <lb/>proprie dicto <lb/>Verticali decli <lb/>nantes ad Ho-<lb/>rizontem.</note>
<note position="left" xlink:label="note-0350-08" xlink:href="note-0350-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0350-09" xlink:href="note-0350-09a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Aſtrono <lb/>mici ab Hori-<lb/>zonte declinan <lb/>tis.</note>
<note position="right" xlink:label="note-0351-01" xlink:href="note-0351-01a" xml:space="preserve">Complemen@@ <lb/>alui<unsure/>udinis poli <lb/>ſupra Horizon <lb/>tem cuiuslibet <lb/>regionis æqua-<lb/>le eſt altitudini <lb/>poli ſupra Ver <lb/>ticalem propria<unsure/> <lb/>dictum eiuſdẽ <lb/>regionis.</note>
<note position="left" xlink:label="note-0351-02" xlink:href="note-0351-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0351-03" xlink:href="note-0351-03a" xml:space="preserve">Deſcribere ho-<lb/>rologiú ab Ho <lb/>rizonte decli <lb/>nãs nihil aliud <lb/>eſt, quàm horo <lb/>logiũ declinãs <lb/>à Verticali de-<lb/>li<unsure/>neare pro ea <lb/>latitudi<unsure/>ne loci. <lb/>quæ cũ propo-<lb/>ſita latitudin<unsure/>e, <lb/>pro qua horolo <lb/>gium conſtrui-<lb/>@@, grad. 90. @@ <lb/>ficit.</note>
<note position="left" xlink:label="note-0351-04" xlink:href="note-0351-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s22401" xml:space="preserve">NAM ſi intelligatur in plano horologii recta C D, æquidiſtare Horizonti, ita vt communis <lb/>
<anchor type="note" xlink:label="note-0351-05a" xlink:href="note-0351-05"/>
ſectio ſit plani horologii ab Horizonte declinantis, &amp; </s>
  <s xml:id="echoid-s22402" xml:space="preserve">Meridiani circuli, erit recta A B, ſectio cõ-<lb/>
<anchor type="note" xlink:label="note-0351-06a" xlink:href="note-0351-06"/>
munis plani eiuſdem horologij declinantis, &amp; </s>
  <s xml:id="echoid-s22403" xml:space="preserve">plani horologij Verticalis. </s>
  <s xml:id="echoid-s22404" xml:space="preserve">Quoniam enim tam <lb/>Meridianus, quàm planum horologij declinantis rectum eſt ad planum horologij Verticalis, ex <lb/>propoſ. </s>
  <s xml:id="echoid-s22405" xml:space="preserve">15. </s>
  <s xml:id="echoid-s22406" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22407" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22408" xml:space="preserve">Theodoſii, quòd &amp; </s>
  <s xml:id="echoid-s22409" xml:space="preserve">Meridianus, &amp; </s>
  <s xml:id="echoid-s22410" xml:space="preserve">maximus circulus, cui planum horologij <lb/>declinantis æquidiſtat, per polos plani horologii Verticalis ducatur, nempe per communes ſectio-<lb/>nes Meridiani atque Horizontis; </s>
  <s xml:id="echoid-s22411" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s22412" xml:space="preserve">communis eorum ſectio CD, ad idem planum horologij <lb/>
<anchor type="note" xlink:label="note-0351-07a" xlink:href="note-0351-07"/>
Verticalis recta, atque adeò &amp; </s>
  <s xml:id="echoid-s22413" xml:space="preserve">ad communem ſectionem plani horologii declinantis, &amp; </s>
  <s xml:id="echoid-s22414" xml:space="preserve">plani ho <lb/>rologij Verticalis, ex defin. </s>
  <s xml:id="echoid-s22415" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22416" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22417" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22418" xml:space="preserve">Euclidis, perpendicularis erit. </s>
  <s xml:id="echoid-s22419" xml:space="preserve">Si igitur planũ horologij Ver-<lb/>ticalis ponatur duci per punctum E, erit recta A B, quæ ad C D, perpendicularis ducta eſt, com-<lb/>munis ſectio plani horologij declinantis, &amp; </s>
  <s xml:id="echoid-s22420" xml:space="preserve">plani horologij Verticalis. </s>
  <s xml:id="echoid-s22421" xml:space="preserve">Quocirca ſi planum per <lb/>rectas A B, E F, E D, ductum intelligatur moueri circa rectam A B, donec Verticali circulo æquidi <lb/>
<anchor type="note" xlink:label="note-0351-08a" xlink:href="note-0351-08"/>
ſtet, atque adeo cũ plano horologii Verticalis coniungatur, ſit vt cũ D E F, ſit angulus inclinationis <lb/>plani ad Horizontem, reliquus A E F, ex recto ſit angulus complementi dictæ inclinationis, qua-<lb/>lem videlicet Meridianus cum plano declinante conſtituit; </s>
  <s xml:id="echoid-s22422" xml:space="preserve">ac propterea recta E F, communis ſe-<lb/>ctio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s22423" xml:space="preserve">horologij Verticalis. </s>
  <s xml:id="echoid-s22424" xml:space="preserve">Deinde quia tam planum. </s>
  <s xml:id="echoid-s22425" xml:space="preserve">Meridiani, quàm planum <lb/>horologij declinantis rectum eſt ad planum Verticalis horologii, vt dictum eſt, erit cõmunis eo-<lb/>rum ſectio C E, ad idem planum Verticalis horologij recta; </s>
  <s xml:id="echoid-s22426" xml:space="preserve">ac proinde ad rectam E F, in eo exi-<lb/>
<anchor type="note" xlink:label="note-0351-09a" xlink:href="note-0351-09"/>
ſtentem, cum oſtẽſa ſit eius linea meridiana, ſeu communis eius ſectio cum Meridiano, per defin. <lb/></s>
  <s xml:id="echoid-s22427" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22428" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22429" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22430" xml:space="preserve">Euclidis, perpendicularis erit. </s>
  <s xml:id="echoid-s22431" xml:space="preserve">Igitur ſi triangulum β E C, moueri intelligatur circa C E, <lb/>donec cum plano Meridiani per rectas C E, E F, ducto coniungatur, congruet angulus rectus <lb/>β E C, angulo recto C E F, &amp; </s>
  <s xml:id="echoid-s22432" xml:space="preserve">punctum β, puncto F, ob æqualitatem rectarum E β E F. </s>
  <s xml:id="echoid-s22433" xml:space="preserve">Quare <lb/>
<anchor type="note" xlink:label="note-0351-10a" xlink:href="note-0351-10"/>
recta β C, conſtituens in eo ſitu cum meridiana linea E F, horologii Verticalis angulum E β C, <lb/>altitudinis poli ſupra Verticalem circulum verſus partes poli occulti, erit axis mundi occurrens <lb/>plano horologij declinantis in C, puncto; </s>
  <s xml:id="echoid-s22434" xml:space="preserve">ac idcirco, ex coroll. </s>
  <s xml:id="echoid-s22435" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s22436" xml:space="preserve">21. </s>
  <s xml:id="echoid-s22437" xml:space="preserve">primi libri, C, cen-<lb/>trum erit horologij declinantis. </s>
  <s xml:id="echoid-s22438" xml:space="preserve">Axis enim cum linea meridiana horologij Verticalis ad meri-<lb/>diem ſpectantis conſtituit angulum altitudinis poli ſupra Verticalem circulum verſus partes po-<lb/>li occulti, vt ex propoſ. </s>
  <s xml:id="echoid-s22439" xml:space="preserve">13. </s>
  <s xml:id="echoid-s22440" xml:space="preserve">ſuperioris libri conſtat, maxime ex portione Analemmatis ibi-<lb/>dem deſcripta.</s>
  <s xml:id="echoid-s22441" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1139" type="float" level="2" n="2">
<note position="right" xlink:label="note-0351-05" xlink:href="note-0351-05a" xml:space="preserve">Demonſtrati@ <lb/>conſtructionis <lb/>horologii ab <lb/>Horizonte de-<lb/>clinantis.</note>
<note position="left" xlink:label="note-0351-06" xlink:href="note-0351-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0351-07" xlink:href="note-0351-07a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0351-08" xlink:href="note-0351-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0351-09" xlink:href="note-0351-09a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0351-10" xlink:href="note-0351-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s22442" xml:space="preserve">RVRSVS ſi concipiatur animo moueri triangulum E F G, circa E G, donec cum plano ho-<lb/>rologii Verticalis coniungatur, oſtendemus, vt in propoſ. </s>
  <s xml:id="echoid-s22443" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22444" xml:space="preserve">huius libri rectam C G, eſſe lineam <lb/>ſtyli, ſeu indicis, &amp; </s>
  <s xml:id="echoid-s22445" xml:space="preserve">C H, axem mundi, angulumq́ue G C H, eſſe angulum altitudinis poli ſu-<lb/>pra planum declinans. </s>
  <s xml:id="echoid-s22446" xml:space="preserve">Reliqua demonſtrabuntur, vt in dicta propoſ. </s>
  <s xml:id="echoid-s22447" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22448" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s22449" xml:space="preserve">Ordo
<pb o="336" file="0352" n="352" rhead="GNOMONICES"/>
autem horarum idem erit tam in ſuperiori horologio, quàm in inferiori, qui in horizontali, vt pa <lb/>
<anchor type="note" xlink:label="note-0352-01a" xlink:href="note-0352-01"/>
tet, ſi circulus ex L, deſcriptus vna cum horologio in proprio ſitu intelligatur eſſe poſitus; </s>
  <s xml:id="echoid-s22450" xml:space="preserve">adeo vt <lb/>in ſuperiori horologio linea meridiana indicet horam 12. </s>
  <s xml:id="echoid-s22451" xml:space="preserve">meridiei: </s>
  <s xml:id="echoid-s22452" xml:space="preserve">In inferiori verò horam 12. <lb/></s>
  <s xml:id="echoid-s22453" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0352-01a" xlink:href="fig-0352-01"/>
<anchor type="note" xlink:label="note-0352-02a" xlink:href="note-0352-02"/>
<anchor type="note" xlink:label="note-0352-03a" xlink:href="note-0352-03"/>
<anchor type="note" xlink:label="note-0352-04a" xlink:href="note-0352-04"/>
mediæ noctis; </s>
  <s xml:id="echoid-s22454" xml:space="preserve">quæ verò ipſam in vtroque horologio præcedunt, vel ſequuntur ad partes orienta-<lb/>
<anchor type="note" xlink:label="note-0352-05a" xlink:href="note-0352-05"/>
les, monſtrent horas poſt meridiem, quæ verò ab eadem verſus occidentales partes recedunt, ho-<lb/>ras poſt mediam noctem indicent. </s>
  <s xml:id="echoid-s22455" xml:space="preserve">Quæ porrò partes horologii dicantur orientales, occidenta-<lb/>lesve, ſi cum meridiana linea conferantur, facile percipietur, ſi horologium in proprio ſitu collo-<lb/>catum eſſe í<unsure/>ntelligatur. </s>
  <s xml:id="echoid-s22456" xml:space="preserve">Eſt tamen hoc diſcrimen attendendum. </s>
  <s xml:id="echoid-s22457" xml:space="preserve">In ſuperiori horologio proxi-<lb/>mam lineam ipſi lineæ meridianæ verſus partes orientales indicare horam 1. </s>
  <s xml:id="echoid-s22458" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s22459" xml:space="preserve">ſequen <lb/>tem pertinere ad 2. </s>
  <s xml:id="echoid-s22460" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22461" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22462" xml:space="preserve">Item proximam verſus occidentales partes oſtendere horam 11. </s>
  <s xml:id="echoid-s22463" xml:space="preserve">à media <lb/>nocte, &amp; </s>
  <s xml:id="echoid-s22464" xml:space="preserve">ſequentem dare horam 10. </s>
  <s xml:id="echoid-s22465" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22466" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22467" xml:space="preserve">In inferiori autem horologio proximam lineam verſus <lb/>orientales partes monſtrare horam 11. </s>
  <s xml:id="echoid-s22468" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s22469" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22470" xml:space="preserve">ſequentem ſignificare 10. </s>
  <s xml:id="echoid-s22471" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22472" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22473" xml:space="preserve">Item proximam li <lb/>
<anchor type="note" xlink:label="note-0352-06a" xlink:href="note-0352-06"/>
neam verſus partes occidentales pertinere ad horam 1. </s>
  <s xml:id="echoid-s22474" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s22475" xml:space="preserve">noct. </s>
  <s xml:id="echoid-s22476" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22477" xml:space="preserve">ſequentem ad 2. </s>
  <s xml:id="echoid-s22478" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22479" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22480" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1140" type="float" level="2" n="3">
<note position="left" xlink:label="note-0352-01" xlink:href="note-0352-01a" xml:space="preserve">Ordo horarum <lb/>in horologio de <lb/>clinante ab Ho <lb/>rizonte idem <lb/>eſt, qui in hori-<lb/>zontali horolo-<lb/>gie.</note>
  <figure xlink:label="fig-0352-01" xlink:href="fig-0352-01a">
    <image file="0352-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0352-01"/>
  </figure>
<note position="left" xlink:label="note-0352-02" xlink:href="note-0352-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0352-03" xlink:href="note-0352-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0352-04" xlink:href="note-0352-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0352-05" xlink:href="note-0352-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0352-06" xlink:href="note-0352-06a" xml:space="preserve">Alia deſcriptio <lb/>linearum hora <lb/>riarum in ho-<lb/>rologio declinã <lb/>te ab Horizon <lb/>te, beneſicio ho <lb/>rologii Vertica <lb/>lis.</note>
</div>
<p>
  <s xml:id="echoid-s22481" xml:space="preserve">QVOD attinet ad alteram rationem ducendarum linearum horariarum, hoc ſolum notan-<lb/>
<anchor type="note" xlink:label="note-0352-07a" xlink:href="note-0352-07"/>
dum eſt, rectas ex F, egredientes, rectamq́ue A B, ſecantes, efficere debere cum E F, eoſdem an-<lb/>gulos, quos in horologio Verticali propoſ. </s>
  <s xml:id="echoid-s22482" xml:space="preserve">13. </s>
  <s xml:id="echoid-s22483" xml:space="preserve">ſuperioris libri deſcripto lineæ horariæ cum meri-<lb/>diana linea conſtituunt: </s>
  <s xml:id="echoid-s22484" xml:space="preserve">quia, vt oſtendimus, recta E F, eſt hic linea meridiana Verticalis horolo-<lb/>
<anchor type="note" xlink:label="note-0352-08a" xlink:href="note-0352-08"/>
gii, non autem horizontalis, vt in horologio declinante à Verticali; </s>
  <s xml:id="echoid-s22485" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22486" xml:space="preserve">punctum F, centrum eſt <lb/>eiuſdem horologii, cum in illud axis mundi cadat, vt probauimus.</s>
  <s xml:id="echoid-s22487" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1141" type="float" level="2" n="4">
<note position="left" xlink:label="note-0352-07" xlink:href="note-0352-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0352-08" xlink:href="note-0352-08a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>ab Horizon@e <lb/>declinantis, ex <lb/>altitudine poli <lb/>ſupra planum <lb/>declinans, &amp; ex <lb/>inclinatione <lb/>Meridiani eiuſ <lb/>dem plani de-<lb/>clinátis ad Me <lb/>ridian um Ho-<lb/>rizontis.</note>
</div>
<p>
  <s xml:id="echoid-s22488" xml:space="preserve">PRO ſecundo modo conſtruendi horologii declinantis, inuenimus per propoſ. </s>
  <s xml:id="echoid-s22489" xml:space="preserve">29. </s>
  <s xml:id="echoid-s22490" xml:space="preserve">primili-<lb/>bri altitudinem poli ſupra planum propoſitum grad. </s>
  <s xml:id="echoid-s22491" xml:space="preserve">35. </s>
  <s xml:id="echoid-s22492" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s22493" xml:space="preserve">25. </s>
  <s xml:id="echoid-s22494" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22495" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s22496" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22497" xml:space="preserve">eiuſdem libri, <lb/>inclinationem proprii Meridiani propoſiti plani ad Meridianum Horizontis grad. </s>
  <s xml:id="echoid-s22498" xml:space="preserve">37. </s>
  <s xml:id="echoid-s22499" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s22500" xml:space="preserve">50. <lb/></s>
  <s xml:id="echoid-s22501" xml:space="preserve">Vnde facile horologium ab Horizonte declinans cõficiemus per ea, quæ propoſ. </s>
  <s xml:id="echoid-s22502" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22503" xml:space="preserve">huius libri tra-<lb/>didimus, conſtructa prius portione Analemmatis A B C, pro altitudine poli inuenta, &amp; </s>
  <s xml:id="echoid-s22504" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22505" xml:space="preserve">vt videre <lb/>eſt prope horologium huius propoſ. </s>
  <s xml:id="echoid-s22506" xml:space="preserve">in ſemicirculo, ſiue portione Analem matis A B C. </s>
  <s xml:id="echoid-s22507" xml:space="preserve">Vt aute@
<pb o="337" file="0353" n="353" rhead="LIBER TERTIVS."/>
ſciatur, in quamnam partem à puncto N, in circulo ex L, deſcripto computari debeat inclinatio <lb/>proprii Meridiani plani declinantis ad Meridianum Horizontis, diligenter attendenda ſunt ea, <lb/>
<anchor type="note" xlink:label="note-0353-01a" xlink:href="note-0353-01"/>
quæ mox præcipiemus. </s>
  <s xml:id="echoid-s22508" xml:space="preserve">Quando planum ad Zenith pertinet, reſpicitq́ue occaſum, quale eſt no-<lb/>ſtrum planum, numeranda eſt dicta inclinatio ab N, ſiniſtram verſus, hoc eſt, ad partes orientales <lb/>verſus A, vſque ad O, quia tunc Meridianus Horizontis per O, ductus orientalior eſt Meridiano <lb/>proprio plani declinantis per N, ducti, propterea quòd polus plani declinantis, per quem eius Me <lb/>ridianus proprius ducitur, conſtitutus eſt in quadrante Verticalis circuli ſuperiori, &amp; </s>
  <s xml:id="echoid-s22509" xml:space="preserve">occidentali, <lb/>vt patet, ſi rectè intelligatur propria poſitio plani declinantis. </s>
  <s xml:id="echoid-s22510" xml:space="preserve">Omnes enim circuli poſitionum, <lb/>quorum vni horologium ab Horizonte declinans æquidiſtat, polos habent in Verticali circulo. <lb/></s>
  <s xml:id="echoid-s22511" xml:space="preserve">
<anchor type="note" xlink:label="note-0353-02a" xlink:href="note-0353-02"/>
Nam cum omnes illi tranſeant per polos Verticalis circuli, hoc eſt, per communes ſectione<unsure/>s Me. <lb/></s>
  <s xml:id="echoid-s22512" xml:space="preserve">
<anchor type="note" xlink:label="note-0353-03a" xlink:href="note-0353-03"/>
ridiani ac Horizontis, tranſibit viciſſim circulus Verticalis per illorum polos, vt in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s22513" xml:space="preserve">15. </s>
  <s xml:id="echoid-s22514" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22515" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22516" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s22517" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s22518" xml:space="preserve">Si verò planum ad Zenith quidem pertineat, ſed ad or-<lb/>tum vergat, ſupputanda eſt eadẽ inclinatio ab N, dextrã verſus, id eſt, ad occidentales partes verſus <lb/>B; </s>
  <s xml:id="echoid-s22519" xml:space="preserve">quoniã tunc Meridianus Horizontis occidentalior eſt proprio Meridiano plani declinantis.</s>
  <s xml:id="echoid-s22520" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1142" type="float" level="2" n="5">
<note position="right" xlink:label="note-0353-01" xlink:href="note-0353-01a" xml:space="preserve">Quam in par-<lb/>tem numeran-<lb/>da ſit in circu-<lb/>lo ex L, deſcri-<lb/>pto inclinatio; <lb/>Meridiani ip-<lb/>ſius plani decli <lb/>nantis ad Me-<lb/>ridianum Ho-<lb/>riz onus.</note>
<note position="right" xlink:label="note-0353-02" xlink:href="note-0353-02a" xml:space="preserve">Omnes circuli <lb/>poſitionũ polos <lb/>habent in Ver <lb/>ticali proprie <lb/>dicto.</note>
<note position="left" xlink:label="note-0353-03" xlink:href="note-0353-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s22521" xml:space="preserve">EX his facile quiuis intelliget, quam in partem dicta inclinatio numeranda ſit ab N, in infe-<lb/>riori horologio, ſi diligenter cõſideret, an Meridianus Horizontis in hemiſphærio infero ſit orien <lb/>talior Meridiano proprio plani declinantis, an occidentalior, &amp;</s>
  <s xml:id="echoid-s22522" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22523" xml:space="preserve">vt in propoſ. </s>
  <s xml:id="echoid-s22524" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22525" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22526" xml:space="preserve">dixi-<lb/>mus. </s>
  <s xml:id="echoid-s22527" xml:space="preserve">Abſtinuimus autem à præceptis huius rei tradendis, ne multitudine præceptorum confu-<lb/>ſionem pareremus lectori: </s>
  <s xml:id="echoid-s22528" xml:space="preserve">maximè quod ſatius eſt inferius horologium ex ſuperiori deducere, <lb/>vt in ſequenti ſcholio docebimus, quàm propria illud arte delineare.</s>
  <s xml:id="echoid-s22529" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s22530" xml:space="preserve">PRO modo denique tertio &amp; </s>
  <s xml:id="echoid-s22531" xml:space="preserve">vltimo reperimus ex propoſ. </s>
  <s xml:id="echoid-s22532" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22533" xml:space="preserve">primi libri, arcum plani decli-<lb/>
<anchor type="note" xlink:label="note-0353-05a" xlink:href="note-0353-05"/>
nantis inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s22534" xml:space="preserve">Meridianum proprium plani declinantis grad. </s>
  <s xml:id="echoid-s22535" xml:space="preserve">24. </s>
  <s xml:id="echoid-s22536" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s22537" xml:space="preserve">14. </s>
  <s xml:id="echoid-s22538" xml:space="preserve">Hic autem arcus computandus erit à recta C D, verſus A, ſi horologium fuerit ſuperius, &amp; </s>
  <s xml:id="echoid-s22539" xml:space="preserve">in <lb/>occaſum vergat; </s>
  <s xml:id="echoid-s22540" xml:space="preserve">verſus B, autem, ſi ſuperius fuerit, &amp; </s>
  <s xml:id="echoid-s22541" xml:space="preserve">reſpiciat ortum Solis: </s>
  <s xml:id="echoid-s22542" xml:space="preserve">quia ibi Meridianus <lb/>proprius plani declinantis occidentalior eſt Meridiano Horizontis in ſupero hemiſphærio, ac <lb/>propterea C P, eius ſectio communis cum plano horologii orientalior debet eſſe in horologio, <lb/>quàm meridiana linea C D: </s>
  <s xml:id="echoid-s22543" xml:space="preserve">Hic autem Meridianus proprius plani orientalior eſt Meridiano Ho-<lb/>rizontis, ac proinde C P, ſectio eius cõmunis cum plano horologij occidentalior eſſe debet, quàm <lb/>linea meridiana C D, in horologio. </s>
  <s xml:id="echoid-s22544" xml:space="preserve">Dubium autem non eſt, in horologio ſuperiori partes à recta <lb/>C D, vergentes verſus A, eſſe orientales, partes verò verſus B, occidentales.</s>
  <s xml:id="echoid-s22545" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1143" type="float" level="2" n="6">
<note position="right" xlink:label="note-0353-05" xlink:href="note-0353-05a" xml:space="preserve">Ali a deſcriptio <lb/>e<unsure/>iuſdem horo-<lb/>logii ab Hori-<lb/>zonte declina@ <lb/>tis.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s22546" xml:space="preserve">FACILE ex his intelliges, quid agere debeas in horologio inferiori, in quo centrum C, ver-<lb/>git ad Boream, &amp; </s>
  <s xml:id="echoid-s22547" xml:space="preserve">arcus D P, ad auſtrum, ſi attente conſideres per ea, quæ proximè dicta ſunt, num <lb/>Meridianus proprius plani declinantis in inferiori horologio ſit orientalior in hemiſphærio infe-<lb/>ro, quàm Meridianus Horizontis, an verò occidentalior. </s>
  <s xml:id="echoid-s22548" xml:space="preserve">Nam prout fuerit orientalior, occiden-<lb/>taliorve, ita numerandus erit dictus arcus à recta CD, in horologio ad contrarias partes, nempe ad <lb/>occidentales, orientalesve. </s>
  <s xml:id="echoid-s22549" xml:space="preserve">Itaque horologium Aſtronomicum ab Horizonte declinans, &amp; </s>
  <s xml:id="echoid-s22550" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22551" xml:space="preserve">de-<lb/>ſcripſimus, quod faciendum erat.</s>
  <s xml:id="echoid-s22552" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1145" type="section" level="1" n="274">
<head xml:id="echoid-head284" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s22553" xml:space="preserve">VTRVMQVE horologium declinans ab Horizonte, tam ſuperius, quàm inferius, ita in plano <lb/>
<anchor type="note" xlink:label="note-0353-08a" xlink:href="note-0353-08"/>
declinante statuendum eſt, vt meridiana linea C D, æquidistet lineæ meridianæ in plano, quod Horizon-<lb/>ti par allelum eſt, inuentæ, (quod facile fiet, ſi recta linea quæpiam ſecans in horologio rectam A B, ad <lb/>angulos rectos conſtituatur in ipſamet linea meridiana inuenta, ita vt tota toti congruat) &amp; </s>
  <s xml:id="echoid-s22554" xml:space="preserve">ipſum ho-<lb/>rologium, ſi ſuperius fuerit ſpectans ad occaſum, eleuetur ex parte orientis; </s>
  <s xml:id="echoid-s22555" xml:space="preserve">vel ſi ad ortum pertineat, ex <lb/>parte occidentis, ſecundum inclinationem plani, nempe in noſtro exemplo, grad. </s>
  <s xml:id="echoid-s22556" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22557" xml:space="preserve">it a tamen, vt illa pars <lb/>eleuetur, in qua linea horę 6. </s>
  <s xml:id="echoid-s22558" xml:space="preserve">æquinoctialem lineam ſecat. </s>
  <s xml:id="echoid-s22559" xml:space="preserve">Ex quo fit, vt recta A B, directè ab ortu in <lb/>occaſum porrigatur, hoc eſt, parallela ſit circulo Verticali propriè dicto, ſecet{q́ue}, ad angulos rectos lineam <lb/>illam meridianam in plano, quod Horizonti æquidiſtat, cui debere congruere diximus rectam illam, quæ <lb/>in horologio perpendicularis eſt ad rectam A B. </s>
  <s xml:id="echoid-s22560" xml:space="preserve">Si autem inferius fuerit horologium ad ortum ſpectans, <lb/>
<anchor type="note" xlink:label="note-0353-09a" xlink:href="note-0353-09"/>
eodem modo attollatur ex parte orientis: </s>
  <s xml:id="echoid-s22561" xml:space="preserve">vel ſi ad occaſum ſpectet, ex parte occidentis, ea tamen lege, <lb/>vt linea horæ 6. </s>
  <s xml:id="echoid-s22562" xml:space="preserve">æquinoctialem lineam ſecans exiſtat infra meridianam lineam C D. </s>
  <s xml:id="echoid-s22563" xml:space="preserve">Hæc verò eleuatio <lb/>it a commodè fieri poterit. </s>
  <s xml:id="echoid-s22564" xml:space="preserve">In plano, quod Horizonti æquidiſtat, inuentam lineam meridianam ſecet alia <lb/>linea ad rectos angulos. </s>
  <s xml:id="echoid-s22565" xml:space="preserve">Si enim cum hac conſtituat recta A B, quam in horologio duximus, angulum in-<lb/>clinationis plani ad Horizontem, it a vt omnes lineæ ex quibuſcunque punctis rectæ A B, demiſſæ ad pla <lb/>num Horizonti æquidiſtans perpendiculares cadant in rectam, quæ meridianam lineam in eodem plano <lb/>ad angulos rectos ſecat, proprium ſitum horologium habebit, ſi ea tamen pars horologii eleuata fuerit, <lb/>quam proximè docuimus eſſe attollendam; </s>
  <s xml:id="echoid-s22566" xml:space="preserve">addito etiam hoc, in ſuperiori horologio centrum C, collo-<lb/>candum eſſe vltra rectam A B, verſus meridiem, in inferiori autem verſus boream citra eandem re-<lb/>ctam A B.</s>
  <s xml:id="echoid-s22567" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1145" type="float" level="2" n="1">
<note position="right" xlink:label="note-0353-08" xlink:href="note-0353-08a" xml:space="preserve">Quomodo col <lb/>locandum ſit <lb/>horologium ab <lb/>Horizonte de-<lb/>clinans, vt ho-<lb/>ras indicet.</note>
<note position="left" xlink:label="note-0353-09" xlink:href="note-0353-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s22568" xml:space="preserve">STYLVS in vtroque horologio erit I K, in puncto K, affigendus, vt perpendicularis ſit ad planũ <lb/>
<anchor type="note" xlink:label="note-0353-10a" xlink:href="note-0353-10"/>
<pb o="338" file="0354" n="354" rhead="GNOMONICES"/>
horologii: </s>
  <s xml:id="echoid-s22569" xml:space="preserve">vel certè ſi triangulum C I G, rectum ſiatuatur ad horologĳ planum, vmbra axis C I, hor{as} <lb/>indicabit, veluti in ſuperioribus dictum eſt.</s>
  <s xml:id="echoid-s22570" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1146" type="float" level="2" n="2">
<note position="right" xlink:label="note-0353-10" xlink:href="note-0353-10a" xml:space="preserve">Stylus horolo-<lb/>gii.</note>
</div>
<p style="it">
  <s xml:id="echoid-s22571" xml:space="preserve">SI inipſo plano declinante ab Horizonte, quod ſtabile ſit, quale eſſet tectum aliquod directè ortum, <lb/>
<anchor type="note" xlink:label="note-0354-01a" xlink:href="note-0354-01"/>
vel occaſum reſpiciens, ita vt neque in meridiem, neque in borcam deflecteret, (quod qua ratione ſit ex-<lb/>plorandum, docuimus propoſ. </s>
  <s xml:id="echoid-s22572" xml:space="preserve">23. </s>
  <s xml:id="echoid-s22573" xml:space="preserve">primi libri) borologium ſit deſcribendum, non au<unsure/>@@m in quouis alio pla-<lb/>no, ex quo in planum declinans transferatur, vt in hac propoſ. </s>
  <s xml:id="echoid-s22574" xml:space="preserve">feci@@us, ducenda erit in plano declinan-<lb/>te recta C D, Horizonti æquidiſtans pro linea meridiana, &amp; </s>
  <s xml:id="echoid-s22575" xml:space="preserve">ad eam perpendicularis excitanda A B, <lb/>reliqua autem conſtruenda, vt in primo modo dixim{us}. </s>
  <s xml:id="echoid-s22576" xml:space="preserve">Quòd ſi poſterioribus duobus modis rem per age-<lb/>re malueris, ducenda quo que erit ante omnia pro linea meridiana recta C D, Horizonti æquid@ſtans, de-<lb/>inde ducenda recta C P, it @ vt rectæ C D, C P, inter cipiant arcum D P, vt in tertio modo dictum eſt, <lb/>
<anchor type="note" xlink:label="note-0354-02a" xlink:href="note-0354-02"/>
verſus quid@m partes orient ales horologii ſuperioris, &amp; </s>
  <s xml:id="echoid-s22577" xml:space="preserve">occaſum reſpicientis; </s>
  <s xml:id="echoid-s22578" xml:space="preserve">verſus autem occidentales <lb/>partes ſuperioris horologii, &amp; </s>
  <s xml:id="echoid-s22579" xml:space="preserve">ſpect antis ad ortum, &amp; </s>
  <s xml:id="echoid-s22580" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22581" xml:space="preserve">Reliqua omnia fiãt omnino, vt in propoſ. </s>
  <s xml:id="echoid-s22582" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22583" xml:space="preserve">huius <lb/>libri præcepimus, hoc eſt, ducatur ad C P, linea G H, perpendicularis pro linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s22584" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22585" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1147" type="float" level="2" n="3">
<note position="left" xlink:label="note-0354-01" xlink:href="note-0354-01a" xml:space="preserve">Q@i<unsure/>ratloae <lb/>@n plano @abili <lb/>declinante ab <lb/>Horizonte de-<lb/>ſcribendum ſit <lb/>borologium.</note>
<note position="left" xlink:label="note-0354-02" xlink:href="note-0354-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s22586" xml:space="preserve">S I lineamenta horologĳ ſuperioris ad occaſum ſpectantis ordinem inter ſe permutent, vt ſiniſtra in <lb/>
<anchor type="note" xlink:label="note-0354-03a" xlink:href="note-0354-03"/>
dextra, &amp; </s>
  <s xml:id="echoid-s22587" xml:space="preserve">dextra in ſiniſtra con@ertantur, (vocamus autem nunc partem dextram, ſinistramve, quæ <lb/>nobis ad horologium conuerſis, &amp; </s>
  <s xml:id="echoid-s22588" xml:space="preserve">ad a@ſtrum, dextra eſt, vel ſiniſtra) adeo vt eum ſitum nanciſcantur, <lb/>quem haberent in facie oppoſita plani deſcripta, it a vt ſingulæ lineæ ſingulis lineis congruerent; </s>
  <s xml:id="echoid-s22589" xml:space="preserve">confe-<lb/>ctum erit horologium aliud ſuperius ad ortum ſpectans, totidemq́, gradib{us}, quot illud, ab Horizonte <lb/>declinans: </s>
  <s xml:id="echoid-s22590" xml:space="preserve">commutatis tamen horarum numeris in earundem complementa vſque ad 12 qu@madmodũ <lb/>de horologio declinante à Verticali diximus in ſcbolio propoſ. </s>
  <s xml:id="echoid-s22591" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22592" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s22593" xml:space="preserve">Eadem enim demonstratio <lb/>
<anchor type="note" xlink:label="note-0354-04a" xlink:href="note-0354-04"/>
huc accommodari poterit. </s>
  <s xml:id="echoid-s22594" xml:space="preserve">Eadem ratione ex horologio ſuperiori ad ortum ſpectante conſlruetur aliud <lb/>ſuperius ſpectans ad occaſum, ſi illa permutatio linearum, &amp; </s>
  <s xml:id="echoid-s22595" xml:space="preserve">horarum fiat. </s>
  <s xml:id="echoid-s22596" xml:space="preserve">Idem{q́ue} dicendum est de in-<lb/>feriori horologio.</s>
  <s xml:id="echoid-s22597" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1148" type="float" level="2" n="4">
<note position="left" xlink:label="note-0354-03" xlink:href="note-0354-03a" xml:space="preserve">Quo pa@o ex <lb/>horologio ad <lb/>occaſum ſpectã <lb/>te fiat aliud ſpe <lb/>ctã@ ad ortum, <lb/>&amp; contra.</note>
<note position="left" xlink:label="note-0354-04" xlink:href="note-0354-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s22598" xml:space="preserve">IAM verò ſi horologium ſuperius quodcunque inuertatur, ita vt nobis conuerſis ad ipſum verſus <lb/>
<anchor type="note" xlink:label="note-0354-05a" xlink:href="note-0354-05"/>
ortum, ſi in occaſum ſpectet, aut verſus occaſum, ſi ſpectet in ortum, pars ſuperior fiat inferior, &amp; </s>
  <s xml:id="echoid-s22599" xml:space="preserve">con-<lb/>tra; </s>
  <s xml:id="echoid-s22600" xml:space="preserve">(quę mutatio facile percipietur, ſi intelligatur planum horologii circa rectam C D, circumuolui, do-<lb/>nec lineamenta ipſius ad Nadir ſpectent, iaceant{q́ue} in facie plani oppoſita, ac inferiori) &amp; </s>
  <s xml:id="echoid-s22601" xml:space="preserve">quæ in eo ſitu <lb/>nobis iterum ad horologium ex altera parte plani conuerſis dextra est, euadat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s22602" xml:space="preserve">è contrario; <lb/></s>
  <s xml:id="echoid-s22603" xml:space="preserve">confectum erit horologium inferius eiuſdem declinationis ab Horizonte, ſed in facie plani oppoſita, &amp; </s>
  <s xml:id="echoid-s22604" xml:space="preserve"><lb/>inferiori collocandum, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s22605" xml:space="preserve">13. </s>
  <s xml:id="echoid-s22606" xml:space="preserve">ſuperioris libri demonſtratum eſt. </s>
  <s xml:id="echoid-s22607" xml:space="preserve">Hoc autem horolo-<lb/>
<anchor type="note" xlink:label="note-0354-06a" xlink:href="note-0354-06"/>
gium inferius pulchrè exprimunt lineamenta ſuperioris horologii in facie oppoſita deſcripta, vt ſingulæ <lb/>lineæ ſingulis lineis congruant. </s>
  <s xml:id="echoid-s22608" xml:space="preserve">Nam hacfacta deſcriptione, ſi faciem oppoſitam ad nes conuertam{us}, <lb/>ita vt centrum C, habemus ad dextram, ſi ſuperius horologium ad occaſum ſpecte; </s>
  <s xml:id="echoid-s22609" xml:space="preserve">vel ad ſiniſtram, ſi <lb/>ſuperius ortum reſpicit, obtinebimus inferius horologium in facie inferiori, &amp; </s>
  <s xml:id="echoid-s22610" xml:space="preserve">oppoſita collocandum.</s>
  <s xml:id="echoid-s22611" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1149" type="float" level="2" n="5">
<note position="left" xlink:label="note-0354-05" xlink:href="note-0354-05a" xml:space="preserve">Qua ratione ex <lb/>Superiore horo <lb/>logio declin an <lb/>teab Horizon-<lb/>te gignatur In-<lb/>ferius horolo-<lb/>gium in facie <lb/>oppoſita plani <lb/>horologii de-<lb/>ſcribeadum.</note>
<note position="left" xlink:label="note-0354-06" xlink:href="note-0354-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s22612" xml:space="preserve">IMMO eodem labore, &amp; </s>
  <s xml:id="echoid-s22613" xml:space="preserve">opera, quemadmoaum de Verticali horologio declinante in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s22614" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22615" xml:space="preserve">huius libri diximus, quatuor horologia ab Horizonte declinantia inter ſe diuerſa, ſerua<unsure/>ta tamen <lb/>eadem ſemper quantitate inclinationis ad Horizontem, deſtribere licebit. </s>
  <s xml:id="echoid-s22616" xml:space="preserve">Si namque horologium ſupe-<lb/>rius declinans v. </s>
  <s xml:id="echoid-s22617" xml:space="preserve">g. </s>
  <s xml:id="echoid-s22618" xml:space="preserve">ab Horizonte verſus occaſum grad. </s>
  <s xml:id="echoid-s22619" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22620" xml:space="preserve">deſcribamus, partem{q́ue} eius dextram mute-<lb/>mus in ſiniſtrã, (vocamus nunc partem dextrã, quæ nobis ad horologiũ conuerſis verſus ortum, ſi ipſum <lb/>ad occaſum ſpectet, vel verſus occaſum, ſi ad ortum portineat, dextra cſt) ex qua quidẽ mutatione fit, vt <lb/>
<anchor type="note" xlink:label="note-0354-07a" xlink:href="note-0354-07"/>
pars etiam ſup<unsure/>erior fiat inferior, &amp; </s>
  <s xml:id="echoid-s22621" xml:space="preserve">centrum C, ad boream vergat, ſi nimirum mutatio hæc in inſtitua-<lb/>tur, vt horologium moueri intelligatur circa eius axem, nempe stylum I K; </s>
  <s xml:id="echoid-s22622" xml:space="preserve">deſcriptum erit quoque ho-<lb/>rologium inferius ad occaſum ſpectans ab Horizonte declinans grad 30. </s>
  <s xml:id="echoid-s22623" xml:space="preserve">Si verò eiuſdem horologii ſupe-<lb/>rioris omnia lineamenta defcribantur in alio plano, ita vt quæ ſunt ad dextram ipſius lineæ meridianę <lb/>C D, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s22624" xml:space="preserve">quę ad ſiniſtram, dextra; </s>
  <s xml:id="echoid-s22625" xml:space="preserve">aut (quod idem eſt) quæ ſita ſunt vltra lineam meridia-<lb/>nam verſus ortum, collocentur ve rſus occaſum, &amp; </s>
  <s xml:id="echoid-s22626" xml:space="preserve">contra, conſtructum erit aliud horologium ſuperius <lb/>ortum Solis reſpiciens, &amp; </s>
  <s xml:id="echoid-s22627" xml:space="preserve">ab Horizonte declinans grad. </s>
  <s xml:id="echoid-s22628" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22629" xml:space="preserve">commutatis horarum numeris in earum <lb/>complementa vſque ad 12. </s>
  <s xml:id="echoid-s22630" xml:space="preserve">Huiuſm<unsure/>odi ſunt lineamenta ſuperioris horologii ad occaſum ſpectantis in par <lb/>te oppoſita, &amp; </s>
  <s xml:id="echoid-s22631" xml:space="preserve">inferiori deſcripta, vt ſingulæ lineæ ſingulis lineis reſpondeant, dummodo ita ſtatuatur in <lb/>plano ſuperiori, quod ad ortum ſpectat, vt eadem pars, in quam cadit hora 6. </s>
  <s xml:id="echoid-s22632" xml:space="preserve">occupet ſuperiorem locũ. <lb/></s>
  <s xml:id="echoid-s22633" xml:space="preserve">
<anchor type="note" xlink:label="note-0354-08a" xlink:href="note-0354-08"/>
Si denique non ſolum lineamenta orientalia fiant occidentalia, &amp; </s>
  <s xml:id="echoid-s22634" xml:space="preserve">contra, ſed &amp; </s>
  <s xml:id="echoid-s22635" xml:space="preserve">pars ſuperior mutetur <lb/>in inferiorem, &amp; </s>
  <s xml:id="echoid-s22636" xml:space="preserve">è contrario, ita vt centrum C, rurſus in boream vergat, fabricatum erit horologium <lb/>inferius ad ortum ſpectans. </s>
  <s xml:id="echoid-s22637" xml:space="preserve">Eadem ratione, ſi deſcribatur horologium ſuperius orientale, deducemus ex <lb/>eo alia tria ciuſdem declinationis. </s>
  <s xml:id="echoid-s22638" xml:space="preserve">Quæ omnia ex ĳs, quæ ad finem ſcholii propoſ. </s>
  <s xml:id="echoid-s22639" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22640" xml:space="preserve">huius libri ſcripſimus, <lb/>facile colligi poſſunt, cuius etiam ſcholii postrema figura refert typum horologii ſuperioris ad ortum ſpc-<lb/>ctantis, quod ab Horizonte declinat grad. </s>
  <s xml:id="echoid-s22641" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22642" xml:space="preserve">ſed ad latitudinem loci grad. </s>
  <s xml:id="echoid-s22643" xml:space="preserve">48. </s>
  <s xml:id="echoid-s22644" xml:space="preserve">quia in eo conſtruendo cõ <lb/>ſtitutus eſt angulus E β C, in figura propoſ. </s>
  <s xml:id="echoid-s22645" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22646" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22647" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s22648" xml:space="preserve">42. </s>
  <s xml:id="echoid-s22649" xml:space="preserve">quanta nimirum eſt altitudo poli ſupra <lb/>Verticalem circulum in regione, cuius latitudo continet grad. </s>
  <s xml:id="echoid-s22650" xml:space="preserve">48.</s>
  <s xml:id="echoid-s22651" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1150" type="float" level="2" n="6">
<note position="left" xlink:label="note-0354-07" xlink:href="note-0354-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0354-08" xlink:href="note-0354-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s22652" xml:space="preserve">CAETERVM tam Superius horologium orientale, quàm Inferius ſtatim horas monſlrat, orien-<lb/>te Sole, licet plures horæ in Superiore contineantur, quàm in Inferiore. </s>
  <s xml:id="echoid-s22653" xml:space="preserve">Tam autem Superius, quàm <lb/>Inferius occidentale horas indicat vſque ad Solis occaſum; </s>
  <s xml:id="echoid-s22654" xml:space="preserve">ita vt tam orientale Superius, &amp; </s>
  <s xml:id="echoid-s22655" xml:space="preserve">occiden-
<pb o="339" file="0355" n="355" rhead="LIBER TERTIVS."/>
tale Inferius ſimul, quàm orientale Inferius, &amp; </s>
  <s xml:id="echoid-s22656" xml:space="preserve">occidentale ſuperius ſimul, contineant omnes ho-<lb/>r{as} diurn{as}.</s>
  <s xml:id="echoid-s22657" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s22658" xml:space="preserve">PRAXIS Andreę Schoneri, qua deſcribit horologium, etiamſi in linea æquinoctiali nulla puncta <lb/>inuenta ſint pro horariis lineis, eadem hic eſt, quę in horologio declinante à Verticali. </s>
  <s xml:id="echoid-s22659" xml:space="preserve">Id quod perſpicuũ <lb/>eſt ex figura huius propoſ. </s>
  <s xml:id="echoid-s22660" xml:space="preserve">ſi cum figura propoſ. </s>
  <s xml:id="echoid-s22661" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22662" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22663" xml:space="preserve">conferatur.</s>
  <s xml:id="echoid-s22664" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s22665" xml:space="preserve">QVOD ſi idem horologium ab Horizonte declinans ſit deſcribendum in plano dato ad quamcunque <lb/>
<anchor type="note" xlink:label="note-0355-01a" xlink:href="note-0355-01"/>
gnomonis magnitudinem, cuius etiam locus in plano datus ſit, vt in puncto K, aggrediemur rem hoc mo-<lb/>do. </s>
  <s xml:id="echoid-s22666" xml:space="preserve">Ducantur per K, locum ſtyli duæ rectæ A B, F D, ſe mutuo ſecantes in K, ad rectos angulos: </s>
  <s xml:id="echoid-s22667" xml:space="preserve">Vel <lb/>
<anchor type="figure" xlink:label="fig-0355-01a" xlink:href="fig-0355-01"/>
<anchor type="note" xlink:label="note-0355-02a" xlink:href="note-0355-02"/>
<anchor type="note" xlink:label="note-0355-03a" xlink:href="note-0355-03"/>
<anchor type="note" xlink:label="note-0355-04a" xlink:href="note-0355-04"/>
ſiplanum declinans ab Horizonte ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s22668" xml:space="preserve">ad Verticalem rectum, ducatur bcneficio libellæ per K, <lb/>locum ſtyli recta F D, Horizonti æquidistans, quam in K, ad angulos rectos ſecet A B. </s>
  <s xml:id="echoid-s22669" xml:space="preserve">In recta autem <lb/>F D, ſumpta longitudine dati ſtyli K F, ſiue ſupra rectam A B, ſiue infra, deſcribatur ex F, vt centro <lb/>verſus rectam A B, arcus circuli D H, verſus B, quidem, ſi planum horologĳ ad occaſum ſpectat, &amp; </s>
  <s xml:id="echoid-s22670" xml:space="preserve">ad <lb/>Zenith, vel ad ortum &amp; </s>
  <s xml:id="echoid-s22671" xml:space="preserve">ad Nadir; </s>
  <s xml:id="echoid-s22672" xml:space="preserve">verſus A, vero, ſi horologium Superius eſt, &amp; </s>
  <s xml:id="echoid-s22673" xml:space="preserve">ortum reſpicit, vel <lb/>Inferius, ſpectat{q́ue} ad occaſum. </s>
  <s xml:id="echoid-s22674" xml:space="preserve">In hoc arcu numerata declinatione ab Horizonte à puncto D, vſque ad <lb/>H, quam rurſum ponimus grad. </s>
  <s xml:id="echoid-s22675" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22676" xml:space="preserve">ita vt horologium Superius occaſum reſpiciat, ducta{q́ue} recta F H, ſe-<lb/>
<anchor type="note" xlink:label="note-0355-05a" xlink:href="note-0355-05"/>
cante ipſam A B, in E, agatur per E, recta C E, ipſi F D, parallela, ſeu ad A B, perpendicularis. </s>
  <s xml:id="echoid-s22677" xml:space="preserve">Nam <lb/>C E, erit linea meridiana, ſiue horæ 12. </s>
  <s xml:id="echoid-s22678" xml:space="preserve">Deinde in arcu H D, ad alteram partem rectæ F D, producto <lb/>ſupputetur cõplementum declinationis D N, ducatur{q́ue} recta F N; </s>
  <s xml:id="echoid-s22679" xml:space="preserve">vel certe ducatur recta F α, ad F E, <lb/>perpendicularis ſecans A B, in α. </s>
  <s xml:id="echoid-s22680" xml:space="preserve">Per punctum enim α, ducenda eſt &amp; </s>
  <s xml:id="echoid-s22681" xml:space="preserve">linea horizontalis, æquinoctia-<lb/>lis{q́ue}, &amp; </s>
  <s xml:id="echoid-s22682" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s22683" xml:space="preserve">Sumpta quoque in A B, recta E β, ſiue ad dextram, ſiue ad ſiniſtram lineę meri-<lb/>dianę C E, quæ ipſi E F, æqualis ſit, deſcribatur ex β, verſus C E, arcus circuli, vltra quidem rectam <lb/>A B, in borologio Superiore, citra vero eandem A B, in inferiore horologio, in quo numerato complemen <lb/>to altitudinis poli, initio facto à recta A B, ducatur ex β ad finem ſupputationis recta ſecans C E, in C, <lb/>puncto, quod centrum erit horologĳ. </s>
  <s xml:id="echoid-s22684" xml:space="preserve">Ducta autem ex C, per K, locum styli recta C K, pro linea ſtyli, <lb/>quam recta ex a, ducta ſecet ad angulos rectos in G, erit recta α G, linea æquinoctialis. </s>
  <s xml:id="echoid-s22685" xml:space="preserve">Poſt hæc exci-<lb/>
<anchor type="note" xlink:label="note-0355-06a" xlink:href="note-0355-06"/>
tetur ex K, recta K I, ad C k, per pendicularis, &amp; </s>
  <s xml:id="echoid-s22686" xml:space="preserve">ſtylo K F, æqualis, iungatur{q́ue} rectæ C I, G I, quæ in <lb/>I, angulum rectum cõtinebunt; </s>
  <s xml:id="echoid-s22687" xml:space="preserve">adeo vt ſi prius ducatur recta C I, &amp; </s>
  <s xml:id="echoid-s22688" xml:space="preserve">ad eam excitetur perpendicula-<lb/>ris I G, ſecans lineam ſtyli in G, punctum G, ſit illud, per quod ex α, ducenda eſt linea ęquinoctialis α G, <lb/>ad C K, perpendicularis. </s>
  <s xml:id="echoid-s22689" xml:space="preserve">Erit autem C I, axis mundi. </s>
  <s xml:id="echoid-s22690" xml:space="preserve">I am vero in linea ſtyli C K, ſumpta recta G L, <lb/>ipſi G I, ęquali, deſcribatur ex L, circulus cuiuſuis magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s22691" xml:space="preserve">ęquales diſtribuatur, <lb/>initio facto à recta L M, quę ex L, ducitur per punctum M, vbi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s22692" xml:space="preserve">meridiana ſe in-<lb/>terſecant, quæ quidem recta L M, ſi erratum non eſt, neceſſario perpendicularis erit ad ductam rectam <lb/>L α. </s>
  <s xml:id="echoid-s22693" xml:space="preserve">Reliqua autem omnia abſoluantur, vt in principio huius propoſ. </s>
  <s xml:id="echoid-s22694" xml:space="preserve">explicatum eſt.</s>
  <s xml:id="echoid-s22695" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1151" type="float" level="2" n="7">
<note position="right" xlink:label="note-0355-01" xlink:href="note-0355-01a" xml:space="preserve">Conftructio ho <lb/>rologii ab Ho-<lb/>rizonte decli-<lb/>nantis ad datã <lb/>longitudinem <lb/>ſtyli, cuius etiã <lb/>locus datus ſit.</note>
  <figure xlink:label="fig-0355-01" xlink:href="fig-0355-01a">
    <image file="0355-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0355-01"/>
  </figure>
<note position="left" xlink:label="note-0355-02" xlink:href="note-0355-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0355-03" xlink:href="note-0355-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0355-04" xlink:href="note-0355-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0355-05" xlink:href="note-0355-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0355-06" xlink:href="note-0355-06a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Demonſtratie <lb/>præcedentis @@ <lb/>ſtructionis.</note>
<p style="it">
  <s xml:id="echoid-s22696" xml:space="preserve">SIC autem conſtructionem hanc demonſtrabimus. </s>
  <s xml:id="echoid-s22697" xml:space="preserve">Intelligatur in horologii plano recta F D, Hori-<lb/>zonti æquidiſtare, it a vt ſit communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s22698" xml:space="preserve">illius circuli poſitionis, qui per polos plani <lb/>horologĳ, &amp; </s>
  <s xml:id="echoid-s22699" xml:space="preserve">per communes ſectiones Meridiani &amp; </s>
  <s xml:id="echoid-s22700" xml:space="preserve">Horizontis ducitur. </s>
  <s xml:id="echoid-s22701" xml:space="preserve">Hic enim circulus per ſtylum
<pb o="340" file="0356" n="356" rhead="GNOMONICES"/>
F K, ducitur, (quòd ſtylus productus in polum plani horologĳ cadat, cum ſit ſegmentum axis ipſius ho <lb/>rology) facit{q́ue} ſectionem ęquidiſta@tem Horizonti. </s>
  <s xml:id="echoid-s22702" xml:space="preserve">Nam cum planum horologii ab Horizonte declinan-<lb/>tis æquidiſtet communi ſectioni dicti circuli poſitionũ &amp; </s>
  <s xml:id="echoid-s22703" xml:space="preserve">Horizontis, nempe axi Verticalis circuli, erunt <lb/>
<anchor type="figure" xlink:label="fig-0356-01a" xlink:href="fig-0356-01"/>
<anchor type="note" xlink:label="note-0356-01a" xlink:href="note-0356-01"/>
<anchor type="note" xlink:label="note-0356-02a" xlink:href="note-0356-02"/>
per propoſ. </s>
  <s xml:id="echoid-s22704" xml:space="preserve">18. </s>
  <s xml:id="echoid-s22705" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22706" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22707" xml:space="preserve">ſectiones, quas horologii planum cum illo circulo &amp; </s>
  <s xml:id="echoid-s22708" xml:space="preserve">cum Horizonte facit, paralle-<lb/>
<anchor type="note" xlink:label="note-0356-03a" xlink:href="note-0356-03"/>
læ inter ſe; </s>
  <s xml:id="echoid-s22709" xml:space="preserve">atque adeo communis ſectio plani horologii &amp; </s>
  <s xml:id="echoid-s22710" xml:space="preserve">dicti circuli poſitionum, cum æquidiſtet com-<lb/>muni ſectioni eiuſdem horologii &amp; </s>
  <s xml:id="echoid-s22711" xml:space="preserve">Horizontis, ipſi Horizonti ęquidiſtabit, propterea recta F D, ſi po-<lb/>natur Horizonti parallela, communis ſectio erit dicti circuli poſitionum, &amp; </s>
  <s xml:id="echoid-s22712" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s22713" xml:space="preserve">Hinc ſequi-<lb/>tur, rectam A B, eſſe ſectionem communem Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s22714" xml:space="preserve">e<unsure/>iuſdem plani horologii. </s>
  <s xml:id="echoid-s22715" xml:space="preserve">Quoniã enim <lb/>tam planum Verticalis circuli proprie dicti, quàm planum horologii ab Horizonte declinantis, ad præ-<lb/>dictum circulum poſitionum rectum eſt, erit &amp; </s>
  <s xml:id="echoid-s22716" xml:space="preserve">communis eorum ſectio ad eundem recta; </s>
  <s xml:id="echoid-s22717" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s22718" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0356-04a" xlink:href="note-0356-04"/>
ad rectam F D, in eo circulo exiſtentem perpendicularis erit, ex defin. </s>
  <s xml:id="echoid-s22719" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22720" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22721" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22722" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s22723" xml:space="preserve">Quare recta A B, <lb/>cum ſit ad F D, perpendicularis, ex conſtructione, communis ſectio eſt Verticalis circuli per centrũ mun <lb/>di, &amp; </s>
  <s xml:id="echoid-s22724" xml:space="preserve">per ſtylum tranſeuntis, &amp; </s>
  <s xml:id="echoid-s22725" xml:space="preserve">plani horologii.</s>
  <s xml:id="echoid-s22726" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1152" type="float" level="2" n="8">
  <figure xlink:label="fig-0356-01" xlink:href="fig-0356-01a">
    <image file="0356-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-01"/>
  </figure>
<note position="left" xlink:label="note-0356-01" xlink:href="note-0356-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0356-02" xlink:href="note-0356-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0356-03" xlink:href="note-0356-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0356-04" xlink:href="note-0356-04a" xml:space="preserve">19. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s22727" xml:space="preserve">DEINDE quia E F K, angulus est declinationis plani horologii ab Horizonte, erit F E K, angu-<lb/>
<anchor type="note" xlink:label="note-0356-05a" xlink:href="note-0356-05"/>
lus complementi eiuſdem declinationis, qualem nimirum Meridianus cum plano declinante conſtituit. <lb/></s>
  <s xml:id="echoid-s22728" xml:space="preserve">Quare ſi triangulum E F K, circa E K, moueatur, donec rectum ſit ad planum horologii in proprio ſitu <lb/>poſitum, erit F E, communis ſectio Verticalis ac Meridiani per F, verticem ſtyli ducti; </s>
  <s xml:id="echoid-s22729" xml:space="preserve">ac proinde per <lb/>E, ducenda erit linea m@ridiana, id eſt, communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s22730" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s22731" xml:space="preserve">Quia verò hæc <lb/>communis ſectio paraliela eſt, per propoſ. </s>
  <s xml:id="echoid-s22732" xml:space="preserve">18. </s>
  <s xml:id="echoid-s22733" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22734" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22735" xml:space="preserve">communi ſectioni plani horologii &amp; </s>
  <s xml:id="echoid-s22736" xml:space="preserve">ſupradicti circu <lb/>li poſitionum, hoc est, ipſi rectę F D, propterea quòd planum horologii ęquidiſtat communi ſectioni Me-<lb/>ridiani &amp; </s>
  <s xml:id="echoid-s22737" xml:space="preserve">illius circuli poſitionum; </s>
  <s xml:id="echoid-s22738" xml:space="preserve">erit recta C E, quæ ipſi F D, ducta eſt parallela, linea meridiana. </s>
  <s xml:id="echoid-s22739" xml:space="preserve">Et <lb/>quoniam arcus H N, quadrans eſt, erit angulus E F α, rectus; </s>
  <s xml:id="echoid-s22740" xml:space="preserve">ac proinde recta F α, cõmunis ſectio Ver <lb/>ticalis atque Horizontis. </s>
  <s xml:id="echoid-s22741" xml:space="preserve">Cum enim tam Verticalis quàm Horizon ad Meridianum rectus ſit, erit &amp; </s>
  <s xml:id="echoid-s22742" xml:space="preserve"><lb/>eorum ſectio communis ad eundem recta, ac proinde, per defin. </s>
  <s xml:id="echoid-s22743" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22744" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22745" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22746" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s22747" xml:space="preserve">ad rectam F E, in Meri-<lb/>
<anchor type="note" xlink:label="note-0356-06a" xlink:href="note-0356-06"/>
<anchor type="note" xlink:label="note-0356-07a" xlink:href="note-0356-07"/>
diano exiſtentem perpendicularis in F, centro mundi. </s>
  <s xml:id="echoid-s22748" xml:space="preserve">Quare F α, quæ ad F E, perpendicularis eſt, com-<lb/>munis ſe@tio eſt Verticalis atque Horizontis. </s>
  <s xml:id="echoid-s22749" xml:space="preserve">Habet autem Aequator eandem communem ſectionem <lb/>cum Verticali, Horizonte, &amp; </s>
  <s xml:id="echoid-s22750" xml:space="preserve">circulo horę 6. </s>
  <s xml:id="echoid-s22751" xml:space="preserve">nempe axem Meridiani, cum quatuor hi circuli ad Meri-<lb/>dianum recti tranſeant, per propoſ. </s>
  <s xml:id="echoid-s22752" xml:space="preserve">13. </s>
  <s xml:id="echoid-s22753" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22754" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22755" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s22756" xml:space="preserve">per polos Meridiani. </s>
  <s xml:id="echoid-s22757" xml:space="preserve">Igitur tam Horizon, quàm <lb/>Aequator, circulus{q́ue} horæ 6. </s>
  <s xml:id="echoid-s22758" xml:space="preserve">per rectam F α, ducitur, occurritq́, plano horologii declinantis in puncto <lb/>α; </s>
  <s xml:id="echoid-s22759" xml:space="preserve">atque adeo per α, ducenda erit tam linea horizontalis, quàm æquinoctialis, atque linea horæ ſextæ.</s>
  <s xml:id="echoid-s22760" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1153" type="float" level="2" n="9">
<note position="left" xlink:label="note-0356-05" xlink:href="note-0356-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0356-06" xlink:href="note-0356-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0356-07" xlink:href="note-0356-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s22761" xml:space="preserve">MANENTE, adhuc triangulo E F K, ad horologĳ planum recto, quoniam tam planum horolo-<lb/>gĳ, quàm planum Meridiani rectum eſt ad Verticalem, erit quoque communis eorum ſectio C E, ad eun-<lb/>
<anchor type="note" xlink:label="note-0356-08a" xlink:href="note-0356-08"/>
dem recta, atque adeo, per defin. </s>
  <s xml:id="echoid-s22762" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22763" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22764" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22765" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s22766" xml:space="preserve">ad rectam F E, in Verticali exiſtentem in illo ſitu per-<lb/>pendicularis; </s>
  <s xml:id="echoid-s22767" xml:space="preserve">ac proinde angulus C E F, rectus erit. </s>
  <s xml:id="echoid-s22768" xml:space="preserve">Siigitur triangulum β E C, moueri intelligatur <lb/>circa rectam C E, donec recta β E, rectæ F E, &amp; </s>
  <s xml:id="echoid-s22769" xml:space="preserve">punctum β, puncto F, congruat, propter rectos angu<unsure/>
<pb o="341" file="0357" n="357" rhead="LIBER TERTIVS."/>
los β E C, F E C, &amp; </s>
  <s xml:id="echoid-s22770" xml:space="preserve">æqualitatem rectarum E β, E F, erit β C, axis mundi; </s>
  <s xml:id="echoid-s22771" xml:space="preserve">quandoquidem in plano <lb/>Meridiani per rectas F E, E C, ducti cum F E, meridiana linea Verticalis in F, centro mundi angulum <lb/>conſtituit E β C, complemento altitudinis poli ſupra Horizontem æqualem. </s>
  <s xml:id="echoid-s22772" xml:space="preserve">Igitur per coroll. </s>
  <s xml:id="echoid-s22773" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s22774" xml:space="preserve">21. <lb/></s>
  <s xml:id="echoid-s22775" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s22776" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22777" xml:space="preserve">punctum C, in plano horologii, in quod axis cadit, centrum erit horologii. </s>
  <s xml:id="echoid-s22778" xml:space="preserve">Hinc fit, rectam C K, eſ-<lb/>ſe lineam ſtyli, quemadmodum &amp; </s>
  <s xml:id="echoid-s22779" xml:space="preserve">in prima deſcriptione huius propoſ. </s>
  <s xml:id="echoid-s22780" xml:space="preserve">linea styli C G, ducta eſt ex cen-<lb/>tro C, per k, locum ſtyli. </s>
  <s xml:id="echoid-s22781" xml:space="preserve">Pari ratione efficitur, rectam α G, quæ ad lineam ſtyli perpendicularis eſt, eſ-<lb/>ſe lineam æquinoctialem, quandoquidem per punctum α, ducenda eſt, vt nuper oſtendimus, &amp; </s>
  <s xml:id="echoid-s22782" xml:space="preserve">angulos <lb/>rectos facit cum linea ſtyli, vt in priori deſcriptione horologĳ declinantis à Verticali propoſ. </s>
  <s xml:id="echoid-s22783" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22784" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22785" xml:space="preserve"><lb/>demonſtratum eſt à nobis. </s>
  <s xml:id="echoid-s22786" xml:space="preserve">Reliqua omnia demonſtrabuntur, vt in priori deſcriptione propoſ. </s>
  <s xml:id="echoid-s22787" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22788" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22789" xml:space="preserve"><lb/>eius{q́ue} ſcholio, vbi horologium declinans à Verticali ad datum ſtylum, eius locum conſtruximus.</s>
  <s xml:id="echoid-s22790" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1154" type="float" level="2" n="10">
<note position="left" xlink:label="note-0356-08" xlink:href="note-0356-08a" xml:space="preserve">19. vndec.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s22791" xml:space="preserve">PER Ellipſim in plano horologii deſcriptã, cuius diametri inueniuntur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s22792" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22793" xml:space="preserve">huius <lb/>
<anchor type="note" xlink:label="note-0357-02a" xlink:href="note-0357-02"/>
lib. </s>
  <s xml:id="echoid-s22794" xml:space="preserve">conſtruemus idẽ horologium ab Horizonte declinans, &amp; </s>
  <s xml:id="echoid-s22795" xml:space="preserve">cõmodiſſime quidem, quoad illas boras, quę <lb/>vix ęquinoctialem lineã interſecant, quales in noſtro exẽplo ſunt horę 8. </s>
  <s xml:id="echoid-s22796" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22797" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22798" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s22799" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s22800" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s22801" xml:space="preserve">Exem-<lb/>plum huius deſcriptionis non confecimus, quia ſine vllo labore res ipſa per cipi poteſt ex figura, quam in <lb/>dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s22802" xml:space="preserve">1. </s>
  <s xml:id="echoid-s22803" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22804" xml:space="preserve">construximus. </s>
  <s xml:id="echoid-s22805" xml:space="preserve">Refert enim ea figura horologiũ ab Horizonte declinans <lb/>grad. </s>
  <s xml:id="echoid-s22806" xml:space="preserve">30. </s>
  <s xml:id="echoid-s22807" xml:space="preserve">ex parte orientali, ita vt occaſum reſpiciat, fabricatum ad latitudinem gr. </s>
  <s xml:id="echoid-s22808" xml:space="preserve">48. </s>
  <s xml:id="echoid-s22809" xml:space="preserve">quæ nimirũ com-<lb/>plementũ est illius latitudinis, ad quã illud horologiũ à Verticali declinans cõſtructũ eſt; </s>
  <s xml:id="echoid-s22810" xml:space="preserve">mutatis tamen <lb/>numeris horarum in earundem complementa vſque ad 12. </s>
  <s xml:id="echoid-s22811" xml:space="preserve">Vt manifestum eſt ex iis, quæ ad initium huius <lb/>propoſ. </s>
  <s xml:id="echoid-s22812" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s22813" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1155" type="float" level="2" n="11">
<note position="right" xlink:label="note-0357-02" xlink:href="note-0357-02a" xml:space="preserve">Deſcript io eiuſ <lb/>dem horologii <lb/>ex @llipſi.</note>
</div>
</div>
<div xml:id="echoid-div1157" type="section" level="1" n="275">
<head xml:id="echoid-head285" xml:space="preserve">PROBLEMA 14. PROPOSITIO 14.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s22814" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in horologio, <lb/>quod ab Horizonte declinat, figurare.</s>
  <s xml:id="echoid-s22815" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s22816" xml:space="preserve">PRORSVS ijſdem modis in hoc horologio arcus ſignorum deſcribentur, quibus deſcri-<lb/>
<anchor type="note" xlink:label="note-0357-04a" xlink:href="note-0357-04"/>
<anchor type="figure" xlink:label="fig-0357-01a" xlink:href="fig-0357-01"/>
<anchor type="note" xlink:label="note-0357-05a" xlink:href="note-0357-05"/>
<anchor type="note" xlink:label="note-0357-06a" xlink:href="note-0357-06"/>
<anchor type="note" xlink:label="note-0357-07a" xlink:href="note-0357-07"/>
pti ſunt in horologio declinante à Verticali, vt in ſubiecta figura apparet. </s>
  <s xml:id="echoid-s22817" xml:space="preserve">Duximus ã<unsure/>utem in f<unsure/>i-<lb/>gura radiorum ex C, lineas illis duntaxat horis reſpondentes, quæ in horologio ad ſiniſtram lineę
<pb o="342" file="0358" n="358" rhead="GNOMONICES"/>
ſtyli poſitæ ſunt, vt confuſio, quæ ex multitudine linearum oriri ſolet, vitetur, quemadmodũ pro-<lb/>poſ. </s>
  <s xml:id="echoid-s22818" xml:space="preserve">2. </s>
  <s xml:id="echoid-s22819" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s22820" xml:space="preserve">monuimus. </s>
  <s xml:id="echoid-s22821" xml:space="preserve">Nam in horologio ex parte dextra eiuſdẽ lineæ ſtyli duximus lineas <lb/>occultas, quales ſunt illæ minutis quibuſdam lineis diſtinctæ, quæ cum horis ad ſiniſtram poſitis <lb/>
<anchor type="figure" xlink:label="fig-0358-01a" xlink:href="fig-0358-01"/>
<anchor type="note" xlink:label="note-0358-01a" xlink:href="note-0358-01"/>
<anchor type="note" xlink:label="note-0358-02a" xlink:href="note-0358-02"/>
<anchor type="note" xlink:label="note-0358-03a" xlink:href="note-0358-03"/>
e<unsure/>aſdem diſtantias à linea ſtyli ſeruant; </s>
  <s xml:id="echoid-s22822" xml:space="preserve">non ſecus atque horæ in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s22823" xml:space="preserve">Vertica <lb/>li æqualiter hincinde à meridiana linea remouentur; </s>
  <s xml:id="echoid-s22824" xml:space="preserve">atque ita horaria interualla poſita inter pun <lb/>ctum C, &amp; </s>
  <s xml:id="echoid-s22825" xml:space="preserve">radios ſignorum translata ſunt ex horologii centro C, vna eademq́ue opera &amp; </s>
  <s xml:id="echoid-s22826" xml:space="preserve">in ho-<lb/>ras ad ſiniſtram lineæ ſtyli poſitas, &amp; </s>
  <s xml:id="echoid-s22827" xml:space="preserve">in lineas illas occultas ad dextram eiuſdem exiſtentes, &amp;</s>
  <s xml:id="echoid-s22828" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s22829" xml:space="preserve">Duximus tamen etiam in figura radiorum lineam CE, reſpondentem lineæ meridianæ, quamuis <lb/>ea non contineatur ad ſiniſtram partem lineæ indicis, ſed ad dextram, hanc ſolum ob cauſam, vt <lb/>per eam inueniremus punctum F, à quo diuiſio circuli ex A, deſcripto principium habere debet, <lb/>
<anchor type="note" xlink:label="note-0358-04a" xlink:href="note-0358-04"/>
vt videlicet eaſdem horarias lineas ex C, ſecundum praxim Andreæ Schoneri ducere poſſimus, vt <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s22830" xml:space="preserve">2. </s>
  <s xml:id="echoid-s22831" xml:space="preserve">huius libri tradidimus. </s>
  <s xml:id="echoid-s22832" xml:space="preserve">In quo quidem circulo puncta diuiſionum à puncto <lb/>F, verſus B, in quod linea indicis cadit, progrediendo pertinent ad horas, quæ in horologio à li-<lb/>nea meridiana verſus lineam indicis ducuntur, ita vt in noſtro exemplo proximum punctum in-<lb/>fra F, verſus B, ſpectet ad horam primam à meridie, ſequens ad 2. </s>
  <s xml:id="echoid-s22833" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s22834" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22835" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1157" type="float" level="2" n="1">
<note position="right" xlink:label="note-0357-04" xlink:href="note-0357-04a" xml:space="preserve">Deſcriptio @@-<lb/>cuum ſignorũ <lb/>in hologio de<unsure/>-<lb/>clinante ab Ho <lb/>siaont<unsure/>e.</note>
  <figure xlink:label="fig-0357-01" xlink:href="fig-0357-01a">
    <image file="0357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0357-01"/>
  </figure>
<note position="left" xlink:label="note-0357-05" xlink:href="note-0357-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0357-06" xlink:href="note-0357-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0357-07" xlink:href="note-0357-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0358-01" xlink:href="fig-0358-01a">
    <image file="0358-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0358-01"/>
  </figure>
<note position="left" xlink:label="note-0358-01" xlink:href="note-0358-01a" xml:space="preserve">01<unsure/></note>
<note position="left" xlink:label="note-0358-02" xlink:href="note-0358-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0358-03" xlink:href="note-0358-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0358-04" xlink:href="note-0358-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s22836" xml:space="preserve">PORRO in Superiori horologio, quod ab Horizonte declinat, paralleli ſeu arcus ſignorum <lb/>
<anchor type="note" xlink:label="note-0358-05a" xlink:href="note-0358-05"/>
inter centrum C, &amp; </s>
  <s xml:id="echoid-s22837" xml:space="preserve">lineam æquinoctialem poſiti pertinent ad ſigna borealia, qui verò à centro C, <lb/>longius abſunt, quàm æquinoctialis linea, ad auſtralia, quemadmodum in horizontali horologio. <lb/></s>
  <s xml:id="echoid-s22838" xml:space="preserve">In horologio autem inferiori contrarium omnino intelligatur. </s>
  <s xml:id="echoid-s22839" xml:space="preserve">Nam in eo arcus ſignorum inter <lb/>centrum C, &amp; </s>
  <s xml:id="echoid-s22840" xml:space="preserve">æquinoctialem lineam ad auſtralia ſigna, alii autem ad borealia pertinent. </s>
  <s xml:id="echoid-s22841" xml:space="preserve">Id quod <lb/>
<anchor type="note" xlink:label="note-0358-06a" xlink:href="note-0358-06"/>
facile percipi poteſt, ſi vtrumque horologium in proprio ſitu poſitum eſſe intelligatur Fiet enim, <lb/>vt Sole exiſtente in ſignis auſtralibus, vmbra ſtyli proiiciatur in partem borealem horologij, eo-<lb/>dem verò in ſignis borealibus exiſtente, in partem auſtralem, &amp;</s>
  <s xml:id="echoid-s22842" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22843" xml:space="preserve">Aequinoctialis autem linea ſepa <lb/>rat partem horologii auſtralem à boreali, vt conſtat, quemadmodũ in omnibus alijs horologijs.</s>
  <s xml:id="echoid-s22844" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1158" type="float" level="2" n="2">
<note position="left" xlink:label="note-0358-05" xlink:href="note-0358-05a" xml:space="preserve">Qui arcus in <lb/>horologio pe@ti <lb/>neant ad ſigna <lb/>bo<unsure/>realia, &amp; qui <lb/>ad auſtr<unsure/>alia.</note>
<note position="left" xlink:label="note-0358-06" xlink:href="note-0358-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s22845" xml:space="preserve">LINEA horizontalis ducenda eſt per horam 6. </s>
  <s xml:id="echoid-s22846" xml:space="preserve">in linea æquinoctiali ipſi lineæ meridianæ, <lb/>
<anchor type="note" xlink:label="note-0358-07a" xlink:href="note-0358-07"/>
ſeu horæ 12. </s>
  <s xml:id="echoid-s22847" xml:space="preserve">parallela. </s>
  <s xml:id="echoid-s22848" xml:space="preserve">Quoniam enim Sol exiſtens in Aequatore oritur, &amp; </s>
  <s xml:id="echoid-s22849" xml:space="preserve">occidit hora 6. </s>
  <s xml:id="echoid-s22850" xml:space="preserve">fit, vt <lb/>tempore horæ 6. </s>
  <s xml:id="echoid-s22851" xml:space="preserve">Horizõtem quoque occupet. </s>
  <s xml:id="echoid-s22852" xml:space="preserve">Quare tempore ortus Solis, vel occaſus radius So-<lb/>laris per verticem ſtyli porrectus cadet, per propoſ. </s>
  <s xml:id="echoid-s22853" xml:space="preserve">11. </s>
  <s xml:id="echoid-s22854" xml:space="preserve">primi libri, in communes ſectiones, quas <lb/>in plano horologii faciunt circulus horæ 6. </s>
  <s xml:id="echoid-s22855" xml:space="preserve">Aequator, &amp; </s>
  <s xml:id="echoid-s22856" xml:space="preserve">Horizon, cum in his tunc Sol exiſtat. <lb/></s>
  <s xml:id="echoid-s22857" xml:space="preserve">Liquido ergo conſtat, communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s22858" xml:space="preserve">plani horologii, id eſt, lineam hori-<lb/>zontalem, per horam 6. </s>
  <s xml:id="echoid-s22859" xml:space="preserve">in linea æquinoctiali ducendam eſſe, vbi nimirum ſe mutuo ſecant linea
<pb o="343" file="0359" n="359" rhead="LIBER TERTIVS."/>
horæ 6. </s>
  <s xml:id="echoid-s22860" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22861" xml:space="preserve">æquinoctialis; </s>
  <s xml:id="echoid-s22862" xml:space="preserve">alias non caderet radius Solis in omnes tres ſectiones, quas planum ho-<lb/>rologij cum illis tribus circulis facit. </s>
  <s xml:id="echoid-s22863" xml:space="preserve">quod eſt abſurdum. </s>
  <s xml:id="echoid-s22864" xml:space="preserve">Quòd autem eadem parallela eſſe de-<lb/>beat lineæ meridianæ, perſpicuè colligitur ex propoſ. </s>
  <s xml:id="echoid-s22865" xml:space="preserve">18. </s>
  <s xml:id="echoid-s22866" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s22867" xml:space="preserve">Quia enim Meridianus, Ho-<lb/>rizon, &amp; </s>
  <s xml:id="echoid-s22868" xml:space="preserve">circulus maximus, cui horologium æquidiſtat, communem ſectionem habent axem Ver <lb/>ticalis circuli, erunt communes ſectiones, quas Meridianus, &amp; </s>
  <s xml:id="echoid-s22869" xml:space="preserve">Horizon cum plano horologij fa-<lb/>ciunt, parallelæ inter ſeſe, vt in dicta propoſ. </s>
  <s xml:id="echoid-s22870" xml:space="preserve">18. </s>
  <s xml:id="echoid-s22871" xml:space="preserve">demonſtratum eſt.</s>
  <s xml:id="echoid-s22872" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1159" type="float" level="2" n="3">
<note position="left" xlink:label="note-0358-07" xlink:href="note-0358-07a" xml:space="preserve">Horizontalis li <lb/>nea quomodo <lb/>d<unsure/>ucatur.</note>
</div>
<p>
  <s xml:id="echoid-s22873" xml:space="preserve">HANC eandem lineam horizontalem ducemus hac ratione. </s>
  <s xml:id="echoid-s22874" xml:space="preserve">Per K, locum ſtyli agatur re-<lb/>
<anchor type="note" xlink:label="note-0359-01a" xlink:href="note-0359-01"/>
cta K A, meridianæ lineæ parallela, ad quam ex quolibet puncto B, excitetur perpendicularis B D, <lb/>verſus illam partem horologii, vbi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s22875" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s22876" xml:space="preserve">ſe interſecant. </s>
  <s xml:id="echoid-s22877" xml:space="preserve">Deinde <lb/>ſumpta recta A B, quæ ſtylo I K, æqualis ſit, conſtituatur in A, angulus B A D, complemento de-<lb/>
<anchor type="note" xlink:label="note-0359-02a" xlink:href="note-0359-02"/>
clinationis plani ab Horizonte æqualis, ſecetq́ue recta A D, rectam B D, in D. </s>
  <s xml:id="echoid-s22878" xml:space="preserve">Nam per punctum <lb/>D, acta ipſi meridianæ lineæ<unsure/> parallela dabit horizontalem lineam, vt prius, quæ neceſſario per ho-<lb/>ram 6. </s>
  <s xml:id="echoid-s22879" xml:space="preserve">in line@ æquinoctiali tranſibit, ſi erratum non eſt. </s>
  <s xml:id="echoid-s22880" xml:space="preserve">Atque hoc modo ducendo lineam ho-<lb/>rizontalem facile examinabimus, an hora 6. </s>
  <s xml:id="echoid-s22881" xml:space="preserve">ſit rectè deſcripta, necne. </s>
  <s xml:id="echoid-s22882" xml:space="preserve">Quòd autem linea hori-<lb/>zontalis ducenda ſit per punctum D, hac arte inuentum, (Ipſam enim duci per horam 6. </s>
  <s xml:id="echoid-s22883" xml:space="preserve">in linea <lb/>æquinoctiali, &amp; </s>
  <s xml:id="echoid-s22884" xml:space="preserve">parallelam eſſe lineæ meridianæ, proximè iam demonſtratum eſt) hoc modo ma-<lb/>nifeſtabimus. </s>
  <s xml:id="echoid-s22885" xml:space="preserve">Intelligatur triangulum A B D, circa rectam B D, moueri, vſque dum ad horologij <lb/>planum ſit rectam, &amp; </s>
  <s xml:id="echoid-s22886" xml:space="preserve">ſtylus I K, in K, rectus cogitetur eſſe ad horologium. </s>
  <s xml:id="echoid-s22887" xml:space="preserve">Erunt hac ratione re-<lb/>ctæ I K, A B inter ſe parallelæ, quòd vtraque ad planum horologij recta ſit; </s>
  <s xml:id="echoid-s22888" xml:space="preserve">ipſa quidem I k, ex <lb/>
<anchor type="note" xlink:label="note-0359-03a" xlink:href="note-0359-03"/>
poſitione, at verò A B, ex defin. </s>
  <s xml:id="echoid-s22889" xml:space="preserve">4. </s>
  <s xml:id="echoid-s22890" xml:space="preserve">lib 11. </s>
  <s xml:id="echoid-s22891" xml:space="preserve">Euclidis. </s>
  <s xml:id="echoid-s22892" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s22893" xml:space="preserve">æquales inter ſe ſint, erit &amp; </s>
  <s xml:id="echoid-s22894" xml:space="preserve">re-<lb/>
<anchor type="note" xlink:label="note-0359-04a" xlink:href="note-0359-04"/>
cta A I, ducta ex A, ad I, (poſita vtraque linea I K, A B, ad planum recta) parallela ipſi B K. </s>
  <s xml:id="echoid-s22895" xml:space="preserve">Ho-<lb/>
<anchor type="note" xlink:label="note-0359-05a" xlink:href="note-0359-05"/>
rizon ergo tranſiens per I, verticem ſtyli, æquidiſtansq́ue meridianæ lineæ, ac proinde &amp; </s>
  <s xml:id="echoid-s22896" xml:space="preserve">ipſi <lb/>B K, ducetur per rectam A I, atque adeo per punctum A. </s>
  <s xml:id="echoid-s22897" xml:space="preserve">Et quia angulus B A D, ex conſtructio-<lb/>ne, complemento declinationis plani ab Horizonte ęqualis eſt, erit reliquus A D B, ipſi declinatio-<lb/>niæqualis. </s>
  <s xml:id="echoid-s22898" xml:space="preserve">Quare Horizon per rectam A D, ducetur, cum hac ratione plano horologii occurrat <lb/>ſecua<unsure/>dum angulum declinationis A D B, ita vt A D, communis ſectio ſit Horizontis, &amp; </s>
  <s xml:id="echoid-s22899" xml:space="preserve">trianguli <lb/>A B D. </s>
  <s xml:id="echoid-s22900" xml:space="preserve">Quocirca Horizon plano horologii occurret in D, puncto, ac propterea per D, ducenda <lb/>erit linea horizontalis.</s>
  <s xml:id="echoid-s22901" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1160" type="float" level="2" n="4">
<note position="right" xlink:label="note-0359-01" xlink:href="note-0359-01a" xml:space="preserve">Alia deſcriptio <lb/>lineæ horizon-<lb/>talis.</note>
<note position="left" xlink:label="note-0359-02" xlink:href="note-0359-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0359-03" xlink:href="note-0359-03a" xml:space="preserve">6. vndec.</note>
<note position="left" xlink:label="note-0359-04" xlink:href="note-0359-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0359-05" xlink:href="note-0359-05a" xml:space="preserve">33. primi.</note>
</div>
<p>
  <s xml:id="echoid-s22902" xml:space="preserve">DENIQVE eadem horizontalis linea ducetur hac arte. </s>
  <s xml:id="echoid-s22903" xml:space="preserve">Ex figura radiorum, ſi horologium <lb/>
<anchor type="note" xlink:label="note-0359-06a" xlink:href="note-0359-06"/>
Superius ad occaſum ſpecter, ſumantur interualla horæ ſeptimæ à meridie, inter C, &amp; </s>
  <s xml:id="echoid-s22904" xml:space="preserve">radium ho <lb/>
<anchor type="note" xlink:label="note-0359-07a" xlink:href="note-0359-07"/>
rarum 14. </s>
  <s xml:id="echoid-s22905" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22906" xml:space="preserve">horæ 5. </s>
  <s xml:id="echoid-s22907" xml:space="preserve">à meridie inter C, &amp; </s>
  <s xml:id="echoid-s22908" xml:space="preserve">radium horarum 10. </s>
  <s xml:id="echoid-s22909" xml:space="preserve">vel ſi ad ortum vergat, horæ 5. </s>
  <s xml:id="echoid-s22910" xml:space="preserve">à <lb/>media nocte inter C, &amp; </s>
  <s xml:id="echoid-s22911" xml:space="preserve">radium horarum 14. </s>
  <s xml:id="echoid-s22912" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22913" xml:space="preserve">horæ 7. </s>
  <s xml:id="echoid-s22914" xml:space="preserve">à media nocte inter C, &amp; </s>
  <s xml:id="echoid-s22915" xml:space="preserve">radium horarũ <lb/>10 &amp; </s>
  <s xml:id="echoid-s22916" xml:space="preserve">transferantur ex C, centro horologii in reſpondentes lineas, imprimendo puncta in ipſis. <lb/></s>
  <s xml:id="echoid-s22917" xml:space="preserve">Per hæc enim puncta erit horizontalis linea ducenda: </s>
  <s xml:id="echoid-s22918" xml:space="preserve">quoniam Sol in eo parallelo exiſtens, cuius <lb/>arcus diurnus continet horas 14. </s>
  <s xml:id="echoid-s22919" xml:space="preserve">qui quidem, per ea, quæ demonſtrata ſunt, tranſit in horologio <lb/>per inuenta puncta in hora 7. </s>
  <s xml:id="echoid-s22920" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s22921" xml:space="preserve">hora 5. </s>
  <s xml:id="echoid-s22922" xml:space="preserve">à media nocte, occidit hora 7. </s>
  <s xml:id="echoid-s22923" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s22924" xml:space="preserve"><lb/>oritur hora 5. </s>
  <s xml:id="echoid-s22925" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s22926" xml:space="preserve">Exiſtens verò in illo parallelo, cuius arcus diurnus complectitur <lb/>horas 10. </s>
  <s xml:id="echoid-s22927" xml:space="preserve">qui ex demonſtratis quoque tranſit in horologio per puncta inuenta in hora 5. </s>
  <s xml:id="echoid-s22928" xml:space="preserve">à meri-<lb/>die<unsure/>, &amp; </s>
  <s xml:id="echoid-s22929" xml:space="preserve">hora 7. </s>
  <s xml:id="echoid-s22930" xml:space="preserve">à media nocte, occidit hora 5. </s>
  <s xml:id="echoid-s22931" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s22932" xml:space="preserve">oritur hora 7. </s>
  <s xml:id="echoid-s22933" xml:space="preserve">à media nocte; </s>
  <s xml:id="echoid-s22934" xml:space="preserve">ac proin <lb/>de per dictas horas in nominatis arcubus diurnis horizontalis linea ducenda erit, quæ vt ante de-<lb/>
<anchor type="note" xlink:label="note-0359-08a" xlink:href="note-0359-08"/>
monſtrauimu<unsure/>s, neceſſario per horam 6. </s>
  <s xml:id="echoid-s22935" xml:space="preserve">in linea æquinoctiali tranſibit, &amp; </s>
  <s xml:id="echoid-s22936" xml:space="preserve">lineæ meridianæ paral-<lb/>lela exiſtet. </s>
  <s xml:id="echoid-s22937" xml:space="preserve">Adducimus tot modos ducendæ lineæ horizontalis, quia &amp; </s>
  <s xml:id="echoid-s22938" xml:space="preserve">iucundum eſt cernere, <lb/>tanta varietate ad eundem ſemper ſcopum nos poſſe peruenire, &amp; </s>
  <s xml:id="echoid-s22939" xml:space="preserve">certi eſſe poſſumus, in horarum <lb/>deſcriptione nullum errorem fuiſſe commiſſum, ſi omnes modi concordes conſentientesq́ue in-<lb/>ter ſe fuerint.</s>
  <s xml:id="echoid-s22940" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1161" type="float" level="2" n="5">
<note position="right" xlink:label="note-0359-06" xlink:href="note-0359-06a" xml:space="preserve">Horizontalis li <lb/>neæ deſcriptio <lb/>alia.</note>
<note position="left" xlink:label="note-0359-07" xlink:href="note-0359-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0359-08" xlink:href="note-0359-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s22941" xml:space="preserve">HÆC autem linea horizontalis totum horologium diuidit in duo, quorum maius eſt Supe-<lb/>
<anchor type="note" xlink:label="note-0359-09a" xlink:href="note-0359-09"/>
rius, &amp; </s>
  <s xml:id="echoid-s22942" xml:space="preserve">minus Inferius, vt in præcedentibus oſtenſum eſt; </s>
  <s xml:id="echoid-s22943" xml:space="preserve">dummodo partes Inferioris immuten-<lb/>tur, vt in præcedenti propoſ. </s>
  <s xml:id="echoid-s22944" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s22945" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1162" type="float" level="2" n="6">
<note position="right" xlink:label="note-0359-09" xlink:href="note-0359-09a" xml:space="preserve">Horizontalis Ii<unsure/> <lb/>nea dirimit to-<lb/>tum horologiũ <lb/>in Superius In-<lb/>feriusq́ue, &amp; in <lb/>diurnum no-<lb/>cturnumque.</note>
</div>
<p>
  <s xml:id="echoid-s22946" xml:space="preserve">SECATVR horologium quoque totum ab eadem horizontali linea in diurnum, &amp; </s>
  <s xml:id="echoid-s22947" xml:space="preserve">noctur <lb/>num, veluti in ſuperioribus dictum eſt. </s>
  <s xml:id="echoid-s22948" xml:space="preserve">Parallelos igitur, ſiue arcus, &amp;</s>
  <s xml:id="echoid-s22949" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22950" xml:space="preserve">figurauimus. </s>
  <s xml:id="echoid-s22951" xml:space="preserve">quod <lb/>
<anchor type="note" xlink:label="note-0359-10a" xlink:href="note-0359-10"/>
faciendum erat.</s>
  <s xml:id="echoid-s22952" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1163" type="float" level="2" n="7">
<note position="left" xlink:label="note-0359-10" xlink:href="note-0359-10a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1165" type="section" level="1" n="276">
<head xml:id="echoid-head286" xml:space="preserve">PROBLEMA 15. PROPOSITIO 15.</head>
<p>
  <s xml:id="echoid-s22953" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio, quod <lb/>ab Horizonte declinat, deſcribere.</s>
  <s xml:id="echoid-s22954" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Areuum diu@-<lb/>n<unsure/>orum deſcri-<lb/>ptio in eodem<unsure/> <lb/>horologio dec<unsure/>li <lb/>nanteab Hori-<lb/>zon<unsure/>te.</note>
<p>
  <s xml:id="echoid-s22955" xml:space="preserve">IN his parallelis deſcribendis nihil difficultatis eſt, cum eodem modo deſcribantur, quo pa-<lb/>ralleli ſignorum Zodiaci in præcedenti propoſ. </s>
  <s xml:id="echoid-s22956" xml:space="preserve">delineati ſunt, vt patet, ſi pro ſignorum paralle-
<pb o="344" file="0360" n="360" rhead="GNOMONICES"/>
lis ſumantur paralleli arcuum diurnorum, &amp;</s>
  <s xml:id="echoid-s22957" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22958" xml:space="preserve">Parallelos ergo arcuum diurnorum, &amp;</s>
  <s xml:id="echoid-s22959" xml:space="preserve">c. </s>
  <s xml:id="echoid-s22960" xml:space="preserve">de-<lb/>ſcripſimus. </s>
  <s xml:id="echoid-s22961" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s22962" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1166" type="section" level="1" n="277">
<head xml:id="echoid-head287" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s22963" xml:space="preserve">HIC etiam, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s22964" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22965" xml:space="preserve">huius libri monuimus, per arcus diurnos duci poterunt lineæ il-<lb/>
<anchor type="note" xlink:label="note-0360-01a" xlink:href="note-0360-01"/>
larum horarum, quę vix æquinoctialem lineam interſecant, quales ſunt in noſtro exemplo 8. </s>
  <s xml:id="echoid-s22966" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22967" xml:space="preserve">9. </s>
  <s xml:id="echoid-s22968" xml:space="preserve">tam à <lb/>meridie, quàm à media nocte. </s>
  <s xml:id="echoid-s22969" xml:space="preserve">Cum enim, die continente horas 16. </s>
  <s xml:id="echoid-s22970" xml:space="preserve">Sol occidat hora 8. </s>
  <s xml:id="echoid-s22971" xml:space="preserve">à meridie, tran-<lb/>ſibit hora 8. </s>
  <s xml:id="echoid-s22972" xml:space="preserve">à meridie per illud punctum lineæ horizont alis, vbi ab arcu circuli ad interuallum rectę in <lb/>figura radiorum, quæ horę 8. </s>
  <s xml:id="echoid-s22973" xml:space="preserve">à meridie reſpondet, inter ceptæ inter C, &amp; </s>
  <s xml:id="echoid-s22974" xml:space="preserve">radium horarum 16. </s>
  <s xml:id="echoid-s22975" xml:space="preserve">deſcripti <lb/>
<anchor type="note" xlink:label="note-0360-02a" xlink:href="note-0360-02"/>
ſecatur. </s>
  <s xml:id="echoid-s22976" xml:space="preserve">Hæc autem hora vltra centrum C, producta dabit horam 8. </s>
  <s xml:id="echoid-s22977" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s22978" xml:space="preserve">Similiter quoniam, <lb/>cum dies continet horas 18. </s>
  <s xml:id="echoid-s22979" xml:space="preserve">Sol occidit hora 9. </s>
  <s xml:id="echoid-s22980" xml:space="preserve">à meridie, ducenda erit hora 9. </s>
  <s xml:id="echoid-s22981" xml:space="preserve">à meridie per punctum <lb/>in linea horizontali, in quo ab arcu circuli ad interuallum rectæ in figura radiorum, quæ horæ 9. </s>
  <s xml:id="echoid-s22982" xml:space="preserve">à meri-<lb/>diereſpondet, interiectæ inter C, &amp; </s>
  <s xml:id="echoid-s22983" xml:space="preserve">radiũ horarum 18. </s>
  <s xml:id="echoid-s22984" xml:space="preserve">deſcripti diuiditur. </s>
  <s xml:id="echoid-s22985" xml:space="preserve">Atque hæc hora producta vl-<lb/>tra centrum C, dabit horam 9. </s>
  <s xml:id="echoid-s22986" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s22987" xml:space="preserve">In horologio autem ſpectante ad ortum, idem faciendum <lb/>erit de horis 4. </s>
  <s xml:id="echoid-s22988" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s22989" xml:space="preserve">3. </s>
  <s xml:id="echoid-s22990" xml:space="preserve">à media nocte, &amp;</s>
  <s xml:id="echoid-s22991" xml:space="preserve">c.</s>
  <s xml:id="echoid-s22992" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1166" type="float" level="2" n="1">
<note position="left" xlink:label="note-0360-01" xlink:href="note-0360-01a" xml:space="preserve">Quo artificio <lb/>per<unsure/> arcus diur-<lb/>nos illę horæ <lb/>deſcribantur, <lb/>quæ uix æqui-<lb/>noctialẽ lineã <lb/>ſecant.</note>
<note position="left" xlink:label="note-0360-02" xlink:href="note-0360-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s22993" xml:space="preserve">SED commodius ea puncta in linea horizontali inueniemus per arcus illos diurnos priori modo, nem <lb/>pe ex Analemmate, deſcriptos: </s>
  <s xml:id="echoid-s22994" xml:space="preserve">quia horæ illæ, quæ vix æquinoctialem lineam ſecant, duci nequeunt in fi-<lb/>gura radiorum, niſi praxi Andreæ Schoneri vti velimus.</s>
  <s xml:id="echoid-s22995" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1168" type="section" level="1" n="278">
<head xml:id="echoid-head288" xml:space="preserve">PROBLEMA 16. PROPOSITIO 16.</head>
<p>
  <s xml:id="echoid-s22996" xml:space="preserve">CIRCVLOS Verticales in eodem horologio, quod ab Horizon-<lb/>te declinat, delineare.</s>
  <s xml:id="echoid-s22997" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s22998" xml:space="preserve">DVCTA per K, locum ſtyli, &amp; </s>
  <s xml:id="echoid-s22999" xml:space="preserve">punctum D, vbi linea horæ 6. </s>
  <s xml:id="echoid-s23000" xml:space="preserve">horizontalis, &amp; </s>
  <s xml:id="echoid-s23001" xml:space="preserve">æquinoctia-<lb/>
<anchor type="note" xlink:label="note-0360-04a" xlink:href="note-0360-04"/>
lis ſe interſecant, linea recta ſecante meridianam lineam in B, erigatur ex K, ad B D, perpendicu <lb/>laris K A, ſtylo I K, æqualis; </s>
  <s xml:id="echoid-s23002" xml:space="preserve">iunctaq́ue recta D A, abſcindatur ei æqualis D E. </s>
  <s xml:id="echoid-s23003" xml:space="preserve">Centro deinde E, <lb/>
<anchor type="note" xlink:label="note-0360-05a" xlink:href="note-0360-05"/>
deſcribatur ad quodcunque interuallum circulus, qui in grad. </s>
  <s xml:id="echoid-s23004" xml:space="preserve">360. </s>
  <s xml:id="echoid-s23005" xml:space="preserve">aut in pauciores partes, vt in <lb/>præcedentibus dictum eſt, ſecetur, initio facto à recta D E. </s>
  <s xml:id="echoid-s23006" xml:space="preserve">Si enim per centrum E, &amp; </s>
  <s xml:id="echoid-s23007" xml:space="preserve">diuiſionum <lb/>puncta egrediantur rectæ, ſecabitur ab his linea horizontalis in punctis, per quæ ex puncto B, <lb/>emiſſæ rectæ dabunt Verticales circulos, id eſt, communes eorum, &amp; </s>
  <s xml:id="echoid-s23008" xml:space="preserve">plani horologij ſectio-<lb/>nes, ita vt B D, ſit communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s23009" xml:space="preserve">Verticalis propriè dicti. </s>
  <s xml:id="echoid-s23010" xml:space="preserve">Quod hac ra-<lb/>tione conſirmabimus.</s>
  <s xml:id="echoid-s23011" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1168" type="float" level="2" n="1">
<note position="left" xlink:label="note-0360-04" xlink:href="note-0360-04a" xml:space="preserve">Vertica liũ cir-<lb/>culorum in eo-<lb/>dem horologio <lb/>declinante ab <lb/>Horizonte de-<lb/>lineatio.</note>
<note position="left" xlink:label="note-0360-05" xlink:href="note-0360-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s23012" xml:space="preserve">CONCIPIATVR animo triangulum A D K, moueri circa D K, donec rectum ſit ad pla <lb/>
<anchor type="note" xlink:label="note-0360-06a" xlink:href="note-0360-06"/>
num horologij, ac proinde punctum A, cum vertice ſtyli, ſeu centro mundi coniungatur, &amp; </s>
  <s xml:id="echoid-s23013" xml:space="preserve">ip-<lb/>ſum triangulum cum plano Verticalis circuli proprie dicti, quod &amp; </s>
  <s xml:id="echoid-s23014" xml:space="preserve">hic Verticalis ad planum ho-<lb/>rologij rectus ſit, tranſeatq́ue per A K, ſtylum, necnon per punctum D. </s>
  <s xml:id="echoid-s23015" xml:space="preserve">Quoniam enim circu-<lb/>
<anchor type="note" xlink:label="note-0360-07a" xlink:href="note-0360-07"/>
lus maximus, cui horologium æquidiſtat, per polos Verticalis propriè dicti ductus ad Vertica-<lb/>lem, per propoſ. </s>
  <s xml:id="echoid-s23016" xml:space="preserve">15. </s>
  <s xml:id="echoid-s23017" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23018" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23019" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s23020" xml:space="preserve">rectus eſt, erit viciſſim Verticalis ad illum circulũ rectus, atque <lb/>adeo &amp; </s>
  <s xml:id="echoid-s23021" xml:space="preserve">ad planum horologij, quod ei circulo æquidiſtat. </s>
  <s xml:id="echoid-s23022" xml:space="preserve">Cum ergo omnia plana per axẽ A K, du-<lb/>cta ad idem planum horologij recta ſint, tranſibit Verticalis per ſtylum A K, quandoquidem per <lb/>
<anchor type="note" xlink:label="note-0360-08a" xlink:href="note-0360-08"/>
verticem ipſius ducitur. </s>
  <s xml:id="echoid-s23023" xml:space="preserve">Quia vero Sole exiſtente in puncto, vbi mutuo ſe interſecant Aequator, <lb/>Horizon, circulus horæ 6. </s>
  <s xml:id="echoid-s23024" xml:space="preserve">nec non Verticalis proprie dictus, vmbra ſtyli cadit in D, punctum <lb/>horæ 6. </s>
  <s xml:id="echoid-s23025" xml:space="preserve">in æquinoctiali linea, vt ſupra diximus, fit vt per D, tranſeat communis quoque ſectio <lb/>Verticalis, &amp; </s>
  <s xml:id="echoid-s23026" xml:space="preserve">plani horologij, cum per propoſ. </s>
  <s xml:id="echoid-s23027" xml:space="preserve">11. </s>
  <s xml:id="echoid-s23028" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23029" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23030" xml:space="preserve">vmbra ſtyli tunc cadat in cõmunem hanc <lb/>ſectionem. </s>
  <s xml:id="echoid-s23031" xml:space="preserve">Igitur B D, communis ſectio erit plani horologii, &amp; </s>
  <s xml:id="echoid-s23032" xml:space="preserve">Verticalis proprie dicti. </s>
  <s xml:id="echoid-s23033" xml:space="preserve">Recta <lb/>autem A D, communis erit ſectio trianguli A D K, &amp; </s>
  <s xml:id="echoid-s23034" xml:space="preserve">Horizontis per verticem ſtyli A, &amp; </s>
  <s xml:id="echoid-s23035" xml:space="preserve">pun-<lb/>
<anchor type="note" xlink:label="note-0360-09a" xlink:href="note-0360-09"/>
ctum D, ducti. </s>
  <s xml:id="echoid-s23036" xml:space="preserve">Si igitur intelligamus circulum ex E, deſcriptum circa lineam horizontalem <lb/>moueri, donec punctum E, cum vertice ſtyli A, &amp; </s>
  <s xml:id="echoid-s23037" xml:space="preserve">recta E D, cum recta A D, coniungatur, ob <lb/>æqualitatem rectarum E D, A D, erit quoque E D, vel A D, communis ſectio Verticalis proprie <lb/>dicti, atque Horizontis; </s>
  <s xml:id="echoid-s23038" xml:space="preserve">immo ipſe circulus ex E, deſcriptus in plano Horizontis erit collocatus, <lb/>eiusq́ue centrum idem erit, quod centrum mundi. </s>
  <s xml:id="echoid-s23039" xml:space="preserve">Rectæ igitur aliæ per centrum E, emiſſæ di-<lb/>uidentes circulum ex E, deſcriptum, ac proinde &amp; </s>
  <s xml:id="echoid-s23040" xml:space="preserve">Horizontem ex eodem centro A, quod tunc <lb/>idem eſt, quod E, &amp; </s>
  <s xml:id="echoid-s23041" xml:space="preserve">in eodem plano deſcriptum, in partes æquales, communes ſectiones erunt <lb/>Horizontis &amp; </s>
  <s xml:id="echoid-s23042" xml:space="preserve">reliquorum Verticalium circulorum. </s>
  <s xml:id="echoid-s23043" xml:space="preserve">Quare Verticales circuli occurrent plano <lb/>horologii in punctis, in quibus horizontalis linea à rectis illis ex centro E, emiſſis diuiditur. <lb/></s>
  <s xml:id="echoid-s23044" xml:space="preserve">Quoniam verò omnes etiam ſe mutuo interſecant per propoſ. </s>
  <s xml:id="echoid-s23045" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23046" xml:space="preserve">primi libri, in puncto B, in <lb/>quod eorum communis ſectio, nempe axis Horizontis cadit, ita vt B, ſit Zenith, ſeu vertex capi-
<pb o="345" file="0361" n="361" rhead="LIBER TERTIVS."/>
tis; </s>
  <s xml:id="echoid-s23047" xml:space="preserve">(quia enim Meridianus, &amp; </s>
  <s xml:id="echoid-s23048" xml:space="preserve">Verticalis per centrum mundi A, &amp; </s>
  <s xml:id="echoid-s23049" xml:space="preserve">per punctum B, ducuntur, <lb/>erit ducta recta A B, e<unsure/>orum communis ſectio, hoc e<unsure/>ſt, axis Horizontis) erunt rectæ per B, &amp; </s>
  <s xml:id="echoid-s23050" xml:space="preserve">pun <lb/>
<anchor type="figure" xlink:label="fig-0361-01a" xlink:href="fig-0361-01"/>
<anchor type="note" xlink:label="note-0361-01a" xlink:href="note-0361-01"/>
<anchor type="note" xlink:label="note-0361-02a" xlink:href="note-0361-02"/>
<anchor type="note" xlink:label="note-0361-03a" xlink:href="note-0361-03"/>
<anchor type="note" xlink:label="note-0361-04a" xlink:href="note-0361-04"/>
cta in horizontali linea inuenta ductæ communes ſectiones Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s23051" xml:space="preserve">plani ho-<lb/>rologii. </s>
  <s xml:id="echoid-s23052" xml:space="preserve">Linea autem meridiana erit nonageſimus Verticalis. </s>
  <s xml:id="echoid-s23053" xml:space="preserve">Itaque circulos Verticales in eo-<lb/>dem horologio, quod ab Horizonte declinat, delineauimus. </s>
  <s xml:id="echoid-s23054" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23055" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1169" type="float" level="2" n="2">
<note position="left" xlink:label="note-0360-06" xlink:href="note-0360-06a" xml:space="preserve">Demonſtra tio <lb/>præcedentis cõ<unsure/> <lb/>@ructionis.</note>
<note position="left" xlink:label="note-0360-07" xlink:href="note-0360-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0360-08" xlink:href="note-0360-08a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0360-09" xlink:href="note-0360-09a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0361-01" xlink:href="fig-0361-01a">
    <image file="0361-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0361-01"/>
  </figure>
<note position="left" xlink:label="note-0361-01" xlink:href="note-0361-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0361-02" xlink:href="note-0361-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0361-03" xlink:href="note-0361-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0361-04" xlink:href="note-0361-04a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1171" type="section" level="1" n="279">
<head xml:id="echoid-head289" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">50</note>
<p style="it">
  <s xml:id="echoid-s23056" xml:space="preserve">EX iis, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s23057" xml:space="preserve">14. </s>
  <s xml:id="echoid-s23058" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23059" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23060" xml:space="preserve">ostendimus, liquido conſtat, portionem minorem horologii à <lb/>linea horizontali abſciſſam exhibere quoque nobis circulos Verticales in horologio Inferiori, ſi eius par <lb/>tes permutentur, vt ſupra dictum eſt.</s>
  <s xml:id="echoid-s23061" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s23062" xml:space="preserve">QVONIAM vero demonſtrauimus, Horizontem per rectam A D, &amp; </s>
  <s xml:id="echoid-s23063" xml:space="preserve">Meridianum per A B, <lb/>duci, ſi triangulum A B D, rectum ſtatuatur ad horologii planum in recta B D, efficitur, angulum <lb/>A D B, eſſe angulum inclinationis plani ad Horizontem, quem videlicet Horizon cum plano declinan-<lb/>te facit in plano Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s23064" xml:space="preserve">A B D, angulum complementi eiuſdem inclinationis, nempe quem <lb/>Meridianus cum eodẽ plano declinante conſtituit in Verticalis circuli plano. </s>
  <s xml:id="echoid-s23065" xml:space="preserve">Quamobrem neceſſe est, re-<lb/>liquum angulum B A D, rectum eſſe in triangulo A B D. </s>
  <s xml:id="echoid-s23066" xml:space="preserve">Id quod perſpicuum etiam eſſe poteſt ex horo-<lb/>logio, quod in ſcholio propoſ. </s>
  <s xml:id="echoid-s23067" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23068" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s23069" xml:space="preserve">ad datam ſtyli longitudinem conſtruximus. </s>
  <s xml:id="echoid-s23070" xml:space="preserve">Ibi enim linea F E, <lb/>reſpondet hic lineæ A B, &amp; </s>
  <s xml:id="echoid-s23071" xml:space="preserve">linea F α, ibi eadem eſt, quæ bic linea A D.</s>
  <s xml:id="echoid-s23072" xml:space="preserve"/>
</p>
<pb o="346" file="0362" n="362" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1172" type="section" level="1" n="280">
<head xml:id="echoid-head290" xml:space="preserve">PROBLEMA 17. PROPOSITIO 17.</head>
<p>
  <s xml:id="echoid-s23073" xml:space="preserve">PARALLELOS Horizontis in eodem horologio declinante ab <lb/>Horizonte reponere.</s>
  <s xml:id="echoid-s23074" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23075" xml:space="preserve">DESCRIBEMVS in hoc horologio parallelos Horizontis, vt in polari e<unsure/>oſdem deſignaui <lb/>
<anchor type="note" xlink:label="note-0362-01a" xlink:href="note-0362-01"/>
mus propoſ. </s>
  <s xml:id="echoid-s23076" xml:space="preserve">41. </s>
  <s xml:id="echoid-s23077" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23078" xml:space="preserve">dummodo ea, quæ ſequuntur, diligenter obſeruentur. </s>
  <s xml:id="echoid-s23079" xml:space="preserve">In priori <lb/>modo circulus Analemmatis A B C, referet Verticalem propriè dictum, qui nimirum per ſtylum <lb/>tranſiens ad planum horologij rectus eſt, facitq́ue fectionem B D: </s>
  <s xml:id="echoid-s23080" xml:space="preserve">Paralleli autem Horizontis nõ <lb/>
<anchor type="note" xlink:label="note-0362-02a" xlink:href="note-0362-02"/>
mutantur. </s>
  <s xml:id="echoid-s23081" xml:space="preserve">Rurſus pro axe E F, ducenda erit diameter, ſeu communis ſectio Verticalis, &amp; </s>
  <s xml:id="echoid-s23082" xml:space="preserve">circuli <lb/>maximi, cui horologiũ æquidiſtat, ita vt tam arcus C E, quàm B F, æqualis ſit declinationi propo-<lb/>
<anchor type="figure" xlink:label="fig-0362-01a" xlink:href="fig-0362-01"/>
ſitæ ab Horizonte. </s>
  <s xml:id="echoid-s23083" xml:space="preserve">Huicautẽ diametro ducẽda <lb/>eſt parallela R Q, pro magnitudine ſtyli I K, vel <lb/>A K, ita vt recta D I, rectam R Q, ad rectos a<unsure/>n-<lb/>gulos ſecans ſit ſtylo I K, æqualis. </s>
  <s xml:id="echoid-s23084" xml:space="preserve">Puncta deni-<lb/>que L, M, N, O, P, accepta ex T, puncto, vbi <lb/>Horizon B C, rectam R Q, ſecat, tran sferenda <lb/>erunt in rectam B D, ex D, puncto horizonta-<lb/>lis lineæ verſus B, in ſuperiori horologio: </s>
  <s xml:id="echoid-s23085" xml:space="preserve">In in-<lb/>
<anchor type="note" xlink:label="note-0362-03a" xlink:href="note-0362-03"/>
feriori autem transferẽda erunt interualla S T, <lb/>&amp; </s>
  <s xml:id="echoid-s23086" xml:space="preserve">alia, ſi qua fuerint, ex D, in eandem rectam <lb/>B D, ſed vltra D, productam. </s>
  <s xml:id="echoid-s23087" xml:space="preserve">Nam ſectiones <lb/>conicæ circa diametros L Q, M Q, N Q, &amp;</s>
  <s xml:id="echoid-s23088" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s23089" xml:space="preserve">ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s23090" xml:space="preserve">8. </s>
  <s xml:id="echoid-s23091" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23092" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23093" xml:space="preserve">deſcri-<lb/>ptæ, &amp; </s>
  <s xml:id="echoid-s23094" xml:space="preserve">translatæ in horologium, ita vt diame-<lb/>tri earum rectæ B D, congruant, tranſeantq́ue <lb/>per puncta translata L, M, N, O, P, S, &amp;</s>
  <s xml:id="echoid-s23095" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23096" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23097" xml:space="preserve"><lb/>cornua earum à linea horizontali auertantur, <lb/>dabunt parallelos Horizontis.</s>
  <s xml:id="echoid-s23098" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1172" type="float" level="2" n="1">
<note position="left" xlink:label="note-0362-01" xlink:href="note-0362-01a" xml:space="preserve">Defcriptio pa-<lb/>rallel orum Ho <lb/>rizontis in eo-<lb/>dem horologio <lb/>declinante ab <lb/>Horizonte.</note>
<note position="left" xlink:label="note-0362-02" xlink:href="note-0362-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0362-01" xlink:href="fig-0362-01a">
    <image file="0362-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0362-01"/>
  </figure>
<note position="left" xlink:label="note-0362-03" xlink:href="note-0362-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s23099" xml:space="preserve">IN poſteriori autem modo recta A D, ſu-<lb/>menda eſt æqualis rectæ A B, quæ ex vertice ſtyli A, in figura præcedentis propoſ. </s>
  <s xml:id="echoid-s23100" xml:space="preserve">in Zenith B, <lb/>cadit, &amp; </s>
  <s xml:id="echoid-s23101" xml:space="preserve">in rectam A B, transferenda ſunt interualla inter E, &amp; </s>
  <s xml:id="echoid-s23102" xml:space="preserve">lineas Verticales in linea hori-<lb/>zontali, &amp;</s>
  <s xml:id="echoid-s23103" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23104" xml:space="preserve">Pro linea autem meridiana, quæ dat Verticalem grad. </s>
  <s xml:id="echoid-s23105" xml:space="preserve">90. </s>
  <s xml:id="echoid-s23106" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23107" xml:space="preserve">horizontalem lineã <lb/>non ſecat, ducenda eſt D F, ipſi A B, parallela, &amp; </s>
  <s xml:id="echoid-s23108" xml:space="preserve">in alteram partem transferendæ lineæ, quæ ex <lb/>D, emiſ@æ rectam A B, ſecant, ſicut in lineis horarijs factum eſt in horizontali horologio. </s>
  <s xml:id="echoid-s23109" xml:space="preserve">Eſt <lb/>enim hic A D, tanquam axis; </s>
  <s xml:id="echoid-s23110" xml:space="preserve">A B, veluti radius Aequatoris, quanquam re uera radius ſit Horizon <lb/>tis; </s>
  <s xml:id="echoid-s23111" xml:space="preserve">rectæ ex A, ductæ ſunt inſtar radiorum ſignorum, &amp;</s>
  <s xml:id="echoid-s23112" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23113" xml:space="preserve">Demonſtratio huius operationis eadẽ <lb/>eſt, quæ in horizontali horologio, ſi recta A D, rectæ A B, axi Horizontis congruat, punctumq́ue <lb/>A, puncto A, &amp; </s>
  <s xml:id="echoid-s23114" xml:space="preserve">punctum D, puncto B, &amp; </s>
  <s xml:id="echoid-s23115" xml:space="preserve">circa illam figura A D F, in qua continentur radij paral <lb/>
<anchor type="note" xlink:label="note-0362-05a" xlink:href="note-0362-05"/>
lelorum Horizontis, circumuertatur, quemadmodum in horologio horizontali figuram radio-<lb/>rum circa axem mundi moueri intelligimus, &amp;</s>
  <s xml:id="echoid-s23116" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23117" xml:space="preserve">Nam in hac ita ſe habent lineæ Verticales, vt <lb/>ibilineæ horariæ, ita vt punctum B, reſpondeat centro horologij, in quod axis A B, cadit, &amp; </s>
  <s xml:id="echoid-s23118" xml:space="preserve">linea <lb/>horizontalis ſit veluti æquinoctialis linea, &amp;</s>
  <s xml:id="echoid-s23119" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23120" xml:space="preserve">Quapropter parallelos Horizontis in eodem horo <lb/>logio declinante ab Horizonte repoſnimus. </s>
  <s xml:id="echoid-s23121" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s23122" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1173" type="float" level="2" n="2">
<note position="left" xlink:label="note-0362-05" xlink:href="note-0362-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1175" type="section" level="1" n="281">
<head xml:id="echoid-head291" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s23123" xml:space="preserve">PER ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s23124" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23125" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23126" xml:space="preserve">ſcripſimus, non erit difficile iudicare, quinam paral <lb/>
<anchor type="note" xlink:label="note-0362-06a" xlink:href="note-0362-06"/>
<anchor type="note" xlink:label="note-0362-07a" xlink:href="note-0362-07"/>
leli Horizontis in plano horologĳ ſint hyperbolę, &amp; </s>
  <s xml:id="echoid-s23127" xml:space="preserve">qui parabolæ, aut Ellipſes. </s>
  <s xml:id="echoid-s23128" xml:space="preserve">Quando enim in figure, <lb/>in qua continentur radii parallelorum Horizontis, recta ex puncto D, egrediens, ſecans{q́ue} rectam A B, <lb/>in puncto, quod puncto A, eſt omnium propinquiſſimum, ſecat duos radios parallelorum oppoſitos ex A, <lb/>eductos, fient duæ hyperbolæ oppoſitæ, vt in exemplo nostro contingit in radĳs parallelorum grad. </s>
  <s xml:id="echoid-s23129" xml:space="preserve">15. <lb/></s>
  <s xml:id="echoid-s23130" xml:space="preserve">Si verò eadem recta ex puncto D, emiſſa æquidiſtet alicui radio ad ſiniſtram rectæ A B, poſito, erit pa-<lb/>rallelus radii oppoſiti Parabole. </s>
  <s xml:id="echoid-s23131" xml:space="preserve">Si denique recta eadem ex D, educta quempiam radiorum ad ſiniſtram <lb/>rectæ A B, neque ſecet, neque ei æquidiſtet, erit parallelus ex radio oppoſito deſcriptus, Ellipſis, vt ac-<lb/>cidit in propoſito exemplo in radiis parallelorum Horizontis grad. </s>
  <s xml:id="echoid-s23132" xml:space="preserve">30. </s>
  <s xml:id="echoid-s23133" xml:space="preserve">45. </s>
  <s xml:id="echoid-s23134" xml:space="preserve">60. </s>
  <s xml:id="echoid-s23135" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s23136" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23137" xml:space="preserve">Quæ omnia ibi-<lb/>dem demonſtrata ſunt.</s>
  <s xml:id="echoid-s23138" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1175" type="float" level="2" n="1">
<note position="left" xlink:label="note-0362-06" xlink:href="note-0362-06a" xml:space="preserve">Qui paralleli <lb/>Horizontis in <lb/>horologio ſint <lb/>Hyperbolæ, Pa <lb/>rabolæ, aut El-<lb/>lipſes.</note>
<note position="left" xlink:label="note-0362-07" xlink:href="note-0362-07a" xml:space="preserve">50</note>
</div>
<pb o="347" file="0363" n="363" rhead="LIBER TERTIVS."/>
</div>
<div xml:id="echoid-div1177" type="section" level="1" n="282">
<head xml:id="echoid-head292" xml:space="preserve">PROBLEMA 18. PROPOSITIO 18.</head>
<p>
  <s xml:id="echoid-s23139" xml:space="preserve">MERIDIANOS, ſiue circulos longitudinum ciuitatum, in co-<lb/>dem horologio declinante ab Horizonte collocare.</s>
  <s xml:id="echoid-s23140" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23141" xml:space="preserve">SVPPVTETVR in circulo ex L, deſcripto à puncto O, diamet<unsure/>ri O L M, verſus partes oc-<lb/>
<anchor type="note" xlink:label="note-0363-01a" xlink:href="note-0363-01"/>
cidentales longitudo loci vſque ad α. </s>
  <s xml:id="echoid-s23142" xml:space="preserve">Diuiſo deinde circulo in partes 360. </s>
  <s xml:id="echoid-s23143" xml:space="preserve">æquales, vel in pau-<lb/>
<anchor type="figure" xlink:label="fig-0363-01a" xlink:href="fig-0363-01"/>
<anchor type="note" xlink:label="note-0363-02a" xlink:href="note-0363-02"/>
<anchor type="note" xlink:label="note-0363-03a" xlink:href="note-0363-03"/>
<anchor type="note" xlink:label="note-0363-04a" xlink:href="note-0363-04"/>
ciores, ducantur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s23144" xml:space="preserve">per centrum L, lineæ occultæ ſecantes æquinoctialem <lb/>lineam in punctis, per quæ ex centro horologii C, emiſſæ rectæ dabunt communes ſectiones pla-<lb/>ni horologij, &amp; </s>
  <s xml:id="echoid-s23145" xml:space="preserve">Meridianorum, vt ex ſuperioribus conſtat. </s>
  <s xml:id="echoid-s23146" xml:space="preserve">Nam diameter circuli ex α, per cen-<lb/>trum L, ducta communis ſectio eſt Aequatoris, &amp; </s>
  <s xml:id="echoid-s23147" xml:space="preserve">Meridiani inſularum Fortunatarum, &amp;</s>
  <s xml:id="echoid-s23148" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23149" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1177" type="float" level="2" n="1">
<note position="right" xlink:label="note-0363-01" xlink:href="note-0363-01a" xml:space="preserve">Meridia nor@ <lb/>deſe<unsure/>riptio in <lb/>horologio eodẽ <lb/>declinante ab <lb/>Horizonte.</note>
  <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a">
    <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0363-01"/>
  </figure>
<note position="left" xlink:label="note-0363-02" xlink:href="note-0363-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0363-03" xlink:href="note-0363-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0363-04" xlink:href="note-0363-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s23150" xml:space="preserve">IN horologio inferiori, quod nobis exhibet portio abſciſſa à linea horizontali, ſi eius partes <lb/>inuertantur, vt ſupra docuimus, aſcribendi ſunt numeri ipſis Meridianis, ſicut in Verticali horo-<lb/>logio tradidimus propoſ. </s>
  <s xml:id="echoid-s23151" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23152" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23153" xml:space="preserve">addendo nimirum numeris eorundem Meridiano-<lb/>rum in ſuperiori horologio grad. </s>
  <s xml:id="echoid-s23154" xml:space="preserve">180. </s>
  <s xml:id="echoid-s23155" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s23156" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23157" xml:space="preserve">Meridianos ergo, ſiue circulos longitudinum in c<unsure/>o-<lb/>dem horologio, &amp;</s>
  <s xml:id="echoid-s23158" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23159" xml:space="preserve">collocauimus. </s>
  <s xml:id="echoid-s23160" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23161" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1179" type="section" level="1" n="283">
<head xml:id="echoid-head293" xml:space="preserve">PROBLEMA 19. PROPOSITIO 19.</head>
<p>
  <s xml:id="echoid-s23162" xml:space="preserve">PARALLELOS ciuitatum, ſeu circulos latitudinum in eodem <lb/>horologio declinante ab Horizonte diſponere.</s>
  <s xml:id="echoid-s23163" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s23164" xml:space="preserve">CVM hi paralleli æquidiſtent Aequatori, vt &amp; </s>
  <s xml:id="echoid-s23165" xml:space="preserve">paralleli ſignorum, non diſcrepabit eorum de-<lb/>
<anchor type="note" xlink:label="note-0363-07a" xlink:href="note-0363-07"/>
ſcriptio ab illorum deſcriptione, quam propoſ. </s>
  <s xml:id="echoid-s23166" xml:space="preserve">14. </s>
  <s xml:id="echoid-s23167" xml:space="preserve">huius libri tradidimus. </s>
  <s xml:id="echoid-s23168" xml:space="preserve">Quare parallelos ci-<lb/>uitatum, ſeu circulos latitudinum in eodem horologio declinante ab Horizonte diſpoſuimus. <lb/></s>
  <s xml:id="echoid-s23169" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s23170" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1179" type="float" level="2" n="1">
<note position="right" xlink:label="note-0363-07" xlink:href="note-0363-07a" xml:space="preserve">Deſcriptio pa-<lb/>ra llelorum lati <lb/>tudinum<unsure/> in eo <lb/>dem horologio <lb/>declinanteab <lb/>H@rizo@t@.</note>
</div>
</div>
<div xml:id="echoid-div1181" type="section" level="1" n="284">
<head xml:id="echoid-head294" xml:space="preserve">PROBLEMA 20. PROPOSITIO 20.</head>
<p>
  <s xml:id="echoid-s23171" xml:space="preserve">DOMOS cœleſtes in eodem horologio declinante ab Hori-<lb/>zonte ponere.</s>
  <s xml:id="echoid-s23172" xml:space="preserve"/>
</p>
<pb o="348" file="0364" n="364" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s23173" xml:space="preserve">CIRCVLVS ex L, deſcriptus propoſ. </s>
  <s xml:id="echoid-s23174" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23175" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s23176" xml:space="preserve">diuidatur in 12. </s>
  <s xml:id="echoid-s23177" xml:space="preserve">partes æquales, vel in <lb/>
<anchor type="note" xlink:label="note-0364-01a" xlink:href="note-0364-01"/>
plures, ſi domorum cęleſtium partes etiam deſiderentur, initio facto à recta L M, vt i<unsure/>n deſcriptio-<lb/>ne horarum à meridie, vel media nocte: </s>
  <s xml:id="echoid-s23178" xml:space="preserve">Et per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s23179" xml:space="preserve">centrum L, rectæ ducantu@ <lb/>
<anchor type="figure" xlink:label="fig-0364-01a" xlink:href="fig-0364-01"/>
<anchor type="note" xlink:label="note-0364-02a" xlink:href="note-0364-02"/>
<anchor type="note" xlink:label="note-0364-03a" xlink:href="note-0364-03"/>
ſecantes lineam æquinoctialem in punctis, per quæ ſi agantur rectæ ipſi meridianæ lineæ, vel hori <lb/>zontali parallelæ, deſcriptæ erunt domus cœleſtes ex ſententia Ioan. </s>
  <s xml:id="echoid-s23180" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s23181" xml:space="preserve">Cum enim Meri-<lb/>
<anchor type="note" xlink:label="note-0364-04a" xlink:href="note-0364-04"/>
dianus, &amp; </s>
  <s xml:id="echoid-s23182" xml:space="preserve">reliqui circuli domorum cœleſtium diuidant Aequatorem, ac proinde circulum quo-<lb/>que ex L, deſcriptum, in partes 12. </s>
  <s xml:id="echoid-s23183" xml:space="preserve">æquales; </s>
  <s xml:id="echoid-s23184" xml:space="preserve">ſit autem ex demonſtratis, recta L M, communis ſe-<lb/>ctio Meridiani, &amp; </s>
  <s xml:id="echoid-s23185" xml:space="preserve">Aequatoris; </s>
  <s xml:id="echoid-s23186" xml:space="preserve">erunt reliquæ lineæ occultæ per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s23187" xml:space="preserve">centrum L, <lb/>ductæ, communes ſectiones reliquorum circulorum cœleſtium domorum, &amp; </s>
  <s xml:id="echoid-s23188" xml:space="preserve">Aequatoris, ſi cir-<lb/>culus ex L, deſcriptus in propria poſitione concipiatur eſſe collocatus. </s>
  <s xml:id="echoid-s23189" xml:space="preserve">Quocirca circuli domorũ <lb/>cœleſtium ſecabunt planum horologij in punctis æquinoctialis lineæ, in quæ cadunt dictæ lineæ <lb/>occultæ; </s>
  <s xml:id="echoid-s23190" xml:space="preserve">ac proinde per eadem puncta communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s23191" xml:space="preserve">plani horo <lb/>logij ducendæ erunt. </s>
  <s xml:id="echoid-s23192" xml:space="preserve">Cum ergo hæ cõmunes ſectiones, per propoſ. </s>
  <s xml:id="echoid-s23193" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23194" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23195" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23196" xml:space="preserve">parallelæ ſint, quòd <lb/>planum horogii æquidiſtet communi ſectioni dictorum circulorum, hoc eſt, axi Verticalis cir-<lb/>culi; </s>
  <s xml:id="echoid-s23197" xml:space="preserve">conſtat rectas horizontali lineæ, vel meridianæ parallelas per inuenta puncta in linea æqui-<lb/>
<anchor type="note" xlink:label="note-0364-05a" xlink:href="note-0364-05"/>
noctiali ductas, eſſe domos cœleſtes ſecundum doctrinam Ioan. </s>
  <s xml:id="echoid-s23198" xml:space="preserve">Regiom.</s>
  <s xml:id="echoid-s23199" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1181" type="float" level="2" n="1">
<note position="left" xlink:label="note-0364-01" xlink:href="note-0364-01a" xml:space="preserve">Domoru<unsure/>m cœ <lb/>leſtium deſcri <lb/>ptio in eodem <lb/>horologio decli <lb/>nante ab Hori <lb/>zonte ſecundũ <lb/>Loan. Regiom.</note>
  <figure xlink:label="fig-0364-01" xlink:href="fig-0364-01a">
    <image file="0364-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0364-01"/>
  </figure>
<note position="left" xlink:label="note-0364-02" xlink:href="note-0364-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0364-03" xlink:href="note-0364-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0364-04" xlink:href="note-0364-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0364-05" xlink:href="note-0364-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s23200" xml:space="preserve">SED, vt vult Campanus, ita eaſdẽ domos delineabimus. </s>
  <s xml:id="echoid-s23201" xml:space="preserve">Ex K, loco ſtyli ducatur lineæ meri-<lb/>
<anchor type="note" xlink:label="note-0364-06a" xlink:href="note-0364-06"/>
dianæ æquidiſtans K A, &amp; </s>
  <s xml:id="echoid-s23202" xml:space="preserve">ſtylo æqualis. </s>
  <s xml:id="echoid-s23203" xml:space="preserve">Centro autem A, circulus deſcriptus ſecetur in 12. </s>
  <s xml:id="echoid-s23204" xml:space="preserve">partes <lb/>æquales, initio facto à ducta recta A D, vel A B; </s>
  <s xml:id="echoid-s23205" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23206" xml:space="preserve">per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s23207" xml:space="preserve">centrum A, ducan-<lb/>tur rectæ occultæ ſecantes lineam Verticalem D B, quam propoſ. </s>
  <s xml:id="echoid-s23208" xml:space="preserve">16. </s>
  <s xml:id="echoid-s23209" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s23210" xml:space="preserve">duximus, in pun-<lb/>ctis, per quæ ſi agantur rurſus parallelæ ipſi meridianæ lineæ, vel horizontali, habebimus domos <lb/>cœleſtes ſecundum Campanum. </s>
  <s xml:id="echoid-s23211" xml:space="preserve">Quoniam enim, vt ſupra oſtendimus propoſ. </s>
  <s xml:id="echoid-s23212" xml:space="preserve">16. </s>
  <s xml:id="echoid-s23213" xml:space="preserve">huius libri, re-<lb/>cta A D, communis ſectio eſt Verticalis, &amp; </s>
  <s xml:id="echoid-s23214" xml:space="preserve">Horizontis; </s>
  <s xml:id="echoid-s23215" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23216" xml:space="preserve">A B, Verticalis ac Meridiani, ſuntq́ue <lb/>Meridianus, &amp; </s>
  <s xml:id="echoid-s23217" xml:space="preserve">Horizon ex numero circulorum domorum cœleſtium, erunt reliquæ lineæ occul-<lb/>tæ per puncta diuiſionum circuli ex A, deſcripti, &amp; </s>
  <s xml:id="echoid-s23218" xml:space="preserve">per centrum A, ductæ, ſectiones communes <lb/>
<anchor type="note" xlink:label="note-0364-07a" xlink:href="note-0364-07"/>
Verticalis, &amp; </s>
  <s xml:id="echoid-s23219" xml:space="preserve">reliquorum circulorum domorum cœleſtium. </s>
  <s xml:id="echoid-s23220" xml:space="preserve">Igitur circuli cœleſtium domorum <lb/>plano horologii occurrent in punctis Verticalis lineæ DB, in quæ cadunt dictæ occultæ lineæ, ac <lb/>proinde per eadem puncta communes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s23221" xml:space="preserve">plani horologii tranſi-<lb/>bunt. </s>
  <s xml:id="echoid-s23222" xml:space="preserve">Cum ergo, vt proximè oſtendimus, parallelæ ſint hæ ſectiones communes, liquet parallelas <lb/>illas per puncta lineæ Verticalis ductas, eſſe domos cœleſtes, ex ſententia Campani. </s>
  <s xml:id="echoid-s23223" xml:space="preserve">Quapropter <lb/>domos cœleſtes in eodem horologio declinante ab Horizonte poſuimus. </s>
  <s xml:id="echoid-s23224" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s23225" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1182" type="float" level="2" n="2">
<note position="left" xlink:label="note-0364-06" xlink:href="note-0364-06a" xml:space="preserve">Deſcriptio eęle <lb/>ſtium domorũ <lb/>ſecundum Cã-<lb/>panum.</note>
<note position="left" xlink:label="note-0364-07" xlink:href="note-0364-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1184" type="section" level="1" n="285">
<head xml:id="echoid-head295" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s23226" xml:space="preserve">QVIA horologium noſtrũ declinare ponimus ab Horizonte grad. </s>
  <s xml:id="echoid-s23227" xml:space="preserve">30. </s>
  <s xml:id="echoid-s23228" xml:space="preserve">ſpectare{q́ue} ad occaſum, fit, vt <lb/>circulus maximus per polos Verticalis circuli tranſiens, per quos omnes circuli domorum cæleſtium du-
<pb o="349" file="0365" n="365" rhead="LIBER TERTIVS."/>
cuntur, &amp; </s>
  <s xml:id="echoid-s23229" xml:space="preserve">per ſtylum, ita vt rect{us} ſit ad planum horologii, ſit circul{us} domus nonæ cœleſtis, ſecundum <lb/>doctrinam Campani, recedens nimirum à Meridiano verſ{us} occaſum grad. </s>
  <s xml:id="echoid-s23230" xml:space="preserve">30. </s>
  <s xml:id="echoid-s23231" xml:space="preserve">quandoquidem circul{us} <lb/>maxim{us}, cui horologium parallelum eſt, &amp; </s>
  <s xml:id="echoid-s23232" xml:space="preserve">circulus maxim{us} ipſum ad angulos rectos ſecans, qua-<lb/>drantem ex Verticali circulo auferunt. </s>
  <s xml:id="echoid-s23233" xml:space="preserve">Quare linea domus nonæ ſecundum Campanum tranſibit per <lb/>locum ſtyli.</s>
  <s xml:id="echoid-s23234" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s23235" xml:space="preserve">IN horologio Inferiori dom{us} duodecima tam procul à linea horizontali excurrit, vt illam ægrè <lb/>recipere poſſit horologĳ planum, id circo duxim{us}, iuxta vtrumque modum, lineam parallelam, quæ in-<lb/>dicet grad. </s>
  <s xml:id="echoid-s23236" xml:space="preserve">15. </s>
  <s xml:id="echoid-s23237" xml:space="preserve">dom{us} duodecimæ, vt in figura apparet.</s>
  <s xml:id="echoid-s23238" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1185" type="section" level="1" n="286">
<head xml:id="echoid-head296" xml:space="preserve">PROBLEMA 21. PROPOSITIO 21.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s23239" xml:space="preserve">SIGNA Zodiaci aſcendentia in horologio eodem, quod ab Ho-<lb/>rizonte declinat, depingerc.</s>
  <s xml:id="echoid-s23240" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23241" xml:space="preserve">NON aliter hæc in horologio declinante ab Horizonte deſcribemus, atque in ſuperioribus, <lb/>
<anchor type="note" xlink:label="note-0365-02a" xlink:href="note-0365-02"/>
licet ea non omnia ex prioribus quatuor tabellis propoſ. </s>
  <s xml:id="echoid-s23242" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23243" xml:space="preserve">ſuperioris libri commodè delineari <lb/>queant; </s>
  <s xml:id="echoid-s23244" xml:space="preserve">propterea quòd vix omnes horæ à meridie, vel ante meridiem, quarum initium ſumitur <lb/>
<anchor type="figure" xlink:label="fig-0365-01a" xlink:href="fig-0365-01"/>
<anchor type="note" xlink:label="note-0365-03a" xlink:href="note-0365-03"/>
<anchor type="note" xlink:label="note-0365-04a" xlink:href="note-0365-04"/>
<anchor type="note" xlink:label="note-0365-05a" xlink:href="note-0365-05"/>
<anchor type="note" xlink:label="note-0365-06a" xlink:href="note-0365-06"/>
à diametro L M, circuli ex L, deſcripti, in lineam æquinoctialem cadunt. </s>
  <s xml:id="echoid-s23245" xml:space="preserve">Sed commodiſſimè in <lb/>linea meridiana inueniemus puncta aſcendentium ſignorum ex tabula ſexta eiuſdem propoſ. </s>
  <s xml:id="echoid-s23246" xml:space="preserve">be-<lb/>neficio mediationum cœli: </s>
  <s xml:id="echoid-s23247" xml:space="preserve">quæ puncta ſi coniungantur rectis lineis cum punctis lineæ horizon <lb/>talis, vbi à parallelis ſignorum ſecatur, vt in præcedentibus docuimus, deſcripta erunt ſigna aſcen <lb/>dentia. </s>
  <s xml:id="echoid-s23248" xml:space="preserve">Nam v. </s>
  <s xml:id="echoid-s23249" xml:space="preserve">g. </s>
  <s xml:id="echoid-s23250" xml:space="preserve">in Superiori horologio, quodad occaſum ſpectat, quale noſtrum eſt, cum Sol <lb/>exiſtens in principio ♋, occidit, vmbra ſtyli cadit in punctum lineæ horizontalis, per quod tropi <lb/>cus ♋, tranſit, oriturq́ue eodem tempore ſignum ♑, ſigno ♋, oppoſitum. </s>
  <s xml:id="echoid-s23251" xml:space="preserve">Igitur per illud pun-<lb/>ctum ducenda erit linea ♑. </s>
  <s xml:id="echoid-s23252" xml:space="preserve">Eodem modo, quando Sol exiſtens in principio ♊, vel ♌, occidit, <lb/>e<unsure/>adit vmbra ſtyli in punctum horizontalis lineæ, per quod parallelus ♊, &amp; </s>
  <s xml:id="echoid-s23253" xml:space="preserve">♌, ducitur, oriturq́ue
<pb o="350" file="0366" n="366" rhead="GNOMONICES"/>
eodem temporis momento ſignum oppoſitum, vt ſignum ♐, vel ♒. </s>
  <s xml:id="echoid-s23254" xml:space="preserve">Per illud ergo punctum du-<lb/>cendæ erunt lineę ♐, &amp; </s>
  <s xml:id="echoid-s23255" xml:space="preserve">♒, &amp; </s>
  <s xml:id="echoid-s23256" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s23257" xml:space="preserve">In horologio verò Superiori, quod ortũ reſpicit, cum <lb/>Sol in principio ♋, exiſtens oritur, proijcitur vmbra gnomonis in punctum lineæ horizontalis, <lb/>per quod tropicus ♋, incedit. </s>
  <s xml:id="echoid-s23258" xml:space="preserve">Igitur per illud punctum ducendum erit ſignum aſcendẽs ♋, &amp;</s>
  <s xml:id="echoid-s23259" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23260" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1185" type="float" level="2" n="1">
<note position="right" xlink:label="note-0365-02" xlink:href="note-0365-02a" xml:space="preserve">A ſcendentium <lb/>ſignorum in eo <lb/>dem hotologio <lb/>declinante ab <lb/>Horizonte do<unsure/>-<lb/>ſcriptio.</note>
  <figure xlink:label="fig-0365-01" xlink:href="fig-0365-01a">
    <image file="0365-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0365-01"/>
  </figure>
<note position="left" xlink:label="note-0365-03" xlink:href="note-0365-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0365-04" xlink:href="note-0365-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0365-05" xlink:href="note-0365-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0365-06" xlink:href="note-0365-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s23261" xml:space="preserve">CÆTERVM puncta in horizontali linea, per quæ arcus ſignorum ducendi ſunt, etiamſi <lb/>
<anchor type="note" xlink:label="note-0366-01a" xlink:href="note-0366-01"/>
ducti non ſint, inueniemus vel ex tabella quinta propoſ. </s>
  <s xml:id="echoid-s23262" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23263" xml:space="preserve">ſuperioris libri, vt in ſuperioribus tradi <lb/>tum eſt; </s>
  <s xml:id="echoid-s23264" xml:space="preserve">(ſi enim ducantur lineæ horariæ indicantes horas, quæ arcus ſemidiurnos terminant, ſe-<lb/>cabitur ab illis linea horizontalis in dictis punctis.) </s>
  <s xml:id="echoid-s23265" xml:space="preserve">Vel ex figura la<unsure/>titudinum ortiu<unsure/>arum, occi-<lb/>duarumve propoſ. </s>
  <s xml:id="echoid-s23266" xml:space="preserve">21. </s>
  <s xml:id="echoid-s23267" xml:space="preserve">ſuperioris libri, hac ratione. </s>
  <s xml:id="echoid-s23268" xml:space="preserve">Sit vt in dicta propoſ. </s>
  <s xml:id="echoid-s23269" xml:space="preserve">21. </s>
  <s xml:id="echoid-s23270" xml:space="preserve">Horizon A B C D, <lb/>cuius centrum E, vnà cum radijs latitudinum ortiuarum, &amp; </s>
  <s xml:id="echoid-s23271" xml:space="preserve">occiduarum. </s>
  <s xml:id="echoid-s23272" xml:space="preserve">Itaque rectæ A D, quæ <lb/>
<anchor type="note" xlink:label="note-0366-02a" xlink:href="note-0366-02"/>
in figura præcedẽtis propoſ. </s>
  <s xml:id="echoid-s23273" xml:space="preserve">continetur, abſcindemus rectam E F, æqualem, ex recta quidem E C, <lb/>producta, ſi horologium ſuperius occaſum reſpicit, ex E A, verò, ſi ad ortum ſpectat; </s>
  <s xml:id="echoid-s23274" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23275" xml:space="preserve">per F, ad <lb/>E F, perpendicularem ducemus. </s>
  <s xml:id="echoid-s23276" xml:space="preserve">Si enim puncta huius lineæ, vbi à radijs latitudinum ortiuarum <lb/>ſecatur, ex puncto F, accepta transſerantur in lineam horizontalem ex puncto D, habebu<unsure/>ntur pun <lb/>cta, per quæ paralleli ſignorum tranſeunt. </s>
  <s xml:id="echoid-s23277" xml:space="preserve">Nam ſi triangulum A B D, in figura præcedentis pro-<lb/>poſ. </s>
  <s xml:id="echoid-s23278" xml:space="preserve">intelligatur rectum ad planum horologij, erit A, centrum mundi, &amp; </s>
  <s xml:id="echoid-s23279" xml:space="preserve">A D, communis ſectio <lb/>Horizontis, ac Verticalis circuli, vt ex demonſtratis conſtat. </s>
  <s xml:id="echoid-s23280" xml:space="preserve">Si igitur Horizon A B C D, figuræ <lb/>latitudinum ortiuarum intelligatur poni in horologio, ita vt centrum eius E, centro A, congruat, <lb/>&amp; </s>
  <s xml:id="echoid-s23281" xml:space="preserve">recta E F, communis ſectio Verticalis &amp; </s>
  <s xml:id="echoid-s23282" xml:space="preserve">Horizontis, rectæ A D, cadet punctũ F, in D, ob æqua-<lb/>litatem rectarum E F, A D. </s>
  <s xml:id="echoid-s23283" xml:space="preserve">Quare perpendicularis per F, ducta congruet horizontali lineæ, cum <lb/>
<anchor type="note" xlink:label="note-0366-03a" xlink:href="note-0366-03"/>
hæc quoque perpendicularis ſitad A D, rectam in illo ſitu; </s>
  <s xml:id="echoid-s23284" xml:space="preserve">ac proinde radij latitudinum ortiua-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s23285" xml:space="preserve">occiduarum cadent in illa puncta, quæ diximus in horizontalem lineam eſſe transferenda <lb/>ex puncto D. </s>
  <s xml:id="echoid-s23286" xml:space="preserve">Quapropter ſigna Zodiaci aſcendentia in horologio eodem, quod ab Horizonte de <lb/>clinat, depinximus. </s>
  <s xml:id="echoid-s23287" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23288" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1186" type="float" level="2" n="2">
<note position="left" xlink:label="note-0366-01" xlink:href="note-0366-01a" xml:space="preserve">Inuentio pun-<lb/>ctorũ in linea <lb/>horizontali, per <lb/>quę arcus ſigno <lb/>t<unsure/>um, &amp; lineę ſi <lb/>gnorum aſcen-<lb/>dentium ducẽ-<lb/>dæ ſunt.</note>
<note position="left" xlink:label="note-0366-02" xlink:href="note-0366-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0366-03" xlink:href="note-0366-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1188" type="section" level="1" n="287">
<head xml:id="echoid-head297" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s23289" xml:space="preserve">EX Andreæ Schoneri doctrina hoc modo eadem ſigna aſcendentia depingem{us}. </s>
  <s xml:id="echoid-s23290" xml:space="preserve">In priori figura ſcho <lb/>
<anchor type="note" xlink:label="note-0366-04a" xlink:href="note-0366-04"/>
lĳ propoſ. </s>
  <s xml:id="echoid-s23291" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23292" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23293" xml:space="preserve">præcedentis, quam in ſcholio propoſ. </s>
  <s xml:id="echoid-s23294" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23295" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s23296" xml:space="preserve">repetiuimus, ex recta E C, vel E A, au-<lb/>feratur recta E M, æqualis interuallo L D, quod in horologio inter cipitur inter L, centrum, &amp; </s>
  <s xml:id="echoid-s23297" xml:space="preserve">punctum <lb/>
<anchor type="note" xlink:label="note-0366-05a" xlink:href="note-0366-05"/>
D, vbi conueniunt linea horizontalis, æquinoctialis, &amp; </s>
  <s xml:id="echoid-s23298" xml:space="preserve">horæ 6. </s>
  <s xml:id="echoid-s23299" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23300" xml:space="preserve">in M, ad rectam E M, conſtituatur <lb/>angulus E M N, æqualis angulo, quem recta L D, (ſi ducta eſſet) cu<unsure/>m æquinoctiali linea facit in horo-<lb/>logio, ea conditione, vt centro E, poſito in centro L, &amp; </s>
  <s xml:id="echoid-s23301" xml:space="preserve">puncto M, in puncto D, recta M N, lineæ æquino <lb/>ctiali congruat. </s>
  <s xml:id="echoid-s23302" xml:space="preserve">Poſt hæc interualla rectæ M N, inter M, &amp; </s>
  <s xml:id="echoid-s23303" xml:space="preserve">line{as} ſignorum interpoſitæ transferantur <lb/>in lineam æquinoctialem ex puncto D, eo ordine, quem haberent, ſi recta M N, ęquinoctiali lineę con-<lb/>grueret, imprimendo in linea æquinoctiali puncta. </s>
  <s xml:id="echoid-s23304" xml:space="preserve">Si enim per hæc puncta agantur parallelę occultæ ipſi <lb/>lineæ horizontali, vel meridianæ, ſecabuntur tropici in punctis, per quæ erunt aſcendentia ſigna ducenda, <lb/>hoc ordine ſeruato. </s>
  <s xml:id="echoid-s23305" xml:space="preserve">In horologio ad occaſum ſpectante, punctum, vbi linea horizontalis à tropico ♋, ſe-<lb/>
<anchor type="note" xlink:label="note-0366-06a" xlink:href="note-0366-06"/>
catur, pertinet ad ♑; </s>
  <s xml:id="echoid-s23306" xml:space="preserve">ſequens in eodem tropico infra lineam horizont alem, ad ♐, &amp; </s>
  <s xml:id="echoid-s23307" xml:space="preserve">ſequens ad ♏, &amp; </s>
  <s xml:id="echoid-s23308" xml:space="preserve"><lb/>ſic deinceps, contra ſignorum ſucceſſionem. </s>
  <s xml:id="echoid-s23309" xml:space="preserve">Puncta verò, quæ ab eiſdem parallelis in tropico ♑, mon-<lb/>
<anchor type="note" xlink:label="note-0366-07a" xlink:href="note-0366-07"/>
ſtrantur, ſpectant ad ſigna oppoſita. </s>
  <s xml:id="echoid-s23310" xml:space="preserve">In horologio autem, quod ortum reſpicit, punctum, quod commune eſt <lb/>tropico ♋, &amp; </s>
  <s xml:id="echoid-s23311" xml:space="preserve">lineę horizontali, tribuendum eſt ſigno ♋; </s>
  <s xml:id="echoid-s23312" xml:space="preserve">ſequens verſus lineam meridianam, ſigno ♌, <lb/>&amp; </s>
  <s xml:id="echoid-s23313" xml:space="preserve">ita deinceps ſecundum ſeriem ſignorum. </s>
  <s xml:id="echoid-s23314" xml:space="preserve">Puncta verò quæ in tropico ♑, ab eiſdem parallelis indicã-<lb/>tur, ad oppoſita ſigna pertinebunt.</s>
  <s xml:id="echoid-s23315" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1188" type="float" level="2" n="1">
<note position="left" xlink:label="note-0366-04" xlink:href="note-0366-04a" xml:space="preserve">Qua ratione <lb/>eadẽ<unsure/> ſigna aſc@ <lb/>dentia ſecun-<lb/>dum praxim <lb/>Andreæ Scho-<lb/>neri deſcriban-<lb/>tur in eodẽ ho-<lb/>rologio decſinã <lb/>te ab Horizon-<lb/>@e.</note>
<note position="left" xlink:label="note-0366-05" xlink:href="note-0366-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0366-06" xlink:href="note-0366-06a" xml:space="preserve">Ordo ſignor@ <lb/>aſcendentium <lb/>in tropicis.</note>
<note position="left" xlink:label="note-0366-07" xlink:href="note-0366-07a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s23316" xml:space="preserve">RVRSVS in figura postriori dicti ſcholii propoſ. </s>
  <s xml:id="echoid-s23317" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23318" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23319" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23320" xml:space="preserve">quam etiã in ſcholio propoſ. </s>
  <s xml:id="echoid-s23321" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23322" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s23323" xml:space="preserve">repetiuimus, ex recta E C, abſcindatur recta E M, æqualis eidem interuallo L D, quod in horologio in-<lb/>ter L, &amp; </s>
  <s xml:id="echoid-s23324" xml:space="preserve">D, ponitur; </s>
  <s xml:id="echoid-s23325" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23326" xml:space="preserve">in M, ad rectam E M, conſtituatur angul{us} E M N, æqualis angulo, quem <lb/>dicta recta L D, (ſi ducta eſſet) cum linea æquinoctiali facit in D; </s>
  <s xml:id="echoid-s23327" xml:space="preserve">ita vt centro E, poſito in centro L, <lb/>&amp; </s>
  <s xml:id="echoid-s23328" xml:space="preserve">puncto F, in puncto D, recta F G, congruat lineæ æquinoctiali. </s>
  <s xml:id="echoid-s23329" xml:space="preserve">Deinde interualla rectę M N, inter <lb/>M, &amp; </s>
  <s xml:id="echoid-s23330" xml:space="preserve">line{as} ſignorum interiecta in lineam æquinoctialem transferantur ex puncto D, eo ordine, quem <lb/>
<anchor type="note" xlink:label="note-0366-08a" xlink:href="note-0366-08"/>
haberent, ſi recta M N, congrueret lineæ æquinoctiali, imprimendo puncta in æquinoctiali linea. </s>
  <s xml:id="echoid-s23331" xml:space="preserve">Nam ſi <lb/>hæc puncta æquinoctialis lineæ rectis lineis cõnectantur cum punctis reſpondentibus tropicorum iam in-<lb/>uentis, deſc<unsure/>ripta erunt aſcendentia ſigna, vt pri{us}. </s>
  <s xml:id="echoid-s23332" xml:space="preserve">Signorum autem ordo in æquinoctiali linea hic eſt. <lb/></s>
  <s xml:id="echoid-s23333" xml:space="preserve">
<anchor type="note" xlink:label="note-0366-09a" xlink:href="note-0366-09"/>
Quando horologium ad ortum ſpectat, pertinebit primum punctum infra horizontalem lineam ad ♉, &amp; </s>
  <s xml:id="echoid-s23334" xml:space="preserve"><lb/>ſequens ad ♊, &amp; </s>
  <s xml:id="echoid-s23335" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s23336" xml:space="preserve">ſic conſequenter, vt in poſteriori figura dicta collocantur. </s>
  <s xml:id="echoid-s23337" xml:space="preserve">Proximum verò pun <lb/>ctum ſupra lineam horizontale@ conueniet ſigno ♓, &amp; </s>
  <s xml:id="echoid-s23338" xml:space="preserve">ſequens ſignis ♒, &amp; </s>
  <s xml:id="echoid-s23339" xml:space="preserve">♍, atque ita deinceps, <lb/>prout poſita ſunt ſigna in prædicta figura. </s>
  <s xml:id="echoid-s23340" xml:space="preserve">Si verò in occaſum ſpectet horologium, contrarius prorſus or-<lb/>do ſeruand{us} erit. </s>
  <s xml:id="echoid-s23341" xml:space="preserve">Nam primum punctum infra lineam horizontalem dandum erit ſigno ♓, &amp; </s>
  <s xml:id="echoid-s23342" xml:space="preserve">ſequens <lb/>ad ♒, &amp; </s>
  <s xml:id="echoid-s23343" xml:space="preserve">♍, pertinebit, &amp;</s>
  <s xml:id="echoid-s23344" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23345" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1189" type="float" level="2" n="2">
<note position="left" xlink:label="note-0366-08" xlink:href="note-0366-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0366-09" xlink:href="note-0366-09a" xml:space="preserve">Ordo ſignorũ<unsure/> <lb/>aſcendentium <lb/>in ęquinoctiali <lb/>linea.</note>
</div>
<p style="it">
  <s xml:id="echoid-s23346" xml:space="preserve">QVOD ſi ſigna aſcendentia vltra horizontalem lineam producantur, habebimus eadẽ ſigna in horo <lb/>logio inferiori, ſi partes illius portionis, quam linea horizontalis aufert, inuertantur, vt dictũ e<unsure/>ſt ſupra.</s>
  <s xml:id="echoid-s23347" xml:space="preserve"/>
</p>
<pb o="351" file="0367" n="367" rhead="LIBER TERTIVS."/>
</div>
<div xml:id="echoid-div1191" type="section" level="1" n="288">
<head xml:id="echoid-head298" xml:space="preserve">PROBLEMA 22. PROPOSITIO 22.</head>
<p>
  <s xml:id="echoid-s23348" xml:space="preserve">HOROLOGIVM Italicum declinans ab Horizonte com-<lb/>ponere.</s>
  <s xml:id="echoid-s23349" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23350" xml:space="preserve">SI circulus ex L, deſcriptus ſecetur in arcum diurnum paralleli ♋, a Nb, &amp; </s>
  <s xml:id="echoid-s23351" xml:space="preserve">arcum diurnum <lb/>
<anchor type="note" xlink:label="note-0367-01a" xlink:href="note-0367-01"/>
paralleli ♑, d N e, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s23352" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23353" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23354" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23355" xml:space="preserve">tradidimus, ita vt rectæ a b, d e, rectam L M, quæ <lb/>communis ſectio eſt Meridiani, &amp; </s>
  <s xml:id="echoid-s23356" xml:space="preserve">Aequatoris, ſecent ad angulos rectos, deſcribemus horas ab <lb/>
<anchor type="note" xlink:label="note-0367-02a" xlink:href="note-0367-02"/>
<anchor type="figure" xlink:label="fig-0367-01a" xlink:href="fig-0367-01"/>
<anchor type="note" xlink:label="note-0367-03a" xlink:href="note-0367-03"/>
<anchor type="note" xlink:label="note-0367-04a" xlink:href="note-0367-04"/>
<anchor type="note" xlink:label="note-0367-05a" xlink:href="note-0367-05"/>
occaſu in hoc horologio, quemadmodum in horologio declinante à Verticali propoſ. </s>
  <s xml:id="echoid-s23357" xml:space="preserve">10. </s>
  <s xml:id="echoid-s23358" xml:space="preserve">huius <lb/>libri factum eſt. </s>
  <s xml:id="echoid-s23359" xml:space="preserve">Exemplum habes in hora 21. </s>
  <s xml:id="echoid-s23360" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s23361" xml:space="preserve">Nam recta ex m, puncto horæ 21. </s>
  <s xml:id="echoid-s23362" xml:space="preserve">tro <lb/>pici ♑, ducta per L, ſecat æquinoctialem lineam in n; </s>
  <s xml:id="echoid-s23363" xml:space="preserve">recta autem ex C, per n, ducta ſecat tropicũ <lb/>♑, in p, puncto horæ 21. </s>
  <s xml:id="echoid-s23364" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s23365" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23366" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1191" type="float" level="2" n="1">
<note position="right" xlink:label="note-0367-01" xlink:href="note-0367-01a" xml:space="preserve">Conſt ructio ho <lb/>rologii Italici <lb/>ab Horizonte <lb/>declinantis.</note>
<note position="left" xlink:label="note-0367-02" xlink:href="note-0367-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0367-01" xlink:href="fig-0367-01a">
    <image file="0367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0367-01"/>
  </figure>
<note position="left" xlink:label="note-0367-03" xlink:href="note-0367-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0367-04" xlink:href="note-0367-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0367-05" xlink:href="note-0367-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s23367" xml:space="preserve">SIC etiam ex arcubus diurnis horarum 14. </s>
  <s xml:id="echoid-s23368" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23369" xml:space="preserve">10. </s>
  <s xml:id="echoid-s23370" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23371" xml:space="preserve">nocturnis horarum 10. </s>
  <s xml:id="echoid-s23372" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23373" xml:space="preserve">14. </s>
  <s xml:id="echoid-s23374" xml:space="preserve">eaſdem <lb/>
<anchor type="note" xlink:label="note-0367-06a" xlink:href="note-0367-06"/>
<anchor type="note" xlink:label="note-0367-07a" xlink:href="note-0367-07"/>
horas in hoc horologio, vt in præcedentibus, delineabimus, ſi tamen, cum hora aliqua ab occaſu <lb/>non habet punctũ in arcubus diurnis, accipiatur eiuſdem numeri hora ab ortu, &amp;</s>
  <s xml:id="echoid-s23375" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23376" xml:space="preserve">Exempli gra-<lb/>tia, quia hora 12. </s>
  <s xml:id="echoid-s23377" xml:space="preserve">ab occaſu in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s23378" xml:space="preserve">nullum habet punctum ex tabula tertia <lb/>propoſ. </s>
  <s xml:id="echoid-s23379" xml:space="preserve">33. </s>
  <s xml:id="echoid-s23380" xml:space="preserve">primi libri, accipiemus horam 12. </s>
  <s xml:id="echoid-s23381" xml:space="preserve">ab ortu, eamq́ue ſecundum tabulam tertiam dictæ <lb/>propoſ. </s>
  <s xml:id="echoid-s23382" xml:space="preserve">ducemus per horam 5. </s>
  <s xml:id="echoid-s23383" xml:space="preserve">à meridie in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s23384" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23385" xml:space="preserve">ſecundum tabulam ſex-<lb/>tam per horam 6. </s>
  <s xml:id="echoid-s23386" xml:space="preserve">à meridie in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s23387" xml:space="preserve">Hæc enim producta vltra lineam me-<lb/>ridianam, hoc eſt, vltra parallelum omnium ſemper apparentium maximum, qui horam 12. </s>
  <s xml:id="echoid-s23388" xml:space="preserve">ab <lb/>ortu, vel occaſu in linea meridiana tangit, dabit horam 12. </s>
  <s xml:id="echoid-s23389" xml:space="preserve">ab occaſu, vt ſupra oſtendimus. </s>
  <s xml:id="echoid-s23390" xml:space="preserve">Eodern <lb/>modo pro hora 13. </s>
  <s xml:id="echoid-s23391" xml:space="preserve">ab occaſu duximus horam 13. </s>
  <s xml:id="echoid-s23392" xml:space="preserve">ab ortu per horam 6. </s>
  <s xml:id="echoid-s23393" xml:space="preserve">à meridie in arcu diurno <lb/>horarum 14. </s>
  <s xml:id="echoid-s23394" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23395" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s23396" xml:space="preserve">à meridie in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s23397" xml:space="preserve">Ita etiam pro hora 14. </s>
  <s xml:id="echoid-s23398" xml:space="preserve">ab <lb/>@ccaſu, quæ v@icum punctum habet, nempe horam 9. </s>
  <s xml:id="echoid-s23399" xml:space="preserve">à media nocte, in arcu diurno horarum 14.</s>
  <s xml:id="echoid-s23400" xml:space="preserve">
<pb o="352" file="0368" n="368" rhead="GNOMONICES"/>
accepimus horam 14. </s>
  <s xml:id="echoid-s23401" xml:space="preserve">ab ortu, quę ducenda eſt per horam 7. </s>
  <s xml:id="echoid-s23402" xml:space="preserve">à meridie in arcu noct<unsure/>urno horarum <lb/>10. </s>
  <s xml:id="echoid-s23403" xml:space="preserve">atque ita per hæc puncta rectam duximus, cuius portio in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s23404" xml:space="preserve">ducta per <lb/>horam 9. </s>
  <s xml:id="echoid-s23405" xml:space="preserve">à media nocte horam 14. </s>
  <s xml:id="echoid-s23406" xml:space="preserve">ab occaſu, altera verò per horam 7. </s>
  <s xml:id="echoid-s23407" xml:space="preserve">à meridie ducta in arcu <lb/>nocturno horarum 10. </s>
  <s xml:id="echoid-s23408" xml:space="preserve">horam eandem 14. </s>
  <s xml:id="echoid-s23409" xml:space="preserve">ab ortu indicabit, &amp; </s>
  <s xml:id="echoid-s23410" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s23411" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1192" type="float" level="2" n="2">
<note position="left" xlink:label="note-0367-06" xlink:href="note-0367-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0367-07" xlink:href="note-0367-07a" xml:space="preserve">Deſcriptio e<unsure/>iuſ <lb/>dem horologi@ <lb/>Italici ab Hori <lb/>zon te declinan <lb/>tis per arcus <lb/>diurnos, n@-<lb/>cturnosq́ue.</note>
</div>
<note position="left" xml:space="preserve">Eiuſdem horo-<lb/>l<unsure/>ogii Italici de-<lb/>ſcriptio per<unsure/> ta-<lb/>bulas propoſ. <lb/>20. lib. 1.</note>
<p>
  <s xml:id="echoid-s23412" xml:space="preserve">DENIQVE horas eaſdem ab occaſu deſcribemus per mutuas earum ſectiones cum horis à <lb/>meridie, vel media nocte in linea horizontali, ſeu horæ 24. </s>
  <s xml:id="echoid-s23413" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23414" xml:space="preserve">horæ 12. </s>
  <s xml:id="echoid-s23415" xml:space="preserve">ab ortu, vel occaſu, &amp;</s>
  <s xml:id="echoid-s23416" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23417" xml:space="preserve">vt <lb/>in tabulis propoſ. </s>
  <s xml:id="echoid-s23418" xml:space="preserve">20. </s>
  <s xml:id="echoid-s23419" xml:space="preserve">primi libri apparet. </s>
  <s xml:id="echoid-s23420" xml:space="preserve">Linea autem horæ 12. </s>
  <s xml:id="echoid-s23421" xml:space="preserve">ab ortu, vel occaſu ducenda eſt <lb/>per horam 6. </s>
  <s xml:id="echoid-s23422" xml:space="preserve">à meridie, vel media nocte in æquinoctiali linea, &amp; </s>
  <s xml:id="echoid-s23423" xml:space="preserve">per punctum A, lineæ meridia-<lb/>næ, ſeu horæ 12. </s>
  <s xml:id="echoid-s23424" xml:space="preserve">à media nocte, per quod arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s23425" xml:space="preserve">ducitur, vt conſtat ex tabula <lb/>ſeptima, &amp; </s>
  <s xml:id="echoid-s23426" xml:space="preserve">tabulis 5. </s>
  <s xml:id="echoid-s23427" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23428" xml:space="preserve">6. </s>
  <s xml:id="echoid-s23429" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s23430" xml:space="preserve">33. </s>
  <s xml:id="echoid-s23431" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s23432" xml:space="preserve">Itaque horologium Italicum declinans ab Ho-<lb/>
<anchor type="note" xlink:label="note-0368-02a" xlink:href="note-0368-02"/>
rizonte compoſuimus. </s>
  <s xml:id="echoid-s23433" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23434" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1193" type="float" level="2" n="3">
<note position="left" xlink:label="note-0368-02" xlink:href="note-0368-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1195" type="section" level="1" n="289">
<head xml:id="echoid-head299" xml:space="preserve">PROBLEMA 23. PROPOSITIO 23.</head>
<p>
  <s xml:id="echoid-s23435" xml:space="preserve">HOROLOGIVM Babylonicum ab Horizonte declinans <lb/>conſtituere.</s>
  <s xml:id="echoid-s23436" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23437" xml:space="preserve">IISDEM omnino vijs Babylonicum horologium, quibus Italicum, conſtruemus. </s>
  <s xml:id="echoid-s23438" xml:space="preserve">Id quod <lb/>
<anchor type="note" xlink:label="note-0368-03a" xlink:href="note-0368-03"/>
apertè figura præcedentis propoſ.</s>
  <s xml:id="echoid-s23439" xml:space="preserve"><unsure/> declarat, in qua continentur &amp; </s>
  <s xml:id="echoid-s23440" xml:space="preserve">horæ à meridie, vel media nocte, <lb/>
<anchor type="note" xlink:label="note-0368-04a" xlink:href="note-0368-04"/>
&amp; </s>
  <s xml:id="echoid-s23441" xml:space="preserve">horæ tam ab occaſu, quàm ab ortu, vt in ſuperioribus etiam horologiis.</s>
  <s xml:id="echoid-s23442" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1195" type="float" level="2" n="1">
<note position="left" xlink:label="note-0368-03" xlink:href="note-0368-03a" xml:space="preserve">Babylonici ho <lb/>rologii ab Ho-<lb/>rizonte decli-<lb/>nantis compoſi <lb/>tio.</note>
<note position="left" xlink:label="note-0368-04" xlink:href="note-0368-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s23443" xml:space="preserve">CAETERVM in horologio Inferiori, vbi omnia mutantur, ducta eſt hora 1. </s>
  <s xml:id="echoid-s23444" xml:space="preserve">ab ortu per <lb/>horam 6. </s>
  <s xml:id="echoid-s23445" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s23446" xml:space="preserve">in quem mutatur arcus diurnus horarũ 10. <lb/></s>
  <s xml:id="echoid-s23447" xml:space="preserve">ſuperioris horologij, &amp; </s>
  <s xml:id="echoid-s23448" xml:space="preserve">per horam 8. </s>
  <s xml:id="echoid-s23449" xml:space="preserve">à media nocte in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s23450" xml:space="preserve">in quem conuer <lb/>titur arcus diurnus horarum 14. </s>
  <s xml:id="echoid-s23451" xml:space="preserve">horologij ſuperioris, conſtat autem ex ſcholio propoſ. </s>
  <s xml:id="echoid-s23452" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23453" xml:space="preserve">ſupe-<lb/>rioris libri, in horologio inferiori horas à media nocte eſſe numerandas, quæ in ſuperiori ſuppu-<lb/>tantur à meridie, &amp; </s>
  <s xml:id="echoid-s23454" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s23455" xml:space="preserve">Vel certè pro hora 1. </s>
  <s xml:id="echoid-s23456" xml:space="preserve">ab ortu ducemus horam 1. </s>
  <s xml:id="echoid-s23457" xml:space="preserve">ab occaſu per horã <lb/>8. </s>
  <s xml:id="echoid-s23458" xml:space="preserve">à meridie in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s23459" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23460" xml:space="preserve">per horam 6.</s>
  <s xml:id="echoid-s23461" xml:space="preserve"><unsure/> à meridie in arcu nocturno horarum <lb/>14. </s>
  <s xml:id="echoid-s23462" xml:space="preserve">prout tabulæ propoſ. </s>
  <s xml:id="echoid-s23463" xml:space="preserve">33. </s>
  <s xml:id="echoid-s23464" xml:space="preserve">primi libri indicant. </s>
  <s xml:id="echoid-s23465" xml:space="preserve">Hæc enim in inferiori horologio erit hora 1. </s>
  <s xml:id="echoid-s23466" xml:space="preserve"><lb/>ab ortu, vt in ſcholio propoſ, 23. </s>
  <s xml:id="echoid-s23467" xml:space="preserve">ſuperioris libri docuimus. </s>
  <s xml:id="echoid-s23468" xml:space="preserve">Horologium igitur Babylonicum ab <lb/>
<anchor type="note" xlink:label="note-0368-05a" xlink:href="note-0368-05"/>
Horizonte declinans conſtituimus. </s>
  <s xml:id="echoid-s23469" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s23470" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1196" type="float" level="2" n="2">
<note position="left" xlink:label="note-0368-05" xlink:href="note-0368-05a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1198" type="section" level="1" n="290">
<head xml:id="echoid-head300" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s23471" xml:space="preserve">HORAE ab ortu, vel occaſu ſuperioris horologii productæ vltra lineam horizontalem dant quo-<lb/>que hic in facie oppoſita, &amp; </s>
  <s xml:id="echoid-s23472" xml:space="preserve">inferiori eaſdem hor{as}, vt in præcedentibus dictum eſt.</s>
  <s xml:id="echoid-s23473" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s23474" xml:space="preserve">PARI ratione, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s23475" xml:space="preserve">11. </s>
  <s xml:id="echoid-s23476" xml:space="preserve">huius libri, ita &amp; </s>
  <s xml:id="echoid-s23477" xml:space="preserve">hic vno, eodem{q́ue} labore quatuor diuer-<lb/>ſa horologia Italica, &amp; </s>
  <s xml:id="echoid-s23478" xml:space="preserve">Babylonica c<unsure/>onſtituemus: </s>
  <s xml:id="echoid-s23479" xml:space="preserve">quemadmodum in ſcholio propoſ. </s>
  <s xml:id="echoid-s23480" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23481" xml:space="preserve">hui{us} lib. </s>
  <s xml:id="echoid-s23482" xml:space="preserve">de ho-<lb/>rologio Aſtronomico monuimus. </s>
  <s xml:id="echoid-s23483" xml:space="preserve">Id quod difficile non erit, ſi obſeruemus ea, quę in ſcholio propoſ. </s>
  <s xml:id="echoid-s23484" xml:space="preserve">11. </s>
  <s xml:id="echoid-s23485" xml:space="preserve">hu-<lb/>ius libri tradidim{us} de mut atione horarum ab ortu, vel occaſu in earum complementa vſque ad 24. </s>
  <s xml:id="echoid-s23486" xml:space="preserve">ad-<lb/>
<anchor type="note" xlink:label="note-0368-06a" xlink:href="note-0368-06"/>
ditis etiam iis, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s23487" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23488" xml:space="preserve">eiuſdem libri ſcripſimus.</s>
  <s xml:id="echoid-s23489" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1198" type="float" level="2" n="1">
<note position="left" xlink:label="note-0368-06" xlink:href="note-0368-06a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1200" type="section" level="1" n="291">
<head xml:id="echoid-head301" xml:space="preserve">PROBLEMA 24. PROPOSITIO 24.</head>
<p>
  <s xml:id="echoid-s23490" xml:space="preserve">HOROLOGIVM Antiquum ab Horizonte declinans <lb/>conſtruere.</s>
  <s xml:id="echoid-s23491" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23492" xml:space="preserve">CONSTRVEMVS hoc horologium, vt declinans à Verticali propoſ. </s>
  <s xml:id="echoid-s23493" xml:space="preserve">12. </s>
  <s xml:id="echoid-s23494" xml:space="preserve">huius libri. <lb/></s>
  <s xml:id="echoid-s23495" xml:space="preserve">
<anchor type="note" xlink:label="note-0368-07a" xlink:href="note-0368-07"/>
Nam exempli gratia, quod ad priorem rationem attinet, ex f, puncto horæ 4. </s>
  <s xml:id="echoid-s23496" xml:space="preserve">inæqualis tropici ♋, <lb/>
<anchor type="note" xlink:label="note-0368-08a" xlink:href="note-0368-08"/>
per L, ducta recta ſecta lineam æquinoctialem in g; </s>
  <s xml:id="echoid-s23497" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23498" xml:space="preserve">recta C g, tropicum ♋, ſecat in h, puncto <lb/>horæ 4. </s>
  <s xml:id="echoid-s23499" xml:space="preserve">inæqualis, &amp; </s>
  <s xml:id="echoid-s23500" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s23501" xml:space="preserve">Pro hora autem 1. </s>
  <s xml:id="echoid-s23502" xml:space="preserve">in horologio inferiori duximus ex m, pun-<lb/>cto horæ 1. </s>
  <s xml:id="echoid-s23503" xml:space="preserve">nocturnæ tropici ♑, per L, rectam, quæ ſecat æquinoctialem lineam in n. </s>
  <s xml:id="echoid-s23504" xml:space="preserve">Recta nam-<lb/>que C n, ſecat tropicum ♑, in p, puncto horæ 1. </s>
  <s xml:id="echoid-s23505" xml:space="preserve">inæqualis nocturnæ. </s>
  <s xml:id="echoid-s23506" xml:space="preserve">Recta igitur ex p, per horã <lb/>7. </s>
  <s xml:id="echoid-s23507" xml:space="preserve">à meridie in linea æquinoctiali ducta dabit horam 1. </s>
  <s xml:id="echoid-s23508" xml:space="preserve">nocturnam inæqualem in portione horo <lb/>logii nocturna: </s>
  <s xml:id="echoid-s23509" xml:space="preserve">hæc autem in horologio inferiori erit hora 1. </s>
  <s xml:id="echoid-s23510" xml:space="preserve">inæqualis diurna, &amp;</s>
  <s xml:id="echoid-s23511" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23512" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1200" type="float" level="2" n="1">
<note position="left" xlink:label="note-0368-07" xlink:href="note-0368-07a" xml:space="preserve">Conſtructio ho <lb/>rologiii Anti-<lb/>qui ab Horizõ-<lb/>te<unsure/> declinantis.</note>
<note position="left" xlink:label="note-0368-08" xlink:href="note-0368-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s23513" xml:space="preserve">QVOD attinet ad rationem poſteriorem, notauimus in horis à media nocte 9. </s>
  <s xml:id="echoid-s23514" xml:space="preserve">10 {1/2}. </s>
  <s xml:id="echoid-s23515" xml:space="preserve">12. </s>
  <s xml:id="echoid-s23516" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23517" xml:space="preserve"><lb/>in horis à meridie 1 {1/2}. </s>
  <s xml:id="echoid-s23518" xml:space="preserve">3. </s>
  <s xml:id="echoid-s23519" xml:space="preserve">4 {1/2}. </s>
  <s xml:id="echoid-s23520" xml:space="preserve">6. </s>
  <s xml:id="echoid-s23521" xml:space="preserve">7 {1/2}. </s>
  <s xml:id="echoid-s23522" xml:space="preserve">9. </s>
  <s xml:id="echoid-s23523" xml:space="preserve">puncta arcus diurni horarum 18. </s>
  <s xml:id="echoid-s23524" xml:space="preserve">per quæ ducenda ſunt <lb/>horæ inæquales, vt ex tabula 11. </s>
  <s xml:id="echoid-s23525" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s23526" xml:space="preserve">33. </s>
  <s xml:id="echoid-s23527" xml:space="preserve">primi libri colligitur. </s>
  <s xml:id="echoid-s23528" xml:space="preserve">He<unsure/>rologium ergo Antiquum <lb/>ab Horizonte declinans conſtruximus. </s>
  <s xml:id="echoid-s23529" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23530" xml:space="preserve"/>
</p>
<pb o="353" file="0369" n="369" rhead="LIBER TERTIVS."/>
  <figure>
    <image file="0369-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0369-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1202" type="section" level="1" n="292">
<head xml:id="echoid-head302" xml:space="preserve">DE HOROLOGIIS <lb/>ad Horizontem inclinatis.</head>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1203" type="section" level="1" n="293">
<head xml:id="echoid-head303" xml:space="preserve">PROBLEMA 25. PROPOSITIO 25.</head>
<p>
  <s xml:id="echoid-s23531" xml:space="preserve">HOROLOGIVM Aſtronomicum, quod inclinatum eſt ad <lb/>Horizontem; </s>
  <s xml:id="echoid-s23532" xml:space="preserve">id eſt, lineas horarum à meridie, vel media nocte in pla-<lb/>no, quod circulo cuipiam maximo ad Horizontem inclinato, &amp; </s>
  <s xml:id="echoid-s23533" xml:space="preserve">ad Me-<lb/>ridianum recto ęquidiſtat, deſcribere.</s>
  <s xml:id="echoid-s23534" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horologii A-<lb/>ſtronomici ad <lb/>Horizontẽ in-<lb/>clinati deſcri-<lb/>ptio ſex præc@-<lb/>ptis con tenta.</note>
<p>
  <s xml:id="echoid-s23535" xml:space="preserve">QVONIAM ſex modis ſe habere poteſt planum, quod ad Horizontem eſt inclinatum, &amp; </s>
  <s xml:id="echoid-s23536" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0369-06a" xlink:href="note-0369-06"/>
rectum ad Meridianum, vt mox explicabimus, vniuerſam doctrinam de horologiis in huiuſmodi <lb/>plano deſcribendis ſex etiam præceptis complectemur, vt facilius res ipſa percipiatur.</s>
  <s xml:id="echoid-s23537" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1203" type="float" level="2" n="1">
<note position="left" xlink:label="note-0369-06" xlink:href="note-0369-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1205" type="section" level="1" n="294">
<head xml:id="echoid-head304" xml:space="preserve">PRÆCEPTVM I.</head>
<p>
  <s xml:id="echoid-s23538" xml:space="preserve">QVANDO planum ex parte Septentrionis inclinatum, cuius ſcilicet ſuperior facies meri-<lb/>
<anchor type="note" xlink:label="note-0369-07a" xlink:href="note-0369-07"/>
diem reſpicit, inclinationem habet altitudini poli æqualem, non differet eius horologium à Pola-<lb/>ri horologio, quod propoſ. </s>
  <s xml:id="echoid-s23539" xml:space="preserve">37. </s>
  <s xml:id="echoid-s23540" xml:space="preserve">ſuperioris libri deſcripſimus.</s>
  <s xml:id="echoid-s23541" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1205" type="float" level="2" n="1">
<note position="right" xlink:label="note-0369-07" xlink:href="note-0369-07a" xml:space="preserve">Quando plani <lb/>inclinatio ex <lb/>parte Septen-<lb/>trionis altitudi <lb/>ni poli eſt ęqua <lb/>lis.</note>
</div>
</div>
<div xml:id="echoid-div1207" type="section" level="1" n="295">
<head xml:id="echoid-head305" xml:space="preserve">PRAECEPTVM II.</head>
<p>
  <s xml:id="echoid-s23542" xml:space="preserve">CVM verò idem planum inclinationem habuerit altitudine poli minorem, detrahenda erit <lb/>
<anchor type="note" xlink:label="note-0369-08a" xlink:href="note-0369-08"/>
inclinatio ab altitudine poli: </s>
  <s xml:id="echoid-s23543" xml:space="preserve">relinquetur enim altitudo poli ſupra planum inclinatum: </s>
  <s xml:id="echoid-s23544" xml:space="preserve">De<unsure/>inde <lb/>ad hanc poli altitudinem inuentam horologium horizontale deſcribendum, vt tradidimus pro-<lb/>poſ. </s>
  <s xml:id="echoid-s23545" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23546" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23547" xml:space="preserve">Quod ita collocandũ erit, vt linea æquinoctialis æquidiſtet lineæ rectæ, quæ
<pb o="354" file="0370" n="370" rhead="GNOMONICES"/>
in plano, quod Horizonti æquidiſtat, lineam meridianã ad angulos rectos ſecat; </s>
  <s xml:id="echoid-s23548" xml:space="preserve">(quod facile fiet, <lb/>ſi recta quæpiam linea meridianam lineam horologii ad angulos rectos ſecans ſtatuatur in plano, <lb/>quod Horizonti parallelum eſt, perpendicularis ad lineam meridianam in eo plano inuentam) &amp; </s>
  <s xml:id="echoid-s23549" xml:space="preserve"><lb/>ipſum horologium eleuetur ex parte boreali ſecundum inclinationem plani, ita vt eius linea me-<lb/>ridiana cum meridiana linea Horizontis ad partes Septentrionis contineat angulum inclinatio-<lb/>nis: </s>
  <s xml:id="echoid-s23550" xml:space="preserve">hac tamen lege, vt in ſuperiori facie plani, quę ad Zenith, &amp; </s>
  <s xml:id="echoid-s23551" xml:space="preserve">meridiem conuertitur, centrũ <lb/>horologij infra lineam æquinoctialem exiſtat: </s>
  <s xml:id="echoid-s23552" xml:space="preserve">in oppoſita autem facie &amp; </s>
  <s xml:id="echoid-s23553" xml:space="preserve">inferiori, ſupra eandem. <lb/></s>
  <s xml:id="echoid-s23554" xml:space="preserve">Ordo horarum hic erit. </s>
  <s xml:id="echoid-s23555" xml:space="preserve">In ſuperiori horologio horæ poſt mediam noctem ſunt nobis ad horolo <lb/>gium conuerſis ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s23556" xml:space="preserve">pomeridianæ ad dextram; </s>
  <s xml:id="echoid-s23557" xml:space="preserve">portioq́; </s>
  <s xml:id="echoid-s23558" xml:space="preserve">lineæ meridianæ à centro ho-<lb/>rologii verſus æquinoctialem lineam excurrens indicat horam 12. </s>
  <s xml:id="echoid-s23559" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s23560" xml:space="preserve">reliqua portio ab <lb/>
<anchor type="note" xlink:label="note-0370-01a" xlink:href="note-0370-01"/>
eodem centro inchoata, ad horam 12. </s>
  <s xml:id="echoid-s23561" xml:space="preserve">mediæ noctis pertinet. </s>
  <s xml:id="echoid-s23562" xml:space="preserve">In horologio autem inferiori con-<lb/>trario modo ſe res habet. </s>
  <s xml:id="echoid-s23563" xml:space="preserve">Nam in eo horæ poſt mediam noctem ſunt nobis conuerſis ad horolo-<lb/>gium ad dextram, &amp; </s>
  <s xml:id="echoid-s23564" xml:space="preserve">pomeridianæ ad ſiniſtram; </s>
  <s xml:id="echoid-s23565" xml:space="preserve">atque portio lineæ meridianæ à centro verſus li-<lb/>neam æquinoctialem monſtrat horam 12. </s>
  <s xml:id="echoid-s23566" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s23567" xml:space="preserve">reliqua portio à centro etiam inchoa-<lb/>ta horam 12. </s>
  <s xml:id="echoid-s23568" xml:space="preserve">meridiei.</s>
  <s xml:id="echoid-s23569" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1207" type="float" level="2" n="1">
<note position="right" xlink:label="note-0369-08" xlink:href="note-0369-08a" xml:space="preserve">Quando incli-<lb/>natio plani ex <lb/>parte Septen-<lb/>trionis altitudi <lb/>ne poli minor <lb/>eſt.</note>
<note position="left" xlink:label="note-0370-01" xlink:href="note-0370-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1209" type="section" level="1" n="296">
<head xml:id="echoid-head306" xml:space="preserve">PRAECEPTVM III.</head>
<p>
  <s xml:id="echoid-s23570" xml:space="preserve">CVM denique idem planum habuerit inclinationem maiorem poli altitudine, auferenda <lb/>
<anchor type="note" xlink:label="note-0370-02a" xlink:href="note-0370-02"/>
erit altitudo poli ab inclinatione: </s>
  <s xml:id="echoid-s23571" xml:space="preserve">remanebit enim altitudo poli ſupra planum inclinatum. </s>
  <s xml:id="echoid-s23572" xml:space="preserve">Poſtea <lb/>ad hanc poli eleuationem horologium horizontale, ex doctrina propoſ. </s>
  <s xml:id="echoid-s23573" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23574" xml:space="preserve">ſuperioris libri, fabri-<lb/>candum. </s>
  <s xml:id="echoid-s23575" xml:space="preserve">Quod collocandũ erit non aliter atque illud, de quo in antecedenti præcepto egimus, <lb/>
<anchor type="note" xlink:label="note-0370-03a" xlink:href="note-0370-03"/>
hoc dempto; </s>
  <s xml:id="echoid-s23576" xml:space="preserve">quòd hic in ſuperiori horologio centrum horologii ſtatuendum eſt ſupra lineam <lb/>æquinoctialem, infra verò eandem in inferiori. </s>
  <s xml:id="echoid-s23577" xml:space="preserve">ordo quoque horarum idem hic eſt omnino, qui <lb/>in præcedenti præcepto declaratus eſt.</s>
  <s xml:id="echoid-s23578" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1209" type="float" level="2" n="1">
<note position="left" xlink:label="note-0370-02" xlink:href="note-0370-02a" xml:space="preserve">Quando incli-<lb/>natio plani ex <lb/>parte Septẽtrio <lb/>@is altitudine <lb/>poli maior eſt.</note>
<note position="left" xlink:label="note-0370-03" xlink:href="note-0370-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1211" type="section" level="1" n="297">
<head xml:id="echoid-head307" xml:space="preserve">PRAECEPTVM IIII.</head>
<p>
  <s xml:id="echoid-s23579" xml:space="preserve">RVRSVS, quando planum ex parte auſtrali inclinatum, cuius nimirum ſuperior facies bo-<lb/>
<anchor type="note" xlink:label="note-0370-04a" xlink:href="note-0370-04"/>
ream reſpicit, inclinationem æqualem habet cõplemento altitudinis poli, idem prorſus erit eius <lb/>horologium, quod æquinoctiale propoſ. </s>
  <s xml:id="echoid-s23580" xml:space="preserve">49. </s>
  <s xml:id="echoid-s23581" xml:space="preserve">præcedentis libri conſtructum.</s>
  <s xml:id="echoid-s23582" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1211" type="float" level="2" n="1">
<note position="left" xlink:label="note-0370-04" xlink:href="note-0370-04a" xml:space="preserve">Quando incli-<lb/>natio plani ex <lb/>parte auſtrali <lb/>complemento <lb/>alt@udinis po-<lb/>li æqualis eſt.</note>
</div>
</div>
<div xml:id="echoid-div1213" type="section" level="1" n="298">
<head xml:id="echoid-head308" xml:space="preserve">PRAECEPTVM V.</head>
<p>
  <s xml:id="echoid-s23583" xml:space="preserve">CVM autem idem planum inclinationem minorem habuerit complemento altitudinis poli, <lb/>
<anchor type="note" xlink:label="note-0370-05a" xlink:href="note-0370-05"/>
addenda erit inclinatio altitudini poli. </s>
  <s xml:id="echoid-s23584" xml:space="preserve">Ita enim conflabitur altitudo poli ſupra planum inclina-<lb/>
<anchor type="note" xlink:label="note-0370-06a" xlink:href="note-0370-06"/>
rum. </s>
  <s xml:id="echoid-s23585" xml:space="preserve">Ad hanc deinde poli altitudinem, per ea, quæ propoſ. </s>
  <s xml:id="echoid-s23586" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23587" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s23588" xml:space="preserve">tradita ſunt, horologium <lb/>horizontale conſtruendum. </s>
  <s xml:id="echoid-s23589" xml:space="preserve">Quod collocandum eſt, vt in ſecundo præcepto præſcripſimus, niſi <lb/>quòd hoc horologium eleuandum eſt ex parte auſtrali ſecundum inclinationem plani, ita vt eius <lb/>meridiana linea cum linea meridiana Horizontis conſtituat angulum inclinationis ad partes au-<lb/>ſtrales; </s>
  <s xml:id="echoid-s23590" xml:space="preserve">hac etiam conditione adiecta, vt in ſuperiori horologio cẽtrum horologij ſedem habeat <lb/>ſupra lineam æquinoctialem, infra verò eandem in inferiori. </s>
  <s xml:id="echoid-s23591" xml:space="preserve">Ordo horarum idem hic erit in ſu-<lb/>periori horologio, qui in inferiori ſecundi præcepti: </s>
  <s xml:id="echoid-s23592" xml:space="preserve">In inferiori autẽ idem, qui in ſuperiori eiuſ-<lb/>dem præcepti: </s>
  <s xml:id="echoid-s23593" xml:space="preserve">Veruntamen in ſuperiori portio meridianæ lineæ à centro verſus æquinoctialem <lb/>lineam extenſa horam 12. </s>
  <s xml:id="echoid-s23594" xml:space="preserve">meridiei, in inferiori vertò 12. </s>
  <s xml:id="echoid-s23595" xml:space="preserve">mediæ noctis ſignificat.</s>
  <s xml:id="echoid-s23596" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1213" type="float" level="2" n="1">
<note position="left" xlink:label="note-0370-05" xlink:href="note-0370-05a" xml:space="preserve">Quando incli-<lb/>natio plani ex <lb/>parte auſtrali <lb/>complemento <lb/>altitudinis poli <lb/>minor eſt.</note>
<note position="left" xlink:label="note-0370-06" xlink:href="note-0370-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1215" type="section" level="1" n="299">
<head xml:id="echoid-head309" xml:space="preserve">PRAECEPTVM VI.</head>
<note position="left" xml:space="preserve">Quando incli-<lb/>na<unsure/>tio plani ex <lb/>patte auſtrali <lb/>maior eſt com <lb/>plemento alti-<lb/>tudinis poli.</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s23597" xml:space="preserve">CVM denique idem planum maiorem inclinationem habuerit complemento altitudinis po <lb/>li, addendum erit complementum inclinationis complemento altitudinis poli. </s>
  <s xml:id="echoid-s23598" xml:space="preserve">Hac enim ratione <lb/>conficietur altitudo poli ſupra planum inclinatum. </s>
  <s xml:id="echoid-s23599" xml:space="preserve">Pro hac deinde altitudine poli horologium <lb/>horizontale deſcribendum, vt propoſ. </s>
  <s xml:id="echoid-s23600" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23601" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23602" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23603" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s23604" xml:space="preserve">Quod collocandum erit, vt in antece-<lb/>denti præcepto dictum eſt; </s>
  <s xml:id="echoid-s23605" xml:space="preserve">ita tamen, vt in ſuperiori horologio centrum ſit infra lineam æqui-<lb/>noctialem, ſupra verò eandem in inferiori. </s>
  <s xml:id="echoid-s23606" xml:space="preserve">Ordo quoque horarum erit idem hic, qui in præce-<lb/>denti præcepto, hoc excepto, quòd hic in ſuperiori horologio portio meridianæ lineæ à centro <lb/>verſus lineam æquinoctialem oſtendit horam 12. </s>
  <s xml:id="echoid-s23607" xml:space="preserve">mediæ noctis, in inferiori autem horam duo-<lb/>decimam meridiei.</s>
  <s xml:id="echoid-s23608" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23609" xml:space="preserve">HAEC autem omnia ita demonſtrabimus. </s>
  <s xml:id="echoid-s23610" xml:space="preserve">Sit Meridianus Analemmatis A B C D, cuius <lb/>
<anchor type="note" xlink:label="note-0370-09a" xlink:href="note-0370-09"/>
<anchor type="note" xlink:label="note-0370-10a" xlink:href="note-0370-10"/>
centrum E; </s>
  <s xml:id="echoid-s23611" xml:space="preserve">Horizontis diameter B D; </s>
  <s xml:id="echoid-s23612" xml:space="preserve">Verticalis A C; </s>
  <s xml:id="echoid-s23613" xml:space="preserve">Axis mundi F G; </s>
  <s xml:id="echoid-s23614" xml:space="preserve">polus arcticus F; </s>
  <s xml:id="echoid-s23615" xml:space="preserve">antar-<lb/>cticus G; </s>
  <s xml:id="echoid-s23616" xml:space="preserve">Aequatoris diameter H I. </s>
  <s xml:id="echoid-s23617" xml:space="preserve">Quoniam igitur planum ad Horizõtem inclinatum ponitur <lb/>rectum ad Meridianum, metietur Meridianus &amp; </s>
  <s xml:id="echoid-s23618" xml:space="preserve">inclinationem plani ad Horizonrem, &amp; </s>
  <s xml:id="echoid-s23619" xml:space="preserve">altitudi-<lb/>nem poli ſupra ipſum: </s>
  <s xml:id="echoid-s23620" xml:space="preserve">Perſpicuum autem eſt, ſi planum eleuetur ex parte poli arctici, ita vt eius <lb/>inclinatio æqualis ſit altitudini poli D F, planum à circulo horæ 6. </s>
  <s xml:id="echoid-s23621" xml:space="preserve">à meridie vel media nocte per <lb/>axem F G, ducto, &amp; </s>
  <s xml:id="echoid-s23622" xml:space="preserve">ad Meridianum recto, non differre; </s>
  <s xml:id="echoid-s23623" xml:space="preserve">ac proinde horologium in eo plano de-<lb/>ſcriptum, eſſe idem, quod polare, vt in primo præcepto diximus. </s>
  <s xml:id="echoid-s23624" xml:space="preserve">Si verò plani K L, inclinatio <lb/>D k, ex parte eiuſdem poli arctici minor fuerit altitudine poli D F, vt in prima figura, liquet in-<lb/>clinationem D K, ex altitudine poli D F, ablatam relinquere K F, altitudinem poli ſupra planum <lb/>per K L, ductum, veluti in ſecundo præcepto docuimus. </s>
  <s xml:id="echoid-s23625" xml:space="preserve">Si denique eiuſdem plani K L, inclina-<lb/>tio D K, ex eadem parte poli arctici fuerit maior altitudine poli D F, vt in ſecunda figura, quis nõ
<pb o="355" file="0371" n="371" rhead="LIBER TERTIVS."/>
videt, altitudinem poli D F, ex inclinatione D K, detractam relinquere K F, altitudinem poli ſu-<lb/>pra planum K L? </s>
  <s xml:id="echoid-s23626" xml:space="preserve">Rurſus ſi planum K L, ſupra Horizontem attollatur ad partes auſtrales, ita vt <lb/>eius inclinatio æqualis ſit altitudini Aequatoris, ſeu complemento altitudinis poli B H, luce cla-<lb/>rius exiſtit, planum ab Aequatore non differre, &amp;</s>
  <s xml:id="echoid-s23627" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23628" xml:space="preserve">Si vero B K, inclinatio plani K L, ex parte ea-<lb/>dem auſtrali minor exiſtat complemento altitudinis poli B H, dubium non eſt, quin inclinatio <lb/>
<anchor type="figure" xlink:label="fig-0371-01a" xlink:href="fig-0371-01"/>
<anchor type="note" xlink:label="note-0371-01a" xlink:href="note-0371-01"/>
B K, addita altitudini poli B G, componat arcum K G, altitudinis poli ſupra planum K L, vt in <lb/>tertia figura apparet. </s>
  <s xml:id="echoid-s23629" xml:space="preserve">Si denique eiuſdem plani K L, inclinatio B K, ex auſtrali parte ſuperet com-<lb/>plementum altitudinis poli B H, vt in quarta figura, liquido conſtat, cõplementum inclinationis <lb/>A K, complemento altitudinis poli A F, adiunctum conſtituere arcum K F, altitudinis poli ſupra <lb/>
<anchor type="note" xlink:label="note-0371-02a" xlink:href="note-0371-02"/>
planum K L. </s>
  <s xml:id="echoid-s23630" xml:space="preserve">Rectè igitur in ſuperioribus præceptis inuentio altitudinis poli ſupra planum in-<lb/>clinatum tradita eſt. </s>
  <s xml:id="echoid-s23631" xml:space="preserve">Quare ſi fabricemus horologium Aſtronomicum ad inuentam poli altitu-<lb/>dinem, habebimus horas à meridie vel media nocte in plano inclinato delineatas, cum ipſum pla <lb/>num inclinatum ſit Horizon quidam, quem Meridianus proprius loci, in quo horologium con-<lb/>ſtruitur, ad rectos angulos ſecat, vt &amp; </s>
  <s xml:id="echoid-s23632" xml:space="preserve">Horizontem loci.</s>
  <s xml:id="echoid-s23633" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1215" type="float" level="2" n="1">
<note position="left" xlink:label="note-0370-09" xlink:href="note-0370-09a" xml:space="preserve">Demonſtratio <lb/>ſex præceptorũ <lb/>ante cedentiu.</note>
<note position="left" xlink:label="note-0370-10" xlink:href="note-0370-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0371-01" xlink:href="fig-0371-01a">
    <image file="0371-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0371-01"/>
  </figure>
<note position="left" xlink:label="note-0371-01" xlink:href="note-0371-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0371-02" xlink:href="note-0371-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s23634" xml:space="preserve">QVOD ſi ipſi K L, communi ſectioni plani inclinati &amp; </s>
  <s xml:id="echoid-s23635" xml:space="preserve">Meridiani ducamus duas parallelas <lb/>M N, O P, ita vt per M N, infra centrum ductam tranſire intelligatur planum horologij Superio-<lb/>ris, cum verticem A, reſpiciat; </s>
  <s xml:id="echoid-s23636" xml:space="preserve">at vero per O P, ſupra centrum ductam planum inferioris horolo-<lb/>gij duci intelligatur, cum ſeſe ad C, oppoſitum Verticis conuertat, dicto citius cognoſcemus, <lb/>in quonam horologio centrum, id eſt, punctum, vbi axis mundi planum horologii ſecat, vt ex <lb/>propoſ. </s>
  <s xml:id="echoid-s23637" xml:space="preserve">21. </s>
  <s xml:id="echoid-s23638" xml:space="preserve">primilibri patet, ſtatuendum ſit infra lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s23639" xml:space="preserve">in quo ſupra eandem; <lb/></s>
  <s xml:id="echoid-s23640" xml:space="preserve">
<anchor type="note" xlink:label="note-0371-03a" xlink:href="note-0371-03"/>
prout nimirum axis F G, parallelas M N, O P, ſecat ſupra, aut infra lineam æquinoctialem H I, vt <lb/>in figuris apparet; </s>
  <s xml:id="echoid-s23641" xml:space="preserve">quarum prima reſpondet ſecundo præcepto; </s>
  <s xml:id="echoid-s23642" xml:space="preserve">ſecunda tertio; </s>
  <s xml:id="echoid-s23643" xml:space="preserve">tertia quinto, &amp; </s>
  <s xml:id="echoid-s23644" xml:space="preserve"><lb/>quarta ſexto. </s>
  <s xml:id="echoid-s23645" xml:space="preserve">Ita enim vides in prima figura M, centrum horologii ſuperioris eſſe infra N, pun-<lb/>ctum, per quod linea æquinoctialis ducenda eſt ad meridianam lineam M N, perpendicularis, vt <lb/>propoſ. </s>
  <s xml:id="echoid-s23646" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23647" xml:space="preserve">præcedentis libri oſtendimus. </s>
  <s xml:id="echoid-s23648" xml:space="preserve">In inferioriautem centrum O, eſſe ſupra P, punctũ æqui-<lb/>noctialis lineæ, &amp; </s>
  <s xml:id="echoid-s23649" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s23650" xml:space="preserve">Semper enim in figuris occurrit axis F G, plano horologii ſuperio <lb/>ris in M, &amp; </s>
  <s xml:id="echoid-s23651" xml:space="preserve">Aequator in N: </s>
  <s xml:id="echoid-s23652" xml:space="preserve">plano autem inferioris horologij occurrit axis in O, &amp; </s>
  <s xml:id="echoid-s23653" xml:space="preserve">Aequator in <lb/>P. </s>
  <s xml:id="echoid-s23654" xml:space="preserve">Ordo quoque horarum ex eiſdem figuris facile colligitur, ſi Meridianus A B C D, in proprio <lb/>ſitu cogitetur eſſe collocatus. </s>
  <s xml:id="echoid-s23655" xml:space="preserve">Nam vt in prima, &amp; </s>
  <s xml:id="echoid-s23656" xml:space="preserve">ſecunda figura apparet, axis proiicit vmbram <lb/>in meridianam lineam M N, horologii ſuperioris, cum Sol exiſtit in ſemicirculo F A G, qui per <lb/>
<anchor type="note" xlink:label="note-0371-04a" xlink:href="note-0371-04"/>
verticem, &amp; </s>
  <s xml:id="echoid-s23657" xml:space="preserve">punctum meridiei tranſit: </s>
  <s xml:id="echoid-s23658" xml:space="preserve">at verò in lineam meridianam O P, inferioris horologii <lb/>idem axis vmbram proiicit, cum Sol in oppoſito ſemicirculo F C G, exiſtit, qui per Nadir, &amp; </s>
  <s xml:id="echoid-s23659" xml:space="preserve">pun <lb/>ctum mediæ noctis ducitur. </s>
  <s xml:id="echoid-s23660" xml:space="preserve">Ex quo fit lineam meridianam M N, ſuperioris horologii à centro <lb/>M, verſus punctum Aequatoris N, pertinere ad horam 12. </s>
  <s xml:id="echoid-s23661" xml:space="preserve">meridiei, lineam verò meridianã O P, <lb/>horologii inferioris à centro O, verſus punctum Aequatoris P, ad horam 12. </s>
  <s xml:id="echoid-s23662" xml:space="preserve">mediæ noctis, vt in <lb/>2. </s>
  <s xml:id="echoid-s23663" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23664" xml:space="preserve">3. </s>
  <s xml:id="echoid-s23665" xml:space="preserve">præcepto declarauimus. </s>
  <s xml:id="echoid-s23666" xml:space="preserve">Conuerſis etiam nobis ad horologium ſuperius, ita vt faciem con <lb/>uertamus ad Boream, proijcientur vmbræ pomeridiano rempore in partem horologij, quæ nobis <lb/>ad dextram collocatur, eſtq́ue orientalis; </s>
  <s xml:id="echoid-s23667" xml:space="preserve">in partem verò occidentalem, quæ nobis ſiniſtra eſt, an-<lb/>temeridiano tempore, ſiue poſt mediã noctem. </s>
  <s xml:id="echoid-s23668" xml:space="preserve">Conuerſis item nobis ad inferius horologium, <lb/>ita vt faciem ad meridiem conuertamus, cadent vmbræ in partem orientalem tempore pomeridia <lb/>
<anchor type="note" xlink:label="note-0371-05a" xlink:href="note-0371-05"/>
no, quæ quidem nobis ſiniſtra eſt; </s>
  <s xml:id="echoid-s23669" xml:space="preserve">in partem verò occidentalem nobis ad dextram collocatam, an-<lb/>temeridiano tempore, ſiue poſt mediam noctem. </s>
  <s xml:id="echoid-s23670" xml:space="preserve">Rurſus, vt in tertia figura patet, vmbra axis proii-<lb/>citur in meridianam lineam M N, horologii ſuperioris, Sole exiſtente in ſemicirculo meridiei <lb/>F A G; </s>
  <s xml:id="echoid-s23671" xml:space="preserve">in meridianam vero lineam O P, inferioris horologij, eodem in ſemicirculo mediæ noctis <lb/>F C G, exiſtente. </s>
  <s xml:id="echoid-s23672" xml:space="preserve">Vnde illa ad meridiem, hæc verò ad mediam noctem pertinebit: </s>
  <s xml:id="echoid-s23673" xml:space="preserve">contrarium <lb/>cernitur in quarta figura. </s>
  <s xml:id="echoid-s23674" xml:space="preserve">Conuerſis quoque nobis in 3. </s>
  <s xml:id="echoid-s23675" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23676" xml:space="preserve">4. </s>
  <s xml:id="echoid-s23677" xml:space="preserve">figura ad ſuperius horologium, ita <lb/>vt faciem verſus meridiem vertamus, cadentvmbræ in partem occidentalem, quæ nobis dextra <lb/>eſt, poſt mediam noctem, ſeu tempore antemeridiano; </s>
  <s xml:id="echoid-s23678" xml:space="preserve">in partem vero orientalem, &amp; </s>
  <s xml:id="echoid-s23679" xml:space="preserve">nobis ſini-<lb/>ſtram, pomeridiano tempore. </s>
  <s xml:id="echoid-s23680" xml:space="preserve">At nobis ad inferius horologium conuerſis, ita vt conuertamus fa-<lb/>ciem verſus ſeptentrionem, contrarium omnino accidit. </s>
  <s xml:id="echoid-s23681" xml:space="preserve">Rectè igitur ordinem horarum in præ-<lb/>ceptis ſuperioribus præſcripſimus.</s>
  <s xml:id="echoid-s23682" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1216" type="float" level="2" n="2">
<note position="left" xlink:label="note-0371-03" xlink:href="note-0371-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0371-04" xlink:href="note-0371-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0371-05" xlink:href="note-0371-05a" xml:space="preserve">50</note>
</div>
<pb o="356" file="0372" n="372" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s23683" xml:space="preserve">EXEMPLVM omnium hoc ſit. </s>
  <s xml:id="echoid-s23684" xml:space="preserve">Proponatur planum ad Horizontem inclinatum ex par-<lb/>
<anchor type="note" xlink:label="note-0372-01a" xlink:href="note-0372-01"/>
te meridiei, grad. </s>
  <s xml:id="echoid-s23685" xml:space="preserve">68. </s>
  <s xml:id="echoid-s23686" xml:space="preserve">Quoniam igitur inclinatio complemento altitudinis poli maior eſt, cum in <lb/>Horizõte Romano, ad quẽ omnia horologia in noſtra hac Gnomonica deſcribimus, complemen <lb/>
<anchor type="figure" xlink:label="fig-0372-01a" xlink:href="fig-0372-01"/>
<anchor type="note" xlink:label="note-0372-02a" xlink:href="note-0372-02"/>
<anchor type="note" xlink:label="note-0372-03a" xlink:href="note-0372-03"/>
<anchor type="note" xlink:label="note-0372-04a" xlink:href="note-0372-04"/>
<anchor type="note" xlink:label="note-0372-05a" xlink:href="note-0372-05"/>
tum altitudinis poli complectatur grad. </s>
  <s xml:id="echoid-s23687" xml:space="preserve">48. </s>
  <s xml:id="echoid-s23688" xml:space="preserve">addemus, vt in ſexto præcepto (cui reſpondet quar-<lb/>ta figura ex ſuperioribus) tradidimus, complementum inclinationis, nempe grad. </s>
  <s xml:id="echoid-s23689" xml:space="preserve">22. </s>
  <s xml:id="echoid-s23690" xml:space="preserve">complemen <lb/>to altitudinis poli, quod grad. </s>
  <s xml:id="echoid-s23691" xml:space="preserve">48. </s>
  <s xml:id="echoid-s23692" xml:space="preserve">diximus complecti, efficiemusq́ue altitudinem poli ſupra planũ <lb/>propoſitum grad. </s>
  <s xml:id="echoid-s23693" xml:space="preserve">70. </s>
  <s xml:id="echoid-s23694" xml:space="preserve">Ad hanc igitur altitudinem horologium Aſtronomicum deſcribemus, vt in <lb/>
<anchor type="note" xlink:label="note-0372-06a" xlink:href="note-0372-06"/>
horizontali horologio dictum eſt, propoſ. </s>
  <s xml:id="echoid-s23695" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23696" xml:space="preserve">ſuperioris libri, veluti in appoſita figura apparet; </s>
  <s xml:id="echoid-s23697" xml:space="preserve">in <lb/>qua, quoniam horologium in ſuperiori facie plani collocandum eſt, centrum horologij H, infra <lb/>lineam æquinoctialem poſitum eſt, portioq́ue lineæ meridianæ ab H, verſus I, porrecta horam 12. <lb/></s>
  <s xml:id="echoid-s23698" xml:space="preserve">mediæ noctis, reliqua autem ab H, verſus alteram partem educta horam 12. </s>
  <s xml:id="echoid-s23699" xml:space="preserve">meridiei indicat, vt <lb/>in 6. </s>
  <s xml:id="echoid-s23700" xml:space="preserve">præcepto docuimus, &amp; </s>
  <s xml:id="echoid-s23701" xml:space="preserve">facile ex 4. </s>
  <s xml:id="echoid-s23702" xml:space="preserve">figura colligitur. </s>
  <s xml:id="echoid-s23703" xml:space="preserve">Horologium igitur Aſtronomicum, <lb/>quod inclinatum eſt ad Horizontem, &amp;</s>
  <s xml:id="echoid-s23704" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23705" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s23706" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23707" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1217" type="float" level="2" n="3">
<note position="left" xlink:label="note-0372-01" xlink:href="note-0372-01a" xml:space="preserve">Exemplum ho <lb/>rologu ad Ho-<lb/>rizontem in cli-<lb/>nau.</note>
  <figure xlink:label="fig-0372-01" xlink:href="fig-0372-01a">
    <image file="0372-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0372-01"/>
  </figure>
<note position="left" xlink:label="note-0372-02" xlink:href="note-0372-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0372-03" xlink:href="note-0372-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0372-04" xlink:href="note-0372-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0372-05" xlink:href="note-0372-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0372-06" xlink:href="note-0372-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1219" type="section" level="1" n="300">
<head xml:id="echoid-head310" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s23708" xml:space="preserve">IDEM hoc horologium, ſi omnes ei{us} partes inuertantur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s23709" xml:space="preserve">13. </s>
  <s xml:id="echoid-s23710" xml:space="preserve">præcedentis li-<lb/>hri docuimus, indicabit hor{as} in facie plani inferiori, vt ibidem demonſtr auim{us}.</s>
  <s xml:id="echoid-s23711" xml:space="preserve"/>
</p>
<pb o="357" file="0373" n="373" rhead="LIBER TERTIVS."/>
<p style="it">
  <s xml:id="echoid-s23712" xml:space="preserve">SI planum ad Horizontem inclinatum fuerit ſtabile, it a rem aggrediemur. </s>
  <s xml:id="echoid-s23713" xml:space="preserve">In plano ducemus Hori-<lb/>
<anchor type="note" xlink:label="note-0373-01a" xlink:href="note-0373-01"/>
zonti lineam æquidiſtantem F K, pro linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s23714" xml:space="preserve">ad eam ducemus per pendicularem H E, pro <lb/>linea meridiana, quæ illam ſecet in I. </s>
  <s xml:id="echoid-s23715" xml:space="preserve">Deinde ex I, verſus partem inferiorem, ſi centrum horologĳ infra <lb/>æquinoctialem lineam cadit, aut verſus ſuperiorem partem, ſi horologĳ centrum cadit ſupra lineam æqui <lb/>noctialem, (Id quod ſuperiora ſex præcepta clariſſime docent) transferemus ex portione Analemmatis <lb/>rectam H I, in lineam meridianam H E, vſque ad punctum H, quod centrum erit horologĳ. </s>
  <s xml:id="echoid-s23716" xml:space="preserve">Item in ean <lb/>dem lineam meridianam ex portione Analemmatis transferem{us} rectam I D, ex I, vſque ad E. </s>
  <s xml:id="echoid-s23717" xml:space="preserve">Po-<lb/>stremo ex E, deſcripto circulo, eoq́, di@iſo in 24 hor{as}, &amp;</s>
  <s xml:id="echoid-s23718" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23719" xml:space="preserve">reliqua perficiem{us}, vt prius.</s>
  <s xml:id="echoid-s23720" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1219" type="float" level="2" n="1">
<note position="right" xlink:label="note-0373-01" xlink:href="note-0373-01a" xml:space="preserve">Qua ratione in <lb/>plano ad Hori-<lb/>zonæm in@lina <lb/>to ſtabili horo-<lb/>logium ſit con-<lb/>ſtruendum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s23721" xml:space="preserve">SI vero idem horologium deſcribendum ſit in plano dato, ſine portione Analemmatis ſeorſum con-<lb/>
<anchor type="note" xlink:label="note-0373-02a" xlink:href="note-0373-02"/>
ſtructa, ad quamcunque longitudinem ſtyli, cuius etiam loc{us} dat{us} ſit, progrediemur hac via. </s>
  <s xml:id="echoid-s23722" xml:space="preserve">Sit lon-<lb/>
<anchor type="note" xlink:label="note-0373-03a" xlink:href="note-0373-03"/>
gitudo styli data D G, eiusq́, loc{us} in plano horologii punctum G. </s>
  <s xml:id="echoid-s23723" xml:space="preserve">Si igitur planum horologii fuerit quod-<lb/>
<anchor type="figure" xlink:label="fig-0373-01a" xlink:href="fig-0373-01"/>
<anchor type="note" xlink:label="note-0373-04a" xlink:href="note-0373-04"/>
<anchor type="note" xlink:label="note-0373-05a" xlink:href="note-0373-05"/>
cunque, vt horologium in eo deſcriptum in proprio deinde fitu collocetur, vel in planum ſtabile, quod ad <lb/>Horizontem ſit inclinatum, transfer atur, ducem{us} per G, locum ſtyli lineam rectam vtcunque H E, pro <lb/>linea meridiana: </s>
  <s xml:id="echoid-s23724" xml:space="preserve">Si autem planum horologii proponatur ſtabile, &amp; </s>
  <s xml:id="echoid-s23725" xml:space="preserve">ad Horizontem inclinatum, duce-<lb/>
<anchor type="note" xlink:label="note-0373-06a" xlink:href="note-0373-06"/>
m{us} per G, lineam Horizonti par allelam D G, ad quam in G, excitabimus perpendicularem H E, pro <lb/>linea meridiana: </s>
  <s xml:id="echoid-s23726" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23727" xml:space="preserve">ex G D, abſcindemus rectam G D, dato ſtylo ęqualem. </s>
  <s xml:id="echoid-s23728" xml:space="preserve">Ex centro autem D, arcum <lb/>circuli deſcribemus, in eoq́, à recta D G, ad partes G, producta numer abim{us} complementum altitudi-<lb/>nis poli ſupra planum inclinatum inuentæ, verſus quidẽ partem inferiorem horologii, (quam nunc poni-<lb/>mus eſſe à puncto G, verſ{us} H) ſi centrũ horologii infra lineam æquinoctialẽ cadit, (quod quando contin-<lb/>gat, ex ſuperiorib{us} præceptis colligitur) verſ{us} partem autem ſuperiorem, ſi centrum horologii ſupra <lb/>lineam ęquinoctialem exiſtit; </s>
  <s xml:id="echoid-s23729" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23730" xml:space="preserve">ex D, per finem ſupputationis rectam educem{us}, quę meridianam lineã <lb/>ſecet in H, centro horologii. </s>
  <s xml:id="echoid-s23731" xml:space="preserve">In eodem quoque arcu ab eadem recta D G, verſ{us} oppoſitam partem nu-<lb/>merabimus ipſam altitudinem poli ſupra planum inclinatum inuentam, &amp; </s>
  <s xml:id="echoid-s23732" xml:space="preserve">per finem numer ationis ex D, <lb/>rectam ducem{us}, quæ ad D H, perpendicularis erit, ſecabit{q́ue} meridianam lineam in puncto I, per quod <lb/>
<anchor type="note" xlink:label="note-0373-07a" xlink:href="note-0373-07"/>
ducenda eſt linea æquinoctialis F K, ad meridianam lineam perpendicularis. </s>
  <s xml:id="echoid-s23733" xml:space="preserve">Sumpta iam recta I E, ipſi <lb/>I D, æquali, deſcripto{q́ue} circulo ex E, qui in partes 24. </s>
  <s xml:id="echoid-s23734" xml:space="preserve">æquales ſecetun, abſoluem{us} reliqua, vt pri{us}. <lb/></s>
  <s xml:id="echoid-s23735" xml:space="preserve">Demonſtratio hui{us} rei ab ea non differt, quam in ſcholio propoſ. </s>
  <s xml:id="echoid-s23736" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23737" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23738" xml:space="preserve">ſcripſim{us}, cum horo-<lb/>logium horizontale ad datam ſtyli longitudinem conſtrueremus. </s>
  <s xml:id="echoid-s23739" xml:space="preserve">Eſt enim planum ad Horizontem inclin-<lb/>natum Horizon quidam, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s23740" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1220" type="float" level="2" n="2">
<note position="right" xlink:label="note-0373-02" xlink:href="note-0373-02a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>ad Horizontẽ <lb/>inclinati pro <lb/>data ſ@yli lon gi <lb/>@udine, cuius e-<lb/>tiam locus da-<lb/>tus fit, ſine por-<lb/>tione Analem <lb/>matis ſeorſum <lb/>conſtru@ta.</note>
<note position="left" xlink:label="note-0373-03" xlink:href="note-0373-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0373-01" xlink:href="fig-0373-01a">
    <image file="0373-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0373-01"/>
  </figure>
<note position="left" xlink:label="note-0373-04" xlink:href="note-0373-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0373-05" xlink:href="note-0373-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0373-06" xlink:href="note-0373-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0373-07" xlink:href="note-0373-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s23741" xml:space="preserve">PER Ellipſim quoque in plano horologii deſcriptam, cui{us} maior ſemidiameter eſt H I, minon au-<lb/>
<anchor type="note" xlink:label="note-0373-08a" xlink:href="note-0373-08"/>
tem I D, &amp; </s>
  <s xml:id="echoid-s23742" xml:space="preserve">centrum H, deſcribem{us} idem horologium, vt horizont ale deſcripſim{us} in ſcholio propoſ. </s>
  <s xml:id="echoid-s23743" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s23744" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s23745" xml:space="preserve">Id quod ex figura, quam in eo ſcholio appoſuimus, facile intelligi poteſt. </s>
  <s xml:id="echoid-s23746" xml:space="preserve">Refert enim ea <lb/>figur a in regione, cui{us} latitudo complectitur grad. </s>
  <s xml:id="echoid-s23747" xml:space="preserve">60. </s>
  <s xml:id="echoid-s23748" xml:space="preserve">horologium inclinatum ad Horizontem gr. </s>
  <s xml:id="echoid-s23749" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23750" xml:space="preserve">ex <lb/>parte boreali: </s>
  <s xml:id="echoid-s23751" xml:space="preserve">quia tunc pol{us} arctic{us} habet ſupr a illud planum altitudinem grad, 42. </s>
  <s xml:id="echoid-s23752" xml:space="preserve">quemadmodum <lb/>&amp; </s>
  <s xml:id="echoid-s23753" xml:space="preserve">ſupra Horizontem illi{us} loci, pro quo illud horizontale horologium conſtruxim{us}.</s>
  <s xml:id="echoid-s23754" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1221" type="float" level="2" n="3">
<note position="right" xlink:label="note-0373-08" xlink:href="note-0373-08a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii <lb/>beneficio Elli-<lb/>pſis.</note>
</div>
<pb o="358" file="0374" n="374" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1223" type="section" level="1" n="301">
<head xml:id="echoid-head311" xml:space="preserve">PROBLEMA 26. PROPOSITIO 26.</head>
<p>
  <s xml:id="echoid-s23755" xml:space="preserve">PARALLELOS, ſeu arcus ſignorum Zodiaci, in eodem horo-<lb/>logio ad Horizontem inclinato ponere.</s>
  <s xml:id="echoid-s23756" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23757" xml:space="preserve">HABITA ratione altitudinis poli inuentæ ſupra planum inclinatum, deſcribentur paralle <lb/>
<anchor type="note" xlink:label="note-0374-01a" xlink:href="note-0374-01"/>
li ſignorum in hoc horologio, quemadmodum in horizontali, vt propoſ. </s>
  <s xml:id="echoid-s23758" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23759" xml:space="preserve">antecedentis libri <lb/>tradidimus &amp; </s>
  <s xml:id="echoid-s23760" xml:space="preserve">in ſubiectis figuris apparet.</s>
  <s xml:id="echoid-s23761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1223" type="float" level="2" n="1">
<note position="left" xlink:label="note-0374-01" xlink:href="note-0374-01a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſigno-<lb/>rum in eodem <lb/>horologio ad <lb/>Horizõtem in-<lb/>clinato.</note>
</div>
<p>
  <s xml:id="echoid-s23762" xml:space="preserve">QVI autem arcus ad ſigna borealia, &amp; </s>
  <s xml:id="echoid-s23763" xml:space="preserve">qui ad auſtralia pertineant, pulchrè quatuor illa Ana-<lb/>
<anchor type="note" xlink:label="note-0374-02a" xlink:href="note-0374-02"/>
<anchor type="note" xlink:label="note-0374-03a" xlink:href="note-0374-03"/>
lemmata in propoſ. </s>
  <s xml:id="echoid-s23764" xml:space="preserve">antecedenti declarant. </s>
  <s xml:id="echoid-s23765" xml:space="preserve">Quoniam enim in primo Analemmate puncta qua-<lb/>drantis Borealis F H, (appellamus nunc ſemicirculum borealem Meridiani H F I, &amp; </s>
  <s xml:id="echoid-s23766" xml:space="preserve">auſtralem <lb/>
<anchor type="figure" xlink:label="fig-0374-01a" xlink:href="fig-0374-01"/>
<anchor type="note" xlink:label="note-0374-04a" xlink:href="note-0374-04"/>
<anchor type="note" xlink:label="note-0374-05a" xlink:href="note-0374-05"/>
H G I) proiiciunt vmbram in meridie per centrum E, in portionem meridianæ lineæ M N, ſupe-<lb/>rioris horologij poſitam inter centrum, &amp; </s>
  <s xml:id="echoid-s23767" xml:space="preserve">lineam æquinoctialem: </s>
  <s xml:id="echoid-s23768" xml:space="preserve">puncta verò quadrantis auſtra-<lb/>lis G I, vmbram proiiciunt per centrum E, in portionem lineæ meridianæ O P, poſitam inter <lb/>
<anchor type="note" xlink:label="note-0374-06a" xlink:href="note-0374-06"/>
centrum, &amp; </s>
  <s xml:id="echoid-s23769" xml:space="preserve">æquinoctialem lineam inferioris horologij; </s>
  <s xml:id="echoid-s23770" xml:space="preserve">efficitur, vt in ſuperiori horologio ex par-<lb/>te boreali eleuato, cuius inclinatio minor eſt altitudine poli, vt in Analemmate primo apparet, <lb/>arcus ſignorum borealium contineantur inter centrum horologij, &amp; </s>
  <s xml:id="echoid-s23771" xml:space="preserve">æquinoctialem lineam; </s>
  <s xml:id="echoid-s23772" xml:space="preserve">ar-<lb/>cus vero auſtralium ſignorum vltra lineam æquinoctialem: </s>
  <s xml:id="echoid-s23773" xml:space="preserve">In horologio autẽ inferiori contra. <lb/></s>
  <s xml:id="echoid-s23774" xml:space="preserve">Rurſus quia in ſecundo Analemmate puncta quadrantis borealis F H, proijciunt vmbram per <lb/>cẽtrum E, in portionẽ meridianæ lineæ M N, ſuperioris horologij vltra lineã æquinoctialem per <lb/>N, productã: </s>
  <s xml:id="echoid-s23775" xml:space="preserve">puncta verò quadrantis auſtralis G I, vmbram proiiciunt per E, centrum in portionẽ <lb/>meridianæ lineæ OP, inferioris horologij vltra æquinoctialẽ lineam per P, productã fit, vt in ſupe-<lb/>riori horologio ex parte boreali eleuato, cuius inclinatio maior eſt altitudine poli, vt in ſecundo <lb/>Analẽmate conſpicitur, arcus ſignorum borealium exiſtant vltra lineã æquinoctialem, &amp; </s>
  <s xml:id="echoid-s23776" xml:space="preserve">auſtraliũ <lb/>
<anchor type="note" xlink:label="note-0374-07a" xlink:href="note-0374-07"/>
inter centrum, &amp; </s>
  <s xml:id="echoid-s23777" xml:space="preserve">eandẽ æquinoctialem lineam: </s>
  <s xml:id="echoid-s23778" xml:space="preserve">In inferiori autem horologio contra ſe res ha-<lb/>beat. </s>
  <s xml:id="echoid-s23779" xml:space="preserve">Præterea quia in tertio Analemmate puncta quadrantis borealis F H, vmbram proii-<lb/>ciuntin portionem meridianæ lineæ M N, horologii ſuperioris poſitam inter centrum, &amp; </s>
  <s xml:id="echoid-s23780" xml:space="preserve">li-<lb/>neam æquinoctialem: </s>
  <s xml:id="echoid-s23781" xml:space="preserve">puncta verò quadrantis auſtralis G I, vmbram proijciunt in portionem <lb/>meridianæ lineæ O P, poſitam inter centrum, &amp; </s>
  <s xml:id="echoid-s23782" xml:space="preserve">lineam æquinoctialem inferioris horologii; </s>
  <s xml:id="echoid-s23783" xml:space="preserve">fit, vt <lb/>in horologio ſuperiori ex parte auſtrali eleuato, cuius inclinatio minor eſt complemento altitudi <lb/>nis poli, vt in tertio Analemmate, arcus ſignorum borealium ſint inter centrum, &amp; </s>
  <s xml:id="echoid-s23784" xml:space="preserve">lineam æqui-<lb/>noctialem, &amp; </s>
  <s xml:id="echoid-s23785" xml:space="preserve">auſtralium vltra æquinoctialem lineam: </s>
  <s xml:id="echoid-s23786" xml:space="preserve">In inferiori autem è contrario. </s>
  <s xml:id="echoid-s23787" xml:space="preserve">Poſtremo <lb/>quoniam in Analemmate quarto puncta quadrantis borealis F I, proijciunt vmbram in portionẽ <lb/>meridianæ lineæ M N, ſuperioris horologii poſitam inter centrum, &amp; </s>
  <s xml:id="echoid-s23788" xml:space="preserve">lineam ęquinoctialem: </s>
  <s xml:id="echoid-s23789" xml:space="preserve">pun <lb/>cta verò quadrantis auſtralis G H, vmbram proijciunt in portionem lineæ meridianæ O P, horo-
<pb o="359" file="0375" n="375" rhead="LIBER TERTIVS."/>
logij inferioris poſitam inter centrum, &amp; </s>
  <s xml:id="echoid-s23790" xml:space="preserve">æquinoctialem lineam; </s>
  <s xml:id="echoid-s23791" xml:space="preserve">efficitur, vt in ſuperiori horo-<lb/>logio ex parte auſtrali eleuato, cuius inclinatio complementum altitudinis poli ſuperat, vt in quar <lb/>to Analemmate apparet, &amp; </s>
  <s xml:id="echoid-s23792" xml:space="preserve">quale eſt horologium nobis propoſitum, arcus ſignorum borealium <lb/>inter cẽtrum, &amp; </s>
  <s xml:id="echoid-s23793" xml:space="preserve">lineam æquinoctia <lb/>
<anchor type="figure" xlink:label="fig-0375-01a" xlink:href="fig-0375-01"/>
lem comprehendantur, &amp; </s>
  <s xml:id="echoid-s23794" xml:space="preserve">auſtraliũ <lb/>ſignorum vltra eandem lineam æ-<lb/>quinoctialem: </s>
  <s xml:id="echoid-s23795" xml:space="preserve">At in horologio in-<lb/>ferior contra. </s>
  <s xml:id="echoid-s23796" xml:space="preserve">Quæ omnia perſpi <lb/>cua ſunt, ſi attentè dicta Analem-<lb/>mata conſiderentur. </s>
  <s xml:id="echoid-s23797" xml:space="preserve">Quòd autem <lb/>
<anchor type="note" xlink:label="note-0375-01a" xlink:href="note-0375-01"/>
puncta quędã ſemicirculi borealis <lb/>H F I, in vtroque Analemmate po-<lb/>ſteriori proiiciant quoque vmbram <lb/>vltra centrum M, argumento eſt, <lb/>arcus ſignorum eſſe tunc Ellipſes, <lb/>ita vt ſinguli duobus in locis ſecent <lb/>lineam meridianam, quorum vnũ <lb/>neceſſario inter centrum M, &amp; </s>
  <s xml:id="echoid-s23798" xml:space="preserve">æqui <lb/>noctialem lineam exiſtit; </s>
  <s xml:id="echoid-s23799" xml:space="preserve">adeò vt ve <lb/>rum ſemper ſit, arcus cõtentos in-<lb/>
<anchor type="note" xlink:label="note-0375-02a" xlink:href="note-0375-02"/>
ter centrum, &amp; </s>
  <s xml:id="echoid-s23800" xml:space="preserve">ęquinoctialem li-<lb/>neam ſuperioris horologii in poſte-<lb/>rioribus duobus Analẽmatibus per-<lb/>tinere ad ſigna borealia, quamuis <lb/>aliqua puncta quadrantis borealis <lb/>F I, in tertio Analemmate, &amp; </s>
  <s xml:id="echoid-s23801" xml:space="preserve">qua-<lb/>drantis borealis F H, in quarto vm-<lb/>bram ſuam vltra centrum M, pro-<lb/>ijciant in lineam meridianam.</s>
  <s xml:id="echoid-s23802" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1224" type="float" level="2" n="2">
<note position="left" xlink:label="note-0374-02" xlink:href="note-0374-02a" xml:space="preserve">Qui arcus@ ad <lb/>ſigna borealia, <lb/>&amp; qui ad au-<lb/>ſtralia perti-<lb/>neant.</note>
<note position="left" xlink:label="note-0374-03" xlink:href="note-0374-03a" xml:space="preserve">01</note>
  <figure xlink:label="fig-0374-01" xlink:href="fig-0374-01a">
    <image file="0374-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0374-01"/>
  </figure>
<note position="left" xlink:label="note-0374-04" xlink:href="note-0374-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0374-05" xlink:href="note-0374-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0374-06" xlink:href="note-0374-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0374-07" xlink:href="note-0374-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0375-01" xlink:href="fig-0375-01a">
    <image file="0375-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0375-01"/>
  </figure>
<note position="left" xlink:label="note-0375-01" xlink:href="note-0375-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0375-02" xlink:href="note-0375-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s23803" xml:space="preserve">IN noſtro exemplo tam arcus ♋, in ſuperiori horologio, &amp; </s>
  <s xml:id="echoid-s23804" xml:space="preserve">arcus ♑, in inferiori, quàm arcus <lb/>
<anchor type="note" xlink:label="note-0375-03a" xlink:href="note-0375-03"/>
♊, &amp; </s>
  <s xml:id="echoid-s23805" xml:space="preserve">♌, in ſuperiori, &amp; </s>
  <s xml:id="echoid-s23806" xml:space="preserve">arcus ♐, &amp; </s>
  <s xml:id="echoid-s23807" xml:space="preserve">♒, in inferiori, Ellipſis eſt, vt ex coroll. </s>
  <s xml:id="echoid-s23808" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s23809" xml:space="preserve">7. </s>
  <s xml:id="echoid-s23810" xml:space="preserve">primi libri <lb/>colligitur: </s>
  <s xml:id="echoid-s23811" xml:space="preserve">quoniam declinatio horum ſignorum excedit complementum altitudinis poli ſupra <lb/>planum propoſitum: </s>
  <s xml:id="echoid-s23812" xml:space="preserve">quamuis poſterior arcus fere ſit parabola, cum illorum ſignorum declina-<lb/>tio fermè ęqualis ſit complemento altitudinis poli ſupra planum inclinatum: </s>
  <s xml:id="echoid-s23813" xml:space="preserve">Eſt enim differen-<lb/>tia Minutorum 12. </s>
  <s xml:id="echoid-s23814" xml:space="preserve">duntaxat, vt patet. </s>
  <s xml:id="echoid-s23815" xml:space="preserve">At verò arcus ♉, &amp; </s>
  <s xml:id="echoid-s23816" xml:space="preserve">♍, in ſuperiori horologio, &amp; </s>
  <s xml:id="echoid-s23817" xml:space="preserve">arcus <lb/>♏, &amp; </s>
  <s xml:id="echoid-s23818" xml:space="preserve">♓, in inferiori Hyperbola eſt, vt in coroll. </s>
  <s xml:id="echoid-s23819" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s23820" xml:space="preserve">6. </s>
  <s xml:id="echoid-s23821" xml:space="preserve">eiuſdem primi libri expoſuimus; </s>
  <s xml:id="echoid-s23822" xml:space="preserve">pro-<lb/>pterea quod declinatio horum ſignorum minor eſt complemento altitudinis poli ſupra planum <lb/>inclinatum propoſitum. </s>
  <s xml:id="echoid-s23823" xml:space="preserve">Idem etiam facile concludi poteſt ex iis, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s23824" xml:space="preserve">2. </s>
  <s xml:id="echoid-s23825" xml:space="preserve">ſuperio <lb/>ris libri ſcripſimus.</s>
  <s xml:id="echoid-s23826" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1225" type="float" level="2" n="3">
<note position="left" xlink:label="note-0375-03" xlink:href="note-0375-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s23827" xml:space="preserve">HORIZONTALIS linea ita ducetur. </s>
  <s xml:id="echoid-s23828" xml:space="preserve">Per G, locum ſtyli ducatur ad meridianam lineã <lb/>
<anchor type="note" xlink:label="note-0375-04a" xlink:href="note-0375-04"/>
<anchor type="note" xlink:label="note-0375-05a" xlink:href="note-0375-05"/>
perpendicularis G A, ex qua abſcindatur G A, longitudini ſtyli æqualis. </s>
  <s xml:id="echoid-s23829" xml:space="preserve">Deinde in A, conſtitua-<lb/>tur angulus G A B, complemento inclinationis plani ad Horizontem æqualis, ſurſum quidem <lb/>verſus in ſuperiori horologio, deorſum autem verſus in inferiori. </s>
  <s xml:id="echoid-s23830" xml:space="preserve">(Quod facile fiet, ſi ex A, ver-<lb/>ſus meridianam lineam arcus circuli deſcribatur, in quo à recta A G, complementum inclinatio-<lb/>nis ſupputetur, &amp;</s>
  <s xml:id="echoid-s23831" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s23832" xml:space="preserve">ſecet autem recta A B, meridianam lineam in B. </s>
  <s xml:id="echoid-s23833" xml:space="preserve">Dico rectam per B, ductam <lb/>ęquinoctiali lineæ parallelam, vel perpendicularem ad lineam meridianam, eſſe lineam horizon <lb/>talem, hoc eſt, communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s23834" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s23835" xml:space="preserve">Si enim triangulũ A B G, <lb/>circa B G, moueatur, donec rectum ſit ad planum horologij, atque adeo in Meridiani plano con-<lb/>ſiſtat, &amp; </s>
  <s xml:id="echoid-s23836" xml:space="preserve">A, vertex ſtyli cum centro mundi coniungatur, cum angulus G A B, ſit inclinationis com-<lb/>plemento æqualis, erit A B G, angulus inclinationis; </s>
  <s xml:id="echoid-s23837" xml:space="preserve">ac proinde cum Horizon per A, verticem <lb/>
<anchor type="note" xlink:label="note-0375-06a" xlink:href="note-0375-06"/>
ſtyli incedat, erit recta A B, communis ſectio eius, &amp; </s>
  <s xml:id="echoid-s23838" xml:space="preserve">Meridiani faciens in plano Meridiani cum <lb/>meridiana linea horologij angulum inclinationis, vt res poſtulat. </s>
  <s xml:id="echoid-s23839" xml:space="preserve">Quare cum in B, Horizon pla-<lb/>no horologij occurrat, ducenda erit linea horizontalis per B, punctum: </s>
  <s xml:id="echoid-s23840" xml:space="preserve">quæ ipſi lineæ ęquino-<lb/>ctiali parallela neceſſario eſt, ex propoſ. </s>
  <s xml:id="echoid-s23841" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23842" xml:space="preserve">primi libri, cum Aequator, Horizon, &amp; </s>
  <s xml:id="echoid-s23843" xml:space="preserve">circulus ma-<lb/>ximus, cui horologium ęquidiſtat, habeant vnam eademq́ue communem ſectionem, &amp;</s>
  <s xml:id="echoid-s23844" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23845" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1226" type="float" level="2" n="4">
<note position="left" xlink:label="note-0375-04" xlink:href="note-0375-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0375-05" xlink:href="note-0375-05a" xml:space="preserve">Linea horizo@-<lb/>talis qua ratio-<lb/>ne deſcribatur.</note>
<note position="left" xlink:label="note-0375-06" xlink:href="note-0375-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s23846" xml:space="preserve">IDEM punctum B, reperiemus hac ratione. </s>
  <s xml:id="echoid-s23847" xml:space="preserve">Ex figura radiorum accipiemus portionẽ lineæ <lb/>
<anchor type="note" xlink:label="note-0375-07a" xlink:href="note-0375-07"/>
horæ 12. </s>
  <s xml:id="echoid-s23848" xml:space="preserve">ad mediam noctem pertinentis inter H, &amp; </s>
  <s xml:id="echoid-s23849" xml:space="preserve">radium diurnum horarum 24. </s>
  <s xml:id="echoid-s23850" xml:space="preserve">qualis in no-<lb/>ſtro exemplo eſt recta H I, eamq́ue ex H, centro horologij in portionem lineæ meridianæ, quæ ho <lb/>ram 12. </s>
  <s xml:id="echoid-s23851" xml:space="preserve">mediæ noctis, ſeu, (quod idem eſt) à meridie indicat, transferemus vſque ad B. </s>
  <s xml:id="echoid-s23852" xml:space="preserve">Per pun <lb/>ctum enim B, arcus diurni horarum 24. </s>
  <s xml:id="echoid-s23853" xml:space="preserve">ducenda erit linea horizontalis, ſeu horæ 24. </s>
  <s xml:id="echoid-s23854" xml:space="preserve">ab ortu, vel <lb/>occaſu, vt ex tabula 7. </s>
  <s xml:id="echoid-s23855" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s23856" xml:space="preserve">33. </s>
  <s xml:id="echoid-s23857" xml:space="preserve">primi libri conſtat.</s>
  <s xml:id="echoid-s23858" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1227" type="float" level="2" n="5">
<note position="right" xlink:label="note-0375-07" xlink:href="note-0375-07a" xml:space="preserve">Alia deſcriptio <lb/>lineæ horizon-<lb/>talis.</note>
</div>
<pb o="360" file="0376" n="376" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s23859" xml:space="preserve">HAEC autem horizontalis linea totum horologium dirimit in duo, ſuperius, &amp; </s>
  <s xml:id="echoid-s23860" xml:space="preserve">inferius, nec <lb/>non in diurnum, &amp; </s>
  <s xml:id="echoid-s23861" xml:space="preserve">nocturnum, vt de Verticali horologio, &amp; </s>
  <s xml:id="echoid-s23862" xml:space="preserve">alijs diximus. </s>
  <s xml:id="echoid-s23863" xml:space="preserve">Parallelos ergo, ſeu <lb/>arcus ſignorum Zodiaci in eodem horologio ad Horizontem inclinato poſuimus. </s>
  <s xml:id="echoid-s23864" xml:space="preserve">Quod fa-<lb/>ciendum erat.</s>
  <s xml:id="echoid-s23865" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1229" type="section" level="1" n="302">
<head xml:id="echoid-head312" xml:space="preserve">PROBLEMA 27. PROPOSITIO 27.</head>
<p>
  <s xml:id="echoid-s23866" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio ad <lb/>Horizontem inclinato locare.</s>
  <s xml:id="echoid-s23867" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſignorũ <lb/>in horologio <lb/>ad Horizõtem <lb/>inclinato.</note>
<p>
  <s xml:id="echoid-s23868" xml:space="preserve">SI loco parallelorum, qui per ſigna Zodiaci deſcribuntur, ſumantur paralleli arcuum diur-<lb/>norum, delineabuntur arcus diurni, vt arcus ſignorum, veluti in præcedentibus factum eſt. </s>
  <s xml:id="echoid-s23869" xml:space="preserve">Itaque <lb/>parallelos arcuum diurnorum in eodem horologio ad Horizontem inclinato locauimus. </s>
  <s xml:id="echoid-s23870" xml:space="preserve">Quod <lb/>erat faciendum.</s>
  <s xml:id="echoid-s23871" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1230" type="section" level="1" n="303">
<head xml:id="echoid-head313" xml:space="preserve">PROBLEMA 28. PROPOSITIO 28.</head>
<p>
  <s xml:id="echoid-s23872" xml:space="preserve">CIRCVLOS Verticales in eodem horologio inclinato ad Ho-<lb/>rizontem delineare.</s>
  <s xml:id="echoid-s23873" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s23874" xml:space="preserve">DVCATVR ex G, loco ſtyli ad meridianam lineam perpendicularis G A, ſtylo æqua<unsure/>lis, &amp; </s>
  <s xml:id="echoid-s23875" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0376-04a" xlink:href="note-0376-04"/>
in A, ad G A, conſtituatur angulus G A C, inclinationi plani æqualis, deorſum quidem in horo-<lb/>logio ſuperiori, ſurſum verò in inferiori, nempe in contrariam partem ei, in quam in propoſ. </s>
  <s xml:id="echoid-s23876" xml:space="preserve">26. <lb/></s>
  <s xml:id="echoid-s23877" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0376-01a" xlink:href="fig-0376-01"/>
<anchor type="note" xlink:label="note-0376-05a" xlink:href="note-0376-05"/>
<anchor type="note" xlink:label="note-0376-06a" xlink:href="note-0376-06"/>
<anchor type="note" xlink:label="note-0376-07a" xlink:href="note-0376-07"/>
huius libri recta A B, ducta eſt ad inueniendum punctum B, pro linea horizontali ducenda: </s>
  <s xml:id="echoid-s23878" xml:space="preserve">ſecet <lb/>autem recta A C, meridianam lineam in C. </s>
  <s xml:id="echoid-s23879" xml:space="preserve">Poſtea ductæ rectæ A B, abſcindatur æqualis B D, in <lb/>linea meridiana ſurſum, vel deorſum verſus: </s>
  <s xml:id="echoid-s23880" xml:space="preserve">Centro autem D, circulus deſcriptus in partes 360. <lb/></s>
  <s xml:id="echoid-s23881" xml:space="preserve">vel pauciores diuidatur, &amp; </s>
  <s xml:id="echoid-s23882" xml:space="preserve">per centrum D, &amp; </s>
  <s xml:id="echoid-s23883" xml:space="preserve">diuiſionum puncta rectæ emittantur ſecantes hori-<lb/>zontalem lineam in punctis, per quæ ſi ex C, rectæ emittantur, deſcripti erunt circuli Verticales, <lb/>nempe communes eorum, &amp; </s>
  <s xml:id="echoid-s23884" xml:space="preserve">plani horologij ſectiones, quarum principium ſtatuitur in Vertica-<lb/>li linea, quæ per punctum C, inuentum parallela ducitur lineæ æquinoctiali. </s>
  <s xml:id="echoid-s23885" xml:space="preserve">Quæ omnia ita <lb/>oſtendemus.</s>
  <s xml:id="echoid-s23886" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1230" type="float" level="2" n="1">
<note position="left" xlink:label="note-0376-04" xlink:href="note-0376-04a" xml:space="preserve">Deſcriptio cir-<lb/>culorum Verti <lb/>calium in eodẽ <lb/>horologio ad <lb/>Horizõtem in-<lb/>slinato.</note>
  <figure xlink:label="fig-0376-01" xlink:href="fig-0376-01a">
    <image file="0376-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0376-01"/>
  </figure>
<note position="left" xlink:label="note-0376-05" xlink:href="note-0376-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0376-06" xlink:href="note-0376-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0376-07" xlink:href="note-0376-07a" xml:space="preserve">50</note>
</div>
<pb o="361" file="0377" n="377" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s23887" xml:space="preserve">INTELLIGATVR triangulum A B C, ad planum horologij rectum, ita vt in plano Me <lb/>
<anchor type="note" xlink:label="note-0377-01a" xlink:href="note-0377-01"/>
ridiani iaceat, vertexq́ue ſtyli A, idem ſit, quod centrum mundi. </s>
  <s xml:id="echoid-s23888" xml:space="preserve">Et quia, vt in propoſ. </s>
  <s xml:id="echoid-s23889" xml:space="preserve">26. </s>
  <s xml:id="echoid-s23890" xml:space="preserve">huius li-<lb/>bri demonſtrauimus, recta A B communis ſectio eſt Horizontis, ac Meridiani; </s>
  <s xml:id="echoid-s23891" xml:space="preserve">eſtq́ue angulus <lb/>B A C, rectus, quippe qui ex angulo inclinationis G A C, &amp; </s>
  <s xml:id="echoid-s23892" xml:space="preserve">angulo complementi inclinationis <lb/>G A B, componatur; </s>
  <s xml:id="echoid-s23893" xml:space="preserve">erit recta A C, communis ſectio Verticalis proprie dicti, &amp; </s>
  <s xml:id="echoid-s23894" xml:space="preserve">Meridiani, ita vt <lb/>C, punctum ſit Verticale, in quod nimirum axis Horizontis cadit. </s>
  <s xml:id="echoid-s23895" xml:space="preserve">Quoniam enim tam Meridia-<lb/>nus, quàm Verticalis ad Horizontem rectus eſt, erit eorum communis ſectio (nempe axis Hori-<lb/>zontis) ad eundem Horizontem recta; </s>
  <s xml:id="echoid-s23896" xml:space="preserve">atque adeo per defin. </s>
  <s xml:id="echoid-s23897" xml:space="preserve">3. </s>
  <s xml:id="echoid-s23898" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s23899" xml:space="preserve">11. </s>
  <s xml:id="echoid-s23900" xml:space="preserve">Euclidis, ad rectam A B, in <lb/>
<anchor type="note" xlink:label="note-0377-02a" xlink:href="note-0377-02"/>
Horizonte exiſtentem perpendicularis in centro mundi A. </s>
  <s xml:id="echoid-s23901" xml:space="preserve">Recta igitur A C, in plano Meridiani <lb/>perpendicularis exiſtens ad A B, communis ſectio eſt Meridiani, &amp; </s>
  <s xml:id="echoid-s23902" xml:space="preserve">Verticalis propriè dicti, ac pro-<lb/>
<anchor type="note" xlink:label="note-0377-03a" xlink:href="note-0377-03"/>
inde &amp; </s>
  <s xml:id="echoid-s23903" xml:space="preserve">omnium Verticalium. </s>
  <s xml:id="echoid-s23904" xml:space="preserve">Quod etiam inde manifeſtum eſſe poteſt, quòd angulus A C G, cõ-<lb/>plemento inclinationis æqualis eſt, qualem nimirum facit planum inclinatum cum Verticali. </s>
  <s xml:id="echoid-s23905" xml:space="preserve">Iam <lb/>verò ſi circulus ex D, deſcriptus intelligatur moueri circa horizontalem lineam, donec centrum <lb/>eius D, cum centro mundi A, &amp; </s>
  <s xml:id="echoid-s23906" xml:space="preserve">recta B D, cum recta B A, coniungatur, ob æqualitatem rectarum <lb/>B D, B A, iacebit dictus circulus in plano Horizontis circa eius centrum deſcriptus. </s>
  <s xml:id="echoid-s23907" xml:space="preserve">Quare cum <lb/>Verticales circuli ſecent Horizontem, atque adeò &amp; </s>
  <s xml:id="echoid-s23908" xml:space="preserve">circulum ex D, deſcriptũ illi concentricum, <lb/>in partes æquales, initio facto à Verticali, vel Meridiano, qui vnus etiam eſt ex Verticalibus circu-<lb/>lis, erunt rectæ per D, &amp; </s>
  <s xml:id="echoid-s23909" xml:space="preserve">per puncta diuiſionum ductæ, communes ſectiones Verticalium circu-<lb/>lorum, &amp; </s>
  <s xml:id="echoid-s23910" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s23911" xml:space="preserve">Igitur Verticales circuli plano horologij occurrent in punctis lineæ hori-<lb/>zontalis, in quæ dictæ rectæ cadunt, ac proinde per illa puncta ducendæ erunt communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0377-04a" xlink:href="note-0377-04"/>
nes Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s23912" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s23913" xml:space="preserve">Cum ergo eædem ſectiones coeant omnes quo-<lb/>que in C, puncto, per propoſ. </s>
  <s xml:id="echoid-s23914" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23915" xml:space="preserve">primi libri, in quod cadit axis Horizontis, ſeu eorum ſectio cõ-<lb/>munis, erunt rectæ per C, &amp; </s>
  <s xml:id="echoid-s23916" xml:space="preserve">per puncta inuenta in linea horizontali ductæ communes ſectiones <lb/>Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s23917" xml:space="preserve">plani horologij. </s>
  <s xml:id="echoid-s23918" xml:space="preserve">Communis porrò ſectio Verticalis proprie dicti, &amp; </s>
  <s xml:id="echoid-s23919" xml:space="preserve"><lb/>plani horologii per C, ducta, parallela eſt, ex eadem propoſ. </s>
  <s xml:id="echoid-s23920" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23921" xml:space="preserve">primi libri, lineæ ęquinoctiali, <lb/>vel etiam horizontali; </s>
  <s xml:id="echoid-s23922" xml:space="preserve">propterea quòd Aequator, Horizon, Verticalis proprie dictus, &amp; </s>
  <s xml:id="echoid-s23923" xml:space="preserve">circulus <lb/>maximus, cui horologium æquidiſtat, vnam eandemq́ue communem ſectionem habeant. </s>
  <s xml:id="echoid-s23924" xml:space="preserve">Quo-<lb/>circa circulos Verticales in eodem horologio inclinato ad Horizontem delineauimus. </s>
  <s xml:id="echoid-s23925" xml:space="preserve">Quod <lb/>erat faciendum.</s>
  <s xml:id="echoid-s23926" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1231" type="float" level="2" n="2">
<note position="right" xlink:label="note-0377-01" xlink:href="note-0377-01a" xml:space="preserve">Demonſtratio <lb/>de@cripti@is cir <lb/>culorum Verti <lb/>calium.</note>
<note position="right" xlink:label="note-0377-02" xlink:href="note-0377-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0377-03" xlink:href="note-0377-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0377-04" xlink:href="note-0377-04a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1233" type="section" level="1" n="304">
<head xml:id="echoid-head314" xml:space="preserve">PROBLEMA 29. PROPOSITIO 29.</head>
<p>
  <s xml:id="echoid-s23927" xml:space="preserve">PARALLELOS Horizontis in eodem horologio ad Horizon-<lb/>tem inclinato depingere.</s>
  <s xml:id="echoid-s23928" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23929" xml:space="preserve">IN hoc horologio parallelos Horizontis ita deſcribemus, vt in polari horologio propoſ. </s>
  <s xml:id="echoid-s23930" xml:space="preserve">41. </s>
  <s xml:id="echoid-s23931" xml:space="preserve">ſu-<lb/>
<anchor type="note" xlink:label="note-0377-06a" xlink:href="note-0377-06"/>
<anchor type="figure" xlink:label="fig-0377-01a" xlink:href="fig-0377-01"/>
perioris libri, paucis mutatis. </s>
  <s xml:id="echoid-s23932" xml:space="preserve">Nam loco axis <lb/>E F, (quod ad priorem rationem attinet) du-<lb/>cenda erit E F, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s23933" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0377-07a" xlink:href="note-0377-07"/>
plani inclinati, ita vt arcus C E, inclinatio-<lb/>nem plani ſupra Horizontem metiatur; </s>
  <s xml:id="echoid-s23934" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23935" xml:space="preserve"><lb/>huic communi ſectioni E F, ducenda paralle-<lb/>la Q R, vt ibi, pro data ſtyli magnitudine. <lb/></s>
  <s xml:id="echoid-s23936" xml:space="preserve">Deinde puncta K, L, M, N, O, ex puncto T, <lb/>accepta, vbi Horizon B C, rectam Q R, ſe-<lb/>cat, transferenda erunt in lineam meridia-<lb/>nam horologii ex B, puncto Horizontis, ver-<lb/>ſus punctum Verticale C, in horologio ſupe-<lb/>riori: </s>
  <s xml:id="echoid-s23937" xml:space="preserve">in inferiori vero interualla T S, &amp; </s>
  <s xml:id="echoid-s23938" xml:space="preserve">alia, <lb/>
<anchor type="note" xlink:label="note-0377-08a" xlink:href="note-0377-08"/>
ſi qua fuerint, ex B, transferenda erunt in al-<lb/>teram partem meridiane lineæ, &amp;</s>
  <s xml:id="echoid-s23939" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23940" xml:space="preserve">Demon-<lb/>ſtratio eadem omnino eſt, quæ in propoſ. </s>
  <s xml:id="echoid-s23941" xml:space="preserve">41. <lb/></s>
  <s xml:id="echoid-s23942" xml:space="preserve">ſuperioris libri, ſi Meridianus Analemmatis <lb/>A B C, in propria poſitione intelligatur eſſe <lb/>conſtitutus, ita vt punctum C, ad boream, ſi <lb/>planum ex parte ſeptentrionali eleuetur, ſpe-<lb/>ctet; </s>
  <s xml:id="echoid-s23943" xml:space="preserve">ad auſtrum verò, ſi ex auſtrali parte at-<lb/>tollatur, vt in noſtro exemplo, &amp;</s>
  <s xml:id="echoid-s23944" xml:space="preserve">c.</s>
  <s xml:id="echoid-s23945" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1233" type="float" level="2" n="1">
<note position="right" xlink:label="note-0377-06" xlink:href="note-0377-06a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis in eo-<lb/>dem horologio <lb/>ad Horizontẽ <lb/>inclinato.</note>
  <figure xlink:label="fig-0377-01" xlink:href="fig-0377-01a">
    <image file="0377-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0377-01"/>
  </figure>
<note position="left" xlink:label="note-0377-07" xlink:href="note-0377-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0377-08" xlink:href="note-0377-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s23946" xml:space="preserve">QVOD verò ſpectat ad poſteriorem viam, ſumenda eſt A D, æqualis axi Horizontis A C, in <lb/>figura præcedentis propoſ. </s>
  <s xml:id="echoid-s23947" xml:space="preserve">hoc eſt, rectæ, quæ ex A, vertice ſtyli in C, Zenith cadit; </s>
  <s xml:id="echoid-s23948" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s23949" xml:space="preserve">in rectam
<pb o="362" file="0378" n="378" rhead="GNOMONICES"/>
A B, transferenda omnia interualla inter D, &amp; </s>
  <s xml:id="echoid-s23950" xml:space="preserve">lineas Verticales in horizontali linea. </s>
  <s xml:id="echoid-s23951" xml:space="preserve">Reliqua au-<lb/>tem perficienda, vt in propoſ. </s>
  <s xml:id="echoid-s23952" xml:space="preserve">41. </s>
  <s xml:id="echoid-s23953" xml:space="preserve">præcedentis libri dictum eſt. </s>
  <s xml:id="echoid-s23954" xml:space="preserve">Eadem enim demonſtratio hua<unsure/> <lb/>
<anchor type="figure" xlink:label="fig-0378-01a" xlink:href="fig-0378-01"/>
<anchor type="note" xlink:label="note-0378-01a" xlink:href="note-0378-01"/>
<anchor type="note" xlink:label="note-0378-02a" xlink:href="note-0378-02"/>
<anchor type="note" xlink:label="note-0378-03a" xlink:href="note-0378-03"/>
accommodari poteſt. </s>
  <s xml:id="echoid-s23955" xml:space="preserve">Parallelos igitur Horizontis in eodem horologio ad Horizontem inclina-<lb/>to depinximus. </s>
  <s xml:id="echoid-s23956" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23957" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1234" type="float" level="2" n="2">
  <figure xlink:label="fig-0378-01" xlink:href="fig-0378-01a">
    <image file="0378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0378-01"/>
  </figure>
<note position="left" xlink:label="note-0378-01" xlink:href="note-0378-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0378-02" xlink:href="note-0378-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0378-03" xlink:href="note-0378-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1236" type="section" level="1" n="305">
<head xml:id="echoid-head315" xml:space="preserve">PROBLEMA 30. PROPOSITIO 30.</head>
<p>
  <s xml:id="echoid-s23958" xml:space="preserve">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in eo-<lb/>dem horologio ad Horizontem inclinato diſponere.</s>
  <s xml:id="echoid-s23959" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23960" xml:space="preserve">NON aliter hic, atque in antecedentibus horologijs, Meridianos deſcribemus; </s>
  <s xml:id="echoid-s23961" xml:space="preserve">ſi nimirum <lb/>
<anchor type="note" xlink:label="note-0378-04a" xlink:href="note-0378-04"/>
<anchor type="note" xlink:label="note-0378-05a" xlink:href="note-0378-05"/>
in circulo ex E, deſcripto in propoſ. </s>
  <s xml:id="echoid-s23962" xml:space="preserve">25. </s>
  <s xml:id="echoid-s23963" xml:space="preserve">huius libri, à communi ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s23964" xml:space="preserve">Aequato-<lb/>ris E I, verſus partes occidentales numeretur loci longitudo vſque ad punctum O, initio facto à <lb/>puncto illius ſectionis, quod meridiem reſpicit, quale eſt in noſtro exemplo punctum M, in ſupe-<lb/>riori horologio; </s>
  <s xml:id="echoid-s23965" xml:space="preserve">vt patet, ſi circulus dictus in propria poſitione concipiatur eſſe collocatus. </s>
  <s xml:id="echoid-s23966" xml:space="preserve">Nam <lb/>recta occulta per centrum E, ex N, puncto, quod puncto O, inſularum Fortunatarum opponitur, <lb/>ducta dabit in linea æquinoctiali Meridianum grad. </s>
  <s xml:id="echoid-s23967" xml:space="preserve">180. </s>
  <s xml:id="echoid-s23968" xml:space="preserve">nempe ſemicirculum oppoſitum ſemi-<lb/>circulo per inſulas Fortunatas ducto: </s>
  <s xml:id="echoid-s23969" xml:space="preserve">ſed Meridianus hic vltra centrum horologij H, productus <lb/>dabit oppoſitum ſemicirculum, qui nimirum per Inſulas Fortunatas incedit, per ea, <lb/>quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s23970" xml:space="preserve">1. </s>
  <s xml:id="echoid-s23971" xml:space="preserve">ſuperioris libri ſcripſimus. </s>
  <s xml:id="echoid-s23972" xml:space="preserve">Cætera patent ex ſi-<lb/>
<anchor type="note" xlink:label="note-0378-06a" xlink:href="note-0378-06"/>
gura. </s>
  <s xml:id="echoid-s23973" xml:space="preserve">Vbi etiam vides in inferiori horologio Meridianis appoſitos <lb/>eſſe numeros, qui fiunt ex additione grad. </s>
  <s xml:id="echoid-s23974" xml:space="preserve">180. </s>
  <s xml:id="echoid-s23975" xml:space="preserve">ad numeros <lb/>Meridianorum ſuperioris horologij, &amp;</s>
  <s xml:id="echoid-s23976" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23977" xml:space="preserve">vt in <lb/>propoſ. </s>
  <s xml:id="echoid-s23978" xml:space="preserve">18. </s>
  <s xml:id="echoid-s23979" xml:space="preserve">ſuperioris libri declaraui-<lb/>mus. </s>
  <s xml:id="echoid-s23980" xml:space="preserve">Meridianos ergo, ſeu cir <lb/>culos longitudinum, &amp;</s>
  <s xml:id="echoid-s23981" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s23982" xml:space="preserve">diſpoſuimus. </s>
  <s xml:id="echoid-s23983" xml:space="preserve">Quod <lb/>faciendum <lb/>erat.</s>
  <s xml:id="echoid-s23984" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1236" type="float" level="2" n="1">
<note position="left" xlink:label="note-0378-04" xlink:href="note-0378-04a" xml:space="preserve">Deſcriptio Me <lb/>ridianorum in <lb/>eodem horolo-<lb/>gio ad Horizon <lb/>tem inclinato.</note>
<note position="left" xlink:label="note-0378-05" xlink:href="note-0378-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0378-06" xlink:href="note-0378-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1238" type="section" level="1" n="306">
<head xml:id="echoid-head316" xml:space="preserve">SEQVITVR FIGVRA.</head>
<pb o="363" file="0379" n="379" rhead="LIBER TERTIVS."/>
  <figure>
    <image file="0379-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0379-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1239" type="section" level="1" n="307">
<head xml:id="echoid-head317" xml:space="preserve">PROBLEMA 31. PROPOSITIO 31.</head>
<p>
  <s xml:id="echoid-s23985" xml:space="preserve">PARALLELOS ciuitatum, circulosve latitudinum, in eodem <lb/>horologio ad Horizontem inclinato figurare.</s>
  <s xml:id="echoid-s23986" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s23987" xml:space="preserve">QVONIAM Paralleli per vertices locorum ducti Aequatori æquidiſtant, quemadmodum <lb/>
<anchor type="note" xlink:label="note-0379-05a" xlink:href="note-0379-05"/>
<anchor type="note" xlink:label="note-0379-06a" xlink:href="note-0379-06"/>
&amp; </s>
  <s xml:id="echoid-s23988" xml:space="preserve">paralleli ſignorum, liquido conſtat, eandem eſſe illorum deſcriptionem, &amp; </s>
  <s xml:id="echoid-s23989" xml:space="preserve">horum, vt in præce-<lb/>dentibus monuimus. </s>
  <s xml:id="echoid-s23990" xml:space="preserve">Igitur parallelos ciuitatum, circulosve latitudinum, &amp;</s>
  <s xml:id="echoid-s23991" xml:space="preserve">c. </s>
  <s xml:id="echoid-s23992" xml:space="preserve">figurauimus. <lb/></s>
  <s xml:id="echoid-s23993" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s23994" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1239" type="float" level="2" n="1">
<note position="left" xlink:label="note-0379-05" xlink:href="note-0379-05a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0379-06" xlink:href="note-0379-06a" xml:space="preserve">Deſcriptio cit-<lb/>culorum latitu<unsure/> <lb/>dinum in eod@ <lb/>horologio ad <lb/>Horizontem in <lb/>clinato.</note>
</div>
</div>
<div xml:id="echoid-div1241" type="section" level="1" n="308">
<head xml:id="echoid-head318" xml:space="preserve">PROBLEMA 32. PROPOSITIO 32.</head>
<p>
  <s xml:id="echoid-s23995" xml:space="preserve">DOMOS cœleſtes in horologio eodem ad Horizontem incli-<lb/>
<anchor type="note" xlink:label="note-0379-07a" xlink:href="note-0379-07"/>
nato fabricare.</s>
  <s xml:id="echoid-s23996" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1241" type="float" level="2" n="1">
<note position="right" xlink:label="note-0379-07" xlink:href="note-0379-07a" xml:space="preserve">Domorum cœ-<lb/>le<unsure/>ſtium deſcri-<lb/>ptio ſecuudum <lb/>loan. Regiom. <lb/>in eodem horo <lb/>logio ad Hori-<lb/>zontem inclina <lb/>to.</note>
</div>
<p>
  <s xml:id="echoid-s23997" xml:space="preserve">DISTRIBVATVR circulus ex E, deſcriptus, beneficio cuius in propoſ. </s>
  <s xml:id="echoid-s23998" xml:space="preserve">25. </s>
  <s xml:id="echoid-s23999" xml:space="preserve">huius libri ho <lb/>rologium Aſtronomicum conſtruximus, in 12. </s>
  <s xml:id="echoid-s24000" xml:space="preserve">partes æquales, initio facto à meridiana linea. </s>
  <s xml:id="echoid-s24001" xml:space="preserve">Nã
<pb o="364" file="0380" n="380" rhead="GNOMONICES"/>
rectæ ex centro E, per diuiſionum puncta emiſſæ dabunt in linea æquinoctiali puncta, per quæ ſi <lb/>ex B, puncto, vbi meridiana linea, &amp; </s>
  <s xml:id="echoid-s24002" xml:space="preserve">horizontalis ſe mutuo interſecant, rectæ educantur, habe-<lb/>buntur communes ſectiones plani horologij, &amp; </s>
  <s xml:id="echoid-s24003" xml:space="preserve">circulorum maximorum per domorum initia du <lb/>ctorum, &amp; </s>
  <s xml:id="echoid-s24004" xml:space="preserve">ex ſententia Ioan. </s>
  <s xml:id="echoid-s24005" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s24006" xml:space="preserve">qui huiuſmodi circulos per diuiſiones Aequatoris ducit. <lb/></s>
  <s xml:id="echoid-s24007" xml:space="preserve">Si enim circulus ex E, deſcriptus intelligatur in plano Aequatoris potitus, ita vt eius centrum E, à <lb/>centro mundi non differat, &amp; </s>
  <s xml:id="echoid-s24008" xml:space="preserve">E I, ſit communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s24009" xml:space="preserve">Meridiani; </s>
  <s xml:id="echoid-s24010" xml:space="preserve">erunt rectæ ex E, <lb/>per puncta diuiſionum eiuſdem circuli emiſſæ, communes ſectiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s24011" xml:space="preserve">circulorum <lb/>domorum cœleſtium, ſecundum Ioan. </s>
  <s xml:id="echoid-s24012" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s24013" xml:space="preserve">quandoquidem Æquatorem, atqueadeò &amp; </s>
  <s xml:id="echoid-s24014" xml:space="preserve">circu <lb/>lum illum ſibi concentricum, in 12. </s>
  <s xml:id="echoid-s24015" xml:space="preserve">partes æquales partiuntur. </s>
  <s xml:id="echoid-s24016" xml:space="preserve">Occurrent igitur circuli domorũ <lb/>cœleſtium plano horologij in punctis æquinoctialis lineæ, in quæ illæ rectæ ex E, ductæ cadunt, <lb/>
<anchor type="note" xlink:label="note-0380-01a" xlink:href="note-0380-01"/>
ideoq́ue per ea puncta lineæ domorum cœleſtium ducendæ erunt, nempe communes ſectiones <lb/>plani horologij, &amp; </s>
  <s xml:id="echoid-s24017" xml:space="preserve">circulorum domorum cœleſtium. </s>
  <s xml:id="echoid-s24018" xml:space="preserve">Cum ergo cædem tranſeant, per propoſ. <lb/></s>
  <s xml:id="echoid-s24019" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24020" xml:space="preserve">primi libri, per punctum B, in quod cadit axis Verticalis A B, in quo omnes circuli domo-<lb/>rum cœleſtium ſe ſecant, perſpicuum eſt, rectas ex B, per puncta inuenta in linea æquínoctiali du <lb/>ctas, eſſe lineas cœleſtium domorum.</s>
  <s xml:id="echoid-s24021" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1242" type="float" level="2" n="2">
<note position="left" xlink:label="note-0380-01" xlink:href="note-0380-01a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">Deſcriptio do-<lb/>morum cœle-<lb/>ſtium ſecundũ <lb/>Campanum in <lb/>eodem horolo-<lb/>gio ad Horizõ-<lb/>tem inclinato.</note>
<p>
  <s xml:id="echoid-s24022" xml:space="preserve">DOMOS autem cœleſtes, prout à Campano intelliguntur, ita fabricabimus. </s>
  <s xml:id="echoid-s24023" xml:space="preserve">Ex loco ſtyli <lb/>
<anchor type="figure" xlink:label="fig-0380-01a" xlink:href="fig-0380-01"/>
<anchor type="note" xlink:label="note-0380-03a" xlink:href="note-0380-03"/>
<anchor type="note" xlink:label="note-0380-04a" xlink:href="note-0380-04"/>
<anchor type="note" xlink:label="note-0380-05a" xlink:href="note-0380-05"/>
<anchor type="note" xlink:label="note-0380-06a" xlink:href="note-0380-06"/>
G, ducta ad meridianam lineam perpendiculari G A, quæ gnomoni æqualis ſit, conſtituatur in A, <lb/>ad A G, angulus inclinationis G A C, ita vt per ea, quæ in propoſ. </s>
  <s xml:id="echoid-s24024" xml:space="preserve">28. </s>
  <s xml:id="echoid-s24025" xml:space="preserve">huius libri demõſtrauimus,
<pb o="365" file="0381" n="381" rhead="LIBER TERTIVS."/>
A C, ſit axis Horizontis, &amp; </s>
  <s xml:id="echoid-s24026" xml:space="preserve">C, punctum Verticale; </s>
  <s xml:id="echoid-s24027" xml:space="preserve">recta autem per C, ducta ad meridianam li-<lb/>neam perpendicularis, communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s24028" xml:space="preserve">Verticalis. </s>
  <s xml:id="echoid-s24029" xml:space="preserve">Sumpta deinde recta C D, <lb/>æquali ipſi C A, deſcribatur ex D, circulus, quo in partes 12. </s>
  <s xml:id="echoid-s24030" xml:space="preserve">æquales ſecto, initio facto à meridia-<lb/>na linea, ducantur ex D, per diuiſionum puncta lineæ rectæ ſecãtes Verticalem lineam in punctis, <lb/>quæ cũ puncto B, vt prius, coniuncta dabunt lineas cœleſtium domorũ, vt eas ſumit Campanus; <lb/></s>
  <s xml:id="echoid-s24031" xml:space="preserve">cuiuſmodi ſunt lineæ minutis illis lineis diſtinctæ in noſtro exemplo. </s>
  <s xml:id="echoid-s24032" xml:space="preserve">Si namque triangulum <lb/>G A C, intelligatur rectum ad planum horologij, &amp; </s>
  <s xml:id="echoid-s24033" xml:space="preserve">circulus ex D, deſcriptus circa Verticalem <lb/>lineam moueri, donec centrum D, cum A, centro mundi coniungatur, ob æqualitatem rectarum <lb/>C A, C D, erit circulus ex D, deſcriptus in plano circuli Verticalis idem cum ipſo habens centrũ. </s>
  <s xml:id="echoid-s24034" xml:space="preserve"><lb/>Quare rectæ ex D, emiſſæ per puncta diuiſionum erunt communes ſectiones Verticalis, &amp; </s>
  <s xml:id="echoid-s24035" xml:space="preserve">circulo <lb/>
<anchor type="note" xlink:label="note-0381-01a" xlink:href="note-0381-01"/>
rum domorum cœleſtium; </s>
  <s xml:id="echoid-s24036" xml:space="preserve">atque adeo horologij planum in illis punctis Verticalis lineę, in quæ <lb/>dictæ rectæ cadunt, ſecabitur à circulis domorum cœleſtium, &amp;</s>
  <s xml:id="echoid-s24037" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24038" xml:space="preserve">Itaque domos cœleſtes in horo <lb/>logio eodem ad Horizontem inclinato fabricauimus. </s>
  <s xml:id="echoid-s24039" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s24040" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1243" type="float" level="2" n="3">
  <figure xlink:label="fig-0380-01" xlink:href="fig-0380-01a">
    <image file="0380-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0380-01"/>
  </figure>
<note position="left" xlink:label="note-0380-03" xlink:href="note-0380-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0380-04" xlink:href="note-0380-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0380-05" xlink:href="note-0380-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0380-06" xlink:href="note-0380-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0381-01" xlink:href="note-0381-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1245" type="section" level="1" n="309">
<head xml:id="echoid-head319" xml:space="preserve">PROBLEMA 33. PROPOSITIO 33.</head>
<p>
  <s xml:id="echoid-s24041" xml:space="preserve">SIGNA aſcendentia Zodiaci in eodem horologio ad Horizontem <lb/>inclinato deſignare.</s>
  <s xml:id="echoid-s24042" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s24043" xml:space="preserve">DESIGNABIMVS ſigna Zodiaci aſcendentia eiſdem prorſus vijs, quibus in præcedenti-<lb/>
<anchor type="note" xlink:label="note-0381-03a" xlink:href="note-0381-03"/>
bus vſi ſumus, vt in ſubiecta figura apparet. </s>
  <s xml:id="echoid-s24044" xml:space="preserve">Vt exempli gratia, ſi in ſuperiori horologio deſcri-<lb/>
<anchor type="figure" xlink:label="fig-0381-01a" xlink:href="fig-0381-01"/>
<anchor type="note" xlink:label="note-0381-04a" xlink:href="note-0381-04"/>
<anchor type="note" xlink:label="note-0381-05a" xlink:href="note-0381-05"/>
<anchor type="note" xlink:label="note-0381-06a" xlink:href="note-0381-06"/>
bendum ſit ſignum ♉, aſcendens. </s>
  <s xml:id="echoid-s24045" xml:space="preserve">Video in 1. </s>
  <s xml:id="echoid-s24046" xml:space="preserve">tabula propoſ. </s>
  <s xml:id="echoid-s24047" xml:space="preserve">9. </s>
  <s xml:id="echoid-s24048" xml:space="preserve">ſuperioris libri, illud, Sole exi-<lb/>ſtente in principio ♈, aſcendere hora 4. </s>
  <s xml:id="echoid-s24049" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24050" xml:space="preserve">51. </s>
  <s xml:id="echoid-s24051" xml:space="preserve">ante meridiem. </s>
  <s xml:id="echoid-s24052" xml:space="preserve">Sed quia eiuſmodi hora æqui <lb/>noctialem lineam non ſecat, quæro idem ſignum in 2. </s>
  <s xml:id="echoid-s24053" xml:space="preserve">tabula, &amp; </s>
  <s xml:id="echoid-s24054" xml:space="preserve">reperio illud, Sole exiſtente in <lb/>principio ♎, aſcendere hora 7. </s>
  <s xml:id="echoid-s24055" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24056" xml:space="preserve">8. </s>
  <s xml:id="echoid-s24057" xml:space="preserve">poſt meridiem, quæ quidem hora æquinoctialem lineã
<pb o="366" file="0382" n="382" rhead="GNOMONICES"/>
ſecat. </s>
  <s xml:id="echoid-s24058" xml:space="preserve">Per hanc ergo horam inuenio punctum in linea æquinoctiali, per quod ducendum eſt ſi-<lb/>gnum ♉, aſcendens. </s>
  <s xml:id="echoid-s24059" xml:space="preserve">Deinde ex 3. </s>
  <s xml:id="echoid-s24060" xml:space="preserve">tabula, Sole exiſtente in principio ♋, reperio idem ſignum <lb/>♉, aſcendere hora 10. </s>
  <s xml:id="echoid-s24061" xml:space="preserve">Min 50. </s>
  <s xml:id="echoid-s24062" xml:space="preserve">ante meridiem, hoc eſt, hora 1. </s>
  <s xml:id="echoid-s24063" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24064" xml:space="preserve">10. </s>
  <s xml:id="echoid-s24065" xml:space="preserve">poſt mediam noctem, <lb/>atque ita per hanc horam offendo punctum in arcu ♋, per quod ducendum eſt idem ſignum. <lb/></s>
  <s xml:id="echoid-s24066" xml:space="preserve">Linea ergo recta connectens hoc punctum cum priori in linea æquinoctiali inuẽto dabit ſignum <lb/>aſcendens ♉, &amp; </s>
  <s xml:id="echoid-s24067" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s24068" xml:space="preserve">Per eaſdem tabulas commodiſſimè eadem ſigna aſcendentia deli-<lb/>neabuntur in horologio inferiori, in quo arcus ♋, mutatur in arcum ♑. </s>
  <s xml:id="echoid-s24069" xml:space="preserve">Vt idem ſignum ♉, in <lb/>inferiori horologio ducendum erit in linea æquinoctiali per horam 4. </s>
  <s xml:id="echoid-s24070" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24071" xml:space="preserve">51. </s>
  <s xml:id="echoid-s24072" xml:space="preserve">ante meridiem, <lb/>vt ex 1. </s>
  <s xml:id="echoid-s24073" xml:space="preserve">tabula colligitur, &amp; </s>
  <s xml:id="echoid-s24074" xml:space="preserve">in tropico ♑, per horam 1. </s>
  <s xml:id="echoid-s24075" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24076" xml:space="preserve">10. </s>
  <s xml:id="echoid-s24077" xml:space="preserve">poſt meridiem, vt vult quarta <lb/>tabula, &amp;</s>
  <s xml:id="echoid-s24078" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24079" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1245" type="float" level="2" n="1">
<note position="right" xlink:label="note-0381-03" xlink:href="note-0381-03a" xml:space="preserve">Signorum aſc@ <lb/>dentium in eo <lb/>dem horologio <lb/>ad Horizó<unsure/>tem <lb/>inclinato de-<lb/>ſcriptio.</note>
  <figure xlink:label="fig-0381-01" xlink:href="fig-0381-01a">
    <image file="0381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0381-01"/>
  </figure>
<note position="left" xlink:label="note-0381-04" xlink:href="note-0381-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0381-05" xlink:href="note-0381-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0381-06" xlink:href="note-0381-06a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s24080" xml:space="preserve">PVNCTA autem in linea horizontali, per quæ tranſeunt arcus ſignorum, itemq́ue lineæ <lb/>
<anchor type="note" xlink:label="note-0382-02a" xlink:href="note-0382-02"/>
aſcendentium ſignorum, vt in ſuperioribus dictum eſt, ita deprehendemus. </s>
  <s xml:id="echoid-s24081" xml:space="preserve">In figura radiorum <lb/>latitudinum ortiuarum propoſ. </s>
  <s xml:id="echoid-s24082" xml:space="preserve">9 huius libri ex recta E B, ſi horologium ſeptentrionem reſpicit, <lb/>vel ex E D, ſi ad meridiem ſpectat, auferatur recta E L, æqualis rectæ A B, per quam in figura pro-<lb/>poſ. </s>
  <s xml:id="echoid-s24083" xml:space="preserve">26. </s>
  <s xml:id="echoid-s24084" xml:space="preserve">huius libri punctum B, per quod horizontalis linea ducitur, inuenimus; </s>
  <s xml:id="echoid-s24085" xml:space="preserve">atque per L, ad <lb/>rectam B D, perpendicularis in vtramque partem educatur, quæ radios latitudinum ortiuarum <lb/>&amp; </s>
  <s xml:id="echoid-s24086" xml:space="preserve">occiduarum ſecabit in punctis, quæ beneficio circini accepta ex L, &amp; </s>
  <s xml:id="echoid-s24087" xml:space="preserve">in lineam horizontalem <lb/>translata ex puncto B, dabunt puncta, per quæ tranſire debent paralleli ſignorum. </s>
  <s xml:id="echoid-s24088" xml:space="preserve">Nam quia, ſi <lb/>triangulum A B G, in figura propoſ. </s>
  <s xml:id="echoid-s24089" xml:space="preserve">26. </s>
  <s xml:id="echoid-s24090" xml:space="preserve">huius libri intelligatur eſſe rectum ad horologii planum, <lb/>recta A B, eſt communis ſectio Horizontis, ac Meridiani, fit vt ſi Horizon A B C D, in figura pro-<lb/>
<anchor type="note" xlink:label="note-0382-03a" xlink:href="note-0382-03"/>
poſ. </s>
  <s xml:id="echoid-s24091" xml:space="preserve">9. </s>
  <s xml:id="echoid-s24092" xml:space="preserve">huius libri, in quo radij latitudinum ortiuarum continentur, intelligatur poni in horolo-<lb/>gio, ita vt centrum eius E, centro mundi A, congruat, &amp; </s>
  <s xml:id="echoid-s24093" xml:space="preserve">recta E L, rectæ A B, punctum L, cadat <lb/>in punctum B, ob æqualitatem rectarum E L, A B; </s>
  <s xml:id="echoid-s24094" xml:space="preserve">atque adeò &amp; </s>
  <s xml:id="echoid-s24095" xml:space="preserve">perpendicularis per L, ducta <lb/>horizontali lineæ congruat, &amp;</s>
  <s xml:id="echoid-s24096" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24097" xml:space="preserve">Eadem quoque puncta in horizontali linea inueniri poſſunt ex <lb/>tabella 5. </s>
  <s xml:id="echoid-s24098" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24099" xml:space="preserve">9. </s>
  <s xml:id="echoid-s24100" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24101" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24102" xml:space="preserve">vt etiam in ſuperioribus factum eſt.</s>
  <s xml:id="echoid-s24103" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1246" type="float" level="2" n="2">
<note position="left" xlink:label="note-0382-02" xlink:href="note-0382-02a" xml:space="preserve">Inuentio pun-<lb/>ctorum in linea <lb/>horizontali, per <lb/>quę arcus ſigno <lb/>rum ducendi <lb/>ſunt.</note>
<note position="left" xlink:label="note-0382-03" xlink:href="note-0382-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s24104" xml:space="preserve">QVONIAM verò, Sole exiſtente in principio ♋, cuius arcus in noſtro exemplo Ellipſis eſt, <lb/>
<anchor type="note" xlink:label="note-0382-04a" xlink:href="note-0382-04"/>
vt oſtendimus ſupra, ſignum ♈, oritur, cum principium ♋, in Meridiano circulo exiſtit ſub Ho-<lb/>rizonte, hoc eſt, hora 12. </s>
  <s xml:id="echoid-s24105" xml:space="preserve">mediæ noctis, ducenda erit linea ♈, per punctum lineæ meridianæ ſu-<lb/>pra lineam horizontalem, per quod arcus ♋, tranſit: </s>
  <s xml:id="echoid-s24106" xml:space="preserve">hoc enim punctum ad mediam noctem per-<lb/>tinet. </s>
  <s xml:id="echoid-s24107" xml:space="preserve">Rurſus quia, Sole in principio ♋, exiſtente, ſignum ♎, oritur, cum principium ♋, in meri-<lb/>
<anchor type="note" xlink:label="note-0382-05a" xlink:href="note-0382-05"/>
die ſtatuitur, ducenda erit linea ♎, per aliud punctum lineæ horizontalis infra horizontalem li-<lb/>neam, per quod arcus ♋, tranſit, cum hoc punctum ad meridiẽ pertineat, vt ſupra diximus. </s>
  <s xml:id="echoid-s24108" xml:space="preserve">Vtra-<lb/>que autem linea tam ♈, quàm ♎, parallela eſt horizontali lineæ, vel æquinoctiali, ex propoſ. </s>
  <s xml:id="echoid-s24109" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s24110" xml:space="preserve">primi libri; </s>
  <s xml:id="echoid-s24111" xml:space="preserve">propterea quòd tunc Horizon, Aequator, Ecliptica, &amp; </s>
  <s xml:id="echoid-s24112" xml:space="preserve">circulus maximus, cui æquidi-<lb/>ſtat horologij planum, habent vnam, eandemq́ue communem ſectionem, nempe axem Meridia <lb/>ni circuli, cum omnes illi circuli ad Meridianum recti ſint, vt conſtat ex ſphæra materiali, vel cer <lb/>tè ex Elementis ſphæricis Theod. </s>
  <s xml:id="echoid-s24113" xml:space="preserve">facile colligi poteſt. </s>
  <s xml:id="echoid-s24114" xml:space="preserve">Non ducta eſt autem in propoſito exemplo <lb/>linea ♎, quia in puncto nimis remoto ellipſis ♋, meridianam lineam ſecat infra lineam horizon <lb/>talem. </s>
  <s xml:id="echoid-s24115" xml:space="preserve">Signa ergo aſcendentia Zodiaci in eodem horologio ad Horizontem inclinato deſigna-<lb/>uimus. </s>
  <s xml:id="echoid-s24116" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s24117" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1247" type="float" level="2" n="3">
<note position="left" xlink:label="note-0382-04" xlink:href="note-0382-04a" xml:space="preserve">Lineæ Arietis, <lb/>&amp; Libræ, quo <lb/>pacto ducendę <lb/>fint.</note>
<note position="left" xlink:label="note-0382-05" xlink:href="note-0382-05a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1249" type="section" level="1" n="310">
<head xml:id="echoid-head320" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s24118" xml:space="preserve">ASCENDENTIA ſigna ſecundum Andream Schonerum hac ratione depingem{us}. </s>
  <s xml:id="echoid-s24119" xml:space="preserve">In prio-<lb/>
<anchor type="note" xlink:label="note-0382-07a" xlink:href="note-0382-07"/>
ri eius figura abſcindatur ex diametro B D, recta E P, ęqualis rectæ E I, horologĳ inter centrum E, &amp; </s>
  <s xml:id="echoid-s24120" xml:space="preserve"><lb/>lineam æquinoctialem, (quę in noſtro exemplo œqualis eſt omnino ſemidiametro E B) &amp; </s>
  <s xml:id="echoid-s24121" xml:space="preserve">per P, ad B D, <lb/>perpendicularis educatur in vtramque partem. </s>
  <s xml:id="echoid-s24122" xml:space="preserve">Hæc enim line{as} ſignorum in punctis ſecabit, quæ bene-<lb/>ficio circini accepta ex P, &amp; </s>
  <s xml:id="echoid-s24123" xml:space="preserve">in æquinoctialem lineam horologĳ ex I, translata dabunt puncta, ex qui-<lb/>bus per B, punctum, vbi conueniunt meridiana linea, &amp; </s>
  <s xml:id="echoid-s24124" xml:space="preserve">horizontalis, rectæ occultæ emiſſæ ſecabunt tro <lb/>picum ♋, vel etiam vtrumque tropicum, quando vterque in horologio deſcriptus eſt, in punctis, per quæ <lb/>
<anchor type="note" xlink:label="note-0382-08a" xlink:href="note-0382-08"/>
ſigna aſcendentia ducenda ſunt: </s>
  <s xml:id="echoid-s24125" xml:space="preserve">quorum ordinem facile intelliges ex tabula 3. </s>
  <s xml:id="echoid-s24126" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24127" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24128" xml:space="preserve">propos. </s>
  <s xml:id="echoid-s24129" xml:space="preserve">9. </s>
  <s xml:id="echoid-s24130" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24131" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s24132" xml:space="preserve">Nam quia v. </s>
  <s xml:id="echoid-s24133" xml:space="preserve">g. </s>
  <s xml:id="echoid-s24134" xml:space="preserve">per punctum meridianæ lineę ſupra horizontalem lineam in noſtro exemplo ducitur ſi-<lb/>gnum ♈, &amp; </s>
  <s xml:id="echoid-s24135" xml:space="preserve">Sole exiſtente in tropico ♋, ſignum ♉, oritur poſt mediam noctem, vel ante meridiem, vt <lb/>in 3. </s>
  <s xml:id="echoid-s24136" xml:space="preserve">tabula habetur, perſpicuum eſt, primum punctum in parte antemeridiana horologĳ, hoc eſt, in oc-<lb/>cidentali, poſt illud punctum ♈, conuenire ſigno ♉, &amp; </s>
  <s xml:id="echoid-s24137" xml:space="preserve">ſequens ſigno ♊, &amp;</s>
  <s xml:id="echoid-s24138" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24139" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1249" type="float" level="2" n="1">
<note position="left" xlink:label="note-0382-07" xlink:href="note-0382-07a" xml:space="preserve">Eorundem ſi-<lb/>gnorum aſcen-<lb/>dentium deſcri <lb/>ptio ex praxi <lb/>Andræ Scho-<lb/>neri.</note>
<note position="left" xlink:label="note-0382-08" xlink:href="note-0382-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s24140" xml:space="preserve">RVRSVS in posteriori figura ex diametro B D, detrabatur recta E P, æqualis rectę E I, vt <lb/>prius, (quæ rurſus æqualis eſt ſemidiametro E D,) &amp; </s>
  <s xml:id="echoid-s24141" xml:space="preserve">per P, ad B D, excitetur perpendicularis, quæ <lb/>lineas ſignorum ſecabit in punctis, quę accepta beneficio circini ex puncto P, &amp; </s>
  <s xml:id="echoid-s24142" xml:space="preserve">in lineam æquinoctia-<lb/>lem ex I, translata dabunt puncta, per quæ ducenda ſunt aſcendentia ſigna: </s>
  <s xml:id="echoid-s24143" xml:space="preserve">quorum ordinem ex tabu-<lb/>la 1. </s>
  <s xml:id="echoid-s24144" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24145" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24146" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24147" xml:space="preserve">9. </s>
  <s xml:id="echoid-s24148" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24149" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24150" xml:space="preserve">facile colligemus. </s>
  <s xml:id="echoid-s24151" xml:space="preserve">Quoniam enim v. </s>
  <s xml:id="echoid-s24152" xml:space="preserve">g. </s>
  <s xml:id="echoid-s24153" xml:space="preserve">Sole exiſtente in principio ♈, ſignum <lb/>♉, oritur hora 4. </s>
  <s xml:id="echoid-s24154" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24155" xml:space="preserve">51. </s>
  <s xml:id="echoid-s24156" xml:space="preserve">ante meridiem, quæ in noſtro horologio lineam æquinoctialem non ſecat, recur
<pb o="367" file="0383" n="383" rhead="LIBER TERTIVS."/>
remus ad 2. </s>
  <s xml:id="echoid-s24157" xml:space="preserve">tabulam, in qua inueniemus, Sole existente in principio ♎, ſignum ♉, oriri hora 7. </s>
  <s xml:id="echoid-s24158" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24159" xml:space="preserve">8. <lb/></s>
  <s xml:id="echoid-s24160" xml:space="preserve">post meridiem, ſignum verò ♊, hora 8. </s>
  <s xml:id="echoid-s24161" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24162" xml:space="preserve">34. </s>
  <s xml:id="echoid-s24163" xml:space="preserve">poſt meridiem, concludo ſignum ♉, ducendum eſſe in <lb/>parte horologĳ orientali, ſiue pomeridiana, per punctum remotius in linea æquinoctiali, quàm ſi-<lb/>gnum ♊, &amp;</s>
  <s xml:id="echoid-s24164" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24165" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s24166" xml:space="preserve">IDEM ordo ex dicta poſteriori figura facile etiam colligi poteſt. </s>
  <s xml:id="echoid-s24167" xml:space="preserve">Cognito enim puncto, per quod ſi-<lb/>gnum ♉, ducendum eſt, quod ſemper remotius eſt omnibus alĳs, ſequentur deinde alia ſigna, prout in <lb/>dicta figura continentur. </s>
  <s xml:id="echoid-s24168" xml:space="preserve">Vt quoniam ſignum ♉, ducendum est per remotiſſimum punctum lineę æquino-<lb/>ctialis in parte pomeridiana horologii, ducenda erunt per ſequens punctum ſigna ♊, &amp; </s>
  <s xml:id="echoid-s24169" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s24170" xml:space="preserve">per ſe-<lb/>quens punctum ſignum ♋, &amp;</s>
  <s xml:id="echoid-s24171" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24172" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1251" type="section" level="1" n="311">
<head xml:id="echoid-head321" xml:space="preserve">PROBLEMA 34. PROPOSITIO 34.</head>
<p>
  <s xml:id="echoid-s24173" xml:space="preserve">HOROLOGIVM Italicum ad Horizontem inclinatum <lb/>conſtruere.</s>
  <s xml:id="echoid-s24174" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24175" xml:space="preserve">CIRCVLVS ex E, deſcriptus diuidatur, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s24176" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24177" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24178" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24179" xml:space="preserve">docuimus, in arcum <lb/>
<anchor type="note" xlink:label="note-0383-02a" xlink:href="note-0383-02"/>
diurnum tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s24180" xml:space="preserve">nocturnum a M b. </s>
  <s xml:id="echoid-s24181" xml:space="preserve">Deinde idem, initio facto à puncto b, occiden-<lb/>tali, ſecetur in partes 24. </s>
  <s xml:id="echoid-s24182" xml:space="preserve">æquales, &amp; </s>
  <s xml:id="echoid-s24183" xml:space="preserve">reliqua fiant, vt in præcedentibus, deſcriptumq́ue erit horo-<lb/>
<anchor type="note" xlink:label="note-0383-03a" xlink:href="note-0383-03"/>
<anchor type="figure" xlink:label="fig-0383-01a" xlink:href="fig-0383-01"/>
<anchor type="note" xlink:label="note-0383-04a" xlink:href="note-0383-04"/>
<anchor type="note" xlink:label="note-0383-05a" xlink:href="note-0383-05"/>
<anchor type="note" xlink:label="note-0383-06a" xlink:href="note-0383-06"/>
logium Italicem. </s>
  <s xml:id="echoid-s24184" xml:space="preserve">Exempli gratia, ſit ducenda linea horæ 9. </s>
  <s xml:id="echoid-s24185" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s24186" xml:space="preserve">Ex F, puncto horæ 9. </s>
  <s xml:id="echoid-s24187" xml:space="preserve">per <lb/>E, centrum ducta recta ſecat æquinoctialem lineam in puncto L; </s>
  <s xml:id="echoid-s24188" xml:space="preserve">recta autem ex L, ad H, centrũ <lb/>horologij extenſa ſecat tropicum ♋, in M, puncto horæ 9. </s>
  <s xml:id="echoid-s24189" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s24190" xml:space="preserve">Et quoniam, vt ex tabula <lb/>6. </s>
  <s xml:id="echoid-s24191" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24192" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24193" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24194" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24195" xml:space="preserve">conſtat, hora 9. </s>
  <s xml:id="echoid-s24196" xml:space="preserve">ab occaſu tranſit etiam per horam 3. </s>
  <s xml:id="echoid-s24197" xml:space="preserve">à media nocte in arcu no-<lb/>cturno horarum 12. </s>
  <s xml:id="echoid-s24198" xml:space="preserve">quem exhibet in noſtro horologio linea æquinoctialis, cum tota ſupra hori-<lb/>zontalem lineam exiſtat; </s>
  <s xml:id="echoid-s24199" xml:space="preserve">vel certè ducitur per horam 3. </s>
  <s xml:id="echoid-s24200" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s24201" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s24202" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s24203" xml:space="preserve">in linea æquinoctiali <lb/>ſimpliciter, ſiue ea arcum diurnum, ſiue nocturnum referat, vt conſtat ex tabula propoſ. </s>
  <s xml:id="echoid-s24204" xml:space="preserve">19. </s>
  <s xml:id="echoid-s24205" xml:space="preserve">libri 1. <lb/></s>
  <s xml:id="echoid-s24206" xml:space="preserve">dabit recta ex M, per horam 3. </s>
  <s xml:id="echoid-s24207" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s24208" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s24209" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s24210" xml:space="preserve">in linea æquinoctiali, quæ quidem in propo-
<pb o="368" file="0384" n="384" rhead="GNOMONICES"/>
ſito exemplo eſt hora 3. </s>
  <s xml:id="echoid-s24211" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s24212" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s24213" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s24214" xml:space="preserve">horam 9. </s>
  <s xml:id="echoid-s24215" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s24216" xml:space="preserve">Quo-<lb/>niam verò ſi velimus ducere lineam horæ 21. </s>
  <s xml:id="echoid-s24217" xml:space="preserve">ab occaſu, recta ex K, puncto horæ 21. </s>
  <s xml:id="echoid-s24218" xml:space="preserve">ab occaſu nõ <lb/>prius tranſit per centrum E, quàm per æquinoctialem lineam, accipiemus punctum oppoſitum <lb/>F, quod ſemper ab illo diſtat ſemicirculo integro, ſiue horis 12. </s>
  <s xml:id="echoid-s24219" xml:space="preserve">ita vt F, ſit punctum horæ 9. </s>
  <s xml:id="echoid-s24220" xml:space="preserve">ab <lb/>occaſu; </s>
  <s xml:id="echoid-s24221" xml:space="preserve">(quæ quidem habetur, ſi ad 21. </s>
  <s xml:id="echoid-s24222" xml:space="preserve">adijciamus 12. </s>
  <s xml:id="echoid-s24223" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24224" xml:space="preserve">ex ſumma, quoniam ſuperat 24. </s>
  <s xml:id="echoid-s24225" xml:space="preserve">abijcia-<lb/>mus 24.) </s>
  <s xml:id="echoid-s24226" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24227" xml:space="preserve">ex F, ducemus per E, &amp; </s>
  <s xml:id="echoid-s24228" xml:space="preserve">K, rectam, quæ ſecet æquinoctialem lineam in L. </s>
  <s xml:id="echoid-s24229" xml:space="preserve">Nam recta <lb/>L H, ſecabit tropicum ♋, in M, puncto horæ 9. </s>
  <s xml:id="echoid-s24230" xml:space="preserve">ab occaſu, vt proximè dictum eſt, producta autem <lb/>vltra centrum H, ſecabit eundem tropicum in O, puncto horæ 21. </s>
  <s xml:id="echoid-s24231" xml:space="preserve">ab occaſu, vt demonſtrauimus <lb/>propoſ. </s>
  <s xml:id="echoid-s24232" xml:space="preserve">10. </s>
  <s xml:id="echoid-s24233" xml:space="preserve">ſuperioris libri. </s>
  <s xml:id="echoid-s24234" xml:space="preserve">Cum ergo hora 21. </s>
  <s xml:id="echoid-s24235" xml:space="preserve">ducatur quoque, vt habetur in tabula propoſ. </s>
  <s xml:id="echoid-s24236" xml:space="preserve">19. <lb/></s>
  <s xml:id="echoid-s24237" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24238" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24239" xml:space="preserve">per horam 3. </s>
  <s xml:id="echoid-s24240" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s24241" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s24242" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s24243" xml:space="preserve">in linea æquinoctiali, indicabit recta per O, punctum, &amp; </s>
  <s xml:id="echoid-s24244" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0384-01a" xlink:href="note-0384-01"/>
per horam 3. </s>
  <s xml:id="echoid-s24245" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s24246" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s24247" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s24248" xml:space="preserve">in linea æquinoctiali ducta horam 21. </s>
  <s xml:id="echoid-s24249" xml:space="preserve">ab occaſ<unsure/>u. </s>
  <s xml:id="echoid-s24250" xml:space="preserve">Sic etiam du-<lb/>cta recta ex P, puncto horæ 1. </s>
  <s xml:id="echoid-s24251" xml:space="preserve">ab occaſu per E, centrum, &amp; </s>
  <s xml:id="echoid-s24252" xml:space="preserve">per R, punctum horæ 13. </s>
  <s xml:id="echoid-s24253" xml:space="preserve">ab occaſu ſe-<lb/>cat lineam æquinoctialem in A; </s>
  <s xml:id="echoid-s24254" xml:space="preserve">recta autem A H, ſecat tropicum ♋, in B, puncto horæ 1. </s>
  <s xml:id="echoid-s24255" xml:space="preserve">ab oc-<lb/>caſu, producta autem ſecat eundem in C, puncto horæ 13. </s>
  <s xml:id="echoid-s24256" xml:space="preserve">ab occaſu, &amp;</s>
  <s xml:id="echoid-s24257" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24258" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1251" type="float" level="2" n="1">
<note position="right" xlink:label="note-0383-02" xlink:href="note-0383-02a" xml:space="preserve">Compoſitio ho <lb/>rologii Italici <lb/>ad Horizontẽ<unsure/> <lb/>inclinati.</note>
<note position="left" xlink:label="note-0383-03" xlink:href="note-0383-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0383-01" xlink:href="fig-0383-01a">
    <image file="0383-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0383-01"/>
  </figure>
<note position="left" xlink:label="note-0383-04" xlink:href="note-0383-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0383-05" xlink:href="note-0383-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0383-06" xlink:href="note-0383-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0384-01" xlink:href="note-0384-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s24259" xml:space="preserve">IN alijs modis nulla eſt difficultas. </s>
  <s xml:id="echoid-s24260" xml:space="preserve">Per ſolum enim arcum diurnum horarum 14. </s>
  <s xml:id="echoid-s24261" xml:space="preserve">in ſuperio-<lb/>
<anchor type="note" xlink:label="note-0384-02a" xlink:href="note-0384-02"/>
ri horologio, qui in portione nocturna eſt arcus nocturnus horarum 10. </s>
  <s xml:id="echoid-s24262" xml:space="preserve">commodiſſimè horæ ab <lb/>occaſu deſcribentur ſecundum tabulas propoſ. </s>
  <s xml:id="echoid-s24263" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24264" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s24265" xml:space="preserve">Sed quoniam pro ſingulis horis ab <lb/>occaſu ſingula tantum puncta habemus in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s24266" xml:space="preserve">ſumemus pro eiſdem nume <lb/>ro horis ab ortu alia puncta, ſiue in eodem arcu diurno horarum 14. </s>
  <s xml:id="echoid-s24267" xml:space="preserve">ſiue in nocturno horarũ 10. <lb/></s>
  <s xml:id="echoid-s24268" xml:space="preserve">vt tabulæ propoſ. </s>
  <s xml:id="echoid-s24269" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24270" xml:space="preserve">primi libri indicant. </s>
  <s xml:id="echoid-s24271" xml:space="preserve">Vt hora 23. </s>
  <s xml:id="echoid-s24272" xml:space="preserve">ab occaſu tranſit per horam 6. </s>
  <s xml:id="echoid-s24273" xml:space="preserve">à meridie <lb/>
<anchor type="note" xlink:label="note-0384-03a" xlink:href="note-0384-03"/>
in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s24274" xml:space="preserve">at hora 23. </s>
  <s xml:id="echoid-s24275" xml:space="preserve">ab ortu per horam 4. </s>
  <s xml:id="echoid-s24276" xml:space="preserve">à media nocte in arcu nocturno ho <lb/>rarum 10. </s>
  <s xml:id="echoid-s24277" xml:space="preserve">Si igitur duo hæc puncta iungantur per lineam rectam, habebitur quidem in ſuperio-<lb/>ri horologio diurno hora 23. </s>
  <s xml:id="echoid-s24278" xml:space="preserve">ab occaſu, in nocturno verò hora 23. </s>
  <s xml:id="echoid-s24279" xml:space="preserve">ab ortu, vt ex demonſtratis ma-<lb/>nifeſtum eſt. </s>
  <s xml:id="echoid-s24280" xml:space="preserve">Hęc enim linea tangit maximum parallelorum ſemper apparentium. </s>
  <s xml:id="echoid-s24281" xml:space="preserve">Vnde vna pars <lb/>indicabit horam ab occaſu, &amp; </s>
  <s xml:id="echoid-s24282" xml:space="preserve">altera horam ab ortu. </s>
  <s xml:id="echoid-s24283" xml:space="preserve">Hac etiam ratione pro hora 20. </s>
  <s xml:id="echoid-s24284" xml:space="preserve">ab occaſu du <lb/>ximus horam 20. </s>
  <s xml:id="echoid-s24285" xml:space="preserve">ab ortu per horam 1. </s>
  <s xml:id="echoid-s24286" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s24287" xml:space="preserve">nocte in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s24288" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24289" xml:space="preserve">per horam <lb/>2. </s>
  <s xml:id="echoid-s24290" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s24291" xml:space="preserve">Hæc namque producta dat horam quoque 20. </s>
  <s xml:id="echoid-s24292" xml:space="preserve">ab <lb/>occaſu, &amp;</s>
  <s xml:id="echoid-s24293" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24294" xml:space="preserve">Propter anguſtiam autem ſpatij non eſt deſcripta tota Ellipſis ♋, quam ſecare deberẽt <lb/>horæ ſequentes ab occaſu 14. </s>
  <s xml:id="echoid-s24295" xml:space="preserve">15. </s>
  <s xml:id="echoid-s24296" xml:space="preserve">16. </s>
  <s xml:id="echoid-s24297" xml:space="preserve">17. </s>
  <s xml:id="echoid-s24298" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24299" xml:space="preserve">19. </s>
  <s xml:id="echoid-s24300" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24301" xml:space="preserve">horæ ab ortu, de quibus in propoſ. </s>
  <s xml:id="echoid-s24302" xml:space="preserve">ſequenti <lb/>agemus, V. </s>
  <s xml:id="echoid-s24303" xml:space="preserve">VI. </s>
  <s xml:id="echoid-s24304" xml:space="preserve">VII. </s>
  <s xml:id="echoid-s24305" xml:space="preserve">VIII. </s>
  <s xml:id="echoid-s24306" xml:space="preserve">IX. </s>
  <s xml:id="echoid-s24307" xml:space="preserve">X.</s>
  <s xml:id="echoid-s24308" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1252" type="float" level="2" n="2">
<note position="left" xlink:label="note-0384-02" xlink:href="note-0384-02a" xml:space="preserve">E<unsure/>iuſdem Itali-<lb/>ci horologii de <lb/>ſcriptio per ar-<lb/>cus diurnos, no <lb/>cturnosq́ue.</note>
<note position="left" xlink:label="note-0384-03" xlink:href="note-0384-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s24309" xml:space="preserve">APTE etiam eaſdem horas deſcribemus ex tabula 7. </s>
  <s xml:id="echoid-s24310" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24311" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24312" xml:space="preserve">primi libri, ſi prius arcum <lb/>diurnum horarum 24. </s>
  <s xml:id="echoid-s24313" xml:space="preserve">deſignemus, qui lineas horarum 24. </s>
  <s xml:id="echoid-s24314" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24315" xml:space="preserve">12. </s>
  <s xml:id="echoid-s24316" xml:space="preserve">tanget, &amp;</s>
  <s xml:id="echoid-s24317" xml:space="preserve">c.</s>
  <s xml:id="echoid-s24318" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24319" xml:space="preserve">QVOD ſi per mutuas ſectiones horarum à meridie vel media nocte, &amp; </s>
  <s xml:id="echoid-s24320" xml:space="preserve">ab ortu vel occaſu in-<lb/>ter ſe, quæ quidem in tabulis propoſ. </s>
  <s xml:id="echoid-s24321" xml:space="preserve">19. </s>
  <s xml:id="echoid-s24322" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24323" xml:space="preserve">20. </s>
  <s xml:id="echoid-s24324" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24325" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24326" xml:space="preserve">continentur, horologium deſcribere alicui <lb/>placeat, ducenda erit linea horæ 12. </s>
  <s xml:id="echoid-s24327" xml:space="preserve">ab ortu vel occaſu hoc modo. </s>
  <s xml:id="echoid-s24328" xml:space="preserve">In portione Analemmatis pro-<lb/>
<anchor type="note" xlink:label="note-0384-05a" xlink:href="note-0384-05"/>
poſ. </s>
  <s xml:id="echoid-s24329" xml:space="preserve">25. </s>
  <s xml:id="echoid-s24330" xml:space="preserve">huius libri à polo E, vtrinque numeretur altitudo poli ſupra Horizontem regionis, pro <lb/>qua horologium deſcribitur, vſque ad M, N, ducaturq́ue recta M N, quæ communis ſectio erit <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s24331" xml:space="preserve">paralleli omnium ſemper apparentium maximi, ſi polus E, fuerit ſeptentrionalis; </s>
  <s xml:id="echoid-s24332" xml:space="preserve">vel <lb/>maximi ſemper latentium, ſi E, ſit auſtralis polus. </s>
  <s xml:id="echoid-s24333" xml:space="preserve">Ductis deinde ex punctis M, N, per centrum <lb/>D, rectis M D, N D, erit vna illarum communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s24334" xml:space="preserve">Horizontis, &amp; </s>
  <s xml:id="echoid-s24335" xml:space="preserve">altera <lb/>
<anchor type="note" xlink:label="note-0384-06a" xlink:href="note-0384-06"/>
ſectio communis Meridiani, &amp; </s>
  <s xml:id="echoid-s24336" xml:space="preserve">circuli horæ 12. </s>
  <s xml:id="echoid-s24337" xml:space="preserve">ab ortu, vel occaſu; </s>
  <s xml:id="echoid-s24338" xml:space="preserve">cum Horizon, &amp; </s>
  <s xml:id="echoid-s24339" xml:space="preserve">di-<lb/>ctus circulus parallelum illum maximum tangant in punctis M, N, Meridiani circuli. </s>
  <s xml:id="echoid-s24340" xml:space="preserve">Vtra <lb/>autem illarum ſit communis ſectio Horizontis, vel circuli horæ 12. </s>
  <s xml:id="echoid-s24341" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24342" xml:space="preserve">Meridiani, &amp; </s>
  <s xml:id="echoid-s24343" xml:space="preserve">an E, ſit <lb/>polus arcticus, an artarcticus ſupra planum horologii eleuatus, apertè docebunt quatuor Ana-<lb/>lemmata propoſ. </s>
  <s xml:id="echoid-s24344" xml:space="preserve">25. </s>
  <s xml:id="echoid-s24345" xml:space="preserve">huius libri deſcripta. </s>
  <s xml:id="echoid-s24346" xml:space="preserve">Conſiderandum enim eſt, an Horizontis ſemi-<lb/>diameter auſtralis B E, an Borealis D E, per centrum extenſa occurrat plano ſuperioris horo-<lb/>logii M N; </s>
  <s xml:id="echoid-s24347" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24348" xml:space="preserve">in qua parte, an ſcilicet inter centrum M, &amp; </s>
  <s xml:id="echoid-s24349" xml:space="preserve">punctum Aequatoris N, an verò vl-<lb/>tra centrum M, vel punctum N. </s>
  <s xml:id="echoid-s24350" xml:space="preserve">Nam in primo Analemmate Horizontis ſemidiameter auſtra-<lb/>lis B E, vltra centrum E, producta occurrit plano horologij M N, vltra N, punctum Aequato-<lb/>ris. </s>
  <s xml:id="echoid-s24351" xml:space="preserve">In ſecundo verò eadem ſemidiameter eidem plano occurrit inter centrum horologij M, &amp; </s>
  <s xml:id="echoid-s24352" xml:space="preserve">N, <lb/>
<anchor type="note" xlink:label="note-0384-07a" xlink:href="note-0384-07"/>
punctum Aequatoris. </s>
  <s xml:id="echoid-s24353" xml:space="preserve">In tertio autem ſemidiameter borealis Horizontis D E, vltra centrum E, <lb/>extenſa ſecat planum horologij M N, vltra M, centrum horologii. </s>
  <s xml:id="echoid-s24354" xml:space="preserve">In quarto denique eadem ſemi <lb/>diameter borealis idem planum ſecat inter M, &amp; </s>
  <s xml:id="echoid-s24355" xml:space="preserve">centrum horologij, &amp; </s>
  <s xml:id="echoid-s24356" xml:space="preserve">N, punctum Aequatoris. <lb/></s>
  <s xml:id="echoid-s24357" xml:space="preserve">Ex his non difficile erit cognoſcere, quænam linea in dicta portione Analemmatis ſit communis <lb/>ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s24358" xml:space="preserve">Horizontis, ac proinde, quæ communis ſectio ſit circuli horæ 12. </s>
  <s xml:id="echoid-s24359" xml:space="preserve">ab ortu, <lb/>vel occaſu; </s>
  <s xml:id="echoid-s24360" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24361" xml:space="preserve">an polus E, ſupra planum horologii eleuatus ſit arcticus, vel antarcticus. </s>
  <s xml:id="echoid-s24362" xml:space="preserve">Nam in <lb/>noſtro exemplo, quoniam planum inclinatum ex parte auſtrali ſupra Horizontem attollitur, ha-<lb/>betq́ue inclinationem maiorem complemento altitudinis poli, reſpondebit ei quartum Analem-<lb/>ma propoſitionis 25. </s>
  <s xml:id="echoid-s24363" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s24364" xml:space="preserve">Quare borealis ſemidiameter Horizontis planum horologii ſu <lb/>perioris ſecabit inter centrum horologij, &amp; </s>
  <s xml:id="echoid-s24365" xml:space="preserve">linea æquinoctialem; </s>
  <s xml:id="echoid-s24366" xml:space="preserve">atque adeo recta M D, in dicta <lb/>portione Analemmatis eiuſdem propoſ. </s>
  <s xml:id="echoid-s24367" xml:space="preserve">25. </s>
  <s xml:id="echoid-s24368" xml:space="preserve">ſecans rectam per G, ductam inter H, centrum horo-
<pb o="369" file="0385" n="385" rhead="LIBER TERTIVS."/>
logij, &amp; </s>
  <s xml:id="echoid-s24369" xml:space="preserve">punctum I, per quod æquinoctialis linea ducitur, communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s24370" xml:space="preserve"><lb/>Horizontis; </s>
  <s xml:id="echoid-s24371" xml:space="preserve">altera vero linea N D, erit proinde ſectio communis Meridiani, &amp; </s>
  <s xml:id="echoid-s24372" xml:space="preserve">circuli horæ 12. <lb/></s>
  <s xml:id="echoid-s24373" xml:space="preserve">ab ortu, vel occaſu; </s>
  <s xml:id="echoid-s24374" xml:space="preserve">eritq́ue E, polus ſeptentrionalis ſupra planum horologii per rectam H I, du-<lb/>ctum eleuatus, quippe cum axis F G, ex polo atctico F, per centrum E, in quarto Analemmate ex-<lb/>tenſus cadat in M, centrum horologii. </s>
  <s xml:id="echoid-s24375" xml:space="preserve">Eadem ratione in primo &amp; </s>
  <s xml:id="echoid-s24376" xml:space="preserve">tertio Analemmate attolletur <lb/>
<anchor type="note" xlink:label="note-0385-01a" xlink:href="note-0385-01"/>
polus arcticus ſupra planum ſuperioris horologij, in ſecundo autem antarcticus, propterea quòd <lb/>in illis axis ex polo arctico per centrum extenſus, in hoc vero ex antarctico cadit in centrum horo <lb/>logij. </s>
  <s xml:id="echoid-s24377" xml:space="preserve">Oppoſitus autem ſemper polus ſupra planum inferioris horologij eleuabitur, vt manifeſtũ <lb/>eſt ex eiſdem Analemmatibus. </s>
  <s xml:id="echoid-s24378" xml:space="preserve">Itaque ſi in propoſito noſtro exemplo rectam H O, ex portione <lb/>Analemmatis propoſ. </s>
  <s xml:id="echoid-s24379" xml:space="preserve">25. </s>
  <s xml:id="echoid-s24380" xml:space="preserve">huius libri transferamus in lineam meridianã horologii ex H, centro <lb/>
<anchor type="note" xlink:label="note-0385-02a" xlink:href="note-0385-02"/>
<anchor type="note" xlink:label="note-0385-03a" xlink:href="note-0385-03"/>
horologij verſus æquinoctialem lineam, inueniemus punctum B, per quod linea horizontalis du <lb/>citur ad lineam meridianam perpendicularis: </s>
  <s xml:id="echoid-s24381" xml:space="preserve">ſi autem rectam H P, transferamus ex H, in alterã <lb/>partem, offendemus punctum D, per quod linea horæ 12. </s>
  <s xml:id="echoid-s24382" xml:space="preserve">ab ortu, vel occaſu ducenda eſt, quæ ne-<lb/>ceſſario per propoſ. </s>
  <s xml:id="echoid-s24383" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24384" xml:space="preserve">primi lib. </s>
  <s xml:id="echoid-s24385" xml:space="preserve">lineę æquinoctiali, vel horizontali, vel etiam horæ 6. </s>
  <s xml:id="echoid-s24386" xml:space="preserve">à meridie, <lb/>vel media nocte æquidiſtabit, cum harum linearum circuli maximi, nec non circulus maximus, <lb/>cui horologium parallelum eſt, habeant vnam, eandemq́ue communem ſectionem. </s>
  <s xml:id="echoid-s24387" xml:space="preserve">Quare recta <lb/>per D, ducta parallela æquinoctiali lineę dabit horam 12. </s>
  <s xml:id="echoid-s24388" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s24389" xml:space="preserve">Horologium igi-<lb/>tur Italicum ad Horizontem inclinatum conſtruximus. </s>
  <s xml:id="echoid-s24390" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s24391" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1253" type="float" level="2" n="3">
<note position="left" xlink:label="note-0384-05" xlink:href="note-0384-05a" xml:space="preserve">Linea horæ 12. <lb/>ab or. vel occ. <lb/>quomodo de-<lb/>ſctibatur.</note>
<note position="left" xlink:label="note-0384-06" xlink:href="note-0384-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0384-07" xlink:href="note-0384-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0385-01" xlink:href="note-0385-01a" xml:space="preserve">An polus arcti-<lb/>cus, an antatcti <lb/>cus eleuetur ſu <lb/>pra planum ho <lb/>rologii prope<unsure/>-<lb/>ſi ti.</note>
<note position="left" xlink:label="note-0385-02" xlink:href="note-0385-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0385-03" xlink:href="note-0385-03a" xml:space="preserve">Deſcriptio alia <lb/>lineæ horizon-<lb/>talis.</note>
</div>
</div>
<div xml:id="echoid-div1255" type="section" level="1" n="312">
<head xml:id="echoid-head322" xml:space="preserve">PROBLEMA 35. PROPOSITIO 35.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s24392" xml:space="preserve">HOROLOGIVM Babylonicum ad Horizontem inclina-<lb/>tum conficerc.</s>
  <s xml:id="echoid-s24393" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24394" xml:space="preserve">EADEM prorſus ratione horologium Babylonicum delineabimus, qua Italicum deſcripſi-<lb/>
<anchor type="note" xlink:label="note-0385-05a" xlink:href="note-0385-05"/>
mus: </s>
  <s xml:id="echoid-s24395" xml:space="preserve">ſed in priori modo diuiſio circuli ex E, deſcripti inchoanda eſt à puncto a, orientali. </s>
  <s xml:id="echoid-s24396" xml:space="preserve">Exem-<lb/>plum habes in præcedenti figura, in qua horæ ab ortu notantur characteribus numerorum anti-<lb/>quis: </s>
  <s xml:id="echoid-s24397" xml:space="preserve">vbi vides pro hora 11. </s>
  <s xml:id="echoid-s24398" xml:space="preserve">ab ortu ductam eſſe in circulo, cuius centrum E, ex T, puncto oppo-<lb/>
<anchor type="note" xlink:label="note-0385-06a" xlink:href="note-0385-06"/>
ſito horæ 11. </s>
  <s xml:id="echoid-s24399" xml:space="preserve">nempe ex hora 23. </s>
  <s xml:id="echoid-s24400" xml:space="preserve">ab ortu, per centrum E, &amp; </s>
  <s xml:id="echoid-s24401" xml:space="preserve">per punctum S, horæ 11. </s>
  <s xml:id="echoid-s24402" xml:space="preserve">ab ortu rectã, <lb/>quæ æquinoctialem lineam ſecat in V. </s>
  <s xml:id="echoid-s24403" xml:space="preserve">Recta enim ex V, per centrum horologij H, ducta ſecabit <lb/>tropicum ♋, in puncto X. </s>
  <s xml:id="echoid-s24404" xml:space="preserve">horæ 23. </s>
  <s xml:id="echoid-s24405" xml:space="preserve">ab ortu (quæ quidem in portione nocturna horologij, quem-<lb/>admodum &amp; </s>
  <s xml:id="echoid-s24406" xml:space="preserve">punctum T, in arcu nocturno tropici ♋, continetur) producta autem vltra centrũ <lb/>H, ſecabit eundem tropicum ♋, in Y, puncto horæ 11. </s>
  <s xml:id="echoid-s24407" xml:space="preserve">ab ortu, &amp;</s>
  <s xml:id="echoid-s24408" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24409" xml:space="preserve">Quocirca horologium Baby-<lb/>lonicum ad Horizontem inclinatum confecimus. </s>
  <s xml:id="echoid-s24410" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s24411" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1255" type="float" level="2" n="1">
<note position="right" xlink:label="note-0385-05" xlink:href="note-0385-05a" xml:space="preserve">Conſtructio ho <lb/>rologii Babylo <lb/>nici ad Hori-<lb/>zentem inelina<unsure/> <lb/>ti.</note>
<note position="left" xlink:label="note-0385-06" xlink:href="note-0385-06a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1257" type="section" level="1" n="313">
<head xml:id="echoid-head323" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">40</note>
<p style="it">
  <s xml:id="echoid-s24412" xml:space="preserve">HORAE ab ortu, &amp; </s>
  <s xml:id="echoid-s24413" xml:space="preserve">occaſu ſuperioris horologii productæ vltra horizontalem lineam dant eaſdẽ <lb/>
<anchor type="note" xlink:label="note-0385-08a" xlink:href="note-0385-08"/>
horas in inferiori, ſeruato tamen ordine, quem in Verticali horologio præſcripſimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s24414" xml:space="preserve">22. <lb/></s>
  <s xml:id="echoid-s24415" xml:space="preserve">ſuperioris libri: </s>
  <s xml:id="echoid-s24416" xml:space="preserve">ita vt illæ horæ, quæ in portione horologii nocturna numer antur ab ortu Solis, quales <lb/>ſunt 23. </s>
  <s xml:id="echoid-s24417" xml:space="preserve">22. </s>
  <s xml:id="echoid-s24418" xml:space="preserve">21. </s>
  <s xml:id="echoid-s24419" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s24420" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24421" xml:space="preserve">in inferiori horologio ab occaſu ſupputentur; </s>
  <s xml:id="echoid-s24422" xml:space="preserve">quę verò ab occaſu numerantur, <lb/>quales ſunt 1. </s>
  <s xml:id="echoid-s24423" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24424" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24425" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24426" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s24427" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24428" xml:space="preserve">numerentur ab ortu.</s>
  <s xml:id="echoid-s24429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1257" type="float" level="2" n="1">
<note position="right" xlink:label="note-0385-08" xlink:href="note-0385-08a" xml:space="preserve">Quomodo ho-<lb/>rologium Infe-<lb/>rius Italicũ &amp; <lb/>Babylonicum <lb/>ex Superiori or<unsure/> <lb/>tum habeat<unsure/>.</note>
</div>
</div>
<div xml:id="echoid-div1259" type="section" level="1" n="314">
<head xml:id="echoid-head324" xml:space="preserve">PROBLEMA 36. PROPOSITIO 36.</head>
<p>
  <s xml:id="echoid-s24430" xml:space="preserve">HOROLOGIVM Antiquum ad Horizontem inclinatum <lb/>
<anchor type="note" xlink:label="note-0385-09a" xlink:href="note-0385-09"/>
componere.</s>
  <s xml:id="echoid-s24431" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1259" type="float" level="2" n="1">
<note position="left" xlink:label="note-0385-09" xlink:href="note-0385-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s24432" xml:space="preserve">FIGVRA ipſa declarat, non aliter Antiquum horologium ad Horizontem inclinatum de-<lb/>
<anchor type="note" xlink:label="note-0385-10a" xlink:href="note-0385-10"/>
ſcribi, ac ſuperiora conſtructa ſunt. </s>
  <s xml:id="echoid-s24433" xml:space="preserve">Nam exempli gratia, puncto A, horæ 3. </s>
  <s xml:id="echoid-s24434" xml:space="preserve">tinæqualis in circulo <lb/>ex E, deſcripto accepimus punctum oppoſitum C, duximusq́ue rectam C E A, quæ lineam æqui-<lb/>noctialem ſecat in D, puncto, per quod recta per H, centrum horologij extenſa, ſecat quidem <lb/>tropicum ♋, in arcu nocturno in puncto quodam, quod puncto C, dicti circuli in arcu noctur-<lb/>no debetur, vltra autem H, ſecat eundem tropicum in arcu diurno in F, puncto horæ 3. </s>
  <s xml:id="echoid-s24435" xml:space="preserve">inæqua-<lb/>lis, &amp;</s>
  <s xml:id="echoid-s24436" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24437" xml:space="preserve">Sed idem horologium aptiſſimè delineabitur beneficio ſolius arcus nocturni tropici ♋, <lb/>in noſtro exemplo. </s>
  <s xml:id="echoid-s24438" xml:space="preserve">Ita enim vides rectam ex I, puncto horæ vndecimæ in arcu nocturno tro-
<pb o="370" file="0386" n="386" rhead="GNOMONICES"/>
pici ♋, per E, ductam ſecare æquinoctialem lineam in L, rectam autem L H, ſecare arcum noctur <lb/>num ♋, in M, puncto horæ 11. </s>
  <s xml:id="echoid-s24439" xml:space="preserve">nocturnæ. </s>
  <s xml:id="echoid-s24440" xml:space="preserve">Si igitur ex M, per horam quintam à media nocte in <lb/>
<anchor type="figure" xlink:label="fig-0386-01a" xlink:href="fig-0386-01"/>
<anchor type="note" xlink:label="note-0386-01a" xlink:href="note-0386-01"/>
<anchor type="note" xlink:label="note-0386-02a" xlink:href="note-0386-02"/>
<anchor type="note" xlink:label="note-0386-03a" xlink:href="note-0386-03"/>
arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s24441" xml:space="preserve">hoc eſt, in linea æquinoctiali, vt conſtat ex tabula 14. </s>
  <s xml:id="echoid-s24442" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24443" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24444" xml:space="preserve">pri-<lb/>mi libri, ducamus rectam lineam, habebimus horam 11. </s>
  <s xml:id="echoid-s24445" xml:space="preserve">inæqualem nocturnam, quæ producta <lb/>vltra lineam horizontalem dabit etiam horam 11. </s>
  <s xml:id="echoid-s24446" xml:space="preserve">diurnam, vt ex demonſtratis colligitur. </s>
  <s xml:id="echoid-s24447" xml:space="preserve">Eo-<lb/>
<anchor type="note" xlink:label="note-0386-04a" xlink:href="note-0386-04"/>
dem modo reliquas horas reperiemus.</s>
  <s xml:id="echoid-s24448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1260" type="float" level="2" n="2">
<note position="right" xlink:label="note-0385-10" xlink:href="note-0385-10a" xml:space="preserve">Antiqui horo-<lb/>logii ad Hori-<lb/>zontem inclina <lb/>ti conſtructie<unsure/>.</note>
  <figure xlink:label="fig-0386-01" xlink:href="fig-0386-01a">
    <image file="0386-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0386-01"/>
  </figure>
<note position="left" xlink:label="note-0386-01" xlink:href="note-0386-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0386-02" xlink:href="note-0386-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0386-03" xlink:href="note-0386-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0386-04" xlink:href="note-0386-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s24449" xml:space="preserve">QVOD ad deſcriptionem attinet, quæ per arcum diurnum horarum 18. </s>
  <s xml:id="echoid-s24450" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24451" xml:space="preserve">nocturnum ho-<lb/>rarum 6. </s>
  <s xml:id="echoid-s24452" xml:space="preserve">conſicitur, res planè perſpicua eſt ex figura, &amp; </s>
  <s xml:id="echoid-s24453" xml:space="preserve">tabulis propoſ. </s>
  <s xml:id="echoid-s24454" xml:space="preserve">33. </s>
  <s xml:id="echoid-s24455" xml:space="preserve">primi libri. </s>
  <s xml:id="echoid-s24456" xml:space="preserve">Quare ho <lb/>rologium Antiquum ad Horizontem inclinatum compoſuimus. </s>
  <s xml:id="echoid-s24457" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s24458" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1262" type="section" level="1" n="315">
<head xml:id="echoid-head325" xml:space="preserve">DE HOROLOGIIS ET A VERTICALI</head>
<head xml:id="echoid-head326" xml:space="preserve">declinantibus, &amp; ad Horizontem inclinatis.</head>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1263" type="section" level="1" n="316">
<head xml:id="echoid-head327" xml:space="preserve">PROBLEMA 37. PROPOSITIO 37.</head>
<p>
  <s xml:id="echoid-s24459" xml:space="preserve">HOROLOGIVM Aſtronomicum &amp; </s>
  <s xml:id="echoid-s24460" xml:space="preserve">à Verticali declinans, &amp; </s>
  <s xml:id="echoid-s24461" xml:space="preserve"><lb/>ad Horizontem inclinatum conſtruere: </s>
  <s xml:id="echoid-s24462" xml:space="preserve">hoc eſt, lineas horarum à me-<lb/>ridie vel media nocte in plano, quod circulo cuipiam maximo æquidi-<lb/>ſtat, qui &amp; </s>
  <s xml:id="echoid-s24463" xml:space="preserve">à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s24464" xml:space="preserve">ad Horizontem inclinatus eſt, <lb/>deſcribere.</s>
  <s xml:id="echoid-s24465" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24466" xml:space="preserve">VT facilius omnia horologia, quæ à Verticali circulo declinant, &amp; </s>
  <s xml:id="echoid-s24467" xml:space="preserve">ad Horizontem ſunt incli-
<pb o="371" file="0387" n="387" rhead="LIBER TERTIVS."/>
nata, deſcribamus, præcepta trademus de ſuperioribus duntaxat deſcribendis, quæ videlicet Ze-<lb/>nith, ſiue verticem capitis reſpiciunt. </s>
  <s xml:id="echoid-s24468" xml:space="preserve">Ita enim fiet, vt res tota, quæ aliquantulum difficilis eſt, &amp; </s>
  <s xml:id="echoid-s24469" xml:space="preserve"><lb/>obſcura, planius percipiatur. </s>
  <s xml:id="echoid-s24470" xml:space="preserve">Deſcripto autem horologio quouis ſuperiore, nullo negotic ex ip-<lb/>ſo inferius fabricabimus, quod nimirum in facie eiuſdem plani inferiori delineatur, ſi eius par-<lb/>tes inuertantur omnes, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s24471" xml:space="preserve">14. </s>
  <s xml:id="echoid-s24472" xml:space="preserve">ſuperioris libri demonſtratum eſt à nobis. </s>
  <s xml:id="echoid-s24473" xml:space="preserve">His <lb/>adde, quòd facile ex præceptis his quilibet ſibi alia præcepta pro inferioribus comparare queat, vt <lb/>&amp; </s>
  <s xml:id="echoid-s24474" xml:space="preserve">nos in præcedentibus fecimus, præſertim ſi attentè legantur ea, quæ in propoſ. </s>
  <s xml:id="echoid-s24475" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24476" xml:space="preserve">huius libri <lb/>de boreali horologio declinante à Verticali circulo ſcripſimus.</s>
  <s xml:id="echoid-s24477" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24478" xml:space="preserve">TOTVM autem hoc negotium ſex exemplis, ſiue figuris abſoluemus. </s>
  <s xml:id="echoid-s24479" xml:space="preserve">Tot enim varietates <lb/>
<anchor type="note" xlink:label="note-0387-01a" xlink:href="note-0387-01"/>
in vniuerſum eſſe videntur, vt ex ſequentibus fiet perſpicuum. </s>
  <s xml:id="echoid-s24480" xml:space="preserve">In prima figura ponimus declina <lb/>
<anchor type="note" xlink:label="note-0387-02a" xlink:href="note-0387-02"/>
tionem plani à meridie in ortum grad. </s>
  <s xml:id="echoid-s24481" xml:space="preserve">40. </s>
  <s xml:id="echoid-s24482" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24483" xml:space="preserve">inclinationem ad Horizontem grad. </s>
  <s xml:id="echoid-s24484" xml:space="preserve">20. </s>
  <s xml:id="echoid-s24485" xml:space="preserve">In ſecun-<lb/>da declinationem à meridie in occaſum grad. </s>
  <s xml:id="echoid-s24486" xml:space="preserve">20. </s>
  <s xml:id="echoid-s24487" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24488" xml:space="preserve">inclinationem ad Horizontem grad. </s>
  <s xml:id="echoid-s24489" xml:space="preserve">70. </s>
  <s xml:id="echoid-s24490" xml:space="preserve">In <lb/>tertia declinationem à meridie in ortum grad. </s>
  <s xml:id="echoid-s24491" xml:space="preserve">45. </s>
  <s xml:id="echoid-s24492" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24493" xml:space="preserve">inclinationem ad Horizontem grad. </s>
  <s xml:id="echoid-s24494" xml:space="preserve">51. <lb/></s>
  <s xml:id="echoid-s24495" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24496" xml:space="preserve">51. </s>
  <s xml:id="echoid-s24497" xml:space="preserve">In quarta declinationem à ſeptentrione in occaſum grad. </s>
  <s xml:id="echoid-s24498" xml:space="preserve">20. </s>
  <s xml:id="echoid-s24499" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24500" xml:space="preserve">inclinationem ad Hori-<lb/>
<anchor type="note" xlink:label="note-0387-03a" xlink:href="note-0387-03"/>
zontem grad. </s>
  <s xml:id="echoid-s24501" xml:space="preserve">30. </s>
  <s xml:id="echoid-s24502" xml:space="preserve">In quinta declinationem à ſeptentrione in ortum grad. </s>
  <s xml:id="echoid-s24503" xml:space="preserve">60. </s>
  <s xml:id="echoid-s24504" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24505" xml:space="preserve">inclinationem <lb/>ad Horizontem grad. </s>
  <s xml:id="echoid-s24506" xml:space="preserve">80. </s>
  <s xml:id="echoid-s24507" xml:space="preserve">In ſexta denique ſtatuimus declinationem plani à ſeptentrione in ortũ <lb/>grad. </s>
  <s xml:id="echoid-s24508" xml:space="preserve">30. </s>
  <s xml:id="echoid-s24509" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24510" xml:space="preserve">inclinationem ad Horizontem grad. </s>
  <s xml:id="echoid-s24511" xml:space="preserve">52. </s>
  <s xml:id="echoid-s24512" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s24513" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24514" xml:space="preserve">Itaque in prioribus tribus exemplis <lb/>planum inclinatum eſt ad Horizontem ad partes boreales, eiuſq́; </s>
  <s xml:id="echoid-s24515" xml:space="preserve">facies ſuperior reſpicit Zenith, <lb/>&amp; </s>
  <s xml:id="echoid-s24516" xml:space="preserve">auſtralem plagam; </s>
  <s xml:id="echoid-s24517" xml:space="preserve">in tribus autẽ poſterioribus planum ad Horizontem inclinatum eſt ex par-<lb/>te auſtrali, reſpicitq́ue facies eius ſuperior Zenith, &amp; </s>
  <s xml:id="echoid-s24518" xml:space="preserve">plagam borealem: </s>
  <s xml:id="echoid-s24519" xml:space="preserve">Hoc eſt, planum priorum <lb/>
<anchor type="note" xlink:label="note-0387-04a" xlink:href="note-0387-04"/>
trium figurarum ſecat Meridianum circulum ſupra Horizontem ex parte boreali, planum autem <lb/>trium poſteriorum figurarum ex auſtrali parte.</s>
  <s xml:id="echoid-s24520" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1263" type="float" level="2" n="1">
<note position="right" xlink:label="note-0387-01" xlink:href="note-0387-01a" xml:space="preserve">Sex figuris con <lb/>tinetur deſcri-<lb/>ptio horologii <lb/>à Verticali de-<lb/>elina ntis, &amp; ad <lb/>Horizontem in <lb/>clinati.</note>
<note position="left" xlink:label="note-0387-02" xlink:href="note-0387-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0387-03" xlink:href="note-0387-03a" xml:space="preserve">Declinationes <lb/>planorum hu-<lb/>ius propoſitio-<lb/>nis à Vercicali, <lb/>&amp; corddeni ad <lb/>Horizontẽ in-<lb/>clinationes.</note>
<note position="left" xlink:label="note-0387-04" xlink:href="note-0387-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s24521" xml:space="preserve">ITAQVE vt ſuperius horologium declinans à Verticali, &amp; </s>
  <s xml:id="echoid-s24522" xml:space="preserve">ad Horizontem inclinatum de-<lb/>
<anchor type="note" xlink:label="note-0387-05a" xlink:href="note-0387-05"/>
ſcribatur, ducantur in plano aliquo duæ rectæ A B, C D, ſe ſe ad angulos rectos ſecantes in E, <lb/>
<anchor type="figure" xlink:label="fig-0387-01a" xlink:href="fig-0387-01"/>
<anchor type="note" xlink:label="note-0387-06a" xlink:href="note-0387-06"/>
<anchor type="note" xlink:label="note-0387-07a" xlink:href="note-0387-07"/>
<anchor type="note" xlink:label="note-0387-08a" xlink:href="note-0387-08"/>
Deinde ad rectam C D, in puncto E, conſtituatur angulus declinationis per propoſ. </s>
  <s xml:id="echoid-s24523" xml:space="preserve">23. </s>
  <s xml:id="echoid-s24524" xml:space="preserve">primi libri <lb/>inuentæ, hoc ſeruato ordine. </s>
  <s xml:id="echoid-s24525" xml:space="preserve">In its, quæ declinant à meridie in ortũ, conſtituendus eſt dictus angu <lb/>lus D E F, infra rectam A B, verſus A; </s>
  <s xml:id="echoid-s24526" xml:space="preserve">verſus autẽ B, in ijs, quæ à meridie in occaſum declinant:</s>
  <s xml:id="echoid-s24527" xml:space="preserve">
<pb o="372" file="0388" n="388" rhead="GNOMONICES"/>
In planis verò, quæ à ſeptentrione in ortum deflectunt, idem angulus conſtituendus eſt infra re-<lb/>ctam A B, verſus B; </s>
  <s xml:id="echoid-s24528" xml:space="preserve">verſus A, autem in iis, quæ declinant à ſeptentrione in occaſum. </s>
  <s xml:id="echoid-s24529" xml:space="preserve">Dicatur au-<lb/>
<anchor type="note" xlink:label="note-0388-01a" xlink:href="note-0388-01"/>
tem recta EF, linea declinationis.</s>
  <s xml:id="echoid-s24530" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1264" type="float" level="2" n="2">
<note position="right" xlink:label="note-0387-05" xlink:href="note-0387-05a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Aſtro-<lb/>nom ici Supe <lb/>rioris, quod &amp; <lb/>à Verticali de-<lb/>clinat, &amp; ad Ho <lb/>rizontem eſt in <lb/>elinatum:</note>
  <figure xlink:label="fig-0387-01" xlink:href="fig-0387-01a">
    <image file="0387-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0387-01"/>
  </figure>
<note position="left" xlink:label="note-0387-06" xlink:href="note-0387-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0387-07" xlink:href="note-0387-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0387-08" xlink:href="note-0387-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0388-01" xlink:href="note-0388-01a" xml:space="preserve">Linea declina-<lb/>@o@is.</note>
</div>
<p>
  <s xml:id="echoid-s24531" xml:space="preserve">POST hæc in recta A B, ſumpto puncto quocunque β, ſiue ad dextram, ſiue ad ſiniſtram, vt <lb/>
<anchor type="figure" xlink:label="fig-0388-01a" xlink:href="fig-0388-01"/>
<anchor type="note" xlink:label="note-0388-02a" xlink:href="note-0388-02"/>
<anchor type="note" xlink:label="note-0388-03a" xlink:href="note-0388-03"/>
<anchor type="note" xlink:label="note-0388-04a" xlink:href="note-0388-04"/>
in propoſ. </s>
  <s xml:id="echoid-s24532" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24533" xml:space="preserve">huius libri diximus, conſtituatur ad rectam A B, in puncto β, angulus altitudinis <lb/>
<anchor type="note" xlink:label="note-0388-05a" xlink:href="note-0388-05"/>
poli E β C, verſus rectam C D, &amp; </s>
  <s xml:id="echoid-s24534" xml:space="preserve">ſupra rectam A B, vel infra eandem, ita vt recta β C, ſecet re-<lb/>ctam C D, in C.</s>
  <s xml:id="echoid-s24535" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1265" type="float" level="2" n="3">
  <figure xlink:label="fig-0388-01" xlink:href="fig-0388-01a">
    <image file="0388-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0388-01"/>
  </figure>
<note position="left" xlink:label="note-0388-02" xlink:href="note-0388-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0388-03" xlink:href="note-0388-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0388-04" xlink:href="note-0388-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0388-05" xlink:href="note-0388-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s24536" xml:space="preserve">DEINDE ad rectam C D, in E, puncto conſtituatur angulus inclinationis plani ad Horizon-<lb/>tem per propo@. </s>
  <s xml:id="echoid-s24537" xml:space="preserve">23. </s>
  <s xml:id="echoid-s24538" xml:space="preserve">primi libri inuentæ D E γ, infra rectam A B, &amp; </s>
  <s xml:id="echoid-s24539" xml:space="preserve">in quamcunque partem: </s>
  <s xml:id="echoid-s24540" xml:space="preserve">ap-<lb/>pelletur autem recta E γ, linea inclinationis. </s>
  <s xml:id="echoid-s24541" xml:space="preserve">Ducta autem ex D, puncto quolibet rectæ C D, ad <lb/>
<anchor type="note" xlink:label="note-0388-06a" xlink:href="note-0388-06"/>
linea inclinationis. </s>
  <s xml:id="echoid-s24542" xml:space="preserve">Ducta autem ex D, puncto quolibet rectæ C D, ad lineam inclinationis E γ, <lb/>linea perpendiculari D γ, abſcindatur ex E D, recta E δ, rectæ E γ, æqualis. </s>
  <s xml:id="echoid-s24543" xml:space="preserve">Ductis quoque per <lb/>puncta D, δ, rectis D ε, δ θ, rectæ A B, parallelis, vel ad C D, perpendicularibus, quarum δ θ, li-<lb/>neam declinationis E F, ſecet in θ, abſcindatur recta D ε, ipſi δ θ, æqualis, &amp; </s>
  <s xml:id="echoid-s24544" xml:space="preserve">ex ε, per E, recta edu <lb/>catur ε E, quæ linea erit meridiana, ſiue horæ 12. </s>
  <s xml:id="echoid-s24545" xml:space="preserve">à meridie, vel media nocte in plano horologii, <lb/>
<anchor type="note" xlink:label="note-0388-07a" xlink:href="note-0388-07"/>
<anchor type="note" xlink:label="note-0388-08a" xlink:href="note-0388-08"/>
vt demonſtrabimus.</s>
  <s xml:id="echoid-s24546" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1266" type="float" level="2" n="4">
<note position="left" xlink:label="note-0388-06" xlink:href="note-0388-06a" xml:space="preserve">Linea inclina-<lb/>tionis.</note>
<note position="left" xlink:label="note-0388-07" xlink:href="note-0388-07a" xml:space="preserve">Linea meridia <lb/>na.</note>
<note position="left" xlink:label="note-0388-08" xlink:href="note-0388-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s24547" xml:space="preserve">INVENIEMVS quoque eandem lineam horæ 12. </s>
  <s xml:id="echoid-s24548" xml:space="preserve">hac ratione. </s>
  <s xml:id="echoid-s24549" xml:space="preserve">Ex aſſumpto puncto F, vt-<lb/>cunque in linea declinationis E F, ducatur ad A B, perpendicularis F ψ, vel (quod magis probo, <lb/>quando linea declinationis E F, parum à recta A B, diſtat) ex aſſumpto vtlibet puncto ψ, in recta <lb/>E A, vel in E B, prout declinationis linea E F, cadit ad ſiniſtram, vel dextram rectæ C D, ducatur <lb/>ipſi C D, parallela ψ p, ſecans lineam declinationis E F, in F. </s>
  <s xml:id="echoid-s24550" xml:space="preserve">Item ad F ψ, excitetur perpendicula <lb/>ris F n. </s>
  <s xml:id="echoid-s24551" xml:space="preserve">Conſtituto deinde in ψ, angulo inclinationis F ψ n, ita vt recta ψ n, dictum angulum cũ <lb/>ψ F, continens ſecet perpendicularem F n, in n, abſcindatur ex ψ F, producta ad partes F, recta <lb/>ψ p, ipſi ψ n, æqualis, &amp; </s>
  <s xml:id="echoid-s24552" xml:space="preserve">ex E, per p, recta educatur E p, quæ rurſus erit linea meridiana in plano <lb/>inclinato, vt oſtendemus. </s>
  <s xml:id="echoid-s24553" xml:space="preserve">Aliam quoque inuentionem eiuſdem meridianæ lineæ trademus in <lb/>ſcholio huius propoſ.</s>
  <s xml:id="echoid-s24554" xml:space="preserve"/>
</p>
<pb o="373" file="0389" n="389" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s24555" xml:space="preserve">AD hæc, ducta ex θ, ad lin eam declinationis E F, perpendiculari θ λ, verſus rectam A B, &amp; </s>
  <s xml:id="echoid-s24556" xml:space="preserve">ipſi <lb/>D γ, æquali, ducatur recta E λ, per puncta E, λ, interminatæ magnitudinis. </s>
  <s xml:id="echoid-s24557" xml:space="preserve">Conſtituatur quo-<lb/>que in F, ad rectã E F, quæ rectæ aſſumptę E β, ſit æqualis, angulus angulo altitudinis poli E β γ, <lb/>æqualis, ducta recta F μ, ita vt F μ, cadat ſemper in contrariã partẽ rectæ Eλ, nempe in dextram ip-<lb/>ſius E F, ſi E λ, in ſiniſtram eiuſdẽ E F, ducta eſt, vel contra. </s>
  <s xml:id="echoid-s24558" xml:space="preserve">Angulus autem altitudinis poli, quem <lb/>recta F μ, cum recta EF, conſtituit, vergere debet verſus E, hoc eſt, ſurſum verſus, ſi planum au-<lb/>ſtrum reſpicit, ita vt angulus E F μ, ſit angulo altitudinis poli æqualis; </s>
  <s xml:id="echoid-s24559" xml:space="preserve">ſi vero planum ad boreã <lb/>ſpectat, ad partes oppoſitas ipſi E, conſtituen dus idem angulus erit, ita vt angulus E F μ, vna cum <lb/>angulo altitudinis poli compleat duos rectos. </s>
  <s xml:id="echoid-s24560" xml:space="preserve">Recta autem μ F, per F, producta verſus ξ, vt in <lb/>prima figura, quarta, quinta, &amp; </s>
  <s xml:id="echoid-s24561" xml:space="preserve">ſexta, ſecet rectam ex E, per λ, ductam; </s>
  <s xml:id="echoid-s24562" xml:space="preserve">vel certè ipſa F μ, ad par-<lb/>
<anchor type="note" xlink:label="note-0389-01a" xlink:href="note-0389-01"/>
tes μ, extenſa, vt in ſecunda figura, ſecet rectam λ E, per E, protractam in puncto π, rectæq́; </s>
  <s xml:id="echoid-s24563" xml:space="preserve">E π, <lb/>ex linea horæ 12. </s>
  <s xml:id="echoid-s24564" xml:space="preserve">E ε, abſcindatur æqualis recta E ρ, infra quidem punctum E, ſi punctum π, cadit <lb/>vel in ipſam E λ, vel in eam productam ad partes λ, ſupra verò idem punctum E, ſi punctum π, <lb/>in ipſam E λ, per E, productam cadit, vt in ſecunda figura accidit. </s>
  <s xml:id="echoid-s24565" xml:space="preserve">Punctum enim ρ, erit centrũ <lb/>
<anchor type="note" xlink:label="note-0389-02a" xlink:href="note-0389-02"/>
horologii, in quo omnes lineæ horarum à meridie, vel media nocte conuenient. </s>
  <s xml:id="echoid-s24566" xml:space="preserve">Quod ſi quando <lb/>contingat, rectam F μ, nullo modo ſecare rectam per puncta E, λ, ductam, ſed ei æquidiſtare, nõ <lb/>
<anchor type="note" xlink:label="note-0389-03a" xlink:href="note-0389-03"/>
habebit horologium centrum, in quo eius horariæ lineæ coeant, ſed omnes inter ſe parallelæ <lb/>erunt, vt accidit in planis inclinatis per polum mundi tranſeuntibus. </s>
  <s xml:id="echoid-s24567" xml:space="preserve">cuius rei exemplum habes <lb/>in tertia figura.</s>
  <s xml:id="echoid-s24568" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1267" type="float" level="2" n="5">
<note position="left" xlink:label="note-0389-01" xlink:href="note-0389-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0389-02" xlink:href="note-0389-02a" xml:space="preserve">Centrum he-<lb/>rologu.</note>
<note position="right" xlink:label="note-0389-03" xlink:href="note-0389-03a" xml:space="preserve">Quæ plana ho-<lb/>rologiorum @@ <lb/>tro careant.</note>
</div>
<p>
  <s xml:id="echoid-s24569" xml:space="preserve">PRAETEREA ad rectam A B, in puncto E, conſtituatur angulus D E γ, æqualis angulo <lb/>
<anchor type="note" xlink:label="note-0389-04a" xlink:href="note-0389-04"/>
inclinationis plani ſiue verſus B, ſiue verſus A; </s>
  <s xml:id="echoid-s24570" xml:space="preserve">ſitq́ue recta E φ, dictũ angulum conſtituens æqua-<lb/>lis rectæ E C, qui angulus conſtituatur ſupra rectam A B, ſi planum ad auſtrum ſpectat, vt in prio-<lb/>ribus tribus figuris, ſi verò ad boream, infra eandem, vtin tribus figuris poſterioribus factum eſt. <lb/></s>
  <s xml:id="echoid-s24571" xml:space="preserve">Ex puncto autem φ, ad C D, ducatur perpendicularis φ χ. </s>
  <s xml:id="echoid-s24572" xml:space="preserve">Item ex F, ad A B, ducta perpendi-<lb/>culari F ψ, conſtituatur ad eam in puncto ψ, ſiue ad dextram, ſiue ad ſiniſtram partem, angulus <lb/>F ψ ω, angulo inclinationis D E γ, æqualis, ſitq́ue recta ψ ω, rectæ ψ F, æqualis, &amp; </s>
  <s xml:id="echoid-s24573" xml:space="preserve">ex ω, ad ψ F, <lb/>
<anchor type="note" xlink:label="note-0389-05a" xlink:href="note-0389-05"/>
perpendicularis excitetur ω d. </s>
  <s xml:id="echoid-s24574" xml:space="preserve">Recta namque per χ d, ducta erit ſtyli linea, tranſibitq́ue neceſſa-<lb/>rio per centrum horologij ρ, vel certè, vbi non eſt centrum horologii, vt in tertia figura, ipſi lineæ <lb/>meridianæ E ε, parallela erit; </s>
  <s xml:id="echoid-s24575" xml:space="preserve">ita vt in recta χ d, ſtylus horarum index ſit collocandus ad planum <lb/>horologii rectus. </s>
  <s xml:id="echoid-s24576" xml:space="preserve">Satis autem erit, ſi alterum punctorum, nempe vel χ, vel d, inueniatur, vt li-<lb/>
<anchor type="note" xlink:label="note-0389-06a" xlink:href="note-0389-06"/>
nea indicis ſeu ſtyli poſſit duci. </s>
  <s xml:id="echoid-s24577" xml:space="preserve">Recta enim ex ρ, centro horologii per illud punctum inuentum <lb/>ducta, vel certè, vbi non eſt centrum horologij, ducta per illud punctum parallela ipſi lineæ me-<lb/>ridianæ E ε, erit linea ſtyli: </s>
  <s xml:id="echoid-s24578" xml:space="preserve">Rectius tamen eadem linea ducetur, ſi vtrumque punctum inuenia-<lb/>tur, præſertim quando punctum, quod primo inuentum eſt, parum à centro horologii ρ, diſtat.</s>
  <s xml:id="echoid-s24579" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1268" type="float" level="2" n="6">
<note position="left" xlink:label="note-0389-04" xlink:href="note-0389-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0389-05" xlink:href="note-0389-05a" xml:space="preserve">Linea ſtyli, vel <lb/>indieis.</note>
<note position="left" xlink:label="note-0389-06" xlink:href="note-0389-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s24580" xml:space="preserve">INSVPER ex χ, d, punctis educantur ad lineam indicis χ d, duæ perpendiculares χ e, <lb/>d f, rectis χ φ, d ω, æquales, ſingulæ ſingulis, ex vna, &amp; </s>
  <s xml:id="echoid-s24581" xml:space="preserve">eadem quidem parte ipſius rectæ χ d, <lb/>dextra videlicet, vel ſiniſtra, ſi planum in auſtrum ſpectat, vt in prioribus tribus figuris, ſi verò bo-<lb/>ream reſpicit, ad partes diuerſas, nempe vna ad dextram ipſius χ d, &amp; </s>
  <s xml:id="echoid-s24582" xml:space="preserve">ad ſiniſtram altera, vt fa-<lb/>ctum eſt in tribus ſiguris poſterioribus. </s>
  <s xml:id="echoid-s24583" xml:space="preserve">Recta enim e f, ducta, quæ omnino per ρ, centrum horo-<lb/>logii tranſibit, vel certe, vbi non eſt centrum, ipſi lineæ meridianæ E ε, æquidiſtabit, erit axis <lb/>
<anchor type="note" xlink:label="note-0389-07a" xlink:href="note-0389-07"/>
<anchor type="note" xlink:label="note-0389-08a" xlink:href="note-0389-08"/>
mundi ſupra lineam ſtyli χ d, eleuandus pro magnitudine perpendicularium χ e, d f, quæ re-<lb/>ctæ ſint ad planum horologii. </s>
  <s xml:id="echoid-s24584" xml:space="preserve">Cæterum quoniam axis e f, productus ſecat lineam ſtyli χ d, pro-<lb/>ductam in centro horologii ρ, vbi centrum habetur in horologio, aſſnmenda eſt ſemper pars illa <lb/>axis, quæ ex centro ρ, per f, emittitur, non autem illa, quæ per e: </s>
  <s xml:id="echoid-s24585" xml:space="preserve">quod intelligendum eſt, quando <lb/>χ e, d f, ad diuerſas partes lineæ ſtyli ducuntur, vt fit in planis ad boream ſpectantibus, nempe in <lb/>poſterioribus tribus figuris. </s>
  <s xml:id="echoid-s24586" xml:space="preserve">Nam vbi ex eadem parte lineæ ſtyli ducuntur, vt in planis ad auſtrũ <lb/>ſpectantibus contingit, vt diximus, qualia per priores tres figuras exprimuntur, accipiendus eſt to-<lb/>tus axis ρ e f, per puncta e, f, ex ρ, ductus; </s>
  <s xml:id="echoid-s24587" xml:space="preserve">vel certe totus axis e f, vtrinque productus in horolo-<lb/>gio, quod centro caret, cuiuſmodi eſt illud, quod in tertia figura deſcriptum eſt.</s>
  <s xml:id="echoid-s24588" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1269" type="float" level="2" n="7">
<note position="left" xlink:label="note-0389-07" xlink:href="note-0389-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0389-08" xlink:href="note-0389-08a" xml:space="preserve">Axis mundi.</note>
</div>
<p>
  <s xml:id="echoid-s24589" xml:space="preserve">IAM vero aſſumpto in axis portione, quæ ex ρ, per f, ducitur, puncto quolibet I, ducatur ex <lb/>
<anchor type="note" xlink:label="note-0389-09a" xlink:href="note-0389-09"/>
eo ad axem perpendicularis I G, ſecans lineam indicis in G, puncto, per quod ad lineam ſtyli per-<lb/>pendicularis excitetur G H. </s>
  <s xml:id="echoid-s24590" xml:space="preserve">Hæc enim erit ęquinoctialis linea horologij. </s>
  <s xml:id="echoid-s24591" xml:space="preserve">Cadet autem punctum <lb/>
<anchor type="note" xlink:label="note-0389-10a" xlink:href="note-0389-10"/>
G, vel in rectam A B, vt in prioribus tribus figuris vides, vel infra eam, vt in quarta figura, vel ſu-<lb/>pra, vt in quinta &amp; </s>
  <s xml:id="echoid-s24592" xml:space="preserve">ſexta figura cõtingit. </s>
  <s xml:id="echoid-s24593" xml:space="preserve">Quando tamen commodè fieri poteſt, ſuaderem, vt prius <lb/>in linea ſtyli acciperetur punctum G, vbi ſe mutuo ſecant linea ſtyli, &amp; </s>
  <s xml:id="echoid-s24594" xml:space="preserve">recta A B, &amp; </s>
  <s xml:id="echoid-s24595" xml:space="preserve">ex eo ad axem <lb/>ex ρ, per f, ductum perpendicularis duceretur G I, vt in prioribus tribus figuris factũ eſt: </s>
  <s xml:id="echoid-s24596" xml:space="preserve">(quod <lb/>quidem in figura quarta fieri nequit, quia ex puncto, vbi ſe ſecant linea ſtyli, &amp; </s>
  <s xml:id="echoid-s24597" xml:space="preserve">recta A B, non po-<lb/>teſt cadere linea perpendicularis in portionem axis ρ f, ſed in portionem ρ e.) </s>
  <s xml:id="echoid-s24598" xml:space="preserve">Deinde per idem <lb/>
<anchor type="note" xlink:label="note-0389-11a" xlink:href="note-0389-11"/>
punctum G, ad lineam ſtyli perpendicularis excitaretur G H, pro linea æquinoctiali. </s>
  <s xml:id="echoid-s24599" xml:space="preserve">Ex I, quoq; <lb/></s>
  <s xml:id="echoid-s24600" xml:space="preserve">ad lineam ſtyli demittatur perpendicularis IK. </s>
  <s xml:id="echoid-s24601" xml:space="preserve">Erit enim recta I K, longitudo ſtyli, eiusq́ue locus <lb/>in K. </s>
  <s xml:id="echoid-s24602" xml:space="preserve">Angulus autem G ρ f, erit angulus altitudinis poli ſupra planũ propoſitũ, vt monſtrabitur.</s>
  <s xml:id="echoid-s24603" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1270" type="float" level="2" n="8">
<note position="left" xlink:label="note-0389-09" xlink:href="note-0389-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0389-10" xlink:href="note-0389-10a" xml:space="preserve">Aequin octialis <lb/>linea.</note>
<note position="right" xlink:label="note-0389-11" xlink:href="note-0389-11a" xml:space="preserve">Longitudo ſty-<lb/>li eiusq́; locus: <lb/>&amp; angulus alti <lb/>tudinis poli ſu <lb/>pra planũ pro-<lb/>poſitum.</note>
</div>
<pb o="374" file="0390" n="390" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s24604" xml:space="preserve">POSTREMO in linea ſtyli χ d, ſumpta recta G L, ſiue ſupra G, ſiue infra, rectæ G I, æqua-<lb/>li, deſcribatur ex L, circulus ciusuis magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s24605" xml:space="preserve">æquales ſecetur, initio facto <lb/>à recta L M, quæ per L, centrum circuli, &amp; </s>
  <s xml:id="echoid-s24606" xml:space="preserve">punctum M, ducitur, vbi linea æquinoctialis lineam <lb/>
<anchor type="figure" xlink:label="fig-0390-01a" xlink:href="fig-0390-01"/>
<anchor type="note" xlink:label="note-0390-01a" xlink:href="note-0390-01"/>
<anchor type="note" xlink:label="note-0390-02a" xlink:href="note-0390-02"/>
<anchor type="note" xlink:label="note-0390-03a" xlink:href="note-0390-03"/>
meridianam E ε, interſecat, veluti in horologio declinante à Verticali fit. </s>
  <s xml:id="echoid-s24607" xml:space="preserve">Quod ſi contingat li <lb/>neam ęquinoctialem eſſe parallelam lineæ meridianę, vt accidit in plano horologij, quod circu-<lb/>lo maximo æquidiſtat, qui Meridianum circulum in eodẽ puncto ſecat, in quo ab Aequatore di-<lb/>uiditur, vt paulo infra demoſtrabimus, inchoanda erit diuiſio dicti circuli ex L, deſcripti à recta, <lb/>quæ per L, centrum circuli parallela ducitur lineæ æquinoctiali, vel meridianæ, vt in ſexta figura <lb/>huius propoſ. </s>
  <s xml:id="echoid-s24608" xml:space="preserve">apparet in linea M O. </s>
  <s xml:id="echoid-s24609" xml:space="preserve">Hic autem, quoniam plerunque accidit, vt centrum L, &amp; </s>
  <s xml:id="echoid-s24610" xml:space="preserve"><lb/>punctum M, tam vicina inter ſe ſint, vt vix ſine errore aliquo recta L M, à qua diuiſio circuli de-<lb/>
<anchor type="note" xlink:label="note-0390-04a" xlink:href="note-0390-04"/>
bet incipere, duci poſſit, adhibendum omnino erit remedium illud, quod in propoſ. </s>
  <s xml:id="echoid-s24611" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24612" xml:space="preserve">huius libri <lb/>de horologio declinante à Verticali tradidimus, vt nimirum prius lineam horæ 6. </s>
  <s xml:id="echoid-s24613" xml:space="preserve">vel alterius cu-<lb/>iuſpiam horæ ducamus, &amp; </s>
  <s xml:id="echoid-s24614" xml:space="preserve">c. </s>
  <s xml:id="echoid-s24615" xml:space="preserve">vt paulo infra docebimus poſt demonſtrationem. </s>
  <s xml:id="echoid-s24616" xml:space="preserve">Rectæ enim per <lb/>centrum L, &amp; </s>
  <s xml:id="echoid-s24617" xml:space="preserve">puncta diuiſionum emiſſæ ſecabunt æquinoctialem lineam in punctis, per quæ re-<lb/>ctæ emiſſæ per ρ, centrum horologij, vel vbi centrum non eſt, vt in tertia figura, rectæ ipſi lineæ <lb/>meridianæ parallelæ, vel ad lineam æquinoctialem perpendiculares, dabunt horas à meridie, vel <lb/>
<anchor type="note" xlink:label="note-0390-05a" xlink:href="note-0390-05"/>
media nocte, hoc ordine. </s>
  <s xml:id="echoid-s24618" xml:space="preserve">In planis, quæ ad auſtrum ſpectant, portio lineæ meridianæ à centro ho <lb/>
<anchor type="note" xlink:label="note-0390-06a" xlink:href="note-0390-06"/>
rologij ρ, verſus lineam æquinoctialem extenſa, vt in prioribus duabus figuris, vel tota linea me-<lb/>ridiana, vbi centrum deeſt, vt in tertia figura, demonſtrat horam 12. </s>
  <s xml:id="echoid-s24619" xml:space="preserve">meridiei, quæ verò ei ſunt ad <lb/>dexteram in linea æquinoctiali, horas pomeridianas, &amp; </s>
  <s xml:id="echoid-s24620" xml:space="preserve">quæ ad ſiniſtram, antemeridianas ſigni-<lb/>
<anchor type="note" xlink:label="note-0390-07a" xlink:href="note-0390-07"/>
ficant: </s>
  <s xml:id="echoid-s24621" xml:space="preserve">reliqua verò portio lineæ meridianæ à centro quoque incipiens oſtendit horam 12. </s>
  <s xml:id="echoid-s24622" xml:space="preserve">medię <lb/>noctis. </s>
  <s xml:id="echoid-s24623" xml:space="preserve">In planis autem boream reſpicientibus, exiſtente quidem linea æquinoctiali infra centrũ <lb/>horologii ρ, in linea indicis, vt in quarta figura conſpicitur, denotabit portio meridianæ lineæ à <lb/>centro ρ, verſus lineam æquinoctialem porrecta horam 12. </s>
  <s xml:id="echoid-s24624" xml:space="preserve">meridiei, quæ verò ei ſunt ad dexterã <lb/>in linea æquinoctiali, antemeridianas horas, &amp; </s>
  <s xml:id="echoid-s24625" xml:space="preserve">quæ ad ſiniſtram, pomeridianas indicant; </s>
  <s xml:id="echoid-s24626" xml:space="preserve">reliqua <lb/>autem portio meridianæ lineæ vltra centrum verſus ſuperiores partes tendens, ad horam 12. </s>
  <s xml:id="echoid-s24627" xml:space="preserve">me-<lb/>diæ noctis pertinet. </s>
  <s xml:id="echoid-s24628" xml:space="preserve">Exiſtente verò æquinoctiali linea ſupra horologii centrum ρ, in linea indicis, <lb/>ſeu ſtyli, vt in poſterioribus duabus figuris huius deſcriptionis cernitur, portio lineæ meridianæ <lb/>à centro horologij ρ, verſus lineam æquinoctialem producta, vel certè ad ſuperiores partes ten-<lb/>dens, vbi parallelæ ſunt linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s24629" xml:space="preserve">meridiana, vt in ſexta figura, monſtrabit horam <lb/>12. </s>
  <s xml:id="echoid-s24630" xml:space="preserve">mediæ noctis, horæ verò ad dextram lineæ meridianæ in æquinoctiali linea deſcendẽtes ſunt
<pb o="375" file="0391" n="391" rhead="LIBER TERTIVS."/>
antemeridianæ, &amp; </s>
  <s xml:id="echoid-s24631" xml:space="preserve">pomeridianæ ad ſiniſtram: </s>
  <s xml:id="echoid-s24632" xml:space="preserve">reliqua verò portio meridianæ lineæ infra centrum <lb/>horologii ρ, ad horam 12. </s>
  <s xml:id="echoid-s24633" xml:space="preserve">meridiei ſpectat.</s>
  <s xml:id="echoid-s24634" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1271" type="float" level="2" n="9">
  <figure xlink:label="fig-0390-01" xlink:href="fig-0390-01a">
    <image file="0390-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0390-01"/>
  </figure>
<note position="left" xlink:label="note-0390-01" xlink:href="note-0390-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0390-02" xlink:href="note-0390-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0390-03" xlink:href="note-0390-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0390-04" xlink:href="note-0390-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0390-05" xlink:href="note-0390-05a" xml:space="preserve">Lineæ horariæ.</note>
<note position="left" xlink:label="note-0390-06" xlink:href="note-0390-06a" xml:space="preserve">Ordo horarũ.</note>
<note position="left" xlink:label="note-0390-07" xlink:href="note-0390-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s24635" xml:space="preserve">QVOD ſi quando recta per aliquod punctum diuiſionis circuli ex L, deſcripti, &amp; </s>
  <s xml:id="echoid-s24636" xml:space="preserve">per centrũ <lb/>L, ducta, parallela fuerit lineæ æquinoctiali, tum ducta per ρ, centrum horologii linea recta æqui <lb/>noctiali lineæ parallela dabit illam horam, quæcunque fuerit, vt in propoſ. </s>
  <s xml:id="echoid-s24637" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24638" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s24639" xml:space="preserve">de Verti-<lb/>cali declinante diximus. </s>
  <s xml:id="echoid-s24640" xml:space="preserve">Eadem enim hic demonſtratio eſt, ſi pro C, ſumatur ſemper ρ, centrum <lb/>horologii in demonſtratione ibi allata.</s>
  <s xml:id="echoid-s24641" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s24642" xml:space="preserve">CONSTRVCTIONEM autem hanc demonſtrabimus hac ratione. </s>
  <s xml:id="echoid-s24643" xml:space="preserve">Intelligatur in pla <lb/>
<anchor type="note" xlink:label="note-0391-01a" xlink:href="note-0391-01"/>
no horologii proprium ſitum habentis recta A B, Horizonti eſſe parallela ita vt ſit ſectio cõmu-<lb/>nis plani horologii horizontalis, &amp; </s>
  <s xml:id="echoid-s24644" xml:space="preserve">plani horologii declinantis ſimul &amp; </s>
  <s xml:id="echoid-s24645" xml:space="preserve">inclinati, &amp; </s>
  <s xml:id="echoid-s24646" xml:space="preserve">planum per <lb/>
<anchor type="note" xlink:label="note-0391-02a" xlink:href="note-0391-02"/>
rectas A B, E F, E D, ductum concipiatur moueri circa rectam A B, donec Horizonti æquidiſtet, <lb/>atque adeo idem fiat, quod planum horologii horizontalis. </s>
  <s xml:id="echoid-s24647" xml:space="preserve">Quo in ſitu, cum D E F, ſit angulus <lb/>declinationis plani horologii à Verticali, erit reliquus A E F, vel B E F, angulus complementi eiuſ-<lb/>dem declinationis, qualem nimirum Meridianus facit cum linea, quæ in plano declinante Hori-<lb/>zonti æquidiſtat, vel potius cum plano, quod per illam rectam ducitur, rectumq́ue eſt ad Hori-<lb/>zontem. </s>
  <s xml:id="echoid-s24648" xml:space="preserve">Quamobrem recta E F, communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s24649" xml:space="preserve">plani horologii horizonta-<lb/>lis, ac proinde Meridianus planum horologii declinantis ſimul &amp; </s>
  <s xml:id="echoid-s24650" xml:space="preserve">inclinati ſecabit in puncto E.</s>
  <s xml:id="echoid-s24651" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1272" type="float" level="2" n="10">
<note position="right" xlink:label="note-0391-01" xlink:href="note-0391-01a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>horologii à Ver <lb/>ticali declinan<unsure/> <lb/>tis, &amp; ad Hori-<lb/>zontẽ inclinati.</note>
<note position="left" xlink:label="note-0391-02" xlink:href="note-0391-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s24652" xml:space="preserve">QVOD ſi triangulum rectangulum D E γ, circa D E, conuertatur, donec ad planum <lb/>horologii rectum ſit, erit recta A E, (quæ in plano horologij perpendicularis eſt ad D E, <lb/>communem ſectionem trianguli D E γ, &amp; </s>
  <s xml:id="echoid-s24653" xml:space="preserve">plani inclinati) perpendicularis per defin. </s>
  <s xml:id="echoid-s24654" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24655" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s24656" xml:space="preserve">
<anchor type="note" xlink:label="note-0391-03a" xlink:href="note-0391-03"/>
11. </s>
  <s xml:id="echoid-s24657" xml:space="preserve">Euclidis, ad triangulum D E γ, atque adeo per defin. </s>
  <s xml:id="echoid-s24658" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24659" xml:space="preserve">eiuſdem libri, &amp; </s>
  <s xml:id="echoid-s24660" xml:space="preserve">ad rectam E γ. <lb/></s>
  <s xml:id="echoid-s24661" xml:space="preserve">Quare cum utraque linea D E, γ E, perpendicularis ſit ad rectam A E, erit D E γ, angulus <lb/>inclinationis plani propoſiti ad planum per rectas A E, E γ, ductum ex deſin. </s>
  <s xml:id="echoid-s24662" xml:space="preserve">6. </s>
  <s xml:id="echoid-s24663" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24664" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24665" xml:space="preserve">Eucli-<lb/>dis; </s>
  <s xml:id="echoid-s24666" xml:space="preserve">quandoquidem A E, communis ſectio eſt plani propoſiti, &amp; </s>
  <s xml:id="echoid-s24667" xml:space="preserve">dicti plani per rectas A E, <lb/>E γ, ducti. </s>
  <s xml:id="echoid-s24668" xml:space="preserve">Cum igitur angulus D E γ, ſumptus ſit æqualis inclinationi plani propoſiti ad Ho-<lb/>rizontem, atque adeò &amp; </s>
  <s xml:id="echoid-s24669" xml:space="preserve">ad planũ horologij horizontalis Horizonti parallelum, erit planum per <lb/>rectas A E, E γ, ductum, idem quod horologij horizontalis planum, ac propterea recta E γ, in ho <lb/>rizontalis horologij plano iacebit; </s>
  <s xml:id="echoid-s24670" xml:space="preserve">cui quoniã ſumpta eſt æqualis E δ, ſi triangulũ E δ θ, uel potius <lb/>planum per rectas A B, E θ, E δ, ductum, in quo dictum triangulum exiſtit, circa rectam A B, <lb/>concipiatur moueri, donec cum horizontalis horologij plano coniungatur, ita ut E δ, à plano <lb/>
<anchor type="note" xlink:label="note-0391-04a" xlink:href="note-0391-04"/>
D E γ, ad planum inclinatum recto non recedat, ſed ſemper rectum angulum cum A E, conſti-<lb/>tuat, ipſaq́; </s>
  <s xml:id="echoid-s24671" xml:space="preserve">δ θ, æquidiſtet ſemper ipſi A E, fiet E δ, eadem quæ E γ, &amp; </s>
  <s xml:id="echoid-s24672" xml:space="preserve">punctum δ, idem quod γ. <lb/></s>
  <s xml:id="echoid-s24673" xml:space="preserve">Quoniam autem rectæ δ θ, D ε, quarum illa in horologij horizontalis plano, ut modo diximus, <lb/>hæc uerò in plano inclinato exiſtit, ęquidiſtantes, per conſtructionẽ, ipſi A B, inter ſe quoque paral <lb/>
<anchor type="note" xlink:label="note-0391-05a" xlink:href="note-0391-05"/>
lelæ ſunt, poſitæq́ue ſunt æquales, erunt quoque rectæ extrema earum puncta connectentes paral-<lb/>
<anchor type="note" xlink:label="note-0391-06a" xlink:href="note-0391-06"/>
lelæ inter ſe, &amp; </s>
  <s xml:id="echoid-s24674" xml:space="preserve">æquales, nimirum recta γ D, ex puncto γ, uel δ, in plano horizontalis horologij <lb/>ad D, punctum demiſſa, &amp; </s>
  <s xml:id="echoid-s24675" xml:space="preserve">recta θ ε, ex puncto θ, plani horizontalis horologij ad punctum ε, dedu <lb/>cta. </s>
  <s xml:id="echoid-s24676" xml:space="preserve">Cum igitur recta D γ, ſit per defin. </s>
  <s xml:id="echoid-s24677" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24678" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24679" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24680" xml:space="preserve">Euclidis ad planum horizontalis horologij per-<lb/>pendicularis, (propterea quòd in plano D E γ, exiſtens perpendicularis eſt ad E γ, cõmunem ſectio <lb/>nem plani horologij horizontalis, &amp;</s>
  <s xml:id="echoid-s24681" xml:space="preserve">plani D E γ, quod ad planum horizontalis horologij rectum <lb/>
<anchor type="note" xlink:label="note-0391-07a" xlink:href="note-0391-07"/>
eſt. </s>
  <s xml:id="echoid-s24682" xml:space="preserve">quoniam enim A E, oſtenſa eſt recta ad planum D E γ, erit quoque planũ horologii horizonta <lb/>lis per A E, ductum, ad idem planũ per D E γ, rectum, ac uiciſſim idcirco &amp; </s>
  <s xml:id="echoid-s24683" xml:space="preserve">planum D E γ, re-<lb/>
<anchor type="note" xlink:label="note-0391-08a" xlink:href="note-0391-08"/>
ctum ad planum horologij horizontalis) erit quoque ε θ, ad idem planum horizontalis horolo-<lb/>
<anchor type="note" xlink:label="note-0391-09a" xlink:href="note-0391-09"/>
gij perpendicularis, atque adeo per defin. </s>
  <s xml:id="echoid-s24684" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24685" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24686" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24687" xml:space="preserve">Euclidis, &amp; </s>
  <s xml:id="echoid-s24688" xml:space="preserve">ad rectam E θ. </s>
  <s xml:id="echoid-s24689" xml:space="preserve">Ex quo efficitur, re-<lb/>ctam θ ε, in plano Meridiani exiſtere: </s>
  <s xml:id="echoid-s24690" xml:space="preserve">alioqui cum &amp; </s>
  <s xml:id="echoid-s24691" xml:space="preserve">perpẽdicularis ex θ, ad ε θ, cõmunem ſectio-<lb/>nem plani horologij horizontalis, &amp; </s>
  <s xml:id="echoid-s24692" xml:space="preserve">Meridiani in plano Meridiani ducta, ſit per definitionem 4. <lb/></s>
  <s xml:id="echoid-s24693" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24694" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24695" xml:space="preserve">Euclidis, ad planum horologij horizontalis perpendicularis, ducerentur ex eodem puncto <lb/>θ, ad idem planum horologij horizontalis duæ perpendiculares, quod fieri non poteſt. </s>
  <s xml:id="echoid-s24696" xml:space="preserve">Quam-<lb/>
<anchor type="note" xlink:label="note-0391-10a" xlink:href="note-0391-10"/>
obrem Meridianus plano inclinato occurret in puncto ε, atque adeò, cum eidem occurrat in pun-<lb/>cto E, ut paulo ante oſtendimus, (ducitur enim Meridianus per E F, lineam meridianam horolo-<lb/>
<anchor type="note" xlink:label="note-0391-11a" xlink:href="note-0391-11"/>
gij horizontalis) erit recta E ε, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s24697" xml:space="preserve">plani inclinati, hoc eſt, linea meri-<lb/>diana, ſeu horæ 12. </s>
  <s xml:id="echoid-s24698" xml:space="preserve">in plano horologij declinantis ſimul &amp; </s>
  <s xml:id="echoid-s24699" xml:space="preserve">inclinati.</s>
  <s xml:id="echoid-s24700" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1273" type="float" level="2" n="11">
<note position="left" xlink:label="note-0391-03" xlink:href="note-0391-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0391-04" xlink:href="note-0391-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0391-05" xlink:href="note-0391-05a" xml:space="preserve">9. vndec.</note>
<note position="right" xlink:label="note-0391-06" xlink:href="note-0391-06a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0391-07" xlink:href="note-0391-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0391-08" xlink:href="note-0391-08a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0391-09" xlink:href="note-0391-09a" xml:space="preserve">8. vndec.</note>
<note position="right" xlink:label="note-0391-10" xlink:href="note-0391-10a" xml:space="preserve">13. vndec.</note>
<note position="left" xlink:label="note-0391-11" xlink:href="note-0391-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s24701" xml:space="preserve">RECTAM autem E p, eſſe quoque lineam meridianam, ita oſtendi poteſt. </s>
  <s xml:id="echoid-s24702" xml:space="preserve">Intelligatur trian <lb/>gulum E F ψ, circa rectam E ψ, moueri, donec Horizonti æquidiſtet, hoc eſt, cum plano horolo-<lb/>gij horizontalis coniungatur, ita ut F E, ſit rurſus communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s24703" xml:space="preserve">plani horologij <lb/>horizõtalis. </s>
  <s xml:id="echoid-s24704" xml:space="preserve">Deinde in hoc ſitu cõcipiatur circa rectam ψ F, circumferri triangulum ψ F n, donec <lb/>&amp; </s>
  <s xml:id="echoid-s24705" xml:space="preserve">ad planum horologij inclinati, &amp; </s>
  <s xml:id="echoid-s24706" xml:space="preserve">ad planum horologij horizontalis rectum ſit; </s>
  <s xml:id="echoid-s24707" xml:space="preserve">quod quidem <lb/>factum erit, cum recta n ψ, perpendicularis fuerit ad A B. </s>
  <s xml:id="echoid-s24708" xml:space="preserve">Tunc enim recta A B, perpendicularis <lb/>exiſtens ad rectas ψ F, ψ n, perpendicularis erit ad planum triãguli ψ F n, per illas rectas ductum. <lb/></s>
  <s xml:id="echoid-s24709" xml:space="preserve">
<anchor type="note" xlink:label="note-0391-12a" xlink:href="note-0391-12"/>
Igitur &amp; </s>
  <s xml:id="echoid-s24710" xml:space="preserve">planum horologij tam inclinati, quàm horizõtalis per A B, ductum ad idem planum triã <lb/>
<anchor type="note" xlink:label="note-0391-13a" xlink:href="note-0391-13"/>
guli ψ F n, rectum erit, atque adeò uiciſſim hoc ad utrumque illorum rectum exiſtet. </s>
  <s xml:id="echoid-s24711" xml:space="preserve">Quamob-
<pb o="376" file="0392" n="392" rhead="GNOMONICES"/>
rem cum F ψ n, ſit angulus inclinationis plani ad Horizontem, &amp; </s>
  <s xml:id="echoid-s24712" xml:space="preserve">ψ F, Horizonti æquidiſtet, iace-<lb/>bit ψ n, in plano inclinato, hoc eſt, cum recta ψ p, coniuncta erit in dicto plano. </s>
  <s xml:id="echoid-s24713" xml:space="preserve">Quare pun-<lb/>ctum n, in punctum p, cadet, ob æqualitatẽ rectarum ψ n, ψ p. </s>
  <s xml:id="echoid-s24714" xml:space="preserve">cum ergo Meridianus rectus exi-<lb/>
<anchor type="figure" xlink:label="fig-0392-01a" xlink:href="fig-0392-01"/>
<anchor type="note" xlink:label="note-0392-01a" xlink:href="note-0392-01"/>
<anchor type="note" xlink:label="note-0392-02a" xlink:href="note-0392-02"/>
<anchor type="note" xlink:label="note-0392-03a" xlink:href="note-0392-03"/>
ſtens ad planum trianguli ψ F E, in plano horologij horizõtalis exiſtentis tranſeat per E F, atque <lb/>adeo per F n, (quod F n, per defin. </s>
  <s xml:id="echoid-s24715" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24716" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24717" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24718" xml:space="preserve">Euclidis, recta ſit ad planum trianguli E F ψ, propterea <lb/>
<anchor type="note" xlink:label="note-0392-04a" xlink:href="note-0392-04"/>
quòd ad ψ F, communem ſectionem triangulorũ E F ψ, ψ F n, perpendicularis eſt ex conſtructio-<lb/>ne) occurret Meridianus plano inclinato in puncto p, ac proinde recta E p, communis ſectio <lb/>erit Meridiani, &amp; </s>
  <s xml:id="echoid-s24719" xml:space="preserve">plani inclinati.</s>
  <s xml:id="echoid-s24720" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1274" type="float" level="2" n="12">
<note position="right" xlink:label="note-0391-12" xlink:href="note-0391-12a" xml:space="preserve">4. vndec.</note>
<note position="right" xlink:label="note-0391-13" xlink:href="note-0391-13a" xml:space="preserve">18. vndec.</note>
  <figure xlink:label="fig-0392-01" xlink:href="fig-0392-01a">
    <image file="0392-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0392-01"/>
  </figure>
<note position="left" xlink:label="note-0392-01" xlink:href="note-0392-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0392-02" xlink:href="note-0392-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0392-03" xlink:href="note-0392-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0392-04" xlink:href="note-0392-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s24721" xml:space="preserve">ITAQVE cum θ λ, ad E θ, perpendicularis ſit, &amp; </s>
  <s xml:id="echoid-s24722" xml:space="preserve">æqualis rectæ D γ, hoc eſt, rectæ θ ε, ex θ, <lb/>puncto plani horologii horizontalis ad ε, punctum plani inclinati demiſſæ, erit triangulum <lb/>E θ λ, æquale omnino triangulo E θ ε, in plano Meridiani exiſtenti, cuius latus E θ, in horizonta-<lb/>lis horologij plano, E ε, in plano inclinato, &amp; </s>
  <s xml:id="echoid-s24723" xml:space="preserve">θ ε, in plano Meridiani exiſtit; </s>
  <s xml:id="echoid-s24724" xml:space="preserve">rectaq́ue E λ, rectæ <lb/>E ε, æqualis erit, &amp; </s>
  <s xml:id="echoid-s24725" xml:space="preserve">angulus θ E λ, angulo θ E ε, in Meridiani plano. </s>
  <s xml:id="echoid-s24726" xml:space="preserve">Quocirca ſi concipiatur triã-<lb/>gulum E θ λ, circa rectam E θ, in plano horologij horizontalis exiſtentem circumduci, donec cum <lb/>plano Meridiani coniungatur, efficietur prorſus idem triangulum E θ λ, quod triangulum E θ ε, <lb/>
<anchor type="note" xlink:label="note-0392-05a" xlink:href="note-0392-05"/>
in plano Meridiani exiſtens, punctumq́ue λ, in punctum ε, cadet. </s>
  <s xml:id="echoid-s24727" xml:space="preserve">Quia verò horologio inclina-<lb/>to in propria poſitione conſtituto, ita vt recta E F, in plano horologii horizontalis exiſtens ſit com <lb/>munis ſectio ipſius, ac Meridiani, recta μ F, circumducta, donec ad planum Meridiani, vel trian-<lb/>guli E θ λ, quod iam idem eſſe demonſtrauimus, quod E θ ε, in Meridiani plano exiſtens, perue-<lb/>niat, ea tamen lege, ut eundem ſemper angulum E F μ, conficiat, axis mundi eſt; </s>
  <s xml:id="echoid-s24728" xml:space="preserve">propterea quod <lb/>angulus E F μ, in planis auſtrũ reſpicientibus ſumptus eſt æqualis altitudini poli, in planis autem <lb/>ad boream ſpectantibus conſtituit una cum angulo altitudinis poli duos rectos, ex conſtructione; <lb/></s>
  <s xml:id="echoid-s24729" xml:space="preserve">ac idcirco recta F μ, ad partes μ, producta per polum arcticum trãſit, fit ut punctum, in quo occur <lb/>rit plano inclinato, uel rectę E λ, quæ eadem iam eſt, quæ E ε, ut oſtendimus, ſit illud, in quo om-<lb/>nes lineæ horarum à meridie, vel media nocte conueniunt, ex coroll. </s>
  <s xml:id="echoid-s24730" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24731" xml:space="preserve">21. </s>
  <s xml:id="echoid-s24732" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24733" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24734" xml:space="preserve">quod qui-<lb/>dem centrum horologij appellari ſolet. </s>
  <s xml:id="echoid-s24735" xml:space="preserve">Vnde cum axis μ F, ſecet rectam E λ, in π, ſi recta E π, in
<pb o="377" file="0393" n="393" rhead="LIBER TERTIVS."/>
rectam E ε, transferatur uſque ad punctum ρ, erit ρ, centrum horologij. </s>
  <s xml:id="echoid-s24736" xml:space="preserve">Nam axis μ F, ſi vnà <lb/>cum triangulo E θ λ, circa rectam E θ, in plano horologij horizontalis exiſtentem circumuol-<lb/>uatur, donec cum Meridiano coniungatur, propriumq́ue ſitum adipiſcatur, in eo puncto oc-<lb/>curret plano propoſito, vt ex demonſtratis patet. </s>
  <s xml:id="echoid-s24737" xml:space="preserve">Non difficile autem erit intelligere, an axis <lb/>
<anchor type="note" xlink:label="note-0393-01a" xlink:href="note-0393-01"/>
plano inclinato occurrat infra rectam A B, an ſupra. </s>
  <s xml:id="echoid-s24738" xml:space="preserve">Si enim axis μ F, per F, productus ſecet <lb/>rectam E λ, vel ipſam productam ad partes λ, vt in prima, quarta, quinta, &amp; </s>
  <s xml:id="echoid-s24739" xml:space="preserve">ſexta figuris con-<lb/>tingit, erit centrum ρ, infra rectam A B, quia recta E λ, cadit in rectam E ε, infra rectam A B, cum <lb/>punctum λ, in punctum ε, cadat, vt dictum eſt: </s>
  <s xml:id="echoid-s24740" xml:space="preserve">Si verò axis μ F, ad partes μ, productus ſecet re-<lb/>ctam E λ, per E, productam, vt in ſecunda figura cernitur, erit centrum ρ, ſupra rectam A B, quòd <lb/>recta E λ, per E, protracta cadat in rectam E ε, per E, protractam, vt ex dictis conſtat, quandoqui-<lb/>
<anchor type="note" xlink:label="note-0393-02a" xlink:href="note-0393-02"/>
dem punctum λ, in punctum ε, cadit. </s>
  <s xml:id="echoid-s24741" xml:space="preserve">Quod ſi axis F μ, nullo modo rectam E λ, ſecet æquidiſta-<lb/>bit planũ inclinatum axi F μ, ac proinde horologium in eo deſcriptum centrum non habebit, ſed <lb/>omnes lineæ horariæ in eo parallelæ erunt, ut conſtat ex coroll. </s>
  <s xml:id="echoid-s24742" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24743" xml:space="preserve">22. </s>
  <s xml:id="echoid-s24744" xml:space="preserve">primi libri.</s>
  <s xml:id="echoid-s24745" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1275" type="float" level="2" n="13">
<note position="left" xlink:label="note-0392-05" xlink:href="note-0392-05a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">An cẽrrum he <lb/>rologii ſit infra <lb/>rectam A B, ſu <lb/>mendum, an <lb/>ſupra, quo mo-<lb/>do cognoſe<unsure/>a-<lb/>tur.</note>
<note position="left" xlink:label="note-0393-02" xlink:href="note-0393-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s24746" xml:space="preserve">QVONIAM autem linea indicis, in qua uidelicet ſtylus affigendus eſt, talis eſſe debet, ut <lb/>ſtylus, uel alia linea ex quocunque eius puncto ad planũ horologij perpendicularis ducta in axem <lb/>mundi cadat, ita ut planum per illam perpendicularẽ, &amp; </s>
  <s xml:id="echoid-s24747" xml:space="preserve">axem mundi ductum rectũ ſit ad planũ <lb/>
<anchor type="note" xlink:label="note-0393-03a" xlink:href="note-0393-03"/>
horologij, inſtar proprii cuiuſdã Meridiani ipſius plani horologij, ut propoſ. </s>
  <s xml:id="echoid-s24748" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24749" xml:space="preserve">huius libri oſtendi <lb/>mus; </s>
  <s xml:id="echoid-s24750" xml:space="preserve">demonſtrabimus talem eſſe rectam χ d, hac ratione. </s>
  <s xml:id="echoid-s24751" xml:space="preserve">Si triangulum rectangulũ E φ χ, circa <lb/>rectam E χ, moueatur, donec rectum ſit ad planum inclinatum, in planis quidem auſtrum reſpi-<lb/>cientibus, ſurſum uerſus, in planis autem boream reſpicientibus deorſum uerſus, erit per defi-<lb/>
<anchor type="note" xlink:label="note-0393-04a" xlink:href="note-0393-04"/>
nitionem 4. </s>
  <s xml:id="echoid-s24752" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24753" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24754" xml:space="preserve">Euclidis, recta A E, in plano inclinato exiſtens, quæ perpendicularis eſt ad <lb/>E χ, cõmunem ſectionem plani inclinati &amp; </s>
  <s xml:id="echoid-s24755" xml:space="preserve">trianguli E φ χ, eam poſitionem habentis, perpen-<lb/>dicularis ad triangulum E φ χ, atque adeo &amp; </s>
  <s xml:id="echoid-s24756" xml:space="preserve">ad rectam E φ, ex defin. </s>
  <s xml:id="echoid-s24757" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24758" xml:space="preserve">eiuſdem libri. </s>
  <s xml:id="echoid-s24759" xml:space="preserve">Quia ergo <lb/>utraque linea E χ, E φ, perpendicularis eſt ad rectam A E, erit angulus φ E χ, angulus inclinatio-<lb/>nis plani propoſiti ad planum per rectas A E, E φ, ductum, ex defin. </s>
  <s xml:id="echoid-s24760" xml:space="preserve">6. </s>
  <s xml:id="echoid-s24761" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24762" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24763" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24764" xml:space="preserve">cum A E, <lb/>communis ſectio ſit propoſiti plani, &amp; </s>
  <s xml:id="echoid-s24765" xml:space="preserve">eius, quod per rectas A E, E φ, ducitur. </s>
  <s xml:id="echoid-s24766" xml:space="preserve">Cum igitur angulus <lb/>φ E χ, ſit æqualis complemento inclinationis plani propoſiti ad Horizontem (nam angulus <lb/>B E φ, uel A E φ, ſumptus eſt æqualis inclinationi plani ad Horizontẽ) hoc eſt, æqualis inclinatio-<lb/>nis plani ad Verticalem illum circulum, qui per rectam A B, ducitur, erit planum per rectas A E, <lb/>E φ, ductum idem, quod Verticalis illius circuli planum; </s>
  <s xml:id="echoid-s24767" xml:space="preserve">ac propterea recta E φ, in Verticali illo <lb/>
<anchor type="note" xlink:label="note-0393-05a" xlink:href="note-0393-05"/>
circulo exiſtet. </s>
  <s xml:id="echoid-s24768" xml:space="preserve">Et quoniam recta E φ, ſumpta eſt æqualis rectæ E C, &amp; </s>
  <s xml:id="echoid-s24769" xml:space="preserve">recta E F, rectæ E β, tran-<lb/>ſibit axis mundi F μ, occurrens plano horizontalis horologij in F, per punctum φ, in dicto illo <lb/>circulo Verticali; </s>
  <s xml:id="echoid-s24770" xml:space="preserve">quia hac ratione axis F μ, conſtituet cum meridiana linea horologij horizon-<lb/>talis E F, in F, angulum altitudinis poli ſupra Horizontem uerſus partes boreales, cum recta uero <lb/>E φ, per quam dictus ille Verticalis, immo &amp; </s>
  <s xml:id="echoid-s24771" xml:space="preserve">Verticalis propriè dictus ducitur, angulum comple <lb/>mẽti altitudinis poli ſupra Horizontẽ, adeo ut axis F μ, cõſtituat triangulum cum rectis E F, E φ, <lb/>rectangulum in plano Meridiani circuli, &amp; </s>
  <s xml:id="echoid-s24772" xml:space="preserve">omnino æquale, &amp; </s>
  <s xml:id="echoid-s24773" xml:space="preserve">ſimile triangulo E β C, quia non <lb/>ſolum E F, ſed et E φ, in illo ſitu in Meridiani plano exiſtit, angulusq́ue F E φ, rectus eſt: </s>
  <s xml:id="echoid-s24774" xml:space="preserve">quod <lb/>ita oſtendemus. </s>
  <s xml:id="echoid-s24775" xml:space="preserve">Quoniã Verticalis ille circulus per rectas A B, E φ, ductus, rectus eſt ad horizon-<lb/>talis horologii planũ, erit per defin. </s>
  <s xml:id="echoid-s24776" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24777" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24778" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24779" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24780" xml:space="preserve">recta E φ, in illo Verticali exiſtens, quæ oſtenſa <lb/>
<anchor type="note" xlink:label="note-0393-06a" xlink:href="note-0393-06"/>
eſt perpendicularis ad A E, cõmunem ſectionẽ dicti Verticalis, &amp; </s>
  <s xml:id="echoid-s24781" xml:space="preserve">plani horologij horizõtalis, ad <lb/>planum horlogij horizontalis perpendicularis; </s>
  <s xml:id="echoid-s24782" xml:space="preserve">ac proinde, per defin. </s>
  <s xml:id="echoid-s24783" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24784" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24785" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24786" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24787" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s24788" xml:space="preserve">ad rectã <lb/>E F, in plano horologij horizontalis exiſtentẽ. </s>
  <s xml:id="echoid-s24789" xml:space="preserve">Rectus ergo eſt angulus F E φ. </s>
  <s xml:id="echoid-s24790" xml:space="preserve">Ex quo fit, rectam <lb/>E φ, in plano Meridiani exiſtere: </s>
  <s xml:id="echoid-s24791" xml:space="preserve">alioquin cum &amp; </s>
  <s xml:id="echoid-s24792" xml:space="preserve">perpendicularis ex E, ad E F, cõmunem ſectio-<lb/>nem plani horologii horizontalis, ac Meridiani ducta in plano Meridiani ſit ad horologij hori-<lb/>zontalis planum perpendicularis, ex defin. </s>
  <s xml:id="echoid-s24793" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24794" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24795" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24796" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24797" xml:space="preserve">ducerentur ex eodem puncto E, ad <lb/>idem planum horologij horizontalis duæ perpendiculares; </s>
  <s xml:id="echoid-s24798" xml:space="preserve">quod fieri non poteſt. </s>
  <s xml:id="echoid-s24799" xml:space="preserve">Cauſa autem, <lb/>
<anchor type="note" xlink:label="note-0393-07a" xlink:href="note-0393-07"/>
propter quam triangulum E φ χ, moueri debeat ſurſum uerſus in planis auſtrum reſpicientibus <lb/>deorſum verò uerſus in ijs, quæ in boream ſpectant, ſi tamen in illis triangulum E φ χ, ſupra <lb/>rectam A B, in his autem infra eandem, vt præcepimus, conſtruatur, hæc eſt: </s>
  <s xml:id="echoid-s24800" xml:space="preserve">quoniam nimirum <lb/>in illis axis mundi F μ, per punctum F, in plano horologij horizontalis tranſiens occurrit Verti-<lb/>
<anchor type="note" xlink:label="note-0393-08a" xlink:href="note-0393-08"/>
cali illi circulo per rectam A B, ducto, ſupra rectam A B, in his uero infra rectam A B, poſtquam <lb/>iam plano inclinato occurrit, ut perſpicuum eſt, ſi plana inclinata, planum horologij horizonta-<lb/>lis, dictus Verticalis, &amp; </s>
  <s xml:id="echoid-s24801" xml:space="preserve">axis mundi F μ, in proprijs poſitionibus cõcipiantur. </s>
  <s xml:id="echoid-s24802" xml:space="preserve">Rurſus ſi triangu-<lb/>lum rectangulum ψ d ω, circa rectam ψ d, ſurſum uerſus moueatur, donec rectum ſit ad planũ <lb/>inclinatum, erit per defin. </s>
  <s xml:id="echoid-s24803" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24804" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24805" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24806" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24807" xml:space="preserve">recta A ψ, in plano inclinato exiſtens, rectoſq́ue angu-<lb/>los faciens cum ψ d, communi ſectione trianguli ψ d ω, &amp; </s>
  <s xml:id="echoid-s24808" xml:space="preserve">plani inclinati, perpendicularis ad <lb/>triangulum ψ d ω, atque adeo per defin. </s>
  <s xml:id="echoid-s24809" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24810" xml:space="preserve">eiuſdem libri, &amp; </s>
  <s xml:id="echoid-s24811" xml:space="preserve">ad rectam ψ ω. </s>
  <s xml:id="echoid-s24812" xml:space="preserve">Quia uero utraque <lb/>recta ψ ω, ψ d, perpendicularis eſt ad rectam A ψ, erit per defin. </s>
  <s xml:id="echoid-s24813" xml:space="preserve">6. </s>
  <s xml:id="echoid-s24814" xml:space="preserve">eiuſdem libri, ω ψ d, angu-<lb/>lus inclinationis plani propoſiti ad planum per rectas A ψ, ψ ω, ductũ, cum A ψ, ſit communis <lb/>ſectio propoſiti plani, &amp; </s>
  <s xml:id="echoid-s24815" xml:space="preserve">eius, quod per rectas A ψ, ψ ω, ducitur. </s>
  <s xml:id="echoid-s24816" xml:space="preserve">Cum ergo angulus ω ψ d, ſum-
<pb o="378" file="0394" n="394" rhead="GNOMONICES"/>
ptus ſit æqualis inclinationi plani propoſiti ad Horizontem, atque adeo &amp; </s>
  <s xml:id="echoid-s24817" xml:space="preserve">ad planum horologij <lb/>horizontalis Horizonti parallelum, erit planum per rectas A ψ, ψ ω, ductum, idem quod pla-<lb/>num horologij horizontalis, ac proinde recta ψ ω, in plano horologij horizontalis iacebit; </s>
  <s xml:id="echoid-s24818" xml:space="preserve">quę <lb/>
<anchor type="figure" xlink:label="fig-0394-01a" xlink:href="fig-0394-01"/>
<anchor type="note" xlink:label="note-0394-01a" xlink:href="note-0394-01"/>
<anchor type="note" xlink:label="note-0394-02a" xlink:href="note-0394-02"/>
<anchor type="note" xlink:label="note-0394-03a" xlink:href="note-0394-03"/>
quoniam æqualis ſumpta eſt rectæ ψ F, ſi triangulum E F ψ, circa rectam E ψ, moueatur, donec <lb/>cum plano horologij horizontalis coniungatur, fiet ψ ω, eadem, quæ ψ F, &amp; </s>
  <s xml:id="echoid-s24819" xml:space="preserve">punctum ω, idem <lb/>quod F, propterea quòd in illo motu recta F ψ, ſemper rectos angulos facit cum E ψ, manetq́ue <lb/>ſemper in plano trianguli ψ ω d; </s>
  <s xml:id="echoid-s24820" xml:space="preserve">alias in plano horizontalis horologii ducerentur ad rectam E ψ, <lb/>in puncto ψ, duæ perpendiculares ω ψ, F ψ, quod eſt abſurdum. </s>
  <s xml:id="echoid-s24821" xml:space="preserve">Cum ergo axis mundi F μ, tran <lb/>ſeat per F, punctum horizontalis horologij, ſit vt etiam per punctum ω, trianguli ψ d ω, illum <lb/>ſitum habentis incedat. </s>
  <s xml:id="echoid-s24822" xml:space="preserve">Hæc cum ita ſint, quoniam tam recta φ χ, quàm recta ω d, ad planum in-<lb/>clinatum, per defin. </s>
  <s xml:id="echoid-s24823" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24824" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24825" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24826" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24827" xml:space="preserve">perpendicularis eſt, (ſi in illo ſitu intelligantur poſita eſſe triã-<lb/>
<anchor type="note" xlink:label="note-0394-04a" xlink:href="note-0394-04"/>
gula E φ χ, ψ ω d,) ac idcirco etiam ad rectam χ d, ex defin. </s>
  <s xml:id="echoid-s24828" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24829" xml:space="preserve">eiuſdem libri, fit, vt rectæ φ χ, <lb/>
<anchor type="note" xlink:label="note-0394-05a" xlink:href="note-0394-05"/>
ω d, parallelæ ſint, &amp; </s>
  <s xml:id="echoid-s24830" xml:space="preserve">ideo in eodem plano, quod per rectas φ χ, ω d, ducitur; </s>
  <s xml:id="echoid-s24831" xml:space="preserve">quod quidem <lb/>rectum eſt ad planum inclinatum, tranſitq́ue per axem mundi, quem per puncta φ, ω, incedere <lb/>demonſtrauimus. </s>
  <s xml:id="echoid-s24832" xml:space="preserve">Quare planum per rectas φ χ, ω d, χ d, ductum, rectumq́ue exiſtens ad planũ <lb/>inclinatũ, erit inſtar noui, ac proprij cuiuſdam Meridiani ipſius plani inclinati, in quo nouo Me-<lb/>ridiano omnes lineæ perpendiculares ductæ ad rectam χ d, perpendiculares quoque ſunt, per de-<lb/>fin. </s>
  <s xml:id="echoid-s24833" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24834" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24835" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24836" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24837" xml:space="preserve">ad planum inclinatum, occurruntq́ue axi per puncta φ, ω, tranſeunti. </s>
  <s xml:id="echoid-s24838" xml:space="preserve">Quo-<lb/>circa recta χ d, linea indicis erit, nempe communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s24839" xml:space="preserve">proprij illius Me-<lb/>ridiani dicti, tanquàm linea meridiana, ſi circulus, cui horologium ęquidiſtat, eſſet Horizon, quã-<lb/>doquidem ſtylus quicunque in illa ad planum inclinatum erectus axem mundi ſecat, vt diximus, <lb/>
<anchor type="note" xlink:label="note-0394-06a" xlink:href="note-0394-06"/>
quemadmodum &amp; </s>
  <s xml:id="echoid-s24840" xml:space="preserve">in aliis horologiis fit. </s>
  <s xml:id="echoid-s24841" xml:space="preserve">Quod autem linea hæc in dicis χ d, in horologijs centrũ <lb/>habentibus ducenda ſit per centrũ horologii ρ, perſpicuum eſt. </s>
  <s xml:id="echoid-s24842" xml:space="preserve">Cum enim axis tranſeat per ρ, cen <lb/>trum, ſecabit omnino planum illud rectum ad horologii planum, &amp; </s>
  <s xml:id="echoid-s24843" xml:space="preserve">per axem tranſiens, nempe <lb/>nouus ille Meridianus, planum horologii in ρ, ac propterea communis ſectio illius, &amp; </s>
  <s xml:id="echoid-s24844" xml:space="preserve">plani horo <lb/>logii per ρ, tranſibit. </s>
  <s xml:id="echoid-s24845" xml:space="preserve">In horologiis denique centro carentibus, eandem lineam indicis χ d, pa-<lb/>rallelam eſſe meridianæ lineæ, ſeu horæ 12. </s>
  <s xml:id="echoid-s24846" xml:space="preserve">hoc modo fiet manifeſtum. </s>
  <s xml:id="echoid-s24847" xml:space="preserve">Quoniam tam Meridia <lb/>nus Horizontis, quàm proprius ille Meridianus plani inclinati, qui nimirũ in plano facit lineam <lb/>indicis χ d, per axem mundi tranſit, erunt ſectiones, quas in plano inclinato faciunt, hoc eſt, li-<lb/>nea meridiana, &amp; </s>
  <s xml:id="echoid-s24848" xml:space="preserve">linea indicis, parallelæ, per propoſ. </s>
  <s xml:id="echoid-s24849" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24850" xml:space="preserve">primi libri, quandoquidem planum ho-<lb/>rologii axi æquidiſtat, cum illud non ſecet, vt dictum eſt.</s>
  <s xml:id="echoid-s24851" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1276" type="float" level="2" n="14">
<note position="right" xlink:label="note-0393-03" xlink:href="note-0393-03a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0393-04" xlink:href="note-0393-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0393-05" xlink:href="note-0393-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0393-06" xlink:href="note-0393-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0393-07" xlink:href="note-0393-07a" xml:space="preserve">13. vndec.</note>
<note position="left" xlink:label="note-0393-08" xlink:href="note-0393-08a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0394-01" xlink:href="fig-0394-01a">
    <image file="0394-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0394-01"/>
  </figure>
<note position="left" xlink:label="note-0394-01" xlink:href="note-0394-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0394-02" xlink:href="note-0394-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0394-03" xlink:href="note-0394-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0394-04" xlink:href="note-0394-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0394-05" xlink:href="note-0394-05a" xml:space="preserve">6. et 7. vnde. <lb/>18. &amp; 7. vn <lb/>dec.</note>
<note position="left" xlink:label="note-0394-06" xlink:href="note-0394-06a" xml:space="preserve">50</note>
</div>
<pb o="379" file="0395" n="395" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s24852" xml:space="preserve">INTELLIGANTVR quoque rectæ χ e, d f, moueri circa rectam χ d, donec perpendi-<lb/>culares ſint ad planum inclinatum, ambæ quidem ſurſum verſus in illis horologiis, quæ auſtrum <lb/>reſpiciunt, at verò in ijs, quæ ſpectant ad boream, recta quidem χ e, deorſum, recta verò d f, ſur-<lb/>ſum verſus. </s>
  <s xml:id="echoid-s24853" xml:space="preserve">Fient enim hac ratione puncta e, f, cadem, quæ φ, &amp; </s>
  <s xml:id="echoid-s24854" xml:space="preserve">ω, propter æqualitatem linea-<lb/>rum χ φ, χ e, &amp; </s>
  <s xml:id="echoid-s24855" xml:space="preserve">d ω, d f. </s>
  <s xml:id="echoid-s24856" xml:space="preserve">Cum igitur axis mundi per puncta φ, ω, tranſeat, vt iam demonſtra-<lb/>uimus, tranſibit idem per puncta e, f, in illo ſitu. </s>
  <s xml:id="echoid-s24857" xml:space="preserve">Quia verò axis tranſit quoque per centrum ρ, vel <lb/>vbi centrum non eſt, æquidiſtat lineæ indicis χ d, (vt enim paulo ante demonſtrauimus, idcirco <lb/>linea meridiana, &amp; </s>
  <s xml:id="echoid-s24858" xml:space="preserve">linea indicis in horologio, vbi centrum non eſt, parallelæ ſunt, quia vtraque <lb/>parallela eſt axi mundi, vt conſtat ex demonſtratione propoſ. </s>
  <s xml:id="echoid-s24859" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24860" xml:space="preserve">primi libri) fit vt recta e f, tran-<lb/>
<anchor type="note" xlink:label="note-0395-01a" xlink:href="note-0395-01"/>
ſeat quoque per centrum ρ, vel ipſi χ d, æquidiſtet. </s>
  <s xml:id="echoid-s24861" xml:space="preserve">Nam ſi circumducatur vnà cum rectis χ e, <lb/>d f, circa χ d, coniungetur cum axe, ita vt idem ſit axis, quæ recta e f. </s>
  <s xml:id="echoid-s24862" xml:space="preserve">Quamobrem axis eleuan-<lb/>dus eſt ex centro ρ, ſecundum angulum f ρ d, vel e ρ χ, qui quidem eſt angulus altitudinis poli <lb/>ſupra planum inclinatum: </s>
  <s xml:id="echoid-s24863" xml:space="preserve">(quia huiuſmodi angulus æqualis eſt ei, quem axis mundi, &amp; </s>
  <s xml:id="echoid-s24864" xml:space="preserve">commu <lb/>
<anchor type="note" xlink:label="note-0395-02a" xlink:href="note-0395-02"/>
nis ſectio noui Meridiani ipſius plani inclinati, &amp; </s>
  <s xml:id="echoid-s24865" xml:space="preserve">circuli maximi, cui planum horologii inclina-<lb/>ti æquidiſtat, conſtituunt; </s>
  <s xml:id="echoid-s24866" xml:space="preserve">propterea quod hæc communis ſectio parallela eſt.</s>
  <s xml:id="echoid-s24867" xml:space="preserve"><unsure/> rectæ χ d, in plano <lb/>
<anchor type="note" xlink:label="note-0395-03a" xlink:href="note-0395-03"/>
horologii. </s>
  <s xml:id="echoid-s24868" xml:space="preserve">Manifeſtum autem eſt, hunc angulum in Meridiano proprio plani inclinati conſtiru-<lb/>tum in centro mundi inſiſtere arcui altitudinis poli ſupra illum circulum maximum, cui horolo-<lb/>gium æquidiſtat) vel certè, vbi centrum non habetur, vt in tertia figura, eleuandus eſt ſecundum <lb/>perpendiculares χ e, d f, quæ æquales ſunt inter ſe, propterea quòd axis e f, lineæ indicis χ d, <lb/>æquidiſtat, vt probatum eſt. </s>
  <s xml:id="echoid-s24869" xml:space="preserve">Facile autem erit intelligere, cur in planis auſtrum reſpicientibus <lb/>
<anchor type="note" xlink:label="note-0395-04a" xlink:href="note-0395-04"/>
utraque linea χ e, d f, ducenda ſit eadem ex parte recte χ d, in planis autem, quæ boreales partes <lb/>reſpiciunt, una ex parte dextra, &amp; </s>
  <s xml:id="echoid-s24870" xml:space="preserve">altera ex ſiniſtra. </s>
  <s xml:id="echoid-s24871" xml:space="preserve">Quoniam enim in illis, ut diximus, vtrumque <lb/>triangulum E φ χ, φ ω d, ſurſum uerſus uoluitur circa rectas E χ, φ d, donec rectum ſit ad pla-<lb/>num inclinatum, ducenda eſt utraque linea χ e, d f, ex eadem parte rectæ χ d, ut cum utraque <lb/>circumuertitur, donec perpẽdicularis ſit ad planum inclinatum ex parte ſuperiori, puncta e, f, ca-<lb/>dant in puncta φ, ω, per quæ axis ducitur, &amp; </s>
  <s xml:id="echoid-s24872" xml:space="preserve">quorum utrumque ex parte ſuperiori exiſtit. </s>
  <s xml:id="echoid-s24873" xml:space="preserve">Quia <lb/>uerò in his triangulum E φ χ, deorſum, &amp; </s>
  <s xml:id="echoid-s24874" xml:space="preserve">φ ω d, ſurſum uerſus moueri intelligitur circa rectas <lb/>E φ, φ d, vt diximus, donec rectum ſit ad planum inclinatum, neceſſe eſt, unam ex una parte, <lb/>&amp; </s>
  <s xml:id="echoid-s24875" xml:space="preserve">ex altera alteram duci, ut cum utraque circumducitur, donec ad planum inclinatum ſit perpẽ-<lb/>dicularis, recta quidem d f, ex parte ſuperiori plani ſit erecta, punctumq́; </s>
  <s xml:id="echoid-s24876" xml:space="preserve">f, in punctum ω, (quod <lb/>
<anchor type="note" xlink:label="note-0395-05a" xlink:href="note-0395-05"/>
et iam ſupra planum eſt) cadat, recta verò χ e, ex parte inferiori erigatur, punctumq́ue e, idem <lb/>fiat, quod φ, punctum infra planum quoque exiſtens. </s>
  <s xml:id="echoid-s24877" xml:space="preserve">Ita enim fiet, vt recta ef, axem mundi, quẽ <lb/>per puncta φ, ω, tranſire oſtendimus, referat; </s>
  <s xml:id="echoid-s24878" xml:space="preserve">immò ſequetur, vt eadem linea conſtituatur ex e f, <lb/>&amp; </s>
  <s xml:id="echoid-s24879" xml:space="preserve">axe mundi. </s>
  <s xml:id="echoid-s24880" xml:space="preserve">Similiter patet ratio, cur in prioribus horologijs accipiatur totus axis ρ fe, in po-<lb/>ſterioribus autem portio duntaxat ρ f, &amp; </s>
  <s xml:id="echoid-s24881" xml:space="preserve">non ρ e: </s>
  <s xml:id="echoid-s24882" xml:space="preserve">quia videlicet in illis totus axis ρ f e, extat ſupra <lb/>planum inclinatum, quòd &amp; </s>
  <s xml:id="echoid-s24883" xml:space="preserve">puncta f, e, ſupra idem planum exiſtant; </s>
  <s xml:id="echoid-s24884" xml:space="preserve">In his verò portio axis ρ f, <lb/>exiſtit quidem ſupra planum, at ρ e, infra, propterea quòd &amp; </s>
  <s xml:id="echoid-s24885" xml:space="preserve">punctum f, ſupra idem, at punctum <lb/>e, infra exiſtit, vt ex dictis perſpicuum eſt.</s>
  <s xml:id="echoid-s24886" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1277" type="float" level="2" n="15">
<note position="left" xlink:label="note-0395-01" xlink:href="note-0395-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0395-02" xlink:href="note-0395-02a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0395-03" xlink:href="note-0395-03a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0395-04" xlink:href="note-0395-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0395-05" xlink:href="note-0395-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s24887" xml:space="preserve">QVIA verò axis mundi ρ f, rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s24888" xml:space="preserve">10. </s>
  <s xml:id="echoid-s24889" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24890" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24891" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s24892" xml:space="preserve">ad Æquatorem, tranſitq́; <lb/></s>
  <s xml:id="echoid-s24893" xml:space="preserve">per eius centrum, atque adeò rectos angulos facit, per defin. </s>
  <s xml:id="echoid-s24894" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24895" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24896" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24897" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24898" xml:space="preserve">cum quacunque recta <lb/>
<anchor type="note" xlink:label="note-0395-06a" xlink:href="note-0395-06"/>
ex centro Aequatoris in eius plano ducta, efficitur, vt ſi punctum I, in axe pro centro mundi, ſiue <lb/>Æquatoris accipiatur, (poteſt enim quodcunque punctum axis ρ f, pro centro mundi ſumi, cum <lb/>inſenſibilis ſit, ac imperceptibilis eius diſtantia à centro mundi, ſi cum diſtantia ipſius à Sole cõ-<lb/>feratur, vt in ſphæra oſtendimus) recta G I, quæ perpendicularis eſt ad axem e f, ſecatq́ue lineam <lb/>indicis in G, ſit communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s24899" xml:space="preserve">plani per rectas χ e, d f, quæ ad planum incli-<lb/>natum perpendiculares ſunt, &amp; </s>
  <s xml:id="echoid-s24900" xml:space="preserve">per lineam indicis χ d, atquc axem e f, ducti, quod quidem pla-<lb/>
<anchor type="note" xlink:label="note-0395-07a" xlink:href="note-0395-07"/>
num rectum eſt ad planum inclinatum, inſtar noui cuiuſdam, ac proprii Meridiani ipſius plani <lb/>inclinati: </s>
  <s xml:id="echoid-s24901" xml:space="preserve">adeò vt recta G I, non ſolum ſit in plano G I f d, ſed etiam in plano Aequatoris, quan-<lb/>doquidem axis cum ea in plano G I f d, exiſtente angulum rectum facit in I: </s>
  <s xml:id="echoid-s24902" xml:space="preserve">alias ſi Aequator nõ <lb/>tranſiret per rectam I G, ſed per aliam quampiam ex puncto I, quod pro centro Aequatoris acce-<lb/>ptum eſt, ductam, eſſet axis, per defin. </s>
  <s xml:id="echoid-s24903" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24904" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24905" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24906" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24907" xml:space="preserve">ad hanc quoque perpendicularis, propte-<lb/>
<anchor type="note" xlink:label="note-0395-08a" xlink:href="note-0395-08"/>
rea quòd rectus eſt ad planum Aequatoris. </s>
  <s xml:id="echoid-s24908" xml:space="preserve">Quare in plano G I f d, duæ perpendiculares ad axẽ <lb/>in puncto I, ducerentur, quod eſt abſurdum. </s>
  <s xml:id="echoid-s24909" xml:space="preserve">Occurret igitur Aequatoris planum per rectam I G, <lb/>ductum plano horologii inclinati in puncto G, lineæ indicis, ibiq́ue ipſum ſecabit; </s>
  <s xml:id="echoid-s24910" xml:space="preserve">ac proinde <lb/>per punctum G, ducenda erit linea æquinoctialis, hoc eſt, ſectio communis Aequatoris, &amp; </s>
  <s xml:id="echoid-s24911" xml:space="preserve">plani <lb/>
<anchor type="note" xlink:label="note-0395-09a" xlink:href="note-0395-09"/>
horologii inclinati. </s>
  <s xml:id="echoid-s24912" xml:space="preserve">Quoniam verò planum G I f d, rectum eſt ad Aequatorem, propterea quòd <lb/>axis e f, per quem ducitur, ad eundem rectus eſt, vt diximus, (quod idem ex propoſ. </s>
  <s xml:id="echoid-s24913" xml:space="preserve">15. </s>
  <s xml:id="echoid-s24914" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24915" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s24916" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s24917" xml:space="preserve">conſtare poteſt, propterea quòd planum G I f d, per axem Aequatoris e f, atque adeo per <lb/>eius polos ductum ſit) erit viciſſim &amp; </s>
  <s xml:id="echoid-s24918" xml:space="preserve">Aequator ad planum G I f d, rectus: </s>
  <s xml:id="echoid-s24919" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s24920" xml:space="preserve">planum <lb/>horologij inclinati rectũ ad idem planũ G I f d, eò quòd hoc ad illud proximè oſtenſum ſit rectũ. </s>
  <s xml:id="echoid-s24921" xml:space="preserve"><lb/>Igitur &amp; </s>
  <s xml:id="echoid-s24922" xml:space="preserve">communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s24923" xml:space="preserve">plani horologij inclinati ad idem planum G I f d, <lb/>
<anchor type="note" xlink:label="note-0395-10a" xlink:href="note-0395-10"/>
<pb o="380" file="0396" n="396" rhead="GNOMONICES"/>
recta erit, ac proinde &amp;</s>
  <s xml:id="echoid-s24924" xml:space="preserve">, per defin. </s>
  <s xml:id="echoid-s24925" xml:space="preserve">3. </s>
  <s xml:id="echoid-s24926" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24927" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24928" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24929" xml:space="preserve">ad lineã indicis χ d, in eo plano exiſtentem per-<lb/>pendicularis erit. </s>
  <s xml:id="echoid-s24930" xml:space="preserve">Quocirca cũ dicta cõmunis ſectio ducenda ſit per punctũ G, vt proximè mõſtra <lb/>u<unsure/>imus, erit G H, ducta perpendicularis ad χ d, cõmunis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s24931" xml:space="preserve">plani horologij in-<lb/>
<anchor type="figure" xlink:label="fig-0396-01a" xlink:href="fig-0396-01"/>
<anchor type="note" xlink:label="note-0396-01a" xlink:href="note-0396-01"/>
<anchor type="note" xlink:label="note-0396-02a" xlink:href="note-0396-02"/>
<anchor type="note" xlink:label="note-0396-03a" xlink:href="note-0396-03"/>
clinati, id eſt, linea æquinoctialis. </s>
  <s xml:id="echoid-s24932" xml:space="preserve">Et quia punctũ I, pro cẽtro mũdi acceptũ eſt, ex quo cadit recta <lb/>I K, perpendicularis ad planũ horologij inclinati, ex deſin. </s>
  <s xml:id="echoid-s24933" xml:space="preserve">4. </s>
  <s xml:id="echoid-s24934" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24935" xml:space="preserve">11. </s>
  <s xml:id="echoid-s24936" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s24937" xml:space="preserve">propterea quòd perpen <lb/>
<anchor type="note" xlink:label="note-0396-04a" xlink:href="note-0396-04"/>
dicularis ducta eſt ad lineã indicis χ d, cõmunem ſectionẽ plani horologii, &amp; </s>
  <s xml:id="echoid-s24938" xml:space="preserve">plani G I f d, quod <lb/>ad illud rectum eſt; </s>
  <s xml:id="echoid-s24939" xml:space="preserve">erit recta I K, longitudo ſtyli, eiusq́ue locus in K, puncto lineę indicis, quia <lb/>nulla alia linea ad planum horologij recta, præter K I, in centrũ mundi I, cadere poteſt, vt patet.</s>
  <s xml:id="echoid-s24940" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1278" type="float" level="2" n="16">
<note position="left" xlink:label="note-0395-06" xlink:href="note-0395-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0395-07" xlink:href="note-0395-07a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0395-08" xlink:href="note-0395-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0395-09" xlink:href="note-0395-09a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0395-10" xlink:href="note-0395-10a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0396-01" xlink:href="fig-0396-01a">
    <image file="0396-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0396-01"/>
  </figure>
<note position="left" xlink:label="note-0396-01" xlink:href="note-0396-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0396-02" xlink:href="note-0396-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0396-03" xlink:href="note-0396-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0396-04" xlink:href="note-0396-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s24941" xml:space="preserve">IAM verò ſi planum circuli ex L, deſcripti intelligatur circumduci circa lineam æquinoctia-<lb/>lem G H, don ec centrum eius L, cum centro mundi I, coniungatur, (coniungetur autem omni-<lb/>no cum eo, propterea quòd rectæ G I, G L, æquales inter ſe ſunt, &amp; </s>
  <s xml:id="echoid-s24942" xml:space="preserve">vtraque ad lineam æquino-<lb/>ctialem perpendicularis eſt, ſi planum G I f d, concipiatur rectum eſſe ad planum horologii) erũt <lb/>rectæ per centrum L, quod tunc idem eſt, quod centrũ Aequatoris, &amp; </s>
  <s xml:id="echoid-s24943" xml:space="preserve">per diuiſiones circuli emiſ-<lb/>ſæ, communes ſectiones Aequatoris, &amp; </s>
  <s xml:id="echoid-s24944" xml:space="preserve">circulorum horarum à meridie, vel media nocte, vt in ho <lb/>rologio horizontali oſtendimus propoſ. </s>
  <s xml:id="echoid-s24945" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24946" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24947" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24948" xml:space="preserve">In illa enim poſitione circulus dictus idem cen-<lb/>trum cum Aequatore habens exiſtit in plano Aequatoris. </s>
  <s xml:id="echoid-s24949" xml:space="preserve">Incipit autem diuiſio dicti circuli à re-<lb/>
<anchor type="note" xlink:label="note-0396-05a" xlink:href="note-0396-05"/>
cta L M, quæ per centrum L, &amp; </s>
  <s xml:id="echoid-s24950" xml:space="preserve">punctum M, vbi linea meridiana, &amp; </s>
  <s xml:id="echoid-s24951" xml:space="preserve">æquinoctialis ſe interſecant, <lb/>ducta eſt, vel quæ per L, ipſi lineæ meridianæ parallela acta eſt, quando linea meridiana, &amp; </s>
  <s xml:id="echoid-s24952" xml:space="preserve">æqui <lb/>noctialis ſemutuo non ſecant, ſed parallelæ ſunt; </s>
  <s xml:id="echoid-s24953" xml:space="preserve">quoniam ea linea communis ſectio eſt Aequa-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s24954" xml:space="preserve">Meridiani, ſeu circuli horæ 12. </s>
  <s xml:id="echoid-s24955" xml:space="preserve">propterea quòd plano horologii occurrit in puncto M, <lb/>per quod linea meridiana, &amp; </s>
  <s xml:id="echoid-s24956" xml:space="preserve">æquinoctialis incedunt; </s>
  <s xml:id="echoid-s24957" xml:space="preserve">vel certè parallela eſt lineæ meridianæ, vt <lb/>ratio poſtulat, quando meridiana linea, &amp; </s>
  <s xml:id="echoid-s24958" xml:space="preserve">æquinoctialis ſunt parallelæ, quod quidem fit, cum pla <lb/>num horologij æquidiſtat circulo maximo, qui Meridianum in eodem puncto ſecat, in quo ab <lb/>Aequatore ſecatur. </s>
  <s xml:id="echoid-s24959" xml:space="preserve">Nam cum hac ratione planum horologii æquidiſtet communi ſectioni Meri-<lb/>diani, &amp; </s>
  <s xml:id="echoid-s24960" xml:space="preserve">Aequatoris, cum per illam tranſeat circulus maximus, cui planum horologii æquidiſtat, <lb/>erit communis ſectio facta à plano horologij in Meridiano, hoc eſt, ipſa linea meridiana, commu
<pb o="381" file="0397" n="397" rhead="LIBER TERTIVS."/>
ni ſectioni Meridiani, &amp; </s>
  <s xml:id="echoid-s24961" xml:space="preserve">Aequatoris parallela, vt conſtat ex demõſtratione propoſ. </s>
  <s xml:id="echoid-s24962" xml:space="preserve">18. </s>
  <s xml:id="echoid-s24963" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s24964" xml:space="preserve">Quę <lb/>cum ita ſint, ſecabunt circuli horarij planum horologij inclinati in ijſdem punctis, in quibus re-<lb/>ctæ per centrum L, &amp; </s>
  <s xml:id="echoid-s24965" xml:space="preserve">diuiſionum puncta in circulo ex L, deſcripto eductæ, tanquam commu-<lb/>nes ſectiones dictorum circulorum, &amp; </s>
  <s xml:id="echoid-s24966" xml:space="preserve">Aequatoris, occurrunt lineæ æquinoctiali; </s>
  <s xml:id="echoid-s24967" xml:space="preserve">atque adeo cõ-<lb/>munes ſectiones eorundem circulorum, &amp; </s>
  <s xml:id="echoid-s24968" xml:space="preserve">plani horologij inclinati, hoc eſt, lineæ horariæ, per <lb/>eadem puncta erunt ducendæ. </s>
  <s xml:id="echoid-s24969" xml:space="preserve">Cum ergo eædem per coroll. </s>
  <s xml:id="echoid-s24970" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s24971" xml:space="preserve">21. </s>
  <s xml:id="echoid-s24972" xml:space="preserve">primi libri, ſe mutuo ſe-<lb/>cent in ρ, centro horologii, vel, vbi centrum non habetur, parallelæ ſint inter ſe, ex coroll. </s>
  <s xml:id="echoid-s24973" xml:space="preserve">propoſ. <lb/></s>
  <s xml:id="echoid-s24974" xml:space="preserve">22. </s>
  <s xml:id="echoid-s24975" xml:space="preserve">eiuſdem libri, erunt rectæ per puncta lineæ æquinoctialis, &amp; </s>
  <s xml:id="echoid-s24976" xml:space="preserve">per punctum ρ, ductæ, vel certè, <lb/>vbi non eſt centrum horologii, ipſi lineæ meridianæ parallelæ, lineæ horarum à meridie, vel me-<lb/>dia nocte, id eſt, communes ſectiones plani horologij, &amp; </s>
  <s xml:id="echoid-s24977" xml:space="preserve">circulorum horariorum à meridie, vel <lb/>
<anchor type="note" xlink:label="note-0397-01a" xlink:href="note-0397-01"/>
media nocte. </s>
  <s xml:id="echoid-s24978" xml:space="preserve">Quæ autem ſint horæ à meridie, &amp; </s>
  <s xml:id="echoid-s24979" xml:space="preserve">quæ à media nocte, facile intelligi poteſt, ſi cir-<lb/>culus ex L, deſcriptus concipiatur vna cum horologio in propria poſitione, &amp; </s>
  <s xml:id="echoid-s24980" xml:space="preserve">ea diligenter con-<lb/>ſiderentur, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s24981" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24982" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s24983" xml:space="preserve">2. </s>
  <s xml:id="echoid-s24984" xml:space="preserve">ſcripſimus de interſectionibus æquinoctialis lineæ, &amp; </s>
  <s xml:id="echoid-s24985" xml:space="preserve"><lb/>rectarum circuli ex L, deſcripti, obſeruando ſemper, ſi horologium, &amp; </s>
  <s xml:id="echoid-s24986" xml:space="preserve">dictus circulus intelligan-<lb/>tur in propria poſitione, puncta diuiſionum, quæ ſequuntur communem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s24987" xml:space="preserve"><lb/>Aequatoris, (qualis eſt recta L M,) verſus occidentem ex parte ſuperiori, referre horas à meri-<lb/>die, puncta verò, quæ eandem rectam L M, ſequuntur verſus orientem ex parte inferiori, horas à <lb/>media nocte. </s>
  <s xml:id="echoid-s24988" xml:space="preserve">Et quoniam, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s24989" xml:space="preserve">1. </s>
  <s xml:id="echoid-s24990" xml:space="preserve">ſuperioris libri docuimus, lineæ rectæ prius trã-<lb/>ſire debent per centrum L, quàm occurrant lineæ æquinoctiali, facile cognoſci poterit, quænam <lb/>puncta æquinoctialis lineæ indicent horas à meridie, &amp; </s>
  <s xml:id="echoid-s24991" xml:space="preserve">quæ à media nocte: </s>
  <s xml:id="echoid-s24992" xml:space="preserve">Ita vt rectè ordo ho-<lb/>
<anchor type="note" xlink:label="note-0397-02a" xlink:href="note-0397-02"/>
rarum à nobis ſupra deſcriptus ſit. </s>
  <s xml:id="echoid-s24993" xml:space="preserve">Nam ſi rectè diligenterq́ue rem perpendamus, deprehende-<lb/>
<anchor type="note" xlink:label="note-0397-03a" xlink:href="note-0397-03"/>
mus lineam æquinoctialem in horologiis, quæ ad Zenith pertinent, &amp; </s>
  <s xml:id="echoid-s24994" xml:space="preserve">auſtrum reſpiciunt, eſſe ſe-<lb/>ctionem plani horologij, &amp; </s>
  <s xml:id="echoid-s24995" xml:space="preserve">Aequatoris, in quam cadunt radij Solis in ſemicirculo Aequatoris ſu-<lb/>pra Horizontem exiſtentis. </s>
  <s xml:id="echoid-s24996" xml:space="preserve">Vndelineæ meridianæ portio lineam æquinoctialem ſecans in illis <lb/>horologijs horam 12. </s>
  <s xml:id="echoid-s24997" xml:space="preserve">meridiei indicabit; </s>
  <s xml:id="echoid-s24998" xml:space="preserve">lineæ verò verſus partes orientales monſtrabunt horas <lb/>poſt meridiem, quales ſunt illæ, quæ nobis ad horologia conuerſis ad dextram ſunt poſitæ. </s>
  <s xml:id="echoid-s24999" xml:space="preserve">Idem <lb/>contingit in horologijs, quæ ad Zenith pertinent, ſpectantq́ue in boream, &amp; </s>
  <s xml:id="echoid-s25000" xml:space="preserve">habent lineam æqui <lb/>noctialem infra centrum horologij, ſed partes orientales ſitæ ſunt nobis ad horologia conuerſis. <lb/></s>
  <s xml:id="echoid-s25001" xml:space="preserve">ad ſiniſtram. </s>
  <s xml:id="echoid-s25002" xml:space="preserve">In horologijs autem ad Zenith pertinentibus, &amp; </s>
  <s xml:id="echoid-s25003" xml:space="preserve">quæ boream reſpiciunt, habentq́; </s>
  <s xml:id="echoid-s25004" xml:space="preserve"><lb/>æquinoctialem lineam ſupra centrum horologij, linea æquinoctialis communis ſectio eſt Aequa-<lb/>
<anchor type="note" xlink:label="note-0397-04a" xlink:href="note-0397-04"/>
toris, &amp; </s>
  <s xml:id="echoid-s25005" xml:space="preserve">plani horologij, in quam vmbræ cadunt, Sole exiſtente in ſemicirculo Aequatoris infra <lb/>Horizontem. </s>
  <s xml:id="echoid-s25006" xml:space="preserve">Quamobrem portio lineæ meridianæ lineam æquinoctialem ſecans oſtendet in his <lb/>horologiis horam 12. </s>
  <s xml:id="echoid-s25007" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s25008" xml:space="preserve">lineæ verſus partes occidentales, quæ nobis dextræ ſunt, ſi <lb/>faciem ad horologia conuertamus, horas poſt mediam noctem dabunt, vt ſupra diximus.</s>
  <s xml:id="echoid-s25009" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1279" type="float" level="2" n="17">
<note position="left" xlink:label="note-0396-05" xlink:href="note-0396-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0397-01" xlink:href="note-0397-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0397-02" xlink:href="note-0397-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0397-03" xlink:href="note-0397-03a" xml:space="preserve">Quomodo iudi <lb/>ca<unsure/>dum ſit, quæ <lb/>horę à mer. &amp; <lb/>quę@à med noc. <lb/>co<unsure/>putãdæ ſint.</note>
<note position="left" xlink:label="note-0397-04" xlink:href="note-0397-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s25010" xml:space="preserve">QVOD ſi ex F, egrediantur rectæ efficientes cum E F, linea declinationis, quam oſtendimus <lb/>
<anchor type="note" xlink:label="note-0397-05a" xlink:href="note-0397-05"/>
eſſe lineam meridianam in horologio horizontali, eoſdem angulos, quos cum linea meridiana <lb/>conſtituunt lineæ horariæ in horizontali horologio, nempelinea horæ 6. </s>
  <s xml:id="echoid-s25011" xml:space="preserve">qualis eſt F α, angulum <lb/>rectum α F E, &amp; </s>
  <s xml:id="echoid-s25012" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25013" xml:space="preserve">ſecabitur recta A B, in punctis, per quæ rectæ emiſſæ ex centro ρ, vel, vbi non eſt <lb/>centrum, ipſi meridianæ lineæ parallelæ ductæ, dabunt horarias lineas, vt prius; </s>
  <s xml:id="echoid-s25014" xml:space="preserve">veluti demonſtra <lb/>uimus propoſ. </s>
  <s xml:id="echoid-s25015" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25016" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s25017" xml:space="preserve">Qua de re vide, quæ ibi ſcripſimus circa perpendicularem F α, vt per <lb/>
<anchor type="note" xlink:label="note-0397-06a" xlink:href="note-0397-06"/>
illam, vel aliquam aliam lineam ex F, egredientem diuiſio circuli ex L, deſcripti recte inſtituatur, <lb/>quemadmodum ſupra quoque in hac propoſ. </s>
  <s xml:id="echoid-s25018" xml:space="preserve">monuimus.</s>
  <s xml:id="echoid-s25019" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1280" type="float" level="2" n="18">
<note position="right" xlink:label="note-0397-05" xlink:href="note-0397-05a" xml:space="preserve">Alia deſcriptio <lb/>horarum ex ho <lb/>rologio horizõ-<lb/>tali.</note>
<note position="left" xlink:label="note-0397-06" xlink:href="note-0397-06a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Conſtructio a-<lb/>lia horologii de <lb/>clinantis ſi<unsure/>mul <lb/>&amp; inclinati, ad <lb/>ſimilitudinem <lb/>horologii hori-<lb/>zontalis.</note>
<p>
  <s xml:id="echoid-s25020" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s25021" xml:space="preserve">Conſtruemus quoque horologium idem declinans ſimul &amp; </s>
  <s xml:id="echoid-s25022" xml:space="preserve">inclinatum, ad ſi-<lb/>militudinem horizontalis horologij, quemadmodum &amp; </s>
  <s xml:id="echoid-s25023" xml:space="preserve">in declinante horologio à Verticali ſcri-<lb/>pſimus propoſ. </s>
  <s xml:id="echoid-s25024" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25025" xml:space="preserve">huius libri, hacarte. </s>
  <s xml:id="echoid-s25026" xml:space="preserve">Conſtituatur primum portio Analemmatis, vt in propoſ. <lb/></s>
  <s xml:id="echoid-s25027" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25028" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s25029" xml:space="preserve">in qua contineantur ſectiones communes Meridiani proprii ipſius plani decli-<lb/>nanus ſimul &amp; </s>
  <s xml:id="echoid-s25030" xml:space="preserve">inclinati cum Horizonte, Verticali, &amp; </s>
  <s xml:id="echoid-s25031" xml:space="preserve">Aequatore, &amp; </s>
  <s xml:id="echoid-s25032" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25033" xml:space="preserve">(circulus autem maximus, <lb/>cui planum horologij declinantis ſimul &amp; </s>
  <s xml:id="echoid-s25034" xml:space="preserve">inclinati æquidiſtat, vices gerit Horizontis, &amp; </s>
  <s xml:id="echoid-s25035" xml:space="preserve">alius <lb/>circulus maximus ſecans illum ad angulos rectos, tranſiensq́ue per communes ſectiones Aequa-<lb/>toris, &amp; </s>
  <s xml:id="echoid-s25036" xml:space="preserve">dicti Horizontis, munere Verticalis circuli fungitur) ita vt arcus C E, metiatur altitudi-<lb/>
<anchor type="note" xlink:label="note-0397-08a" xlink:href="note-0397-08"/>
nem poli ſupra planum declinãs ſimul &amp; </s>
  <s xml:id="echoid-s25037" xml:space="preserve">inclinatum, &amp; </s>
  <s xml:id="echoid-s25038" xml:space="preserve">recta D G, ſitæqualis ſtylo horologij de-<lb/>clinantis ſimul &amp; </s>
  <s xml:id="echoid-s25039" xml:space="preserve">inclinati cuiusuis magnitudinis aſſumpto, &amp; </s>
  <s xml:id="echoid-s25040" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25041" xml:space="preserve">In noſtro exemplo, quod ſextæ <lb/>figuræ accõmodauimus, prope quam dictam portionem Analemmatis deſcripſimus, arcus C E, <lb/>
<anchor type="note" xlink:label="note-0397-09a" xlink:href="note-0397-09"/>
continet grad. </s>
  <s xml:id="echoid-s25042" xml:space="preserve">66. </s>
  <s xml:id="echoid-s25043" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25044" xml:space="preserve">47. </s>
  <s xml:id="echoid-s25045" xml:space="preserve">Tanta enim ferè eſt altitudo poli inuenta ſupra planum illud inclina-<lb/>rum; </s>
  <s xml:id="echoid-s25046" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25047" xml:space="preserve">recta D G, ſumpta eſt æqualis ſtylo I K, eiuſdem horologij. </s>
  <s xml:id="echoid-s25048" xml:space="preserve">In prima autem figura idem <lb/>arcus C E, ſi portio Analemmatis conſtruatur figuræ illi reſpondens, continebit grad. </s>
  <s xml:id="echoid-s25049" xml:space="preserve">25. </s>
  <s xml:id="echoid-s25050" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25051" xml:space="preserve">43. <lb/></s>
  <s xml:id="echoid-s25052" xml:space="preserve">In ſecunda grad. </s>
  <s xml:id="echoid-s25053" xml:space="preserve">25. </s>
  <s xml:id="echoid-s25054" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25055" xml:space="preserve">18. </s>
  <s xml:id="echoid-s25056" xml:space="preserve">In tertia grad. </s>
  <s xml:id="echoid-s25057" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25058" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25059" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25060" xml:space="preserve">In quarta grad. </s>
  <s xml:id="echoid-s25061" xml:space="preserve">68. </s>
  <s xml:id="echoid-s25062" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25063" xml:space="preserve">13. </s>
  <s xml:id="echoid-s25064" xml:space="preserve">In quinta de-<lb/>nique grad. </s>
  <s xml:id="echoid-s25065" xml:space="preserve">27. </s>
  <s xml:id="echoid-s25066" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25067" xml:space="preserve">50. </s>
  <s xml:id="echoid-s25068" xml:space="preserve">Tantæ enim ferè ſunt altitudines poli ſupra illa plana inclinata repertæ, <lb/>iuxta doctrinam propoſ. </s>
  <s xml:id="echoid-s25069" xml:space="preserve">29. </s>
  <s xml:id="echoid-s25070" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25071" xml:space="preserve">1.</s>
  <s xml:id="echoid-s25072" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1281" type="float" level="2" n="19">
<note position="left" xlink:label="note-0397-08" xlink:href="note-0397-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0397-09" xlink:href="note-0397-09a" xml:space="preserve">Altitu dines po <lb/>li ſupra plana <lb/>ſex figuratum <lb/>huiuſce propo-<lb/>ſiu<unsure/>onis.</note>
</div>
<p>
  <s xml:id="echoid-s25073" xml:space="preserve">POST hæc ducãtur rectæ G N, G H, ſeſe ad rectos angulos ſecantes in G, quarum G N, re-<lb/>ferat ſectionem communem plani horologii, &amp; </s>
  <s xml:id="echoid-s25074" xml:space="preserve">Meridiani proprii ipſius plani, inſtar lineæ cuiuſ-
<pb o="382" file="0398" n="398" rhead="GNOMONICES"/>
dam meridianæ, in qua ſtylus collocandus eſt, &amp; </s>
  <s xml:id="echoid-s25075" xml:space="preserve">G H, lineam æquinoctialem, quemadmodũ <lb/>in horizontali horologio recta H E, meridiana linea eſt, hoc eſt, communis ſectio plani horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s25076" xml:space="preserve">Meridiani<unsure/>, in qua ſtylus collocatur, recta autem F K, munere lineæ æquinoctialis fungitur. <lb/></s>
  <s xml:id="echoid-s25077" xml:space="preserve">In rectam autem G N, quæ inſtar eſt lineæ meridianæ, ſi planum inclinatum pro Horizonte <lb/>quopiam accipiatur, transferenda eſt recta H I, quæ in portione Analemmatis inter axem, &amp; </s>
  <s xml:id="echoid-s25078" xml:space="preserve">dia-<lb/>metrum Æquatoris interponitur, initio facto à linea æquinoctiali in puncto G, uſque ad pun-<lb/>ctum ρ, ut centrum horologii habeatur; </s>
  <s xml:id="echoid-s25079" xml:space="preserve">ſicut etiam in horologio horizontali in recta H E, linea <lb/>I H, inter lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s25080" xml:space="preserve">centrum horologii æqualis eſt rectæ H I, in portione Analem <lb/>matis. </s>
  <s xml:id="echoid-s25081" xml:space="preserve">Sed quoniam in hiſce horologiis declinantibus ſimul &amp; </s>
  <s xml:id="echoid-s25082" xml:space="preserve">inclinatis centrum ρ, exiſtit ali-<lb/>quando infra lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s25083" xml:space="preserve">aliquando ſupra eandem, ut ſciamus, quando infra ip-<lb/>
<anchor type="note" xlink:label="note-0398-01a" xlink:href="note-0398-01"/>
ſam cẽtrum exiſtat, ac proinde infra eandem recta H I, transferenda ſit, ut centrum ρ, habeamus, <lb/>&amp; </s>
  <s xml:id="echoid-s25084" xml:space="preserve">quando ſupra, &amp; </s>
  <s xml:id="echoid-s25085" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25086" xml:space="preserve">inueſtigandus erit, per propoſ. </s>
  <s xml:id="echoid-s25087" xml:space="preserve">28. </s>
  <s xml:id="echoid-s25088" xml:space="preserve">primi libri arcus Meridiani interiectus <lb/>inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s25089" xml:space="preserve">Horizontem. </s>
  <s xml:id="echoid-s25090" xml:space="preserve">Ex hoc enim cognito ſine ullo negotio id, quod quę-<lb/>ritur, aſſequemur. </s>
  <s xml:id="echoid-s25091" xml:space="preserve">In prima figura deprehendimus hunc arcum ex parte boreali ſupra Horizontẽ <lb/>
<anchor type="note" xlink:label="note-0398-02a" xlink:href="note-0398-02"/>
gr. </s>
  <s xml:id="echoid-s25092" xml:space="preserve">15. </s>
  <s xml:id="echoid-s25093" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25094" xml:space="preserve">35. </s>
  <s xml:id="echoid-s25095" xml:space="preserve">In ſecunda autẽ grad. </s>
  <s xml:id="echoid-s25096" xml:space="preserve">68. </s>
  <s xml:id="echoid-s25097" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25098" xml:space="preserve">50. </s>
  <s xml:id="echoid-s25099" xml:space="preserve">In tertia denique gr. </s>
  <s xml:id="echoid-s25100" xml:space="preserve">42. </s>
  <s xml:id="echoid-s25101" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25102" xml:space="preserve">o adeò ut planum <lb/>huius figuræ per polum tranſeat. </s>
  <s xml:id="echoid-s25103" xml:space="preserve">Rurſus in quarta figura inuenimus eundem arcum ex parte au-<lb/>ſtrali ſupra Horizontẽ grad. </s>
  <s xml:id="echoid-s25104" xml:space="preserve">28. </s>
  <s xml:id="echoid-s25105" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25106" xml:space="preserve">29. </s>
  <s xml:id="echoid-s25107" xml:space="preserve">In quinta autem, grad. </s>
  <s xml:id="echoid-s25108" xml:space="preserve">72. </s>
  <s xml:id="echoid-s25109" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25110" xml:space="preserve">57. </s>
  <s xml:id="echoid-s25111" xml:space="preserve">In 6. </s>
  <s xml:id="echoid-s25112" xml:space="preserve">denique gra. <lb/></s>
  <s xml:id="echoid-s25113" xml:space="preserve">48. </s>
  <s xml:id="echoid-s25114" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25115" xml:space="preserve">o. </s>
  <s xml:id="echoid-s25116" xml:space="preserve">adeò ut planum huius figuræ per punctum illud Meridiani tranſeat, ubi ab Æquato-<lb/>re ſecatur. </s>
  <s xml:id="echoid-s25117" xml:space="preserve">Si igitur planum ex parte boreali ad Horizontem fuerit inclinatum, fueritq́ue arcus <lb/>
<anchor type="note" xlink:label="note-0398-03a" xlink:href="note-0398-03"/>
Meridiani inter ipſum, &amp; </s>
  <s xml:id="echoid-s25118" xml:space="preserve">Horizontem poſitus minor altitudine poli ſupra Horizontem, ſumen-<lb/>
<anchor type="note" xlink:label="note-0398-04a" xlink:href="note-0398-04"/>
da eſt ex portione Analemmatis recta H I, transferendaq́ue in lineam G N, ex G, infra lineam æ-<lb/>quinoctialem uſq; </s>
  <s xml:id="echoid-s25119" xml:space="preserve">ad punctum ρ, quod centrum erit horologii; </s>
  <s xml:id="echoid-s25120" xml:space="preserve">quia tunc centrum horologii <lb/>infra lineã ęquinoctialem exiſtit, ut in prima figura contingit: </s>
  <s xml:id="echoid-s25121" xml:space="preserve">quoniam axis mundi tunc occurrit <lb/>ſuperiori faciei plani horologii ex parte auſtrali non ſecus, ac in horizontali horologio.</s>
  <s xml:id="echoid-s25122" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1282" type="float" level="2" n="20">
<note position="left" xlink:label="note-0398-01" xlink:href="note-0398-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0398-02" xlink:href="note-0398-02a" xml:space="preserve">Quanti ſint ar <lb/>@us Meridiani <lb/>inter Horizon-<lb/>tẽ &amp; plana ſex <lb/>figurarum hu-<lb/>ius propoſ. in-<lb/>terpoſiti.</note>
<note position="left" xlink:label="note-0398-03" xlink:href="note-0398-03a" xml:space="preserve">Quando cen-<lb/>trum horologii <lb/>eſt infra lineã <lb/>ęquinocti alem, <lb/>&amp; quando ſu-<lb/>pra.</note>
<note position="left" xlink:label="note-0398-04" xlink:href="note-0398-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s25123" xml:space="preserve">SI uerò plano ex eadem parte boreali ſupra Horizontem eleuato arcus Meridiani inter ipſum, <lb/>&amp; </s>
  <s xml:id="echoid-s25124" xml:space="preserve">Horizontem poſitus fuerit altitudine poli ſupra Horizontem maior, transferenda eſt recta H I, <lb/>ex portione Analemmatis in rectam G N, ex G, ſupra lineam æquinoctialẽ uſque ad punctum ρ, <lb/>quod centrum erit horologii ſupra lineam æquinoctialem exiſtens, ut in ſecunda figura conſpici-<lb/>tur; </s>
  <s xml:id="echoid-s25125" xml:space="preserve">quia tunc axis mundi ſuperiori faciei plani horologit<unsure/> occurrit ad partes ſuperiores, ſiue borea-<lb/>les, ita ut cum linea ſtyli ea facie deſcripta faciat angulum acutum uerſus polum oppoſitum, ſeu <lb/>
<anchor type="note" xlink:label="note-0398-05a" xlink:href="note-0398-05"/>
uerſus partes inferiores, ut in Verticali horologio auſtrali contingit.</s>
  <s xml:id="echoid-s25126" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1283" type="float" level="2" n="21">
<note position="left" xlink:label="note-0398-05" xlink:href="note-0398-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s25127" xml:space="preserve">SI denique plano ex eadem parte boreali eleuato ſupra Horizontem, arcus Meridiani inter <lb/>ipſum &amp; </s>
  <s xml:id="echoid-s25128" xml:space="preserve">Horizontem poſitus æqualis altitudini poli fuerit, ita ut planum per polos mundi tran <lb/>ſeat, carebit horologium centro, ut accidit in tertia figura. </s>
  <s xml:id="echoid-s25129" xml:space="preserve">Vnde nihil tunc transferendum eſt, ſed <lb/>alio modo horologium conſtruendum, ut paulo infra docebimus.</s>
  <s xml:id="echoid-s25130" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25131" xml:space="preserve">QVOD ſi planum ex parte auſtrali inclinatum fuerit ad Horizontem, fueritq́ue arcus inter <lb/>ipſum, &amp; </s>
  <s xml:id="echoid-s25132" xml:space="preserve">Horizontem incluſus minor complemento altitudi@s poli ſupra Horizontem, trans-<lb/>ferenda erit eadem recta H I, ex portione Analemmatis in rectam G N, ex G, ſupra lineam æ-<lb/>quinoctialem uſque ad punctum ρ, quod centrum horologii erit ſupra lineam æquinoctialem <lb/>exiſtens, ut in quarta figura uidere licet; </s>
  <s xml:id="echoid-s25133" xml:space="preserve">quoniam tunc axis mundi faciei ſuperiori plani horolo-<lb/>
<anchor type="note" xlink:label="note-0398-06a" xlink:href="note-0398-06"/>
gii occurrit ſupra lineã æquinoctialem uerſus partes ſuperiores, hoc eſt, auſtrales, ut in horizon-<lb/>tali horologio.</s>
  <s xml:id="echoid-s25134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1284" type="float" level="2" n="22">
<note position="left" xlink:label="note-0398-06" xlink:href="note-0398-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s25135" xml:space="preserve">POSTREMO ſi planum ex eadem parte auſtrali fuerit inclinatum ad Horizontem, &amp; </s>
  <s xml:id="echoid-s25136" xml:space="preserve">ar-<lb/>cus Meridiani inter ipſum, &amp; </s>
  <s xml:id="echoid-s25137" xml:space="preserve">Horizontem extiterit uel æqualis, uel maior complemento altitudi-<lb/>nis poli ſupra Horizontem, transferenda erit recta H I, ex portione Analemmatis in rectã G N, ex <lb/>G, infra lineam æquinoctialem uſque ad punctum ρ, quod centrum erit horologii infra lineam æ-<lb/>quinoctialem exiſtens, ut in poſtremis duabus figuris apparet; </s>
  <s xml:id="echoid-s25138" xml:space="preserve">quoniam quando æqualis aut <lb/>maior eſt arcus dictus complemento altitudinis poli, ſecabit axis mundi faciem ſuperiorem pla-<lb/>ni horologii ad partes inferiores, ſiue boreales, ita ut cum linea ſtyli in ea facie deſcripta angulum <lb/>acutum faciat uerſus polum arcticum, ſeu uerſus partes ſuperiores, quemadmodum in horologio <lb/>
<anchor type="note" xlink:label="note-0398-07a" xlink:href="note-0398-07"/>
Verticali boreali ſolet contingere.</s>
  <s xml:id="echoid-s25139" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1285" type="float" level="2" n="23">
<note position="left" xlink:label="note-0398-07" xlink:href="note-0398-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s25140" xml:space="preserve">HÆC eriã omnia luce clarius colligũtur ex quatuor illis Analemmatibus in propoſ. </s>
  <s xml:id="echoid-s25141" xml:space="preserve">27. </s>
  <s xml:id="echoid-s25142" xml:space="preserve">huius <lb/>
<anchor type="note" xlink:label="note-0398-08a" xlink:href="note-0398-08"/>
libri poſitis. </s>
  <s xml:id="echoid-s25143" xml:space="preserve">Si enim in prioribus duobus intelligatur ex parte boreali arcus D K, æqualis arcui Me <lb/>ridiani inter planum &amp; </s>
  <s xml:id="echoid-s25144" xml:space="preserve">Horizontem poſito, in duobus uerò poſterioribus ex parte auſtrali ponatur <lb/>arcus B K, eidem arcui Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s25145" xml:space="preserve">Horizontem æqualis, erit recta K L, commu-<lb/>nis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s25146" xml:space="preserve">circuli maximi, cui horologii planũ æquidiſtat. </s>
  <s xml:id="echoid-s25147" xml:space="preserve">Igitur M N, ipſi K L, pa-<lb/>rallela communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s25148" xml:space="preserve">plani horologii illi maximo circulo æquidiſtantis, nem-<lb/>pelinea meridiana in horologio inclinato. </s>
  <s xml:id="echoid-s25149" xml:space="preserve">Meridianus enim ſecans dictum circulum maximum, <lb/>&amp; </s>
  <s xml:id="echoid-s25150" xml:space="preserve">planum horologii illi æquidiſtans facit ſectiones parallelas. </s>
  <s xml:id="echoid-s25151" xml:space="preserve">Vnde ubi axis mundi F G, recta <lb/>
<anchor type="note" xlink:label="note-0398-09a" xlink:href="note-0398-09"/>
M N, ſecat in M, ibi centrum erit horologii in linea meridiana, punctum autem N, in eadem me<unsure/> <lb/>ridiana linea erit illud, per quod linea æquinoctialis ducitur, cum in eo Æquator lineam meridia-
<pb o="383" file="0399" n="399" rhead="LIBER TERTIVS."/>
nã ſecet. </s>
  <s xml:id="echoid-s25152" xml:space="preserve">Ex quo etiã fit, ſi portio axis E M, ſumatur æqualis portioni axis ρ I, in ſuperioribus ho-<lb/>rologiis inter centrũ mundi I, &amp; </s>
  <s xml:id="echoid-s25153" xml:space="preserve">centrum horologii ρ, ubi lineam meridianam ſecat axis mundi, <lb/>&amp; </s>
  <s xml:id="echoid-s25154" xml:space="preserve">per M, ducatur ipſi K L, parallela M N, (dũmodo arcus D K, uel B K, æqualis ſit arcui Meridiani <lb/>inter planum, &amp; </s>
  <s xml:id="echoid-s25155" xml:space="preserve">Horizontẽ inuento) ſecans Æquatoris diametrum in N, rectã M N, æqualẽ eſſe <lb/>rectæ ρ M, hoc eſt, portioni lineæ meridianæ inter centrum horologii ρ, &amp; </s>
  <s xml:id="echoid-s25156" xml:space="preserve">punctum M, lineæ æ-<lb/>quinoctialis; </s>
  <s xml:id="echoid-s25157" xml:space="preserve">rectam autẽ EN, æqualem rectæ illi in horologio, quæ ex vertice ſtyli, ſeu centro mũ-<lb/>di I, in ſublimi poſito cadit in punctum M. </s>
  <s xml:id="echoid-s25158" xml:space="preserve">Sicut enim triangulum E M N, conſtituitur in Ana-<lb/>lemmate ex axe E M, communi ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s25159" xml:space="preserve">plani horologii inclinati M N, &amp; </s>
  <s xml:id="echoid-s25160" xml:space="preserve">commu-<lb/>ni ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s25161" xml:space="preserve">Æquatoris E N, ita quoque in horologio triangulum ρ I M, in plano <lb/>Meridiani exiſtens, ſi axis ρ I, in proprio ſitu eſle intelligatur, (tranſit enim Meridianus per axem <lb/>
<anchor type="note" xlink:label="note-0399-01a" xlink:href="note-0399-01"/>
ρ I, &amp; </s>
  <s xml:id="echoid-s25162" xml:space="preserve">per punctum M,) ex eiſdem lineis conſtat, atque illi omnino æquale eſt. </s>
  <s xml:id="echoid-s25163" xml:space="preserve">Quoniam enim <lb/>angulus E M N, in Analemmate, quem axis cum linea meridiana horologii facit, æqualis eſt an-<lb/>gulo I ρ M, in horologio, quem axis, ſi in proprio ſitu collocetur, cum linea meridiana conſtituit, <lb/>&amp; </s>
  <s xml:id="echoid-s25164" xml:space="preserve">angulus M E N, rectus angulo recto ρ I M; </s>
  <s xml:id="echoid-s25165" xml:space="preserve">(Nam Aequator ſecat axem in I, ad rectos angulos, <lb/>ac proinde per defin. </s>
  <s xml:id="echoid-s25166" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25167" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25168" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25169" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25170" xml:space="preserve">axis cum recta I M, in Aequatore exiſtente rectos angulos fa-<lb/>cit) ponitur autem &amp; </s>
  <s xml:id="echoid-s25171" xml:space="preserve">recta E M, rectę I ρ, æqualis; </s>
  <s xml:id="echoid-s25172" xml:space="preserve">erit quoque recta M N, rectę ρ M, &amp; </s>
  <s xml:id="echoid-s25173" xml:space="preserve">recta E N, <lb/>
<anchor type="note" xlink:label="note-0399-02a" xlink:href="note-0399-02"/>
rectæ I M, æqualis. </s>
  <s xml:id="echoid-s25174" xml:space="preserve">Iam uerò ipſamet Analemmata perſpicuè indicãt, an centrum horologii ſit in-<lb/>fra lineam æquinoctialem, an uero ſupra eãdem. </s>
  <s xml:id="echoid-s25175" xml:space="preserve">Quoniam enim in Analemmate primo &amp; </s>
  <s xml:id="echoid-s25176" xml:space="preserve">quar-<lb/>to centrum M, in linea meridiana M N, horologii ſuperioris infra punctum N, per quod linea æ-<lb/>quinoctialis ducenda eſt, in aliis autem duobus intermediis ſupra idem punctum N, exiſtit, fit ut <lb/>
<anchor type="note" xlink:label="note-0399-03a" xlink:href="note-0399-03"/>
idem centrum in prioribus duobus infra æquinoctialem lineã, in duobus uerò poſterioribus infra <lb/>eãdem exiſtat. </s>
  <s xml:id="echoid-s25177" xml:space="preserve">Quãdo enim centrũ horologii in linea meridiana exiſtit infra, uel ſupra punctum <lb/>N, æquinoctialis lineæ, idem centrum neceſſario exiſtit quoque infra lineam æquinoctialem uel <lb/>ſupra in linea ſtyli G N. </s>
  <s xml:id="echoid-s25178" xml:space="preserve">Nam quia æquinoctialis linea ſecat lineam ſtyli G N, ad angulos rectos <lb/>liquido conſtat, ſi æquinoctialis linca ſecet meridianam lineam ſupra, uel infra centrum, eandem <lb/>ſecare quoque lineam ſtyli G N, ſupra centrum uel infra, ut ex ſuprapoſitis fig uris manifeſtum eſt.</s>
  <s xml:id="echoid-s25179" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1286" type="float" level="2" n="24">
<note position="left" xlink:label="note-0398-08" xlink:href="note-0398-08a" xml:space="preserve">Qua ratione ex <lb/>quatuor Ana-<lb/>lemmatibus in <lb/>propoſ. 27. hu-<lb/>ius lib. poſitis <lb/>cognoſcatur, <lb/>quando centrũ <lb/>horologii eſt in <lb/>fra lineam ęqui <lb/>noctialem, &amp; <lb/>quando ſupra.</note>
<note position="left" xlink:label="note-0398-09" xlink:href="note-0398-09a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0399-01" xlink:href="note-0399-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0399-02" xlink:href="note-0399-02a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0399-03" xlink:href="note-0399-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s25180" xml:space="preserve">QVOD ſi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s25181" xml:space="preserve">Horizontẽ æqualis fuerit cõplemento altitudinis <lb/>poli ex parte auſtrali, ita ut cõmunis ſectio ipſius plani, &amp; </s>
  <s xml:id="echoid-s25182" xml:space="preserve">Meridiani eadem ſit in Analemmate, <lb/>quæ ſectio cõmunis Meridiani &amp; </s>
  <s xml:id="echoid-s25183" xml:space="preserve">Aequatoris H I, ſecabit axis F G, meridianam lineam horologii, <lb/>quæ in Analemmate parallela ducitur ipſi H I, ad angulos rectos: </s>
  <s xml:id="echoid-s25184" xml:space="preserve">atque adeo &amp; </s>
  <s xml:id="echoid-s25185" xml:space="preserve">linea ſtyli G N, ad <lb/>
<anchor type="note" xlink:label="note-0399-04a" xlink:href="note-0399-04"/>
<anchor type="note" xlink:label="note-0399-05a" xlink:href="note-0399-05"/>
eandem lineam meridianam in horologio perpendicularis erit; </s>
  <s xml:id="echoid-s25186" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25187" xml:space="preserve">Æquatoris diameter in eodem <lb/>Anlemmate meridianam lineam horologii, hoc eſt, communem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s25188" xml:space="preserve">plani <lb/>
<anchor type="note" xlink:label="note-0399-06a" xlink:href="note-0399-06"/>
horologii non ſecabit. </s>
  <s xml:id="echoid-s25189" xml:space="preserve">Vnde in horologio parallelæ erunt inter ſelinea meridiana, &amp; </s>
  <s xml:id="echoid-s25190" xml:space="preserve">æquinoctia-<lb/>lis. </s>
  <s xml:id="echoid-s25191" xml:space="preserve">Quæ omnia ita confirmabimus. </s>
  <s xml:id="echoid-s25192" xml:space="preserve">Quoniam tres circuli Æquator, Meridianus, &amp; </s>
  <s xml:id="echoid-s25193" xml:space="preserve">circulus ma-<lb/>ximus, cui horologium æquidiſtat, habent unam eandemq́; </s>
  <s xml:id="echoid-s25194" xml:space="preserve">cõmunem ſectionem H I, in Analem-<lb/>mate, planum autem horologii uni illorum, atque adeo communi huic ſectioni æquidiſtat, erunt <lb/>communes ſectiones, quas reliqu<unsure/>@uo circuli, nempe Æquator, &amp; </s>
  <s xml:id="echoid-s25195" xml:space="preserve">Meridianus in plano horolo-<lb/>gij faciunt, parallelæ, ex propoſ. </s>
  <s xml:id="echoid-s25196" xml:space="preserve">18. </s>
  <s xml:id="echoid-s25197" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25198" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25199" xml:space="preserve">quales ſunt linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s25200" xml:space="preserve">linea meridiana. <lb/></s>
  <s xml:id="echoid-s25201" xml:space="preserve">Cum ergo linea ſtyli ρ G, æquinoctialem lineam ſecet ad angulos rectos, ſecabit eadem &amp; </s>
  <s xml:id="echoid-s25202" xml:space="preserve">meri-<lb/>dianam lineam ad rectos angulos. </s>
  <s xml:id="echoid-s25203" xml:space="preserve">Erit nihilominus adhuc centrum horologii infra lineam æqui <lb/>
<anchor type="note" xlink:label="note-0399-07a" xlink:href="note-0399-07"/>
<anchor type="note" xlink:label="note-0399-08a" xlink:href="note-0399-08"/>
noctialem, vt in ſexta figura apparet.</s>
  <s xml:id="echoid-s25204" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1287" type="float" level="2" n="25">
<note position="left" xlink:label="note-0399-04" xlink:href="note-0399-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0399-05" xlink:href="note-0399-05a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0399-06" xlink:href="note-0399-06a" xml:space="preserve">In quonam ho <lb/>rologio linea <lb/>æquinoctialis, <lb/>&amp; li<unsure/>nea meri-<lb/>diana inter ſe <lb/>parallelę ſint.</note>
<note position="left" xlink:label="note-0399-07" xlink:href="note-0399-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0399-08" xlink:href="note-0399-08a" xml:space="preserve">29. primi.</note>
</div>
<note position="right" xml:space="preserve">Quodnam ho-<lb/>rologium @@-<lb/>tro careat.</note>
<p>
  <s xml:id="echoid-s25205" xml:space="preserve">SI denique arcus Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s25206" xml:space="preserve">Horizontem æqualis fuerit ex par-<lb/>te boreali altitudini poli, ita vt communis ſectio plani, &amp; </s>
  <s xml:id="echoid-s25207" xml:space="preserve">Meridiani non differatab axe F G, per-<lb/>ſpicuum eſt, horologium centro carere, quia axis lineam meridianam ſecare non poteſt, immo <lb/>nec ipſum planum horologii, cum parallelum ſit circulo maximo per axem ducto. </s>
  <s xml:id="echoid-s25208" xml:space="preserve">Rectè igitur <lb/>præſcripſimus, rectam H I, ex portione Analemmatis in rectam G N, quæ eſt linea ſtyli in horolo <lb/>gio, modo infra punctum G, modo ſupra idem eſſe transferendam vſque ad punctum ρ, &amp; </s>
  <s xml:id="echoid-s25209" xml:space="preserve">c.</s>
  <s xml:id="echoid-s25210" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25211" xml:space="preserve">INVENTO hac ratione horologij centro ρ, quod modo infra æquinoctialem lineam eſt, <lb/>modo ſupra eandem, vt tradidimus, progrediemur vlterius in conſtructione horologij hoc mo-<lb/>do. </s>
  <s xml:id="echoid-s25212" xml:space="preserve">Ex portione Analemmatis ſumatur recta D I, nempe portio ſectionis Meridiani, &amp; </s>
  <s xml:id="echoid-s25213" xml:space="preserve">Aequato-<lb/>
<anchor type="note" xlink:label="note-0399-10a" xlink:href="note-0399-10"/>
ris intercepta inter D, centrum Mundi, &amp; </s>
  <s xml:id="echoid-s25214" xml:space="preserve">rectam H I, transferaturq́ue in rectam G N, ex puncto <lb/>G, ſiue ſurſum, ſiue deorſum verſus vſque ad punctum L, ex quo circulus cuiuſuis magnitudinis <lb/>deſcribatur, qui ſecetur in 24. </s>
  <s xml:id="echoid-s25215" xml:space="preserve">partes æquales. </s>
  <s xml:id="echoid-s25216" xml:space="preserve">Verum diuiſio inchoanda hic non eſt à recta G N, <lb/>vt in horologio horizontali à linea H E, incipit, quia linea G N, non eſt hic meridiana, vt ibi H E, <lb/>ſed communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s25217" xml:space="preserve">circuli maximi per polos ipſius plani, &amp; </s>
  <s xml:id="echoid-s25218" xml:space="preserve">polos mundi trã <lb/>ſeuntis, inſtar proprii Meridiani ipſius plani, qui non eſt Meridianus Horizontis. </s>
  <s xml:id="echoid-s25219" xml:space="preserve">Hinc enim fit, <lb/>rectam G N, in circulo ex L, deſcripto non poſſe eſſe ſectionem communem Aequatoris, &amp; </s>
  <s xml:id="echoid-s25220" xml:space="preserve">Meri-<lb/>diani ipſius Horizontis, ſi circulus ex L, deſcriptus in propria poſitione intelligatur eſſe conſtitu <lb/>tus, quemadmodum in horizontali horologio recta I E, in circulo ex E, deſcripto eſt communis <lb/>ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s25221" xml:space="preserve">Aequatoris, ſi dictus circulus proprium ſitum habeat, vt ibi oſtendimus. <lb/></s>
  <s xml:id="echoid-s25222" xml:space="preserve">Vnde cum à communi ſectione dicta Meridiani, &amp; </s>
  <s xml:id="echoid-s25223" xml:space="preserve">Aequatoris, nempe ab hora 12. </s>
  <s xml:id="echoid-s25224" xml:space="preserve">principium
<pb o="384" file="0400" n="400" rhead="GNOMONICES"/>
habere debeat diuiſio dicti circuli ex L, deſcripti, ut in horizontali horologio factum eſt, inuenie-<lb/>mus huiuſimodi ſectionem, ſeu lineam horæ 12. </s>
  <s xml:id="echoid-s25225" xml:space="preserve">in prædicto circulo hac ratione. </s>
  <s xml:id="echoid-s25226" xml:space="preserve">Inquiratur <lb/>per propoſ. </s>
  <s xml:id="echoid-s25227" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25228" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25229" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25230" xml:space="preserve">inclinatio Meridiani proprij ipſius plani ad Meridianum Horizontis: </s>
  <s xml:id="echoid-s25231" xml:space="preserve">quam <lb/>quidem comperimus in prima figura grad. </s>
  <s xml:id="echoid-s25232" xml:space="preserve">14. </s>
  <s xml:id="echoid-s25233" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25234" xml:space="preserve">10. </s>
  <s xml:id="echoid-s25235" xml:space="preserve">In ſecunda grad. </s>
  <s xml:id="echoid-s25236" xml:space="preserve">20. </s>
  <s xml:id="echoid-s25237" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25238" xml:space="preserve">52. </s>
  <s xml:id="echoid-s25239" xml:space="preserve">In terria <lb/>
<anchor type="note" xlink:label="note-0400-01a" xlink:href="note-0400-01"/>
grad. </s>
  <s xml:id="echoid-s25240" xml:space="preserve">33. </s>
  <s xml:id="echoid-s25241" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25242" xml:space="preserve">47. </s>
  <s xml:id="echoid-s25243" xml:space="preserve">In quarta grad. </s>
  <s xml:id="echoid-s25244" xml:space="preserve">27. </s>
  <s xml:id="echoid-s25245" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25246" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25247" xml:space="preserve">In quinta grad. </s>
  <s xml:id="echoid-s25248" xml:space="preserve">75. </s>
  <s xml:id="echoid-s25249" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25250" xml:space="preserve">46. </s>
  <s xml:id="echoid-s25251" xml:space="preserve">In ſexta denique <lb/>grad. </s>
  <s xml:id="echoid-s25252" xml:space="preserve">90. </s>
  <s xml:id="echoid-s25253" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25254" xml:space="preserve">o. </s>
  <s xml:id="echoid-s25255" xml:space="preserve">Hęc enim inclinatio numeranda eſt à puncto N, in circulo ex L, deſcripto uſque <lb/>ad punctum O, hac ſeruata lege. </s>
  <s xml:id="echoid-s25256" xml:space="preserve">Si planum ad Horizontem fuerit inclinatum ad partes boreales, <lb/>hoc eſt, facies eius ſuperior à meridie declinet in ortum, uel occaſum, ſi quidem à meridie in or-<lb/>tum declinet, numeranda eſt dicta inclinatio Meridianorum à puncto N, uerſus ſiniſtram, hoc eſt, <lb/>uerſus partes occidentales, ut in figura prima &amp; </s>
  <s xml:id="echoid-s25257" xml:space="preserve">tertia factum eſt. </s>
  <s xml:id="echoid-s25258" xml:space="preserve">Nam quia tunc circulus maxi-<lb/>
<anchor type="note" xlink:label="note-0400-02a" xlink:href="note-0400-02"/>
mus per polos Horizontis, &amp; </s>
  <s xml:id="echoid-s25259" xml:space="preserve">polos plani inclinati ductus, qui nimirum inclinationem ad Hori-<lb/>zontem metitur, cadit ex parte auſtri in quadrantem hemiſphęrii ſuperi orientalem; </s>
  <s xml:id="echoid-s25260" xml:space="preserve">(Vocamus <lb/>quadrantes hemiſphęrii ſuperi, partes illas, quæ inter Meridianum, Horizontem, &amp; </s>
  <s xml:id="echoid-s25261" xml:space="preserve">Verticalem <lb/>circulum@ propriè dictum continentur. </s>
  <s xml:id="echoid-s25262" xml:space="preserve">Hi enim tres circuli ſe mutuo ad angulos rectos ſecantes <lb/>partiuntur totum hemiſphęrium ſuperum in quatuor partes æquales, quarum duæ auſtrales <lb/>ſunt, una orientalis, &amp; </s>
  <s xml:id="echoid-s25263" xml:space="preserve">occidentalis altera; </s>
  <s xml:id="echoid-s25264" xml:space="preserve">duæ uero boreales, vna orientalis, &amp; </s>
  <s xml:id="echoid-s25265" xml:space="preserve">altera occidenta-<lb/>lis, ut ex ſphæra materiali conſtat) exiſtet polus plani inclinati in eodem quadrante ſupra Ho-<lb/>rizontem. </s>
  <s xml:id="echoid-s25266" xml:space="preserve">Cum enim arcus illius circuli maximi ducti per uerticem loci, &amp; </s>
  <s xml:id="echoid-s25267" xml:space="preserve">polum plani incli-<lb/>nati poſitus inter planum &amp; </s>
  <s xml:id="echoid-s25268" xml:space="preserve">uerticem ſit quadrante minor, arcus autem eiuſdem circuli maximi <lb/>à plano per verticem uſque ad Horizontem porrectus quadrante maior, propterea quòd arcus <lb/>
<anchor type="note" xlink:label="note-0400-03a" xlink:href="note-0400-03"/>
dicti circuli maximi inter uerticem &amp; </s>
  <s xml:id="echoid-s25269" xml:space="preserve">Horizontem interiecti quadrantes ſunt; </s>
  <s xml:id="echoid-s25270" xml:space="preserve">perſpicuum eſt, <lb/>polum plani inclinati, qui terminat quadrantem dicti circuli maximi, quo polus plani inclinati ab <lb/>ipſo plano, per coroll. </s>
  <s xml:id="echoid-s25271" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s25272" xml:space="preserve">16. </s>
  <s xml:id="echoid-s25273" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25274" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25275" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s25276" xml:space="preserve">abeſt, cadere in quadrantẽ hemiſphęrii ſuperi <lb/>orientalem, &amp; </s>
  <s xml:id="echoid-s25277" xml:space="preserve">auſtralem. </s>
  <s xml:id="echoid-s25278" xml:space="preserve">Quare Meridianus Horizontis occidentalior erit in Æquatore ſupra <lb/>Horizontem Meridiano proprio plani inclinati per eius polos, &amp; </s>
  <s xml:id="echoid-s25279" xml:space="preserve">per polosmundi ducto; </s>
  <s xml:id="echoid-s25280" xml:space="preserve">ac pro-<lb/>pterea cum, poſito circulo ex L, deſcripto in proprio ſitu, Meridianus proprius plani inclinati ſe-<lb/>cet dictum circulum ſupra Horizontem in puncto N, numeranda erit ab N, uerſus partes occidẽ-<lb/>tales inclinatio Meridiani huius ad Meridianum Horizontis uſquead punctum O. </s>
  <s xml:id="echoid-s25281" xml:space="preserve">In hoc enim <lb/>puncto eundem circulum ſecabit Meridianus Horizontis, cum ab illo ſecedat in Æquatore ſupra <lb/>Horizontem, atque adeo in circulo ex L, deſcripto, ab N, uerſus occidentẽ, ut dictum eſt. </s>
  <s xml:id="echoid-s25282" xml:space="preserve">Igitur à <lb/>
<anchor type="note" xlink:label="note-0400-04a" xlink:href="note-0400-04"/>
puncto O, inchoanda erit diuiſio circuli ex L, deſcripti. </s>
  <s xml:id="echoid-s25283" xml:space="preserve">Si uerò planum eiuſdem generis, quod <lb/>nimirum ex parte boreali ad Horizontem eſt inclinatum, à meridie deflectat in occaſum, nume-<lb/>randa erit dicta inclinatio duorum Meridianorum ab N, uerſus orientales partes, uſque ad O, <lb/>punctum, quod initium prębeat diuiſionis circuli ex L, deſcripti: </s>
  <s xml:id="echoid-s25284" xml:space="preserve">quia tunc polus plani inclinati <lb/>exiſtit in quadrante hemiſphęrii ſuperi occidentali; </s>
  <s xml:id="echoid-s25285" xml:space="preserve">(quod nõ aliter probabimus, quàm proximè <lb/>oſtendimus, polum plani eſle in quadrãte oriẽtali, quando planum declinabat à meridie in ortũ) <lb/>atque adeò Meridianus Horizontis in Æquatore ſupra Horizontem orientalior eſt Meridiano <lb/>proprii plani inclinati, &amp; </s>
  <s xml:id="echoid-s25286" xml:space="preserve">c.</s>
  <s xml:id="echoid-s25287" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1288" type="float" level="2" n="26">
<note position="left" xlink:label="note-0399-10" xlink:href="note-0399-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0400-01" xlink:href="note-0400-01a" xml:space="preserve">Quanta ſit in <lb/>cli<unsure/>natio Meri <lb/>diani proprii <lb/>ipſius plani in <lb/>clinati ad Meri <lb/>dianum Hori-<lb/>zontis in quali <lb/>bet ſex figura-<lb/>rum huius pro <lb/>poſ.</note>
<note position="left" xlink:label="note-0400-02" xlink:href="note-0400-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0400-03" xlink:href="note-0400-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0400-04" xlink:href="note-0400-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s25288" xml:space="preserve">IN planis autem, quæ ex parte auſtrali inclinata ſunt ad Horizontem, hoc eſt, quorum ſupe-<lb/>riores facies à ſeptentrione deflectunt in ortum, occaſumue, ut ſciamus, quamnã in partem ſuppu-<lb/>
<anchor type="note" xlink:label="note-0400-05a" xlink:href="note-0400-05"/>
tare debeamus dictam inclinationem Meridianorum, inquirẽdi erunt primum per propoſ. </s>
  <s xml:id="echoid-s25289" xml:space="preserve">32. </s>
  <s xml:id="echoid-s25290" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s25291" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25292" xml:space="preserve">arcus circulorum maximorum inclinationes planorum ad Horizontem metientium inter Ho-<lb/>rizontem, &amp; </s>
  <s xml:id="echoid-s25293" xml:space="preserve">circulũ horæ 6. </s>
  <s xml:id="echoid-s25294" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s25295" xml:space="preserve">uel med. </s>
  <s xml:id="echoid-s25296" xml:space="preserve">nocte interiecti. </s>
  <s xml:id="echoid-s25297" xml:space="preserve">In quarta figura huius propoſ. </s>
  <s xml:id="echoid-s25298" xml:space="preserve">inue-<lb/>nimus eiuſmodi arcum (in prioribus enim tribus figuris hiſce arcubus non indigemus, cum <lb/>
<anchor type="note" xlink:label="note-0400-06a" xlink:href="note-0400-06"/>
earum plana ad Horizontem inclinata ſint ex parte boreali) grad. </s>
  <s xml:id="echoid-s25299" xml:space="preserve">40. </s>
  <s xml:id="echoid-s25300" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25301" xml:space="preserve">14. </s>
  <s xml:id="echoid-s25302" xml:space="preserve">In quinta grad. <lb/></s>
  <s xml:id="echoid-s25303" xml:space="preserve">24. </s>
  <s xml:id="echoid-s25304" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25305" xml:space="preserve">14. </s>
  <s xml:id="echoid-s25306" xml:space="preserve">In ſexta denique grad. </s>
  <s xml:id="echoid-s25307" xml:space="preserve">37. </s>
  <s xml:id="echoid-s25308" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25309" xml:space="preserve">57. </s>
  <s xml:id="echoid-s25310" xml:space="preserve">Deinde explorandum erit, an polus plani inclina-<lb/>ti ex parte auſtrali ad Horizontem (qui quidem in huiuſmodi planis perpetuo in alterutrum <lb/>quadrantum borealium hemiſphęrii ſuperi cadit, quemadmodum in planis ex parte boreali ad <lb/>Horizontem inclinatis ſemper cadit in alterutrum quadrantum auſtralium, ut paulo ante oſten-<lb/>dimus) exiſtat infra circulum horæ 6. </s>
  <s xml:id="echoid-s25311" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s25312" xml:space="preserve">uel med. </s>
  <s xml:id="echoid-s25313" xml:space="preserve">nocte, uel in ipſomer circulo, uel deni-<lb/>
<anchor type="note" xlink:label="note-0400-07a" xlink:href="note-0400-07"/>
que ſupra eundem. </s>
  <s xml:id="echoid-s25314" xml:space="preserve">Hoc autem facile aſſequemur, ſi cum arcu proxime inuento conferamus ar-<lb/>cum circuli maximi inclinationem plani ad Horizontem metientis (in quo etiam exiſtit arcus <lb/>proximè inuentus) poſitum inter polum plani inclinati, &amp; </s>
  <s xml:id="echoid-s25315" xml:space="preserve">Horizontem, quem mox reperiemus. <lb/></s>
  <s xml:id="echoid-s25316" xml:space="preserve">Si enim hic arcus minor repertus fuerit illo, manifeſtum eſt, polum plani inclinati cadere infra <lb/>
<anchor type="note" xlink:label="note-0400-08a" xlink:href="note-0400-08"/>
circulum horæ 6. </s>
  <s xml:id="echoid-s25317" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s25318" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s25319" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25320" xml:space="preserve">Si autem æqualis extiterit, polum plani in ipſomer circu <lb/>lo locari: </s>
  <s xml:id="echoid-s25321" xml:space="preserve">ſi denique maior fuerit inuentus, polum plani ſupra eundem circulum cadere, vt per-<lb/>ſpicuum eſt ex figura propoſ. </s>
  <s xml:id="echoid-s25322" xml:space="preserve">32. </s>
  <s xml:id="echoid-s25323" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25324" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25325" xml:space="preserve">vbi M, polus plani inclinati E, cadit infra circulum horæ <lb/>6. </s>
  <s xml:id="echoid-s25326" xml:space="preserve">B K D, quia arcus H M, inter polum plani, &amp; </s>
  <s xml:id="echoid-s25327" xml:space="preserve">Horizontem minor eſt arcu H L, inter circulum <lb/>horæ 6. </s>
  <s xml:id="echoid-s25328" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25329" xml:space="preserve">Horizontem: </s>
  <s xml:id="echoid-s25330" xml:space="preserve">quòd ſi æqualis eſlet, caderet polus in L, ſi verò maior, ſupra L, vt patet. <lb/></s>
  <s xml:id="echoid-s25331" xml:space="preserve">Cæterum arcus dictus inter polum plani, &amp; </s>
  <s xml:id="echoid-s25332" xml:space="preserve">Horizontem dicto citius reperitur, cum perpetuo <lb/>ęqualis ſit complemento inclinationis plani ad Horizontem, ut ex eadem figura propoſ. </s>
  <s xml:id="echoid-s25333" xml:space="preserve">32. </s>
  <s xml:id="echoid-s25334" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25335" xml:space="preserve">1.</s>
  <s xml:id="echoid-s25336" xml:space="preserve">
<pb o="385" file="0401" n="401" rhead="LIBER TERTIVS."/>
manifeſtum eſt. </s>
  <s xml:id="echoid-s25337" xml:space="preserve">Quia enim G I H, ſemicirculus eſt, ex propoſ. </s>
  <s xml:id="echoid-s25338" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25339" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25340" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25341" xml:space="preserve">Theodoſii, &amp; </s>
  <s xml:id="echoid-s25342" xml:space="preserve">arcus M N, <lb/>inter planum, &amp; </s>
  <s xml:id="echoid-s25343" xml:space="preserve">eius polum quadrans, ex coroll, propoſ. </s>
  <s xml:id="echoid-s25344" xml:space="preserve">16. </s>
  <s xml:id="echoid-s25345" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25346" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25347" xml:space="preserve">Theodoſii, erunt reliqui duo <lb/>atcus G N, M H, ſimul quadranti æquales. </s>
  <s xml:id="echoid-s25348" xml:space="preserve">Cum ergo G N, ſit arcus inclinationis, erit arcus M H, <lb/>inter polum plani, &amp; </s>
  <s xml:id="echoid-s25349" xml:space="preserve">Horizontem poſitus complementum inclinationis. </s>
  <s xml:id="echoid-s25350" xml:space="preserve">Vnde cognita inclina-<lb/>tione planiad Horizontem, ſi ea auferatur ex quadrante, relinquetur prædictus arcus inter polũ <lb/>plani, &amp; </s>
  <s xml:id="echoid-s25351" xml:space="preserve">Horizontem. </s>
  <s xml:id="echoid-s25352" xml:space="preserve">Hac arte inuentus eſt huiuſmodi arcus in quarta figura huius propoſ. </s>
  <s xml:id="echoid-s25353" xml:space="preserve">(in <lb/>prioribus enim tribus figuris, cum earum plana polos habeant in parte hemiſphærii ſuperi auſtra <lb/>li, non indigemus dictis arcubus) grad. </s>
  <s xml:id="echoid-s25354" xml:space="preserve">60. </s>
  <s xml:id="echoid-s25355" xml:space="preserve">Min 0. </s>
  <s xml:id="echoid-s25356" xml:space="preserve">In quinta grad. </s>
  <s xml:id="echoid-s25357" xml:space="preserve">10. </s>
  <s xml:id="echoid-s25358" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25359" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25360" xml:space="preserve">In ſexta denique <lb/>grad. </s>
  <s xml:id="echoid-s25361" xml:space="preserve">37. </s>
  <s xml:id="echoid-s25362" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25363" xml:space="preserve">57. </s>
  <s xml:id="echoid-s25364" xml:space="preserve">Qui arcus ſi cum prioribus inter circulum horæ 6. </s>
  <s xml:id="echoid-s25365" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25366" xml:space="preserve">Horizontem poſitis cõ-<lb/>ferantur, deprehendemus polum plani inclinati in quarta figura cadere ſupra circulum horæ 6. <lb/></s>
  <s xml:id="echoid-s25367" xml:space="preserve">
<anchor type="note" xlink:label="note-0401-01a" xlink:href="note-0401-01"/>
In quinta infra eundem; </s>
  <s xml:id="echoid-s25368" xml:space="preserve">In ſexta denique in ipſomet circulo horæ 6. </s>
  <s xml:id="echoid-s25369" xml:space="preserve">exiſtere.</s>
  <s xml:id="echoid-s25370" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1289" type="float" level="2" n="27">
<note position="left" xlink:label="note-0400-05" xlink:href="note-0400-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0400-06" xlink:href="note-0400-06a" xml:space="preserve">Quanti ſint at <lb/>cus circulorum <lb/>maximorũ in-<lb/>clinationes pla <lb/>norum metien <lb/>tium, inter Ho <lb/>rizontem &amp; cir <lb/>culum horæ 6. <lb/>à mer. vel med. <lb/>noc. interiecti <lb/>in poſteriorib’ <lb/>tribus ſiguris <lb/>huius propoſ.</note>
<note position="left" xlink:label="note-0400-07" xlink:href="note-0400-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0400-08" xlink:href="note-0400-08a" xml:space="preserve">An polus plani <lb/>inclinati in tri <lb/>bus poſteriori-<lb/>bus figuris hu-<lb/>ius propoſ. ca-<lb/>dat infra circu <lb/>lum horæ 6. an <lb/>ſupra, an vero <lb/>in ipſummet <lb/>circulum, qua <lb/>ratione cogno-<lb/>@catur.</note>
<note position="left" xlink:label="note-0401-01" xlink:href="note-0401-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s25371" xml:space="preserve">HIS perueſtigatis, ſi planum inclinatum ad Horizontem ex parte auſtrali declinet à Septen-<lb/>trione in occaſum, cadatq́ue eius polus ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s25372" xml:space="preserve">centrum autem horologii exiſtat <lb/>ſupra lineam æquinoctialem, vt in quarta figura contingit, ſupputanda eſt ſupradicta inclinatio <lb/>Meridianorum ab N, verſus partes orientales, ſiue verſus partes, quæ nobis ſunt ad ſiniſtram po-<lb/>ſitæ, ſi conuertamus faciem ad planum horologii, vſque ad punctum O, à quo inchoanda eſt di-<lb/>uiſio circuli ex L, deſcripti. </s>
  <s xml:id="echoid-s25373" xml:space="preserve">Quoniam enim tunc circulus maximus per polos Horizontis, &amp; </s>
  <s xml:id="echoid-s25374" xml:space="preserve">per <lb/>polos plani ductus cadit ex parte boreæ in quadrantem hemiſphærii ſuperi occidentalem, eiuſq́; <lb/></s>
  <s xml:id="echoid-s25375" xml:space="preserve">polus ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s25376" xml:space="preserve">exiſtit, ſecabit Meridianus proprius plani Aequatorem ſupra Hori <lb/>zontem in quadrante occidentali, nempe inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s25377" xml:space="preserve">circulum horæ 6. </s>
  <s xml:id="echoid-s25378" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0401-02a" xlink:href="note-0401-02"/>
Quare Meridianus Horizontis orientalior erit in Aequatore ſupra Horizontem Meridiano pro-<lb/>prio plani inclinati; </s>
  <s xml:id="echoid-s25379" xml:space="preserve">ac proinde, cum poſito circulo ex L, deſcripto in proprio ſitu, Meridianus <lb/>proprius plani inclinati ſecet dictum circulum ſupra Horizontem in puncto N, computanda erit <lb/>ab N, verſus orientem inclinatio huius Meridiani ad Meridianum Horizontis, vt inueniatur pun <lb/>ctum O, per quod Meridianus Horizontis tranſit. </s>
  <s xml:id="echoid-s25380" xml:space="preserve">Si verò ijſdem manentibus, centrum horolo-<lb/>gij infra lineam æquinoctialem extiterit, numeranda erit eadem Meridianorum inclinatio ab N, <lb/>verſus occidentales partes, hoc eſt, verſus dextram: </s>
  <s xml:id="echoid-s25381" xml:space="preserve">quia tunc Meridianus Horizontis in Aequa-<lb/>tore infra Horizontem occidentalior eſt proprio Meridiano plani inclinati, cum (vt diximus) ſu <lb/>pra Horizontem ſit orientalior. </s>
  <s xml:id="echoid-s25382" xml:space="preserve">Quare cum, poſito circulo ex L, deſcripto in proprio ſitu, Meri <lb/>dianus proprius plani inclinati ſecet dictum circulum in N, ſub Horizonte, (Id quod facile intel-<lb/>
<anchor type="note" xlink:label="note-0401-03a" xlink:href="note-0401-03"/>
ligetur, ſi figura quarta inuertatur, ita vt centrum ρ, infra æquinoctialem circulum exiſtat, &amp; </s>
  <s xml:id="echoid-s25383" xml:space="preserve">cir-<lb/>culus N O, propriam poſitionem adipiſcatur, ita vt eius centrum L, cum centro mundi I, coniun <lb/>gatur) computanda erit dicta inclinatio Meridianorum verſus occidentem à puncto N.</s>
  <s xml:id="echoid-s25384" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1290" type="float" level="2" n="28">
<note position="left" xlink:label="note-0401-02" xlink:href="note-0401-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0401-03" xlink:href="note-0401-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s25385" xml:space="preserve">QVOD ſi eiuſdem plani ex parte auſtrali ad Horizontem inclinati, &amp; </s>
  <s xml:id="echoid-s25386" xml:space="preserve">à ſeptentrione in occa-<lb/>ſum declinantis polus præcisè cadat in circulum horæ 6. </s>
  <s xml:id="echoid-s25387" xml:space="preserve">vbicunque centrum horologii exiſtat, <lb/>comprehender dicta Meridianorum inclinatio grad. </s>
  <s xml:id="echoid-s25388" xml:space="preserve">90. </s>
  <s xml:id="echoid-s25389" xml:space="preserve">cum Meridianus proprius plani idem <lb/>tunc ſit, qui circulus horæ 6. </s>
  <s xml:id="echoid-s25390" xml:space="preserve">qui in Aequatore à Meridiano Horizontis per quadrantem remoue-<lb/>tur. </s>
  <s xml:id="echoid-s25391" xml:space="preserve">Quocirca in quamcunque partem numeretur dicta inclinatio à puncto N, inuenietur pun-<lb/>ctum O, à quo diuiſio circuli ex L, deſcripti principium ſumere poteſt.</s>
  <s xml:id="echoid-s25392" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25393" xml:space="preserve">DENIQVE ſi eiuſdem plani polus infra circulum horæ 6. </s>
  <s xml:id="echoid-s25394" xml:space="preserve">cadat, centrum autem horologii <lb/>
<anchor type="note" xlink:label="note-0401-04a" xlink:href="note-0401-04"/>
exiſtat ſupra lineam æquinoctialem, ſupputanda erit eadem inclinatio Meridianorum ab N, ver-<lb/>ſus partes occidentales. </s>
  <s xml:id="echoid-s25395" xml:space="preserve">Quoniam enim tunc polus plani inclinati infra circulum horæ 6. </s>
  <s xml:id="echoid-s25396" xml:space="preserve">in qua-<lb/>drante hemiſphęrii ſuperi boreali, &amp; </s>
  <s xml:id="echoid-s25397" xml:space="preserve">occidentali exiſtit, ſecabit Meridianus proprius plani Aequa <lb/>torem infra Horizontem in quadrante occidentali, ſupra verò Horizontem in quadrante orien-<lb/>tali. </s>
  <s xml:id="echoid-s25398" xml:space="preserve">Vnde Meridianus Horizontis in Æquatore ſupra Horizontem occidentalior erit Meridia-<lb/>no proprio plani inclinati. </s>
  <s xml:id="echoid-s25399" xml:space="preserve">Quamobrem numeranda eſt inclinatio Meridianorum ab N, verſus <lb/>occidentales partes, cum Meridianus proprius plani ſecet circulum N O, ſupra Horizontem in <lb/>N. </s>
  <s xml:id="echoid-s25400" xml:space="preserve">Si verò iiſdem manentibus, centrum horologii extiterit infra lineam æquinoctialem, nume-<lb/>randa eſt eadem inclinatio Meridianorum ab N, verſus orientales partes: </s>
  <s xml:id="echoid-s25401" xml:space="preserve">quia tunc Meridianus <lb/>proprius plani ſecat circulum N O, in N, infra Horizontem, eſtq́ue illo orientalior Meridianus <lb/>Horizontis in Aequatore, ſeu circulo N O, infra Horizontem, vt patet ex dictis.</s>
  <s xml:id="echoid-s25402" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1291" type="float" level="2" n="29">
<note position="left" xlink:label="note-0401-04" xlink:href="note-0401-04a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s25403" xml:space="preserve">SI autem planum ad Horizontem ex parte auſtrali inclinatum à Septentrione in ortum de-<lb/>flectat, fiat omnino contraria ijs, quæ proximè præcepimus in planis à Septentrione in occaſum <lb/>declinantibus obſeruanda eſſe. </s>
  <s xml:id="echoid-s25404" xml:space="preserve">Ita vides inclinationem Meridianorum in quin ta figura numera-<lb/>tam eſſe ab N, verſus partes occidentales vſque ad O: </s>
  <s xml:id="echoid-s25405" xml:space="preserve">quia eius plani polus cadit infra circulum <lb/>horæ 6. </s>
  <s xml:id="echoid-s25406" xml:space="preserve">reperiturq́ue centrum horologii infra lineam æquinoctialem. </s>
  <s xml:id="echoid-s25407" xml:space="preserve">Ratio huius ex dictis fa-<lb/>cile colligi poteſt. </s>
  <s xml:id="echoid-s25408" xml:space="preserve">In ſexta denique figura numerata eſt inclinatio eadem grad. </s>
  <s xml:id="echoid-s25409" xml:space="preserve">90. </s>
  <s xml:id="echoid-s25410" xml:space="preserve">quia ibi polus <lb/>plani cadit præcisè in ipſummet circulum horæ 6. </s>
  <s xml:id="echoid-s25411" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s25412" xml:space="preserve">c.</s>
  <s xml:id="echoid-s25413" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25414" xml:space="preserve">ITAQVE ſi per puncta diuiſionum circuli ex L, deſcripti, &amp; </s>
  <s xml:id="echoid-s25415" xml:space="preserve">per centrum L, ducantur re-<lb/>ctæ occultæ, ſecabitur linea æquinoctialis G H, in punctis, per quæ lineæ eductæ ex centro horo-<lb/>logij ρ, dabunt horas à mer. </s>
  <s xml:id="echoid-s25416" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s25417" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25418" xml:space="preserve">vt in horologio horizontali demonſtrauimus; </s>
  <s xml:id="echoid-s25419" xml:space="preserve">ita ta-
<pb o="386" file="0402" n="402" rhead="GNOMONICES"/>
men, vt tecta ex ρ, ducta per punctum M, æquinoctialis lineæ, in quod cadit recta O L, in horolo-<lb/>giis omnibus, quæ Zenith reſpiciunt &amp; </s>
  <s xml:id="echoid-s25420" xml:space="preserve">auſtrum, &amp; </s>
  <s xml:id="echoid-s25421" xml:space="preserve">in ijs, quæ ad Zenith, &amp; </s>
  <s xml:id="echoid-s25422" xml:space="preserve">boream ſpectant, <lb/>dummodo centrum ſit ſupra lineam æquinoctialem, indicet horam 12. </s>
  <s xml:id="echoid-s25423" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s25424" xml:space="preserve">rectæ illam <lb/>ſequentes in horologio verſus partes orientales (voco partes oriẽtales illas, quæ, horologio in pro-<lb/>pria poſitione locato, vergunt ad ortum Solis, &amp;</s>
  <s xml:id="echoid-s25425" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s25426" xml:space="preserve">monſtrent horas à meridie, &amp;</s>
  <s xml:id="echoid-s25427" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25428" xml:space="preserve">In horologijs <lb/>autem, quæ ad Zenith, boreamque pertinent, habentq́ue centrum infra lineam æquinoctialem, <lb/>eadem recta ρ M, ſignificet horam 12. </s>
  <s xml:id="echoid-s25429" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s25430" xml:space="preserve">quæ ipſam ſequuntur verſus occidentales <lb/>partes, oſtendant horas à media nocte, &amp;</s>
  <s xml:id="echoid-s25431" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25432" xml:space="preserve">In horologio denique, vbi inclinatio Meridiani pro-<lb/>prij ad Meridianum Horizontis continet gr. </s>
  <s xml:id="echoid-s25433" xml:space="preserve">90 rectaq́ ex ρ, ducitur lineæ æquinoctiali parallela <lb/>verſus ſuperiores partes, monſtret quoque horam 12. </s>
  <s xml:id="echoid-s25434" xml:space="preserve">mediæ noctis; </s>
  <s xml:id="echoid-s25435" xml:space="preserve">ſequentes verò eam verſus oc-<lb/>
<anchor type="note" xlink:label="note-0402-01a" xlink:href="note-0402-01"/>
caſum, horas indicent à media nocte, &amp;</s>
  <s xml:id="echoid-s25436" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25437" xml:space="preserve">Cuius rei cauſa ſupra in priori deſcriptione allata eſt.</s>
  <s xml:id="echoid-s25438" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1292" type="float" level="2" n="30">
<note position="left" xlink:label="note-0402-01" xlink:href="note-0402-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s25439" xml:space="preserve">QVANDO planum horologii ex parte boreali inclinatum eſt ad Horizontum, ea lege, ut ar-<lb/>cus Meridiani inter ipſum, &amp; </s>
  <s xml:id="echoid-s25440" xml:space="preserve">Horizontẽ æqualis ſit altitudini poli ſupra Horizontem, ac proinde <lb/>axi æquidiſtet, ut in tertia figura accidit, ita horologium in eo cõſtruemus. </s>
  <s xml:id="echoid-s25441" xml:space="preserve">Ductis rectis G N, G H, <lb/>ſeſe ad rectos angulos in G, ſecantibus, ut prius, accipiemus in G N, ſiue ſupra rectam G H, ſiue <lb/>infra, rectam G L, cuiuſcunque magnitudinis pro ſtylo, &amp; </s>
  <s xml:id="echoid-s25442" xml:space="preserve">ex L, circulum deſcribemus. </s>
  <s xml:id="echoid-s25443" xml:space="preserve">Suppu-<lb/>tata deinde ex puncto N, ubi recta G N, dictum circulum ſecat, inclinatione Meridiani proprii <lb/>plani propoſiti ad Meridianum Horizontis, ad partes quidem occidentales, ſi in ortũ decliner ho <lb/>rologium à meridie, vel ad partes orientales, ſi horologium à meridie in occaſum deflectat, uſque <lb/>ad punctum O, ſecetur circulus ex L, deſcriptus in 24. </s>
  <s xml:id="echoid-s25444" xml:space="preserve">partes æquales, initio facto à puncto O. <lb/></s>
  <s xml:id="echoid-s25445" xml:space="preserve">
<anchor type="note" xlink:label="note-0402-02a" xlink:href="note-0402-02"/>
Rectæ enim ex punctis diuiſionum per centrum L, ductæ ſecabunt lineam æquinoctialem G H, <lb/>in punctis, per quæ ſi ducantur lineæ ad G H, perpendiculares, ut in Meridiano horologio, uel po <lb/>lari, habebuntur lineæ horarum à mer. </s>
  <s xml:id="echoid-s25446" xml:space="preserve">uel med. </s>
  <s xml:id="echoid-s25447" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25448" xml:space="preserve">ita tamen, ut recta per punctum M, æquino <lb/>ctialis lineæ, in quod cadit recta O L, monſtret horam 12. </s>
  <s xml:id="echoid-s25449" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s25450" xml:space="preserve">rectæ ſequentes illam ver <lb/>ſus ortum, oſtendant horas à meridie, &amp;</s>
  <s xml:id="echoid-s25451" xml:space="preserve">c.</s>
  <s xml:id="echoid-s25452" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1293" type="float" level="2" n="31">
<note position="left" xlink:label="note-0402-02" xlink:href="note-0402-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s25453" xml:space="preserve">CAETERVM idẽ horologiũ declinãs, &amp; </s>
  <s xml:id="echoid-s25454" xml:space="preserve">inclinatũ ſimul deſcribemus etiã hoc modo. </s>
  <s xml:id="echoid-s25455" xml:space="preserve">Inue <lb/>
<anchor type="note" xlink:label="note-0402-03a" xlink:href="note-0402-03"/>
niatur per propoſ. </s>
  <s xml:id="echoid-s25456" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25457" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25458" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25459" xml:space="preserve">arcus plani propoſiti interceptus inter Meridianũ Horizontis, &amp; </s>
  <s xml:id="echoid-s25460" xml:space="preserve">Meri <lb/>dianũ ipſius propriũ. </s>
  <s xml:id="echoid-s25461" xml:space="preserve">Itẽ per propoſ. </s>
  <s xml:id="echoid-s25462" xml:space="preserve">29. </s>
  <s xml:id="echoid-s25463" xml:space="preserve">eiuſdẽ lib. </s>
  <s xml:id="echoid-s25464" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25465" xml:space="preserve">altitudo poli ſupra planũ propoſitũ. </s>
  <s xml:id="echoid-s25466" xml:space="preserve">Altitudi-<lb/>nes quidem poli ſupra plana 6. </s>
  <s xml:id="echoid-s25467" xml:space="preserve">figurarum huius propoſ. </s>
  <s xml:id="echoid-s25468" xml:space="preserve">iam antea expoſitæ ſunt ad initium præ-<lb/>cedentis deſcriptionis: </s>
  <s xml:id="echoid-s25469" xml:space="preserve">Arcus uerò plani cuiuslibet propoſiti inter Meridianos dictos poſiti ita ſe <lb/>
<anchor type="note" xlink:label="note-0402-04a" xlink:href="note-0402-04"/>
habent. </s>
  <s xml:id="echoid-s25470" xml:space="preserve">In prima figura dictus arcus continet grad. </s>
  <s xml:id="echoid-s25471" xml:space="preserve">6. </s>
  <s xml:id="echoid-s25472" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25473" xml:space="preserve">15. </s>
  <s xml:id="echoid-s25474" xml:space="preserve">In ſecunda grad 9. </s>
  <s xml:id="echoid-s25475" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25476" xml:space="preserve">15. </s>
  <s xml:id="echoid-s25477" xml:space="preserve">In <lb/>
<anchor type="note" xlink:label="note-0402-05a" xlink:href="note-0402-05"/>
tertia grad. </s>
  <s xml:id="echoid-s25478" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25479" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25480" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25481" xml:space="preserve">In quarta grad. </s>
  <s xml:id="echoid-s25482" xml:space="preserve">25. </s>
  <s xml:id="echoid-s25483" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25484" xml:space="preserve">48. </s>
  <s xml:id="echoid-s25485" xml:space="preserve">In quinta grad. </s>
  <s xml:id="echoid-s25486" xml:space="preserve">61. </s>
  <s xml:id="echoid-s25487" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25488" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25489" xml:space="preserve">In ſexta denique <lb/>grad. </s>
  <s xml:id="echoid-s25490" xml:space="preserve">90. </s>
  <s xml:id="echoid-s25491" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25492" xml:space="preserve">0. </s>
  <s xml:id="echoid-s25493" xml:space="preserve">Deinde in plano aliquo ducatur recta ρ a, utcunque pro linea horæ 12. </s>
  <s xml:id="echoid-s25494" xml:space="preserve">in qua <lb/>ſumpto puncto quolibet ρ, pro centro horologii, deſcribatur ex eo arcus circuli a b, ſupra quidem <lb/>punctum ρ, ſi centrum horologii, infra lineam æquinoctialem cadit, infra uerò punctum ρ, ſi cen <lb/>trum ſupra æquinoctialem lineam ponendum eſt. </s>
  <s xml:id="echoid-s25495" xml:space="preserve">Quando autem horologii centrum infra, uel <lb/>ſupra lineam æquinoctialem cadat, ſatis ſuperq́ue expoſuimus in antecedenti deſcriptione, &amp; </s>
  <s xml:id="echoid-s25496" xml:space="preserve"><lb/>apertiſſime ex quatuor illis Analẽmatibus propoſ. </s>
  <s xml:id="echoid-s25497" xml:space="preserve">25. </s>
  <s xml:id="echoid-s25498" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s25499" xml:space="preserve">intelligi poteſt. </s>
  <s xml:id="echoid-s25500" xml:space="preserve">In illis enim recta <lb/>M N, eſt linea meridiana, ſeu horæ 12. </s>
  <s xml:id="echoid-s25501" xml:space="preserve">in ſuperioribus horologiis. </s>
  <s xml:id="echoid-s25502" xml:space="preserve">Vnde ſi ex data declinatione pla <lb/>ni, eiuſdemq́; </s>
  <s xml:id="echoid-s25503" xml:space="preserve">inclinatione, inueniatur arcus Meridiani inter ipſum planũ &amp; </s>
  <s xml:id="echoid-s25504" xml:space="preserve">Horizontẽ, nẽpe D K, <lb/>uel B K, facile colligi poterit, num cẽtrũ horologii, id eſt, punctũ M, in quod cadit axis F G, exiſtat <lb/>
<anchor type="note" xlink:label="note-0402-06a" xlink:href="note-0402-06"/>
infra ęquinoctialẽ lineam, quę tranſit per punctum N, an uerò ſupra, in ipſa linea meridiana M N, <lb/>atque adeò &amp; </s>
  <s xml:id="echoid-s25505" xml:space="preserve">in meridiana linea ρ a, horologij deſcribendi. </s>
  <s xml:id="echoid-s25506" xml:space="preserve">In arcu autem a b, numeretur à recta <lb/>ρ a, nempe à puncto a, arcus inuentus inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s25507" xml:space="preserve">Meridianum plani pro-<lb/>poſiti uſque ad b, ducaturq́ue recta ρ b, quæ communis ſectio erit plani horologij, &amp; </s>
  <s xml:id="echoid-s25508" xml:space="preserve">Meridiani <lb/>proprij ipſius, ut mox demonſtrabitur. </s>
  <s xml:id="echoid-s25509" xml:space="preserve">Vt autem ſciamus, uerſus quam partem dictus arcus nu-<lb/>merandus ſit, diligenter cõſideranda ſunt ea, quæ in antecedenti deſcriptione tradidimus. </s>
  <s xml:id="echoid-s25510" xml:space="preserve">In pla-<lb/>nis enim, quæ ad Horizontẽ inclinata ſunt ad partes boreales, ſi quidẽ declinẽt à meridie in ortũ, <lb/>ut in prima figura, ſupputandus eſt dictus arcus uerſus partem ſiniſtram, hoc eſt, uerſus partes <lb/>occidentales, quę nobis ad horologium cõuerſis ad ſiniſtram ſitę ſunt: </s>
  <s xml:id="echoid-s25511" xml:space="preserve">quia tunc Meridianus pro-<lb/>prius plani orientalior eſt Meridiano Horizontis; </s>
  <s xml:id="echoid-s25512" xml:space="preserve">ac proinde communis eius ſectio in plano ho-<lb/>
<anchor type="note" xlink:label="note-0402-07a" xlink:href="note-0402-07"/>
rologii, nempe recta ρ b, occidentalior erit meridiana linea ρ a, propterea quod umbra ſtyli, Sole <lb/>in quocunque circulo exiſtente, ſemper in contrariam partem proiiciatur, ut ex dictis conſtat. <lb/></s>
  <s xml:id="echoid-s25513" xml:space="preserve">Si uero plana eiuſmodi à meridie in occaſum deflectant, contrarium omnino faciẽdum eſt, pro-<lb/>pter contrariam etiam cauſam, ut in ſecunda figura factum eſt.</s>
  <s xml:id="echoid-s25514" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1294" type="float" level="2" n="32">
<note position="left" xlink:label="note-0402-03" xlink:href="note-0402-03a" xml:space="preserve">Alia conſtra-<lb/>@io eiuſdẽho-<lb/>rologii declinã <lb/>tis ſimul &amp; in-<lb/>clinati.</note>
<note position="left" xlink:label="note-0402-04" xlink:href="note-0402-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0402-05" xlink:href="note-0402-05a" xml:space="preserve">Quantus ſit ar-<lb/>cus plani incli-<lb/>nati inter pro-<lb/>pri um eius Me <lb/>ridianũ, &amp; Me <lb/>ridianum Hori <lb/>zontis poſitus <lb/>in qualibet ſex <lb/>figuratum hu-<lb/>ius propoſ.</note>
<note position="left" xlink:label="note-0402-06" xlink:href="note-0402-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0402-07" xlink:href="note-0402-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s25515" xml:space="preserve">IN planis autem ex auſtrali parte ad Horizontem inclinatis, addiſcendum erit ex ijs, quæ in <lb/>pręcedenti deſcriptione docuimus, num Meridianus proprius plani propoſiti ſit ſupra Horizon-<lb/>tem, uel infra orientalior, occidentaliorve Meridiano Horizontis. </s>
  <s xml:id="echoid-s25516" xml:space="preserve">Semper enim in contrariam <lb/>partem arcus dictus a b, erit computandus. </s>
  <s xml:id="echoid-s25517" xml:space="preserve">Ita uides in quarta figura dictum arcum numera-<lb/>tum eſſe ad partem ſiniſtram, ſiue uerſus orientem: </s>
  <s xml:id="echoid-s25518" xml:space="preserve">quia illius plani Meridianus proprius occi-<lb/>dentalior eſt ſupra Horizontem Meridiano Horizontis. </s>
  <s xml:id="echoid-s25519" xml:space="preserve">In quinta autem figura idem arcus ſup-
<pb o="387" file="0403" n="403" rhead="LIBER TERTIVS."/>
putatus eſt uerſus dexteram, ſeu partes occidentales, quia eius plani Meridianus ſub Horizonte <lb/>orientalior eſt Meridiano Horizontis. </s>
  <s xml:id="echoid-s25520" xml:space="preserve">In ſexta denique figura nihil intereſt, utrum in hanc, uel in <lb/>illam partem arcus dictus a b, numerctur: </s>
  <s xml:id="echoid-s25521" xml:space="preserve">quia complectitur grad. </s>
  <s xml:id="echoid-s25522" xml:space="preserve">90. </s>
  <s xml:id="echoid-s25523" xml:space="preserve">ita ut recta ρ b, cum ρ a, <lb/>angulum conſtituat rectum in ρ, puncto.</s>
  <s xml:id="echoid-s25524" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25525" xml:space="preserve">POST hæc ex quocunque puncto rectæ ρ b, ut ex G, ducatur ad ipſam perpendicularis G H, <lb/>quę erit linea æquinoctialis, quia, ut mox oſtẽdemus, ρ b, eſt linea indicis, ad quam neceſlario per-<lb/>pendicularis eſt æquinoctialis linea, ut ſupra demonſtrauimus.</s>
  <s xml:id="echoid-s25526" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s25527" xml:space="preserve">AD hæc in puncto ρ, cum recta ρ b, conſtituatur angulus G ρ I, altitudinis poli ſupra planum <lb/>propoſitũ inueatę, per propoſ. </s>
  <s xml:id="echoid-s25528" xml:space="preserve">29. </s>
  <s xml:id="echoid-s25529" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25530" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25531" xml:space="preserve">ut habeatur ρ I, axis mundi, ad quem ex puncto G, exci-<lb/>tetur perpendicularis G I, ac reliqua fiant, ut in prima deſcriptione, hoc eſt, rectæ G I, ſuma-<lb/>
<anchor type="note" xlink:label="note-0403-01a" xlink:href="note-0403-01"/>
tur æqualis G L, &amp; </s>
  <s xml:id="echoid-s25532" xml:space="preserve">circulus ex L, deſcriptus in 24 partes æquales ſecetur, initio facto à recta L M, <lb/>quę ex centro L, ducitur per punctum M, ubi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s25533" xml:space="preserve">meridiana ρ b, ſe interſecant <lb/>uel certè, quæ ex L, parallela ducitur ipſi meridianę lineę, quando æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s25534" xml:space="preserve">meridia <lb/>na parallelę ſunt, ut in ſexta figura, &amp;</s>
  <s xml:id="echoid-s25535" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25536" xml:space="preserve">Gnomon erit I K, ex I, perpendicularis demiſſa ad ρ b, <lb/>vt prius.</s>
  <s xml:id="echoid-s25537" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1295" type="float" level="2" n="33">
<note position="left" xlink:label="note-0403-01" xlink:href="note-0403-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s25538" xml:space="preserve">QVOD autem recta ρ b, communis ſectio ſit plani horologii, &amp; </s>
  <s xml:id="echoid-s25539" xml:space="preserve">Meridiani proprii eiuſdem <lb/>plani, ita demonſtrabimus. </s>
  <s xml:id="echoid-s25540" xml:space="preserve">Quoniam Meridianus Horizontis, &amp; </s>
  <s xml:id="echoid-s25541" xml:space="preserve">Meridianus plani proprius per <lb/>axem mundi ducuntur, occurruntq́ue circulo maximo, cui horologium æquidiſtat, in centro mũ <lb/>di, utpote in I, uertice ſtyli, fit ut dicti Meridiani cum hoc circulo maximo faciant communes <lb/>ſectiones, rectas lineas, quæ in centro angulum contineant, cui ſubtenditur arcus eiuſdem circuli <lb/>
<anchor type="note" xlink:label="note-0403-02a" xlink:href="note-0403-02"/>
maximi inter illos Meridi<unsure/>anos interiectus: </s>
  <s xml:id="echoid-s25542" xml:space="preserve">Quia uerò ijdem Meridiani occurrunt plano horolo-<lb/>
<anchor type="note" xlink:label="note-0403-03a" xlink:href="note-0403-03"/>
gii in ρ, puncto, ubi axis eidem plano occurrit, faciuntq́ue cum eo ſectiones communes, lineas <lb/>
<anchor type="note" xlink:label="note-0403-04a" xlink:href="note-0403-04"/>
rectas, quę illis prioribus in maximo circulo ęquidiſtant, eo quòd eidem maximo circulo paral-<lb/>lelum eſt horologii planam; </s>
  <s xml:id="echoid-s25543" xml:space="preserve">comprehendent huiuſmodi lineæ in plano horologii angulũ æqua-<lb/>lem illi angulo, quem in circulo maximo priores illæ lineæ conſtituunt. </s>
  <s xml:id="echoid-s25544" xml:space="preserve">Quamobrem cum angu <lb/>lus a ρ b, in plano horologii ſit illi in maximo circulo æqualis, quòd arcus a b, ſimilis ſit arcui il-<lb/>lius circuli maximi inter duos Meridianos poſito, quandoquidem per conſtructionem totidem <lb/>gradus, ac Minuta continet: </s>
  <s xml:id="echoid-s25545" xml:space="preserve">ponatur autem ρ a, linea meridiana, erit ρ b, communis ſectio pla-<lb/>ni horologij, &amp; </s>
  <s xml:id="echoid-s25546" xml:space="preserve">Meridiani ipſius proprii: </s>
  <s xml:id="echoid-s25547" xml:space="preserve">Ac proinde ſtylus in ea collocandus erit ad angulos re-<lb/>ctos, cum hac ratione à plano proprii huius Meridiani non recedat, ſed ad ipſum axem mundi in <lb/>
<anchor type="note" xlink:label="note-0403-05a" xlink:href="note-0403-05"/>
eo exiſtentem pertingat. </s>
  <s xml:id="echoid-s25548" xml:space="preserve">Quare ρ b, linea indicis eſt, ſeu ſtyli. </s>
  <s xml:id="echoid-s25549" xml:space="preserve">Vnde reliqua conſtructio demon-<lb/>ſtrabitur, vt prima conſtructio huius propoſ. </s>
  <s xml:id="echoid-s25550" xml:space="preserve">Sed tertiam hanc deſcriptionem aliunde inchoare <lb/>poterimus, &amp; </s>
  <s xml:id="echoid-s25551" xml:space="preserve">forſitan commodius, quàm tradidimus, vt in ſcholio ſequenti prope finem fere pla <lb/>num faciemus.</s>
  <s xml:id="echoid-s25552" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1296" type="float" level="2" n="34">
<note position="left" xlink:label="note-0403-02" xlink:href="note-0403-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0403-03" xlink:href="note-0403-03a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0403-04" xlink:href="note-0403-04a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0403-05" xlink:href="note-0403-05a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Quando planũ <lb/>horologii axi <lb/>æquidiſtat.</note>
<p>
  <s xml:id="echoid-s25553" xml:space="preserve">PORRO in plano ex parte boreali ad Horizontem inclinato, quod nec arcum habeat inter-<lb/>poſitum inter dictos duos Meridianos, neque altitudinem poli ſortiatur, vt contingit in planis, <lb/>quæ æquidiſtant circulis maximis per axem mundi ductis, quale eſt planum tertiæ figuræ, con-<lb/>ſtruendum erit horologium, vt in antecedenti conſtructione; </s>
  <s xml:id="echoid-s25554" xml:space="preserve">vel ſi prius ducatur vtcunque recta <lb/>quæpiam linea E ε, pro linea meridiana, ita procedendum erit. </s>
  <s xml:id="echoid-s25555" xml:space="preserve">Excitetur ad E ε, in quouis pun-<lb/>cto, vt in M, perpendicularis M H, pro linea æquinoctiali. </s>
  <s xml:id="echoid-s25556" xml:space="preserve">Deinde in M, conſtituatur angulus <lb/>
<anchor type="note" xlink:label="note-0403-07a" xlink:href="note-0403-07"/>
E M L, inclinationis Meridiani proprii ipſius plani ad Meridianum Horizontis inuentæ per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s25557" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25558" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25559" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25560" xml:space="preserve">verſus quidem ſiniſtrã, ſi planum à meridie in ortum, at dextrã verſus, ſi à meridie <lb/>in occaſum declinet. </s>
  <s xml:id="echoid-s25561" xml:space="preserve">Sumpto autem in recta M L, puncto L, vt libet, ducatur per illud ipſi E ε, <lb/>parallela L G, ſecans æquinoctialem lineam in G, quæ communis ſectio erit proprii Meridiani, &amp; </s>
  <s xml:id="echoid-s25562" xml:space="preserve"><lb/>plani horologii, &amp; </s>
  <s xml:id="echoid-s25563" xml:space="preserve">ipſa L G, longitudo gnomonis. </s>
  <s xml:id="echoid-s25564" xml:space="preserve">Deſcripto autem circulo ex L, diuiſoq́ue in <lb/>partes 24. </s>
  <s xml:id="echoid-s25565" xml:space="preserve">æquales, initio ſumpto à recta M L, ſi ex punctis diuiſionum per L, rectæ ducantur, ſe-<lb/>cabitur æquinoctialis linea in punctis, per quæ ducendæ ſunt lineæ horariæ ad æquinoctialem li-<lb/>neam perpendiculares, &amp; </s>
  <s xml:id="echoid-s25566" xml:space="preserve">inter ſe parallelæ, vt prius. </s>
  <s xml:id="echoid-s25567" xml:space="preserve">Nam hac ratione deſcriptum erit huiuſmo-<lb/>di horologium non aliter, atque in præcedenti deſcriptione, quando prius linea ſtyli G N, duce-<lb/>batur: </s>
  <s xml:id="echoid-s25568" xml:space="preserve">quia angulus N L O, æqualis eſt angulo E M L, inclinationis Meridianorum, externus in-<lb/>
<anchor type="note" xlink:label="note-0403-08a" xlink:href="note-0403-08"/>
terno. </s>
  <s xml:id="echoid-s25569" xml:space="preserve">Horologium igitur Aſtronomicum, &amp; </s>
  <s xml:id="echoid-s25570" xml:space="preserve">à Verticali declinans, &amp; </s>
  <s xml:id="echoid-s25571" xml:space="preserve">ad Horizontem inclinatũ <lb/>
<anchor type="note" xlink:label="note-0403-09a" xlink:href="note-0403-09"/>
conſtruximus, &amp;</s>
  <s xml:id="echoid-s25572" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25573" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s25574" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1297" type="float" level="2" n="35">
<note position="left" xlink:label="note-0403-07" xlink:href="note-0403-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0403-08" xlink:href="note-0403-08a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0403-09" xlink:href="note-0403-09a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1299" type="section" level="1" n="317">
<head xml:id="echoid-head328" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s25575" xml:space="preserve">TOTAM hanc deſcriptionem horologĳ à Verticali declinantis, &amp; </s>
  <s xml:id="echoid-s25576" xml:space="preserve">ſimul ad Horizontem inclinati <lb/>ſex figuris abſoluimus, vt omnis varietas in huiuſmodi horologĳs patefieret: </s>
  <s xml:id="echoid-s25577" xml:space="preserve">quarum priores tres ad ea <lb/>borologia ſuperiorapertinent, quæ auſtrum reſpiciunt, in quibus centrum horologĳ uel eſt infra æquinoctia <lb/>lem lineam, vel ſupra eandem, uel certe omnes lineæ horariæ ſunt parallelæ ſecantes lineam æquinoctia-<lb/>lem ad angulos rectos, horologium{q́ue} centro caret; </s>
  <s xml:id="echoid-s25578" xml:space="preserve">poſteriores uerò tres referunt ea horologia ſuperiora, <lb/>quæ ad boreã ſpectant, in quibus linea horæ 12. </s>
  <s xml:id="echoid-s25579" xml:space="preserve">vel meridiana æquinoctialẽ lineam ſecat, uel infra centrũ
<pb o="388" file="0404" n="404" rhead="GNOMONICES"/>
horologĳ, uel ſupra idem, uel certè ipſi æquinoctiali lineæ parallela eſt. </s>
  <s xml:id="echoid-s25580" xml:space="preserve">Cæterum in prima figura, tertia &amp; </s>
  <s xml:id="echoid-s25581" xml:space="preserve"><lb/>ſexta omnia lineamenta horarum duximus, in intermedĳs autem illa duntaxat expreſſa ſunt, quæ ad co-<lb/>gnitionem deſcriptionis requiruntur, omiſſis lineis horarĳs, ut confuſionem linearum vitaremus. </s>
  <s xml:id="echoid-s25582" xml:space="preserve">Facile <lb/>enim quiuis in his, ut in illis, lineas horarias ducere poterit, ſi præcepta, quæ à nobis tradita ſunt, atten-<lb/>te, diligenter{q́ue} conſideret.</s>
  <s xml:id="echoid-s25583" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s25584" xml:space="preserve">ITA autem horologium hactenus delineatum in proprio ſitu collocabimus. </s>
  <s xml:id="echoid-s25585" xml:space="preserve">In priore deſcriptione re <lb/>
<anchor type="note" xlink:label="note-0404-01a" xlink:href="note-0404-01"/>
cta A B, æquidiſtare debet Horizonti, puncto A, ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s25586" xml:space="preserve">B, ad dextram exiſtente, commu-<lb/>nis{q́ue} ipſius, &amp; </s>
  <s xml:id="echoid-s25587" xml:space="preserve">Horizontis ſectio conſtituere debet cum linea meridiana in plano, quod Horizonti æqui-<lb/>diſtat, inuenta angulum complementi declinationis, ad auſtrum quidem, &amp; </s>
  <s xml:id="echoid-s25588" xml:space="preserve">occaſum, ſi planum horologĳ à <lb/>meridie in ortum declinat, ad auſtrum uerò, &amp; </s>
  <s xml:id="echoid-s25589" xml:space="preserve">ortum, ſi à meridie in occaſum; </s>
  <s xml:id="echoid-s25590" xml:space="preserve">at uerò ad boream, &amp; </s>
  <s xml:id="echoid-s25591" xml:space="preserve">oc-<lb/>
<anchor type="note" xlink:label="note-0404-02a" xlink:href="note-0404-02"/>
caſum, ſi planum à ſeptentrione in ortum, ad boream autem, &amp; </s>
  <s xml:id="echoid-s25592" xml:space="preserve">ortum, ſi à ſeptentrione in occaſum de-<lb/>flectit. </s>
  <s xml:id="echoid-s25593" xml:space="preserve">Ita enim debitam declinationem obtinebit horologium. </s>
  <s xml:id="echoid-s25594" xml:space="preserve">Deinde recta C D, cum recta in plano <lb/>Horizontis communem ſectionem horologĳ, &amp; </s>
  <s xml:id="echoid-s25595" xml:space="preserve">Horizontis ad rectos angulos ſecante angulum conſtitue-<lb/>re debet inclinationis ad partes quidem boreales, ſi horologiũ ad austrum ſpectat, ad auſtrales uerò, ſi ad <lb/>boream. </s>
  <s xml:id="echoid-s25596" xml:space="preserve">Hac etenim ratione collocato horologio, ſi axis ρ I, in triangulo ρ I G, uel axis e f, in rectangu-<lb/>loefd χ, ubi non eſt centrum, ad planum horologĳ recto intelligatur filum extenſum, uel ferrum ali-<lb/>quod ſubtile, indicabit eius umbra ſingulas horas a mer@uel med. </s>
  <s xml:id="echoid-s25597" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25598" xml:space="preserve">quamdiu Sol ipſum horologium illu-<lb/>minabit; </s>
  <s xml:id="echoid-s25599" xml:space="preserve">uel certè uertex I, styli I K, recti ad horologĳ planum in puncto K, idem pręstabit, ut de horolo <lb/>gio horizontali dictum eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s25600" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25601" xml:space="preserve">præcedentis libri. </s>
  <s xml:id="echoid-s25602" xml:space="preserve">Idem præstabit axis ρ I, uel e f, ſi trian <lb/>gulo ρ 1 G, uel rectangulum e f d χ, ex materia aliqua ſolida conſtruatur, rectum{q́ue} ad planum horolo-<lb/>
<anchor type="note" xlink:label="note-0404-03a" xlink:href="note-0404-03"/>
gĳ ſtatuatur.</s>
  <s xml:id="echoid-s25603" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1299" type="float" level="2" n="1">
<note position="left" xlink:label="note-0404-01" xlink:href="note-0404-01a" xml:space="preserve">Qua ratione <lb/>collocandũ ſit <lb/>horologium de <lb/>clinans ſimul <lb/>&amp; inclinatum.</note>
<note position="left" xlink:label="note-0404-02" xlink:href="note-0404-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0404-03" xlink:href="note-0404-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s25604" xml:space="preserve">SI autem poſterioribus duabus deſcriptionibus horologium fuerit conſtructum, inquirendus erit per <lb/>propoſ. </s>
  <s xml:id="echoid-s25605" xml:space="preserve">31. </s>
  <s xml:id="echoid-s25606" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25607" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25608" xml:space="preserve">arcus plani propoſiti, cui horologium æquidiſtat, inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s25609" xml:space="preserve">circu <lb/>lum maximum, qui inclinationem plani ad Horizontem metitur, interceptus: </s>
  <s xml:id="echoid-s25610" xml:space="preserve">qui arcus in prima figura <lb/>
<anchor type="note" xlink:label="note-0404-04a" xlink:href="note-0404-04"/>
comprehendit grad. </s>
  <s xml:id="echoid-s25611" xml:space="preserve">38. </s>
  <s xml:id="echoid-s25612" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25613" xml:space="preserve">15. </s>
  <s xml:id="echoid-s25614" xml:space="preserve">In ſecundagrad. </s>
  <s xml:id="echoid-s25615" xml:space="preserve">7. </s>
  <s xml:id="echoid-s25616" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25617" xml:space="preserve">6. </s>
  <s xml:id="echoid-s25618" xml:space="preserve">Intertia grad. </s>
  <s xml:id="echoid-s25619" xml:space="preserve">31. </s>
  <s xml:id="echoid-s25620" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25621" xml:space="preserve">42. </s>
  <s xml:id="echoid-s25622" xml:space="preserve">In quarta grad. <lb/></s>
  <s xml:id="echoid-s25623" xml:space="preserve">17. </s>
  <s xml:id="echoid-s25624" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25625" xml:space="preserve">30. </s>
  <s xml:id="echoid-s25626" xml:space="preserve">In quinta grad. </s>
  <s xml:id="echoid-s25627" xml:space="preserve">16. </s>
  <s xml:id="echoid-s25628" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25629" xml:space="preserve">46. </s>
  <s xml:id="echoid-s25630" xml:space="preserve">In ſexta deniq; </s>
  <s xml:id="echoid-s25631" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s25632" xml:space="preserve">19. </s>
  <s xml:id="echoid-s25633" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s25634" xml:space="preserve">33. </s>
  <s xml:id="echoid-s25635" xml:space="preserve">Deinde ex quolibet puncto li-<lb/>neæ meridianæ, ſeu horæ 12. </s>
  <s xml:id="echoid-s25636" xml:space="preserve">ut ex E, deſcripto arcu circuli m h, ex parte ſuperiori, numeretur in eo ex m, <lb/>arcus inuẽtus uſque ad h, ſiniſtrã quidem uerſus, ſi horologium à meridie in ortũ uel à ſeptentrione in oc-<lb/>caſum declinet; </s>
  <s xml:id="echoid-s25637" xml:space="preserve">at uerò uerſus dextram, ſi declinet horologium à meridie in occaſum, uel à ſeptentrione <lb/>in ortum: </s>
  <s xml:id="echoid-s25638" xml:space="preserve">quia in illis circulus maximus inclinationem plani metiens recedit a Meridiano ſupra Horizon <lb/>
<anchor type="note" xlink:label="note-0404-05a" xlink:href="note-0404-05"/>
tem verſus ſiniſtram, in his autem uerſus dextrã, ut liquido conſtat, ſi rectè conſiderentur in ſuis poſitio-<lb/>nibus dicti circuli, &amp; </s>
  <s xml:id="echoid-s25639" xml:space="preserve">planum horologĳ. </s>
  <s xml:id="echoid-s25640" xml:space="preserve">Quod ſi arcus m h, deſcribatur ex parte inferiori, contrarium <lb/>omnino faciendum erit in numer atione dicti arcus, ut manifestum eſt, &amp; </s>
  <s xml:id="echoid-s25641" xml:space="preserve">in figuris factum eſſe cernis. </s>
  <s xml:id="echoid-s25642" xml:space="preserve">Ex <lb/>h, autem per E, ducatur recta h E, quæ communis ſectio erit plani horologĳ, &amp; </s>
  <s xml:id="echoid-s25643" xml:space="preserve">circuli maximi eius in-<lb/>clinationem ad Horizontem metientis. </s>
  <s xml:id="echoid-s25644" xml:space="preserve">Nam ſi ex E, intelligatur attolli in ſublime communis ſectio <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s25645" xml:space="preserve">dicti circuli maximi uſque ad centrum mundi, facient bi duo circuli cum circulo maximo, <lb/>cui horologium æquidistat, communes ſectiones, duas rectas, quæ in centro mundi angulum conſtituunt, <lb/>cui ſubtenditur arcus per propoſ. </s>
  <s xml:id="echoid-s25646" xml:space="preserve">31. </s>
  <s xml:id="echoid-s25647" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25648" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25649" xml:space="preserve">inuentus. </s>
  <s xml:id="echoid-s25650" xml:space="preserve">Quoniam uerò ĳdem duo circuli occurrunt plano <lb/>horologĳ in E, vbi eorum communis ſectio eidem plano occurrit, faciunt cum eo ſectiones communes, <lb/>duas rect{as}, quę illis in circulo maximo parallelæ ſunt, cum huic circulo maximo horologĳ planum æqui-<lb/>
<anchor type="note" xlink:label="note-0404-06a" xlink:href="note-0404-06"/>
distet, comprehendent hæ duæ lineæ in plano horologĳ angulum æqualem illi angulo, quem in circulo ma-<lb/>
<anchor type="note" xlink:label="note-0404-07a" xlink:href="note-0404-07"/>
<anchor type="note" xlink:label="note-0404-08a" xlink:href="note-0404-08"/>
ximo priores illæ lineæ efficiunt. </s>
  <s xml:id="echoid-s25651" xml:space="preserve">Quare cum angulus m E h, ſit illi ęqualis, quòd arcus m h, ſimilis ſit ar <lb/>cui illius circuli maximi inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s25652" xml:space="preserve">circulum maximum inclinationem illius ad <lb/>Horizontem metientem interiecto, quia totidem gradus, ac Minuta complectitur; </s>
  <s xml:id="echoid-s25653" xml:space="preserve">ponatur autem m E, <lb/>linea meridiana, id eſt, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s25654" xml:space="preserve">plani horologĳ, erit h E, communis ſectio plani ho <lb/>rologĳ, &amp; </s>
  <s xml:id="echoid-s25655" xml:space="preserve">circuli maximi inclinationem eius metientis. </s>
  <s xml:id="echoid-s25656" xml:space="preserve">Quòd ſi per E, ad h E, ducatur perpendicularis <lb/>A B, erit hæc communis ſectio plani horologĳ, &amp; </s>
  <s xml:id="echoid-s25657" xml:space="preserve">Horizontis per E, ducti. </s>
  <s xml:id="echoid-s25658" xml:space="preserve">Cum enim tam Horizon, <lb/>quàm planum horologĳ rectum ſit ad circulum maximum, qui inclinationem horologĳ metitur, ſectio-<lb/>nem{q́ue} facit h E; </s>
  <s xml:id="echoid-s25659" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s25660" xml:space="preserve">communis illorum ſectio ad eundem circulum maximum, atque adeò per defin. <lb/></s>
  <s xml:id="echoid-s25661" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25662" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25663" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25664" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25665" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25666" xml:space="preserve">ad h E, communem ſectionem dicti circuli maximi, &amp; </s>
  <s xml:id="echoid-s25667" xml:space="preserve">plani horologĳ, perpendicula-<lb/>ris, qualis eſt A B. </s>
  <s xml:id="echoid-s25668" xml:space="preserve">Itaque ſirurſus A B, ſtatuatur parallela Horizonti, &amp; </s>
  <s xml:id="echoid-s25669" xml:space="preserve">reliqua fiant, ut paulo an-<lb/>te diximus, proprium ſitum ſortietur horologium.</s>
  <s xml:id="echoid-s25670" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1300" type="float" level="2" n="2">
<note position="left" xlink:label="note-0404-04" xlink:href="note-0404-04a" xml:space="preserve">Quantus ſit ar-<lb/>cus plani incli-<lb/>nati inter Meri <lb/>dianum Hori-<lb/>zontis, &amp; circu-<lb/>lum maximũ, <lb/>qui inclinatio-<lb/>nem plani me-<lb/>@itur, poſitus, in <lb/>qualibet ſex ſi-<lb/>gurarum huius <lb/>propoſ.</note>
<note position="left" xlink:label="note-0404-05" xlink:href="note-0404-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0404-06" xlink:href="note-0404-06a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0404-07" xlink:href="note-0404-07a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0404-08" xlink:href="note-0404-08a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<note position="left" xml:space="preserve">Qua ratione <lb/>horologiũ de-<lb/>elinans ſimul <lb/>&amp; inclina tũ in <lb/>plano ſtabili ſit <lb/>deſcribendum.</note>
<p style="it">
  <s xml:id="echoid-s25671" xml:space="preserve">QVOD ſi in ipſo muro inclinato deſcribendum ſit horologium, non autem in alio quopiam plano, ex <lb/>quo in murum inclinatum transferatur, ut hactenus fecimus, efficietur id hoc modo. </s>
  <s xml:id="echoid-s25672" xml:space="preserve">In ipſo muro incli-<lb/>nato ducatur recta A B, Horizonti parallela beneficio libellæ, &amp; </s>
  <s xml:id="echoid-s25673" xml:space="preserve">perpẽdiculi, quam ad rectos angulos ſe-<lb/>cet alia recta C D, in puncto E. </s>
  <s xml:id="echoid-s25674" xml:space="preserve">Reliqua autẽ fiant, vt in priori deſcriptione præcepimus, hoc est, duca-<lb/>
<anchor type="note" xlink:label="note-0404-11a" xlink:href="note-0404-11"/>
tur linea declinationis E F, &amp; </s>
  <s xml:id="echoid-s25675" xml:space="preserve">linea meridiana inueniatur E ε, quam hoc etiam modo reperiemus. </s>
  <s xml:id="echoid-s25676" xml:space="preserve">Ex <lb/>E, deſcribatur arcus circuli h m, verſus partem ſuperiorem, in quo ſupputetur vſque ad m, arcus plani <lb/>inclinati inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s25677" xml:space="preserve">circulum maximum, qui inclinationem plani dimetitur, inuen <lb/>tus per propoſ. </s>
  <s xml:id="echoid-s25678" xml:space="preserve">31. </s>
  <s xml:id="echoid-s25679" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25680" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25681" xml:space="preserve">verſus quidem partem dextram, ſi horologium à meridie in ortum, vel à ſepten <lb/>trione in occaſum declinet; </s>
  <s xml:id="echoid-s25682" xml:space="preserve">verſus autem ſiniſtram, ſi planum horologĳ deflectat à meridie in occaſum,
<pb o="389" file="0405" n="405" rhead="LIBER TERTIVS."/>
vel à ſeptentrione in ortum. </s>
  <s xml:id="echoid-s25683" xml:space="preserve">Nam recta m E, erit linea me<unsure/>ridiana, nempe communis ſectio Meridiani, <lb/>&amp; </s>
  <s xml:id="echoid-s25684" xml:space="preserve">plani horologĳ. </s>
  <s xml:id="echoid-s25685" xml:space="preserve">Quod ex eo, quòd h E, eſt communis ſectio plani horologĳ, &amp; </s>
  <s xml:id="echoid-s25686" xml:space="preserve">circuli maximi inclina <lb/>tionem eius ad Horizontem metientis, comprobabimus non aliter, quam proximè oſtenſum eſt, rectam <lb/>h E, eſſe communem ſectionem plani horologĳ, &amp; </s>
  <s xml:id="echoid-s25687" xml:space="preserve">circuli maximi inclinationem ipſius ad Horizontem <lb/>metientis, ex eo, quòd m E, ponebatur linea meridiana, &amp;</s>
  <s xml:id="echoid-s25688" xml:space="preserve">c. </s>
  <s xml:id="echoid-s25689" xml:space="preserve">Vel certè hac ratione eandem meridianam <lb/>
<anchor type="note" xlink:label="note-0405-01a" xlink:href="note-0405-01"/>
lineam ducemus, vt in quarta figura apparet. </s>
  <s xml:id="echoid-s25690" xml:space="preserve">in alĳs enim, vt uitemus linearum confuſionem, exemplum <lb/>non ponimus. </s>
  <s xml:id="echoid-s25691" xml:space="preserve">Ducta recta A B, Horizonti parallela, ſtatuatur iuxta planum inclinatum, planum ali-<lb/>quod Horizonti æquidiſtans, ita vt eius, &amp; </s>
  <s xml:id="echoid-s25692" xml:space="preserve">plani inclinati communis ſectio ſit A B. </s>
  <s xml:id="echoid-s25693" xml:space="preserve">Vt nunc, exempli gra <lb/>tia, in dicta quarta figura, planum infra rectã A B, intelligatur Horizonti eſſe æquidistans, planum au-<lb/>tem ſupra eandem A B, inclinatum eſſe ad Horizontem. </s>
  <s xml:id="echoid-s25694" xml:space="preserve">Itaque in plano, quod Horizonti parallelum <lb/>
<anchor type="note" xlink:label="note-0405-02a" xlink:href="note-0405-02"/>
eſt, inueniatur per ea, quę lib. </s>
  <s xml:id="echoid-s25695" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25696" xml:space="preserve">docuimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s25697" xml:space="preserve">23. </s>
  <s xml:id="echoid-s25698" xml:space="preserve">linea meridiana E F, quam alia recta t u, <lb/>ſecet ad anguios rectos in q. </s>
  <s xml:id="echoid-s25699" xml:space="preserve">Deinde in t u, ſumantur vtrinque duæ rectę æquales inter ſe q t, q u. </s>
  <s xml:id="echoid-s25700" xml:space="preserve">Si enim <lb/>beneficio circini ex punctis t, &amp; </s>
  <s xml:id="echoid-s25701" xml:space="preserve">u, duo arcus circulorum in plano inclinato deſcribantur ſe mutuo inter-<lb/>ſecantes in l, habebimus in plano inclinato punctum hoc interſectionis l, ex quo per punctum E, in quo <lb/>E F, linea meridiana Horizontis rectę A B, occurrit, emiſſa recta dabit lineam meridianam in plano ho-<lb/>rologĳ. </s>
  <s xml:id="echoid-s25702" xml:space="preserve">Ratio est, quia cum Meridianus per meridianam lineam E F, plani Horizonti æquidistantis du-<lb/>ctus ad idem planum rectum ſit, erit per defin. </s>
  <s xml:id="echoid-s25703" xml:space="preserve">4. </s>
  <s xml:id="echoid-s25704" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25705" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25706" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25707" xml:space="preserve">recta t u, quæ ad angulos rectos ſecat me-<lb/>ridianam lineam E F, eiuſdem plani, nempe communem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s25708" xml:space="preserve">dicti plani, ad Meri-<lb/>dianum perpendicularis; </s>
  <s xml:id="echoid-s25709" xml:space="preserve">atque adeo per defin. </s>
  <s xml:id="echoid-s25710" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25711" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s25712" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25713" xml:space="preserve">ad omnes rectas in Meridiano ipſam <lb/>tangentes in q. </s>
  <s xml:id="echoid-s25714" xml:space="preserve">Cum ergo t u, perpendicularis ſit ad rectam, quæ ex puncto q, plani Horizonti æquidi-<lb/>
<anchor type="note" xlink:label="note-0405-03a" xlink:href="note-0405-03"/>
<anchor type="note" xlink:label="note-0405-04a" xlink:href="note-0405-04"/>
ſtantis ducitur ad punctum l, plani inclinati, vbi ſe interſecant mutuo dicti duo arcus circulorum ex t, <lb/>u, deſcripti; </s>
  <s xml:id="echoid-s25715" xml:space="preserve">ut patet, ſi concipiantur animo duo triangula, quorum baſes ſunt rectæ lineæ t l, u l, inter <lb/>ſe æquales, cum ſint ſemidiametri circulorum æqualium, latera uerò rectæ æquales q t, q u, &amp; </s>
  <s xml:id="echoid-s25716" xml:space="preserve">recta com <lb/>munis ex q, ad l, ducta; </s>
  <s xml:id="echoid-s25717" xml:space="preserve">erit recta ex q, ad l, ducta in plano Meridiani circuli: </s>
  <s xml:id="echoid-s25718" xml:space="preserve">ali{as} ſi extra ipſum eſ-<lb/>ſet, foret t q, ad du{as} rect{as} in puncto q, perpendicularis in plano per t q, &amp; </s>
  <s xml:id="echoid-s25719" xml:space="preserve">rectam ex q, ad l, ductam <lb/>tranſiens, nempe ad rectam ex q, ad l, ductam, ut ostendimus, &amp; </s>
  <s xml:id="echoid-s25720" xml:space="preserve">ad rectam, quæ ex q, in plano Meri-<lb/>diani ducitur exiſtens in eodem plano, in quo rectę t q, &amp; </s>
  <s xml:id="echoid-s25721" xml:space="preserve">recta ex q, per l, ducta, hoc est, ad commu-<lb/>nem ſectionem Meridiani, &amp; </s>
  <s xml:id="echoid-s25722" xml:space="preserve">plani per t q, &amp; </s>
  <s xml:id="echoid-s25723" xml:space="preserve">rectam q l, ducti, ex defin. </s>
  <s xml:id="echoid-s25724" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25725" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25726" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25727" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25728" xml:space="preserve">ut dictum eſt. <lb/></s>
  <s xml:id="echoid-s25729" xml:space="preserve">quod eſt abſurdum. </s>
  <s xml:id="echoid-s25730" xml:space="preserve">Quare Meridianus per punctum l, tranſibit in plano inclinato: </s>
  <s xml:id="echoid-s25731" xml:space="preserve">Tranſit autem &amp; </s>
  <s xml:id="echoid-s25732" xml:space="preserve"><lb/>per punctum E. </s>
  <s xml:id="echoid-s25733" xml:space="preserve">Igitur recta l E, communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s25734" xml:space="preserve">plani inclinati. </s>
  <s xml:id="echoid-s25735" xml:space="preserve">Inuenta autem linea <lb/>
<anchor type="note" xlink:label="note-0405-05a" xlink:href="note-0405-05"/>
meridiana, poterimus in plano inclinato horologium delineare, ut intertio modo tradidimus, ſi forte pri <lb/>mus nimis longus uideatur. </s>
  <s xml:id="echoid-s25736" xml:space="preserve">Idem fieri poterit per ſecundum modum, ſi prius linea ſtyli inueniatur, quam <lb/>quidem reperiemus, ſi primum per propoſ. </s>
  <s xml:id="echoid-s25737" xml:space="preserve">31. </s>
  <s xml:id="echoid-s25738" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25739" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25740" xml:space="preserve">inueſtigetur arcus plani inclinati inter proprium Me-<lb/>ridianum ipſius, &amp; </s>
  <s xml:id="echoid-s25741" xml:space="preserve">circulum maximum eiuſdem inclinationem metientem: </s>
  <s xml:id="echoid-s25742" xml:space="preserve">deinde diligenter obſeruetur, <lb/>num Meridianus proprius ab illo circulo maximo recedat uerſus ortum, an ad occaſum uergat, &amp;</s>
  <s xml:id="echoid-s25743" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s25744" xml:space="preserve">Sed commodior eſt deſcriptio ſecundum tertium modum, atq; </s>
  <s xml:id="echoid-s25745" xml:space="preserve">facilior. </s>
  <s xml:id="echoid-s25746" xml:space="preserve">Immo tertius hic modus aptiſſimè <lb/>
<anchor type="note" xlink:label="note-0405-06a" xlink:href="note-0405-06"/>
inchoari poteſt a duabus perpendicularibus A B, C D, non ſecus, ac ſi in ipſo muro ſtatim horologium eſſet <lb/>conſtruendum, ut proximè tradidimus. </s>
  <s xml:id="echoid-s25747" xml:space="preserve">Ita enim fiet, ut horologium proprium ſitum ſortiatur, ſi recta <lb/>A B, Horizonti æquidiſtans ſtatuatur, &amp;</s>
  <s xml:id="echoid-s25748" xml:space="preserve">c.</s>
  <s xml:id="echoid-s25749" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1301" type="float" level="2" n="3">
<note position="left" xlink:label="note-0404-11" xlink:href="note-0404-11a" xml:space="preserve">Linea meridia-<lb/>na quomodo <lb/>in plano decli-<lb/>nante ſimul &amp; <lb/>inclinato repe-<lb/>riatur aliter, <lb/>quàm ſupratra <lb/>ditum eſt.</note>
<note position="right" xlink:label="note-0405-01" xlink:href="note-0405-01a" xml:space="preserve">Alia inuentio <lb/>lineę meridia-<lb/>næ.</note>
<note position="left" xlink:label="note-0405-02" xlink:href="note-0405-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0405-03" xlink:href="note-0405-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0405-04" xlink:href="note-0405-04a" xml:space="preserve">8. primi.</note>
<note position="left" xlink:label="note-0405-05" xlink:href="note-0405-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0405-06" xlink:href="note-0405-06a" xml:space="preserve">Qu o pacto ter-<lb/>tius modus de-<lb/>ſcribendi horo <lb/>logium decli-<lb/>nans ſimul &amp; <lb/>inclinatum in-<lb/>choari poffit <lb/>aliunde, quà@ <lb/>ſupta tradi-<lb/>mus.</note>
</div>
<p style="it">
  <s xml:id="echoid-s25750" xml:space="preserve">TRADIT Andreas Schonerus aliũ modũ deſcribendi horologĳ declinantis a Verticali, &amp; </s>
  <s xml:id="echoid-s25751" xml:space="preserve">ad Ho <lb/>
<anchor type="note" xlink:label="note-0405-07a" xlink:href="note-0405-07"/>
rizontem inclinati, non diſſimilẽ illi, quem in alĳs horologĳs explicauimus, qui quidẽ perutilis eſt ad non-<lb/>nullas horas ducendas, quæ uix per priorem deſcriptionẽ haberi poſſunt. </s>
  <s xml:id="echoid-s25752" xml:space="preserve">Eſt autem modus ferè huiuſmodi. <lb/></s>
  <s xml:id="echoid-s25753" xml:space="preserve">Ex E, ducatur ad β C, perpendicularis E Y, &amp; </s>
  <s xml:id="echoid-s25754" xml:space="preserve">ad E F, alia perpendicularis E Q, quæipſi E Y, ſit æqua <lb/>lis, ſupra rectam A B. </s>
  <s xml:id="echoid-s25755" xml:space="preserve">Ducta deinde recta Q F, quæ ſecet A B, in R, agatur per R, lineæ meridianæ <lb/>E ε, parallela R S, quæ ſecet lineam horæ 6. </s>
  <s xml:id="echoid-s25756" xml:space="preserve">in S. </s>
  <s xml:id="echoid-s25757" xml:space="preserve">Poſtremo ex S, excitetur ad R S, perpendicularis <lb/>S T, ſit{q́ue} S T, ipſi R S, ęqualis; </s>
  <s xml:id="echoid-s25758" xml:space="preserve">facto{q́ue} T, centro circulus deſcribatur, qui in 24. </s>
  <s xml:id="echoid-s25759" xml:space="preserve">partes æquales <lb/>diſtribuatur, initio facto à recta S T. </s>
  <s xml:id="echoid-s25760" xml:space="preserve">Nam ſi ex centro T, per diuiſionum puncta ducantur rectę oc-<lb/>cultæ, ſecabitur recta R S, in punctis, per quę lineæ horarię ducendæ ſunt ex centro horologĳ ρ. </s>
  <s xml:id="echoid-s25761" xml:space="preserve">Exem-<lb/>plum habes in prima figura. </s>
  <s xml:id="echoid-s25762" xml:space="preserve">In tertia autem figura, ubi centrum horologĳ non eſt, deſcriptio hæc lo-<lb/>cum non habet, quia recta, quam diximus ducendam eſſe parallelam lineę meridianę, lineam horæ 6. </s>
  <s xml:id="echoid-s25763" xml:space="preserve">non <lb/>
<anchor type="note" xlink:label="note-0405-08a" xlink:href="note-0405-08"/>
ſecat, ſed ei<unsure/> æquidiſtat. </s>
  <s xml:id="echoid-s25764" xml:space="preserve">In alĳs autem figuris exempla non poſuimus confuſionis uitandę cauſa, quę ex tan <lb/>ta linearum multitudine oriretur.</s>
  <s xml:id="echoid-s25765" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1302" type="float" level="2" n="4">
<note position="left" xlink:label="note-0405-07" xlink:href="note-0405-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0405-08" xlink:href="note-0405-08a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio eiuſ<unsure/> <lb/>dem horologii <lb/>declinantis ſi-<lb/>mul &amp; inclina <lb/>ti pro data ſtyli <lb/>longitudine, c<unsure/>n <lb/>ius etiam locus <lb/>datus ſit.</note>
<p style="it">
  <s xml:id="echoid-s25766" xml:space="preserve">SI idem horologium declinans ſimul &amp; </s>
  <s xml:id="echoid-s25767" xml:space="preserve">inclinatum deſcribendum ſit in dato plano ad quamcunque <lb/>ſtyli magnitudinem, cuius etiam locus datus ſit, hoc artificio utemur. </s>
  <s xml:id="echoid-s25768" xml:space="preserve">Sit data longitudo ſtyli K β, <lb/>eius{q́ue} locus in plano horologĳ punctum K. </s>
  <s xml:id="echoid-s25769" xml:space="preserve">Si igitur planum horologĳ fuerit quodcunque, ut horologium <lb/>in eo deſcriptum in proprio deinde ſitu collocetur, uel in planum ſtabile, quod a Verticali declinet, &amp; </s>
  <s xml:id="echoid-s25770" xml:space="preserve">ad <lb/>Horizontem ſit inclinatum, transferatur, ducemus per K, locum styli du{as} rectas A B, C D, ſeſe in K, <lb/>ad angulos rectos ſecantes: </s>
  <s xml:id="echoid-s25771" xml:space="preserve">Si autem planum ſtabile ſit declinans ſimul &amp; </s>
  <s xml:id="echoid-s25772" xml:space="preserve">inclinatum, ducemus per lo-<lb/>cum ſtyli K, beneficio libellę &amp; </s>
  <s xml:id="echoid-s25773" xml:space="preserve">perpendiculi rectam A B, Horizonti parallelam, quam in K, recta <lb/>C D, ſecet ad rectos angulos. </s>
  <s xml:id="echoid-s25774" xml:space="preserve">Sumpta autem in A B, recta K β, ſtylo æquali ſiue ad dexteram, ſiue ad <lb/>ſiniſtram, deſcribatur ex β, uerſus C D, arcus circuli, in quo numerata inclinatione plani ad Horizon-
<pb o="390" file="0406" n="406" rhead="GNOMONICES"/>
tem, (ſumimus autem hic eadem plana cum eiſdem inclinationibus, declinationibus{q́ue}, quę prius) ini-<lb/>tio facto a recta A B, deorſum uerſus, ducatur per finem numer ationis ex β, recta β D, ſecans C D, in <lb/>D, puncto, per quod meridia-<lb/>na linea ducenda erit. </s>
  <s xml:id="echoid-s25775" xml:space="preserve">Suppu <lb/>tato quoque in eodẽ arcu ſur-<lb/>
<anchor type="figure" xlink:label="fig-0406-01a" xlink:href="fig-0406-01"/></s>
<s xml:id="echoid-s25776" xml:space="preserve">ſum uerſus complemento in-
clinationis, ducatur ex β, per
finẽ ſupputationis recta β C,
quæ perpendicularis erit ad
β D, ſecans C D, in C, pun-
<anchor type="note" xlink:label="note-0406-01a" xlink:href="note-0406-01"/>
cto, per quod recta C E, du-
cta ad C D, perpendicularis
erit linea horizontalis.</s>
  <s xml:id="echoid-s25777" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1303" type="float" level="2" n="5">
  <figure xlink:label="fig-0406-01" xlink:href="fig-0406-01a">
    <image file="0406-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0406-01"/>
<caption xml:id="echoid-caption1" xml:space="preserve">1. figura</caption>
  </figure>
<note position="left" xlink:label="note-0406-01" xlink:href="note-0406-01a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">Linea horiz<unsure/>on <lb/>talis.</note>
<p style="it">
  <s xml:id="echoid-s25778" xml:space="preserve">DEINDE in recta C D, <lb/>ipſi C β, ſumpta æquali C F, <lb/>ſiue ſurſum uerſus, ſiue deor-<lb/>ſum, deſcribatur ex F, verſus <lb/>C E, arcus circuli, in quo nu-<lb/>merata à recta C D, declina <lb/>tione plani à Verticali circu-<lb/>
<anchor type="note" xlink:label="note-0406-03a" xlink:href="note-0406-03"/>
lo ad dexteram quidem, ſi pla <lb/>num a meridie in ortum, uel <lb/>a Septẽtrione in occaſum<unsure/> de-<lb/>flectit, ut in prima, tertia, &amp; </s>
  <s xml:id="echoid-s25779" xml:space="preserve"><lb/>quarta figura, ad ſiniſtram au <lb/>tem, ſi planum declinat à me <lb/>ridie in occaſum, uel a ſepten <lb/>trione in ortum, ut in ſecun-<lb/>da, quinta, &amp; </s>
  <s xml:id="echoid-s25780" xml:space="preserve">ſexta figura, du <lb/>catur ex F, per finem numera <lb/>tionis recta F E, ſecans ho-<lb/>
<anchor type="note" xlink:label="note-0406-04a" xlink:href="note-0406-04"/>
rizontalem lineam C E, in E. </s>
  <s xml:id="echoid-s25781" xml:space="preserve">Nam recta D E, per D, &amp; </s>
  <s xml:id="echoid-s25782" xml:space="preserve">E, in utramq; </s>
  <s xml:id="echoid-s25783" xml:space="preserve">partem eiecta dabit lineam me-<lb/>ridianam. </s>
  <s xml:id="echoid-s25784" xml:space="preserve">Supputato quoq; </s>
  <s xml:id="echoid-s25785" xml:space="preserve">in eodem arcu a recta C D, in contrariam partem complemento declinationis <lb/>
<anchor type="note" xlink:label="note-0406-05a" xlink:href="note-0406-05"/>
ducatur ex F, per finem ſupputationis recta F α, quę ad F E, perpendicularis erit, ſecans lineam horizon <lb/>talem in puncto α, per quod linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s25786" xml:space="preserve">linea horę 6. </s>
  <s xml:id="echoid-s25787" xml:space="preserve">ducenda est.</s>
  <s xml:id="echoid-s25788" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1304" type="float" level="2" n="6">
<note position="left" xlink:label="note-0406-03" xlink:href="note-0406-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0406-04" xlink:href="note-0406-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0406-05" xlink:href="note-0406-05a" xml:space="preserve">Linea meridia-<lb/>na.</note>
</div>
<p style="it">
  <s xml:id="echoid-s25789" xml:space="preserve">RVRSVS ducta recta α K, quæ neceſſario ad meridianam lineam D E, perpendicularis erit ſi er-<lb/>ratum non fuerit, deſcribantur ex D, &amp; </s>
  <s xml:id="echoid-s25790" xml:space="preserve">E, duo arcus ad interualla recta<unsure/>rum D β, E F, ſecantes ſeſe <lb/>neceſſario, ſi erratum non eſt, in recta α K, ut in puncto H; </s>
  <s xml:id="echoid-s25791" xml:space="preserve">ſiue autem hocfiat ex parte dextra, ſiue <lb/>ex ſiniſtra, nihil intereſt. </s>
  <s xml:id="echoid-s25792" xml:space="preserve">Ex quo fit, neceſſarium non eſſe, ut recta α K, ducatur, ſed utile tantum, ut <lb/>nimirũ accuratior fiat deſcriptio. </s>
  <s xml:id="echoid-s25793" xml:space="preserve">ſi enim nõ tranſiret per punctũ H, inuentũ, corrigendus eſſet error com <lb/>miſſus. </s>
  <s xml:id="echoid-s25794" xml:space="preserve">Sic etiã ducta recta α K, ſatis eſſet, ſi uel ex D, deſcriberetur arcus ad interuallũ D β, duntaxat, <lb/>
<anchor type="note" xlink:label="note-0406-06a" xlink:href="note-0406-06"/>
uel (ſi cõmodius uiſum fuerit) arcus ex E, ad interuallum E F. </s>
  <s xml:id="echoid-s25795" xml:space="preserve">Nam ubi alter horum arcuũ rectam α K, <lb/>ſecat, ibi erit punctũ H, ut prius. </s>
  <s xml:id="echoid-s25796" xml:space="preserve">Ducta quoque recta H E, deſcribatur ex H, arcus circuli in quo a recta <lb/>H E, uerſus rectam H D, numeretur complementum altitudinis poli ſuper Horizontem, ſi planum ho-<lb/>rologĳ a meridie declinat, &amp; </s>
  <s xml:id="echoid-s25797" xml:space="preserve">per finẽ numerationis ex H, ducatur recta Hb, ſecans meridianam lineam in <lb/>M, puncto, per quod æquinoctialis linea ducenda eſt ex puncto α, iampridẽ inuento. </s>
  <s xml:id="echoid-s25798" xml:space="preserve">Et ſi in eodem arcu in <lb/>
<anchor type="note" xlink:label="note-0406-07a" xlink:href="note-0406-07"/>
cõtrariã partẽ a recta H E, numeretur altitudo poli, et ex fine numer ationis per H, recta Hd, ducatur, quę <lb/>ad H b, perpẽdicularis erit, ſecabitur eadẽ linea meridiana in puncto ρ, quod centrũ erit horologĳ. </s>
  <s xml:id="echoid-s25799" xml:space="preserve">Quod <lb/>
<anchor type="note" xlink:label="note-0406-08a" xlink:href="note-0406-08"/>
ſi quãdo accidat, rectã hãc H d, ultimo loco per H, ductã parallelam eſſe lineæ meridianæ, ut contingit in <lb/>tertia figura, ubi prior recta H b, trãſit per locũ ſtyli K, &amp; </s>
  <s xml:id="echoid-s25800" xml:space="preserve">per punctũ α, ita ut a recta α K, non differat, <lb/>carebit horologium centro, omneſ{q́ue} horariæ lineæ inter ſe æquidiſtãtes erit. </s>
  <s xml:id="echoid-s25801" xml:space="preserve">Si uero horologĳ planum decli <lb/>
<anchor type="note" xlink:label="note-0406-09a" xlink:href="note-0406-09"/>
net a Septẽtrione, numerãda erit altitudo poli in dicto ar cu circuli a recta H E, uerſus rectã H D. </s>
  <s xml:id="echoid-s25802" xml:space="preserve">Recta <lb/>enim H b, ducta ex H, per finẽ numer ationis ſecabit meridianã lineã in ρ, cẽtro horologĳ: </s>
  <s xml:id="echoid-s25803" xml:space="preserve">Et ſi in eodẽ ar <lb/>cuin cõtrariã partem a recta H E, ſupputetur cõplementũ altitudinis poli, atq; </s>
  <s xml:id="echoid-s25804" xml:space="preserve">ex fine numer ationis per <lb/>H, traiiciatur recta Hd, quæ ad H b, perpẽdicularis erit, ſecabitur linea meridiana in puncto M, per quod <lb/>linea æquinoctialis ex α, ducenda eſt. </s>
  <s xml:id="echoid-s25805" xml:space="preserve">Quod ſi quando contingat, hanc rectam H d, ultimo loco ductam pa-<lb/>rallelam eſſe meridianæ lineæ, ut in figura ſexta apparet, ubi prior recta H b, tranſit per K, locum styli, <lb/>adeo ut a recta α K, non differat, ducenda erit linea æquinoctialis per α, ipſi lineæ meridianæ parallela.</s>
  <s xml:id="echoid-s25806" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1305" type="float" level="2" n="7">
<note position="left" xlink:label="note-0406-06" xlink:href="note-0406-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0406-07" xlink:href="note-0406-07a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="left" xlink:label="note-0406-08" xlink:href="note-0406-08a" xml:space="preserve">Centrum horo <lb/>logii.</note>
<note position="left" xlink:label="note-0406-09" xlink:href="note-0406-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s25807" xml:space="preserve">IAM uero ſi ex ρ, centro horologĳ per k, locum styli recta ducatur ρ K, habebimus lineam ſtyli, <lb/>
<anchor type="note" xlink:label="note-0406-10a" xlink:href="note-0406-10"/>
quæ neceſſario lineam æquinoctialem ex α, ductam ad angulos rectos ſecabit. </s>
  <s xml:id="echoid-s25808" xml:space="preserve">Sed ubi centrum horologii <lb/>non habetur, ducenda erit linea ſtyli per K, locum ſtyli parallela lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s25809" xml:space="preserve">ad æquinoctialem
<pb o="391" file="0407" n="407" rhead="LIBER TERTIVS."/>
lineam perpendicularis, ut in tertia figura. </s>
  <s xml:id="echoid-s25810" xml:space="preserve">Item ubi æquinoctialis linea meridianę lineæ æquidiſtat, erit <lb/>linea ſtyli ρ K, non ſolum ad æquinoctialem lineam, ſed etiã ad lineam meridianã perpendicularis. </s>
  <s xml:id="echoid-s25811" xml:space="preserve">Itaq; <lb/></s>
  <s xml:id="echoid-s25812" xml:space="preserve">
<anchor type="note" xlink:label="note-0407-01a" xlink:href="note-0407-01"/>
ſi primo loco linea æquinoctialis per inuenta puncta α, M, ducatur, ducenda erit linea ſtyli ad ipſam per-<lb/>
<anchor type="figure" xlink:label="fig-0407-01a" xlink:href="fig-0407-01"/>
<anchor type="figure" xlink:label="fig-0407-02a" xlink:href="fig-0407-02"/>
<anchor type="note" xlink:label="note-0407-02a" xlink:href="note-0407-02"/>
<anchor type="note" xlink:label="note-0407-03a" xlink:href="note-0407-03"/>
<anchor type="note" xlink:label="note-0407-04a" xlink:href="note-0407-04"/>
pendicularis per locum ſtyli K, ex centro ρ, vel vbi centrum nõ adeſt, per K, locum ſtyli dunt axat: </s>
  <s xml:id="echoid-s25813" xml:space="preserve">Si uero
primo loco ducatur linea ſtyli ex ρ, centro per K, uel vbi centrum non eſt, per K, æquidistans lineæ meri-
dianæ, ducenda erit linea æquinoctialis ad ipſam ex α, perpendicularis.</s>
  <s xml:id="echoid-s25814" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1306" type="float" level="2" n="8">
<note position="left" xlink:label="note-0406-10" xlink:href="note-0406-10a" xml:space="preserve">Linea ſtyli.</note>
<note position="right" xlink:label="note-0407-01" xlink:href="note-0407-01a" xml:space="preserve">26. primi.</note>
  <figure xlink:label="fig-0407-01" xlink:href="fig-0407-01a">
    <image file="0407-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0407-01"/>
<caption xml:id="echoid-caption2" xml:space="preserve">2. figura.</caption>
  </figure>
  <figure xlink:label="fig-0407-02" xlink:href="fig-0407-02a">
    <image file="0407-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0407-02"/>
<caption xml:id="echoid-caption3" xml:space="preserve">3. figura.</caption>
  </figure>
<note position="left" xlink:label="note-0407-02" xlink:href="note-0407-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0407-03" xlink:href="note-0407-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0407-04" xlink:href="note-0407-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s25815" xml:space="preserve">POST hæc ex K, loco ſtyli excitetur ad lineã ſtyli linea perpendicularis K I, ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s25816" xml:space="preserve">ex <lb/>
<anchor type="note" xlink:label="note-0407-05a" xlink:href="note-0407-05"/>
cẽtro ρ, per I, recta emittatur ρ I, pro axe mũdi. </s>
  <s xml:id="echoid-s25817" xml:space="preserve">At ubi centrũ nõ eſt, ducẽdus erit axis per I, æquidiſtãs <lb/>lineæ ſtyli, uel lineæ meridianę. </s>
  <s xml:id="echoid-s25818" xml:space="preserve">Quod ſi ex I, ad axem perpendicularis educatur, ſecabit ea lineam ſtyli <lb/>in puncto G, per quod æquinoctialis linea ducitur, niſi error commiſſus ſit. </s>
  <s xml:id="echoid-s25819" xml:space="preserve">Vnde ubi horologium centro <lb/>caret, atque adeo axis lineæ styli æquidiſtat, cadet dicta perpendicularis in K, locum styli, &amp; </s>
  <s xml:id="echoid-s25820" xml:space="preserve">ab æqui-<lb/>noctiali linea non differet. </s>
  <s xml:id="echoid-s25821" xml:space="preserve">Itaque ſi primo loco ductus fuerit axis mundi per I, inueniemus beneficio li-<lb/>neæ I G, ad axem perpendicularis in linea ſtyli aliud punctum G, per quod ęquinoctialis linea ex puncto <lb/>
<anchor type="note" xlink:label="note-0407-06a" xlink:href="note-0407-06"/>
α, ducenda est, quę neceſſario cum linea ſtyli angulos rectos efficiet.</s>
  <s xml:id="echoid-s25822" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1307" type="float" level="2" n="9">
<note position="right" xlink:label="note-0407-05" xlink:href="note-0407-05a" xml:space="preserve">Ax<unsure/>is m<unsure/>undi.</note>
<note position="left" xlink:label="note-0407-06" xlink:href="note-0407-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s25823" xml:space="preserve">AD extremum ſumpta recta G L, in linea indicis, quæ æqualis ſit ipſi G I, deſcribatur ex L, circu-<lb/>lus cuiuslibet magnitudinis, qui in 24. </s>
  <s xml:id="echoid-s25824" xml:space="preserve">partes æquales diſtribuatur, initio facto arecta L M, quę ex cen-<lb/>tro L, ducitur per punctum M, ubi æquinoctialis linea &amp; </s>
  <s xml:id="echoid-s25825" xml:space="preserve">meridiana ſe interſecant, vel a recta L α, du-<lb/>cta ex eodem centro L, per punctum α, ubi coeunt horizontalis linea, &amp; </s>
  <s xml:id="echoid-s25826" xml:space="preserve">æquinoctialis, ſeu linea horæ 6. <lb/></s>
  <s xml:id="echoid-s25827" xml:space="preserve">Neceſſe eſt autem duas rectas L M, &amp; </s>
  <s xml:id="echoid-s25828" xml:space="preserve">L α, ſeſe in L, ad rectos angulos interſecare, ſi nulla in re com <lb/>miſſus fuerit error. </s>
  <s xml:id="echoid-s25829" xml:space="preserve">Quòd ſi æquinoctialis linea parallela ſit meridiànæ lineæ, ducẽda erit loco rectæ L M, <lb/>recta eidem meridianæ lineæ parallela, quærectam L α, angulos rectos ſecet. </s>
  <s xml:id="echoid-s25830" xml:space="preserve">I am ſi ex L, per diuiſio-<lb/>num puncta rectæ occultæ ducantur, ſecabitur ęquinoctialis linea in punctis, per quæ ex centro ρ, du-<lb/>
<anchor type="note" xlink:label="note-0407-07a" xlink:href="note-0407-07"/>
cendę ſunt lineæ horarum à mer. </s>
  <s xml:id="echoid-s25831" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25832" xml:space="preserve">med. </s>
  <s xml:id="echoid-s25833" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25834" xml:space="preserve">Vel quando centro caret horologium, per quæ ipſi lineę me <lb/>
<anchor type="note" xlink:label="note-0407-08a" xlink:href="note-0407-08"/>
ridianæ, vel lineę ſtyli, axive ducendę ſunt parallelę, &amp; </s>
  <s xml:id="echoid-s25835" xml:space="preserve">ad ęquinoctialẽ lineã perpendiculares, pro horis <lb/>à mer. </s>
  <s xml:id="echoid-s25836" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s25837" xml:space="preserve">med. </s>
  <s xml:id="echoid-s25838" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s25839" xml:space="preserve">Ordo horarũ idem est hic, qui ſupra in prima deſcriptione huius propoſ. </s>
  <s xml:id="echoid-s25840" xml:space="preserve">expoſitus eſt.</s>
  <s xml:id="echoid-s25841" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1308" type="float" level="2" n="10">
<note position="right" xlink:label="note-0407-07" xlink:href="note-0407-07a" xml:space="preserve">Lineę<unsure/> horariæ.</note>
<note position="left" xlink:label="note-0407-08" xlink:href="note-0407-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s25842" xml:space="preserve">VIDES ergo, deſcriptionem hanc multo eſſe pręſtantiorem ea, quam primo loco in hac propoſ. </s>
  <s xml:id="echoid-s25843" xml:space="preserve">ex-<lb/>plicauimus, cùm hęc vltro nos ducat in locum centri horologĳ, ita vt non op{us} ſit conſiderare, an centrũ <lb/>horologĳ statuendum ſit infra lineam ęquinoctialem, an ſupra, quemadmodum in illa deſcriptione.</s>
  <s xml:id="echoid-s25844" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s25845" xml:space="preserve">DEMONSTRABIMVS autem omnia, quę in hac deſcriptione ſunt dicta, hoc modo. </s>
  <s xml:id="echoid-s25846" xml:space="preserve">In-<lb/>
<anchor type="note" xlink:label="note-0407-09a" xlink:href="note-0407-09"/>
telligatur triangulum β C D, cuius angulus β, rect{us} eſt, ob quadrantem circuli, ex β, deſcripti inter re-<lb/>ctas β D, β C, interiectum, moueri circa rectam C D, donec rectum ſit ad planum horologĳ, atque adeo <lb/>vertex styli β, cum centro mundi coniungatur. </s>
  <s xml:id="echoid-s25847" xml:space="preserve">Quia igitur angulus K β C, æqualis eſt complemento in-<lb/>clinationis, erit β C K, angulus inclinationis; </s>
  <s xml:id="echoid-s25848" xml:space="preserve">ac proinde cum Horizon per β, verticem ſtyli incedat, <lb/>erit recta β C, communis ſectio ipſius, &amp; </s>
  <s xml:id="echoid-s25849" xml:space="preserve">circuli maximi inclinationem metientis, fæ<unsure/>ciens cum recta
<pb o="392" file="0408" n="408" rhead="GNOMONICES"/>
C D, angulum inclinationis, vt res poſtulat. </s>
  <s xml:id="echoid-s25850" xml:space="preserve">Quare Horizon plano horologĳ in C, occurret, &amp; </s>
  <s xml:id="echoid-s25851" xml:space="preserve">propte-<lb/>rea per punctum C, linea horizontalis ducenda erit ad C D, perpendicularis. </s>
  <s xml:id="echoid-s25852" xml:space="preserve">Cum enim tam Horizon, <lb/>quàm planum horologĳ rectum ſit ad circulum maximum, qui inclinationem plani metitur, duciturq́, per <lb/>rectam C D, erit &amp; </s>
  <s xml:id="echoid-s25853" xml:space="preserve">communis illorum ſectio, nempe linea horizontalis, ad eundem circulum maximum <lb/>
<anchor type="note" xlink:label="note-0408-01a" xlink:href="note-0408-01"/>
recta, atque adeo, per defin. </s>
  <s xml:id="echoid-s25854" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25855" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25856" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25857" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25858" xml:space="preserve">ad rectam C D, in illo circulo exiſtentem perpendicularis in <lb/>puncto C. </s>
  <s xml:id="echoid-s25859" xml:space="preserve">Rurſus quoniam tam circulus maximus inclinationem horologĳ metiens, quàm Meridianus ad <lb/>Horizontem rectus eſt, erit <lb/>quoque communis eorum ſe <lb/>
<anchor type="note" xlink:label="note-0408-02a" xlink:href="note-0408-02"/>
<anchor type="figure" xlink:label="fig-0408-01a" xlink:href="fig-0408-01"/>
ctio ad euudẽ recta, ac pro-
pterea, per defin. </s>
  <s xml:id="echoid-s25860" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25861" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25862" xml:space="preserve">11.</s>
  <s xml:id="echoid-s25863" xml:space="preserve">
<anchor type="note" xlink:label="note-0408-03a" xlink:href="note-0408-03"/>
Eucl. </s>
  <s xml:id="echoid-s25864" xml:space="preserve">ad rectam β C, in Ho
rizonte exiſtentem perpen-
dicularis in centro mundi
β, per quod omnes circuli
maximi ducuntur. </s>
  <s xml:id="echoid-s25865" xml:space="preserve">Cum er-
go recta β D, ſit in plano cir
culi maximi inclinationem
borologĳ metiẽtis, rectum{q́ue}
faciat angulum cum β C, vt
diximus, erit ipſa β D, com
<anchor type="note" xlink:label="note-0408-04a" xlink:href="note-0408-04"/>
munis ſectio dicti circuli
maximi, &amp; </s>
  <s xml:id="echoid-s25866" xml:space="preserve">Meridiani. </s>
  <s xml:id="echoid-s25867" xml:space="preserve">Oc-
currit igitur Meridianus
plano horologĳ in pũcto D.</s>
  <s xml:id="echoid-s25868" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1309" type="float" level="2" n="11">
<note position="right" xlink:label="note-0407-09" xlink:href="note-0407-09a" xml:space="preserve">Demonſtratio<unsure/> <lb/>proximæ deſ@r@ <lb/>ptionis.</note>
<note position="left" xlink:label="note-0408-01" xlink:href="note-0408-01a" xml:space="preserve">19. vn<unsure/>dec<unsure/>.</note>
<note position="left" xlink:label="note-0408-02" xlink:href="note-0408-02a" xml:space="preserve">19. vn<unsure/>dec<unsure/>.</note>
  <figure xlink:label="fig-0408-01" xlink:href="fig-0408-01a">
    <image file="0408-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0408-01"/>
<caption xml:id="echoid-caption4" xml:space="preserve">4. figura</caption>
  </figure>
<note position="left" xlink:label="note-0408-03" xlink:href="note-0408-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0408-04" xlink:href="note-0408-04a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s25869" xml:space="preserve">MOVEATVR quo-<lb/>que triangulum α F E, cir-<lb/>ca rectam α E, donec cum <lb/>plano Horizontis coniunga <lb/>tur, punctumq́, F, cum cen-<lb/>tro mundi β, ob æqualitatẽ <lb/>
<anchor type="note" xlink:label="note-0408-05a" xlink:href="note-0408-05"/>
rectarum C F, C β. </s>
  <s xml:id="echoid-s25870" xml:space="preserve">Quo <lb/>facto, cũ C F E, ſit angulus <lb/>declinationis plani à Verti-<lb/>cali, erit C E F, angulus complementi eiuſdem declinationis, qualem nimirum cõmunis ſectio plani horo <lb/>logĳ &amp; </s>
  <s xml:id="echoid-s25871" xml:space="preserve">Horizoutis cum communi ſectione Horizontis ac Meridiani facit. </s>
  <s xml:id="echoid-s25872" xml:space="preserve">Cum igitur Meridian{us} per <lb/>F, ducatur, hoc eſt, per centrum mundi, in quo punctum F, poſuimus, erit recta F E, faciens cum linea <lb/>horizontali C E, angulum complementi declinationis, communis ſectio Horizontis ac Meridiani, cum <lb/>exiſtat in Horizonte per centrum mundi F, &amp; </s>
  <s xml:id="echoid-s25873" xml:space="preserve">punctum E, ducto. </s>
  <s xml:id="echoid-s25874" xml:space="preserve">Quare Meridianus plano horologĳ <lb/>occurret in puncto E: </s>
  <s xml:id="echoid-s25875" xml:space="preserve">Occurrit autem eidem in puncto D, vt oſtendimus. </s>
  <s xml:id="echoid-s25876" xml:space="preserve">Igitur recta D E, in vtram-<lb/>que partem eiecta erit linea meridiana. </s>
  <s xml:id="echoid-s25877" xml:space="preserve">Quoniam vero tam Aequator, quàm Horizon ad Meridianum <lb/>rectus eſt, erit etiam eorum communis ſectio ad eundem recta, ac proinde, per defin. </s>
  <s xml:id="echoid-s25878" xml:space="preserve">3. </s>
  <s xml:id="echoid-s25879" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25880" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25881" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25882" xml:space="preserve">ad <lb/>
<anchor type="note" xlink:label="note-0408-06a" xlink:href="note-0408-06"/>
<anchor type="note" xlink:label="note-0408-07a" xlink:href="note-0408-07"/>
rectam F E, in Meridiano exiſtentem perpendicularis in F, centro mundi. </s>
  <s xml:id="echoid-s25883" xml:space="preserve">Quocirca cum recta F α, ſit <lb/>in Horizonte per centrum mundi F, &amp; </s>
  <s xml:id="echoid-s25884" xml:space="preserve">punctum α, ducto, faciat{q́ue} cum F E, in Meridiano exiſtentem an <lb/>gulum rectum in F, ob quadrantem circuli ex F, deſcripti inter rectas F E, F α, interiectum, erit ipſa <lb/>F α, communis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s25885" xml:space="preserve">Aequatoris: </s>
  <s xml:id="echoid-s25886" xml:space="preserve">Quamobrem Aequator plano horologii occurret in <lb/>α, ac idcirco per α, ducenda erit linea æquinoctialis.</s>
  <s xml:id="echoid-s25887" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1310" type="float" level="2" n="12">
<note position="left" xlink:label="note-0408-05" xlink:href="note-0408-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0408-06" xlink:href="note-0408-06a" xml:space="preserve">@@. vn<unsure/>dec.</note>
<note position="left" xlink:label="note-0408-07" xlink:href="note-0408-07a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s25888" xml:space="preserve">CONCIPIATVR rurſum per polum plani horologii, atque adeo per ſtylum K β, qui portio <lb/>eſt axis eiuſdem plani, &amp; </s>
  <s xml:id="echoid-s25889" xml:space="preserve">per polum Meridiani duci circul{us} maximus faciens in horologio ſectionem li-<lb/>ueam rectam, quæneceſſario per α, punctum tranſibit. </s>
  <s xml:id="echoid-s25890" xml:space="preserve">Quoniam enim Aequator, &amp; </s>
  <s xml:id="echoid-s25891" xml:space="preserve">Horizon tranſeũt <lb/>quoque per polos Meridiani, habebunt Aequator, Horizon, &amp; </s>
  <s xml:id="echoid-s25892" xml:space="preserve">dictus circulus maximus eandem commu <lb/>nem ſectionem. </s>
  <s xml:id="echoid-s25893" xml:space="preserve">Quare in horologio facient tres ſectiones, lineas rectas, in eo puncto coeuntes, per pro-<lb/>
<anchor type="note" xlink:label="note-0408-08a" xlink:href="note-0408-08"/>
poſ. </s>
  <s xml:id="echoid-s25894" xml:space="preserve">18. </s>
  <s xml:id="echoid-s25895" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25896" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25897" xml:space="preserve">in quod communis eorum ſectio cadit. </s>
  <s xml:id="echoid-s25898" xml:space="preserve">Cum ergo communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s25899" xml:space="preserve">Aequa-<lb/>toris cadat in punctum α, quòd ibi ſe mutuo ſecent horizontalis linea, &amp; </s>
  <s xml:id="echoid-s25900" xml:space="preserve">ęquinoctialis, vt oſtendimus, <lb/>tranſibit quoque communis ſectio prędicti circuli maximi, &amp; </s>
  <s xml:id="echoid-s25901" xml:space="preserve">plani horologii per punctum α: </s>
  <s xml:id="echoid-s25902" xml:space="preserve">Tranſit <lb/>autem idem circulus maximus per K, locum ſtyli. </s>
  <s xml:id="echoid-s25903" xml:space="preserve">Igitur recta α K, communis ſectio eſt plani horologii, <lb/>&amp; </s>
  <s xml:id="echoid-s25904" xml:space="preserve">dicti circuli maximi. </s>
  <s xml:id="echoid-s25905" xml:space="preserve">Quia vero dictus circulus rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s25906" xml:space="preserve">15. </s>
  <s xml:id="echoid-s25907" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25908" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25909" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s25910" xml:space="preserve">ad Meridia-<lb/>num, &amp; </s>
  <s xml:id="echoid-s25911" xml:space="preserve">ad planum horologii, cum per horum polos ducatur, erit viciſſim tam planum horologii, quàm <lb/>planum Meridiani ad dictum circulum rectum. </s>
  <s xml:id="echoid-s25912" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s25913" xml:space="preserve">communis illorum ſectio, hoc eſt, linea meri-<lb/>diana E ρ, ad eundem circulum recta erit, ac proinde &amp; </s>
  <s xml:id="echoid-s25914" xml:space="preserve">ad rectam α K, in illo circulo exiſtentem per-<lb/>
<anchor type="note" xlink:label="note-0408-09a" xlink:href="note-0408-09"/>
pendicularis. </s>
  <s xml:id="echoid-s25915" xml:space="preserve">Secabit ergo neceſſario recta α K, meridianam lineam ad angulos rectos in puncto a. </s>
  <s xml:id="echoid-s25916" xml:space="preserve">Hinc <lb/>fit eandem rectam α K, tranſire omnino per punctum H, vbi ſe interſecant arcus deſcripti ex D, E, ad
<pb o="393" file="0409" n="409" rhead="LIBER TERTIVS."/>
interualla D β, E F. </s>
  <s xml:id="echoid-s25917" xml:space="preserve">Nam ſi triangulum D E H, concipiatur moueri circa rectam D E, permanebit per-<lb/>petuo recta H a, in plano dicti circuli maximi ſectionem α K, facientis; </s>
  <s xml:id="echoid-s25918" xml:space="preserve">quia ad hunc motum recta H a, <lb/>ſemper angulum rectum faciet cum meridiana linea, ita vt neque ad hanc, neque ad illam partem incli-<lb/>net, ſicut nec planum illi{us} <lb/>circuli in hanc vel illam par <lb/>
<anchor type="figure" xlink:label="fig-0409-01a" xlink:href="fig-0409-01"/>
tem inclinatum eſt ad pla-
num horologĳ, ſed rectum
est ad ipſum. </s>
  <s xml:id="echoid-s25919" xml:space="preserve">Quòd ſi trian
gulum D β C, rectum ſtatua
tur ad horologii planum in
<anchor type="note" xlink:label="note-0409-01a" xlink:href="note-0409-01"/>
recta C D, ita vt ſty’<unsure/>{us} β k,
rectus ſit ad idem planum;</s>
  <s xml:id="echoid-s25920" xml:space="preserve">
intelligatur autem &amp; </s>
  <s xml:id="echoid-s25921" xml:space="preserve">trian
gulum E F α, circa rectam
α E, moueri, donec recta
C F, rectæ C β, congruat, et
punctum F, centro mundi β,
ob æqualitatẽ rectarũ C F,
C β, at que adeo triangulum
ipſun E F α, cum Horizon-
<anchor type="note" xlink:label="note-0409-02a" xlink:href="note-0409-02"/>
teper rectam α E, &amp; </s>
  <s xml:id="echoid-s25922" xml:space="preserve">cen-
trum mundi β, ducto coniun
gatur, rectaq́, E F, rectę E β,
in plano Meridiani; </s>
  <s xml:id="echoid-s25923" xml:space="preserve">item co
gitetur quoque triangulum
D H E, circa meridianam li
neam D E, circumagi, donec
cum plano Meridiani coniun
gatur, congruet omnino triã-
gulum D H E, triangulo
<anchor type="note" xlink:label="note-0409-03a" xlink:href="note-0409-03"/>
D β F, in eodem plano Me-
ridiani exiſtẽti, adeo vt pun
ctum H, in centrum mundi
β, cadat: </s>
  <s xml:id="echoid-s25924" xml:space="preserve">alioquin in plano
Meridiani ſuper rectã D E,
<anchor type="note" xlink:label="note-0409-04a" xlink:href="note-0409-04"/>
<anchor type="note" xlink:label="note-0409-05a" xlink:href="note-0409-05"/>
educerentur ex D, duæ re-
ctæ inter ſe ęquales D β,
D H, &amp; </s>
  <s xml:id="echoid-s25925" xml:space="preserve">ex E, alię duæ in-
ter ſe ęquales E β, quæ eadẽ
eſt, quę E F, &amp; </s>
  <s xml:id="echoid-s25926" xml:space="preserve">E H, quę ipſi
<anchor type="note" xlink:label="note-0409-06a" xlink:href="note-0409-06"/>
E F, ſumpta eſt ęqualis. </s>
  <s xml:id="echoid-s25927" xml:space="preserve">quod est abſurdũ. </s>
  <s xml:id="echoid-s25928" xml:space="preserve">Ex quo efficitur, rectam E H, in eo ſitu eſſe cõmunem ſectio-
nem Horizontis ac Meridiani. </s>
  <s xml:id="echoid-s25929" xml:space="preserve">Igitur cum in planis à meridie declinantibus, vt in trib{us} priorib{us} fi-
guris, angul{us} d H E, verſ{us} partes boreales ſit ęqualis altitudini poli, qualem nimirum axis mundi ſu-
pra Horizontem cum recta H E, communi ſectione Horizontis ac Meridiani facit verſ{us} partes borea-
les, erit recta d H, axis mundi, occurrens meridianę lineę horologĳ in ρ; </s>
  <s xml:id="echoid-s25930" xml:space="preserve">ac proinde ρ, centrum erit ho-
rologii, ex coroll. </s>
  <s xml:id="echoid-s25931" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s25932" xml:space="preserve">21. </s>
  <s xml:id="echoid-s25933" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25934" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25935" xml:space="preserve">Si vero axis d H, æquidiſtet lineæ meridianæ D E, non habebit horo-
logium centrum. </s>
  <s xml:id="echoid-s25936" xml:space="preserve">In planis autem à ſeptentrione declinantib{us}, vt in poſteriorib{us} trib{us} figuris, quo-
niam angul{us} b H E, æqualis eſt altitudini poli, qualem nimirum axis mundi infra Horizontem cum re-
cta H E, communi ſectione Horizontis ac Meridiani facit verſus partes auſtrales, erit recta b H, axis
mundi, ac idcirco, vt antea, ρ, centrum erit horologii. </s>
  <s xml:id="echoid-s25937" xml:space="preserve">Hinc fit tam in illis planis, quàm in his, rectam
H M, in plano Meridiani exiſtentem, facientem{q́ue} cum axe H ρ, angulum rectum b H d, ob quadrantem
b d, eſſe communem ſectionem Meridiani &amp; </s>
  <s xml:id="echoid-s25938" xml:space="preserve">Aequatoris, cum axis mundi in centro mundi H, neceſſario
<anchor type="note" xlink:label="note-0409-07a" xlink:href="note-0409-07"/>
ſit perpendicularis, per defin. </s>
  <s xml:id="echoid-s25939" xml:space="preserve">3 lib. </s>
  <s xml:id="echoid-s25940" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25941" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25942" xml:space="preserve">ad eiuſmodi communem ſectionem, propterea quòd axis ad
Aequatoris planum rect{us} eſt, ex propoſ. </s>
  <s xml:id="echoid-s25943" xml:space="preserve">10. </s>
  <s xml:id="echoid-s25944" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25945" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25946" xml:space="preserve">Theod Occurrit igitur Aequator plano horologii in
puncto M, propterea{q́ue} per M, ex α, ducenda eſt linea æquinoctialis. </s>
  <s xml:id="echoid-s25947" xml:space="preserve">Quòd ſi H M, communis ſectio Me
ridiani at que Aequatoris paralle<unsure/>la ſit lineæ ipſi meridianę D E, æquidiſtabit planum horologii per D E,
duct@m eidem communi ſectioni H M, cum eam non ſecet. </s>
  <s xml:id="echoid-s25948" xml:space="preserve">Quare per propoſ. </s>
  <s xml:id="echoid-s25949" xml:space="preserve">18. </s>
  <s xml:id="echoid-s25950" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25951" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25952" xml:space="preserve">ſectiones, qu{as}
Meridian{us}, &amp; </s>
  <s xml:id="echoid-s25953" xml:space="preserve">Aequator cum plano horologii faciunt, parallelæ erunt; </s>
  <s xml:id="echoid-s25954" xml:space="preserve">atque idcirco per α, ducenda
erit linea æquinoctialis æquidiſtans meridianæ lineę D E.</s>
  <s xml:id="echoid-s25955" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1311" type="float" level="2" n="13">
<note position="left" xlink:label="note-0408-08" xlink:href="note-0408-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0408-09" xlink:href="note-0408-09a" xml:space="preserve">@@. vndec.</note>
  <figure xlink:label="fig-0409-01" xlink:href="fig-0409-01a">
    <image file="0409-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0409-01"/>
<caption xml:id="echoid-caption5" xml:space="preserve">5. figura</caption>
  </figure>
<note position="left" xlink:label="note-0409-01" xlink:href="note-0409-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0409-02" xlink:href="note-0409-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0409-03" xlink:href="note-0409-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0409-04" xlink:href="note-0409-04a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0409-05" xlink:href="note-0409-05a" xml:space="preserve">7. pri<gap/></note>
<note position="left" xlink:label="note-0409-06" xlink:href="note-0409-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0409-07" xlink:href="note-0409-07a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s25956" xml:space="preserve">RECTAM autem ρ K, ductam ex centro horologii per locum ſtyli, eſſe lineam ſtyli, hoc eſt, com-<lb/>munem ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s25957" xml:space="preserve">Meridiani ipſi{us} proprĳ, perſpicuum eſt. </s>
  <s xml:id="echoid-s25958" xml:space="preserve">Quoniam enim Meridia-
<pb o="394" file="0410" n="410" rhead="GNOMONICES"/>
nus ille per H ρ, axem ductus, occurrit plano horologĳ in ρ, centro horologĳ, ducenda erit communis ei{us} <lb/>cum horologio ſectio per ρ. </s>
  <s xml:id="echoid-s25959" xml:space="preserve">Rurſus quia idem Meridianus ad planum horologĳ rectus eſt, tranſibit ne-<lb/>ceſſario per stylum, cum omnia plana per stylum ducta ſint recta ad planum horologĳ; </s>
  <s xml:id="echoid-s25960" xml:space="preserve">atque adeo di-<lb/>
<anchor type="note" xlink:label="note-0410-01a" xlink:href="note-0410-01"/>
cta communis ſectio, hoc eſt, linea ſtyli per K, ducenda erit, cuiuſmodi eſt recta ρ K, quæ æquinoctialem <lb/>lineam ſecabit ad angulos rectos, <lb/>vt in ſuperioribus demonstratum <lb/>
<anchor type="figure" xlink:label="fig-0410-01a" xlink:href="fig-0410-01"/>
est. </s>
  <s xml:id="echoid-s25961" xml:space="preserve">Nam quia tam planum Ae-
quatoris, quàm planum horologĳ
rectum eſt ad Meridianum pro-
prium plani horologĳ, erit quoque
<anchor type="note" xlink:label="note-0410-02a" xlink:href="note-0410-02"/>
communis eorum ſectio, nempe
æquinoctialis linea α M, ad eun-
dem recta, atque adeo, per defin.</s>
  <s xml:id="echoid-s25962" xml:space="preserve">
<anchor type="note" xlink:label="note-0410-03a" xlink:href="note-0410-03"/>
3. </s>
  <s xml:id="echoid-s25963" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25964" xml:space="preserve">11. </s>
  <s xml:id="echoid-s25965" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s25966" xml:space="preserve">ad lineam ſtyli
ρ K, in eodem Meridiano exiſten-
tem perpendicularis. </s>
  <s xml:id="echoid-s25967" xml:space="preserve">Quod ſi cen
tro careat horologium, ducenda
erit linea styli per K, locum styli
parallela lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s25968" xml:space="preserve">ad
æquinoctialem lineam perpendi-
<anchor type="note" xlink:label="note-0410-04a" xlink:href="note-0410-04"/>
cularis. </s>
  <s xml:id="echoid-s25969" xml:space="preserve">Quia enim tunc pla-
num horologii axi mundi, quem
non ſecat, hoc eſt, communi ſe-
ctioni Meridiani Horizontis, et
Meridiani proprĳ ipſius horolo-
gĳ, æquidiſtat, erunt per propoſ.</s>
  <s xml:id="echoid-s25970" xml:space="preserve">
18. </s>
  <s xml:id="echoid-s25971" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s25972" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25973" xml:space="preserve">communes ſectiones pla
ni horologii, &amp; </s>
  <s xml:id="echoid-s25974" xml:space="preserve">ipſorum Meridia-
norum, hoc est, linea meridiana,
&amp; </s>
  <s xml:id="echoid-s25975" xml:space="preserve">linea ſtyli, parallelæ inter ſe, ſecabit{q́ue}<unsure/> linea styli lineam æquinoctialem ad angulos rectos, vt proxi-
me demonſtr auim{us}.</s>
  <s xml:id="echoid-s25976" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1312" type="float" level="2" n="14">
<note position="left" xlink:label="note-0410-01" xlink:href="note-0410-01a" xml:space="preserve">18. vndec.</note>
  <figure xlink:label="fig-0410-01" xlink:href="fig-0410-01a">
    <image file="0410-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0410-01"/>
<caption xml:id="echoid-caption6" xml:space="preserve">6. figura</caption>
  </figure>
<note position="left" xlink:label="note-0410-02" xlink:href="note-0410-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0410-03" xlink:href="note-0410-03a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0410-04" xlink:href="note-0410-04a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s25977" xml:space="preserve">QVOD autem recta ρ I, ſit axis mundi, ita vt cum linea ſtyli ρ K, quæ communis ſectio eſt Meri-<lb/>diani proprii plani inclinati, &amp; </s>
  <s xml:id="echoid-s25978" xml:space="preserve">plani horologii, comprehendat angulum I ρ K, altitudinis poli ſupra pla <lb/>num inclinatum, manifestum eſt. </s>
  <s xml:id="echoid-s25979" xml:space="preserve">Si enim triangulum I K ρ, circa K ρ, moueatur, donec rectum fiat ad <lb/>planum horologii, &amp; </s>
  <s xml:id="echoid-s25980" xml:space="preserve">ſtylus I K, ad idem rectus, ac idcirco punctum I, centro mundi congruat, erit recta <lb/>ρ I, axis mundi, quandoquidem axis mundi per centrum mundi, &amp; </s>
  <s xml:id="echoid-s25981" xml:space="preserve">centrum horologĳ ducitur. </s>
  <s xml:id="echoid-s25982" xml:space="preserve">Quod etiã <lb/>hac ratione perſpicuum fiet. </s>
  <s xml:id="echoid-s25983" xml:space="preserve">quoniam circumuoluto triangulo ρ H E, circa meridianam lineam ρ E, do-<lb/>nec cum plano Meridiani coniungatur, punctum H, centro mundi congruit, vt ſupra oſtendim{us}, at que <lb/>adeo &amp; </s>
  <s xml:id="echoid-s25984" xml:space="preserve">puncto I, congruet quoque recta ρ H, rectæ ρ I: </s>
  <s xml:id="echoid-s25985" xml:space="preserve">Oſtendimus autem ρ H, eſſe axem mundi. </s>
  <s xml:id="echoid-s25986" xml:space="preserve">Igi-<lb/>tur &amp; </s>
  <s xml:id="echoid-s25987" xml:space="preserve">ρ I, axis mundi erit. </s>
  <s xml:id="echoid-s25988" xml:space="preserve">In horologĳs, quæ centro carent, ducend{us} eſt axis mundi per I, lineæ ſtyli <lb/>æquidiſtans, quia ſi ipſam ſecaret, eſſet punctum ſectionis centrum horologĳ, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s25989" xml:space="preserve">Reliqua <lb/>
<anchor type="note" xlink:label="note-0410-06a" xlink:href="note-0410-06"/>
perſpicua ſunt ex demonſtratione primæ deſcriptionis in hac propoſ. </s>
  <s xml:id="echoid-s25990" xml:space="preserve">traditæ.</s>
  <s xml:id="echoid-s25991" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1313" type="float" level="2" n="15">
<note position="left" xlink:label="note-0410-06" xlink:href="note-0410-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s25992" xml:space="preserve">POSTREMO idem horologium declinans ſimul &amp; </s>
  <s xml:id="echoid-s25993" xml:space="preserve">inclinatum deſcribemus beneficio Ellipſis in <lb/>horologĳ plano deſcriptæ, non ſec{us} ac docuimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s25994" xml:space="preserve">1. </s>
  <s xml:id="echoid-s25995" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s25996" xml:space="preserve">Semidiametri circulorũ, <lb/>
<anchor type="note" xlink:label="note-0410-07a" xlink:href="note-0410-07"/>
qui determinant longitudinem &amp; </s>
  <s xml:id="echoid-s25997" xml:space="preserve">latitudinem Ellipſis, ex centro horologĳ ρ, deſcribendorum ſunt ρ G, <lb/>G I: </s>
  <s xml:id="echoid-s25998" xml:space="preserve">Vel ſi maiores deſiderentur, ſumatur pro maiore ſemidiametro quant acunque portio ex linea ſtyli, <lb/>nempe ρ L, pro minore autem recta, quæ ex puncto, quod maiorem terminat, vt ex L, cadit in axem ρ I, <lb/>perpendicularis: </s>
  <s xml:id="echoid-s25999" xml:space="preserve">Et quod ad demonſtrationem attinet, circa G I, vel illam perpendicularem ex L, caden <lb/>tem in axem, deſcribendus eſt circulus in plano Aequatoris ex cẽtro mundi, quod in axe eſt, pro baſe cy-<lb/>lindri. </s>
  <s xml:id="echoid-s26000" xml:space="preserve">Diuiſio autem circulorum ex<unsure/> ρ, deſcriptorum inchoanda eſt à recta, quæ in cẽtro ρ, cum linea ſty-<lb/>li verſus lineam meridianam angulum comprehendat angulo ρ L M, nempe inclinationi Meridiani pro-<lb/>
<anchor type="note" xlink:label="note-0410-08a" xlink:href="note-0410-08"/>
prii ipſius plani inclinati ad Meridianum Horizontis, æqualem. </s>
  <s xml:id="echoid-s26001" xml:space="preserve">Vnde quoniam in ſexta figura inclina-<lb/>tio Meridianorum complectitur grad. </s>
  <s xml:id="echoid-s26002" xml:space="preserve">90. </s>
  <s xml:id="echoid-s26003" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26004" xml:space="preserve">recta L M, cum linea ſtyli angulum efficit rectum, initium <lb/>habebit diuiſio circulorum ex ρ, deſcriptorum à linea meridiana, cum hæc cum linea ſl<unsure/>yli rectos etiã con-<lb/>tineat angulos, vt ex ſuperioribus conſtat. </s>
  <s xml:id="echoid-s26005" xml:space="preserve">Hæc porro deſcriptio locum non habet in horologiis centro cæ <lb/>rentibus, vt in tertia figura: </s>
  <s xml:id="echoid-s26006" xml:space="preserve">quia planum horologĳ, cum axi mundi, ſiue cylindri, ex cuius ſectione Elli-<lb/>pſis illa oritur, æquidiſtet, non efficit Ellipſim, ſed parallelogrammum, vt à Sereno Antinſenſi demon-<lb/>ſtratur lib. </s>
  <s xml:id="echoid-s26007" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26008" xml:space="preserve">de ſectione cylindri.</s>
  <s xml:id="echoid-s26009" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1314" type="float" level="2" n="16">
<note position="left" xlink:label="note-0410-07" xlink:href="note-0410-07a" xml:space="preserve">Eiuſdem horo-<lb/>logii deſcriptio<unsure/> <lb/>ex Ellipſi.</note>
<note position="left" xlink:label="note-0410-08" xlink:href="note-0410-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s26010" xml:space="preserve">IAM verò ſi horologium quodcunque ſuperi{us} inuertatur, ita vt ſuperior pars euadat inferior, &amp; </s>
  <s xml:id="echoid-s26011" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0410-09a" xlink:href="note-0410-09"/>
quæ poſt hanc inuerſionem nobis dextra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s26012" xml:space="preserve">è contrario, vt in præcedentibus non ſemel de-<lb/>clarauim{us}, habebim{us} horologium in facie plani oppoſita, ac inferiori collocandum, vt demonſtratum
<pb o="395" file="0411" n="411" rhead="LIBER TERTIVS."/>
eſt in ſcholio propoſ. </s>
  <s xml:id="echoid-s26013" xml:space="preserve">13. </s>
  <s xml:id="echoid-s26014" xml:space="preserve">libri ſuperioris. </s>
  <s xml:id="echoid-s26015" xml:space="preserve">Sed tunc lineæ horarum, quæ prius in ſuperiori horologio indi-<lb/>cabant hor{as} à meridie, ostendent hor{as} à media nocte, &amp; </s>
  <s xml:id="echoid-s26016" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s26017" xml:space="preserve">Pulchrè autem, vt &amp; </s>
  <s xml:id="echoid-s26018" xml:space="preserve">in anteceden-<lb/>tib{us}, inuerſionẽ hanc declarant lineamẽta horologĳ ſuperioris deſcripta in facie oppoſita, ita vt ſingula <lb/>ſingulis reſpondeant ad vnguem, dummodo pars ſuperior faciei oppoſitæ fiat inferior, &amp; </s>
  <s xml:id="echoid-s26019" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s26020" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1315" type="float" level="2" n="17">
<note position="left" xlink:label="note-0410-09" xlink:href="note-0410-09a" xml:space="preserve">Qua ratione ex <lb/>horologio Su-<lb/>periori genere-<lb/>tur Inferius.</note>
</div>
</div>
<div xml:id="echoid-div1317" type="section" level="1" n="318">
<head xml:id="echoid-head329" xml:space="preserve">PROBLEMA 38. PROPOSITIO 38.</head>
<p>
  <s xml:id="echoid-s26021" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in eodem horo-<lb/>logio, quod &amp; </s>
  <s xml:id="echoid-s26022" xml:space="preserve">à Verticali circulo declinat, &amp; </s>
  <s xml:id="echoid-s26023" xml:space="preserve">ad Horizontem eſt incli-<lb/>
<anchor type="note" xlink:label="note-0411-01a" xlink:href="note-0411-01"/>
natum, depingere.</s>
  <s xml:id="echoid-s26024" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1317" type="float" level="2" n="1">
<note position="left" xlink:label="note-0411-01" xlink:href="note-0411-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s26025" xml:space="preserve">ALTITVDINE poli ſupra planum declinans, &amp; </s>
  <s xml:id="echoid-s26026" xml:space="preserve">inclinatum ex propoſ. </s>
  <s xml:id="echoid-s26027" xml:space="preserve">29. </s>
  <s xml:id="echoid-s26028" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26029" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26030" xml:space="preserve">inuenta, <lb/>
<anchor type="note" xlink:label="note-0411-02a" xlink:href="note-0411-02"/>
quam quidem in horologio ſecundum priorem deſcriptionem fabricato in pręcedẽti propoſ. </s>
  <s xml:id="echoid-s26031" xml:space="preserve">uel <lb/>in eo, ubi ſtylus eiusq́ue locus dabatur in ſcholio eiuſdem propoſ. </s>
  <s xml:id="echoid-s26032" xml:space="preserve">oſtendit angulus K ρ I, quem <lb/>
<anchor type="figure" xlink:label="fig-0411-01a" xlink:href="fig-0411-01"/>
<anchor type="note" xlink:label="note-0411-03a" xlink:href="note-0411-03"/>
<anchor type="note" xlink:label="note-0411-04a" xlink:href="note-0411-04"/>
<anchor type="note" xlink:label="note-0411-05a" xlink:href="note-0411-05"/>
linea ſtyli cum axc mundi efficit, vt diximus, conſtituatur ad ipſam Analemma, ut in propoſ. </s>
  <s xml:id="echoid-s26033" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s26034" xml:space="preserve">præcedentis libri, ita ut arcus CE, in Analemmate comprehendat gradus altitudinis poli in-<lb/>
<anchor type="note" xlink:label="note-0411-06a" xlink:href="note-0411-06"/>
uentæ, uel certe angulus CDE, in Analemmate æqualis ſit angulo altitudinis poli K ρ I, in <lb/>horologio inclinato. </s>
  <s xml:id="echoid-s26035" xml:space="preserve">Deinde in eodem Analemmate accipiatur recta DG, æqualis ſtylo I K, <lb/>quem nobis offert prima deſcriptio præcedentis propoſ. </s>
  <s xml:id="echoid-s26036" xml:space="preserve">uel quem in ſecunda deſcriptione aſ-<lb/>ſumpſimus in portione Analemmatis, einſdem propoſ. </s>
  <s xml:id="echoid-s26037" xml:space="preserve">quæ portioni Analemmatis propoſ. </s>
  <s xml:id="echoid-s26038" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s26039" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26040" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26041" xml:space="preserve">reſpondet, uel certe quem aſſumpſimus in deſcriptione tradita in ſcholio præcedentis <lb/>propoſ. </s>
  <s xml:id="echoid-s26042" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26043" xml:space="preserve">per G, agatur recta OR, parallela ipſi BC. </s>
  <s xml:id="echoid-s26044" xml:space="preserve">Hac etenim ratione in recta R O, in-<lb/>ueniemus diametros conicatum ſectionum, quemadmodum earundem diametros K R, L R, <lb/>MR, NO PO, QO, in horizontali horologio reperiemus propoſ. </s>
  <s xml:id="echoid-s26045" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26046" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26047" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26048" xml:space="preserve">Vnde ut ibi <lb/>docuimus, ita etiam deſcribentur hic ſectiones conicæ inuentarum diametrorum, hoc eſt, arcus, <lb/>paralleli ſignorum Zodiaci. </s>
  <s xml:id="echoid-s26049" xml:space="preserve">Nam ſicut in horologio horizontali circulus Analemmatis A B C,
<pb o="396" file="0412" n="412" rhead="GNOMONICES"/>
repreſentat Meridianũ Horizontis, &amp; </s>
  <s xml:id="echoid-s26050" xml:space="preserve">recta OR, cõmunem ſectionẽ plani horologij horizontalis, <lb/>&amp; </s>
  <s xml:id="echoid-s26051" xml:space="preserve">Meridiani, hoc eſt, lineam meridianam; </s>
  <s xml:id="echoid-s26052" xml:space="preserve">ita in horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26053" xml:space="preserve">inclinato idẽ cir-<lb/>culus refert Meridianum proprium plani inclinati, id eſt, circulum maximum per polos mundi <lb/>&amp; </s>
  <s xml:id="echoid-s26054" xml:space="preserve">per polos plani declinantis ductum; </s>
  <s xml:id="echoid-s26055" xml:space="preserve">recta autem OR, communem ſectionem exprimit dicti <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s26056" xml:space="preserve">plani horologij declinantis, ac inclinati, hoc eſt, lineam ſtyli.</s>
  <s xml:id="echoid-s26057" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1318" type="float" level="2" n="2">
<note position="right" xlink:label="note-0411-02" xlink:href="note-0411-02a" xml:space="preserve">Arcus fignor@ <lb/>quo pacto ex <lb/>Analemmate <lb/>deſcribantur.</note>
  <figure xlink:label="fig-0411-01" xlink:href="fig-0411-01a">
    <image file="0411-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0411-01"/>
  </figure>
<note position="left" xlink:label="note-0411-03" xlink:href="note-0411-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0411-04" xlink:href="note-0411-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0411-05" xlink:href="note-0411-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0411-06" xlink:href="note-0411-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s26058" xml:space="preserve">ALITER. </s>
  <s xml:id="echoid-s26059" xml:space="preserve">Ducta recta ρ I, pro axe mundi, erigatur ad eam in I, perpendicularis IG, pro ra-<lb/>
<anchor type="note" xlink:label="note-0412-01a" xlink:href="note-0412-01"/>
dio Æquatoris, ad cuius utramque partem radij aliorũ ſignorũ educãtur, ut in ſuperioribus factũ <lb/>eſt, ſitq́ue I ρ, æqualis portioni axis ρ I, in horologio, &amp; </s>
  <s xml:id="echoid-s26060" xml:space="preserve">recta IG, æqualis rectæ IG, uel LG, in <lb/>
<anchor type="figure" xlink:label="fig-0412-01a" xlink:href="fig-0412-01"/>
<anchor type="note" xlink:label="note-0412-02a" xlink:href="note-0412-02"/>
<anchor type="note" xlink:label="note-0412-03a" xlink:href="note-0412-03"/>
<anchor type="note" xlink:label="note-0412-04a" xlink:href="note-0412-04"/>
<anchor type="note" xlink:label="note-0412-05a" xlink:href="note-0412-05"/>
eodem horologio; </s>
  <s xml:id="echoid-s26061" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26062" xml:space="preserve">ex ρ, per G, recta emittatur ρ G: </s>
  <s xml:id="echoid-s26063" xml:space="preserve">quam fortaſſis commodius ducemus, fi <lb/>ex ρ, educamus rectam ρ G, quæ cum ρ I, conſtituat angulum G ρ I, æqualem angulo G ρ I, quẽ <lb/>in horologio conſtituunt axis ρ I, &amp; </s>
  <s xml:id="echoid-s26064" xml:space="preserve">linea ſtyli ρ G, nempe angulo altitudinis poli ſupra planum <lb/>horologij. </s>
  <s xml:id="echoid-s26065" xml:space="preserve">Erit hac ratione triangulum hoc G ρ I, æquale omnino triangulo G ρ I, in horologio <lb/>
<anchor type="note" xlink:label="note-0412-06a" xlink:href="note-0412-06"/>
inclinato, atque adeo exiſtente ρ I, in hac figura axe mundi, recta ρ G, linea ſtyli erit. </s>
  <s xml:id="echoid-s26066" xml:space="preserve">Quod ſi re-<lb/>liqua fiant, ut in propoſ. </s>
  <s xml:id="echoid-s26067" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26068" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s26069" xml:space="preserve">in eius ſcholio tradidimus, accipiendo ſemper hic li-<lb/>teram ρ, pro litera C, cuius ibi mentio fit, deſcripti erunt paralleli, ſiue arcus ſignorum Zodiaci.</s>
  <s xml:id="echoid-s26070" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1319" type="float" level="2" n="3">
<note position="left" xlink:label="note-0412-01" xlink:href="note-0412-01a" xml:space="preserve">Alia deſcriptio <lb/>arcuum ſigno-<lb/>@@m.</note>
  <figure xlink:label="fig-0412-01" xlink:href="fig-0412-01a">
    <image file="0412-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0412-01"/>
  </figure>
<note position="left" xlink:label="note-0412-02" xlink:href="note-0412-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0412-03" xlink:href="note-0412-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0412-04" xlink:href="note-0412-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0412-05" xlink:href="note-0412-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0412-06" xlink:href="note-0412-06a" xml:space="preserve">4. vel 26. <lb/>primi.</note>
</div>
<p>
  <s xml:id="echoid-s26071" xml:space="preserve">EXEMPLVM ſubiecimus reſpondens ultimo horologio Superiori ex illis ſex præcedentis <lb/>
<anchor type="note" xlink:label="note-0412-07a" xlink:href="note-0412-07"/>
propoſ. </s>
  <s xml:id="echoid-s26072" xml:space="preserve">Vbi quoniam linea ſtyli eadem eſt, quæ linea horæ 6. </s>
  <s xml:id="echoid-s26073" xml:space="preserve">ſingulis lineis horarijs ex puncto ρ, <lb/>figurę radiorum ſignorum Zodiaci, ex qua arcus ſignorum deſcribuntur, egredientibus appoſi-<lb/>ti ſunt bini numeri horarum æqualiter hinc inde à linea horæ 6. </s>
  <s xml:id="echoid-s26074" xml:space="preserve">hoc eſt, à linea ſtyli diſtantiũ, ut <lb/>in propoſ. </s>
  <s xml:id="echoid-s26075" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26076" xml:space="preserve">huius libri monimus. </s>
  <s xml:id="echoid-s26077" xml:space="preserve">Rurſus hic recta ρ V, radio Æquatoris æquidiſtans exhibet ho <lb/>ram 12. </s>
  <s xml:id="echoid-s26078" xml:space="preserve">quoniam huius horæ linea in horologio equidiſtat ęquinoctiali lineæ: </s>
  <s xml:id="echoid-s26079" xml:space="preserve">quemadmodum in <lb/>horizontali horologio recta HV, radio Æquatoris æquidiſtans in figura radiorum propoſ. </s>
  <s xml:id="echoid-s26080" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26081" xml:space="preserve">ſupe <lb/>rioris lib. </s>
  <s xml:id="echoid-s26082" xml:space="preserve">refert horã 6. </s>
  <s xml:id="echoid-s26083" xml:space="preserve">quia huiuſce horę linea etiã æquinoctiali lineæ æquidiſtat in horologio.</s>
  <s xml:id="echoid-s26084" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1320" type="float" level="2" n="4">
<note position="left" xlink:label="note-0412-07" xlink:href="note-0412-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s26085" xml:space="preserve">ADDIDIMVS quoque aliã figurã radiorũ Zodiaci, cũ lineis horarijs ex ρ, egredientibus <lb/>reſpondenté primo horologio antecedẽtis propoſ in quo linea ſtvli, neq; </s>
  <s xml:id="echoid-s26086" xml:space="preserve">vna eſt ex lineis horariis, <lb/>aeque æqualiter à duabus hinc inde poſitis diſtat. </s>
  <s xml:id="echoid-s26087" xml:space="preserve">Vnde fit ut ſingulę lineæ ex ρ, emiſſę ſingulos
<pb o="397" file="0413" n="413" rhead="LIBER TERTIVS."/>
quoq; </s>
  <s xml:id="echoid-s26088" xml:space="preserve">numeros habeant affixos. </s>
  <s xml:id="echoid-s26089" xml:space="preserve">Ex hac igitur figura in dicto horologio arcus ſignorũ deſcribere <lb/>licebit, cũ res tulerit. </s>
  <s xml:id="echoid-s26090" xml:space="preserve">Partiti autẽ ſumus figuram hanc, ut cernis, in duas, quia alioquin nimis inter <lb/>ſe cõfunderentur lineæ, propterea quòd linea ſtyli primi horologij parum diſtat à linea horæ 11. <lb/></s>
  <s xml:id="echoid-s26091" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0413-01a" xlink:href="fig-0413-01"/>
<anchor type="note" xlink:label="note-0413-01a" xlink:href="note-0413-01"/>
<anchor type="note" xlink:label="note-0413-02a" xlink:href="note-0413-02"/>
In priori harum figurarũ continẽcur lineæ horarum, quæ in horologio poſitæ ſunt ad ſiniſtram li-<lb/>neæ ſtyli, quales ſunt 5. </s>
  <s xml:id="echoid-s26092" xml:space="preserve">6. </s>
  <s xml:id="echoid-s26093" xml:space="preserve">7. </s>
  <s xml:id="echoid-s26094" xml:space="preserve">8. </s>
  <s xml:id="echoid-s26095" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26096" xml:space="preserve">10. </s>
  <s xml:id="echoid-s26097" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26098" xml:space="preserve">11. </s>
  <s xml:id="echoid-s26099" xml:space="preserve">In poſteriori uerò reliquæ horæ ad dextram eiuſdem <lb/>lineæ ſtyli ſitæ, nempe 12. </s>
  <s xml:id="echoid-s26100" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26101" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26102" xml:space="preserve">3. </s>
  <s xml:id="echoid-s26103" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26104" xml:space="preserve">5. </s>
  <s xml:id="echoid-s26105" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s26106" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26107" xml:space="preserve">Id quod iam pridem in propoſ. </s>
  <s xml:id="echoid-s26108" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26109" xml:space="preserve">huius libri mo-<lb/>nuimus faciendum eſſe in horologiis declinantibus, atque adeò inclinatis, in quibus huiuſmodi <lb/>confuſio linearum reperitur.</s>
  <s xml:id="echoid-s26110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1321" type="float" level="2" n="5">
  <figure xlink:label="fig-0413-01" xlink:href="fig-0413-01a">
    <image file="0413-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0413-01"/>
  </figure>
<note position="left" xlink:label="note-0413-01" xlink:href="note-0413-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0413-02" xlink:href="note-0413-02a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s26111" xml:space="preserve">POSTREMO, vt videas, quid agendum ſit in tertio horologio præcedentis propoſ. </s>
  <s xml:id="echoid-s26112" xml:space="preserve">in quo <lb/>lineæ horariæ ſunt æquidiſtantes, deſcripſimus etiam in eo arcus ſignorum, qui quidem deſcribũ-<lb/>
<anchor type="figure" xlink:label="fig-0413-02a" xlink:href="fig-0413-02"/>
<anchor type="note" xlink:label="note-0413-04a" xlink:href="note-0413-04"/>
<anchor type="note" xlink:label="note-0413-05a" xlink:href="note-0413-05"/>
tur, vt in Meridiano horologio, vel polati, hoc excepto, quòd hic lineæ horariæ in figura radiorum <lb/>radium Aequatoris ad angulos rectos ſecantes habent ſingulæ ſingulos numeros, non autem bi-<lb/>nos, vt ibi, niſi cum linea ſtyli vna eſt ex lineis horarijs, vel certè à duabus proximis hinc inde po-<lb/>ſiris æqualiter diſtat, quemadmodum in alijs horologijs declinantibus contingere ſolet.</s>
  <s xml:id="echoid-s26113" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1322" type="float" level="2" n="6">
  <figure xlink:label="fig-0413-02" xlink:href="fig-0413-02a">
    <image file="0413-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0413-02"/>
  </figure>
<note position="left" xlink:label="note-0413-04" xlink:href="note-0413-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0413-05" xlink:href="note-0413-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s26114" xml:space="preserve">LINEA horizontalis in horologio, quod in ſcholio præcedentis propoſ. </s>
  <s xml:id="echoid-s26115" xml:space="preserve">ſecundum datam
<pb o="398" file="0414" n="414" rhead="GNOMONICES"/>
magnitudinem ſtyli, eiuſq́ue locum deſcripſimus, iam deſcripta eſt. </s>
  <s xml:id="echoid-s26116" xml:space="preserve">Oſtendimus enim ibi, rectam <lb/>α E, eſſe horizontalem lineam. </s>
  <s xml:id="echoid-s26117" xml:space="preserve">In aliis autem horologiis eadem linea horizontalis hac ratione <lb/>deſcribetur. </s>
  <s xml:id="echoid-s26118" xml:space="preserve">Ex quocunque puncto A, in linea meridiana aſſumpto deſcribatur arcus circuli m h, <lb/>
<anchor type="note" xlink:label="note-0414-01a" xlink:href="note-0414-01"/>
in quo ex m, vel ad ſiniſtram, vel ad dextram meridianæ lineæ, vt in ſcholio præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s26119" xml:space="preserve">docuimus, cum de collocatione horologii ſecũdum poſteriores deſcriptiones fabricati ageremus, <lb/>prout arcus m h, ſupra punctum A, vel infra deſcriptus fuerit, &amp;</s>
  <s xml:id="echoid-s26120" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26121" xml:space="preserve">numeretur arcus plani propo-<lb/>ſiti, cui horologium æquidiſtat, inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s26122" xml:space="preserve">circulum maximum, qui incli-<lb/>nationem plani ad Horizontem dimetitur, interceptus vſq; </s>
  <s xml:id="echoid-s26123" xml:space="preserve">ad h; </s>
  <s xml:id="echoid-s26124" xml:space="preserve">(qui quanam ratione inuenien-<lb/>dus ſit, in propoſ. </s>
  <s xml:id="echoid-s26125" xml:space="preserve">31. </s>
  <s xml:id="echoid-s26126" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26127" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26128" xml:space="preserve">demonſtrauimus) &amp; </s>
  <s xml:id="echoid-s26129" xml:space="preserve">ex A, per h, recta ducatur A h. </s>
  <s xml:id="echoid-s26130" xml:space="preserve">Nam recta ducta <lb/>ad A h, perpendicularis ex puncto, vbi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s26131" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s26132" xml:space="preserve">ſe interſecant, dabit <lb/>
<anchor type="note" xlink:label="note-0414-02a" xlink:href="note-0414-02"/>
lineam horizontalem. </s>
  <s xml:id="echoid-s26133" xml:space="preserve">Quod ita oſtendemus. </s>
  <s xml:id="echoid-s26134" xml:space="preserve">Quoniam vt in dicto ſcholio præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s26135" xml:space="preserve">demonſtrauimus de recta E h, linea recta A h, communis ſectio eſt plani horologij, &amp; </s>
  <s xml:id="echoid-s26136" xml:space="preserve">circuli ma-<lb/>ximi inclinationem plani ad Horizontem metientis &amp; </s>
  <s xml:id="echoid-s26137" xml:space="preserve">eandem ad angulos rectos ſecat commu-<lb/>nis ſectio eiuſdem plani horologii, &amp; </s>
  <s xml:id="echoid-s26138" xml:space="preserve">Horizontis, efficitur, vt cùm communis ſectio Horizontis, <lb/>&amp; </s>
  <s xml:id="echoid-s26139" xml:space="preserve">plani horologij tranſeat per horam 6. </s>
  <s xml:id="echoid-s26140" xml:space="preserve">in æquinoctiali linea, vt in præcedentibus non ſemel di-<lb/>ctum eſt, atque demonſtratum, recta, quæ rectam A h, ad angulos rectos ſecat, ſit ſectio commu-<lb/>nis Horizontis, ac plani horologii, hoc eſt, linea horizontalis.</s>
  <s xml:id="echoid-s26141" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1323" type="float" level="2" n="7">
<note position="left" xlink:label="note-0414-01" xlink:href="note-0414-01a" xml:space="preserve">Horizontalis li <lb/>nea quomodo <lb/>deſeribatur.</note>
<note position="left" xlink:label="note-0414-02" xlink:href="note-0414-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s26142" xml:space="preserve">ALIO modo ita eandem lineam horizontalem ducemus. </s>
  <s xml:id="echoid-s26143" xml:space="preserve">Ducta recta A h, ut prius, excitabi-<lb/>
<anchor type="note" xlink:label="note-0414-03a" xlink:href="note-0414-03"/>
musad ipſam ex K, loco gnomonis perpendicularem K B, in qua producta ſumemus rectam B C, <lb/>gnomoni K I, æqualem, &amp; </s>
  <s xml:id="echoid-s26144" xml:space="preserve">in C, conſtituemus ſurſum uerſus angulum B C D, complemento in-<lb/>
<anchor type="note" xlink:label="note-0414-04a" xlink:href="note-0414-04"/>
clinationis plani ad Horizontem æqualem, ita ut recta C D, ſecet rectam A h, in D. </s>
  <s xml:id="echoid-s26145" xml:space="preserve">Dico rectam <lb/>per D, ductam ad angulos rectos ipſi A h, eſſe lineam horizontalem. </s>
  <s xml:id="echoid-s26146" xml:space="preserve">Nam ſi triangulum B C D, <lb/>circa B D, moueri intelligatur, donec rectum fiat ad planum horologii, erit per defin. </s>
  <s xml:id="echoid-s26147" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26148" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26149" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s26150" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s26151" xml:space="preserve">B C, ad planum horologii perpendicularis. </s>
  <s xml:id="echoid-s26152" xml:space="preserve">Si igitur &amp; </s>
  <s xml:id="echoid-s26153" xml:space="preserve">ſtylus K I, concipiatur rectus ad idẽ <lb/>planum horologii, erunt inter ſe æquidiſtantes recta B C, &amp; </s>
  <s xml:id="echoid-s26154" xml:space="preserve">ſtylus K I. </s>
  <s xml:id="echoid-s26155" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s26156" xml:space="preserve">recta connectẽs <lb/>
<anchor type="note" xlink:label="note-0414-05a" xlink:href="note-0414-05"/>
puncta C, I, in ſublimi exiſtentia parallela erit ipſi B K, &amp; </s>
  <s xml:id="echoid-s26157" xml:space="preserve">æqualis. </s>
  <s xml:id="echoid-s26158" xml:space="preserve">Quoniam uerò Horizon pla-<lb/>
<anchor type="note" xlink:label="note-0414-06a" xlink:href="note-0414-06"/>
num horologii ſecat per rectam lineã perpendicularem ad A h, ut in ſcholio præcedentis propoſ. <lb/></s>
  <s xml:id="echoid-s26159" xml:space="preserve">oſtendimus, cum de collocatione horologii ageremus, erit hæc communis ſectio ipſi K B, paralle-<lb/>
<anchor type="note" xlink:label="note-0414-07a" xlink:href="note-0414-07"/>
la. </s>
  <s xml:id="echoid-s26160" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s26161" xml:space="preserve">ducta C I, eidem B K, parallela ſit oſtenſa, erunt quoque communis ſectio plani <lb/>horologii, &amp; </s>
  <s xml:id="echoid-s26162" xml:space="preserve">Horizontis, ac recta C I, parallelæ inter ſe; </s>
  <s xml:id="echoid-s26163" xml:space="preserve">ac proinde in eodem exiſtent plano, per <lb/>
<anchor type="note" xlink:label="note-0414-08a" xlink:href="note-0414-08"/>
<anchor type="note" xlink:label="note-0414-09a" xlink:href="note-0414-09"/>
defin. </s>
  <s xml:id="echoid-s26164" xml:space="preserve">parallelarum. </s>
  <s xml:id="echoid-s26165" xml:space="preserve">Quare cum Horizon per communem illam ſectionem ductus tranſeat per I, <lb/>verticẽ ſtyli, ſeu centrum mundi, tranſibit quoque idem per rectam I C, atque adeo per punctum <lb/>C. </s>
  <s xml:id="echoid-s26166" xml:space="preserve">Quapropter cum angulus B C D, complemento inclinationis plani ad Horizontem ſit factus <lb/>æqualis, &amp; </s>
  <s xml:id="echoid-s26167" xml:space="preserve">ob id B D C, angulus ſit ipſius inclinationis, incedet Horizon per rectam C D; </s>
  <s xml:id="echoid-s26168" xml:space="preserve">quã-<lb/>doquidem hac ratione plano inclinato occurrit ſecundum angulum inclinationis B D C, ita ut <lb/>C D, communis ſectio ſit Horizontis, &amp; </s>
  <s xml:id="echoid-s26169" xml:space="preserve">trianguli B C D. </s>
  <s xml:id="echoid-s26170" xml:space="preserve">Quamobrem Horizon plano horologii <lb/>occurret in puncto D. </s>
  <s xml:id="echoid-s26171" xml:space="preserve">Cum ergo, ut ante demonſtrauimus, communis ipſius, &amp; </s>
  <s xml:id="echoid-s26172" xml:space="preserve">plani horologii <lb/>ſectio perpendiculatis ſit ad rectam A h, perſpicuum eſt, perpendicularem ad A h, per D, ductã <lb/>eſſe lineam horizontalem. </s>
  <s xml:id="echoid-s26173" xml:space="preserve">Tranſibit autem omnino horizontalis linea per D, ducta, per horam 6. <lb/></s>
  <s xml:id="echoid-s26174" xml:space="preserve">in linea æquinoctiali, ſi erratum non fuerit in deſcriptione.</s>
  <s xml:id="echoid-s26175" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1324" type="float" level="2" n="8">
<note position="left" xlink:label="note-0414-03" xlink:href="note-0414-03a" xml:space="preserve">Alia deſcriptio <lb/>lineæ horizon-<lb/>talis.</note>
<note position="left" xlink:label="note-0414-04" xlink:href="note-0414-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0414-05" xlink:href="note-0414-05a" xml:space="preserve">6. vndec.</note>
<note position="left" xlink:label="note-0414-06" xlink:href="note-0414-06a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0414-07" xlink:href="note-0414-07a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0414-08" xlink:href="note-0414-08a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0414-09" xlink:href="note-0414-09a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s26176" xml:space="preserve">ITEM alia adhuc uia horizontalem lineam deſcribemus. </s>
  <s xml:id="echoid-s26177" xml:space="preserve">Ex figura radiorum Zodiaci inue-<lb/>
<anchor type="note" xlink:label="note-0414-11a" xlink:href="note-0414-11"/>
niatur in portione lineæ meridianæ horologii, quæ ad mediam noctem ſpectat, hoc eſt, quæ me-<lb/>diam noctem, uel horam 12. </s>
  <s xml:id="echoid-s26178" xml:space="preserve">poſt meridiem indicat, punctum E, per quod arcus diurnus horarum <lb/>24. </s>
  <s xml:id="echoid-s26179" xml:space="preserve">ducendus eſt: </s>
  <s xml:id="echoid-s26180" xml:space="preserve">uel in portione eiuſdem meridianæ lineæ ad meridiem ſpectantis, hoc eſt, quæ <lb/>meridiem, ſeu horã 12. </s>
  <s xml:id="echoid-s26181" xml:space="preserve">poſt mediam noctem oſtendit; </s>
  <s xml:id="echoid-s26182" xml:space="preserve">reperiatur punctum E, arcus diurni hora-<lb/>rum 0. </s>
  <s xml:id="echoid-s26183" xml:space="preserve">uel arcus nocturni horarum 24. </s>
  <s xml:id="echoid-s26184" xml:space="preserve">quia aliquando arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s26185" xml:space="preserve">non ſecat <lb/>portionem lineæ meridianæ ad mediam noctem pertinentem, ſed arcus nocturnus horarum 24. <lb/></s>
  <s xml:id="echoid-s26186" xml:space="preserve">eam portionem lineæ meridianæ interſecat, quæ ad meridiem ſpectat. </s>
  <s xml:id="echoid-s26187" xml:space="preserve">Per punctum enim E, du-<lb/>cenda erit horizontalis linea, cum Sol oriatur hora 12. </s>
  <s xml:id="echoid-s26188" xml:space="preserve">poſt meridiem, die continente horas 24. </s>
  <s xml:id="echoid-s26189" xml:space="preserve"><lb/>uel hora 12. </s>
  <s xml:id="echoid-s26190" xml:space="preserve">poſt mediam noctem, die continente horas 0. </s>
  <s xml:id="echoid-s26191" xml:space="preserve">uel quando nox horas 24. </s>
  <s xml:id="echoid-s26192" xml:space="preserve">compre-<lb/>hendit, ut ex tabulis arcus diurni horarum 24. </s>
  <s xml:id="echoid-s26193" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26194" xml:space="preserve">arcus nocturni horarum 24. </s>
  <s xml:id="echoid-s26195" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s26196" xml:space="preserve">33. </s>
  <s xml:id="echoid-s26197" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26198" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26199" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0414-12a" xlink:href="note-0414-12"/>
perſpicuum eſt. </s>
  <s xml:id="echoid-s26200" xml:space="preserve">Eadem ratione ſi in linea horæ 5. </s>
  <s xml:id="echoid-s26201" xml:space="preserve">poſt mediam noctem inueniatur punctum <lb/>F, arcus diurni horarum 14. </s>
  <s xml:id="echoid-s26202" xml:space="preserve">uel in linea horæ 7. </s>
  <s xml:id="echoid-s26203" xml:space="preserve">a media nocte, punctum F, arcus diurni ho-<lb/>rarum 10. </s>
  <s xml:id="echoid-s26204" xml:space="preserve">habebimus quoque punctum F, per quod linea horizontalis ducenda eſt, ut patet. </s>
  <s xml:id="echoid-s26205" xml:space="preserve">Ita-<lb/>que cum minimum quatuor puncta habebimus, per quæ horizontalis linea duci debet, nempa<unsure/> <lb/>D, E, F, &amp; </s>
  <s xml:id="echoid-s26206" xml:space="preserve">punctum horæ 6. </s>
  <s xml:id="echoid-s26207" xml:space="preserve">in linea æquinoctiali. </s>
  <s xml:id="echoid-s26208" xml:space="preserve">Eodem pacto tranſibit linea horizontalis per <lb/>punctum arcus diurni horarum 10. </s>
  <s xml:id="echoid-s26209" xml:space="preserve">ubi a linea horæ 5. </s>
  <s xml:id="echoid-s26210" xml:space="preserve">a meridie ſecatur: </s>
  <s xml:id="echoid-s26211" xml:space="preserve">Item per punctum ar-<lb/>
<anchor type="note" xlink:label="note-0414-13a" xlink:href="note-0414-13"/>
cus diurni horarum 14. </s>
  <s xml:id="echoid-s26212" xml:space="preserve">ubi a linea horæ 7. </s>
  <s xml:id="echoid-s26213" xml:space="preserve">à meridie ſecatur.</s>
  <s xml:id="echoid-s26214" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1325" type="float" level="2" n="9">
<note position="left" xlink:label="note-0414-11" xlink:href="note-0414-11a" xml:space="preserve">Alia deſcriptio <lb/>eiuſdem lineæ <lb/>horizontalis.</note>
<note position="left" xlink:label="note-0414-12" xlink:href="note-0414-12a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0414-13" xlink:href="note-0414-13a" xml:space="preserve">Horizontalis li <lb/>nea partitur ho <lb/>rologium in <lb/>Superius, Infe-<lb/>riusq́ue, &amp; in <lb/>Diurnum, no-<lb/>cturnumque.</note>
</div>
<p>
  <s xml:id="echoid-s26215" xml:space="preserve">CÆTERVM linea horizontalis totum horologium hactenus deſcriptum diuidit, ut &amp; </s>
  <s xml:id="echoid-s26216" xml:space="preserve">in <lb/>præcedentibus dictum eſt, in ſuperius &amp; </s>
  <s xml:id="echoid-s26217" xml:space="preserve">inferius, quorum ſuperius eſt pars illa, quæ infra lineã <lb/>horizontalem continetur: </s>
  <s xml:id="echoid-s26218" xml:space="preserve">Reliqua autem pars dabit inferius, ſi tamen memor ſis, omnia debere
<pb o="399" file="0415" n="415" rhead="LIBER TERTIVS."/>
inuerti, &amp; </s>
  <s xml:id="echoid-s26219" xml:space="preserve">horas, quę prius à media nocte computabãtur, à meridie numerãdas eſſe, ut in propoſ. <lb/></s>
  <s xml:id="echoid-s26220" xml:space="preserve">13. </s>
  <s xml:id="echoid-s26221" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26222" xml:space="preserve">14. </s>
  <s xml:id="echoid-s26223" xml:space="preserve">pręcedentis libri oſtendimus. </s>
  <s xml:id="echoid-s26224" xml:space="preserve">Item eadem horizontalis linea dirimit totum horologiũ <lb/>in diurnum, atque nocturnum, ut ex eadem propoſ. </s>
  <s xml:id="echoid-s26225" xml:space="preserve">14. </s>
  <s xml:id="echoid-s26226" xml:space="preserve">præcedentis lib perſpicuum eſt. </s>
  <s xml:id="echoid-s26227" xml:space="preserve">Itaque <lb/>parallelos, ſiue arcus ſignorum Zodiaci, &amp; </s>
  <s xml:id="echoid-s26228" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26229" xml:space="preserve">depinximus. </s>
  <s xml:id="echoid-s26230" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s26231" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1327" type="section" level="1" n="319">
<head xml:id="echoid-head330" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s26232" xml:space="preserve">QVI arcus in horol gio ad ſigna borealia pertineant, &amp; </s>
  <s xml:id="echoid-s26233" xml:space="preserve">qui ad auſtralia, non difficile erit iudicare, <lb/>
<anchor type="note" xlink:label="note-0415-01a" xlink:href="note-0415-01"/>
ſi quatuor illa Analemmata, quæ in propoſ. </s>
  <s xml:id="echoid-s26234" xml:space="preserve">25. </s>
  <s xml:id="echoid-s26235" xml:space="preserve">hui{us} libri deſcripſim{us}, attentè conſiderentur. </s>
  <s xml:id="echoid-s26236" xml:space="preserve">Nam <lb/>in horologĳs, quæ ad meridiem, &amp; </s>
  <s xml:id="echoid-s26237" xml:space="preserve">ad verticem, ſeu polum Horizontis ſpectant, ſi quidem centrum ho-<lb/>
<anchor type="note" xlink:label="note-0415-02a" xlink:href="note-0415-02"/>
rologĳ fuerit infra lineam æquinoctialem, continentur arcus ſignorum borealium inter centrũ, &amp; </s>
  <s xml:id="echoid-s26238" xml:space="preserve">æqui-<lb/>noctialem lineam, vt ex primo Analemmate dictæ propoſ. </s>
  <s xml:id="echoid-s26239" xml:space="preserve">conſtat; </s>
  <s xml:id="echoid-s26240" xml:space="preserve">quia puncta quadrantis borealis <lb/>H F, proĳ ciunt in meridie vmbras in portionem meridianæ lineæ M N, inter centrum M, &amp; </s>
  <s xml:id="echoid-s26241" xml:space="preserve">punctum <lb/>N, per quod æquinoctialis linea ducitur: </s>
  <s xml:id="echoid-s26242" xml:space="preserve">Si verò horologĳ centrum ſupra lineam æquinoctialem exti-<lb/>terit, arcus auſtralium ſignorum inter centrum, &amp; </s>
  <s xml:id="echoid-s26243" xml:space="preserve">æquinoctialem lineam comprehenduntur, vt ex ſe-<lb/>cundo Analemmate manifeſtum eſt; </s>
  <s xml:id="echoid-s26244" xml:space="preserve">quoniam puncta quadrantis auſtralis G H, proĳciunt in meridie <lb/>vmbras in portionem lineæ meridianæ M N, inter centrum M, &amp; </s>
  <s xml:id="echoid-s26245" xml:space="preserve">lineam æquinoctialem, quæ per N, du <lb/>citur. </s>
  <s xml:id="echoid-s26246" xml:space="preserve">Quòd ſi horologium centro careat, pertinebunt arcus infr a æquinoctialom lineam ad ſigna borea-<lb/>lia, vt perſpicuum eſt ex primo Analemmate, ſi duceretur infra E, linea parallela axi F G, quæ commu <lb/>nis ſectio eſſet Meridiani, ac plani horologĳ. </s>
  <s xml:id="echoid-s26247" xml:space="preserve">Nam tunc puncta quadrantis borealis H F, proĳcerent <lb/>
<anchor type="note" xlink:label="note-0415-03a" xlink:href="note-0415-03"/>
vmbras in meridie in portionem lineæ meridianæ infra punctum, per quod linea æquinoctialis eſſet ducẽ-<lb/>da. </s>
  <s xml:id="echoid-s26248" xml:space="preserve">At verò in horologĳs, quæ ad ſeptentrionem, &amp; </s>
  <s xml:id="echoid-s26249" xml:space="preserve">ad verticem pertinent, vbicunque centrum horolo-<lb/>gĳ exiſtat, perpetuo arcus ſignorum borealium inter centrum, &amp; </s>
  <s xml:id="echoid-s26250" xml:space="preserve">æquinoctialem lineam continentur. </s>
  <s xml:id="echoid-s26251" xml:space="preserve">Id <lb/>quod ex poſteriorib{us} duob{us} Analemmatib{us} liquido conſtat. </s>
  <s xml:id="echoid-s26252" xml:space="preserve">In tertio enim puncta quadrantis borea <lb/>lis H F, vmbr{as} ſu{as} proĳciunt in portionem meridianæ lineæ M N, inter cẽtrum M, &amp; </s>
  <s xml:id="echoid-s26253" xml:space="preserve">punctum N, <lb/>lineæ æquinoctialis: </s>
  <s xml:id="echoid-s26254" xml:space="preserve">Idem{q́ue} cernitur in quadrante boreali F I, quarti Analemmatis, vbi in media no-<lb/>cte proĳciuntur vmbræ in portionem lineæ meridianæ M N, inter centrum &amp; </s>
  <s xml:id="echoid-s26255" xml:space="preserve">lineam æquinoctialem: <lb/></s>
  <s xml:id="echoid-s26256" xml:space="preserve">Neque obſtat, quòd aliquando puncta quædam ſemicirculi borealis H F I, in vtroque Analemmate po-<lb/>ſteriori proĳciant quoque vmbr{as} ſu{as} vltra centrum M, vt in quadrante F H, quarti Analemmatis <lb/>contingit, quia tunc arc{us} ſignorum ſunt Ellipſes, ita vt ſinguli in duob{us} punctis meridianam lineam ſe <lb/>
<anchor type="note" xlink:label="note-0415-04a" xlink:href="note-0415-04"/>
cent, quorum vnum neceſſario inter centrum, &amp; </s>
  <s xml:id="echoid-s26257" xml:space="preserve">æquinoctialem lineam exiſtit; </s>
  <s xml:id="echoid-s26258" xml:space="preserve">adeò vt verum ſemper <lb/>ſit, arc{us} contentos inter centrum, &amp; </s>
  <s xml:id="echoid-s26259" xml:space="preserve">æquinoctialem lineam pertinere ad ſigna borealia. </s>
  <s xml:id="echoid-s26260" xml:space="preserve">Quòd ſi horolo <lb/>gium it a ex parte auſtrali eleuatum ſit, vt arc{us} Meridiani inter ipſum, &amp; </s>
  <s xml:id="echoid-s26261" xml:space="preserve">Horizontem ęqualis ſit al-<lb/>titudini Aequatoris, ſeu complemento altitudinis poli, ac proinde linea meridiana M N, diametro Ae-<lb/>quatoris H I, ęquidiſtet, perſpicuum quoque eſt, tunc arc{us} ſignorum prope centrum pertinere ad bo-<lb/>realia ſigna, propterea quòd vmbræ punctorum ſemicirculi borealis H F I, cadunt in meridianam lineã, <lb/>in cui{us} medio centrum M, existit, vt patet.</s>
  <s xml:id="echoid-s26262" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1327" type="float" level="2" n="1">
<note position="right" xlink:label="note-0415-01" xlink:href="note-0415-01a" xml:space="preserve">Qui arcus ad <lb/>ſigna borealia, <lb/>&amp; qui ad au-<lb/>ſtralia peru-<lb/>neant.</note>
<note position="left" xlink:label="note-0415-02" xlink:href="note-0415-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0415-03" xlink:href="note-0415-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0415-04" xlink:href="note-0415-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s26263" xml:space="preserve">IN horologĳs, quæ ad Nadir ſpectant, hoc eſt, in Inferiorib{us}, contrarium prorſ{us} intelligendum <lb/>eſt, vt eadem quatuor Analemmata demonſtrant.</s>
  <s xml:id="echoid-s26264" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s26265" xml:space="preserve">RVRSVS arcus ſignorum in illis horologĳs, in quib{us} horariæ lineæ parallelæ ſunt, cuiuſmodi est <lb/>
<anchor type="note" xlink:label="note-0415-05a" xlink:href="note-0415-05"/>
<anchor type="note" xlink:label="note-0415-06a" xlink:href="note-0415-06"/>
horologium tertium præcedenti propoſ. </s>
  <s xml:id="echoid-s26266" xml:space="preserve">deſcriptum, omnes ſunt hyperbolæ, quemadmodum in Polari ho <lb/>rologio, vt ad propoſ. </s>
  <s xml:id="echoid-s26267" xml:space="preserve">38. </s>
  <s xml:id="echoid-s26268" xml:space="preserve">præcedentis libri dictum est. </s>
  <s xml:id="echoid-s26269" xml:space="preserve">Eadem enim hic eſt ratio. </s>
  <s xml:id="echoid-s26270" xml:space="preserve">In alĳs autem iudica <lb/>bim{us}, vt in propoſ. </s>
  <s xml:id="echoid-s26271" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26272" xml:space="preserve">eiuſdem libri tradidim{us}, quinam arc{us} ſint hyperbolæ, qui parabolæ, &amp; </s>
  <s xml:id="echoid-s26273" xml:space="preserve">qui El-<lb/>lipſes. </s>
  <s xml:id="echoid-s26274" xml:space="preserve">Vel certè idem ex propoſ. </s>
  <s xml:id="echoid-s26275" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26276" xml:space="preserve">5. </s>
  <s xml:id="echoid-s26277" xml:space="preserve">6. </s>
  <s xml:id="echoid-s26278" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26279" xml:space="preserve">7. </s>
  <s xml:id="echoid-s26280" xml:space="preserve">primi libri petatur.</s>
  <s xml:id="echoid-s26281" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1328" type="float" level="2" n="2">
<note position="left" xlink:label="note-0415-05" xlink:href="note-0415-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0415-06" xlink:href="note-0415-06a" xml:space="preserve">Qui arcus R-<lb/>gnorũ ſint hy-<lb/>perbolæ, &amp; qui <lb/>parabolæ, vel <lb/>Ellipſes.</note>
</div>
<p style="it">
  <s xml:id="echoid-s26282" xml:space="preserve">QVOD ſi ex figura radiorum Zodiaci maius, aut minus horologium deſcribendum ſit, pro datalon <lb/>
<anchor type="note" xlink:label="note-0415-07a" xlink:href="note-0415-07"/>
gitudine gnomonis, fiet id hoc modo. </s>
  <s xml:id="echoid-s26283" xml:space="preserve">Deſcribatur ſeorſum, veluti iuxta figuram radiorum huius propoſ. <lb/></s>
  <s xml:id="echoid-s26284" xml:space="preserve">factum eſt, triangulum ρ I G, ex horologio, quod in propoſ. </s>
  <s xml:id="echoid-s26285" xml:space="preserve">præcedenti conſtruximus, vel ex ipſa figura <lb/>radiorum deſumptum, in quo axis mundi eſt ρ I; </s>
  <s xml:id="echoid-s26286" xml:space="preserve">Aequator I G; </s>
  <s xml:id="echoid-s26287" xml:space="preserve">linea styli, in quam gnomon I K, ad an-<lb/>gulos rectos cadit ρ G. </s>
  <s xml:id="echoid-s26288" xml:space="preserve">Deinde productis rectis I ρ, I G, I K, ſi ſumatur in I K, recta I A, dato gno-<lb/>moni æqualis, ſiue is maior existat ſtylo I K, ſiue minor, &amp; </s>
  <s xml:id="echoid-s26289" xml:space="preserve">per A, ipſi ρ G, parallela agatur B D, erit <lb/>triangulum B I D, triangulo ρ I G, per coroll. </s>
  <s xml:id="echoid-s26290" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s26291" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26292" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26293" xml:space="preserve">6. </s>
  <s xml:id="echoid-s26294" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s26295" xml:space="preserve">ſimile. </s>
  <s xml:id="echoid-s26296" xml:space="preserve">Itaque ſi axis I B, transſera-<lb/>
<anchor type="note" xlink:label="note-0415-08a" xlink:href="note-0415-08"/>
tur in figuram radiorum ex ρ, vſque ad B, verſus I, &amp; </s>
  <s xml:id="echoid-s26297" xml:space="preserve">reliqua fiant, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s26298" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26299" xml:space="preserve">huius libri <lb/>præcepimus, mutando ſemper literam C, ibi poſitam in literam ρ, hic notatam, deſcribentur arcus ſigno <lb/>rum pro magnitudine ſtyli dati I A, &amp; </s>
  <s xml:id="echoid-s26300" xml:space="preserve">c.</s>
  <s xml:id="echoid-s26301" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1329" type="float" level="2" n="3">
<note position="right" xlink:label="note-0415-07" xlink:href="note-0415-07a" xml:space="preserve">Qua ratione ex <lb/>figura radiorũ <lb/>ad datam ſtyli <lb/>longitudinem <lb/>maius au mi-<lb/>nus horologiũ <lb/>deſcribatur.</note>
<note position="left" xlink:label="note-0415-08" xlink:href="note-0415-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1331" type="section" level="1" n="320">
<head xml:id="echoid-head331" xml:space="preserve">PROBLEMA 39. PROPOSITIQ 39.</head>
<p>
  <s xml:id="echoid-s26302" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio de-<lb/>clinante ſimul &amp; </s>
  <s xml:id="echoid-s26303" xml:space="preserve">inclinato delineare.</s>
  <s xml:id="echoid-s26304" xml:space="preserve"/>
</p>
<pb o="400" file="0416" n="416" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s26305" xml:space="preserve">SÆPIVS iam in præcedentibus declaratũ eſt, nulla in re deſcriptionem arcuum diurnorũ in <lb/>
<anchor type="note" xlink:label="note-0416-01a" xlink:href="note-0416-01"/>
quouis horologio a deſcriptione parallelorum ſignorum Zodiaci differre, ſi loco radiorum pa-<lb/>rallelorum Zodiaci accipiantur radii parallelorum arcuum diurnorum. </s>
  <s xml:id="echoid-s26306" xml:space="preserve">Vnde ſuperuacaneum e-<lb/>rit, noua hoc loco pręcepta tradere, cum ea, quæ in propoſ. </s>
  <s xml:id="echoid-s26307" xml:space="preserve">præcedenti ſcripſimus, ſufficiant. </s>
  <s xml:id="echoid-s26308" xml:space="preserve">Pa-<lb/>rallelos igitur arcuum diurnorum in eodem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26309" xml:space="preserve">inclinato delineaui-<lb/>mus. </s>
  <s xml:id="echoid-s26310" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s26311" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1331" type="float" level="2" n="1">
<note position="left" xlink:label="note-0416-01" xlink:href="note-0416-01a" xml:space="preserve">Areus diurni <lb/>quomodo de-<lb/>ſcribantur in <lb/>eodem horolo-<lb/>gio.</note>
</div>
</div>
<div xml:id="echoid-div1333" type="section" level="1" n="321">
<head xml:id="echoid-head332" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s26312" xml:space="preserve">SI hic repetantur ea, quę in ſcholio propoſ. </s>
  <s xml:id="echoid-s26313" xml:space="preserve">3. </s>
  <s xml:id="echoid-s26314" xml:space="preserve">huius libri tradidimus, facile deſcribere poterimus li-<lb/>neas illas horarias, quæ vix, aut nullo modo æquinoctialem lineam interſecant.</s>
  <s xml:id="echoid-s26315" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1334" type="section" level="1" n="322">
<head xml:id="echoid-head333" xml:space="preserve">PROBLEMA 40. PROPOSITIO 40.</head>
<p>
  <s xml:id="echoid-s26316" xml:space="preserve">CIRCVLOS Verticales in eodem horologio declinante ſimul <lb/>&amp; </s>
  <s xml:id="echoid-s26317" xml:space="preserve">inclinato ſtatuere.</s>
  <s xml:id="echoid-s26318" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s26319" xml:space="preserve">EXLOGO ſtyli K, ducta ad horizontalem lineam perpendiculari K B, ad quam excitetur a-<lb/>
<anchor type="note" xlink:label="note-0416-03a" xlink:href="note-0416-03"/>
<anchor type="figure" xlink:label="fig-0416-01a" xlink:href="fig-0416-01"/>
<anchor type="note" xlink:label="note-0416-04a" xlink:href="note-0416-04"/>
<anchor type="note" xlink:label="note-0416-05a" xlink:href="note-0416-05"/>
<anchor type="note" xlink:label="note-0416-06a" xlink:href="note-0416-06"/>
<anchor type="note" xlink:label="note-0416-07a" xlink:href="note-0416-07"/>
lia perpendicularis K A, ſtylo K I, æqualis, ductaq́ue recta A B, ſumatur ei æqualis B D, in recta <lb/>K B, producta: </s>
  <s xml:id="echoid-s26320" xml:space="preserve">centro autem D, circulus deſcribatur, qui in 360. </s>
  <s xml:id="echoid-s26321" xml:space="preserve">partes æquales ſecetur, uel in
<pb o="401" file="0417" n="417" rhead="LIBER TERTIVS."/>
pauciores, ut in præcedentibus diximus, initio facto à recta D E, ducta ex centro D, ad punctum <lb/>E, ubi linea æquinoctialis, horizõtalis, &amp; </s>
  <s xml:id="echoid-s26322" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s26323" xml:space="preserve">ſe interſecãt. </s>
  <s xml:id="echoid-s26324" xml:space="preserve">Nam rectæ occultæ ex D, per <lb/>diuiſionum puncta emiſſę ſecabunt lineam horizontalem in punctis, quæ ſi cõnectantur rectis li-<lb/>neis cum puncto C, ubi recta B K, meridianam lineam ſecat, deſcripti erunt Verticales circuli, <lb/>id eſt, communes ipſorum, &amp; </s>
  <s xml:id="echoid-s26325" xml:space="preserve">plani horologii ſectiones, ita ut C E, communis ſectio ſit plani ho-<lb/>rologii, &amp; </s>
  <s xml:id="echoid-s26326" xml:space="preserve">Verticalis circuli proprie dicti. </s>
  <s xml:id="echoid-s26327" xml:space="preserve">Quod ita demonſtrabimus.</s>
  <s xml:id="echoid-s26328" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1334" type="float" level="2" n="1">
<note position="left" xlink:label="note-0416-03" xlink:href="note-0416-03a" xml:space="preserve">Verticaliũ eir-<lb/>culorum in eo-<lb/>dem horologio <lb/>deſcriptio.</note>
  <figure xlink:label="fig-0416-01" xlink:href="fig-0416-01a">
    <image file="0416-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0416-01"/>
  </figure>
<note position="left" xlink:label="note-0416-04" xlink:href="note-0416-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0416-05" xlink:href="note-0416-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0416-06" xlink:href="note-0416-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0416-07" xlink:href="note-0416-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s26329" xml:space="preserve">INTELLIGATVR triangulum A B K, moueri circa B K, donec rectum ſit ad horologij <lb/>
<anchor type="note" xlink:label="note-0417-01a" xlink:href="note-0417-01"/>
planum, atque adeò punctum A, cum vertice ſtvli, ſeu centro mundi I, coniungatur, &amp; </s>
  <s xml:id="echoid-s26330" xml:space="preserve">ipſum <lb/>triangulum cum plano Verticalis circuli, quiad planum horologij rectus eſt, duciturq́ue per ſty-<lb/>lum ipſum, &amp; </s>
  <s xml:id="echoid-s26331" xml:space="preserve">inclinationem plani ſupra Horizontem metitur, ita ut recta B K, communis ſe-<lb/>
<anchor type="note" xlink:label="note-0417-02a" xlink:href="note-0417-02"/>
ctio ſit huius Verticalis, &amp; </s>
  <s xml:id="echoid-s26332" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s26333" xml:space="preserve">Quoniam igitur &amp; </s>
  <s xml:id="echoid-s26334" xml:space="preserve">meridiana linea communis ſe-<lb/>ctio eſt eiuſdem plani horologii, ac Meridiani, qui unus quoque eſt ex circulis Verticalibus, con-<lb/>uenient neceſſario meridiana linea, &amp; </s>
  <s xml:id="echoid-s26335" xml:space="preserve">B K, in eo puncto, in quod cadit communis ſectio om-<lb/>nium Verticalium, hoc eſt, axis Horizontis, ut ex propoſ. </s>
  <s xml:id="echoid-s26336" xml:space="preserve">18. </s>
  <s xml:id="echoid-s26337" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26338" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26339" xml:space="preserve">perſpicuum eſt. </s>
  <s xml:id="echoid-s26340" xml:space="preserve">Conue-<lb/>
<anchor type="note" xlink:label="note-0417-03a" xlink:href="note-0417-03"/>
niuntautem in C. </s>
  <s xml:id="echoid-s26341" xml:space="preserve">Igitur C, punctũ erit Verticale, in quo omnes lineæ Verticales coeunt. </s>
  <s xml:id="echoid-s26342" xml:space="preserve">Et quia, <lb/>ut in propoſ. </s>
  <s xml:id="echoid-s26343" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26344" xml:space="preserve">huius libri ſcripſimus, cõmunis ſectio plani horologij cuiuſcunque, &amp; </s>
  <s xml:id="echoid-s26345" xml:space="preserve">Verticalis <lb/>circuli proprie dicti tranſit per punctũ E, ubi ſe mutuo interſecant linea æquinoctialis, horizonta-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s26346" xml:space="preserve">linea horæ 6. </s>
  <s xml:id="echoid-s26347" xml:space="preserve">erit recta C E, communis ſectio Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s26348" xml:space="preserve">plani horologii. <lb/></s>
  <s xml:id="echoid-s26349" xml:space="preserve">Rurſus quia manente triangulo A B K, ad horologij planum recto, recta A B, communis ſectio <lb/>eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s26350" xml:space="preserve">dicti trianguli, ſeu Verticalis facientis ſectionem B K, quòd Horizon, &amp; </s>
  <s xml:id="echoid-s26351" xml:space="preserve">per <lb/>
<anchor type="note" xlink:label="note-0417-04a" xlink:href="note-0417-04"/>
verticem ſtyli A, &amp; </s>
  <s xml:id="echoid-s26352" xml:space="preserve">per punctũ B, tranſeat; </s>
  <s xml:id="echoid-s26353" xml:space="preserve">ſi circulus ex D, deſcriptus concipiatur animo moueri <lb/>circa horizontalem lineam, donec cius centrum D, cum puncto A, coniungatur, &amp; </s>
  <s xml:id="echoid-s26354" xml:space="preserve">recta D B, cũ <lb/>recta A B, ob æqualitatem rectarum D B, A B, atque adeo circulus ipſe in plano Horizontis circa <lb/>centrum mundi ſit deſcriptus, erit recta D E, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s26355" xml:space="preserve">Verticalis proprie <lb/>dicti, cum Verticalis per centrum mundi, quod idem tunc eſt quod D, ac per punctum E, ut di-<lb/>ximus, ducatur. </s>
  <s xml:id="echoid-s26356" xml:space="preserve">Recta autem D F, ducta ex D, ad punctum F, ubi meridiana linea horizontalem <lb/>ſecat, communis ſectio erit Horizontis, ac Meridiani; </s>
  <s xml:id="echoid-s26357" xml:space="preserve">quandoquidem Meridianus &amp; </s>
  <s xml:id="echoid-s26358" xml:space="preserve">per centrũ <lb/>mundi D, &amp; </s>
  <s xml:id="echoid-s26359" xml:space="preserve">per punctum F, in horologio incedit. </s>
  <s xml:id="echoid-s26360" xml:space="preserve">Ex quo fit angulum E D F, rectum eſſe, cum <lb/>Meridianus, &amp; </s>
  <s xml:id="echoid-s26361" xml:space="preserve">Verticalis proprie dictus ſe mutuò in mundi centro ad angulos rectos ſecent. </s>
  <s xml:id="echoid-s26362" xml:space="preserve">Ita-<lb/>que cum diuiſio circuli à recta D E, principium habeat, erunt reliquæ occultæ ex D, per di-<lb/>
<anchor type="note" xlink:label="note-0417-05a" xlink:href="note-0417-05"/>
uiſionum puncta emiſlæ, communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s26363" xml:space="preserve">aliorum circulorum Verticalium. <lb/></s>
  <s xml:id="echoid-s26364" xml:space="preserve">Quare ubi horizontalem lineam diuident, per illa puncta ducendę erunt ex C, vertice commu-<lb/>nes ſectiones Verticalium circulorum, &amp; </s>
  <s xml:id="echoid-s26365" xml:space="preserve">plani horologij, cum in illis punctis lineæ horizontalis <lb/>omnes circuli Verticales plano horologij occurrant, itemq́ue omnes per Verticale punctum C, <lb/>ducantur, in quod cadit axis Horizontis, cuiuſmodi eſt ducta recta A C, quippe quæ ſit commu-<lb/>nis omnium Verticalium circulorum ſectio, quandoquidem omnes, &amp; </s>
  <s xml:id="echoid-s26366" xml:space="preserve">per centrum mundi A, &amp; </s>
  <s xml:id="echoid-s26367" xml:space="preserve"><lb/>per Verticale punctum C, ducuntur. </s>
  <s xml:id="echoid-s26368" xml:space="preserve">Vnde niſi erratum fuerit, neceſſe eſt angulum B A C, eſſe <lb/>rectum, &amp; </s>
  <s xml:id="echoid-s26369" xml:space="preserve">C A K, angulum inclinationis plani ad Horizontem, &amp; </s>
  <s xml:id="echoid-s26370" xml:space="preserve">A C K, angulum complemẽ-<lb/>ti inclinationis, quemadmodum &amp; </s>
  <s xml:id="echoid-s26371" xml:space="preserve">A B K, angulus eſt inclinationis, quem nimirum Horizon cũ <lb/>plano inclinato conſtituit, &amp; </s>
  <s xml:id="echoid-s26372" xml:space="preserve">B A K, angulus complementi inclinationis. </s>
  <s xml:id="echoid-s26373" xml:space="preserve">Quocirca inuenietur <lb/>
<anchor type="note" xlink:label="note-0417-06a" xlink:href="note-0417-06"/>
<anchor type="note" xlink:label="note-0417-07a" xlink:href="note-0417-07"/>
punctum Verticale, ſi in A, cum ſtylo conſtituatur angulus C A K, inclinationis plani ad Hori-<lb/>zontem, uel ſi ad A B, ducatur perpendicularis A C. </s>
  <s xml:id="echoid-s26374" xml:space="preserve">Recta enim A C, ſecabit meridianam lineam <lb/>in uertice C. </s>
  <s xml:id="echoid-s26375" xml:space="preserve">Numeri autem Verticaliũ linearum initium ſumunt à recta C E, progrediunturq́ue <lb/>in utráque partem, ita ut linea meridiana det nonageſimum Verticalem. </s>
  <s xml:id="echoid-s26376" xml:space="preserve">Circulos igitur Vertica-<lb/>les in eodem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26377" xml:space="preserve">inclinato ſtatuimus. </s>
  <s xml:id="echoid-s26378" xml:space="preserve">quod erat faciendum.</s>
  <s xml:id="echoid-s26379" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1335" type="float" level="2" n="2">
<note position="right" xlink:label="note-0417-01" xlink:href="note-0417-01a" xml:space="preserve">Demonſtratio <lb/>pr<unsure/>ædictæ deſcri <lb/>p<unsure/>tionis circulo <lb/>rum Vertica-<lb/>lium.</note>
<note position="left" xlink:label="note-0417-02" xlink:href="note-0417-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0417-03" xlink:href="note-0417-03a" xml:space="preserve">Verticale pun<unsure/>-<lb/>ctum quod ſi@.</note>
<note position="left" xlink:label="note-0417-04" xlink:href="note-0417-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0417-05" xlink:href="note-0417-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0417-06" xlink:href="note-0417-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0417-07" xlink:href="note-0417-07a" xml:space="preserve">Verticale pu@-<lb/>ctum qua ratio <lb/>ne inueniatur.</note>
</div>
</div>
<div xml:id="echoid-div1337" type="section" level="1" n="323">
<head xml:id="echoid-head334" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s26380" xml:space="preserve">IN nostro exẽplo Verticalis circul{us} gr. </s>
  <s xml:id="echoid-s26381" xml:space="preserve">60. </s>
  <s xml:id="echoid-s26382" xml:space="preserve">trãſit præcisè per K, locũ ſtyli, adeo vt eius ſectio, <lb/>quim in horologii plano facit, ſit recta C D: </s>
  <s xml:id="echoid-s26383" xml:space="preserve">quia Verticalis inclinationem plani ad Horizontem metiẽs <lb/>
<anchor type="note" xlink:label="note-0417-08a" xlink:href="note-0417-08"/>
diſcedit à Meridiano grad. </s>
  <s xml:id="echoid-s26384" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26385" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26386" xml:space="preserve">à Verticali proprie dicto grad. </s>
  <s xml:id="echoid-s26387" xml:space="preserve">60. </s>
  <s xml:id="echoid-s26388" xml:space="preserve">cum planum noſtri horologĳ defle-<lb/>ctere ponam{us} à Verticali grad. </s>
  <s xml:id="echoid-s26389" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26390" xml:space="preserve">Id quod etiam in propoſ. </s>
  <s xml:id="echoid-s26391" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26392" xml:space="preserve">hui{us} libri euenit.</s>
  <s xml:id="echoid-s26393" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1337" type="float" level="2" n="1">
<note position="left" xlink:label="note-0417-08" xlink:href="note-0417-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s26394" xml:space="preserve">ACCIDIT nonnunquam, rectas aliqu{as} occultas ex centro D, per diuiſionum puncta emiſſas <lb/>
<anchor type="note" xlink:label="note-0417-09a" xlink:href="note-0417-09"/>
vix, aut nullo modo horizontalem lineam interſecare, vt difficile admodum ſit Verticales lineas illis re-<lb/>ſpondentes ex vertice C, in horologio ſine errore deſcribere. </s>
  <s xml:id="echoid-s26395" xml:space="preserve">Id quod in nostro exemplo contingit in Ver <lb/>ticalib{us} lineis grad. </s>
  <s xml:id="echoid-s26396" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26397" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26398" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26399" xml:space="preserve">Vnde querenda erunt puncta in æquinoctiali linea, per quę Verticales <lb/>lineæ du<unsure/>cendę ſunt, quando punctis in linea horizontali deſtituimur, hoc modo. </s>
  <s xml:id="echoid-s26400" xml:space="preserve">Reperiatur hora, qua Sol <lb/>in Aequatore existens ad Verticalem illum circulum perueniat, cuius lineam ducere volumus. </s>
  <s xml:id="echoid-s26401" xml:space="preserve">Nam <lb/>vbi linea illi{us} horæ<unsure/> (quam quidem occultè ducem{us} ſecundum doctrinam propoſ. </s>
  <s xml:id="echoid-s26402" xml:space="preserve">37. </s>
  <s xml:id="echoid-s26403" xml:space="preserve">hui{us} lib.) </s>
  <s xml:id="echoid-s26404" xml:space="preserve">æquino-<lb/>ctialem lineam ſecabit, per illud punctum ex C, linea illa Verticalis ducenda erit. </s>
  <s xml:id="echoid-s26405" xml:space="preserve">Vt quoniam Sol in <lb/>Aequatore exiſtens peruenit ad Verticalem grad. </s>
  <s xml:id="echoid-s26406" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26407" xml:space="preserve">ex parte orientali hora 3. </s>
  <s xml:id="echoid-s26408" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26409" xml:space="preserve">17. </s>
  <s xml:id="echoid-s26410" xml:space="preserve">ante meri-
<pb o="402" file="0418" n="418" rhead="GNOMONICES"/>
diem, hoc eſt, hora S. </s>
  <s xml:id="echoid-s26411" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26412" xml:space="preserve">43. </s>
  <s xml:id="echoid-s26413" xml:space="preserve">poſt mediam noctem: </s>
  <s xml:id="echoid-s26414" xml:space="preserve">Linea autem hui{us} horæ ſecat lineam æquinoctia-<lb/>lem in G. </s>
  <s xml:id="echoid-s26415" xml:space="preserve">Igitur ducta recta C G, dabit Verticalem grad. </s>
  <s xml:id="echoid-s26416" xml:space="preserve">30 Sic quoque quoniam Sol in Aequatore <lb/>exiſtens attingit Verticalem grad. </s>
  <s xml:id="echoid-s26417" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26418" xml:space="preserve">hora 2. </s>
  <s xml:id="echoid-s26419" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26420" xml:space="preserve">15. </s>
  <s xml:id="echoid-s26421" xml:space="preserve">ante meridiem, hoc eſt, hora 9. </s>
  <s xml:id="echoid-s26422" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26423" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26424" xml:space="preserve">poſt <lb/>mediam noctem; </s>
  <s xml:id="echoid-s26425" xml:space="preserve">ſecat autem linea huius horæ æquinoctialem lineam in H, dabit recta ducta C H, Ver <lb/>ticalem grad. </s>
  <s xml:id="echoid-s26426" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26427" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26428" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s26429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1338" type="float" level="2" n="2">
<note position="right" xlink:label="note-0417-09" xlink:href="note-0417-09a" xml:space="preserve">Quo pacto Ver <lb/>ticales illæ li-<lb/>neæ ducendæ <lb/>ſint, quę vix, <lb/>aut nunquam <lb/>horizontalem <lb/>lineam interſe-<lb/>cant.</note>
</div>
<p style="it">
  <s xml:id="echoid-s26430" xml:space="preserve">IT Aautem horam, qua Sol Aequatorem percurrens ad propoſitum Verticalem perueniat, inquire <lb/>
<anchor type="note" xlink:label="note-0418-01a" xlink:href="note-0418-01"/>
mus. </s>
  <s xml:id="echoid-s26431" xml:space="preserve">Sit Horizon A B C D; </s>
  <s xml:id="echoid-s26432" xml:space="preserve">Meridianus A C; </s>
  <s xml:id="echoid-s26433" xml:space="preserve">Aequator B E D; </s>
  <s xml:id="echoid-s26434" xml:space="preserve">Verticalis propriè<unsure/> dictus B F D; </s>
  <s xml:id="echoid-s26435" xml:space="preserve">Ver <lb/>
<anchor type="figure" xlink:label="fig-0418-01a" xlink:href="fig-0418-01"/>
ticalis ali{us} quicunque F I H, ſecans Horizontem <lb/>in quarta orientali, &amp; </s>
  <s xml:id="echoid-s26436" xml:space="preserve">auſtrali A B, &amp; </s>
  <s xml:id="echoid-s26437" xml:space="preserve">Aequatorẽ <lb/>in I. </s>
  <s xml:id="echoid-s26438" xml:space="preserve">Quærendus igitur eſt arc{us} E I, in Aequatore. <lb/></s>
  <s xml:id="echoid-s26439" xml:space="preserve">
<anchor type="note" xlink:label="note-0418-02a" xlink:href="note-0418-02"/>
Quoniam in triangulo ſphærico E F I, angulus E, re-<lb/>ct{us} eſt, erit per propoſ. </s>
  <s xml:id="echoid-s26440" xml:space="preserve">18. </s>
  <s xml:id="echoid-s26441" xml:space="preserve">lib 4. </s>
  <s xml:id="echoid-s26442" xml:space="preserve">Ioan Regiom. </s>
  <s xml:id="echoid-s26443" xml:space="preserve">de <lb/>triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s26444" xml:space="preserve">14 lib. </s>
  <s xml:id="echoid-s26445" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26446" xml:space="preserve">Gebri, vel per <lb/>propoſ. </s>
  <s xml:id="echoid-s26447" xml:space="preserve">42. </s>
  <s xml:id="echoid-s26448" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt <lb/>ſinus anguli E F I, (qui notus eſt, cum eius arcus <lb/>A H, ſit complementum distantię Verticalis F H, <lb/>à Verticali propriè dicto F B,) ad ſinum totum, ita <lb/>ſin{us} complementi anguli E I F, ad ſinum comple-<lb/>menti arc{us} E F, altitudinis poli: </s>
  <s xml:id="echoid-s26449" xml:space="preserve">Et conuertendo, <lb/>vt ſinus totus ad ſinum anguli E F I, hoc eſt, ad ſi-<lb/>
<anchor type="note" xlink:label="note-0418-03a" xlink:href="note-0418-03"/>
num complementi diſtantiæ Verticalis propoſiti à <lb/>propriè dicto Verticali, ita ſinus complementi altitu <lb/>dinis poli ad ſinum complementi anguli E I F. </s>
  <s xml:id="echoid-s26450" xml:space="preserve">Qua-<lb/>ve angulus E I F, notus erit. </s>
  <s xml:id="echoid-s26451" xml:space="preserve">Quoniam verò rurſus eſt, per propoſ. </s>
  <s xml:id="echoid-s26452" xml:space="preserve">16. </s>
  <s xml:id="echoid-s26453" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26454" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26455" xml:space="preserve">Ioan Regiom. </s>
  <s xml:id="echoid-s26456" xml:space="preserve">de triangu-<lb/>lis, vel per propoſ. </s>
  <s xml:id="echoid-s26457" xml:space="preserve">13. </s>
  <s xml:id="echoid-s26458" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26459" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26460" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s26461" xml:space="preserve">41. </s>
  <s xml:id="echoid-s26462" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus <lb/>anguli E I F, proximè inuenti ad ſinum arcus E F, altitudinis poli, ita ſinus anguli E F I, complementi <lb/>distantiæ Verticalis propoſiti à Verticali propriè dicto ad ſinum arcus E I, distantię Solis à meridie: <lb/></s>
  <s xml:id="echoid-s26463" xml:space="preserve">Si fiat, vt ſinus tot{us} ad ſinum complementi diſtantiæ Verticalis propoſiti à propriè dicto Verticali, ita <lb/>ſinus complementi altitudinis poli ad aliud, reperietur ſinus, cui{us} arc{us} complementum ſeruetur. </s>
  <s xml:id="echoid-s26464" xml:space="preserve">Et <lb/>ſi rurſus fiat, vt ſin{us} hui{us} complementi ſeruati ad ſinum altitudinis poli, ita ſinus complementi diſtan <lb/>tiæ propoſiti Verticalis à Verticali propriè dicto ad aliud, inuenietur ſinus diſtantiæ Solis à meridie. </s>
  <s xml:id="echoid-s26465" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0418-04a" xlink:href="note-0418-04"/>
Exemplum. </s>
  <s xml:id="echoid-s26466" xml:space="preserve">Ponatur diſtare Verticalis F H, à puncto B, veri ortus verſ{us} auſtrum grad. </s>
  <s xml:id="echoid-s26467" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26468" xml:space="preserve">Si igi-<lb/>
<anchor type="note" xlink:label="note-0418-05a" xlink:href="note-0418-05"/>
tur fiat, vt 100000. </s>
  <s xml:id="echoid-s26469" xml:space="preserve">ſinus totus ad 86602. </s>
  <s xml:id="echoid-s26470" xml:space="preserve">ſinum complementi diſtantiæ dicti Verticalis à puncto veri <lb/>ortus, ita 74314. </s>
  <s xml:id="echoid-s26471" xml:space="preserve">ſin{us} complementi altitudinis poli ad aliud, offendem{us} hunc ferè ſinum 64357. </s>
  <s xml:id="echoid-s26472" xml:space="preserve">cui{us} <lb/>arcus cõplementum continet grad. </s>
  <s xml:id="echoid-s26473" xml:space="preserve">49. </s>
  <s xml:id="echoid-s26474" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26475" xml:space="preserve">56. </s>
  <s xml:id="echoid-s26476" xml:space="preserve">ferè. </s>
  <s xml:id="echoid-s26477" xml:space="preserve">Quòd ſi rurſum fiat, vt 76529. </s>
  <s xml:id="echoid-s26478" xml:space="preserve">ſinus arcus gr. </s>
  <s xml:id="echoid-s26479" xml:space="preserve">49. <lb/></s>
  <s xml:id="echoid-s26480" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26481" xml:space="preserve">56. </s>
  <s xml:id="echoid-s26482" xml:space="preserve">proximè inuenti ad 66913. </s>
  <s xml:id="echoid-s26483" xml:space="preserve">ſinum altitudinis poli, ita 86602. </s>
  <s xml:id="echoid-s26484" xml:space="preserve">ſinus complementi diſtantiæ Ver <lb/>ticalis propoſiti à propriè dicto Verticali ad aliud, inuenietur hic propemodum ſinus 75720. </s>
  <s xml:id="echoid-s26485" xml:space="preserve">cui{us} ar-<lb/>cus grad. </s>
  <s xml:id="echoid-s26486" xml:space="preserve">49. </s>
  <s xml:id="echoid-s26487" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26488" xml:space="preserve">13. </s>
  <s xml:id="echoid-s26489" xml:space="preserve">dabit diſtantiam Solis tunc à meridie hor. </s>
  <s xml:id="echoid-s26490" xml:space="preserve">3. </s>
  <s xml:id="echoid-s26491" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26492" xml:space="preserve">17. </s>
  <s xml:id="echoid-s26493" xml:space="preserve">Et quoniam hæc diſtantia <lb/>ante meridiem eſt, quod Verticalis F H, poſit{us} ſit diſtare à vero ortu verſus auſtrum grad. </s>
  <s xml:id="echoid-s26494" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26495" xml:space="preserve">aufere-<lb/>m{us} eam ex ſemicirculo, hoc eſt, ex 12. </s>
  <s xml:id="echoid-s26496" xml:space="preserve">horis, vt remaneat hora 8. </s>
  <s xml:id="echoid-s26497" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26498" xml:space="preserve">43 poſt mediam noctem. </s>
  <s xml:id="echoid-s26499" xml:space="preserve">Fodẽ <lb/>pacto, ſi ponatur idem Verticalis diſtare grad. </s>
  <s xml:id="echoid-s26500" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26501" xml:space="preserve">inueniemus horam 2. </s>
  <s xml:id="echoid-s26502" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26503" xml:space="preserve">15. </s>
  <s xml:id="echoid-s26504" xml:space="preserve">ante meridiem, id eſt <lb/>
<anchor type="note" xlink:label="note-0418-06a" xlink:href="note-0418-06"/>
horam 9. </s>
  <s xml:id="echoid-s26505" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26506" xml:space="preserve">45. </s>
  <s xml:id="echoid-s26507" xml:space="preserve">poſt mediam noctem.</s>
  <s xml:id="echoid-s26508" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1339" type="float" level="2" n="3">
<note position="left" xlink:label="note-0418-01" xlink:href="note-0418-01a" xml:space="preserve">Quo pacto ho-<lb/>ra@nueniatur, <lb/>qua Sol in Ae-<lb/>quato re exiſtẽ<unsure/>s <lb/>ad quẽ cunque <lb/>Verticalẽ per-<lb/>@eniat.</note>
  <figure xlink:label="fig-0418-01" xlink:href="fig-0418-01a">
    <image file="0418-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0418-01"/>
  </figure>
<note position="left" xlink:label="note-0418-02" xlink:href="note-0418-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0418-03" xlink:href="note-0418-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0418-04" xlink:href="note-0418-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0418-05" xlink:href="note-0418-05a" xml:space="preserve">Exemplum<unsure/>.</note>
<note position="left" xlink:label="note-0418-06" xlink:href="note-0418-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s26509" xml:space="preserve">IAM verò ſi Verticalis F M, diſtet à vero occaſu D, verſ{us} auſtrum grad. </s>
  <s xml:id="echoid-s26510" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26511" xml:space="preserve">vel 45. </s>
  <s xml:id="echoid-s26512" xml:space="preserve">reperiem{us} <lb/>tunc eodem artificio horam 3. </s>
  <s xml:id="echoid-s26513" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26514" xml:space="preserve">17. </s>
  <s xml:id="echoid-s26515" xml:space="preserve">poſt meridiem, vel horam 2. </s>
  <s xml:id="echoid-s26516" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26517" xml:space="preserve">15.</s>
  <s xml:id="echoid-s26518" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s26519" xml:space="preserve">QVOD ſi propoſitus Verticalis recedat à verò ortu, occaſuve verſ{us} boream, ac proinde Aequa-<lb/>
<anchor type="note" xlink:label="note-0418-07a" xlink:href="note-0418-07"/>
torem ſub Horizonte ſecet, qualis eſt Verticalis F N O, vel F L K, ſecabit quoque idem Verticalis <lb/>Aequatorem ſupra Horizontem in puncto oppoſito, vt in P, vel I. </s>
  <s xml:id="echoid-s26520" xml:space="preserve">Quare vt prius, diſtantiam Solis E P, <lb/>poſt meridiem, vel E I, ante meridiem inueſtigabimus. </s>
  <s xml:id="echoid-s26521" xml:space="preserve">Hęc enim ęqualis eſt diſtantię puncti O, poſt me-<lb/>diam noctem, vel puncti K, ante mediam noctem, &amp; </s>
  <s xml:id="echoid-s26522" xml:space="preserve">c.</s>
  <s xml:id="echoid-s26523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1340" type="float" level="2" n="4">
<note position="left" xlink:label="note-0418-07" xlink:href="note-0418-07a" xml:space="preserve">Quando Verti <lb/>calis propoſitus <lb/>deflectit à vero <lb/>ortu, occaſuve <lb/>in boream.</note>
</div>
<p style="it">
  <s xml:id="echoid-s26524" xml:space="preserve">RVRSVS ſi quando contingat, vt hora à meridie, vel media nocte inuenta, per quam linea Verti <lb/>
<anchor type="note" xlink:label="note-0418-08a" xlink:href="note-0418-08"/>
calis propoſita ducenda eſt in æquinoctiali linea, non ſecet lineam æquinoctialem, quæremus horam oppo-<lb/>
<anchor type="note" xlink:label="note-0418-09a" xlink:href="note-0418-09"/>
ſitam in lineaę quinoctiali, &amp; </s>
  <s xml:id="echoid-s26525" xml:space="preserve">per eam ducem{us} lineam Verticalem. </s>
  <s xml:id="echoid-s26526" xml:space="preserve">Hæc namque a Verticali puncto C, <lb/>verſus æquinoctialem lineam prote<unsure/>nſa referet ſemicir culum Verticalis propoſiti oppoſitum, at vltra <lb/>Verticale punctum C, reliquum ſemicirculum, cuius linea deſideratur. </s>
  <s xml:id="echoid-s26527" xml:space="preserve">Vt ſi hac arte ducere velim{us} <lb/>lineam Verticalem grad. </s>
  <s xml:id="echoid-s26528" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26529" xml:space="preserve">ita vt ei{us} circul{us} Verticalis recedat a vero occaſu verſ{us} auſtrum grad. <lb/></s>
  <s xml:id="echoid-s26530" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26531" xml:space="preserve">inueniem{us} Solem in Aequatore exiſtentem peruenturum ad eum Verticalem hora 3. </s>
  <s xml:id="echoid-s26532" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26533" xml:space="preserve">17. </s>
  <s xml:id="echoid-s26534" xml:space="preserve">poſt <lb/>meridiem: </s>
  <s xml:id="echoid-s26535" xml:space="preserve">Et quia hęc hora post meridiem in noſtro horologio lineam æquinoctialem non poteſt ſecare, <lb/>inueniemus in linea ęquinoctiali punctum L, horæ 3. </s>
  <s xml:id="echoid-s26536" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26537" xml:space="preserve">17. </s>
  <s xml:id="echoid-s26538" xml:space="preserve">poſt mediam noctem. </s>
  <s xml:id="echoid-s26539" xml:space="preserve">Nam recta C L, da-<lb/>bit communem ſectionem Verticalis circuli a vero ortu recedentis in boream grad. </s>
  <s xml:id="echoid-s26540" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26541" xml:space="preserve">portio verò eiuſ-<lb/>dem vltra C, producta communem ſectionẽ Verticalis circuli a vero occaſu in auſtrum recedentis gr. </s>
  <s xml:id="echoid-s26542" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26543" xml:space="preserve"><lb/>Idem{q́ue} fiat in cæteris.</s>
  <s xml:id="echoid-s26544" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1341" type="float" level="2" n="5">
<note position="left" xlink:label="note-0418-08" xlink:href="note-0418-08a" xml:space="preserve">Quid agẽ<unsure/>dum <lb/>ſit, cum hora, <lb/>qua Sol in Ae-<lb/>quatore exiſtẽs, <lb/>ad propoſitum <lb/>Verticalem per <lb/>tienit, lineã æ-<lb/>quinoctial em <lb/>@on ſecat.</note>
<note position="left" xlink:label="note-0418-09" xlink:href="note-0418-09a" xml:space="preserve">50</note>
</div>
<pb o="403" file="0419" n="419" rhead="LIBER TERTIVS."/>
<p style="it">
  <s xml:id="echoid-s26545" xml:space="preserve">HAC induſtria vti quoque poterimus in præcedentibus, quando lineæ nonnullæ Verticales vix, aut <lb/>
<anchor type="note" xlink:label="note-0419-01a" xlink:href="note-0419-01"/>
nullo modo, niſi in punctis remotiſſimis lineam horizontalem interſecant. </s>
  <s xml:id="echoid-s26546" xml:space="preserve">Immo eodem artificio omnes <lb/>lineas Verticales deſcribere licebit.</s>
  <s xml:id="echoid-s26547" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1342" type="float" level="2" n="6">
<note position="right" xlink:label="note-0419-01" xlink:href="note-0419-01a" xml:space="preserve">Prędicto artifi-<lb/>cio vti quis po-<lb/>te<unsure/>ſt in omni-<lb/>bus Verti<unsure/>cali-<lb/>bus ducẽdis in <lb/>quoe<unsure/>unque ho <lb/>rologio hacte. <lb/>nus deſcripto.</note>
</div>
<p style="it">
  <s xml:id="echoid-s26548" xml:space="preserve">QVOD ſi forte aliqua linearum occultarum ex D, ductarum parallela fuerit lineæ horizontali, <lb/>ducenda erit tunc line<unsure/>a Verticalis per C, eidem lineæ horizontali parallela. </s>
  <s xml:id="echoid-s26549" xml:space="preserve">Nam quia tunc parallela <lb/>illa occulta per D, ducta communis ſectio eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s26550" xml:space="preserve">Verticalis per eam ducti, cui quidem com-<lb/>muni ſectioni, ſi circulus ex D, deſcriptus in proprio ſitu intelligatur eſſe poſitus, æquidiſtat planum ho-<lb/>rologii, (alioquin occulta illa par allela producta ſecaret planum horologĳ, at que adeò in aliquo puncto <lb/>horizontalis lineæ, cùm ſecundum hanc lineam duntaxat Horizon plano horologĳ occurrat. </s>
  <s xml:id="echoid-s26551" xml:space="preserve">Igitur ea-<lb/>dem parallela lineam horizontalem ſecaret: </s>
  <s xml:id="echoid-s26552" xml:space="preserve">quod abſurdum est, cum horizontali lineæ ponatur paralle-<lb/>
<anchor type="note" xlink:label="note-0419-02a" xlink:href="note-0419-02"/>
la) erunt per propoſ. </s>
  <s xml:id="echoid-s26553" xml:space="preserve">18. </s>
  <s xml:id="echoid-s26554" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26555" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26556" xml:space="preserve">parallelæ inter ſe communes ſectiones factæ a plano horologĳ in Horizon-<lb/>te, &amp; </s>
  <s xml:id="echoid-s26557" xml:space="preserve">dicto Verticali, hoc est, linea horizontalis, &amp; </s>
  <s xml:id="echoid-s26558" xml:space="preserve">linea Verticalis prædicta. </s>
  <s xml:id="echoid-s26559" xml:space="preserve">Ita vides in propoſito <lb/>exemplo Verticalem lineam grad. </s>
  <s xml:id="echoid-s26560" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26561" xml:space="preserve">parallelam eſſe horizontali lineæ, quoniam occulta recta M N, <lb/>quæ communis ſectio eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s26562" xml:space="preserve">Verticalis grad. </s>
  <s xml:id="echoid-s26563" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26564" xml:space="preserve">parallela eſt horizontali lineæ. </s>
  <s xml:id="echoid-s26565" xml:space="preserve">Cum enim <lb/>inter rectas D M, D B, intercipiatur quadrans, (Nam a recta M D, communi ſectione Horizontis, &amp; </s>
  <s xml:id="echoid-s26566" xml:space="preserve"><lb/>Verticalis grad. </s>
  <s xml:id="echoid-s26567" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26568" xml:space="preserve">vſque ad F D, communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s26569" xml:space="preserve">Meridiani, ſeu Verticalis gr. <lb/></s>
  <s xml:id="echoid-s26570" xml:space="preserve">90. </s>
  <s xml:id="echoid-s26571" xml:space="preserve">numer antur grad. </s>
  <s xml:id="echoid-s26572" xml:space="preserve">60. </s>
  <s xml:id="echoid-s26573" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26574" xml:space="preserve">a recta F D, vſque ad B D, communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s26575" xml:space="preserve">Vertica-<lb/>lis grad. </s>
  <s xml:id="echoid-s26576" xml:space="preserve">60. </s>
  <s xml:id="echoid-s26577" xml:space="preserve">computantur grad. </s>
  <s xml:id="echoid-s26578" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26579" xml:space="preserve">qui cum grad. </s>
  <s xml:id="echoid-s26580" xml:space="preserve">60. </s>
  <s xml:id="echoid-s26581" xml:space="preserve">efficiunt grad. </s>
  <s xml:id="echoid-s26582" xml:space="preserve">90.) </s>
  <s xml:id="echoid-s26583" xml:space="preserve">erit angulus ad D, rectus. </s>
  <s xml:id="echoid-s26584" xml:space="preserve"><lb/>Cum igitur &amp; </s>
  <s xml:id="echoid-s26585" xml:space="preserve">angul{us} ad B, rectus ſit, erunt rectæ M N, B E, parallelæ inter ſe.</s>
  <s xml:id="echoid-s26586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1343" type="float" level="2" n="7">
<note position="left" xlink:label="note-0419-02" xlink:href="note-0419-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve">28. primi.</note>
</div>
<div xml:id="echoid-div1345" type="section" level="1" n="324">
<head xml:id="echoid-head335" xml:space="preserve">PROBLEMA 41. PROPOSITIO 41.</head>
<p>
  <s xml:id="echoid-s26587" xml:space="preserve">PARALLELOS Horizontis in eodem horologio declinante <lb/>ſimul &amp; </s>
  <s xml:id="echoid-s26588" xml:space="preserve">inclinato deſignare.</s>
  <s xml:id="echoid-s26589" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s26590" xml:space="preserve">SICVT propoſ. </s>
  <s xml:id="echoid-s26591" xml:space="preserve">41. </s>
  <s xml:id="echoid-s26592" xml:space="preserve">libri ſuperioris parallelos Horizontis in horologio polari deſcripſi-<lb/>mus, ita eoſdem in horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26593" xml:space="preserve">inclinato deſcribemus, ſi ea, quæ dicturi ſu-<lb/>mus, recte percipiantur. </s>
  <s xml:id="echoid-s26594" xml:space="preserve">Quod <lb/>
<anchor type="figure" xlink:label="fig-0419-01a" xlink:href="fig-0419-01"/>
<anchor type="note" xlink:label="note-0419-05a" xlink:href="note-0419-05"/>
ad priorem modum attinet, <lb/>circulus Analemmatis A B C, <lb/>
<anchor type="note" xlink:label="note-0419-06a" xlink:href="note-0419-06"/>
referet hoc loco Verticalem il <lb/>lum circulum, qui per ſtylum <lb/>tranſiens ad planum horolo-<lb/>gii rectus eſt, facitq́ue in pla-<lb/>no horologii ſectionem C D, <lb/>qualis in præcedenti propoſ. <lb/></s>
  <s xml:id="echoid-s26595" xml:space="preserve">eſt ille, qui per ſtylum I K, du <lb/>ctus ſectionem facit C D: </s>
  <s xml:id="echoid-s26596" xml:space="preserve">Pa-<lb/>ralleli autem Horizõtis in eo-<lb/>dem Analemmate non mutan <lb/>
<anchor type="note" xlink:label="note-0419-07a" xlink:href="note-0419-07"/>
tur. </s>
  <s xml:id="echoid-s26597" xml:space="preserve">Deinde loco axis E F, du-<lb/>cenda erit diameter, ſeu com-<lb/>munis ſectio dicti Verticalis, <lb/>&amp; </s>
  <s xml:id="echoid-s26598" xml:space="preserve">circuli maximi, cui horolo <lb/>gium æquidiſtat, ita ut tam ar-<lb/>cus C E, quàm B F, æqualis ſit <lb/>inclinationi plani propoſiti ad <lb/>Horizõtem. </s>
  <s xml:id="echoid-s26599" xml:space="preserve">Huic autẽ diame <lb/>tro ducẽda eſt parallela R Q, <lb/>pro magnitudine ſtyli I k, vel <lb/>
<anchor type="note" xlink:label="note-0419-08a" xlink:href="note-0419-08"/>
AK, ita ut recta DI, rectã RQ, <lb/>ad rectos angulos ſecans ſit ſtylo I K, ęqualis. </s>
  <s xml:id="echoid-s26600" xml:space="preserve">Poſtremo puncta L, M, N, &amp;</s>
  <s xml:id="echoid-s26601" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26602" xml:space="preserve">accepta ex puncto T, <lb/>ubi Horizon B C, rectam R Q, ſecat, transferenda erunt in rectam B C, ex B, puncto horizonta-<lb/>lis lineæ uerſus C, in ſuperiori horologio; </s>
  <s xml:id="echoid-s26603" xml:space="preserve">in inferiori autem transferenda erunt interualla T S, &amp; </s>
  <s xml:id="echoid-s26604" xml:space="preserve"><lb/>alia, ſi qua fuerint, ex B, in eãdem rectam B D, ultra B, productã. </s>
  <s xml:id="echoid-s26605" xml:space="preserve">Nam ſectiones conicæ circa dia-<lb/>metros L Q, M Q, N Q, &amp;</s>
  <s xml:id="echoid-s26606" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26607" xml:space="preserve">ſecundum doctrinã propoſ. </s>
  <s xml:id="echoid-s26608" xml:space="preserve">8. </s>
  <s xml:id="echoid-s26609" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s26610" xml:space="preserve">deſcriptæ, &amp; </s>
  <s xml:id="echoid-s26611" xml:space="preserve">in horologiũ <lb/>trãslatæ, ita ut diametri ipſarũ rectæ B C, cõgruant, trãſeantq́ue per pũcta translata L, M, N, &amp;</s>
  <s xml:id="echoid-s26612" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s26613" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26614" xml:space="preserve">earum cornua à linea horizontali auertantur, dabunt parallelos Horizontis.</s>
  <s xml:id="echoid-s26615" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1345" type="float" level="2" n="1">
  <figure xlink:label="fig-0419-01" xlink:href="fig-0419-01a">
    <image file="0419-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0419-01"/>
  </figure>
<note position="right" xlink:label="note-0419-05" xlink:href="note-0419-05a" xml:space="preserve">Deſcriptio pa-<lb/>rallelorum Ho <lb/>rizontis in eo-<lb/>dem horologio <lb/>declinante ſi-<lb/>mul &amp; inclina <lb/>@o.</note>
<note position="left" xlink:label="note-0419-06" xlink:href="note-0419-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0419-07" xlink:href="note-0419-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0419-08" xlink:href="note-0419-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s26616" xml:space="preserve">QVOD ad modum poſteriorem ſpectat, ſumenda eſt recta A D, æqualis rectæ A C, quæ ex <lb/>
<anchor type="note" xlink:label="note-0419-09a" xlink:href="note-0419-09"/>
A, vertice ſtyli in figura antecedentis propoſ. </s>
  <s xml:id="echoid-s26617" xml:space="preserve">cadit in Zenith, ſeu uerticẽ C; </s>
  <s xml:id="echoid-s26618" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26619" xml:space="preserve">in rectã A B, trans-<lb/>ferenda ſunt interualla inter centrum D, &amp; </s>
  <s xml:id="echoid-s26620" xml:space="preserve">lineas Verticales in linea horizontali, &amp;</s>
  <s xml:id="echoid-s26621" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26622" xml:space="preserve">Reliqua
<pb o="404" file="0420" n="420" rhead="GNOMONICES"/>
autem omnia abſoluenda erunt, ut in prędicta propoſ. </s>
  <s xml:id="echoid-s26623" xml:space="preserve">41. </s>
  <s xml:id="echoid-s26624" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s26625" xml:space="preserve">traditum eſt. </s>
  <s xml:id="echoid-s26626" xml:space="preserve">Eſt enim &amp; </s>
  <s xml:id="echoid-s26627" xml:space="preserve"><lb/>hic linea horizontalis, tanquam linea quædam æquinoctialis, &amp; </s>
  <s xml:id="echoid-s26628" xml:space="preserve">lineæ Verticales, ueluti lineæ ho-<lb/>rariæ, quarum centrum eſt Zenith, ſeu uertex C. </s>
  <s xml:id="echoid-s26629" xml:space="preserve">Item A D, in hac appoſita figura inſtar axis mũ-<lb/>di, nempe axis Horizontis, qui nunc inſtar Æquatoris; </s>
  <s xml:id="echoid-s26630" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26631" xml:space="preserve">A B, ueluti radius Æquatoris, &amp; </s>
  <s xml:id="echoid-s26632" xml:space="preserve">a-<lb/>lię rectæ ex A, emiſſæ, tanquam radij aliorum ſignorum; </s>
  <s xml:id="echoid-s26633" xml:space="preserve">rectæ uerò ex D, cadentes inſtar hora-<lb/>riarum linearum, &amp;</s>
  <s xml:id="echoid-s26634" xml:space="preserve">c.</s>
  <s xml:id="echoid-s26635" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1346" type="float" level="2" n="2">
<note position="right" xlink:label="note-0419-09" xlink:href="note-0419-09a" xml:space="preserve">Alia deſcriptio <lb/>parallelorum <lb/>Horizontia<unsure/>.</note>
</div>
  <figure>
    <image file="0420-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0420-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s26636" xml:space="preserve">IN exemplo propoſito in pręcedenti propoſ. </s>
  <s xml:id="echoid-s26637" xml:space="preserve">quoniã recta C D, una eſt ex lineis Verticalibus, <lb/>fit ut ipſa æqualiter diſtet à binis quibusuis lineis Verticalibus hinc inde poſitis, quæ æquali nu-<lb/>mero graduum ab ea recedunt, ita ut interualla bina inter D, centrum, &amp; </s>
  <s xml:id="echoid-s26638" xml:space="preserve">lineam horizontalem <lb/>æqualia ſint, cuiuſmodi ſunt v. </s>
  <s xml:id="echoid-s26639" xml:space="preserve">g. </s>
  <s xml:id="echoid-s26640" xml:space="preserve">D F, D G, Verticaliũ linearum grad. </s>
  <s xml:id="echoid-s26641" xml:space="preserve">90. </s>
  <s xml:id="echoid-s26642" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26643" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26644" xml:space="preserve">quarum utraque <lb/>30. </s>
  <s xml:id="echoid-s26645" xml:space="preserve">gradibus abeſt à Verticali linea C D, graduum 60. </s>
  <s xml:id="echoid-s26646" xml:space="preserve">Quoniam enim in triãgulis figuræ pręcedẽ-<lb/>tis propoſ. </s>
  <s xml:id="echoid-s26647" xml:space="preserve">D B F, D B G, (ſi recta linea duceretur ex D, in G,) anguli ad B, recti ſunt &amp;</s>
  <s xml:id="echoid-s26648" xml:space="preserve">æquales, nec <lb/>non &amp; </s>
  <s xml:id="echoid-s26649" xml:space="preserve">anguli ad D, æquales, cum æqualibus arcubus gra. </s>
  <s xml:id="echoid-s26650" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26651" xml:space="preserve">inſiſtãt; </s>
  <s xml:id="echoid-s26652" xml:space="preserve">ac præterea latus D B, com-<lb/>mune exiſtit, erunt &amp; </s>
  <s xml:id="echoid-s26653" xml:space="preserve">reliqua latera D F, F B, reliquis lateribus D G, G B, æqualia, &amp; </s>
  <s xml:id="echoid-s26654" xml:space="preserve">ſic de cæ-<lb/>
<anchor type="note" xlink:label="note-0420-05a" xlink:href="note-0420-05"/>
teris. </s>
  <s xml:id="echoid-s26655" xml:space="preserve">Hinc fit, ſingulas rectas in hac figura ex D, eductas habere binos numeros, ut in figura appa-<lb/>
<anchor type="note" xlink:label="note-0420-06a" xlink:href="note-0420-06"/>
ret; </s>
  <s xml:id="echoid-s26656" xml:space="preserve">atque adeo ſingula interualla rectarum ex D, cadentium inter D, &amp; </s>
  <s xml:id="echoid-s26657" xml:space="preserve">rectas ex A, egreſſas tranſ-<lb/>ferenda eſſe in binas Verticales ex Zenith C, æqualiter à recta C D, diſtantes, quemadmodum in <lb/>deſcriptione arcuum ſignorum in horizontali horologio factũ eſt propoſ. </s>
  <s xml:id="echoid-s26658" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26659" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s26660" xml:space="preserve">obſer-<lb/>uando tamen, ut interualla rectarum ex D, cadentium, quę rectam A B, ſecant, transferantur in <lb/>illas Verticales lineas, quæ horizontalem lineã ſecant in horologio, quales in noſtro exemplo ſunt <lb/>omnes, quæ ſupra Verticalem lineam grad. </s>
  <s xml:id="echoid-s26661" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26662" xml:space="preserve">horizontali lineæ parallelam continentur: </s>
  <s xml:id="echoid-s26663" xml:space="preserve">Inter-<lb/>ualla autem aliarum rectarum, quæ ſitæ ſunt ad dextram rectæ D F, grad. </s>
  <s xml:id="echoid-s26664" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26665" xml:space="preserve">ipſi A B, æquidiſtan-<lb/>tis, ductæq́; </s>
  <s xml:id="echoid-s26666" xml:space="preserve">ſunt ea lege, ut anguli, quos cum D F, faciunt, æquales ſint angulis, quos cum eadem <lb/>D F, rectæ ad ſiniſtram ipſius collocatę conſtituunt, transferantur in portiones Verticalium li-<lb/>nearum, quæ horizontalem lineam non ſecant; </s>
  <s xml:id="echoid-s26667" xml:space="preserve">cuiuſmodi ſunt omnes lineæ Verticales in dato <lb/>exemplo, quæ infra Verticalem lineam C G, grad. </s>
  <s xml:id="echoid-s26668" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26669" xml:space="preserve">horizontali lineæ parallelam cadunt.</s>
  <s xml:id="echoid-s26670" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1347" type="float" level="2" n="3">
<note position="left" xlink:label="note-0420-05" xlink:href="note-0420-05a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0420-06" xlink:href="note-0420-06a" xml:space="preserve">50</note>
</div>
<pb o="405" file="0421" n="421" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s26671" xml:space="preserve">QVOD ſi quando recta C D, non fuerit una ex Verticalibus lineis, ſed tamen æqualiter <lb/>diſtiterit à duabus hinc inde poſitis, continebunt eodem modo ſingulæ lineæ ex D, emiſſæ bi-<lb/>nos numeros: </s>
  <s xml:id="echoid-s26672" xml:space="preserve">ſuprema tamen D E, quæ rectæ C D, in horologio reſpondet, nullum habebit <lb/>affixum numerum. </s>
  <s xml:id="echoid-s26673" xml:space="preserve">Si uero C D, neque una fuerit ex lineis Verticalibus, neque ęqualiter à pro-<lb/>
<anchor type="note" xlink:label="note-0421-01a" xlink:href="note-0421-01"/>
ximis duabus hinc inde poſitis receſſerit, aſcribendi erunt ſingulis rectis ex D, prodeuntibus <lb/>ſinguli numeri duntaxat, quia tunc interualla omnia inter D, &amp; </s>
  <s xml:id="echoid-s26674" xml:space="preserve">horizontalem lineam inæqua-<lb/>lia erunt. </s>
  <s xml:id="echoid-s26675" xml:space="preserve">Quoniam uerò tunc nulla linea Verticalis lineæ horizontali parallela eſt, ducenda <lb/>erit per C, linea occulta lineæ horizontali æquidiſtans in horologio, cui reſpondebit recta D F, <lb/>in proxima figura rectæ A B, æquidiſtans. </s>
  <s xml:id="echoid-s26676" xml:space="preserve">Deinde ad dextram rectę D F, transferendę erunt om-<lb/>nes rectæ ad ſiniſtram eiuſdem D F, poſitæ. </s>
  <s xml:id="echoid-s26677" xml:space="preserve">Hæ enim reſpondebunt lineis Verticalibus, quæ hori-<lb/>
<anchor type="note" xlink:label="note-0421-02a" xlink:href="note-0421-02"/>
zontalem lineam nõ ſecant, ſed vltra punctum C, ſunt productæ, quemadmodum de lineis hora-<lb/>riis diximus in horologio declinante à Vert@cali circulo propoſ. </s>
  <s xml:id="echoid-s26678" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26679" xml:space="preserve">huius libri. </s>
  <s xml:id="echoid-s26680" xml:space="preserve">Id quod in noſtro <lb/>etiam exemplo intueri licet. </s>
  <s xml:id="echoid-s26681" xml:space="preserve">Nam quemadmodum in proxima figura linea D 15. </s>
  <s xml:id="echoid-s26682" xml:space="preserve">75. </s>
  <s xml:id="echoid-s26683" xml:space="preserve">ad ſini-<lb/>ſtram rectæ D F, reſpondet in horologio Verticalibus lineis gra. </s>
  <s xml:id="echoid-s26684" xml:space="preserve">15. </s>
  <s xml:id="echoid-s26685" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26686" xml:space="preserve">75. </s>
  <s xml:id="echoid-s26687" xml:space="preserve">quæ horizontalem li-<lb/>neam ſecantes æqualiter à C D, abſunt, cuiuſmodi ſunt lineæ quæ tertio loco in horologio rectam <lb/>C D, ſequuntur in utramque partem, ita quoque linea D 75. </s>
  <s xml:id="echoid-s26688" xml:space="preserve">@5. </s>
  <s xml:id="echoid-s26689" xml:space="preserve">ad dexteram rectæ D F, in proxi-<lb/>ma figura reſpondet<unsure/> dictis Verticalibus lineis ultra Zenith C, productis, &amp;</s>
  <s xml:id="echoid-s26690" xml:space="preserve">c.</s>
  <s xml:id="echoid-s26691" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1348" type="float" level="2" n="4">
<note position="right" xlink:label="note-0421-01" xlink:href="note-0421-01a" xml:space="preserve">Quid agend@ <lb/>ſit, quando re-<lb/>cta C D, in horo<unsure/> <lb/>logio anteced@ <lb/>tis propoſ. in-<lb/>@qualiter diſtar <lb/>à Verticali bus <lb/>lineis hinc i@-<lb/>de poſitis.</note>
<note position="left" xlink:label="note-0421-02" xlink:href="note-0421-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s26692" xml:space="preserve">EX radiis parallelorum Horizontis ex A, eductis ad ſiniſtram radii Horizontis A B, deſcribun <lb/>tur paralleli Horizontis ſupra lineam horizon<unsure/>talem, qui quidem ad inferius horologium perti-<lb/>nent, ſi pars ſupra horizontalem lineam inuertatur, vt ſępius dictum eſt in ſuperioribus, ut &amp; </s>
  <s xml:id="echoid-s26693" xml:space="preserve">in <lb/>
<anchor type="note" xlink:label="note-0421-03a" xlink:href="note-0421-03"/>
propoſ. </s>
  <s xml:id="echoid-s26694" xml:space="preserve">41. </s>
  <s xml:id="echoid-s26695" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26696" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26697" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s26698" xml:space="preserve">Parallelos igitur Horizontis in eodem horologio declinante ſimul <lb/>&amp; </s>
  <s xml:id="echoid-s26699" xml:space="preserve">inclinato deſignauimus. </s>
  <s xml:id="echoid-s26700" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s26701" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1349" type="float" level="2" n="5">
<note position="left" xlink:label="note-0421-03" xlink:href="note-0421-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1351" type="section" level="1" n="325">
<head xml:id="echoid-head336" xml:space="preserve">PROBLEMA 42. PROPOSITIO 42.</head>
<p>
  <s xml:id="echoid-s26702" xml:space="preserve">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in co-<lb/>dem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26703" xml:space="preserve">inclinato deſcribere.</s>
  <s xml:id="echoid-s26704" xml:space="preserve"/>
</p>
  <figure>
    <image file="0421-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0421-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<note position="left" xml:space="preserve">50</note>
<pb o="406" file="0422" n="422" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s26705" xml:space="preserve">HI circuli deſcribentur, ut lineæ horarum à meridie, vel media nocte, vt propoſ. </s>
  <s xml:id="echoid-s26706" xml:space="preserve">37. </s>
  <s xml:id="echoid-s26707" xml:space="preserve">huius <lb/>
<anchor type="note" xlink:label="note-0422-01a" xlink:href="note-0422-01"/>
libri tradidimus, propterea quòd per polos mundi ducuntur, quemadmodum &amp; </s>
  <s xml:id="echoid-s26708" xml:space="preserve">horarii circuli. <lb/></s>
  <s xml:id="echoid-s26709" xml:space="preserve">Sed diuiſio circuli ex L, deſcripti in horologio propoſ. </s>
  <s xml:id="echoid-s26710" xml:space="preserve">37. </s>
  <s xml:id="echoid-s26711" xml:space="preserve">huius libri inchoanda non eſt à recta <lb/>L M, ſed ab alia quadam, quæ à puncto M, uerſus occaſum (poſito horologio, &amp; </s>
  <s xml:id="echoid-s26712" xml:space="preserve">dicto circulo <lb/>in propria poſitione) tot gradibus recedit, quot in longitudine loci comprehenduntur, ut in da-<lb/>to exemplo gr. </s>
  <s xml:id="echoid-s26713" xml:space="preserve">36. </s>
  <s xml:id="echoid-s26714" xml:space="preserve">Nam hæc linea communis erit ſectio Æquatoris, ac Meridiani primi per In-<lb/>ſulas Fortunatas ducti, qualis in appoſita figura eſt recta L A.</s>
  <s xml:id="echoid-s26715" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1351" type="float" level="2" n="1">
<note position="left" xlink:label="note-0422-01" xlink:href="note-0422-01a" xml:space="preserve">Meridianorũ <lb/>circulorum de-<lb/>ſcrip@o in eo-<lb/>de norologio.</note>
</div>
<p>
  <s xml:id="echoid-s26716" xml:space="preserve">IN horologio inferiori, quod in facie inferiori plani deſcribitur, quale eſt illud, quod horizon <lb/>talis linea abſcindit, ſi omnes eius partes inuertantur, vt in pręcedentibus dictum eſt, apponen-<lb/>di ſunt numeri Meridianis ipſis, quemadmodum in horologio Verticali docuimus propoſ. </s>
  <s xml:id="echoid-s26717" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s26718" xml:space="preserve">
<anchor type="note" xlink:label="note-0422-02a" xlink:href="note-0422-02"/>
lib. </s>
  <s xml:id="echoid-s26719" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26720" xml:space="preserve">addẽdo uidelicet numeris eorundem Meridianorũ in ſuperiori horologio gradus 180. </s>
  <s xml:id="echoid-s26721" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s26722" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s26723" xml:space="preserve">ut in præcedenti figura apparet. </s>
  <s xml:id="echoid-s26724" xml:space="preserve">Itaque Meridianos, ſeu circulos longitudinum ciuitatum, &amp;</s>
  <s xml:id="echoid-s26725" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26726" xml:space="preserve"><lb/>deſcripſimus. </s>
  <s xml:id="echoid-s26727" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s26728" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1352" type="float" level="2" n="2">
<note position="left" xlink:label="note-0422-02" xlink:href="note-0422-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1354" type="section" level="1" n="326">
<head xml:id="echoid-head337" xml:space="preserve">PROBLEMA 43. PROPOSITIO 43.</head>
<p>
  <s xml:id="echoid-s26729" xml:space="preserve">PARALLELOS ciuitatum, circulosve latitudinum in eodem <lb/>horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26730" xml:space="preserve">inclinato reponere.</s>
  <s xml:id="echoid-s26731" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s26732" xml:space="preserve">NVLLA in re horum parallelorũ deſcriptio differt à deſcriptione arcuum ſignorum, de <lb/>
<anchor type="note" xlink:label="note-0422-03a" xlink:href="note-0422-03"/>
<anchor type="note" xlink:label="note-0422-04a" xlink:href="note-0422-04"/>
quibus propoſ. </s>
  <s xml:id="echoid-s26733" xml:space="preserve">38. </s>
  <s xml:id="echoid-s26734" xml:space="preserve">huius libri egimus. </s>
  <s xml:id="echoid-s26735" xml:space="preserve">Id quod ſæpius iam in præcedentibus monuimus. </s>
  <s xml:id="echoid-s26736" xml:space="preserve">Paral-<lb/>lelos igitur ciuitatum, circulosve latitudinum in eodem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26737" xml:space="preserve">inclina-<lb/>to repoſuimus. </s>
  <s xml:id="echoid-s26738" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s26739" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1354" type="float" level="2" n="1">
<note position="left" xlink:label="note-0422-03" xlink:href="note-0422-03a" xml:space="preserve">Circulorum la <lb/>ti tudinum in <lb/>eodem horolo-<lb/>gio deſcriptio.</note>
<note position="left" xlink:label="note-0422-04" xlink:href="note-0422-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1356" type="section" level="1" n="327">
<head xml:id="echoid-head338" xml:space="preserve">PROBLEMA 44. PROPOSITIO 44.</head>
<p>
  <s xml:id="echoid-s26740" xml:space="preserve">DOMOS cœleſtes in eodem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s26741" xml:space="preserve">in-<lb/>clinato collocare.</s>
  <s xml:id="echoid-s26742" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s26743" xml:space="preserve">SECETVR circulus ex L, deſcriptus propoſ. </s>
  <s xml:id="echoid-s26744" xml:space="preserve">37. </s>
  <s xml:id="echoid-s26745" xml:space="preserve">huius libri in partes 12. </s>
  <s xml:id="echoid-s26746" xml:space="preserve">æquales, vel <lb/>
<anchor type="note" xlink:label="note-0422-06a" xlink:href="note-0422-06"/>
etiam in plures, ſi partes domorum cæleſtium deſiderentur, facto initio à recta L M, vt in de-<lb/>ſcriptione horarum à meridie, uel media nocte; </s>
  <s xml:id="echoid-s26747" xml:space="preserve">ac per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s26748" xml:space="preserve">centrum L, emit-<lb/>tantur rectæ ſecantes æquinoctialem lineam in punctis, per quę ſi ducantur ex puncto E, vbi li-<lb/>nea horizontalis meridianam lineam interſecat, rectæ lineæ, deſcriptæ erunt, ſecundum doctrinam <lb/>loan. </s>
  <s xml:id="echoid-s26749" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s26750" xml:space="preserve">domus cœleſtes. </s>
  <s xml:id="echoid-s26751" xml:space="preserve">Quod perinde demonſtrabimus, vt in propoſ. </s>
  <s xml:id="echoid-s26752" xml:space="preserve">8. </s>
  <s xml:id="echoid-s26753" xml:space="preserve">huius libri idẽ <lb/>oſtendimus de horologio declinante.</s>
  <s xml:id="echoid-s26754" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1356" type="float" level="2" n="1">
<note position="left" xlink:label="note-0422-06" xlink:href="note-0422-06a" xml:space="preserve">Domotum cœ-<lb/>leſtium ſecun <lb/>dum loan. Re-<lb/>@@@@@. deſcti <lb/>@@@@ in eodem <lb/>horologio.</note>
</div>
<p>
  <s xml:id="echoid-s26755" xml:space="preserve">VT autem à Campano conſtituuntur domus cæleſtes, ita eas in horologio depingemus. </s>
  <s xml:id="echoid-s26756" xml:space="preserve">Ex K, <lb/>
<anchor type="note" xlink:label="note-0422-07a" xlink:href="note-0422-07"/>
loco ſtyli ad Verticalem lineam propriè dictam C B, quam in propoſ. </s>
  <s xml:id="echoid-s26757" xml:space="preserve">40. </s>
  <s xml:id="echoid-s26758" xml:space="preserve">huius libri deſcripſi-<lb/>mus, perpendicularis excite@ur K B D, ad quam erigatur alia perpendicularis K A, ſtylo æqualis, <lb/>
<anchor type="note" xlink:label="note-0422-08a" xlink:href="note-0422-08"/>
iungaturq́ue recta A B. </s>
  <s xml:id="echoid-s26759" xml:space="preserve">Sumpta deinde recta B D, æquali ipſi A B, deſcribatur ex D, circulus cu-<lb/>iusuis magnitudinis, quo diuiſo in 12. </s>
  <s xml:id="echoid-s26760" xml:space="preserve">partes, vel plures æquales, initio ſumpto à recta D C, <lb/>quę ex centro D, ad Zenith C, ducitur, emittãtur ex D, per diuiſionũ puncta lineæ occultæ ſecan-<lb/>tes Verticalem lineam C B, in punctis, per quæ ſi ex E, puncto, vbi meridiana linea, atque hori-<lb/>zontalis ſe mutuo interſecant, rectæ lineæ educantur, cuiuſmodi ſunt illæ, quæ in propoſita figu-<lb/>ra minutis illis lineis diſtinctæ ſunt, deſcriptæ erunt domus cæleſtes ex ſententia Cãpani. </s>
  <s xml:id="echoid-s26761" xml:space="preserve">Quod <lb/>hac ratione demonſtrabimus.</s>
  <s xml:id="echoid-s26762" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1357" type="float" level="2" n="2">
<note position="left" xlink:label="note-0422-07" xlink:href="note-0422-07a" xml:space="preserve">Cœleſtium do-<lb/>morum deſcri-<lb/>ptio in eodem <lb/>horologio ſecũ <lb/>dum Gampa-<lb/>num.</note>
<note position="left" xlink:label="note-0422-08" xlink:href="note-0422-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s26763" xml:space="preserve">CONCIPIATVR triangulum A B K, moueri circa B K, donec rectum ſitad planũ ho-<lb/>
<anchor type="note" xlink:label="note-0422-09a" xlink:href="note-0422-09"/>
rologij, ac proinde &amp; </s>
  <s xml:id="echoid-s26764" xml:space="preserve">ſtylus A K, @d idem rectus. </s>
  <s xml:id="echoid-s26765" xml:space="preserve">Item circulus ex D, deſcriptus intelligatur con-<lb/>uerti circa lineam Verticalem C B, donec eius centrum cum centro mundi, ſeu vertice ſtyli A, <lb/>
<anchor type="note" xlink:label="note-0422-10a" xlink:href="note-0422-10"/>
coniungatur; </s>
  <s xml:id="echoid-s26766" xml:space="preserve">coniungetur autem neceſſario, propter æqualitatẽ rectarum A B, B D. </s>
  <s xml:id="echoid-s26767" xml:space="preserve">Quibus po-<lb/>ſitis, conſtitutus erit circulus ex D, deſcriptus in plano Verticalis circuli proprie dicti, &amp; </s>
  <s xml:id="echoid-s26768" xml:space="preserve">circa <lb/>idem cum eo centrum. </s>
  <s xml:id="echoid-s26769" xml:space="preserve">Nam circulus Verticalis per centrum mundi, ſeu uerticem ſtyli A, &amp; </s>
  <s xml:id="echoid-s26770" xml:space="preserve">re-<lb/>ctam C B, ducitur, quemadmodum &amp; </s>
  <s xml:id="echoid-s26771" xml:space="preserve">dictus circulus ex D, deſcriptus in eo ſitu. </s>
  <s xml:id="echoid-s26772" xml:space="preserve">Igitur D C, com <lb/>munis ſectio erit Verticalis, ac Meridiani, cum Meridianus per centrum D, trãſeat, ſecetq́ue pla-<lb/>num horologii in C: </s>
  <s xml:id="echoid-s26773" xml:space="preserve">reliquæ autem lineæ occultæ communes ſectiones erunt Verticalis circuli, <lb/>&amp; </s>
  <s xml:id="echoid-s26774" xml:space="preserve">circulorum aliarum domorum cæleſtium. </s>
  <s xml:id="echoid-s26775" xml:space="preserve">Quare, ut in propoſ. </s>
  <s xml:id="echoid-s26776" xml:space="preserve">8. </s>
  <s xml:id="echoid-s26777" xml:space="preserve">huius libri, oſtendemus re-<lb/>ctè deſcriptas eſſe domos cæleſtes ſecundum Campani ſententiam. </s>
  <s xml:id="echoid-s26778" xml:space="preserve">Recta autem D F, quę commu <lb/>nis ſectio eſt Horizontis, &amp; </s>
  <s xml:id="echoid-s26779" xml:space="preserve">Verticalis, cum D C, communi ſectione Meridiani, ac Verticalis re-<lb/>ctum angulum in centro D, conſtituet, propterea quòd inter Meridianum, &amp; </s>
  <s xml:id="echoid-s26780" xml:space="preserve">Horizontem qua-
<pb o="407" file="0423" n="423" rhead="LIBER TERTIVS."/>
<anchor type="figure" xlink:label="fig-0423-01a" xlink:href="fig-0423-01"/>
<anchor type="note" xlink:label="note-0423-01a" xlink:href="note-0423-01"/>
<anchor type="note" xlink:label="note-0423-02a" xlink:href="note-0423-02"/>
<anchor type="note" xlink:label="note-0423-03a" xlink:href="note-0423-03"/>
<anchor type="note" xlink:label="note-0423-04a" xlink:href="note-0423-04"/>
drans circuli Verticalis proprie dicti includatur. </s>
  <s xml:id="echoid-s26781" xml:space="preserve">Domos ergo cæleſtes in eodem horologio decli-<lb/>nante ſimul &amp; </s>
  <s xml:id="echoid-s26782" xml:space="preserve">inclinato collocauimus. </s>
  <s xml:id="echoid-s26783" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s26784" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1358" type="float" level="2" n="3">
<note position="left" xlink:label="note-0422-09" xlink:href="note-0422-09a" xml:space="preserve">Demon ſtratio <lb/>proximę deſcri <lb/>ptionis.</note>
<note position="left" xlink:label="note-0422-10" xlink:href="note-0422-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0423-01" xlink:href="fig-0423-01a">
    <image file="0423-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0423-01"/>
  </figure>
<note position="left" xlink:label="note-0423-01" xlink:href="note-0423-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0423-02" xlink:href="note-0423-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0423-03" xlink:href="note-0423-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0423-04" xlink:href="note-0423-04a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1360" type="section" level="1" n="328">
<head xml:id="echoid-head339" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s26785" xml:space="preserve">NECESSE eſt autem, rectam K B D, quæ perpendicularis ducta eſt ad Verticalem lineam, vltra <lb/>K, locum ſtyli productam tranſire per punctum E, vbi ſe interſecant mutuo meridiana linea, &amp; </s>
  <s xml:id="echoid-s26786" xml:space="preserve">linea <lb/>
<anchor type="note" xlink:label="note-0423-05a" xlink:href="note-0423-05"/>
horizontalis: </s>
  <s xml:id="echoid-s26787" xml:space="preserve">quoniam communis ſectio eſt plani horologĳ, &amp; </s>
  <s xml:id="echoid-s26788" xml:space="preserve">circuli poſitionis, qui ad planum horolo-<lb/>gĳ rect{us} eſt, tranſit{q́ue} per communes ſectiones Meridiani, atque Horizontis, atque adeo planum horolo-<lb/>gĳ ſecat in puncto E, ſicut &amp; </s>
  <s xml:id="echoid-s26789" xml:space="preserve">reliqui circuli poſitionum, ſiue domorum cœleſtium, vt in propoſ. </s>
  <s xml:id="echoid-s26790" xml:space="preserve">8. </s>
  <s xml:id="echoid-s26791" xml:space="preserve">huius <lb/>libri demonſtratum est. </s>
  <s xml:id="echoid-s26792" xml:space="preserve">Nam quia circulus poſitionis per polos Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s26793" xml:space="preserve">plani horologĳ <lb/>duct{us}, rectus eſt &amp; </s>
  <s xml:id="echoid-s26794" xml:space="preserve">ad Verticalem circulum, &amp; </s>
  <s xml:id="echoid-s26795" xml:space="preserve">ad planum horologĳ, ex propoſ. </s>
  <s xml:id="echoid-s26796" xml:space="preserve">15. </s>
  <s xml:id="echoid-s26797" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26798" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26799" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s26800" xml:space="preserve">tran-<lb/>ſibit idem omnino per ſtylum A K, in proprio ſitu poſitum; </s>
  <s xml:id="echoid-s26801" xml:space="preserve">(quòd omnia plana per stylum d@@@a ad pla <lb/>
<anchor type="note" xlink:label="note-0423-06a" xlink:href="note-0423-06"/>
num horologĳ recta ſint) at que adeò per punctum K. </s>
  <s xml:id="echoid-s26802" xml:space="preserve">Quia verò è contr ario ad dictum circulum poſitio-<lb/>nis rectum eſt &amp; </s>
  <s xml:id="echoid-s26803" xml:space="preserve">planum Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s26804" xml:space="preserve">planum horologĳ, erit quoque communis horum ſectio, <lb/>hoc est, Verticalis linea C B, ad eundem circulum poſitionis perpendicularis, ac proinde, per defin. </s>
  <s xml:id="echoid-s26805" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s26806" xml:space="preserve">
<anchor type="note" xlink:label="note-0423-07a" xlink:href="note-0423-07"/>
lib. </s>
  <s xml:id="echoid-s26807" xml:space="preserve">11. </s>
  <s xml:id="echoid-s26808" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s26809" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26810" xml:space="preserve">ad communem ſectionem eiuſdem circuli, ac plani horologĳ in eo exiſtentem. </s>
  <s xml:id="echoid-s26811" xml:space="preserve">Cum ergo <lb/>C B, ad K B, perpendicularis ſit ex conſtructione, erit K B, communis ſectio dicti circuli poſitionis, &amp;</s>
  <s xml:id="echoid-s26812" xml:space="preserve">
<pb o="408" file="0424" n="424" rhead="GNOMONICES"/>
plani horologĳ, atque adeò per punctum E, tranſibit, vt &amp; </s>
  <s xml:id="echoid-s26813" xml:space="preserve">reliquæ ſectiones communes circulorum do-<lb/>morum cœleſtium, &amp; </s>
  <s xml:id="echoid-s26814" xml:space="preserve">plani horologĳ.</s>
  <s xml:id="echoid-s26815" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1360" type="float" level="2" n="1">
<note position="left" xlink:label="note-0423-05" xlink:href="note-0423-05a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0423-06" xlink:href="note-0423-06a" xml:space="preserve">18. vndec.</note>
<note position="right" xlink:label="note-0423-07" xlink:href="note-0423-07a" xml:space="preserve">19. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s26816" xml:space="preserve">IAM verò quoniam in deſcriptione domorum cœleſtium ſecundum opinionem Campani vſu inter-<lb/>
<anchor type="note" xlink:label="note-0424-01a" xlink:href="note-0424-01"/>
dum venit, aliqu{as} rect{as} line{as} occult{as} ex centro D, emiſſas vix, aut nullo modo Verticalem lineam <lb/>C B, ſecare adeò vt difficile admodum ſit line{as} domorum cœlestium illis reſpondentes in horologio ex <lb/>puncto E, ſine errore aliquo deſcribere, vt in nostro exemplo contingit in linea ſecundæ dom{us} cœle-<lb/>ſtis in portione nocturna horologĳ, quæ in inferiori horologio dat domum octauam, quæ illi oppoſita eſt; <lb/></s>
  <s xml:id="echoid-s26817" xml:space="preserve">inueſtiganda erunt puncta in linea æquinoctiali, per quæ lineæ domorum cœleſtium ſunt ducendæ, quand@ <lb/>punctis destituimur in linea Verticali, hoc modo. </s>
  <s xml:id="echoid-s26818" xml:space="preserve">Inquiratur hora, qua Sol in Aequatore existens ad <lb/>circulum illius domus cœleſtis perueniat, cuius lineam deſcribere volumus. </s>
  <s xml:id="echoid-s26819" xml:space="preserve">Nam vbi linea illius horæ <lb/>(quam occultè ducemus, vt in propoſ. </s>
  <s xml:id="echoid-s26820" xml:space="preserve">37. </s>
  <s xml:id="echoid-s26821" xml:space="preserve">huius libri tradidimus) æquinoctialem lineam ſecabit, per illud <lb/>
<anchor type="note" xlink:label="note-0424-02a" xlink:href="note-0424-02"/>
punctum ex E, ducenda erit dom{us} cœleſtis quæſita. </s>
  <s xml:id="echoid-s26822" xml:space="preserve">Vt quia Sol in Aequatore exiſtens perucnit motis<unsure/> <lb/>diurno ad circulum ſecundæ domus cœleſtis, quæ in horologio inferiori eſt domus octaua, quæ illi opponi-<lb/>tur, hora 3. </s>
  <s xml:id="echoid-s26823" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26824" xml:space="preserve">29. </s>
  <s xml:id="echoid-s26825" xml:space="preserve">post mediam noctem; </s>
  <s xml:id="echoid-s26826" xml:space="preserve">linea autem huius horæ æquinoctialem lineam ſecat in pun-<lb/>cto G; </s>
  <s xml:id="echoid-s26827" xml:space="preserve">ducenda erit linea dictę domus ex E, per G, &amp; </s>
  <s xml:id="echoid-s26828" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s26829" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1361" type="float" level="2" n="2">
<note position="left" xlink:label="note-0424-01" xlink:href="note-0424-01a" xml:space="preserve">Quomodo de-<lb/>ſcribantur do-<lb/>mus illæ cœle-<lb/>ftcs, quæ vix, <lb/>aut nullo mo-<lb/>do Verticalem <lb/>lineam interſ@-<lb/>@@nt.</note>
<note position="left" xlink:label="note-0424-02" xlink:href="note-0424-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s26830" xml:space="preserve">REPERIEMVS autem horam, qua Sol Aequatorem percurrens ad propoſitum circulum do-<lb/>mus cœleſtis peruenit, ex doctrina ſinuum bac arte.</s>
  <s xml:id="echoid-s26831" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s26832" xml:space="preserve">SIT Horizon A B C D; </s>
  <s xml:id="echoid-s26833" xml:space="preserve">Meridianus A E C; <lb/></s>
  <s xml:id="echoid-s26834" xml:space="preserve">
<anchor type="note" xlink:label="note-0424-03a" xlink:href="note-0424-03"/>
Aequator B E D; </s>
  <s xml:id="echoid-s26835" xml:space="preserve">Verticalis B F D; </s>
  <s xml:id="echoid-s26836" xml:space="preserve">circulus dom{us} <lb/>cœleſtis A G C K, ſecans Verticalem, &amp; </s>
  <s xml:id="echoid-s26837" xml:space="preserve">Aequato <lb/>
<anchor type="note" xlink:label="note-0424-04a" xlink:href="note-0424-04"/>
rem ex parte quidem orientali, ſiue ſupra Horizon-<lb/>tem, ſiue infra, in punctis G, H, ex parte verò occi-<lb/>dentali in punctis I, K. </s>
  <s xml:id="echoid-s26838" xml:space="preserve">Quęrendus eſt igitur arcus <lb/>Aequatoris E H, vel E K. </s>
  <s xml:id="echoid-s26839" xml:space="preserve">Quoniam in triangulo <lb/>B G H, vel D I K, angulus G, vel I, rectus eſt, per <lb/>propoſitionem 15. </s>
  <s xml:id="echoid-s26840" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26841" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26842" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s26843" xml:space="preserve">erit per propoſ. </s>
  <s xml:id="echoid-s26844" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s26845" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26846" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26847" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s26848" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s26849" xml:space="preserve">de triãgulis, vel per propoſ. </s>
  <s xml:id="echoid-s26850" xml:space="preserve">14. </s>
  <s xml:id="echoid-s26851" xml:space="preserve"><lb/>lib. </s>
  <s xml:id="echoid-s26852" xml:space="preserve">1. </s>
  <s xml:id="echoid-s26853" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s26854" xml:space="preserve">42. </s>
  <s xml:id="echoid-s26855" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s26856" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s26857" xml:space="preserve">vt ſinus anguli B, vel D, nempe altitudinis po-<lb/>li, quem Aequator cum Verticali conſtituit, ad ſinũ <lb/>
<anchor type="note" xlink:label="note-0424-05a" xlink:href="note-0424-05"/>
totum, ita ſinus complementi anguli H, vel K, <lb/>ad ſinum complementi arcus B G, vel D I, Verticalis circuli inter Horizontem, &amp; </s>
  <s xml:id="echoid-s26858" xml:space="preserve">circulum A G C K, <lb/>poſiti: </s>
  <s xml:id="echoid-s26859" xml:space="preserve">Et conuertendo vt ſinus totus ad ſinum anguli altitudinis poli B, vel D, ita ſinus complementi <lb/>arcus B G, vel D I, ad ſinum complementi anguli H, vel K. </s>
  <s xml:id="echoid-s26860" xml:space="preserve">Cognito ergo hoc complemento, cogn<unsure/>oſcetur <lb/>&amp; </s>
  <s xml:id="echoid-s26861" xml:space="preserve">angulus H, vel K. </s>
  <s xml:id="echoid-s26862" xml:space="preserve">Rurſ{us} quia eſt, per propoſ. </s>
  <s xml:id="echoid-s26863" xml:space="preserve">16. </s>
  <s xml:id="echoid-s26864" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26865" xml:space="preserve">4. </s>
  <s xml:id="echoid-s26866" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s26867" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s26868" xml:space="preserve">de triangulis, vel per propoſ. <lb/></s>
  <s xml:id="echoid-s26869" xml:space="preserve">13. </s>
  <s xml:id="echoid-s26870" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s26871" xml:space="preserve">Gebri, vel per propoſ.</s>
  <s xml:id="echoid-s26872" xml:space="preserve"><unsure/> 41. </s>
  <s xml:id="echoid-s26873" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s26874" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s26875" xml:space="preserve">vt ſinus anguli H, vel K, proximè inuenti <lb/>ad ſinum arc{us} B G, vel D I, ita ſin{us} tot{us} anguli recti G, vel I, ad ſinum arcus Aequatoris B H, vel <lb/>D K, complementi diſtantiæ Solis à meridie, vel media nocte: </s>
  <s xml:id="echoid-s26876" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum altitudi-<lb/>nis poli, ita ſinus complementi arcus Verticalis circuli inter Horizontem, &amp; </s>
  <s xml:id="echoid-s26877" xml:space="preserve">circulum dom{us} cœleſtis <lb/>propoſitę interiecti, ad aliud, inuenietur ſinus, cuius arcus complementum ſeruetur. </s>
  <s xml:id="echoid-s26878" xml:space="preserve">Rurſus ſi fiat, vt <lb/>ſin{us} hui{us} complementi ſeruati ad ſinum arcus Verticalis circuli poſiti inter Horizontem, &amp; </s>
  <s xml:id="echoid-s26879" xml:space="preserve">circulum <lb/>
<anchor type="note" xlink:label="note-0424-06a" xlink:href="note-0424-06"/>
dom{us} cœleſtis propoſitæ, it a ſin{us} tot{us} ad aliud, reperietur ſinus complementi diſtantiæ Solis à meri-<lb/>die, ſi dom{us} cœleſtis ſupra Horizontem extierit, vel a media nocte, ſi infra Horizontem data cœleſtis <lb/>domus latuerit. </s>
  <s xml:id="echoid-s26880" xml:space="preserve">Exemplum. </s>
  <s xml:id="echoid-s26881" xml:space="preserve">Exiſtat Sol in principio dom{us} ſecundæ, cui{us} circul{us} infra Horizontẽ <lb/>
<anchor type="note" xlink:label="note-0424-07a" xlink:href="note-0424-07"/>
latet grad. </s>
  <s xml:id="echoid-s26882" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26883" xml:space="preserve">ex parte orientali, qui quidem grad{us} in Verticali circulo numerantur. </s>
  <s xml:id="echoid-s26884" xml:space="preserve">Itaque ſi fiat, vt <lb/>100000. </s>
  <s xml:id="echoid-s26885" xml:space="preserve">ſinus totus ad 66913. </s>
  <s xml:id="echoid-s26886" xml:space="preserve">ſinum altitudinis poli, ita 86602. </s>
  <s xml:id="echoid-s26887" xml:space="preserve">ſinus complementi arcus grad. </s>
  <s xml:id="echoid-s26888" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26889" xml:space="preserve">ad <lb/>aliud, inuenietur hic fermè ſin{us} 57950. </s>
  <s xml:id="echoid-s26890" xml:space="preserve">cui{us} arcus continet grad. </s>
  <s xml:id="echoid-s26891" xml:space="preserve">35. </s>
  <s xml:id="echoid-s26892" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26893" xml:space="preserve">25. </s>
  <s xml:id="echoid-s26894" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26895" xml:space="preserve">huius complementũ <lb/>grad. </s>
  <s xml:id="echoid-s26896" xml:space="preserve">54. </s>
  <s xml:id="echoid-s26897" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26898" xml:space="preserve">35. </s>
  <s xml:id="echoid-s26899" xml:space="preserve">dabit angulum B H G. </s>
  <s xml:id="echoid-s26900" xml:space="preserve">Deinde ſi fiat, vt 81495. </s>
  <s xml:id="echoid-s26901" xml:space="preserve">ſinus anguli B H G, quem proximè <lb/>offendim{us} ad 50000. </s>
  <s xml:id="echoid-s26902" xml:space="preserve">ſinum arcus Verticalis circuli inter circulum domus propoſitæ, &amp; </s>
  <s xml:id="echoid-s26903" xml:space="preserve">Horizontem <lb/>interiecti, ita 100000. </s>
  <s xml:id="echoid-s26904" xml:space="preserve">ſinus totus ad aliud, reperietur hic ferèſinus 61353. </s>
  <s xml:id="echoid-s26905" xml:space="preserve">cuius arcus B H, grad. </s>
  <s xml:id="echoid-s26906" xml:space="preserve">37. <lb/></s>
  <s xml:id="echoid-s26907" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26908" xml:space="preserve">51. </s>
  <s xml:id="echoid-s26909" xml:space="preserve">dabit complementum, id est, diſtantiam Solis poſt mediam noctem, cum tunc Sol existat inter <lb/>
<anchor type="note" xlink:label="note-0424-08a" xlink:href="note-0424-08"/>
Meridianum, &amp; </s>
  <s xml:id="echoid-s26910" xml:space="preserve">Horizontem ſub terra ex parte orientali, grad. </s>
  <s xml:id="echoid-s26911" xml:space="preserve">52. </s>
  <s xml:id="echoid-s26912" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26913" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26914" xml:space="preserve">hoc eſt, hor{as} 3. </s>
  <s xml:id="echoid-s26915" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s26916" xml:space="preserve">29. <lb/></s>
  <s xml:id="echoid-s26917" xml:space="preserve">Hęc autem diſtantia eſſet ante meridiem, ſi circulus domus cœleſtis tranſiret per principium domus duo-<lb/>decimæ, ita vt arc{us} Verticalis inter Horizo<unsure/>ntem, &amp; </s>
  <s xml:id="echoid-s26918" xml:space="preserve">circulum dictum ſupra Horizontem ex parte <lb/>orientali contineret grad. </s>
  <s xml:id="echoid-s26919" xml:space="preserve">30. </s>
  <s xml:id="echoid-s26920" xml:space="preserve">poſt meridiem verò, ſi idem circulus duceretur per initium domus octa-<lb/>@@æ. </s>
  <s xml:id="echoid-s26921" xml:space="preserve">Denique ante mediam noctem, ſi per principium domus ſextæincederet.</s>
  <s xml:id="echoid-s26922" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1362" type="float" level="2" n="3">
<note position="left" xlink:label="note-0424-03" xlink:href="note-0424-03a" xml:space="preserve">Qu@ r<unsure/>atione <lb/>exploretur ho-<lb/>ra, qua Sol in<unsure/> <lb/>Aequatore exi-<lb/>ſtens ad prope<unsure/> <lb/>ſitum circulũ <lb/>domus co@leſtis <lb/>gerueni@@.</note>
<note position="left" xlink:label="note-0424-04" xlink:href="note-0424-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0424-05" xlink:href="note-0424-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0424-06" xlink:href="note-0424-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0424-07" xlink:href="note-0424-07a" xml:space="preserve">@xemplum<unsure/>.</note>
<note position="left" xlink:label="note-0424-08" xlink:href="note-0424-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1364" type="section" level="1" n="329">
<head xml:id="echoid-head340" xml:space="preserve">PROBLEMA 45. PROPOSITIO 45.</head>
<p>
  <s xml:id="echoid-s26923" xml:space="preserve">SIGNA aſcendentia Zodiaci in eodem horologio declinante ſi-<lb/>mul &amp; </s>
  <s xml:id="echoid-s26924" xml:space="preserve">inclinato reponere.</s>
  <s xml:id="echoid-s26925" xml:space="preserve"/>
</p>
<pb o="409" file="0425" n="425" rhead="LIBER TERTIVS."/>
<p>
  <s xml:id="echoid-s26926" xml:space="preserve">EISDEM prorſus uijs, quibus in præcedentibus uſi ſumus, deſcribemus hoc loco aſcenden <lb/>
<anchor type="note" xlink:label="note-0425-01a" xlink:href="note-0425-01"/>
tia ſigna, ut ex appoſita figura perſpicuum fiet. </s>
  <s xml:id="echoid-s26927" xml:space="preserve">Nam ex prioribus duabus tabellis propoſ. </s>
  <s xml:id="echoid-s26928" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26929" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26930" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s26931" xml:space="preserve">indagabimus in linea æquinoctiali puncta, per quæ lineæ ♈, ♉, ♊, ♋, ♎, ♏, ♒, &amp; </s>
  <s xml:id="echoid-s26932" xml:space="preserve">♓, tranſeunt. </s>
  <s xml:id="echoid-s26933" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0425-01a" xlink:href="fig-0425-01"/>
<anchor type="note" xlink:label="note-0425-02a" xlink:href="note-0425-02"/>
<anchor type="note" xlink:label="note-0425-03a" xlink:href="note-0425-03"/>
<anchor type="note" xlink:label="note-0425-04a" xlink:href="note-0425-04"/>
Ex tertia autem tabella eiuſdem propoſ. </s>
  <s xml:id="echoid-s26934" xml:space="preserve">inueniemus in tropico ♋, puncta pro ♈, ♉, ♊, ♋, &amp; </s>
  <s xml:id="echoid-s26935" xml:space="preserve">♎, <lb/>Pro ♏, autem ♒, &amp; </s>
  <s xml:id="echoid-s26936" xml:space="preserve">♓, puncta inueniemus in linea meridiana ex tabella ſexta eiuſdem propoſ. <lb/></s>
  <s xml:id="echoid-s26937" xml:space="preserve">
<anchor type="note" xlink:label="note-0425-05a" xlink:href="note-0425-05"/>
Deinde pro ♌, reperiemus punctum in tropico ♋, ex tertia tabella eiuſdẽ propoſ. </s>
  <s xml:id="echoid-s26938" xml:space="preserve">per quod du-<lb/>ximus lineam ♌, trãſeuntem per punctum illud horizõtalis lineæ, ubi à parallelo ♊, &amp; </s>
  <s xml:id="echoid-s26939" xml:space="preserve">♌, ſeca-<lb/>tur. </s>
  <s xml:id="echoid-s26940" xml:space="preserve">Pro ♍, tandem offendimus unum punctum in tropico ♋, ex tertia tabella dictæ propoſ. </s>
  <s xml:id="echoid-s26941" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26942" xml:space="preserve"><lb/>alterum in meridiana linea ex ſexta tabella propoſ. </s>
  <s xml:id="echoid-s26943" xml:space="preserve">eiuſdem. </s>
  <s xml:id="echoid-s26944" xml:space="preserve">Lineæ autem ♐, &amp; </s>
  <s xml:id="echoid-s26945" xml:space="preserve">♑, uix in noſtro <lb/>exemplo deſcribi poſſunt, cum nimis procul excurrãt, vt ex dictis tabellis facile colligi poteſt. </s>
  <s xml:id="echoid-s26946" xml:space="preserve">Trã-<lb/>ſibũtautem omnes lineæ aſcendentium ſignorum per puncta lineæ horizontalis, vbi eam arcus ſi-<lb/>gnorum ſecant, quæ quidem puncta ſine dictis arcubus inueſtigari etiam poſſunt vel ex tabella <lb/>quinta propoſ. </s>
  <s xml:id="echoid-s26947" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26948" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26949" xml:space="preserve">2. </s>
  <s xml:id="echoid-s26950" xml:space="preserve">vt ex ſuperioribus patet, vel ex figura latitudinum ortiuarum, occidua-<lb/>rumve propoſ. </s>
  <s xml:id="echoid-s26951" xml:space="preserve">21. </s>
  <s xml:id="echoid-s26952" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s26953" xml:space="preserve">hac arte.</s>
  <s xml:id="echoid-s26954" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1364" type="float" level="2" n="1">
<note position="right" xlink:label="note-0425-01" xlink:href="note-0425-01a" xml:space="preserve">Aſcẽdentia ſi-<lb/>gna quo pacto <lb/>in eodem horo <lb/>logio depingan <lb/>tur.</note>
  <figure xlink:label="fig-0425-01" xlink:href="fig-0425-01a">
    <image file="0425-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0425-01"/>
  </figure>
<note position="left" xlink:label="note-0425-02" xlink:href="note-0425-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0425-03" xlink:href="note-0425-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0425-04" xlink:href="note-0425-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0425-05" xlink:href="note-0425-05a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Inuentio pun-<lb/>ctorum, per quę <lb/>aſcendentia ſi-<lb/>gna ducuntur <lb/>in linea hori-<lb/>zontali.</note>
<p>
  <s xml:id="echoid-s26955" xml:space="preserve">IN figura latitudinum ortiuarum, &amp; </s>
  <s xml:id="echoid-s26956" xml:space="preserve">occiduarum, quam in propoſ. </s>
  <s xml:id="echoid-s26957" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26958" xml:space="preserve">huius libri repetiuimus <lb/>
<anchor type="note" xlink:label="note-0425-07a" xlink:href="note-0425-07"/>
conſtituatur B E G, angulus declinationis plani propoſiti à Verticali circulo, ad partes quidẽ me-<lb/>ridiei uerſus occaſum, ſi planum à ſeptentrionem in ortum declinet, vt in dato exemplo contin-<lb/>git, vel verſus ortum, ſi in occaſum uergat: </s>
  <s xml:id="echoid-s26959" xml:space="preserve">at uerò ad partes ſeptentrionis verſus ortum, ſi horo-<lb/>logium deflectat à meridie in occaſum, vel verſus occaſum, ſi uergat à meridie in ortũ. </s>
  <s xml:id="echoid-s26960" xml:space="preserve">Poſt hæc <lb/>accipiatur recta E G, ęqualis rectę A B, in figura propoſ. </s>
  <s xml:id="echoid-s26961" xml:space="preserve">40. </s>
  <s xml:id="echoid-s26962" xml:space="preserve">huius libri, &amp; </s>
  <s xml:id="echoid-s26963" xml:space="preserve">per G, ad E G, perpendi <lb/>cularis excitetur G H. </s>
  <s xml:id="echoid-s26964" xml:space="preserve">Si enim puncta huius perpendicularis, vbi à radiis latitudinũ ortiuarũ ſe-<lb/>catur, ex puncto H, accepta trãsferantur in lineam horizontalẽ ex puncto F, vbi meridiana linea, <lb/>&amp; </s>
  <s xml:id="echoid-s26965" xml:space="preserve">horizontalis ſe mutuo interſecãt, inuenta erunt puncta, per quæ arcus ſignorũ ducuntur. </s>
  <s xml:id="echoid-s26966" xml:space="preserve">Ducta <lb/>enim ex K, loco gnomonis ad horizontalẽ lineã perpendiculari K B, &amp; </s>
  <s xml:id="echoid-s26967" xml:space="preserve">ad hanc alia perpendicula <lb/>ri K A, quæ ſtylo æqualis ſit, iungatur recta A B, quæ eadem eſt, quę prædicta in propoſ. </s>
  <s xml:id="echoid-s26968" xml:space="preserve">40. </s>
  <s xml:id="echoid-s26969" xml:space="preserve">hu-<lb/>ius libri, atque adeò rectæ E G, in figura latitudinum ortiuarum propoſ. </s>
  <s xml:id="echoid-s26970" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26971" xml:space="preserve">huius libri æqualis; </s>
  <s xml:id="echoid-s26972" xml:space="preserve">ſi
<pb o="410" file="0426" n="426" rhead="GNOMONICES"/>
triangulum A B K, concipiatur animo conuerti circa B K, donec rectum ſit ad horologii planũ, <lb/>ac proinde in plano Verticalis circuli inclinationem plani ad Horizontem metientis, &amp; </s>
  <s xml:id="echoid-s26973" xml:space="preserve">per B K, <lb/>ducti, erit recta A B, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s26974" xml:space="preserve">dicti Verticalis, &amp; </s>
  <s xml:id="echoid-s26975" xml:space="preserve">iuncta recta A F, cõmu-<lb/>nis ſectio Horizontis, ac Meridiani, propterea quod tam Horizon, quàm Meridianus per cen-<lb/>trum Mundi A, &amp; </s>
  <s xml:id="echoid-s26976" xml:space="preserve">per pũctum F, ducitur, Quare angulus A F B, quem linea meridiana A F, Ho-<lb/>rizontis cum linea horizontali F B, plani horologij conſtituit, æqualis erit complemento decli-<lb/>nationis horologij à Verticali proprie dicto; </s>
  <s xml:id="echoid-s26977" xml:space="preserve">ac proinde cum angulus A B F, rectus ſit (quoniá <lb/>enim triangulum A B K, rectum eſt, &amp; </s>
  <s xml:id="echoid-s26978" xml:space="preserve">ad planum horologij, &amp; </s>
  <s xml:id="echoid-s26979" xml:space="preserve">ad Horizontem, erunt quoque <lb/>duo hæc plana ad triangulum recta. </s>
  <s xml:id="echoid-s26980" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s26981" xml:space="preserve">cõmunis eorũ ſectio F B, ad idẽ perpendicularis erit <lb/>
<anchor type="note" xlink:label="note-0426-01a" xlink:href="note-0426-01"/>
<anchor type="note" xlink:label="note-0426-02a" xlink:href="note-0426-02"/>
ac propterea &amp; </s>
  <s xml:id="echoid-s26982" xml:space="preserve">ad rectam B A, perpendicularis erit, ex defin. </s>
  <s xml:id="echoid-s26983" xml:space="preserve">3. </s>
  <s xml:id="echoid-s26984" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s26985" xml:space="preserve">11. </s>
  <s xml:id="echoid-s26986" xml:space="preserve">Eucl.) </s>
  <s xml:id="echoid-s26987" xml:space="preserve">erit reliquus an-<lb/>gulus B A F, declinationi horologii à Verticali proprie dicto æqualis, hoc eſt, angulo B E G, in <lb/>figura latitudinum ortiuarum propoſ. </s>
  <s xml:id="echoid-s26988" xml:space="preserve">9. </s>
  <s xml:id="echoid-s26989" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s26990" xml:space="preserve">Quoniá igitur anguli E, G, trianguli G E H, <lb/>in figura latitudinum ortiuarum æquales ſunt angulis A, B, trianguli B A F, in ſigura huius pro-<lb/>poſ. </s>
  <s xml:id="echoid-s26991" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s26992" xml:space="preserve">latera E G, A B, quibus dicti anguli adiacent, æqualia quoque ex conſtructione, erũt quo-<lb/>que latera E H, H G, lateribus A F, F B, æqualia, &amp; </s>
  <s xml:id="echoid-s26993" xml:space="preserve">angulus H, angulo A F B. </s>
  <s xml:id="echoid-s26994" xml:space="preserve">Quamcbrem ſi <lb/>
<anchor type="note" xlink:label="note-0426-03a" xlink:href="note-0426-03"/>
recta E G, figuræ latitudinum ortiuarum rectę A B, in horologio congruat, congruet quoque re-<lb/>cta E H, rectæ A F, &amp; </s>
  <s xml:id="echoid-s26995" xml:space="preserve">recta H G, rectæ F B, ob æqualitaté angulorum, &amp; </s>
  <s xml:id="echoid-s26996" xml:space="preserve">denique tota H G, pro <lb/>ducta in utramque partem toti horizontali lineæ congruet; </s>
  <s xml:id="echoid-s26997" xml:space="preserve">atque idcirco radii latitudinum orti-<lb/>uarum, occiduarumve lineę horizontali occurrent in punctis tanto ſpatio à pũcto B, vel F, diſtá-<lb/>tibus, quanto ſpatio à puncto G, vel H, abſunt puncta, vbi radii latitudinum rectam G H, ſecát, <lb/>
<anchor type="note" xlink:label="note-0426-04a" xlink:href="note-0426-04"/>
&amp; </s>
  <s xml:id="echoid-s26998" xml:space="preserve">c. </s>
  <s xml:id="echoid-s26999" xml:space="preserve">Signa igitur aſcendentia Zodiaci in eodem horologio declinante ſimul &amp; </s>
  <s xml:id="echoid-s27000" xml:space="preserve">inclinato repoſui-<lb/>mus. </s>
  <s xml:id="echoid-s27001" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27002" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1365" type="float" level="2" n="2">
<note position="left" xlink:label="note-0425-07" xlink:href="note-0425-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0426-01" xlink:href="note-0426-01a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0426-02" xlink:href="note-0426-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0426-03" xlink:href="note-0426-03a" xml:space="preserve">26. primi.</note>
<note position="left" xlink:label="note-0426-04" xlink:href="note-0426-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1367" type="section" level="1" n="330">
<head xml:id="echoid-head341" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s27003" xml:space="preserve">SI eadem aſcendentia ſigna deſcribere velim{us} ſecundum doctrinam Andreæ Schoneri, vtemur <lb/>
<anchor type="note" xlink:label="note-0426-05a" xlink:href="note-0426-05"/>
hac arte. </s>
  <s xml:id="echoid-s27004" xml:space="preserve">Inpriori figura ſcholĳ propoſ. </s>
  <s xml:id="echoid-s27005" xml:space="preserve">9. </s>
  <s xml:id="echoid-s27006" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27007" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27008" xml:space="preserve">ex recta E D, vel E B, abſcindatur recta E H, æqualis <lb/>rectæ L M, quæ in horologio intercipitur inter centrum L, &amp; </s>
  <s xml:id="echoid-s27009" xml:space="preserve">punctum M, vbi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s27010" xml:space="preserve"><lb/>meridiana ſe interſecant, &amp; </s>
  <s xml:id="echoid-s27011" xml:space="preserve">in H, conſtituatur cum recta B D, angul{us} æqualis ei, quem in horologio li-<lb/>nea æquinoctialis cum recta L M, efficit, hac tamen lege, vt poſito centro E, in centro L, &amp; </s>
  <s xml:id="echoid-s27012" xml:space="preserve">recta E D, <lb/>
<anchor type="note" xlink:label="note-0426-06a" xlink:href="note-0426-06"/>
ſupra rectam L M, recta per punctum H, ducta, &amp; </s>
  <s xml:id="echoid-s27013" xml:space="preserve">dictum angulum conſtituens congruat lineæ æqui-<lb/>noctiali. </s>
  <s xml:id="echoid-s27014" xml:space="preserve">Deinde interualla prædictæ rectæ per H, ductæinter H, &amp; </s>
  <s xml:id="echoid-s27015" xml:space="preserve">lineas ſignorum interiecta transfe-<lb/>rantur in lineam æquinoctialem ex puncto M, imprimendo puncta in ipſa æquinoctiali linea. </s>
  <s xml:id="echoid-s27016" xml:space="preserve">Si enim ex <lb/>puncto, vbi meridiana linea, &amp; </s>
  <s xml:id="echoid-s27017" xml:space="preserve">horizontalis ſe interſecant, per hæc puncta æquinoctialis lineæ ducantur <lb/>rectæ occultæ, ſecabuntur ambo tropici in punctis, per quæ ſigna aſcendẽtia erunt ducenda, hoc ordine ſer <lb/>
<anchor type="note" xlink:label="note-0426-07a" xlink:href="note-0426-07"/>
uato. </s>
  <s xml:id="echoid-s27018" xml:space="preserve">Si horologium vergat in ortum, pertinebit punctũ, vbi tropic{us} ♑, lineam horizontalẽ interſecat, <lb/>ad ♑, punctum verò, in quo ſe interſecant tropic{us} ♋, &amp; </s>
  <s xml:id="echoid-s27019" xml:space="preserve">horizontalis linea, ad ♋. </s>
  <s xml:id="echoid-s27020" xml:space="preserve">Proximum deinde <lb/>punctum in tropico infra horizontalem lineam debetur illi ſigno, quod proximè oritur post ♑, vel ♋, <lb/>vt ſigno ♒, vel ♌, &amp; </s>
  <s xml:id="echoid-s27021" xml:space="preserve">ita deinceps ſecundum ſucceſſionem ſignorum. </s>
  <s xml:id="echoid-s27022" xml:space="preserve">Si autem in occaſum deflectat ho-<lb/>rologium, tribuendum erit punctum, vbitropicus ♑, &amp; </s>
  <s xml:id="echoid-s27023" xml:space="preserve">linea horizontalis ſe mutuo ſecant, ſigno ♋; <lb/></s>
  <s xml:id="echoid-s27024" xml:space="preserve">punctum vero, vbi tropicus ♋, eandem horizontalem lineam ſecat, conueniet ſigno ♑. </s>
  <s xml:id="echoid-s27025" xml:space="preserve">Deinde proxi-<lb/>
<anchor type="note" xlink:label="note-0426-08a" xlink:href="note-0426-08"/>
mum punctum infra lineam horizontalem illi ſigno reſpondebit, quod ante ♑, vel ♋, oritur, vt ſigno <lb/>♐, vel ♊, &amp; </s>
  <s xml:id="echoid-s27026" xml:space="preserve">ſic deinceps contra ſignorum ſucceſſionem. </s>
  <s xml:id="echoid-s27027" xml:space="preserve">Exhis facili negotio intelligem{us}, quib{us} ſi-<lb/>gnis reſpondeant puncta tropicorum ſupra horizontalem lineam inuenta. </s>
  <s xml:id="echoid-s27028" xml:space="preserve">Nam ſi infra ſeruant ordinẽ <lb/>ſecundum ſucceſſionem ſignorum, ſeruabunt ſupra horizontalem lineam ordinem contra ſucceſſionem ſi-<lb/>gnorum, &amp; </s>
  <s xml:id="echoid-s27029" xml:space="preserve">contra, vt ex figuris aſcendentium ſignorum, qu{as} hactenus in varĳs planis conſtruxim{us}, <lb/>perſpicuum eſt. </s>
  <s xml:id="echoid-s27030" xml:space="preserve">Semper autem quælibet recta occulta ex puncto, vbi ſe interſecant meridiana linea, at-<lb/>que horizontalis, ducta per puncta in linea æquinoctiali inuenta, pertinet ad duo ſigna oppoſita, quem-<lb/>admodum &amp; </s>
  <s xml:id="echoid-s27031" xml:space="preserve">in priori figura radiorum ſignorum aſcendentium quælibet linea ad duo oppoſita ſigna per-<lb/>tinet: </s>
  <s xml:id="echoid-s27032" xml:space="preserve">ita vt ſi v. </s>
  <s xml:id="echoid-s27033" xml:space="preserve">g. </s>
  <s xml:id="echoid-s27034" xml:space="preserve">vnum punctum, per quod dicta linea occulta tranſit, pertinet ad ♊, alterum pun-<lb/>ctum, quod eadem recta monſtr at ſiue in oppoſito tropico, ſiue in eodem, pertineat ad ♐, &amp; </s>
  <s xml:id="echoid-s27035" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27036" xml:space="preserve">vt ex ſu-<lb/>
<anchor type="note" xlink:label="note-0426-09a" xlink:href="note-0426-09"/>
periorib{us} figuris ſignorum aſcendentium, qu{as} in varĳs planis depinximus, manifestum eſt.</s>
  <s xml:id="echoid-s27037" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1367" type="float" level="2" n="1">
<note position="left" xlink:label="note-0426-05" xlink:href="note-0426-05a" xml:space="preserve">Aſcendentis <lb/>figna, quo pa-<lb/>cto ex doctina <lb/>Andreæ Scho-<lb/>neri deſcriban <lb/>tur.</note>
<note position="left" xlink:label="note-0426-06" xlink:href="note-0426-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0426-07" xlink:href="note-0426-07a" xml:space="preserve">Ordo ſignorũ <lb/>aſcendentium <lb/>in tropicis.</note>
<note position="left" xlink:label="note-0426-08" xlink:href="note-0426-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0426-09" xlink:href="note-0426-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s27038" xml:space="preserve">IN propoſito exemplo, vbi meridiana linea, atque æquinoctialis æquidiſtantes ſunt, recta L M, <lb/>
<anchor type="note" xlink:label="note-0426-10a" xlink:href="note-0426-10"/>
ęquinoctialem lineam non ſecat, ſed ei parallela eſt, vnde cum ea angulum conſtituere non poteſt. </s>
  <s xml:id="echoid-s27039" xml:space="preserve">In <lb/>priori ergo figura ſignorum ducenda erit ipſi E D, linea parallela reſpondens æquinoctiali lineæ in horolo <lb/>gio, hac ratione. </s>
  <s xml:id="echoid-s27040" xml:space="preserve">Ex E C, ſumatur E K, æqualis rectæ, quæ in horologio inter centrum L, &amp; </s>
  <s xml:id="echoid-s27041" xml:space="preserve">punctum, <lb/>vbi linea horizontalis æquinoctialem diuidit, intercipitur, &amp; </s>
  <s xml:id="echoid-s27042" xml:space="preserve">per K, excitetur ad E K, perpendicularis <lb/>ſecans lineas ſignorum in punctis, quæ accepta ex puncto K, &amp; </s>
  <s xml:id="echoid-s27043" xml:space="preserve">translata in lineam æquinoctialem ex di-<lb/>cto puncto, vbi ſe ſecant linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s27044" xml:space="preserve">horizontalis, dabunt in æquinoctiali linea pun-<lb/>cta, vt pri{us}.</s>
  <s xml:id="echoid-s27045" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1368" type="float" level="2" n="2">
<note position="left" xlink:label="note-0426-10" xlink:href="note-0426-10a" xml:space="preserve">Quuando æqui <lb/>noctialis linea, <lb/>&amp; meridiana <lb/>parallelæ ſunt, <lb/>quid agendum <lb/>in aſcendenti-<lb/>bus ſignis deli-<lb/>meandis.</note>
</div>
<p style="it">
  <s xml:id="echoid-s27046" xml:space="preserve">QVOD ſi in horologio primæ figuræ propoſ. </s>
  <s xml:id="echoid-s27047" xml:space="preserve">37. </s>
  <s xml:id="echoid-s27048" xml:space="preserve">hui{us} lib. </s>
  <s xml:id="echoid-s27049" xml:space="preserve">deſcribenda ſint aſcendentia ſigna, con-
<pb o="411" file="0427" n="427" rhead="LIBER TERTIVS."/>
ſtituend{us} erit angulus E H Q, æqualis ei, quem in horologio recta L M, cum æquinoctiali linea confi-<lb/>cit, vt in priori figura radiorum aſcendentium ſignorum ſactum eft.</s>
  <s xml:id="echoid-s27050" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s27051" xml:space="preserve">RVRSVS in figura poſteriori eiuſdem ſcholĳ propoſ. </s>
  <s xml:id="echoid-s27052" xml:space="preserve">9. </s>
  <s xml:id="echoid-s27053" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27054" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27055" xml:space="preserve">ex recta E C, auferatur E K, æqua-<lb/>lis rectæ, quæ in horologio inter cipitur inter centrum L, &amp; </s>
  <s xml:id="echoid-s27056" xml:space="preserve">punctum, in quo ſe mutuo diuidunt linea ho-<lb/>rizontalis, &amp; </s>
  <s xml:id="echoid-s27057" xml:space="preserve">æquinoctialis: </s>
  <s xml:id="echoid-s27058" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27059" xml:space="preserve">in K, cum E K, fiat angulus æqualis ei, quem æquinoctialis linea consti <lb/>tuit cum recta ducta ex L, per dictum punctum, vbi horizontalis linea æquinoctialem ſecat, ea tamen <lb/>lege, &amp; </s>
  <s xml:id="echoid-s27060" xml:space="preserve">conditione, vt poſito centro E, in centro L, &amp; </s>
  <s xml:id="echoid-s27061" xml:space="preserve">recta E C, ſupra rectam ductam ex L, per pun-<lb/>ctum, vbi ſe interſecant linea horizontalis, atque æquinoctialis, recta per K, ducta congruat lineę æqui-<lb/>noctiali. </s>
  <s xml:id="echoid-s27062" xml:space="preserve">In noſtro exemplo dict{us} angul{us} rect{us} eſt. </s>
  <s xml:id="echoid-s27063" xml:space="preserve">In primo autem horologio propoſ. </s>
  <s xml:id="echoid-s27064" xml:space="preserve">37. </s>
  <s xml:id="echoid-s27065" xml:space="preserve">hui{us} lib. <lb/></s>
  <s xml:id="echoid-s27066" xml:space="preserve">quoniam linea horizontalis ſecat æquinoctialem lineam in H, ſumem{us} rectæ L H, æqualem E K, in po-<lb/>
<anchor type="note" xlink:label="note-0427-01a" xlink:href="note-0427-01"/>
ſteriori figura dicti ſcholĳ, &amp; </s>
  <s xml:id="echoid-s27067" xml:space="preserve">angulum E K Q, æqualem conſtituem{us} angulo illi, quem in horologio re-<lb/>cta L H, cum æquinoctiali linea efficit, &amp; </s>
  <s xml:id="echoid-s27068" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27069" xml:space="preserve">Deinde interualla rectæ per K, ductæ inter K, &amp; </s>
  <s xml:id="echoid-s27070" xml:space="preserve">lineas ſi-<lb/>gnorum transferantur in lineam æquinoctialem ex puncto, quod lineæ horizont ali, &amp; </s>
  <s xml:id="echoid-s27071" xml:space="preserve">æquinoctiali com-<lb/>mune eſt, eo ordine, quem haberent, ſi recta per K, ducta lineę æquinoctiali congrueret. </s>
  <s xml:id="echoid-s27072" xml:space="preserve">Hęc enim pun-<lb/>cta cum reſpondentib{us} punctis, quæ in tropicis inuenta ſunt, coniuncta lineis rectis dabunt aſcendentia <lb/>ſigna, quorum ordo in horologio ſpectante ad ortum hic eſt in linea æquinoctiali. </s>
  <s xml:id="echoid-s27073" xml:space="preserve">Primum punctum infra <lb/>
<anchor type="note" xlink:label="note-0427-02a" xlink:href="note-0427-02"/>
horizontalem lineam inuentum ex poſteriori figura pertinet ad ♉, ſequens ad ♊, &amp; </s>
  <s xml:id="echoid-s27074" xml:space="preserve">♏, &amp; </s>
  <s xml:id="echoid-s27075" xml:space="preserve">ita deinceps <lb/>eo ordine, vt in figura prædicta ſunt deſcripta. </s>
  <s xml:id="echoid-s27076" xml:space="preserve">Proximum autem punctum ſupralineam horizontalẽ <lb/>reſpondet ſigno ♓, ſequens ſignis ♒, &amp; </s>
  <s xml:id="echoid-s27077" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s27078" xml:space="preserve">ſic deinceps, prout ſequuntur in figura. </s>
  <s xml:id="echoid-s27079" xml:space="preserve">In horologio au-<lb/>tem in occaſum declinante contrarius erit ordo. </s>
  <s xml:id="echoid-s27080" xml:space="preserve">Nam primum punctum infra lineam horizontalem per-<lb/>
<anchor type="note" xlink:label="note-0427-03a" xlink:href="note-0427-03"/>
tinebit ad ♓, ſequens ad ♒, &amp; </s>
  <s xml:id="echoid-s27081" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s27082" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27083" xml:space="preserve">Proximum autem punctum ſupra lineam horizontalem ſpecta-<lb/>bit ad ♉, ſequens ad ♊, &amp; </s>
  <s xml:id="echoid-s27084" xml:space="preserve">♒, &amp; </s>
  <s xml:id="echoid-s27085" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27086" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1369" type="float" level="2" n="3">
<note position="left" xlink:label="note-0427-01" xlink:href="note-0427-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0427-02" xlink:href="note-0427-02a" xml:space="preserve">Ordo ſignorũ <lb/>aſcenden tium <lb/>in linea ęqui-<lb/>noctiali.</note>
<note position="left" xlink:label="note-0427-03" xlink:href="note-0427-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1371" type="section" level="1" n="331">
<head xml:id="echoid-head342" xml:space="preserve">PROBLEMA 46. PROPOSITIO 46.</head>
<p>
  <s xml:id="echoid-s27087" xml:space="preserve">HOROLOGIVM Italicum, quod &amp; </s>
  <s xml:id="echoid-s27088" xml:space="preserve">à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s27089" xml:space="preserve"><lb/>inclinatum eſt ad Horizontem, componere.</s>
  <s xml:id="echoid-s27090" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27091" xml:space="preserve">VT in pręcedentibus horologiis, &amp; </s>
  <s xml:id="echoid-s27092" xml:space="preserve">in hoc lineas horarum ab occaſu ducemus, ſi circulum ex <lb/>
<anchor type="note" xlink:label="note-0427-04a" xlink:href="note-0427-04"/>
<anchor type="note" xlink:label="note-0427-05a" xlink:href="note-0427-05"/>
L, deſcrptum partiamur in arcum diurnum paralleli ♋, a M b, &amp; </s>
  <s xml:id="echoid-s27093" xml:space="preserve">diurnum paralleli ♑, d M e, <lb/>ita ut rectæ a b, d e, ſecent rectam L M, quæ communis ſectio eſt Meridiani, &amp; </s>
  <s xml:id="echoid-s27094" xml:space="preserve">Æquatoris, ad <lb/>angulos rectos, vt ad propoſ. </s>
  <s xml:id="echoid-s27095" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27096" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27097" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27098" xml:space="preserve">tradidimns, dummodo diuiſio circuli in 24. </s>
  <s xml:id="echoid-s27099" xml:space="preserve">horas ęqua-<lb/>les principium habeat à punctis occidentalibus b, e. </s>
  <s xml:id="echoid-s27100" xml:space="preserve">Sed quoniã in noſtro horologio tropicus ♑, <lb/>deſcribi non poteſt, ſatis erit, ſi inueniãtur puncta horarum ab occaſu in tropico ♋, beneficio ar-<lb/>cus diurni eiuſdem ttopici. </s>
  <s xml:id="echoid-s27101" xml:space="preserve">Reperiemus autem in ſuperiori horologio noſtri exempli, hoc eſt, in <lb/>portione infra horizontalem lineam contenta, puncta duntaxat horarum ab occaſu à 9. </s>
  <s xml:id="echoid-s27102" xml:space="preserve">uſque <lb/>ad 16. </s>
  <s xml:id="echoid-s27103" xml:space="preserve">incluſiue, quia hæ omnes horę continentur in arcu circuli a M, ex cuius punctis lineæ re-<lb/>ctę ductæ per centrum L, occurruntlineæ æquinoctiali, poſtquam per centrum L, ductę ſunt. <lb/></s>
  <s xml:id="echoid-s27104" xml:space="preserve">Hæc autem puncta lineis rectis coniuncta cum horis reſpondentibus in linea æquinoctiali, vt ex <lb/>tabulis arcus diurni, &amp; </s>
  <s xml:id="echoid-s27105" xml:space="preserve">arcus nocturni horarum 12. </s>
  <s xml:id="echoid-s27106" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s27107" xml:space="preserve">33. </s>
  <s xml:id="echoid-s27108" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27109" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27110" xml:space="preserve">poſitis conſtat, <lb/>
<anchor type="note" xlink:label="note-0427-06a" xlink:href="note-0427-06"/>
vel ex tabula propoſ 19. </s>
  <s xml:id="echoid-s27111" xml:space="preserve">eiuſdẽ libri, deſcriptæ erũt horæ ab occaſu in ſuperiori horologio à 9 ho <lb/>ra uſq; </s>
  <s xml:id="echoid-s27112" xml:space="preserve">ad 16. </s>
  <s xml:id="echoid-s27113" xml:space="preserve">incluſiue. </s>
  <s xml:id="echoid-s27114" xml:space="preserve">Puncta autẽ horarũ 17. </s>
  <s xml:id="echoid-s27115" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27116" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27117" xml:space="preserve">ab occaſu ita inueniemus in tropico ♋. </s>
  <s xml:id="echoid-s27118" xml:space="preserve">Ex <lb/>punctis hor. </s>
  <s xml:id="echoid-s27119" xml:space="preserve">5. </s>
  <s xml:id="echoid-s27120" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27121" xml:space="preserve">6. </s>
  <s xml:id="echoid-s27122" xml:space="preserve">ab occaſu in circulo a M b N, quæ cõtinentur in arcu a N, opponunturq́; </s>
  <s xml:id="echoid-s27123" xml:space="preserve">dictis <lb/>horis 17. </s>
  <s xml:id="echoid-s27124" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27125" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27126" xml:space="preserve">ducemus lineas occultas per centrũ L. </s>
  <s xml:id="echoid-s27127" xml:space="preserve">Beneficio enim earũ reperiemus in tropi-<lb/>co ♋, in portione nocturna puncta pro hor. </s>
  <s xml:id="echoid-s27128" xml:space="preserve">5. </s>
  <s xml:id="echoid-s27129" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27130" xml:space="preserve">6. </s>
  <s xml:id="echoid-s27131" xml:space="preserve">à quibus rectę occultę per ρ, centrum horolo-<lb/>gii ductæ dabunt in eodẽ tropico ♋, puncta horarũ 17. </s>
  <s xml:id="echoid-s27132" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27133" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27134" xml:space="preserve">vt ex demonſtratis in propoſ. </s>
  <s xml:id="echoid-s27135" xml:space="preserve">10. </s>
  <s xml:id="echoid-s27136" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s27137" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27138" xml:space="preserve">colligitur. </s>
  <s xml:id="echoid-s27139" xml:space="preserve">Erit auté linea horę 18. </s>
  <s xml:id="echoid-s27140" xml:space="preserve">ab occaſu in plano nobis propoſito parallela lineę ęquinoctia <lb/>li, &amp; </s>
  <s xml:id="echoid-s27141" xml:space="preserve">meridianæ; </s>
  <s xml:id="echoid-s27142" xml:space="preserve">quia ſi ſecaret lineam ęquinoctialem, neceſſario hoc contingeret in hora 12. </s>
  <s xml:id="echoid-s27143" xml:space="preserve">à <lb/>mer. </s>
  <s xml:id="echoid-s27144" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27145" xml:space="preserve">nocte, vt ex tabula propoſ. </s>
  <s xml:id="echoid-s27146" xml:space="preserve">19. </s>
  <s xml:id="echoid-s27147" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27148" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27149" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s27150" xml:space="preserve">Cum ergo hora 12. </s>
  <s xml:id="echoid-s27151" xml:space="preserve">æquinoctialem <lb/>lineam in noſtro exemplo non ſecet, ſed ei æquidiſtet, perſpicuum eſt, neque horam 18. </s>
  <s xml:id="echoid-s27152" xml:space="preserve">poſ@e <lb/>
<anchor type="note" xlink:label="note-0427-07a" xlink:href="note-0427-07"/>
eandem ſecare. </s>
  <s xml:id="echoid-s27153" xml:space="preserve">Quare parallela ei erit. </s>
  <s xml:id="echoid-s27154" xml:space="preserve">Idem dicendum eſt de hora 6. </s>
  <s xml:id="echoid-s27155" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s27156" xml:space="preserve">hæc e-<lb/>nim parallela etiam eſt lineæ æquinoctiali, &amp; </s>
  <s xml:id="echoid-s27157" xml:space="preserve">meridianę. </s>
  <s xml:id="echoid-s27158" xml:space="preserve">Quod facile hac quoq; </s>
  <s xml:id="echoid-s27159" xml:space="preserve">ratione demõſtra <lb/>ri poteſt. </s>
  <s xml:id="echoid-s27160" xml:space="preserve">Quoniam per propoſ. </s>
  <s xml:id="echoid-s27161" xml:space="preserve">16. </s>
  <s xml:id="echoid-s27162" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27163" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27164" xml:space="preserve">circuli hor. </s>
  <s xml:id="echoid-s27165" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27166" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27167" xml:space="preserve">6. </s>
  <s xml:id="echoid-s27168" xml:space="preserve">ab ortu, vel occaſu cum Æquatore <lb/>
<anchor type="note" xlink:label="note-0427-08a" xlink:href="note-0427-08"/>
eandem communem ſectionem habent, nec non per propoſ. </s>
  <s xml:id="echoid-s27169" xml:space="preserve">17. </s>
  <s xml:id="echoid-s27170" xml:space="preserve">eiuſdem libri, eandem cũ Me-<lb/>ridiano, neceſſe eſt, illos tranſire per communem ſectionẽ Meridiani, &amp; </s>
  <s xml:id="echoid-s27171" xml:space="preserve">Æquatoris, adeò vt hæc <lb/>cõmunis ſectio ſit cõmunis ſectio illorũ circulorũ, &amp; </s>
  <s xml:id="echoid-s27172" xml:space="preserve">Æquatoris, ac Meridiani Cum ergo planũ <lb/>horologii huic ſectioni cõmuni æquidiſtet, quod parallelũ ſit circulo maximo declinanti à Verti <lb/>cali, &amp; </s>
  <s xml:id="echoid-s27173" xml:space="preserve">ad Horizontẽ inclinato, qui per dictam ſectionẽ ducitur; </s>
  <s xml:id="echoid-s27174" xml:space="preserve">erunt per propoſ. </s>
  <s xml:id="echoid-s27175" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27176" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27177" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27178" xml:space="preserve">paral-<lb/>lelæ inter ſeſe ſectiones illę, quas nominati circuli in horologii plano efficiũt, nẽpe linea æquino-<lb/>ctialis, linea meridiana, &amp; </s>
  <s xml:id="echoid-s27179" xml:space="preserve">lineæ hor. </s>
  <s xml:id="echoid-s27180" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27181" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27182" xml:space="preserve">6. </s>
  <s xml:id="echoid-s27183" xml:space="preserve">ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s27184" xml:space="preserve">Hora verò 17. </s>
  <s xml:id="echoid-s27185" xml:space="preserve">ducẽda eſt per
<pb o="412" file="0428" n="428" rhead="GNOMONICES"/>
horam 11. </s>
  <s xml:id="echoid-s27186" xml:space="preserve">@ mer. </s>
  <s xml:id="echoid-s27187" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27188" xml:space="preserve">nocte in linea æquinoctiali, atque ita abſolutum erit horologium I@@-<lb/>licum ſuperius, cum uix plures horæ ab occaſu deſcribi poſſint in propoſito plano.</s>
  <s xml:id="echoid-s27189" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1371" type="float" level="2" n="1">
<note position="left" xlink:label="note-0427-04" xlink:href="note-0427-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0427-05" xlink:href="note-0427-05a" xml:space="preserve">Horologii Ita-<lb/>li@i dccl<unsure/>nantis <lb/>ſimul &amp; incli-<lb/>nati conſtru -<lb/>ctio.</note>
<note position="left" xlink:label="note-0427-06" xlink:href="note-0427-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0427-07" xlink:href="note-0427-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0427-08" xlink:href="note-0427-08a" xml:space="preserve">Linea æquino<unsure/>-<lb/>ctialis, linea me <lb/>ridiana, &amp; li <lb/>neę hor. 6 &amp; 18. <lb/>ab or. &amp; occ pa <lb/>rallelę ſunt in <lb/>propoſito horo<unsure/> <lb/>logio.</note>
</div>
  <figure>
    <image file="0428-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0428-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s27190" xml:space="preserve">VT autem conficiamus horologium Italicum inferius, deſcribendę erũt in portione noctur-<lb/>na horologii horæ ab ortu, nempe 23. </s>
  <s xml:id="echoid-s27191" xml:space="preserve">22. </s>
  <s xml:id="echoid-s27192" xml:space="preserve">21. </s>
  <s xml:id="echoid-s27193" xml:space="preserve">20. </s>
  <s xml:id="echoid-s27194" xml:space="preserve">19. </s>
  <s xml:id="echoid-s27195" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27196" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s27197" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27198" xml:space="preserve">Hæ enim, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s27199" xml:space="preserve">23. <lb/></s>
  <s xml:id="echoid-s27200" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27201" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27202" xml:space="preserve">oſtendimus, numerantur in inferiori horologio ab occaſu. </s>
  <s xml:id="echoid-s27203" xml:space="preserve">Continentur autem dictæ horæ <lb/>in portionea N b, circuli ex L, deſcripti, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s27204" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27205" xml:space="preserve">COMMODIVS multo eædem horæ ab occaſu deſcribentur per arcum diurnum horarũ <lb/>
<anchor type="note" xlink:label="note-0428-05a" xlink:href="note-0428-05"/>
<anchor type="note" xlink:label="note-0428-06a" xlink:href="note-0428-06"/>
24. </s>
  <s xml:id="echoid-s27206" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27207" xml:space="preserve">per arcum diurnum horarum 14. </s>
  <s xml:id="echoid-s27208" xml:space="preserve">qui in portione nocturna horologii mutatur in arcum <lb/>nocturnum hor. </s>
  <s xml:id="echoid-s27209" xml:space="preserve">10. </s>
  <s xml:id="echoid-s27210" xml:space="preserve">Omnes enim lineæ horarum ab occaſu tangunt arcum diurnum horarũ 24. <lb/></s>
  <s xml:id="echoid-s27211" xml:space="preserve">in punctis horarum à mer. </s>
  <s xml:id="echoid-s27212" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27213" xml:space="preserve">nocte, vt in propoſ. </s>
  <s xml:id="echoid-s27214" xml:space="preserve">14. </s>
  <s xml:id="echoid-s27215" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27216" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27217" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s27218" xml:space="preserve">Vnde fe-<lb/>rè ſemper in deſcriptione horarum ab occaſu habebimus pro ſingulis horis terna puncta, vnum <lb/>videlicet in arcu diurno horarum 24. </s>
  <s xml:id="echoid-s27219" xml:space="preserve">alterum in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s27220" xml:space="preserve">vel nocturno hora-<lb/>rum 10. </s>
  <s xml:id="echoid-s27221" xml:space="preserve">tertium denique in linea æquinoctiali, ſeu arcu diurno, nocturnove horarum 12. </s>
  <s xml:id="echoid-s27222" xml:space="preserve">vt <lb/>ex tabulis in lib. </s>
  <s xml:id="echoid-s27223" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27224" xml:space="preserve">poſitis conſtat. </s>
  <s xml:id="echoid-s27225" xml:space="preserve">Cuius rei non opus eſt ex@mplum ponere, c<unsure/>um perfacilis ſit.</s>
  <s xml:id="echoid-s27226" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1372" type="float" level="2" n="2">
<note position="left" xlink:label="note-0428-05" xlink:href="note-0428-05a" xml:space="preserve">Eiufdem horo <lb/>logii Italici de <lb/>ſcriptio per ar-<lb/>cus diurnos no <lb/>cturno@q́ue.</note>
<note position="left" xlink:label="note-0428-06" xlink:href="note-0428-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s27227" xml:space="preserve">IAM vero quod ad ſectiones mutuas horarum ab or. </s>
  <s xml:id="echoid-s27228" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s27229" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27230" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s27231" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27232" xml:space="preserve">nocteattinet, <lb/>res admodum perſpicua eſt ex tabulis propoſ. </s>
  <s xml:id="echoid-s27233" xml:space="preserve">19. </s>
  <s xml:id="echoid-s27234" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27235" xml:space="preserve">20. </s>
  <s xml:id="echoid-s27236" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27237" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27238" xml:space="preserve">Itaque horologium Italicũ, quod <lb/>&amp; </s>
  <s xml:id="echoid-s27239" xml:space="preserve">à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s27240" xml:space="preserve">inclinatum eſtad Horizontem, compoſuimus. </s>
  <s xml:id="echoid-s27241" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s27242" xml:space="preserve"/>
</p>
<pb o="413" file="0429" n="429" rhead="LIBER TERTIVS."/>
</div>
<div xml:id="echoid-div1374" type="section" level="1" n="332">
<head xml:id="echoid-head343" xml:space="preserve">PROBLEMA 47. PROPOSITIO 47.</head>
<p>
  <s xml:id="echoid-s27243" xml:space="preserve">HOROLOGIVM Babylonicum, quod &amp; </s>
  <s xml:id="echoid-s27244" xml:space="preserve">à Verticali declinat, <lb/>&amp; </s>
  <s xml:id="echoid-s27245" xml:space="preserve">ad Horizontem eſt inclinatum, conſtruere.</s>
  <s xml:id="echoid-s27246" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27247" xml:space="preserve">PRORSVS ijſdem uijs horologium Babylonicum in plano propoſito conficiemus, quibus <lb/>
<anchor type="note" xlink:label="note-0429-01a" xlink:href="note-0429-01"/>
Italicum deſcripſimus, vt liquido ex figura præcedentis propoſ. </s>
  <s xml:id="echoid-s27248" xml:space="preserve">apparet; </s>
  <s xml:id="echoid-s27249" xml:space="preserve">Vbi cõtinentur &amp; </s>
  <s xml:id="echoid-s27250" xml:space="preserve">horæ <lb/>à mer. </s>
  <s xml:id="echoid-s27251" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27252" xml:space="preserve">nocte, &amp; </s>
  <s xml:id="echoid-s27253" xml:space="preserve">tam ab ortu, quàm ab occaſu, quemadmodum in ſuperioribus horolo-<lb/>giis. </s>
  <s xml:id="echoid-s27254" xml:space="preserve">Sed in primo modo diuiſio circuli a M b N, inchoanda eſt à punctis orientalibus a, &amp; </s>
  <s xml:id="echoid-s27255" xml:space="preserve">d. <lb/></s>
  <s xml:id="echoid-s27256" xml:space="preserve">Horologium ergo Babylonicum, quod &amp; </s>
  <s xml:id="echoid-s27257" xml:space="preserve">à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s27258" xml:space="preserve">ad Horizontem eſt inclinatum, <lb/>
<anchor type="note" xlink:label="note-0429-02a" xlink:href="note-0429-02"/>
conſtruximus. </s>
  <s xml:id="echoid-s27259" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27260" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1374" type="float" level="2" n="1">
<note position="right" xlink:label="note-0429-01" xlink:href="note-0429-01a" xml:space="preserve">Compoſitio ho <lb/>rologii Babylo <lb/>nici declinan-<lb/>tis ſimul &amp; in-<lb/>clinati.</note>
<note position="left" xlink:label="note-0429-02" xlink:href="note-0429-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1376" type="section" level="1" n="333">
<head xml:id="echoid-head344" xml:space="preserve">PROBLEMA 48. PROPOSITIO 48.</head>
<p>
  <s xml:id="echoid-s27261" xml:space="preserve">HOROLOGIVM Antiquum à Verticali declinans ſimul &amp; </s>
  <s xml:id="echoid-s27262" xml:space="preserve"><lb/>inclinatum ad Horizontem conficere.</s>
  <s xml:id="echoid-s27263" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27264" xml:space="preserve">HOC etiam horologium conſtruemus in plano declinante à Verticali circulo, &amp; </s>
  <s xml:id="echoid-s27265" xml:space="preserve">ad Horizon-<lb/>
<anchor type="note" xlink:label="note-0429-03a" xlink:href="note-0429-03"/>
tem inclinato eiſdem rationibus, quibus in alijs planis uſi ſumus, vt ipſa figura indicat, in qua <lb/>
<anchor type="note" xlink:label="note-0429-04a" xlink:href="note-0429-04"/>
<anchor type="figure" xlink:label="fig-0429-01a" xlink:href="fig-0429-01"/>
<anchor type="note" xlink:label="note-0429-05a" xlink:href="note-0429-05"/>
<anchor type="note" xlink:label="note-0429-06a" xlink:href="note-0429-06"/>
<anchor type="note" xlink:label="note-0429-07a" xlink:href="note-0429-07"/>
arcum diurnum horarum 18. </s>
  <s xml:id="echoid-s27266" xml:space="preserve">delineauimus, qui in portione horologij nocturna in arcũ noctur-<lb/>num horarum 6. </s>
  <s xml:id="echoid-s27267" xml:space="preserve">commutatur. </s>
  <s xml:id="echoid-s27268" xml:space="preserve">Quamobrem horologium Antiquum à Verticali declinans ſimul <lb/>&amp; </s>
  <s xml:id="echoid-s27269" xml:space="preserve">inclinatum ad Horizontem confecimus. </s>
  <s xml:id="echoid-s27270" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27271" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1376" type="float" level="2" n="1">
<note position="right" xlink:label="note-0429-03" xlink:href="note-0429-03a" xml:space="preserve">Antiqui horo-<lb/>logii declinan-<lb/>tis fimul &amp; in-<lb/>c<unsure/>linati delinea <lb/>@o.</note>
<note position="left" xlink:label="note-0429-04" xlink:href="note-0429-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0429-01" xlink:href="fig-0429-01a">
    <image file="0429-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0429-01"/>
  </figure>
<note position="left" xlink:label="note-0429-05" xlink:href="note-0429-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0429-06" xlink:href="note-0429-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0429-07" xlink:href="note-0429-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1378" type="section" level="1" n="334">
<head xml:id="echoid-head345" style="it" xml:space="preserve">FINIS TERTII LIBRI.</head>
<pb o="414" file="0430" n="430"/>
</div>
<div xml:id="echoid-div1379" type="section" level="1" n="335">
<head xml:id="echoid-head346" xml:space="preserve">GNOMONICES</head>
<head xml:id="echoid-head347" xml:space="preserve">LIBER QVARTVS.</head>
  <figure>
    <image file="0430-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0430-01"/>
  </figure>
</div>
<div xml:id="echoid-div1380" type="section" level="1" n="336">
<head xml:id="echoid-head348" style="it" xml:space="preserve">AVCTORE</head>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1381" type="section" level="1" n="337">
<head xml:id="echoid-head349" xml:space="preserve">CHRISTOPHORO CLAVIO BAMBER GENSI</head>
<head xml:id="echoid-head350" xml:space="preserve">SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s27272" xml:space="preserve">SVPERIORIBVS proximis duobus libris præcepta tradi-<lb/>dimus, quibus deſcriptio horarum omnis generis, aliarumq<unsure/>; <lb/></s>
  <s xml:id="echoid-s27273" xml:space="preserve">rerum, quæ ex vmbra Gnomonis cognoſci poſſunt, abſoluatur <lb/>ad datam quamcũque latitudinem loci inter Æquatorem, &amp; </s>
  <s xml:id="echoid-s27274" xml:space="preserve"><lb/>polum arcticum conſtituti, &amp; </s>
  <s xml:id="echoid-s27275" xml:space="preserve">in omnibus planis, quæ poſſunt <lb/>
<anchor type="note" xlink:label="note-0430-02a" xlink:href="note-0430-02"/>
excogitari. </s>
  <s xml:id="echoid-s27276" xml:space="preserve">Reſtat vt doceamus, quo pacto earundem rerum <lb/>
<anchor type="note" xlink:label="note-0430-03a" xlink:href="note-0430-03"/>
deſcriptio inſtituenda ſit in eiſdem planis in ſphæra recta exi-<lb/>ſtentibus, vbi nulla eſt altitudo poli ſupra Horizontem, nec <lb/>non in ſphæra obliquiſſima, vbi polus arcticus grad. </s>
  <s xml:id="echoid-s27277" xml:space="preserve">90. </s>
  <s xml:id="echoid-s27278" xml:space="preserve">ſupra <lb/>Horizontem attollitur. </s>
  <s xml:id="echoid-s27279" xml:space="preserve">Deinde quomodo apud antipodas quibus polus antarcti-<lb/>cus huic noſtro oppoſitus ſupra Horizontem eleuatur, eadem horologia deſcripta <lb/>ſe habeant, quo ad numerum, &amp; </s>
  <s xml:id="echoid-s27280" xml:space="preserve">ordinem horarum: </s>
  <s xml:id="echoid-s27281" xml:space="preserve">qui omnino apud antipodas <lb/>mutari debet, vt infra exponemus. </s>
  <s xml:id="echoid-s27282" xml:space="preserve">Quamuis enim omnia hæc ex ſuperioribus præ-<lb/>ceptis poſſint facile colligi, tamen quia nonnulla breuius hic deſcribuntur, &amp; </s>
  <s xml:id="echoid-s27283" xml:space="preserve">quę-<lb/>dam alia diuerſas regulas poſtulant, viſum eſt ea hoc libro ſeorſum explicare. </s>
  <s xml:id="echoid-s27284" xml:space="preserve">Po-<lb/>
<anchor type="note" xlink:label="note-0430-04a" xlink:href="note-0430-04"/>
ſtremo vno aut altero exemplo docebimus, quæ diuerſitates conſequantur in ho-<lb/>rologiorum lineamentis diuerſam poli eleuationẽ tum apud nos, tum apud antipo <lb/>das. </s>
  <s xml:id="echoid-s27285" xml:space="preserve">Hac enim re ignorata, facile cõtingeret cuipiam in deſcribendis varijs horolo-<lb/>gijs interdum hærere, præſertim in horis ab or. </s>
  <s xml:id="echoid-s27286" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27287" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s27288" xml:space="preserve">quæ aliquando, etiam ſi in in-<lb/>finitũ producantur, duos tropicos non ſecãt, ſed alios duos parallelos intra tropicos <lb/>contingunt. </s>
  <s xml:id="echoid-s27289" xml:space="preserve">His omnibus tria adijciemus problemata, quibus demonſtrabimus, <lb/>qua ratione ſtylus, ſiue gnomon cuiuſque horologij proprio in loco collocari de-<lb/>beat, vt ad planum horologii rectus ſit: </s>
  <s xml:id="echoid-s27290" xml:space="preserve">quo item modo eius vertex, ſi quando à pro-<lb/>pria ſede deflexerit, in eandem poſſit reſtitui. </s>
  <s xml:id="echoid-s27291" xml:space="preserve">Inſuper, qua via inueſtigandum ſit, ad <lb/>quam altitudinem poli datum horologiũ ſit fabricatum, cuius ſtylus, eiuſque locus <lb/>datus ſit. </s>
  <s xml:id="echoid-s27292" xml:space="preserve">Item quam declinationem habeat à Verticali, &amp; </s>
  <s xml:id="echoid-s27293" xml:space="preserve">inclinationem ad Hori-<lb/>
<anchor type="note" xlink:label="note-0430-05a" xlink:href="note-0430-05"/>
zontem, ſi declinans eſt, aut inclinatũ, nec non quanta ſit altitudo poli ſupra ipſum <lb/>planum declinans, aut inclinatum: </s>
  <s xml:id="echoid-s27294" xml:space="preserve">Et contra, quo pacto, dato horologio, vna cum <lb/>altitudine poli, ad quam conſtructum eſt, nec non inclinatione eius ad Horizontẽ, <lb/>ſi inclinatum eſt, inquirenda ſit longitudo ſtyli eiuſque locus, vna cum declinatio-<lb/>ne à Verticali, ſi horologium declinans eſt, nec non altitudine poli ſupra ipſum <lb/>planum declinans, inclinatumve. </s>
  <s xml:id="echoid-s27295" xml:space="preserve">Tandem qua arte horologium quodcumque in <lb/>maiorem, minoremve formam redigendum ſit, oſtendemus, manente eadem ſem-<lb/>per proportione lineamentorum &amp; </s>
  <s xml:id="echoid-s27296" xml:space="preserve">vmbrarum; </s>
  <s xml:id="echoid-s27297" xml:space="preserve">quod nõ raro vſu venire ſolet, præ-<lb/>ſertim quando horologium quodpiam in charta deſcriptum, aut in quauis alia <lb/>
<anchor type="note" xlink:label="note-0430-06a" xlink:href="note-0430-06"/>
materia, in murum, pro quo delineatum eſt, transferendum ſit.</s>
  <s xml:id="echoid-s27298" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1381" type="float" level="2" n="1">
<note position="left" xlink:label="note-0430-02" xlink:href="note-0430-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0430-03" xlink:href="note-0430-03a" xml:space="preserve">Argumentu@ <lb/>quarti libri.</note>
<note position="left" xlink:label="note-0430-04" xlink:href="note-0430-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0430-05" xlink:href="note-0430-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0430-06" xlink:href="note-0430-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1383" type="section" level="1" n="338">
<head xml:id="echoid-head351" xml:space="preserve">PROBLEMA 1. PROPOSITIO 1.</head>
<p>
  <s xml:id="echoid-s27299" xml:space="preserve">HOROLOGIA horizontalia in ſphęra recta deſcribere.</s>
  <s xml:id="echoid-s27300" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27301" xml:space="preserve">HORÆ à meridie, &amp; </s>
  <s xml:id="echoid-s27302" xml:space="preserve">media nocte in horologio horizontali ſphæ ę rectę, &amp; </s>
  <s xml:id="echoid-s27303" xml:space="preserve">paral-<lb/>
<anchor type="note" xlink:label="note-0430-07a" xlink:href="note-0430-07"/>
leli ſiguorum Zodiaci, nec non paralleli ciuitatum, ſiue circuli latitudinum de-<lb/>ſcribentur, vt in horologio polari, de quo in lib. </s>
  <s xml:id="echoid-s27304" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27305" xml:space="preserve">egimus: </s>
  <s xml:id="echoid-s27306" xml:space="preserve">propterea quòd Ho-<lb/>rizon ſphæræ rectæ per polos mundi ducitur, non ſecus, atque circulus horæ 6. </s>
  <s xml:id="echoid-s27307" xml:space="preserve">@ <lb/>mer. </s>
  <s xml:id="echoid-s27308" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27309" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s27310" xml:space="preserve">cui horologium polareæquidiſtat. </s>
  <s xml:id="echoid-s27311" xml:space="preserve">Immo circulus horæ 6. <lb/></s>
  <s xml:id="echoid-s27312" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s27313" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s27314" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s27315" xml:space="preserve">ab Horizonte ſphæræ rectæ non differt. </s>
  <s xml:id="echoid-s27316" xml:space="preserve">Sed horizontalis linea in horizon-
<pb o="415" file="0431" n="431" rhead="LIBER QVARTVS."/>
tali horologio ſphæræ rectæ ducenda non eſt, ſient nec in horizontali horologio ſphæræ obli-<lb/>quæ ducitur, cum Horizon illam ltneam faciens planum horologii horizontalis ſiue in ſphæra <lb/>recta, ſiue in obli <lb/>
<anchor type="figure" xlink:label="fig-0431-01a" xlink:href="fig-0431-01"/>
qua, nõ ſecet. </s>
  <s xml:id="echoid-s27317" xml:space="preserve">Ita-<lb/>que ſi polare ho <lb/>rologium lib. </s>
  <s xml:id="echoid-s27318" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s27319" xml:space="preserve">deſcriptũ in ſphę <lb/>ra recta ſtatuatur <lb/>Horizonti æqui-<lb/>diſtãs, ita vt linea <lb/>
<anchor type="note" xlink:label="note-0431-01a" xlink:href="note-0431-01"/>
meridiana pro-<lb/>prium ſitum ha-<lb/>beat, punctumq́; <lb/></s>
  <s xml:id="echoid-s27320" xml:space="preserve">D, ad borealem <lb/>polum, &amp; </s>
  <s xml:id="echoid-s27321" xml:space="preserve">E, ad <lb/>auſtralem vergat, <lb/>habebunt nume <lb/>ri horarum, &amp; </s>
  <s xml:id="echoid-s27322" xml:space="preserve">ſi-<lb/>gna Zodiaci eun <lb/>dem ordinẽ, quẽ <lb/>
<anchor type="note" xlink:label="note-0431-02a" xlink:href="note-0431-02"/>
in polari horologio, hoc eſt, horæ à media nocte ſitæ erunt nobis ad polum antarcticum conuer <lb/>ſis ad dexteram, ſiue ad occaſum; </s>
  <s xml:id="echoid-s27323" xml:space="preserve">horę verò à meridie ad ſiniſtram ſiue ad ortum. </s>
  <s xml:id="echoid-s27324" xml:space="preserve">Signa item be-<lb/>realia ad auſtrum, &amp; </s>
  <s xml:id="echoid-s27325" xml:space="preserve">auſtralia ad boream erunt poſita, vt appoſita figura demonſtrat, in qua ex om <lb/>nibus parallelis ſolos duos tropicos deſcripſimus.</s>
  <s xml:id="echoid-s27326" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1383" type="float" level="2" n="1">
<note position="left" xlink:label="note-0430-07" xlink:href="note-0430-07a" xml:space="preserve">Horologiũ ho-<lb/>tizontale cum <lb/>parallelis ſigno <lb/>rum, &amp; latitu-<lb/>dinum ciuita-<lb/>tum, quomodo <lb/>in ſphęra recta <lb/>deſcribatur.</note>
  <figure xlink:label="fig-0431-01" xlink:href="fig-0431-01a">
    <image file="0431-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0431-01"/>
  </figure>
<note position="left" xlink:label="note-0431-01" xlink:href="note-0431-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0431-02" xlink:href="note-0431-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s27327" xml:space="preserve">PARALLELI arcuum diurnorum in ſphæra recta nulli ſunt, quia ibi nulla eſt dierum in <lb/>
<anchor type="note" xlink:label="note-0431-03a" xlink:href="note-0431-03"/>
æqualitas, ſed quilibet dies artiſicialis comprehendit horas 12. </s>
  <s xml:id="echoid-s27328" xml:space="preserve">toridemq́ue nox artificialis, per-<lb/>petuumq́ue efficitur æquinoctium, vt in ſphæra explicauimus, adeo vt quiuis parallelus, ſeu arcus <lb/>ſigni, dici poſſit arcus diurnus horarum 12.</s>
  <s xml:id="echoid-s27329" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1384" type="float" level="2" n="2">
<note position="right" xlink:label="note-0431-03" xlink:href="note-0431-03a" xml:space="preserve">Arcus diurai<unsure/> <lb/>in ſp<unsure/>hæra recta <lb/>nulii ſunt, quia <lb/>omnes comple <lb/>ctuntur horas <lb/>12.</note>
</div>
<p>
  <s xml:id="echoid-s27330" xml:space="preserve">LINEÆ horarũ abortu, &amp; </s>
  <s xml:id="echoid-s27331" xml:space="preserve">occaſu à lineis horarum à meridie, &amp; </s>
  <s xml:id="echoid-s27332" xml:space="preserve">media nocte non differũt, <lb/>
<anchor type="note" xlink:label="note-0431-04a" xlink:href="note-0431-04"/>
ſolum numeri horarum mutãdi ſunt. </s>
  <s xml:id="echoid-s27333" xml:space="preserve">Quoniam enim perpetuo in ſphęra recta Sol oritur hora 6. <lb/></s>
  <s xml:id="echoid-s27334" xml:space="preserve">
<anchor type="note" xlink:label="note-0431-05a" xlink:href="note-0431-05"/>
à media nocte, &amp; </s>
  <s xml:id="echoid-s27335" xml:space="preserve">24 ab ortu, &amp; </s>
  <s xml:id="echoid-s27336" xml:space="preserve">12. </s>
  <s xml:id="echoid-s27337" xml:space="preserve">ab occaſu, dabit hora 7. </s>
  <s xml:id="echoid-s27338" xml:space="preserve">à media nocte horam 1. </s>
  <s xml:id="echoid-s27339" xml:space="preserve">ab ortu &amp; </s>
  <s xml:id="echoid-s27340" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s27341" xml:space="preserve">ab occaſu; </s>
  <s xml:id="echoid-s27342" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27343" xml:space="preserve">hora 8. </s>
  <s xml:id="echoid-s27344" xml:space="preserve">à media nocte horam 2. </s>
  <s xml:id="echoid-s27345" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s27346" xml:space="preserve">14. </s>
  <s xml:id="echoid-s27347" xml:space="preserve">ab occaſu, &amp;</s>
  <s xml:id="echoid-s27348" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27349" xml:space="preserve">vt in ſigura ap-<lb/>poſita apparet, in qua numeri ad lineam æquinoctialem poſiti pertinẽt ad horas aſtronomicas, ſi-<lb/>ue à meridie, &amp; </s>
  <s xml:id="echoid-s27350" xml:space="preserve">media nocte, numeri verò ad tropicum ♑, indicant horas ab ortn Solis, &amp; </s>
  <s xml:id="echoid-s27351" xml:space="preserve">reli-<lb/>qui iuxta tropicum ♋, horas ab occaſu Solis demonſtrant.</s>
  <s xml:id="echoid-s27352" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1385" type="float" level="2" n="3">
<note position="right" xlink:label="note-0431-04" xlink:href="note-0431-04a" xml:space="preserve">Horologium <lb/>Italicum, ac Ba <lb/>bylo@icum in <lb/>ſphæra recta ſo <lb/>lo numero ho-<lb/>ratum diftert <lb/>ab Aſtronomi-<lb/>co.</note>
<note position="left" xlink:label="note-0431-05" xlink:href="note-0431-05a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Horologium <lb/>Antiquum in <lb/>phæra recta @ <lb/>Pabylonico no<unsure/> <lb/>diftert.</note>
<p>
  <s xml:id="echoid-s27353" xml:space="preserve">HORÆ autem inæquales locum non habent in ſphæra recta, cum ſemper dies, &amp; </s>
  <s xml:id="echoid-s27354" xml:space="preserve">noctes æ-<lb/>quales ſint, comprehendantq́ue horas 12. </s>
  <s xml:id="echoid-s27355" xml:space="preserve">æquales inter ſe. </s>
  <s xml:id="echoid-s27356" xml:space="preserve">Vnde horæ ab ortu indi<unsure/>cant duodeci-<lb/>mas partes diei tranſactas, quemadmodum horæ inæquales in ſphæra obliqua.</s>
  <s xml:id="echoid-s27357" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27358" xml:space="preserve">VERTICALES quoque circuli, &amp; </s>
  <s xml:id="echoid-s27359" xml:space="preserve">paralleli Horizontis eadem ratione hic, qua in horo-<lb/>
<anchor type="note" xlink:label="note-0431-07a" xlink:href="note-0431-07"/>
logio horizontali deſcribentur. </s>
  <s xml:id="echoid-s27360" xml:space="preserve">Nam lineæ Verticales tranſeunt per locum ſtyli, hoc eſt, per pũ-<lb/>ctum, vbi linea meridiana, &amp; </s>
  <s xml:id="echoid-s27361" xml:space="preserve">æquinoctialis ſe mutuo ſecant, &amp; </s>
  <s xml:id="echoid-s27362" xml:space="preserve">linea æquinoctialis dabit Verti-<lb/>
<anchor type="note" xlink:label="note-0431-08a" xlink:href="note-0431-08"/>
calem proprie dictum, à quo reliqui Verticales numerantur; </s>
  <s xml:id="echoid-s27363" xml:space="preserve">quia Verticalis, &amp; </s>
  <s xml:id="echoid-s27364" xml:space="preserve">Æquator in ſphę-<lb/>ra recta unum eundemq́ue circulum conſtituunt. </s>
  <s xml:id="echoid-s27365" xml:space="preserve">Paralleli autem Horizontis ex eo dem loco ſtyli, <lb/>vt centro deſcribuntur, &amp;</s>
  <s xml:id="echoid-s27366" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27367" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1386" type="float" level="2" n="4">
<note position="right" xlink:label="note-0431-07" xlink:href="note-0431-07a" xml:space="preserve">Verticaliũ cir-<lb/>culorũ, &amp; pa ral <lb/>lelorum Hori-<lb/>zontis in horo <lb/>logio horizon-<lb/>tali ſphætæ re-<lb/>ctæ deſcriptio.</note>
<note position="left" xlink:label="note-0431-08" xlink:href="note-0431-08a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Meridiani cir-<lb/>culi in horolo-<lb/>gio horizontali <lb/>ſphæ@ę rectæ <lb/>quo pacto de-<lb/>ſcr@bantur.</note>
<p>
  <s xml:id="echoid-s27368" xml:space="preserve">MERIDIANI porro circuli, ſiue circuli longitudinum ciuitatum deſcribentur hic, vt <lb/>in horologio polari, ſi in circulo, beneficio cuius horæ aſtronomicæ ſunt delineatæ, numeretur <lb/>longitudo loci à meridiana linea D E, uerſus occaſum, uſque ad Meridianum Inſularum Fortu-<lb/>natarum, &amp;</s>
  <s xml:id="echoid-s27369" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27370" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Domorum cœ <lb/>leſtium deſcri-<lb/>p@o in horizon <lb/>tali horolog@o <lb/>@phæræ rectæ.</note>
<p>
  <s xml:id="echoid-s27371" xml:space="preserve">RVRSVS domus cœleſtes depingentur in Horizonte recto, vt in obliquo. </s>
  <s xml:id="echoid-s27372" xml:space="preserve">Sunt namque &amp; </s>
  <s xml:id="echoid-s27373" xml:space="preserve"><lb/>hic inter ſe parallelæ lineæ domorum cœleſtium, &amp; </s>
  <s xml:id="echoid-s27374" xml:space="preserve">ſingula ſpatia inter binas lineas unam domũ <lb/>
<anchor type="note" xlink:label="note-0431-11a" xlink:href="note-0431-11"/>
intercipientes poſita complectuntur binas horas. </s>
  <s xml:id="echoid-s27375" xml:space="preserve">Vnde linea horæ 8. </s>
  <s xml:id="echoid-s27376" xml:space="preserve">à media nocte dabit initiũ <lb/>domus duodecimæ &amp; </s>
  <s xml:id="echoid-s27377" xml:space="preserve">linea horæ 10 à media nocte principium domus vndecimæ; </s>
  <s xml:id="echoid-s27378" xml:space="preserve">linea uerò me-<lb/>ridiana initium decimæ domus, &amp; </s>
  <s xml:id="echoid-s27379" xml:space="preserve">linea horæ 2. </s>
  <s xml:id="echoid-s27380" xml:space="preserve">à meridie initium domus nonæ; </s>
  <s xml:id="echoid-s27381" xml:space="preserve">linea denique <lb/>horæ 4. </s>
  <s xml:id="echoid-s27382" xml:space="preserve">à meridie initium domus octauæ. </s>
  <s xml:id="echoid-s27383" xml:space="preserve">Vno autem modo hic deſcribuntur domus cœleſtes, <lb/>quia Æquator, &amp; </s>
  <s xml:id="echoid-s27384" xml:space="preserve">Verticalis circulus in ſphæra recta non differunt. </s>
  <s xml:id="echoid-s27385" xml:space="preserve">Vnde eædem domus ſunt <lb/>ſecundum Ioan. </s>
  <s xml:id="echoid-s27386" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s27387" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27388" xml:space="preserve">Campanum.</s>
  <s xml:id="echoid-s27389" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1387" type="float" level="2" n="5">
<note position="left" xlink:label="note-0431-11" xlink:href="note-0431-11a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Signa aſcendẽ<unsure/>-<lb/>tia qua ui<unsure/>a in <lb/>horologi<unsure/>o hoti <lb/>zontali ſphæræ <lb/>rectæ depingan <lb/>tur.</note>
<p>
  <s xml:id="echoid-s27390" xml:space="preserve">ASCENDENTIA denique ſigna hic etiã deſcribentur, vt in ſuperioribus horologijs, ſi <lb/>prius cõponantut tabulæ continentes horas, quibus principia ſignorum ſupra Horizontem aſcẽ-<lb/>dunt in ſphæra recta. </s>
  <s xml:id="echoid-s27391" xml:space="preserve">Hæ autem componentur, vt docuimus lib. </s>
  <s xml:id="echoid-s27392" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27393" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s27394" xml:space="preserve">9. </s>
  <s xml:id="echoid-s27395" xml:space="preserve">ſi loco aſcenſionũ <lb/>obliquarum aſſumantur aſcenſiones rectæ. </s>
  <s xml:id="echoid-s27396" xml:space="preserve">Ita compoſitæ ſunt ſequentes quatuor tabellę.</s>
  <s xml:id="echoid-s27397" xml:space="preserve"/>
</p>
<pb o="416" file="0432" n="432" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1389" type="section" level="1" n="339">
<head xml:id="echoid-head352" style="it" xml:space="preserve">I. SOLE EXISTENTE IN PRINCIPIO ♈.</head>
<note position="right" xml:space="preserve"> <lb/>♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓ <lb/>Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Post \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel\\ añ mer. # Ante \\ mer. # Ante \\ mer. <lb/>H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. <lb/>6. 0. # 4. 8. # 2. 9. # 0. 0. # 2. 9. # 4. 8. # 6. 0. # 7. 52. # 9. 51. # 12. 0. # 9. 51. # 7. 52. <lb/></note>
</div>
<div xml:id="echoid-div1390" type="section" level="1" n="340">
<head xml:id="echoid-head353" style="it" xml:space="preserve">II. SOLE EXISTENTE IN PRINCIPIO ♎.</head>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>♎ # ♏ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍ <lb/>Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer. <lb/>H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. <lb/>6. 0. # 4. 8. # 2. 9. # 0. 0. # 2. 9. # 4. 8. # 6. 0. # 7. 52. # 9. 51. # 12. 0. # 9. 51. # 7. 52. <lb/></note>
</div>
<div xml:id="echoid-div1391" type="section" level="1" n="341">
<head xml:id="echoid-head354" style="it" xml:space="preserve">III. SOLE EXISTENTE IN PRINCIPIO ♋.</head>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊ <lb/>Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer. <lb/>H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. <lb/>6. 0. # 3. 51. # 1. 52. # 0. 0. # 1. 52. # 3. 51. # 6. 0. # 8. 9. # 10. 8. # 12. 0. # 10. 8. # 8. 9. <lb/></note>
</div>
<div xml:id="echoid-div1392" type="section" level="1" n="342">
<head xml:id="echoid-head355" style="it" xml:space="preserve">IIII. SOLE EXISTENTE IN PRINCIPIO ♑.</head>
<note position="right" xml:space="preserve"> <lb/>♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ <lb/>
Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer.
H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M.
6. 0. # 3. 51. # 1. 52. # 0. 0. # 1. 52. # 3. 51. # 0. 0. # 8. 9. # 10. 8. # 12. 0. # 10. 8. # 8. 9.
</note>
<p>
  <s xml:id="echoid-s27398" xml:space="preserve">EADEM ratione componi poterunt tabellę mediationum cœli, &amp; </s>
  <s xml:id="echoid-s27399" xml:space="preserve">angulorum terrę: </s>
  <s xml:id="echoid-s27400" xml:space="preserve">Item <lb/>aliæ duæ tabellæ continentes puncta Eclipticæ in circulo horæ 5. </s>
  <s xml:id="echoid-s27401" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27402" xml:space="preserve">7. </s>
  <s xml:id="echoid-s27403" xml:space="preserve">à meridie, vel media nocte <lb/>exiſtentia, eorumq́ue declinationes, cum principia 12. </s>
  <s xml:id="echoid-s27404" xml:space="preserve">ſignorum in ſphęra recta ſupra Horizon-<lb/>tem emergunt, vt ibidem explicauimus.</s>
  <s xml:id="echoid-s27405" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s27406" xml:space="preserve">FIGVRA autem radiorum latitudinum ortiuarum, &amp; </s>
  <s xml:id="echoid-s27407" xml:space="preserve">occiduarum in propoſ. </s>
  <s xml:id="echoid-s27408" xml:space="preserve">21. </s>
  <s xml:id="echoid-s27409" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27410" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27411" xml:space="preserve">de-<lb/>
<anchor type="note" xlink:label="note-0432-09a" xlink:href="note-0432-09"/>
ſcripta à figura radiorum Zodiaci non differt, proptera quod amplitudines ortiuæ, occiduęve <lb/>punctorum Eclipticæ æquales ſunt in ſphæra recta eorundẽ declinationibus, cum Horizon rectus <lb/>per polos mundi ductus metiatur &amp; </s>
  <s xml:id="echoid-s27412" xml:space="preserve">declinationes, &amp; </s>
  <s xml:id="echoid-s27413" xml:space="preserve">amplitudines ortiuas, occiduasve. </s>
  <s xml:id="echoid-s27414" xml:space="preserve">Horolo-<lb/>gia igitur horizontalia in ſphęra recta deſcripſimus. </s>
  <s xml:id="echoid-s27415" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27416" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1392" type="float" level="2" n="1">
<note position="left" xlink:label="note-0432-09" xlink:href="note-0432-09a" xml:space="preserve">Amplitudines <lb/>ortiuæ occiduę <lb/>ve punctorum <lb/>Eclipticę in <lb/>ſphęra recta ę <lb/>quales ſunt co-<lb/>rundem decli-<lb/>nationibus.</note>
</div>
</div>
<div xml:id="echoid-div1394" type="section" level="1" n="343">
<head xml:id="echoid-head356" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
<p>
  <s xml:id="echoid-s27417" xml:space="preserve">HOROLOGIA Verticalia in ſphæra recta conſtruere.</s>
  <s xml:id="echoid-s27418" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s27419" xml:space="preserve">DESCRIBENTVR horæ à meridie, &amp; </s>
  <s xml:id="echoid-s27420" xml:space="preserve">media nocte, &amp; </s>
  <s xml:id="echoid-s27421" xml:space="preserve">paralleli ſignorum Zodiaci, vna <lb/>
<anchor type="note" xlink:label="note-0432-11a" xlink:href="note-0432-11"/>
cum parallelis, circulisve latitudinum ciuitatum in Verticali horologio ſphæræ rectæ non aliter, <lb/>ac in horologio æquinoctiali. </s>
  <s xml:id="echoid-s27422" xml:space="preserve">Nã inter ſe non differũt circulus Verticalis propriè dictus in ſphæ-<lb/>ra recta, &amp; </s>
  <s xml:id="echoid-s27423" xml:space="preserve">Æquator, vt patet. </s>
  <s xml:id="echoid-s27424" xml:space="preserve">Verum horizontalis linea ducenda eſt per centrum horologii, ſiue <lb/>locum gnomonis, ad meridianam lineam perpendicularis, ita vt à linea horæ 6. </s>
  <s xml:id="echoid-s27425" xml:space="preserve">à meridie, vel <lb/>media nocte non differat: </s>
  <s xml:id="echoid-s27426" xml:space="preserve">propterea quod in ſphæra recta Horizon, &amp; </s>
  <s xml:id="echoid-s27427" xml:space="preserve">circulus horæ 6. </s>
  <s xml:id="echoid-s27428" xml:space="preserve">à meridie <lb/>vel media nocte non differunt, vt in ſequentibus figuris apparet.</s>
  <s xml:id="echoid-s27429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1394" type="float" level="2" n="1">
<note position="left" xlink:label="note-0432-11" xlink:href="note-0432-11a" xml:space="preserve">Horologii Ver <lb/>ticalis vnà cũ <lb/>parallelis ſigno <lb/>rum, &amp; latitu-<lb/>dinum ciuita-<lb/>tum in ſphęra <lb/>recta delinea-<lb/>tio.</note>
</div>
<note position="left" xml:space="preserve">Horæ ab ortu <lb/>&amp; occaſu in ho <lb/>rologio Verti-<lb/>cali ſphęrę re-<lb/>ctæ.</note>
<p>
  <s xml:id="echoid-s27430" xml:space="preserve">QVOD ad horas ab ortu, &amp; </s>
  <s xml:id="echoid-s27431" xml:space="preserve">occaſu attinet; </s>
  <s xml:id="echoid-s27432" xml:space="preserve">Item ad inæquales, idem hic dicendum eſt, quod <lb/>in pręcedenti propoſ. </s>
  <s xml:id="echoid-s27433" xml:space="preserve">Numeri enim medio loco poſiti ad horas à meridie, &amp; </s>
  <s xml:id="echoid-s27434" xml:space="preserve">media nocte, ſupe-<lb/>riores ad horas ab occaſu, &amp; </s>
  <s xml:id="echoid-s27435" xml:space="preserve">inferiores ad horas ab ortu pertinent.</s>
  <s xml:id="echoid-s27436" xml:space="preserve"/>
</p>
<pb o="417" file="0433" n="433" rhead="LIBER QVARTVS."/>
  <figure>
    <image file="0433-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0433-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve">Verticales eit-<lb/>culi, &amp; paralleli <lb/>Horizontis in <lb/>Verticali horo <lb/>logio ſphæræ <lb/>rectę.</note>
<p>
  <s xml:id="echoid-s27437" xml:space="preserve">VERTICALES autem circuli, &amp; </s>
  <s xml:id="echoid-s27438" xml:space="preserve">paralleli Horizontis ita hic delineabuntur, vt in horo-<lb/>logio Verticali ſphæræ obliquæ. </s>
  <s xml:id="echoid-s27439" xml:space="preserve">Eadem namque vtrobique demonſtratio eſt.</s>
  <s xml:id="echoid-s27440" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Meridiani cit-<lb/>euli in Vertica <lb/>li horologio <lb/>ſphæræ tectæ.</note>
<p>
  <s xml:id="echoid-s27441" xml:space="preserve">MERIDIANI quoque deſcribentur, vt horæ à meridie, vel media nocte, ſi prius à meri-<lb/>diana linea ſupputetur longitudo loci, ita vt recta ex centro horologij per finẽ numerationis du-<lb/>cta, Meridianumq́; </s>
  <s xml:id="echoid-s27442" xml:space="preserve">Inſularum Fortunatarum referens, in parte orientali horologii exiſtat, qualis <lb/>eſt linea in vtroque horologio punctis diſtincta, ſi longitudo loci in ſphæra recta fuerit grad. </s>
  <s xml:id="echoid-s27443" xml:space="preserve">36.</s>
  <s xml:id="echoid-s27444" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Domus cœle-<lb/>ſtes in Vertica-<lb/>li horologio <lb/>ſphærę rectæ.</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s27445" xml:space="preserve">DOMVS uerò cœleſtes ab horis à meridie, &amp; </s>
  <s xml:id="echoid-s27446" xml:space="preserve">media nocte non diſcrepant, cum ijdem ſint <lb/>circuli domorum cœleſtium in ſphæra recta, qui horarum à meridie, &amp; </s>
  <s xml:id="echoid-s27447" xml:space="preserve">media nocte: </s>
  <s xml:id="echoid-s27448" xml:space="preserve">Ita vt ho-<lb/>ra 6. </s>
  <s xml:id="echoid-s27449" xml:space="preserve">à media nocte, ſiue linea horizontalis ex parte occidentis, præbeat initium domus 1. </s>
  <s xml:id="echoid-s27450" xml:space="preserve">hora <lb/>autem 8. </s>
  <s xml:id="echoid-s27451" xml:space="preserve">à media nocte principium domus 12. </s>
  <s xml:id="echoid-s27452" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27453" xml:space="preserve">ſic de cæteris, vt in præcedenti propoſ. </s>
  <s xml:id="echoid-s27454" xml:space="preserve">ſcripſi-<lb/>@us, adeò vt hora 6. </s>
  <s xml:id="echoid-s27455" xml:space="preserve">à meridie, ſeu linea horizontalis, ex parte orientis offerat initium domus 7.</s>
  <s xml:id="echoid-s27456" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27457" xml:space="preserve">POSTREMO ſigna Zodiaci aſcendentia commodiſſimè hoc loco deſcribentur per puncta <lb/>
<anchor type="note" xlink:label="note-0433-08a" xlink:href="note-0433-08"/>
lineæ horizontalis, vbi ab arcubus ſignorum ſecatur, vt in præcedentibus diximus, &amp; </s>
  <s xml:id="echoid-s27458" xml:space="preserve">per media-<lb/>tiones cœli, angulosq́ue terræ, ſi prius huiuſmodi tabulę conficiantur pro ſphæra recta; </s>
  <s xml:id="echoid-s27459" xml:space="preserve">vel certè <lb/>per horas tropici ♋, &amp; </s>
  <s xml:id="echoid-s27460" xml:space="preserve">♑, prout tabulæ ſuperioris propoſ. </s>
  <s xml:id="echoid-s27461" xml:space="preserve">indicant, deſcribendo hos tropicos <lb/>occultè ſupra lineam horizontalem unà cum lineis horariis à meridie, vel media nocte. </s>
  <s xml:id="echoid-s27462" xml:space="preserve">In horis <lb/>
<anchor type="note" xlink:label="note-0433-09a" xlink:href="note-0433-09"/>
enim tropici ♋, &amp; </s>
  <s xml:id="echoid-s27463" xml:space="preserve">♑, in quibus ſigna oriuntur, tangent lineæ ſignorum aſcendentium tropi-<lb/>cos dictos, tranſibuntq́ue per puncta horizontalis lineæ. </s>
  <s xml:id="echoid-s27464" xml:space="preserve">Ita vides in auſtrali horologio lineam <lb/>aſcendentis ♒, punctis diſtinctã tangere tropicum ♑, in hor. </s>
  <s xml:id="echoid-s27465" xml:space="preserve">3. </s>
  <s xml:id="echoid-s27466" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s27467" xml:space="preserve">51. </s>
  <s xml:id="echoid-s27468" xml:space="preserve">ante meridiem, trãſireq́ <lb/>per punctum horizontalis lineæ, vbi ab arcu ♒, ſecatur ex parte occidentis. </s>
  <s xml:id="echoid-s27469" xml:space="preserve">Sic in boreali horo-<lb/>logio linea aſcendentis ♉, tang et tropicum ♋, ſupra lineam horizontalem in hor. </s>
  <s xml:id="echoid-s27470" xml:space="preserve">10. </s>
  <s xml:id="echoid-s27471" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s27472" xml:space="preserve">8. <lb/></s>
  <s xml:id="echoid-s27473" xml:space="preserve">ante meridiem, tranſibitq́ue per punctum lineæ horizontalis, vbi ab arcu ♉, ſecatur ad partes oc-<lb/>cidentales. </s>
  <s xml:id="echoid-s27474" xml:space="preserve">Itaque horologia Verticalia in ſphæra conſtruximus. </s>
  <s xml:id="echoid-s27475" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s27476" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1395" type="float" level="2" n="2">
<note position="right" xlink:label="note-0433-08" xlink:href="note-0433-08a" xml:space="preserve">Aſeendentia ſi <lb/>gna in horolo-<lb/>gio Verticali <lb/>ſphęræ rectę.</note>
<note position="left" xlink:label="note-0433-09" xlink:href="note-0433-09a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1397" type="section" level="1" n="344">
<head xml:id="echoid-head357" xml:space="preserve">PROBLEMA 3. PROPOSITIO 3.</head>
<p>
  <s xml:id="echoid-s27477" xml:space="preserve">HOROLOGIA Meridiana in ſphęra recta componere.</s>
  <s xml:id="echoid-s27478" xml:space="preserve"/>
</p>
<pb o="418" file="0434" n="434" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s27479" xml:space="preserve">HÆC horologia conſtruentur hic, quemadmodum in ſphæra obliqua, quod attinet ad ho-<lb/>
<anchor type="note" xlink:label="note-0434-01a" xlink:href="note-0434-01"/>
<anchor type="figure" xlink:label="fig-0434-01a" xlink:href="fig-0434-01"/>
ras à meridie, &amp; </s>
  <s xml:id="echoid-s27480" xml:space="preserve"><lb/>media nocte, ni <lb/>ſi quod linea ho <lb/>ræ 6. </s>
  <s xml:id="echoid-s27481" xml:space="preserve">in ſphæra <lb/>recta à linea ho-<lb/>rizõtali nõ dif-<lb/>fert, atque adeò <lb/>ęquinoctialis li-<lb/>nea ipſam ad an <lb/>
<anchor type="note" xlink:label="note-0434-02a" xlink:href="note-0434-02"/>
gulos rectos ſe-<lb/>cans ad Horizõ <lb/>tem perpendicu <lb/>laris exiſtit. </s>
  <s xml:id="echoid-s27482" xml:space="preserve">In <lb/>parallelis autẽ, <lb/>ſiue arcubus ſi-<lb/>gnorum, &amp; </s>
  <s xml:id="echoid-s27483" xml:space="preserve">lati-<lb/>tudinum ciuita <lb/>tum nullum eſt <lb/>diſcrimen in v-<lb/>
<anchor type="note" xlink:label="note-0434-03a" xlink:href="note-0434-03"/>
traque ſphæra dummodo obſeruentur, parallelos ab æquinoctiali linea in auſtrum recedentes <lb/>pertinere ad ſigna, &amp; </s>
  <s xml:id="echoid-s27484" xml:space="preserve">oppida borealia; </s>
  <s xml:id="echoid-s27485" xml:space="preserve">reliquos verò ad auſtralia.</s>
  <s xml:id="echoid-s27486" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1397" type="float" level="2" n="1">
<note position="left" xlink:label="note-0434-01" xlink:href="note-0434-01a" xml:space="preserve">Horę ã mer. <lb/>vel med. noc. <lb/>arcus ſignorũ, <lb/>&amp; circuli latitu <lb/>dinũ ciuitatũ <lb/>in horologio <lb/>Meridiano <lb/>ſphæræ rectæ.</note>
  <figure xlink:label="fig-0434-01" xlink:href="fig-0434-01a">
    <image file="0434-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0434-01"/>
  </figure>
<note position="left" xlink:label="note-0434-02" xlink:href="note-0434-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0434-03" xlink:href="note-0434-03a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">Horę ab o@. &amp; <lb/>occ. in horolo-<lb/>gio Meridiano <lb/>ſphæræ rectæ.</note>
<p>
  <s xml:id="echoid-s27487" xml:space="preserve">HORÆ verò ab ortu, &amp; </s>
  <s xml:id="echoid-s27488" xml:space="preserve">occaſu in eiſdem lineis horarum à meridie, &amp; </s>
  <s xml:id="echoid-s27489" xml:space="preserve">media nocte nume-<lb/>randę ſunt, vt in propoſ. </s>
  <s xml:id="echoid-s27490" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27491" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s27492" xml:space="preserve">tradidimus, veluti ex appoſitis figuris liquet, in quibus nu-<lb/>meri diſpoſiti ſunt, vt in horologio horizõtali ſphæræ rectæ. </s>
  <s xml:id="echoid-s27493" xml:space="preserve">Itaque Meridianum horologiũ in <lb/>ſphæra recta ab horizontali eiuſdem ſphærę non differt, ſi lineamenta reſpiciamus; </s>
  <s xml:id="echoid-s27494" xml:space="preserve">ſolũ numeri <lb/>mutantur, vt patet: </s>
  <s xml:id="echoid-s27495" xml:space="preserve">adeò vt horizontale horologium ſphæræ rectæ, ſi collocetur, vt Meridiano cir <lb/>
<anchor type="note" xlink:label="note-0434-05a" xlink:href="note-0434-05"/>
culo æquidiſtet, prębeat horologium Meridianum in eadem ſphæra.</s>
  <s xml:id="echoid-s27496" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1398" type="float" level="2" n="2">
<note position="left" xlink:label="note-0434-05" xlink:href="note-0434-05a" xml:space="preserve">Verticales cir-<lb/>culi, &amp; paralle-<lb/>li Horizontis <lb/>in horologio <lb/>Meridiano <lb/>ſphæræ rectæ.</note>
</div>
<p>
  <s xml:id="echoid-s27497" xml:space="preserve">CIRCVLI etiam Verticales, &amp; </s>
  <s xml:id="echoid-s27498" xml:space="preserve">paralleli Horizontis reponentur hic, vt in meridiano horo-<lb/>logio Horizontis obliqui, ſed linea æquinoctialis dabit Verticalem circulum propriè dictum, vt <lb/>
<anchor type="note" xlink:label="note-0434-06a" xlink:href="note-0434-06"/>
in horizontali horologio ſphæræ rectæ diximus.</s>
  <s xml:id="echoid-s27499" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1399" type="float" level="2" n="3">
<note position="left" xlink:label="note-0434-06" xlink:href="note-0434-06a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Meridiani cir-<lb/>culi, &amp; domus <lb/>cœleſtes in Me <lb/>ridiano horolo <lb/>gio ſphęræ re-<lb/>ctæ.</note>
<p>
  <s xml:id="echoid-s27500" xml:space="preserve">SIMILITER Meridiani circuli, &amp; </s>
  <s xml:id="echoid-s27501" xml:space="preserve">domus cœleſtes depingentur hic, vt in horologio Me-<lb/>ridiano ſphæræ obliquæ, ita tamen, vt domus cœleſtes eundem hic ordinem habeant, quem in <lb/>horizontali horologio ſphæræ rectæ pręſcripſimus.</s>
  <s xml:id="echoid-s27502" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27503" xml:space="preserve">POSTREMO ſigna aſcendentia eandem deſcriptionem etiam habent hic, quam in horo-<lb/>
<anchor type="note" xlink:label="note-0434-08a" xlink:href="note-0434-08"/>
logio Meridiano ſphæræ obliquæ. </s>
  <s xml:id="echoid-s27504" xml:space="preserve">Quamobrem horologia Meridiana in ſphæra recta compoſui <lb/>mus. </s>
  <s xml:id="echoid-s27505" xml:space="preserve">Quod erat ſaciendum.</s>
  <s xml:id="echoid-s27506" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1400" type="float" level="2" n="4">
<note position="left" xlink:label="note-0434-08" xlink:href="note-0434-08a" xml:space="preserve">Signa aſcendẽ-<lb/>tia in horolo-<lb/>gio Meridiano <lb/>ſphæræ rectę.</note>
</div>
</div>
<div xml:id="echoid-div1402" type="section" level="1" n="345">
<head xml:id="echoid-head358" xml:space="preserve">PROBLEMA 4. PROPOSITIO 4.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s27507" xml:space="preserve">HOROLOGIA polaria in ſphęra recta delineare.</s>
  <s xml:id="echoid-s27508" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27509" xml:space="preserve">NVLLA in re differunt polaria horologia ſphæræ rectæ ab Horizontalibus eiuſdem ſphæ-<lb/>
<anchor type="note" xlink:label="note-0434-10a" xlink:href="note-0434-10"/>
ræ; </s>
  <s xml:id="echoid-s27510" xml:space="preserve">cum circulus horæ 6. </s>
  <s xml:id="echoid-s27511" xml:space="preserve">à meridie vel media nocte, cui polaria horologia æquidiſtant, ab Hori-<lb/>zonte, cui parallela ſunt horologia horizontalia, non differat. </s>
  <s xml:id="echoid-s27512" xml:space="preserve">Horologia ergo polaria in ſphæra <lb/>recta delineauimus. </s>
  <s xml:id="echoid-s27513" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27514" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1402" type="float" level="2" n="1">
<note position="left" xlink:label="note-0434-10" xlink:href="note-0434-10a" xml:space="preserve">Polaria horo-<lb/>logia in ſphæra <lb/>recta.</note>
</div>
</div>
<div xml:id="echoid-div1404" type="section" level="1" n="346">
<head xml:id="echoid-head359" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
<p>
  <s xml:id="echoid-s27515" xml:space="preserve">HOROLOGIA æquinoctialia in ſphæra recta figurare.</s>
  <s xml:id="echoid-s27516" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<note position="left" xml:space="preserve">Aequinoctialia <lb/>horologia in <lb/>ſphęra rect a.</note>
<p>
  <s xml:id="echoid-s27517" xml:space="preserve">NEQVE verò æquinoctialia horologia ſphæræ rectæ à Verticalibus horologijs eiuſdem ſphæ <lb/>ræ diuerſa ſunt, quod idem circulus ſit Æquator, &amp; </s>
  <s xml:id="echoid-s27518" xml:space="preserve">Verticalis in ſphæra recta. </s>
  <s xml:id="echoid-s27519" xml:space="preserve">Quocirca horo-<lb/>logia æquinoctialia in ſphæra recta figurauimus. </s>
  <s xml:id="echoid-s27520" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s27521" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1405" type="section" level="1" n="347">
<head xml:id="echoid-head360" xml:space="preserve">PROBLEMA 6. PROPOSITIO 6.</head>
<p>
  <s xml:id="echoid-s27522" xml:space="preserve">HOROLOGIA à Verticali circulo declinantia in ſphęra recta <lb/>depingere.</s>
  <s xml:id="echoid-s27523" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27524" xml:space="preserve">DVCTIS duabus rectis A B, C H, ſeſe in H, ad angulos rectos ſecantibus, conſtituatur ad
<pb o="419" file="0435" n="435" rhead="LIBER QVARTVS."/>
rectam C H, in H, angulus declinationis CHD, verſus quidem punctum B, ſi planum à meri-<lb/>
<anchor type="note" xlink:label="note-0435-01a" xlink:href="note-0435-01"/>
die in occaſum, vel à ſeptentrione in ortum declinet; </s>
  <s xml:id="echoid-s27525" xml:space="preserve">verſus autem punctum A, ſi à meridie in <lb/>ortum, vel à borea in occaſum deflectat. </s>
  <s xml:id="echoid-s27526" xml:space="preserve">In noſtro exemplo ponimus planum declinare grad. </s>
  <s xml:id="echoid-s27527" xml:space="preserve">60. <lb/></s>
  <s xml:id="echoid-s27528" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0435-01a" xlink:href="fig-0435-01"/>
<anchor type="note" xlink:label="note-0435-02a" xlink:href="note-0435-02"/>
<anchor type="note" xlink:label="note-0435-03a" xlink:href="note-0435-03"/>
<anchor type="note" xlink:label="note-0435-04a" xlink:href="note-0435-04"/>
à meridie in occaſum. </s>
  <s xml:id="echoid-s27529" xml:space="preserve">Sumpto autem puncto D, vt libet, in recta H D, ducaur ad H D, perpen-<lb/>dicularis D I, ſecans A B, in I, &amp; </s>
  <s xml:id="echoid-s27530" xml:space="preserve">per I, ducatur ad A B, perpendicularis I F. </s>
  <s xml:id="echoid-s27531" xml:space="preserve">Deinde abſciſſa recta <lb/>I E, ipſi D I, æquali, deſcribantur ex E, circulus vt libet, quo diuiſo in 24. </s>
  <s xml:id="echoid-s27532" xml:space="preserve">partes æquales, initio <lb/>facto à recta A B, emittantur ex E, per diuiſionum puncta rectæ occultæ ſecantes rectam I F, in <lb/>punctis, per quæ ſi ex H, rectæ educantur, habebuntur lineę horariæ, quarum ordo hic eſt. </s>
  <s xml:id="echoid-s27533" xml:space="preserve">Re-<lb/>cta C H, dat horam 12. </s>
  <s xml:id="echoid-s27534" xml:space="preserve">ſeu lineam meridianam, quæ verò ei ſunt ad ſiniſtram, indicant horas à <lb/>media nocte in horologijs à meridie declinantibus, quæ verò ad dextram ſunt collocatæ, ad ho-<lb/>ras à meridie pertinent. </s>
  <s xml:id="echoid-s27535" xml:space="preserve">Contrarium intelligatur in horologijs, quæ à ſeptentrione deflectunt.</s>
  <s xml:id="echoid-s27536" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1405" type="float" level="2" n="1">
<note position="right" xlink:label="note-0435-01" xlink:href="note-0435-01a" xml:space="preserve">Horologiũ A-<lb/>ſtronomicum <lb/>declinãs à Ver <lb/>ticali in ſphæra <lb/>recta, quo pacto <lb/>deſcribatur.</note>
  <figure xlink:label="fig-0435-01" xlink:href="fig-0435-01a">
    <image file="0435-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0435-01"/>
  </figure>
<note position="left" xlink:label="note-0435-02" xlink:href="note-0435-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0435-03" xlink:href="note-0435-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0435-04" xlink:href="note-0435-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s27537" xml:space="preserve">DEMONSTRATIO huius deſcriptionis perfacilis eſt. </s>
  <s xml:id="echoid-s27538" xml:space="preserve">Si enim (poſito horologio in <lb/>
<anchor type="note" xlink:label="note-0435-06a" xlink:href="note-0435-06"/>
proprio ſitu, vt recta A B, Horizonti ęquidiſtet, ſitq̀ue communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s27539" xml:space="preserve">Ho-<lb/>rizontis, ſiue circuli horæ 6. </s>
  <s xml:id="echoid-s27540" xml:space="preserve">à meridie, vel media nocte) intelligatur triangulum H D I, moueri <lb/>circa rectam H I, donec ad planum horologij rectum ſit, &amp; </s>
  <s xml:id="echoid-s27541" xml:space="preserve">cum Horizonte coniungatur, ſeu <lb/>circulo horæ ſextæ a meridie, vel media nocte, cum C H D, ſit angulus declinationis à Ver-<lb/>ticali, erit D H I, angulus declinationis à Meridiano circulo, ac proinde H D, communis erit <lb/>ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s27542" xml:space="preserve">Horizontis, hoc eſt, axis mundi. </s>
  <s xml:id="echoid-s27543" xml:space="preserve">Quare D I, ad axem perpendicularis <lb/>communis ſectio erit Æquatoris, &amp; </s>
  <s xml:id="echoid-s27544" xml:space="preserve">eiuſdem Horizontis: </s>
  <s xml:id="echoid-s27545" xml:space="preserve">ac propterea cum Meridianus pla-<lb/>no horologii occurrat in H, &amp; </s>
  <s xml:id="echoid-s27546" xml:space="preserve">Æquator in I, ducenda erit linea meridiana per H, &amp; </s>
  <s xml:id="echoid-s27547" xml:space="preserve">æquino-<lb/>ctialis per I. </s>
  <s xml:id="echoid-s27548" xml:space="preserve">Quoniam verò tam planum borologii, quàm Meridiani ad Horizontem eſt re-<lb/>
<anchor type="note" xlink:label="note-0435-07a" xlink:href="note-0435-07"/>
ctum, erit eorum communis ſectio ad eundem recta, ac proinde per defin. </s>
  <s xml:id="echoid-s27549" xml:space="preserve">3. </s>
  <s xml:id="echoid-s27550" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27551" xml:space="preserve">11. </s>
  <s xml:id="echoid-s27552" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s27553" xml:space="preserve">
<anchor type="note" xlink:label="note-0435-08a" xlink:href="note-0435-08"/>
ad rectam A B, in Horizonte exiſtentem perpendicularis. </s>
  <s xml:id="echoid-s27554" xml:space="preserve">Quamobrem C H, ad A B, per-<lb/>pendicularis communis erit ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s27555" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s27556" xml:space="preserve">Eadem ratione oſtende-<lb/>mus I F, eſſe communem ſectionem Æquatoris, &amp; </s>
  <s xml:id="echoid-s27557" xml:space="preserve">plani horologii; </s>
  <s xml:id="echoid-s27558" xml:space="preserve">propterea quòd etiam tam <lb/>planum horologii, quàm Æquatoris rectum eſt ad Horizontem. </s>
  <s xml:id="echoid-s27559" xml:space="preserve">Exiſtente autem triangulo eo-<lb/>dem H D I, ad planũ horologii recto, ſi circulus ex E, deſcriptus moueri concipiatur circa æqui-<lb/>noctialem lineam I F, donec eius centrum E, cum D, centro mundi coniungatur, propter æqua-<lb/>litatem rectarum I D, I E, atque adeo in plano Æquatoris per rectas I D, I F, ducto exiſtat, oſten-<lb/>demus, vt in horologio horizontali propoſ. </s>
  <s xml:id="echoid-s27560" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27561" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27562" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27563" xml:space="preserve">recte eſſe deſcriptas horas à meridie, &amp; </s>
  <s xml:id="echoid-s27564" xml:space="preserve">me-<lb/>dia nocte. </s>
  <s xml:id="echoid-s27565" xml:space="preserve">Eſt enim Horizon rectus, ſeu circulus horæ 6. </s>
  <s xml:id="echoid-s27566" xml:space="preserve">à meridie, vel media nocte, veluti Me-<lb/>ridianus reſpectu plani horologii declinantis, &amp; </s>
  <s xml:id="echoid-s27567" xml:space="preserve">ipſe Meridianus inſtar circuli horæ 6. </s>
  <s xml:id="echoid-s27568" xml:space="preserve">à me-
<pb o="420" file="0436" n="436" rhead="GNOMONICES"/>
ridie, vel media nocte, ita vt recta H I, communis ſectio Horizontis recti, ſeu circuli horæ 6. </s>
  <s xml:id="echoid-s27569" xml:space="preserve">à <lb/>meridie vel media nocte, eum locum hic habeat, quem linea meridiana in horologio horizon-<lb/>tali ſphæræ obliquæ, &amp; </s>
  <s xml:id="echoid-s27570" xml:space="preserve">eundem linea meridiana C H, quem linea horæ 6. </s>
  <s xml:id="echoid-s27571" xml:space="preserve">à meridie, vel media <lb/>nocte. </s>
  <s xml:id="echoid-s27572" xml:space="preserve">Erũt autem interualla horaria ex altera parte meridianæ lineæ C H, æqualia horariis inter-<lb/>uallis inter meridianam lineam, &amp; </s>
  <s xml:id="echoid-s27573" xml:space="preserve">ęquinoctialem, ſingula ſingulis, vtpote quæ ortum habeant <lb/>ex horariis interuallis in linea ęquinoctiali ſupra punctum I, quæ interuallis horariis in eadem <lb/>linea æquinoctiali infra punctum I, ęqualia eſſe oſtendimus, ſingula ſingulis, in propoſ. </s>
  <s xml:id="echoid-s27574" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27575" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27576" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s27577" xml:space="preserve">Vnde non neceſſarium eſt, vt integrum horologium deſcribatur, ſed ſatis eſt, ſi trans ferantur ho-<lb/>rariæ lineę æquinoctialem lineam ſecantes in alterã partem lineę meridianę Stylus eſt recta D G, <lb/>cadens ex D, centro mundi in rectam A B, ad angulos rectos, eiusq́ue locus punctum G.</s>
  <s xml:id="echoid-s27578" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1406" type="float" level="2" n="2">
<note position="right" xlink:label="note-0435-06" xlink:href="note-0435-06a" xml:space="preserve">Demonſtratio <lb/>an@ecedẽtis de-<lb/>ſcriptionis.</note>
<note position="left" xlink:label="note-0435-07" xlink:href="note-0435-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0435-08" xlink:href="note-0435-08a" xml:space="preserve">19. vndec.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s27579" xml:space="preserve">SI in plano declinante detur locus ſtyli in G, eiuſq́ue longitudo G D, ita deſcribemus horolo-<lb/>
<anchor type="note" xlink:label="note-0436-02a" xlink:href="note-0436-02"/>
gium. </s>
  <s xml:id="echoid-s27580" xml:space="preserve">P er G, locum ſtyli ducemus rectam A B, Horizonti parallelã, ad quam excitabimus ex G, <lb/>loco ſtyli perdendicularem G D, ſtylo æqualem. </s>
  <s xml:id="echoid-s27581" xml:space="preserve">Deinde in D, conſtituemus G D H, angulum de-<lb/>clinationis verſus A, ſi planum à meridie in occaſum declinet, vel à ſeptentrione in ortum, verſus <lb/>autẽ B, ſi cõtra à meridie in ortũ, vel à ſeptenttione in occaſum declinet, ita vt recta D H, ſecet re-<lb/>ctam A B, in H: </s>
  <s xml:id="echoid-s27582" xml:space="preserve">Ex altera verò parte in D, conſtituemus G D I, angulũ cõplementi declinationis, <lb/>ita vt recta D I, ſecet rectã A B, in I. </s>
  <s xml:id="echoid-s27583" xml:space="preserve">Reliqua denique perſiciemus, vt prius. </s>
  <s xml:id="echoid-s27584" xml:space="preserve">Ratio huiuſce rei eſt, <lb/>
<anchor type="note" xlink:label="note-0436-03a" xlink:href="note-0436-03"/>
quòd angulus declinationis C H D, in priori deſcriptione conſtitutus equalis eſt angulo alterno <lb/>G D H, ac proinde ei, quem in D, conſtruximus in poſteriori hac deſcriptione, &amp;</s>
  <s xml:id="echoid-s27585" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1407" type="float" level="2" n="3">
<note position="left" xlink:label="note-0436-02" xlink:href="note-0436-02a" xml:space="preserve">Deſcriptio eiuſ <lb/>dem horologii, <lb/>@@ locus ſtyli, <lb/>@iusq́ue longi-<lb/>tudo detur in <lb/>plano declinan <lb/>rc.</note>
<note position="left" xlink:label="note-0436-03" xlink:href="note-0436-03a" xml:space="preserve">Moræ ab or. &amp; <lb/>o@c. atque in-<lb/>æquales in ho-<lb/>rologio decli-<lb/>@anæ<unsure/> ſphæræ <lb/>rectæ.</note>
</div>
<p>
  <s xml:id="echoid-s27587" xml:space="preserve">DE horis ab ortu, &amp; </s>
  <s xml:id="echoid-s27588" xml:space="preserve">occaſu, atque inæqualibus idem hic dicendum eſt, quod in horizontali <lb/>
<anchor type="note" xlink:label="note-0436-04a" xlink:href="note-0436-04"/>
horologio ſphæræ rectæ.</s>
  <s xml:id="echoid-s27589" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1408" type="float" level="2" n="4">
<note position="left" xlink:label="note-0436-04" xlink:href="note-0436-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s27590" xml:space="preserve">PARALLELI, ſiue arcus ſignorũ arcus diurni, &amp; </s>
  <s xml:id="echoid-s27591" xml:space="preserve">circuli latitudinum ciuitatum non aliter <lb/>
<anchor type="note" xlink:label="note-0436-05a" xlink:href="note-0436-05"/>
in hoc horologio reponẽtur, ac in horologio horizontali ſphęræ obliquę; </s>
  <s xml:id="echoid-s27592" xml:space="preserve">dũmodo in priori mo-<lb/>do circulus Analemmatis A B C, referat Horizontem rectum, ſeu circulum horæ 6. </s>
  <s xml:id="echoid-s27593" xml:space="preserve">à meridie, <lb/>vel media nocte, &amp; </s>
  <s xml:id="echoid-s27594" xml:space="preserve">recta B C, communem ſectionem ipſius, &amp; </s>
  <s xml:id="echoid-s27595" xml:space="preserve">circuli maximi, cui horologii pla-<lb/>num per rectam R O, ductum æquidiſtat; </s>
  <s xml:id="echoid-s27596" xml:space="preserve">arcus autem C E, æqualis ſit complemẽto declinationis <lb/>plani à Verticali, vel (quod idem eſt,) declinationi à Meridiano, quæ ſemper æqualis eſt altitu-<lb/>dini poli ſupra planum. </s>
  <s xml:id="echoid-s27597" xml:space="preserve">In modo verò poſteriori recta H I, repreſentet lineam horæ 6. </s>
  <s xml:id="echoid-s27598" xml:space="preserve">à meridie <lb/>vel media nocte, &amp; </s>
  <s xml:id="echoid-s27599" xml:space="preserve">recta H V, lineam meridianam, &amp;</s>
  <s xml:id="echoid-s27600" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27601" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1409" type="float" level="2" n="5">
<note position="left" xlink:label="note-0436-05" xlink:href="note-0436-05a" xml:space="preserve">Arcus ſignotũ, <lb/>arcus diurni, &amp; <lb/>&amp; circuli lati<unsure/>tu <lb/>dinum ciuita-<lb/>tum in horolo <lb/>gio declinante <lb/>@phæræ rectæ.</note>
</div>
<p>
  <s xml:id="echoid-s27602" xml:space="preserve">SIGNA porrò borealia in huiuſmodi horologiis ſemper ad partes auſtrales, &amp; </s>
  <s xml:id="echoid-s27603" xml:space="preserve">auſtralia ad <lb/>
<anchor type="note" xlink:label="note-0436-06a" xlink:href="note-0436-06"/>
<anchor type="note" xlink:label="note-0436-07a" xlink:href="note-0436-07"/>
boreales ſunt poſita. </s>
  <s xml:id="echoid-s27604" xml:space="preserve">ſuntautem partes horologii boreales inter centrum H, &amp; </s>
  <s xml:id="echoid-s27605" xml:space="preserve">lineam æquinoctia-<lb/>lem, ſi horologium à meridie declinet: </s>
  <s xml:id="echoid-s27606" xml:space="preserve">ſed ſi à ſeptentrione deflectat, continebuntur partes au-<lb/>ſtrales inter centrum, &amp; </s>
  <s xml:id="echoid-s27607" xml:space="preserve">lineam æquinoctialem.</s>
  <s xml:id="echoid-s27608" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1410" type="float" level="2" n="6">
<note position="left" xlink:label="note-0436-06" xlink:href="note-0436-06a" xml:space="preserve">Qui arc@s ad <lb/>ſigha borealia <lb/>pertinean@, &amp; <lb/>qui ad auſtra-<lb/>@ia.</note>
<note position="left" xlink:label="note-0436-07" xlink:href="note-0436-07a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s27609" xml:space="preserve">CIRCVLI Verticales ita ducentur. </s>
  <s xml:id="echoid-s27610" xml:space="preserve">Ex puncto D, prioris figuræ huius propoſ. </s>
  <s xml:id="echoid-s27611" xml:space="preserve">deſcribatur <lb/>
<anchor type="note" xlink:label="note-0436-08a" xlink:href="note-0436-08"/>
circulus, &amp; </s>
  <s xml:id="echoid-s27612" xml:space="preserve">in 360. </s>
  <s xml:id="echoid-s27613" xml:space="preserve">partes æquales ſecetur, vel in pauciores, facto initio diuiſionis à recta D H, vel <lb/>D I. </s>
  <s xml:id="echoid-s27614" xml:space="preserve">Nam ſi ex D, per puncta diuiſionum egrediantur rectæ, ſecabitur horizontalis linea H I, in <lb/>punctis, per quæ ſi agantur meridianæ lineæ, vel æquinoctiali æquidiſtantes rectæ, ſiue ad H I, <lb/>perpendiculares, deſcripti erunt Verticales circuli. </s>
  <s xml:id="echoid-s27615" xml:space="preserve">Si namque circulus ex D, deſcriptus circa re-<lb/>ctam H I, circumuertatur, donec ad horologii planum rectus fiat, &amp; </s>
  <s xml:id="echoid-s27616" xml:space="preserve">in plano Horizontis exiſtat, <lb/>atque adeò centrum D, cum centro mundi, ſeu vertice ſtyli coniungatur; </s>
  <s xml:id="echoid-s27617" xml:space="preserve">cum recta D H, ſit com-<lb/>
<anchor type="note" xlink:label="note-0436-09a" xlink:href="note-0436-09"/>
munis ſectio Meridiani ac Horizontis, &amp; </s>
  <s xml:id="echoid-s27618" xml:space="preserve">D I, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s27619" xml:space="preserve">eiuſdem Horizon-<lb/>tis, vt paulo ante in hac propoſ. </s>
  <s xml:id="echoid-s27620" xml:space="preserve">demonſtrauimus, erunt reliquę lineæ ex D, eductę communes ſe-<lb/>ctiones Horizontis, &amp; </s>
  <s xml:id="echoid-s27621" xml:space="preserve">reliquorum Verticalium circulorum. </s>
  <s xml:id="echoid-s27622" xml:space="preserve">Quare vt in propoſ. </s>
  <s xml:id="echoid-s27623" xml:space="preserve">4 pręcedentis li-<lb/>bri oſtenſum eſt, rectè deſcripti ſunt circuli Verticales. </s>
  <s xml:id="echoid-s27624" xml:space="preserve">Erit autem æquinoctialis linea I F, com-<lb/>munis ſectio Verticalis proprie dicti, &amp; </s>
  <s xml:id="echoid-s27625" xml:space="preserve">plani horologii propterca quòd Æ quator in ſphera re-<lb/>cta eſt Verticalis primarius, vt patet; </s>
  <s xml:id="echoid-s27626" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27627" xml:space="preserve">linea meridiana C H, ſectio communis plani horologii, &amp; </s>
  <s xml:id="echoid-s27628" xml:space="preserve"><lb/>circuli Verticalis grad. </s>
  <s xml:id="echoid-s27629" xml:space="preserve">90. </s>
  <s xml:id="echoid-s27630" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s27631" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27632" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1411" type="float" level="2" n="7">
<note position="left" xlink:label="note-0436-08" xlink:href="note-0436-08a" xml:space="preserve">Verticales cir-<lb/>culi in horolo-<lb/>gio declinante <lb/>a Verticali in <lb/>ſphæra recta.</note>
<note position="left" xlink:label="note-0436-09" xlink:href="note-0436-09a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">Para@@eli Hori <lb/>zontis in codé <lb/>horologio.</note>
<p>
  <s xml:id="echoid-s27633" xml:space="preserve">PARALLELI Horizontis candem hoc loco deſcriptionem habent, quam in horologio <lb/>declinante à Verticali ſphæræ obliquæ.</s>
  <s xml:id="echoid-s27634" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27635" xml:space="preserve">PARI ratione &amp; </s>
  <s xml:id="echoid-s27636" xml:space="preserve">Meridiani circuli depingentur, vt in præcedentibus dictum eſt, ſi in circulo <lb/>
<anchor type="note" xlink:label="note-0436-11a" xlink:href="note-0436-11"/>
<anchor type="note" xlink:label="note-0436-12a" xlink:href="note-0436-12"/>
ex E, deſcripto in priori figura huius propoſ. </s>
  <s xml:id="echoid-s27637" xml:space="preserve">à ſuperiori puncto rectæ, quæ per E, ad H E, perpen <lb/>dicularis ducitur, numeretur longitudo loci verſus partes occidentales, quales ſunt in noſtro exẽ-<lb/>plo partes verſus punctum B, vt patet, ſi horologium ponatur in proprio ſitu, vnà cum circulo ex <lb/>E, deſcripto, ita vt centrum E, in D, centro mundi ſtatuatur. </s>
  <s xml:id="echoid-s27638" xml:space="preserve">Erit enim tunc recta illa cum A B, <lb/>in E, rectos angulos faciens, communis ſectio Aequatoris ac Meridiani, &amp; </s>
  <s xml:id="echoid-s27639" xml:space="preserve">punctum B, in oc-<lb/>caſum verget.</s>
  <s xml:id="echoid-s27640" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1412" type="float" level="2" n="8">
<note position="left" xlink:label="note-0436-11" xlink:href="note-0436-11a" xml:space="preserve">Meridiani cir-<lb/>@uli in eodem <lb/>horologio de-<lb/>clinante a Ver <lb/>gicali ſphæræ <lb/>rectæ.</note>
<note position="left" xlink:label="note-0436-12" xlink:href="note-0436-12a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s27641" xml:space="preserve">QVOD ad domos cœleſtes attinet, idem hic intelligatur, quod in horologio horizontali <lb/>
<anchor type="note" xlink:label="note-0436-13a" xlink:href="note-0436-13"/>
ſphæræ rectæ ſcripſimus. </s>
  <s xml:id="echoid-s27642" xml:space="preserve">Non enim earum circuli à circulis horarum à meridie, vel media nocte <lb/>diuerſi ſunt. </s>
  <s xml:id="echoid-s27643" xml:space="preserve">Vnde neque earum lineæ à lineis dictarum horarum different.</s>
  <s xml:id="echoid-s27644" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1413" type="float" level="2" n="9">
<note position="left" xlink:label="note-0436-13" xlink:href="note-0436-13a" xml:space="preserve">Domus cœle-<lb/>ſtes in eodem <lb/>horologio.</note>
</div>
<note position="left" xml:space="preserve">Signa a ſcendẽ-<lb/>tia in eodem <lb/>horologio.</note>
<p>
  <s xml:id="echoid-s27645" xml:space="preserve">AD extremum ſigna aſcendentia figurabuntur, vt in præcedentibus. </s>
  <s xml:id="echoid-s27646" xml:space="preserve">Quamobrem horolo-<lb/>gia à Verticali circulo declinantia in ſphæra recta depinximus. </s>
  <s xml:id="echoid-s27647" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s27648" xml:space="preserve"/>
</p>
<pb o="421" file="0437" n="437" rhead="LIBER QVARTVS."/>
  <figure>
    <image file="0437-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0437-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1415" type="section" level="1" n="348">
<head xml:id="echoid-head361" xml:space="preserve">PROBLEMA 7. PROPOSITIO 7.</head>
<p>
  <s xml:id="echoid-s27649" xml:space="preserve">HOROLOGIA ab Horizonte declinantia in ſphæra recta <lb/>conſtruere.</s>
  <s xml:id="echoid-s27650" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27651" xml:space="preserve">DVCTIS duabus rectis A B, C D, ſe ſe in A, ad rectosangulos ſecantibus, conſtituatur in <lb/>
<anchor type="note" xlink:label="note-0437-05a" xlink:href="note-0437-05"/>
A, ad rectam C D, angulus declinationis plani ab Horizonte D A E, verſus quidem punctum D, <lb/>
<anchor type="note" xlink:label="note-0437-06a" xlink:href="note-0437-06"/>
ſi planum ad occaſum ſpectet, verſus autem punctum C, ſi in ortum. </s>
  <s xml:id="echoid-s27652" xml:space="preserve">Nos planum propoſitum <lb/>ponimus declinare grad. </s>
  <s xml:id="echoid-s27653" xml:space="preserve">40. </s>
  <s xml:id="echoid-s27654" xml:space="preserve">ſpectareq́ue ad occaſum. </s>
  <s xml:id="echoid-s27655" xml:space="preserve">Ex aſſumpto quoque puncto E, vtcunque <lb/>in recta A E, ducatur ad A E, perpendicularis E D, ſecans C D, in D. </s>
  <s xml:id="echoid-s27656" xml:space="preserve">Item ex E, deſcribatur cir-<lb/>culus, qui in partes 24. </s>
  <s xml:id="echoid-s27657" xml:space="preserve">æquales diſtribuatur, initio facto à recta E D, vel E A. </s>
  <s xml:id="echoid-s27658" xml:space="preserve">Emiſſis autem ex <lb/>E, per diuiſionum puncta rectis occultis, ſecabitur C D, in punctis, è quibus ad C D, excitatæ <lb/>perpendiculares dabunt horas à meridie, &amp; </s>
  <s xml:id="echoid-s27659" xml:space="preserve">media nocte, hoc ordine. </s>
  <s xml:id="echoid-s27660" xml:space="preserve">Semper recta per D, ducta <lb/>erit linea horæ 12. </s>
  <s xml:id="echoid-s27661" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27662" xml:space="preserve">reliquæ lineæ verſus A, dabunt in horologio ad occaſum ſpectante horas <lb/>à meridie, in eo verò, quod ſpectat ad ortum, horas à media nocte, ita vt in illo recta A B, det ho <lb/>
<anchor type="note" xlink:label="note-0437-07a" xlink:href="note-0437-07"/>
ram 6. </s>
  <s xml:id="echoid-s27663" xml:space="preserve">à meridie; </s>
  <s xml:id="echoid-s27664" xml:space="preserve">in hoc verò horam 6. </s>
  <s xml:id="echoid-s27665" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s27666" xml:space="preserve">Quod ita oſtendemus.</s>
  <s xml:id="echoid-s27667" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1415" type="float" level="2" n="1">
<note position="right" xlink:label="note-0437-05" xlink:href="note-0437-05a" xml:space="preserve">Horologium <lb/>Aſtronomicũ <lb/>ab Horizonte <lb/>declinans in <lb/>ſphæra recta.</note>
<note position="left" xlink:label="note-0437-06" xlink:href="note-0437-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0437-07" xlink:href="note-0437-07a" xml:space="preserve">Demonſtratio <lb/>præcedentis de <lb/>ſeriptionis.</note>
</div>
<p>
  <s xml:id="echoid-s27668" xml:space="preserve">CONCIPIATVR horologium in proprio ſitu, ita vt recta A B, Horizonti æquidiſtet,
<pb o="422" file="0438" n="438" rhead="GNOMONICES"/>
communisq́ue ſectio ſit Horizontis, atque plani horologii. </s>
  <s xml:id="echoid-s27669" xml:space="preserve">Et quoniam tam planum horologii@ <lb/>quàm planum Horizontis, per propoſ. </s>
  <s xml:id="echoid-s27670" xml:space="preserve">15. </s>
  <s xml:id="echoid-s27671" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27672" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27673" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s27674" xml:space="preserve">ad Aequatorem rectum eſt, quòd <lb/>vtrumque per polos Aequatoris, ſeu mundi ducatur, nimirum per communes ſectiones Meridia <lb/>
<anchor type="figure" xlink:label="fig-0438-01a" xlink:href="fig-0438-01"/>
<anchor type="note" xlink:label="note-0438-01a" xlink:href="note-0438-01"/>
ni atque Hori-<lb/>zontis, erit quo <lb/>que communis <lb/>illorum ſectio <lb/>A B, ad eundem <lb/>perpẽdicularis, <lb/>atque adeo per <lb/>
<anchor type="note" xlink:label="note-0438-02a" xlink:href="note-0438-02"/>
defin. </s>
  <s xml:id="echoid-s27675" xml:space="preserve">3. </s>
  <s xml:id="echoid-s27676" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27677" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s27678" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s27679" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27680" xml:space="preserve">ad re-<lb/>ctam in Aequa-<lb/>tore exiſtentem, <lb/>quæ communis <lb/>ſectio ſit Aequa <lb/>toris, &amp; </s>
  <s xml:id="echoid-s27681" xml:space="preserve">plani ho <lb/>rologii. </s>
  <s xml:id="echoid-s27682" xml:space="preserve">Cũ ergo <lb/>angulus B A D, <lb/>rectus ſit, erit <lb/>
<anchor type="note" xlink:label="note-0438-03a" xlink:href="note-0438-03"/>
C D, communis <lb/>ſectio Aequato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s27683" xml:space="preserve">plani ho-<lb/>rologij. </s>
  <s xml:id="echoid-s27684" xml:space="preserve">Itaquo <lb/>ſi planum, in quo circulus ex E, deſcriptus, &amp; </s>
  <s xml:id="echoid-s27685" xml:space="preserve">triangulum A D E, exiſtit, circumuertatur circa <lb/>rectam A D, donec rectum ſit ad planum horologii, &amp; </s>
  <s xml:id="echoid-s27686" xml:space="preserve">centrum E, cum centro mundi con-<lb/>iungatur, erit circulus ipſe in plano Aequatoris circa idem centrum E, quòd &amp; </s>
  <s xml:id="echoid-s27687" xml:space="preserve">Aequator per <lb/>centrum mundi E, &amp; </s>
  <s xml:id="echoid-s27688" xml:space="preserve">rectam C D, ductus ad planum horologii ſit rectus. </s>
  <s xml:id="echoid-s27689" xml:space="preserve">Quare recta E A, <lb/>in plano Aequatoris, ſiue Verticalis circuli ſphæræ rectæ exiſtens, ſaciensq́ue angulum declinatio-<lb/>nis ab Horizonte E A D, communis ſectio erit Horizontis, ſeu circuli horæ 6. </s>
  <s xml:id="echoid-s27690" xml:space="preserve">à meridie, vel me-<lb/>
<anchor type="note" xlink:label="note-0438-04a" xlink:href="note-0438-04"/>
dia nocte, &amp; </s>
  <s xml:id="echoid-s27691" xml:space="preserve">Aequatoris, ſiue circuli Verticalis; </s>
  <s xml:id="echoid-s27692" xml:space="preserve">atque idcirco E D, communis ſectio Meridiani, <lb/>&amp; </s>
  <s xml:id="echoid-s27693" xml:space="preserve">eiuſdem Aequatoris. </s>
  <s xml:id="echoid-s27694" xml:space="preserve">Cum enim tam Meridianus, quàm Aequator in ſphæra recta ad Hori-<lb/>zontem rectus ſit, erit quoque eorum ſectio communis ad eundem perpendicularis, atque adeò <lb/>
<anchor type="note" xlink:label="note-0438-05a" xlink:href="note-0438-05"/>
&amp; </s>
  <s xml:id="echoid-s27695" xml:space="preserve">ad rectam A E, in Horizonte exiſtentem, in centro mundi E, perpendicularis erit; </s>
  <s xml:id="echoid-s27696" xml:space="preserve">ac propte-<lb/>rea E D, ad A E, perpendicularis in E, centro mundi communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s27697" xml:space="preserve">Aequa-<lb/>toris. </s>
  <s xml:id="echoid-s27698" xml:space="preserve">Vnde ſequitur, reliquas occultas ex E, emiſſas communes ſectiones eſſe Aequaroris, &amp; </s>
  <s xml:id="echoid-s27699" xml:space="preserve"><lb/>aliorum circulorum horariorum. </s>
  <s xml:id="echoid-s27700" xml:space="preserve">Quocirca cum lineæ horariæ in hoc plano ſint parallelæ ipſi <lb/>meridianæ lineæ, ex propoſ. </s>
  <s xml:id="echoid-s27701" xml:space="preserve">18. </s>
  <s xml:id="echoid-s27702" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27703" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27704" xml:space="preserve">eruntrectæ illæ perpendiculares ductæ ad C D, per puncta, <lb/>in quæ cadunt lineæ illæ occultæ, communes ſectiones horariorum circulorum, &amp; </s>
  <s xml:id="echoid-s27705" xml:space="preserve">plani horolo-<lb/>gii. </s>
  <s xml:id="echoid-s27706" xml:space="preserve">Stylus autem erit perpendicularis E F, ex E, ad rectam C D, demiſſa, eiuſq́ue locus in F.</s>
  <s xml:id="echoid-s27707" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1416" type="float" level="2" n="2">
  <figure xlink:label="fig-0438-01" xlink:href="fig-0438-01a">
    <image file="0438-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0438-01"/>
  </figure>
<note position="left" xlink:label="note-0438-01" xlink:href="note-0438-01a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0438-02" xlink:href="note-0438-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0438-03" xlink:href="note-0438-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0438-04" xlink:href="note-0438-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0438-05" xlink:href="note-0438-05a" xml:space="preserve">19. vndec.</note>
</div>
<note position="left" xml:space="preserve">Eiuſdẽ<unsure/> horolo-<lb/>gii deſcriptio, ſi <lb/>longitudo ſtyli <lb/>eiuſque locus <lb/>detur in plano <lb/>declinante ab <lb/>Horizonte.</note>
<p>
  <s xml:id="echoid-s27708" xml:space="preserve">QVOD ſi detur longitudo ſtyli E F, eiuſq́ue locus in puncto F, in plano declinante ab Hori-<lb/>
<anchor type="note" xlink:label="note-0438-07a" xlink:href="note-0438-07"/>
zonte, deſcribemus horologium hac ratione. </s>
  <s xml:id="echoid-s27709" xml:space="preserve">Per F, locum ſtyli ducemus rectam F E, Horizon-<lb/>ti æquidiſtantem, &amp; </s>
  <s xml:id="echoid-s27710" xml:space="preserve">ſtylo æqualem, quam in F, loco ſtyli ad angulos rectos ſecabimus linea C D. <lb/></s>
  <s xml:id="echoid-s27711" xml:space="preserve">Deinde in E, verſus partes ſuperiores plani conſtituemus F E A, angulum complementi declina-<lb/>tionis plani ab Horizonte, ita vt recta E A, ſecet rectam C D, in A. </s>
  <s xml:id="echoid-s27712" xml:space="preserve">Item in E, eſticiemus F E D, <lb/>verſus partes inſeriores plani angulum declinationis ab Horizonte, ita vt recta E D, rectam C D, <lb/>ſecet in D. </s>
  <s xml:id="echoid-s27713" xml:space="preserve">Reliqua autem abſoluemus, vt prius. </s>
  <s xml:id="echoid-s27714" xml:space="preserve">Nam hac ratione erit E A F, angulus declinatio-<lb/>
<anchor type="note" xlink:label="note-0438-08a" xlink:href="note-0438-08"/>
nis plani ab Horizonte, &amp;</s>
  <s xml:id="echoid-s27715" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27716" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1417" type="float" level="2" n="3">
<note position="left" xlink:label="note-0438-07" xlink:href="note-0438-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0438-08" xlink:href="note-0438-08a" xml:space="preserve">Horæ ab or. &amp; <lb/>occ. Itẽ inæqua <lb/>les in eodẽ ho-<lb/>rologio.</note>
</div>
<p>
  <s xml:id="echoid-s27717" xml:space="preserve">HORAE ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s27718" xml:space="preserve">inæquales ſe ſe habent hoc loco, vt in horizontali horologio <lb/>ſphæræ rectæ, quemadmodum ante tradidimus.</s>
  <s xml:id="echoid-s27719" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Arcus ſignotũ, <lb/>arcus diurni, &amp; <lb/>circuli latitudi <lb/>num ciuitatum <lb/>in horologio <lb/>eodem declinã <lb/>te ab Horizõte.</note>
<p>
  <s xml:id="echoid-s27720" xml:space="preserve">PARALLELI, arcusve ſignorum Zodiaci, arcus diurni, &amp; </s>
  <s xml:id="echoid-s27721" xml:space="preserve">paralleli ciuitatum deſcribun-<lb/>
<anchor type="note" xlink:label="note-0438-10a" xlink:href="note-0438-10"/>
tur hic, vt in horologio Meridiano, &amp; </s>
  <s xml:id="echoid-s27722" xml:space="preserve">polari ſphæræ obliquæ. </s>
  <s xml:id="echoid-s27723" xml:space="preserve">Transferenda enim ſunt inter-<lb/>ualla horaria inter centrum E, &amp; </s>
  <s xml:id="echoid-s27724" xml:space="preserve">æquinoctialem lineam C D, in radium Aequatoris, &amp;</s>
  <s xml:id="echoid-s27725" xml:space="preserve">c. </s>
  <s xml:id="echoid-s27726" xml:space="preserve">vt in <lb/>ſequenti ſigura apparet.</s>
  <s xml:id="echoid-s27727" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1418" type="float" level="2" n="4">
<note position="left" xlink:label="note-0438-10" xlink:href="note-0438-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s27728" xml:space="preserve">VERTICALES circuli, &amp; </s>
  <s xml:id="echoid-s27729" xml:space="preserve">paralleli Horizontis collocabuntur etiam in hoc horologio, <lb/>
<anchor type="note" xlink:label="note-0438-11a" xlink:href="note-0438-11"/>
veluti in horologio declinante ab Horizonte ſphæræ obliquæ.</s>
  <s xml:id="echoid-s27730" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1419" type="float" level="2" n="5">
<note position="left" xlink:label="note-0438-11" xlink:href="note-0438-11a" xml:space="preserve">Circuli Verti-<lb/>cales, &amp; paralle <lb/>li Horizõtis in <lb/>eodem horolo <lb/>gio.</note>
</div>
<p>
  <s xml:id="echoid-s27731" xml:space="preserve">MERIDIANI quoque ducentur, vt lineæ horariæ, ſi in circulo ex E, deſcrip@o numeretur <lb/>à puncto G, meridiei verſus occidentales partes longitudo loci, vt Meridianus Inſularum Fortu-<lb/>
<anchor type="note" xlink:label="note-0438-12a" xlink:href="note-0438-12"/>
natarum habeatur.</s>
  <s xml:id="echoid-s27732" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1420" type="float" level="2" n="6">
<note position="left" xlink:label="note-0438-12" xlink:href="note-0438-12a" xml:space="preserve">Circuli Meri-<lb/>diani in eodem <lb/>horologio.</note>
</div>
<p>
  <s xml:id="echoid-s27733" xml:space="preserve">LINEÆ cœleſtium domorum eædem ſunt, vt in præcedentibus diximus, quæ horarum à <lb/>
<anchor type="note" xlink:label="note-0438-13a" xlink:href="note-0438-13"/>
meridie, &amp; </s>
  <s xml:id="echoid-s27734" xml:space="preserve">media nocte.</s>
  <s xml:id="echoid-s27735" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1421" type="float" level="2" n="7">
<note position="left" xlink:label="note-0438-13" xlink:href="note-0438-13a" xml:space="preserve">Domus cœle-<lb/>ſtes in eodem <lb/>horologio.</note>
</div>
<pb o="423" file="0439" n="439" rhead="LIBER QVARTVS."/>
  <figure>
    <image file="0439-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0439-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve">Aſcendentia ſi<unsure/> <lb/>gna in eodem <lb/>horologio.</note>
<p>
  <s xml:id="echoid-s27736" xml:space="preserve">SIGNA tandem aſcendentia, vt in ſuperioribus, delineabuntur. </s>
  <s xml:id="echoid-s27737" xml:space="preserve">Quapropter horologia ab <lb/>Horizonte declinantia in ſphæra recta conſtruximus. </s>
  <s xml:id="echoid-s27738" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s27739" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1423" type="section" level="1" n="349">
<head xml:id="echoid-head362" xml:space="preserve">PROBLEMA 8. PROPOSITIO 8.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s27740" xml:space="preserve">HOROLOGIA ad Horizontem inclinata in ſphæra recta <lb/>delineare.</s>
  <s xml:id="echoid-s27741" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horologiu@ <lb/>Aſtronomicũ <lb/>ad Horizõtem <lb/>ſphęrę rectæ in <lb/>clinatum quo <lb/>modo deſcriba <lb/>tur.</note>
<p>
  <s xml:id="echoid-s27742" xml:space="preserve">QVONIAM inclinatio plani ad Horizontem in ſphęra recta (loquimur autem de planis ad <lb/>Meridianũ rectis, &amp; </s>
  <s xml:id="echoid-s27743" xml:space="preserve">quorum circuli maximi quibus æquidiſtant, per polos Meridiani, id eſt, per <lb/>ſectiones cõmunes Horizontis, &amp; </s>
  <s xml:id="echoid-s27744" xml:space="preserve">Æquatoris ducuntur) altitudinẽ poli ſupra idẽ planũ metitur, <lb/>ſit vt horologia aſtronomica ad Horizontem inclinata in ſphæra recta deſcribantur, vt horizonta <lb/>lia in ſphæra obliqua, ſi pro altitudine poli in portione Analemmatis propoſ. </s>
  <s xml:id="echoid-s27745" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27746" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27747" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27748" xml:space="preserve">accipiatur <lb/>
<anchor type="note" xlink:label="note-0439-06a" xlink:href="note-0439-06"/>
arcus C E, inclinationi plani ad Horizontẽ æqualis; </s>
  <s xml:id="echoid-s27749" xml:space="preserve">ita vt axis mundi E D, cõmunis ſectio ſit Ho <lb/>rizontis recti, ac meridiani; </s>
  <s xml:id="echoid-s27750" xml:space="preserve">E, polus mundi, ſiue arcticus, ſiue antarcticus; </s>
  <s xml:id="echoid-s27751" xml:space="preserve">B C, ſectio communis <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s27752" xml:space="preserve">circuli maximi, cui horologiũ æquidiſtat; </s>
  <s xml:id="echoid-s27753" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27754" xml:space="preserve">H I, cõmunis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s27755" xml:space="preserve">plani <lb/>horologii. </s>
  <s xml:id="echoid-s27756" xml:space="preserve">Vnde quoniã Horizon rectus, ſiue circulus horæ 6. </s>
  <s xml:id="echoid-s27757" xml:space="preserve">à meridie vel media nocte per axẽ <lb/>E D, ductus occurrit plano horologii in H, cẽtro horologii, per quod ducitur linea horæ 6. </s>
  <s xml:id="echoid-s27758" xml:space="preserve">à me-<lb/>ridie, vel media nocte ad meridianam lineam perpendicularis, dabit in hoc horologio linea horæ <lb/>6. </s>
  <s xml:id="echoid-s27759" xml:space="preserve">à meridie, vel media nocte lineam horizontalem, quæ ſemper ſuperiorem locum occupabit, <lb/>conſtituto horologio in proprio ſitu. </s>
  <s xml:id="echoid-s27760" xml:space="preserve">Ordo horarum in horologio, quod ex parte auſtrali eleuatur <lb/>
<anchor type="note" xlink:label="note-0439-07a" xlink:href="note-0439-07"/>
ſupra Horizontem, ſpectatq́ue ad boream, idem eſt, qui in horologio horizõtali ſphæræ obliquę, <lb/>quia polus arcticus, ſupra planum horologij eleuatur; </s>
  <s xml:id="echoid-s27761" xml:space="preserve">adeò vt horizontale horologium, quod ad <lb/>
<anchor type="note" xlink:label="note-0439-08a" xlink:href="note-0439-08"/>
initium libri 2. </s>
  <s xml:id="echoid-s27762" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s27763" xml:space="preserve">42. </s>
  <s xml:id="echoid-s27764" xml:space="preserve">deſcripſimus, eleuatum ex parte auſtrali grad. </s>
  <s xml:id="echoid-s27765" xml:space="preserve">42. </s>
  <s xml:id="echoid-s27766" xml:space="preserve">exhi-<lb/>beat horologium inclinatum grad. </s>
  <s xml:id="echoid-s27767" xml:space="preserve">42. </s>
  <s xml:id="echoid-s27768" xml:space="preserve">in ſphæra recta, ita tamen vt linea horæ 6. </s>
  <s xml:id="echoid-s27769" xml:space="preserve">à meridie, vel <lb/>media nocte ſit linea horizontalis. </s>
  <s xml:id="echoid-s27770" xml:space="preserve">Quòd ſi horologium ad auſtrum ſpectet, eleueturq́ue ex par-<lb/>te boreali, erit idem ordo horarum, qui in Verticali horologio ſphærę obliquæ auſtrali, quia po-<lb/>lus antarcticus eleuatur ſupra planum horologii, adeò vt Verticale horologium ad auſtrum ſpe-<lb/>ctans, quod in lib. </s>
  <s xml:id="echoid-s27771" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27772" xml:space="preserve">deſcripſimus propoſ. </s>
  <s xml:id="echoid-s27773" xml:space="preserve">13. </s>
  <s xml:id="echoid-s27774" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s27775" xml:space="preserve">14. </s>
  <s xml:id="echoid-s27776" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s27777" xml:space="preserve">42. </s>
  <s xml:id="echoid-s27778" xml:space="preserve">eleuatum ex par-<lb/>te boreali grad. </s>
  <s xml:id="echoid-s27779" xml:space="preserve">48. </s>
  <s xml:id="echoid-s27780" xml:space="preserve">(quanta nimirum eſt poli altitudo ſupra Verticalem circulum) præbeat in <lb/>ſphæra recta horologium inclinatum grad. </s>
  <s xml:id="echoid-s27781" xml:space="preserve">48. </s>
  <s xml:id="echoid-s27782" xml:space="preserve">ita vt rurſus linea horæ 6. </s>
  <s xml:id="echoid-s27783" xml:space="preserve">à meridie, uel media <lb/>nocte det lineam horizontalem. </s>
  <s xml:id="echoid-s27784" xml:space="preserve">Quę omnia clara ſunt, &amp; </s>
  <s xml:id="echoid-s27785" xml:space="preserve">perſpicua, ſi horologium ad Horizon-<lb/>
<anchor type="note" xlink:label="note-0439-09a" xlink:href="note-0439-09"/>
tem inclinatum in proprio ſitu cogitetur eſſe collocatum.</s>
  <s xml:id="echoid-s27786" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1423" type="float" level="2" n="1">
<note position="left" xlink:label="note-0439-06" xlink:href="note-0439-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0439-07" xlink:href="note-0439-07a" xml:space="preserve">Ordo horarum <lb/>in prædicto h@ <lb/>rologio.</note>
<note position="left" xlink:label="note-0439-08" xlink:href="note-0439-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0439-09" xlink:href="note-0439-09a" xml:space="preserve">Quando lon-<lb/>gitudo ſtyli <lb/>vna cum eius <lb/>loco data eſt.</note>
</div>
<p>
  <s xml:id="echoid-s27787" xml:space="preserve">QVOD ſi detur longitudo ſtyli, eiuſque locus in plano inclinato, procedemus, vt in horolo-
<pb o="424" file="0440" n="440" rhead="GNOMONICES"/>
gio horizontali, dummodo pro altitudine poli eiusq́ue complemento accipiamus inclinationem <lb/>plani ad Horizontem, eiuſq́ue complementum, numerando complementum inclinationis ſem-<lb/>
<anchor type="note" xlink:label="note-0440-01a" xlink:href="note-0440-01"/>
per verſus partes ſuperiores plani, &amp; </s>
  <s xml:id="echoid-s27788" xml:space="preserve">ipſam inclinationem verſus inſeriores, &amp;</s>
  <s xml:id="echoid-s27789" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27790" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1424" type="float" level="2" n="2">
<note position="left" xlink:label="note-0440-01" xlink:href="note-0440-01a" xml:space="preserve">Horæ ab or. &amp; <lb/>occ. atque in-<lb/>ęquales in eo <lb/>dé horologio.</note>
</div>
<p>
  <s xml:id="echoid-s27791" xml:space="preserve">HORÆ ab ortu, &amp; </s>
  <s xml:id="echoid-s27792" xml:space="preserve">occaſu, atque inæquales numerantur hic, vt in propoſ. </s>
  <s xml:id="echoid-s27793" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27794" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s27795" xml:space="preserve">tra <lb/>ditum eſt.</s>
  <s xml:id="echoid-s27796" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27797" xml:space="preserve">ARCVS autem ſignorum, arcus diurni, &amp; </s>
  <s xml:id="echoid-s27798" xml:space="preserve">paralleli ciuitatum deſcribuntur, vt in horizon-<lb/>
<anchor type="note" xlink:label="note-0440-02a" xlink:href="note-0440-02"/>
tali horologio ſphęræ obliquę dictum eſt, eundemq́ue ordinem habent, quem in horizontali, ſeu <lb/>Verticali, prout horologium ad boream ſpectat, vel ad auſtrum.</s>
  <s xml:id="echoid-s27799" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1425" type="float" level="2" n="3">
<note position="left" xlink:label="note-0440-02" xlink:href="note-0440-02a" xml:space="preserve">Arcus ſignorũ, <lb/>arcus diu@ni, &amp; <lb/>citculi latitudi <lb/>num ciuitatũ <lb/>in eodem horo <lb/>logio.</note>
</div>
<p>
  <s xml:id="echoid-s27800" xml:space="preserve">VERTICALES circuli, &amp; </s>
  <s xml:id="echoid-s27801" xml:space="preserve">paralleli Horizontis depingentur, vt in horologio inclinato ad <lb/>Horizontem ſphæræ obliquæ, veluti propoſ. </s>
  <s xml:id="echoid-s27802" xml:space="preserve">28. </s>
  <s xml:id="echoid-s27803" xml:space="preserve">ſuperioris libri docuimus. </s>
  <s xml:id="echoid-s27804" xml:space="preserve">Si enim ex portione <lb/>
<anchor type="note" xlink:label="note-0440-03a" xlink:href="note-0440-03"/>
<anchor type="note" xlink:label="note-0440-04a" xlink:href="note-0440-04"/>
Analemmatis in propoſ. </s>
  <s xml:id="echoid-s27805" xml:space="preserve">1. </s>
  <s xml:id="echoid-s27806" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27807" xml:space="preserve">2. </s>
  <s xml:id="echoid-s27808" xml:space="preserve">poſita ſumatur rectæ H D, (Reſpondet autem recta illa H D, ſi <lb/>angulus D H I, inclinationi plani æqualis fuerit, rectæ A B, in figura propoſ. </s>
  <s xml:id="echoid-s27809" xml:space="preserve">28. </s>
  <s xml:id="echoid-s27810" xml:space="preserve">ſuperioris lib.) </s>
  <s xml:id="echoid-s27811" xml:space="preserve">in <lb/>linea meridiana æqualis recta, facto initio à centro horologij H, hoc eſt, à puncto, vbi horizonta-<lb/>lis linea, ſeu horæ ſextæ, meridianam lineam interſecat, &amp; </s>
  <s xml:id="echoid-s27812" xml:space="preserve">circulus deſcribatur, inueniemus <lb/>puncta in linea horæ ſextæ à meridie, vel media nocte, ſeu horizontali, quæ cum puncto, vbi <lb/>meridiana linea, &amp; </s>
  <s xml:id="echoid-s27813" xml:space="preserve">æquinoctialis ſe mutuo ſecant, coniuncta lineis rectis, dabunt circulos Ver <lb/>ticales. </s>
  <s xml:id="echoid-s27814" xml:space="preserve">Eſtnamque linea ęquinoctialis eadem, quæ Verticalis, &amp; </s>
  <s xml:id="echoid-s27815" xml:space="preserve">linea meridiana dat Vertica-<lb/>lem grad. </s>
  <s xml:id="echoid-s27816" xml:space="preserve">90. </s>
  <s xml:id="echoid-s27817" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s27818" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27819" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1426" type="float" level="2" n="4">
<note position="left" xlink:label="note-0440-03" xlink:href="note-0440-03a" xml:space="preserve">Circuli Verti-<lb/>cales, &amp; paralle <lb/>li Horizontis.</note>
<note position="left" xlink:label="note-0440-04" xlink:href="note-0440-04a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s27820" xml:space="preserve">MERIDIANI, domus cœleſtes, &amp; </s>
  <s xml:id="echoid-s27821" xml:space="preserve">aſcendentia ſigna Zodiaci figurabuntur, vt in præce-<lb/>
<anchor type="note" xlink:label="note-0440-05a" xlink:href="note-0440-05"/>
dentibus dictum eſt. </s>
  <s xml:id="echoid-s27822" xml:space="preserve">Quocirca horologia ad Horizontem inclinata in ſphæra recta delineauimus. <lb/></s>
  <s xml:id="echoid-s27823" xml:space="preserve">
<anchor type="note" xlink:label="note-0440-06a" xlink:href="note-0440-06"/>
Quod faciendum erat.</s>
  <s xml:id="echoid-s27824" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1427" type="float" level="2" n="5">
<note position="left" xlink:label="note-0440-05" xlink:href="note-0440-05a" xml:space="preserve">Circuli Meri-<lb/>diani, domus <lb/>cœleſtes, &amp; ſi-<lb/>gna aſcenden-<lb/>tia.</note>
<note position="left" xlink:label="note-0440-06" xlink:href="note-0440-06a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1429" type="section" level="1" n="350">
<head xml:id="echoid-head363" xml:space="preserve">PROBLEMA 9. PROPOSITIO 9.</head>
<p>
  <s xml:id="echoid-s27825" xml:space="preserve">HOROLOGIA à Verticali circulo declinantia, &amp; </s>
  <s xml:id="echoid-s27826" xml:space="preserve">ſimul ad Ho <lb/>rizontem inclinata in ſphæra recta componere.</s>
  <s xml:id="echoid-s27827" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27828" xml:space="preserve">DVCANTVR duæ rectæ A B, C D, ſe ſe in E, ad rectos angulos ſecantes, &amp; </s>
  <s xml:id="echoid-s27829" xml:space="preserve">in E, ad rectã <lb/>
<anchor type="note" xlink:label="note-0440-07a" xlink:href="note-0440-07"/>
C D, conſtituatur angulus declinationis D E F, ſeruato illo ordine, quem in propoſ. </s>
  <s xml:id="echoid-s27830" xml:space="preserve">37. </s>
  <s xml:id="echoid-s27831" xml:space="preserve">ſuperio-<lb/>ris libri pręſcripſimus, hoc eſt, in plano, quod à meridie in ortum, vel à ſeptentrione in occaſum <lb/>
<anchor type="note" xlink:label="note-0440-08a" xlink:href="note-0440-08"/>
declinat, infra rectam A B, uerſus punctum A. </s>
  <s xml:id="echoid-s27832" xml:space="preserve">At verſus punctum B, infra eandem rectam A B, <lb/>in plano, quod à meridie in occaſum, vel à ſeptentrione in ortum vergit. </s>
  <s xml:id="echoid-s27833" xml:space="preserve">Loquimur autem hic <lb/>de ſuperiori horologio, vt in dicta propoſ. </s>
  <s xml:id="echoid-s27834" xml:space="preserve">37. </s>
  <s xml:id="echoid-s27835" xml:space="preserve">ſuperioris libri. </s>
  <s xml:id="echoid-s27836" xml:space="preserve">Ex hoc enim facile inferius horo-<lb/>logium deducetur, vt in præcedentibus duobus libris tradidimus. </s>
  <s xml:id="echoid-s27837" xml:space="preserve">Dicetur autem E F, linea decli-<lb/>nationis. </s>
  <s xml:id="echoid-s27838" xml:space="preserve">Nos planum propoſitum declinare ponimus à meridie in ortum grad. </s>
  <s xml:id="echoid-s27839" xml:space="preserve">60. </s>
  <s xml:id="echoid-s27840" xml:space="preserve">inclinatum <lb/>verò eſſe ad Horizontem grad. </s>
  <s xml:id="echoid-s27841" xml:space="preserve">70.</s>
  <s xml:id="echoid-s27842" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1429" type="float" level="2" n="1">
<note position="left" xlink:label="note-0440-07" xlink:href="note-0440-07a" xml:space="preserve">Qua ratione <lb/>horologium à <lb/>Verticali circu <lb/>lo declinans, &amp; <lb/>ad Horizontem <lb/>inclinatum in <lb/>ſphęra recta de <lb/>ſcribatur.</note>
<note position="left" xlink:label="note-0440-08" xlink:href="note-0440-08a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s27843" xml:space="preserve">DEINDE ex puncto F, vtcunque in linea declinationis E F, aſſumpto excitetur ad A B, <lb/>perpendicularis F ψ, vel potius ex aſſumpto puncto ψ, in recta A B, ducatur ad A B, perpendi-<lb/>cularis ψ F, ſecans lineam declinationis E F, in F, puncto ex quo ad ψ F, perpendicularis educatur <lb/>F n. </s>
  <s xml:id="echoid-s27844" xml:space="preserve">Conſtituto deinde in ψ, ad ψ F, angulo inclination is plani ad Horizontem F ψ n, ita vt re-<lb/>
<anchor type="note" xlink:label="note-0440-09a" xlink:href="note-0440-09"/>
cta ψ n, ſecet rectam F n, in n, abſcindatur ex ψ F, producta ipſi ψ n, æqualis ψ p, ducaturq́ue re-<lb/>cta E p, quæ linea erit meridiana, ſiue horæ 12 à meridie vel media nocte, ur demonſtrabimus.</s>
  <s xml:id="echoid-s27845" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1430" type="float" level="2" n="2">
<note position="left" xlink:label="note-0440-09" xlink:href="note-0440-09a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s27846" xml:space="preserve">POST hæc, ducta ex F, ad ψ n, perpendiculari F G, auferatur ex ψ F, ipſi ψ G, recta æqua-<lb/>lis ψ H. </s>
  <s xml:id="echoid-s27847" xml:space="preserve">Ducta namque recta E H, erit linea indicis, ſiue ſtyli: </s>
  <s xml:id="echoid-s27848" xml:space="preserve">ſtylus autem erit recta F G, in H, col-<lb/>locandus ad planum horologii rectus.</s>
  <s xml:id="echoid-s27849" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27850" xml:space="preserve">RVRSVS erigatur ex H, ad lineam ſtyli E H, perpendicularis H I, ſtylo F G, æqualis, &amp; </s>
  <s xml:id="echoid-s27851" xml:space="preserve">ex E, <lb/>per I, emittatur recta E I, quæ axem mundi referet, adeò vt H E I, ſit angulus altitudinis poli ſu-<lb/>pra planum propoſitum. </s>
  <s xml:id="echoid-s27852" xml:space="preserve">Ducta autem ex I, ad axem E I, perpendiculari I K, ſecante lineam indi-<lb/>cis in K, excitetur per K, ad lineam indicis perpendicularis K M, pro linea æquinoctiali, quæ ne-<lb/>ceſſario, ſi erratum non eſt, per punctum p, tranſibit vt demonſtrabimus.</s>
  <s xml:id="echoid-s27853" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s27854" xml:space="preserve">POSTREMO ſumpta in linea ſtyli recta K L, ipſi K I, æquali, deſcribatur ex K, circulus <lb/>cuiuſuis magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s27855" xml:space="preserve">ſecetur, initio facto à recta L M, quæ ex centro L, per <lb/>punctum M, vbi ſe mutuo ſecant linea meridiana, &amp; </s>
  <s xml:id="echoid-s27856" xml:space="preserve">æquinoctialis, ducitur: </s>
  <s xml:id="echoid-s27857" xml:space="preserve">vel à recta L α, quæ <lb/>ducitur ex centro L, per punctum α, vbi æquinoctialis linea rectam A B, interſecat. </s>
  <s xml:id="echoid-s27858" xml:space="preserve">Si enim ex L, <lb/>per diuiſionum puncta emittantur rectæ, ſecabitur æquinoctialis linea K M, in punctis, per quæ <lb/>ex E, rectæ emiſſæ dabunt horas à meridie, vel media nocte hoc ordine. </s>
  <s xml:id="echoid-s27859" xml:space="preserve">Poſito horologio in pro-<lb/>prio ſitu, ita vt recta A B, Horizonti æquidiſter, horæ, quæ meridianam lineam ſequuntur verſus <lb/>ortum, (quæ uidelicet nobis ad horologium à meridie declinans conuerſis ad dextram ſitæ ſunt, <lb/>ad ſiniſtram verò, ſi horologium declinet à ſeptentrione) à meridie computandę ſunt, quemad-<lb/>modum &amp; </s>
  <s xml:id="echoid-s27860" xml:space="preserve">in horologio declinante, &amp; </s>
  <s xml:id="echoid-s27861" xml:space="preserve">inclinato ſimul in ſphæra obliqua, de quo in propoſ. </s>
  <s xml:id="echoid-s27862" xml:space="preserve">37. <lb/></s>
  <s xml:id="echoid-s27863" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s27864" xml:space="preserve">egimus.</s>
  <s xml:id="echoid-s27865" xml:space="preserve"/>
</p>
<pb o="425" file="0441" n="441" rhead="LIBER QVARTVS."/>
<p>
  <s xml:id="echoid-s27866" xml:space="preserve">HANC autem conſtructionem hoc modo demonſtrabimus. </s>
  <s xml:id="echoid-s27867" xml:space="preserve">In plano horologii proprium <lb/>
<anchor type="note" xlink:label="note-0441-01a" xlink:href="note-0441-01"/>
ſitum habentis intelligatur A B, Horizonti æquidiſtans, ita vt ſit communis ſectio plani horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s27868" xml:space="preserve">Horizontis, &amp; </s>
  <s xml:id="echoid-s27869" xml:space="preserve">triangulum E F ψ, moueri concipiatur circa rectam E ψ, donec cum Hori-<lb/>zonte coniungatur, in eoque iaceat. </s>
  <s xml:id="echoid-s27870" xml:space="preserve">Et quoniam D E F, angulus eſt declinationis plani à Vertica-<lb/>
<anchor type="figure" xlink:label="fig-0441-01a" xlink:href="fig-0441-01"/>
<anchor type="note" xlink:label="note-0441-02a" xlink:href="note-0441-02"/>
<anchor type="note" xlink:label="note-0441-03a" xlink:href="note-0441-03"/>
<anchor type="note" xlink:label="note-0441-04a" xlink:href="note-0441-04"/>
li, erit reliquus A E F, angulus complementi dictæ declinationis, qualem nimirum facit Meri-<lb/>dianus cum linea, quæ in plano declinante, &amp; </s>
  <s xml:id="echoid-s27871" xml:space="preserve">inclinato æquidiſtat Horizonti, vel potius cum pla <lb/>no per illam rectam ducto, &amp; </s>
  <s xml:id="echoid-s27872" xml:space="preserve">ad Horizontem recto. </s>
  <s xml:id="echoid-s27873" xml:space="preserve">Quare E F, in illo ſitu communis ſectio erit <lb/>Meridiani, &amp; </s>
  <s xml:id="echoid-s27874" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s27875" xml:space="preserve">Quia verò in ſphæra recta axis mundi communis ſectio eſt Horizon -<lb/>tis, ac Meridiani, erit E F, axis mundi occurrens plano horologij in E, puncto, quod centrum erit <lb/>horologii, in quo omnes horariæ lineæ conueniunt, vt in ſuperioribus demonſtratum eſt.</s>
  <s xml:id="echoid-s27876" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1431" type="float" level="2" n="3">
<note position="right" xlink:label="note-0441-01" xlink:href="note-0441-01a" xml:space="preserve">Demonſtratio <lb/>deſcriptionis <lb/>horologii præ-<lb/>dicti.</note>
  <figure xlink:label="fig-0441-01" xlink:href="fig-0441-01a">
    <image file="0441-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0441-01"/>
  </figure>
<note position="left" xlink:label="note-0441-02" xlink:href="note-0441-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0441-03" xlink:href="note-0441-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0441-04" xlink:href="note-0441-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s27877" xml:space="preserve">RVRSVS triangulo E F ψ, habente illum ſitum, quem diximus, intelligatur circa F ψ, con-<lb/>
<anchor type="note" xlink:label="note-0441-05a" xlink:href="note-0441-05"/>
uerti triangulum F n ψ, deorſum verſus, donec &amp; </s>
  <s xml:id="echoid-s27878" xml:space="preserve">ad planum horologii, &amp; </s>
  <s xml:id="echoid-s27879" xml:space="preserve">ad Horizontem ſit <lb/>rectum: </s>
  <s xml:id="echoid-s27880" xml:space="preserve">quod tum demum fiet, cum recta ψ n, perpendicularis fuerit ad A B. </s>
  <s xml:id="echoid-s27881" xml:space="preserve">Tunc enim recta <lb/>A B, perpendicularis exiſtens ad rectas ψ F, ψ n, recta erit ad planum trianguli ψ F n, per illas re-<lb/>
<anchor type="note" xlink:label="note-0441-06a" xlink:href="note-0441-06"/>
ctas ductum. </s>
  <s xml:id="echoid-s27882" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s27883" xml:space="preserve">tam planum horologii, quàm Horizontis, per rectam A B, ductum, ad idẽ <lb/>planum trianguli ψ F n, rectum erit; </s>
  <s xml:id="echoid-s27884" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s27885" xml:space="preserve">viciſſim hoc ad vtrumque illorum rectum exi <lb/>
<anchor type="note" xlink:label="note-0441-07a" xlink:href="note-0441-07"/>
ſtet. </s>
  <s xml:id="echoid-s27886" xml:space="preserve">Quocirca cum F ψ n, angulus ſit inclinationis plani ad Horizontem, &amp; </s>
  <s xml:id="echoid-s27887" xml:space="preserve">per rectam F ψ, in <lb/>eo ſitu ducatur Horizon, iacebit ψ n, in plano inclinato, coniunctaq́; </s>
  <s xml:id="echoid-s27888" xml:space="preserve">erit cum recta ψ p, in eodẽ <lb/>plano exiſtente, atque adeò punctum n, in punctum p, cadet, ob æqualitatem rectarum ψ n, ψ p. <lb/></s>
  <s xml:id="echoid-s27889" xml:space="preserve">Cum ergo Meridianus rectus exiſtens ad Horizontem, ac idcirco &amp; </s>
  <s xml:id="echoid-s27890" xml:space="preserve">ad planum trianguli E F ψ, <lb/>
<anchor type="note" xlink:label="note-0441-08a" xlink:href="note-0441-08"/>
in plano Horizontis exiſtentis in dicto ſitu, tranſeat per rectam E F, vt demonſtrauimus, ac pro-<lb/>inde &amp; </s>
  <s xml:id="echoid-s27891" xml:space="preserve">per rectam F n, in illo ſitu, (propterea quod F n, per defin. </s>
  <s xml:id="echoid-s27892" xml:space="preserve">4. </s>
  <s xml:id="echoid-s27893" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27894" xml:space="preserve">11. </s>
  <s xml:id="echoid-s27895" xml:space="preserve">Euclidis recta eſt ad <lb/>planum trianguli E F ψ, cum perpendicularis ſit, ex conſtructione, ad F ψ, cõmunem ſectione m <lb/>triangulorum E F ψ, ψ F n, quorum vnum ad alterum rectum eſt) occurret Meridianus plano <lb/>horologii inclinati in puncto p; </s>
  <s xml:id="echoid-s27896" xml:space="preserve">ac proinde recta E p, communis ſectio erit Meridiani, ac plani <lb/>horologii inclinati. </s>
  <s xml:id="echoid-s27897" xml:space="preserve">Hanc autem eandem meridianam lineam inueniemus etiam alio modo, vt <lb/>ad principium propoſ. </s>
  <s xml:id="echoid-s27898" xml:space="preserve">37. </s>
  <s xml:id="echoid-s27899" xml:space="preserve">ſuperioris libri docuimus.</s>
  <s xml:id="echoid-s27900" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1432" type="float" level="2" n="4">
<note position="left" xlink:label="note-0441-05" xlink:href="note-0441-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0441-06" xlink:href="note-0441-06a" xml:space="preserve">4. vndec.</note>
<note position="right" xlink:label="note-0441-07" xlink:href="note-0441-07a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0441-08" xlink:href="note-0441-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s27901" xml:space="preserve">QVONIAM autem, triangulis E F ψ, ψ F n, in iiſdem poſitionibus adhuc conſtitutis, re-<lb/>cta F G, ad ψ n, cõmunem ſectionem plani horologii, &amp; </s>
  <s xml:id="echoid-s27902" xml:space="preserve">trianguli F n ψ, ad horologii planum re <lb/>cti exiſtentis, perpendicularis eſt, exiſtitq́ue in plano trianguli F n ψ, erit per deſin. </s>
  <s xml:id="echoid-s27903" xml:space="preserve">4. </s>
  <s xml:id="echoid-s27904" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27905" xml:space="preserve">11. </s>
  <s xml:id="echoid-s27906" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s27907" xml:space="preserve">@adem F G, ad planum hologii recta in puncto G, quod idem tunc eſt, quod H. </s>
  <s xml:id="echoid-s27908" xml:space="preserve">Cum ergo eius
<pb o="426" file="0442" n="442" rhead="GNOMONICES"/>
extremum punctum F, cadat in axem E F, (oſtenſum enim eſt, E F, in eo ſitu eſſe axem mundi) <lb/>erit punctum F, centrum mundi, cum per illud ducatur &amp; </s>
  <s xml:id="echoid-s27909" xml:space="preserve">Meridianus, &amp; </s>
  <s xml:id="echoid-s27910" xml:space="preserve">Horizon, recta autõ <lb/>F G, ſtylus erit, ſiue gnomon; </s>
  <s xml:id="echoid-s27911" xml:space="preserve">ac proinde recta E H, per locum ſtyli ducta erit linea indicis, adeo <lb/>vt circulus maximus per ipſam, &amp; </s>
  <s xml:id="echoid-s27912" xml:space="preserve">ſtylum ductus, necnon per polos mundi, ad planum horologii <lb/>rectus ſit, inſtar proprii cuiuſdam Meridiani.</s>
  <s xml:id="echoid-s27913" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s27914" xml:space="preserve">IAM verò ſi triangulum E I K, circa rectam E K, circumuertatur, vſque dum rectum ſit ad <lb/>planum horologii, erit recta H I, ad idẽ perpendicularis, ex defin. </s>
  <s xml:id="echoid-s27915" xml:space="preserve">4. </s>
  <s xml:id="echoid-s27916" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s27917" xml:space="preserve">11. </s>
  <s xml:id="echoid-s27918" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s27919" xml:space="preserve">Cum ergo ſum-<lb/>pta ſit æqualis ſtylo F G, cadet punctum I, in centrum mundi F, hoc eſt, recta H I, ſtylo congruet, <lb/>&amp; </s>
  <s xml:id="echoid-s27920" xml:space="preserve">recta E I, axi mundi E F; </s>
  <s xml:id="echoid-s27921" xml:space="preserve">ac proinde H E I, angulus erit altitudinis poli ſupra planum horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s27922" xml:space="preserve">I K, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s27923" xml:space="preserve">trianguli E I K, ſiue Meridiani proprii ipſius plani <lb/>
<anchor type="note" xlink:label="note-0442-01a" xlink:href="note-0442-01"/>
horologii. </s>
  <s xml:id="echoid-s27924" xml:space="preserve">Quare vt in præcedentibus oſtenſum eſt, erit K M, linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s27925" xml:space="preserve">horariæ li-<lb/>neæ erunt deſcriptæ, vt diximus. </s>
  <s xml:id="echoid-s27926" xml:space="preserve">Quia vero Aequator in ſphæra recta ad Horizontem rectus eſt, <lb/>tranſitq́ue per F, verticem ſtyli, efficitur, vt per rectam F n, quam oſtendimus eſſe rectam ad Hori <lb/>zontem, ſiue ad triangulum E F ψ, in Horizonte iacens, ducatur, ac proinde plano horologii in <lb/>puncto p, occurrat. </s>
  <s xml:id="echoid-s27927" xml:space="preserve">Quare linea æquinoctialis K M, omnino per punctum p, tranſibit.</s>
  <s xml:id="echoid-s27928" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1433" type="float" level="2" n="5">
<note position="left" xlink:label="note-0442-01" xlink:href="note-0442-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s27929" xml:space="preserve">PARALLELI autem ſignorum Zodiaci, &amp; </s>
  <s xml:id="echoid-s27930" xml:space="preserve">latitudinum ciuitatum in hoc horologio incli <lb/>
<anchor type="note" xlink:label="note-0442-02a" xlink:href="note-0442-02"/>
nato, &amp; </s>
  <s xml:id="echoid-s27931" xml:space="preserve">declinante ſimul deſcribentur, vt in horologio inclinato, &amp; </s>
  <s xml:id="echoid-s27932" xml:space="preserve">declinante in ſphæra obli-<lb/>qua, veluti propoſ. </s>
  <s xml:id="echoid-s27933" xml:space="preserve">38. </s>
  <s xml:id="echoid-s27934" xml:space="preserve">ſuperioris libri tradidimus.</s>
  <s xml:id="echoid-s27935" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1434" type="float" level="2" n="6">
<note position="left" xlink:label="note-0442-02" xlink:href="note-0442-02a" xml:space="preserve">Paralleli ſigno <lb/>rum, &amp; latitu-<lb/>dinum ciuita-<lb/>tum.</note>
</div>
<p>
  <s xml:id="echoid-s27936" xml:space="preserve">HORAE ab ortu, &amp; </s>
  <s xml:id="echoid-s27937" xml:space="preserve">occaſu, nec non inæquales conueniunt, quo ad lineamenta, cum horis <lb/>
<anchor type="note" xlink:label="note-0442-03a" xlink:href="note-0442-03"/>
à meridie, &amp; </s>
  <s xml:id="echoid-s27938" xml:space="preserve">media nocte, in numero ſolum differunt, vt &amp; </s>
  <s xml:id="echoid-s27939" xml:space="preserve">in aliis horologiis ſphæræ re-<lb/>
<anchor type="note" xlink:label="note-0442-04a" xlink:href="note-0442-04"/>
ctæ diximus.</s>
  <s xml:id="echoid-s27940" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1435" type="float" level="2" n="7">
<note position="left" xlink:label="note-0442-03" xlink:href="note-0442-03a" xml:space="preserve">Horæab or. &amp; <lb/>occ. una cum <lb/>inæqualibus.</note>
<note position="left" xlink:label="note-0442-04" xlink:href="note-0442-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s27941" xml:space="preserve">CIRCVLI Verticales, paralleli Horizontis, Meridiani, &amp; </s>
  <s xml:id="echoid-s27942" xml:space="preserve">ſigna aſcendentia, non aliter <lb/>
<anchor type="note" xlink:label="note-0442-05a" xlink:href="note-0442-05"/>
etiam hic depingentur, atque in horologio declinante, &amp; </s>
  <s xml:id="echoid-s27943" xml:space="preserve">ſimul inclinato in ſphæra obliqua.</s>
  <s xml:id="echoid-s27944" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1436" type="float" level="2" n="8">
<note position="left" xlink:label="note-0442-05" xlink:href="note-0442-05a" xml:space="preserve">Circuli Verti-<lb/>cales, paralleli <lb/>Horizontis, Me <lb/>ridiani, atque <lb/>aſcendentia ſi-<lb/>gna.</note>
</div>
<p>
  <s xml:id="echoid-s27945" xml:space="preserve">CAELESTES denique domus per lineas horarias hic exprimuntur, quemadmodum in <lb/>aliis horologiis ſphæræ rectæ, vt dictum eſt. </s>
  <s xml:id="echoid-s27946" xml:space="preserve">Horologia igitur à Verticali circulo declinantia, &amp; </s>
  <s xml:id="echoid-s27947" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0442-06a" xlink:href="note-0442-06"/>
ſimul ad Horizontem inclinata in ſphæra recta compoſuimus. </s>
  <s xml:id="echoid-s27948" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s27949" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1437" type="float" level="2" n="9">
<note position="left" xlink:label="note-0442-06" xlink:href="note-0442-06a" xml:space="preserve">Domus cœle-<lb/>@tes.</note>
</div>
</div>
<div xml:id="echoid-div1439" type="section" level="1" n="351">
<head xml:id="echoid-head364" xml:space="preserve">PROBLEMA 10. PROPOSITIO 10.</head>
<p>
  <s xml:id="echoid-s27950" xml:space="preserve">HOROLOGIA in ſphęra obliquiſſima, vbi polus arcticus ſupra <lb/>
<anchor type="note" xlink:label="note-0442-07a" xlink:href="note-0442-07"/>
Horizontem attollitur grad. </s>
  <s xml:id="echoid-s27951" xml:space="preserve">90. </s>
  <s xml:id="echoid-s27952" xml:space="preserve">conficere.</s>
  <s xml:id="echoid-s27953" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1439" type="float" level="2" n="1">
<note position="left" xlink:label="note-0442-07" xlink:href="note-0442-07a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s27954" xml:space="preserve">QVONIAM in huiuſmodi ſphæra continuus dies eſt, dum Sol ſex ſigna borealia percur-<lb/>
<anchor type="note" xlink:label="note-0442-08a" xlink:href="note-0442-08"/>
rit, ita vt tunc Sol neque oriatur, neque occidat, neque ad meridiem, aut mediam noctem perue-<lb/>niat, ſed perpetuo ſupra Horizontem exiſtat: </s>
  <s xml:id="echoid-s27955" xml:space="preserve">continua item nox, dum Sol in ſex aliis ſignis au-<lb/>ſtralibus moratur: </s>
  <s xml:id="echoid-s27956" xml:space="preserve">efficitur vt, ſi propriè loqui velimus, neque horæ computari poſſint ab ortu, <lb/>occaſuve, neque à meridie, aut media nocte, neque horæ 12. </s>
  <s xml:id="echoid-s27957" xml:space="preserve">inæquales aſſignari, cum non ſint ibi <lb/>arcus diurni, nocturnive, qui in partes 12. </s>
  <s xml:id="echoid-s27958" xml:space="preserve">æquales diſtribuantur. </s>
  <s xml:id="echoid-s27959" xml:space="preserve">Quare neque horologiũ Aſtro-<lb/>nomicum, neque Italicum, Babylonicumve, aut Antiquum in dicta ſphæra conſtrui poteſt. </s>
  <s xml:id="echoid-s27960" xml:space="preserve">Ve-<lb/>runtamen ſi concipiantur 12. </s>
  <s xml:id="echoid-s27961" xml:space="preserve">circuli horarii per polos mundi incedentes, Aequatoremq́ue in <lb/>
<anchor type="note" xlink:label="note-0442-09a" xlink:href="note-0442-09"/>
24. </s>
  <s xml:id="echoid-s27962" xml:space="preserve">partes æquales diuidentes fixi, &amp; </s>
  <s xml:id="echoid-s27963" xml:space="preserve">immobiles, licebit eorum lineas horarias deſcribere tam in <lb/>plano, quod Horizonti æquidiſtat, quàm in eo, quod rectum eſt, vel inclinatum ad Horizontem, <lb/>hoc modo.</s>
  <s xml:id="echoid-s27964" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1440" type="float" level="2" n="2">
<note position="left" xlink:label="note-0442-08" xlink:href="note-0442-08a" xml:space="preserve">Qua ratione <lb/>horologia in <lb/>ſphæra obli-<lb/>quiſſima. vbi al <lb/>titudo poli at-<lb/>ctici continet <lb/>grad. 90. deſcri <lb/>bi poſſint.</note>
<note position="left" xlink:label="note-0442-09" xlink:href="note-0442-09a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">Horizõ<unsure/>tale ho-<lb/>rologium in <lb/>ſphæra obli-<lb/>quiſſima, vbi <lb/>polus arcticus <lb/>in polo Hori-<lb/>zontis conſti-<lb/>tui tur.</note>
<p>
  <s xml:id="echoid-s27965" xml:space="preserve">PRO horologio horizontali ſumatur horologiũ Æquinoctiale, ita tamen vt integri paralleli <lb/>ſignorum Zodiaci deſcribantur, ſine linea horizõtali. </s>
  <s xml:id="echoid-s27966" xml:space="preserve">Quoniam enim Horizon in dicta ſphæra ab <lb/>Æquatore non differt, non ſecabitur planum horologii horizontalis ab Horizonte, neque ab <lb/>ęqninoctiali horologio differet. </s>
  <s xml:id="echoid-s27967" xml:space="preserve">Ordo autem horarum idem omnino erit in hoc horizontali ho-<lb/>rologio, qui in æquinoctiali, hoc ſolum excepto, quod hic non eſt opus indagare lineam meridia <lb/>nam, vt ibi, ſed collocato horologio, ita vt Horizonti æquidiſtet, initium horarum à quacunque <lb/>linea ſumi poteſt.</s>
  <s xml:id="echoid-s27968" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s27969" xml:space="preserve">HOROLOGIVM autem ad Horizontem rectum (quale eſt Verticale, vel à Verticali de-<lb/>
<anchor type="note" xlink:label="note-0442-12a" xlink:href="note-0442-12"/>
clinans) non diſcrepabit ab horologio polari; </s>
  <s xml:id="echoid-s27970" xml:space="preserve">cum circulus maximus, cui æquidiſtat, per polos <lb/>mundi incedat. </s>
  <s xml:id="echoid-s27971" xml:space="preserve">Initium tamen horarum ſtatui poteſt in quacunque linea horaria, &amp; </s>
  <s xml:id="echoid-s27972" xml:space="preserve">earum <lb/>ordo à ſiniſtra verſus dextram ſumitur. </s>
  <s xml:id="echoid-s27973" xml:space="preserve">Æquinoctialis autem linea eadem erit, quæ horizontalis.</s>
  <s xml:id="echoid-s27974" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1441" type="float" level="2" n="3">
<note position="left" xlink:label="note-0442-12" xlink:href="note-0442-12a" xml:space="preserve">Horologium<unsure/> <lb/>Verticale, &amp; à <lb/>Verticali decli <lb/>nans in eadem <lb/>ſphæra obli-<lb/>quiſſima.</note>
</div>
<p>
  <s xml:id="echoid-s27975" xml:space="preserve">SI denique planum horologii ad Horizontem fuerit inclinatum, dabit complementum in-<lb/>
<anchor type="note" xlink:label="note-0442-13a" xlink:href="note-0442-13"/>
clinationis altitudinem poli ſupra ipſum planum inclinatum, vt patet. </s>
  <s xml:id="echoid-s27976" xml:space="preserve">Quare ſi ad illam altitu-<lb/>dinem fabricetur horologiũ horizontale, vt ad initium libri 2. </s>
  <s xml:id="echoid-s27977" xml:space="preserve">tradidimus, in eoq́; </s>
  <s xml:id="echoid-s27978" xml:space="preserve">linea horizon-<lb/>talis ducatur, vt in alijs inclinatis horologiis ſphęrę obliquæ, deſcriptũ erit horologium inclinatũ <lb/>ad Horizontem. </s>
  <s xml:id="echoid-s27979" xml:space="preserve">Verum ex omnibus iſtis horologiis non cognoſcemus, vt diximus, quot horę ef-<lb/>fluxerint à meridie, vel media nocte, aut ab ortu vel occaſu, ſed quot horę ęquales ab aliquo pun-
<pb o="427" file="0443" n="443" rhead="LIBER QVARTVS."/>
cto fixo, quod animo concipimus, tranſierint ex illis 24. </s>
  <s xml:id="echoid-s27980" xml:space="preserve">quibus Sol integram reuolutionem ab <lb/>eodem puncto ad idem punctum perficit.</s>
  <s xml:id="echoid-s27981" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1442" type="float" level="2" n="4">
<note position="left" xlink:label="note-0442-13" xlink:href="note-0442-13a" xml:space="preserve">Horologium <lb/>inclinatum ad <lb/>Horizõtem in <lb/>eadẽ obliquiſ-<lb/>fima ſphæra.</note>
</div>
<p>
  <s xml:id="echoid-s27982" xml:space="preserve">VERTICALES circuli, quoniam à circulis horariis non diſcrepant, cum per polos mun-<lb/>di ducantur, deſcribentur, vt horariæ lineæ, ſtatuendo quamlibet lineam Verticalem pro commu <lb/>
<anchor type="note" xlink:label="note-0443-01a" xlink:href="note-0443-01"/>
ni ſectione Verticalis proprii dicti, &amp; </s>
  <s xml:id="echoid-s27983" xml:space="preserve">plani horologii, à qua cæteræ computari debent.</s>
  <s xml:id="echoid-s27984" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1443" type="float" level="2" n="5">
<note position="right" xlink:label="note-0443-01" xlink:href="note-0443-01a" xml:space="preserve">Verticales cir-<lb/>@ uli.</note>
</div>
<p>
  <s xml:id="echoid-s27985" xml:space="preserve">PARALLELI Horizontis, &amp; </s>
  <s xml:id="echoid-s27986" xml:space="preserve">latitudinum ciuitatum depingentur etiam, vt paralleli ſi-<lb/>
<anchor type="note" xlink:label="note-0443-02a" xlink:href="note-0443-02"/>
gnorum Zodiaci, ſi loco radiorum Zodiaci deſcribantur radij integri quadrantis, &amp;</s>
  <s xml:id="echoid-s27987" xml:space="preserve">c.</s>
  <s xml:id="echoid-s27988" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1444" type="float" level="2" n="6">
<note position="right" xlink:label="note-0443-02" xlink:href="note-0443-02a" xml:space="preserve">Paralleli Hori <lb/>zonris, &amp; lat@@ <lb/>dinum ciuita-<lb/>t<unsure/>u m.</note>
</div>
<p>
  <s xml:id="echoid-s27989" xml:space="preserve">MERIDIANI figurabũtur quoque, vt lineæ horariæ, ſi prius perſpecta fuerit poſitio primi <lb/>Meridiani per Inſulas Fortunatas ducti. </s>
  <s xml:id="echoid-s27990" xml:space="preserve">Cognoſci autẽ poterit ſitus primi illius Meridiani hac ra-<lb/>
<anchor type="note" xlink:label="note-0443-03a" xlink:href="note-0443-03"/>
tione. </s>
  <s xml:id="echoid-s27991" xml:space="preserve">Obſeruetur ſitus alicuius vrbis notam habentis longitudinem, quæ à loco ſub polo conſti-<lb/>
<anchor type="note" xlink:label="note-0443-04a" xlink:href="note-0443-04"/>
tuto diſtet aliquot milliariis, &amp; </s>
  <s xml:id="echoid-s27992" xml:space="preserve">in plano, quod Horizonti ſit parallelum, à propoſito loco ſub po-<lb/>lo ducatur linea recta verſus illam ciuitatem, cuius longitudo nota eſt, &amp; </s>
  <s xml:id="echoid-s27993" xml:space="preserve">ex puncto in ea vt libet <lb/>aſſumpto, circulus deſcribatur. </s>
  <s xml:id="echoid-s27994" xml:space="preserve">Nam quoniam illa recta communis ſectio eſt plani horologii ho-<lb/>rizontalis, &amp; </s>
  <s xml:id="echoid-s27995" xml:space="preserve">Meridiani per illam ciuitatem ducti, ſi ab ea verſus occidentales partes, hoc eſt, cõ-<lb/>tra ſucceſſionem ſignorum, ſecundum motum Solis diurnum, numeretur longitudo dictę ci-<lb/>uitatis, &amp; </s>
  <s xml:id="echoid-s27996" xml:space="preserve">à fine numerationis per centrum linea recta ducatur, habebitur communis ſectio Me-<lb/>ridiani primarij, &amp; </s>
  <s xml:id="echoid-s27997" xml:space="preserve">plani horizontalis horologii, vt patet. </s>
  <s xml:id="echoid-s27998" xml:space="preserve">Quandocunque ergo vmbra ſtyli in <lb/>hanc lineam cadet, facili negotio in aliis planis ex umbra gnomonis aliam lineam ducemus ei <lb/>reſpondentem, pro Meridiano Inſularum Fortunatarum.</s>
  <s xml:id="echoid-s27999" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1445" type="float" level="2" n="7">
<note position="right" xlink:label="note-0443-03" xlink:href="note-0443-03a" xml:space="preserve">Meridiani c<unsure/>i@-<lb/>culi.</note>
<note position="left" xlink:label="note-0443-04" xlink:href="note-0443-04a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s28000" xml:space="preserve">DOMVS autem cœleſtes locum in hac ſphæra non habent, propterea quod neque Meridia-<lb/>
<anchor type="note" xlink:label="note-0443-05a" xlink:href="note-0443-05"/>
<anchor type="note" xlink:label="note-0443-06a" xlink:href="note-0443-06"/>
nus, neque Verticalis propriè dictus per puncta veri ortus, &amp; </s>
  <s xml:id="echoid-s28001" xml:space="preserve">occaſus incedens aſſignari poſſit, <lb/>vt diximus.</s>
  <s xml:id="echoid-s28002" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1446" type="float" level="2" n="8">
<note position="left" xlink:label="note-0443-05" xlink:href="note-0443-05a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0443-06" xlink:href="note-0443-06a" xml:space="preserve">Domu<unsure/>s cœ<unsure/>le<unsure/>-<lb/>@es in obliquiſ <lb/>@ma ſphæra <lb/>nullæ ſunt.</note>
</div>
<p>
  <s xml:id="echoid-s28003" xml:space="preserve">SIGNA denique aſcendentia nulla quoque ſunt, cum perpetuo ſex ſigna ſupra Horizontem <lb/>
<anchor type="note" xlink:label="note-0443-07a" xlink:href="note-0443-07"/>
appareant, &amp; </s>
  <s xml:id="echoid-s28004" xml:space="preserve">ſex infra eundem abſcondantur. </s>
  <s xml:id="echoid-s28005" xml:space="preserve">Horologia igitur in ſphæra obliquiſſima, &amp;</s>
  <s xml:id="echoid-s28006" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28007" xml:space="preserve">con-<lb/>fecimus. </s>
  <s xml:id="echoid-s28008" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s28009" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1447" type="float" level="2" n="9">
<note position="right" xlink:label="note-0443-07" xlink:href="note-0443-07a" xml:space="preserve">Signa aſcendẽ-<lb/>tia in eadem <lb/>ſph<unsure/>ęra obliquiſ <lb/>@ma nulla @@@.</note>
</div>
</div>
<div xml:id="echoid-div1449" type="section" level="1" n="352">
<head xml:id="echoid-head365" xml:space="preserve">PROBLEMA 11. PROPOSITIO 11.</head>
<p>
  <s xml:id="echoid-s28010" xml:space="preserve">HOROLOGIA in ſphęra obliqua, in qua antarcticus polus ſu-<lb/>pra Horizontem attollitur, deſcribere.</s>
  <s xml:id="echoid-s28011" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s28012" xml:space="preserve">QVONIAM omnia præcepta, quæ in 2. </s>
  <s xml:id="echoid-s28013" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28014" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28015" xml:space="preserve">libro de horologiorum deſcriptionibus tradi <lb/>dimus, ad eam ſphęram obliquam ſpectant, quæ polum arcticum habet conſpicuum, viſum eſt <lb/>hoc problemmate paucis perſtringere, quomodo ſe gerere debeat is, qui horologia deſcribere ve-<lb/>lit in altera ſphæra obliqua, in qua antarcticus polus ſupra Horizontem eleuatur. </s>
  <s xml:id="echoid-s28016" xml:space="preserve">Hoc enim ſolũ <lb/>deeſſe videtur, vt per tradita præcepta horologia quis deſcribere in quacunque orbis terreni re-<lb/>gione poſſit: </s>
  <s xml:id="echoid-s28017" xml:space="preserve">quandoquidem hoc etiam libro regulas præſcripſimus, quibus &amp; </s>
  <s xml:id="echoid-s28018" xml:space="preserve">in ſphæra recta, <lb/>&amp; </s>
  <s xml:id="echoid-s28019" xml:space="preserve">in obliquiſſima, vbi polus arcticus ſupra Horizontem extollitur grad. </s>
  <s xml:id="echoid-s28020" xml:space="preserve">90. </s>
  <s xml:id="echoid-s28021" xml:space="preserve">horologia poſ-<lb/>ſint confici.</s>
  <s xml:id="echoid-s28022" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28023" xml:space="preserve">DESCRIPTVRI igitur in hemiſphærio auſtrali horologia, vtemur iiſdem omnino præ-<lb/>
<anchor type="note" xlink:label="note-0443-09a" xlink:href="note-0443-09"/>
<anchor type="note" xlink:label="note-0443-10a" xlink:href="note-0443-10"/>
ceptis, quæ lib. </s>
  <s xml:id="echoid-s28024" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28025" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28026" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28027" xml:space="preserve">dedimus, hac vna re animaduerſa, atque notata, vt quicquid ibi dictum eſt <lb/>de polo arctico, &amp; </s>
  <s xml:id="echoid-s28028" xml:space="preserve">horis ante meridiem, hic intelligatur de antarctico polo, horisq́ue pomeridia-<lb/>nis. </s>
  <s xml:id="echoid-s28029" xml:space="preserve">Et quod ibidem in horologijs Verticalibus, declinantibus, inclinatis, &amp;</s>
  <s xml:id="echoid-s28030" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28031" xml:space="preserve">ſcripſimus de par-<lb/>re auſtrali, ac boreali, transferatur hic ad partem borealem, atque auſtralem. </s>
  <s xml:id="echoid-s28032" xml:space="preserve">Denique quæcunque <lb/>ibi de ſignis borealibus, auſtralibusve præcepimus, contrario modo hic de auſtralibus, boreali-<lb/>busve accipiantur eſſe dicta: </s>
  <s xml:id="echoid-s28033" xml:space="preserve">adeò vt ſi hæc commutatio polorum, horarum ante, &amp; </s>
  <s xml:id="echoid-s28034" xml:space="preserve">poſt meridiẽ, <lb/>partis auſtralis, &amp; </s>
  <s xml:id="echoid-s28035" xml:space="preserve">borealis, ac ſignorum borealium, auſtraliumq́ue fiat, quodlibet horologiũ lib. <lb/></s>
  <s xml:id="echoid-s28036" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28037" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28038" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28039" xml:space="preserve">delineatum, verbi gratia, ad latitudinem grad. </s>
  <s xml:id="echoid-s28040" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28041" xml:space="preserve">in hemiſphærio borali, exhibeat quoque <lb/>horologium in auſtrali hemiſphærio ad latitudinem grad. </s>
  <s xml:id="echoid-s28042" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28043" xml:space="preserve">fabricatum. </s>
  <s xml:id="echoid-s28044" xml:space="preserve">Quod vt planius fiat, <lb/>per varia horologia in ſuperioribus libris deſcripta breuiter percurremus, declarantes in vnoquo-<lb/>
<anchor type="note" xlink:label="note-0443-11a" xlink:href="note-0443-11"/>
que, quomodo in auſtrali hemiſphærio collocandum, quidque in eo immutandum ſit, vt ho-<lb/>ras commonſtret.</s>
  <s xml:id="echoid-s28045" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1449" type="float" level="2" n="1">
<note position="left" xlink:label="note-0443-09" xlink:href="note-0443-09a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0443-10" xlink:href="note-0443-10a" xml:space="preserve">Qua ration<unsure/>e in <lb/>ſphæra obli-<lb/>qua, quę<unsure/> c<unsure/>olu<unsure/>m <lb/>antarcticum ha <lb/>bet con pi<unsure/>e@ũ, <lb/>deſcriban<unsure/>tur.</note>
<note position="left" xlink:label="note-0443-11" xlink:href="note-0443-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s28046" xml:space="preserve">HORIZONTALE ergo horologium in ſphæra obliqua, vbi polus antarcticus ſupra <lb/>
<anchor type="note" xlink:label="note-0443-12a" xlink:href="note-0443-12"/>
Horizontem eleuatur, ita collocandum eſt, vt centrum ipſius in boream, &amp; </s>
  <s xml:id="echoid-s28047" xml:space="preserve">linea æquinoctialis in <lb/>auſtrum vergat, quia hac ratione axis mundi per centrum horologii, &amp; </s>
  <s xml:id="echoid-s28048" xml:space="preserve">verticem gnomonis tran-<lb/>ſiens proprium ſitum habebit, hoc eſt, per polos mundi incedet. </s>
  <s xml:id="echoid-s28049" xml:space="preserve">Arcus quoque ſignorum borea <lb/>lium mutandi ſunt in arcus ſignorum auſtralium, &amp; </s>
  <s xml:id="echoid-s28050" xml:space="preserve">arcus auſtralium in arcus borealium, ita vt <lb/>ſigna inter centrum, &amp; </s>
  <s xml:id="echoid-s28051" xml:space="preserve">æquinoctialem lineam pertineant ad ſigna auſtralia, &amp; </s>
  <s xml:id="echoid-s28052" xml:space="preserve">reliqua ad borealia@ <lb/>quoniam ibi principium ♑, in meridie maximè ad Zenith accedit, principium vero ♋, ab eo-<lb/>d<unsure/>em maximè recedit. </s>
  <s xml:id="echoid-s28053" xml:space="preserve">Horæ denique mutandę ſunt in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s28054" xml:space="preserve">ſi à me-
<pb o="428" file="0444" n="444" rhead="GNOMONICES"/>
ridie, vel media nocte computentur, in complementa verò earundem vſque ad 24. </s>
  <s xml:id="echoid-s28055" xml:space="preserve">ſi numerentur <lb/>ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s28056" xml:space="preserve">quæ in ſphæra obliqua boreali à meridie cõputabantur, in hac altera à me-<lb/>dia nocte ſupputentur, &amp; </s>
  <s xml:id="echoid-s28057" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s28058" xml:space="preserve">Quæ verò ab ortu ibi numerari ſolebant, numerentur hic ab <lb/>occaſu, &amp; </s>
  <s xml:id="echoid-s28059" xml:space="preserve">e contrario; </s>
  <s xml:id="echoid-s28060" xml:space="preserve">adeò vt ex Italico horologio fiat Babylonicum, &amp; </s>
  <s xml:id="echoid-s28061" xml:space="preserve">Italicum ex Babylonico, <lb/>quod ad lineamenta attinet. </s>
  <s xml:id="echoid-s28062" xml:space="preserve">Nam numeri horarum mutantur in complementa vſque ad 24. </s>
  <s xml:id="echoid-s28063" xml:space="preserve">vt <lb/>diximus. </s>
  <s xml:id="echoid-s28064" xml:space="preserve">Pari ratione numeri horarum inæqualium mutandi ſunt in earum complementa vſque <lb/>ad 12. </s>
  <s xml:id="echoid-s28065" xml:space="preserve">Ratio autem huius mutationis perſpicua eſt, ſi diligenter ſitus horologii conſideretur. </s>
  <s xml:id="echoid-s28066" xml:space="preserve">Nã <lb/>quæ pars horologii in ſphæra obliqua boreali vergebat in ortum, atque adeo horas continebat <lb/>poſt meridiem, vel ab occaſu, ſpectat in auſtrali ſphæra obliqua in occaſum, horasq́ue complecti-<lb/>tur ante meridiem, vel ab ortu, &amp; </s>
  <s xml:id="echoid-s28067" xml:space="preserve">è contrario. </s>
  <s xml:id="echoid-s28068" xml:space="preserve">Exemplum hic habes in horologio horizontali ad <lb/>
<anchor type="note" xlink:label="note-0444-01a" xlink:href="note-0444-01"/>
<anchor type="figure" xlink:label="fig-0444-01a" xlink:href="fig-0444-01"/>
<anchor type="note" xlink:label="note-0444-02a" xlink:href="note-0444-02"/>
latitudinem auſtralem grad. </s>
  <s xml:id="echoid-s28069" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28070" xml:space="preserve">cõſtructo. </s>
  <s xml:id="echoid-s28071" xml:space="preserve">Vbi perſpicue cernis, horologium Babylonicũ in ſphæ <lb/>ra boreali, eſſe in auſtrali Italicum, &amp; </s>
  <s xml:id="echoid-s28072" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s28073" xml:space="preserve">Item horas, quæ ibi à meridie numerantur, compu-<lb/>tari hic à med. </s>
  <s xml:id="echoid-s28074" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28075" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28076" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s28077" xml:space="preserve">Lineæ punctis notatæ pertinent ad horas aſtronomicas, quarum <lb/>
<anchor type="note" xlink:label="note-0444-03a" xlink:href="note-0444-03"/>
numeri prope ęquinoctialem lineam ſunt poſiti; </s>
  <s xml:id="echoid-s28078" xml:space="preserve">lineæ vero vltra tropicos productæ horas ab oc-<lb/>caſu ſignificant, &amp; </s>
  <s xml:id="echoid-s28079" xml:space="preserve">reliquæ horas ab ortu.</s>
  <s xml:id="echoid-s28080" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1450" type="float" level="2" n="2">
<note position="right" xlink:label="note-0443-12" xlink:href="note-0443-12a" xml:space="preserve">Quomodo he-<lb/>rologium hoti <lb/>zontale pro <lb/>ſphæra obliqua <lb/>boreali fabrica <lb/>tum collocan-<lb/>dũ ſit in ſphæ-<lb/>ra obliqua au-<lb/>ſt@ali, &amp; qua ra <lb/>tione numeri <lb/>horarum ſins<unsure/> <lb/>mu andi.</note>
<note position="left" xlink:label="note-0444-01" xlink:href="note-0444-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0444-01" xlink:href="fig-0444-01a">
    <image file="0444-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0444-01"/>
  </figure>
<note position="left" xlink:label="note-0444-02" xlink:href="note-0444-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0444-03" xlink:href="note-0444-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">A reus diurni <lb/>in ſphæra obli <lb/>qua auſtrali.</note>
<p>
  <s xml:id="echoid-s28081" xml:space="preserve">NVMERI porrò arcubus diurnis aſcripti non mutantur, licet ipſimet arcus non iidem per-<lb/>maneant. </s>
  <s xml:id="echoid-s28082" xml:space="preserve">Arcus etenim diurni plures horas, quàm 12. </s>
  <s xml:id="echoid-s28083" xml:space="preserve">continentes ſunt in obliqua ſphæra bo-<lb/>reali boreales, in auſtrali verò ſphæra obliqua ijdem auſtrales ſunt, &amp;</s>
  <s xml:id="echoid-s28084" xml:space="preserve">c.</s>
  <s xml:id="echoid-s28085" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28086" xml:space="preserve">VERTICALES circuli, &amp; </s>
  <s xml:id="echoid-s28087" xml:space="preserve">paralleli Horizontis mutandi quoque non ſunt, ſiue lineamen <lb/>
<anchor type="note" xlink:label="note-0444-05a" xlink:href="note-0444-05"/>
ta, ſiue numeri conſiderentur.</s>
  <s xml:id="echoid-s28088" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1451" type="float" level="2" n="3">
<note position="left" xlink:label="note-0444-05" xlink:href="note-0444-05a" xml:space="preserve">Verticales cir-<lb/>culi, &amp; paralle-<lb/>li Horizontis.</note>
</div>
<p>
  <s xml:id="echoid-s28089" xml:space="preserve">MERIDIANI deſcribendi ſunt in auſtrali hemiſphærio, vt in boreali, ſi à meridiana linea <lb/>
<anchor type="note" xlink:label="note-0444-06a" xlink:href="note-0444-06"/>
in circulo, beneſicio cuius horę aſtronomicæ ſunt deſcriptæ, numeretur longitudo loci verſus par <lb/>tes occidentales, quæ nobis ad polum antarcticum conuerſis dextræ ſunt.</s>
  <s xml:id="echoid-s28090" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1452" type="float" level="2" n="4">
<note position="left" xlink:label="note-0444-06" xlink:href="note-0444-06a" xml:space="preserve">Meridiani cir-<lb/>culi.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s28091" xml:space="preserve">LINEÆ quoque cœleſtium domorum eædẽ remanent, numeri duntaxat permutandi ſunt. <lb/></s>
  <s xml:id="echoid-s28092" xml:space="preserve">
<anchor type="note" xlink:label="note-0444-08a" xlink:href="note-0444-08"/>
Nam quiad ſiniſtram poſiti ſunt, collocandi erunt ad dextram, &amp; </s>
  <s xml:id="echoid-s28093" xml:space="preserve">contra, ita vt ex domo 12. </s>
  <s xml:id="echoid-s28094" xml:space="preserve">fiat <lb/>domus 8. </s>
  <s xml:id="echoid-s28095" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28096" xml:space="preserve">ex domo 11. </s>
  <s xml:id="echoid-s28097" xml:space="preserve">domus 9. </s>
  <s xml:id="echoid-s28098" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28099" xml:space="preserve">c.</s>
  <s xml:id="echoid-s28100" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1453" type="float" level="2" n="5">
<note position="left" xlink:label="note-0444-08" xlink:href="note-0444-08a" xml:space="preserve">Domus cœle-<lb/>ſtes.</note>
</div>
<p>
  <s xml:id="echoid-s28101" xml:space="preserve">SIGNA tandẽ aſcendentia depingenda ſunt in ſphæra obliqua auſtrali, vt in boreali, ſi prius <lb/>
<anchor type="note" xlink:label="note-0444-09a" xlink:href="note-0444-09"/>
tabulæ conſtruantur, pro data latitudine loci auſtralis, ſimiles illis, quas in propoſ. </s>
  <s xml:id="echoid-s28102" xml:space="preserve">9. </s>
  <s xml:id="echoid-s28103" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28104" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28105" xml:space="preserve">com-<lb/>poſuimus: </s>
  <s xml:id="echoid-s28106" xml:space="preserve">hoc diligenter obſeruato, aſcenſiones obliquas omnium ſignorum in boreali ſphæta <lb/>obliqua conuenire in auſtrali ſphæra ſignis oppoſitis. </s>
  <s xml:id="echoid-s28107" xml:space="preserve">Item arcus diurnos, ſemidiurnosve in ſphę <lb/>ra boreali ſupputatos, tribuendos eſſe in auſtrali ſignis oppoſitis, &amp;</s>
  <s xml:id="echoid-s28108" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28109" xml:space="preserve">Quæ omnia copiose oſten-<lb/>ſa à nobis ſunt in rebus aſtronomicis.</s>
  <s xml:id="echoid-s28110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1454" type="float" level="2" n="6">
<note position="left" xlink:label="note-0444-09" xlink:href="note-0444-09a" xml:space="preserve">Aſcendentia<unsure/> <lb/>ſigna.</note>
</div>
<p>
  <s xml:id="echoid-s28111" xml:space="preserve">OMNIA hæc in aliis etiam horologiis obſeruanda ſunt, ſed quod ad eorum deſcriptionẽ, <lb/>
<anchor type="note" xlink:label="note-0444-10a" xlink:href="note-0444-10"/>
&amp; </s>
  <s xml:id="echoid-s28112" xml:space="preserve">collocationem attinet, quicquid in ſphęra obliqua boreali de parte auſtrali, &amp; </s>
  <s xml:id="echoid-s28113" xml:space="preserve">orientali dixi-<lb/>
<anchor type="note" xlink:label="note-0444-11a" xlink:href="note-0444-11"/>
mus, in hac altera obliqua auſtrali intelligendum eſt de parte boreali, &amp; </s>
  <s xml:id="echoid-s28114" xml:space="preserve">occidentali, &amp; </s>
  <s xml:id="echoid-s28115" xml:space="preserve">contra. <lb/></s>
  <s xml:id="echoid-s28116" xml:space="preserve">Hoc eſt, Auſtrale horologium, quod propoſ. </s>
  <s xml:id="echoid-s28117" xml:space="preserve">13. </s>
  <s xml:id="echoid-s28118" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28119" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28120" xml:space="preserve">delineauimus ad latitudinem borealem <lb/>grad. </s>
  <s xml:id="echoid-s28121" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28122" xml:space="preserve">ſpectare debet in ſphæra auſtrali eiuſdem latitudinis ad boream, quia ex ea parte meri-<lb/>dies efficitur, &amp; </s>
  <s xml:id="echoid-s28123" xml:space="preserve">pars quę ibi vergebat in ortum, poni hic debet verſus occaſum, &amp; </s>
  <s xml:id="echoid-s28124" xml:space="preserve">è contrario. </s>
  <s xml:id="echoid-s28125" xml:space="preserve"><lb/>Rurſus Meridianum horologium orientale propoſ. </s>
  <s xml:id="echoid-s28126" xml:space="preserve">25. </s>
  <s xml:id="echoid-s28127" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28128" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28129" xml:space="preserve">deſcriptum pro eadem latitudine bo <lb/>reali grad. </s>
  <s xml:id="echoid-s28130" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28131" xml:space="preserve">erit in auſtrali ſphæra eiuſdem latitudinis occidentale, &amp; </s>
  <s xml:id="echoid-s28132" xml:space="preserve">contra, occidentale fiet <lb/>orientale, ita tamen vtrumque collocandum erit, vt pars, quæ prius in auſtrum vergebat, nunc in <lb/>boream ſpectet, &amp; </s>
  <s xml:id="echoid-s28133" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s28134" xml:space="preserve">Sic etiam declinantia horologia immutanda erunt, vt quod prius de-<lb/>clinabat à meridie in ortum, nunc à ſeptentrione deflectat in occaſum, &amp;</s>
  <s xml:id="echoid-s28135" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28136" xml:space="preserve">Eadem ratione decli-
<pb o="429" file="0445" n="445" rhead="LIBER QVARTVS."/>
nantia ab Horizonte ponenda ſunt, vt quod prius in occaſum, nunc in ortum ſpectet, &amp; </s>
  <s xml:id="echoid-s28137" xml:space="preserve">quæ pars <lb/>erat auſtralis, fiat nunc borealis, &amp;</s>
  <s xml:id="echoid-s28138" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28139" xml:space="preserve">In omnibus autem mutandi ſunt horarum numeri in com-<lb/>plementa vſque ad 12. </s>
  <s xml:id="echoid-s28140" xml:space="preserve">ſi de horis à meridie, vel media nocte ſermo ſit, &amp; </s>
  <s xml:id="echoid-s28141" xml:space="preserve">quæ prius à meridie nu <lb/>merabantur, nunc à media nocte ſumendæ ſunt, &amp; </s>
  <s xml:id="echoid-s28142" xml:space="preserve">è contrario: </s>
  <s xml:id="echoid-s28143" xml:space="preserve">ſi verò ad fuerint horę ab ortu, vel <lb/>occaſu, accipienda erunt earum complementa vſque ad 24. </s>
  <s xml:id="echoid-s28144" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28145" xml:space="preserve">quæ prius ab ortu ſupputabantur, nu <lb/>merandæ nunc erunt ab occaſu, &amp; </s>
  <s xml:id="echoid-s28146" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s28147" xml:space="preserve">Cætera perſpicua ſunt ex ſe, ſi rectè concipiatur poſi-<lb/>tio cuiuſuis horologii. </s>
  <s xml:id="echoid-s28148" xml:space="preserve">Quapropter horologia in ſphæra obliqua, in qua antarcticus polus ſupra <lb/>Horizontem attollitur, deſcripſimus. </s>
  <s xml:id="echoid-s28149" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s28150" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1455" type="float" level="2" n="7">
<note position="left" xlink:label="note-0444-10" xlink:href="note-0444-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0444-11" xlink:href="note-0444-11a" xml:space="preserve">Quo pacto alia <lb/>horologia pro <lb/>ſphæra obliqua <lb/>boreali conſt ru <lb/>cta, col<unsure/>locanda <lb/>ſint in ſphæra <lb/>obliqua auſtra <lb/>li.</note>
</div>
</div>
<div xml:id="echoid-div1457" type="section" level="1" n="353">
<head xml:id="echoid-head366" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s28151" xml:space="preserve">VISVM eſt operæpretium hoc loco paucis declarare, quam diuerſitatem lineæ horarum ab or. </s>
  <s xml:id="echoid-s28152" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28153" xml:space="preserve"><lb/>occ. </s>
  <s xml:id="echoid-s28154" xml:space="preserve">ad aliam atq; </s>
  <s xml:id="echoid-s28155" xml:space="preserve">aliã altitudinẽ poli tam arctici, quàm antarctici ſupra Horizontẽ nanciſcantur, ne in <lb/>deſcribendis huiuſmodi lineis hæreat quiſpiam aut impediatur, quòd videat, non eodẽ modo vbiuis gen-<lb/>
<anchor type="note" xlink:label="note-0445-02a" xlink:href="note-0445-02"/>
tium ſeſe habere horas ab or. </s>
  <s xml:id="echoid-s28156" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28157" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28158" xml:space="preserve">Quoniam enim in 2. </s>
  <s xml:id="echoid-s28159" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28160" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28161" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28162" xml:space="preserve">omnia illa, quæ centũ &amp; </s>
  <s xml:id="echoid-s28163" xml:space="preserve">octo proble <lb/>matib{us} deſcripſim{us}, pertinent ad eam ſphær am obliquam, in qua polus arcticus eleuatur grad. </s>
  <s xml:id="echoid-s28164" xml:space="preserve">42. </s>
  <s xml:id="echoid-s28165" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28166" xml:space="preserve"><lb/>quæ hoc libro tradidimus, ad ſphæram rectam ſpectant, fit vt lineæ horarum ab or. </s>
  <s xml:id="echoid-s28167" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28168" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28169" xml:space="preserve">in quocunque <lb/>horologio vtrumque tropicum ſecent. </s>
  <s xml:id="echoid-s28170" xml:space="preserve">Quando enim minor eſt altitudo poli quàm grad. </s>
  <s xml:id="echoid-s28171" xml:space="preserve">66. </s>
  <s xml:id="echoid-s28172" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s28173" xml:space="preserve">30. </s>
  <s xml:id="echoid-s28174" xml:space="preserve">id <lb/>
<anchor type="note" xlink:label="note-0445-03a" xlink:href="note-0445-03"/>
eſt, quàm complementum maximæ declinationis Solis, tropicus vterque Horizontem ſecat, atque adeo <lb/>parallelus omnium ſemper apparentium maximus, quem circuli horarum ab or. </s>
  <s xml:id="echoid-s28175" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28176" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28177" xml:space="preserve">tangunt, vt pro-<lb/>
<anchor type="note" xlink:label="note-0445-04a" xlink:href="note-0445-04"/>
poſ. </s>
  <s xml:id="echoid-s28178" xml:space="preserve">10. </s>
  <s xml:id="echoid-s28179" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28180" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28181" xml:space="preserve">oſtendimus, inter tropicum &amp; </s>
  <s xml:id="echoid-s28182" xml:space="preserve">polum exiſtit. </s>
  <s xml:id="echoid-s28183" xml:space="preserve">Quare ĳdem circuli horarĳ tropicum in ſphę <lb/>ra, ac proinde &amp; </s>
  <s xml:id="echoid-s28184" xml:space="preserve">in horologio quocunque earundem horarum lineę arcum ♋, vel ♑, interſecabunt, vt <lb/>in ſuperioribus exemplis omnibus factum eſt. </s>
  <s xml:id="echoid-s28185" xml:space="preserve">Fit autem nonnunquam, vt dictarum horarum lineæ tan-<lb/>gant ſolum tropicum in illis punctis, vbi à lineis horarum à mer. </s>
  <s xml:id="echoid-s28186" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s28187" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28188" xml:space="preserve">diuiditur: </s>
  <s xml:id="echoid-s28189" xml:space="preserve">aliquando ve-<lb/>ro, vt nullo modo ad tropicum perueniant, ſed tangant alium parallelum inter tropicum, &amp; </s>
  <s xml:id="echoid-s28190" xml:space="preserve">lineam æqui <lb/>
<anchor type="note" xlink:label="note-0445-05a" xlink:href="note-0445-05"/>
noctialem. </s>
  <s xml:id="echoid-s28191" xml:space="preserve">Nam quando altitudo poli æqualis eſt complemento maximæ declinationis Solis, hoc eſt, com <lb/>plectitur grad. </s>
  <s xml:id="echoid-s28192" xml:space="preserve">66. </s>
  <s xml:id="echoid-s28193" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s28194" xml:space="preserve">30. </s>
  <s xml:id="echoid-s28195" xml:space="preserve">tropicus Horizontem tangit, &amp; </s>
  <s xml:id="echoid-s28196" xml:space="preserve">a parallelo omnium ſemper apparentium <lb/>maximo non differt. </s>
  <s xml:id="echoid-s28197" xml:space="preserve">Vnde in ſphæra circuli horarum ab or. </s>
  <s xml:id="echoid-s28198" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28199" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28200" xml:space="preserve">tropicum, &amp; </s>
  <s xml:id="echoid-s28201" xml:space="preserve">in quocunque horolo-<lb/>gio lineæ earundem horarum arcum ♋, vel ♑, tangent in punctis, in quibus alineis horarum a mer. </s>
  <s xml:id="echoid-s28202" xml:space="preserve">vel <lb/>
<anchor type="note" xlink:label="note-0445-06a" xlink:href="note-0445-06"/>
med. </s>
  <s xml:id="echoid-s28203" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28204" xml:space="preserve">ſecatur. </s>
  <s xml:id="echoid-s28205" xml:space="preserve">Quando vero altitudo poli maior eſt complemento maximæ declinationis Solis, hoc <lb/>
<anchor type="note" xlink:label="note-0445-07a" xlink:href="note-0445-07"/>
est, maior, quàm grad. </s>
  <s xml:id="echoid-s28206" xml:space="preserve">66. </s>
  <s xml:id="echoid-s28207" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s28208" xml:space="preserve">30. </s>
  <s xml:id="echoid-s28209" xml:space="preserve">extat tropicus totus ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s28210" xml:space="preserve">alius parallelus maior <lb/>Horizontem tangit. </s>
  <s xml:id="echoid-s28211" xml:space="preserve">Quamobrem cum in ſphæra circuli horarum ab or. </s>
  <s xml:id="echoid-s28212" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28213" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28214" xml:space="preserve">bunc parallelum tan-<lb/>gant, &amp; </s>
  <s xml:id="echoid-s28215" xml:space="preserve">ad tropicum nullo modo perueniant, tangent in quolibet horologio lineæ earundem horarum ar-<lb/>cum illi{us} paralleli, &amp; </s>
  <s xml:id="echoid-s28216" xml:space="preserve">ad arcum ♋, vel ♑, nequaquam peruenient. </s>
  <s xml:id="echoid-s28217" xml:space="preserve">Quæ omnia ex ĳs, quæ lib. </s>
  <s xml:id="echoid-s28218" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28219" xml:space="preserve">de cir-<lb/>culis horarĳs, &amp; </s>
  <s xml:id="echoid-s28220" xml:space="preserve">de contactibus linearum horarum ab or. </s>
  <s xml:id="echoid-s28221" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28222" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28223" xml:space="preserve">quos cum parallelis omnium ſemper <lb/>apparentium, &amp; </s>
  <s xml:id="echoid-s28224" xml:space="preserve">latentium maximis faciunt, ſcripſimus, manifeſtò colligi poſſunt. </s>
  <s xml:id="echoid-s28225" xml:space="preserve">Vt tamen res hæc ma-<lb/>gis adhuc fiat perſpicua, adiecimus hoc loco duo horologia, quorum primum ad latitudinem borealem <lb/>grad. </s>
  <s xml:id="echoid-s28226" xml:space="preserve">66. </s>
  <s xml:id="echoid-s28227" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s28228" xml:space="preserve">30. </s>
  <s xml:id="echoid-s28229" xml:space="preserve">conſtructum, horizontale eſt, continet{q́ue} horas tum a mer. </s>
  <s xml:id="echoid-s28230" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28231" xml:space="preserve">med. </s>
  <s xml:id="echoid-s28232" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28233" xml:space="preserve">tum ab or. </s>
  <s xml:id="echoid-s28234" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28235" xml:space="preserve"><lb/>occ. </s>
  <s xml:id="echoid-s28236" xml:space="preserve">quarum poſteriores tangunt arcum ♋, qui vices gerit paralleli omnium ſemper apparentium maxi-<lb/>mi, in punctis, vbi a prioribus ſecatur: </s>
  <s xml:id="echoid-s28237" xml:space="preserve">alterum vero ad latitudinem ſeptentrionalem grad. </s>
  <s xml:id="echoid-s28238" xml:space="preserve">69. </s>
  <s xml:id="echoid-s28239" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s28240" xml:space="preserve">
<anchor type="note" xlink:label="note-0445-08a" xlink:href="note-0445-08"/>
48. </s>
  <s xml:id="echoid-s28241" xml:space="preserve">fabricatum, polare eſt cum iiſdem horis, in quo horæ ab or. </s>
  <s xml:id="echoid-s28242" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28243" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s28244" xml:space="preserve">non perueniunt vſque ad tropicos, <lb/>ſed tangunt parallelos ♊, &amp; </s>
  <s xml:id="echoid-s28245" xml:space="preserve">♐, qui in ea latitudine funguntur munere parallelorum ſemper apparentiũ, <lb/>ſemperq́, latentium maximorum, in punctis, in quibus ab horis a mer. </s>
  <s xml:id="echoid-s28246" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28247" xml:space="preserve">med. </s>
  <s xml:id="echoid-s28248" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28249" xml:space="preserve">ſecantur. </s>
  <s xml:id="echoid-s28250" xml:space="preserve">Quia vero <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s28251" xml:space="preserve">10. </s>
  <s xml:id="echoid-s28252" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28253" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28254" xml:space="preserve">demonſtratum eſt a nobis, vnam portionem lineæ cuiuſque horariæ paralle-<lb/>lum omnium ſemper apparentium, vel ſemper latentium maximum tangentis, indicare horam ab occaſu, <lb/>reliquam vero ad horam eandem numero ab ortu pertinere, (quarum vtramque portionem punctum con <lb/>
<anchor type="note" xlink:label="note-0445-09a" xlink:href="note-0445-09"/>
tactus dirimit) ſecernem{us} hor{as} ab occ. </s>
  <s xml:id="echoid-s28255" xml:space="preserve">ab horis ab or. </s>
  <s xml:id="echoid-s28256" xml:space="preserve">hoc modo. </s>
  <s xml:id="echoid-s28257" xml:space="preserve">In horologio horizontali ſegmenta <lb/>linearum tangentium, quæ a punctis contactuum ad dextram lineæ meridianæ, hoc eſt, ad partes horolo-<lb/>gii occidentales, ſurſum verſus ducuntur, pertinent ad hor{as} ab occ. </s>
  <s xml:id="echoid-s28258" xml:space="preserve">quæ vero deorſum verſus tendunt, <lb/>ad horas ab ortu. </s>
  <s xml:id="echoid-s28259" xml:space="preserve">Contrarium intelligatur in lineis, quæ per puncta contactuum ad ſiniſtram lineæ meri-<lb/>dianæ, ſiue ad partes orientales horologii, ducuntur: </s>
  <s xml:id="echoid-s28260" xml:space="preserve">quæ enim ſurſum verſus porriguntur, horas ab or. <lb/></s>
  <s xml:id="echoid-s28261" xml:space="preserve">
<anchor type="note" xlink:label="note-0445-10a" xlink:href="note-0445-10"/>
monſtrant, quæ autem deorſum verſus extenduntur, ad hor{as} ab occ. </s>
  <s xml:id="echoid-s28262" xml:space="preserve">ſpectant. </s>
  <s xml:id="echoid-s28263" xml:space="preserve">Illius denique lineæ, quæ <lb/>in hora 12. </s>
  <s xml:id="echoid-s28264" xml:space="preserve">aſtronomica parallelum ſemper apparentium maximum tangit, portio occidentalis indicat <lb/>horam 12. </s>
  <s xml:id="echoid-s28265" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s28266" xml:space="preserve">reliqua vero horam 12. </s>
  <s xml:id="echoid-s28267" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s28268" xml:space="preserve">Vnde ſi deſcribendum ſit horologium Italicum dun-<lb/>
<anchor type="note" xlink:label="note-0445-11a" xlink:href="note-0445-11"/>
taxat, vel Babylonicum, non erunt lineæ horariæ tangentes in vtramque partem punctorum contactuum <lb/>educendæ, ſed in illam partem tantum, quæ ad horas ab occ. </s>
  <s xml:id="echoid-s28269" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s28270" xml:space="preserve">pertinent. </s>
  <s xml:id="echoid-s28271" xml:space="preserve">In horologio polari <lb/>facile cognoſcentur horæ ab occ. </s>
  <s xml:id="echoid-s28272" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s28273" xml:space="preserve">ex iis, quę lib. </s>
  <s xml:id="echoid-s28274" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28275" xml:space="preserve">de polari horologio ſcripſimus.</s>
  <s xml:id="echoid-s28276" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1457" type="float" level="2" n="1">
<note position="right" xlink:label="note-0445-02" xlink:href="note-0445-02a" xml:space="preserve">Ad quam lati-<lb/>tudinem ora-<lb/>nia horologia <lb/>ſuperiora de-<lb/>ſcripta ſint.</note>
<note position="right" xlink:label="note-0445-03" xlink:href="note-0445-03a" xml:space="preserve">In latitudine <lb/>minore, quam <lb/>grad. 66. Min. <lb/>30. lineæ hora-<lb/>ratum ab or. &amp; <lb/>occ. ſecant tro-<lb/>picũ vtrumq;.</note>
<note position="left" xlink:label="note-0445-04" xlink:href="note-0445-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0445-05" xlink:href="note-0445-05a" xml:space="preserve">In latitudina <lb/>grad. 66. Min. <lb/>30. lineę hora-<lb/>rum ab or. &amp; <lb/>occ. tangunt <lb/>tropicum.</note>
<note position="right" xlink:label="note-0445-06" xlink:href="note-0445-06a" xml:space="preserve">In latitudine <lb/>maiore, quàm <lb/>grad. 66. Min. <lb/>30. lineę hora-<lb/>rum ab or. &amp; <lb/>occ. neque ſecãt <lb/>tropicũ, neque <lb/>tangunt, ſed r<unsure/>ã <lb/>gunt alium pa-<lb/>rallelum pro-<lb/>pinquiorem li-<lb/>nee æquino<unsure/>-<lb/>ctiali.</note>
<note position="left" xlink:label="note-0445-07" xlink:href="note-0445-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0445-08" xlink:href="note-0445-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0445-09" xlink:href="note-0445-09a" xml:space="preserve">Quæ ſegmenta <lb/>lincarum tan-<lb/>gentium ad ho <lb/>ras ab occ. &amp; <lb/>quæ ad horas <lb/>ab or. peruneãt</note>
<note position="left" xlink:label="note-0445-10" xlink:href="note-0445-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0445-11" xlink:href="note-0445-11a" xml:space="preserve">Quando locus <lb/>ſtyli in horolo-<lb/>giis horizonta-<lb/>libus cadat ex-<lb/>tra tropicos, &amp; <lb/>quando in tro <lb/>picu m præci-<lb/>ſe, aut intra tro <lb/>picos, aut in ip <lb/>ſam d enique li <lb/>neam æquino-<lb/>ctialem.</note>
</div>
<p style="it">
  <s xml:id="echoid-s28277" xml:space="preserve">NON videtur etiam prætereundum hoc loco, locum ſtyli in horologiis horizont alibus poſſe variis <lb/>ſe modis habere, pro varia altitudine poli ſupra Horizontem. </s>
  <s xml:id="echoid-s28278" xml:space="preserve">Nam quando altitudo poli maior eſt ma-<lb/>xima Solis declinatione, cadit locus styli extra tropicos inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s28279" xml:space="preserve">tropicum: </s>
  <s xml:id="echoid-s28280" xml:space="preserve">Quando <lb/>autem maximæ Solis declinationi æqualis eſt altitudo poli, locus ſtyli cadit præciſe in tropicum: </s>
  <s xml:id="echoid-s28281" xml:space="preserve">Quando
<pb o="430" file="0446" n="446" rhead="GNOMONICES"/>
<anchor type="figure" xlink:label="fig-0446-01a" xlink:href="fig-0446-01"/>
<anchor type="note" xlink:label="note-0446-01a" xlink:href="note-0446-01"/>
<anchor type="note" xlink:label="note-0446-02a" xlink:href="note-0446-02"/>
vero minor est altitudo poli declinatione maxima Solis, cadit locus ſtyli inter tropicum, &amp; </s>
  <s xml:id="echoid-s28282" xml:space="preserve">æquinoctia-<lb/>lem lineam: </s>
  <s xml:id="echoid-s28283" xml:space="preserve">Quando denique poli altitudo nulla eſt, vt in ſphæra recta, collocandus eſt ſtylus in ipſa li-<lb/>nea æquinoctiali. </s>
  <s xml:id="echoid-s28284" xml:space="preserve">Quæ omnia aperte ex Analemmate, quod propoſ. </s>
  <s xml:id="echoid-s28285" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28286" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28287" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28288" xml:space="preserve">conſtruximus, colliguntur. <lb/></s>
  <s xml:id="echoid-s28289" xml:space="preserve">Quia enim in eo altitudo poli A F, maior eſt maxima Solis declinatione, fit vt radius ♋, per centrum D, <lb/>
<anchor type="note" xlink:label="note-0446-03a" xlink:href="note-0446-03"/>
emiſſus cadat in lineam meridianã R O, ad punctum K, vltra locum ſtyli G, ita vt punctum G, ſit inter <lb/>H, centrum horologii, &amp; </s>
  <s xml:id="echoid-s28290" xml:space="preserve">K, punctum ♋. </s>
  <s xml:id="echoid-s28291" xml:space="preserve">Quare locus ſtyli extra tropicos omnino exiſtet. </s>
  <s xml:id="echoid-s28292" xml:space="preserve">Quòd ſi altitu <lb/>
<anchor type="figure" xlink:label="fig-0446-02a" xlink:href="fig-0446-02"/>
<anchor type="note" xlink:label="note-0446-04a" xlink:href="note-0446-04"/>
<anchor type="note" xlink:label="note-0446-05a" xlink:href="note-0446-05"/>
do poli A F, æqualis eſſet maximę Solis declinationi, ita vt diameter paralleli ♋, ſecaret Meridianũ <lb/>in puncto A, non differret radius ♋, ex A, per centrum D, eiectus a diametro Verticalis; </s>
  <s xml:id="echoid-s28293" xml:space="preserve">ac proinde <lb/>locus styli eſſet in puncto G, vbi radius ♋, meridianam lineã ſecaret. </s>
  <s xml:id="echoid-s28294" xml:space="preserve">Si vero altitudo poli minor eſſet <lb/>maxima declinatione Solis, ita vt diameter paralleli ♋, Meridianum ſecaret inter A, verticem, &amp; </s>
  <s xml:id="echoid-s28295" xml:space="preserve">po <lb/>lum mundi E, liquido conſtat, radium ♋, per centrum D, tranſeuntem cadere tunc inter H, centrum ho <lb/>rologii, &amp; </s>
  <s xml:id="echoid-s28296" xml:space="preserve">G, locum ſtyli; </s>
  <s xml:id="echoid-s28297" xml:space="preserve">adeo vt tunc locus ſtyli exiſteret inter tropicum ♋, &amp; </s>
  <s xml:id="echoid-s28298" xml:space="preserve">æquinoctialem lineam. <lb/></s>
  <s xml:id="echoid-s28299" xml:space="preserve">Si denique altitudo poli nulla foret, ita vt diameter Aequatoris a diametro Verticalis non differret, <lb/>quis non videt, locum ſtyli tunc cadere in illud punctum lineæ meridianæ, in quo Aequator plano horo-<lb/>logĳ occurreret?</s>
  <s xml:id="echoid-s28300" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1458" type="float" level="2" n="2">
  <figure xlink:label="fig-0446-01" xlink:href="fig-0446-01a">
    <image file="0446-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0446-01"/>
  </figure>
<note position="left" xlink:label="note-0446-01" xlink:href="note-0446-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0446-02" xlink:href="note-0446-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0446-03" xlink:href="note-0446-03a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0446-02" xlink:href="fig-0446-02a">
    <image file="0446-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0446-02"/>
  </figure>
<note position="left" xlink:label="note-0446-04" xlink:href="note-0446-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0446-05" xlink:href="note-0446-05a" xml:space="preserve">50</note>
</div>
<pb o="431" file="0447" n="447" rhead="LIBER QVARTVS."/>
<p style="it">
  <s xml:id="echoid-s28301" xml:space="preserve">HAEC omnia alĳs quoque horologĳs conueniunt, prout altitudo poli ſuper circulos maximos, qui-<lb/>
<anchor type="note" xlink:label="note-0447-01a" xlink:href="note-0447-01"/>
bus eorum plana æquidiſtant, maior fuerit, æqualiſue, aut minor maxima Solis declinatione, aut denique <lb/>nulla. </s>
  <s xml:id="echoid-s28302" xml:space="preserve">Ita k<unsure/>ides in horologĳs, quæ lib. </s>
  <s xml:id="echoid-s28303" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28304" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28305" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28306" xml:space="preserve">deſcripſimus, nempe in horizontali, verticali, Aequinoctia <lb/>li, Declinante à verticali, Declinante ab Horizonte, Inclinato ad Horizontem, &amp; </s>
  <s xml:id="echoid-s28307" xml:space="preserve">in Declinante ſimul <lb/>ac inclinato, in quo propoſ. </s>
  <s xml:id="echoid-s28308" xml:space="preserve">38. </s>
  <s xml:id="echoid-s28309" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s28310" xml:space="preserve">arcus ſignorum delineauimus, locum ſtyli extra tropicos <lb/>eſſe conſtitutum; </s>
  <s xml:id="echoid-s28311" xml:space="preserve">quia altitudo poli ſupra maximos circulos, quibus ea horologia ſunt parallela, maximã <lb/>Solis declinationem ſuperat: </s>
  <s xml:id="echoid-s28312" xml:space="preserve">In horologio autem horizontali, quod in ſcholio propoſ. </s>
  <s xml:id="echoid-s28313" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28314" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28315" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28316" xml:space="preserve">contine-<lb/>tur, locum ſtyli intra tropicum cadere; </s>
  <s xml:id="echoid-s28317" xml:space="preserve">quoniã altitudo poli ſupra illum Horizontem minor eſt maxima <lb/>declinatione Solis: </s>
  <s xml:id="echoid-s28318" xml:space="preserve">In horologio denique Meridiano, Polari, Declinante ſimul ac inclinato, quod tertio <lb/>loco conſtruximus propoſ. </s>
  <s xml:id="echoid-s28319" xml:space="preserve">37. </s>
  <s xml:id="echoid-s28320" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s28321" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28322" xml:space="preserve">in horologiis ſphæræ rectæ hoc lib. </s>
  <s xml:id="echoid-s28323" xml:space="preserve">compoſitis, ſtylum ca-<lb/>
<anchor type="note" xlink:label="note-0447-02a" xlink:href="note-0447-02"/>
dere in ipſam lineam æquinoctialem, propterea quòd nulla eſt altitudo poli ſupra circulos maximos, qui-<lb/>bus ca horologia æquidiſtant.</s>
  <s xml:id="echoid-s28324" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1459" type="float" level="2" n="3">
<note position="right" xlink:label="note-0447-01" xlink:href="note-0447-01a" xml:space="preserve">Quomodo idé <lb/>ſciatur in aliis <lb/>horologiis.</note>
<note position="left" xlink:label="note-0447-02" xlink:href="note-0447-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1461" type="section" level="1" n="354">
<head xml:id="echoid-head367" xml:space="preserve">PROBLEMA 12. PROPOSITIO 12.</head>
<p>
  <s xml:id="echoid-s28325" xml:space="preserve">GNOMONEM cuiuſcunque horologii proprio in loco ita col-<lb/>locare, vt ad planum horologij rectus ſit, eiuſq́; </s>
  <s xml:id="echoid-s28326" xml:space="preserve">verticem in propriam <lb/>ſedem, ſi quando ab ea deflexerit, reſtituere.</s>
  <s xml:id="echoid-s28327" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s28328" xml:space="preserve">SIT ſtylus, ſiue gnomon cuiuſuis horologii A B, eiuſq́ue locus in puncto A, in quo ita eum <lb/>oporteat horologio infigere, vt ad planum horologii rectus ſit, &amp;</s>
  <s xml:id="echoid-s28329" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28330" xml:space="preserve">Ex A, loco ſtyli circulus in <lb/>
<anchor type="note" xlink:label="note-0447-04a" xlink:href="note-0447-04"/>
horologii plano deſcribatur C D E, cuiuslibet magnitudinis, in quo tria puncta eligantur vtcun-<lb/>que C, D, E. </s>
  <s xml:id="echoid-s28331" xml:space="preserve">Deinde in A, erigatur ſtylus A B, eiuſq́ue vertex B, hinc inde moueatur, donec be-<lb/>neficio circini deprehendantur æquales tres rectæ, quæ ex punctis C, D, E, ad verticem B, perti-<lb/>nent. </s>
  <s xml:id="echoid-s28332" xml:space="preserve">Dico tunc gnomonem A B, ad <lb/>planum horologii, in quo circulus <lb/>
<anchor type="figure" xlink:label="fig-0447-01a" xlink:href="fig-0447-01"/>
C D E, exiſtit, rectum eſſe. </s>
  <s xml:id="echoid-s28333" xml:space="preserve">Si enim <lb/>nõ dicatur eſſe rectus, demitti intel-<lb/>ligatur ex vertice B, ad planũ horo-<lb/>
<anchor type="note" xlink:label="note-0447-05a" xlink:href="note-0447-05"/>
logii alia linea perpendicularis B F, <lb/>ſi fieri poteſt, cadens in punctum F, <lb/>diuerſum ab A. </s>
  <s xml:id="echoid-s28334" xml:space="preserve">Ductis rectis C F, <lb/>D F, E F, erit per defin. </s>
  <s xml:id="echoid-s28335" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28336" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28337" xml:space="preserve">11. </s>
  <s xml:id="echoid-s28338" xml:space="preserve">Eu <lb/>clidis ad omnes has recta B F, per-<lb/>pendicularis, atque adeo triangula <lb/>B F C, B F D, B F E, rectãgula erunt; <lb/></s>
  <s xml:id="echoid-s28339" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s28340" xml:space="preserve">quadratum ex B C, <lb/>quadratis ex B F, F C, &amp; </s>
  <s xml:id="echoid-s28341" xml:space="preserve">quadratũ ex <lb/>B D, quadratis ex B F, F D, &amp; </s>
  <s xml:id="echoid-s28342" xml:space="preserve">quadra-<lb/>tũ ex B E, quadratis ex B F, F E, ęqua-<lb/>
<anchor type="note" xlink:label="note-0447-06a" xlink:href="note-0447-06"/>
<anchor type="note" xlink:label="note-0447-07a" xlink:href="note-0447-07"/>
le erit. </s>
  <s xml:id="echoid-s28343" xml:space="preserve">Quia verò quadrata trium li-<lb/>nearum B C, B D, B E, quæ æquales <lb/>ponuntur, æqualia ſunt, erunt qua-<lb/>drata ex B F, F C, tam quadratis ex <lb/>B F, F D, quàm quadratis ex B F, <lb/>F E, æqualia. </s>
  <s xml:id="echoid-s28344" xml:space="preserve">Ablato ergo commu-<lb/>ni quadrato rectę B F, æqualia remanebunt quadrata rectarum F C, F D, F E; </s>
  <s xml:id="echoid-s28345" xml:space="preserve">ac idcirco &amp; </s>
  <s xml:id="echoid-s28346" xml:space="preserve">ipſę <lb/>rectæ æquales erunt. </s>
  <s xml:id="echoid-s28347" xml:space="preserve">Punctum ergo F, centrum erit circuli C D E, quod eſt abſurdum. </s>
  <s xml:id="echoid-s28348" xml:space="preserve">Eſt enim <lb/>
<anchor type="note" xlink:label="note-0447-08a" xlink:href="note-0447-08"/>
A, centrum dicti circuli. </s>
  <s xml:id="echoid-s28349" xml:space="preserve">Non igitur ex B, vertice ſtyli ad planum horologii perpendicularis de-<lb/>
<anchor type="note" xlink:label="note-0447-09a" xlink:href="note-0447-09"/>
miſſa cadet in F, punctum ab A, diuerſum, ac proinde in A, cadet. </s>
  <s xml:id="echoid-s28350" xml:space="preserve">Quare recta A B, ita erecta, ut <lb/>tres rectæ C B, D B, E B, ſint æquales, ad planum propoſitum perpendicularis erit.</s>
  <s xml:id="echoid-s28351" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1461" type="float" level="2" n="1">
<note position="right" xlink:label="note-0447-04" xlink:href="note-0447-04a" xml:space="preserve">Qua ratione <lb/>ſlylus rectus ad <lb/>planum horelo <lb/>gii fit colloc@@-<lb/>dus.</note>
  <figure xlink:label="fig-0447-01" xlink:href="fig-0447-01a">
    <image file="0447-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0447-01"/>
  </figure>
<note position="left" xlink:label="note-0447-05" xlink:href="note-0447-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0447-06" xlink:href="note-0447-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0447-07" xlink:href="note-0447-07a" xml:space="preserve">49. primi.</note>
<note position="right" xlink:label="note-0447-08" xlink:href="note-0447-08a" xml:space="preserve">9. tertĳ.</note>
<note position="left" xlink:label="note-0447-09" xlink:href="note-0447-09a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Quantum in-<lb/>ter ſe diſtare de <lb/>beant erura eir <lb/>cini, vt benefi-<lb/>cio circuli ſty-<lb/>lus ad planum <lb/>horologii re-<lb/>ctus ſtatuatur.</note>
<p>
  <s xml:id="echoid-s28352" xml:space="preserve">VT autem ſciamus, quanto interuallo inter ſe diſtare debeãt circini crura, vt vno crure poſito <lb/>in tribus quibuſcunque punctis circunferentię C D E, altero verticem ſtyli B, ad horologii planũ <lb/>recti attingamus, deſcribemus triangulum rectangulum G H I, cuius latus G H, ſtylo, &amp; </s>
  <s xml:id="echoid-s28353" xml:space="preserve">G I, ſemi-<lb/>diametro A E, ſit æquale. </s>
  <s xml:id="echoid-s28354" xml:space="preserve">Nam interuallum rectæ I H, æquale erit ſingulis interuallis inter pun-<lb/>cta C, D, E, &amp; </s>
  <s xml:id="echoid-s28355" xml:space="preserve">verticem B, ſi ſtylus ad planum horologii rectus fuerit. </s>
  <s xml:id="echoid-s28356" xml:space="preserve">Cum enim duo latera <lb/>G H, G I, trianguli G H I, æqualia ſint duobus lateribus A B, A E, trianguli A B E, habeantq́ue <lb/>angulos G, A, æquales, vtpote rectos, erunt quoque baſes I H, E B, æquales inter ſe; </s>
  <s xml:id="echoid-s28357" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28358" xml:space="preserve">eadem ra-<lb/>
<anchor type="note" xlink:label="note-0447-11a" xlink:href="note-0447-11"/>
tione I H, rectis D B, C B, æqualis oſtendetur. </s>
  <s xml:id="echoid-s28359" xml:space="preserve">Itaque vt ſtylum A B, in puncto A, ita figamus, vt <lb/>rectus ſit ad planum horologii, neceſſe eſt, vt vno pede circini in quouis puncto circunferentię
<pb o="432" file="0448" n="448" rhead="GNOMONICES"/>
C D E, poſito, alter verticem B, attingat, ſi interuallum inter circini pedes interiectum rectæ <lb/>I H, ſuerit æquale, vt ex demonſtratis perſpicuum relinquitur.</s>
  <s xml:id="echoid-s28360" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1462" type="float" level="2" n="2">
<note position="right" xlink:label="note-0447-11" xlink:href="note-0447-11a" xml:space="preserve">4. primi.</note>
</div>
<p>
  <s xml:id="echoid-s28361" xml:space="preserve">IAM verò, ſi quando vertex gnomonis inflectatur, &amp; </s>
  <s xml:id="echoid-s28362" xml:space="preserve">à proprio dimoueatur loco, ita eum re-<lb/>
<anchor type="note" xlink:label="note-0448-01a" xlink:href="note-0448-01"/>
ſtituemus. </s>
  <s xml:id="echoid-s28363" xml:space="preserve">Ex A, loco ſtyli in horo-<lb/>logio ducta recta vtcunque A B, quę <lb/>
<anchor type="figure" xlink:label="fig-0448-01a" xlink:href="fig-0448-01"/>
vel ſtylo ſit æqualis, vt in priore <lb/>triangulo inferiore, vel maior, vt in <lb/>poſteriore, ducemus per B, ad A B, <lb/>perpendicularem C D, rectalq́; </s>
  <s xml:id="echoid-s28364" xml:space="preserve">B C, <lb/>B D, rectę A B, æquales ponemus. <lb/></s>
  <s xml:id="echoid-s28365" xml:space="preserve">
<anchor type="note" xlink:label="note-0448-02a" xlink:href="note-0448-02"/>
Deinde ex A C, rectam A E, ſtylo <lb/>auferemus æqualem, &amp; </s>
  <s xml:id="echoid-s28366" xml:space="preserve">interuallo <lb/>D E, æqualem abſcindomus D F. <lb/></s>
  <s xml:id="echoid-s28367" xml:space="preserve">Dico ſi circino accipiatur interual-<lb/>lum D F, &amp; </s>
  <s xml:id="echoid-s28368" xml:space="preserve">vertex gnomonis hinc <lb/>inde moueatur, donec vno pede cir-<lb/>cini in punctis C, &amp; </s>
  <s xml:id="echoid-s28369" xml:space="preserve">D, poſito, alte-<lb/>ro verticem attingamus, reſtitutum <lb/>eſſe gnomonis verticem, ita vt rur-<lb/>ſum ſtylus ad horologii planum re-<lb/>
<anchor type="note" xlink:label="note-0448-03a" xlink:href="note-0448-03"/>
ctus ſit in puncto A. </s>
  <s xml:id="echoid-s28370" xml:space="preserve">Intelligatur <lb/>enim in A, ſtylus A G, ad planum <lb/>horologii rectus, coniunganturq́; </s>
  <s xml:id="echoid-s28371" xml:space="preserve">re-<lb/>ctæ D E, D G, G C. </s>
  <s xml:id="echoid-s28372" xml:space="preserve">Et quoniam late <lb/>ra B A, B C, æqualia ſunt, erunt an-<lb/>
<anchor type="note" xlink:label="note-0448-04a" xlink:href="note-0448-04"/>
guli A, C, æquales. </s>
  <s xml:id="echoid-s28373" xml:space="preserve">Exiſtente ergo B. <lb/></s>
  <s xml:id="echoid-s28374" xml:space="preserve">recto, erit angulus B A C, ſemirectus, cum omnes tres anguli trianguli A B C, duobus ſint <lb/>
<anchor type="note" xlink:label="note-0448-05a" xlink:href="note-0448-05"/>
rectis æquales. </s>
  <s xml:id="echoid-s28375" xml:space="preserve">Eadem ratione ſemirectus oſtendetur angulus B A D, ac proinde totus <lb/>C A D, rectus erit, nec non rectę A C, A D, inter ſe erunt æquales, ob triangula A B C, <lb/>
<anchor type="note" xlink:label="note-0448-06a" xlink:href="note-0448-06"/>
A B D, in quibus duo latera B A, B C, duobus lateribus B A, B D, ſunt æqualia, angulosq́; <lb/></s>
  <s xml:id="echoid-s28376" xml:space="preserve">
<anchor type="note" xlink:label="note-0448-07a" xlink:href="note-0448-07"/>
comprehendunt æquales ad B, nempe rectos. </s>
  <s xml:id="echoid-s28377" xml:space="preserve">Rurſus quia G A, perpendicularis eſt ad pla-<lb/>num horologii, in quo triangulum A C D, exiſtit, erunt quoque per defin. </s>
  <s xml:id="echoid-s28378" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28379" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28380" xml:space="preserve">11 Euclid. </s>
  <s xml:id="echoid-s28381" xml:space="preserve">angu <lb/>li G A C, G A D, recti. </s>
  <s xml:id="echoid-s28382" xml:space="preserve">Itaque quoniam duo latera D A, A E, trianguli D A E duobus lateribus <lb/>D A, A G, trianguli D A G, ſunt æqualia, continentq́; </s>
  <s xml:id="echoid-s28383" xml:space="preserve">angulos ad A, æquales, vtpote rectos, erunt <lb/>quoque baſes D E, D G, æquales inter ſe. </s>
  <s xml:id="echoid-s28384" xml:space="preserve">Eodemq́ue modo oſtendemus æquales inter ſe eſle i<unsure/>e-<lb/>
<anchor type="note" xlink:label="note-0448-08a" xlink:href="note-0448-08"/>
ctas D E, C G, propter triangula D A E, C A G, quorum duo latera D A, A E, duobus lateribus <lb/>C A, A G, æqualia ſunt, continentq́ue æquales angulos D A E, C A G, nimirum rec@os. </s>
  <s xml:id="echoid-s28385" xml:space="preserve">Cum er-<lb/>go recta D E, atque adeò recta D F, quæ ipſi D E, æqualis ſumpta eſt, æqualis ſit tam rectæ D G, <lb/>quàm rectæ C G, quarum vtraque ex D, &amp; </s>
  <s xml:id="echoid-s28386" xml:space="preserve">C, ad verticem ſtyli G, rectos angulos cum plano ho-<lb/>rologii facientis ducitur, neceſſe eſt, vt vno pede circini collocato tam in D, quàm in C, altero ver <lb/>
<anchor type="note" xlink:label="note-0448-09a" xlink:href="note-0448-09"/>
ticem ſtyli G, attingamus, ſi ſpatium inter circini pedes incluſum rectæ D F, fuerit æquale, ipſeq́; <lb/></s>
  <s xml:id="echoid-s28387" xml:space="preserve">ſtylus rectos cum horologii plano angulos fecetit, vt ex demonſtratis liquet. </s>
  <s xml:id="echoid-s28388" xml:space="preserve">Gnomonem igitur <lb/>cuiuſque horologii proprio in loco collocauimus, &amp;</s>
  <s xml:id="echoid-s28389" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28390" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s28391" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1463" type="float" level="2" n="3">
<note position="left" xlink:label="note-0448-01" xlink:href="note-0448-01a" xml:space="preserve">Qua uia ſtylus <lb/>in propriam ſe <lb/>dem, @i quando <lb/>ao<unsure/> ca deflexe <lb/>@, reitituatut.</note>
  <figure xlink:label="fig-0448-01" xlink:href="fig-0448-01a">
    <image file="0448-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0448-01"/>
  </figure>
<note position="left" xlink:label="note-0448-02" xlink:href="note-0448-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0448-03" xlink:href="note-0448-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0448-04" xlink:href="note-0448-04a" xml:space="preserve">5. primi.</note>
<note position="left" xlink:label="note-0448-05" xlink:href="note-0448-05a" xml:space="preserve">32. primi.</note>
<note position="left" xlink:label="note-0448-06" xlink:href="note-0448-06a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0448-07" xlink:href="note-0448-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0448-08" xlink:href="note-0448-08a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0448-09" xlink:href="note-0448-09a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1465" type="section" level="1" n="355">
<head xml:id="echoid-head368" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s28392" xml:space="preserve">IN horologiis, quæ non declinant, vt in horizontali, verticali, polari, æquinostiali, &amp; </s>
  <s xml:id="echoid-s28393" xml:space="preserve">inclinato ad <lb/>
<anchor type="note" xlink:label="note-0448-10a" xlink:href="note-0448-10"/>
Horizontem, recta A B, pręcedentis trianguli abſcindenda eſt ex linea meridiana, vt factum eſſe vides <lb/>in horizontali horologio propoſ. </s>
  <s xml:id="echoid-s28394" xml:space="preserve">4. </s>
  <s xml:id="echoid-s28395" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s28396" xml:space="preserve">in quo circuli V erticales, &amp; </s>
  <s xml:id="echoid-s28397" xml:space="preserve">paralleli Horizontis ſunt deſcri-<lb/>pti. </s>
  <s xml:id="echoid-s28398" xml:space="preserve">In aliis autem, quæ declinant, eadem recta A B, ſumenda est in linea ſtyli, vt factum eſſe cernis in <lb/>horologio declinante a Verticali propoſ. </s>
  <s xml:id="echoid-s28399" xml:space="preserve">6. </s>
  <s xml:id="echoid-s28400" xml:space="preserve">ſuperioris libri continente circulos Meridianos. </s>
  <s xml:id="echoid-s28401" xml:space="preserve">Quod tamen <lb/>
<anchor type="note" xlink:label="note-0448-11a" xlink:href="note-0448-11"/>
neceſſarium non eſt. </s>
  <s xml:id="echoid-s28402" xml:space="preserve">Potest enim recta A B, ex loco gnomonis educi vtcunque, &amp; </s>
  <s xml:id="echoid-s28403" xml:space="preserve">triangulum prædi-<lb/>ctum construi. </s>
  <s xml:id="echoid-s28404" xml:space="preserve">Ita enim conſpicis in horologio Italico declinante a Verticoli propoſ. </s>
  <s xml:id="echoid-s28405" xml:space="preserve">10. </s>
  <s xml:id="echoid-s28406" xml:space="preserve">ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s28407" xml:space="preserve">triangulum huiuſmodi eſſe confectum, ita vt recta A B, baſim trianguli bifariam diuidens maior ſit, <lb/>quàm ſtylus, &amp; </s>
  <s xml:id="echoid-s28408" xml:space="preserve">extra lineam ſtyli accepta. </s>
  <s xml:id="echoid-s28409" xml:space="preserve">Eodem modo dictum triangulum in quocunque horologio <lb/>deſcribi poteſt. </s>
  <s xml:id="echoid-s28410" xml:space="preserve">Quod ſi quando locus gnomonis intratropicos fucrit conſtitutus, vt contingit in polari <lb/>horologio, &amp; </s>
  <s xml:id="echoid-s28411" xml:space="preserve">nonnullis alĳs, vt ſupra in ſcholio propoſ. </s>
  <s xml:id="echoid-s28412" xml:space="preserve">præcedentis docuimus, latera A C, A D, præ-<lb/>dicti trianguli, cum lineas horologii interſecent, deleri poterunt, &amp; </s>
  <s xml:id="echoid-s28413" xml:space="preserve">ſola baſis C D, relinqui, vel cer-<lb/>tè ſegmenta ipſorum laterum, quæ extra tropicos cadunt, deſcribi tantum poterunt: </s>
  <s xml:id="echoid-s28414" xml:space="preserve">cuius rei <lb/>exemplum habes in horologio polari ſignorum aſcendentium propoſ. </s>
  <s xml:id="echoid-s28415" xml:space="preserve">45. </s>
  <s xml:id="echoid-s28416" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s28417" xml:space="preserve">Poterit quoque, ſi <lb/>placet, interuallum D F, transferri ex C, vſque ad H. </s>
  <s xml:id="echoid-s28418" xml:space="preserve">Item in poſteriori triangulo, in quo recta A B,
<pb o="433" file="0449" n="449" rhead="LIBER QVARTVS."/>
maior eſt ſtylo, abſcindi recta B I, ſtylo æqualis, vt ſi quando stylus amittatur, aut frangatur, ei-<lb/>æqualem poſſimus exhibere.</s>
  <s xml:id="echoid-s28419" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1465" type="float" level="2" n="1">
<note position="left" xlink:label="note-0448-10" xlink:href="note-0448-10a" xml:space="preserve">Quæ in variis <lb/>horologiis ob-<lb/>ſeruanda ſint <lb/>in conſtructio-<lb/>ne trianguli, <lb/>quo ſtylus in <lb/>proprium ſitũ <lb/>@@ſtituatur.</note>
<note position="left" xlink:label="note-0448-11" xlink:href="note-0448-11a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1467" type="section" level="1" n="356">
<head xml:id="echoid-head369" xml:space="preserve">PROBLEMA 13. PROPOSITIO 13.</head>
<p>
  <s xml:id="echoid-s28420" xml:space="preserve">DATO horologio, vna cum ſtylo, eiuſq́; </s>
  <s xml:id="echoid-s28421" xml:space="preserve">loco, ad quam poli al-<lb/>titudinem fabricatum ſit, &amp; </s>
  <s xml:id="echoid-s28422" xml:space="preserve">quam declinationem habeat à Verticali, <lb/>&amp; </s>
  <s xml:id="echoid-s28423" xml:space="preserve">inclinationem ad Horizontem, ſi declinans eſt, aut inclinatum, nec <lb/>
<anchor type="note" xlink:label="note-0449-01a" xlink:href="note-0449-01"/>
non quanta ſit altitudo poli ſupra ipſum planum declinans, aut inclina-<lb/>tum, cognoſcere. </s>
  <s xml:id="echoid-s28424" xml:space="preserve">Et contra, dato horologio, vna cum altitudine <lb/>poli, ad quam conſtructum eſt, nec non inclinatione eius ad Horizon <lb/>tem, ſi inclinatum eſt, longitudinem ſtyli, eiusq; </s>
  <s xml:id="echoid-s28425" xml:space="preserve">locum, vna cum de-<lb/>clinatione à Verticali, ſi horologium declinans eſt, atque altitudinem <lb/>poli ſupra ipſum planum declinans, inclinatumve, inueſtigare.</s>
  <s xml:id="echoid-s28426" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1467" type="float" level="2" n="1">
<note position="left" xlink:label="note-0449-01" xlink:href="note-0449-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s28427" xml:space="preserve">FREQVENTER accidit, vt ignoretur, ad quam eleuationem poli horologium aliquod <lb/>oblatum ſit conſtructum, aut quantus debeat eſſe eius ſtylus, (ſi fortè is aut amiſſus fuerit, aut con <lb/>
<anchor type="note" xlink:label="note-0449-02a" xlink:href="note-0449-02"/>
fractus) &amp; </s>
  <s xml:id="echoid-s28428" xml:space="preserve">in quo ſtatuendus loco, vt horas indicet. </s>
  <s xml:id="echoid-s28429" xml:space="preserve">Vtrumque igitur hac ratione cognoſcemus.</s>
  <s xml:id="echoid-s28430" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1468" type="float" level="2" n="2">
<note position="left" xlink:label="note-0449-02" xlink:href="note-0449-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s28431" xml:space="preserve">SIT primum horologium horizontale A, in quo æquinoctialis linea B C, &amp; </s>
  <s xml:id="echoid-s28432" xml:space="preserve">meridiana D E, <lb/>
<anchor type="note" xlink:label="note-0449-03a" xlink:href="note-0449-03"/>
ſtylus autem F G, in puncto F, collocandus. </s>
  <s xml:id="echoid-s28433" xml:space="preserve">Excitetur ex F, loco ſtyli ad meridianam lineam per-<lb/>pendicularis F H, ſtylo F G, æqualis. </s>
  <s xml:id="echoid-s28434" xml:space="preserve">Ducta autem recta I H, ex puncto I, vbi meridiana linea, &amp; </s>
  <s xml:id="echoid-s28435" xml:space="preserve"><lb/>æquinoctialis ſe interſecant, ad H, erigatur ex H, ad I H, perpendicularis H D, ſecans lineam meri <lb/>dianam in D. </s>
  <s xml:id="echoid-s28436" xml:space="preserve">Dico I D H, eſſe angulum altitudinis poli, ad quam horologium eſt fabricatum. <lb/></s>
  <s xml:id="echoid-s28437" xml:space="preserve">Quoniam enim, vt ex de-<lb/>
<anchor type="figure" xlink:label="fig-0449-01a" xlink:href="fig-0449-01"/>
monſtratis in propoſ. </s>
  <s xml:id="echoid-s28438" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28439" xml:space="preserve">li-<lb/>bri ſuperioris conſtat, re-<lb/>cta H I, communis ſectio <lb/>
<anchor type="note" xlink:label="note-0449-04a" xlink:href="note-0449-04"/>
eſt (ſi triangulum D H I, <lb/>ſtatuatur rectum ad planũ <lb/>horologii, hoc eſt, in Me-<lb/>ridiani plano) Aequato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s28440" xml:space="preserve">Meridiani, axisq́ue <lb/>mundi per verticem ſtyli <lb/>H, tranſiens rectus eſt ad <lb/>planum Aequatoris, atque <lb/>adeò per defin. </s>
  <s xml:id="echoid-s28441" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28442" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28443" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s28444" xml:space="preserve">Euclidis, ad H I, perpendi <lb/>
<anchor type="note" xlink:label="note-0449-05a" xlink:href="note-0449-05"/>
cularis, erit H D, quæ per-<lb/>pendicularis ducta eſt ad <lb/>H I, axis mundi occurrens <lb/>meridianæ lineæ, &amp; </s>
  <s xml:id="echoid-s28445" xml:space="preserve">plano <lb/>horologii in D. </s>
  <s xml:id="echoid-s28446" xml:space="preserve">Eſt igitur <lb/>H D I, angulus altitudinis <lb/>poli ſupra Horizontem, <lb/>quem nimirum axis mun <lb/>di cum meridiana linea ſa <lb/>cit in plano horizontalis <lb/>horologii.</s>
  <s xml:id="echoid-s28447" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1469" type="float" level="2" n="3">
<note position="right" xlink:label="note-0449-03" xlink:href="note-0449-03a" xml:space="preserve">Qua ratione in <lb/>horologio hori <lb/>zontali ex da@o <lb/>ſtylo, eiu@q́ue <lb/>loc<unsure/>o, ad quam <lb/>poli altitudinẽ <lb/>fabricatum ſit, <lb/>inueſtigetur.</note>
  <figure xlink:label="fig-0449-01" xlink:href="fig-0449-01a">
    <image file="0449-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0449-01"/>
  </figure>
<note position="left" xlink:label="note-0449-04" xlink:href="note-0449-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0449-05" xlink:href="note-0449-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s28448" xml:space="preserve">QVOD ſi in linea meridiana datum fuerit D, centrum horologii, in quo omnes lineæ hora-<lb/>rum à meridie &amp; </s>
  <s xml:id="echoid-s28449" xml:space="preserve">media nocte coeunt, facilius inueniemus eandem altitudinem poli, ſi ex D, ad <lb/>H, rectam ducamus D H. </s>
  <s xml:id="echoid-s28450" xml:space="preserve">Erit enim rurſus D H, axis mundi (cum per centrum mundi H, &amp; </s>
  <s xml:id="echoid-s28451" xml:space="preserve">per <lb/>D, centrum horologii ducatur) &amp; </s>
  <s xml:id="echoid-s28452" xml:space="preserve">H D I, angulus altitudinis poli.</s>
  <s xml:id="echoid-s28453" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Qua uia ſtylus <lb/>eiusque locus <lb/>in horizont<unsure/>ali <lb/>horologio in-<lb/>quiratur ex da <lb/>ta altitudine <lb/>poli, ad quam <lb/>fabricatum eſt <lb/>horologium.</note>
<p>
  <s xml:id="echoid-s28454" xml:space="preserve">IAM verò ſit nota altitudo poli, ad quam fabricatum eſt horologium, ſed ſtylus ignotus, nec <lb/>non &amp; </s>
  <s xml:id="echoid-s28455" xml:space="preserve">locus eiuſdem, quem ita inquiremus. </s>
  <s xml:id="echoid-s28456" xml:space="preserve">Circa rectam D I, inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s28457" xml:space="preserve">æqui <lb/>noctialem lineam interiectam deſcribemus ſemicirculum D H I, &amp; </s>
  <s xml:id="echoid-s28458" xml:space="preserve">ex D, centro horologii axem <lb/>mundi educemus D H, facientem cum meridiana linea angulum altitudinis poli H D I, qui cir-<lb/>culum ſecet in H. </s>
  <s xml:id="echoid-s28459" xml:space="preserve">Nam ex H, ad lineam meridianam demiſſa perpendicularis H F, erit longitu-<lb/>do ſtyli, eiuſq́ue ſedes in puncto F. </s>
  <s xml:id="echoid-s28460" xml:space="preserve">Ducta enim recta H I, erit angulus D H I, rectus in ſemicircu-<lb/>
<anchor type="note" xlink:label="note-0449-08a" xlink:href="note-0449-08"/>
<pb o="434" file="0450" n="450" rhead="GNOMONICES"/>
lo; </s>
  <s xml:id="echoid-s28461" xml:space="preserve">acproinde recta H I, communis ſectio erit Meridiani, &amp; </s>
  <s xml:id="echoid-s28462" xml:space="preserve">Æquatoris, ſi triangulum D H I, ſta-<lb/>tuatur in plano Meridiani, hoc eſt, rectum ad<unsure/> planum horologii. </s>
  <s xml:id="echoid-s28463" xml:space="preserve">Quia verò axis mundi occurrit <lb/>Æquatori in centro mundi, erit H, centrum mundi. </s>
  <s xml:id="echoid-s28464" xml:space="preserve">Quare H F, perpendicularis ex centro mun-<lb/>di cadens in lineam meridianam ſtylus erit, &amp; </s>
  <s xml:id="echoid-s28465" xml:space="preserve">eius locus F. </s>
  <s xml:id="echoid-s28466" xml:space="preserve">Idem aſlequemur, ſi ex I, puncto ę-<lb/>
<anchor type="figure" xlink:label="fig-0450-01a" xlink:href="fig-0450-01"/>
quinoctialis liueæ emitta <lb/>mus rectam I H, facien-<lb/>tem cum linea meridia-<lb/>na angulum complemen <lb/>ti altitudinis poli H I D, <lb/>quæ eundem circulum ſe <lb/>
<anchor type="note" xlink:label="note-0450-01a" xlink:href="note-0450-01"/>
cet in H. </s>
  <s xml:id="echoid-s28467" xml:space="preserve">Nam rurſus de-<lb/>miſſa ex H. </s>
  <s xml:id="echoid-s28468" xml:space="preserve">ad meridianã <lb/>lineã perpẽdicularis H F, <lb/>erit ſtyli longitudo, lo-<lb/>cusq́ue ipſius in puncto <lb/>F. </s>
  <s xml:id="echoid-s28469" xml:space="preserve">Ducta enim recta H D, <lb/>
<anchor type="note" xlink:label="note-0450-02a" xlink:href="note-0450-02"/>
erit angulus I H D, in ſe<unsure/>-<lb/>micirculo rectus: </s>
  <s xml:id="echoid-s28470" xml:space="preserve">ac pro-<lb/>pterea in triãgulo D H I, <lb/>reliquus angulus H D I, al <lb/>
<anchor type="note" xlink:label="note-0450-03a" xlink:href="note-0450-03"/>
titudini poli æqualis erit. <lb/></s>
  <s xml:id="echoid-s28471" xml:space="preserve">Quare vt prius H F, erit <lb/>ſtylus in F, erigendus.</s>
  <s xml:id="echoid-s28472" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1470" type="float" level="2" n="4">
<note position="right" xlink:label="note-0449-08" xlink:href="note-0449-08a" xml:space="preserve">31. tertĳ.</note>
  <figure xlink:label="fig-0450-01" xlink:href="fig-0450-01a">
    <image file="0450-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0450-01"/>
  </figure>
<note position="left" xlink:label="note-0450-01" xlink:href="note-0450-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0450-02" xlink:href="note-0450-02a" xml:space="preserve">35. tertĳ.</note>
<note position="left" xlink:label="note-0450-03" xlink:href="note-0450-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s28473" xml:space="preserve">QVOD ſi D, centrũ <lb/>horologii datum nõ fue-<lb/>rit, ita rem propoſitã exe-<lb/>quemur. </s>
  <s xml:id="echoid-s28474" xml:space="preserve">Si horologium <lb/>fuerit Aſtronomicum cõ-<lb/>tinens horas à meridie, &amp; </s>
  <s xml:id="echoid-s28475" xml:space="preserve"><lb/>media nocte, producemus lineã K D, horæ 6. </s>
  <s xml:id="echoid-s28476" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s28477" xml:space="preserve">B D, aut 7. </s>
  <s xml:id="echoid-s28478" xml:space="preserve">vel denique cuiuſcunque alterius <lb/>
<anchor type="note" xlink:label="note-0450-04a" xlink:href="note-0450-04"/>
horæ, quæ meridianã lineam ſecet in D. </s>
  <s xml:id="echoid-s28479" xml:space="preserve">Erit namque D, centrum horologii, cum omnes lineæ ho <lb/>rarum à meridie, ac media nocte lineam meridianã ſecent in centro horologii, vt in coroll. </s>
  <s xml:id="echoid-s28480" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s28481" xml:space="preserve">21. </s>
  <s xml:id="echoid-s28482" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28483" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28484" xml:space="preserve">demonſtratum eſt. </s>
  <s xml:id="echoid-s28485" xml:space="preserve">Si autem fuerit horologium Babylonicum, vel Italicum horas ab <lb/>ortu, vel occaſu complectens, producemus duas horas ab crtu, vel occaſu ſecantes horam 6. </s>
  <s xml:id="echoid-s28486" xml:space="preserve">à me <lb/>ridie, vel media nocte in vno eodemq́; </s>
  <s xml:id="echoid-s28487" xml:space="preserve">puncto, vt ex tabula lineæ horæ 6. </s>
  <s xml:id="echoid-s28488" xml:space="preserve">à meridie, vel media no-<lb/>cte poſita in ſcholio propoſ. </s>
  <s xml:id="echoid-s28489" xml:space="preserve">20. </s>
  <s xml:id="echoid-s28490" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28491" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28492" xml:space="preserve">conſtat, quales ſunt linea B k, horæ 23. </s>
  <s xml:id="echoid-s28493" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s28494" xml:space="preserve">linea <lb/>C K, horæ 13. </s>
  <s xml:id="echoid-s28495" xml:space="preserve">ab occaſ<unsure/>u ſecantes ſeſe in K. </s>
  <s xml:id="echoid-s28496" xml:space="preserve">Si igitur per K, ducamus lineæ æquinoctiali parallelam <lb/>K D, quæ meridianam lineam in D, ſecet, erit K D, linea horæ 6. </s>
  <s xml:id="echoid-s28497" xml:space="preserve">à meridie, vel media nocte, cum <lb/>per punctum K, tranſeat huiuſmodi linea, vt ex dicta tabula perſpicuum eſt, parallelaq́ue ſit æqui <lb/>noctiali lineæ in horizontali horologio, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s28498" xml:space="preserve">22. </s>
  <s xml:id="echoid-s28499" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28500" xml:space="preserve">1 oſtenſum eſt. </s>
  <s xml:id="echoid-s28501" xml:space="preserve">Quamobrem <lb/>
<anchor type="note" xlink:label="note-0450-05a" xlink:href="note-0450-05"/>
D, centrum erit horologii, ac proinde ſi circa D I, ſemicirculum deſcribamus, inueniemus ſtylũ, <lb/>eiuſq́ue ſedem, veluti prius. </s>
  <s xml:id="echoid-s28502" xml:space="preserve">Eadem linea horæ 6. </s>
  <s xml:id="echoid-s28503" xml:space="preserve">à meridie, vel media nocte tranſit per punctum <lb/>commune horarum 22. </s>
  <s xml:id="echoid-s28504" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28505" xml:space="preserve">14. </s>
  <s xml:id="echoid-s28506" xml:space="preserve">ab ortu vel occaſu. </s>
  <s xml:id="echoid-s28507" xml:space="preserve">Item 21. </s>
  <s xml:id="echoid-s28508" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28509" xml:space="preserve">15 aut 20. </s>
  <s xml:id="echoid-s28510" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28511" xml:space="preserve">16. </s>
  <s xml:id="echoid-s28512" xml:space="preserve">aut 1. </s>
  <s xml:id="echoid-s28513" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28514" xml:space="preserve">11. </s>
  <s xml:id="echoid-s28515" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28516" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28517" xml:space="preserve">vt <lb/>ex eadem tabula lineæ horæ 6. </s>
  <s xml:id="echoid-s28518" xml:space="preserve">à meridie, vel media nocte liquet. </s>
  <s xml:id="echoid-s28519" xml:space="preserve">Vnde vt certi ſimus, num li-<lb/>nea K D, ducta æquinoctiali lineæ parallela indicet verè horam 6. </s>
  <s xml:id="echoid-s28520" xml:space="preserve">à meridie, vel media nocte, in-<lb/>ueſtiganda erunt duo, aut tria, quatuorve, aut etiam plura puncta, ex prædicta tabula, per quæ li-<lb/>nea horæ 6. </s>
  <s xml:id="echoid-s28521" xml:space="preserve">à meridie, vel media nocte ducenda eſt. </s>
  <s xml:id="echoid-s28522" xml:space="preserve">Si enim per vnum illorum ducta lineæ æqui <lb/>noctiali parallela tranſierit per reliqua puncta, haud dubie accuratiſſimè deſcripta erit linea ho-<lb/>ræ 6. </s>
  <s xml:id="echoid-s28523" xml:space="preserve">à meridie, vel media nocte, ac propterea &amp; </s>
  <s xml:id="echoid-s28524" xml:space="preserve">centrum horologii rectè inuentum erit. </s>
  <s xml:id="echoid-s28525" xml:space="preserve">Si for-<lb/>taſſis commodè duci non poſſit in horologio linea horæ 6. </s>
  <s xml:id="echoid-s28526" xml:space="preserve">à meridie, vel media nocte, inquire-<lb/>mus ex quacunque alia tabula lineæ alicuius horę à meridie, vel media nocte poſita in eodẽſcho-<lb/>
<anchor type="note" xlink:label="note-0450-06a" xlink:href="note-0450-06"/>
lio propoſ. </s>
  <s xml:id="echoid-s28527" xml:space="preserve">20. </s>
  <s xml:id="echoid-s28528" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28529" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28530" xml:space="preserve">alia puncta, per quæ illa linea horæ à meridie, vel media nocte duci debet. <lb/></s>
  <s xml:id="echoid-s28531" xml:space="preserve">Ducta namque illa linea ſecabitur rurſum meridiana linea in centro horologii. </s>
  <s xml:id="echoid-s28532" xml:space="preserve">Vt ſi velimus du <lb/>cere lineam horæ 5. </s>
  <s xml:id="echoid-s28533" xml:space="preserve">à meridie, vel media nocte, producemus tam horas 22. </s>
  <s xml:id="echoid-s28534" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28535" xml:space="preserve">12. </s>
  <s xml:id="echoid-s28536" xml:space="preserve">ab ortu, vel oc-<lb/>
<anchor type="note" xlink:label="note-0450-07a" xlink:href="note-0450-07"/>
caſu, quàm 16. </s>
  <s xml:id="echoid-s28537" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28538" xml:space="preserve">18. </s>
  <s xml:id="echoid-s28539" xml:space="preserve">aut 3. </s>
  <s xml:id="echoid-s28540" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28541" xml:space="preserve">7. </s>
  <s xml:id="echoid-s28542" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28543" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28544" xml:space="preserve">Per puncta enim, vbi mutuo ſe diuident huiuſmodi horæ, <lb/>ducenda erit hora 5. </s>
  <s xml:id="echoid-s28545" xml:space="preserve">à meridie, vel media nocte, vt pater ex tabula lineæ horæ 5. </s>
  <s xml:id="echoid-s28546" xml:space="preserve">à meridie, vel me <lb/>dia nocte in ſcholio propoſ. </s>
  <s xml:id="echoid-s28547" xml:space="preserve">20. </s>
  <s xml:id="echoid-s28548" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28549" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28550" xml:space="preserve">poſita.</s>
  <s xml:id="echoid-s28551" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1471" type="float" level="2" n="5">
<note position="left" xlink:label="note-0450-04" xlink:href="note-0450-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0450-05" xlink:href="note-0450-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0450-06" xlink:href="note-0450-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0450-07" xlink:href="note-0450-07a" xml:space="preserve">Quo pacto ex <lb/>loco ſtyli longi <lb/>tudo eiuſdem <lb/>inueſtigãda ſit <lb/>vna cum cen-<lb/>tro horologii <lb/>horizontalis, &amp; <lb/>poli altitudo, <lb/>ad quam horo <lb/>logium fabrica <lb/>@@m eſt.</note>
</div>
<p>
  <s xml:id="echoid-s28552" xml:space="preserve">NON aliter ſi ſtyli locus F, duntaxat detur ſine eius longitudine, altitudine poli, &amp; </s>
  <s xml:id="echoid-s28553" xml:space="preserve">centro ho <lb/>rologii, indagabimus &amp; </s>
  <s xml:id="echoid-s28554" xml:space="preserve">horologii centrum, &amp; </s>
  <s xml:id="echoid-s28555" xml:space="preserve">poli eleuationem, &amp; </s>
  <s xml:id="echoid-s28556" xml:space="preserve">longitudinem ſtyli. </s>
  <s xml:id="echoid-s28557" xml:space="preserve">Inuenta <lb/>enim, vt proximè docuimus, linea horæ 6. </s>
  <s xml:id="echoid-s28558" xml:space="preserve">vel alterius cuiuſque à meridie, vel media nocte, vbi <lb/>hæc lineam meridianam ſecabit, ibi erit centrum horologii D. </s>
  <s xml:id="echoid-s28559" xml:space="preserve">Quod facilius inueniemus, ſi ho-
<pb o="435" file="0451" n="451" rhead="LIBER QVARTVS."/>
@ologium fuerit Aſtronomicum. </s>
  <s xml:id="echoid-s28560" xml:space="preserve">Nam quælibet linea horaria illius producta ſecabit meridianam <lb/>lineam in D, centro horologii. </s>
  <s xml:id="echoid-s28561" xml:space="preserve">Deſcripto autem circa D I, ſemicirculo, ſi ex F, loco ſtyli educatur <lb/>F H, ad lineam meridianam perpendicularis, quæ circunferentiam ſecet in H, erit F H, ſtyli ma-<lb/>gnitudo, &amp; </s>
  <s xml:id="echoid-s28562" xml:space="preserve">ducta recta D H, dabit angulum altitudinis poli H D I. </s>
  <s xml:id="echoid-s28563" xml:space="preserve">Nam ducta recta H I, erit in <lb/>ſemicirculo angulus D H I, rectus. </s>
  <s xml:id="echoid-s28564" xml:space="preserve">Cum ergo ſtylus in centro mundi occurrat axi, &amp; </s>
  <s xml:id="echoid-s28565" xml:space="preserve">communi <lb/>
<anchor type="note" xlink:label="note-0451-01a" xlink:href="note-0451-01"/>
ſectioni Aequatoris, ac Meridiani, vbi ſe ad angulos rectos interſecant, vt ex demonſtratis mani-<lb/>feſtum eſt, erit H, centrum mundi; </s>
  <s xml:id="echoid-s28566" xml:space="preserve">F H, ſtylus; </s>
  <s xml:id="echoid-s28567" xml:space="preserve">D H, axis mundi; </s>
  <s xml:id="echoid-s28568" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28569" xml:space="preserve">HI, communis ſectio Aequa <lb/>toris, ac Meridiani. </s>
  <s xml:id="echoid-s28570" xml:space="preserve">Nam ſi F H, non dicatur eſſe ſtylus, ſed longior quædam linea, quàm F H, vel <lb/>breuior, conueniet axis cum communi ſectione Aequatoris, &amp; </s>
  <s xml:id="echoid-s28571" xml:space="preserve">Meridiani vel infra H, in ſtylo, <lb/>vel ſupra, atque ita fiet angulus vel obtuſus, vel acutus, maior videlicet, vel minor angulo recto <lb/>
<anchor type="note" xlink:label="note-0451-02a" xlink:href="note-0451-02"/>
D H I, quod eſt abſurdum.</s>
  <s xml:id="echoid-s28572" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1472" type="float" level="2" n="6">
<note position="right" xlink:label="note-0451-01" xlink:href="note-0451-01a" xml:space="preserve">31. tertĳ.</note>
<note position="left" xlink:label="note-0451-02" xlink:href="note-0451-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s28573" xml:space="preserve">DEINDE ſit Verticale horologium A, idem quod Horizontale, in quo rurſus æquinoctialis <lb/>
<anchor type="note" xlink:label="note-0451-03a" xlink:href="note-0451-03"/>
linea B C, &amp; </s>
  <s xml:id="echoid-s28574" xml:space="preserve">meridiana D E, ſtylus autem F G, eiusq́ue ſedes punctum F, in quo meridiana linea <lb/>horizontalem lineam (ſi ea ducta eſt) interſecat. </s>
  <s xml:id="echoid-s28575" xml:space="preserve">Excitetur ex F, ad meridianam lineam perpen-<lb/>dieularis F H, ſtylo F G, æqualis, ducaturq́ue recta I H. </s>
  <s xml:id="echoid-s28576" xml:space="preserve">Dico D I H, angulum eſſe altitudinis poli <lb/>ſupra Horizontem. </s>
  <s xml:id="echoid-s28577" xml:space="preserve">Intelligatur enim triangulum F H I, moueri circa meridianam lineam, donec <lb/>rectum ſit ad planum horologii, &amp; </s>
  <s xml:id="echoid-s28578" xml:space="preserve">in plano Meridiani conſtituatur. </s>
  <s xml:id="echoid-s28579" xml:space="preserve">Et quoniam Aequator tran-<lb/>ſit per I, &amp; </s>
  <s xml:id="echoid-s28580" xml:space="preserve">per H, centrum mundi, erit H I, communis ſectio Aequatoris, ac Meridiani. </s>
  <s xml:id="echoid-s28581" xml:space="preserve">Cum er -<lb/>go Aequator cum Verticali contineat angulum altitudinis poli, propterea quòd arcus Meridiani <lb/>inter Verticalem, &amp; </s>
  <s xml:id="echoid-s28582" xml:space="preserve">Aequatorem interiectus æqualis ſit arcui altitudinis poli, vt in ſphæra oſten-<lb/>
<anchor type="note" xlink:label="note-0451-04a" xlink:href="note-0451-04"/>
dimus, cum de Horizonte ageremus, erit D I H, angulus altitudinis poli ſupra Horizontem, ad <lb/>quam Verticale horologium fabricatum eſt.</s>
  <s xml:id="echoid-s28583" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1473" type="float" level="2" n="7">
<note position="right" xlink:label="note-0451-03" xlink:href="note-0451-03a" xml:space="preserve">Quomodo in <lb/>Verticali horo <lb/>log@o cognoſca <lb/>tur ex dato ſty <lb/>lo, eiuſque lo-<lb/>co, ad quam al <lb/>titudinem po-<lb/>li ſit con@@ru-<lb/>ctum.</note>
<note position="left" xlink:label="note-0451-04" xlink:href="note-0451-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s28584" xml:space="preserve">QVOD ſi ex D, centro horologii (quod quidem inueniemus, ſi notatum non fuerit, vt in ho <lb/>rizontali horologio proximè docuimus) rectam ducamus D H, erit H D I, angulus complemen-<lb/>ti altitudinis poli ſupra Horizontem; </s>
  <s xml:id="echoid-s28585" xml:space="preserve">ac proinde in rectangulo triangulo D F H, reliquus D H F, <lb/>angulus erit altitudinis poli. </s>
  <s xml:id="echoid-s28586" xml:space="preserve">Erit namque D H, axis mundi, cum per D, centrum horologii, &amp; </s>
  <s xml:id="echoid-s28587" xml:space="preserve"><lb/>H, centrum mundi extendatur; </s>
  <s xml:id="echoid-s28588" xml:space="preserve">ac propterea F D H, angulus erit complementi altitudinis poli, <lb/>
<anchor type="note" xlink:label="note-0451-05a" xlink:href="note-0451-05"/>
quem videlicet axis cum Verticali conſtituit.</s>
  <s xml:id="echoid-s28589" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1474" type="float" level="2" n="8">
<note position="right" xlink:label="note-0451-05" xlink:href="note-0451-05a" xml:space="preserve">Quo pacto in <lb/>hotologio Vet <lb/>ticali inuenien <lb/>dus ſit ſtylus <lb/>eiuſque locus <lb/>ex data al@itu-<lb/>dine pol@, ad <lb/>quam horolo-<lb/>gium conſtru-<lb/>ctum eſt.</note>
</div>
<p>
  <s xml:id="echoid-s28590" xml:space="preserve">SIT iam altitudo poli nota, ad quam horologium Verticale conſtructum eſt, &amp; </s>
  <s xml:id="echoid-s28591" xml:space="preserve">oporteat in-<lb/>ueſtigare &amp; </s>
  <s xml:id="echoid-s28592" xml:space="preserve">magnitudinem, &amp; </s>
  <s xml:id="echoid-s28593" xml:space="preserve">locum ſtyli. </s>
  <s xml:id="echoid-s28594" xml:space="preserve">Circa rectam D I, poſitam inter centrum horologii <lb/>D, (quod, vt prius, reperiemus, ſi datum non fuerit) &amp; </s>
  <s xml:id="echoid-s28595" xml:space="preserve">æquinoctialem lineam ſemicirculus de-<lb/>
<anchor type="note" xlink:label="note-0451-06a" xlink:href="note-0451-06"/>
ſcribatur D H I, &amp; </s>
  <s xml:id="echoid-s28596" xml:space="preserve">ex I, egrediatur recta I H, faciens angulum altitudinis poli H I D, ſupra Hori-<lb/>zontem, ſecansq́ue circunferentiam in H. </s>
  <s xml:id="echoid-s28597" xml:space="preserve">Dico demiſſam perpendicularem H F, ad meridianam <lb/>lineam eſſe ſtyli magnitudinem, eiuſq́ue locum in F. </s>
  <s xml:id="echoid-s28598" xml:space="preserve">Ducta enim recta H D, erit angulus D H I, <lb/>
<anchor type="note" xlink:label="note-0451-07a" xlink:href="note-0451-07"/>
in ſemicirculo rectus. </s>
  <s xml:id="echoid-s28599" xml:space="preserve">Quocirca cum I H, ſit commun is ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s28600" xml:space="preserve">Meridiani, propte-<lb/>rea quod cum linea meridiana angulum altitudinis poli conſtituit, erit H D, occurrens ei ex cen-<lb/>tro horologii educta ad angulos rectos, axis mundi. </s>
  <s xml:id="echoid-s28601" xml:space="preserve">Cum ergo axis mundi Aequatori occurrat <lb/>in centro mundi, erit H, centrum mundi: </s>
  <s xml:id="echoid-s28602" xml:space="preserve">ac propterea H F, ex centro mundi cadens in meridia-<lb/>nam lineam perpendicularis, erit ſtylus, eiusq́ue ſedes in puncto F. </s>
  <s xml:id="echoid-s28603" xml:space="preserve">Obtinebimus idem, ſi ex D, <lb/>centro horologii emittamus rectam D H, facientem cum linea meridiana angulum complemen <lb/>ti altitudinis poli H D I, quæ eundem circulum in H, ſecet. </s>
  <s xml:id="echoid-s28604" xml:space="preserve">Erit enim rurſus demiſſa perpendi-<lb/>
<anchor type="note" xlink:label="note-0451-08a" xlink:href="note-0451-08"/>
cularis ex H, ad lineam meridianam longitudo ſtyli, &amp; </s>
  <s xml:id="echoid-s28605" xml:space="preserve">locus eiuſdem in F, puncto. </s>
  <s xml:id="echoid-s28606" xml:space="preserve">Nam ducta re <lb/>cta HI, erit in ſemicirculo angulus D H I, rectus, ac proinde in triangulo rectangulo D H I, reli-<lb/>
<anchor type="note" xlink:label="note-0451-09a" xlink:href="note-0451-09"/>
quus angulus D I H, altitudini poli æqualis erit. </s>
  <s xml:id="echoid-s28607" xml:space="preserve">Quare vt ante oſtendimus, erit H, centrum mun <lb/>di, &amp; </s>
  <s xml:id="echoid-s28608" xml:space="preserve">H F, ſtylus in F, collocandus.</s>
  <s xml:id="echoid-s28609" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1475" type="float" level="2" n="9">
<note position="left" xlink:label="note-0451-06" xlink:href="note-0451-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0451-07" xlink:href="note-0451-07a" xml:space="preserve">31. tertĳ.</note>
<note position="left" xlink:label="note-0451-08" xlink:href="note-0451-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0451-09" xlink:href="note-0451-09a" xml:space="preserve">31. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s28610" xml:space="preserve">PARI ratione ſi detur duntaxat locus ſtyli F, inueniemus eius longitudinem, altitudinem <lb/>
<anchor type="note" xlink:label="note-0451-10a" xlink:href="note-0451-10"/>
poli, &amp; </s>
  <s xml:id="echoid-s28611" xml:space="preserve">centrum horologii, veluti paulo ante in horologio horizontali. </s>
  <s xml:id="echoid-s28612" xml:space="preserve">Ducta enim, vt ibi, linea <lb/>horæ 6. </s>
  <s xml:id="echoid-s28613" xml:space="preserve">à meridie, vel media nocte, vel alterius cuiuſpiam horæ à meridie, vel media nocte, inue-<lb/>niemus centrum horologii D, nempe punctum, in quo meridianã lineam ſecat hora quæcunque <lb/>à meridie, vel media nocte. </s>
  <s xml:id="echoid-s28614" xml:space="preserve">Deinde deſcripto circa D I, ſemicirculo, excitabimus ex F, ad meri-<lb/>dianam lineam perpendicularem F H, quæ circulum ſecet in H. </s>
  <s xml:id="echoid-s28615" xml:space="preserve">Nam F H, erit longitudo ſtyli, &amp; </s>
  <s xml:id="echoid-s28616" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0451-11a" xlink:href="note-0451-11"/>
ducta recta I H, dabit angulum altitudinis poli ſupra Horizontem. </s>
  <s xml:id="echoid-s28617" xml:space="preserve">Ducta enim recta H D, erit <lb/>angulus D H I, in ſemicirculo rectus. </s>
  <s xml:id="echoid-s28618" xml:space="preserve">Quapropter, vt ante in horologio horizontali diximus, erit <lb/>
<anchor type="note" xlink:label="note-0451-12a" xlink:href="note-0451-12"/>
H, centrum mundi; </s>
  <s xml:id="echoid-s28619" xml:space="preserve">D H, axis mundi, &amp; </s>
  <s xml:id="echoid-s28620" xml:space="preserve">H I, communis ſectio Aequatoris, ac Meridiani, propte <lb/>rea quod hæ tres lineæ in centro mundi coeunt, &amp; </s>
  <s xml:id="echoid-s28621" xml:space="preserve">poſteriores duæ angulum conficiunt rectum. <lb/></s>
  <s xml:id="echoid-s28622" xml:space="preserve">Si enim F H, non dicatur ſtylus, ſed maior quædam linea, aut breuior, quàm F H, conuenient axis <lb/>ex centro horologii D, cadens, &amp; </s>
  <s xml:id="echoid-s28623" xml:space="preserve">communis ſectio Aequatoris, ac Meridiani ducta ex I, communi <lb/>ſectione lineæ meridianæ, atque æquinoctialis lineæ, in recta F H, infra H, vel ſupra ad angulum <lb/>obtuſum, acutumve, nempe maiorem, vel minorem angulo D H I; </s>
  <s xml:id="echoid-s28624" xml:space="preserve">quandoquidem in vertice ſtyli <lb/>conueniuntaxis, &amp; </s>
  <s xml:id="echoid-s28625" xml:space="preserve">communis ſectio Aequatoris ac Meridiani. </s>
  <s xml:id="echoid-s28626" xml:space="preserve">quod abſurdum eſt.</s>
  <s xml:id="echoid-s28627" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1476" type="float" level="2" n="10">
<note position="right" xlink:label="note-0451-10" xlink:href="note-0451-10a" xml:space="preserve">Qua ratione ex <lb/>loco ſtyli in <lb/>Verticali horo <lb/>logio eius lon-<lb/>gitudo, altitu-<lb/>do poli, &amp; cen-<lb/>trum horologii <lb/>inueſtigetur.</note>
<note position="left" xlink:label="note-0451-11" xlink:href="note-0451-11a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0451-12" xlink:href="note-0451-12a" xml:space="preserve">31. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s28628" xml:space="preserve">EX his facili etiam negotio diſcemus, ad quas altitudines poli fabricata ſint horologia illa,
<pb o="436" file="0452" n="452" rhead="GNOMONICES"/>
quæ in Germania, aut Gallia confecta communiter circumferuntur, conſtantq́ue ex duabus tabel-<lb/>
<anchor type="note" xlink:label="note-0452-01a" xlink:href="note-0452-01"/>
lis planis, &amp; </s>
  <s xml:id="echoid-s28629" xml:space="preserve">quadratis ad angulum rectum coniunctis, quarum inferior, in qua acus continetur <lb/>Magnete illita, horologium horizontale continet<unsure/>; </s>
  <s xml:id="echoid-s28630" xml:space="preserve">altera verò, quæ ſupra hanc erigitur ad angulos <lb/>rectos, Verticale. </s>
  <s xml:id="echoid-s28631" xml:space="preserve">Nam cum huiuſmodi horologia plerunque ſint aſtronomica, habeantq<unsure/>ue fi-<lb/>lum per centra horologiorum extenſum pro axe mundi, quod horas indicet; </s>
  <s xml:id="echoid-s28632" xml:space="preserve">ſi conſtruatur trian-<lb/>gulum rectangulum, cuius vnum latus circa rectum angulum æquale ſit portioni meridianæ li-<lb/>neæ in horizontali horologio inter filum, ſeu centrum horologii, &amp; </s>
  <s xml:id="echoid-s28633" xml:space="preserve">alteram tabellam interpoſitę, <lb/>alterum verò ſegmento lineæ meridianæ in Verticali horologio inter filum, centrumve horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s28634" xml:space="preserve">priorem tabellam interiectæ, continebit reliquum latus angulo recto obiectum cum meri-<lb/>diana linea horologii horizõ talis angulum altitudinis poli, ad quam conſtructum eſt horologiũ, <lb/>
<anchor type="note" xlink:label="note-0452-02a" xlink:href="note-0452-02"/>
cum meridiana verò linea Verticalis horologii angulum complementi altitudinis poli, vt con-<lb/>ſtat. </s>
  <s xml:id="echoid-s28635" xml:space="preserve">At vero ſi huiuſmodi horologia loco fili habeant triangulum rectangulum in horologio ho <lb/>rizontali, quod erigi, &amp; </s>
  <s xml:id="echoid-s28636" xml:space="preserve">deprimi poteſt, (Id quod in multis accidit) ita vt eo erecto, ſuprema linea <lb/>angulo recto oppoſita, tanquàm axis, horas indicet, conficiemus ei triangulum omnino æquale. <lb/></s>
  <s xml:id="echoid-s28637" xml:space="preserve">Nam angulus reſpondens inferiori angulo in horizontali horologio continebit altitudinem po-<lb/>li, alter verò complementum altitudims poli.</s>
  <s xml:id="echoid-s28638" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1477" type="float" level="2" n="11">
<note position="left" xlink:label="note-0452-01" xlink:href="note-0452-01a" xml:space="preserve">Ad quas altitu <lb/>dines poli fa <lb/>bricata fint ho <lb/>rologia horizõ <lb/>talia, Vertica <lb/>liaque, quæ vul <lb/>go cicuterun-<lb/>tur cũ acu Ma <lb/>gnete illita, quo <lb/>modo cogno-<lb/>ſca@ur.</note>
<note position="left" xlink:label="note-0452-02" xlink:href="note-0452-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s28639" xml:space="preserve">RVRSVS detur ho <lb/>rologium Meridianũ B, <lb/>
<anchor type="note" xlink:label="note-0452-03a" xlink:href="note-0452-03"/>
<anchor type="figure" xlink:label="fig-0452-01a" xlink:href="fig-0452-01"/>
ſiue orientale, ſiue occi-<lb/>dentale, in quo æquino-<lb/>ctialis linea A C, horizõ-<lb/>
<anchor type="note" xlink:label="note-0452-04a" xlink:href="note-0452-04"/>
talis D E, &amp; </s>
  <s xml:id="echoid-s28640" xml:space="preserve">ſtylus A G, <lb/>eiusq́ue locus A. </s>
  <s xml:id="echoid-s28641" xml:space="preserve">Angu-<lb/>lus acutus C A E, quem <lb/>æquinoctialis linea cum <lb/>horizontali facit, æqualis <lb/>eſt complemento altitu-<lb/>dinis poli: </s>
  <s xml:id="echoid-s28642" xml:space="preserve">Item acutus <lb/>E A F, quem linea horæ <lb/>6. </s>
  <s xml:id="echoid-s28643" xml:space="preserve">à meridie, vel media <lb/>nocte (quæ quidem per <lb/>
<anchor type="note" xlink:label="note-0452-05a" xlink:href="note-0452-05"/>
A, locum ſtyli ducitur ad <lb/>æquinoctialem lineã per <lb/>pendicularis) conſtituit <lb/>cum linea æquinoctiali, <lb/>æqualis eſt altitudini po-<lb/>li. </s>
  <s xml:id="echoid-s28644" xml:space="preserve">Longitudo autem ſty-<lb/>li ſemper æqualis eſt ſpa-<lb/>tio in linea æquinoctiali <lb/>inter A, &amp; </s>
  <s xml:id="echoid-s28645" xml:space="preserve">punctum C, <lb/>per quod hora 9. </s>
  <s xml:id="echoid-s28646" xml:space="preserve">à me-<lb/>
<anchor type="note" xlink:label="note-0452-06a" xlink:href="note-0452-06"/>
dia nocte, &amp; </s>
  <s xml:id="echoid-s28647" xml:space="preserve">hora 3. </s>
  <s xml:id="echoid-s28648" xml:space="preserve">ab <lb/>ortu; </s>
  <s xml:id="echoid-s28649" xml:space="preserve">Item hora 15. </s>
  <s xml:id="echoid-s28650" xml:space="preserve">ab occaſu ducitur in orientali horologio, vel hora 3. </s>
  <s xml:id="echoid-s28651" xml:space="preserve">à meridie, &amp; </s>
  <s xml:id="echoid-s28652" xml:space="preserve">hora 9. </s>
  <s xml:id="echoid-s28653" xml:space="preserve">ab <lb/>ortu; </s>
  <s xml:id="echoid-s28654" xml:space="preserve">Item hora 21. </s>
  <s xml:id="echoid-s28655" xml:space="preserve">ab occaſu in horologio occidentali. </s>
  <s xml:id="echoid-s28656" xml:space="preserve">Sedes autem eiuſdem eſt punctum A, vbi <lb/>coeunt linea æquinoctialis, horizontalis, linea horæ 6. </s>
  <s xml:id="echoid-s28657" xml:space="preserve">à meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s28658" xml:space="preserve">horæ 12. </s>
  <s xml:id="echoid-s28659" xml:space="preserve">ab <lb/>ortu, vel occaíu. </s>
  <s xml:id="echoid-s28660" xml:space="preserve">Quæ omnia ex demonſtratis in libro 2. </s>
  <s xml:id="echoid-s28661" xml:space="preserve">perſpicua ſunt.</s>
  <s xml:id="echoid-s28662" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1478" type="float" level="2" n="12">
<note position="left" xlink:label="note-0452-03" xlink:href="note-0452-03a" xml:space="preserve">Quo pacto pro <lb/>blema propoſi-<lb/>tum abſolua-<lb/>tur in horolo-<lb/>gio Meridiano</note>
  <figure xlink:label="fig-0452-01" xlink:href="fig-0452-01a">
    <image file="0452-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0452-01"/>
  </figure>
<note position="left" xlink:label="note-0452-04" xlink:href="note-0452-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0452-05" xlink:href="note-0452-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0452-06" xlink:href="note-0452-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s28663" xml:space="preserve">QVARTO ſit horologium polare C, in quo æquinoctialis linea A B, meridiana B D, hori-<lb/>
<anchor type="note" xlink:label="note-0452-07a" xlink:href="note-0452-07"/>
zontalis D E, ſtylus B F, eiusq́ue locus in B, vbi ſe interſecant linea meridiana, &amp; </s>
  <s xml:id="echoid-s28664" xml:space="preserve">æquinoctialis. </s>
  <s xml:id="echoid-s28665" xml:space="preserve">Ex <lb/>puncto A, vbi hora 3. </s>
  <s xml:id="echoid-s28666" xml:space="preserve">à meridie, vel 9 à media nocte, aut 9. </s>
  <s xml:id="echoid-s28667" xml:space="preserve">ab ortu, aut 21. </s>
  <s xml:id="echoid-s28668" xml:space="preserve">ab occaſu, vel deniq; <lb/></s>
  <s xml:id="echoid-s28669" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28670" xml:space="preserve">ab ortu, vel 15. </s>
  <s xml:id="echoid-s28671" xml:space="preserve">ab occaſu æquinoctialem lineam diuidit, ad punctum D, in quo mutuo ſe diui-<lb/>dunt linea meridiana, &amp; </s>
  <s xml:id="echoid-s28672" xml:space="preserve">horizontalis, ducatur recta A D. </s>
  <s xml:id="echoid-s28673" xml:space="preserve">Angulus enim A D B, ęqualis erit alti-<lb/>
<anchor type="note" xlink:label="note-0452-08a" xlink:href="note-0452-08"/>
tudini poli ſupra Horizontem dati horologii, ſeu inclinationi eiuſdem ad Horizontem. </s>
  <s xml:id="echoid-s28674" xml:space="preserve">Styli ve-<lb/>rò longitudo perpetuo æqualis eſt ſpatio in linea æquinoctiali inter B, &amp; </s>
  <s xml:id="echoid-s28675" xml:space="preserve">punctum A, per quod di <lb/>ctæ horæ ducuntur, eiuſq́ue locus in B, vt ex iis, quæ lib. </s>
  <s xml:id="echoid-s28676" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28677" xml:space="preserve">demõſtrauimus, manifeſtum eſt. </s>
  <s xml:id="echoid-s28678" xml:space="preserve">Quod <lb/>
<anchor type="note" xlink:label="note-0452-09a" xlink:href="note-0452-09"/>
ſi horizontalis linea deſcripta non fuerit, contineatq́ue horologium horas duntaxat à meridie, &amp; </s>
  <s xml:id="echoid-s28679" xml:space="preserve"><lb/>media nocte monſtrabit horologium dictas horas in omni regione, ſi vt in propoſ. </s>
  <s xml:id="echoid-s28680" xml:space="preserve">38. </s>
  <s xml:id="echoid-s28681" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s28682" xml:space="preserve">do-<lb/>cuimus, in proprio ſitu collocetur.</s>
  <s xml:id="echoid-s28683" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1479" type="float" level="2" n="13">
<note position="left" xlink:label="note-0452-07" xlink:href="note-0452-07a" xml:space="preserve">Idem proble-<lb/>ma in horolo-<lb/>gio polari, quo <lb/>modo abſolua-<lb/>@ur.</note>
<note position="left" xlink:label="note-0452-08" xlink:href="note-0452-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0452-09" xlink:href="note-0452-09a" xml:space="preserve">Qua ratione <lb/>horologium po <lb/>lare Aſtrono-<lb/>mieum ſit vni-<lb/>uerſale.</note>
</div>
<p>
  <s xml:id="echoid-s28684" xml:space="preserve">QVINTO datum ſit æquinoctiale horologium D, in quo meridiana linea A B; </s>
  <s xml:id="echoid-s28685" xml:space="preserve">horizonta-<lb/>
<anchor type="note" xlink:label="note-0452-10a" xlink:href="note-0452-10"/>
lis A C; </s>
  <s xml:id="echoid-s28686" xml:space="preserve">ſtylus B E, eiuſq́ue locus in B, centro, vbi omnes horæ à meridie, &amp; </s>
  <s xml:id="echoid-s28687" xml:space="preserve">media nocte ſe inter-<lb/>ſecant. </s>
  <s xml:id="echoid-s28688" xml:space="preserve">Ex B, excitetur ad lineam meridianam perpendicularis B F, ſtylo ęqualis, (quę quidem in <lb/>horologio Aſtronomico eadem erit, quæ linea horæ 6. </s>
  <s xml:id="echoid-s28689" xml:space="preserve">à meridie, vel media nocte) &amp; </s>
  <s xml:id="echoid-s28690" xml:space="preserve">iungatur
<pb o="437" file="0453" n="453" rhead="LIBER QVARTVS."/>
recta F A; </s>
  <s xml:id="echoid-s28691" xml:space="preserve">Erit enim A F B, angulus altitudinis poli, &amp; </s>
  <s xml:id="echoid-s28692" xml:space="preserve">B A F, angulus inclinationis horologij ad <lb/>Horizontem, nempe altitudinis Aequatoris ſupra Horizontem. </s>
  <s xml:id="echoid-s28693" xml:space="preserve">Styli porrò longitudo, cuius lo-<lb/>cus eſt in centro B, vbi conueniunt lineæ horarum à meridie, &amp; </s>
  <s xml:id="echoid-s28694" xml:space="preserve">media nocte, inuenietur ex nota <lb/>poli altitudine, hac ratione. </s>
  <s xml:id="echoid-s28695" xml:space="preserve">Ex A, puncto, vbi meridiana linea, &amp; </s>
  <s xml:id="echoid-s28696" xml:space="preserve">horizontalis ſe interſecant, egre-<lb/>diatur recta A F, faciens angulum BAF, complemento altitudinis poli æqualem, &amp; </s>
  <s xml:id="echoid-s28697" xml:space="preserve">ex B, centro <lb/>educta perpendicularis B F, ad meridianam lineam ſecet A F, in F. </s>
  <s xml:id="echoid-s28698" xml:space="preserve">Erit namque B F, longitudo <lb/>ſtyli, vt conſtat ex iis, quæ in ſuperiori libro demonſtrata ſunt. </s>
  <s xml:id="echoid-s28699" xml:space="preserve">Si verò horologium contineat ſo-<lb/>
<anchor type="note" xlink:label="note-0453-01a" xlink:href="note-0453-01"/>
lum horas à meridie, &amp; </s>
  <s xml:id="echoid-s28700" xml:space="preserve">media nocte, careatq́ue linea horizontali, indicabit horologium horas <lb/>vbique gentium, ſi, vt in propoſ. </s>
  <s xml:id="echoid-s28701" xml:space="preserve">49. </s>
  <s xml:id="echoid-s28702" xml:space="preserve">libri 2. </s>
  <s xml:id="echoid-s28703" xml:space="preserve">tradidimus, ponatur in ſitu propriu, poteritq́ue ſtylus <lb/>cuiuſque longitudinis aſſumi, ſi circuli ſignorum in horologio deſcripti non fuerint.</s>
  <s xml:id="echoid-s28704" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1480" type="float" level="2" n="14">
<note position="left" xlink:label="note-0452-10" xlink:href="note-0452-10a" xml:space="preserve">Explicatio pro-<lb/>blematis in ho <lb/>@ologio æqui-<lb/>@octiali.</note>
<note position="right" xlink:label="note-0453-01" xlink:href="note-0453-01a" xml:space="preserve">Horologium <lb/>æquinoctiale <lb/>Aſtronomieú<unsure/> <lb/>quo pacto ſit <lb/>vniuerſale.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve">Problema ex-<lb/>plicatur in ho-<lb/>@ologio decli-<lb/>nante à Verri-<lb/>cali.</note>
<p>
  <s xml:id="echoid-s28705" xml:space="preserve">PROPONATVR ſexto horologium à Verticali declinans A, vt in ſequentibus figuris, <lb/>(Erit autem declinans à Verticali, quando linea horizontalis per locum ſtyli ducitur, vt in horo-<lb/>logijs Verticalibus, at lineæ æquinoctiali non æquidiſtat, quod quidẽ in Verticalibus horologijs <lb/>fit, ſed eam ſecat, non tamen in loco ſtyli, vt in Meridianis horologijs accidit) in quo meridiana <lb/>linea B C; </s>
  <s xml:id="echoid-s28706" xml:space="preserve">æquinoctialis D E; </s>
  <s xml:id="echoid-s28707" xml:space="preserve">horizontalis D F; </s>
  <s xml:id="echoid-s28708" xml:space="preserve">ſtylus F G, eiuſq́ue locus in F; </s>
  <s xml:id="echoid-s28709" xml:space="preserve">linea ſtyli E F, quæ ſi <lb/>
<anchor type="figure" xlink:label="fig-0453-01a" xlink:href="fig-0453-01"/>
<anchor type="note" xlink:label="note-0453-04a" xlink:href="note-0453-04"/>
<anchor type="note" xlink:label="note-0453-05a" xlink:href="note-0453-05"/>
fortaſſis ducta non eſt, habebitur, ſi per F, locũ ſtyli ad æquinoctialem lineam excitetur perpen-<lb/>dicularis F E. </s>
  <s xml:id="echoid-s28710" xml:space="preserve">Ita igitur altitudinem poli ſupra Horizontem, ad quam fabricatum eſt horologiũ, <lb/>eiuſq́ue declinationem à Verticali, &amp; </s>
  <s xml:id="echoid-s28711" xml:space="preserve">altitudinem poli ſupra ipſum planum declinans inquire-<lb/>mus. </s>
  <s xml:id="echoid-s28712" xml:space="preserve">Ex F, loco ſtyli erigemus ad lineam ſtyli E F, perpendicularem F H, ſtylo F G, æqualem, &amp; </s>
  <s xml:id="echoid-s28713" xml:space="preserve"><lb/>ex B, centro horologii, in quo videlicet linea ſtyli producta cum meridiana linea conuenit, per H, <lb/>rectam ducemus B H, quæ ſecet æquinoctialem lineam in I. </s>
  <s xml:id="echoid-s28714" xml:space="preserve">Deinde per E, vbi æquinoctialem <lb/>lineam ſecat linea ſtyli, ducta recta E C, parallela lineæ horizontali, excitabimus ad eam perpen-<lb/>
<anchor type="note" xlink:label="note-0453-06a" xlink:href="note-0453-06"/>
dicularem E K, rectæ E I, æqualem, iungemuſq́ue rectam K C. </s>
  <s xml:id="echoid-s28715" xml:space="preserve">Poſtremo ſumpta recta C L, ipſi <lb/>C K, æquali, ducemus rectam L B. </s>
  <s xml:id="echoid-s28716" xml:space="preserve">Nam B L C, angulus erit altitudinis poli ſupra Horizontem; <lb/></s>
  <s xml:id="echoid-s28717" xml:space="preserve">K C M, angulus declinationis à Verticali; </s>
  <s xml:id="echoid-s28718" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28719" xml:space="preserve">E B I, angulus altitudinis poli ſupra planum decli-<lb/>nans. </s>
  <s xml:id="echoid-s28720" xml:space="preserve">Ipſum autem horologium à meridie declinabit, ſi centrum B, extiterit ſupra lineam hori-<lb/>zontalem, à borea verò, ſi infra; </s>
  <s xml:id="echoid-s28721" xml:space="preserve">atque in ortum verget à meridie, ſi ex parte dextra linea æqui-<lb/>noctialis infra lineam horizontalem cadit, in occaſum autem, ſi ex parte ſiniſtra. </s>
  <s xml:id="echoid-s28722" xml:space="preserve">At verò à borea <lb/>deflectet in ortum, ſi linea æquinoctialis ex parte ſiniſtra cadit infra horizontalem lineam, in oc-<lb/>caſum verò, ſi ex parte dextra. </s>
  <s xml:id="echoid-s28723" xml:space="preserve">Quæ omnia liquido colliguntur ex ijs, quę in propoſ. </s>
  <s xml:id="echoid-s28724" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28725" xml:space="preserve">ſuperio-<lb/>ris libri à nobis ſunt demonſtrata, ſi attente conſidere@ur conſtructio horologii à Verticali decli <lb/>nantis eo loco tradita.</s>
  <s xml:id="echoid-s28726" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1481" type="float" level="2" n="15">
  <figure xlink:label="fig-0453-01" xlink:href="fig-0453-01a">
    <image file="0453-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0453-01"/>
  </figure>
<note position="left" xlink:label="note-0453-04" xlink:href="note-0453-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0453-05" xlink:href="note-0453-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0453-06" xlink:href="note-0453-06a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s28727" xml:space="preserve">SED data iam ſit altitudo poli ſupra Horizontem, ad quam conſtructum eſt horologium, <lb/>oporteatq́ue inueſtigare longitudinem ſtyli, (cuius quidem locus ſemper eſt in huiuſmodi horo-<lb/>logio in puncto, vbi linea ſtyli horizontalem interſecat,) declinationemq́ue à Verticali, &amp; </s>
  <s xml:id="echoid-s28728" xml:space="preserve">altitu-<lb/>dinem pol iſupra planum declinans. </s>
  <s xml:id="echoid-s28729" xml:space="preserve">Ex B, centro horologii, vbi conueniunt linea horizontalis, <lb/>&amp; </s>
  <s xml:id="echoid-s28730" xml:space="preserve">linea ſtyli, egrediatur recta B L, faciens cum meridiana linea angulum C B L, complementi <lb/>altitudinis poli ſupra Horizontem: </s>
  <s xml:id="echoid-s28731" xml:space="preserve">ductaq́ue ex E, puncto, quod linea ſtyli &amp; </s>
  <s xml:id="echoid-s28732" xml:space="preserve">æquinoctiali com-<lb/>mune eſt, recta E C, horizontali lineæ parallela ſecet B L, in L, &amp; </s>
  <s xml:id="echoid-s28733" xml:space="preserve">meridianam lineam in C. </s>
  <s xml:id="echoid-s28734" xml:space="preserve">De-<lb/>inde ex E, ad E C, excitetur perpendicularis E K, &amp; </s>
  <s xml:id="echoid-s28735" xml:space="preserve">ex C, arcus circuli ad interuallum rectę C L, <lb/>deſcribatur ſecans E K, in K, ducaturq́ue recta C K. </s>
  <s xml:id="echoid-s28736" xml:space="preserve">Poſtremo abſcindatur in linea æquinoctiali <lb/>rectæ E K, æqualis E I, iunctaq́ue recta I B, excitetur ad lineam ſtyli ex F, loco ſtyli perpendicula-
<pb o="438" file="0454" n="454" rhead="GNOMONICES"/>
ris F H, ſecans I B, in H. </s>
  <s xml:id="echoid-s28737" xml:space="preserve">Erit ergo F H, longitudo ſtyli in F, ponendi, &amp; </s>
  <s xml:id="echoid-s28738" xml:space="preserve">K C M, angulus decli-<lb/>nationis à Verticali; </s>
  <s xml:id="echoid-s28739" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28740" xml:space="preserve">E B I, angulus altitudinis poli ſupra planum declinans, vt conſtat ex ijs, <lb/>quæ in conſtructione huiuſce horologii propoſ. </s>
  <s xml:id="echoid-s28741" xml:space="preserve">1. </s>
  <s xml:id="echoid-s28742" xml:space="preserve">ſuperioris libri demõſtrauimus. </s>
  <s xml:id="echoid-s28743" xml:space="preserve">Vtrum autem <lb/>horologium declinet à meridie, vel ſeptentrione in ortum, occaſumve, cognoſcemus, vt prius <lb/>dictum eſt.</s>
  <s xml:id="echoid-s28744" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28745" xml:space="preserve">SEPTIMO datum ſit horologium B, ab Horizonte declinans, (tunc autem ab Horizonte <lb/>
<anchor type="note" xlink:label="note-0454-01a" xlink:href="note-0454-01"/>
declinabit, cum linea horizontalis meridianæ lineæ fuerit parallela) in quo linea meridiana A C; <lb/></s>
  <s xml:id="echoid-s28746" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0454-01a" xlink:href="fig-0454-01"/>
<anchor type="note" xlink:label="note-0454-02a" xlink:href="note-0454-02"/>
<anchor type="note" xlink:label="note-0454-03a" xlink:href="note-0454-03"/>
æquinoctialis D E; </s>
  <s xml:id="echoid-s28747" xml:space="preserve">horizontalis D N; </s>
  <s xml:id="echoid-s28748" xml:space="preserve">ſtylus F G, eiuſq́ue locus in F; </s>
  <s xml:id="echoid-s28749" xml:space="preserve">linea ſtyli E F, ducta ex F, lo-<lb/>co ſtyli ad lineam æquinoctialem perpendicularis, ſecanſq́ue producta lineam meridianam in A, <lb/>centro horologii. </s>
  <s xml:id="echoid-s28750" xml:space="preserve">Ducatur ex F, loco ſtyli ad lineam ſtyli perpendicularis F H, ſtylo F G, æqualis, <lb/>&amp; </s>
  <s xml:id="echoid-s28751" xml:space="preserve">ex A, centro horologii per H, recta ducta ſecet æquinoctialem lineam in I. </s>
  <s xml:id="echoid-s28752" xml:space="preserve">Rurſus per E, pun-<lb/>ctum, vbi ſe interſecant linea ſtyli, &amp; </s>
  <s xml:id="echoid-s28753" xml:space="preserve">æquinoctialis, excitetur ad meridianam lineam petpendi-<lb/>
<anchor type="note" xlink:label="note-0454-04a" xlink:href="note-0454-04"/>
cularis E C, ad quam ex E, alia perdendicularis erigatur E K, ipſi E I, æqualis, iungaturq́ue recta <lb/>K C. </s>
  <s xml:id="echoid-s28754" xml:space="preserve">Sumpta tandem C L, æquali ipſi C K, ducatur recta L A. </s>
  <s xml:id="echoid-s28755" xml:space="preserve">Erit igitur A L C, angulus altitu-<lb/>dinis poli ſupra Horizontem; </s>
  <s xml:id="echoid-s28756" xml:space="preserve">K C M, angulus inclinationis ad Horizontem, ſeu declinationis ab <lb/>Horizonte, &amp; </s>
  <s xml:id="echoid-s28757" xml:space="preserve">E A I, angulus altitudinis poli ſupra planum horologii. </s>
  <s xml:id="echoid-s28758" xml:space="preserve">Vtrum autem horologi-<lb/>um ad occaſum ſpecter, an ad ortũ, (Loquor autem hic de ſuperioribus duntaxat horologiis, quæ <lb/>videlicet ad Zenith pertinẽt, quod &amp; </s>
  <s xml:id="echoid-s28759" xml:space="preserve">in duobus ſequentibus generibus faciemus, propterea quod <lb/>inferiora, quæ nimirum ad Nadir ſpectant, minus in vſu ſunt, &amp; </s>
  <s xml:id="echoid-s28760" xml:space="preserve">illis doctrina de ſuperioribus <lb/>tradita facile poteſt accommodari) facile intelligemus. </s>
  <s xml:id="echoid-s28761" xml:space="preserve">Si enim poſito horologio, vt centrum A, <lb/>ad meridiem vergat, horizontalis linea fuerit orientalior, quàm meridiana, ſpectabit ad occaſum, <lb/>ad octum verò, ſi horizontalis linea occidentalior extiterit, quàm meridiana. </s>
  <s xml:id="echoid-s28762" xml:space="preserve">Quæ omnia patent <lb/>
<anchor type="note" xlink:label="note-0454-05a" xlink:href="note-0454-05"/>
ex demonſtratis in conſtructione huiuſmodi horologii propoſ. </s>
  <s xml:id="echoid-s28763" xml:space="preserve">13. </s>
  <s xml:id="echoid-s28764" xml:space="preserve">ſuperioris libri.</s>
  <s xml:id="echoid-s28765" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1482" type="float" level="2" n="16">
<note position="left" xlink:label="note-0454-01" xlink:href="note-0454-01a" xml:space="preserve">In horologio, <lb/>quod ab Hori-<lb/>@onte declinat, <lb/>idẽ pro blema <lb/>@@peditu<unsure/>r.</note>
  <figure xlink:label="fig-0454-01" xlink:href="fig-0454-01a">
    <image file="0454-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0454-01"/>
  </figure>
<note position="left" xlink:label="note-0454-02" xlink:href="note-0454-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0454-03" xlink:href="note-0454-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0454-04" xlink:href="note-0454-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0454-05" xlink:href="note-0454-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s28766" xml:space="preserve">NOTA iam ſit altitudo poli ſupra Horizontem, ad quam fabricatum eſt horologium, opor-<lb/>teatq́ue indagare reliqua. </s>
  <s xml:id="echoid-s28767" xml:space="preserve">Ex A, centro horologii, vbi meridiana linea à linea ſtyli producta ſeca-<lb/>tur, emittatur recta A L, faciens angulum C A L, complementi altitudinis poli, ſecetq́ue recta <lb/>A L, perpendicularem E C, quæ ex E, ad meridianam lineam ducitur, in L. </s>
  <s xml:id="echoid-s28768" xml:space="preserve">Ducta quoque E K, <lb/>ad E C, perpendiculari, deſcribatur ex C, ad interuallum rectæ C L, arcus circuli ſecans E K, in K, <lb/>ducaturq́ue recta C K. </s>
  <s xml:id="echoid-s28769" xml:space="preserve">Deinde in æquinoctiali linea ſumatur E I, rectæ E K, æqualis, &amp; </s>
  <s xml:id="echoid-s28770" xml:space="preserve">iungatur <lb/>recta I A. </s>
  <s xml:id="echoid-s28771" xml:space="preserve">Poſtremo vel ducta ex D, puncto, vbi ſe ſe interſecant linea horizontalis, &amp; </s>
  <s xml:id="echoid-s28772" xml:space="preserve">æquinoctia <lb/>lis, ad horizontalem lineam perpendiculari D F, ſecante lineam ſtyli in F, ducatur ex F, ad lineam <lb/>ſtyli perpendicularis F H, ſecans rectam A I, in H; </s>
  <s xml:id="echoid-s28773" xml:space="preserve">vel deſcripto ſemicirculo A H E, circa A E, ſe-<lb/>
<anchor type="note" xlink:label="note-0454-06a" xlink:href="note-0454-06"/>
cante rectam A I, in H, ducatur ex H, ad lineam ſtyli perpendicularis H F, ſecans lineam ſtyli in <lb/>F. </s>
  <s xml:id="echoid-s28774" xml:space="preserve">Erit namque F H, longitudo ſtyli, eiuſq́ue locus in F; </s>
  <s xml:id="echoid-s28775" xml:space="preserve">at K C M, erit angulus declinationis ab <lb/>Horizonte, &amp; </s>
  <s xml:id="echoid-s28776" xml:space="preserve">E A I, angulus altitudinis poli ſupra planum horologii. </s>
  <s xml:id="echoid-s28777" xml:space="preserve">Quod ex demonſtratis in <lb/>propoſ. </s>
  <s xml:id="echoid-s28778" xml:space="preserve">13. </s>
  <s xml:id="echoid-s28779" xml:space="preserve">ſuperioris libri facile colligitur.</s>
  <s xml:id="echoid-s28780" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1483" type="float" level="2" n="17">
<note position="left" xlink:label="note-0454-06" xlink:href="note-0454-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s28781" xml:space="preserve">OCTAVO ſit propoſitum horologium C, inclinatum ad Horizontem, (Erit autem tunc <lb/>
<anchor type="note" xlink:label="note-0454-07a" xlink:href="note-0454-07"/>
inclinatum ad Horizontem, cum linea horizontalis lineę æquinoctiali fuerit parallela, nõ tamen <lb/>per locum ſtyli trãſierit, vt in Verticalibus horologiis fieri ſolet) in quo linea meridiana A B; </s>
  <s xml:id="echoid-s28782" xml:space="preserve">æqui <lb/>noctialis D E; </s>
  <s xml:id="echoid-s28783" xml:space="preserve">horizontalis A F; </s>
  <s xml:id="echoid-s28784" xml:space="preserve">ſtylus G H, eiusq́ue locus in G. </s>
  <s xml:id="echoid-s28785" xml:space="preserve">Primum omnium conſiderandũ <lb/>erit, num horologium ad meridiem ſpectet, an ad boream, hoc eſt, an ex parte ſeptentrionis ſupra <lb/>Horizontem eleuetur, an ex parte meridiei. </s>
  <s xml:id="echoid-s28786" xml:space="preserve">Hoc autem ex ordine horarum ſine magno labore
<pb o="439" file="0455" n="455" rhead="LIBER QVARTVS."/>
conſequemur. </s>
  <s xml:id="echoid-s28787" xml:space="preserve">Si namque horologio ad nos conuerſo, vt horizontalis linea ſupra ſtylum exiſtat, <lb/>horæ pomeridianæ ad ſiniſtram lineæ meridianæ collocatæ ſint, &amp; </s>
  <s xml:id="echoid-s28788" xml:space="preserve">antemeridianæ ad dextram, <lb/>(ſunt autem in aſtronomico horologio horæ pomeridianę hæ, 1. </s>
  <s xml:id="echoid-s28789" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28790" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28791" xml:space="preserve">4. </s>
  <s xml:id="echoid-s28792" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28793" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28794" xml:space="preserve">In Italico hæ, 24. <lb/></s>
  <s xml:id="echoid-s28795" xml:space="preserve">23. </s>
  <s xml:id="echoid-s28796" xml:space="preserve">22. </s>
  <s xml:id="echoid-s28797" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28798" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28799" xml:space="preserve">in Babylonico verò antem eridianæ ſunt iſtæ, 1. </s>
  <s xml:id="echoid-s28800" xml:space="preserve">2. </s>
  <s xml:id="echoid-s28801" xml:space="preserve">3. </s>
  <s xml:id="echoid-s28802" xml:space="preserve">4. </s>
  <s xml:id="echoid-s28803" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s28804" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s28805" xml:space="preserve">inclinatum erit horolo-<lb/>gium ad partes auſtri, ſpectabitq́ue ad ſeptentrionem: </s>
  <s xml:id="echoid-s28806" xml:space="preserve">Contra verò, ſi poſitæ ſint horæ pomeri-<lb/>dianæ ad dextram lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s28807" xml:space="preserve">ad ſiniſtram antemeridianæ, ex parte ſeptentrionis inclina <lb/>tum erit horologium ad Horizontem, ſpectabitq́ue in auſtrum. </s>
  <s xml:id="echoid-s28808" xml:space="preserve">Deinde intueri oportebit, an pla <lb/>num ex parte boreæ eleuatum minorem habeat inclinationem ad Horizontem altitudine poli ſu <lb/>pra Horizontem, an verò maiorem; </s>
  <s xml:id="echoid-s28809" xml:space="preserve">Item num planum ex auſtrali parte eleuatum minorem ha-<lb/>beat ad Horizontem inclinationem, an maiorem complemento altitudinis poli ſupra Horizon-<lb/>
<anchor type="note" xlink:label="note-0455-01a" xlink:href="note-0455-01"/>
tem, hoc eſt, altitudine Aequatoris ſupra Horizontem. </s>
  <s xml:id="echoid-s28810" xml:space="preserve">Quod quidem ex quatuor illis Analem-<lb/>matibus in propoſ. </s>
  <s xml:id="echoid-s28811" xml:space="preserve">25. </s>
  <s xml:id="echoid-s28812" xml:space="preserve">ſuperioris libri poſitis clariſſime<unsure/> intelligemus. </s>
  <s xml:id="echoid-s28813" xml:space="preserve">Horologia enim ex parte <lb/>boreali eleuata, quorum centra infra lineam æquinoctialem exiſtunt, minorem habent inclinatio-<lb/>nem ad Horizontem altitudine poli ſupra Horizontem, quorum verò centra ſupra lineam æqui-<lb/>noctialem reperiuntur, maiorem. </s>
  <s xml:id="echoid-s28814" xml:space="preserve">Et ſi horologium aliquod careat centro, ita vt lineæ horarum <lb/>à meridie, &amp; </s>
  <s xml:id="echoid-s28815" xml:space="preserve">media nocte parallelæ ſint, aut ſtylus ponatur in communi ſectione lineæ meridia-<lb/>næ, &amp; </s>
  <s xml:id="echoid-s28816" xml:space="preserve">æquinoctialis, inclinatio æqualis erit altitudini poli, &amp; </s>
  <s xml:id="echoid-s28817" xml:space="preserve">horologium idem erit, quod pola-<lb/>re. </s>
  <s xml:id="echoid-s28818" xml:space="preserve">Contra verò horologia ex auſtrali parte eleuata, quorum centra infra lineam æquinoctialem <lb/>continentur, maiorem obtinent inclinationem altitudine Aequatoris, minorem verò, quorum <lb/>centra ſupra æquinoctialem lineam exiſtunt. </s>
  <s xml:id="echoid-s28819" xml:space="preserve">Quod ſi horologium aliquod habeat ſedem ſtyli in <lb/>
<anchor type="note" xlink:label="note-0455-02a" xlink:href="note-0455-02"/>
ipſo centro horologij, æqualis erit eius inclinatio ad Horizontem altitudini Aequatoris, &amp; </s>
  <s xml:id="echoid-s28820" xml:space="preserve">ab <lb/>æquinoctiali horologio non differet.</s>
  <s xml:id="echoid-s28821" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1484" type="float" level="2" n="18">
<note position="left" xlink:label="note-0454-07" xlink:href="note-0454-07a" xml:space="preserve">Tract@tur pro-<lb/>poſitum proble <lb/>m<unsure/>a in horolo-<lb/>gio ad Horizon <lb/>tem inclinato.</note>
<note position="left" xlink:label="note-0455-01" xlink:href="note-0455-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0455-02" xlink:href="note-0455-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s28822" xml:space="preserve">HIS ita poſitis, exequemur id, quod proponitur, hac ratione. </s>
  <s xml:id="echoid-s28823" xml:space="preserve">Ex G, loco ſtyli erigatur ad <lb/>meridianam lineam perpendicularis G I, ſtylo G H, æqualis, &amp; </s>
  <s xml:id="echoid-s28824" xml:space="preserve">ex I, ad centrũ horologij B, quod <lb/>inuenietur, vt paulo ante in horizontali horologio diximus, &amp; </s>
  <s xml:id="echoid-s28825" xml:space="preserve">ad punctum A, vbi meridiana li-<lb/>nea horizontalem interſecat, rectæ ducantur I B, I A. </s>
  <s xml:id="echoid-s28826" xml:space="preserve">Nam G B I, erit angulus altitudinis poli <lb/>ſupra planum inclinatum, &amp; </s>
  <s xml:id="echoid-s28827" xml:space="preserve">G A I, angulus inclinationis eiuſdem plani ad Horizontem, vt con-<lb/>ſtat ex demonſtratis propoſ. </s>
  <s xml:id="echoid-s28828" xml:space="preserve">25. </s>
  <s xml:id="echoid-s28829" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28830" xml:space="preserve">26. </s>
  <s xml:id="echoid-s28831" xml:space="preserve">ſuperioris libri.</s>
  <s xml:id="echoid-s28832" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28833" xml:space="preserve">EX his autem duobus, &amp; </s>
  <s xml:id="echoid-s28834" xml:space="preserve">ijs, quæ proximè ſcripſimus, facile altitudinem poli, ad quam pro-<lb/>poſitum horologium fabricatum eſt, eliciemus. </s>
  <s xml:id="echoid-s28835" xml:space="preserve">Nam ſi horologium ex parte ſeptentrionali ſupra <lb/>Horizontem attollatur, habeatq́ue minorem inclinationem altitudine poli ſupra Horizontem, ad-<lb/>
<anchor type="note" xlink:label="note-0455-03a" xlink:href="note-0455-03"/>
denda erit altitudo poli ſupra planum inuenta inclinationi eiuſdem plani inuentæ. </s>
  <s xml:id="echoid-s28836" xml:space="preserve">Numerus <lb/>enim conflatus dabit altitudinem poli ſupra Horizontem: </s>
  <s xml:id="echoid-s28837" xml:space="preserve">ſi verò maiorem habeat inclinationem <lb/>altitudine poli ſupra Horizontem, detrahenda erit altitudo poli ſupra planum ex eius inclinatio-<lb/>ne, vt relinquatur altitudo poli ſupra Horizontem. </s>
  <s xml:id="echoid-s28838" xml:space="preserve">Quod ſi horologium eleuetur ex auſtrali par <lb/>te, habeatq́ue minorem inclinationem altitudine Aequatoris ſupra Horizontem, ſiue complemẽ <lb/>to altitudinis poli ſupra Horizontem, addendum erit complementum inuentæ altitudinis poli <lb/>ſupra planum inclinationi inuentæ. </s>
  <s xml:id="echoid-s28839" xml:space="preserve">Habebitur enim ex hac additione complementum altitudi-<lb/>nis poli ſupra Horizontem, ex quo ſtatim ipſa altitudo poli nota fiet. </s>
  <s xml:id="echoid-s28840" xml:space="preserve">Si verò inclinationem ha-<lb/>beat maiorem altitudine Aequatoris ſupra Horizontem, ſeu complemento altitudinis poli ſupra <lb/>Horizontem, auferendum erit complementum inuentæ altitudinis poli ſupra planum ex inclina <lb/>
<anchor type="note" xlink:label="note-0455-04a" xlink:href="note-0455-04"/>
tione inuenta. </s>
  <s xml:id="echoid-s28841" xml:space="preserve">Relinquetur enim poſt hanc ſubtractionem complementum altitudinis poli ſupra <lb/>Horizontẽ, ex quo rurſus altitudo ipſa poli elicietur. </s>
  <s xml:id="echoid-s28842" xml:space="preserve">Quæ omnia ex dictis Analemmatibus pro-<lb/>poſ. </s>
  <s xml:id="echoid-s28843" xml:space="preserve">25. </s>
  <s xml:id="echoid-s28844" xml:space="preserve">ſuperioris libri perſpicua ſunt.</s>
  <s xml:id="echoid-s28845" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1485" type="float" level="2" n="19">
<note position="left" xlink:label="note-0455-03" xlink:href="note-0455-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0455-04" xlink:href="note-0455-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s28846" xml:space="preserve">VERVM data ſit altitudo poli ſupra Horizontem, ad quam horologium eſt conſtructum, <lb/>vna cum inclinatione plani ſupra Horizontem, (Nam ex ſola altitudine poli ſupra Horizontem <lb/>nihil certi colligi poteſt) oporteatq́ue ex his inueſtigare &amp; </s>
  <s xml:id="echoid-s28847" xml:space="preserve">altitudinem poli ſupra planum, &amp; </s>
  <s xml:id="echoid-s28848" xml:space="preserve">lon <lb/>gitudinem ſtyli, eiusq́ue locum. </s>
  <s xml:id="echoid-s28849" xml:space="preserve">Primum itaque ex ordine horarum, &amp; </s>
  <s xml:id="echoid-s28850" xml:space="preserve">ſitu centri horologii di-<lb/>ſcemus, vt paulo ante docuimus, an planum horologii eleuatum ſit ex parte boreali, an auſtrali, &amp; </s>
  <s xml:id="echoid-s28851" xml:space="preserve"><lb/>an inclinatio illius maior ſit, minorve altitudine poli, Aequatorisve ſupra Horizontem. </s>
  <s xml:id="echoid-s28852" xml:space="preserve">Nam ſi <lb/>eleuetur ex parte boreali, habeatq́ue inclinationem minorem altitudine poli ſupra Horizontem, <lb/>
<anchor type="note" xlink:label="note-0455-05a" xlink:href="note-0455-05"/>
ſubtrahenda erit inclinatio ex poli altitudine, ſi verò maiorem habeat inclinationem, auferenda <lb/>erit altitudo poli ex inclinatione. </s>
  <s xml:id="echoid-s28853" xml:space="preserve">Vtrobique enim relinquetur altitudo poli ſupra planum. </s>
  <s xml:id="echoid-s28854" xml:space="preserve">At ſi <lb/>horologium ex parte auſtrali eleuetur, habeatq́ue inclinationem minorem altitudine Aequatoris, <lb/>auferenda erit inclinatio ex altitudine Aequatoris, ſi verò maiorem habeat inclinationem, demen <lb/>da erit ex inclinatione altitudo Aequatoris. </s>
  <s xml:id="echoid-s28855" xml:space="preserve">Ita enim ſemper reliquum erit complementum al-<lb/>titudinis poli ſupra planum, vt ex dictis Analemmatibus conſtat: </s>
  <s xml:id="echoid-s28856" xml:space="preserve">Vnde &amp; </s>
  <s xml:id="echoid-s28857" xml:space="preserve">altitudo ipſa poli co-<lb/>gnita erit. </s>
  <s xml:id="echoid-s28858" xml:space="preserve">Ex qua dicto citius ſtyli magnitudinem, locumq́ue inquiremus. </s>
  <s xml:id="echoid-s28859" xml:space="preserve">Deſcripto enim ſe-<lb/>micirculo B I D, circa portionem meridianæ lineæ B D, inter centrum horologii, (quod inuenie-<lb/>mus, vt ante tradidimus in horizontali horologio) &amp; </s>
  <s xml:id="echoid-s28860" xml:space="preserve">lineam æquinoctialem, ducemus ex B, cen-<lb/>tro horologij rectam B I, facientem cum B D, angulum D B I, altitudinis poli ſupra planum, quæ
<pb o="440" file="0456" n="456" rhead="GNOMONICES"/>
ſecet circumferentiam circuli in I. </s>
  <s xml:id="echoid-s28861" xml:space="preserve">Demiſſa enim ex I, ad B D, perpendicularis I G, dabit longitu-<lb/>dinem ſtyli, eiusq́ue locus erit in G; </s>
  <s xml:id="echoid-s28862" xml:space="preserve">vt paulo ante oſtendimus in horologi<unsure/>o horizontali.</s>
  <s xml:id="echoid-s28863" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1486" type="float" level="2" n="20">
<note position="left" xlink:label="note-0455-05" xlink:href="note-0455-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s28864" xml:space="preserve">QVOD ſi detur locus duntaxat ſtyli in G, reperiemus omnia alia hoc modo. </s>
  <s xml:id="echoid-s28865" xml:space="preserve">Deſcripto ſemi <lb/>circulo, vt prius, B I D, erigemus ad lineam meridianam ex G, loco ſtyli perpendicularem G I, quę <lb/>circulum ſecet in I, ducemusq́ue rectas I B, I A. </s>
  <s xml:id="echoid-s28866" xml:space="preserve">Nam G I, erit longitudo ſtyli; </s>
  <s xml:id="echoid-s28867" xml:space="preserve">I B G, angulus alti <lb/>tudinis poli ſupra planum; </s>
  <s xml:id="echoid-s28868" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s28869" xml:space="preserve">I A G, angulus inclinationis, vt ex dictis liquet. </s>
  <s xml:id="echoid-s28870" xml:space="preserve">Vnde, vt prius, alti-<lb/>tudinem poli ſupra Horizontem colligemus.</s>
  <s xml:id="echoid-s28871" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28872" xml:space="preserve">OFFERATVR tandem nono horologium &amp; </s>
  <s xml:id="echoid-s28873" xml:space="preserve">declinans à Verticali, &amp; </s>
  <s xml:id="echoid-s28874" xml:space="preserve">ad Horizontem in-<lb/>
<anchor type="note" xlink:label="note-0456-01a" xlink:href="note-0456-01"/>
clinatum (cognoſcemus autem huiuſmodi horologium, ſi linea horizontalis neque æquinoctia-<lb/>li lineæ, vt in inclinatis ad Horizontem, neque lineæ meridianæ, vt in declinantibus ab Hori-<lb/>
<anchor type="note" xlink:label="note-0456-02a" xlink:href="note-0456-02"/>
zonte, parallela eſt, neque meridianam lineam ad angulos rectos ſecat, neque ſtylus in horizon-<lb/>tali linea collo<unsure/>catur, vt in declinantibns à Verticali) in quo linea meridiana E ε; </s>
  <s xml:id="echoid-s28875" xml:space="preserve">æquinoctialis <lb/>G H; </s>
  <s xml:id="echoid-s28876" xml:space="preserve">horizontalis H M; </s>
  <s xml:id="echoid-s28877" xml:space="preserve">ſtylus K L; </s>
  <s xml:id="echoid-s28878" xml:space="preserve">eiuſque locus in K. </s>
  <s xml:id="echoid-s28879" xml:space="preserve">Ante omnia conſiderandum hic quoque <lb/>
<anchor type="figure" xlink:label="fig-0456-01a" xlink:href="fig-0456-01"/>
<anchor type="note" xlink:label="note-0456-03a" xlink:href="note-0456-03"/>
<anchor type="note" xlink:label="note-0456-04a" xlink:href="note-0456-04"/>
eſt, vt in præcedenti horologio, num propoſitũ horlogium ad meridiem ſpectet, an ad boream; <lb/></s>
  <s xml:id="echoid-s28880" xml:space="preserve">quod quidem eodem modo cognoſcemus. </s>
  <s xml:id="echoid-s28881" xml:space="preserve">Deinde ex K, loco ſtyli ad lineam horizontalem per-<lb/>
<anchor type="note" xlink:label="note-0456-05a" xlink:href="note-0456-05"/>
pendicularis excitetur K M, &amp; </s>
  <s xml:id="echoid-s28882" xml:space="preserve">ad hancalia perpendicularis K N, ſtylo K L, æqualis, iungaturq́ue <lb/>recta N M. </s>
  <s xml:id="echoid-s28883" xml:space="preserve">Erit enim K M N, angulus inclinationis plani propoſiti ad Horizontem. </s>
  <s xml:id="echoid-s28884" xml:space="preserve">Rurſus ex <lb/>loco ſtyli ad lineam indicis erigatur perpendidularis K I, ſtylo etiã æqualis, &amp; </s>
  <s xml:id="echoid-s28885" xml:space="preserve">per I, &amp; </s>
  <s xml:id="echoid-s28886" xml:space="preserve">centrũ ho-<lb/>rologii ρ, (Inuenietur autem linea ſtyli, ſi ex K, ad æquinoctialem lineam perpendicularis duca-<lb/>tur K G: </s>
  <s xml:id="echoid-s28887" xml:space="preserve">centrum autem horlogii punctum erit, vbi linea meridiana lineam ſtyli interſecat) <lb/>ducatur recta I ρ e, quæ axis mundi erit. </s>
  <s xml:id="echoid-s28888" xml:space="preserve">Quod ſi horologium centro careat, quod tunc demum <lb/>continget, cum linea ſtyli, &amp; </s>
  <s xml:id="echoid-s28889" xml:space="preserve">meridiana ſunt parallelæ, ducenda erit per I, linea æquidiſtans lineæ <lb/>meridianæ, &amp; </s>
  <s xml:id="echoid-s28890" xml:space="preserve">lineæ ſtyli pro axe mundi. </s>
  <s xml:id="echoid-s28891" xml:space="preserve">Poſt hæc ſumpto vtcunque puncto χ, in linea ſtyli, du-<lb/>catur per illud ad horizontalem lineam perpendicularis E D, ſecans meridianam lineam in E, <lb/>puncto, in quo conſtituatur cum E D, angulus inclinationis plani D E γ, &amp; </s>
  <s xml:id="echoid-s28892" xml:space="preserve">ad E γ, ex D, <lb/>
<anchor type="note" xlink:label="note-0456-06a" xlink:href="note-0456-06"/>
puncto vt libet aſſumpto in recta E D, excitetur perpendicularis D γ. </s>
  <s xml:id="echoid-s28893" xml:space="preserve">Abſciſſa autem E δ, ipſi E γ, <lb/>æquali, ducantur per puncta D, δ, ad D E, duæ perpendi culares D ε, δ θ, quarum D ε, meri-<lb/>dianam ſecet in ε. </s>
  <s xml:id="echoid-s28894" xml:space="preserve">Per ε, quoque ducta ipſi D E, parallela ſecet δ θ, in θ, atque ex E, per θ, recta <lb/>emittatur E θ. </s>
  <s xml:id="echoid-s28895" xml:space="preserve">Nam θ E D, erit angulus declinationis plani à Verticali circulo. </s>
  <s xml:id="echoid-s28896" xml:space="preserve">Præterea ex α, vbi <lb/>linea horæ 6. </s>
  <s xml:id="echoid-s28897" xml:space="preserve">à meridie, vel media nocte rectam A B, quę per E, horizontali lineæ parallela du-<lb/>citur, interſecat, (eſt autem hora 6<unsure/>. </s>
  <s xml:id="echoid-s28898" xml:space="preserve">ducenda per ρ, centrum horologii, &amp; </s>
  <s xml:id="echoid-s28899" xml:space="preserve">per punctum H, vbi <lb/>horizontalis linea, &amp; </s>
  <s xml:id="echoid-s28900" xml:space="preserve">ęquinoctialis ſe interſecant; </s>
  <s xml:id="echoid-s28901" xml:space="preserve">vel certè per punctum H, parallela ducenda eſt <lb/>lineę meridianę, quando centro caret horologium) excitetur ad lineam declinationis E θ, per-<lb/>pendicularis α F. </s>
  <s xml:id="echoid-s28902" xml:space="preserve">Poſtremo ad A B, in E, conſtituatur B E φ, angulus inclinationis, deorſum qui-<lb/>dem in planis ad boream ſpectantibus, ſurſum autem in iis, quę meridiem reſpiciunt, &amp; </s>
  <s xml:id="echoid-s28903" xml:space="preserve">ducta
<pb o="441" file="0457" n="457" rhead="LIBER QVARTVS."/>
ex χ, ad E D, perpendiculari χ φ, ſecer eam recta E φ, in puncto φ. </s>
  <s xml:id="echoid-s28904" xml:space="preserve">Producta autem recta D E, <lb/>ad partes E, ſumatur E C, rectæ E φ, &amp; </s>
  <s xml:id="echoid-s28905" xml:space="preserve">in A B, recta E β<unsure/>, rectę E F, æqualis, iungaturq́ue recta <lb/>β C, eritq́ue E β C, angulus altitudinis poli ſupra Horizontem.</s>
  <s xml:id="echoid-s28906" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1487" type="float" level="2" n="21">
<note position="left" xlink:label="note-0456-01" xlink:href="note-0456-01a" xml:space="preserve">Explicatio pro-<lb/>blematis propo <lb/>fiti in horolo-<lb/>gio declinante <lb/>ſimul ac incli-<lb/>@ato.</note>
<note position="left" xlink:label="note-0456-02" xlink:href="note-0456-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0456-01" xlink:href="fig-0456-01a">
    <image file="0456-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0456-01"/>
  </figure>
<note position="left" xlink:label="note-0456-03" xlink:href="note-0456-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0456-04" xlink:href="note-0456-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0456-05" xlink:href="note-0456-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0456-06" xlink:href="note-0456-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s28907" xml:space="preserve">HVIVS rei ratio perſpicua ſatis eſt ex ipſa conſtructione horologiorum à Verticali declinan-<lb/>tium, &amp; </s>
  <s xml:id="echoid-s28908" xml:space="preserve">ad Horizontem inclinatorum. </s>
  <s xml:id="echoid-s28909" xml:space="preserve">Quemadmodum enim ibi ex loco ſtyli ducta eſt recta <lb/>Horizonti parallela, &amp; </s>
  <s xml:id="echoid-s28910" xml:space="preserve">ſumpta ſtylo æqualis B C, in propoſ. </s>
  <s xml:id="echoid-s28911" xml:space="preserve">38. </s>
  <s xml:id="echoid-s28912" xml:space="preserve">ſuperioris libri, &amp; </s>
  <s xml:id="echoid-s28913" xml:space="preserve">per angulum <lb/>in C, conſtitutum complemento inclinationis æqualem, inuentum punctum D, per quod hori-<lb/>zontalis linea ducenda erat; </s>
  <s xml:id="echoid-s28914" xml:space="preserve">ita hic vice verſa ex puncto M, lineæ horizontalis ducta recta M N, <lb/>ad extremum rectæ K N, quæ ſtylo æqualis eſt, dabit angulum K N M, complemento inclinatio-<lb/>nis æqualem, &amp; </s>
  <s xml:id="echoid-s28915" xml:space="preserve">propterea reliquus K M N, angulus erit inclinationis. </s>
  <s xml:id="echoid-s28916" xml:space="preserve">Rurſus quemadmodum <lb/>
<anchor type="note" xlink:label="note-0457-01a" xlink:href="note-0457-01"/>
ibi ex linea declinationis E θ, &amp; </s>
  <s xml:id="echoid-s28917" xml:space="preserve">angulo inclinationis D E γ, &amp; </s>
  <s xml:id="echoid-s28918" xml:space="preserve">rectis δ θ, D E, inuenta eſt linea <lb/>meridiana E ε, ita hic viciſſim ex linea meridiana E ε, &amp; </s>
  <s xml:id="echoid-s28919" xml:space="preserve">inclinationis angulo D E γ, &amp; </s>
  <s xml:id="echoid-s28920" xml:space="preserve">rectis <lb/>D E, δ θ, reperitur linea declinationis E θ. </s>
  <s xml:id="echoid-s28921" xml:space="preserve">Eſſe autem I ρ K, angulum altitudinis poli ſupra pla-<lb/>num horologii, perſpicuum eſt, cum axis mundi per centrum horologii, &amp; </s>
  <s xml:id="echoid-s28922" xml:space="preserve">per verticem ſtyli, <lb/>id eſt, per centrum mundi tranſeat. </s>
  <s xml:id="echoid-s28923" xml:space="preserve">Ad hæc, vt ibi, conſtituto triangulo E β C, rectangulo, cuius <lb/>angulus E β C, æqualis ſit angulo altitudinis poli ſupta Horizontem, accepimus in linea decli-<lb/>nationis rectam E F, rectæ E β, æqualem, ductaq́ue ex F, ad lineam declinationis perpendicula-<lb/>ri F A, reperimus in recta A B, punctum α, per quod linea horæ 6. </s>
  <s xml:id="echoid-s28924" xml:space="preserve">à meridie, vel media no-<lb/>cte eſt ducenda; </s>
  <s xml:id="echoid-s28925" xml:space="preserve">ita è contrario hic ex puncto α, rectæ A B, per quod linea horæ 6. </s>
  <s xml:id="echoid-s28926" xml:space="preserve">ducitur, exci-<lb/>tata perpendicularis α F, ad lineam declinationis abſcindit ex linea declinationis rectam E F, æ-<lb/>
<anchor type="note" xlink:label="note-0457-02a" xlink:href="note-0457-02"/>
qualem rectę E β, dicti trianguli E β C, beneficio cuius horologium conſtruitur. </s>
  <s xml:id="echoid-s28927" xml:space="preserve">Poſtremo, quẽ-<lb/>admodum ibi ducta recta E φ, faciente cum A B, angulum inclinationis plani ad Horizontem, <lb/>ſiue deorſum, ſiue ſurſum verſus, prout horologium ad boream, aut meridiem ſpectat, abſciſſa <lb/>eſt E φ, æqualis rectæ E C, eiuſdem trianguli E β C, &amp; </s>
  <s xml:id="echoid-s28928" xml:space="preserve">ex φ, ducta perpendicularis φ, χ, ad rectã <lb/>C D, oſtendit in recta C D, punctum, per quod traiicienda eſt linea ſtyli; </s>
  <s xml:id="echoid-s28929" xml:space="preserve">ita contra hoc loco ex <lb/>puncto χ, ducta perpendiculari χ φ, ad C D, &amp; </s>
  <s xml:id="echoid-s28930" xml:space="preserve">conſtituto angulo B E φ, inclinationis, ſecat re-<lb/>cta E φ, rectam χ φ, in φ, ita vt E φ, æqualis ſit rectæ E C, dicti trianguli E β C, &amp;</s>
  <s xml:id="echoid-s28931" xml:space="preserve">c.</s>
  <s xml:id="echoid-s28932" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1488" type="float" level="2" n="22">
<note position="left" xlink:label="note-0457-01" xlink:href="note-0457-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0457-02" xlink:href="note-0457-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s28933" xml:space="preserve">COGNITO autem, an horologium ſpectet ad auſtrum, boreamve, facili negotio ex linea de <lb/>clinationis E θ, percipiemus, num idem in ortum vergat, an ad occaſum, prout linea declinationis <lb/>ad ſiniſtram rectæ D E, ducitur, vel ad dexteram, quemadmodum ducendam eſſe docuimus ad <lb/>
<anchor type="note" xlink:label="note-0457-03a" xlink:href="note-0457-03"/>
initium propoſ. </s>
  <s xml:id="echoid-s28934" xml:space="preserve">37. </s>
  <s xml:id="echoid-s28935" xml:space="preserve">ſuperioris libri.</s>
  <s xml:id="echoid-s28936" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1489" type="float" level="2" n="23">
<note position="left" xlink:label="note-0457-03" xlink:href="note-0457-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s28937" xml:space="preserve">VERVM ſit iam cogmta altitudo poli ſupra Horizontem, ad quam conſtructum horologiũ <lb/>eſt, vna cum inclinatione plani ad Horizontem, (quia &amp; </s>
  <s xml:id="echoid-s28938" xml:space="preserve">hic nihil certi ex ſola altitudine poli col <lb/>ligi poteſt) oporteatq́ue inueſtigare reliqua. </s>
  <s xml:id="echoid-s28939" xml:space="preserve">Sumpto in linea ſtyli quocunque puncto χ, ductaq́; <lb/></s>
  <s xml:id="echoid-s28940" xml:space="preserve">per χ, perpendiculari E D, ad lineam horizontalem, inueniemus, vt paulo ante, lineam declina-<lb/>tionis E θ, beneſicio meridianæ lineæ E ε, &amp; </s>
  <s xml:id="echoid-s28941" xml:space="preserve">anguli inclinationis D E γ, &amp;</s>
  <s xml:id="echoid-s28942" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28943" xml:space="preserve">Deinde ex declinatio-<lb/>ne nota, &amp; </s>
  <s xml:id="echoid-s28944" xml:space="preserve">inclinatione inueſtigetur per propoſ. </s>
  <s xml:id="echoid-s28945" xml:space="preserve">27. </s>
  <s xml:id="echoid-s28946" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s28947" xml:space="preserve">primi inclinatio plani ad Meridianum, &amp; </s>
  <s xml:id="echoid-s28948" xml:space="preserve"><lb/>ex hac, &amp; </s>
  <s xml:id="echoid-s28949" xml:space="preserve">altitudine poli ſupra Horizontem, per propoſ. </s>
  <s xml:id="echoid-s28950" xml:space="preserve">28. </s>
  <s xml:id="echoid-s28951" xml:space="preserve">eiuſdem libri, &amp; </s>
  <s xml:id="echoid-s28952" xml:space="preserve">eius coroll. </s>
  <s xml:id="echoid-s28953" xml:space="preserve">arcus Me-<lb/>ridiani inter planum, &amp; </s>
  <s xml:id="echoid-s28954" xml:space="preserve">polum mũdi, &amp; </s>
  <s xml:id="echoid-s28955" xml:space="preserve">tandem per propoſ. </s>
  <s xml:id="echoid-s28956" xml:space="preserve">29. </s>
  <s xml:id="echoid-s28957" xml:space="preserve">eiuſdem libri altitudo poli ſupra <lb/>planum horologij. </s>
  <s xml:id="echoid-s28958" xml:space="preserve">Si enim huius altitudinis angulus conſtituatur G ρ I, cum linea ſtyli in centro <lb/>horologij, &amp; </s>
  <s xml:id="echoid-s28959" xml:space="preserve">circa portionem lineæ ſtyli G ρ, inter æquinoctialem lineam, &amp; </s>
  <s xml:id="echoid-s28960" xml:space="preserve">centrum horologij <lb/>
<anchor type="note" xlink:label="note-0457-04a" xlink:href="note-0457-04"/>
comprehenſam ſemicirculus deſcribatur ſecans ρ I, axem mundi, in I, erit ex I, demiſſa perpendi-<lb/>cularis I K, ad lineam ſtyli, longitudo gnomonis, eiusq́ue locus in K, puncto. </s>
  <s xml:id="echoid-s28961" xml:space="preserve">Cæterum axis mun <lb/>di alia ratione inuenietur hoc modo.</s>
  <s xml:id="echoid-s28962" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1490" type="float" level="2" n="24">
<note position="left" xlink:label="note-0457-04" xlink:href="note-0457-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s28963" xml:space="preserve">EX χ, puncto, vbi ſe interſecant linea ſtyli, &amp; </s>
  <s xml:id="echoid-s28964" xml:space="preserve">recta D E, ducatur ad rectam D E, perpendicula-<lb/>ris χ φ, quam in φ, ſecet recta E φ, faciens cum A B, angulum inclinationis B E φ. </s>
  <s xml:id="echoid-s28965" xml:space="preserve">Poſtea ex eo-<unsure/> <lb/>dem puncto χ, ad lineam ſtyli excitetur perpendicularis χ e, ipſi χ φ, æqualis. </s>
  <s xml:id="echoid-s28966" xml:space="preserve">Nam recta per e, <lb/>&amp; </s>
  <s xml:id="echoid-s28967" xml:space="preserve">centrum horlogii ducta erit axis mundi, vt ex demonſtratis in conſtructione horum horolo-<lb/>giorum liquido conſtare poteſt. </s>
  <s xml:id="echoid-s28968" xml:space="preserve">In planis autem per polum mundi ductis, in quibus parallelę <lb/>ſuntlineę horarum à meridie, vel media nocte, erit recta χ e, longitudo ſtyli, eiusq́ue locus in <lb/>puncto, vbi linea ſtyli lineam æquinoctialem interſecat, vt conſtat ex tertia figura propoſ. </s>
  <s xml:id="echoid-s28969" xml:space="preserve">37. </s>
  <s xml:id="echoid-s28970" xml:space="preserve">ſu-<lb/>
<anchor type="note" xlink:label="note-0457-05a" xlink:href="note-0457-05"/>
perioris libri.</s>
  <s xml:id="echoid-s28971" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1491" type="float" level="2" n="25">
<note position="left" xlink:label="note-0457-05" xlink:href="note-0457-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s28972" xml:space="preserve">SI autem locus duntaxat gnomonis detur in puncto K, inquiremus omnia alia hac ratione. <lb/></s>
  <s xml:id="echoid-s28973" xml:space="preserve">Deſcripto circa portionem lineæ indicis G ρ, (quæ ſemper ducitur ex loco gnomonis ad æquino-<lb/>ctialem lineam perpendicularis) inter lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s28974" xml:space="preserve">centrum horologij poſitam ſe-<lb/>micirculo G I ρ, ducemus ex K, loco ſtyli ad lineam indicis perpendicularem K I, quæ ſecet circu-<lb/>lum in I. </s>
  <s xml:id="echoid-s28975" xml:space="preserve">Ita enim habebimus longitudinem ſtyli I k, vt in præcedentibus etiam horologiis <lb/>oſtendimus. </s>
  <s xml:id="echoid-s28976" xml:space="preserve">Vnde reliqua omnia indagabimus, vt prius, quando dabatur longitudo ſtyli, <lb/>eiuſq́ue locus.</s>
  <s xml:id="echoid-s28977" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28978" xml:space="preserve">IDEM porro problema hoc facile eſt in ſphæra recta, vt ex conſtructione horologiorum in <lb/>dicta ſphæra perſpicuum eſt. </s>
  <s xml:id="echoid-s28979" xml:space="preserve">Intelligetur autem, horologium aliquod pro ſphæra recta eſſe con-
<pb o="442" file="0458" n="458" rhead="GNOMONICES"/>
ſtructum, cum horizontalis linea indicat horam 6. </s>
  <s xml:id="echoid-s28980" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s28981" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s28982" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s28983" xml:space="preserve">Quod ſi horizontalis li-<lb/>nea non adſit, ſint autem lineæ horariæ parallelæ, erit propoſitum horologium in ſphæra recta ho <lb/>rizontale. </s>
  <s xml:id="echoid-s28984" xml:space="preserve">Quamobrem, dato horologio, vna cum ſtylo, eiusq́ue loco; </s>
  <s xml:id="echoid-s28985" xml:space="preserve">ad quam poli altitudinẽ <lb/>fabricatum ſit, &amp;</s>
  <s xml:id="echoid-s28986" xml:space="preserve">c. </s>
  <s xml:id="echoid-s28987" xml:space="preserve">inueſtigauimus. </s>
  <s xml:id="echoid-s28988" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s28989" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1493" type="section" level="1" n="357">
<head xml:id="echoid-head370" xml:space="preserve">PROBLEMA 14. PROPOSITIO 14.</head>
<p>
  <s xml:id="echoid-s28990" xml:space="preserve">HOROLOGIVM quodcunque deſcriptum ad maiorem, mi-<lb/>noremve formam, pro data magnitudine ſtyli, reducere.</s>
  <s xml:id="echoid-s28991" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s28992" xml:space="preserve">PROPONATVR doctrinæ cauſa horologium Babylonicum declinans ab Horizonte, <lb/>quod propoſ. </s>
  <s xml:id="echoid-s28993" xml:space="preserve">22. </s>
  <s xml:id="echoid-s28994" xml:space="preserve">ſuperioris libri deſcripſimus, cuiuſque ſtylus eſt A B, augendum vel diminuen-<lb/>dum ſecundum proportionem ſtyli cuiuſuis dati C D, ita vt, quam proportionem habet ſtylus <lb/>A B, ad ſtylum C D, eandem habeant omnia lineamenta, atque vmbræ à ſtylo A B, cadentes ad <lb/>lineamenta reſpondentia, ac vmbras à ſtylo C D, proiectas: </s>
  <s xml:id="echoid-s28995" xml:space="preserve">permutandoq́ue, vt ſe habet ſtylus <lb/>A B, ad lineamenta, &amp; </s>
  <s xml:id="echoid-s28996" xml:space="preserve">vmbras ſui horologii, ita ſe habeat ſtylus C D, ad reſpondentia lineamen <lb/>ta, atque vmbras in horologio, quod fabricandum eſt.</s>
  <s xml:id="echoid-s28997" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s28998" xml:space="preserve">PRIMVM omnium ducantur ſeorſum in plano quopiam duæ rectæ E F, E G, facientes in <lb/>
<anchor type="note" xlink:label="note-0458-02a" xlink:href="note-0458-02"/>
E, angulum quemcunque, &amp; </s>
  <s xml:id="echoid-s28999" xml:space="preserve">ipſi E F, parallela vtcunque agatur H I: </s>
  <s xml:id="echoid-s29000" xml:space="preserve">In E F, autem ſ@matur recta <lb/>
<anchor type="note" xlink:label="note-0458-03a" xlink:href="note-0458-03"/>
E K, ſtylo A B, &amp; </s>
  <s xml:id="echoid-s29001" xml:space="preserve">in E G, recta E L, ſtylo C D, æqualis, iungaturq́ue recta K L, ſecans H I, in M; </s>
  <s xml:id="echoid-s29002" xml:space="preserve">ac <lb/>poſtremo per E, ipſi K L, parallela agatur E H, ſecans H I, in H. </s>
  <s xml:id="echoid-s29003" xml:space="preserve">Ita enim parata erit figura, per quã <lb/>horologium propoſitum ſine magno labore ad maiorem minoremve figuram redigetur.</s>
  <s xml:id="echoid-s29004" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1493" type="float" level="2" n="1">
<note position="left" xlink:label="note-0458-02" xlink:href="note-0458-02a" xml:space="preserve">Quo pacto ho-<lb/>rologium pro-<lb/>poſitum ad ma <lb/>iorem mino <lb/>re@@ ve formã <lb/>redigatur, pro <lb/>data magnitu-<lb/>dine ſtyli.</note>
<note position="left" xlink:label="note-0458-03" xlink:href="note-0458-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s29005" xml:space="preserve">DEINDE in propoſito horologio per A, locum ſtyli ducantur duæ rectæ occultæ A P, A a, <lb/>ſeſe ad rectos angulos in A, ſecantes, quarum altera in horologiis ad Horizontem rectis eadem <lb/>ſit, quæ linea horizontalis per locum ſtyli ducta, &amp; </s>
  <s xml:id="echoid-s29006" xml:space="preserve">altera ad Horizontem perpendicularis. </s>
  <s xml:id="echoid-s29007" xml:space="preserve">In ho-<lb/>rologijs autem inclinatis vna ſit horizontali lineæ æquidiſtans, &amp; </s>
  <s xml:id="echoid-s29008" xml:space="preserve">altera idcirco communis ſectio <lb/>plani horologij, &amp; </s>
  <s xml:id="echoid-s29009" xml:space="preserve">Verticalis circuli inclinationem ipſius ad Horizontem metientis. </s>
  <s xml:id="echoid-s29010" xml:space="preserve">Pari ratione <lb/>in muro, vel in plano aliquo, in quo horologium amplificandum eſt, aut diminuendum, eligatur <lb/>C, locus ſtyli C D, &amp; </s>
  <s xml:id="echoid-s29011" xml:space="preserve">per C, duæ quoque rectæ occultæ ducantur ſeſe ad angulos rectos ſecantes <lb/>in C, quarum vna reſpondeat horizontali lineæ propoſiti horologij, vel certè ei, quæ lineæ hori-<lb/>
<anchor type="note" xlink:label="note-0458-04a" xlink:href="note-0458-04"/>
zontali parallela eſt, altera verò alteri: </s>
  <s xml:id="echoid-s29012" xml:space="preserve">hoc eſt, ſi hoiologium propoſitum rectum eſt ad Horizon <lb/>tem, &amp; </s>
  <s xml:id="echoid-s29013" xml:space="preserve">offeratur murus, ſeu planum aliquod ſtabile, ac firmum, in quo horologium eſt delinean-<lb/>dum maius, aut minus, vna ex dictis lineis per locum ſtyli C, ducta Horizonti æquidiſter, @ſitq́ue <lb/>horizontalis linea, altera verò ad Horizontem ſit perpendicularis: </s>
  <s xml:id="echoid-s29014" xml:space="preserve">at verò, ſi horologium oblatum <lb/>non eſt rectum ad Horizontem, vna dictarum linearum in muro, vel plano firmo, ac ſtabili æqui-<lb/>diſtet quidem Horizonti, ſed altera ſit ſectio communis ipſius, &amp; </s>
  <s xml:id="echoid-s29015" xml:space="preserve">Verticalis circuli, qui inclina-<lb/>tionem plani ad Horizontem metitur. </s>
  <s xml:id="echoid-s29016" xml:space="preserve">Harum autem linearum in horologijs horizontalibus, vbi <lb/>linea horizontalis duci non poteſt, vna ſit linea meridiana, &amp; </s>
  <s xml:id="echoid-s29017" xml:space="preserve">altera lineæ ęquinoctiali æquidiſtãs. <lb/></s>
  <s xml:id="echoid-s29018" xml:space="preserve">Deſcripto quoque ex A, circulo P O, cuiuſque magnitudinis, ei æqualis Q R, ex centro C, <lb/>deſcribatur.</s>
  <s xml:id="echoid-s29019" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1494" type="float" level="2" n="2">
<note position="left" xlink:label="note-0458-04" xlink:href="note-0458-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s29020" xml:space="preserve">QVIBVS confectis, ita amplificationem diminutionemve horologij abſoluemus. </s>
  <s xml:id="echoid-s29021" xml:space="preserve">Ex cen-<lb/>tro A, per N, punctum horæ 6. </s>
  <s xml:id="echoid-s29022" xml:space="preserve">ab ortu, in tropico ♋, verbi gratia, ducatur recta occulta A N, ſe-<lb/>cans circumferentiam circuli in O, &amp; </s>
  <s xml:id="echoid-s29023" xml:space="preserve">arcui P O, ſumatur æqualis arcus Q R, in altero circulo, du-<lb/>caturq́ue recta C R. </s>
  <s xml:id="echoid-s29024" xml:space="preserve">Sumptis deinde in E F, H G, rectis E S, H T, ipſi A N, ęqualibus, iungatur <lb/>recta S T, ſecans E G, in V, &amp; </s>
  <s xml:id="echoid-s29025" xml:space="preserve">ex C R, rectæ E V, æqualis abſcindatur C X. </s>
  <s xml:id="echoid-s29026" xml:space="preserve">Dico, Sole exiſtente in <lb/>principio ♋, &amp; </s>
  <s xml:id="echoid-s29027" xml:space="preserve">in circulo horæ 6. </s>
  <s xml:id="echoid-s29028" xml:space="preserve">ab ortu, vmbram ſtyli C D, cadere in punctum X, quemadmo <lb/>dum eodem illo tempore vmbra ſtyli A B, in punctum N, cadit. </s>
  <s xml:id="echoid-s29029" xml:space="preserve">Si enim circulus maximus, cui <lb/>horologium vtrumque æquidiſtat, concipiatur eſſe Horizon aliquis, ita vt tam ſtylus A B, quàm <lb/>C D, ſit axis ipſius, per quem omnes ipſius Verticales circuli ducuntur, vt in horologio horizonta <lb/>li contingit; </s>
  <s xml:id="echoid-s29030" xml:space="preserve">erit recta A N, communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s29031" xml:space="preserve">circuli illius Verticalis reſpectu <lb/>
<anchor type="note" xlink:label="note-0458-06a" xlink:href="note-0458-06"/>
dicti Horizontis, qui tunc per centrum Solis ducitur, atque adeò eadem A N, longitudo erit vm-<lb/>bræ in prædicta hora 6. </s>
  <s xml:id="echoid-s29032" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s29033" xml:space="preserve">Quoniam autem ille Verticalis eandem poſitionem habet in om <lb/>nibus planis parallelis, ita vt cum recta C Q, quæ rectæ A P, reſpondet, æqualem faciat angulum <lb/>angulo N A P, fit vt cum angulus R C Q, æqualis ſit angulo O A P, propterea quod &amp; </s>
  <s xml:id="echoid-s29034" xml:space="preserve">arcus Q R, <lb/>
<anchor type="note" xlink:label="note-0458-07a" xlink:href="note-0458-07"/>
arcui P O, æqualis eſt, recta C R, ſit quoque communis ſectio dicti Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s29035" xml:space="preserve">plani ho-<lb/>rologii, in quo ſtylus C D. </s>
  <s xml:id="echoid-s29036" xml:space="preserve">Quare vmbra ſtyli C D, tunc temporis in rectam C R, cadet. </s>
  <s xml:id="echoid-s29037" xml:space="preserve">Quia <lb/>verò rectæ E S, H T, æquales inter ſe ſunt, (vtraque enim ſumpta eſt æqualis rectæ A N,) &amp; </s>
  <s xml:id="echoid-s29038" xml:space="preserve">pa-<lb/>rallelæ, erunt quoque E H, S T, æquales, &amp; </s>
  <s xml:id="echoid-s29039" xml:space="preserve">parallelæ. </s>
  <s xml:id="echoid-s29040" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s29041" xml:space="preserve">K L, ipſi E H, ſit, ex conſtructio <lb/>
<anchor type="note" xlink:label="note-0458-08a" xlink:href="note-0458-08"/>
ne, parallela, erunt &amp; </s>
  <s xml:id="echoid-s29042" xml:space="preserve">K L, S T, inter ſe parallelæ. </s>
  <s xml:id="echoid-s29043" xml:space="preserve">Igitur erit, vt E K, hoc eſt, vt A B, ſtylus ad E S, <lb/>
<anchor type="note" xlink:label="note-0458-09a" xlink:href="note-0458-09"/>
hoc eſt, ad A N, vmbram, ita E L, hoc eſt, ita C D, ſtylus, ad E V, hoc eſt, ad C X. </s>
  <s xml:id="echoid-s29044" xml:space="preserve">Quocirca cum <lb/>
<anchor type="note" xlink:label="note-0458-10a" xlink:href="note-0458-10"/>
<pb o="443" file="0459" n="459" rhead="LIBER QVARTVS."/>
omnes ſtyli in @odem plano, vel in planis parallelis proportionales ſint ſuis vmbris, propterea <lb/>quod eandem proportionem haber quicunque ſtylus ad ſuam vmbram, quam ſinus altitudinis So <lb/>lis ſupra illud planum, in quo vmbra excipitur, ad ſinum complementi eiuſdem altitudinis, vt in <lb/>
<anchor type="figure" xlink:label="fig-0459-01a" xlink:href="fig-0459-01"/>
<anchor type="note" xlink:label="note-0459-01a" xlink:href="note-0459-01"/>
<anchor type="note" xlink:label="note-0459-02a" xlink:href="note-0459-02"/>
<anchor type="note" xlink:label="note-0459-03a" xlink:href="note-0459-03"/>
<anchor type="note" xlink:label="note-0459-04a" xlink:href="note-0459-04"/>
<anchor type="note" xlink:label="note-0459-05a" xlink:href="note-0459-05"/>
ſequenti libro demonſtrabimus; </s>
  <s xml:id="echoid-s29045" xml:space="preserve">erit C X, longitudo vmbræ in prædicta hora 6. </s>
  <s xml:id="echoid-s29046" xml:space="preserve">ab ortu à ſtylo <lb/>C D, proiectæ. </s>
  <s xml:id="echoid-s29047" xml:space="preserve">Simili modo, ſi ex centro A, per Y, punctum horæ 6. </s>
  <s xml:id="echoid-s29048" xml:space="preserve">ab ortu in tropico ♑, duca-<lb/>tur recta occulta A Y, ſecans circulum in Z, &amp; </s>
  <s xml:id="echoid-s29049" xml:space="preserve">arcuia Z, ſumatur in alio circulo æqualis arcus <lb/>b d, ducaturq́ue recta C d, oſtendemus tunc temporis, Sole exiſtente in principio ♑, vmbram ſty-
<pb o="444" file="0460" n="460" rhead="GNOMONICES"/>
li C D, cadere in rectam C D. </s>
  <s xml:id="echoid-s29050" xml:space="preserve">Et ſi rectæ A Y, ſumantur æquales E F, H I, iungaturq́ue recta F I, <lb/>ſecans E G, in G; </s>
  <s xml:id="echoid-s29051" xml:space="preserve">ac poſtremo rectæ E G, æqualis abſcindatur C e, probabimus, vt prius, vmbram <lb/>ſtyli C D, cadere in punctum e. </s>
  <s xml:id="echoid-s29052" xml:space="preserve">Quapropter recta e X, connectens horam 6. </s>
  <s xml:id="echoid-s29053" xml:space="preserve">in tropico ♋, cum <lb/>hora 6. </s>
  <s xml:id="echoid-s29054" xml:space="preserve">in tropico ♑, erit linea horæ 6. </s>
  <s xml:id="echoid-s29055" xml:space="preserve">ab ortu.</s>
  <s xml:id="echoid-s29056" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1495" type="float" level="2" n="3">
<note position="left" xlink:label="note-0458-06" xlink:href="note-0458-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0458-07" xlink:href="note-0458-07a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0458-08" xlink:href="note-0458-08a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0458-09" xlink:href="note-0458-09a" xml:space="preserve">30. primi.</note>
<note position="left" xlink:label="note-0458-10" xlink:href="note-0458-10a" xml:space="preserve">2. vel 4. ſexti</note>
  <figure xlink:label="fig-0459-01" xlink:href="fig-0459-01a">
    <image file="0459-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0459-01"/>
  </figure>
<note position="left" xlink:label="note-0459-01" xlink:href="note-0459-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0459-02" xlink:href="note-0459-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0459-03" xlink:href="note-0459-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0459-04" xlink:href="note-0459-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0459-05" xlink:href="note-0459-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s29057" xml:space="preserve">QVOD ſi non velimus tot rectas lineas ex A, &amp; </s>
  <s xml:id="echoid-s29058" xml:space="preserve">C, educere, poterimus loco illarum appli-<lb/>
<anchor type="note" xlink:label="note-0460-01a" xlink:href="note-0460-01"/>
care regulam aliquam ad centrum A, &amp; </s>
  <s xml:id="echoid-s29059" xml:space="preserve">ad punctum, quod transferre cupimus: </s>
  <s xml:id="echoid-s29060" xml:space="preserve">quo facto pun-<lb/>ctum in circulo à regula abſciſſa notabimus. </s>
  <s xml:id="echoid-s29061" xml:space="preserve">Deinde eandem regulam apponemus puncto C, ita <lb/>vt auferat ex circulo arcum æqualem illi, quem prius in alio circulo abſcidit, &amp; </s>
  <s xml:id="echoid-s29062" xml:space="preserve">in latere regulæ <lb/>vmbræ longitudinem ſignabimus, imprimendo punctum in horologii plano, &amp;</s>
  <s xml:id="echoid-s29063" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29064" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1496" type="float" level="2" n="4">
<note position="left" xlink:label="note-0460-01" xlink:href="note-0460-01a" xml:space="preserve">Loco rectarum <lb/>ex A, &amp; C. egre <lb/>dientium uſur <lb/>pari poteſt re-<lb/>gula@ &amp;c.</note>
</div>
<p>
  <s xml:id="echoid-s29065" xml:space="preserve">NON alia ratione in horlogium ſtyli C D, transferemus omnia puncta horologii propoſiti, <lb/>
<anchor type="note" xlink:label="note-0460-02a" xlink:href="note-0460-02"/>
ſi per ea rectas ducamus ex centro A, eorumq́ue diſtantias ex A, transferamus in rectas E F, H I, <lb/>&amp;</s>
  <s xml:id="echoid-s29066" xml:space="preserve">c. </s>
  <s xml:id="echoid-s29067" xml:space="preserve">Vt ſi transferre velimus punctum h, vbi æquinoctialis linea horam 4. </s>
  <s xml:id="echoid-s29068" xml:space="preserve">ab ortu diuidit, duce-<lb/>mus rectam A h, quæ ſecet circulum in l, &amp; </s>
  <s xml:id="echoid-s29069" xml:space="preserve">ſumpto arcu Q l, arcui P i, ęquali, ducemus rectam <lb/>C l. </s>
  <s xml:id="echoid-s29070" xml:space="preserve">Deinde ſumptis rectis E n, H p, rectæ A h, æqualibus, ductaq́ue recta n p, ſecante E G, in q, <lb/>abſcindemus rectæ E q, æqualem C m; </s>
  <s xml:id="echoid-s29071" xml:space="preserve">cadetq́ue vmbra ſtyli C D, hora 4 ab ortu in punctum m, <lb/>Sole in Æquatore exiſtente, quemadmodum eodem tempore vmbra gnomonis A B, in punctũ <lb/>h, cadit. </s>
  <s xml:id="echoid-s29072" xml:space="preserve">Et ſic de cæteris.</s>
  <s xml:id="echoid-s29073" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1497" type="float" level="2" n="5">
<note position="left" xlink:label="note-0460-02" xlink:href="note-0460-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s29074" xml:space="preserve">SED in lineis, quæ interminatæ ſunt, qualis eſt linea ſtyli, linea meridiana, horizontalis, <lb/>
<anchor type="note" xlink:label="note-0460-03a" xlink:href="note-0460-03"/>
&amp; </s>
  <s xml:id="echoid-s29075" xml:space="preserve">æquinoctialis, ſatis eſt, vt vnum pro qualibet punctum inueniamus in horologio futuro, ſecun-<lb/>dum doctrinam iam traditam. </s>
  <s xml:id="echoid-s29076" xml:space="preserve">Si enim pef<unsure/> illud punctum ducatur recta faciens cum alia quapiã <lb/>
<anchor type="note" xlink:label="note-0460-04a" xlink:href="note-0460-04"/>
linea iam ducta angulum æqualem ei, quem eadem linea in propoſito horologio cum reſpon-<lb/>dente linea conſtituit, deſcripta erit linea illa, cuius punctum inuentum eſt. </s>
  <s xml:id="echoid-s29077" xml:space="preserve">Vt quoniam linea <lb/>ſtyli tranſire debet per locum ſtyli C, ſi per C, ducatur recta C g, faciens cum C Q, vel cum C b, <lb/>angulum æqualem ei, quem linea ſtyli A f, cum reſpondente recta A P, vel A a, conficit, deſcri-<lb/>pta erit linea ſtyli. </s>
  <s xml:id="echoid-s29078" xml:space="preserve">Rurſus inuento puncto g, per quod meridiana linea ducenda eſt, quod reſpon <lb/>deat puncto f, &amp; </s>
  <s xml:id="echoid-s29079" xml:space="preserve">per g, emittatur recta faciens cum linea ſtyli angulum æqualem angulo, quem <lb/>in f, linea meridiana cum linea ſtyli conſtituit, deſcripta quoque erit linea meridiana. </s>
  <s xml:id="echoid-s29080" xml:space="preserve">Ita etiam <lb/>quia in dato exemplo recta A P, ad partes A, producta ſecat lineam horizontalem ad angulos re-<lb/>ctos; </s>
  <s xml:id="echoid-s29081" xml:space="preserve">ſi in C Q, recta ad partes C, producta inueniamus punctũ, per quod horizontalis linea ducẽ-<lb/>da eſt, &amp; </s>
  <s xml:id="echoid-s29082" xml:space="preserve">per illud perpẽdicularem ad C Q, excitemus, habebimus lineam horizontalem. </s>
  <s xml:id="echoid-s29083" xml:space="preserve">Poſtre-<lb/>
<anchor type="note" xlink:label="note-0460-05a" xlink:href="note-0460-05"/>
mo inuento puncto in linea ſtyli horologii futuri, vel in linea meridiana, vel in horizontali, per <lb/>quod æquinoctialis linea eſt traiicienda, ſi per illud rectam educamus facientem cum linea ſtyli, <lb/>vel meridiana, vel horizontali angulum ęqualem illi angulo, quem linea æquinoctialis in horolo-<lb/>gio propoſito facit cum reſpondente linea ſtyli, vel meridiana, vel horizontali, ducta quoque erit <lb/>æquinoctialis linea in horologio futuro. </s>
  <s xml:id="echoid-s29084" xml:space="preserve">Secabunt autem ſe mutuo linea meridiana, &amp; </s>
  <s xml:id="echoid-s29085" xml:space="preserve">ęquino-<lb/>ctialis, ſi non errauimus, in hora 6. </s>
  <s xml:id="echoid-s29086" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s29087" xml:space="preserve">18. </s>
  <s xml:id="echoid-s29088" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s29089" xml:space="preserve">6. </s>
  <s xml:id="echoid-s29090" xml:space="preserve">inæquali. </s>
  <s xml:id="echoid-s29091" xml:space="preserve">Item linea æquinoctia <lb/>lis, &amp; </s>
  <s xml:id="echoid-s29092" xml:space="preserve">horizontalis ſe ſe interſecabunt in hora 12. </s>
  <s xml:id="echoid-s29093" xml:space="preserve">ab ortu, vel occaſu, &amp; </s>
  <s xml:id="echoid-s29094" xml:space="preserve">6. </s>
  <s xml:id="echoid-s29095" xml:space="preserve">à meridie, vel media no-<lb/>cte, nec non linea ſtyli lineam æquinoctialem ſemper ad angulos rectos diuidet. </s>
  <s xml:id="echoid-s29096" xml:space="preserve">Quæ omnia ex <lb/>demonſtratis in deſcriptione horologiorum conſtant, &amp; </s>
  <s xml:id="echoid-s29097" xml:space="preserve">vtilia ſunt, ſi diligenter aduertantur, vt <lb/>rectè in horologio huiuſmodi lineæ deſcribi poſſint.</s>
  <s xml:id="echoid-s29098" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1498" type="float" level="2" n="6">
<note position="left" xlink:label="note-0460-03" xlink:href="note-0460-03a" xml:space="preserve">De lineis intet <lb/>minatis quid <lb/>agendum.</note>
<note position="left" xlink:label="note-0460-04" xlink:href="note-0460-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0460-05" xlink:href="note-0460-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s29099" xml:space="preserve">POSSVMVS quoque alio modo inueſtigare longitudines vnibrarum, quę ad ſtylum C D, <lb/>
<anchor type="note" xlink:label="note-0460-06a" xlink:href="note-0460-06"/>
<anchor type="note" xlink:label="note-0460-07a" xlink:href="note-0460-07"/>
eaſdem habeant proportiones, quas vnibræ in horologio propoſito ad ſtylum A B, habent. </s>
  <s xml:id="echoid-s29100" xml:space="preserve">In re-<lb/>cta enim quacunque α β γ, ſit α β, ſtylo A B, &amp; </s>
  <s xml:id="echoid-s29101" xml:space="preserve">α γ, ſtylo C D, æqualis, &amp; </s>
  <s xml:id="echoid-s29102" xml:space="preserve">per β, γ, ducantur vt-<lb/>cunque duæ lineę parallelæ inter ſe β θ, γ λ. </s>
  <s xml:id="echoid-s29103" xml:space="preserve">Deinde beneficio circini transferatur recta A N, lon <lb/>gitudo ſcilicet vmbrę in hora 6. </s>
  <s xml:id="echoid-s29104" xml:space="preserve">ab ortu in tropico ♋, ex α, in parallelam β θ, quæ per terminum <lb/>ſtyli propoſiti ducitur, vſque ad punctum δ, iungaturq́ue recta α δ, ſecans alteram parallelam in <lb/>ε. </s>
  <s xml:id="echoid-s29105" xml:space="preserve">Dico rectam α ε, beneficio circini translatam ex C, in lineam vmbræ C R, vſque ad X, exhibe-<lb/>re nobis X, punctum horæ 6. </s>
  <s xml:id="echoid-s29106" xml:space="preserve">ab ortu in tropico ♋. </s>
  <s xml:id="echoid-s29107" xml:space="preserve">Nam quoniam ex coroll. </s>
  <s xml:id="echoid-s29108" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s29109" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29110" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29111" xml:space="preserve">6. </s>
  <s xml:id="echoid-s29112" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s29113" xml:space="preserve">triangula α β δ, α γ ε, ſimilia ſunt, erit vt α β, ſtylo A B, æqualis ad α δ, vmbrę A N, æqualem, <lb/>
<anchor type="note" xlink:label="note-0460-08a" xlink:href="note-0460-08"/>
ita α γ, ſtylo C D, æqualis ad α ε, vmbræ C X, æqualem. </s>
  <s xml:id="echoid-s29114" xml:space="preserve">Eadem ratione, ſi ſumamus α θ, æqua-<lb/>lem vmbræ A Y, iungamusq́ue rectam α θ, quæ parallelam γ λ, ſecet in λ, &amp; </s>
  <s xml:id="echoid-s29115" xml:space="preserve">rectæ α λ, æqualem <lb/>
<anchor type="note" xlink:label="note-0460-09a" xlink:href="note-0460-09"/>
auferamus C e, habebimus punctum e, horæ 6. </s>
  <s xml:id="echoid-s29116" xml:space="preserve">ab ortu in tropico ♑, &amp; </s>
  <s xml:id="echoid-s29117" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s29118" xml:space="preserve">Verũ prior <lb/>via commodior videtur: </s>
  <s xml:id="echoid-s29119" xml:space="preserve">quoniam in hac poſteriori vmbræ longiores nimis obliquè parallelas <lb/>α θ, γ λ, ſecant, vt patet in recta α π ρ; </s>
  <s xml:id="echoid-s29120" xml:space="preserve">In priori autem parallelæ E H, k M, S T, &amp;</s>
  <s xml:id="echoid-s29121" xml:space="preserve">c. </s>
  <s xml:id="echoid-s29122" xml:space="preserve">eodem ſem-<lb/>per modo rectam E G, in qua vmbrarum longitudines terminantur, diuidunt. </s>
  <s xml:id="echoid-s29123" xml:space="preserve">Rurſus in poſte-<lb/>riori, quando vmbræ ſunt breuiores, vt ſit in horis prope ſtylum in viciniori tropico, neceſſe eſt <lb/>ducere alias duas parallelas β μ, γ ξ, quæ tam prope accedant ad punctum α, vt breues illæ vmbrę <lb/>in parallelam β μ, transferri poſſint. </s>
  <s xml:id="echoid-s29124" xml:space="preserve">Ita vides vmbram horę 7. </s>
  <s xml:id="echoid-s29125" xml:space="preserve">ab ortu in tropico ♋, translatam <lb/>eſſe vſque ad μ, rectam autem α ξ, eſſe longitudinem vmbræ eiuſdem horæ in futuro horologio. <lb/></s>
  <s xml:id="echoid-s29126" xml:space="preserve">Hac autem cautione in priori via non indigemus, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s29127" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1499" type="float" level="2" n="7">
<note position="left" xlink:label="note-0460-06" xlink:href="note-0460-06a" xml:space="preserve">A lia inuentio <lb/>longitudinum <lb/>vmbrarum pro <lb/>dato ſtylo.</note>
<note position="left" xlink:label="note-0460-07" xlink:href="note-0460-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0460-08" xlink:href="note-0460-08a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0460-09" xlink:href="note-0460-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s29128" xml:space="preserve">VERVM poſterior hęc via cõmodius inſtituetur, ſi longitudines vmbrarum horologij pro-
<pb o="445" file="0461" n="461" rhead="LIBER QVARTVS."/>
poſiti transferantnt in rectam β θ, non ex puncto α, ſed ex puncto β. </s>
  <s xml:id="echoid-s29129" xml:space="preserve">Ita enim opus non erit du-<lb/>
<anchor type="note" xlink:label="note-0461-01a" xlink:href="note-0461-01"/>
cere alias duas parallelas propinquiores. </s>
  <s xml:id="echoid-s29130" xml:space="preserve">Sed tunc in futurum horologium transferendæ ſunt vm <lb/>bræ acceptæ non ex puncto α, ſed ex puncto γ, in recta γ λ. </s>
  <s xml:id="echoid-s29131" xml:space="preserve">Vt ſi vmbra translata eſſet recta β δ, <lb/>transferenda foret vmbra γ ε: </s>
  <s xml:id="echoid-s29132" xml:space="preserve">quia ob triangulorum ſimilitudinem, eadem proportio eſt ſtyli <lb/>
<anchor type="note" xlink:label="note-0461-02a" xlink:href="note-0461-02"/>
α β, ad vmbram ſuam β δ, quæ ſtyli α γ, ad rectam γ ε, &amp; </s>
  <s xml:id="echoid-s29133" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1500" type="float" level="2" n="8">
<note position="right" xlink:label="note-0461-01" xlink:href="note-0461-01a" xml:space="preserve">Longitudines <lb/>vmbrarum ali-<lb/>ter inueſtigan-<lb/>tur.</note>
<note position="right" xlink:label="note-0461-02" xlink:href="note-0461-02a" xml:space="preserve">4. ſexti.</note>
</div>
<p>
  <s xml:id="echoid-s29135" xml:space="preserve">QVAMVIS autem propoſitum horologium in maiorem formam redegimus in noſtro <lb/>exemplo, eiſdem tamen vijs idem ad minorem reducemus, ſi ex E G, vel ex α β, abſcindamus rectã <lb/>minori propoſito ſtylo æqualem. </s>
  <s xml:id="echoid-s29136" xml:space="preserve">Itaque horologium quodcunque deſcriptum ad maiorem, mi-<lb/>noremve formam, pro data magnitudine ſtyli, reduximus. </s>
  <s xml:id="echoid-s29137" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s29138" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1502" type="section" level="1" n="358">
<head xml:id="echoid-head371" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s29139" xml:space="preserve">FORT ASSIS idem hoc problema abſoluem{us} facili{us} hoc modo. </s>
  <s xml:id="echoid-s29140" xml:space="preserve">In recta linea quacunque ſu-<lb/>
<anchor type="note" xlink:label="note-0461-04a" xlink:href="note-0461-04"/>
mantur quot cunque rectæ A B, B C, C D, D E, E F, ſtylo A B, propoſiti horologii æquales, itatamen <lb/>vt tota linea ex illis rectis compoſita minor non ſit longiſſima vmbra ex ſtylo A B, cadente; </s>
  <s xml:id="echoid-s29141" xml:space="preserve">Et in alia <lb/>quapiam recta linea totidem rectæ accipiantur G H, H I, I K, K L, L M, ſtylo C D, futuri horologĳ, <lb/>ſiue maior is fuerit ſtylo A B, ſiue minor, æquales. </s>
  <s xml:id="echoid-s29142" xml:space="preserve">Deinde diuiſis ſingulis partibus prioris lineæ in <lb/>quot cunque partes æquales, (hortarer ego, vt primum ſingulæ diuidantur bifariam, deinde ſingulæ par-<lb/>ticulæ rurſus bifariam, &amp; </s>
  <s xml:id="echoid-s29143" xml:space="preserve">ſic deinceps, quo ad commodè fieri poterit, quo enim plures extiterint par-<lb/>tes, eo accuratius futurum horologium deſcribetur; </s>
  <s xml:id="echoid-s29144" xml:space="preserve">quæ quidem diuiſio omnium facillima est) ſecentur <lb/>
<anchor type="note" xlink:label="note-0461-05a" xlink:href="note-0461-05"/>
ſingulæ partes lineæ poſterioris in totidem, aſcriptis numeris, vt in præcedenti figura apparet. </s>
  <s xml:id="echoid-s29145" xml:space="preserve">Iam verò <lb/>ſi ex A, loco styli horologii propoſiti per omnia puncta horologii, quæ transferenda ſunt, ducantur rectæ <lb/>lineæ, eis{q́ue} ſimiles ex C, loco styli futuri horologii beneficio circuli ex C; </s>
  <s xml:id="echoid-s29146" xml:space="preserve">deſcripti emittãtur; </s>
  <s xml:id="echoid-s29147" xml:space="preserve">atque inter-<lb/>ualla omnium punctorum ex A, accepta transferantur in rectam A F, quibus ſimilia interualla in re-<lb/>cta G M, acceptatransfer antur in rectas ex C, emiſſas, reſpondentes{q́ue} rectis ex A, emiſſis, translata <lb/>erunt omnia puncta propoſiti horologii in horologiũ futurum. </s>
  <s xml:id="echoid-s29148" xml:space="preserve">Vnde ſi reſpondentia puncta rectis lineis <lb/>connectantur, deſcriptum erit horologium pro ſtylo C D. </s>
  <s xml:id="echoid-s29149" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s29150" xml:space="preserve">Interuallum A N, complecti <lb/>tur inrecta A F, partes 5. </s>
  <s xml:id="echoid-s29151" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s29152" xml:space="preserve">paulo amplius, quàm tertiam partem vnius. </s>
  <s xml:id="echoid-s29153" xml:space="preserve">Igitur ſi in recta G M, ſu-<lb/>mãtur quoque partes 5. </s>
  <s xml:id="echoid-s29154" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s29155" xml:space="preserve">paulo amplius, quàm tertia pars vnius, trãsferãtur{q́ue} in rectã C R, quę rectæ <lb/>A O, reſpõdet, propter æquales arcus P O, Q R, inueniemus punctũ X, reſpondens puncto N: </s>
  <s xml:id="echoid-s29156" xml:space="preserve">quia quam<unsure/> <lb/>
<anchor type="note" xlink:label="note-0461-06a" xlink:href="note-0461-06"/>
proportionẽ habet recta A B, ſtylo horologĳ propoſiti æqualis ad partes 5 {1/3}. </s>
  <s xml:id="echoid-s29157" xml:space="preserve">eandem habet recta G H, <lb/>ſtylo futuri horologĳ æqualis ad partes 5 {1/3}. </s>
  <s xml:id="echoid-s29158" xml:space="preserve">Eodẽ modo interuallum A Y, continet in recta A F, partes <lb/>7 {1/3}. </s>
  <s xml:id="echoid-s29159" xml:space="preserve">ſi igitur in recta G M, ſumantur totidem partes, &amp; </s>
  <s xml:id="echoid-s29160" xml:space="preserve">referantur in rectã C d, rectæ A Z, reſponden <lb/>tem, reperietur punctum e, reſpondens puncto Y. </s>
  <s xml:id="echoid-s29161" xml:space="preserve">Recta ergo connexa X e, reſpondebit rectæ N Y. </s>
  <s xml:id="echoid-s29162" xml:space="preserve">Ita <lb/>quoque, quoniam interuallum inter A, &amp; </s>
  <s xml:id="echoid-s29163" xml:space="preserve">horam 14. </s>
  <s xml:id="echoid-s29164" xml:space="preserve">ab ortu in tropico ♋, comprehendit partes 5. </s>
  <s xml:id="echoid-s29165" xml:space="preserve">præ-<lb/>cisè in linea A F, ſi totidem partes rectæ G M, transferantur ex C, in lineã vmbræ reſpondentem lineæ <lb/>vmbræ ex A, eductæ, habebitur punctum horæ 14. </s>
  <s xml:id="echoid-s29166" xml:space="preserve">ab ortu in tropico ♋, horologii futuri, &amp; </s>
  <s xml:id="echoid-s29167" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29168" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1502" type="float" level="2" n="1">
<note position="right" xlink:label="note-0461-04" xlink:href="note-0461-04a" xml:space="preserve">Qua uia aliter <lb/>augendum, vel <lb/>minuẽdum ſit <lb/>datum horolo-<lb/>gium.</note>
<note position="left" xlink:label="note-0461-05" xlink:href="note-0461-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0461-06" xlink:href="note-0461-06a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s29169" xml:space="preserve">HIC etiam loco linearum ex A, &amp; </s>
  <s xml:id="echoid-s29170" xml:space="preserve">C, emiſſarum vti poterimus regula aliqua, vt ſupra diximus.</s>
  <s xml:id="echoid-s29171" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s29172" xml:space="preserve">CVM Daniele autem Barbaro in fine ſuæ Perſpectiuæ, quam Italico ſermone conſcripſit, eandem <lb/>
<anchor type="note" xlink:label="note-0461-07a" xlink:href="note-0461-07"/>
hanc rationem ita instituemus. </s>
  <s xml:id="echoid-s29173" xml:space="preserve">Fiant duæ regulæ planæ, quæ habeant partes omnino æquales partibus <lb/>rectarum A F, G M, &amp; </s>
  <s xml:id="echoid-s29174" xml:space="preserve">in extremitatibus ſubtiliſſimos clauiculos affixos, ita vt circa ipſos in punctis <lb/>
<anchor type="note" xlink:label="note-0461-08a" xlink:href="note-0461-08"/>
A, &amp; </s>
  <s xml:id="echoid-s29175" xml:space="preserve">C, conſtitutos regulæ ipſę poſſint liberè circumduci, reſecentur{q́ue} partes ſuperfluæ, ita vt reliquę <lb/>ſint extremæ lineæ rectæ ex clauiculis, tanquam centris, prodeuntes, inſtar lineæ fiduciæ, ut vocant, <lb/>in aſtrolabio. </s>
  <s xml:id="echoid-s29176" xml:space="preserve">Poſt hæc diuiſo circulo ex A, deſcripto in quotcunque partes ſiue æquales, ſiue inæquales <lb/>ſecetur in eaſdem partes circulus ex C, deſcriptus. </s>
  <s xml:id="echoid-s29177" xml:space="preserve">Itaque poſita regula priore, quæ diuiſiones rectæ <lb/>A F, continet, in centro A, &amp; </s>
  <s xml:id="echoid-s29178" xml:space="preserve">circumducta liberè, donec eius linea fiduciæ per propoſitum punctum ho-<lb/>rologii tranſeat, notabimus in circumferentia circuli partem à linea fiducię abſciſſam, &amp; </s>
  <s xml:id="echoid-s29179" xml:space="preserve">partẽ, quam <lb/>punctum propoſitum in eadem linea fiducię monſtrat. </s>
  <s xml:id="echoid-s29180" xml:space="preserve">Nam ſi regulam poſteriorem collocemus in centro <lb/>C, circumducamuſ{q́ue}, donec eius linea fiduciæ abſcindat ex circumferentia circuli eandem partem, ſigna-<lb/>bimus in plano punctum, quod parti prædictæ in linea fiducię reſpondet. </s>
  <s xml:id="echoid-s29181" xml:space="preserve">Hoc enim erit punctum, quod <lb/>quæritur. </s>
  <s xml:id="echoid-s29182" xml:space="preserve">Exempli cauſa. </s>
  <s xml:id="echoid-s29183" xml:space="preserve">Prior regula in centro A, constituta, &amp; </s>
  <s xml:id="echoid-s29184" xml:space="preserve">ad punctũ horæ 14. </s>
  <s xml:id="echoid-s29185" xml:space="preserve">ab ortu, in tropico <lb/>
<anchor type="note" xlink:label="note-0461-09a" xlink:href="note-0461-09"/>
♋, admota ſecat circulum in ſ, punctum autem dictæ horæ cadit in eius partem quintam: </s>
  <s xml:id="echoid-s29186" xml:space="preserve">ſi igitur poſte-<lb/>rior regula in centro C, ſtatuatur, moueaturq́, donec eius linea fiducię abſcindat ex circulo arcum t u, <lb/>arcuir ſ, æqualem, notabimus in plano punctum, quod terminat partem ipſius quintã pro hora 14. </s>
  <s xml:id="echoid-s29187" xml:space="preserve">ab or <lb/>tuin tropico ♋, &amp; </s>
  <s xml:id="echoid-s29188" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29189" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1503" type="float" level="2" n="2">
<note position="right" xlink:label="note-0461-07" xlink:href="note-0461-07a" xml:space="preserve">Abſoluitur <lb/>problema alie<unsure/> <lb/>modo.</note>
<note position="left" xlink:label="note-0461-08" xlink:href="note-0461-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0461-09" xlink:href="note-0461-09a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Quando @@ylus <lb/>dari horologii <lb/>ad ſtylum horo <lb/>logii futuri pro <lb/>portionem ha-<lb/>bet multiplicẽ, <lb/>vel ſubmulti-<lb/>plicem, quo pa-<lb/>cto problema <lb/>abſoluatur fa-<lb/>cilius.</note>
<p style="it">
  <s xml:id="echoid-s29190" xml:space="preserve">QVOD ſi ſtylus A B, horologĳ propoſiti ad ſtylum C D, datum proportionem habeat multiplicẽ, <lb/>vel ſubmultiplicem, quod non raro vſu venire ſolet, quando horologium pro muro aliquo fabricatum in <lb/>ipſum murum ſub maiori forma eſt transferendum, (deſcripto enim horologio, licebit nobis ſtylum eli-<lb/>gere, qui prioris ſit vel duplus, triplus, decuplus, vel vigecuplus, &amp; </s>
  <s xml:id="echoid-s29191" xml:space="preserve">c. </s>
  <s xml:id="echoid-s29192" xml:space="preserve">prout horologĳ deſcribendi ma-<lb/>gnitudo exiget) expeditiſſimè maius, aut minus horologium conſtruemus, ſi omnia interualla horologii <lb/>propoſiti in eadem proportione multiplici, ſubmultiplicive, quam ſtylus ad ſtylum habet, accipiamus.</s>
  <s xml:id="echoid-s29193" xml:space="preserve">
<pb o="446" file="0462" n="462" rhead="GNOMONICES"/>
Vt ſi v. </s>
  <s xml:id="echoid-s29194" xml:space="preserve">g. </s>
  <s xml:id="echoid-s29195" xml:space="preserve">propoſitum horologium decies ſit maius conficiendum, ita vt ſtylus ad ſtylum, &amp; </s>
  <s xml:id="echoid-s29196" xml:space="preserve">ſingula in-<lb/>terualla ad ſingula interualla proportionem habeant decuplam, transferemus interuallum A N, decies <lb/>in rectam C R, quę rectæ A O, reſpondet, ita vt recta C X, decupla ſit rectæ A N, &amp; </s>
  <s xml:id="echoid-s29197" xml:space="preserve">c. </s>
  <s xml:id="echoid-s29198" xml:space="preserve">Vnde ſi rectè <lb/>deſcriptum eſt horologium, neceſſe eſt, vt ſingula interualla horologii, in quo ſtylus decies maior eſt ſtylo <lb/>horologĳ propoſiti, qualia ſunt interualla horaria in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s29199" xml:space="preserve">horizontali, nec non ſegmenta <lb/>linearum horariarum inter lineam æquinoctialem, &amp; </s>
  <s xml:id="echoid-s29200" xml:space="preserve">tropicos ♋, &amp; </s>
  <s xml:id="echoid-s29201" xml:space="preserve">♑, &amp; </s>
  <s xml:id="echoid-s29202" xml:space="preserve">c. </s>
  <s xml:id="echoid-s29203" xml:space="preserve">ſingulorum interuallorũ <lb/>reſpondentium ſint decupla. </s>
  <s xml:id="echoid-s29204" xml:space="preserve">Quocirca vt accuratè, quoad eius fieri poteſt, horologium eiuſmodi deſcri-<lb/>batur, ducendæ erunt prius linea ſtyli, æquinoctialis, &amp; </s>
  <s xml:id="echoid-s29205" xml:space="preserve">horizontalis: </s>
  <s xml:id="echoid-s29206" xml:space="preserve">deinde ſingula interualla lineæ <lb/>ęquinoctialis inter lineam ſtyli, &amp; </s>
  <s xml:id="echoid-s29207" xml:space="preserve">lineas horarias propoſiti horologĳ decuplanda in futuro horologio, <lb/>vel multiplicanda ſecundum proportionem ſtyli, minuendave in æquinoctiali linea, à ſtyli linea initio <lb/>
<anchor type="note" xlink:label="note-0462-01a" xlink:href="note-0462-01"/>
facto; </s>
  <s xml:id="echoid-s29208" xml:space="preserve">idem{q́ue} faciendum de interuallis in linea horizontali inter lineam ęquinoctialem, &amp; </s>
  <s xml:id="echoid-s29209" xml:space="preserve">lineas hora-<lb/>rias. </s>
  <s xml:id="echoid-s29210" xml:space="preserve">Nam ſi lineę horariæ puncta horarum reſpondentia, quæ in tropicis inuenta ſunt, connectentes, per <lb/>puncta illo modo inuenta in linea æquinoctiali, vel horizontali tranſierint, accuratiſſimè delineatum erit <lb/>borologium. </s>
  <s xml:id="echoid-s29211" xml:space="preserve">Quòd ſi viſum fuerit expedire, duci poterit in dato horologio linea vtcunque vel <lb/>æquinoctiali lineę, vel horizontali æquidistans, vel ad horizontalem lineam perpendicula-<lb/>ris, quę commode lineas horarias ſecet: </s>
  <s xml:id="echoid-s29212" xml:space="preserve">Deinde in futuro horologio alia duci illi <lb/>reſpondens ſecundum proportionem ſtyli. </s>
  <s xml:id="echoid-s29213" xml:space="preserve">Nam ſi omnia interual-<lb/>la prioris lineę multiplicentur ſecundum datam propor-<lb/>tionem in linea poſteriori, inuenta erunt pun-<lb/>cta, per quæ ducendæ ſunt ho-<lb/>
<anchor type="note" xlink:label="note-0462-02a" xlink:href="note-0462-02"/>
rariæ lineæ, &amp; </s>
  <s xml:id="echoid-s29214" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29215" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1504" type="float" level="2" n="3">
<note position="left" xlink:label="note-0462-01" xlink:href="note-0462-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0462-02" xlink:href="note-0462-02a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1506" type="section" level="1" n="359">
<head xml:id="echoid-head372" style="it" xml:space="preserve">FINIS QV ARTI LIBRI.</head>
<pb o="447" file="0463" n="463"/>
</div>
<div xml:id="echoid-div1507" type="section" level="1" n="360">
<head xml:id="echoid-head373" xml:space="preserve">GNOMONICES</head>
<head xml:id="echoid-head374" xml:space="preserve">LIBER QVINTVS.</head>
  <figure>
    <image file="0463-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0463-01"/>
  </figure>
</div>
<div xml:id="echoid-div1508" type="section" level="1" n="361">
<head xml:id="echoid-head375" style="it" xml:space="preserve">AVCTORE</head>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1509" type="section" level="1" n="362">
<head xml:id="echoid-head376" xml:space="preserve">CHRISTOPHORO CLAVIO BAMBERGENSI <lb/>SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s29216" xml:space="preserve">QVONIAM plerique, qui parum ſunt exercitati in ducendis <lb/>lineis perpendicularibus, &amp; </s>
  <s xml:id="echoid-s29217" xml:space="preserve">parallelis, quarum frequentiffi-<lb/>mus vſus eſt in horologiorum deſcriptionibus, quas ſuperiori-<lb/>bus libris tradidimus, difficultate rei perterriti diffidunt, ſe poſ-<lb/>ſe aliquando horologium aliquod ſine errore delineare, quod <lb/>
<anchor type="note" xlink:label="note-0463-02a" xlink:href="note-0463-02"/>
putent, fieri non poſſe, vt in tot perpendicularibus lineis, pa-<lb/>rallelisque occultis ducendis, quæ ad rectam horologii deſcri-<lb/>ptionem requiruntur, errorem aliquem non committant; </s>
  <s xml:id="echoid-s29218" xml:space="preserve">vi-<lb/>ſum eſt hoc libro viam, ac rationem præſcribere, qua quiuis, <lb/>qui vel mediocriter in tabula ſinuum verſatus ſit, proprio Marte ſibi tabulas quaſ-<lb/>dam poffit ſupputare, ex quibus deinde horas cuiuſcunque generis ſine moleſtia <lb/>vlla, laboreve in quocunque plano propoſito deſcribere queat, ad datam etiam ſty-<lb/>li magnitudinem quamcunque. </s>
  <s xml:id="echoid-s29219" xml:space="preserve">Negare enim non poſſum, perdifficile eſſe, ne di-<lb/>cam, fieri omnino non poſſe, vt in tanta multitudine occultarum linearum perpen <lb/>dicularium, atque parallelarum in nullum errorem labatur quis, etiamſi ea in re <lb/>
<anchor type="note" xlink:label="note-0463-03a" xlink:href="note-0463-03"/>
diu, multumq́ue ſeſe exercuerit. </s>
  <s xml:id="echoid-s29220" xml:space="preserve">Quod in deſcriptione horarum per tabulas, quas <lb/>iam iam ſupputabimus, contingere tam facile non poteſt, vt ex ſequentibus fiet <lb/>perſpicuum.</s>
  <s xml:id="echoid-s29221" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1509" type="float" level="2" n="1">
<note position="left" xlink:label="note-0463-02" xlink:href="note-0463-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0463-03" xlink:href="note-0463-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1511" type="section" level="1" n="363">
<head xml:id="echoid-head377" xml:space="preserve">PROBLEMA 1. PROPOSITIO 1.</head>
<p>
  <s xml:id="echoid-s29222" xml:space="preserve">ALTITVDINEM Solis ſupra quemcunque circulum maxi-<lb/>mum ſphærę pro ſingulis horis inueſtigare.</s>
  <s xml:id="echoid-s29223" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s29224" xml:space="preserve">QVA ratione altitudo Solis ſupra Horizontem ex data hora ſit ſupputanda, abundè <lb/>
<anchor type="note" xlink:label="note-0463-04a" xlink:href="note-0463-04"/>
docuimus propoſ. </s>
  <s xml:id="echoid-s29225" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29226" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29227" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29228" xml:space="preserve">nunc eandem inquiremus ſupra quemcunque circulũ <lb/>maximum, qui ab Horizonte differat, hoc modo. </s>
  <s xml:id="echoid-s29229" xml:space="preserve">Primum quæratur, per propoſ. <lb/></s>
  <s xml:id="echoid-s29230" xml:space="preserve">29. </s>
  <s xml:id="echoid-s29231" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29232" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29233" xml:space="preserve">altitudo poli ſupra circulum propoſitum: </s>
  <s xml:id="echoid-s29234" xml:space="preserve">Deinde ad hanc altitudinem <lb/>altitudo Solis meridiana, eiuſdemq́ue depreſſio inueniatur, vt in ſcholio huius <lb/>propoſ. </s>
  <s xml:id="echoid-s29235" xml:space="preserve">docebimus, ſumaturq́ue dimidium rectæ compoſitæ ex ſinu dictæ altitu-<lb/>dinis meridianæ, &amp; </s>
  <s xml:id="echoid-s29236" xml:space="preserve">ſinu depreſſionis meridianæ. </s>
  <s xml:id="echoid-s29237" xml:space="preserve">Poſtremo diſtantia Solis à Meridiano circulo <lb/>
<anchor type="note" xlink:label="note-0463-05a" xlink:href="note-0463-05"/>
proprio dati circuli maximi, hoc eſt, à circulo per polos mundi, &amp; </s>
  <s xml:id="echoid-s29238" xml:space="preserve">per polos circuli propoſiti du-<lb/>cto, inſtar Meridiani, inueſtigetur. </s>
  <s xml:id="echoid-s29239" xml:space="preserve">Quam ita inueniemus. </s>
  <s xml:id="echoid-s29240" xml:space="preserve">In circulis, ad quorum plana Meridia-<lb/>nus Horizontis rectus eſt, qualis eſt Verticalis circulus proprie dictus, circulus horę 6. </s>
  <s xml:id="echoid-s29241" xml:space="preserve">à meridie, <lb/>vel media nocte. </s>
  <s xml:id="echoid-s29242" xml:space="preserve">cui horologium polare æquidiſtat, Æquator, &amp; </s>
  <s xml:id="echoid-s29243" xml:space="preserve">circulus ad Horizontem incli-<lb/>
<anchor type="note" xlink:label="note-0463-06a" xlink:href="note-0463-06"/>
natus, &amp; </s>
  <s xml:id="echoid-s29244" xml:space="preserve">ad Meridianum rectus, ſumitur diſtantia à Meridiano, vt in Horizonte docuimus ad <lb/>initium propoſ. </s>
  <s xml:id="echoid-s29245" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29246" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29247" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29248" xml:space="preserve">quia Meridianus Horizontis eſt etiã illorum circulorum Meridianus, vt <lb/>patet. </s>
  <s xml:id="echoid-s29249" xml:space="preserve">In aliis autem circulis explorandum prius erit per propoſ. </s>
  <s xml:id="echoid-s29250" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29251" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29252" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29253" xml:space="preserve">quanta ſit inclinatio <lb/>proprii Meridiani cuiuſque illorum ad Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s29254" xml:space="preserve">in quam partem proprius il-<lb/>le Meridianus vergat, hoc eſt, an in ortũ, occaſumve à Meridiano Horizontis recedat; </s>
  <s xml:id="echoid-s29255" xml:space="preserve">quod qui-<lb/>dem facile percipiemus ex ſitu poli circuli maximi propoſiti, vt in lib. </s>
  <s xml:id="echoid-s29256" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29257" xml:space="preserve">docuimus propoſ. </s>
  <s xml:id="echoid-s29258" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29259" xml:space="preserve">13. <lb/></s>
  <s xml:id="echoid-s29260" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s29261" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29262" xml:space="preserve">Hac enim re perſpecta, difficile non erit, quantam diſtantiã à proprio Meridiano propoſiti <lb/>circuli habeat Sol qualibet hora, cognoſcere. </s>
  <s xml:id="echoid-s29263" xml:space="preserve">Nam ſi Meridianus proprius circuli maximi propo-<lb/>ſiti à Meridiano Horizontis in ſumpto hemiſpherio recedat in ortum, ſumenda erit diſtantia <lb/>Solis à meridie, vt ad initium propoſ. </s>
  <s xml:id="echoid-s29264" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29265" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29266" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29267" xml:space="preserve">ſcripſimus, ad quam ſi fuerit poſt meridiem, adij-
<pb o="448" file="0464" n="464" rhead="GNOMONICES"/>
cienda erit inclinatio Meridianorum, vt diſtãtia à proprio Meridiano circuli propoſiti habeatur; <lb/></s>
  <s xml:id="echoid-s29268" xml:space="preserve">ſi vero ante meridiem fuerit, &amp; </s>
  <s xml:id="echoid-s29269" xml:space="preserve">diſtantia à meridie minor inclinatione Meridianorum, detrahẽ-<lb/>da erit diſtantia à meridie ex inclinatione Meridianorum: </s>
  <s xml:id="echoid-s29270" xml:space="preserve">at ſi maior, ipſa inclinatio ex diſtantia <lb/>à meridie auferenda erit, vt diſtantia à Meridiano proprio circuli propoſiti relinquatur. </s>
  <s xml:id="echoid-s29271" xml:space="preserve">Quod <lb/>ſi quando accidat, diſtantiam Solis à meridie ante meridiem æqualem eſſe inclinationi Meridia-<lb/>norum, conſtitutus erit Sol in ipſo Meridiano circuli propoſiti. </s>
  <s xml:id="echoid-s29272" xml:space="preserve">Si autem Meridianus propoſiti <lb/>circuli in eodem hemiſphęrio ſuperno recedat à Meridiano Horizontis in occaſum, contrario <lb/>prorſus modo agendum erit. </s>
  <s xml:id="echoid-s29273" xml:space="preserve">Nam diſtantia Solis à meridie, ſi fueritante meridiem, addenda <lb/>erit inclinationi Meridianorum, vt diſtantia à meridiano circuli propoſiti habeatur; </s>
  <s xml:id="echoid-s29274" xml:space="preserve">ſi verò poſt <lb/>meridiem data fuerit hora, &amp; </s>
  <s xml:id="echoid-s29275" xml:space="preserve">eius diſtantia à meridie minor inclinatione Meridianorum, aufe-<lb/>
<anchor type="note" xlink:label="note-0464-01a" xlink:href="note-0464-01"/>
renda erit diſtantia à meridie inuenta ex inclinatione Meridianorum; </s>
  <s xml:id="echoid-s29276" xml:space="preserve">at ſi maior, inclinatio ipſa <lb/>ex diſtantia à meridie ſubtrahenda, vt reliqua ſit diſtantia Solis à Meridiano circuli propoſiti. <lb/></s>
  <s xml:id="echoid-s29277" xml:space="preserve">At verò ſi Meridianus proprius circuli propoſiti à Meridiano Horizontis infra Horizontem rece-<lb/>dat in ortum, vt contingit in faciebus circulorum, quas Sol illuminaret media nocte, ſi à rerra <lb/>non impediretur, (quales ſunt facies inferiorum circulorum poſitionum, &amp; </s>
  <s xml:id="echoid-s29278" xml:space="preserve">boreales circulorum <lb/>Verticalium in regionibus, quarum vertex capitis citra tropicum ♋, conſtituitur &amp;</s>
  <s xml:id="echoid-s29279" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s29280" xml:space="preserve">accipien-<lb/>da erit diſtantia Solis à media nocte; </s>
  <s xml:id="echoid-s29281" xml:space="preserve">ad quam, ſi fuerit ante mediam noctem, adiicienda erit in-<lb/>clinatio Meridianorum: </s>
  <s xml:id="echoid-s29282" xml:space="preserve">Si verò poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s29283" xml:space="preserve">diſtantia inuenta à media nocte minor <lb/>fuerit inclinatione Meridianorum, detrahenda erit ipſamet diſtantia ab inclinatione; </s>
  <s xml:id="echoid-s29284" xml:space="preserve">ſi autẽ ma-<lb/>ior, auferenda erit inclinatio ipſa ex diſtantia à media nocte, vt habeatur diſtãtia Solis à Meridia-<lb/>
<anchor type="note" xlink:label="note-0464-02a" xlink:href="note-0464-02"/>
no proprio circuli propoſiti infra Horizontem. </s>
  <s xml:id="echoid-s29285" xml:space="preserve">Si autem Meridianus circuli propoſiti à Meridia-<lb/>no Horizontis in hemiſphærio infero recedat in occaſum, contrarium omnino faciendum erit. <lb/></s>
  <s xml:id="echoid-s29286" xml:space="preserve">Quod vt planius fiat, apponemus exempla in Meridiano Horizontis, ac nonnullis alijs circulis, <lb/>quibus horologia in lib. </s>
  <s xml:id="echoid-s29287" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29288" xml:space="preserve">deſcripta æquidiſtant, &amp; </s>
  <s xml:id="echoid-s29289" xml:space="preserve">ad quos Meridianus Horizõtis rectus nõ eſt.</s>
  <s xml:id="echoid-s29290" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1511" type="float" level="2" n="1">
<note position="left" xlink:label="note-0463-04" xlink:href="note-0463-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0463-05" xlink:href="note-0463-05a" xml:space="preserve">Diſtantia Solis <lb/>à Meridiano <lb/>proprio cuiuſ-<lb/>cunque circuli <lb/>maximi qua at <lb/>te exploretut.</note>
<note position="left" xlink:label="note-0463-06" xlink:href="note-0463-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0464-01" xlink:href="note-0464-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0464-02" xlink:href="note-0464-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s29291" xml:space="preserve">IN Meridiano igitur circulo, quoniam circulus horæ 6. </s>
  <s xml:id="echoid-s29292" xml:space="preserve">à meridie, vel media nocte eſt inſta@ <lb/>
<anchor type="note" xlink:label="note-0464-03a" xlink:href="note-0464-03"/>
Meridiani ipſius, receditq́ue ab eodem grad. </s>
  <s xml:id="echoid-s29293" xml:space="preserve">90. </s>
  <s xml:id="echoid-s29294" xml:space="preserve">tam in ortum, quàm in occaſum, ſupputandæ <lb/>erunt omnes diſtantię Solis à ſexta hora à media nocte, vel à meridie; </s>
  <s xml:id="echoid-s29295" xml:space="preserve">adeò vt hora 9. </s>
  <s xml:id="echoid-s29296" xml:space="preserve">poſt mediã <lb/>noctem diſter Sol à proprio Meridiano orientali ipſius circuli Meridiani, id eſt, ab hora 6. </s>
  <s xml:id="echoid-s29297" xml:space="preserve">à me-<lb/>dia nocte hor. </s>
  <s xml:id="echoid-s29298" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29299" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s29300" xml:space="preserve">45. </s>
  <s xml:id="echoid-s29301" xml:space="preserve">at verò hora quinta poſt mediam noctem diſtet per horam 1. <lb/></s>
  <s xml:id="echoid-s29302" xml:space="preserve">ſiue grad. </s>
  <s xml:id="echoid-s29303" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29304" xml:space="preserve">Sic etiam hora 2. </s>
  <s xml:id="echoid-s29305" xml:space="preserve">poſt meridiem diſtabit Sol à proprio Meridiano occidentali ip-<lb/>
<anchor type="note" xlink:label="note-0464-04a" xlink:href="note-0464-04"/>
ſius circuli Meridiani, hoc eſt, ab hora 6. </s>
  <s xml:id="echoid-s29306" xml:space="preserve">à meridie horis quatuor, ſeu grad. </s>
  <s xml:id="echoid-s29307" xml:space="preserve">60. </s>
  <s xml:id="echoid-s29308" xml:space="preserve">At verò hora 6.</s>
  <s xml:id="echoid-s29309" xml:space="preserve">{1/2}. <lb/></s>
  <s xml:id="echoid-s29310" xml:space="preserve">à meridie diſtabit ab eodem proprio Meridiano hor. </s>
  <s xml:id="echoid-s29311" xml:space="preserve">{1/2}, vel grad. </s>
  <s xml:id="echoid-s29312" xml:space="preserve">7. </s>
  <s xml:id="echoid-s29313" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29314" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29315" xml:space="preserve">In facie enim circu-<lb/>li Meridiani orientali ſupputandæ ſunt dictæ diſtantiæ ab hora 6. </s>
  <s xml:id="echoid-s29316" xml:space="preserve">à media nocte. </s>
  <s xml:id="echoid-s29317" xml:space="preserve">In facie verò oc-<lb/>cidentali ab hora 6. </s>
  <s xml:id="echoid-s29318" xml:space="preserve">à meridie.</s>
  <s xml:id="echoid-s29319" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1512" type="float" level="2" n="2">
<note position="left" xlink:label="note-0464-03" xlink:href="note-0464-03a" xml:space="preserve">Diſtantiæ So-<lb/>lis à Meridia-<lb/>no proprio Me <lb/>ridiani Hori-<lb/>zontis, hoc eſt, <lb/>à circulo horæ <lb/>6. a mer. vel <lb/>med. noc.</note>
<note position="left" xlink:label="note-0464-04" xlink:href="note-0464-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s29320" xml:space="preserve">DEINDE in Verticali circulo, qui à meridie in ortum declinat grad. </s>
  <s xml:id="echoid-s29321" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29322" xml:space="preserve">cui horologium <lb/>
<anchor type="note" xlink:label="note-0464-05a" xlink:href="note-0464-05"/>
æquidiſtans delineauimus propoſ. </s>
  <s xml:id="echoid-s29323" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29324" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29325" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29326" xml:space="preserve">quoniam eius Meridianus à Meridiano Horizontis re-<lb/>cedit in ortum grad. </s>
  <s xml:id="echoid-s29327" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29328" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29329" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29330" xml:space="preserve">fermè, vt ibidem diximus, ſi ad horam 2. </s>
  <s xml:id="echoid-s29331" xml:space="preserve">à meridie, hoc eſt, ad <lb/>grad. </s>
  <s xml:id="echoid-s29332" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29333" xml:space="preserve">quibus Sol à Meridiano Horizontis abeſt pomeridiano tempore, adijciamus grad. </s>
  <s xml:id="echoid-s29334" xml:space="preserve">40. <lb/></s>
  <s xml:id="echoid-s29335" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29336" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29337" xml:space="preserve">efficiemus grad. </s>
  <s xml:id="echoid-s29338" xml:space="preserve">70. </s>
  <s xml:id="echoid-s29339" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29340" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29341" xml:space="preserve">pro diſtantia Solis à Meridiano dicti Verticalis illo tempo <lb/>re. </s>
  <s xml:id="echoid-s29342" xml:space="preserve">Si autem tempore horæ 10 {1/2}. </s>
  <s xml:id="echoid-s29343" xml:space="preserve">poſt mediam noctem diſtantiam Solis à Meridiano Ho-<lb/>
<anchor type="note" xlink:label="note-0464-06a" xlink:href="note-0464-06"/>
rizontis, id eſt, grad. </s>
  <s xml:id="echoid-s29344" xml:space="preserve">22. </s>
  <s xml:id="echoid-s29345" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29346" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29347" xml:space="preserve">detrahamus ex grad. </s>
  <s xml:id="echoid-s29348" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29349" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29350" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29351" xml:space="preserve">remanebunt grad. </s>
  <s xml:id="echoid-s29352" xml:space="preserve">18. </s>
  <s xml:id="echoid-s29353" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29354" xml:space="preserve">18. <lb/></s>
  <s xml:id="echoid-s29355" xml:space="preserve">pro diſtãtia Solis à Meridiano eiuſdem Verticalis illo tempore. </s>
  <s xml:id="echoid-s29356" xml:space="preserve">Denique ſi tempore horæ 7. </s>
  <s xml:id="echoid-s29357" xml:space="preserve">poſt <lb/>mediam noctem ex diſtantia Solis, quam à meridie habet, nempe ex grad. </s>
  <s xml:id="echoid-s29358" xml:space="preserve">105. </s>
  <s xml:id="echoid-s29359" xml:space="preserve">deducamus grad. </s>
  <s xml:id="echoid-s29360" xml:space="preserve"><lb/>40. </s>
  <s xml:id="echoid-s29361" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29362" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29363" xml:space="preserve">relinquentur pro diſtantia Solis à Meridiano eiuſdem Verticalis illo tempore grad. </s>
  <s xml:id="echoid-s29364" xml:space="preserve"><lb/>64. </s>
  <s xml:id="echoid-s29365" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29366" xml:space="preserve">12. </s>
  <s xml:id="echoid-s29367" xml:space="preserve">Verum in facie eiuſdem Verticalis boreali, quoniam Sol in meridie eam non illumi <lb/>nat, ſed media nocte illam illuſtraret, ſi terra non impediret eius radios, inueniemus diſtantiam <lb/>Solis à Meridiano proprio dictæ faciei hora 8. </s>
  <s xml:id="echoid-s29368" xml:space="preserve">poſt meridiem hoc modo. </s>
  <s xml:id="echoid-s29369" xml:space="preserve">Diſtantia tunc Solis à <lb/>media nocte continet horas 4. </s>
  <s xml:id="echoid-s29370" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s29371" xml:space="preserve">60. </s>
  <s xml:id="echoid-s29372" xml:space="preserve">quæ quidem ante mediam noctem eſt. </s>
  <s xml:id="echoid-s29373" xml:space="preserve">Et quia <lb/>Meridianus proprius infra Horizontem recedit à Meridiano Horizõtis occaſum verſus grad. </s>
  <s xml:id="echoid-s29374" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29375" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s29376" xml:space="preserve">48. </s>
  <s xml:id="echoid-s29377" xml:space="preserve">eſtq́ue diſtantia inuenta maior hac inclinatione, auferenda erit inclinatio ex dicta diſtan <lb/>tia, vt relinquantur grad. </s>
  <s xml:id="echoid-s29378" xml:space="preserve">19. </s>
  <s xml:id="echoid-s29379" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29380" xml:space="preserve">12. </s>
  <s xml:id="echoid-s29381" xml:space="preserve">pro diſtantia Solis à proprio Meridiano dicti Verticalis in <lb/>
<anchor type="note" xlink:label="note-0464-07a" xlink:href="note-0464-07"/>
facie boreali.</s>
  <s xml:id="echoid-s29382" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1513" type="float" level="2" n="3">
<note position="left" xlink:label="note-0464-05" xlink:href="note-0464-05a" xml:space="preserve">Diſtantiæ So <lb/>lis à Meridia <lb/>no proprio cir-<lb/>cu@@ Verticalis, <lb/>qui à meridie <lb/>in ortum decli <lb/>nat grad. 30.</note>
<note position="left" xlink:label="note-0464-06" xlink:href="note-0464-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0464-07" xlink:href="note-0464-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s29383" xml:space="preserve">RVRSVS in circulo poſitionis declinante ab Horizonte grad. </s>
  <s xml:id="echoid-s29384" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29385" xml:space="preserve">cuius facies ſuperior ad <lb/>
<anchor type="note" xlink:label="note-0464-08a" xlink:href="note-0464-08"/>
occaſum ſpectat, cui horologium æquidiſtans propoſ. </s>
  <s xml:id="echoid-s29386" xml:space="preserve">13. </s>
  <s xml:id="echoid-s29387" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29388" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29389" xml:space="preserve">deſcripſimus, quia eius Meridianus <lb/>à Meridiano Horizontis in occaſum recedit grad. </s>
  <s xml:id="echoid-s29390" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29391" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29392" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29393" xml:space="preserve">ſi ad horam 7. </s>
  <s xml:id="echoid-s29394" xml:space="preserve">poſt mediam noctẽ, <lb/>hoc eſt, ad grad. </s>
  <s xml:id="echoid-s29395" xml:space="preserve">105. </s>
  <s xml:id="echoid-s29396" xml:space="preserve">quibus Sol à Meridiano Horizontis abeſt tempore antemeridiano, addamus <lb/>grad. </s>
  <s xml:id="echoid-s29397" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29398" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29399" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29400" xml:space="preserve">conficiemus grad. </s>
  <s xml:id="echoid-s29401" xml:space="preserve">142. </s>
  <s xml:id="echoid-s29402" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29403" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29404" xml:space="preserve">pro diſtantia Solis à Meridiano dicti circuli po-<lb/>ſitionis. </s>
  <s xml:id="echoid-s29405" xml:space="preserve">Si verò tempore horæ 17. </s>
  <s xml:id="echoid-s29406" xml:space="preserve">ab occaſu, Sole exiſtente in principio ♋, (cum meridies fit <lb/>hora 16. </s>
  <s xml:id="echoid-s29407" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29408" xml:space="preserve">28. </s>
  <s xml:id="echoid-s29409" xml:space="preserve">ab occaſu, ad latitudinem grad. </s>
  <s xml:id="echoid-s29410" xml:space="preserve">42.) </s>
  <s xml:id="echoid-s29411" xml:space="preserve">auferamus ex grad. </s>
  <s xml:id="echoid-s29412" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29413" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29414" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29415" xml:space="preserve">diſtantiam <lb/>Solis à meridie, nempe grad. </s>
  <s xml:id="echoid-s29416" xml:space="preserve">8. </s>
  <s xml:id="echoid-s29417" xml:space="preserve">reliqua erit diſtantia Solis à Meridiano dicti circuli poſitionis <lb/>grad. </s>
  <s xml:id="echoid-s29418" xml:space="preserve">29. </s>
  <s xml:id="echoid-s29419" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29420" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29421" xml:space="preserve">Si denique tempore horæ 7. </s>
  <s xml:id="echoid-s29422" xml:space="preserve">à meridie ex diſtantia Solis, quam à Meridiano
<pb o="449" file="0465" n="465" rhead="LIBER QVARTVS."/>
Horizontis habet, hoc eſt, ex grad. </s>
  <s xml:id="echoid-s29423" xml:space="preserve">105. </s>
  <s xml:id="echoid-s29424" xml:space="preserve">ſubtrahantur grad. </s>
  <s xml:id="echoid-s29425" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29426" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29427" xml:space="preserve">50. </s>
  <s xml:id="echoid-s29428" xml:space="preserve">relinquetur diſtantia So-<lb/>lis à Meridiano eiuſdem circuli poſitionis grad. </s>
  <s xml:id="echoid-s29429" xml:space="preserve">67. </s>
  <s xml:id="echoid-s29430" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29431" xml:space="preserve">10.</s>
  <s xml:id="echoid-s29432" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1514" type="float" level="2" n="4">
<note position="left" xlink:label="note-0464-08" xlink:href="note-0464-08a" xml:space="preserve">Diſtantiæ So-<lb/>lis à Meridia-<lb/>no proprio cir-<lb/>culi poſitionis, <lb/>qui ab Horizõ <lb/>@e declinat gr. <lb/>30. faciesq́ue <lb/>eius ſuperior <lb/>in occaſum ſpe <lb/>ctat.</note>
</div>
<note position="right" xml:space="preserve">Diſtantiæ Solis <lb/>a<unsure/> Meridiano <lb/>proprio circuli <lb/>maximi, qui a <lb/>borea in ortũ <lb/>declinat grad. <lb/>60. inclinatu@q́; <lb/>eſt ad Herizon <lb/>t@m grad. 80.</note>
<p>
  <s xml:id="echoid-s29433" xml:space="preserve">AD hęc in circulo maximo, qui à ſeptentrione in ortum declinat grad. </s>
  <s xml:id="echoid-s29434" xml:space="preserve">60. </s>
  <s xml:id="echoid-s29435" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s29436" xml:space="preserve">ad Horizontem <lb/>inclinatus eſt grad. </s>
  <s xml:id="echoid-s29437" xml:space="preserve">80. </s>
  <s xml:id="echoid-s29438" xml:space="preserve">cui æquidiſtat horologium quintum propoſ. </s>
  <s xml:id="echoid-s29439" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29440" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29441" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29442" xml:space="preserve">deſcriptum, quia <lb/>Meridianus ipſius à Meridiano Horizontis diſtat verſus ortum grad. </s>
  <s xml:id="echoid-s29443" xml:space="preserve">75. </s>
  <s xml:id="echoid-s29444" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29445" xml:space="preserve">46. </s>
  <s xml:id="echoid-s29446" xml:space="preserve">vt ibidem di-<lb/>ximus, inueniemus diſtantias Solis ſingulis horis à dicto Meridiano propoſiti circuli maximi, <lb/>quemadmodum in præcedentibus, &amp;</s>
  <s xml:id="echoid-s29447" xml:space="preserve">c.</s>
  <s xml:id="echoid-s29448" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s29449" xml:space="preserve">IAM verò his ita inuentis, ſi ſiat, vt ſinus totus ad ſinum verſum diſtantiæ Solis à Meridiano <lb/>
<anchor type="note" xlink:label="note-0465-02a" xlink:href="note-0465-02"/>
proprio circuli propoſiti, ita medietas rectæ compoſitæ ex ſinu altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s29450" xml:space="preserve">ſinu de-<lb/>preſſionis meridianæ, ad aliud, reperietur differentia inter ſinum altitudinis Solis ſupra propoſi-<lb/>
<anchor type="note" xlink:label="note-0465-03a" xlink:href="note-0465-03"/>
tum circulum tempore obſeruationis, &amp; </s>
  <s xml:id="echoid-s29451" xml:space="preserve">ſinum altitudinis meridianæ. </s>
  <s xml:id="echoid-s29452" xml:space="preserve">Ablata igitur hac differen <lb/>tia ex ſinu altitudinis meridianæ, notus relinquetur ſinus altitudinis Solis quęſitæ.</s>
  <s xml:id="echoid-s29453" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1515" type="float" level="2" n="5">
<note position="right" xlink:label="note-0465-02" xlink:href="note-0465-02a" xml:space="preserve">Altitudo Solis <lb/>@upra quemcũ-<lb/>que citculum <lb/>maximũ ſphæ-<lb/>ræ ad datã ho-<lb/>ram quomodo <lb/>ſupputetur.</note>
<note position="left" xlink:label="note-0465-03" xlink:href="note-0465-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s29454" xml:space="preserve">QVOD ſi quando differentia hæc inuenta fuerit maior ſinu altitudinis meridianæ, non con <lb/>
<anchor type="note" xlink:label="note-0465-04a" xlink:href="note-0465-04"/>
tinebitur hora illa, cuius diſtantiæ à Meridiano ſinum verſum accepimus, ſupra faciem circuli <lb/>propoſitam, ſed cadet in alteram faciem. </s>
  <s xml:id="echoid-s29455" xml:space="preserve">Vnde ſi tunc è contrario ſinum altitudinis meridianæ <lb/>ex differentia inuenta auferamus, relinquetur ſinus altitudinis Solis ſupra faciem oppoſitam dati <lb/>circuli maximi, ad illam horam. </s>
  <s xml:id="echoid-s29456" xml:space="preserve">Exempli gratia; </s>
  <s xml:id="echoid-s29457" xml:space="preserve">Inuenienda ſit altitudo Solis ſupra faciem au-<lb/>ſtralem Verticalis circuli ad latitudinem grad. </s>
  <s xml:id="echoid-s29458" xml:space="preserve">42. </s>
  <s xml:id="echoid-s29459" xml:space="preserve">pro hora 5. </s>
  <s xml:id="echoid-s29460" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s29461" xml:space="preserve">Quoniam polus antar <lb/>cticus ſupra illam faciem eleuatur grad. </s>
  <s xml:id="echoid-s29462" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29463" xml:space="preserve">erit complementum huius altitudinis grad. </s>
  <s xml:id="echoid-s29464" xml:space="preserve">42. </s>
  <s xml:id="echoid-s29465" xml:space="preserve">e qui-<lb/>bus ſi deducatur maxima declinatio Solis grad. </s>
  <s xml:id="echoid-s29466" xml:space="preserve">23. </s>
  <s xml:id="echoid-s29467" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29468" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29469" xml:space="preserve">remanebit altitudo meridiaua princi-<lb/>
<anchor type="note" xlink:label="note-0465-05a" xlink:href="note-0465-05"/>
pij ♋, ſupra dictam faciem grad. </s>
  <s xml:id="echoid-s29470" xml:space="preserve">18. </s>
  <s xml:id="echoid-s29471" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29472" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29473" xml:space="preserve">vt ex ſequenti ſcholio erit manifeſtum, cuius ſinus <lb/>eſt 31730. </s>
  <s xml:id="echoid-s29474" xml:space="preserve">ſinus autem depreſſionis meridianæ grad. </s>
  <s xml:id="echoid-s29475" xml:space="preserve">65. </s>
  <s xml:id="echoid-s29476" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29477" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29478" xml:space="preserve">eſt 90996. </s>
  <s xml:id="echoid-s29479" xml:space="preserve">Et medietas aggrega-<lb/>ti ex dictis ſinubus 61363. </s>
  <s xml:id="echoid-s29480" xml:space="preserve">Itaque ſi fiat vt 100000. </s>
  <s xml:id="echoid-s29481" xml:space="preserve">ſinus totus ad 74119. </s>
  <s xml:id="echoid-s29482" xml:space="preserve">ſinum verſum diſtantiæ <lb/>Solis à meridie, ita 61363. </s>
  <s xml:id="echoid-s29483" xml:space="preserve">medietas prędicta ad aliud, inuenietur hic ferè numerus 45481. </s>
  <s xml:id="echoid-s29484" xml:space="preserve">à quo, <lb/>quoniam maior eſt, ſi detrahatur ſinus altitudinis meridianæ 31730. </s>
  <s xml:id="echoid-s29485" xml:space="preserve">reliquus erit ſinus altitudi-<lb/>nis Solis ſupra faciem Verticalis circuli borealem hora 5. </s>
  <s xml:id="echoid-s29486" xml:space="preserve">à meridie, vel 7. </s>
  <s xml:id="echoid-s29487" xml:space="preserve">à media nocte, paralle-<lb/>li ♋, 13751. </s>
  <s xml:id="echoid-s29488" xml:space="preserve">cui reſpondent grad. </s>
  <s xml:id="echoid-s29489" xml:space="preserve">7. </s>
  <s xml:id="echoid-s29490" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29491" xml:space="preserve">54. </s>
  <s xml:id="echoid-s29492" xml:space="preserve">pro altitudine Solis quæſita. </s>
  <s xml:id="echoid-s29493" xml:space="preserve">Rurſus eadem altitudo <lb/>quæratur ad horam 11. </s>
  <s xml:id="echoid-s29494" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s29495" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s29496" xml:space="preserve">ſinus totus ad 196592. </s>
  <s xml:id="echoid-s29497" xml:space="preserve">ſinum verſum diſtantiæ <lb/>Solis à meridie, ita 61363. </s>
  <s xml:id="echoid-s29498" xml:space="preserve">medietas prædicta ad aliud, inuenieturq́ue hic numerus 120634. </s>
  <s xml:id="echoid-s29499" xml:space="preserve">à quo <lb/>ſi dematur ſinus altitudinis meridianæ 31730. </s>
  <s xml:id="echoid-s29500" xml:space="preserve">relinquetur pro ſinu altitudinis Solis ſupra eandẽ <lb/>
<anchor type="note" xlink:label="note-0465-06a" xlink:href="note-0465-06"/>
faciem oppoſitam, nempe borealem Verticalis circuli, hic fere numerus 88904. </s>
  <s xml:id="echoid-s29501" xml:space="preserve">cui debentur gr. <lb/></s>
  <s xml:id="echoid-s29502" xml:space="preserve">62. </s>
  <s xml:id="echoid-s29503" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29504" xml:space="preserve">45. </s>
  <s xml:id="echoid-s29505" xml:space="preserve">pro altitudine Solis quæſita. </s>
  <s xml:id="echoid-s29506" xml:space="preserve">Itaque ſi diſtantiæ Solis à Meridiano cuiuſque circuli <lb/>maximi propoſiti ſupra Horizontem, vel infra accipiantur in ſingulis horis, inuenientur altitu-<lb/>dines Solis ſupra vtramque eius faciem. </s>
  <s xml:id="echoid-s29507" xml:space="preserve">Nam cum differentia inuenta detrahitur à ſinu altitudi-<lb/>nis meridianæ parallelli ♋, altitudines inuentæ erunt ſupra faciem, ſupra quam accepta eſt altitu-<lb/>do meridiana, &amp; </s>
  <s xml:id="echoid-s29508" xml:space="preserve">depreſſio: </s>
  <s xml:id="echoid-s29509" xml:space="preserve">cum verò viciſſim ſinus altitudinis meridianæ à dicta inuenta diffe-<lb/>rentia ſubducitur, ſupra faciem oppoſitam, vt diximus. </s>
  <s xml:id="echoid-s29510" xml:space="preserve">Ego eligerem ſemper diſtantias Solis à <lb/>Meridiano ſupra Horizontem, conſiderando diligenter, ſupra quam faciem plani cadat radius So <lb/>lis in Meridiano propoſiti circuli ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s29511" xml:space="preserve">in eo parallelo exiſtentis, cuius horarum <lb/>altitudines indagantur; </s>
  <s xml:id="echoid-s29512" xml:space="preserve">necnon vter polorum ſupra eandem faciem ſit eleuatus, vt oblati paralle-<lb/>
<anchor type="note" xlink:label="note-0465-07a" xlink:href="note-0465-07"/>
li altitudo meridiana poſſit inueniri, vt mox in ſequenti ſcholio docebimus.</s>
  <s xml:id="echoid-s29513" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1516" type="float" level="2" n="6">
<note position="right" xlink:label="note-0465-04" xlink:href="note-0465-04a" xml:space="preserve">Quando diffe-<lb/>rentia inter fi-<lb/>num altitudi-<lb/>nis Solis, &amp; ſi-<lb/>num altitudi-<lb/>nis meridianæ <lb/>maior eſt ſinu <lb/>altitudinis me-<lb/>ridianæ, non c@ <lb/>dit hora illa, <lb/>pro qua altitu-<lb/>do inueſtiga-<lb/>tur, in faciẽ cir <lb/>culi propoſitã, <lb/>ſed in alteram <lb/>faciem.</note>
<note position="left" xlink:label="note-0465-05" xlink:href="note-0465-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0465-06" xlink:href="note-0465-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0465-07" xlink:href="note-0465-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s29514" xml:space="preserve">DEMONSTRATIO huius rationis inueniendæ altitudinis Solis petatur ex propoſ. </s>
  <s xml:id="echoid-s29515" xml:space="preserve">36. <lb/></s>
  <s xml:id="echoid-s29516" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s29517" xml:space="preserve">Eadem enim ratio hic eſt, quæ in Horizonte, cum quilibet circulus maximus vices gerat <lb/>Horizontis in aliqua regione. </s>
  <s xml:id="echoid-s29518" xml:space="preserve">Quod veròattinet ad altitudinem Solis ſupra faciem circuli oppo <lb/>ſitam, concipiatur in ſecundo circulo primæ figuræ propoſ. </s>
  <s xml:id="echoid-s29519" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29520" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29521" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29522" xml:space="preserve">recta T R, eſſe communis <lb/>ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s29523" xml:space="preserve">circuli maximi, ſupra quem altitudo Solis inueſtigatur, ita vt K T, ſit ſinus <lb/>altitudinis meridianæ. </s>
  <s xml:id="echoid-s29524" xml:space="preserve">Si igitur Sol ponatur in S, vltra dictum circulum, ita vt illuſtret oppoſi-<lb/>tam faciem verſus alterum polum G, inuenietur recta K N, ex dicta ſupputatione maior, quàm <lb/>K T, ſinus altitudinis meridianæ. </s>
  <s xml:id="echoid-s29525" xml:space="preserve">Vnde ablato ſinu altitudinis meridianę K T, ex inuenta recta <lb/>K N, remanebit N T, ſinus altitudinis Solis ſupra faciem oppoſitam circuli propoſiti.</s>
  <s xml:id="echoid-s29526" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s29527" xml:space="preserve">VTIMVR autem in altitudine Solis perueſtiganda ſolo illo modo, quem vltimo loco pro-<lb/>poſuimus propoſ. </s>
  <s xml:id="echoid-s29528" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29529" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s29530" xml:space="preserve">ante triangula ſphærica, quia clariſſimus inter omnes, &amp; </s>
  <s xml:id="echoid-s29531" xml:space="preserve">apertiſſi-<lb/>mus eſt, atque ad omnes parallelos ad quamcumque latitudinem poli ſupra circulum maximum <lb/>propoſitum pertinet, vt ibidem monuimus. </s>
  <s xml:id="echoid-s29532" xml:space="preserve">Vide tamen ea, quæ ad finem ſcholij propoſ. </s>
  <s xml:id="echoid-s29533" xml:space="preserve">36. </s>
  <s xml:id="echoid-s29534" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s29535" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29536" xml:space="preserve">ſcripſimus, quando parallelus vel tangit circulum maximũ propoſitũ, vel totus ſupra eum ex-<lb/>tat, tanquam ſupra Horizontem. </s>
  <s xml:id="echoid-s29537" xml:space="preserve">Nullius autem negotij erit reliquos modos, quos in dicta pro-<lb/>poſ. </s>
  <s xml:id="echoid-s29538" xml:space="preserve">præſcripſimus, huc accommodare, ſi viſum fuerit.</s>
  <s xml:id="echoid-s29539" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Altitudo Solis <lb/>ſu pra Meridia <lb/>num Horizon <lb/>tis tam @recti, <lb/>quàm obliqui, <lb/>qua ratione i@ <lb/>quiratur.</note>
<p>
  <s xml:id="echoid-s29540" xml:space="preserve">ALTITVDINEM quoque Solis ſupra Meridianum Horizontis tam recti, quam obliqui, <lb/>quam metitur circulus maximus per polos Meridiani, hoc eſt, per communes ſectiones Æquato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s29541" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s29542" xml:space="preserve">à meridie, vel media nocte, vel Horizontis, ac per centrum Solis ductus, <lb/>ita explorabimus, Sit Horizon rectus, vel circulus horæ 6. </s>
  <s xml:id="echoid-s29543" xml:space="preserve">à meridie, vel media nocte A B C D;</s>
  <s xml:id="echoid-s29544" xml:space="preserve">
<pb o="450" file="0466" n="466" rhead="GNOMONICES"/>
Meridianus ipſius A E C; </s>
  <s xml:id="echoid-s29545" xml:space="preserve">parallelus Solis ſiueborealis, ſiue auſtralis F G, in quo exiſtat Sol in <lb/>puncto H, per quod &amp; </s>
  <s xml:id="echoid-s29546" xml:space="preserve">polos A, C, circulus horarius, vel declinationis ducatur A H C, ſecans <lb/>Æquatorem in K, ita vt E K, ſit diſtantia Solis à Meridiano. </s>
  <s xml:id="echoid-s29547" xml:space="preserve">Ducatur quoque per B, polum Me-<lb/>ridiani, &amp; </s>
  <s xml:id="echoid-s29548" xml:space="preserve">punctum H, circulus maximus B H I, ita vt H I, ſit arcus altitudinis Solis ſupra Meri-<lb/>dianum A E C. </s>
  <s xml:id="echoid-s29549" xml:space="preserve">Quoniam igitur in triangulo ſphærico rectangulo B H K, angulus k, rectus eſt, <lb/>erit per propoſ. </s>
  <s xml:id="echoid-s29550" xml:space="preserve">19. </s>
  <s xml:id="echoid-s29551" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29552" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29553" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s29554" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0466-01a" xlink:href="fig-0466-01"/>
Regiom. </s>
  <s xml:id="echoid-s29555" xml:space="preserve">de triangulis, vel per <lb/>propoſ. </s>
  <s xml:id="echoid-s29556" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29557" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29558" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29559" xml:space="preserve">Gebri, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s29560" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29561" xml:space="preserve">noſtrorum trian <lb/>gulorum ſphęricorum vt ſinus <lb/>
<anchor type="note" xlink:label="note-0466-01a" xlink:href="note-0466-01"/>
complementi arcus H K, decli-<lb/>nationis ad ſinum totum, ita ſi-<lb/>nus complemẽti arcus B H, hoc <lb/>eſt, ita ſinus arcus H I, altitudinis <lb/>Solis ſupra Meridianum, ad ſinũ <lb/>complementi arcus B K, id eſt, <lb/>ad ſinum arcus E K, diſtantiæ <lb/>Solis à meridie, vel media nocte. <lb/></s>
  <s xml:id="echoid-s29562" xml:space="preserve">Et conuertendo, vt ſinus totus <lb/>ad ſinum complementi declina-<lb/>
<anchor type="note" xlink:label="note-0466-02a" xlink:href="note-0466-02"/>
tionis, ita ſinus diſtantiæ Solis à <lb/>meridie, vel media nocte ad ſi-<lb/>num altitudinis Solis ſupra Me-<lb/>ridianũ. </s>
  <s xml:id="echoid-s29563" xml:space="preserve">Quod breuius ita demõ <lb/>ſtrabimus. </s>
  <s xml:id="echoid-s29564" xml:space="preserve">Quia in triãgulo ſphę <lb/>rico A H I, vel C H I, angulus I, <lb/>rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s29565" xml:space="preserve">16. </s>
  <s xml:id="echoid-s29566" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s29567" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29568" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s29569" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s29570" xml:space="preserve">de triãgulis, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s29571" xml:space="preserve">13. </s>
  <s xml:id="echoid-s29572" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29573" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29574" xml:space="preserve">Gebri, vel <lb/>per propoſ. </s>
  <s xml:id="echoid-s29575" xml:space="preserve">41. </s>
  <s xml:id="echoid-s29576" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus totus anguli recti I, ad ſinum ar-<lb/>
<anchor type="note" xlink:label="note-0466-03a" xlink:href="note-0466-03"/>
cus A H, vel C H, complementi declinationis, ita ſinus anguli A, vel C, diſtantię Solis à Meri-<lb/>diano ad ſinum arcus H I, altitudinis Solis ſupra Meridianum. </s>
  <s xml:id="echoid-s29577" xml:space="preserve">Quamobrem ſi fiat, vt ſinus to-<lb/>tus ad ſinum complementi declinationis, ita ſinus diſtantiæ Solis à meridie, vel media no-<lb/>cte ad aliud, proueniet ſinus altitudinis Solis ſupra Meridianum. </s>
  <s xml:id="echoid-s29578" xml:space="preserve">Exempli gratia, Sole posſiden-<lb/>te prin cipium ♋, vel ♑, quęrenda ſitaltitudo ipſius ſupra Meridianum hora 5. </s>
  <s xml:id="echoid-s29579" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s29580" xml:space="preserve">poſt meri-<lb/>diem, vel mediam noctem, ita vt diſtantia Solis à meridie, vel media nocte contineat horas quin <lb/>que, hoc eſt, grad. </s>
  <s xml:id="echoid-s29581" xml:space="preserve">75. </s>
  <s xml:id="echoid-s29582" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s29583" xml:space="preserve">ſinus totus ad 91706. </s>
  <s xml:id="echoid-s29584" xml:space="preserve">ſinum complementi declinationis, <lb/>ita 96592. </s>
  <s xml:id="echoid-s29585" xml:space="preserve">ſinus diſtantiæ Solis à meridie, vel media nocte, ad aliud, inuenieturq́ue hic ſinus ferè <lb/>88580. </s>
  <s xml:id="echoid-s29586" xml:space="preserve">cuius arcus grad. </s>
  <s xml:id="echoid-s29587" xml:space="preserve">62. </s>
  <s xml:id="echoid-s29588" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29589" xml:space="preserve">21. </s>
  <s xml:id="echoid-s29590" xml:space="preserve">dabit altitudinem Solis ſupra Meridianum quæſitam.</s>
  <s xml:id="echoid-s29591" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1517" type="float" level="2" n="7">
  <figure xlink:label="fig-0466-01" xlink:href="fig-0466-01a">
    <image file="0466-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0466-01"/>
  </figure>
<note position="left" xlink:label="note-0466-01" xlink:href="note-0466-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0466-02" xlink:href="note-0466-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0466-03" xlink:href="note-0466-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s29592" xml:space="preserve">SOLE Æquatorem percurrente, erit ipſa diſtantia Solis à meridie altitudo ipſius ſupra Me-<lb/>
<anchor type="note" xlink:label="note-0466-04a" xlink:href="note-0466-04"/>
ridianum, propterea quod Æquator per polos Meridiani ductus rectus eſt ad Meridianum, per <lb/>propoſ. </s>
  <s xml:id="echoid-s29593" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29594" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29595" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29596" xml:space="preserve">Theodoſii.</s>
  <s xml:id="echoid-s29597" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1518" type="float" level="2" n="8">
<note position="left" xlink:label="note-0466-04" xlink:href="note-0466-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s29598" xml:space="preserve">RVRSVS hora 6. </s>
  <s xml:id="echoid-s29599" xml:space="preserve">à meridie, vel media nocte erit complementum declinationis A F, vel <lb/>C F, altitudo Solis ſupra eundem Meridianum; </s>
  <s xml:id="echoid-s29600" xml:space="preserve">quia circulus horæ 6. </s>
  <s xml:id="echoid-s29601" xml:space="preserve">à meridie vel media nocte <lb/>rectus eſt ad Meridianum, exeadem propoſ. </s>
  <s xml:id="echoid-s29602" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29603" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29604" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29605" xml:space="preserve">Theodoſii.</s>
  <s xml:id="echoid-s29606" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s29607" xml:space="preserve">NON diſſimili ratione inueſtigabimus Solis altitudinem ſupra Horizontem rectum, ſeu cir <lb/>
<anchor type="note" xlink:label="note-0466-05a" xlink:href="note-0466-05"/>
culum horæ 6. </s>
  <s xml:id="echoid-s29608" xml:space="preserve">à meridie, vel media nocte, quam metitur circulus maximus per polos Horizon <lb/>tis recti, ſiue circuli horæ 6. </s>
  <s xml:id="echoid-s29609" xml:space="preserve">à meridie, vel media nocte, hoc eſt, per cõmunes ſectiones Meridia-<lb/>ni, &amp; </s>
  <s xml:id="echoid-s29610" xml:space="preserve">Æquatoris, ac per centrum Solis ductus, qualis eſt circulus E H L, ita vt altitudo Solis ſu-<lb/>pra circulum horæ 6. </s>
  <s xml:id="echoid-s29611" xml:space="preserve">ſit arcus H L, exiſtente Sole in puncto H. </s>
  <s xml:id="echoid-s29612" xml:space="preserve">Quoniam enim in triangulo <lb/>
<anchor type="note" xlink:label="note-0466-06a" xlink:href="note-0466-06"/>
ſphærico E H K, angulus K, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s29613" xml:space="preserve">19. </s>
  <s xml:id="echoid-s29614" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29615" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29616" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s29617" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s29618" xml:space="preserve">detriangulis, <lb/>vel per propoſ. </s>
  <s xml:id="echoid-s29619" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29620" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29621" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29622" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s29623" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29624" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt <lb/>ſinus complementi arcus H K, declinationis ad ſinum totum, ita ſinus arcus E H, hoc eſt, ſinus <lb/>arcus H L, altitudinis Solis ſupra Horizontem rectum, aut circulum horæ 6. </s>
  <s xml:id="echoid-s29625" xml:space="preserve">ad ſinum comple-<lb/>menti arcus E K, diſtantiæ Solis à meridie, vel media nocte. </s>
  <s xml:id="echoid-s29626" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſi-<lb/>num complementi declinationis, ita ſinus complementi diſtantię Solis à meridie, vel media no-<lb/>cte ad ſinum altitudinis Solis ſupra Horizontem rectum, aut circulum horæ 6. </s>
  <s xml:id="echoid-s29627" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s29628" xml:space="preserve">vel med. <lb/></s>
  <s xml:id="echoid-s29629" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s29630" xml:space="preserve">Quod breuius hoc modo oſtendemus. </s>
  <s xml:id="echoid-s29631" xml:space="preserve">Quoniam in triangulo ſphærico A H L, vel C H L, <lb/>angulus L, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s29632" xml:space="preserve">16. </s>
  <s xml:id="echoid-s29633" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29634" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29635" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s29636" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s29637" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s29638" xml:space="preserve">13. </s>
  <s xml:id="echoid-s29639" xml:space="preserve"><lb/>libri 1. </s>
  <s xml:id="echoid-s29640" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s29641" xml:space="preserve">41. </s>
  <s xml:id="echoid-s29642" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus totus anguli <lb/>recti L, ad ſinum arcus A H, vel C H, complementi declinationis, ita ſinus anguli A, vel C, cõ-
<pb o="451" file="0467" n="467" rhead="LIBER QVINTVS."/>
plementi diſtantiæ Solis à meridie, vel media nocte ad ſinum arcus H L, altitudinis Solis ſupra <lb/>Horizontem rectum, vel circulum horæ 6. </s>
  <s xml:id="echoid-s29643" xml:space="preserve">Quocirca ſi fiat, vt ſinus totus ad ſinum complemẽ-<lb/>ti declinationis, ita ſinus complementi diſtantiæ Solis à meridie, vel media nocte ad aliud, proue-<lb/>niet ſinus altitudinis Solis ſupra circulũ horę 6. </s>
  <s xml:id="echoid-s29644" xml:space="preserve">à meridie, vel media nocte, vel Horizontẽ rectum.</s>
  <s xml:id="echoid-s29645" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1519" type="float" level="2" n="9">
<note position="left" xlink:label="note-0466-05" xlink:href="note-0466-05a" xml:space="preserve">Altitudo Solis <lb/>ſupra Horizon <lb/>tem rectũ, aut <lb/>circulum horæ <lb/>6. à mer. vel <lb/>med. noc. qua <lb/>ratione explo-<lb/>retur.</note>
<note position="left" xlink:label="note-0466-06" xlink:href="note-0466-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s29646" xml:space="preserve">SOLE Æquatorẽ percurrẽte, erit cõplementũ diſtãtiæ Solis à meridie, vel media nocte altitu-<lb/>do ipſius ſupra Horizontẽ rectum, ſiue circulũ horæ 6. </s>
  <s xml:id="echoid-s29647" xml:space="preserve">à meridie vel media nocte. </s>
  <s xml:id="echoid-s29648" xml:space="preserve">quoniã Æqua <lb/>tor, per propoſ. </s>
  <s xml:id="echoid-s29649" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29650" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29651" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29652" xml:space="preserve">Theodoſii, ad dictum circulum rectus eſt, cum per eius polos ducatur.</s>
  <s xml:id="echoid-s29653" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s29654" xml:space="preserve">RVRSVS in meridie, vel media nocte, complementum declinationis A M, vel C M, dabit <lb/>altitudinem Solis ſupra eundem circulum, quod &amp; </s>
  <s xml:id="echoid-s29655" xml:space="preserve">Meridianus ad ipſum rectus ſit.</s>
  <s xml:id="echoid-s29656" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s29657" xml:space="preserve">DENIQVE ſupra circulum maximum per polos mundi ductum, qui ad Meridianum in-<lb/>
<anchor type="note" xlink:label="note-0467-01a" xlink:href="note-0467-01"/>
<anchor type="note" xlink:label="note-0467-02a" xlink:href="note-0467-02"/>
clinatus ſit, cuiuſmodi eſt circulus maximus, cui tertium horologium propoſ. </s>
  <s xml:id="echoid-s29658" xml:space="preserve">37. </s>
  <s xml:id="echoid-s29659" xml:space="preserve">lib 3. </s>
  <s xml:id="echoid-s29660" xml:space="preserve">deſcri-<lb/>ptum æquidiſtat, eodem modo altitudinem Solis inquiremus; </s>
  <s xml:id="echoid-s29661" xml:space="preserve">ſi quæramus diſtantias Solis à Me-<lb/>ridiano proprio ipſius, vt ſupra docuimus, &amp; </s>
  <s xml:id="echoid-s29662" xml:space="preserve">loco diſtantiæ Solis à meridie, vel media nocte ac-<lb/>cipiamus diſtantiam eiuſdem à proprio Meridiano dicti circuli.</s>
  <s xml:id="echoid-s29663" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1520" type="float" level="2" n="10">
<note position="left" xlink:label="note-0467-01" xlink:href="note-0467-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0467-02" xlink:href="note-0467-02a" xml:space="preserve">Altitudo Solis <lb/>ſupra quemcũ-<lb/>que circulum <lb/>maximum per <lb/>polos mundi <lb/>ductum quo pa <lb/>cto reperiatur.</note>
</div>
<p>
  <s xml:id="echoid-s29664" xml:space="preserve">SATIS autem eſt, ſi ſupputentur altitudines Solis ſupra circulos maximos per polos mun-<lb/>
<anchor type="note" xlink:label="note-0467-03a" xlink:href="note-0467-03"/>
di ductos, dum in ſignis borealibus exiſtit, vel in auſtralibus. </s>
  <s xml:id="echoid-s29665" xml:space="preserve">Nam in eiſdem horis æquales alti-<lb/>tudines habet Sol ſupra Meridianum, ſeu circulum horæ 6. </s>
  <s xml:id="echoid-s29666" xml:space="preserve">à meridie, vel media nocte, Hori-<lb/>zontemve rectum, vel etiam circulum quemcunque maximum per polos mundi tranſeuntem, <lb/>dum eſt in oppoſitis parallelis. </s>
  <s xml:id="echoid-s29667" xml:space="preserve">Quod ita demonſtrabimus. </s>
  <s xml:id="echoid-s29668" xml:space="preserve">Quoniam in triangulis A H I, C H I, <lb/>anguli ad I, recti ſunt, &amp; </s>
  <s xml:id="echoid-s29669" xml:space="preserve">anguli A, C, æquales, cum ſint anguli diſtantiarum Solis à Meridiano, <lb/>
<anchor type="note" xlink:label="note-0467-04a" xlink:href="note-0467-04"/>
habentq́ue latera A H, C H, quæ rectis angulis ſubtenduntur, æqualia, cum ſint complementa <lb/>declinationum æqualium, erunt per propoſ. </s>
  <s xml:id="echoid-s29670" xml:space="preserve">21. </s>
  <s xml:id="echoid-s29671" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29672" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29673" xml:space="preserve">Menelai ex traditione Franciſci Mauro-<lb/>lyci, vel per propoſ. </s>
  <s xml:id="echoid-s29674" xml:space="preserve">21. </s>
  <s xml:id="echoid-s29675" xml:space="preserve">noſtrorum triangulorum ſphæricorum, &amp; </s>
  <s xml:id="echoid-s29676" xml:space="preserve">arcus H I, H I, altitudines So-<lb/>lis ſupra Meridianum metientes æquales. </s>
  <s xml:id="echoid-s29677" xml:space="preserve">Eadem ratione, quia in triangulis A H L, C H L, an-<lb/>guli ad L, recti ſunt, &amp; </s>
  <s xml:id="echoid-s29678" xml:space="preserve">anguli A, C, æquales, cum ſint anguli complementorum diſtantiarum <lb/>Solis à Meridiano, habentq́ue latera A H, C H, vt diximus, æqualia, erunt per eandem propoſ. <lb/></s>
  <s xml:id="echoid-s29679" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s29680" xml:space="preserve">arcus H L, H L, qui Solis altitudines ſupra Horizontem rectum, vel circulum horæ 6. </s>
  <s xml:id="echoid-s29681" xml:space="preserve">à meri <lb/>die, vel media nocte metiuntur, æquales.</s>
  <s xml:id="echoid-s29682" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1521" type="float" level="2" n="11">
<note position="right" xlink:label="note-0467-03" xlink:href="note-0467-03a" xml:space="preserve">Satis eſt, ſi ſu-<lb/>pra circulos ma <lb/>ximos, qui per <lb/>polos mundi <lb/>ducuntur, inue <lb/>ſtigentur altitu <lb/>dines Solis, dũ <lb/>in ſignis borea <lb/>libus, vel auſtra <lb/>libus exiſtit.</note>
<note position="left" xlink:label="note-0467-04" xlink:href="note-0467-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s29683" xml:space="preserve">PRAETEREA Sol ſupra Meridianum qualibet hora habet altitudinem eandem, quam <lb/>
<anchor type="note" xlink:label="note-0467-05a" xlink:href="note-0467-05"/>
habet ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s29684" xml:space="preserve">à meridie, vel media nocte in alia hora, quæ tantum abeſt à circulo <lb/>
<anchor type="note" xlink:label="note-0467-06a" xlink:href="note-0467-06"/>
horæ 6. </s>
  <s xml:id="echoid-s29685" xml:space="preserve">quantum illa à Meridiano diſtat, cuiuſmodi ſunt v. </s>
  <s xml:id="echoid-s29686" xml:space="preserve">g. </s>
  <s xml:id="echoid-s29687" xml:space="preserve">hora 11. </s>
  <s xml:id="echoid-s29688" xml:space="preserve">aut 1. </s>
  <s xml:id="echoid-s29689" xml:space="preserve">à meridie, vel me-<lb/>dia nocte reſpectu Meridiani, &amp; </s>
  <s xml:id="echoid-s29690" xml:space="preserve">hora 5. </s>
  <s xml:id="echoid-s29691" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s29692" xml:space="preserve">à meridie, vel media nocte reſpectu circuli horæ <lb/>6. </s>
  <s xml:id="echoid-s29693" xml:space="preserve">à meridie, vel media nocte, quia vtraque à ſuo circulo diſtat per horam vnam, ſiue grad. </s>
  <s xml:id="echoid-s29694" xml:space="preserve">15. <lb/></s>
  <s xml:id="echoid-s29695" xml:space="preserve">Quod ita conſirmabimus. </s>
  <s xml:id="echoid-s29696" xml:space="preserve">Ponatur Sol in N, ita vt circulus declinationis C N A, contineat cum <lb/>circulo horæ 6. </s>
  <s xml:id="echoid-s29697" xml:space="preserve">angulum N C O, æqualem angulo H C I, hoc eſt, diſtantia Solis in N, à circulo <lb/>horæ 6. </s>
  <s xml:id="echoid-s29698" xml:space="preserve">æqualis ſit diſtantiæ eiuſdem in H, à Meridiano. </s>
  <s xml:id="echoid-s29699" xml:space="preserve">Quoniam igitur in triangulis C H I, <lb/>C N O, anguli ad I, O, recti ſunt, &amp; </s>
  <s xml:id="echoid-s29700" xml:space="preserve">anguli H C I, N C O, æquales, habentq́ue arcus C H, C N, <lb/>æquales, vtpote complementa declinationis eiuſdem, erunt per eandem propoſ. </s>
  <s xml:id="echoid-s29701" xml:space="preserve">21. </s>
  <s xml:id="echoid-s29702" xml:space="preserve">arcus altitu-<lb/>dinum H I, N O, æquales.</s>
  <s xml:id="echoid-s29703" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1522" type="float" level="2" n="12">
<note position="right" xlink:label="note-0467-05" xlink:href="note-0467-05a" xml:space="preserve">Eandem altitu <lb/>dinem habet <lb/>Sol in quauis <lb/>hora, ſupra Me <lb/>ridianum Ho-<lb/>rizontis, quam <lb/>ſupra circulum <lb/>horæ 6. à mer. <lb/>vel med. noc. <lb/>in alia hora, <lb/>quæ tãtum ab-<lb/>eſt ab hoc cir-<lb/>culo, quantum <lb/>illa à Meridia-<lb/>no diſtat.</note>
<note position="left" xlink:label="note-0467-06" xlink:href="note-0467-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s29704" xml:space="preserve">ITAQVE ſi ſupputatę ſint altitudines Solis ſupra Meridianum ad ſingulas horas à meridie, <lb/>
<anchor type="note" xlink:label="note-0467-07a" xlink:href="note-0467-07"/>
vel media nocte, accommodabuntur eædem altitudines ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s29705" xml:space="preserve">à meridie, vel me <lb/>dia nocte ad ſingulas horas, quæ tantum diſtent à circulo horæ 6. </s>
  <s xml:id="echoid-s29706" xml:space="preserve">à meridie, vel media nocte, <lb/>quantum illæ à Meridiano abſunt. </s>
  <s xml:id="echoid-s29707" xml:space="preserve">Vt binarum horarum in <lb/>
<anchor type="figure" xlink:label="fig-0467-01a" xlink:href="fig-0467-01"/>
priore tabella hic appoſita altitudines ſupra Meridianum cir-<lb/>culum, æquales ſunt binarum horarum in poſteriore tabella al-<lb/>titudinibus ſupra Horizontem rectum, vel circulum horæ 6. </s>
  <s xml:id="echoid-s29708" xml:space="preserve">à <lb/>meridie, vel media nocte, &amp; </s>
  <s xml:id="echoid-s29709" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s29710" xml:space="preserve">Id quod ex ſupputatione <lb/>
<anchor type="note" xlink:label="note-0467-08a" xlink:href="note-0467-08"/>
quoque ipſa liquido conſtat.</s>
  <s xml:id="echoid-s29711" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1523" type="float" level="2" n="13">
<note position="left" xlink:label="note-0467-07" xlink:href="note-0467-07a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0467-01" xlink:href="fig-0467-01a">
    <image file="0467-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0467-01"/>
  </figure>
<note position="right" xlink:label="note-0467-08" xlink:href="note-0467-08a" xml:space="preserve">Altitudo Solis <lb/>ſupra Aequato <lb/>rem ſemper æ-<lb/>qualis eſt decli <lb/>nationi eiuſdẽ.</note>
</div>
<p>
  <s xml:id="echoid-s29712" xml:space="preserve">SVPRA Aequatorem non eſt opus indagare altitudines <lb/>Solis, quia Sole exiſtente in quouis patallelo, tota die Solis altitudo ſupra Aequatorem æqualis <lb/>
<anchor type="note" xlink:label="note-0467-09a" xlink:href="note-0467-09"/>
eſt declinationi ipſius paralleli, vt patet.</s>
  <s xml:id="echoid-s29713" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1524" type="float" level="2" n="14">
<note position="left" xlink:label="note-0467-09" xlink:href="note-0467-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s29714" xml:space="preserve">QVONIAM verò quilibet circulus maximus ad Horizontem, aut Meridianum inclinatus <lb/>
<anchor type="note" xlink:label="note-0467-10a" xlink:href="note-0467-10"/>
duplicem faciem habet, ſuperiorem alteram, &amp; </s>
  <s xml:id="echoid-s29715" xml:space="preserve">alteram inferiorem, vel vnam auſtralem, &amp; </s>
  <s xml:id="echoid-s29716" xml:space="preserve">alte-<lb/>ram borealem; </s>
  <s xml:id="echoid-s29717" xml:space="preserve">ſupputandę erunt altitudines Solis ſupra quamcunque illarum pro illis horis, quę <lb/>in portione cuiuſuis paralleli ſupra illam extante, inſtar arcus cuiuſdam diurni, comprehendun-<lb/>tur. </s>
  <s xml:id="echoid-s29718" xml:space="preserve">Nam in illis tantum Sol ſupra faciem dicti circuli eleuatur. </s>
  <s xml:id="echoid-s29719" xml:space="preserve">Quo pacto autem cognoſcere <lb/>poſſimus horas in illa portione paralleli exiſtentes, in ſubſequenti ſcholio aperiemus. </s>
  <s xml:id="echoid-s29720" xml:space="preserve">Verum hoc <lb/>ipſa quoque ſupputatio altitudinum declarabit. </s>
  <s xml:id="echoid-s29721" xml:space="preserve">Nam ſi diſſerentia inuenta inter ſinum altitudi-<lb/>nis meridianę, &amp; </s>
  <s xml:id="echoid-s29722" xml:space="preserve">ſinum altitudinis tempore obſeruationis fuerit minor ſinu altitudinis meridia-<lb/>næ, extabit hora altitudinis inuentæ in portione paralleli ſupra faciem circuli propoſitam; </s>
  <s xml:id="echoid-s29723" xml:space="preserve">ſi au-<lb/>tem maior, in reliqua portione ſupra faciem oppoſitam, vt paulo ante ſcripſimus. </s>
  <s xml:id="echoid-s29724" xml:space="preserve">Altitudi-
<pb o="452" file="0468" n="468" rhead="GNOMONICES"/>
nem igitur Solis ſupra quemcunque circulum maximum ſphærę pro ſingulis horis inueſtigaui-<lb/>mus. </s>
  <s xml:id="echoid-s29725" xml:space="preserve">Quod faciendum erat.</s>
  <s xml:id="echoid-s29726" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1525" type="float" level="2" n="15">
<note position="right" xlink:label="note-0467-10" xlink:href="note-0467-10a" xml:space="preserve">Pro quibus ho <lb/>ris altitudines <lb/>Solis ſupra fa-<lb/>ciem vtramuis <lb/>cuiuſque circu <lb/>li maximi inu@ <lb/>ſtigandæ ſint.</note>
</div>
</div>
<div xml:id="echoid-div1527" type="section" level="1" n="364">
<head xml:id="echoid-head378" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s29727" xml:space="preserve">MERIDIANAM altitudinẽ Solis ſupra circulũ maximũ propoſitũ in ſphæra obliqua boreali <lb/>hac arte indagabimus Primũ conſiderandũ eſt, an polus arcticus ſupra planũ circuli eleuetur, an verò an <lb/>tarcticus. </s>
  <s xml:id="echoid-s29728" xml:space="preserve">quod hac ratione fiet. </s>
  <s xml:id="echoid-s29729" xml:space="preserve">In circulis Verticalibus omnibus ſupra facies boreales attollitur polus <lb/>
<anchor type="note" xlink:label="note-0468-01a" xlink:href="note-0468-01"/>
arcticus; </s>
  <s xml:id="echoid-s29730" xml:space="preserve">ſupra facies verò auſtrales antarcticus. </s>
  <s xml:id="echoid-s29731" xml:space="preserve">In circulis autẽ poſitionũ, quibus horologia ab Horizon <lb/>te declinantia æquidiſtant, ſupra facies ſuperiores arcticus pol{us}, ſupra inferiores antarcticus eleuatur. <lb/></s>
  <s xml:id="echoid-s29732" xml:space="preserve">
<anchor type="note" xlink:label="note-0468-02a" xlink:href="note-0468-02"/>
In alĳs autẽ circulis ad Horizontẽ inclinatis, ſiue recti ſint ad Meridianũ, ſiue non, ſi quidem ad partes <lb/>auſtrales ad Horizontẽ fuerint inclinati, ita vt facies eorũ ſuperiores ad boreã ſpectent, extollitur ſupra <lb/>facies ſuperiores arcticus polus, antarcticus verò ſupra inferiores: </s>
  <s xml:id="echoid-s29733" xml:space="preserve">At verò ſi ad boreales partes incli-<lb/>nati fuerint ad Horizontem, ita vt eorum facies ſuperiores ſpectent in auſtrum, inueſtigandus erit, ex <lb/>coroll. </s>
  <s xml:id="echoid-s29734" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s29735" xml:space="preserve">28. </s>
  <s xml:id="echoid-s29736" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29737" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29738" xml:space="preserve">arcus Meridiani Horizontis interiectus inter Horizontem, &amp; </s>
  <s xml:id="echoid-s29739" xml:space="preserve">circulum pro-<lb/>poſitum. </s>
  <s xml:id="echoid-s29740" xml:space="preserve">Nam ſi hic arcus (qui neceſſario in huiuſmodi planis ſupra Horizontem extat ex parte boreę, <lb/>vt in ſcholio 1. </s>
  <s xml:id="echoid-s29741" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s29742" xml:space="preserve">28 lib. </s>
  <s xml:id="echoid-s29743" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29744" xml:space="preserve">docuimus) minor fuerit altitudine poli ſupra Horizontem, exaltabi-<lb/>tur polus arcticus ſupra faciem ſuperiorem, ſupra inferiorem verò antarcticus: </s>
  <s xml:id="echoid-s29745" xml:space="preserve">Si autem maior fuerit <lb/>dictus arcus altitudine poliſupra Horizontem, contrarium accidet; </s>
  <s xml:id="echoid-s29746" xml:space="preserve">ſupra enim faciem inferiorem ele-<lb/>uabitur arcticus polus, &amp; </s>
  <s xml:id="echoid-s29747" xml:space="preserve">antarcticus ſupra ſuperiorem: </s>
  <s xml:id="echoid-s29748" xml:space="preserve">Si denique idem arcus deprehenſus fuerit <lb/>
<anchor type="note" xlink:label="note-0468-03a" xlink:href="note-0468-03"/>
æqualis altitudini poli ſupra Horizontem, nulla erit altitudo poli ſupra circulũ datum. </s>
  <s xml:id="echoid-s29749" xml:space="preserve">Quæ omnia per-<lb/>ſpicua ſunt ex ſphęra materiali.</s>
  <s xml:id="echoid-s29750" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1527" type="float" level="2" n="1">
<note position="left" xlink:label="note-0468-01" xlink:href="note-0468-01a" xml:space="preserve">Quo pacto co-<lb/>gnoſca tur, nũ <lb/>polus arcticus, <lb/>an antarcticus <lb/>ſupra datum <lb/>planum circuli <lb/>maximi propo-<lb/>ſi ti eleuetur.</note>
<note position="left" xlink:label="note-0468-02" xlink:href="note-0468-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0468-03" xlink:href="note-0468-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s29751" xml:space="preserve">QVONIAM verò per propoſ. </s>
  <s xml:id="echoid-s29752" xml:space="preserve">19. </s>
  <s xml:id="echoid-s29753" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29754" xml:space="preserve">2. </s>
  <s xml:id="echoid-s29755" xml:space="preserve">Theodosĳ portiones parallelorum Aequatoris, inter <lb/>Aequatorem, &amp; </s>
  <s xml:id="echoid-s29756" xml:space="preserve">polum ſupra faciem circuli propoſiti conſpicuum maiores ſunt, quam ſemicirculi, reli. <lb/></s>
  <s xml:id="echoid-s29757" xml:space="preserve">quorum autem minores, efficitur, vt paralleli boreales habeant maiores portiones ſupra faciem illam, <lb/>ſupra quam polus arcticus eleuatur, reliqui verò minores, vt in Horizonte contingit. </s>
  <s xml:id="echoid-s29758" xml:space="preserve">Contrarium fiet in <lb/>ea facie, ſupra quam antarcticus polus attollitur. </s>
  <s xml:id="echoid-s29759" xml:space="preserve">Itaque ad eam faciem circuli, ſupra quam polus arcti-<lb/>
<anchor type="note" xlink:label="note-0468-04a" xlink:href="note-0468-04"/>
cus eſt conſpicuus, inueſtigabimus altitudinem meridianam, &amp; </s>
  <s xml:id="echoid-s29760" xml:space="preserve">meridianam depreſſionem, ex comple-<lb/>mento altitudinis poli ſupra datum circulum maximum, &amp; </s>
  <s xml:id="echoid-s29761" xml:space="preserve">declinatione paralleli, in quo Sol exiſtit, vt <lb/>in Horizonte, veluti in ſcholio propoſ. </s>
  <s xml:id="echoid-s29762" xml:space="preserve">35. </s>
  <s xml:id="echoid-s29763" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29764" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29765" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s29766" xml:space="preserve">Eadem quoque ratio in eam faciem circuli <lb/>
<anchor type="note" xlink:label="note-0468-05a" xlink:href="note-0468-05"/>
conuenit, quæ polum antarcticum habet exaltatum, dummodo pro borealibus ſignis accipiantur austra-<lb/>lia, &amp; </s>
  <s xml:id="echoid-s29767" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s29768" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1528" type="float" level="2" n="2">
<note position="left" xlink:label="note-0468-04" xlink:href="note-0468-04a" xml:space="preserve">Altitudo Solis <lb/>meridiana ſu-<lb/>pra circulum <lb/>maximum quẽ <lb/>cunque quo pa <lb/>cto indaganda <lb/>ſit.</note>
<note position="left" xlink:label="note-0468-05" xlink:href="note-0468-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s29769" xml:space="preserve">VT autem intelligamus, quænam horæ in portione cuiuſuis paralleli ſupra faciem circuli dati, <lb/>inſtar arcus diurni, exiſtente contineantur, ac propterea qua hora incipiat eadem facies, &amp; </s>
  <s xml:id="echoid-s29770" xml:space="preserve">deſinat à <lb/>
<anchor type="note" xlink:label="note-0468-06a" xlink:href="note-0468-06"/>
Sole illuminari, inquirenda erit per propoſ. </s>
  <s xml:id="echoid-s29771" xml:space="preserve">34. </s>
  <s xml:id="echoid-s29772" xml:space="preserve">libri 1. </s>
  <s xml:id="echoid-s29773" xml:space="preserve">vel potius ex ſcholio propoſ. </s>
  <s xml:id="echoid-s29774" xml:space="preserve">35. </s>
  <s xml:id="echoid-s29775" xml:space="preserve">eiuſdem li-<lb/>bri, (dummodo in planis, ſupra quę polus antarcticus eleuatur, pro borealibus ſignis ſumantur auſtra-<lb/>lia, &amp; </s>
  <s xml:id="echoid-s29776" xml:space="preserve">contra) quantitas arcus illius diurni, acſi facies circuli propoſiti eſſet Horizon aliquis. </s>
  <s xml:id="echoid-s29777" xml:space="preserve">Si enim <lb/>ab illa hora, quæ in Meridianum proprium circuli propoſiti cadit, (quæ quidem cognoſcetur exinclina-<lb/>tione ipſius ad Meridianum Horizontis) vtrinque in parallelo numeretur arcus ſimidiurnus inuentus, <lb/>habebuntur horæ in propoſita portione, ſeu arcu diurno contentæ: </s>
  <s xml:id="echoid-s29778" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s29779" xml:space="preserve">hora, qua Sol illumina <lb/>
<anchor type="note" xlink:label="note-0468-07a" xlink:href="note-0468-07"/>
re incipit, aut deſinit faciem circuli propoſitam. </s>
  <s xml:id="echoid-s29780" xml:space="preserve">Exempligratia. </s>
  <s xml:id="echoid-s29781" xml:space="preserve">Supra faciem australem circuli Verti-<lb/>calis declinantis à Vercicali propriè dicto grad. </s>
  <s xml:id="echoid-s29782" xml:space="preserve">30. </s>
  <s xml:id="echoid-s29783" xml:space="preserve">cui horologium propoſ. </s>
  <s xml:id="echoid-s29784" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29785" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29786" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29787" xml:space="preserve">deſcriptum æqui-<lb/>diſtat, eleuatur polus antarcticus grad. </s>
  <s xml:id="echoid-s29788" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29789" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29790" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29791" xml:space="preserve">Igitur portio paralleli ♑, ſupra illam extans, tan-<lb/>quam arcus diurnus, continebit horas 14. </s>
  <s xml:id="echoid-s29792" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29793" xml:space="preserve">52. </s>
  <s xml:id="echoid-s29794" xml:space="preserve">fere; </s>
  <s xml:id="echoid-s29795" xml:space="preserve">arcus autem ſemidiurnus horas 7. </s>
  <s xml:id="echoid-s29796" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29797" xml:space="preserve">26. <lb/></s>
  <s xml:id="echoid-s29798" xml:space="preserve">Et quoniam Meridianus illius Verticalis diſcedit à Meridiano Horizontis verſus ortum grad. </s>
  <s xml:id="echoid-s29799" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29800" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29801" xml:space="preserve"><lb/>48. </s>
  <s xml:id="echoid-s29802" xml:space="preserve">hoc eſt, hor. </s>
  <s xml:id="echoid-s29803" xml:space="preserve">2. </s>
  <s xml:id="echoid-s29804" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29805" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29806" xml:space="preserve">ferè, cadet hora 9. </s>
  <s xml:id="echoid-s29807" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29808" xml:space="preserve">17. </s>
  <s xml:id="echoid-s29809" xml:space="preserve">à media nocte in dictum Meridianum. </s>
  <s xml:id="echoid-s29810" xml:space="preserve">Qua-<lb/>re ſi vtrinque ab illa hora numeremus arcum ſemidiurnum hor. </s>
  <s xml:id="echoid-s29811" xml:space="preserve">7. </s>
  <s xml:id="echoid-s29812" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29813" xml:space="preserve">26. </s>
  <s xml:id="echoid-s29814" xml:space="preserve">incidemus in hor. </s>
  <s xml:id="echoid-s29815" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29816" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29817" xml:space="preserve"><lb/>51. </s>
  <s xml:id="echoid-s29818" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s29819" xml:space="preserve">in hor. </s>
  <s xml:id="echoid-s29820" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29821" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29822" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29823" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s29824" xml:space="preserve">Omnibus ergo horis ab hora 1. </s>
  <s xml:id="echoid-s29825" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29826" xml:space="preserve">51. </s>
  <s xml:id="echoid-s29827" xml:space="preserve">à media <lb/>nocte vſque ad horam 4. </s>
  <s xml:id="echoid-s29828" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29829" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29830" xml:space="preserve">à meridie illuminaretur illa facies Verticalis circuli à Sole exiſten-<lb/>te in principio ♑, niſi terra obstaret. </s>
  <s xml:id="echoid-s29831" xml:space="preserve">Sed quoniam Sol in principio ♑, ad latitudinem grad. </s>
  <s xml:id="echoid-s29832" xml:space="preserve">42. </s>
  <s xml:id="echoid-s29833" xml:space="preserve">oritur <lb/>
<anchor type="note" xlink:label="note-0468-08a" xlink:href="note-0468-08"/>
hora 7. </s>
  <s xml:id="echoid-s29834" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29835" xml:space="preserve">32. </s>
  <s xml:id="echoid-s29836" xml:space="preserve">à media nocte, &amp; </s>
  <s xml:id="echoid-s29837" xml:space="preserve">occidit hora 4. </s>
  <s xml:id="echoid-s29838" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29839" xml:space="preserve">28. </s>
  <s xml:id="echoid-s29840" xml:space="preserve">à meridie, perſpicuum eſt tota die tunc fa-<lb/>ciem illam à Sole illuminari, demptis Min. </s>
  <s xml:id="echoid-s29841" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29842" xml:space="preserve">quibus ante occaſum illuminari deſinit. </s>
  <s xml:id="echoid-s29843" xml:space="preserve">Portio verò pa-<lb/>ralleli ♋, ſupra eandem faciem exiſtens, inſtar diurni arcus, complectetur hor. </s>
  <s xml:id="echoid-s29844" xml:space="preserve">9. </s>
  <s xml:id="echoid-s29845" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29846" xml:space="preserve">8. </s>
  <s xml:id="echoid-s29847" xml:space="preserve">arcus autem <lb/>ſemidiurnus hor. </s>
  <s xml:id="echoid-s29848" xml:space="preserve">4. </s>
  <s xml:id="echoid-s29849" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29850" xml:space="preserve">34. </s>
  <s xml:id="echoid-s29851" xml:space="preserve">Igitur cum Meridianus dicti Verticalis recedat à Meridiano Horizontis <lb/>in ortum hor. </s>
  <s xml:id="echoid-s29852" xml:space="preserve">2. </s>
  <s xml:id="echoid-s29853" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29854" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29855" xml:space="preserve">vt diximus, cadat{q́ue} in eundem Meridianum dicti Verticalis hora 9. </s>
  <s xml:id="echoid-s29856" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29857" xml:space="preserve">17. <lb/></s>
  <s xml:id="echoid-s29858" xml:space="preserve">à media nocte; </s>
  <s xml:id="echoid-s29859" xml:space="preserve">ſi numeremus vtrinq; </s>
  <s xml:id="echoid-s29860" xml:space="preserve">arcum ſemidiurnum ab hac hora, incidemus in horam 4. </s>
  <s xml:id="echoid-s29861" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29862" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29863" xml:space="preserve"><lb/>à media nocte, &amp; </s>
  <s xml:id="echoid-s29864" xml:space="preserve">in hor. </s>
  <s xml:id="echoid-s29865" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29866" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29867" xml:space="preserve">51. </s>
  <s xml:id="echoid-s29868" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s29869" xml:space="preserve">Quocirca eadem facies dicti Verticalis illustrabitur à <lb/>Sole exiſtente in principio ♋, omnibus horis ab hora 4. </s>
  <s xml:id="echoid-s29870" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29871" xml:space="preserve">43. </s>
  <s xml:id="echoid-s29872" xml:space="preserve">à media nocte vſq; </s>
  <s xml:id="echoid-s29873" xml:space="preserve">ad horam 1. </s>
  <s xml:id="echoid-s29874" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29875" xml:space="preserve"><lb/>51. </s>
  <s xml:id="echoid-s29876" xml:space="preserve">à meridie. </s>
  <s xml:id="echoid-s29877" xml:space="preserve">Vnde cum Sol in principio ♋, ad latitudinem grad. </s>
  <s xml:id="echoid-s29878" xml:space="preserve">42. </s>
  <s xml:id="echoid-s29879" xml:space="preserve">oriatur hora 4. </s>
  <s xml:id="echoid-s29880" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29881" xml:space="preserve">28. </s>
  <s xml:id="echoid-s29882" xml:space="preserve">à media <lb/>nocte, &amp; </s>
  <s xml:id="echoid-s29883" xml:space="preserve">occidat hora 7. </s>
  <s xml:id="echoid-s29884" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29885" xml:space="preserve">32. </s>
  <s xml:id="echoid-s29886" xml:space="preserve">constat, Solem tunc non illuminare illam faciem per totum diem, ſed <lb/>ſolum poſt Min. </s>
  <s xml:id="echoid-s29887" xml:space="preserve">15. </s>
  <s xml:id="echoid-s29888" xml:space="preserve">ab ortu vſque ad boram 1. </s>
  <s xml:id="echoid-s29889" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29890" xml:space="preserve">51. </s>
  <s xml:id="echoid-s29891" xml:space="preserve">à meridie.</s>
  <s xml:id="echoid-s29892" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1529" type="float" level="2" n="3">
<note position="left" xlink:label="note-0468-06" xlink:href="note-0468-06a" xml:space="preserve">Quænam horæ <lb/>in portione cu-<lb/>iusuis paralleli <lb/>ſupra datam fa <lb/>ci@ circuli ma-<lb/>ximi propoſiti <lb/>contineantur, <lb/>qua ratione co <lb/>gnoſcatur; ac <lb/>proinde qua <lb/>hora incipiat <lb/>eadem facies, <lb/>&amp; deſinat à So <lb/>le illuminari.</note>
<note position="left" xlink:label="note-0468-07" xlink:href="note-0468-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0468-08" xlink:href="note-0468-08a" xml:space="preserve">50</note>
</div>
<pb o="453" file="0469" n="469" rhead="LIBER QVINTVS."/>
<p style="it">
  <s xml:id="echoid-s29893" xml:space="preserve">QVAMVIS autem propter impedimentum terrę Sol neutram faciem propoſiti circuli illuminet, <lb/>niſi ſupra Horizontem existat, ſupputandæ ſunt nihilominus altitudines Solis ſupra vtramq; </s>
  <s xml:id="echoid-s29894" xml:space="preserve">faciem pro <lb/>illis etiam horis, quibus Sol infra Horizontem latet, quia per illas facilius horologia, &amp; </s>
  <s xml:id="echoid-s29895" xml:space="preserve">expeditius de-<lb/>ſcribuntur, vt ex ſequentibus patebit.</s>
  <s xml:id="echoid-s29896" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s29897" xml:space="preserve">RVRSVS ſupra faciem borealem eiuſdem circuli Verticalis eleuatur arcticus polus totidem gra-<lb/>dibus, quot antarcticus ſupra priorem faciem, nimirum grad. </s>
  <s xml:id="echoid-s29898" xml:space="preserve">40. </s>
  <s xml:id="echoid-s29899" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29900" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29901" xml:space="preserve">Igitur portio paralleli ♋, ſu-<lb/>pra illam extans, inſtar arcus diurni, comprehendet horas 14. </s>
  <s xml:id="echoid-s29902" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29903" xml:space="preserve">52. </s>
  <s xml:id="echoid-s29904" xml:space="preserve">portio verò paralleli ♑, hor. <lb/></s>
  <s xml:id="echoid-s29905" xml:space="preserve">9. </s>
  <s xml:id="echoid-s29906" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29907" xml:space="preserve">8. </s>
  <s xml:id="echoid-s29908" xml:space="preserve">Recedit autẽ Meridianus dictæ faciei à Meridiano Horizontis infra Horizontẽ hor. </s>
  <s xml:id="echoid-s29909" xml:space="preserve">2. </s>
  <s xml:id="echoid-s29910" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29911" xml:space="preserve"><lb/>43. </s>
  <s xml:id="echoid-s29912" xml:space="preserve">verſus occaſum, ita vt hora 9. </s>
  <s xml:id="echoid-s29913" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s29914" xml:space="preserve">17. </s>
  <s xml:id="echoid-s29915" xml:space="preserve">à meride cadat in dictum Meridianum. </s>
  <s xml:id="echoid-s29916" xml:space="preserve">Quocirca vt pri{us} <lb/>inueniemus horas, quibus Sol in principio ♋, vel ♑, exiſtens dictam faciem borealem illuminaret, niſi <lb/>
<anchor type="note" xlink:label="note-0469-01a" xlink:href="note-0469-01"/>
à terra impediretur.</s>
  <s xml:id="echoid-s29917" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1530" type="float" level="2" n="4">
<note position="left" xlink:label="note-0469-01" xlink:href="note-0469-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s29918" xml:space="preserve">CAETERVM cum Federico Commandino explorabimus quoque ex Analemmate, quot, &amp; </s>
  <s xml:id="echoid-s29919" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0469-02a" xlink:href="note-0469-02"/>
quæ horæ ſupra datam faciẽ cuiuſuis circuli maximi contineantur, atq; </s>
  <s xml:id="echoid-s29920" xml:space="preserve">adeò qua hora Sol eandem faciem <lb/>incipiat, aut deſinat illuminare, hoc modo. </s>
  <s xml:id="echoid-s29921" xml:space="preserve">Deſcribatur Analemma A B C D, cuius centrum E, cum pa <lb/>rallelis ſignorũ (Deſcripſi, <lb/>
<anchor type="figure" xlink:label="fig-0469-01a" xlink:href="fig-0469-01"/>
mus autem tres tantum pa-<lb/>rallelos, nempe F G, ♋; <lb/></s>
  <s xml:id="echoid-s29922" xml:space="preserve">K L, ♉, H I, ♐; </s>
  <s xml:id="echoid-s29923" xml:space="preserve">ne mul-<lb/>titudo cõfuſionem pareret, <lb/>qui quidem inſtar omnium <lb/>
<anchor type="note" xlink:label="note-0469-03a" xlink:href="note-0469-03"/>
erunt. </s>
  <s xml:id="echoid-s29924" xml:space="preserve">Nam F G, funge-<lb/>tur etiam officio paralleli <lb/>♑, cum ♋, &amp; </s>
  <s xml:id="echoid-s29925" xml:space="preserve">♑, æquales <lb/>habeant ab Acquatore de-<lb/>clinationes; </s>
  <s xml:id="echoid-s29926" xml:space="preserve">K L, geret <lb/>vices etiã paralleli ♍, ♓, <lb/>&amp; </s>
  <s xml:id="echoid-s29927" xml:space="preserve">♏, propterea quod hæc <lb/>ſigna &amp; </s>
  <s xml:id="echoid-s29928" xml:space="preserve">♉, æqualiter ab <lb/>Aequatore declinant; </s>
  <s xml:id="echoid-s29929" xml:space="preserve">De-<lb/>nique H I, erit quoque in-<lb/>
<anchor type="note" xlink:label="note-0469-04a" xlink:href="note-0469-04"/>
ſtar par alleli ♒, ♊, &amp; </s>
  <s xml:id="echoid-s29930" xml:space="preserve">♌, <lb/>quia eadem eſt declinatio <lb/>♐, &amp; </s>
  <s xml:id="echoid-s29931" xml:space="preserve">horum ſignorum) cir <lb/>ca diametros autem paral-<lb/>lelorum ſemicirculi deſcri-<lb/>bantur. </s>
  <s xml:id="echoid-s29932" xml:space="preserve">Axis mũdi ſit B D; <lb/></s>
  <s xml:id="echoid-s29933" xml:space="preserve">Horizon M N; </s>
  <s xml:id="echoid-s29934" xml:space="preserve">Verticalis <lb/>12 13. </s>
  <s xml:id="echoid-s29935" xml:space="preserve">Deinde à punctis <lb/>O, P, Q, vbi Horizon dia-<lb/>metros parallelorum ſecat, <lb/>
<anchor type="note" xlink:label="note-0469-05a" xlink:href="note-0469-05"/>
ad diametros ducantur per <lb/>pendiculares Q R, P S, O T. </s>
  <s xml:id="echoid-s29936" xml:space="preserve">Quoniam igitur tam Horizon, quàm parallelus ♋, ad Meridianum rectus <lb/>eſt, erit quoque ad eundem communis eorum ſectio recta; </s>
  <s xml:id="echoid-s29937" xml:space="preserve">at que, adeò per defin. </s>
  <s xml:id="echoid-s29938" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29939" xml:space="preserve">libri 11. </s>
  <s xml:id="echoid-s29940" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s29941" xml:space="preserve">ad vtrã-<lb/>
<anchor type="note" xlink:label="note-0469-06a" xlink:href="note-0469-06"/>
que F G, M N, perpendicularis. </s>
  <s xml:id="echoid-s29942" xml:space="preserve">Quare Q R, quæ in plano paralleli ad F G, perpendicularis eſt, com-<lb/>munis ſectio erit Horizontis &amp; </s>
  <s xml:id="echoid-s29943" xml:space="preserve">paralleli ♋; </s>
  <s xml:id="echoid-s29944" xml:space="preserve">atque adeò F R, erit arcus ſemidiurnus ♋; </s>
  <s xml:id="echoid-s29945" xml:space="preserve">at G R, arcus <lb/>ſemidiurnus ♑. </s>
  <s xml:id="echoid-s29946" xml:space="preserve">Eodem modo erit P S, communis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s29947" xml:space="preserve">paralleli ♉, &amp; </s>
  <s xml:id="echoid-s29948" xml:space="preserve">K S, arcus ſe-<lb/>midiurnus ♉, &amp; </s>
  <s xml:id="echoid-s29949" xml:space="preserve">♍, at L S, arcus ſemidiurnus ♏, &amp; </s>
  <s xml:id="echoid-s29950" xml:space="preserve">♓. </s>
  <s xml:id="echoid-s29951" xml:space="preserve">Item O T, communis ſectio Horizontis ac <lb/>paralleli ♐, &amp; </s>
  <s xml:id="echoid-s29952" xml:space="preserve">H T, arcus ſemidiurnus ♐, &amp; </s>
  <s xml:id="echoid-s29953" xml:space="preserve">♒, at I T, arcus ſemidiurn{us} ♊, &amp; </s>
  <s xml:id="echoid-s29954" xml:space="preserve">♌. </s>
  <s xml:id="echoid-s29955" xml:space="preserve">Poſtremo E D, <lb/>communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s29956" xml:space="preserve">Aequatoris, ſeu paralleli ♈, &amp; </s>
  <s xml:id="echoid-s29957" xml:space="preserve">♎, &amp; </s>
  <s xml:id="echoid-s29958" xml:space="preserve">A D, arcus ſemidiurnus ♈; <lb/></s>
  <s xml:id="echoid-s29959" xml:space="preserve">at C D, arcus ſemidiurnus ♎. </s>
</p>
<p style="it">
  <s xml:id="echoid-s29960" xml:space="preserve">EODEM modo, ſi ex punctis V, X, Y, quibus Verticalis 12 13. </s>
  <s xml:id="echoid-s29961" xml:space="preserve">parallelos ſecat, perpendicula-<lb/>res ad parallelos ducãtur V Z, X α, Y β, erunt hæ communes ſectiones Verticalis, &amp; </s>
  <s xml:id="echoid-s29962" xml:space="preserve">Meridiani, ita <lb/>vt arcus R Z, S α, &amp; </s>
  <s xml:id="echoid-s29963" xml:space="preserve">T β, inter Horizontem, &amp; </s>
  <s xml:id="echoid-s29964" xml:space="preserve">Verticalem interĳciãtur, &amp; </s>
  <s xml:id="echoid-s29965" xml:space="preserve">Verticalis circuli pla-<lb/>num, dum eos Sol percurrit, à Sole non illuminetur ex parte meridiei.</s>
  <s xml:id="echoid-s29966" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1531" type="float" level="2" n="5">
<note position="right" xlink:label="note-0469-02" xlink:href="note-0469-02a" xml:space="preserve">Quæ horę son-<lb/>tineãtur ſupra <lb/>faciem propoſi <lb/>tam dati circu <lb/>li maximi, a@ <lb/>proinde qua <lb/>hora eandem <lb/>illuminare in-<lb/>cipiat, aut deſi-<lb/>nat, quo pacto <lb/>ex Analemma-<lb/>te deprehend@ <lb/>@ur.</note>
  <figure xlink:label="fig-0469-01" xlink:href="fig-0469-01a">
    <image file="0469-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0469-01"/>
  </figure>
<note position="left" xlink:label="note-0469-03" xlink:href="note-0469-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0469-04" xlink:href="note-0469-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0469-05" xlink:href="note-0469-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0469-06" xlink:href="note-0469-06a" xml:space="preserve">19. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s29967" xml:space="preserve">IAM vero ſit γ δ, communis ſectio Meridiani &amp; </s>
  <s xml:id="echoid-s29968" xml:space="preserve">circuli dati ad Meridianum inclinati, quæ fa-<lb/>cile habetur, inuento ex propoſ. </s>
  <s xml:id="echoid-s29969" xml:space="preserve">28. </s>
  <s xml:id="echoid-s29970" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29971" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29972" xml:space="preserve">arcu Meridiani N δ, inter ipſum circulum, ac Horizon-<lb/>tem. </s>
  <s xml:id="echoid-s29973" xml:space="preserve">Inuenta autem per propoſ. </s>
  <s xml:id="echoid-s29974" xml:space="preserve">27. </s>
  <s xml:id="echoid-s29975" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29976" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29977" xml:space="preserve">eiuſdem circuli inclinatione ad Meridianum, inueniatur ex <lb/>propoſ. </s>
  <s xml:id="echoid-s29978" xml:space="preserve">25. </s>
  <s xml:id="echoid-s29979" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29980" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29981" xml:space="preserve">minor diameter Ellipſis, quam perpendiculares à circumferentia circuli inclinati in <lb/>planum Meridiani deductæ faciunt, quæ ſit ε θ, ſecans maiorem diametrum γ δ, ad angulos <lb/>rectos in E, centro; </s>
  <s xml:id="echoid-s29982" xml:space="preserve">atque circa datas diametros γ δ, ε θ, Ellipſis deſcribatur, iuxta ea, quæ in <lb/>ſcholio propoſ. </s>
  <s xml:id="echoid-s29983" xml:space="preserve">26. </s>
  <s xml:id="echoid-s29984" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29985" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29986" xml:space="preserve">tradidimus, ſecans diametros parallelorum in λ, μ, ξ, π, ρ, @, φ, ψ,
<pb o="454" file="0470" n="470" rhead="GNOMONICES"/>
punctis, à quibus ad diametros educantur perpendiculares λ 3, μ 4, ξ 7, π 8, ρ 9, @ 10, φ 11, ψ ω. <lb/></s>
  <s xml:id="echoid-s29987" xml:space="preserve">Dico circulum inclinatum ſecare parallelos in punctis 3, 4, 7, 8, 9, 10, 11, ω. </s>
  <s xml:id="echoid-s29988" xml:space="preserve">Cum enim, poſito ſemi-<lb/>circulo ♋, F R G, in propria poſitione, nimirum ad Meridianum recto, perpendicularis ex 3, in planum <lb/>Meridiani demiſſa cadat in <lb/>
<anchor type="figure" xlink:label="fig-0470-01a" xlink:href="fig-0470-01"/>
F G, communem ſectionem <lb/>
<anchor type="note" xlink:label="note-0470-01a" xlink:href="note-0470-01"/>
ipſius, ac Meridiani, ſit{q́ue} <lb/>propterea ad rectam F G, <lb/>ex defin. </s>
  <s xml:id="echoid-s29989" xml:space="preserve">3. </s>
  <s xml:id="echoid-s29990" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29991" xml:space="preserve">11. </s>
  <s xml:id="echoid-s29992" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s29993" xml:space="preserve">perpendicularis, cadet ne-<lb/>ceſſario ea perpendicularis <lb/>
<anchor type="note" xlink:label="note-0470-02a" xlink:href="note-0470-02"/>
in punctum λ, ne ex pun-<lb/>cto 3, duæ perpendiculares <lb/>dicantur duci ad rectã F G, <lb/>quod fieri non poteſt, vt ad <lb/>propoſ. </s>
  <s xml:id="echoid-s29994" xml:space="preserve">16. </s>
  <s xml:id="echoid-s29995" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s29996" xml:space="preserve">1. </s>
  <s xml:id="echoid-s29997" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s29998" xml:space="preserve">de-<lb/>monſtratum eſt à nobis ex <lb/>Proclo. </s>
  <s xml:id="echoid-s29999" xml:space="preserve">Quare recta 3 λ, <lb/>ad planum Meridiani recta <lb/>eſt, ac propterea, cum ex <lb/>propoſ. </s>
  <s xml:id="echoid-s30000" xml:space="preserve">24. </s>
  <s xml:id="echoid-s30001" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30002" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30003" xml:space="preserve">perpen-<lb/>
<anchor type="note" xlink:label="note-0470-03a" xlink:href="note-0470-03"/>
diculares à circunferentia <lb/>circuli inclinati in planum <lb/>Meridiani demiſſæ cadant <lb/>quoque in Ellipſim, ſecabit <lb/>circunferentia circuli incli-<lb/>nati parallelum ♋, F R G, <lb/>in puncto 3, ex quo videli-<lb/>cet perpendicularis in pla-<lb/>num Meridiani deducta ca-<lb/>dit in λ; </s>
  <s xml:id="echoid-s30004" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30005" xml:space="preserve">ſic de reliquis. <lb/></s>
  <s xml:id="echoid-s30006" xml:space="preserve">Abſcindet ergo circulus inclinatus ex parallelo ♋, arcũ F 3; </s>
  <s xml:id="echoid-s30007" xml:space="preserve">ex parallelo ♑, arcũ G 4; </s>
  <s xml:id="echoid-s30008" xml:space="preserve">ex ♉, &amp; </s>
  <s xml:id="echoid-s30009" xml:space="preserve">♍, ar <lb/>
<anchor type="note" xlink:label="note-0470-04a" xlink:href="note-0470-04"/>
cũ K 7; </s>
  <s xml:id="echoid-s30010" xml:space="preserve">ex ♏, &amp; </s>
  <s xml:id="echoid-s30011" xml:space="preserve">♓, arcum L 8; </s>
  <s xml:id="echoid-s30012" xml:space="preserve">ex ♈, &amp; </s>
  <s xml:id="echoid-s30013" xml:space="preserve">♎, arcum A 9, vel C 10; </s>
  <s xml:id="echoid-s30014" xml:space="preserve">ex ♊, &amp; </s>
  <s xml:id="echoid-s30015" xml:space="preserve">♌, arcum I ω; </s>
  <s xml:id="echoid-s30016" xml:space="preserve">ex ♐ &amp; </s>
  <s xml:id="echoid-s30017" xml:space="preserve"><lb/>♒, arcum H 11: </s>
  <s xml:id="echoid-s30018" xml:space="preserve">qui arcus ſcilicet inter Meridianũ, &amp; </s>
  <s xml:id="echoid-s30019" xml:space="preserve">circulum inclinatum interĳciuntur. </s>
  <s xml:id="echoid-s30020" xml:space="preserve">Vnde ſi tro <lb/>picus ♋, F R G, &amp; </s>
  <s xml:id="echoid-s30021" xml:space="preserve">reliqui paralleli in horas diſtribuantur, initio facto ſiue à Meridiano, nempe à pun-<lb/>cto F, vel G, &amp; </s>
  <s xml:id="echoid-s30022" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30023" xml:space="preserve">more Aſtronomorũ, ſiue ab Horizonte, vt à puncto R, vel S, &amp; </s>
  <s xml:id="echoid-s30024" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30025" xml:space="preserve">more Babyloniorũ, <lb/>Italorumve, liquido conſtabit, quænã hora, aut horæ particula in punctũ 3. </s>
  <s xml:id="echoid-s30026" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s30027" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s30028" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30029" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30030" xml:space="preserve">cadat.</s>
  <s xml:id="echoid-s30031" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1532" type="float" level="2" n="6">
  <figure xlink:label="fig-0470-01" xlink:href="fig-0470-01a">
    <image file="0470-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0470-01"/>
  </figure>
<note position="left" xlink:label="note-0470-01" xlink:href="note-0470-01a" xml:space="preserve">38. vndec.</note>
<note position="left" xlink:label="note-0470-02" xlink:href="note-0470-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0470-03" xlink:href="note-0470-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0470-04" xlink:href="note-0470-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s30032" xml:space="preserve">CAETERVM vt cognoſcamus, an punctum 3. </s>
  <s xml:id="echoid-s30033" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s30034" xml:space="preserve">vel 9, &amp; </s>
  <s xml:id="echoid-s30035" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30036" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s30037" xml:space="preserve">hora, vbi <lb/>parallelus à circulo inclinato ſecatur, ſit ex parte Orientali, Occidentalive, diligenter inſpiciendus erit <lb/>ſitus, ac poſitio circuli inclinati. </s>
  <s xml:id="echoid-s30038" xml:space="preserve">Hoc enim cognito, facile illud intelligemus, vt paulo infra in ſolutione <lb/>eiuſdem huius problematis per doctrinam ſinuum docebimus.</s>
  <s xml:id="echoid-s30039" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s30040" xml:space="preserve">QVOD ſi quando Ellipſis diametrum paralleli duobus in locis ſecet citra pumctum, in quo eadem <lb/>
<anchor type="note" xlink:label="note-0470-05a" xlink:href="note-0470-05"/>
<anchor type="note" xlink:label="note-0470-06a" xlink:href="note-0470-06"/>
diameter ab Horizontis diametro diuiditur, abſcindentur duo arcus ex parallelo, vnus quidem ad par-<lb/>tes Orientis, alter verò ad partes Occidentis. </s>
  <s xml:id="echoid-s30041" xml:space="preserve">Et ſi circuli ſuperior facies ad occaſum ſpectet, erit <lb/>punctum vicinius Meridiano orientale, remotius autem occidentale. </s>
  <s xml:id="echoid-s30042" xml:space="preserve">Contra verò ſi ad ortum ſpectet, vt <lb/>ex ſequentibus magis perſpicuum fiet. </s>
  <s xml:id="echoid-s30043" xml:space="preserve">Hoc autem plerunque accidit in planis per verticem tranſeunti-<lb/>bus, &amp; </s>
  <s xml:id="echoid-s30044" xml:space="preserve">exiguam declinationem habentibus à Verticali circulo, &amp; </s>
  <s xml:id="echoid-s30045" xml:space="preserve">in alĳs nonnullis, vt ex ſphæra ma-<lb/>teriali intelligi poteſt.</s>
  <s xml:id="echoid-s30046" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1533" type="float" level="2" n="7">
<note position="left" xlink:label="note-0470-05" xlink:href="note-0470-05a" xml:space="preserve">Quando circu-<lb/>lus inclinatus <lb/>duobus in locis <lb/>ſecet patallelũ <lb/>Solis propoſi-<lb/>tum.</note>
<note position="left" xlink:label="note-0470-06" xlink:href="note-0470-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s30047" xml:space="preserve">IN circulis ad Meridianũ rectis, qualis eſt Verticalis propriè dictus, &amp; </s>
  <s xml:id="echoid-s30048" xml:space="preserve">omnes circuli, quibus horo <lb/>
<anchor type="note" xlink:label="note-0470-07a" xlink:href="note-0470-07"/>
logia ad Horizontẽ inclinata æquidiſtãt, res propoſita nullius est negotii ex Analẽmate. </s>
  <s xml:id="echoid-s30049" xml:space="preserve">Nam ſi ex pun <lb/>cto, vbi cõmunis ſectio circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s30050" xml:space="preserve">Meridiani diametrũ paralleli cuiuslibet interſecat, ad diame <lb/>trũ paralleli ducatur perpendicularis, ſecabitur circũferentia paralleli in puncto, in quo à dicto circulo <lb/>
<anchor type="note" xlink:label="note-0470-08a" xlink:href="note-0470-08"/>
ſecatur tam ante meridiẽ, quam poſt meridiem. </s>
  <s xml:id="echoid-s30051" xml:space="preserve">Exemplum habes in proxima figura in Verticali circulo, <lb/>cuius diameter eſt 12 13, vbi perpendiculares V Z, X α, E D, Y β, indicant puncta, in quibus paralleli <lb/>à Verticali circulo ſecantur; </s>
  <s xml:id="echoid-s30052" xml:space="preserve">quia vt demonſtratum eſt, illæ perpendiculares communes ſectiones ſunt <lb/>Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s30053" xml:space="preserve">par allelorum. </s>
  <s xml:id="echoid-s30054" xml:space="preserve">Eadem{q́ue} ratio eſt, ſi diameter γ δ, ponatur communis ſectio Me-<lb/>ridiani, &amp; </s>
  <s xml:id="echoid-s30055" xml:space="preserve">alicuius circuli maximi, cuihorologium ad Horizontem inclinatum æquidiſtat, ita vt altitu <lb/>do poli ſupra ipſum ſit arcus δ D. </s>
  <s xml:id="echoid-s30056" xml:space="preserve">Perpendiculares enim ex punctis, vbi γ δ, parallelorum diametros <lb/>ſecat, ad eaſdem diametros eductæ communes ſectiones erunt parallelorum, &amp; </s>
  <s xml:id="echoid-s30057" xml:space="preserve">dicti circuli maximi; <lb/></s>
  <s xml:id="echoid-s30058" xml:space="preserve">quod demonſtrabitur, vt de Verticali circulo, &amp; </s>
  <s xml:id="echoid-s30059" xml:space="preserve">Horizonte dictum eſt.</s>
  <s xml:id="echoid-s30060" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1534" type="float" level="2" n="8">
<note position="left" xlink:label="note-0470-07" xlink:href="note-0470-07a" xml:space="preserve">Quando circu <lb/>lus ad Meridia <lb/>num rectus eſt, <lb/>qua ratione in <lb/>quiratur, quæ <lb/>horæ ſupra v-<lb/>tramuis faciem <lb/>contineantur</note>
<note position="left" xlink:label="note-0470-08" xlink:href="note-0470-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s30061" xml:space="preserve">EX his facile intelligi poteſt, qua hora Sol illuminare incipiat faciem ſuperiorem, inferioremve cir-<lb/>culi inclinati, &amp; </s>
  <s xml:id="echoid-s30062" xml:space="preserve">ad quas horas ſupputandæ ſint altitudines Solis. </s>
  <s xml:id="echoid-s30063" xml:space="preserve">Quando enim circuli facies ſu-
<pb o="455" file="0471" n="471" rhead="LIBER QVINTVS."/>
perior ad occaſum ſpectat, incipiet Sol ſuperiorem faciem illuminare, cum in eo puncto existit, <lb/>quod per ſuperiorem demonſtrationem inuentum eſt, vt in puncto 3, vel 7, vel 9, &amp; </s>
  <s xml:id="echoid-s30064" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30065" xml:space="preserve">Vnde al-<lb/>titudines Solis ſupra faciem ſuperiorem inueſtigandæ erunt pro ſingulis horis ab eo puncto vſque <lb/>ad occaſum Solis; </s>
  <s xml:id="echoid-s30066" xml:space="preserve">niſi quando parallelus ſupra Horizontem duobus in locis à cir culo inclinato ſeca-<lb/>tur: </s>
  <s xml:id="echoid-s30067" xml:space="preserve">tunc enim ſumendæ ſunt horæ duntaxat ab eo puncto vſque ad alterum punctum, quod occidenta-<lb/>lius eſt, quia ibi Sol deſinit illuſtrare faciem ſuperiorem. </s>
  <s xml:id="echoid-s30068" xml:space="preserve">Altitudines verò Solis ſupra faciem inferior@m <lb/>inquirendæ erunt prohoris ab ortu Solis vſque ad dictum punctum: </s>
  <s xml:id="echoid-s30069" xml:space="preserve">Et ſi duobus in locis ſupra Hori-<lb/>zontem à circulo inclinato parallelus ſecatur, pro horis etiam ab occidentaliori puncto vſque ad Solis <lb/>occaſum: </s>
  <s xml:id="echoid-s30070" xml:space="preserve">quia in priori puncto Sol deſinit faciem inferiorem illuſtrare, &amp; </s>
  <s xml:id="echoid-s30071" xml:space="preserve">eandem illuminare rurſus in-<lb/>cipit in puncto poſteriori. </s>
  <s xml:id="echoid-s30072" xml:space="preserve">Quando autem circuli ſuperior facies ad ortum ſpectat, deſinet Sol faciem ſu-<lb/>
<anchor type="note" xlink:label="note-0471-01a" xlink:href="note-0471-01"/>
periorem illuminare, cum in eo puncto exiſtit, quod præccdenti demonſtr atione inuentum eſt. </s>
  <s xml:id="echoid-s30073" xml:space="preserve">Quare alti-<lb/>tudines Solis ſupra faciem ſuperiorẽ inquirendæ erunt pro ſingulis horis ab ortu Solis uſque ad illud pũ-<lb/>ctum. </s>
  <s xml:id="echoid-s30074" xml:space="preserve">Quod ſi cir culus inclinatus duobus in locis parallelum ſecet, accipiendæ erunt illæ horæ duntaxat, <lb/>quæ inter orientalius punctum, &amp; </s>
  <s xml:id="echoid-s30075" xml:space="preserve">occident alius comprehẽduntur: </s>
  <s xml:id="echoid-s30076" xml:space="preserve">quia in priori puncto Sol faciem ſupe <lb/>riorem incipit illustrare. </s>
  <s xml:id="echoid-s30077" xml:space="preserve">Supra faciem autem inferiorem inueniendæ erunt altitudines Solis pro horis à <lb/>puncto inuento vſque ad Solis occaſum: </s>
  <s xml:id="echoid-s30078" xml:space="preserve">Et ſi duobus in locis parallelus à circulo inclinato ſecetur, pro <lb/>horis etiam ab ortu Solis vſque ad orient alius punctum: </s>
  <s xml:id="echoid-s30079" xml:space="preserve">quia in hoc deſinit Sol illuminare faciem inferio <lb/>rem, in occident aliori vero eandcm rurſus illuſtrare incipit.</s>
  <s xml:id="echoid-s30080" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1535" type="float" level="2" n="9">
<note position="left" xlink:label="note-0471-01" xlink:href="note-0471-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s30081" xml:space="preserve">VERVM idem hoc per ſinuum doctrinam expeditius aſſequemur, hac ratione. </s>
  <s xml:id="echoid-s30082" xml:space="preserve">Sit Horizon A B-<lb/>C D; </s>
  <s xml:id="echoid-s30083" xml:space="preserve">Meridianus A E C; </s>
  <s xml:id="echoid-s30084" xml:space="preserve">Aequator B E D; </s>
  <s xml:id="echoid-s30085" xml:space="preserve">parallelus ſiue borealis, ſiue auſtralis F H G; </s>
  <s xml:id="echoid-s30086" xml:space="preserve">circulus maxi <lb/>
<anchor type="note" xlink:label="note-0471-02a" xlink:href="note-0471-02"/>
mus ad Meridianũ inclinatus, ſiue is ad Horizontẽ rectus ſit, ſiue non, R I, ſecans Aequatorẽ in punctis <lb/>K, L, par allelũ borealẽ in punctis M, N, &amp; </s>
  <s xml:id="echoid-s30087" xml:space="preserve">auſtralẽ in punctis R, S, Meridianũ verò in puncto I. </s>
  <s xml:id="echoid-s30088" xml:space="preserve">Inue <lb/>ſtigandus ergo eſt vterq; </s>
  <s xml:id="echoid-s30089" xml:space="preserve">arcus E K, E L, in Aequatore, &amp; </s>
  <s xml:id="echoid-s30090" xml:space="preserve">vter que H M, H N, in parallelo boreali, &amp; </s>
  <s xml:id="echoid-s30091" xml:space="preserve"><lb/>vterq; </s>
  <s xml:id="echoid-s30092" xml:space="preserve">H R, H S, in par allelo auſtrali, hoc eſt, diſtantia Solis ante, vel poſt meridiẽ, cum in plano inclina <lb/>to, &amp; </s>
  <s xml:id="echoid-s30093" xml:space="preserve">in dictis parallelis exiſtit. </s>
  <s xml:id="echoid-s30094" xml:space="preserve">Quoniã vero circulus maximus ad Meridianũ inclinatus quẽlibet paral <lb/>lelum, quem inter ſecat, duobus in punctis ſecat, quorum vnum prop inquius eſt ſemicirculo Meridiani ſu <lb/>pra Horizontem exiſtenti, &amp; </s>
  <s xml:id="echoid-s30095" xml:space="preserve">remotius alterum; </s>
  <s xml:id="echoid-s30096" xml:space="preserve">inquiremus primo loco ar cum illum paralleli, qui inter <lb/>propinquius punctũ, &amp; </s>
  <s xml:id="echoid-s30097" xml:space="preserve">Meridianum interĳ citur: </s>
  <s xml:id="echoid-s30098" xml:space="preserve">ex hoc enim nullo negocio alterum eliciemus, qui inter <lb/>punctum remotius, &amp; </s>
  <s xml:id="echoid-s30099" xml:space="preserve">Meridianum inter cipitur. </s>
  <s xml:id="echoid-s30100" xml:space="preserve">Vt autem cognoſcamus, an punctum propinquius ſit <lb/>orientale, an verò occidentale, diligenter inſpiciendus est ſitus circuli inclinati. </s>
  <s xml:id="echoid-s30101" xml:space="preserve">Nam ex eo facile in-<lb/>
<anchor type="note" xlink:label="note-0471-03a" xlink:href="note-0471-03"/>
telligemus, an minor arcus paralleli inter circulum inclinatum, &amp; </s>
  <s xml:id="echoid-s30102" xml:space="preserve">ſemicirculum Meridiani exiſtentem <lb/>ſupra Horizontem ſit orientalis, an occidentalis, hac arte. </s>
  <s xml:id="echoid-s30103" xml:space="preserve">Quando cir culus maximus ad Meridianum <lb/>
<anchor type="note" xlink:label="note-0471-04a" xlink:href="note-0471-04"/>
rectus est, ſiue per verticem capitis tranſeat, ſiue non, tranſibit neceſſario per communes ſectiones Ae-<lb/>quatoris, &amp; </s>
  <s xml:id="echoid-s30104" xml:space="preserve">Horizontis, nempe per polos Meridiani, ex propoſ. </s>
  <s xml:id="echoid-s30105" xml:space="preserve">14. </s>
  <s xml:id="echoid-s30106" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30107" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30108" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s30109" xml:space="preserve">ſecabit{q́ue} quemuis <lb/>parallelum in duobus punctis æqualiter hinc inde à Meridiano diſtantibus: </s>
  <s xml:id="echoid-s30110" xml:space="preserve">quia Meridianus rectus exi-<lb/>ſtens ad parallelum, &amp; </s>
  <s xml:id="echoid-s30111" xml:space="preserve">circulum illum maximum, ſecat per propoſ. </s>
  <s xml:id="echoid-s30112" xml:space="preserve">9. </s>
  <s xml:id="echoid-s30113" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30114" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30115" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s30116" xml:space="preserve">eorum ſegmenta bi-<lb/>fariam. </s>
  <s xml:id="echoid-s30117" xml:space="preserve">Quando autem idem circulus maximus ad Meridianum inclinatus eſt, &amp; </s>
  <s xml:id="echoid-s30118" xml:space="preserve">per verticem capitis <lb/>tranſit, hoc eſt, ad Horizontem rectus eſt, ſi quidem facies eius australis in occaſum vergat, &amp; </s>
  <s xml:id="echoid-s30119" xml:space="preserve">ver-<lb/>tex capitis inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30120" xml:space="preserve">parallelum borealem propoſitum existat, ſecabitur tam paralle-<lb/>lus ille borealis, quàm auſtralis oppoſitus in duobus punctis, quorum orientale propinquius est ſemicir-<lb/>culo Meridiani ſupra Horizontem exiſtenti, quàm occidentale, propter angulum acutum, quem circulus <lb/>
<anchor type="note" xlink:label="note-0471-05a" xlink:href="note-0471-05"/>
declinans cum Meridiano ad partes orientales, auſtralesq́, constituit: </s>
  <s xml:id="echoid-s30121" xml:space="preserve">Si verò vertex inter Aequato-<lb/>rem, &amp; </s>
  <s xml:id="echoid-s30122" xml:space="preserve">parallelum borealem exiſtat, ſecabitur ille parallelus borealis in duobus punctis occidc<unsure/>ntalibus, <lb/>auſtralis verò oppoſitus in duobus punctis orientalibus. </s>
  <s xml:id="echoid-s30123" xml:space="preserve">Contrarium his accidet, ſi facies circuli decli-<lb/>nantis auſtralis vergat in ortum. </s>
  <s xml:id="echoid-s30124" xml:space="preserve">Nam vertice capitis inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30125" xml:space="preserve">parallelum borealem <lb/>exiſtente, ſecabitur tam parallelus ille borealis, quàm auſtralis oppoſitus in duobus punctis, quorum oc-<lb/>cidentale propinquius eſt ſemicirculo Meridiani ſupra Horizontem exiſtenti, quàm orientale, propte-<lb/>rea quod circulus declinans cum Meridiano angulum acutum efficit ad partes occidentales, auſtrales{q́ue}: <lb/></s>
  <s xml:id="echoid-s30126" xml:space="preserve">Vertice autem inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30127" xml:space="preserve">parallelum borealem exiſtente, ſecabitur parallelus ille borealis <lb/>in duobus punctis orientalibus, auſtralis verò oppoſitus in duobus punctis occidentalibus. </s>
  <s xml:id="echoid-s30128" xml:space="preserve">Quando au-<lb/>tem circulus maximus ad Meridi anum inclinatus non per verticem tranſit, ſi quidem ex parte boreali <lb/>
<anchor type="note" xlink:label="note-0471-06a" xlink:href="note-0471-06"/>
inclinatus ſit, &amp; </s>
  <s xml:id="echoid-s30129" xml:space="preserve">facies eius ſuperior ad occaſum ſpectet, arcus Meridiani inter circulum inclina-<lb/>tum, &amp; </s>
  <s xml:id="echoid-s30130" xml:space="preserve">Horizontem minor ſit arcu Meridiani ex parte boreali inter parallelum borealem, &amp; </s>
  <s xml:id="echoid-s30131" xml:space="preserve">Hori-<lb/>zontem, ita vt planum inclinatum ſecet Meridianum inter Horizontem, &amp; </s>
  <s xml:id="echoid-s30132" xml:space="preserve">parallelum borealem, ſeca-<lb/>bitur quoque tam parallelus ille borealis, quàm auſtr alis oppoſitus in duobus punctis, quorum orientale <lb/>minus à ſemicir culo Meridiani existente ſupra Horizontem diſtat, quàm occidentale, proptcrea quod <lb/>circulus inclinatus cum Meridiano ad partes orientales, australes angulum acutum conſtituit: </s>
  <s xml:id="echoid-s30133" xml:space="preserve">Si ve-<lb/>rò arcus Meridiani inter circulum inclinatum, &amp; </s>
  <s xml:id="echoid-s30134" xml:space="preserve">Horizontem fuerit maior arcu Meridiani ex parte <lb/>boreali inter parallelum borealem propoſitum, atque Horizontem, ita vt planum inclinatum ſecet Me-<lb/>ridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30135" xml:space="preserve">parallelum borealem, ſecabitur parallelus ille borealis in duobus pun-<lb/>ctis occidentalib{us}, parallel{us} vero auſtralis oppoſit{us} in duobus punctis orientalibus. </s>
  <s xml:id="echoid-s30136" xml:space="preserve">Contrarium bis
<pb o="456" file="0472" n="472" rhead="GNOMONICES"/>
accidet, ſi facies ſuperior circuli inclinati ad ortum vergat. </s>
  <s xml:id="echoid-s30137" xml:space="preserve">Idem prorſus dicendum eſt de circulo<unsure/> <lb/>inclinato ex parte australi. </s>
  <s xml:id="echoid-s30138" xml:space="preserve">Si enim facies eius ſuperior occaſum reſpiciat, arcus Meridiani <lb/>ex parte auſtrali inter ipſum, &amp; </s>
  <s xml:id="echoid-s30139" xml:space="preserve">Horizontem minor ſit arcu Meridiani inter parallelum auſtra-<lb/>lem &amp; </s>
  <s xml:id="echoid-s30140" xml:space="preserve">Horizontem, diuidetur tam ille auſtralis parallelus, quam borealis oppoſitus, in duobus <lb/>quoque punctis, quorum orientale minus distat à ſemicirculo Meridiam ſupra Horizontem exi-<lb/>ſtente, quàm occidentale, propter angulum acutum, quem circulus inclinatus cum Meridiano ad partes <lb/>orientales, boreales efficit: </s>
  <s xml:id="echoid-s30141" xml:space="preserve">Si verò arcus Meridiani inter circulum inclinatum, &amp; </s>
  <s xml:id="echoid-s30142" xml:space="preserve">Horizontem ma-<lb/>ior fuerit arcu Meridiani ex parte auſtrali inter parallelum auſtralem, &amp; </s>
  <s xml:id="echoid-s30143" xml:space="preserve">Horizontem, ſecabitur pa-<lb/>rallel{us} ille auſtralis in duobus punctis occidentalibus, parallelus verò borealis oppoſitus in duobus pun <lb/>ctis orientalibus. </s>
  <s xml:id="echoid-s30144" xml:space="preserve">Contrarium his continget, ſi facies ſuperior circuli inclinati in ortum vergat. </s>
  <s xml:id="echoid-s30145" xml:space="preserve">Quod ſi <lb/>
<anchor type="note" xlink:label="note-0472-01a" xlink:href="note-0472-01"/>
planum ex parte australi inclinatum ſit, ſecet Meridianum inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30146" xml:space="preserve">parallelum bo-<lb/>realem, vel inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30147" xml:space="preserve">parallelum borealem, idem dicendum erit, quod ſupra, cum planum <lb/>ex parte boreali inclinatum erat, ſecabat Meriaianum inter Horizontem, &amp; </s>
  <s xml:id="echoid-s30148" xml:space="preserve">parallelum borealem, <lb/>vel inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30149" xml:space="preserve">parallelum borealem. </s>
  <s xml:id="echoid-s30150" xml:space="preserve">Quæ omnia ex ſphæra materiali facile colligi poſſunt, <lb/>at que intelligi.</s>
  <s xml:id="echoid-s30151" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1536" type="float" level="2" n="10">
<note position="left" xlink:label="note-0471-02" xlink:href="note-0471-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0471-03" xlink:href="note-0471-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0471-04" xlink:href="note-0471-04a" xml:space="preserve">An ateus paral <lb/>leli prepoſiti <lb/>inter Meridia-<lb/>num ſupra Ho <lb/>rizontẽ, &amp; cir-<lb/>culum inclina-<lb/>tum ex parte <lb/>orien is minor <lb/>ſitaltero ex par <lb/>te occidẽtis, an <lb/>contra. Item <lb/>quando parall@ <lb/>lus à plano in-<lb/>clina o duobus <lb/>in locis ſecetur <lb/>ex eadem part@ <lb/>ſiue orientali, <lb/>ſiue occidenta-<lb/>li, quo pacto <lb/>cognoſcatur.</note>
<note position="left" xlink:label="note-0471-05" xlink:href="note-0471-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0471-06" xlink:href="note-0471-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0472-01" xlink:href="note-0472-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s30152" xml:space="preserve">IT AQVE hac ratione minores arcus parallelorum inter circulum inclinatum, &amp; </s>
  <s xml:id="echoid-s30153" xml:space="preserve">ſemicirculu@ <lb/>
<anchor type="note" xlink:label="note-0472-02a" xlink:href="note-0472-02"/>
Meridiani exiſtentem ſupra Horizontem, quos ponimus eſſe E K, H M, H R, inueſtigabimus. </s>
  <s xml:id="echoid-s30154" xml:space="preserve">Ex polo <lb/>
<anchor type="figure" xlink:label="fig-0472-01a" xlink:href="fig-0472-01"/>
<anchor type="note" xlink:label="note-0472-03a" xlink:href="note-0472-03"/>
<anchor type="note" xlink:label="note-0472-04a" xlink:href="note-0472-04"/>
<anchor type="note" xlink:label="note-0472-05a" xlink:href="note-0472-05"/>
mundi arctico O, per puncta M, R, circuli maximi declinationum ducantur O M, O R, ſecantes Ae-<lb/>quatorem in P, &amp; </s>
  <s xml:id="echoid-s30155" xml:space="preserve">T. </s>
  <s xml:id="echoid-s30156" xml:space="preserve">Et quoniam in triangulo ſphærico E I K, (cuius angulus E, rectus eſt, &amp; </s>
  <s xml:id="echoid-s30157" xml:space="preserve">angu-<lb/>lus I, inclinationis circuli inclinati ad Meridianum, per propoſ. </s>
  <s xml:id="echoid-s30158" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30159" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30160" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30161" xml:space="preserve">notus, vnà c@m arcu Meri-<lb/>diani E I, inter planum, &amp; </s>
  <s xml:id="echoid-s30162" xml:space="preserve">Aequatorem. </s>
  <s xml:id="echoid-s30163" xml:space="preserve">Cum enim ex coroll. </s>
  <s xml:id="echoid-s30164" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s30165" xml:space="preserve">28. </s>
  <s xml:id="echoid-s30166" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30167" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30168" xml:space="preserve">arcus Meridiani in-<lb/>ter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30169" xml:space="preserve">polum arcticum poſitus ſit notus, &amp; </s>
  <s xml:id="echoid-s30170" xml:space="preserve">inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30171" xml:space="preserve">Aequatorem <lb/>interĳciatur quadrans Meridiani, cognitus quoque erit arcus Meridiani inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30172" xml:space="preserve"><lb/>Aequatorem. </s>
  <s xml:id="echoid-s30173" xml:space="preserve">Nam ſi planum ex parte boreali inclinatum ſit, infra tamen polum, erit arcus Meridiani <lb/>
<anchor type="note" xlink:label="note-0472-06a" xlink:href="note-0472-06"/>
<anchor type="note" xlink:label="note-0472-07a" xlink:href="note-0472-07"/>
inter planum, &amp; </s>
  <s xml:id="echoid-s30174" xml:space="preserve">Aequatorem ſupra Horizontem compoſitus ex quadrante, &amp; </s>
  <s xml:id="echoid-s30175" xml:space="preserve">arcu Meridiani inter <lb/>polum arcticum, &amp; </s>
  <s xml:id="echoid-s30176" xml:space="preserve">planum inclinatum: </s>
  <s xml:id="echoid-s30177" xml:space="preserve">Si autem planum inclinatum ſit ex parte boreali, ſupra tamen <lb/>polum, hoc eſt, ita tamen, vt arcus Meridiani inter Horizontem, &amp; </s>
  <s xml:id="echoid-s30178" xml:space="preserve">planum inclinatum maior ſit altitu <lb/>dine poli ſupra Horizontem, vel ex parte auſtrali, ſupra tamen Aequatorem, hoc est, ita tamen, vt <lb/>arcus Meridiani inter Horizontem, &amp; </s>
  <s xml:id="echoid-s30179" xml:space="preserve">planum inclinatum maior ſit altitudine Aequatoris, relinquetur <lb/>arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s30180" xml:space="preserve">Aequatorem, ſi arcus Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s30181" xml:space="preserve">polum arcticum <lb/>ex quadrante auferatur: </s>
  <s xml:id="echoid-s30182" xml:space="preserve">Si denique planum inclinatum ſit ex parte auſtrali, ſed infra Aequatorem, hoc <lb/>eſt, ſed ar cus Meridiani inter planum at que Horizontem minor ſit altitudine Aequatoris, habebitur ar <lb/>cus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s30183" xml:space="preserve">Aequatorem, ſi quadr ans ex arcu Meridiani inter planum, &amp; </s>
  <s xml:id="echoid-s30184" xml:space="preserve">polum ar-<lb/>cticum detrabatur, vt perſpicuum eſt) per propoſ. </s>
  <s xml:id="echoid-s30185" xml:space="preserve">18. </s>
  <s xml:id="echoid-s30186" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30187" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30188" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s30189" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s30190" xml:space="preserve">de triangulis, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s30191" xml:space="preserve">14. </s>
  <s xml:id="echoid-s30192" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30193" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30194" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s30195" xml:space="preserve">42. </s>
  <s xml:id="echoid-s30196" xml:space="preserve">noſtrorum triangulorum ſphæricorum, eſt, vt ſinus anguli E I K,
<pb o="457" file="0473" n="473" rhead="LIBER QVINTVS."/>
inclinationis plani ad Meridianum, ad ſinum totum, ita ſinus complementi anguli E K I, quem planum <lb/>cum Aequatore facit, ad ſinum complementi arcus Meridiani E I, inter planum, &amp; </s>
  <s xml:id="echoid-s30197" xml:space="preserve">Aequatorem in-<lb/>ter cepti: </s>
  <s xml:id="echoid-s30198" xml:space="preserve">Erit conuertendo, vt ſinus totus ad ſinum anguli inclinationis plani ad Meridianum E I K, <lb/>ita ſinus complementi ar cus Meridani E I, inter planum, &amp; </s>
  <s xml:id="echoid-s30199" xml:space="preserve">Aequatorem, ad ſinum complementi angu-<lb/>li E K I, quem planum cum Aequatore facit. </s>
  <s xml:id="echoid-s30200" xml:space="preserve">Quocirca ſi fiat, vt ſinus totus ad ſinum anguli inclina-<lb/>tionis plani ad Meridianũ, ita ſinus cõplementi arcus Meridiani inter planũ, &amp; </s>
  <s xml:id="echoid-s30201" xml:space="preserve">Aequatorem ad aliud, <lb/>inuenietur ſinus cõplementi anguli E K I, atq; </s>
  <s xml:id="echoid-s30202" xml:space="preserve">adeo angulus ipſe E K I, quẽ planũ cum Aequatore facit, <lb/>cognitus erit. </s>
  <s xml:id="echoid-s30203" xml:space="preserve">Rurſus quia in eodem rectangulo triangulo ſphærico E I K, per propoſ. </s>
  <s xml:id="echoid-s30204" xml:space="preserve">16. </s>
  <s xml:id="echoid-s30205" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30206" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30207" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s30208" xml:space="preserve">
<anchor type="note" xlink:label="note-0473-01a" xlink:href="note-0473-01"/>
Regiom. </s>
  <s xml:id="echoid-s30209" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s30210" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30211" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30212" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30213" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s30214" xml:space="preserve">41. </s>
  <s xml:id="echoid-s30215" xml:space="preserve">nostrorũ triangulorum ſphæ-<lb/>ricorum, eſt, vt ſinus anguli E K I, quem facit planum cum Aequatore, ad ſinum arcus Meridiani E I, <lb/>
<anchor type="note" xlink:label="note-0473-02a" xlink:href="note-0473-02"/>
inter planum, &amp; </s>
  <s xml:id="echoid-s30216" xml:space="preserve">Aequatorem, ita ſinus anguli E I K, inclinationis plani ad Meridianum, ad ſinum ar-<lb/>cus Aequatoris E K, diſtantiæ Solis à meridie: </s>
  <s xml:id="echoid-s30217" xml:space="preserve">Si fiat, vt ſinus anguli inuenti, quem planum cum <lb/>
<anchor type="note" xlink:label="note-0473-03a" xlink:href="note-0473-03"/>
Aequatore facit, ad ſinum arcus Meridiani inter planum &amp; </s>
  <s xml:id="echoid-s30218" xml:space="preserve">Aequatorem, ita ſinus inclinationis plan i <lb/>ad Meridianum ad aliud, inuenietur ſinus minoris distantiæ Solis à meridie, cum Sol in Aequatore exi <lb/>ſtens faciem unam plani inclinati illuminare incipit, &amp; </s>
  <s xml:id="echoid-s30219" xml:space="preserve">alteram illuminare deſinit.</s>
  <s xml:id="echoid-s30220" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1537" type="float" level="2" n="11">
<note position="left" xlink:label="note-0472-02" xlink:href="note-0472-02a" xml:space="preserve">Quota hora an <lb/>te, &amp; poſt meri <lb/>diem circulus <lb/>inclinatus pa-<lb/>rallelos Solis <lb/>interſecet, ae <lb/>proinde quot <lb/>horæ ſupra v-<lb/>tramque faci@ <lb/>eiuſdem circu <lb/>li reperiantur. <lb/>&amp; qua hora <lb/>Sol vtramqu@ <lb/>illuminare in-<lb/>cipiat, aut deſi <lb/>nat, qua uia per <lb/>ſinu@ inquira-<lb/>tur.</note>
  <figure xlink:label="fig-0472-01" xlink:href="fig-0472-01a">
    <image file="0472-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0472-01"/>
  </figure>
<note position="left" xlink:label="note-0472-03" xlink:href="note-0472-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0472-04" xlink:href="note-0472-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0472-05" xlink:href="note-0472-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0472-06" xlink:href="note-0472-06a" xml:space="preserve">Quantus ſit at <lb/>cus Meridiani <lb/>inte r planum <lb/>inclinatum, &amp; <lb/>Aequatorẽ ſu-<lb/>pra Horizon@ẽ, <lb/>quomodo in-<lb/>telligatur.</note>
<note position="left" xlink:label="note-0472-07" xlink:href="note-0472-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0473-01" xlink:href="note-0473-01a" xml:space="preserve">Angulus, quẽ <lb/>planum incli-<lb/>natum cum <lb/>Aequatore fa-<lb/>cit.</note>
<note position="left" xlink:label="note-0473-02" xlink:href="note-0473-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0473-03" xlink:href="note-0473-03a" xml:space="preserve">Diſtantia mi-<lb/>nor Solis à me <lb/>ridie in Aequa <lb/>to re, cum in cir <lb/>culo inclinato <lb/>exiſtit.</note>
</div>
<p style="it">
  <s xml:id="echoid-s30221" xml:space="preserve">DEINDE quoniam in triangulo ſphærico rectangulo K M P, per propoſ. </s>
  <s xml:id="echoid-s30222" xml:space="preserve">16. </s>
  <s xml:id="echoid-s30223" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30224" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30225" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s30226" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s30227" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s30228" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30229" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30230" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30231" xml:space="preserve">Gebri, vel propoſ. </s>
  <s xml:id="echoid-s30232" xml:space="preserve">41. </s>
  <s xml:id="echoid-s30233" xml:space="preserve">noſtrorum triangulorum ſphærico-<lb/>rum, eſt, vt ſinus anguli P K M, quem facit planum inclinatũ cum Aequatore, quem{q́ue} iam cognouimus, <lb/>ad ſinum arcus M P, declinationis paralleli, ita ſinus totus anguli recti K P M, ad ſinum arcus K M, <lb/>plani inclinati inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30234" xml:space="preserve">parallelum: </s>
  <s xml:id="echoid-s30235" xml:space="preserve">Si fiat, vt ſinus anguli inuenti, quem planum in-<lb/>
<anchor type="note" xlink:label="note-0473-04a" xlink:href="note-0473-04"/>
clinatum cum Aequatore facit, ad ſinum declinationis paralleli, ita ſinus totus ad aliud, inuenietur <lb/>ſinus illius arcus plani inclinati, qui inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30236" xml:space="preserve">parallelum interĳcitur. </s>
  <s xml:id="echoid-s30237" xml:space="preserve">Rurſus quia in <lb/>
<anchor type="note" xlink:label="note-0473-05a" xlink:href="note-0473-05"/>
eodem triangulo, per propoſ. </s>
  <s xml:id="echoid-s30238" xml:space="preserve">19. </s>
  <s xml:id="echoid-s30239" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30240" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30241" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s30242" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s30243" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s30244" xml:space="preserve">15. </s>
  <s xml:id="echoid-s30245" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30246" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30247" xml:space="preserve">Gebri, <lb/>vel per propoſ. </s>
  <s xml:id="echoid-s30248" xml:space="preserve">43. </s>
  <s xml:id="echoid-s30249" xml:space="preserve">noſtrorum triangulorum ſphæricorum, est, vt ſinus complementi arcus K M, proxi-<lb/>mè inuenti, ad ſinum complementi arcus M P, declinationis paralleli, ita ſinus complementi arcus K P, <lb/>ad ſinum totum: </s>
  <s xml:id="echoid-s30250" xml:space="preserve">Erit conuertendo, vt ſinus complementi arcus M P, declinationis paralleli, ad ſinum <lb/>complementi arcus K M, proximè inuenti, ita ſinus totus ad ſinum complementi arcus k P. </s>
  <s xml:id="echoid-s30251" xml:space="preserve">Si igitur <lb/>fiat, vt ſinus complementi declinationis paralleli ad ſinum complementi arcus plani inclinati, qui inter <lb/>Aequatorem, &amp; </s>
  <s xml:id="echoid-s30252" xml:space="preserve">parallelum interĳcitur, proxime inuenti, ita ſinus totus ad aliud, inuenietur ſinus <lb/>complementi illius arcus Aequatoris K P, qui inter planum &amp; </s>
  <s xml:id="echoid-s30253" xml:space="preserve">circulum det<unsure/>linationis interĳcitur, ac <lb/>
<anchor type="note" xlink:label="note-0473-06a" xlink:href="note-0473-06"/>
proinde ipſe arcus K P, notus erit, qui æqualis eſt alĳs tribus arcubus K T, L Q, L V. </s>
  <s xml:id="echoid-s30254" xml:space="preserve">Quoniam enim <lb/>
<anchor type="note" xlink:label="note-0473-07a" xlink:href="note-0473-07"/>
duo anguli P K M, T K R, ad verticem, nec non &amp; </s>
  <s xml:id="echoid-s30255" xml:space="preserve">duo Q L N, V L S, per propoſ. </s>
  <s xml:id="echoid-s30256" xml:space="preserve">6. </s>
  <s xml:id="echoid-s30257" xml:space="preserve">noſtrorum tri-<lb/>angulorum ſphæricorum. </s>
  <s xml:id="echoid-s30258" xml:space="preserve">Item angulus E K I, angulo E L I, æqualis, per propoſ. </s>
  <s xml:id="echoid-s30259" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30260" xml:space="preserve">eorundem triangu <lb/>lorum ſphęricorum, erunt duo anguli ad verticem K, duobus angulis ad verticem L, æquales. </s>
  <s xml:id="echoid-s30261" xml:space="preserve">Cum er-<lb/>go anguli ad P, T, Q, V, recti ſint, erunt duo anguli M P K, P K M, trianguli K P M, duobus angu-<lb/>lis R T K, T K R, trianguli K R T, item duobus angulis N Q L, Q L N, trianguli L N Q, &amp; </s>
  <s xml:id="echoid-s30262" xml:space="preserve">duobus <lb/>angulis S V L, V L S, trianguli L S V, æquales: </s>
  <s xml:id="echoid-s30263" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s30264" xml:space="preserve">arcus M P, R T, N Q, S V, oppoſiti <lb/>æqualibus angulis ad K, L, æquales, quod declinationes par allelorum oppoſitorum metiantur, quæ æqua-<lb/>les ſunt. </s>
  <s xml:id="echoid-s30265" xml:space="preserve">Igitur, per propoſ. </s>
  <s xml:id="echoid-s30266" xml:space="preserve">22. </s>
  <s xml:id="echoid-s30267" xml:space="preserve">noſtrorum triangulorum ſphæricorum, &amp; </s>
  <s xml:id="echoid-s30268" xml:space="preserve">reliqui arcus æquales erunt, <lb/>nempe arcus P K, T K, Q L, V L. </s>
  <s xml:id="echoid-s30269" xml:space="preserve">Ex hoc autem arcu Aequatoris inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30270" xml:space="preserve">cir-<lb/>
<anchor type="note" xlink:label="note-0473-08a" xlink:href="note-0473-08"/>
culum declinationis par alleli per Solem ducti, cum in plano inclinato exiſtit, qualis eſt P K, vel T K, <lb/>vel Q L, vel V L, quem proximè inuenimus, ita distantiam minorem Solis à meridie inueſtigabim{us}, hoc <lb/>eſt, arcum H M, &amp; </s>
  <s xml:id="echoid-s30271" xml:space="preserve">arcum H R. </s>
  <s xml:id="echoid-s30272" xml:space="preserve">Quando planum ex parte horeali ſupra Horizontem eleuatur, ſecat{q́ue} <lb/>
<anchor type="note" xlink:label="note-0473-09a" xlink:href="note-0473-09"/>
Meridianum inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30273" xml:space="preserve">Horizontem, vt in prima figura, arcus Aequatoris P K, pro-<lb/>xime inuentus, qui inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30274" xml:space="preserve">circulum declinationis interĳcitur, Sole exiſtente bo-<lb/>reali, addendus eſt arcui Aequatoris E K, ſupra inuento, qui inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30275" xml:space="preserve">Meridianum <lb/>poſitus eſt; </s>
  <s xml:id="echoid-s30276" xml:space="preserve">Sole vero exiſtente auſtrali, arcus T k, quem arcui P K, æqualem oſtendimus, ex eodem <lb/>arcu Aequatoris E K, auferendus eſt. </s>
  <s xml:id="echoid-s30277" xml:space="preserve">Ita enim ex illa additione fiet arcus E P, qui per propoſ. </s>
  <s xml:id="echoid-s30278" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30279" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s30280" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30281" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s30282" xml:space="preserve">arcui H M, metienti in parallelo boreali diſtantiã Solis à meridie ſimilis eſt: </s>
  <s xml:id="echoid-s30283" xml:space="preserve">ex ſubtractione <lb/>verò relinquetur arcus E T, qui per eandem propoſ. </s>
  <s xml:id="echoid-s30284" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30285" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30286" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30287" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s30288" xml:space="preserve">arcui H R, diſtantiæ Solis à <lb/>
<anchor type="note" xlink:label="note-0473-10a" xlink:href="note-0473-10"/>
meridie in parallelo auſtrali oppoſito ſimilis est. </s>
  <s xml:id="echoid-s30289" xml:space="preserve">Quando autem planum inclinatum Meridianum ſecat <lb/>
<anchor type="note" xlink:label="note-0473-11a" xlink:href="note-0473-11"/>
inter polum arcticum &amp; </s>
  <s xml:id="echoid-s30290" xml:space="preserve">parallelum borealem, vt in ſecunda figura, auferendus eſt arcus P K, inuen-<lb/>tus ex arcu inuento E K, vt relinquatur arcus E P, atque adeò ei ſimilis H M, in parallelo boreali di-<lb/>ſtantiam Solis à meridie metiens notus fiat: </s>
  <s xml:id="echoid-s30291" xml:space="preserve">Arcus verò T K, qui æqualis eſt arcui P K, eidem arcui <lb/>E K, adĳciendus eſt, vt fiat arcus E T, notus, qui ſimilis eſt arcui H R, diſtantiam Solis à meridie me-<lb/>tienti in parallelo auſtrali oppoſito. </s>
  <s xml:id="echoid-s30292" xml:space="preserve">Quando denique planum inclinatum ſecat Meridianum inter Aequa <lb/>
<anchor type="note" xlink:label="note-0473-12a" xlink:href="note-0473-12"/>
torem, &amp; </s>
  <s xml:id="echoid-s30293" xml:space="preserve">parallelum borealem, vt in tertia figura, ſi arcus Aequatoris E K, inter planum, &amp; </s>
  <s xml:id="echoid-s30294" xml:space="preserve">Meri-<lb/>dianum interiectus, ex arcu P K, eiuſdem Aequatoris inter planum &amp; </s>
  <s xml:id="echoid-s30295" xml:space="preserve">circulum declinationis poſito <lb/>auferatur, reliquus erit arcus E P, qui arcui H M, diſtantiæ Solis à meridie in parallelo boreali ſimilis <lb/>est: </s>
  <s xml:id="echoid-s30296" xml:space="preserve">Si vero eidem arcui Aequatoris E K, addatur arcus T K, qui arcui P K, æqualis eſt oſtenſus, con-<lb/>ficietur arcus E T, qui ſimilis eſt arcui H R, diſtantiæ Solis à meridie in oppoſito parallelo auſtrali.</s>
  <s xml:id="echoid-s30297" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1538" type="float" level="2" n="12">
<note position="left" xlink:label="note-0473-04" xlink:href="note-0473-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0473-05" xlink:href="note-0473-05a" xml:space="preserve">Arcus Plani in <lb/>clinati inter <lb/>Aequator em, <lb/>&amp; parallelum.</note>
<note position="left" xlink:label="note-0473-06" xlink:href="note-0473-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0473-07" xlink:href="note-0473-07a" xml:space="preserve">Arcus Aequa-<lb/>toris inter pla-<lb/>nũ inclinatũ, &amp; <lb/>circulũ declina <lb/>tionis paralle li <lb/>per Solem du-<lb/>cti, cum in pla-<lb/>no inclinato <lb/>exiſtit.</note>
<note position="left" xlink:label="note-0473-08" xlink:href="note-0473-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0473-09" xlink:href="note-0473-09a" xml:space="preserve">Diſtantia mi-<lb/>nor Solis à me <lb/>ridie, cum in <lb/>plano inclina-<lb/>to Meridianũ <lb/>ſecãte inter po <lb/>lum arcticum, <lb/>&amp; Horizontem <lb/>exiſti@, qua ra-<lb/>tione inueſtige <lb/>tur.</note>
<note position="left" xlink:label="note-0473-10" xlink:href="note-0473-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0473-11" xlink:href="note-0473-11a" xml:space="preserve">Quando pla-<lb/>num ex parte <lb/>boreali inclina <lb/>tum ſecat Me-<lb/>ridianum inter <lb/>polum atcticũ, <lb/>&amp; parallelum <lb/>borealem.</note>
<note position="right" xlink:label="note-0473-12" xlink:href="note-0473-12a" xml:space="preserve">Quando planũ <lb/>ex parte horea-<lb/>li inclinatum <lb/>ſecat Meridia-<lb/>num inter Ae-<lb/>quarorem, &amp; <lb/>parallelum bo. <lb/>realem.</note>
</div>
<pb o="458" file="0474" n="474" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s30298" xml:space="preserve">QVOD ſi planum ex parte auſtr ali eleuetur ſupra Horizontem, ſecet{q́ue} Meridianum inter Hori-<lb/>
<anchor type="note" xlink:label="note-0474-01a" xlink:href="note-0474-01"/>
zontẽ &amp; </s>
  <s xml:id="echoid-s30299" xml:space="preserve">parallelum auſtralem, vt in quarta figura, inuestigabimus diſtantiam Solis à meridie, vt in pri-<lb/>ma figura, vbi planum ex parte boreali inclinatum ſecat Meridianum inter Horizontem, &amp; </s>
  <s xml:id="echoid-s30300" xml:space="preserve">polum ar-<lb/>
<anchor type="figure" xlink:label="fig-0474-01a" xlink:href="fig-0474-01"/>
<anchor type="note" xlink:label="note-0474-02a" xlink:href="note-0474-02"/>
<anchor type="note" xlink:label="note-0474-03a" xlink:href="note-0474-03"/>
cticum. </s>
  <s xml:id="echoid-s30301" xml:space="preserve">Si autem planum ſecet Meridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30302" xml:space="preserve">parallelum australem, vt in quinta <lb/>
<anchor type="note" xlink:label="note-0474-04a" xlink:href="note-0474-04"/>
figura, auferendus eſt arcus Aequatoris E K, inter planum &amp; </s>
  <s xml:id="echoid-s30303" xml:space="preserve">Meridianum ex arcu T K, qui inter pla-<lb/>num, &amp; </s>
  <s xml:id="echoid-s30304" xml:space="preserve">circulum declinationis interĳcitur, vt relinquatur arcus E T, qui ſimilis est arcui H R, di-<lb/>ſtantiæ Solis à meridie in parallelo auſtrali: </s>
  <s xml:id="echoid-s30305" xml:space="preserve">Eidem verò arcui E K, adĳciendus eſt arcus P K, vt con-<lb/>ficiatur arcus E P, qui ſimilis eſt arcui H M, diſtantiæ Solis à meridie in parallelo boreali oppoſito. </s>
  <s xml:id="echoid-s30306" xml:space="preserve">Si <lb/>denique planum inclinatum ex parte auſtrali ſecet Meridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30307" xml:space="preserve">parallelum bo-<lb/>realem, vel inter verticem loci, &amp; </s>
  <s xml:id="echoid-s30308" xml:space="preserve">parallelum borealem, inquirenda erit diſtantia Solis à meridie, vt <lb/>in tertia figura, vbi planum ex parte boreali inclinatum ſecat Meridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30309" xml:space="preserve">pa-<lb/>rallelum borealem; </s>
  <s xml:id="echoid-s30310" xml:space="preserve">vel, vt in ſecunda figura, vbi planum ex parte boreali inclinatum ſecat Meridianum <lb/>inter polum arcticum, &amp; </s>
  <s xml:id="echoid-s30311" xml:space="preserve">par allelum borealem.</s>
  <s xml:id="echoid-s30312" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1539" type="float" level="2" n="13">
<note position="left" xlink:label="note-0474-01" xlink:href="note-0474-01a" xml:space="preserve">Quando planũ <lb/>ex parte auſtra <lb/>li inclinatum <lb/>eſt ad Horizon <lb/>tem vbieunq; <lb/>Meridianũ ſe-<lb/>cet, quo pacto <lb/>diſtãtia minor <lb/>Solis à meri-<lb/>die, cum in ce <lb/>plano exiſtit, in <lb/>@@niatur.</note>
  <figure xlink:label="fig-0474-01" xlink:href="fig-0474-01a">
    <image file="0474-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0474-01"/>
  </figure>
<note position="left" xlink:label="note-0474-02" xlink:href="note-0474-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0474-03" xlink:href="note-0474-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0474-04" xlink:href="note-0474-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Maior diſtan-<lb/>tia Solis à me-<lb/>ridie, cum in <lb/>plano inclina-<lb/>to, &amp; parallelo <lb/>quocunque exi <lb/>ſſit, qua ratio-<lb/>ne inueſtige-<lb/>tut.</note>
<p style="it">
  <s xml:id="echoid-s30313" xml:space="preserve">HACTENVS minorem arcum diſtantiæ Solis à meridie in quouis parallelo inueſtigauimus ex <lb/>
<anchor type="note" xlink:label="note-0474-06a" xlink:href="note-0474-06"/>
minori arcu Aequatoris inter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30314" xml:space="preserve">Meridianum interiecto, qualis est E K. </s>
  <s xml:id="echoid-s30315" xml:space="preserve">Quod ſi <lb/>dictum arcum Aequatoris E K, ex ſemicirculo K L, detr ahamus, remanebit maior arcus Aequatoris <lb/>E L, qui ex altera parte inter planum, &amp; </s>
  <s xml:id="echoid-s30316" xml:space="preserve">Meridianum interĳcitur, per quem explorabimus eodem <lb/>prorſus modo maiorem diſtantiam Solis in quouis parallelo, id eſt, arcu<unsure/>m H N, vel H S, addendo ni-<lb/>mirum arcum Q L, vel V L, arcui E L, aut ſubtrahendo, vt dictum est.</s>
  <s xml:id="echoid-s30317" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1540" type="float" level="2" n="14">
<note position="left" xlink:label="note-0474-06" xlink:href="note-0474-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s30318" xml:space="preserve">QV ANDO planum ſecat Meridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30319" xml:space="preserve">parallelum borealem, vt in tertia <lb/>
<anchor type="note" xlink:label="note-0474-07a" xlink:href="note-0474-07"/>
figura, atq; </s>
  <s xml:id="echoid-s30320" xml:space="preserve">adeò parallelus ipſe ab eodẽ plano duobus in punctis occidẽtalibus, oriẽtalibus ve ſecatur, au <lb/>ferendus eſt arcus Q L, ex arcu E L, vt relinquatur arcus Aequatoris E Q, qui ſimilis eſt arcui H N, <lb/>hoc eſt, maiori diſtantiæ Solis à meridie in parallelo boreali. </s>
  <s xml:id="echoid-s30321" xml:space="preserve">Ex hoc arcu H N, ſi aufer atur minor diſtan-<lb/>tia à meridie H M, notus relinquetur arcus paralleli borealis M N, qui quoniam per propoſ. </s>
  <s xml:id="echoid-s30322" xml:space="preserve">19. </s>
  <s xml:id="echoid-s30323" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30324" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s30325" xml:space="preserve">
<anchor type="note" xlink:label="note-0474-08a" xlink:href="note-0474-08"/>
Theod. </s>
  <s xml:id="echoid-s30326" xml:space="preserve">æqualis est alterno ſegmento paralleli auſtralis oppoſiti, ſi ad arcũ H R, minoris diſtantiæ Solis à <lb/>meridie in parallelo australi adĳciatur arcus æqualis arcui M N, habebitur maior diſtantia Solis à me-<lb/>ridie in parallelo oppoſito auſtrali. </s>
  <s xml:id="echoid-s30327" xml:space="preserve">Quando denique planum ſecat Meridianum inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s30328" xml:space="preserve"><lb/>parallelum australem, vt in quinta figura, atque adeò parallelus ipſe ab eodem plano duobus in punctis <lb/>orientalibus, occidentalibusve ſecatur, auferendus quoque eſt arcus V L, ex arcu E L, vt relinquatur <lb/>arcus Aequatoris E V, qui ſimilis eſt arcui H S, hoc eſt, maiori diſtantiæ Solis à meridie in parallelo <lb/>australi. </s>
  <s xml:id="echoid-s30329" xml:space="preserve">Ex hoc arcu H S, ſi auferatur minor diſtantia Solis à meridie H R, notus relinquetur arcus <lb/>paralleli auſtralis R S, qui quoniam per propoſ. </s>
  <s xml:id="echoid-s30330" xml:space="preserve">19. </s>
  <s xml:id="echoid-s30331" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30332" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30333" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s30334" xml:space="preserve">æqualis eſt alterno ſegmento paralle-<lb/>li borealis oppoſiti, ſi ad ar cum H M, minoris diſtantiæ Solis à meridie in parallelo borcali adĳ ciatur ar-<lb/>cus æqualis arcui R S, habebitur maior diſtantia Solis à meridie in parallelo oppoſito boreali.</s>
  <s xml:id="echoid-s30335" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1541" type="float" level="2" n="15">
<note position="left" xlink:label="note-0474-07" xlink:href="note-0474-07a" xml:space="preserve">Quando paral <lb/>leius duobus <lb/>in punctis ſiue <lb/>ex parte orien-<lb/>tali, ſive occi-<lb/>deatali, à pla-<lb/>no inclinato ſe <lb/>catur, qua tatio <lb/>ne maior diſtã <lb/>tia Solis à me-<lb/>ridie inquira-<lb/>tur.</note>
<note position="left" xlink:label="note-0474-08" xlink:href="note-0474-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s30336" xml:space="preserve">REM hanc totam vnico exemplo illuſtrabimus. </s>
  <s xml:id="echoid-s30337" xml:space="preserve">Ponatur planum ad Horizontem rectum, declinãs <lb/>
<anchor type="note" xlink:label="note-0474-09a" xlink:href="note-0474-09"/>
<pb o="459" file="0475" n="475" rhead="LIBER QVINTVS."/>
verò à Verticali proprie dicto grad. </s>
  <s xml:id="echoid-s30338" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30339" xml:space="preserve">à meridie in ortum, quale est planum horologĳ, quod propoſ. </s>
  <s xml:id="echoid-s30340" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s30341" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30342" xml:space="preserve">3. </s>
  <s xml:id="echoid-s30343" xml:space="preserve">deſcripſimus, ita vt inclinatum ſit ad Meridianum grad. </s>
  <s xml:id="echoid-s30344" xml:space="preserve">60. </s>
  <s xml:id="echoid-s30345" xml:space="preserve">Fiat vt 100000. </s>
  <s xml:id="echoid-s30346" xml:space="preserve">ſinus totus ad <lb/>86602. </s>
  <s xml:id="echoid-s30347" xml:space="preserve">ſinum inclinationis plani ad Meridianum, ita 74314. </s>
  <s xml:id="echoid-s30348" xml:space="preserve">ſinus complementi arcus Meridiani inter <lb/>planum &amp; </s>
  <s xml:id="echoid-s30349" xml:space="preserve">Aequatorem, ad aliud, inuenietur{q́ue} hic ferè ſinus 64357. </s>
  <s xml:id="echoid-s30350" xml:space="preserve">cui reſpondet arcus gr. </s>
  <s xml:id="echoid-s30351" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30352" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30353" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30354" xml:space="preserve"><lb/>cuius complementumgrad. </s>
  <s xml:id="echoid-s30355" xml:space="preserve">49. </s>
  <s xml:id="echoid-s30356" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30357" xml:space="preserve">56. </s>
  <s xml:id="echoid-s30358" xml:space="preserve">dabit angulum E K I, quem planum cum Aequatore facit. </s>
  <s xml:id="echoid-s30359" xml:space="preserve"><lb/>Rurſus fiat, vt 76529. </s>
  <s xml:id="echoid-s30360" xml:space="preserve">ſinus anguli inuenti E K I, ad 66913. </s>
  <s xml:id="echoid-s30361" xml:space="preserve">ſinum arcus Meridiani inter Aequato-<lb/>rem &amp; </s>
  <s xml:id="echoid-s30362" xml:space="preserve">planum, ita 86602. </s>
  <s xml:id="echoid-s30363" xml:space="preserve">ſinus inclinationis plani ad Meridianum, ad aliud, inuenietur{q́ue} hic ferè ſi-<lb/>nus 75720. </s>
  <s xml:id="echoid-s30364" xml:space="preserve">cui debetur arcus grad. </s>
  <s xml:id="echoid-s30365" xml:space="preserve">49. </s>
  <s xml:id="echoid-s30366" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30367" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30368" xml:space="preserve">Tantus eſt arcus Aequitoris E K, continens hor. </s>
  <s xml:id="echoid-s30369" xml:space="preserve">3. </s>
  <s xml:id="echoid-s30370" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s30371" xml:space="preserve">17. </s>
  <s xml:id="echoid-s30372" xml:space="preserve">quibus planum post meridiem illuminatur à Sole ex parte auſtrali, ex parte verò boreali illu-<lb/>ſtrari incipit à Sole hora 3. </s>
  <s xml:id="echoid-s30373" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30374" xml:space="preserve">17. </s>
  <s xml:id="echoid-s30375" xml:space="preserve">à meridie. </s>
</p>
<p style="it">
  <s xml:id="echoid-s30376" xml:space="preserve">POST hæc ſiat, vt 76529. </s>
  <s xml:id="echoid-s30377" xml:space="preserve">ſinus anguli inuenti E K I, quem planum cum Aequatore facit, ad <lb/>39874. </s>
  <s xml:id="echoid-s30378" xml:space="preserve">ſinum declinationis paralleli ♋, vel ♑, ita 100000. </s>
  <s xml:id="echoid-s30379" xml:space="preserve">ſinus totus ad aliud, inuenietur{q́ue} hic fer-<lb/>mè ſinus 52103. </s>
  <s xml:id="echoid-s30380" xml:space="preserve">cui reſpondet arcus grad 31. </s>
  <s xml:id="echoid-s30381" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30382" xml:space="preserve">24. </s>
  <s xml:id="echoid-s30383" xml:space="preserve">Tantus eſt arcus K M, plani inclinati inter <lb/>Aequatorem, &amp; </s>
  <s xml:id="echoid-s30384" xml:space="preserve">parallelum ♋, interiectus: </s>
  <s xml:id="echoid-s30385" xml:space="preserve">Rurſus fias<unsure/>, vt 91706. </s>
  <s xml:id="echoid-s30386" xml:space="preserve">ſinus complementi declinationis pa-<lb/>ralleli ♋, vel ♑, ad 85355. </s>
  <s xml:id="echoid-s30387" xml:space="preserve">ſinum complementi arcus K M, inuenti, quem diximus continere grad. </s>
  <s xml:id="echoid-s30388" xml:space="preserve">31. <lb/></s>
  <s xml:id="echoid-s30389" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30390" xml:space="preserve">24. </s>
  <s xml:id="echoid-s30391" xml:space="preserve">ita 100000. </s>
  <s xml:id="echoid-s30392" xml:space="preserve">ſinus totus ad aliud, inuenietur{q́ue} hic propemodum ſinus 93075. </s>
  <s xml:id="echoid-s30393" xml:space="preserve">cui debetur <lb/>arcus grad. </s>
  <s xml:id="echoid-s30394" xml:space="preserve">68. </s>
  <s xml:id="echoid-s30395" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30396" xml:space="preserve">33. </s>
  <s xml:id="echoid-s30397" xml:space="preserve">cuius complementum grad. </s>
  <s xml:id="echoid-s30398" xml:space="preserve">21. </s>
  <s xml:id="echoid-s30399" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30400" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30401" xml:space="preserve">dabit arcum Aequatoris K P, in-<lb/>ter planum inclinatum, &amp; </s>
  <s xml:id="echoid-s30402" xml:space="preserve">circulum declinationis, qui per Solem in plano inclinato, &amp; </s>
  <s xml:id="echoid-s30403" xml:space="preserve">parallelo ♋, cõ-<lb/>ſtitutum ducitur, cui arcui æquales oſtenſi ſunt arcus K T, L Q, L V.</s>
  <s xml:id="echoid-s30404" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1542" type="float" level="2" n="16">
<note position="left" xlink:label="note-0474-09" xlink:href="note-0474-09a" xml:space="preserve">Exemplum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s30405" xml:space="preserve">IT AQVE quoniam exemplum propoſitum reſpondet ſecundæ figuræ, ſpectat{q́ue} facies plani auſtra <lb/>
<anchor type="note" xlink:label="note-0475-02a" xlink:href="note-0475-02"/>
lis in ortum, ſi arcus K P, grad. </s>
  <s xml:id="echoid-s30406" xml:space="preserve">21. </s>
  <s xml:id="echoid-s30407" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30408" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30409" xml:space="preserve">ex arcu Aequatoris E K, grad. </s>
  <s xml:id="echoid-s30410" xml:space="preserve">49. </s>
  <s xml:id="echoid-s30411" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30412" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30413" xml:space="preserve">detraha-<lb/>tur, reliquus erit arcus E P, atque adeo arcus H M, ei ſimilis, grad. </s>
  <s xml:id="echoid-s30414" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30415" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30416" xml:space="preserve">46. </s>
  <s xml:id="echoid-s30417" xml:space="preserve">qui complectitur <lb/>hor. </s>
  <s xml:id="echoid-s30418" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30419" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30420" xml:space="preserve">51. </s>
  <s xml:id="echoid-s30421" xml:space="preserve">Igitur hor. </s>
  <s xml:id="echoid-s30422" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30423" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30424" xml:space="preserve">51. </s>
  <s xml:id="echoid-s30425" xml:space="preserve">poſt meridiem Sol in parallelo ♋, exiſtens deſinit illuminare <lb/>faciem auſtralem propoſiti plani. </s>
  <s xml:id="echoid-s30426" xml:space="preserve">Quod ſi arcum Aequatoris E K, ex ſemicirculo k L, detrahamus, re-<lb/>manebit arcus E L, grad. </s>
  <s xml:id="echoid-s30427" xml:space="preserve">130. </s>
  <s xml:id="echoid-s30428" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30429" xml:space="preserve">47. </s>
  <s xml:id="echoid-s30430" xml:space="preserve">ex quo ſi rurſum detrahatur arcus L Q, grad. </s>
  <s xml:id="echoid-s30431" xml:space="preserve">21. </s>
  <s xml:id="echoid-s30432" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30433" xml:space="preserve">27. <lb/></s>
  <s xml:id="echoid-s30434" xml:space="preserve">remanebit arcus E Q, vel ei ſimilis H N, grad. </s>
  <s xml:id="echoid-s30435" xml:space="preserve">109. </s>
  <s xml:id="echoid-s30436" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30437" xml:space="preserve">20. </s>
  <s xml:id="echoid-s30438" xml:space="preserve">continens horas 7. </s>
  <s xml:id="echoid-s30439" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30440" xml:space="preserve">17. </s>
  <s xml:id="echoid-s30441" xml:space="preserve">Igitur hora <lb/>4. </s>
  <s xml:id="echoid-s30442" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30443" xml:space="preserve">43. </s>
  <s xml:id="echoid-s30444" xml:space="preserve">poſt mediam noctem Sol in parallelo ♋, exiſtens illuminare incipit faciem australem propo-<lb/>ſiti plani. </s>
  <s xml:id="echoid-s30445" xml:space="preserve">Iam verò ſi eundem arcum K T, vel L V, grad. </s>
  <s xml:id="echoid-s30446" xml:space="preserve">21. </s>
  <s xml:id="echoid-s30447" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30448" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30449" xml:space="preserve">adĳciamus ad arcum E K, grad. </s>
  <s xml:id="echoid-s30450" xml:space="preserve"><lb/>49. </s>
  <s xml:id="echoid-s30451" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30452" xml:space="preserve">13. </s>
  <s xml:id="echoid-s30453" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30454" xml:space="preserve">ad arcum E L, grad. </s>
  <s xml:id="echoid-s30455" xml:space="preserve">130. </s>
  <s xml:id="echoid-s30456" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30457" xml:space="preserve">47. </s>
  <s xml:id="echoid-s30458" xml:space="preserve">inueniemus arcum H R, grad. </s>
  <s xml:id="echoid-s30459" xml:space="preserve">70. </s>
  <s xml:id="echoid-s30460" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30461" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30462" xml:space="preserve">hoc <lb/>eſt, horarum 4. </s>
  <s xml:id="echoid-s30463" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30464" xml:space="preserve">43. </s>
  <s xml:id="echoid-s30465" xml:space="preserve">arcum verò H S, grad. </s>
  <s xml:id="echoid-s30466" xml:space="preserve">152. </s>
  <s xml:id="echoid-s30467" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30468" xml:space="preserve">14. </s>
  <s xml:id="echoid-s30469" xml:space="preserve">hoc eſt, horarum 10. </s>
  <s xml:id="echoid-s30470" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30471" xml:space="preserve">9. </s>
  <s xml:id="echoid-s30472" xml:space="preserve">Igitur <lb/>
<anchor type="note" xlink:label="note-0475-03a" xlink:href="note-0475-03"/>
Sol in parallelo ♑, exiſtens illuminare deſinit faciem plani auſtralem hor. </s>
  <s xml:id="echoid-s30473" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30474" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30475" xml:space="preserve">43. </s>
  <s xml:id="echoid-s30476" xml:space="preserve">poſt meridiem, <lb/>eandem vero illuminare incipit hora 1. </s>
  <s xml:id="echoid-s30477" xml:space="preserve">poſt mediam noctem. </s>
  <s xml:id="echoid-s30478" xml:space="preserve">Has autem diſtantias à meridie etiam ſu-<lb/>pra inuenimus.</s>
  <s xml:id="echoid-s30479" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1543" type="float" level="2" n="17">
<note position="left" xlink:label="note-0475-02" xlink:href="note-0475-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0475-03" xlink:href="note-0475-03a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s30480" xml:space="preserve">VERVM ad altitudines Solis inquirendas non eſt omnino neceſſarium inueſtigare, quot horæ ſupr a <lb/>faciem circuli propoſitam contineantur; </s>
  <s xml:id="echoid-s30481" xml:space="preserve">quia ipſamet ſupputatio nos docebit, num hora propoſita ſit ſu-<lb/>pra oblatam faciem, an vero ſupra oppoſitam, prout differentia inter ſinum altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s30482" xml:space="preserve">ſi-<lb/>num altitudinis Solis tempore obſeruationis minor fuerit, aut maior ſinu altitudinis meridianæ, vt paulo <lb/>ante in hac propoſ. </s>
  <s xml:id="echoid-s30483" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s30484" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s30485" xml:space="preserve">VT autem commodius, atque facilius omnium horarum altitudines ſupputentur, ſumendæ erunt di-<lb/>
<anchor type="note" xlink:label="note-0475-04a" xlink:href="note-0475-04"/>
ſtantiæ à Meridiano circuli propoſiti ſupra Horizontem omnium 24. </s>
  <s xml:id="echoid-s30486" xml:space="preserve">horarum vnius paralleli, &amp; </s>
  <s xml:id="echoid-s30487" xml:space="preserve">earũ-<lb/>
<anchor type="note" xlink:label="note-0475-05a" xlink:href="note-0475-05"/>
dem altitudines ſupputandæ, quarum quæ dam ſupra vnam faciem dati circuli, quædam verò ſupra oppo-<lb/>ſitam cadent. </s>
  <s xml:id="echoid-s30488" xml:space="preserve">Hæ enim æquales erunt altitudinibus earundem horarum paralleli oppoſiti, dummodo, <lb/>quæ prius à meridie numerabantur, nunc à media nocte, &amp; </s>
  <s xml:id="echoid-s30489" xml:space="preserve">contra, &amp; </s>
  <s xml:id="echoid-s30490" xml:space="preserve">quæ ante ab occaſu, nunc ab or-<lb/>tu numerentur, &amp; </s>
  <s xml:id="echoid-s30491" xml:space="preserve">è contrario. </s>
  <s xml:id="echoid-s30492" xml:space="preserve">Item quæ prius ſupra vnam faciem circuli dati cadebant, cadant <lb/>nunc in oppoſitam, vt mox demonſtrabimus, ſi prius rem, vt melius intelligatur, aliquot exem-<lb/>plis illustremus.</s>
  <s xml:id="echoid-s30493" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1544" type="float" level="2" n="18">
<note position="right" xlink:label="note-0475-04" xlink:href="note-0475-04a" xml:space="preserve">Satis eſt, ſi ſup-<lb/>pu@entur altitu <lb/>dines Solis pro <lb/>horis unius pa <lb/>ralleli. He c-<lb/>nim æquales <lb/>ſunt altitudini <lb/>bus Solis pro <lb/>eiſdẽ horis op-<lb/>poſiti paralleli.</note>
<note position="left" xlink:label="note-0475-05" xlink:href="note-0475-05a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s30494" xml:space="preserve">PRIMVM igitur ſupra faciem Verticalis circuli proprè dicti auſtralem eleuatur polus antar cti-<lb/>
<anchor type="note" xlink:label="note-0475-06a" xlink:href="note-0475-06"/>
cus grad. </s>
  <s xml:id="echoid-s30495" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30496" xml:space="preserve">in latitudine grad. </s>
  <s xml:id="echoid-s30497" xml:space="preserve">42. </s>
  <s xml:id="echoid-s30498" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30499" xml:space="preserve">complementum huius altitudinis eſt grad. </s>
  <s xml:id="echoid-s30500" xml:space="preserve">42. </s>
  <s xml:id="echoid-s30501" xml:space="preserve">Igitur altitudo <lb/>meridiana ♋, continebit gr. </s>
  <s xml:id="echoid-s30502" xml:space="preserve">18. </s>
  <s xml:id="echoid-s30503" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30504" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30505" xml:space="preserve">cui reſpondet ſinus 31730. </s>
  <s xml:id="echoid-s30506" xml:space="preserve">depreſſio vero meridiana gr. </s>
  <s xml:id="echoid-s30507" xml:space="preserve">65. <lb/></s>
  <s xml:id="echoid-s30508" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30509" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30510" xml:space="preserve">cui reſpondet ſinus 90996. </s>
  <s xml:id="echoid-s30511" xml:space="preserve">Medietas aggregati ex ſinu altitudinis meridianæ ♋, &amp; </s>
  <s xml:id="echoid-s30512" xml:space="preserve">ſinu de-<lb/>
<anchor type="note" xlink:label="note-0475-07a" xlink:href="note-0475-07"/>
preſſionis, erit 61363. </s>
  <s xml:id="echoid-s30513" xml:space="preserve">Diſtantiæ autem, quas in parallelo ♋, horæ ab occaſu Solis numeratę habent à <lb/>Meridiano ſupra Horizontem. </s>
  <s xml:id="echoid-s30514" xml:space="preserve">(Nam Sol exiſtens in principio ♋, faciem australem circuli Verticalis <lb/>ante &amp; </s>
  <s xml:id="echoid-s30515" xml:space="preserve">poſt meridiem illuminat) ſunt hæ ſequentes, propterea quod circulus horæ 16. </s>
  <s xml:id="echoid-s30516" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30517" xml:space="preserve">28. </s>
  <s xml:id="echoid-s30518" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30519" xml:space="preserve">pa-<lb/>rallelus ♋, ſecant Meridianum ſupra Horizontem in vno eodemque puncto, atque adeò hora 16. </s>
  <s xml:id="echoid-s30520" xml:space="preserve">diſtet <lb/>à Meridiano verſus ortum hor. </s>
  <s xml:id="echoid-s30521" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30522" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30523" xml:space="preserve">28. </s>
  <s xml:id="echoid-s30524" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s30525" xml:space="preserve">7. </s>
  <s xml:id="echoid-s30526" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30527" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30528" xml:space="preserve">Hora autem 17. </s>
  <s xml:id="echoid-s30529" xml:space="preserve">ab eodem verſus <lb/>eccaſum hor. </s>
  <s xml:id="echoid-s30530" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30531" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30532" xml:space="preserve">32. </s>
  <s xml:id="echoid-s30533" xml:space="preserve">id eſt, grad. </s>
  <s xml:id="echoid-s30534" xml:space="preserve">8. </s>
  <s xml:id="echoid-s30535" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30536" xml:space="preserve">0.</s>
  <s xml:id="echoid-s30537" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1545" type="float" level="2" n="19">
<note position="right" xlink:label="note-0475-06" xlink:href="note-0475-06a" xml:space="preserve">Exempla di-<lb/>ſtantiarũ Solia <lb/>à Meridiano <lb/>proprio ua@io-<lb/>rum circulorũ <lb/>maximorum.</note>
<note position="left" xlink:label="note-0475-07" xlink:href="note-0475-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1547" type="section" level="1" n="365">
<head xml:id="echoid-head379" xml:space="preserve">SEQVVNTVR TABELLAE.</head>
<pb o="460" file="0476" n="476" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab occ. # 16 # 15 # 14 # 13 # 12 # 11 # 10 # 9 # 8 # 7 # 6 # 5 <lb/>Diſtantiæ à Me \\ ridiano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 7. 0. # 22. 0. # 37. 0. # 52. 0 # 67. 0. # 82. 0. # 97. 0. # 112. 0. # 127. 0 # 142. 0 # 15 0. # 172. 0 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab occ. # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 # 1 # 2 # 3 # 4 <lb/>
Diſtantiæ à Me \\ ridiano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 8. 0. # 23. 0. # 38. 0. # 53. 0. # 68. 0. # 83. 0. # 98. 0. # 113. 0. # 128. 0. # 143. 0. # 158. 0. # 173. 0.
</note>
<p style="it">
  <s xml:id="echoid-s30538" xml:space="preserve">PARI ratione distantiæ, quas à Meridiano habent horæ ab ortu Solis in eodem parallelo ♋, ſequen <lb/>ti modo ſe habent, propterea quod Meridianus parallelum ♋, ſecat in hora 7. </s>
  <s xml:id="echoid-s30539" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30540" xml:space="preserve">32. </s>
  <s xml:id="echoid-s30541" xml:space="preserve">ab ortu Solis, at-<lb/>queidcirco hora 7. </s>
  <s xml:id="echoid-s30542" xml:space="preserve">ab ortu diſtat à Meridiano verſus ortum hor. </s>
  <s xml:id="echoid-s30543" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30544" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30545" xml:space="preserve">32. </s>
  <s xml:id="echoid-s30546" xml:space="preserve">hoc eſt, grad. </s>
  <s xml:id="echoid-s30547" xml:space="preserve">8. </s>
  <s xml:id="echoid-s30548" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30549" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30550" xml:space="preserve">Ho-<lb/>ra autem 8. </s>
  <s xml:id="echoid-s30551" xml:space="preserve">ab ortu ab eodem verſus occaſum hor. </s>
  <s xml:id="echoid-s30552" xml:space="preserve">0. </s>
  <s xml:id="echoid-s30553" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30554" xml:space="preserve">28. </s>
  <s xml:id="echoid-s30555" xml:space="preserve">id eſt, grad. </s>
  <s xml:id="echoid-s30556" xml:space="preserve">7. </s>
  <s xml:id="echoid-s30557" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30558" xml:space="preserve">0.</s>
  <s xml:id="echoid-s30559" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab or. # 7 # 6 # 5 # 4 # 3 # 2 # 1 # 24 # 23 # 22 # 21 # 20 <lb/>Diſtantiæ à Me \\ ridiano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 8. 0. # 22. 0. # 38. 0. # 53. 0. # 68. 0. # 83. 0. # 98. 0 # 113. 0. # 128. 0 # 14. 0. # 158. 0. # 173. 0 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab or. # 8 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 <lb/>
Diſtantiæ à Me \\ ridiano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 7. 0. # 22. 0. # 37. 0. # 52. 0. # 67. 0. # 82. 0. # 97. 0. # 112. 0. # 127. 0. # 142. 0. # 157. 0. # 172. 0.
</note>
<p style="it">
  <s xml:id="echoid-s30560" xml:space="preserve">DIST ANTIAE verò, quas à Meridiano habent horæ à meridie, &amp; </s>
  <s xml:id="echoid-s30561" xml:space="preserve">media nocte omnium pa-<lb/>rallelorum, cum Meridianus omnes parallelos ſecet in hora 12. </s>
  <s xml:id="echoid-s30562" xml:space="preserve">meridiei, ita ſe habent.</s>
  <s xml:id="echoid-s30563" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve"> <lb/>Hor. à med. no. # 11 # 10 # 9 # 8 # 7 # 6 # 5 # 4 # 3 # 2 # 1 <lb/>
Horæ à merid. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # 11
Diſtantiæ à Me \\ ridiano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 15. 0. # 30. 0. # 45. 0. # 60. 0. # 75. 0. # 90. 0 # 105. 0. # 120. 0. # 135. 0. # 150. 0. # 165. 0.
</note>
<p style="it">
  <s xml:id="echoid-s30564" xml:space="preserve">DEINDE ſupra faciem auſtralem Verticalis circuli à propriè dicto Verticali declinantis in ortũ <lb/>grad. </s>
  <s xml:id="echoid-s30565" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30566" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s30567" xml:space="preserve">42. </s>
  <s xml:id="echoid-s30568" xml:space="preserve">eleuatur polus antarcticus grad. </s>
  <s xml:id="echoid-s30569" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30570" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30571" xml:space="preserve">3. </s>
  <s xml:id="echoid-s30572" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30573" xml:space="preserve">complementum <lb/>huius altitudinis continet grad. </s>
  <s xml:id="echoid-s30574" xml:space="preserve">49. </s>
  <s xml:id="echoid-s30575" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30576" xml:space="preserve">57. </s>
  <s xml:id="echoid-s30577" xml:space="preserve">Igitur altitudo meridiana ♋, complectetur grad. </s>
  <s xml:id="echoid-s30578" xml:space="preserve">26. <lb/></s>
  <s xml:id="echoid-s30579" xml:space="preserve">
<anchor type="note" xlink:label="note-0476-10a" xlink:href="note-0476-10"/>
Min. </s>
  <s xml:id="echoid-s30580" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30581" xml:space="preserve">cui reſpondet ſinus 44541. </s>
  <s xml:id="echoid-s30582" xml:space="preserve">Depreſſio autem meridiana grad. </s>
  <s xml:id="echoid-s30583" xml:space="preserve">73. </s>
  <s xml:id="echoid-s30584" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30585" xml:space="preserve">27. </s>
  <s xml:id="echoid-s30586" xml:space="preserve">cuius ſinus eſt <lb/>95857. </s>
  <s xml:id="echoid-s30587" xml:space="preserve">Medietas aggregati ex dicto ſinu meridianæ altitudinis, &amp; </s>
  <s xml:id="echoid-s30588" xml:space="preserve">ſinu depreſſionis erit 70199. </s>
  <s xml:id="echoid-s30589" xml:space="preserve">Diſtan <lb/>tię autem, quas in parallelo ♋, horæ ab occaſu Solis ſupputatæ habent à Meridiano propoſiti Verticalis <lb/>ſupra Horizontem, (quia Sol in principio ♋, exiſtens auſtralem faciem eiuſdem Verticalis ante &amp; </s>
  <s xml:id="echoid-s30590" xml:space="preserve">poſt <lb/>meridiem illuminat) ſequenti modo ſe<unsure/> habent; </s>
  <s xml:id="echoid-s30591" xml:space="preserve">propterea quod Meridianus illius proprius à Meridiano <lb/>Horizontis verſus ortum recedit grad. </s>
  <s xml:id="echoid-s30592" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30593" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30594" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30595" xml:space="preserve">Vnde cum in eodem parallelo ♋; </s>
  <s xml:id="echoid-s30596" xml:space="preserve">hora 14. </s>
  <s xml:id="echoid-s30597" xml:space="preserve">diſtet <lb/>verſus ortum à meridie grad. </s>
  <s xml:id="echoid-s30598" xml:space="preserve">37. </s>
  <s xml:id="echoid-s30599" xml:space="preserve">ſi hæc diſtantia auferatur à grad. </s>
  <s xml:id="echoid-s30600" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30601" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30602" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30603" xml:space="preserve">relinquentur grad. </s>
  <s xml:id="echoid-s30604" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s30605" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30606" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30607" xml:space="preserve">pro diſtantia horæ 14. </s>
  <s xml:id="echoid-s30608" xml:space="preserve">ab occaſu verſus occaſum à proprio Meridiano Verticalis declinantis. </s>
  <s xml:id="echoid-s30609" xml:space="preserve"><lb/>Item cum hora 13. </s>
  <s xml:id="echoid-s30610" xml:space="preserve">recedat verſus ortum à meridie grad. </s>
  <s xml:id="echoid-s30611" xml:space="preserve">52. </s>
  <s xml:id="echoid-s30612" xml:space="preserve">ſi ex his demantur grad. </s>
  <s xml:id="echoid-s30613" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30614" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30615" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30616" xml:space="preserve"><lb/>remanebunt grad. </s>
  <s xml:id="echoid-s30617" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30618" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30619" xml:space="preserve">12. </s>
  <s xml:id="echoid-s30620" xml:space="preserve">pro diſtantia horæ 13. </s>
  <s xml:id="echoid-s30621" xml:space="preserve">ab illo proprio Meridiano verſus ortum.</s>
  <s xml:id="echoid-s30622" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1547" type="float" level="2" n="1">
<note position="left" xlink:label="note-0476-10" xlink:href="note-0476-10a" xml:space="preserve">50</note>
</div>
<pb o="461" file="0477" n="477" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab occ. # 13 # 12 # 11 # 10 # 9 # 8 # 7 # 6 # 5 # 4 # 3 # 2 <lb/>Diſtantiæ à Me \\ ridiano ꝓprio. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 11. 12. # 26. 12. # 41. 12. # 56. 12. # 71. 12. # 86. 12. # 101. 12. # 116. 12 # 131. 12 # 146. 12 # 161. 12 # 176. 12 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab occ. # 14 # 15 # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 # 1 <lb/>
Diſtantiæ à Me \\ ridiano ꝓprio. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 3. 48. # 18. 48. # 33. 48. # 48. 48. # 63. 48 # 78. 48. # 93. 48. # 108. 48 # 123. 48 # 138. 48 # 153. 48 # 168. 48
</note>
<p style="it">
  <s xml:id="echoid-s30623" xml:space="preserve">SIMILITER diſtantiæ, quas à Meridiano eodẽ proprio habẽt horæ ab ortu in eodẽ parallelo ♋, <lb/>modo qui ſequitur, ſeſe habent, cò quod Meridianus proprius dicti Verticalis declinantis recedat à Meri <lb/>diano Horizontis verſus ortũ gr. </s>
  <s xml:id="echoid-s30624" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30625" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30626" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30627" xml:space="preserve">Vnde cum in parallelo ♋, hora 5. </s>
  <s xml:id="echoid-s30628" xml:space="preserve">ab ortu diſtet verſus or-<lb/>tum à meridie grad. </s>
  <s xml:id="echoid-s30629" xml:space="preserve">38. </s>
  <s xml:id="echoid-s30630" xml:space="preserve">ſi hæc diſtantia ſubtrahatur à grad. </s>
  <s xml:id="echoid-s30631" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30632" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30633" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30634" xml:space="preserve">remanebunt gr. </s>
  <s xml:id="echoid-s30635" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30636" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30637" xml:space="preserve">48. <lb/></s>
  <s xml:id="echoid-s30638" xml:space="preserve">pro diſtantia horę 5. </s>
  <s xml:id="echoid-s30639" xml:space="preserve">ab ortu à proprio Meridiano verſus occaſum Verticalis declinantis. </s>
  <s xml:id="echoid-s30640" xml:space="preserve">Item cum hora <lb/>4. </s>
  <s xml:id="echoid-s30641" xml:space="preserve">ab ortu à meridie verſus ortum distet grad. </s>
  <s xml:id="echoid-s30642" xml:space="preserve">53. </s>
  <s xml:id="echoid-s30643" xml:space="preserve">ſi ex his auferantur grad. </s>
  <s xml:id="echoid-s30644" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30645" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30646" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30647" xml:space="preserve">reliqui erunt <lb/>
<anchor type="note" xlink:label="note-0477-04a" xlink:href="note-0477-04"/>
grad. </s>
  <s xml:id="echoid-s30648" xml:space="preserve">12. </s>
  <s xml:id="echoid-s30649" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30650" xml:space="preserve">12. </s>
  <s xml:id="echoid-s30651" xml:space="preserve">pro diſtantia horæ 4. </s>
  <s xml:id="echoid-s30652" xml:space="preserve">ab ortu ab illo proprio Meridiano verſus ortum.</s>
  <s xml:id="echoid-s30653" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1548" type="float" level="2" n="2">
<note position="left" xlink:label="note-0477-04" xlink:href="note-0477-04a" xml:space="preserve">20</note>
</div>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab or. # 4 # 3 # 2 # 1 # 24 # 23 # 22 # 21 # 20 # 19 # 18 # 17 <lb/>Diſtantiæ à pro \\ prio Meridiano # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 12. 12. # 27. 12. # 42. 12. # 57. 11. # 72. 12. # 87. 12. # 102. 12 # 117. 12 # 132. 12 # 147. 12 # 162. 12 # 177. 12 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋. ab or. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 <lb/>
Diſtantiæ à pro \\ prio Meridiano # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 2. 48. # 17. 48. # 32. 48. # 47. 48. # 62. 48. # 77. 48. # 92. 48. # 107. 48 # 122. 48 # 137. 48 # 152. 48 # 167. 48
</note>
<p style="it">
  <s xml:id="echoid-s30654" xml:space="preserve">AT verò diſtantiæ, quas horæ à meridie, &amp; </s>
  <s xml:id="echoid-s30655" xml:space="preserve">media nocte habent ab eodem Meridiano dicti Ver-<lb/>ticalis in omnibus parallelis, (quòd in omnibus parallelis dictus Meridianus diſtet à meridie, ſiue hora <lb/>12. </s>
  <s xml:id="echoid-s30656" xml:space="preserve">verſus ortum grd. </s>
  <s xml:id="echoid-s30657" xml:space="preserve">40. </s>
  <s xml:id="echoid-s30658" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30659" xml:space="preserve">48. </s>
  <s xml:id="echoid-s30660" xml:space="preserve">atque adeò hora 9. </s>
  <s xml:id="echoid-s30661" xml:space="preserve">à media nocte ab illo Meridiano diſtet ortum <lb/>verſus gr. </s>
  <s xml:id="echoid-s30662" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30663" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30664" xml:space="preserve">12. </s>
  <s xml:id="echoid-s30665" xml:space="preserve">Hora verò 10. </s>
  <s xml:id="echoid-s30666" xml:space="preserve">à media nocte ab eodem recedat verſus occaſum gr. </s>
  <s xml:id="echoid-s30667" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30668" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30669" xml:space="preserve">48.) <lb/></s>
  <s xml:id="echoid-s30670" xml:space="preserve">
<anchor type="note" xlink:label="note-0477-08a" xlink:href="note-0477-08"/>
in ſequenti tabella continentur.</s>
  <s xml:id="echoid-s30671" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1549" type="float" level="2" n="3">
<note position="left" xlink:label="note-0477-08" xlink:href="note-0477-08a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve"> <lb/>Horæ à \\ media \\ nocte # 9 # 8 # 7 # 6 # 5 # 4 # 3 # 2 # 1 # A meri \\ die. # 12 # 11 # 10 <lb/>Diſtãtiæ à \\ ꝓprio Me- \\ @@diano. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. <lb/># 4. 12. # 19. 12. # 34. 12. # 49. 12. # 64. 12. # 79. 12. # 94. 12. # 109. 12 # 124. 12 # # 139. 12 # 154. 12 # 169. 12 <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ à \\ media \\ noct. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 <lb/>Diſtãtiæ à \\ ꝓprio Me- \\ ridiano. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 10. 48. # 25. 48. # 40. 48. # # 55. 48. # 70. 48. # 85. 48. # 100. 48 # 115. 48 # 130. 48 # 145. 48 # 160. 48 # 175. 48 <lb/></note>
<p style="it">
  <s xml:id="echoid-s30672" xml:space="preserve">DANDA verò opera eſt, vt distantiæ illarum horarum ſimul ponantur, quæ in hemiſphærio orien <lb/>tali, vel occidentali continentur, vt facilius in horologiorũ deſcriptione intelligamus, quænã horæ à linea <lb/>styli, quæ inſtar meridianæ eſt, vergant ortũ verſus, &amp; </s>
  <s xml:id="echoid-s30673" xml:space="preserve">quæ in occaſum tendant. </s>
  <s xml:id="echoid-s30674" xml:space="preserve">Ita vides in propoſitis <lb/>omnibus exemplis primo loco poſitas eſſe horas, quæ in hemiſphęrio orientali cõtinentur, deinde verò, quæ <lb/>in occidentali. </s>
  <s xml:id="echoid-s30675" xml:space="preserve">Orientale porro hemiſphęrium ſeparatur ab occidentali à Meridiano circulo proprio pro-<lb/>poſiti circuli maximi, ſupra quem altitudines Solis proponuntur inueſtigandæ.</s>
  <s xml:id="echoid-s30676" xml:space="preserve"/>
</p>
<pb o="462" file="0478" n="478" rhead="GNOMONICES"/>
<p style="it">
  <s xml:id="echoid-s30677" xml:space="preserve">VIDES igitur, diſiantias omnium horarum à proprio Meridiano in vtroque hemiſphærio nulio ne-<lb/>
<anchor type="note" xlink:label="note-0478-01a" xlink:href="note-0478-01"/>
gotio reperiri, ſi prius inuematur diſtantiæ proximarũ duarum horarum hinc inde ab illo Meridiano di-<lb/>ſtantium. </s>
  <s xml:id="echoid-s30678" xml:space="preserve">Nam ſi ad vtramuis diſtantiam apponãtur gr. </s>
  <s xml:id="echoid-s30679" xml:space="preserve">15. </s>
  <s xml:id="echoid-s30680" xml:space="preserve">inuenta erit diſtantia ſequentis horæ, at-<lb/>que ita per additionem continuam grad. </s>
  <s xml:id="echoid-s30681" xml:space="preserve">15. </s>
  <s xml:id="echoid-s30682" xml:space="preserve">omnium horarum distantiæ inuenientur.</s>
  <s xml:id="echoid-s30683" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1550" type="float" level="2" n="4">
<note position="left" xlink:label="note-0478-01" xlink:href="note-0478-01a" xml:space="preserve">Facilis inuentio <lb/>diſtã<unsure/>tiarum So <lb/>lis à Meridiano <lb/>proprio circuli <lb/>ma@imi propoſi <lb/>ri.</note>
</div>
<p style="it">
  <s xml:id="echoid-s30684" xml:space="preserve">QVOD autẽ altitudines omniũ 24. </s>
  <s xml:id="echoid-s30685" xml:space="preserve">horarum cuiusuis paralleli inuẽtæ ſupra quẽuis circulũ maximũ <lb/>æquales ſint altitudinibus earundẽ numero 24. </s>
  <s xml:id="echoid-s30686" xml:space="preserve">horarũ paralleli oppoſiti ſupra eundẽcirculũ maximum, ſi <lb/>quæ prius à meridie, vel ab ortu numer abãtur, nunc numerẽtur a media nocte vel ab occaſu, &amp; </s>
  <s xml:id="echoid-s30687" xml:space="preserve">quæ prius <lb/>
<anchor type="note" xlink:label="note-0478-02a" xlink:href="note-0478-02"/>
cadebant in vnã faciem circuli illius maximi, nunc cadant in oppoſitã, &amp; </s>
  <s xml:id="echoid-s30688" xml:space="preserve">contra, hac ratione cõprobabi-<lb/>mus. </s>
  <s xml:id="echoid-s30689" xml:space="preserve">Intelligatur circulus aliquis horarius per polos mũdi ductus trãſire per illud punctũ cuiusuis paral <lb/>leli, nẽpe ♑, vbi ſecatur a circulo maximo, ſupra quem altitudines ſunt cõputatæ. </s>
  <s xml:id="echoid-s30690" xml:space="preserve">Quoniã igitur circulus <lb/>
<anchor type="note" xlink:label="note-0478-03a" xlink:href="note-0478-03"/>
ille horarius tranſit in parallelo oppoſito, nempe ♋, per punctũ, quod per ſphæræ diametrũ priori puncto <lb/>opponitur, (cũ enim arcus dicti circuli horarĳ, inter punctũ tropici ♑, &amp; </s>
  <s xml:id="echoid-s30691" xml:space="preserve">polũ antarcticũ, æqualis ſit ar-<lb/>cui eiuſdẽ circuli horarĳ inter punctũ tropici ♋, &amp; </s>
  <s xml:id="echoid-s30692" xml:space="preserve">polum arcticũ, quod vterque arcus cõplemẽtum decli <lb/>nationis vtriuſq; </s>
  <s xml:id="echoid-s30693" xml:space="preserve">tropici metiatur; </s>
  <s xml:id="echoid-s30694" xml:space="preserve">ſi addatur cõmunis arcus ſemicirculo minor, inter punctũ tropici ♑, <lb/>et arcticũ polũ, fient arcus cõpoſiti æquales. </s>
  <s xml:id="echoid-s30695" xml:space="preserve">Cum ergo arcus inter duos polos ſit ſemicirculus, erit quoq; </s>
  <s xml:id="echoid-s30696" xml:space="preserve">al <lb/>ter arcus inter duo dicta puncta cõprehenſus ſemicirculus. </s>
  <s xml:id="echoid-s30697" xml:space="preserve">Id quod luce clarius ex ſphęra materiali depre <lb/>hẽdi poteſt, ſi dictus horarius circulus cogitetur eſſe colurus ęquinoctiorũ in quacũque poſitione, ita vt vbi <lb/>ſecat tropicũ ♑, ſupra Horizontẽ, per illud punctũ cõcipiatur trãſire circulus aliquis maximus) efficitur, <lb/>vt idẽ trãſeat neceſſario per punctũ, vbi idẽ circulus maximus oppoſitũ par allelũ ſecat, propterea quod <lb/>ibi horarius circulus bifariã ſecatur, cum illud punctũ per diametrũ opponatur puncto prioris paralleli, <lb/>vt oſtendimus, &amp; </s>
  <s xml:id="echoid-s30698" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s30699" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30700" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30701" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30702" xml:space="preserve">Thedoſii omnes circuli maximi in ſphæra ſe mutuo bifariam <lb/>
<anchor type="note" xlink:label="note-0478-04a" xlink:href="note-0478-04"/>
ſecant. </s>
  <s xml:id="echoid-s30703" xml:space="preserve">Quare ſi prius punctum prioris paralleli pertineat ad aliquam horam a meridie, pertinebit poste-<lb/>rius alterius paralleli ad eandem numero horam a media nocte, &amp; </s>
  <s xml:id="echoid-s30704" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s30705" xml:space="preserve">Sic etiam, ſi prius punctum <lb/>ſpectet ad horas ab occaſu Solis in priori parallelo, ſpectabit poſterius ad horas ab ortu Solis in oppoſito <lb/>parallelo, &amp; </s>
  <s xml:id="echoid-s30706" xml:space="preserve">è contrario, propterea quod hæc puncta in diuerſis ſemicirculis dicti circuli horarĳ exiſtãt, <lb/>vt patet: </s>
  <s xml:id="echoid-s30707" xml:space="preserve">diuer ſos autẽ ſemicirculos ad diuer ſas horas pertinere, ita vt vnus horã a meridie, vel occaſu, <lb/>alter vero horã eandem à media nocte, vel ortu indicet, propoſ. </s>
  <s xml:id="echoid-s30708" xml:space="preserve">9. </s>
  <s xml:id="echoid-s30709" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30710" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30711" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30712" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30713" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s30714" xml:space="preserve">Neq; </s>
  <s xml:id="echoid-s30715" xml:space="preserve">vero re <lb/>fert, circulũ dictum horarium nõ eſſe circulũ horariũ ab ortu, vel occaſu, cum per polos ponatur trãſire, <lb/>quia ſi per eadẽ duo pũcta oppoſitorũ parallelorũ intelligatur duci circulus horarius ab ortu, vel occaſu, <lb/>qui nimirũ tangat parallelũ omniũ ſemper apparentiũ maximũ, exiſtẽt adhuc duo illa puncta in diuerſis <lb/>huius circuli ſemicirculis. </s>
  <s xml:id="echoid-s30716" xml:space="preserve">Ex quo efficitur, vt quantũ a priori puncto diſtã@ horę a meridie vel occaſu con <lb/>
<anchor type="note" xlink:label="note-0478-05a" xlink:href="note-0478-05"/>
tra ſucceſſionẽ ſignorũ procedendo, tãtum quoq; </s>
  <s xml:id="echoid-s30717" xml:space="preserve">a poſteriori puncto diſtent horæ a media nocte, vel ortu, <lb/>&amp; </s>
  <s xml:id="echoid-s30718" xml:space="preserve">cõtra, ita tamen, vt ſi illæ horæ extent ſupra facie borealẽ, ſuperioremve circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s30719" xml:space="preserve">ſint, in <lb/>parallelo auſtrali, hæ exiſtant ſupra faciem oppoſitam, nempe australem, inferioremve, &amp; </s>
  <s xml:id="echoid-s30720" xml:space="preserve">in oppoſito pa <lb/>rallelo boreali, vt ex ſphæra mater alipatet, Cum ergo duo illi paralleli oppoſiti æquales habeãt inclinatio <lb/>nes ad maximum circulum propoſitum, habebunt horæ à meridie, vel occaſu eaſdem altitudines ſupra <lb/>vnam faciem dicti circuli maximi, quas oppoſitæ horæ à media nocte, vel ortu ſupra reliquam faciem <lb/>babent. </s>
  <s xml:id="echoid-s30721" xml:space="preserve">Id quod luce clarius ſupputatio ipſa altitudinum Solis docebit.</s>
  <s xml:id="echoid-s30722" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1551" type="float" level="2" n="5">
<note position="left" xlink:label="note-0478-02" xlink:href="note-0478-02a" xml:space="preserve">Altitudines So-<lb/>lis ſupra vnam <lb/>faeiem circuli <lb/>maximi propo-<lb/>ſiti in ſingulis <lb/>horis vnius pa-<lb/>ralleli æquales <lb/>ſunt altitud ni-<lb/>bus Solis ſupra <lb/>@l eram faciem <lb/>eiuſdem circuli <lb/>in eiſdem horis <lb/>paralleli oppo-<lb/>ſ@ti.</note>
<note position="left" xlink:label="note-0478-03" xlink:href="note-0478-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0478-04" xlink:href="note-0478-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0478-05" xlink:href="note-0478-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s30723" xml:space="preserve">SEQVVNTVR nunc tabellæ altitudinũ Solis ſupra oẽs circulos maximos, quibus horologia lib. <lb/></s>
  <s xml:id="echoid-s30724" xml:space="preserve">2. </s>
  <s xml:id="echoid-s30725" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30726" xml:space="preserve">3. </s>
  <s xml:id="echoid-s30727" xml:space="preserve">æquidiſtant, partim pro horis à meridie, &amp; </s>
  <s xml:id="echoid-s30728" xml:space="preserve">media nocte, partimuero pro horis ab ortu &amp; </s>
  <s xml:id="echoid-s30729" xml:space="preserve">occaſu, <lb/>nec non pro horis inæqualibus, ad latitudinẽ gr. </s>
  <s xml:id="echoid-s30730" xml:space="preserve">42. </s>
  <s xml:id="echoid-s30731" xml:space="preserve">borealem, Sole percurrẽte tropicum ♋, Aequatorẽ, <lb/>
<anchor type="note" xlink:label="note-0478-06a" xlink:href="note-0478-06"/>
&amp; </s>
  <s xml:id="echoid-s30732" xml:space="preserve">tropicum ♑, ſupputatæ. </s>
  <s xml:id="echoid-s30733" xml:space="preserve">Similes autem confici poterunt, per eadem præcepta, pro quibuſcunque alĳs <lb/>circulis maximis, etiam ad quaſcunque alias latitudines, &amp; </s>
  <s xml:id="echoid-s30734" xml:space="preserve">Sole quemcunq; </s>
  <s xml:id="echoid-s30735" xml:space="preserve">parallelum percurrente, ſiue <lb/>pro horis tam ęqualibus, quàm inæqualibus, ſiue hę integræ ſint, ſiue ſemiſſes, quadrantesve hora-<lb/>rum, aut alię horarum particulæ, ſi earum diſtantiæ à Meridianis dictorum maximorum circulorum re-<lb/>ctè accipiantur, vt ſupra docuimus. </s>
  <s xml:id="echoid-s30736" xml:space="preserve">Quælibet autem horæ æqualiter vtrinque à Meridiano proprio pro-<lb/>poſiti circuli maximi diſtantes habent æquales altitudines, vt contingit in Horizonte, Verticali, Meri-<lb/>diano, circulo horæ 6. </s>
  <s xml:id="echoid-s30737" xml:space="preserve">a meridie, vel media nocte, quoad horas à mer. </s>
  <s xml:id="echoid-s30738" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30739" xml:space="preserve">med. </s>
  <s xml:id="echoid-s30740" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s30741" xml:space="preserve">numerat{as}, &amp;</s>
  <s xml:id="echoid-s30742" xml:space="preserve">c.</s>
  <s xml:id="echoid-s30743" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1552" type="float" level="2" n="6">
<note position="left" xlink:label="note-0478-06" xlink:href="note-0478-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s30744" xml:space="preserve">CAETERVM in tabella 3. </s>
  <s xml:id="echoid-s30745" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30746" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30747" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30748" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30749" xml:space="preserve">ſupputauimus altitudines Solis ſupra vtramq; </s>
  <s xml:id="echoid-s30750" xml:space="preserve">faciem <lb/>Verticalis propriè dicti, &amp; </s>
  <s xml:id="echoid-s30751" xml:space="preserve">Verticalis declinantis, vt exemplo etiam diſcas, horas ♋, a meridie habe <lb/>
<anchor type="note" xlink:label="note-0478-07a" xlink:href="note-0478-07"/>
re ſupra faciem australem eaſdem altitudines, quas horæ, ♑ a media nocte habent ſupra faciem borealẽ <lb/>&amp; </s>
  <s xml:id="echoid-s30752" xml:space="preserve">è contrario, vt proxime demonſtr auimus.</s>
  <s xml:id="echoid-s30753" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1553" type="float" level="2" n="7">
<note position="left" xlink:label="note-0478-07" xlink:href="note-0478-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1555" type="section" level="1" n="366">
<head xml:id="echoid-head380" xml:space="preserve">I. Altitudines Solis ſupra Horizontem pro horis à mer. &amp; med. noc. <lb/>ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. noct. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♋, à meridie. # 7 # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 5. 11. # 15. 29. # 26. 19. # 37. 25. # 48. 29. # 58. 59. # 67. 41. # 71. 30. <lb/></note>
<pb o="463" file="0479" n="479" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, à me- \\ dia nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horę ♈, &amp; ♎, à mer. # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 11. 5. # 21. 49. # 31. 42. # 40. 4. # 45. 52. # 48. 0. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à med. nocte. # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♑, à meridie. # 4 # 3 # 2 # 1 # 0 <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M.
# 4. 14. # 12. 25. # 18. 52. # 23. 3. # 24. 30.
</note>
</div>
<div xml:id="echoid-div1556" type="section" level="1" n="367">
<head xml:id="echoid-head381" xml:space="preserve">II. Altitudines Solis ſupra Horizontem pro horis ab occaſu Solis ſup-<lb/>putatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 40. # 10. 35. # 21. 12. # 32. 13. # 43. 21. # 54. 12. # 63. 59. # 70. 36.
Horæ ♋, ab occaſu. # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 70. 20. # 63. 24. # 53. 30. # 42. 36. # 31. 28. # 20. 29. # 9. 54. # 0. 0.
Horæ ♈, &amp; ♎, \\ ab occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18
# 24 # 23 # 22 # 21 # 20 # 19 # 18
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 11. 5. # 21. 49. # 31. 42. # 40. 4. # 45. 52. # 48. 0.
Horę♑, ab occ. # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 8. 14. # 15. 41. # 21. 8. # 24. 5. # 24. 11. # 21. 25. # 16. 7. # 8. 47. # 0. 0.
</note>
</div>
<div xml:id="echoid-div1557" type="section" level="1" n="368">
<head xml:id="echoid-head382" xml:space="preserve">III. Altitudines Solis ſupra faciem auſtralem Verticalis circuli pro horis à mer. &amp; <lb/>med. noc. ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à med. nocte. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♑, à meridie. # 7 # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 7. 54. # 17. 14. # 27. 5. # 37. 6. # 46. 54. # 55. 52. # 62. 45. # 65. 30.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à \\ med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♈, &amp; ♎ à mer. # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 9. 58. # 19. 33. # 28. 14. # 35. 25. # 40. 16. # 42. 0. <lb/></note>
<pb o="464" file="0480" n="480" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. nocte. # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♋, à meridie. # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 36. # 7. 54. # 13. 36. # 17. 14. # 18. 30. <lb/></note>
</div>
<div xml:id="echoid-div1558" type="section" level="1" n="369">
<head xml:id="echoid-head383" xml:space="preserve">IIII. Altitudines Solis ſupra faciem borealem Verticalis circuli pro horis à mer. &amp; <lb/>med. noc. ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♋, à med. nocte. # 7 # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 7. 54 # 17. 14. # 27. 5. # 37. 6. # 46. 54. # 55. 52. # 62. 45. # 65. 30. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à mer. # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horę ♈, &amp; ♎ à me- \\ dia nocte. # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 9. 58. # 19. 33. # 28. 14. # 35 25. # 10. 16. # 42. 0.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♋, à med. nocte. # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 36. # 7. 54. # 13. 36 # 17. 14. # 18. 30. <lb/></note>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1559" type="section" level="1" n="370">
<head xml:id="echoid-head384" xml:space="preserve">V. Altitudines Solis ſupra ſaciem auſtralem Verticalis circuli pro horis ab occaſu <lb/>Solis ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 3. 15. # 12. 11. # 21. 47. # 31. 45. # 41. 44. # 51. 15. # 59. 27. # 64. 41. <lb/></note>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab occaſu. # 20 # 21 # 22 # 23 # 24 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 64. 53. # 59. 55. # 51. 51. # 42. 23. # 32. 27. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ ab occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18 <lb/>
# 24 # 23 # 22 # 21 # 20 # 19 # 18
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 9. 58. # 19. 33. # 28. 14. # 35. 25. # 40. 16. # 42. 0.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 20 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 4. 40. # 11. 10. # 15. 49. # 18. 13. # 18. 8. # 15. 35. # 10. 47. # 4. 11. <lb/></note>
<pb o="465" file="0481" n="481" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1560" type="section" level="1" n="371">
<head xml:id="echoid-head385" xml:space="preserve">VI. Altitudines Solis ſupra vtramque faciem Meridiani circuli pro horis à mer. &amp; med. noc. ſupputatæ, ad quam- cunque latitudinem.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, &amp; ♑, à \\ med. nocte. # 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. <lb/>Horæ ♋, &amp; ♑, à mer. # 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 13. 44. # 27. 18. # 40. 26. # 52. 35. # 62. 21. # 66. 30. <lb/>
</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, a \\ med. nocte. # 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. <lb/>Horę ♈, &amp; ♎, à mer. # 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 15. 0. # 30. 0. # 45. 0. # 60. 0. # 75. 0. # 90. 0. <lb/></note>
</div>
<div xml:id="echoid-div1561" type="section" level="1" n="372">
<head xml:id="echoid-head386" xml:space="preserve">VII. Altitudines Solis ſupra vtramque faciem Meridiani circuli pro horis ab occaſu ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>Horę♋, ab occ. # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 58. 15. # 65. 32. # 65. 15. # 57. 33. # 46. 16. # 33. 30. # 20. 6. # 6. 25. # 7. 20. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>
Horę ♋, ab occaſu. # 18 # 19 # 20 # 21 # 22 # 23 # 24
Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 20. 59. # 34. 22. # 47. 5. # 58. 15. # 65. 32. # 65. 15. # 57. 33.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ab occaſu. # 6. 18. # 7. 17. # 8. 16. # 9. 15. # 10. 14. # 11. 13. # 12 <lb/># 18. 6. # 19. 5. # 20. 4. # 21. 3. # 22. 2. # 23. 1. # 24 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 0. 0. # 15. 0. # 30. 0. # 45. 0. # 60. 0. # 75. 0. # 90. 0.
</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♑, ab \\ occaſu. # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 47. 5. # 34. 22. # 20. 59. # 7. 20. # 6. 25. # 20. 6. # 33. 30. # 46. 16. # 57. 33. <lb/></note>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1562" type="section" level="1" n="373">
<head xml:id="echoid-head387" xml:space="preserve">VIII. Altitudines Solis ſupra vtramque ſaciem circuli horæ 6. à mer. &amp; med. noc. qui eſt Horizon in ſphæra recta, pro horis à mer. &amp; med. noc. ſupputatæ, ad quam cunque latitudinem.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, &amp; ♑, à \\ med. nocte. # 6. 6. # 7. 5. # 8. 4. # 9. 3. # 10. 2. # 11. 1. # 12. 0. <lb/>Horæ ♋, &amp; ♑, à mer. # 6. 6. # 7. 5. # 8. 4. # 9. 3. # 10. 2. # 11. 1. # 12. 0. <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 13. 44 # 27. 18. # 40. 26. # 52. 35. # 62. 21. # 66. 30. <lb/></note>
<pb o="466" file="0482" n="482" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à \\ med. nocte. # 6. 6. # 7. 5. # 8. 4. # 9. 3. # 10. 2. # 11. 1. # 12. 0. <lb/>Horæ ♈, &amp; ♎, à mer. # 6. 6. # 7. 5. # 8. 4. # 9. 3. # 10. 2. # 11. 1. # 12. 0. <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 15. 0. # 0. 0. # 45. 0. # 60. 0. # 75. 0. # 90. 0 <lb/></note>
</div>
<div xml:id="echoid-div1563" type="section" level="1" n="374">
<head xml:id="echoid-head388" xml:space="preserve">IX. Altitudines Solis ſupra faciem ſuperiorem circuli horæ 6. à mer. &amp; med. noc. pro horis ab occaſu ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 11 # 12 # 13 # 14 # 15 # 16 # 17 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 7. 20. # 11. 0. # 34. 22. # 47. 5. # 58. 15. # 65. 32. # 65. 15. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 18 # 19 # 20 # 21 # 22 <lb/>
Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M.
# 57. 35. # 46. 16. # 33. 30. # 20. 6. # 6. 25.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ab occaſu. # 12. # 13. 11. # 14. 10. # 15. 9. # 16. 8. # 17. 7. # 1@. 6. <lb/># 24. # 1. 23. # 2. 22. # 3. 21. # 4. 20. # 5. 19. # 18. 6. <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 15. 0. # 30. 0. # 45. 0. # 60. 0. # 75. 0. # 90. 0. <lb/></note>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve"> <lb/>Horę♑, abocc. # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 33. 30. # 46. 16. # 57. 35. # 65. 15. # 65. 32. # 58. 15. # 47. 5. # 34 22. # 21. 0. <lb/></note>
</div>
<div xml:id="echoid-div1564" type="section" level="1" n="375">
<head xml:id="echoid-head389" xml:space="preserve">X. Altitudines Solis ſupra faciem auſtralem Verticalis circuli declinantis à meridie in ortum grad. 30. pro horis à mer. &amp; med. noc. ſup- putatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♑, à me- \\ dia nocte. # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 1. 28. # 11. 50. # 22. 50. # 34. 12. # 45. 40. # 56. 51. # 60. 51. # 73. 4. # 73. 27. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à med. noc. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3 # 4 <lb/>
Altitudines Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. # G. M.
# 71. 7. # 62. 42. # 52. 0. # # 40. 38. # 29. 10. # 17. 56. # 7. 11.
</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, à \\ med. nocte. # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 8. 15. # 19. 28. # 30. 1. # 39. 17. # 46. 18. # 49. 46. # 49. 57. <lb/></note>
<pb o="467" file="0483" n="483" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à \\ med. noc. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. <lb/># 48. 45. # 43. 34. # 35. 25. # # 25. 29. # 14. 35. # 3. 13. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Hor. ♋, \\ à med. \\ nocte. # 5 # 6 # 7 # 8 # 9 # *** # 10 # 11 # 12 # A meri \\ die. # 1 <lb/>
Altitu \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M.
# 2. 48. # 11. 40 # 18. 54. # 23. 57. # 26. 20. # 26. 27. # 25. 39. # 22. 3. # 15. 57. # # 8. 2.
</note>
<p style="it">
  <s xml:id="echoid-s30754" xml:space="preserve">IN hac tabella, &amp; </s>
  <s xml:id="echoid-s30755" xml:space="preserve">in ſequentibus infra hoc ſignum ***. </s>
  <s xml:id="echoid-s30756" xml:space="preserve">poſita eſt altitudo meridiana, quam nimi-<lb/>
<anchor type="note" xlink:label="note-0483-04a" xlink:href="note-0483-04"/>
rum Sol ſupra circulum propoſitum habet, cum in proprio Meridiano eiuſdem circuli exiſtit. </s>
  <s xml:id="echoid-s30757" xml:space="preserve">Quo-<lb/>niam enim in proprium Meridianum nulla hora integra cadit, libuit loco horę dictum ſignum appone-<lb/>re, ſub quo altitudo meridiana notaretur.</s>
  <s xml:id="echoid-s30758" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1564" type="float" level="2" n="1">
<note position="right" xlink:label="note-0483-04" xlink:href="note-0483-04a" xml:space="preserve">Quid fignum <lb/>crucis ſignificet <lb/>in cabellis.</note>
</div>
</div>
<div xml:id="echoid-div1566" type="section" level="1" n="376">
<head xml:id="echoid-head390" xml:space="preserve">XI. Altitudines Solis ſupra faciem borealem Verticalis circuli declinantis à Septen- trione in occaſum grad. 30. pro horis à mer. &amp; med. noc. ſup- putatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 1. 2. # 11. 50. # 22. 50. # 34. 12. # 45. 40. # 5. 51. # 6. 51. # 73. 4. # 73. 27. <lb/>
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 10 # 11 # 12 # A med. \\ nocte. # 1 # 2 # 3 # 4 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. # G. M. <lb/># 71. 7. # 2. 42. # 52. 0. # # 40. 38. # 29. 10. # 17. 56. # 7. 11. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à mer. # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 8. 15. # 19. 28. # 0. 1. # 39. 17. # 46. 18. # 49. 46. # 49. 57.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à mer. # 10 # 11 # 12 # A med. \\ nocte. # 1 # 2 # 3 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. <lb/># 48. 45. # 43. 34. # 35. 25. # # 25. 29. # 14. 35. # 3. 13. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>
Hor. ♑, \\ à meri- \\ die. # 5 # 6 # 7 # 8 # 9 # *** # 10 # 11 # 12 # A med. \\ nocte. # 1
Altitu \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M.
# 2. 48. # 11. 40 # 20. 7. # 23. 57. # 26. 20. # 26. 27. # 25. 39. # 22. 3. # 15. 57. # # 8. 2.
</note>
<p style="it">
  <s xml:id="echoid-s30759" xml:space="preserve">VIDES igitur in tabella 3. </s>
  <s xml:id="echoid-s30760" xml:space="preserve">4. </s>
  <s xml:id="echoid-s30761" xml:space="preserve">10. </s>
  <s xml:id="echoid-s30762" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30763" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30764" xml:space="preserve">Solem eaſdem altitudines habere in vtraq; </s>
  <s xml:id="echoid-s30765" xml:space="preserve">faeie Vertica-<lb/>lis circuli tam proprie dicti, quàm declinatis, in eiſdẽ numero horis, ſi tamen horæ, quæ in parallelo ♋, <lb/>numerantur a meridie in una facie, numerentur in altera ſacie in parallelo ♑, a med. </s>
  <s xml:id="echoid-s30766" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s30767" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30768" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s30769" xml:space="preserve">Idẽ <lb/>in alĳs planis, quæ ſequuntur, intelligendum est: </s>
  <s xml:id="echoid-s30770" xml:space="preserve">propterea in vna tantum facie horas, earumq, altitudi-<lb/>nes deſcripſimus.</s>
  <s xml:id="echoid-s30771" xml:space="preserve"/>
</p>
<pb o="468" file="0484" n="484" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1567" type="section" level="1" n="377">
<head xml:id="echoid-head391" xml:space="preserve">XII. Altitudines Solis ſupra faciem auſtralem Verticalis circuli declinantis à me- ridie in ortum grad. 30. pro horis ab occaſu ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab occaſu. # 10 # 11 # 12 # 13 # 14 # 15 # 16 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 6. 1. # 16. 55. # 28. 7. # 39. 33. # 50. 57. # 61. 45. # 70. 31. # 73. 27. <lb/></note>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab occaſu. # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 73. 1@. # 67. 40. # 57. @1. # 46. 44. # 35. 16. # 23. 53. # 12. 51. # 2. 24. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, ab occ. # 10 # 11 # 12 # 13 # 14 # 15 # *** <lb/>
Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 8. 15. # 19. 28. # 30. 1. # 39. 17. # 46. 18. # 49. 46. # 49. 57.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, ab occ. # 16 # 17 # 18 # 19 # 20 # 21 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 48. 45. # 43. 34. # 35. 25. # 25. 29. # 14. 35. # 3. 13. <lb/></note>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve"> <lb/>Horæ \\ ♋, ab oc \\ caſu. # 10 # 11 # 12 # 13 # *** # 14 # 15 # 16 # 17 # 18 <lb/>Altitu. \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 7. 42. # 15. 46. # 21. 55. # 25. 36. # 26. 27. # 26. 21. # 24. 5. # 19. 4. # 11. 53. # 3. 3. <lb/></note>
<p style="it">
  <s xml:id="echoid-s30772" xml:space="preserve">VT autem intelligas, qua ratione altitudines Solis ſupra vnam faciem circuli maximi æquales ſint <lb/>
<anchor type="note" xlink:label="note-0484-09a" xlink:href="note-0484-09"/>
altitudinibus Solis ſupra alterã faciem in eiſdẽ horis, mutatis horis a mer. </s>
  <s xml:id="echoid-s30773" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s30774" xml:space="preserve">in horas a med. </s>
  <s xml:id="echoid-s30775" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s30776" xml:space="preserve">vel or. </s>
  <s xml:id="echoid-s30777" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30778" xml:space="preserve">parallelis horealibus in auſtrales, &amp; </s>
  <s xml:id="echoid-s30779" xml:space="preserve">contra, rem perſpicuã faciemus vno aut altero exemplo. </s>
  <s xml:id="echoid-s30780" xml:space="preserve"><lb/>Sit v. </s>
  <s xml:id="echoid-s30781" xml:space="preserve">g. </s>
  <s xml:id="echoid-s30782" xml:space="preserve">inuenienda altitudo Solis ſupra faciem borealem Verticalis circuli declinantis à Septentrione <lb/>
<anchor type="note" xlink:label="note-0484-10a" xlink:href="note-0484-10"/>
in occaſum grad. </s>
  <s xml:id="echoid-s30783" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30784" xml:space="preserve">ad horam 13. </s>
  <s xml:id="echoid-s30785" xml:space="preserve">ab ortu in parallelo ♋. </s>
  <s xml:id="echoid-s30786" xml:space="preserve">Quæro horam 13. </s>
  <s xml:id="echoid-s30787" xml:space="preserve">ab occaſu in parallelo ♑, <lb/>cuius altitudo ſupra faciem auſtralem dicti Verticalis continet grad. </s>
  <s xml:id="echoid-s30788" xml:space="preserve">39. </s>
  <s xml:id="echoid-s30789" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30790" xml:space="preserve">33. </s>
  <s xml:id="echoid-s30791" xml:space="preserve">Tantam ergo altitu <lb/>dinem habet Solhora 13. </s>
  <s xml:id="echoid-s30792" xml:space="preserve">ab ortu in parallelo ♋, ſupra faciem borealem propoſiti Verticalis. </s>
  <s xml:id="echoid-s30793" xml:space="preserve">Eodem <lb/>modo, quia Sol hora 10. </s>
  <s xml:id="echoid-s30794" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s30795" xml:space="preserve">noc, in parallelo ♋, ſupra faciem auſtralem eiuſdem Verticalis habet <lb/>altitudinem gr. </s>
  <s xml:id="echoid-s30796" xml:space="preserve">25. </s>
  <s xml:id="echoid-s30797" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30798" xml:space="preserve">39. </s>
  <s xml:id="echoid-s30799" xml:space="preserve">eandem altitudinem habebit Sol hora 10. </s>
  <s xml:id="echoid-s30800" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s30801" xml:space="preserve">in parallelo ♑, ſupra fa-<lb/>ciem eiuſdem circuli Verticalis borealem, vt ex tabella 10. </s>
  <s xml:id="echoid-s30802" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30803" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30804" xml:space="preserve">perſpicuum eſt. </s>
  <s xml:id="echoid-s30805" xml:space="preserve">Denique quia ſupra <lb/>faciem ſuperiorem circuli maximi declinantis ab Horizonte gr. </s>
  <s xml:id="echoid-s30806" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30807" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30808" xml:space="preserve">ad V@rticalem proprie dictum <lb/>recti, quæ ad Zenith, occaſum{q́ue} ſpectat, Sol hora 4. </s>
  <s xml:id="echoid-s30809" xml:space="preserve">à. </s>
  <s xml:id="echoid-s30810" xml:space="preserve">mer. </s>
  <s xml:id="echoid-s30811" xml:space="preserve">in parallelo ♋, altitudinẽ habet gr. </s>
  <s xml:id="echoid-s30812" xml:space="preserve">67. </s>
  <s xml:id="echoid-s30813" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s30814" xml:space="preserve">24. </s>
  <s xml:id="echoid-s30815" xml:space="preserve">vt ex ſequẽti tabella patet, habebit eandem altitudinẽ Sol hora 4. </s>
  <s xml:id="echoid-s30816" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s30817" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s30818" xml:space="preserve">in parallelo ♑, ſupra <lb/>
<anchor type="note" xlink:label="note-0484-11a" xlink:href="note-0484-11"/>
faciem inferiorem eiuſdem circuli maximi, &amp; </s>
  <s xml:id="echoid-s30819" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30820" xml:space="preserve">Idem in alĳs tabellis omnibus intelligendum est.</s>
  <s xml:id="echoid-s30821" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1567" type="float" level="2" n="1">
<note position="left" xlink:label="note-0484-09" xlink:href="note-0484-09a" xml:space="preserve">Quomodo ex-<lb/>dem altitudi-<lb/>nes ac@ommo-<lb/>dentur faciebus <lb/>oppoſitis circu <lb/>lorum maximo <lb/>ſum.</note>
<note position="left" xlink:label="note-0484-10" xlink:href="note-0484-10a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0484-11" xlink:href="note-0484-11a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1569" type="section" level="1" n="378">
<head xml:id="echoid-head392" xml:space="preserve">XIII. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis ab Horizon-<lb/>te gr. 30. &amp; ad Verticalem proprie dictum recti, quæ ad Zenith, <lb/>occaſumq́ue ſpectat, pro horis à mer. &amp; med. noc. <lb/>ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horę ♋, à \\ med. noc. # 8 # 9 # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. <lb/># 7. 26. # 18. 56. # 0. 52. # 43. 3. # 55. 13. # # 66. 54. # 76. 17. # 78. 5. <lb/></note>
<pb o="469" file="0485" n="485" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 3 # 4 # 5 # 6 # 7 # 8 # 9 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 76. 33. # 67. 24. # 55. 45. # 43. 35. # 31. 24. # 19. 27. # 7. 55. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à \\ med. nocte. # 9 # 10 # 11 # 12 # A meri- \\ die. # 1 # 2 # *** <lb/>
Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M.
# 5. 50. # 17. 54. # 29. 30. # 40. 4. # # 48. 41. # 53. 50. # 54. 35.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à mer. # 3 # 4 # 5 # 6 # 7 # 8 <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 53. 57. # 49. 0. # 40. 30. # 30. 0. # 18. 26. # 6. 22. <lb/>
</note>
<note position="right" xml:space="preserve"> <lb/>Hor. ♑, \\ à med. \\ nocte. # 10 # 11 # 12 # Ameri- \\ die. # 1 # 2 # *** # 3 # 4 # 5 # 6 # 7 <lb/>Altitu. \\Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 2. 55. # 12. 44. # 21. 3. # # 27. 14. # 30. 37. # 31. 5. # 30. 42. # 27. 27. # 21. 23. # 13. 8. # 3. 23. <lb/></note>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1570" type="section" level="1" n="379">
<head xml:id="echoid-head393" xml:space="preserve">XIIII. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis ab Horizon-<lb/>te gr. 30. &amp; ad Verticalem proprie dictum recti, quæ ad Zenith, <lb/>occaſumq́ue ſpectat, pro horis ab ortu ſup-<lb/>putatæ, ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab ortu. # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # *** <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 1. 34. # 12. 43. # 24. 27. # 36. 32. # 48. 45. # 60. 47. # 71. 49. # 78. 4. # 78. 5. <lb/></note>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋, ab ortu. # 11 # 12 # 13 # 14 # 15 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 72. 53. # 62. 5. # 50. 6. # 37. 53. # 25. 47. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, ab ortu. # 3 # 4 # 5 # 6 # 7 # 8 # *** <lb/>
Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 5. 50. # 17. 54. # 29. 30. # 40. 4. # 48. 41. # 53. 50. # 54. 35.
</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, ab ortu. # 9 # 10 # 11 # 12 # 13 # 14 <lb/>Altitudines \\Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 53. 57. # 49. 0. # 40. 30. # 30. 0. # 18. 26. # 6. 22. <lb/></note>
<pb o="470" file="0486" n="486" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horæ \\ ♑, ab \\ ortu. # 3 # 4 # 5 # 6 # *** # 7 # 8 # 9 # 10 # 11 <lb/>Altitu. \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 8. 18. # 17. 24. # 24. 40. # 29. 26. # 31. 5. # 31. 5. # 29. 21. # 24. 31. # 17. 12. # 8. 5. <lb/></note>
</div>
<div xml:id="echoid-div1571" type="section" level="1" n="380">
<head xml:id="echoid-head394" xml:space="preserve">XV. Altitudines Solis ſupra faciem ſuperiorem circuli maximi ad Meridianum recti, <lb/>&amp; ad Horizontem inclinati ex parte auſtrali gr. 68. pro horis à mer. &amp; <lb/>med. noc. ſupputatæ, ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">10</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋, à med. nocte. # 0 # 1 # 2 # 3 # 4 # 5 # 6 <lb/>Horæ ♋, à meridie. # 12 # 11 # 10 # 9 # 8 # 7 # 6 <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 43. 30. # 42. 40. # 40. 16. # 36. 37. # 32. 7. # 27. 7. # 22. 0. <lb/>Horæ ♋, à med. nocte. # 7 # 8 # 9 # 10 # 11 # 12 <lb/>
Horæ ♋, à meridie. # 5 # 4 # 3 # 2 # 1 # 0
Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 17. 9. # 12. 35. # 8. 48. # 5. 55. # 4. 7. # 3. 30.
Horæ ♈, &amp; ♎, à \\ med. noc. # 0 # 1 # 2 # 3 # 4 # 5 # 6
Horæ ♈, &amp; ♎, à mer. # 12 # 11 # 10 # 9 # 8 # 7 # 6
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 20. 0. # 19. 17. # 17. 14. # 14. 0. # 9. 51. # 5. 5. # 0. 0.
</note>
<p style="it">
  <s xml:id="echoid-s30822" xml:space="preserve">SOL in parallelo ♑, exiſtens faciem ſuperiorem hui{us} circuli non illuminat, ſed inferiorem tantũ, <lb/>propterea nullæ ſunt altitudines horarum paralleli ♑, ſupra faciem ſuperiorem; </s>
  <s xml:id="echoid-s30823" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30824" xml:space="preserve">gnomonis vmbra, <lb/>Sole exiſtente in principio ♋, Ellipſim deſcribit.</s>
  <s xml:id="echoid-s30825" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1572" type="section" level="1" n="381">
<head xml:id="echoid-head395" xml:space="preserve">XVI. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à meridie <lb/>in ortum grad. 40. &amp; ad Horizontem ex parte boreali inclinati grad. <lb/>20. pro horis à mer. &amp; med. noc. ſupputatæ, <lb/>ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à me \\ dia nocte. # 5 # 6 # 7 # 8 # 9 # 10 # 11 # *** # 12 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 9. 16. # 22. 2. # 35. 9. # 48. 28. # 61. 56. # 75. 26. # 87. 35. # 87. 47. # 76. 55. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 1 # 2 # 3 # 4 # 5 <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M.
# 63. 26. # 49. 58. # 36. 37. # 23. 29. # 10. 40.
Horę ♈, &amp; ♎, à \\ med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # *** # 12
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 12. 44. # 26. 3. # 30. 53. # 50. 41. # 60. 5. # 64. 16. # 64. 17. # 60. 52.
</note>
<pb o="471" file="0487" n="487" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/># Horæ. ♈, &amp; ♎, à merid. # 1 # 2 # 3 # 4 # 5 <lb/># Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 51. 53. # 40. 16. # 27. 30. # 14. 14. # 0. 45. <lb/># Horę ♑, à med. noct. # 6 # 7 # 8 # 9 # 10 # 11 # *** # 12 <lb/>
# Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 1. 40. # 13. 17. # 23. 45. # 32. 26. # 38. 27. # 40. 46. # 40. 47. # 38. 54.
# Horæ ♑, à meridie. # 1 # 2 # 3 # 4
# Altitudines Solis. # G. M. # G. M. # G. M. # G. M.
# 33. 16. # 24. 49. # 14. 30. # 3. 0.
</note>
</div>
<div xml:id="echoid-div1573" type="section" level="1" n="382">
<head xml:id="echoid-head396" xml:space="preserve">XVII. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à meridie <lb/>in occaſum grad. 20. &amp; ad Horizontem ex parte boreali inclinati grad. <lb/>70. pro horis inæqualibus ſupputatæ, ad lati-<lb/>tudinem grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/># Horæ ♑, in- \\ æquales. # 12 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # *** <lb/>
# Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 11. 37. # 21. 10. # 30. 55. # 40. 48. # 50. 47. # 60. 50. # 70. 56. # 80. 59. # 88. 12.
# Horæ ♑, in- \\ æquales. # 8 # 9 # 10 # 11 # 12 # # # Hora 1. ♐, &amp; ♒
# Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # # # G. M.
# 87. 45. # 78. 21. # 68. 17. # 58. 12. # 48. 9. # # # 17. 25.
</note>
<p style="it">
  <s xml:id="echoid-s30826" xml:space="preserve">APPOSVIMVS autem hic etiam altitudinem Solis pro hora 1. </s>
  <s xml:id="echoid-s30827" xml:space="preserve">inæquali in par allelo ♐, &amp; </s>
  <s xml:id="echoid-s30828" xml:space="preserve"><lb/>♒, quoniã ex longitudine vmbrę huius altitudinis deſcribenda eſt hora 1. </s>
  <s xml:id="echoid-s30829" xml:space="preserve">inæqualis in horologio, quod <lb/>huic circulo maximo æquiſtat, ſupra quem altitudines Solis ſupputatæ ſunt, deſcribenda eſt, vt ſuo lo-<lb/>co manifeſtum erit.</s>
  <s xml:id="echoid-s30830" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve"> <lb/>Horæ \\ ♈, &amp; ♎, \\ inęq<unsure/>les # 2 # 3 # 4 # 5 # 6 # 7 # *** # 8 # 9 # 10 # 11 # 12 <lb/>Altitu. \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 8. 15. # 21. 42. # 34. 47. # 47. 7. # 57. 39. # 64. 4. # 64. 42. # 63. 12. # 55. 36. # 44. 32. # 31. 55. # 18. 47.
Horæ \\ ♋, in- \\ ęquales # 3 # 4 # 5 # 6 # 7 # *** # 8 # 9 # 10 # 11
Altitu. \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 37. # 15. 13. # 27. 52. # 37. 11. # 41. 10. # 41. 12. # 38. 34. # 30. 14. # 18. 9. # 3. 53.
</note>
<pb o="472" file="0488" n="488" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1574" type="section" level="1" n="383">
<head xml:id="echoid-head397" xml:space="preserve">XVIII. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à meridie <lb/>in ortum grad. 45. &amp; ad Hor izontem ex parte boreali inclinati grad. 51. <lb/>Min. 51. pro horis à mer. &amp; med. noc. ſupputatæ, <lb/>ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, &amp; ♑, à \\ med. noc. # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 3. 28. # 17. 10. # 30. 40. # 43. 37. # 55. 21. # 64. 6. # 66. 30.
Horæ ♋, &amp; ♑, à \\ med. noc. # 10 # 11 # 12 # A meri- \\ die. # 1 # 2 # 3
Altitudines \\ Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M.
# 60. 13. # 60. 15. # 49. 40. # # 37. 11. # 23. 54. # 10. 17.
Horæ ♈, &amp; ♎, à \\ med. noe. # 4 # 5 # 6 # 7 # 8 # 9 # ***
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 3. 47. # 18. 47. # 33. 47. # 48. 47. # 63. 47. # 78. 47. # 90. 0.
Horæ ♈, &amp; ♎, à \\ med. noc. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3
Altítudines \\ Solis. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M.
# 86. 13. # 71. 13. # 56. 13. # # 41. 13. # 26. 13. # 11. 13.
</note>
</div>
<div xml:id="echoid-div1575" type="section" level="1" n="384">
<head xml:id="echoid-head398" xml:space="preserve">XIX. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à Septen-<lb/>trione in occaſum grad. 20. &amp; ad Horizontem ex parte auſtrali incli-<lb/>nati grad. 30. pro horis à mer. &amp; med. noc. ſupputatæ, <lb/>ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. noc. # 1 # *** # 2 # 3 # 4 # 5 # 6 <lb/>Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 2. 11. # 1. 43. # 1. 44. # 2. 37. # 4. 47. # 8. 4. # 12. 18. <lb/>Horę ♋, à med. noct. # 7 # 8 # 9 # 10 # 11 # 12 <lb/>
Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 17. 15. # 22. 39. # 28. 12. # 33. 35. # 38. 24. # 42. 14.
Horæ ♋, à meridie. # 1 # *** # 2 # 3 # 4 # 5 # 6
Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 44. 38. # 45. 17. # 45. 15. # 44. 1. # 41. 6. # 36. 53. # 31. 50.
</note>
<pb o="473" file="0489" n="489" rhead="LIBER QVINTVS."/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 26. 21. # 20. 49. # 15. 33. # 10. 48. # 6. 51. # 3. 55. <lb/>Horæ ♈, &amp; ♎, à me- \\ dia nocte. # 8 # 9 # 10 # 11 # 12 # A meri \\ die. # 1 # *** <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M.
# 0. 56. # 6. 24. # 11. 30. # 15. 53. # 19. 13. # # 21. 14. # 21. 47.
Horę ♈, &amp; ♎, à merid. # 2 # 3 # 4 # 5 # 6 # 7
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 21. 46. # 20. 44. # 18. 14. # 14. 31. # 9. 52. # 4. 36.
</note>
<p style="it">
  <s xml:id="echoid-s30831" xml:space="preserve">TROPICVS ♑, hunc circulum maximum non ſecat, ſed totus infra ipſum latet, quemadmodũ <lb/>&amp; </s>
  <s xml:id="echoid-s30832" xml:space="preserve">tropicus ♋, totus ſupra eundem extat. </s>
  <s xml:id="echoid-s30833" xml:space="preserve">Hinc fit, vt Sole existente in principio ♋, gnomonis vmbra <lb/>Ellipſim deſcribat in facie ſuperiori dicti circuli, eodem vero exiſtente in principio ♑, eam faciem non <lb/>illuſtret, ſed inferiorem. </s>
  <s xml:id="echoid-s30834" xml:space="preserve">Vnde nullæ altitudines Solis pro horis tropici ♑, aſcriptæ ſunt.</s>
  <s xml:id="echoid-s30835" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1576" type="section" level="1" n="385">
<head xml:id="echoid-head399" xml:space="preserve">XX. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à ſeptentrione in <lb/>ortum gr. 60. &amp; ad Horizontem ex parte auſtrali inclinati gr. 80. pro horis ab <lb/>occaſu ſupputatę, ad latitudinem. Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 3 # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 4. 24. # 16. 45. # 29. 32. # 42. 36. # 55. 49. # 69. 4. # 81. 46. # 85. 40.
Horę ♋, ab occaſu. # 10 # 11 # 12 # 13 # 14 # 15 # 16
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 82. 11. # 69. 32. # 56. 17. # 43. 4 # 30. 0. # 17. 12. # 4. 50.
Horæ ♈, &amp; ♎, \\ ab occaſu. # 6 # 7 # 8 # 9 # 10 # 11 # ***
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 12. 33. # 25. 35. # 38. 5. # 49. 27. # 58. 19. # 62. 9. # 62. 10.
Horę ♈, &amp; ♎, ab \\ occaſu. # 12 # 13 # 14 # 15 # 16 # 17
Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 59. 0. # 50. 30. # 39. 19. # 26. 54. # 13. 54. # 0. 41.
Horæ \\ ♑, ab \\ occaſu. # 8 # 9 # 10 # 11 # 12 # *** # 13 # 14 # 15 # 16 # 17
Altitu. \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 6. 10. # 17. 3. # 26. 30. # 33. 47. # 37. 58. # 38. 40. # 38. 19. # 34. 44. # 27. 54. # 18. 46. # 8. 5.
</note>
<pb o="474" file="0490" n="490" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1577" type="section" level="1" n="386">
<head xml:id="echoid-head400" xml:space="preserve">XXI. Altitudines Solis ſupra faciem ſuperiorem circuli maximi declinantis à ſeptentrione <lb/>in ortum gr. 30. &amp; ad Horizontem ex parte auſtrali inclinati gr. 52. Min. 3. pro <lb/>horis à mer. &amp; med. noc. ſupputatæ, ad latitudincm Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♋, à meridie. # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>Altitudines \\ Solis # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 17. # 0. 59. # 3. 4. # 6. 22. # 10. 42. # 15. 50. # 21. 30. <lb/>
</note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋, à med. nocte. # 0 # 1 # 2 # 3 # 4 # 5 # 6 <lb/>Horę ♋, à med. nocte. # 12 # 11 # 10 # 9 # 8 # 7 # 6 <lb/>Altitudines \\ Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 21. 30. # 27. 23. # 33. 11. # 38. 28. # 42. 48. # 45. 42. # 46. 43. <lb/>Horæ ♈, &amp; ♎, à med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 <lb/>Horæ ♈, &amp; ♎, à med. nocte. # 6 # 5 # 4 # 3 # 2 # 1 # 0 <lb/>
Altitudines Solis. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 23. 13. # 22. 23. # 19. 58. # 16. 11. # 11. 22. # 5. 51. # 0. 0.
</note>
<p style="it">
  <s xml:id="echoid-s30836" xml:space="preserve">NVLLAE altitudines Solis pro horis ♑, hic ponuntur, quia tropicus ♑, totus extat ſupra <lb/>faciem inferiorem huius circuli, ſicut &amp; </s>
  <s xml:id="echoid-s30837" xml:space="preserve">tropicus ♋, totus ſupra eiuſdem faciem ſuperiorem exiſtit. <lb/></s>
  <s xml:id="echoid-s30838" xml:space="preserve">Vnde Sol in illo exiſtens faciem ſuperiorem non illustrat, eodem vero in hoc exiſtente, vmbra gnomonis <lb/>Ellipſim deſcribit in ſuperiorifacie.</s>
  <s xml:id="echoid-s30839" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1578" type="section" level="1" n="387">
<head xml:id="echoid-head401" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s30840" xml:space="preserve">EX altitudine Solis ſupra quodcunque planum cognita proportio-<lb/>nem gnomonis ad vmbram tam rectam, quàm verſam; </s>
  <s xml:id="echoid-s30841" xml:space="preserve">Et contra ex <lb/>proportione vmbræ ſiue rectæ, ſiue verſæ ad gnomonem altitudinem <lb/>Solis elicere.</s>
  <s xml:id="echoid-s30842" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s30843" xml:space="preserve">DESCRIBATVR circulus A B C D, vna cum diametris A C, B D, ſeſe in centro E, ad <lb/>rectos angulos ſecantibus. </s>
  <s xml:id="echoid-s30844" xml:space="preserve">Intelligatur autem hic circulus duci per centrum Solis in I, conſtitu-<lb/>ti, &amp; </s>
  <s xml:id="echoid-s30845" xml:space="preserve">per A, polum plani propoſiti; </s>
  <s xml:id="echoid-s30846" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30847" xml:space="preserve">recta B D, communis ſectio eiuſdem circuli, &amp; </s>
  <s xml:id="echoid-s30848" xml:space="preserve">circuli ma-<lb/>ximi, cui planum æquidiſtat. </s>
  <s xml:id="echoid-s30849" xml:space="preserve">Quo poſito, erit <lb/>
<anchor type="figure" xlink:label="fig-0490-01a" xlink:href="fig-0490-01"/>
A C, axis propoſiti plani. </s>
  <s xml:id="echoid-s30850" xml:space="preserve">Sit quoque E F, æquua <lb/>
<anchor type="note" xlink:label="note-0490-06a" xlink:href="note-0490-06"/>
lis gnomoni recto ad planum per rectam F G, <lb/>circulo maximo diametri B D, æquidiſtans du-<lb/>ctum; </s>
  <s xml:id="echoid-s30851" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30852" xml:space="preserve">E H, æqualis gnomoni recto ad planũ <lb/>per rectam H G, ductum, æquidiſtansq́ue circu-<lb/>lo maximo, qui per A C, ducitur, rectusq́ue eſt <lb/>ad circulum A B C D: </s>
  <s xml:id="echoid-s30853" xml:space="preserve">Cadatq́ue ex I, centro <lb/>Solis radius I E, per centrum mundi, ſeu verti-<lb/>cem vtriuſque gnomonis tranſiens, qui occurrat <lb/>rectæ F G, in G, &amp; </s>
  <s xml:id="echoid-s30854" xml:space="preserve">rectæ H G, in G. </s>
  <s xml:id="echoid-s30855" xml:space="preserve">Et quoniam <lb/>
<anchor type="note" xlink:label="note-0490-07a" xlink:href="note-0490-07"/>
per propoſ. </s>
  <s xml:id="echoid-s30856" xml:space="preserve">11. </s>
  <s xml:id="echoid-s30857" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30858" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30859" xml:space="preserve">vmbra ſtyli E F, proiicitur <lb/>in rectam F G, communem ſectionem plani, &amp; </s>
  <s xml:id="echoid-s30860" xml:space="preserve"><lb/>circuli maximi A B C D, in quo Sol exiſtit, vm-<lb/>bra verò ſtyli E H, in rectam H G, communem ſe <lb/>ctionem plani alterius, &amp; </s>
  <s xml:id="echoid-s30861" xml:space="preserve">eiuſdem maximi cir-<lb/>culi A B C D, cadit, erit, per ea, quæ in propoſ. </s>
  <s xml:id="echoid-s30862" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s30863" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s30864" xml:space="preserve">1. </s>
  <s xml:id="echoid-s30865" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30866" xml:space="preserve">in Quadrato Geometrico à nobis oſten-<lb/>
<anchor type="note" xlink:label="note-0490-08a" xlink:href="note-0490-08"/>
ſa ſunt, F G, longitudo vmbræ rectæ, &amp; </s>
  <s xml:id="echoid-s30867" xml:space="preserve">H G, longitudo vmbræ verſæ. </s>
  <s xml:id="echoid-s30868" xml:space="preserve">Iam verò, demiſſa ex I, ad <lb/>B D, perpendiculari I K, quoniam triangula E I k, G E F, ſimilia ſunt, quòd angulus G E F, angu-<lb/>lo E I K, æqualis ſit, externus interno, &amp; </s>
  <s xml:id="echoid-s30869" xml:space="preserve">rectus F, recto k, &amp;</s>
  <s xml:id="echoid-s30870" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30871" xml:space="preserve">erit vt I K, ſinus rectus altitu-<lb/>
<anchor type="note" xlink:label="note-0490-09a" xlink:href="note-0490-09"/>
dinis Solis ad K E, ſinum complementi eiuſdem altitudinis, ita E F, gnomon ad F G, vmbram <lb/>
<anchor type="note" xlink:label="note-0490-10a" xlink:href="note-0490-10"/>
<pb o="475" file="0491" n="491" rhead="LIBER QVINTVS."/>
rectam. </s>
  <s xml:id="echoid-s30872" xml:space="preserve">Quamobrem ſi fiat, vt ſinus altitudinis Solis cognitæ ad ſinum complementi eiuſdem <lb/>altitudinis, ita gnomon diuiſus in quotcunque partes æquales (Nos intelligimus eum diuiſum in <lb/>12. </s>
  <s xml:id="echoid-s30873" xml:space="preserve">partes æquales) ad aliud, inuenietur longitudo vmbræ rectæ nota in partibus, quæ æquales <lb/>ſunt illis, in quas gnomon eſt diuiſus. </s>
  <s xml:id="echoid-s30874" xml:space="preserve">Exempligratia. </s>
  <s xml:id="echoid-s30875" xml:space="preserve">Sole habente altitudinem grad. </s>
  <s xml:id="echoid-s30876" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30877" xml:space="preserve">ſi fiat <lb/>vt 50000. </s>
  <s xml:id="echoid-s30878" xml:space="preserve">ſinus altitudinis Solis ad 86602. </s>
  <s xml:id="echoid-s30879" xml:space="preserve">ſinum complementi eiuſdem altitudinis, ita gno-<lb/>mon 12. </s>
  <s xml:id="echoid-s30880" xml:space="preserve">partium ad aliud, inuenietur vmbra recta earum partium 20. </s>
  <s xml:id="echoid-s30881" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30882" xml:space="preserve">47. </s>
  <s xml:id="echoid-s30883" xml:space="preserve">qualium duo-<lb/>decim gnomon ponitur.</s>
  <s xml:id="echoid-s30884" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1578" type="float" level="2" n="1">
  <figure xlink:label="fig-0490-01" xlink:href="fig-0490-01a">
    <image file="0490-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0490-01"/>
  </figure>
<note position="left" xlink:label="note-0490-06" xlink:href="note-0490-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0490-07" xlink:href="note-0490-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0490-08" xlink:href="note-0490-08a" xml:space="preserve">Qua ratio@e @@ <lb/>altitudine Solis <lb/>longitudo vm-<lb/>bræ re@tæ ſit in-<lb/>ueſt ganda.</note>
<note position="left" xlink:label="note-0490-09" xlink:href="note-0490-09a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0490-10" xlink:href="note-0490-10a" xml:space="preserve">4. ſexti.</note>
</div>
<p>
  <s xml:id="echoid-s30885" xml:space="preserve">EADEM ratione, quia triangula GEH, IEK, ſimilia ſunt, quod anguli ad verticẽE, æqua-<lb/>
<anchor type="note" xlink:label="note-0491-01a" xlink:href="note-0491-01"/>
les ſint, &amp; </s>
  <s xml:id="echoid-s30886" xml:space="preserve">anguli H, K, recti, &amp;</s>
  <s xml:id="echoid-s30887" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30888" xml:space="preserve">erit vt E K, ſinus complementi altitudinis Solis, ad K I, ſinum al-<lb/>
<anchor type="note" xlink:label="note-0491-02a" xlink:href="note-0491-02"/>
<anchor type="note" xlink:label="note-0491-03a" xlink:href="note-0491-03"/>
titudinis eiuſdem, ita E H, ſtylus ad H G, vmbram verí<unsure/>am. </s>
  <s xml:id="echoid-s30889" xml:space="preserve">Si ergo fiat, vt ſinus complementi alti-<lb/>
<anchor type="note" xlink:label="note-0491-04a" xlink:href="note-0491-04"/>
tudinis Solis cognitæ ad ſinũ eiuſdem altitudinis, ita gnomon ad aliud, reperietur vmbra verſa in <lb/>partibus, quæ æquales ſunt illis, in quas gnomon diuiditur. </s>
  <s xml:id="echoid-s30890" xml:space="preserve">Vt in eodẽ exemplo. </s>
  <s xml:id="echoid-s30891" xml:space="preserve">ſi fiat, vt 86602. <lb/></s>
  <s xml:id="echoid-s30892" xml:space="preserve">ſinus complementi altitudinis Solis ad 50000. </s>
  <s xml:id="echoid-s30893" xml:space="preserve">ſinum ipſius altitudinis, ita 12. </s>
  <s xml:id="echoid-s30894" xml:space="preserve">ad aliud, inuenie-<lb/>tur vmbra verſa partium 6. </s>
  <s xml:id="echoid-s30895" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30896" xml:space="preserve">56. </s>
  <s xml:id="echoid-s30897" xml:space="preserve">qualium 12. </s>
  <s xml:id="echoid-s30898" xml:space="preserve">gnomon continet.</s>
  <s xml:id="echoid-s30899" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1579" type="float" level="2" n="2">
<note position="right" xlink:label="note-0491-01" xlink:href="note-0491-01a" xml:space="preserve">15. primi.</note>
<note position="right" xlink:label="note-0491-02" xlink:href="note-0491-02a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0491-03" xlink:href="note-0491-03a" xml:space="preserve">Qua via ex alti <lb/>tudine Solis lon <lb/>gitudo vmbræ <lb/>verſæ ſit exple-<lb/>randa.</note>
<note position="left" xlink:label="note-0491-04" xlink:href="note-0491-04a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s30900" xml:space="preserve">RVRSVS ſi vmbra nota fuerit ſiue recta, ſiue verſa, nota erunt quadrata ex vmbra, &amp; </s>
  <s xml:id="echoid-s30901" xml:space="preserve">gno <lb/>mone deſcripta, quæ cum æqualia ſint quadrato rectæ E G, notum etiam erit quadratum rectæ <lb/>
<anchor type="note" xlink:label="note-0491-05a" xlink:href="note-0491-05"/>
E G. </s>
  <s xml:id="echoid-s30902" xml:space="preserve">Et quoniam eſt, ob ſimilitudinem triangulorum E G F, E I K, vt E G, ad E F, ita E I, ſi-<lb/>
<anchor type="note" xlink:label="note-0491-06a" xlink:href="note-0491-06"/>
<anchor type="note" xlink:label="note-0491-07a" xlink:href="note-0491-07"/>
nus totus ad I K, ſinum altitudinis Solis, erit quoque, vt quadratum ex E G, ad quadratum gno-<lb/>
<anchor type="note" xlink:label="note-0491-08a" xlink:href="note-0491-08"/>
monis E F, ita quadratum ſinus totius E I, ad quadratum ſinus altitudinis Solis I K; </s>
  <s xml:id="echoid-s30903" xml:space="preserve">atque adeo <lb/>ex quadrato noto I K, ſinus ipſe I K, notus erit. </s>
  <s xml:id="echoid-s30904" xml:space="preserve">Vel breuius; </s>
  <s xml:id="echoid-s30905" xml:space="preserve">ex quadrato noto E G, ipſa recta E G, <lb/>
<anchor type="note" xlink:label="note-0491-09a" xlink:href="note-0491-09"/>
nota erit. </s>
  <s xml:id="echoid-s30906" xml:space="preserve">Si igitur fiat, vt E G, nota ad gnomonem E F, ita ſinus totus E I, ad aliud, notus fiet I K, <lb/>ſinus altitudinis Solis. </s>
  <s xml:id="echoid-s30907" xml:space="preserve">Eodem pacto cum ſit, ob ſimilitudinem triangulorum E G H, E I K, vt <lb/>E G, ad G H, ita E I, ad I K, erit quoque, vt quadratum rectæ E G, cognitum, ad quadratum vm-<lb/>
<anchor type="note" xlink:label="note-0491-10a" xlink:href="note-0491-10"/>
<anchor type="note" xlink:label="note-0491-11a" xlink:href="note-0491-11"/>
bræ verſæ G H, notum, ita quadratum ſinus totius E I, ad quadratum ſinus altitudinis Solis I K; <lb/></s>
  <s xml:id="echoid-s30908" xml:space="preserve">ac proinde ex quadrato I K, ſinus ipſe I k, cognoſcetur. </s>
  <s xml:id="echoid-s30909" xml:space="preserve">Vel breuius; </s>
  <s xml:id="echoid-s30910" xml:space="preserve">ex quadrato rectæ E G, ipſa <lb/>recta E G, cognita erit. </s>
  <s xml:id="echoid-s30911" xml:space="preserve">Si igitur fiat, vt E G, nota ad vmbram verſam G H, ita ſinus totus E I, ad <lb/>aliud, inuentus erit ſinus I K, altitudinis Solis. </s>
  <s xml:id="echoid-s30912" xml:space="preserve">Quocirca, ex altitudine Solis ſupra quodcunque <lb/>planum cognita, proportionem, &amp;</s>
  <s xml:id="echoid-s30913" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30914" xml:space="preserve">elicuimus. </s>
  <s xml:id="echoid-s30915" xml:space="preserve">Qod erat faciendum.</s>
  <s xml:id="echoid-s30916" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1580" type="float" level="2" n="3">
<note position="right" xlink:label="note-0491-05" xlink:href="note-0491-05a" xml:space="preserve">47. primi.</note>
<note position="right" xlink:label="note-0491-06" xlink:href="note-0491-06a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0491-07" xlink:href="note-0491-07a" xml:space="preserve">22. ſexti.</note>
<note position="right" xlink:label="note-0491-08" xlink:href="note-0491-08a" xml:space="preserve">Quo pacto ex <lb/>longitudine vm <lb/>bræ ſiue rectæ, <lb/>ſiue verſæ, alti-<lb/>tudo Solis in-<lb/>quiratur.</note>
<note position="left" xlink:label="note-0491-09" xlink:href="note-0491-09a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0491-10" xlink:href="note-0491-10a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0491-11" xlink:href="note-0491-11a" xml:space="preserve">22. ſexti.</note>
</div>
</div>
<div xml:id="echoid-div1582" type="section" level="1" n="388">
<head xml:id="echoid-head402" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="left" xml:space="preserve">30</note>
<p style="it">
  <s xml:id="echoid-s30917" xml:space="preserve">QVONIAM vero propter ſimilitudinem triangulorum E F G, E H G, eſt vt F G, vmbra re-<lb/>
<anchor type="note" xlink:label="note-0491-13a" xlink:href="note-0491-13"/>
cta ad E F, gnomonem, ita E H, gnomon ad H G, vmbram verſam, idemq́, verum eſt, ſi ſtylus E L, <lb/>ſumatur æqualis gnomoni E F, vt vmbra verſa ſit L M; </s>
  <s xml:id="echoid-s30918" xml:space="preserve">fit vt gnomon quicunque medio loco proportio-<lb/>nalis ſit inter vmbram rectam, &amp; </s>
  <s xml:id="echoid-s30919" xml:space="preserve">vmbram verſam ab ipſo gnomone proiectam.</s>
  <s xml:id="echoid-s30920" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1582" type="float" level="2" n="1">
<note position="right" xlink:label="note-0491-13" xlink:href="note-0491-13a" xml:space="preserve">Stylus, vel gn@-<lb/>mon medio lo-<lb/>co propotriona <lb/>lis eſt inter eius <lb/>vmbram rectã, <lb/>&amp; verfam.</note>
</div>
<p style="it">
  <s xml:id="echoid-s30921" xml:space="preserve">ITEM quoniam ſi circulus per A C, ductus concipiatur eſſe Horizon, F G, eſt vmbra verſa ſtyli <lb/>
<anchor type="note" xlink:label="note-0491-14a" xlink:href="note-0491-14"/>
E F, eadem videlicet omnino, quæ prius recta er at eiuſdem ſtyli E F, reſpectu Horizontis per B D, du-<lb/>cti, eſtq́, A I, altitudo Solis ſupra Horizontem per A C, ductum, complementum altitudinis E I, ſupra <lb/>priorem Horizontem, efficitur, vt vmbra recta cuiuſcunque altitudinis Solis ſupra Horizontem, eadem <lb/>omnino ſit, quæ vmbra verſa complementi dictæ altitudinis Solis ſupra eundem Horizontem. </s>
  <s xml:id="echoid-s30922" xml:space="preserve">Id quod <lb/>
<anchor type="note" xlink:label="note-0491-15a" xlink:href="note-0491-15"/>
ex demonſtratis etiam patet. </s>
  <s xml:id="echoid-s30923" xml:space="preserve">Quoniam enim eſt, vt ſinus complementi altitudinis Solis ad ſinum ipſius <lb/>altitudinis, ita gnomon ad vmbram verſam, vt demonſtrauimus; </s>
  <s xml:id="echoid-s30924" xml:space="preserve">poſita autem altitudine Solis, quæ cõ-<lb/>plementum ſit altitudinis D I, ita vt D I, ſit viciſſim complementum illius altitudinis, recta I K, eſt <lb/>ſinus complementi altitudinis, &amp; </s>
  <s xml:id="echoid-s30925" xml:space="preserve">E K, ſinus ipſius altitudinis: </s>
  <s xml:id="echoid-s30926" xml:space="preserve">fit, vt cũ ſit, veluti I K, ad K E, ita E F, <lb/>ad F G, recta F G, ſit tunc vmbra verſa, quæ prius vmbra recta erat, &amp;</s>
  <s xml:id="echoid-s30927" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30928" xml:space="preserve">Quæ cum ita ſint, complectetur <lb/>vna eadem{q́ue} tabula &amp; </s>
  <s xml:id="echoid-s30929" xml:space="preserve">vmbras rectas &amp; </s>
  <s xml:id="echoid-s30930" xml:space="preserve">verſas, ſi altitudines Solis in vna parte tabulæ ponantur, &amp; </s>
  <s xml:id="echoid-s30931" xml:space="preserve"><lb/>earundem cõplementa in altera, vt in ſequenti tabula factũ eſſe vides: </s>
  <s xml:id="echoid-s30932" xml:space="preserve">In qua continentur longitudines <lb/>vmbrarum tam rectarum, quam verſarum in partibus, qualium gnomon eſt 12. </s>
  <s xml:id="echoid-s30933" xml:space="preserve">ad ſingulos gradus, &amp; </s>
  <s xml:id="echoid-s30934" xml:space="preserve"><lb/>Minuta altitudinum Solis ſupputatæ. </s>
  <s xml:id="echoid-s30935" xml:space="preserve">Vtemur autem rectis duntaxat vmbris in horologĳs huius lib. <lb/></s>
  <s xml:id="echoid-s30936" xml:space="preserve">(quæ etiam in ſuperioribus libris deſcripſimus.) </s>
  <s xml:id="echoid-s30937" xml:space="preserve">cum ſemper gnomon rectus inſistat planis illorum horo-<lb/>
<anchor type="note" xlink:label="note-0491-16a" xlink:href="note-0491-16"/>
<anchor type="note" xlink:label="note-0491-17a" xlink:href="note-0491-17"/>
logiorum. </s>
  <s xml:id="echoid-s30938" xml:space="preserve">Quod vero diximus de Horizonte, intelligendum etiam eſt de omni plano, cum omnis circu-<lb/>lus maximus, cui planum borologĳ æquidiſtat, Horizon ſit in aliqua regione, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s30939" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1583" type="float" level="2" n="2">
<note position="right" xlink:label="note-0491-14" xlink:href="note-0491-14a" xml:space="preserve">Vmbra recta c@ <lb/>iuſcunque alti-<lb/>tudinis Solis ſu <lb/>pra Horizontẽ <lb/>eadem eſt, quæ <lb/>vmbra verſa cõ <lb/>plementi eiuſdẽ <lb/>altitudinis So-<lb/>lis ſu pra Hor@-<lb/>zontem.</note>
<note position="left" xlink:label="note-0491-15" xlink:href="note-0491-15a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0491-16" xlink:href="note-0491-16a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0491-17" xlink:href="note-0491-17a" xml:space="preserve">Quomodo ex <lb/>ſequenti tabula <lb/>lõgitudines vm <lb/>brarum ſumen-<lb/>dę ſint, ſi ſtylus <lb/>in plures, pau-<lb/>cioresve partes, <lb/>quàna 12. ſeca-<lb/>tur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s30940" xml:space="preserve">QVOD ſi quando gnomon tantæ magnitudinis ſit, vt commode in plures partes diuidi poſſit, vt in <lb/>24. </s>
  <s xml:id="echoid-s30941" xml:space="preserve">duplicandæ erunt ſingulæ vmbræ ſequentis tabulæ. </s>
  <s xml:id="echoid-s30942" xml:space="preserve">Et ſi gnomon diuidatur in partes 36. </s>
  <s xml:id="echoid-s30943" xml:space="preserve">triplicandæ <lb/>crunt, quadruplicandæ autẽ, ſi in 48. </s>
  <s xml:id="echoid-s30944" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30945" xml:space="preserve">quincuplandæ, ſi in 60. </s>
  <s xml:id="echoid-s30946" xml:space="preserve">quia hac ratione ſeruatur eadem ſemper <lb/>proportio, cum partes cũ pariter multiplicibus in eadem ſint ratione. </s>
  <s xml:id="echoid-s30947" xml:space="preserve">Similiter ſi ſtylus tam paruus fue <lb/>
<anchor type="note" xlink:label="note-0491-18a" xlink:href="note-0491-18"/>
rit, vt commode in 12. </s>
  <s xml:id="echoid-s30948" xml:space="preserve">partes diuidi nequeat, diuidatur in 6. </s>
  <s xml:id="echoid-s30949" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30950" xml:space="preserve">ſingularum vmbrarum dimidia ſu-<lb/>mantur, &amp;</s>
  <s xml:id="echoid-s30951" xml:space="preserve">c.</s>
  <s xml:id="echoid-s30952" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1584" type="float" level="2" n="3">
<note position="right" xlink:label="note-0491-18" xlink:href="note-0491-18a" xml:space="preserve">15. quinti.</note>
</div>
</div>
<div xml:id="echoid-div1586" type="section" level="1" n="389">
<head xml:id="echoid-head403" style="it" xml:space="preserve">SEQVITVR TABVLA VMBRARVM.</head>
<pb o="476" file="0492" n="492" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1587" type="section" level="1" n="390">
<head xml:id="echoid-head404" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 0 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # Infinita. # 687. 34 # 343. 44 # 229. 0 # 171. 37 # 137. 10 # 114. 11 # 97. 44 # 85. 23 # 75. 46 # 60 <lb/>1 # 41378. 54 # 676. 20 # 340. 48 # 227. 44 # 170. 55 # 136. 43 # 113. 52 # 97. 30 # 85. 12 # 75. 37 # 59 <lb/>2 # 20689. 27 # 665. 36 # 338. 0 # 226. 28 # 170. 12 # 136. 15 # 113. 33 # 97. 16 # 85. 2 # 75. 29 # 58 <lb/>3 # 13792. 58 # 654. 55 # 335. 15 # 225. 15 # 169. 30 # 135. 48 # 113. 14 # 97. 2 # 84. 51 # 75. 21 # 57 <lb/>4 # 10344. 43 # 644. 41 # 332. 33 # 224. 1 # 168. 48 # 135. 21 # 112. 55 # 97. 48 # 84. 40 # 75. 12 # 56 <lb/>5 # 8275. 47 # 634. 48 # 329. 54 # 222. 48 # 168. 7 # 134. 54 # 112. 36 # 96. 34 # 84. 30 # 75. 3 # 55 <lb/>
6 # 6896. 29 # 625. 12 # 327. 17 # 221. 36 # 167. 26 # 134. 27 # 112. 17 # 96. 21 # 84. 19 # 74. 55 # 54
7 # 5911. 16 # 615. 54 # 324. 43 # 220. 25 # 166. 45 # 134. 1 # 111. 59 # 96. 7 # 84. 9 # 74. 47 # 53
8 # 5172. 22 # 606. 52 # 322. 11 # 219. 15 # 166. 4 # 133. 35 # 111. 40 # 95. 53 # 83. 58 # 74. 38 # 52
9 # 4597. 39 # 597. 47 # 319. 41 # 218. 4 # 165. 24 # 133. 9 # 111. 22 # 95. 40 # 83. 48 # 74. 30 # 51
10 # 4137. 53 # 589. 16 # 317. 14 # 216. 54 # 164. 44 # 132. 43 # 111. 4 # 95. 26 # 83. 37 # 74. 22 # 50
11 # 3761. 43 # 580. 59 # 314. 49 # 215. 46 # 164. 5 # 132. 17 # 110. 46 # 95. 13 # 83. 27 # 74. 14 # 49
12 # 3438. 22 # 572. 56 # 312. 26 # 214. 39 # 163. 26 # 131. 51 # 110. 28 # 94. 59 # 83. 17 # 74. 5 # 48
13 # 3174. 34 # 565. 6 # 310. 5 # 213. 32 # 162. 47 # 131. 26 # 110. 10 # 94. 46 # 83. 6 # 73. 57 # 47
14 # 2948. 22 # 557. 29 # 307. 46 # 212. 26 # 162. 8 # 131. 1 # 109. 52 # 94. 33 # 82. 56 # 73. 49 # 46
15 # 2752. 16 # 550. 4 # 305. 30 # 211. 20 # 161. 30 # 130. 36 # 109. 35 # 94. 20 # 82. 45 # 73. 41 # 45
16 # 2580. 36 # 542. 51 # 303. 10 # 210. 15 # 160. 52 # 130. 10 # 109. 17 # 94. 7 # 82. 36 # 73. 33 # 44
17 # 2429. 6 # 535. 49 # 300. 58 # 209. 11 # 160. 14 # 129. 44 # 108. 59 # 93. 54 # 82. 26 # 73. 25 # 43
18 # 2294. 22 # 528. 58 # 298. 47 # 206. 8 # 159. 37 # 129. 20 # 108. 41 # 93. 41 # 82. 16 # 73. 17 # 42
19 # 2173. 52 # 522. 17 # 296. 38 # 207. 5 # 159. 0 # 128. 57 # 108. 24 # 93. 28 # 82. 6 # 73. 9 # 41
20 # 2065. 23 # 515. 46 # 294. 31 # 206. 3 # 158. 23 # 128. 33 # 108. 7 # 93. 15 # 81. 55 # 73. 1 # 40
21 # 1967. 10 # 509. 24 # 292. 26 # 205. 1 # 157. 46 # 128. 9 # 107. 50 # 93. 2 # 81. 46 # 72. 53 # 39
22 # 1877. 53 # 503. 0 # 290. 23 # 204. 0 # 157. 10 # 127. 45 # 107. 33 # 92. 49 # 81. 36 # 72. 45 # 38
23 # 1793. 40 # 496. 57 # 288. 21 # 203. 0 # 156. 34 # 127. 21 # 107. 16 # 92. 37 # 81. 26 # 72. 37 # 37
24 # 1719. 9 # 491. 3 # 286. 21 # 202. 0 # 155. 58 # 126. 57 # 106. 59 # 92. 24 # 81. 16 # 72. 29 # 36
25 # 1650. 34 # 485. 17 # 284. 23 # 201. 1 # 155. 23 # 126. 34 # 106. 43 # 92. 11 # 81. 6 # 72. 21 # 35
26 # 1587. 15 # 479. 39 # 282. 25 # 202. 2 # 154. 48 # 126. 10 # 106. 26 # 91. 59 # 80. 57 # 72. 14 # 34
27 # 1528. 36 # 474. 9 # 280. 31 # 199. 4 # 154. 13 # 125. 47 # 106. 9 # 91. 46 # 80. 47 # 72. 6 # 33
28 # 1474. 9 # 468. 47 # 278. 37 # 198. 7 # 153. 38 # 125. 24 # 105. 52 # 91. 34 # 80. 37 # 71. 58 # 32
29 # 1423. 13 # 463. 31 # 276. 45 # 197. 10 # 153. 3 # 125. 1 # 105. 36 # 91. 21 # 80. 27 # 71. 50 # 31
30 # 1376. 6 # 458. 22 # 274. 54 # 196. 13 # 152. 29 # 124. 38 # 105. 19 # 91. 9 # 80. 18 # 71. 43 # 30
31 # 1331. 47 # 453. 21 # 273. 1 # 195. 17 # 151. 55 # 124. 15 # 105. 3 # 90. 57 # 80. 8 # 71. 35 # 29
32 # 1290. 15 # 448. 26 # 271. 14 # 194. 22 # 151. 22 # 123. 52 # 104. 47 # 90. 45 # 79. 59 # 71. 27 # 28
33 # 1251. 14 # 443. 37 # 269. 27 # 193. 27 # 150. 48 # 123. 30 # 104. 31 # 90. 33 # 79. 49 # 71. 20 # 27
34 # 1213. 12 # 438. 45 # 267. 42 # 192. 33 # 150. 15 # 123. 7 # 104. 15 # 90. 21 # 79. 40 # 71. 12 # 26
35 # 1178. 43 # 434. 8 # 265. 59 # 191. 38 # 149. 42 # 122 45 # 103. 59 # 90. 8 # 79. 30 # 71. 4 # 25
36 # 1146. 4 # 429. 38 # 264. 17 # 190. 44 # 149. 10 # 122. 23 # 103. 43 # 89. 56 # 79. 21 # 70. 57 # 24
37 # 1115. 10 # 425. 13 # 262. 36 # 189. 51 # 148. 37 # 122. 1 # 103. 27 # 89. 44 # 79. 11 # 70. 49 # 23
38 # 1085. 54 # 420. 53 # 260. 56 # 188. 59 # 148. 5 # 121. 39 # 103. 11 # 89. 32 # 79. 2 # 70. 42 # 22
39 # 1058. 8 # 416. 38 # 259. 18 # 188. 7 # 147. 33 # 121. 18 # 102. 56 # 89. 20 # 78. 53 # 70. 35 # 21
40 # 1031. 45 # 412. 29 # 257. 40 # 187. 16 # 147. 1 # 120. 56 # 102. 40 # 89. 9 # 78. 44 # 70. 27 # 20
41 # 1006. 38 # 408. 24 # 256. 4 # 186. 25 # 146. 29 # 120. 35 # 102. 25 # 88. 57 # 78. 34 # 70. 20 # 19
42 # 982. 43 # 404. 24 # 254. 30 # 185. 34 # 145. 58 # 120. 14 # 102. 9 # 88. 45 # 78. 25 # 70. 12 # 18
43 # 959. 55 # 400. 29 # 252. 56 # 184. 44 # 145. 27 # 119. 53 # 101. 54 # 88. 33 # 78. 16 # 70. 5 # 17
44 # 938. 9 # 396. 38 # 251. 23 # 183. 55 # 144. 57 # 119. 32 # 101. 39 # 88. 22 # 78. 7 # 69. 58 # 16
45 # 917. 21 # 392. 52 # 249. 52 # 183. 6 # 144. 26 # 119. 11 # 101. 24 # 88. 10 # 77. 58 # 69. 50 # 15
46 # 896. 47 # 389. 10 # 248. 22 # 182. 17 # 143. 55 # 118. 50 # 101. 8 # 87. 59 # 77. 49 # 69. 43 # 14
47 # 877. 45 # 385. 25 # 246. 53 # 181. 29 # 143. 25 # 118. 29 # 100. 53 # 87. 47 # 77. 40 # 69. 36 # 13
48 # 859. 31 # 381. 51 # 245. 24 # 180. 41 # 142. 55 # 118. 8 # 100. 38 # 87. 36 # 77. 31 # 69. 29 # 12
49 # 842. 1 # 378. 21 # 243. 54 # 179. 53 # 142. 25 # 117. 48 # 100. 23 # 87. 25 # 77. 22 # 69. 21 # 11
50 # 825. 13 # 374. 55 # 242. 28 # 179. 6 # 141. 56 # 117. 28 # 100. 8 # 87. 14 # 77. 13 # 69. 14 # 10
51 # 809. 4 # 371. 33 # 241. 11 # 178. 20 # 141. 26 # 117. 8 # 99. 54 # 87. 2 # 77. 4 # 69. 7 # 9
52 # 793. 54 # 368. 14 # 239. 39 # 177. 34 # 140. 57 # 116. 47 # 99. 39 # 86. 51 # 76. 56 # 69. 0 # 8
53 # 778. 37 # 364. 59 # 238. 16 # 176. 48 # 140. 28 # 116. 27 # 99. 25 # 86. 40 # 76. 47 # 68. 53 # 7
54 # 764. 14 # 361. 48 # 236. 54 # 176. 2 # 139. 59 # 116. 7 # 99. 10 # 86. 29 # 76. 38 # 68. 46 # 6
55 # 750. 22 # 358. 39 # 235. 32 # 175. 17 # 139. 30 # 115. 48 # 98. 56 # 86. 18 # 76. 29 # 68. 38 # 5
56 # 737. 0 # 355. 34 # 234. 12 # 174. 32 # 139. 2 # 115. 28 # 98. 41 # 86. 7 # 76. 20 # 68. 31 # 4
57 # 724. 6 # 352. 32 # 232. 53 # 173. 48 # 138. 34 # 115. 8 # 98. 27 # 85. 56 # 76. 11 # 68. 24 # 3
58 # 711. 13 # 349. 33 # 231. 34 # 173. 4 # 138. 6 # 114. 49 # 98. 12 # 85. 34 # 76. 3 # 68. 17 # 2
59 # 699. 12 # 346. 37 # 230. 17 # 172. 21 # 138. 38 # 114. 30 # 97. 58 # # 75. 54 # 68. 10 # 1
60 # 687. 34 # 343. 44 # 229. 0 # 171. 37 # 137. 10 # 114. 11 # 97. 44 # 85. 23 # 75. 46 # 68. 3 # 0
# 89 # 88 # 87 # 86 # 85 # 84 # 83 # 82 # 81 # 80
</note>
</div>
<div xml:id="echoid-div1588" type="section" level="1" n="391">
<head xml:id="echoid-head405" style="it" xml:space="preserve">Gradus allitudinum Solis pro vmbris verſis.</head>
<pb o="477" file="0493" n="493" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1589" type="section" level="1" n="392">
<head xml:id="echoid-head406" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G # G. # G. # G. # G. # G # G. # G. <lb/># 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 <lb/>M. # Par. Mi. # P. M. # P. M # P. M # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 68. 3 # 61. 44 # 56. 27 # 51. 59 # 48. 8 # 44. 47 # 41. 51 # 39. 15 # 36. 56 # 34. 51 # 60 <lb/>1 # 67. 57 # 61. 40 # 56. 23 # 51. 55 # 48. 4 # 44. 44 # 41. 48 # 39. 13 # 36. 54 # 34. 49 # 59 <lb/>2 # 67. 49 # 61. 33 # 56. 18 # 51. 50 # 48. 1 # 44. 41 # 41. 45 # 39. 10 # 36. 52 # 34. 47 # 58 <lb/>3 # 67. 43 # 61. 27 # 56. 13 # 51. 46 # 47. 57 # 44. 38 # 41. 43 # 39. 8 # 36. 49 # 34. 45 # 57 <lb/>4 # 67. 36 # 61. 21 # 56. 8 # 51. 42 # 47. 54 # 44. 35 # 41. 40 # 39. 5 # 36. 47 # 34. 43 # 56 <lb/>5 # 67. 29 # 61. 16 # 56. 3 # 51. 38 # 47. 50 # 44. 31 # 41. 37 # 39. 3 # 36. 45 # 34. 41 # 55 <lb/>
6 # 67. 22 # 61. 10 # 55. 59 # 51. 34 # 47. 46 # 44. 28 # 41. 35 # 39. 0 # 36. 43 # 34. 39 # 54
7 # 67. 15 # 61. 4 # 55. 54 # 51. 30 # 47. 43 # 44. 25 # 41. 32 # 38. 58 # 36. 41 # 34. 37 # 53
8 # 67. 9 # 60. 59 # 55. 49 # 51. 26 # 47. 39 # 44. 22 # 41. 29 # 38. 56 # 36. 39 # 34. 35 # 52
9 # 67. 2 # 60. 53 # 55. 44 # 51. 22 # 47. 36 # 44. 19 # 41. 26 # 38. 53 # 36. 36 # 34. 33 # 51
10 # 66. 55 # 60. 47 # 55. 40 # 51. 18 # 47. 32 # 44. 16 # 41. 24 # 38. 51 # 36. 34 # 34. 31 # 50
11 # 66. 48 # 60. 41 # 55. 35 # 51. 14 # 47. 29 # 44. 13 # 41. 21 # 38. 48 # 36. 32 # 34. 30 # 49
12 # 66. 42 # 60. 36 # 55. 30 # 51. 10 # 47. 25 # 44. 10 # 41. 18 # 38. 46 # 36. 30 # 34. 28 # 48
13 # 66. 35 # 60. 31 # 55. 26 # 51. 6 # 47. 22 # 44. 7 # 41. 16 # 38. 44 # 36. 28 # 34. 26 # 47
14 # 66. 28 # 60. 25 # 55. 21 # 51. 2 # 47. 18 # 44. 4 # 41. 13 # 38. 41 # 36. 26 # 34. 24 # 46
15 # 66. 22 # 60. 20 # 55. 16 # 50. 58 # 47. 15 # 44. 1 # 41. 10 # 38. 39 # 36. 23 # 34. 22 # 45
16 # 66. 15 # 60. 14 # 55. 11 # 50. 54 # 47. 12 # 43. 58 # 41. 8 # 38. 36 # 36. 21 # 34. 20 # 44
17 # 66. 9 # 60. 9 # 55. 7 # 50. 50 # 47. 8 # 43. 55 # 41. 5 # 38. 34 # 36. 19 # 34. 18 # 43
18 # 66. 2 # 60. 3 # 55. 2 # 50. 46 # 47. 5 # 43. 52 # 41. 2 # 38. 32 # 36. 17 # 34. 16 # 42
19 # 65. 55 # 59. 58 # 54. 58 # 50. 42 # 47. 1 # 43. 49 # 41. 0 # 38. 29 # 36. 15 # 34. 14 # 41
20 # 65. 49 # 59. 52 # 54. 53 # 50. 38 # 46. 58 # 43. 46 # 40. 57 # 38. 27 # 36. 13 # 34. 12 # 40
21 # 65. 43 # 59. 47 # 54. 48 # 50. 34 # 46. 54 # 43. 43 # 40. 54 # 38. 25 # 36. 11 # 34. 10 # 39
22 # 65. 36 # 59. 42 # 54. 44 # 50. 30 # 46. 51 # 43. 40 # 40. 52 # 38. 22 # 26. 9 # 34. 8 # 38
23 # 65. 29 # 59. 36 # 54 39 # 50. 26 # 46. 48 # 43. 37 # 40. 49 # 38. 20 # 36. 7 # 34. 6 # 37
24 # 65. 23 # 59. 31 # 54. 35 # 50. 22 # 46. 44 # 43. 34 # 40. 46 # 38. 18 # 36. 4 # 34. 5 # 36
25 # 65. 17 # 59. 25 # 54. 30 # 50 18 # 46. 41 # 43. 31 # 40. 44 # 38. 15 # 36. 2 # 34. 3 # 35
26 # 65. 10 # 59. 20 # 54. 26 # 50. 14 # 46. 37 # 43. 28 # 40. 41 # 38. 13 # 36. 0 # 34. 1 # 34
27 # 65. 4 # 59. 15 # 54. 21 # 50. 11 # 46. 34 # 43. 25 # 40. 39 # 38. 11 # 35. 58 # 33. 59 # 33
28 # 64. 57 # 59. 10 # 54. 17 # 50. 7 # 46. 31 # 43. 22 # 40. 36 # 38. 8 # 35. 56 # 33. 57 # 32
29 # 64. 51 # 59. 4 # 54. 12 # 50. 3 # 46. 27 # 43. 19 # 40. 33 # 38. 6 # 35. 54 # 33<unsure/>. 55 # 31
30 # 64. 45 # 58. 59 # 54. 8 # 49. 59 # 46. 24 # 43. 16 # 40. 31 # 38. 4 # 35. 52 # 33. 53 # 30
31 # 64. 39 # 58. 53 # 54. 3 # 49. 55 # 46. 21 # 43. 13 # 40. 28 # 38. 1 # 35. 50 # 33. 51 # 29
32 # 64. 32 # 58. 49 # 53. 59 # 49. 51 # 46. 17 # 43. 10 # 40. 26 # 37. 59 # 35. 48 # 33. 49 # 28
33 # 64. 26 # 58. 43 # 53. 54 # 49. 47 # 46. 14 # 43. 8 # 40. 23 # 37. 57 # 35. 46 # 33. 48 # 27
34 # 64. 23 # 58. 38 # 53. 50 # 49. 44 # 46. 11 # 43. 5 # 40. 20 # 37. 54 # 35. 44 # 33. 46 # 26
35 # 64. 14 # 58. 33 # 53. 46 # 49. 40 # 46. 8 # 43. 2 # 40. 18 # 37. 52 # 35. 42 # 33. 44 # 25
36 # 64. 7 # 58. 28 # 53. 41 # 49. 36 # 46. 4 # 42. 59 # 40. 15 # 37. 50 # 35. 39 # 33. 42 # 24
37 # 64. 1 # 58. 22 # 53. 37 # 49. 32 # 46. 1 # 42. 56 # 40. 12 # 37. 47 # 35. 37 # 33. 40 # 23
38 # 63. 55 # 58. 17 # 53. 32 # 49. 29 # 45. 58 # 42. 53 # 40. 10 # 37. 45 # 35. 35 # 33. 38 # 22
39 # 63. 49 # 58. 12 # 53. 28 # 49. 25 # 45. 54 # 42. 50 # 40. 8 # 37. 43 # 35. 33 # 33. 36 # 21
40 # 63. 43 # 58. 7 # 53. 24 # 49. 21 # 45. 51 # 42. 47 # 40. 5 # 37. 41 # 35. 31 # 33. 35 # 20
41 # 63. 37 # 58. 2 # 53. 19 # 49. 17 # 45. 48 # 42. 44 # 40. 2 # 37. 38 # 35. 29 # 33. 33 # 19
42 # 63. 31 # 57. 57 # 53. 15 # 49. 13 # 45. 45 # 42. 41 # 40. 0 # 37. 36 # 35. 27 # 33. 31 # 18
43 # 63. 24 # 57. 52 # 53. 11 # 49. 10 # 45. 41 # 42. 39 # 39. 57 # 37. 34 # 35. 25 # 33. 29 # 17
44 # 63. 19 # 57. 49 # 53. 6 # 49. 6 # 45. 38 # 42. 36 # 39. 55 # 37. 32 # 35. 23 # 33. 27 # 16
45 # 63. 12 # 57. 42 # 53. 2 # 49. 2 # 45. 35 # 42. 33 # 39. 52 # 37. 29 # 35. 21 # 33. 25 # 15
46 # 63. 7 # 57. 37 # 52. 58 # 48. 59 # 45. 32 # 42. 30 # 39. 50 # 37. 27 # 35. 19 # 33. 24 # 14
47 # 63. 0 # 57. 31 # 52. 53 # 48. 55 # 45. 28 # 42. 27 # 39. 47 # 37. 25 # 35. 17 # 33. 22 # 13
48 # 62. 54 # 57. 26 # 52. 49 # 48. 51 # 45. 25 # 42. 25 # 39. 45 # 37. 23 # 35. 15 # 33. 20 # 12
49 # 62. 49 # 57. 21 # 52. 45 # 48. 48 # 45. 22 # 42. 22 # 39. 42 # 37. 20 # 35. 13 # 33. 18 # 11
50 # 62. 43 # 57. 16 # 52. 41 # 48. 44 # 45. 19 # 42. 19 # 39. 40 # 37. 18 # 35. 11 # 33. 16 # 10
51 # 62. 37 # 57. 11 # 52. 36 # 48. 40 # 45. 16 # 42. 16 # 39. 37 # 37. 16 # 35. 9 # 33. 14 # 9
52 # 62. 29 # 57. 7 # 52. 32 # 48. 37 # 45. 12 # 42. 13 # 39. 35 # 37. 14 # 35. 7 # 33. 13 # 8
53 # 62. 25 # 57. 2 # 52. 28 # 48. 33 # 45. 9 # 42. 10 # 39. 32 # 37. 11 # 35. 5 # 33. 11 # 7
54 # 62. 19 # 56. 57 # 52. 24 # 48. 29 # 45. 6 # 42. 7 # 39. 30 # 37. 9 # 35. 3 # 33. 9 # 6
55 # 62. 13 # 56. 52 # 52. 20 # 48. 26 # 45. 3 # 42. 5 # 39. 27 # 37. 7 # 35. 1 # 33. 7 # 5
56 # 62. 7 # 56. 47 # 52. 16 # 48. 22 # 45. 0 # 42. 2 # 39. 25 # 37. 5 # 34. 59 # 33. 5 # 4
57 # 62. 1 # 56. 42 # 52. 12 # 48. 18 # 44. 57 # 41. 59 # 39. 22 # 37. 3 # 34. 57 # 33. 4 # 3
58 # 61. 56 # 56. 37 # 52. 7 # 48. 15 # 44. 53 # 41. 57 # 39. 20 # 37. 0 # 34. 55 # 33. 2 # 2
59 # 61. 50 # 56. 32 # 52. 3 # 48. 11 # 44. 50 # 41. 54 # 39. 17 # 36. 58 # 34. 53 # 33. 0 # 1
60 # 61. 44 # 56. 27 # 51. 59 # 48. 8 # 44. 47 # 41. 51 # 39. 15 # 36. 56 # 34. 51 # 32. 58 # 0
# 79 # 78 # 77 # 76 # 75 # 74 # 73 # 72 # 71 # 70
</note>
</div>
<div xml:id="echoid-div1590" type="section" level="1" n="393">
<head xml:id="echoid-head407" style="it" xml:space="preserve">Gradus altudinum Solis pro vmbris verſis.</head>
<pb o="478" file="0494" n="494" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1591" type="section" level="1" n="394">
<head xml:id="echoid-head408" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 20 # 21 # 22 # 23 # 24 # 25 # 26 # 27 # 28 # 29 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 32. 58 # 31. 16 # 29. 42 # 28. 16 # 26. 57 # 25. 44 # 24. 36 # 23. 33 # 22. 34 # 21. 39 # 60 <lb/>1 # 32. 56 # 31. 14 # 29. 41 # 28. 15 # 26. 56 # 25. 43 # 24. 35 # 23. 32 # 22. 33 # 21. 38 # 59 <lb/>2 # 32. 55 # 31. 12 # 29. 39 # 28. 13 # 26. 55 # 25. 42 # 24. 34 # 23. 31 # 22. 32 # 21. 37 # 58 <lb/>3 # 32. 53 # 31. 11 # 29. 38 # 28. 12 # 26. 53 # 25. 41 # 24. 33 # 23. 30 # 22. 31 # 21. 36 # 57 <lb/>4 # 32. 51 # 31. 9 # 39. 36 # 28. 11 # 26. 52 # 25. 39 # 24. 32 # 23. 29 # 22. 30 # 21. 35 # 56 <lb/>5 # 32. 49 # 31. 8 # 29. 35 # 28. 9 # 26. 51 # 25. 38 # 24. 31 # 23. 28 # 22. 29 # 21. 34 # 55 <lb/>
6 # 32. 48 # 31. 6 # 29. 33 # 28. 8 # 26. 50 # 25. 37 # 24. 30 # 23. 27 # 22. 28 # 21. 34 # 54
7 # 32. 46 # 31. 4 # 29. 32 # 28. 7 # 26. 48 # 25. 36 # 24. 28 # 23. 26 # 22. 28 # 21. 33 # 53
8 # 32. 44 # 31. 3 # 29. 30 # 28. 5 # 26. 47 # 25. 35 # 24. 27 # 23. 25 # 22. 27 # 21. 32 # 52
9 # 32. 42 # 31. 1 # 29. 29 # 28. 4 # 26. 46 # 25. 34 # 24. 26 # 23. 24 # 22. 26 # 21. 31 # 51
10 # 32. 40 # 31. 0 # 29. 27 # 28. 3 # 26. 45 # 25. 32 # 24. 25 # 23. 23 # 22. 25 # 21. 30 # 50
11 # 32. 39 # 30. 58 # 29. 26 # 28. 1 # 26. 43 # 25. 31 # 24. 24 # 23. 22 # 22. 24 # 21. 29 # 49
12 # 32. 37 # 30. 56 # 29. 24 # 28. 0 # 26. 42 # 25. 30 # 24. 23 # 23. 21 # 22. 23 # 21. 28 # 48
13 # 32. 35 # 30. 55 # 29. 23 # 27. 59 # 26. 41 # 25. 29 # 24. 22 # 23. 20 # 22. 22 # 21. 27 # 47
14 # 32. 33 # 30. 53 # 29. 21 # 27. 57 # 26. 40 # 25. 28 # 24. 21 # 23. 19 # 22. 21 # 21. 27 # 46
15 # 32. 32 # 30. 52 # 29. 20 # 27. 56 # 26. 38 # 25. 27 # 24. 20 # 23. 18 # 22. 20 # 21. 26 # 45
16 # 32. 30 # 30. 50 # 29. 18 # 27. 54 # 26. 37 # 25. 26 # 24. 19 # 23. 17 # 22. 19 # 21. 25 # 44
17 # 32. 28 # 30. 48 # 29. 17 # 27. 53 # 26. 36 # 25. 24 # 24. 18 # 23. 16 # 22. 18 # 21. 24 # 43
18 # 32. 26 # 30. 47 # 29. 16 # 27. 52 # 26. 35 # 25. 23 # 24. 17 # 23. 15 # 22. 17 # 21. 23 # 42
19 # 32. 25 # 30. 45 # 29. 14 # 27. 50 # 26. 33 # 25. 22 # 24. 16 # 23. 14 # 22. 16 # 21. 22 # 41
20 # 32. 23 # 30. 44 # 29. 13 # 27. 49 # 26. 32 # 25. 21 # 24. 15 # 23. 13 # 22. 15 # 21. 21 # 40
21 # 32. 21 # 30. 42 # 29. 11 # 27. 48 # 26. 31 # 25. 20 # 24. 14 # 23. 12 # 22. 14 # 21. 20 # 39
22 # 32. 20 # 30. 40 # 29. 10 # 27. 46 # 26. 30 # 25. 19 # 24. 13 # 23. 11 # 22. 13 # 21. 20 # 38
23 # 32. 18 # 30. 38 # 29. 8 # 27. 45 # 26. 28 # 25. 17 # 24. 12 # 23. 10 # 22. 13 # 21. 19 # 37
24 # 32. 16 # 30. 37 # 29. 7 # 27. 44 # 26. 27 # 25. 16 # 24. 10 # 23. 9 # 22. 12 # 21. 18 # 36
25 # 32. 14 # 30. 36 # 29. 5 # 27. 42 # 26. 26 # 25. 15 # 24. 9 # 23. 8 # 22. 11 # 21. 17 # 35
26 # 32. 13 # 30. 34 # 29. 4 # 27. 41 # 26. 25 # 25. 14 # 24. 8 # 23. 7 # 22. 10 # 21. 16 # 34
27 # 32. 11 # 30. 33 # 29. 3 # 27. 40 # 26. 24 # 25. 13 # 24. 7 # 23. 6 # 22. 9 # 21. 15 # 33
28 # 32. 9 # 30. 31 # 29. 1 # 27. 39 # 26. 22 # 25. 12 # 24. 6 # 23. 5 # 22. 8 # 21. 14 # 32
29 # 32. 8 # 30. 29 # 29. 0 # 27. 37 # 26. 21 # 25. 11 # 24. 5 # 23. 4 # 22. 7 # 21. 13 # 31
30 # 32. 6 # 30. 28 # 28. 58 # 27. 36 # 26. 20 # 25. 10 # 24. 4 # 13. 3 # 22. 6 # 21. 13 # 30
31 # 32. 4 # 30. 26 # 28. 57 # 27. 35 # 26. 19 # 25. 8 # 24. 3 # 23. 2 # 22. 5 # 21. 12 # 29
32 # 32. 2 # 30. 25 # 28. 55 # 27. 33 # 26. 17 # 25. 7 # 24. 2 # 23. 1 # 12. 4 # 21. 11 # 28
33 # 32. 1 # 30. 23 # 28. 54 # 27. 32 # 26. 16 # 25. 6 # 24. 1 # 23. 0 # 22. 3 # 21. 10 # 27
34 # 31. 59 # 30. 22 # 28. 53 # 27. 30 # 26. 15 # 25. 5 # 24. 0 # 22. 59 # 22. 2 # 21. 9 # 26
35 # 31. 57 # 30. 20 # 28. 51 # 27. 29 # 26. 14 # 25. 4 # 23. 59 # 22. 58 # 22. 2 # 21. 8 # 25
36 # 31. 56 # 30. 19 # 28. 50 # 27. 28 # 26. 12 # 25. 3 # 23. 58 # 22. 57 # 22. 1 # 21. 7 # 24
37 # 31. 54 # 30. 17 # 28. 48 # 27. 27 # 26. 11 # 25. 2 # 23. 57 # 22. 56 # 22. 0 # 21. 7 # 23
38 # 31. 52 # 30. 16 # 28. 47 # 27. 25 # 26. 10 # 25. 1 # 23. 56 # 22. 55 # 21. 59 # 21. 6 # 22
39 # 31. 51 # 30. 14 # 28. 45 # 27. 24 # 26. 9 # 24. 59 # 23. 55 # 22. 54 # 21. 58 # 21. 5 # 21
40 # 31. 49 # 30. 12 # 28. 44 # 27. 23 # 26. 8 # 24. 58 # 23. 54 # 22. 53 # 21. 57 # 21. 4 # 20
41 # 31. 47 # 30. 10 # 28. 43 # 27. 21 # 26. 7 # 24. 57 # 23. 53 # 22. 52 # 21. 56 # 21. 3 # 19
42 # 31. 46 # 30. 9 # 28. 41 # 27. 20 # 26. 5 # 24. 56 # 23. 52 # 22. 51 # 21. 55 # 21. 2 # 18
43 # 31. 44 # 30. 8 # 28. 40 # 27. 19 # 26. 4 # 24. 55 # 23. 51 # 22. 50 # 21. 54 # 21. 1 # 17
44 # 31. 42 # 30. 6 # 28. 38 # 27. 18 # 26. 3 # 24. 54 # 23. 50 # 22. 49 # 21. 53 # 21. 1 # 16
45 # 31. 40 # 30. 5 # 28. 37 # 27. 16 # 26. 2 # 24. 53 # 23. 48 # 22. 48 # 21. 52 # 21. 0 # 15
46 # 31. 39 # 30. 3 # 28. 36 # 27. 15 # 26. 0 # 24. 52 # 23. 47 # 22. 48 # 21. 51 # 20. 59 # 14
47 # 31. 37 # 30. 2 # 28. 34 # 27. 14 # 25. 59 # 24. 51 # 23. 46 # 22. 47 # 21. 51 # 20. 58 # 13
48 # 31. 36 # 30. 0 # 28. 33 # 27. 12 # 25. 58 # 24. 49 # 23. 45 # 22. 46 # 21. 50 # 20. 57 # 12
49 # 31. 34 # 29. 59 # 28. 31 # 27. 11 # 25. 57 # 24. 48 # 23. 44 # 22. 45 # 21. 49 # 20. 56 # 11
50 # 31. 32 # 29. 57 # 28. 30 # 27. 10 # 25. 56 # 24. 47 # 23. 43 # 22. 44 # 21. 48 # 20. 56 # 10
51 # 31. 31 # 29. 56 # 28. 28 # 27. 9 # 25. 55 # 24. 46 # 23. 42 # 22. 43 # 21. 47 # 20. 55 # 9
52 # 31. 29 # 29. 54 # 28. 27 # 27. 7 # 25. 53 # 24. 45 # 23. 41 # 22. 42 # 21. 46 # 20. 54 # 8
53 # 31. 27 # 29. 53 # 28. 26 # 27. 6 # 25. 52 # 24. 44 # 23. 40 # 22. 41 # 21. 45 # 20. 53 # 7
54 # 31. 26 # 29. 51 # 28. 24 # 27. 5 # 25. 51 # 24. 43 # 23. 39 # 22. 40 # 21. 44 # 20. 52 # 6
55 # 31. 24 # 29. 50 # 28. 23 # 27. 4 # 25. 50 # 24. 42 # 23. 38 # 22. 39 # 21. 43 # 20. 51 # 5
56 # 31. 22 # 29. 48 # 88. 22 # 27. 2 # 25. 49 # 24. 41 # 23. 37 # 22. 38 # 21. 42 # 20. 50 # 4
57 # 31. 21 # 29. 47 # 28. 20 # 27. 1 # 25. 48 # 24. 40 # 23. 36 # 22. 37 # 21. 42 # 20. 50 # 3
58 # 31. 19 # 29. 45 # 28. 19 # 27. 0 # 25. 46 # 24. 38 # 23. 35 # 22. 36 # 21. 41 # 20. 49 # 2
59 # 31. 17 # 29. 44 # 28. 18 # 26. 58 # 25. 45 # 24. 37 # 23. 34 # 22. 35 # 21. 40 # 20. 48 # 1
60 # 31. 16 # 29. 42 # 28. 16 # 26. 57 # 25. 44 # 24. 36 # 23. 33 # 22. 34 # 21. 39 # 20. 47 # 0
# 69 # 68 # 67 # 66 # 65 # 64 # 63 # 62 # 61 # 60
</note>
</div>
<div xml:id="echoid-div1592" type="section" level="1" n="395">
<head xml:id="echoid-head409" style="it" xml:space="preserve">Graaus altuudinum Solis pro vmbris verſis.</head>
<pb o="479" file="0495" n="495" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1593" type="section" level="1" n="396">
<head xml:id="echoid-head410" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 30 # 31 # 32 # 33 # 34 # 35 # 36 # 37 # 38 # 39 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 20. 47 # 19. 58 # 19. 12 # 18. 29 # 17. 47 # 17. 8 # 16. 31 # 15. 55 # 15. 22 # 14. 49 # 60 <lb/>1 # 20. 46 # 19. 57 # 19. 12 # 18. 28 # 17. 47 # 17. 8 # 16. 30 # 15. 55 # 15. 21 # 14. 49 # 59 <lb/>2 # 20. 45 # 19. 57 # 19. 11 # 18. 27 # 17. 46 # 17. 7 # 16. 30 # 15. 54 # 15. 20 # 14. 48 # 58 <lb/>3 # 20. 45 # 19. 56 # 19. 10 # 18. 27 # 17. 45 # 17. 6 # 16. 29 # 15. 54 # 15. 20 # 14. 47 # 57 <lb/>4 # 20. 44 # 19. 55 # 19. 9 # 18. 26 # 17. 45 # 17. 6 # 16. 29 # 15. 53 # 15. 19 # 14. 47 # 56 <lb/>
5 # 20. 43 # 19. 54 # 19. 9 # 18. 25 # 17. 44 # 17. 5 # 16. 28 # 15. 53 # 15. 19 # 14. 46 # 55
6 # 20. 42 # 19. 54 # 19. 8 # 18. 24 # 17. 43 # 17. 4 # 16. 27 # 15. 52 # 15. 18 # 14. 46 # 54
7 # 20. 41 # 19. 53 # 19. 7 # 18. 24 # 17. 43 # 17. 4 # 16. 27 # 15. 51 # 15. 18 # 14. 45 # 53
8 # 20. 41 # 19. 52 # 19. 6 # 18. 23 # 17. 42 # 17. 3 # 16. 26 # 15. 51 # 15. 17 # 14. 45 # 52
9 # 20. 40 # 19. 51 # 19. 6 # 18. 22 # 17. 41 # 17. 3 # 16. 26 # 15. 50 # 15. 17 # 14 44 # 51
10 # 20. 39 # 19. 50 # 19. 5 # 18. 22 # 17. 41 # 17. 2 # 16. 25 # 15. 50 # 15. 16 # 14. 44 # 50
11 # 20. 38 # 19 50 # 19 4 # 18. 21 # 17. 40 # 17. 1 # 16. 24 # 15. 49 # 15. 16 # 14. 43 # 49
12 # 20. 37 # 19. 49 # 19 3 # 18. 20 # 17. 39 # 17. 1 # 16. 24 # 15. 49 # 15. 15 # 14. 43 # 48
13 # 20. 36 # 19 48 # 19 3 # 18. 20 # 17. 39 # 17. 0 # 16. 23 # 15. 48 # 15. 14 # 14. 42 # 47
14 # 20. 35 # 19 47 # 19. 2 # 18. 19 # 17. 38 # 16. 59 # 16. 23 # 15. 47 # 15. 14 # 14. 42 # 46
15 # 20 35 # 19. 47 # 19. 1 # 18. 18 # 17. 37 # 16. 59 # 16. 22 # 15. 47 # 15. 13 # 14. 41 # 45
16 # 20. 34 # 19. 46 # 19. 0 # 18. 17 # 17. 37 # 16. 58 # 16. 21 # 15. 46 # 15. 13 # 14. 41 # 44
17 # 20. 33 # 19. 45 # 19. 0 # 18. 17 # 17. 36 # 16. 58 # 16. 21 # 15. 46 # 15. 12 # 14. 40 # 43
18 # 20 32 # 19 44 # 18. 59 # 18. 16 # 17. 35 # 16. 57 # 16. 20 # 15. 45 # 15. 12 # 14. 40 # 42
19 # 20. 31 # 19. 44 # 18. 58 # 18. 15 # 17. 35 # 16. 56 # 16. 20 # 15. 45 # 15. 11 # 14. 39 # 41
20 # 20. 31 # 19. 43 # 18. 57 # 18. 15 # 17. 34 # 16. 56 # 16. 19 # 15. 44 # 15. 11 # 14. 39 # 40
21 # 20. 30 # 19. 42 # 18. 57 # 18. 14 # 17. 34 # 16. 55 # 16. 18 # 15. 43 # 15. 10 # 14. 38 # 39
22 # 20. 29 # 19. 41 # 18. 56 # 18. 13 # 17. 33 # 16. 54 # 16. 18 # 15. 43 # 15. 9 # 14. 38 # 38
23 # 20. 28 # 19. 40 # 18. 55 # 18. 13 # 17. 32 # 16. 54 # 16. 17 # 15. 42 # 15. 9 # 14. 37 # 37
24 # 20. 27 # 19. 40 # 18. 55 # 18. 12 # 17. 32 # 16. 53 # 16. 17 # 15. 42 # 15. 8 # 14. 37 # 36
25 # 20. 26 # 19. 39 # 18. 54 # 18. 11 # 17. 31 # 16. 53 # 16. 16 # 15. 41 # 15. 8 # 14. 36 # 35
26 # 20. 26 # 19. 38 # 18. 53 # 18. 11 # 17. 30 # 16. 52 # 16. 15 # 15. 41 # 15. 7 # 14. 35 # 34
27 # 20. 25 # 19. 37 # 18. 52 # 18. 10 # 17. 30 # 16. 51 # 16. 15 # 15. 40 # 15. 7 # 14. 35 # 33
28 # 20. 24 # 19. 36 # 18. 52 # 18. 9 # 17. 29 # 16. 51 # 16. 14 # 15. 39 # 15. 6 # 14. 34 # 32
29 # 20. 23 # 19. 36 # 18. 51 # 18. 8 # 17. 28 # 16. 50 # 16. 14 # 15. 39 # 15. 6 # 14. 34 # 31
30 # 20. 22 # 19. 35 # 18. 50 # 18. 8 # 17. 28 # 16. 49 # 16. 13 # 15. 38 # 15. 5 # 14. 33 # 30
31 # 20. 22 # 19. 34 # 18. 49 # 18. 7 # 17. 27 # 16. 49 # 16. 12 # 15. 38 # 15. 5 # 14. 33 # 29
32 # 20. 21 # 19. 33 # 18. 49 # 18. 6 # 17. 26 # 16. 48 # 16. 12 # 15. 37 # 15. 4 # 14. 32 # 28
33 # 20. 20 # 19. 33 # 18. 48 # 18. 6 # 17. 26 # 16. 48 # 16. 11 # 15. 37 # 15. 4 # 14. 32 # 27
34 # 20. 19 # 19. 32 # 18. 47 # 18. 5 # 17. 25 # 16. 47 # 16. 11 # 15. 36 # 15. 3 # 14. 31 # 26
35 # 20. 18 # 19. 31 # 18. 47 # 18. 4 # 17. 24 # 16. 46 # 16. 10 # 15. 36 # 15. 3 # 14. 31 # 25
36 # 20. 17 # 19. 30 # 18. 46 # 18. 4 # 17. 24 # 16. 46 # 16. 9 # 15. 35 # 15. 2 # 14. 30 # 24
37 # 20. 17 # 19. 30 # 18. 45 # 18. 3 # 17. 23 # 16. 45 # 16. 9 # 15. 34 # 15. 1 # 14. 30 # 23
38 # 20. 16 # 19. 29 # 18. 44 # 18. 2 # 17. 22 # 16. 44 # 16. 8 # 15. 34 # 15. 1 # 14. 29 # 22
39 # 20. 15 # 19. 28 # 18. 44 # 18. 2 # 17. 22 # 16. 44 # 16. 8 # 15. 33 # 15. 0 # 14. 29 # 21
40 # 20. 14 # 19. 27 # 18. 43 # 18. 1 # 17. 21 # 16. 43 # 16. 7 # 15. 33 # 15. 0 # 14. 28 # 20
41 # 20. 13 # 19. 27 # 18. 42 # 18. 0 # 17. 20 # 16. 43 # 16. 6 # 15. 32 # 14. 59 # 14. 28 # 19
42 # 20. 13 # 19. 26 # 18. 42 # 18. 0 # 17. 20 # 16. 42 # 16. 6 # 15. 32 # 14. 59 # 14. 27 # 18
43 # 20. 12 # 19. 25 # 18. 41 # 17. 59 # 17. 19 # 16. 41 # 16. 5 # 15. 31 # 14. 58 # 14. 27 # 17
44 # 20. 11 # 19. 24 # 18. 40 # 17. 58 # 17. 19 # 16. 41 # 16. 5 # 15. 30 # 14. 58 # 14. 26 # 16
45 # 20. 10 # 19. 24 # 18. 39 # 17. 58 # 17. 18 # 16. 40 # 16. 4 # 15. 30 # 14. 57 # 14. 26 # 15
46 # 20. 9 # 19. 23 # 18. 39 # 17. 57 # 17. 17 # 16. 40 # 16. 4 # 15. 29 # 14. 57 # 14. 25 # 14
47 # 20. 9 # 19. 22 # 18. 38 # 17. 56 # 17. 17 # 16. 39 # 16. 3 # 15. 29 # 14. 56 # 14. 25 # 13
48 # 20. 8 # 19. 21 # 18. 37 # 17. 56 # 17. 16 # 16. 38 # 16. 2 # 15. 28 # 14. 55 # 14. 24 # 12
49 # 20. 7 # 19. 20 # 18. 37 # 17. 55 # 17. 15 # 16. 38 # 16. 2 # 15. 28 # 14. 55 # 14. 24 # 11
50 # 20. 6 # 19. 20 # 18. 36 # 17. 54 # 17. 15 # 16. 37 # 16. 1 # 15. 27 # 14. 54 # 14. 23 # 10
51 # 20. 5 # 19. 19 # 18. 35 # 17. 53 # 17. 14 # 16. 36 # 16. 1 # 15. 27 # 14. 54 # 14. 23 # 9
52 # 20. 5 # 19. 18 # 18. 35 # 17. 53 # 17. 13 # 16. 36 # 16. 0 # 15. 26 # 14. 53 # 14. 22 # 8
53 # 20. 4 # 19. 17 # 18. 34 # 17. 52 # 17. 13 # 16. 35 # 16. 0 # 15. 25 # 14. 53 # 14. 22 # 7
54 # 20. 3 # 19. 17 # 18. 33 # 17. 51 # 17. 12 # 16. 35 # 15. 59 # 15. 25 # 14. 52 # 14. 21 # 6
55 # 20. 2 # 19. 16 # 18. 32 # 17. 51 # 17. 11 # 16. 34 # 15. 58 # 15. 24 # 14. 52 # 14. 21 # 5
56 # 20. 1 # 19. 15 # 18. 32 # 17. 50 # 17. 11 # 16. 34 # 15. 58 # 15. 24 # 14. 51 # 14. 20 # 4
57 # 20. 1 # 19. 14 # 18. 31 # 17. 49 # 17. 10 # 16. 33 # 15. 57 # 15. 23 # 14. 51 # 14. 20 # 3
58 # 20. 0 # 19. 14 # 18. 30 # 17. 49 # 17. 10 # 16. 32 # 15. 57 # 15. 23 # 14. 50 # 14. 19 # 2
59 # 19. 59 # 19. 13 # 18. 29 # 17. 48 # 17. 9 # 16. 32 # 15. 56 # 15. 22 # 14. 50 # 14. 19 # 1
60 # 19. 58 # 19. 12 # 18. 29 # 17. 47 # 17. 8 # 16. 31 # 15. 55 # 15. 22 # 14. 49 # 14. 18 # 0
# 59 # 58 # 57 # 56 # 55 # 54 # 53 # 52 # 51 # 50
</note>
</div>
<div xml:id="echoid-div1594" type="section" level="1" n="397">
<head xml:id="echoid-head411" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris verſis.</head>
<pb o="480" file="0496" n="496" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1595" type="section" level="1" n="398">
<head xml:id="echoid-head412" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 40 # 41 # 42 # 43 # 44 # 45 # 46 # 47 # 48 # 49 <lb/>M. # Par. Mi. # P. M. # P. M # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 14. 18 # 13. 48 # 13. 20 # 11. 52 # 12. 26 # 12. 0 # 11. 35 # 11. 11 # 10. 48 # 10. 26 # 60 <lb/>1 # 14 18 # 13. 48 # 13. 19 # 12. 52 # 12. 25 # 12. 0 # 11. 35 # 11. 11 # 10. 48 # 10. 26 # 59 <lb/>2 # 14. 17 # 13. 47 # 13. 19 # 12. 51 # 12. 25 # 11. 59 # 11. 34 # 11. 11 # 10. 48 # 10. 25 # 58 <lb/>3 # 14 17 # 13 47 # 13. 18 # 12. 51 # 12. 24 # 11. 59 # 11. 34 # 11. 10 # 10 47 # 10. 25 # 57 <lb/>4 # 14. 16 # 13. 46 # 13. 18 # 12. 50 # 12. 24 # 11. 58 # 11. 34 # 11. 10 # 10. 47 # 10. 24 # 56 <lb/>
5 # 14. 16 # 13. 46 # 13. 17 # 12. 50 # 12. 23 # 11. 58 # 11. 33 # 11. 9 # 10 46 # 10. 24 # 55
6 # 14. 15 # 13. 45 # 13. 17 # 12. 49 # 12. 23 # 11. 57 # 11. 33 # 11. 9 # 10. 46 # 10. 24 # 54
7 # 14. 15 # 13. 45 # 13. 16 # 12. 49 # 12. 23 # 11. 57 # 11. 32 # 11. 9 # 10. 46 # 10. 23 # 53
8 # 14. 14 # 13. 44 # 13. 16 # 12. 49 # 12 22 # 11. 57 # 11. 32 # 11. 8 # 10. 45 # 10. 23 # 52
9 # 14. 14 # 13 44 # 13. 15 # 12. 48 # 12. 22 # 11. 56 # 11. 32 # 11. 8 # 10. 45 # 10. 23 # 51
10 # 14. 13 # 13. 43 # 13. 15 # 12. 48 # 12. 21 # 11. 56 # 11. 31 # 11. 8 # 10. 45 # 10. 22 # 50
11 # 14. 13 # 13 43 # 13. 15 # 12. 47 # 12. 21 # 11. 55 # 11. 31 # 11. 7 # 10. 44 # 10 22 # 49
12 # 14. 12 # 13. 42 # 13. 14 # 12. 47 # 12. 20 # 11. 55 # 11. 30 # 11. 7 # 10 44 # 10. 21 # 48
13 # 14 12 # 13. 42 # 13. 14 # 12. 46 # 12. 20 # 11. 55 # 11. 30 # 11. 6 # 10. 43 # 10. 21 # 47
14 # 14. 11 # 13. 41 # 13. 13 # 12. 46 # 12. 20 # 11. 54 # 11. 30 # 11. 6 # 10. 43 # 10. 21 # 46
15 # 14. 11 # 13. 4 # 13 13 # 12. 45 # 12. 19 # 11. 54 # 11. 29 # 11. 6 # 10. 43 # 10. 20 # 45
16 # 14. 10 # 13. 41 # 13. 12 # 12. 45 # 12. 19 # 11. 53 # 11. 29 # 11. 5 # 10. 42 # 10. 20 # 44
17 # 14. 9 # 13 40 # 13. 12 # 12. 44 # 12 18 # 11. 53 # 11. 28 # 11. 5 # 10. 42 # 10. 20 # 43
18 # 14. 9 # 13. 40 # 13. 11 # 12. 44 # 12. 18 # 11. 53 # 11. 28 # 11. 4 # 10. 42 # 10. 19 # 42
19 # 14. 8 # 13. 39 # 13. 11 # 12. 44 # 12. 17 # 11. 52 # 11. 28 # 11. 4 # 10. 41 # 10. 19 # 41
20 # 14. 8 # 13. 39 # 13. 10 # 12. 43 # 12. 17 # 11. 52 # 11. 27 # 11. 4 # 10. 41 # 10. 19 # 40
21 # 14. 7 # 13. 38 # 13. 10 # 12. 43 # 12. 17 # 11. 51 # 11. 27 # 11. 3 # 10. 40 # 10. 18 # 39
22 # 14. 7 # 13. 38 # 13. 9 # 12. 42 # 12. 16 # 11. 51 # 11. 26 # 11. 3 # 10. 40 # 10. 18 # 38
23 # 14. 6 # 13 37 # 13. 9 # 12. 42 # 12. 16 # 11. 50 # 11. 26 # 11. 2 # 10. 40 # 10. 17 # 37
24 # 14. 6 # 13. 37 # 13. 8 # 12. 41 # 12. 15 # 11. 50 # 11. 26 # 11. 2 # 10. 39 # 10. 17 # 36
25 # 14. 5 # 13. 36 # 13. 8 # 12. 41 # 12. 15 # 11. 50 # 11. 25 # 11. 2 # 10. 39 # 10. 17 # 35
26 # 14. 5 # 13. 36 # 13. 8 # 12. 40 # 12. 14 # 11. 49 # 11. 25 # 11. 1 # 10. 39 # 10. 16 # 34
27 # 14. 5 # 23. 35 # 13. 7 # 12. 40 # 12. 14 # 11. 49 # 11. 24 # 11. 1 # 10. 38 # 10. 16 # 33
28 # 14. 4 # 13. 35 # 13. 7 # 12. 40 # 12. 14 # 11. 48 # 11. 24 # 11. 1 # 10. 38 # 10. 16 # 32
29 # 14. 4 # 13. 34 # 13. 6 # 12. 39 # 12. 13 # 11. 48 # 11. 24 # 11. 0 # 10. 37 # 10. 15 # 31
30 # 14. 3 # 13. 34 # 13. 6 # 12. 39 # 12. 13 # 11. 48 # 11. 23 # 11. 0 # 10. 37 # 10. 15 # 30
31 # 14. 3 # 13. 33 # 13. 5 # 12. 38 # 12. 12 # 11. 47 # 11. 23 # 10. 59 # 10. 37 # 10. 15 # 29
32 # 14. 2 # 13. 33 # 13. 5 # 12. 38 # 12. 12 # 11. 47 # 11. 22 # 10. 59 # 10. 36 # 10. 14 # 28
33 # 14. 2 # 13. 32 # 13. 4 # 12. 37 # 12. 11 # 11. 46 # 11. 22 # 10. 59 # 10. 36 # 10. 14 # 27
34 # 14. 1 # 13. 32 # 13. 4 # 12. 37 # 12. 11 # 11. 46 # 11. 22 # 10. 58 # 10. 36 # 10. 13 # 26
35 # 14. 1 # 13. 31 # 13. 3 # 12. 37 # 12. 11 # 11. 45 # 11. 21 # 10. 58 # 10. 35 # 10. 13 # 25
36 # 14. 0 # 13. 3@ # 13. 3 # 12. 36 # 12. 10 # 11. 45 # 11. 21 # 10. 57 # 10. 35 # 10. 13 # 24
37 # 14. 0 # 13. 30 # 13. 3 # 12. 36 # 12. 10 # 11. 45 # 11. 20 # 10. 57 # 10. 34 # 10. 12 # 23
38 # 13. 59 # 13. 30 # 13. 2 # 12. 35 # 12. 9 # 11. 44 # 11. 20 # 10. 57 # 10. 34 # 10. 12 # 22
39 # 13 59 # 13 30 # 13. 2 # 12. 35 # 12. 9 # 11. 44 # 11. 20 # 10. 56 # 10. 34 # 10. 12 # 21
40 # 13. 58 # 13. 29 # 13. 1 # 12. 34 # 12. 8 # 11. 43 # 11. 19 # 10. 56 # 10 33 # 10. 11 # 20
41 # 13. 58 # 13. 29 # 13. 1 # 12. 34 # 12. 8 # 11. 43 # 11. 19 # 10. 56 # 10. 33 # 10. 11 # 19
42 # 13. 57 # 13. 28 # 13. 0 # 12. 33 # 12. 8 # 11. 43 # 11. 18 # 10. 55 # 10. 33 # 10. 1@ # 18
43 # 13. 57 # 13. 28 # 13. 0 # 12. 33 # 12. 7 # 11. 42 # 11. 18 # 10 55 # 10. 32 # 10. 10 # 17
44 # 13. 56 # 13. 27 # 12. 59 # 12. 33 # 12. 7 # 11. 42 # 11. 18 # 10. 54 # 10. 32 # 10. 10 # 16
45 # 13. 56 # 13. 27 # 12. 59 # 12. 32 # 12. 6 # 11. 41 # 11. 17 # 10. 54 # 10. 31 # 10. 10 # 15
46 # 13. 55 # 13. 26 # 12. 58 # 12. 32 # 12. 6 # 11. 41 # 11. 17 # 10. 54 # 10. 31 # 10. 9 # 14
47 # 13. 55 # 13. 26 # 12. 58 # 12. 31 # 12. 5 # 11. 41 # 11. 17 # 10. 53 # 10. 31 # 10. 9 # 13
48 # 13. 54 # 13. 25 # 12. 58 # 12. 31 # 12. 5 # 11. 40 # 11. 16 # 10. 53 # 10. 30 # 10. 8 # 12
49 # 13. 54 # 13. 25 # 12. 57 # 12. 30 # 12. 5 # 11. 40 # 11. 16 # 10. 52 # 10. 30 # 10. 8 # 11
50 # 13. 53 # 13. 24 # 12. 57 # 12. 30 # 12. 4 # 11. 39 # 11. 15 # 10. 52 # 10. 30 # 10. 8 # 10
51 # 13. 53 # 13. 24 # 12. 56 # 12. 29 # 12. 4 # 11. 39 # 11. 15 # 10. 52 # 10. 29 # 10. 7 # 9
52 # 13. 52 # 13. 23 # 12. 56 # 12. 29 # 12. 3 # 11. 39 # 11. 15 # 10. 51 # 10. 29 # 10. 7 # 8
53 # 13. 52 # 13. 23 # 12. 55 # 12. 29 # 12. 3 # 11. 38 # 11. 14 # 10. 51 # 10. 28 # 10. 7 # 7
54 # 13. 51 # 13. 22 # 12. 55 # 12. 28 # 12. 3 # 11. 38 # 11. 14 # 10. 51 # 10. 28 # 10. 6 # 6
55 # 13. 51 # 13. 22 # 12. 54 # 12. 28 # 12. 2 # 11. 37 # 11. 13 # 10. 50 # 10. 28 # 10. 6 # 5
56 # 13. 50 # 13. 22 # 12. 54 # 12. 27 # 12. 2 # 11. 37 # 11. 13 # 10. 50 # 10. 27 # 10. 6 # 4
57 # 13. 50 # 13. 21 # 12. 53 # 12. 27 # 12. 1 # 11. 37 # 11. 13 # 10. 49 # 10. 27 # 10. 5 # 3
58 # 13. 49 # 13. 21 # 12. 53 # 12. 26 # 12. 1 # 11. 36 # 11. 12 # 10. 49 # 10. 27 # 10. 5 # 2
59 # 13. 49 # 13. 20 # 12. 53 # 12. 26 # 12. 0 # 11. 36 # 11. 12 # 10. 49 # 10. 26 # 10. 5 # 1
60 # 13. 48 # 13. 20 # 12. 52 # 12. 26 # 12. 0 # 11. 35 # 11. 11 # 10. 48 # 10. 26 # 10. 4 # 0
# 49 # 48 # 47 # 46 # 45 # 44 # 43 # 42 # 41 # 40
</note>
</div>
<div xml:id="echoid-div1596" type="section" level="1" n="399">
<head xml:id="echoid-head413" style="it" xml:space="preserve">Grad{us} altituainum Solis pro vmbris verſis.</head>
<pb o="481" file="0497" n="497" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1597" type="section" level="1" n="400">
<head xml:id="echoid-head414" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 50 # 51 # 52 # 53 # 54 # 55 # 56 # 57 # 58 # 59 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 10. 4 # 9. 43 # 9. 23 # 9. 3 # 8. 43 # 8. 24 # 8. 6 # 7. 48 # 7. 30 # 7. 13 # 60 <lb/>1 # 10. 4 # 9. 43 # 9. 22 # 9. 2 # 8. 43 # 8. 24 # 8. 5 # 7. 47 # 7. 30 # 7. 12 # 59 <lb/>2 # 10. 3 # 9. 42 # 9. 22 # 9. 2 # 8. 42 # 8. 24 # 8. 5 # 7. 47 # 7. 29 # 7. 12 # 58 <lb/>3 # 10. 3 # 9. 42 # 9. 22 # 9. 2 # 8. 42 # 8. 23 # 8. 5 # 7. 47 # 7. 29 # 7. 12 # 57 <lb/>4 # 10. 3 # 9. 42 # 9. 21 # 9. 1 # 8. 42 # 8. 23 # 8. 4 # 7. 46 # 7. 29 # 7. 11 # 56 <lb/>5 # 10. 2 # 9. 41 # 9. 21 # 9. 1 # 8. 41 # 8. 23 # 8. 4 # 7. 46 # 7. 28 # 7. 11 # 55 <lb/>
6 # 10. 2 # 9. 41 # 9. 20 # 9. 1 # 8. 41 # 8. 22 # 8. 4 # 7. 46 # 7. 28 # 7. 11 # 54
7 # 10. 2 # 9. 41 # 9. 20 # 9. 0 # 8. 41 # 8. 22 # 8. 4 # 7. 45 # 7. 28 # 7. 11 # 53
8 # 10. 1 # 9. 40 # 9. 20 # 9. 0 # 8. 40 # 8. 22 # 8. 3 # 7. 45 # 7. 28 # 7. 10 # 52
9 # 10. 1 # 9. 40 # 9. 19 # 9. 0 # 8. 40 # 8. 21 # 8. 3 # 7. 45 # 7. 27 # 7. 10 # 51
10 # 10. 1 # 9. 40 # 9. 19 # 8. 59 # 8. 40 # 8. 21 # 8. 3 # 7. 45 # 7. 27 # 7. 10 # 50
11 # 10. 0 # 9. 39 # 9. 19 # 8. 59 # 8. 40 # 8. 21 # 8. 2 # 7. 44 # 7. 27 # 7. 9 # 49
12 # 10. 0 # 9. 39 # 9. 18 # 8. 59 # 8. 39 # 8. 20 # 8. 2 # 7. 44 # 7. 26 # 7. 9 # 48
13 # 10. 0 # 9. 39 # 9. 18 # 8. 58 # 8. 39 # 8. 20 # 8. 2 # 7. 44 # 7. 26 # 7. 9 # 47
14 # 9. 59 # 9. 38 # 9. 18 # 8. 58 # 8. 39 # 8. 20 # 8. 1 # 7. 43 # 7. 26 # 7. 9 # 46
15 # 9. 59 # 9. 38 # 9. 17 # 8. 58 # 8. 38 # 8. 19 # 8. 1 # 7. 43 # 7. 26 # 7. 8 # 45
16 # 9. 58 # 9. 38 # 9. 17 # 8. 57 # 8. 38 # 8. 19 # 8. 1 # 7. 43 # 7. 25 # 7. 8 # 44
17 # 9. 58 # 9. 37 # 9. 17 # 8. 57 # 8. 38 # 8. 19 # 8. 0 # 7. 43 # 7. 25 # 7. 8 # 43
18 # 9. 58 # 9. 37 # 9. 16 # 8. 57 # 8. 37 # 8. 19 # 8. 0 # 7. 42 # 7. 25 # 7. 8 # 42
19 # 9. 57 # 9. 36 # 9. 16 # 8. 56 # 8. 37 # 8. 18 # 8. 0 # 7. 42 # 7. 24 # 7. 7 # 41
20 # 9. 57 # 9. 36 # 9. 16 # 8. 56 # 8. 37 # 8. 18 # 8. 0 # 7. 42 # 7. 24 # 7. 7 # 40
21 # 9. 57 # 9. 36 # 9. 15 # 8. 56 # 8. 36 # 8. 18 # 7. 59 # 7. 41 # 7. 24 # 7. 7 # 39
22 # 9. 56 # 9. 35 # 9. 15 # 8. 55 # 8. 36 # 8. 17 # 7. 59 # 7. 41 # 7. 24 # 7. 6 # 38
23 # 9. 56 # 9. 35 # 9. 15 # 8. 55 # 8. 36 # 8. 17 # 7. 59 # 7. 41 # 7. 23 # 7. 6 # 37
24 # 9. 56 # 9. 35 # 9. 14 # 8. 55 # 8. 35 # 8. 17 # 7. 58 # 7. 40 # 7. 23 # 7. 6 # 36
25 # 9. 55 # 9. 34 # 9. 14 # 8. 54 # 8. 35 # 8. 16 # 7. 58 # 7. 40 # 7. 23 # 7. 6 # 35
26 # 9. 55 # 9. 34 # 9. 14 # 8. 54 # 8. 35 # 8. 16 # 7. 58 # 7. 40 # 7. 22 # 7. 5 # 34
27 # 9. 55 # 9. 34 # 9. 13 # 8. 54 # 8. 35 # 8. 16 # 7. 57 # 7. 40 # 7. 22 # 7. 5 # 33
28 # 9. 54 # 9. 33 # 9. 13 # 8. 53 # 8. 34 # 8. 15 # 7. 57 # 7. 39 # 7. 22 # 7. 5 # 32
29 # 9. 54 # 9. 33 # 9. 13 # 8. 53 # 8. 34 # 8. 15 # 7. 57 # 7. 39 # 7. 22 # 7. 4 # 31
30 # 9. 54 # 9. 33 # 9. 12 # 8. 53 # 8. 34 # 8. 15 # 7. 57 # 7. 39 # 7. 21 # 7. 4 # 30
31 # 9. 53 # 9. 32 # 9. 12 # 8. 52 # 8. 33 # 8. 15 # 7. 56 # 7. 38 # 7. 21 # 7. 4 # 29
32 # 9. 53 # 9. 32 # 9. 12 # 8. 52 # 8. 33 # 8. 14 # 7. 56 # 7. 38 # 7. 21 # 7. 4 # 28
33 # 9. 52 # 9. 32 # 9. 11 # 8. 52 # 8. 33 # 8. 14 # 7. 56 # 7. 38 # 7. 20 # 7. 3 # 27
34 # 9. 52 # 9. 31 # 9. 11 # 8. 51 # 8. 32 # 8. 14 # 7. 55 # 7. 38 # 7. 20 # 7. 3 # 26
35 # 9. 52 # 9. 31 # 9. 11 # 8. 51 # 8. 32 # 8. 13 # 7. 55 # 7. 37 # 7. 20 # 7. 3 # 25
36 # 9. 51 # 9. 31 # 9. 10 # 8. 51 # 8. 32 # 8. 13 # 7. 55 # 7. 37 # 7. 19 # 7. 2 # 24
37 # 9. 51 # 9. 30 # 9. 10 # 8. 50 # 8. 31 # 8. 13 # 7. 54 # 7. 37 # 7. 19 # 7. 2 # 23
38 # 9. 51 # 9. 30 # 9. 10 # 8. 50 # 8. 31 # 8. 12 # 7. 54 # 7. 36 # 7. 19 # 7. 2 # 22
39 # 9. 50 # 9. 30 # 9. 9 # 8. 50 # 8. 31 # 8. 12 # 7. 54 # 7. 36 # 7. 19 # 7. 2 # 21
40 # 9. 50 # 9. 29 # 9. 9 # 8. 50 # 8. 30 # 8. 12 # 7. 54 # 7. 36 # 7. 18 # 7. 1 # 20
41 # 9. 50 # 9. 29 # 9. 9 # 8. 49 # 8. 30 # 8. 11@ # 7. 53 # 7. 35 # 7. 18 # 7. 1 # 19
42 # 9. 49 # 9. 29 # 9. 8 # 8. 49 # 8. 30 # 8. 11 # 7. 53 # 7. 35 # 7. 18 # 7. 1 # 18
43 # 9. 49 # 9. 28 # 9. 8 # 8. 49 # 8. 29 # 8. 11 # 7. 53 # 7. 35 # 7. 17 # 7. 0 # 17
44 # 9. 49 # 9. 28 # 9. 8 # 8. 48 # 8. 29 # 8. 10 # 7. 53 # 7. 35 # 7. 17 # 7. 0 # 16
45 # 9. 48 # 9. 28 # 9. 7 # 8. 48 # 8. 29 # 8. 10 # 7. 52 # 7. 34 # 7. 17 # 7. 0 # 15
46 # 9. 48 # 9. 27 # 9. 7 # 8. 48 # 8. 29 # 8. 10 # 7. 52 # 7. 34 # 7. 17 # 7. 0 # 14
47 # 9. 48 # 9. 27 # 9. 7 # 8. 47 # 8. 28 # 8. 10 # 7. 52 # 7. 34 # 7. 16 # 6. 59 # 13
48 # 9. 47 # 9. 27 # 9. 7 # 8. 47 # 8. 28 # 8. 9 # 7. 51 # 7. 33 # 7. 16 # 6. 59 # 12
49 # 9. 47 # 9. 26 # 9. 6 # 8. 47 # 8. 28 # 8. 9 # 7. 51 # 7. 33 # 7. 16 # 6. 59 # 11
50 # 9. 47 # 9. 26 # 9. 6 # 8. 46 # 8. 27 # 8. 9 # 7. 51 # 7. 33 # 7. 15 # 6. 59 # 10
51 # 9. 46 # 9. 26 # 9. 6 # 8. 46 # 8. 27 # 8. 8 # 7. 50 # 7. 33 # 7. 15 # 6. 58 # 9
52 # 9. 46 # 9. 25 # 9. 5 # 8. 46 # 8. 27 # 8. 8 # 7. 50 # 7. 32 # 7. 15 # 6. 58 # 8
53 # 9. 45 # 9. 25 # 9. 5 # 8. 45 # 8. 26 # 8. 8 # 7. 50 # 7. 32 # 7. 15 # 6. 58 # 7
54 # 9. 45 # 9. 25 # 9. 5 # 8. 45 # 8. 26 # 8. 7 # 7. 49 # 7. 32 # 7. 14 # 6. 57 # 6
55 # 9. 45 # 9. 24 # 9. 4 # 8. 45 # 2. 26 # 8. 7 # 7. 49 # 7. 31 # 7. 14 # 6. 57 # 5
56 # 9. 44 # 9. 24 # 9. 4 # 8. 44 # 8. 25 # 8. 7 # 7. 49 # 7. 31 # 7. 14 # 6. 57 # 4
57 # 9. 44 # 9. 24 # 9. 4 # 8. 44 # 8. 25 # 8. 7 # 7. 48 # 7. 31 # 7. 13 # 6. 57 # 3
58 # 9. 44 # 9. 23 # 9. 3 # 8. 44 # 8. 25 # 8. 6 # 7. 48 # 7. 30 # 7. 13 # 6. 56 # 2
59 # 9. 43 # 9. 23 # 9. 3 # 8. 43 # 8. 24 # 8. 6 # 7. 48 # 7. 30 # 7. 13 # 6. 56 # 1
60 # 9. 43 # 9. 23 # 9. 3 # 8. 43 # 8. 24 # 8. 6 # 7. 48 # 7. 30 # 7. 13 # 6. 56 # 0
# 39 # 38 # 37 # 36 # 35 # 34 # 33 # 32 # 31 # 30
</note>
</div>
<div xml:id="echoid-div1598" type="section" level="1" n="401">
<head xml:id="echoid-head415" style="it" xml:space="preserve">Grad{us} aitudinum Solis pro vmbris verſis.</head>
<pb o="482" file="0498" n="498" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1599" type="section" level="1" n="402">
<head xml:id="echoid-head416" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 60 # 61 # 62 # 63 # 64 # 65 # 66 # 67 # 68 # 69 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 6. 56 # 6. 39 # 6. 23 # 6. 7 # 5. 51 # 5. 36 # 5. 21 # 5. 6 # 4. 51 # 4. 36 # 60 <lb/>1 # 6. 55 # 6. 39 # 6. 23 # 6. 7 # 5. 51 # 5. 35 # 5. 20 # 5. 5 # 4. 51 # 4. 36 # 59 <lb/>2 # 6. 55 # 6. 39 # 6. 22 # 6. 6 # 5. 51 # 5. 35 # 5. 20 # 5. 5 # 4. 50 # 4. 36 # 58 <lb/>3 # 6. 55 # 6. 38 # 6. 22 # 6. 6 # 5. 50 # 5. 35 # 5. 20 # 5. 5 # 4. 50 # 4. 36 # 57 <lb/>4 # 6. 55 # 6. 38 # 6. 22 # 6. 6 # 5. 50 # 5. 35 # 5. 20 # 5. 5 # 4. 50 # 4. 35 # 56 <lb/>5 # 6. 54 # 6. 38 # 6. 21 # 6. 6 # 5. 50 # 5. 34 # 5. 19 # 5. 4 # 4. 50 # 4. 35 # 55 <lb/>
6 # 6. 54 # 6. 37 # 6. 21 # 6. 5 # 5. 50 # 5. 34 # 5. 19 # 5. 4 # 4. 49 # 4. 35 # 54
7 # 6. 54 # 6. 37 # 6. 21 # 6. 5 # 5. 49 # 5. 34 # 5. 19 # 5. 4 # 4. 49 # 4. 35 # 53
8 # 6. 53 # 6. 37 # 6. 21 # 6. 5 # 5. 49 # 5. 34 # 5. 19 # 5. 4 # 4. 49 # 4. 34 # 52
9 # 6. 53 # 6. 37 # 6. 20 # 6. 4 # 5. 49 # 5. 33 # 5. 18 # 5. 3 # 4. 49 # 4. 34 # 51
10 # 6. 53 # 6. 36 # 6. 20 # 6. 4 # 5. 49 # 5. 33 # 5. 18 # 5. 3 # 4. 48 # 4. 34 # 50
11 # 6. 53 # 6. 36 # 6. 20 # 6. 4 # 5. 48 # 5. 33 # 5. 18 # 5. 3 # 4. 48 # 4. 34 # 49
12 # 6. 52 # 6. 36 # 6. 20 # 6. 4 # 5. 48 # 5. 33 # 5. 18 # 5. 3 # 4. 48 # 4. 34 # 48
13 # 6. 52 # 6. 36 # 6. 19 # 6. 3 # 5. 48 # 5. 32 # 5. 17 # 5. 2 # 4. 48 # 4. 33 # 47
14 # 6. 52 # 6. 35 # 6. 19 # 6. 3 # 5. 48 # 5. 32 # 5. 17 # 5. 2 # 4. 48 # 4. 33 # 46
15 # 6. 52 # 6. 35 # 6. 19 # 6. 3 # 5. 47 # 5. 32 # 5. 17 # 5. 2 # 4. 47 # 4. 33 # 45
16 # 6. 51 # 6. 35 # 6. 19 # 6. 3 # 5. 47 # 5. 32 # 5. 17 # 5. 2 # 4. 47 # 4. 33 # 44
17 # 6. 51 # 6. 34 # 6. 18 # 6. 2 # 5. 47 # 5. 31 # 5. 16 # 5. 1 # 4. 47 # 4. 32 # 43
18 # 6. 51 # 6. 34 # 6. 18 # 6. 2 # 5. 47 # 5. 31 # 5. 16 # 5. 1 # 4. 47 # 4. 32 # 42
19 # 6. 50 # 6. 34 # 6. 18 # 6. 2 # 5. 46 # 5. 31 # 5. 16 # 5. 1 # 4. 46 # 4. 32 # 41
20 # 6. 50 # 6. 34 # 6. 17 # 6. 2 # 5. 46 # 5. 31 # 5. 16 # 5. 1 # 4. 46 # 4. 32 # 40
21 # 6. 50 # 6. 33 # 6. 17 # 6. 1 # 5. 46 # 5. 30 # 5. 15 # 5. 0 # 4. 46 # 4. 31 # 39
22 # 6. 50 # 6. 33 # 6. 17 # 6. 1 # 5. 45 # 5. 30 # 5. 15 # 5. 0 # 4. 46 # 4. 31 # 38
23 # 6. 49 # 6. 33 # 6. 17 # 6. 1 # 5. 45 # 5. 30 # 5. 15 # 5. 0 # 4. 45 # 4. 31 # 37
24 # 6. 49 # 6. 33 # 6. 16 # 6. 1 # 5. 45 # 5. 30 # 5. 15 # 5. 0 # 4. 45 # 4. 31 # 36
25 # 6. 49 # 6. 32 # 6. 16 # 6. 0 # 5. 45 # 5. 29 # 5. 14 # 4. 59 # 4. 45 # 4. 30 # 35
26 # 6. 48 # 6. 32 # 6. 16 # 6. 0 # 5. 44 # 5. 29 # 5. 14 # 4. 59 # 4. 45 # 4. 30 # 34
27 # 6. 48 # 6. 32 # 6. 16 # 6. 0 # 5. 44 # 5. 29 # 5. 14 # 4. 59 # 4. 44 # 4. 30 # 33
28 # 6. 48 # 6. 31 # 6. 15 # 5. 59 # 5. 44 # 5. 29 # 5. 14 # 4. 59 # 4. 44 # 4. 30 # 32
29 # 6. 48 # 6. 31 # 6. 15 # 5. 59 # 5. 44 # 5. 28 # 5. 13 # 4. 58 # 4. 44 # 4. 29 # 31
30 # 6. 47 # 6. 31 # 6. 15 # 5. 59 # 5. 43 # 5. 28 # 5. 13 # 4. 58 # 4. 44 # 4. 29 # 30
31 # 6. 47 # 6. 31 # 6. 15 # 5. 59 # 5. 43 # 5. 28 # 5. 13 # 4. 58 # 4. 43 # 4. 29 # 29
32 # 6. 47 # 6. 30 # 6. 14 # 5. 58 # 5. 43 # 5. 28 # 5. 13 # 4. 58 # 4. 43 # 4. 29 # 28
33 # 6. 47 # 6. 30 # 6. 14 # 5. 58 # 5. 43 # 5. 27 # 5. 12 # 4. 57 # 4. 43 # 4. 28 # 27
34 # 6. 46 # 6. 30 # 6. 14 # 5. 58 # 5. 42 # 5. 27 # 5. 12 # 4. 57 # 4. 43 # 4. 28 # 26
35 # 6. 46 # 6. 30 # 6. 13 # 5. 58 # 5. 42 # 5. 27 # 5. 12 # 4. 57 # 4. 42 # 4. 28 # 25
36 # 6. 46 # 6. 29 # 6. 13 # 5. 57 # 5. 42 # 5. 27 # 5. 12 # 4. 57 # 4. 42 # 4. 28 # 24
37 # 6. 45 # 6. 29 # 6. 13 # 5. 57 # 5. 42 # 5. 26 # 5. 11 # 4. 57 # 4. 42 # 4. 28 # 23
38 # 6. 45 # 6. 29 # 6. 13 # 5. 57 # 5. 41 # 5. 26 # 5. 11 # 4. 56 # 4. 42 # 4. 27 # 22
39 # 6. 45 # 6. 28 # 6. 12 # 5. 57 # 5. 41 # 5. 26 # 5. 11 # 4. 56 # 4. 41 # 4. 27 # 21
40 # 6. 45 # 6. 28 # 6. 12 # 5. 56 # 5. 41 # 5. 26 # 5. 11 # 4. 56 # 4. 41 # 4. 27 # 20
41 # 6. 44 # 6. 28 # 6. 12 # 5. 56 # 5. 41 # 5. 25 # 5. 10 # 4. 56 # 4. 41 # 4. 27 # 19
42 # 6. 44 # 6. 28 # 6. 12 # 5. 56 # 5. 40 # 5. 25 # 5. 10 # 4. 55 # 4. 41 # 4. 26 # 18
43 # 6. 44 # 6. 27 # 6. 11 # 5. 56 # 5. 40 # 5. 25 # 5. 10 # 4. 55 # 4. 40 # 4. 26 # 17
44 # 6. 43 # 6. 27 # 6. 11 # 5. 55 # 5. 40 # 5. 25 # 5. 10 # 4. 55 # 4. 40 # 4. 26 # 16
45 # 6. 43 # 6. 27 # 6. 11 # 5. 55 # 5. 40 # 5. 24 # 5. 9 # 4. 55 # 4. 40 # 4. 26 # 15
46 # 6. 43 # 6. 27 # 6. 11 # 5. 55 # 5. 39 # 5. 24 # 5. 9 # 4. 54 # 4. 40 # 4. 25 # 14
47 # 6. 43 # 6. 26 # 6. 10 # 5. 54 # 5. 39 # 5. 24 # 5. 9 # 4. 54 # 4. 40 # 4. 25 # 13
48 # 6. 42 # 6. 26 # 6. 10 # 5. 54 # 5. 39 # 5. 24 # 5. 9 # 4. 54 # 4. 39 # 4. 25 # 12
49 # 6. 42 # 6. 26 # 6. 10 # 5. 54 # 5. 39 # 5. 23 # 5. 8 # 4. 54 # 4. 39 # 4. 25 # 11
50 # 6. 42 # 6. 26 # 6. 10 # 5. 54 # 5. 38 # 5. 23 # 5. 8 # 4. 53 # 4. 39 # 4. 24 # 10
51 # 6. 42 # 6. 25 # 6. 9 # 5. 53 # 5. 38 # 5. 23 # 5. 8 # 4. 53 # 4. 39 # 4. 24 # 9
52 # 6. 41 # 6. 25 # 6. 9 # 5. 53 # 5. 38 # 5. 23 # 5. 8 # 4. 53 # 4. 38 # 4. 24 # 8
53 # 6. 41 # 6. 25 # 6. 9 # 5. 53 # 5. 38 # 5. 22 # 5. 7 # 4. 53 # 4. 38 # 4. 24 # 7
54 # 6. 41 # 6. 24 # 6. 8 # 5. 53 # 5. 37 # 5. 22 # 5. 7 # 4. 52 # 4. 38 # 4. 23 # 6
55 # 6. 40 # 6. 24 # 6. 8 # 5. 52 # 5. 37 # 5. 22 # 5. 7 # 4. 52 # 4. 38 # 4. 23 # 5
56 # 6. 40 # 6. 24 # 6. 8 # 5. 52 # 5. 37 # 5. 22 # 5. 7 # 4. 52 # 4. 37 # 4. 23 # 4
57 # 6. 40 # 6. 24 # 6. 8 # 5. 52 # 5. 37 # 5. 21 # 5. 6 # 4. 52 # 4. 37 # 4. 23 # 3
58 # 6. 40 # 6. 23 # 6. 7 # 5. 52 # 5. 36 # 5. 21 # 5. 6 # 4. 51 # 4. 37 # 4. 23 # 2
59 # 6. 39 # 6. 23 # 6. 7 # 5. 51 # 5. 36 # 5. 21 # 5. 6 # 4. 51 # 4. 37 # 4. 22 # 1
60 # 6. 39 # 6. 23 # 6. 7 # 5. 51 # 5. 36 # 5. 21 # 5. 6 # 4. 51 # 4. 36 # 4. 22 # 0
# 29 # 28 # 27 # 26 # 25 # 24 # 23 # 22 # 21 # 20
</note>
</div>
<div xml:id="echoid-div1600" type="section" level="1" n="403">
<head xml:id="echoid-head417" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris verſis.</head>
<pb o="483" file="0499" n="499" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1601" type="section" level="1" n="404">
<head xml:id="echoid-head418" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 70 # 71 # 72 # 73 # 74 # 75 # 76 # 77 # 78 # 79 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 4. 22 # 4. 8 # 3. 54 # 3. 40 # 3. 26 # 3. 13 # 3. 0 # 2. 46 # 2. 33 # 2. 20 # 60 <lb/>1 # 4. 22 # 4. 8 # 3. 54 # 3. 40 # 3. 26 # 3. 13 # 2. 59 # 2. 46 # 2. 33 # 2. 20 # 59 <lb/>2 # 4. 22 # 4. 7 # 3. 53 # 3. 40 # 3. 26 # 3. 12 # 2. 59 # 2. 46 # 2. 33 # 2. 20 # 58 <lb/>3 # 4. 21 # 4. 7 # 3. 53 # 3. 39 # 3. 26 # 3. 12 # 2. 59 # 2. 45 # 2. 32 # 2. 19 # 57 <lb/>4 # 4. 21 # 4. 7 # 3. 53 # 3. 39 # 3. 26 # 3. 12 # 2. 59 # 2. 45 # 2. 32 # 2. 19 # 56 <lb/>
5 # 4. 21 # 4. 7 # 3. 53 # 3. 39 # 3. 25 # 3. 12 # 2. 58 # 2. 45 # 2. 32 # 2. 19 # 55
6 # 4. 21 # 4. 7 # 3. 53 # 3. 39 # 3. 25 # 3. 12 # 2. 58 # 2. 45 # 2. 32 # 2. 19 # 54
7 # 4. 20 # 4. 6 # 3. 52 # 3. 39 # 3. 25 # 3. 11 # 2. 58 # 2. 45 # 2. 31 # 2. 19 # 53
8 # 4. 20 # 4. 6 # 3. 52 # 3. 38 # 3. 25 # 3. 11 # 2. 58 # 2. 44 # 2. 31 # 2. 18 # 52
9 # 4. 20 # 4. 6 # 3. 52 # 3. 38 # 3. 24 # 3. 11 # 2. 58 # 2. 44 # 2. 31 # 2. 18 # 51
10 # 4. 20 # 4. 6 # 3. 52 # 3. 38 # 3. 24 # 3. 11 # 2. 57 # 2. 44 # 2. 31 # 2. 18 # 50
11 # 4. 20 # 4. 5 # 3. 51 # 3. 38 # 3. 24 # 3. 10 # 2. 57 # 2. 44 # 2. 31 # 2. 18 # 49
12 # 4. 19 # 4. 5 # 3. 51 # 3. 37 # 3. 24 # 3. 10 # 2. 57 # 2. 44 # 2. 30 # 2. 17 # 48
13 # 4. 19 # 4. 5 # 3. 51 # 3. 37 # 3. 23 # 3. 10 # 2. 57 # 2. 43 # 2. 30 # 2. 17 # 47
14 # 4. 19 # 4. 5 # 3. 51 # 3. 37 # 3. 23 # 3. 10 # 2. 56 # 2. 43 # 2. 30 # 2. 17 # 46
15 # 4. 19 # 4. 4 # 3. 50 # 3. 37 # 3. 23 # 3. 10 # 2. 56 # 2. 43 # 2. 30 # 2. 17 # 45
16 # 4. 18 # 4. 4 # 3. 50 # 3. 36 # 3. 23 # 3. 9 # 2. 56 # 2. 43 # 2. 30 # 2. 16 # 44
17 # 4. 18 # 4. 4 # 3. 50 # 3. 36 # 3. 23 # 3. 9 # 2. 56 # 2. 42 # 2. 29 # 2. 16 # 43
18 # 4. 18 # 4. 4 # 3. 50 # 3. 36 # 3. 22 # 3. 9 # 2. 55 # 2. 42 # 2. 29 # 2. 16 # 42
19 # 4. 18 # 4. 3 # 3. 50 # 3. 36 # 3. 22 # 3. 9 # 2. 55 # 2. 42 # 2. 29 # 2. 16 # 41
20 # 4. 17 # 4. 3 # 3. 49 # 3. 36 # 3. 22 # 3. 8 # 2. 55 # 2. 42 # 2. 29 # 2. 16 # 40
21 # 4. 17 # 4. 3 # 3. 49 # 3. 35 # 3. 22 # 3. 8 # 2. 55 # 2. 42 # 2. 28 # 2. 15 # 39
22 # 4. 17 # 4. 3 # 3. 49 # 3. 35 # 3. 21 # 3. 8 # 2. 55 # 2. 41 # 2. 28 # 2. 15 # 38
23 # 4. 17 # 4. 3 # 3. 49 # 3. 35 # 3. 21 # 3. 8 # 2. 54 # 2. 41 # 2. 28 # 2. 15 # 37
24 # 4. 17 # 4. 2 # 3. 48 # 3. 35 # 3. 21 # 3. 8 # 2. 54 # 2. 41 # 2. 28 # 2. 15 # 36
25 # 4. 16 # 4. 2 # 3. 48 # 3. 34 # 3. 21 # 3. 7 # 2. 54 # 2. 41 # 2. 28 # 2. 15 # 35
26 # 4. 16 # 4. 2 # 3. 48 # 3. 34 # 3. 21 # 3. 7 # 2. 54 # 2. 40 # 2. 27 # 2. 14 # 34
27 # 4. 16 # 4. 2 # 3. 48 # 3. 34 # 3. 20 # 3. 7 # 2. 54 # 2. 40 # 2. 27 # 2. 14 # 33
28 # 4. 16 # 4. 1 # 3. 47 # 3. 34 # 3. 20 # 3. 7 # 2. 53 # 2. 40 # 2. 27 # 2. 14 # 32
29 # 4. 15 # 4. 1 # 3. 47 # 3. 33 # 3. 20 # 3. 6 # 2. 53 # 2. 40 # 2. 27 # 2. 14 # 31
30 # 4. 15 # 4. 1 # 3. 47 # 3. 33 # 3. 20 # 3. 6 # 2. 53 # 2. 40 # 2. 26 # 2. 13 # 30
31 # 4. 15 # 4. 1 # 3. 47 # 3. 33 # 3. 19 # 3. 6 # 2. 53 # 2. 39 # 2. 26 # 2. 13 # 29
32 # 4. 15 # 4. 0 # 3. 47 # 3. 33 # 3. 19 # 3. 6 # 2. 52 # 2. 39 # 2. 26 # 2. 13 # 28
33 # 4. 14 # 4. 0 # 3. 46 # 3. 33 # 3. 19 # 3. 6@ # 2. 52 # 2. 39 # 2. 26 # 2. 13 # 27
34 # 4. 14 # 4. 0 # 3. 46 # 3. 32 # 3. 19 # 3. 5 # 2. 52 # 2. 39 # 2. 26 # 2. 13 # 26
35 # 4. 14 # 4. 0 # 3. 46 # 3. 32 # 3. 19 # 3. 5 # 2. 52 # 2. 39 # 2. 25 # 2. 12 # 25
36 # 4. 14 # 4. 0 # 3. 46 # 3. 32 # 3. 18 # 3. 5 # 2. 52 # 2. 38 # 2. 25 # 2. 12 # 24
37 # 4. 13 # 3. 59 # 3. 45 # 3. 32 # 3. 18 # 3. 5 # 2. 51 # 2. 38 # 2. 25 # 2. 12 # 23
38 # 4. 13 # 3. 59 # 3. 45 # 3. 31 # 3. 18 # 3. 4 # 2. 51 # 2. 38 # 2. 25 # 2. 12 # 22
39 # 4. 13 # 3. 59 # 3. 45 # 3. 31 # 3. 18 # 3. 4 # 2. 51 # 2. 38 # 2. 25 # 2. 11 # 21
40 # 4. 13 # 3. 59 # 3. 45 # 3. 31 # 3. 17 # 3. 4 # 2. 51 # 2. 37 # 2. 24 # 2. 11 # 20
41 # 4. 12 # 3. 58 # 3. 44 # 3. 31 # 3. 17 # 3. 4 # 2. 50 # 2. 37 # 2. 24 # 2. 11 # 19
42 # 4. 12 # 3. 58 # 3. 44 # 3. 31 # 3. 17 # 3. 4 # 2. 50 # 2. 37 # 2. 24 # 2. 11 # 18
43 # 4. 12 # 3. 58 # 3. 44 # 3. 30 # 3. 17 # 3. 3 # 2. 50 # 2. 37 # 2. 24 # 2. 11 # 17
44 # 4. 12 # 3. 58 # 3. 44 # 3. 30 # 3. 17 # 3. 3 # 2. 50 # 2. 37 # 2. 23 # 2. 10 # 16
45 # 4. 11 # 3. 57 # 3. 43 # 3. 30 # 3. 16 # 3. 3 # 2. 50 # 2. 36 # 2. 23 # 2. 10 # 15
46 # 4. 11 # 3. 57 # 3. 43 # 3. 30 # 3. 16 # 3. 3 # 2. 49 # 2. 36 # 2. 23 # 2. 10 # 14
47 # 4. 11 # 3. 57 # 3. 43 # 3. 29 # 3. 16 # 3. 2 # 2. 49 # 2. 36 # 2. 23 # 2. 10 # 13
48 # 4. 11 # 3. 57 # 3. 43 # 3. 29 # 3. 16 # 3. 2 # 2. 49 # 2. 36 # 2. 23 # 2. 10 # 12
49 # 4. 11 # 3. 56 # 3. 43 # 3. 29 # 3. 15 # 3. 2 # 2. 49 # 2. 35 # 2. 22 # 2. 9 # 11
50 # 4. 10 # 3. 56 # 3. 42 # 3. 29 # 3. 15 # 3. 2 # 2. 48 # 2. 35 # 2. 22 # 2. 9 # 10
51 # 4. 10 # 3. 56 # 3. 42 # 3. 28 # 3. 15 # 3. 2 # 2. 48 # 2. 35 # 2. 22 # 2. 9 # 9
52 # 4. 10 # 3. 56 # 3. 42 # 3. 28 # 3. 15 # 3. 1 # 2. 48 # 2. 35 # 2. 22 # 2. 9 # 8
53 # 4. 10 # 3. 56 # 3. 42 # 3. 28 # 3. 14 # 3. 1 # 2. 48 # 2. 35 # 2. 21 # 2. 8 # 7
54 # 4. 9 # 3. 55 # 3. 42 # 3. 28 # 3. 14 # 3. 1 # 2. 48 # 2. 34 # 2. 21 # 2. 8 # 6
55 # 4. 9 # 3. 55 # 3. 41 # 3. 28 # 3. 14 # 3. 1 # 2. 47 # 2. 34 # 2. 21 # 2. 8 # 5
56 # 4. 9 # 3. 55 # 3. 41 # 3. 27 # 3. 14 # 3. 0 # 2. 47 # 2. 34 # 2. 21 # 2. 8 # 4
57 # 4. 9 # 3. 55 # 3. 41 # 3. 27 # 3. 14 # 3. 0 # 2. 47 # 2. 34 # 2. 21 # 2. 8 # 3
58 # 4. 8 # 3. 54 # 3. 41 # 3. 27 # 3. 13 # 3. 0 # 2. 47 # 2. 33 # 2. 20 # 2. 7 # 2
59 # 4. 8 # 3. 54 # 3. 40 # 3. 27 # 3. 13 # 3. 0 # 2. 46 # 2. 33 # 2. 20 # 2. 7 # 1
60 # 4. 8 # 3. 54 # 3. 40 # 3. 26 # 3. 13@ # 3. 0 # 2. 46 # 2. 33 # 2. 20 # 2. 7 # 0
# 19 # 18 # 17 # 16 # 15 # 14 # 13 # 12 # 11 # 10
</note>
</div>
<div xml:id="echoid-div1602" type="section" level="1" n="405">
<head xml:id="echoid-head419" style="it" xml:space="preserve">rad{us} altitu dinum Solis pro vmbris verſis.</head>
<pb o="484" file="0500" n="500" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1603" type="section" level="1" n="406">
<head xml:id="echoid-head420" style="it" xml:space="preserve">Grad{us} altitudinum Solis pro vmbris rectis.</head>
<note position="right" xml:space="preserve"> <lb/># Grad. # G. # G. # G. # G. # G. # G. # G. # G. # G. <lb/># 80 # 81 # 82 # 83 # 84 # 85 # 86 # 87 # 88 # 89 <lb/>M. # Par. Mi. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>0 # 2. 7 # 1. 54 # 1. 41 # 1. 28 # 1. 16 # 1. 3 # 0. 50 # 0. 38 # 0. 25 # 0. 13 # 60 <lb/>1 # 2. 7 # 1. 54 # 1. 41 # 1. 28 # 1. 15 # 1. 3 # 0. 50 # 0. 38 # 0. 25 # 0. 12 # 59 <lb/>2 # 2. 7 # 1. 54 # 1. 41 # 1. 28 # 1. 15 # 1. 3 # 0. 50 # 0. 37 # 0. 25 # 0. 12 # 58 <lb/>3 # 2. 6 # 1. 53 # 1. 41 # 1. 28 # 1. 15 # 1. 2 # 0. 50 # 0. 37 # 0. 25 # 0. 12 # 57 <lb/>4 # 2. 6@ # 1. 53 # 1. 40 # 1. 28 # 1. 15 # 1. 2 # 0. 50 # 0. 37 # 0. 24 # 0. 12 # 56 <lb/>
5 # 2. 6 # 1. 53 # 1. 40 # 1. 27 # 1. 15 # 1. 2 # 0. 49 # 0. 37 # 0. 24@ # 0. 12 # 55
6 # 2. 6 # 1. 53 # 1. 40 # 1. 27 # 1. 14 # 1. 2 # 0. 49 # 0. 36 # 0. 24 # 0. 11 # 54
7 # 2. 5 # 1. 52 # 1. 40 # 1. 27 # 1. 14 # 1. 2 # 0. 49 # 0. 36 # 0. 24 # 0. 11 # 53
8 # 2. 5 # 1. 52 # 1. 39 # 1. 27 # 1. 14 # 1. 1 # 0. 49 # 0. 36 # 0. 23 # 0. 11 # 52
9 # 2. 5 # 1. 52 # 1. 39 # 1. 26 # 1. 14 # 1. 1 # 0. 48 # 0. 36 # 0. 23 # 0. 11 # 51
10 # 2. 5 # 1. 52 # 1. 39 # 1. 26 # 1. 14 # 1. 1 # 0. 48 # 0. 36 # 0. 23 # 0. 10 # 50
11 # 2. 5 # 1. 52 # 1. 39 # 1. 26 # 1. 13 # 1. 1 # 0. 48 # 0. 35 # 0. 23 # 0. 10 # 49
12 # 2. 4 # 1. 51 # 1. 39 # 1. 26 # 1. 13 # 1. 0 # 0. 48 # 0. 35 # 0. 23 # 0. 10 # 48
13 # 2. 4 # 1. 51 # 1. 38 # 1. 26 # 1. 13 # 1. 0 # 0. 48 # 0. 35 # 0. 22 # 0. 10 # 47
14 # 2. 4 # 1. 51 # 1. 38 # 1. 25 # 1. 13 # 1. 0 # 0. 47 # 0. 35 # 0. 22 # 0. 10 # 46
15 # 2. 4 # 1. 51 # 1. 38 # 1. 25 # 1. 12 # 1. 0 # 0. 47 # 0. 35 # 0. 22 # 0. 9 # 45
16 # 2. 4 # 1. 51 # 1. 38 # 1. 25 # 1. 12 # 1. 0 # 0. 47 # 0. 34 # 0. 22 # 0. 9 # 44
17 # 2. 3 # 1. 50 # 1. 38 # 1. 25 # 1. 12 # 0. 59 # 0. 47 # 0. 34 # 0. 22 # 0. 9 # 43
18 # 2. 3 # 1. 50 # 1. 37 # 1. 25 # 1. 12 # 0. 59 # 0. 47 # 0. 34 # 0. 21 # 0. 9 # 42
19 # 2. 3 # 1. 50 # 1. 37 # 1. 24 # 1. 12 # 0. 59 # 0. 46 # 0. 34 # 0. 21 # 0. 9 # 41
20 # 2. 3 # 1. 50 # 1. 37 # 1. 24 # 1. 11 # 0. 59 # 0. 46 # 0. 34 # 0. 21 # 0. 8 # 40
21 # 2. 2 # 1. 50 # 1. 37 # 1. 24 # 1. 11 # 0. 59 # 0. 46 # 0. 33 # 0. 21 # 0. 8 # 39
22 # 2. 2 # 1. 49 # 1. 36 # 1. 24 # 1. 11 # 0. 58 # 0. 46 # 0. 33 # 0. 21 # 0. 8 # 38
23 # 2. 2 # 1. 49 # 1. 36 # 1. 24 # 1. 11 # 0. 58 # 0. 46 # 0. 33 # 0. 20 # 0. 8 # 37
24 # 2. 2 # 1. 49 # 1. 36 # 1. 23 # 1. 11 # 0. 58 # 0. 45 # 0. 33 # 0. 20 # 0. 8 # 36
25 # 2. 2 # 1. 49 # 1. 36 # 1. 23 # 1. 10 # 0. 58 # 0. 45 # 0. 32 # 0. 20 # 0. 7 # 35
26 # 2. 1 # 1. 48 # 1. 36 # 1. 23 # 1. 10 # 0. 58 # 0. 45 # 0. 32 # 0. 20 # 0. 7 # 34
27 # 2. 1 # 1. 48 # 1. 35 # 1. 23 # 1. 10 # 0. 57 # 0. 45 # 0. 32 # 0. 19 # 0. 7 # 33
28 # 2. 1 # 1. 48 # 1. 35 # 1. 22 # 1. 10 # 0. 57 # 0. 44 # 0. 32 # 0. 19 # 0. 7 # 32
29 # 2. 1 # 1. 48 # 1. 35 # 1. 22 # 1. 10 # 0. 57 # 0. 44 # 0. 32 # 0. 19 # 0. 6 # 31
30 # 2. 0 # 1. 48 # 1. 35 # 1. 22 # 1. 9 # 0. 57 # 0. 44 # 0. 31 # 0. 19 # 0. 6 # 30
31 # 2. 0 # 1. 47 # 1. 35 # 1. 22 # 1. 9 # 0. 56 # 0. 44 # 0. 31 # 0. 19 # 0. 6 # 29
32 # 2. 0 # 1. 47 # 1. 34 # 1. 22 # 1. 9 # 0. 56 # 0. 44 # 0. 31 # 0. 18 # 0. 6 # 28
33 # 2. 0 # 1. 47 # 1. 34 # 1. 21 # 1. 9 # 0. 56 # 0. 43 # 0. 31 # 0. 18 # 0. 6 # 27
34 # 2. 0 # 1. 47 # 1. 34 # 1. 21 # 1. 8 # 0. 56 # 0. 43 # 0. 31 # 0. 18 # 0. 5 # 26
35 # 1. 59 # 1. 47 # 1. 34 # 1. 21 # 1. 8 # 0. 56 # 0. 43 # 0. 30 # 0. 18 # 0. 5 # 25
36 # 1. 59 # 1. 46 # 1. 34 # 1. 21 # 1. 8 # 0. 55 # 0. 43 # 0. 30 # 0. 18 # 0. 5 # 24
37 # 1. 59 # 1. 46 # 1. 33 # 1. 21 # 1. 8 # 0. 55 # 0. 43 # 0. 30 # 0. 17 # 0. 5 # 23
38 # 1. 59 # 1. 46 # 1. 33 # 1. 20 # 1. 8 # 0. 55 # 0. 42 # 0. 30 # 0. 17 # 0. 5 # 22
39 # 1. 59 # 1. 46 # 1. 33 # 1. 20 # 1. 7 # 0. 55 # 0. 42 # 0. 30 # 0. 17 # 0. 4 # 21
40 # 1. 58 # 1. 45 # 1. 33 # 1. 20 # 1. 7 # 0. 55 # 0. 42 # 0. 29 # 0. 17 # 0. 4 # 20
41 # 1. 58 # 1. 45 # 1. 32 # 1. 20 # 1. 7 # 0. 54 # 0. 42 # 0. 29 # 0. 17 # 0. 4 # 19
42 # 1. 58 # 1. 45 # 1. 32 # 1. 19 # 1. 7 # 0. 54 # 0. 42 # 0. 29 # 0. 16 # 0. 4 # 18
43 # 1. 58 # 1. 45 # 1. 32 # 1. 19 # 1. 7 # 0. 54 # 0. 41 # 0. 29 # 0. 16 # 0. 4 # 17
44 # 1. 57 # 1. 45 # 1. 32 # 1. 19 # 1. 6 # 0. 54 # 0. 41 # 0. 28 # 0. 16 # 0. 3 # 16
45 # 1. 57 # 1. 44 # 1. 32 # 1. 19 # 1. 6 # 0. 53 # 0. 41 # 0. 28 # 0. 16 # 0. 3 # 15
46 # 1. 57 # 1. 44 # 1. 31 # 1. 19 # 1. 6 # 0. 53 # 0. 41 # 0. 28 # 0. 15 # 0. 3 # 14
47 # 1. 57 # 1. 44 # 1. 31 # 1. 18 # 1. 6 # 0. 53 # 0. 40 # 0. 28 # 0. 15 # 0. 3 # 13
48 # 1. 57 # 1. 44 # 1. 31 # 1. 18 # 1. 6 # 0. 53 # 0. 40 # 0. 28 # 0. 15 # 0. 3 # 12
49 # 1. 56 # 1. 44 # 1. 31 # 1. 18 # 1. 5 # 0. 53 # 0. 40 # 0. 27 # 0. 15 # 0. 2 # 11
50 # 1. 56 # 1. 43 # 1. 31 # 1. 18 # 1. 5 # 0. 52 # 0. 40 # 0. 27 # 0. 15 # 0. 2 # 10
51 # 1. 56 # 1. 43 # 1. 30 # 1. 18 # 1. 5 # 0. 52 # 0. 40 # 0. 27 # 0. 14 # 0. 2 # 9
52 # 1. 56 # 1. 43 # 1. 30 # 1. 17 # 1. 5 # 0. 52 # 0. 39 # 0. 27 # 0. 14 # 0. 2 # 8
53 # 1. 56 # 1. 43 # 1. 30 # 1. 17 # 1. 4 # 0. 52 # 0. 39 # 0. 27 # 0. 14 # 0. 2 # 7
54 # 1. 55 # 1. 42 # 1. 30 # 1. 17 # 1. 4 # 0. 52 # 0. 39 # 0. 26 # 0. 14 # 0. 1 # 6
55 # 1. 55 # 1. 42 # 1. 29 # 1. 17 # 1. 4 # 0. 51 # 0. 39 # 0. 26 # 0. 14 # 0. 1 # 5
56 # 1. 55 # 1. 42 # 1. 29 # 1. 17 # 1. 4 # 0. 51 # 0. 39 # 0. 26 # 0. 13 # 0. 1 # 4
57 # 1. 55 # 1. 42 # 1. 29 # 1. 16 # 1. 4 # 0. 51 # 0. 38 # 0. 26 # 0. 13 # 0. 1 # 3
58 # 1. 54 # 1. 42 # 1. 29 # 1. 16 # 1. 3 # 0. 51 # 0. 38 # 0. 26 # 0. 13 # 0. 0 # 2
59 # 1. 54 # 1. 41 # 1. 29 # 1. 16 # 1. 3 # 0. 51 # 0. 38 # 0. 25 # 0. 13 # 0. 0 # 1
60 # 1. 54 # 1. 41 # 1. 28 # 1. 16 # 1. 3 # 0. 50 # 0. 38 # 0. 25 # 0. 13 # 0. 0 # 0
# 9 # 8 # 7 # 6 # 5 # 4 # 3 # 2 # 1 # 0
</note>
</div>
<div xml:id="echoid-div1604" type="section" level="1" n="407">
<head xml:id="echoid-head421" style="it" xml:space="preserve">Grad{us} altituainum Solis pro vmbris verſis.</head>
<pb o="485" file="0501" n="501" rhead="LIBER QVINTVS."/>
<p style="it">
  <s xml:id="echoid-s30953" xml:space="preserve">VSVS autem huius tabulæ, quæ Generalis eſt, &amp; </s>
  <s xml:id="echoid-s30954" xml:space="preserve">omnibus climatibus accommodata, hic eſt. </s>
  <s xml:id="echoid-s30955" xml:space="preserve">Da-<lb/>
<anchor type="note" xlink:label="note-0501-01a" xlink:href="note-0501-01"/>
ta altitudine Solis, quær antur eius gradus in ſuperiori parte tabulæ, &amp; </s>
  <s xml:id="echoid-s30956" xml:space="preserve">Minuta, ſi qua fuerint, in ſi-<lb/>niſtro latere. </s>
  <s xml:id="echoid-s30957" xml:space="preserve">Mox enim in angulo communi reperientur Partes, &amp; </s>
  <s xml:id="echoid-s30958" xml:space="preserve">Minuta longitudinis umbræ rectæ, <lb/>quatenus gnomon ex eiſdem partibus comprehendit duodecim. </s>
  <s xml:id="echoid-s30959" xml:space="preserve">Quod ſi ſumantur gradus in inferiori <lb/>parte tabulæ, &amp; </s>
  <s xml:id="echoid-s30960" xml:space="preserve">Minuta, ſi qua ſint, in dextro latere, inuenientur in angulo communi Partes, &amp; </s>
  <s xml:id="echoid-s30961" xml:space="preserve">Minu-<lb/>ta vmbræ verſæ. </s>
  <s xml:id="echoid-s30962" xml:space="preserve">Vt ſi quæratur longitudo vmbræ rectæ ad altitudinẽ Solis gr. </s>
  <s xml:id="echoid-s30963" xml:space="preserve">64. </s>
  <s xml:id="echoid-s30964" xml:space="preserve">inueniemus eam conti <lb/>nere par. </s>
  <s xml:id="echoid-s30965" xml:space="preserve">5. </s>
  <s xml:id="echoid-s30966" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30967" xml:space="preserve">51. </s>
  <s xml:id="echoid-s30968" xml:space="preserve">Eadem autem, dum Sol altitudinem habet grad. </s>
  <s xml:id="echoid-s30969" xml:space="preserve">31. </s>
  <s xml:id="echoid-s30970" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30971" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30972" xml:space="preserve">complectetur par. <lb/></s>
  <s xml:id="echoid-s30973" xml:space="preserve">19. </s>
  <s xml:id="echoid-s30974" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30975" xml:space="preserve">35. </s>
  <s xml:id="echoid-s30976" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30977" xml:space="preserve">c. </s>
  <s xml:id="echoid-s30978" xml:space="preserve">Similiter ſi quæratur vmbra verſa ad altitudinem Solis grad. </s>
  <s xml:id="echoid-s30979" xml:space="preserve">26. </s>
  <s xml:id="echoid-s30980" xml:space="preserve">reperiemus eam <lb/>complecti par. </s>
  <s xml:id="echoid-s30981" xml:space="preserve">5. </s>
  <s xml:id="echoid-s30982" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30983" xml:space="preserve">51. </s>
  <s xml:id="echoid-s30984" xml:space="preserve">Eadem autem, dum Sol altitudinem habet grad. </s>
  <s xml:id="echoid-s30985" xml:space="preserve">58. </s>
  <s xml:id="echoid-s30986" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30987" xml:space="preserve">30. </s>
  <s xml:id="echoid-s30988" xml:space="preserve">habebit par. </s>
  <s xml:id="echoid-s30989" xml:space="preserve"><lb/>19. </s>
  <s xml:id="echoid-s30990" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s30991" xml:space="preserve">35. </s>
  <s xml:id="echoid-s30992" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s30993" xml:space="preserve">c.</s>
  <s xml:id="echoid-s30994" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1604" type="float" level="2" n="1">
<note position="right" xlink:label="note-0501-01" xlink:href="note-0501-01a" xml:space="preserve">Vſus præceden <lb/>tis tabulæ lon <lb/>gitudinum vm <lb/>brarum.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p style="it">
  <s xml:id="echoid-s30995" xml:space="preserve">EX hac eadem tabula cognoſcemus longitudines vmbrarum Solſtitialium, æquinoctialium, &amp; </s>
  <s xml:id="echoid-s30996" xml:space="preserve">bru-<lb/>
<anchor type="note" xlink:label="note-0501-03a" xlink:href="note-0501-03"/>
malium ad quamcunque latitudinem loci, pro qua re multi auctores peculiares tabulas condiderunt. </s>
  <s xml:id="echoid-s30997" xml:space="preserve">Si <lb/>enim in Solſtitio vtroque accipiatur altitudo meridiana, dicto citius ex ea longitudinem vmbræ inue-<lb/>niemus. </s>
  <s xml:id="echoid-s30998" xml:space="preserve">Pro vmbra autem æquinoctiali quærendum eſt in tabula complementum altitudinis poli. </s>
  <s xml:id="echoid-s30999" xml:space="preserve">Tan-<lb/>ta enim tunc eſt altitudo meridiana, &amp; </s>
  <s xml:id="echoid-s31000" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31001" xml:space="preserve">Vt ad latitudinem grad. </s>
  <s xml:id="echoid-s31002" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31003" xml:space="preserve">altitudo meridiana principĳ ♋, <lb/>continet grad. </s>
  <s xml:id="echoid-s31004" xml:space="preserve">71. </s>
  <s xml:id="echoid-s31005" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31006" xml:space="preserve">30. </s>
  <s xml:id="echoid-s31007" xml:space="preserve">cui in tabula reſpondent partes 4. </s>
  <s xml:id="echoid-s31008" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31009" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31010" xml:space="preserve">pro longitudine vmbræ rectæ Sol-<lb/>stitialis. </s>
  <s xml:id="echoid-s31011" xml:space="preserve">Rurſus altitudo meridiana principĳ ♈, aut ♎, comprehendit grad. </s>
  <s xml:id="echoid-s31012" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31013" xml:space="preserve">Cui in eadem tabula <lb/>conueniunt par. </s>
  <s xml:id="echoid-s31014" xml:space="preserve">10. </s>
  <s xml:id="echoid-s31015" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31016" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31017" xml:space="preserve">pro vmbr a recta æquinoctiali. </s>
  <s xml:id="echoid-s31018" xml:space="preserve">Altitudo deniq; </s>
  <s xml:id="echoid-s31019" xml:space="preserve">meridiana principĳ ♑, eſt <lb/>grad. </s>
  <s xml:id="echoid-s31020" xml:space="preserve">24. </s>
  <s xml:id="echoid-s31021" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31022" xml:space="preserve">30. </s>
  <s xml:id="echoid-s31023" xml:space="preserve">Igitur vmbra recta brumalis complectetur partes 26. </s>
  <s xml:id="echoid-s31024" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31025" xml:space="preserve">20. </s>
  <s xml:id="echoid-s31026" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31027" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s31028" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1605" type="float" level="2" n="2">
<note position="right" xlink:label="note-0501-03" xlink:href="note-0501-03a" xml:space="preserve">Longitudin es <lb/>vmbrarum Sol <lb/>ſtitialium, æqui <lb/>noctialium, atq; <lb/>brumaliũ, qua <lb/>ratione ex præ-<lb/>ce denti t<unsure/>abula <lb/>co gnoſcantur, <lb/>ad quam@unq; <lb/>loci latitudinẽ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s31029" xml:space="preserve">GEOMETRICE quoque longitudo vmbræ rectæ ad quamcun altitudinem Solis reperietur <lb/>
<anchor type="note" xlink:label="note-0501-04a" xlink:href="note-0501-04"/>
<anchor type="note" xlink:label="note-0501-05a" xlink:href="note-0501-05"/>
hoc modo. </s>
  <s xml:id="echoid-s31030" xml:space="preserve">Ductis in quocunque circulo, vt in eo, quem in hac propoſ. </s>
  <s xml:id="echoid-s31031" xml:space="preserve">ſupra deſcripſimus, duabus re-<lb/>ctis A C, B D, ſeſe ad angulos rectos ſecantibus in centro E; </s>
  <s xml:id="echoid-s31032" xml:space="preserve">ſumatur in A C, recta E F, æqualis gno <lb/>moni, cuius longitudo vmbræ inquiritur, &amp; </s>
  <s xml:id="echoid-s31033" xml:space="preserve">per F, ipſi B D, parallela agatur F G. </s>
  <s xml:id="echoid-s31034" xml:space="preserve">Poſtremo à puncto <lb/>D, vel B, verſus A, numeretur altitudo Solis vſque ad punctum I, quæ in dato exemplo comprehendit <lb/>ferme grad. </s>
  <s xml:id="echoid-s31035" xml:space="preserve">38. </s>
  <s xml:id="echoid-s31036" xml:space="preserve">Nam ductarecta I E, ex I, per centrum E, quæ rectam F G, ſecet in G, erit F G, lon-<lb/>gitudo vmbræ rectæ ad datam altitudinem Solis D I, vt ſupra demonstrauimus. </s>
  <s xml:id="echoid-s31037" xml:space="preserve">Eodem pacto erit H G, <lb/>vmbra verſa, ſi recta E H, ſumpta ſit æqualis gnomoni, &amp; </s>
  <s xml:id="echoid-s31038" xml:space="preserve">per H, ipſi A C, parallela agatur H G.</s>
  <s xml:id="echoid-s31039" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1606" type="float" level="2" n="3">
<note position="left" xlink:label="note-0501-04" xlink:href="note-0501-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0501-05" xlink:href="note-0501-05a" xml:space="preserve">Quomodo Geo <lb/>metricè ex alti-<lb/>tudine Solis lõ-<lb/>gitudo vmbræ <lb/>inueniatur.</note>
</div>
</div>
<div xml:id="echoid-div1608" type="section" level="1" n="408">
<head xml:id="echoid-head422" xml:space="preserve">PROBLEMA 3. PROPOSITIO 3.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s31040" xml:space="preserve">ARCVM cuiuſuis circuli maximi interceptum inter Verticalem <lb/>eius circulum propriè dictum, &amp; </s>
  <s xml:id="echoid-s31041" xml:space="preserve">Verticalem illum, qui qualibet hora <lb/>per centrum Solis ducitur, inueſtigare.</s>
  <s xml:id="echoid-s31042" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s31043" xml:space="preserve">REPETATVR tertia figura propoſ. </s>
  <s xml:id="echoid-s31044" xml:space="preserve">36. </s>
  <s xml:id="echoid-s31045" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31046" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31047" xml:space="preserve">in qua A B C D, ſit circulus maximus propoſi-<lb/>
<anchor type="note" xlink:label="note-0501-07a" xlink:href="note-0501-07"/>
tus, ſiue is Horizon ſit, ſiue nõ; </s>
  <s xml:id="echoid-s31048" xml:space="preserve">Meridianus ipſius proprius B E D, per polos nimirũ eius, &amp; </s>
  <s xml:id="echoid-s31049" xml:space="preserve">per po <lb/>los mundi ductus; </s>
  <s xml:id="echoid-s31050" xml:space="preserve">A F C, Aequator; </s>
  <s xml:id="echoid-s31051" xml:space="preserve">G I, parallelus Solis ſiue borealis, ſiue auſtralis; </s>
  <s xml:id="echoid-s31052" xml:space="preserve">A E C, Vertica <lb/>lis circuli propoſiti proprie dictus, trãſiens videlicet per polos ipſius, &amp; </s>
  <s xml:id="echoid-s31053" xml:space="preserve">per polos Meridiani pro-<lb/>prij; </s>
  <s xml:id="echoid-s31054" xml:space="preserve">E L O, Verticalis per centrũ Solis in L, conſtituti ductus; </s>
  <s xml:id="echoid-s31055" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31056" xml:space="preserve">N L, circulus horarius per polos <lb/>
<anchor type="note" xlink:label="note-0501-08a" xlink:href="note-0501-08"/>
mundi, &amp; </s>
  <s xml:id="echoid-s31057" xml:space="preserve">centrũ Solis tranſiens hora propoſita. </s>
  <s xml:id="echoid-s31058" xml:space="preserve">Erit igitur A O, arcus inter dictos duos Verticales <lb/>
<anchor type="figure" xlink:label="fig-0501-01a" xlink:href="fig-0501-01"/>
<anchor type="note" xlink:label="note-0501-09a" xlink:href="note-0501-09"/>
circulos poſitus: </s>
  <s xml:id="echoid-s31059" xml:space="preserve">quẽita inueniemus. </s>
  <s xml:id="echoid-s31060" xml:space="preserve">Quoniã in triangulo ſphęrico E N L, per propoſ. </s>
  <s xml:id="echoid-s31061" xml:space="preserve">17. </s>
  <s xml:id="echoid-s31062" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31063" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s31064" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s31065" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s31066" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s31067" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31068" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31069" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31070" xml:space="preserve">Gebri, aut per propoſ. </s>
  <s xml:id="echoid-s31071" xml:space="preserve">41. </s>
  <s xml:id="echoid-s31072" xml:space="preserve">noſtrorum trian <lb/>gulorum ſphæricorum, eſt vt ſinus arcus E L, complementi altitudinis Solis ſupra circulum pro-<lb/>poſitum, ad ſinũ anguli E N L, diſtantię Solis à Meridiano circuli propoſiti, ita ſinus arcus N L, <lb/>complementi declinationis ( Sole enim in parallelo auſtrali exiſtente, vt in quarto circulo, arcus <lb/>N L, eundem ſinum habet, quem reliquus arcus ex ſemicirculo, qui inter L, &amp; </s>
  <s xml:id="echoid-s31073" xml:space="preserve">polum alterum
<pb o="486" file="0502" n="502" rhead="GNOMONICES"/>
includitur, complementumq́ue eſt declinationis L M.) </s>
  <s xml:id="echoid-s31074" xml:space="preserve">ad ſinum anguli N E L; </s>
  <s xml:id="echoid-s31075" xml:space="preserve">Si fiat vt ſinus <lb/>complementi altitudinis Solis ad ſinum diſtantiæ Solis à Meridiano propoſiti circuli, i<unsure/>ta ſinus <lb/>complementi declinationis ad aliud, inuenietur ſinus anguli N E L, ſiue arcns D O, cuius comple-<lb/>mentũ eſt A O, arcus quæſitus, quem ita ex arcu D O, inueſtigabimus. </s>
  <s xml:id="echoid-s31076" xml:space="preserve">Si Sol vltra Verticalẽ pro-<lb/>prium verſus polum occultũ extiterit, vt in primo, &amp; </s>
  <s xml:id="echoid-s31077" xml:space="preserve">quarto circulo, (quod qua ratione cogno-<lb/>ſcatur, paulo poſt in ſcholio explicabitur) auferemus arcũ B O, ſinui inuento anguli B E O, debitũ <lb/>(Habet enim angulus hic, vel arcus B O, eundem ſinum, quem angulus N E L, vel arcus D O, <lb/>
<anchor type="figure" xlink:label="fig-0502-01a" xlink:href="fig-0502-01"/>
<anchor type="note" xlink:label="note-0502-01a" xlink:href="note-0502-01"/>
<anchor type="note" xlink:label="note-0502-02a" xlink:href="note-0502-02"/>
cùm duo illi anguli ſint duobus rectis æquales, &amp; </s>
  <s xml:id="echoid-s31078" xml:space="preserve">dicti duo arcus ſemicirculũ conficiant) ex qua-<lb/>drãte A B, remanebitq́ue arcus quæſitus A O, verſus polum occultum notus. </s>
  <s xml:id="echoid-s31079" xml:space="preserve">Si vero Sol citra Ver-<lb/>ticalem proprie dictum verſus polum conſpicuum fuerit inuentus, vt in ſecundo, tertio, &amp; </s>
  <s xml:id="echoid-s31080" xml:space="preserve">ſexto <lb/>circulo, detrahemus arcũ D O, ſinui inuento anguli N E L, reſpondentem ex quadrante A D, re-<lb/>linqueturq́ue arcus quæſitus A O, verſus polum conſpicuum.</s>
  <s xml:id="echoid-s31081" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1608" type="float" level="2" n="1">
<note position="right" xlink:label="note-0501-07" xlink:href="note-0501-07a" xml:space="preserve">Qua via arcus <lb/>cuiuſuis circuli <lb/>maxi<unsure/>mi interce <lb/>pt<unsure/>us inter eius <lb/>Verticalem pro <lb/>p@@è dictum, <lb/>&amp; alium Verti-<lb/>calem, qui per <lb/>Solem ducitur, <lb/>inquirendus ſit.</note>
<note position="left" xlink:label="note-0501-08" xlink:href="note-0501-08a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0501-01" xlink:href="fig-0501-01a">
    <image file="0501-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0501-01"/>
  </figure>
<note position="left" xlink:label="note-0501-09" xlink:href="note-0501-09a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0502-01" xlink:href="fig-0502-01a">
    <image file="0502-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0502-01"/>
  </figure>
<note position="left" xlink:label="note-0502-01" xlink:href="note-0502-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0502-02" xlink:href="note-0502-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s31082" xml:space="preserve">FACILIVS autem redditur problema, Sole exiſtente in Æquatore, propterea quod tunc <lb/>
<anchor type="note" xlink:label="note-0502-03a" xlink:href="note-0502-03"/>
multiplicatio fit per ſin ũ totum. </s>
  <s xml:id="echoid-s31083" xml:space="preserve">Si enim in primo circulo concipiatur parallelus G H I, eſſe Æ-<lb/>quator, ita vt Verticalis proprie dictus tranſeat per G, &amp; </s>
  <s xml:id="echoid-s31084" xml:space="preserve">I, &amp; </s>
  <s xml:id="echoid-s31085" xml:space="preserve">arcus, qui quęritur, ſit G O, erit <lb/>arcus N L, quadrans, cui reſpondet ſinus totus, non autem ſinus complementi declinationis, vt <lb/>
<anchor type="note" xlink:label="note-0502-04a" xlink:href="note-0502-04"/>
prius. </s>
  <s xml:id="echoid-s31086" xml:space="preserve">Vnde ſi fiat, vt ſinus arcus E L, complementi altitudinis Solis ad ſinum anguli E N L, di-<lb/>ſtantiæ Solis à Meridiano propoſiti circuli, ita ſinus totus quadrantis N L, ad aliud, inuenietur ſi-<lb/>nus anguli N E L, ſeu B E O, cuius arcus B O, ex quadrante B G, ſublatus relinquet arcum quæ-<lb/>ſitum G O, &amp;</s>
  <s xml:id="echoid-s31087" xml:space="preserve">c.</s>
  <s xml:id="echoid-s31088" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1609" type="float" level="2" n="2">
<note position="left" xlink:label="note-0502-03" xlink:href="note-0502-03a" xml:space="preserve">Idem arcus faci <lb/>l@us inueſt@ga@ <lb/>tur @ẽpore æqui <lb/>noctiorum.</note>
<note position="left" xlink:label="note-0502-04" xlink:href="note-0502-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Quando dictus <lb/>ar<unsure/>cus aut nihil <lb/>eſt, aut<unsure/> quadrã <lb/>ti æqualis.</note>
<p>
  <s xml:id="echoid-s31089" xml:space="preserve">HIC arcus nihil eſt, Sole exiſtente in Verticali proprie dicto circuli propoſiti: </s>
  <s xml:id="echoid-s31090" xml:space="preserve">quadranti autẽ <lb/>æqualis eſt, eodem conſtituto in Meridiano eiuſdem circuli propoſiti, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s31091" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s31092" xml:space="preserve">EVNDEM arcũ in Meridiano Horizõtis hac ratione inueniemus. </s>
  <s xml:id="echoid-s31093" xml:space="preserve">Repetatur figura propoſ. </s>
  <s xml:id="echoid-s31094" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s31095" xml:space="preserve">huius libri, in qua dictus arcus eſt <lb/>
<anchor type="note" xlink:label="note-0502-06a" xlink:href="note-0502-06"/>
<anchor type="figure" xlink:label="fig-0502-02a" xlink:href="fig-0502-02"/>
E I; </s>
  <s xml:id="echoid-s31096" xml:space="preserve">cum Æquator B E D, ſit Vertica <lb/>lis proprie dictus Meridiani Hori-<lb/>
<anchor type="note" xlink:label="note-0502-07a" xlink:href="note-0502-07"/>
zontis, &amp; </s>
  <s xml:id="echoid-s31097" xml:space="preserve">B H I, Verticalis per B, po <lb/>lum Meridiani, &amp; </s>
  <s xml:id="echoid-s31098" xml:space="preserve">H, locum Solis <lb/>ductus. </s>
  <s xml:id="echoid-s31099" xml:space="preserve">Quia vero in triangulo ſphę <lb/>rico B H K, angulus K, rectus eſt; <lb/></s>
  <s xml:id="echoid-s31100" xml:space="preserve">erit per propoſ. </s>
  <s xml:id="echoid-s31101" xml:space="preserve">16. </s>
  <s xml:id="echoid-s31102" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31103" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31104" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s31105" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s31106" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s31107" xml:space="preserve"><lb/>13. </s>
  <s xml:id="echoid-s31108" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31109" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31110" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s31111" xml:space="preserve">41. </s>
  <s xml:id="echoid-s31112" xml:space="preserve"><lb/>noſtrorum triangulorum ſphærico-<lb/>rum, vt ſinus arcus B H, complemen <lb/>ti altitudinis Solis ſupra Meridianũ <lb/>
<anchor type="note" xlink:label="note-0502-08a" xlink:href="note-0502-08"/>
Horizontis, ad ſinum totum anguli <lb/>recti K, ita ſinus arcus H K, declina-<lb/>tionis ad ſinum anguli H B K, ſeu <lb/>arcus E I, quæſiti. </s>
  <s xml:id="echoid-s31113" xml:space="preserve">Si igitur fiat, vt ſi-<lb/>nus complementi altitudininis So-<lb/>lis ſupra Meridianum ad ſinum to-<lb/>tum, ita ſinus declinationis ad aliud, <lb/>reperietur ſinus arcus Meridiani in-<lb/>ter duos Verticales incluſus, qui <lb/>quæritur.</s>
  <s xml:id="echoid-s31114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1610" type="float" level="2" n="3">
<note position="left" xlink:label="note-0502-06" xlink:href="note-0502-06a" xml:space="preserve">Quo pacto idẽ <lb/>arcus in Meri-<lb/>diano Horizon <lb/>ti<unsure/>s<unsure/> inueniatur.</note>
  <figure xlink:label="fig-0502-02" xlink:href="fig-0502-02a">
    <image file="0502-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0502-02"/>
  </figure>
<note position="left" xlink:label="note-0502-07" xlink:href="note-0502-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0502-08" xlink:href="note-0502-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s31115" xml:space="preserve">POSTREMO arcum quoque eundem in Horizonte recto, circulove horæ 6. </s>
  <s xml:id="echoid-s31116" xml:space="preserve">à meridie,
<pb o="487" file="0503" n="503" rhead="LIBER QVINTVS."/>
vel media nocte reperiemus hoc modo. </s>
  <s xml:id="echoid-s31117" xml:space="preserve">Quoniam in triangulo ſphęrico E H K, angulus K, rectus <lb/>
<anchor type="note" xlink:label="note-0503-01a" xlink:href="note-0503-01"/>
eſt, erit per eandem propoſ. </s>
  <s xml:id="echoid-s31118" xml:space="preserve">16. </s>
  <s xml:id="echoid-s31119" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31120" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31121" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s31122" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s31123" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s31124" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31125" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31126" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31127" xml:space="preserve">Gebri, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s31128" xml:space="preserve">41. </s>
  <s xml:id="echoid-s31129" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus E H, complementi altitudinis So <lb/>lis ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s31130" xml:space="preserve">Horizontem ve rectum, ad ſinum totum anguli recti K, ita ſinus arcus <lb/>H K, declinationis ad ſinum anguli H E K, ſiue arcus B L, inter Verticalem proprie dictum B E D, <lb/>(Æquator enim per E, polum dicti circuli ductus eſt Verticalis eius primarius) &amp; </s>
  <s xml:id="echoid-s31131" xml:space="preserve">Verticalem E L, <lb/>per centrum Solis H, ductum interiecti. </s>
  <s xml:id="echoid-s31132" xml:space="preserve">Quamobrem, ſi fiat, vt ſinus complementi altitudinis <lb/>Solis ſupra circulum horæ 6. </s>
  <s xml:id="echoid-s31133" xml:space="preserve">aut Horizontem rectum, ad ſinum totum, ita ſinus declinationis <lb/>ad aliud, reperietur ſinus arcus dicti circuli inter nominatos d<unsure/>uos Verticales poſiti.</s>
  <s xml:id="echoid-s31134" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1611" type="float" level="2" n="4">
<note position="right" xlink:label="note-0503-01" xlink:href="note-0503-01a" xml:space="preserve">Idem arcus qua <lb/>v@a in Horizon <lb/>te recto, vel cir-<lb/>culo ho@æ 6 à <lb/>mer. &amp; med. <lb/>noc. inquiren-<lb/>dus ſit.</note>
</div>
<p>
  <s xml:id="echoid-s31135" xml:space="preserve">HOSCE autẽ arcus, doctrinæ cauſa, appellabimus latitudines vmbrarum, quia, vt propoſ. </s>
  <s xml:id="echoid-s31136" xml:space="preserve">5. <lb/></s>
  <s xml:id="echoid-s31137" xml:space="preserve">
<anchor type="note" xlink:label="note-0503-02a" xlink:href="note-0503-02"/>
<anchor type="note" xlink:label="note-0503-03a" xlink:href="note-0503-03"/>
huius lib. </s>
  <s xml:id="echoid-s31138" xml:space="preserve">docebimus, ex ipſis cognoſcem<unsure/>us, quantam habeat latitudinem vmbra gnomonis in <lb/>circulo propoſito, hoc eſt, in quam partem proijciatur qualibet hora propoſita. </s>
  <s xml:id="echoid-s31139" xml:space="preserve">Arcum igitur <lb/>cuiuſuis circuli maximi interceptum inter Verticalem eius circulum, &amp;</s>
  <s xml:id="echoid-s31140" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31141" xml:space="preserve">inueſtigauimus. </s>
  <s xml:id="echoid-s31142" xml:space="preserve">Quod <lb/>faciendum erat.</s>
  <s xml:id="echoid-s31143" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1612" type="float" level="2" n="5">
<note position="left" xlink:label="note-0503-02" xlink:href="note-0503-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0503-03" xlink:href="note-0503-03a" xml:space="preserve">Latitudines vm <lb/>brarum quæ ap <lb/>pellentur.</note>
</div>
<note position="right" xml:space="preserve">Latitudines vm <lb/>brarum pro ho-<lb/>ris ſupra vnam <lb/>faciem cir<unsure/>culi <lb/>propoſiti ſuppu <lb/>tatæ, eędem sũt <lb/>pro horis ſupra <lb/>oppoſitam faciẽ <lb/>eiuſdem cir<unsure/>culi, <lb/>ſi horæ à mer. <lb/>&amp; or. mut<unsure/>entur <lb/>in horas<unsure/> à med. <lb/>n@c. &amp; occ. &amp; <lb/>pa ralleli borea-<lb/>les in auſtrales, <lb/>&amp; contra.</note>
</div>
<div xml:id="echoid-div1614" type="section" level="1" n="409">
<head xml:id="echoid-head423" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s31144" xml:space="preserve">SATIS eſt autem, ſi inueſligentur huiuſmodi arcus ad ſingulas hor{as} in vna facie circuli maximi <lb/>propoſiti. </s>
  <s xml:id="echoid-s31145" xml:space="preserve">Hi enim ijdem ſ@nt in altera facie pro eiſdem horis numero, dummodo horæ ab ortu, &amp; </s>
  <s xml:id="echoid-s31146" xml:space="preserve">me-<lb/>ridie in parallelo ♋, mutentur in horas ab occaſu, &amp; </s>
  <s xml:id="echoid-s31147" xml:space="preserve">media nocte in parallelo ♑, &amp; </s>
  <s xml:id="echoid-s31148" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s31149" xml:space="preserve">Nam, vt <lb/>
<anchor type="note" xlink:label="note-0503-05a" xlink:href="note-0503-05"/>
ſupra oſtendimus propoſ. </s>
  <s xml:id="echoid-s31150" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31151" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31152" xml:space="preserve">huiuſmodi horæ, ſi dicta permutatio fiat, eaſdem habent altitudi-<lb/>nes ſupra vtramque faciẽ circuli maximi propoſiti, æquali<unsure/>ter{q́ue} diſtant à Meridiano, vel Horizonte.</s>
  <s xml:id="echoid-s31153" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1614" type="float" level="2" n="1">
<note position="left" xlink:label="note-0503-05" xlink:href="note-0503-05a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s31154" xml:space="preserve">SED vt ſciam{us}, num Sol data hora existat vltra circulum Verticalem, an vero in ipſo Vertica-<lb/>li, aut citra eundem, quando nimirum in parallelo existit, qui à uerticali ſecatur in hemiſphærio ſupra <lb/>propoſitum circulum, (qualis eſt ille, qui inter Aequatorẽ, &amp; </s>
  <s xml:id="echoid-s31155" xml:space="preserve">polum conſpicuum ſupra circulum propoſi <lb/>
<anchor type="note" xlink:label="note-0503-06a" xlink:href="note-0503-06"/>
tum cxiſtit, minorem{q́ue} declinationem habet ipſa altitudine poli ſupra datum circulum. </s>
  <s xml:id="echoid-s31156" xml:space="preserve">Parallelus enim <lb/>inter polum conſpicuum, &amp; </s>
  <s xml:id="echoid-s31157" xml:space="preserve">Aequatorem habens maiorẽ declinationem altitudine poli ſupra datum cir-<lb/>culũ, nulla ratione à Vertic@li ſecatur, parallelus autẽ inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s31158" xml:space="preserve">polum occultu m vel non <lb/>ſecatur à Verticali, vel certe in hemiſphærio infra propoſitum cir culum ſecatur, vt manifeſtum eſt.) </s>
  <s xml:id="echoid-s31159" xml:space="preserve">in-<lb/>ueſtig abim{us} pri{us}, ex ĳs, quę partim propoſ. </s>
  <s xml:id="echoid-s31160" xml:space="preserve">36. </s>
  <s xml:id="echoid-s31161" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31162" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31163" xml:space="preserve">partim vero propoſ. </s>
  <s xml:id="echoid-s31164" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31165" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31166" xml:space="preserve">ostendim{us}, <lb/>
<anchor type="note" xlink:label="note-0503-07a" xlink:href="note-0503-07"/>
<anchor type="note" xlink:label="note-0503-08a" xlink:href="note-0503-08"/>
quanta ſit diſtantia Solis à Meridiano propoſiti circuli, cum in Verticali circulo eiuſdem conſtituitur. <lb/></s>
  <s xml:id="echoid-s31167" xml:space="preserve">Nam ſi data hora habuerit à Meridiano minorem diſtantiam illa inuenta, exiſtet Sol vltra Verticalem; </s>
  <s xml:id="echoid-s31168" xml:space="preserve"><lb/>ſi æqualem, in ipſomet Verticali reperietur; </s>
  <s xml:id="echoid-s31169" xml:space="preserve">ſi denique maiorem, citra Verticalem erit collocatus. </s>
  <s xml:id="echoid-s31170" xml:space="preserve">Vel <lb/>certe inueniemus per ea, quæ in propoſ. </s>
  <s xml:id="echoid-s31171" xml:space="preserve">36. </s>
  <s xml:id="echoid-s31172" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31173" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31174" xml:space="preserve">demonſtrauim{us}, quantam altitudinem Sol habeat in <lb/>proprio Verticali circuli propoſiti. </s>
  <s xml:id="echoid-s31175" xml:space="preserve">Si enim data hora maiorem habuerit altitudinem illa inuenta, exiſtet <lb/>Sol vltra Verticalem; </s>
  <s xml:id="echoid-s31176" xml:space="preserve">ſi æqualem, in ipſomet Verticali; </s>
  <s xml:id="echoid-s31177" xml:space="preserve">ſi denique minorem, citra Verticalem erit col-<lb/>
<anchor type="note" xlink:label="note-0503-09a" xlink:href="note-0503-09"/>
locatus. </s>
  <s xml:id="echoid-s31178" xml:space="preserve">Appellam{us} autem in omnib{us} cir culis maximis illam partẽ citra Verticalem circulum ipſi{us}, <lb/>quæ ab eius Verticali verſ{us} polum conſpicuum, qui nimirum ſupra circulum datum eleuatur, vergit, <lb/>illam vero vltra Verticalem, quę ab eius Verticali verſus polum alterum, qui occult{us} eſt, recedit; </s>
  <s xml:id="echoid-s31179" xml:space="preserve">at-<lb/>que hæc in horologĳs ſemper verſus centrum horologĳ à ſtylo remouetur, illa vero verſus lineam æqui-<lb/>
<anchor type="note" xlink:label="note-0503-10a" xlink:href="note-0503-10"/>
noctialem.</s>
  <s xml:id="echoid-s31180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1615" type="float" level="2" n="2">
<note position="right" xlink:label="note-0503-06" xlink:href="note-0503-06a" xml:space="preserve">An Sol dat<unsure/>a ho <lb/>ra exiſtat in <lb/>Verticali, an <lb/>vero citra, vel <lb/>vltra eundem, <lb/>quo pacto co-<lb/>gnoſcatur.</note>
<note position="left" xlink:label="note-0503-07" xlink:href="note-0503-07a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0503-08" xlink:href="note-0503-08a" xml:space="preserve">Qui paralleli <lb/>Æ quatoris à <lb/>Ver<unsure/>ticali pro-<lb/>prio cuiuſque <lb/>circuli propoſi-<lb/>ti ſecentur, qua <lb/>t<unsure/>atione cognoſ-<lb/>catur.</note>
<note position="right" xlink:label="note-0503-09" xlink:href="note-0503-09a" xml:space="preserve">Quæ pars dica-<lb/>tur citra Verti-<lb/>calem cuiuſque <lb/>cir<unsure/>culi maxi mi <lb/>&amp; quæ vltra <lb/>Verticalem.</note>
<note position="left" xlink:label="note-0503-10" xlink:href="note-0503-10a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Quãdo omnes <lb/>vmbt<unsure/>a@um la@i <lb/>tu dines ſint ci-<lb/>tra Vertical@m <lb/>circulum.</note>
<p style="it">
  <s xml:id="echoid-s31181" xml:space="preserve">QVOD ſi quando parallel{us} inter polum conſpicuum ſupra cir culum maximum propoſitũ, &amp; </s>
  <s xml:id="echoid-s31182" xml:space="preserve">Ae-<lb/>quatorem non ſecet Verticalem proprium ipſius circuli maximi, (quod tum demum accidet, cum decli-<lb/>natio paralleli maior fuerit altitudine poli ſupra circulum maximum propoſitum) crunt omnes huiuſ-<lb/>modi arcus latitudinum vmbrarum citra Verticalem, hoc eſt, verſus polum conſpicuum ſupra datum <lb/>circulum, ſiue verſus lineam æquinoctialem horologĳ, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s31183" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s31184" xml:space="preserve">HAC arte ſupputauimus varias tabellas, in quibus dicti arcus latitudinesve vmbrarum continẽtur <lb/>ad ſingulas horas ſiuc à meridie vel med. </s>
  <s xml:id="echoid-s31185" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31186" xml:space="preserve">ſiue ab or. </s>
  <s xml:id="echoid-s31187" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s31188" xml:space="preserve">ſupputatas, ſiue etiam inæquales in <lb/>eiſdem circulis maximis, ſupra quos in propoſ. </s>
  <s xml:id="echoid-s31189" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31190" xml:space="preserve">altitudines Solis inueſtigauimus; </s>
  <s xml:id="echoid-s31191" xml:space="preserve">quas quidem tabel-<lb/>las in propoſ. </s>
  <s xml:id="echoid-s31192" xml:space="preserve">5. </s>
  <s xml:id="echoid-s31193" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31194" xml:space="preserve">reperies, vbi varia horologia ex hiſce tabellis construem{us}.</s>
  <s xml:id="echoid-s31195" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1617" type="section" level="1" n="410">
<head xml:id="echoid-head424" xml:space="preserve">PROBLEMA 4. PROPOSITIO 4.</head>
<p>
  <s xml:id="echoid-s31196" xml:space="preserve">ARCVM cuiuſuis dati circuli maximi per polos mundi non tran <lb/>ſeuntis, incluſum inter circulum maximum, qui per polos mundi, &amp; </s>
  <s xml:id="echoid-s31197" xml:space="preserve"><lb/>cõmunes ſectiones Aequatoris, datiq́; </s>
  <s xml:id="echoid-s31198" xml:space="preserve">circuli maximi tranſit, (qualis eſt <lb/>circulus horæ 6. </s>
  <s xml:id="echoid-s31199" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31200" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31201" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31202" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31203" xml:space="preserve">in Horizonte, Verticali, omniq́; </s>
  <s xml:id="echoid-s31204" xml:space="preserve">alio <lb/>circulo ad Horizontem quidem inclinato, ad Meridianum autẽ Hori-
<pb o="488" file="0504" n="504" rhead="GNOMONICES"/>
zontis recto) &amp; </s>
  <s xml:id="echoid-s31205" xml:space="preserve">quemuis alium horariũ circulum, qui per polos mun <lb/>di, &amp; </s>
  <s xml:id="echoid-s31206" xml:space="preserve">centrum Solis qualibet hora ducitur, indagare.</s>
  <s xml:id="echoid-s31207" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s31208" xml:space="preserve">SIT circulus maximus A B C D, ſiue is Horizon ſit, ſiue nõ, dummodo per polos mundi non <lb/>
<anchor type="note" xlink:label="note-0504-01a" xlink:href="note-0504-01"/>
tranſeat; </s>
  <s xml:id="echoid-s31209" xml:space="preserve">Meridianus ipſius proprius A E C, tranſiens per F, G, polos mundi; </s>
  <s xml:id="echoid-s31210" xml:space="preserve">Æquator B E D; <lb/></s>
  <s xml:id="echoid-s31211" xml:space="preserve">circulus horarius per eoſdem polos ductus F H G, ſecans Æquatorem in H, &amp; </s>
  <s xml:id="echoid-s31212" xml:space="preserve">circulum propoſi-<lb/>
<anchor type="figure" xlink:label="fig-0504-01a" xlink:href="fig-0504-01"/>
tum in I, ſitq́uearcus E H, diſtantiæ Solis à Meridia-<lb/>no minor quadrante, ſiue ſex horis. </s>
  <s xml:id="echoid-s31213" xml:space="preserve">Inquirẽdus eſt ar-<lb/>cus I B, circuli propoſiti inter B, cõmunem ſectionem <lb/>eius, &amp; </s>
  <s xml:id="echoid-s31214" xml:space="preserve">Æquatoris, (per quã nimirũ ducitur horarius <lb/>
<anchor type="note" xlink:label="note-0504-02a" xlink:href="note-0504-02"/>
circulus inſtar circuli horæ 6. </s>
  <s xml:id="echoid-s31215" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31216" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31217" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31218" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31219" xml:space="preserve">in Ho <lb/>rizonte) atq; </s>
  <s xml:id="echoid-s31220" xml:space="preserve">horariũ circulũ F H G. </s>
  <s xml:id="echoid-s31221" xml:space="preserve">Quoniã in trian-<lb/>gulo ſphęrico A G I, angulus A, rectus eſt, erit per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s31222" xml:space="preserve">18. </s>
  <s xml:id="echoid-s31223" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31224" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31225" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s31226" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s31227" xml:space="preserve">de triangulis, vel per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s31228" xml:space="preserve">14. </s>
  <s xml:id="echoid-s31229" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31230" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31231" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s31232" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31233" xml:space="preserve">noſtrorũ trian-<lb/>gulorũ ſphæricorũ, vt ſinus anguli G, diſtantiæ Solis à <lb/>Meridiano proprio propoſiti circuli, ad ſinũ totũ, ita <lb/>ſinus cõplementi anguli I, ad ſinum cõplementi arcus <lb/>A G, altitudinis poli ſupra circulum propoſitum. </s>
  <s xml:id="echoid-s31234" xml:space="preserve">Et <lb/>conuertendo; </s>
  <s xml:id="echoid-s31235" xml:space="preserve">vt ſinus totus ad ſinum diſtantiæ Solis <lb/>
<anchor type="note" xlink:label="note-0504-03a" xlink:href="note-0504-03"/>
à Meridiano proprio dati circuli, ita ſinus complemen <lb/>ti altitudinis poli ad ſinum complementi anguli I. <lb/></s>
  <s xml:id="echoid-s31236" xml:space="preserve">Eſt autem in triangulo B H I, per propoſ. </s>
  <s xml:id="echoid-s31237" xml:space="preserve">16. </s>
  <s xml:id="echoid-s31238" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31239" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31240" xml:space="preserve"><lb/>Ioan. </s>
  <s xml:id="echoid-s31241" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s31242" xml:space="preserve">de triangulis, vel per propoſ. </s>
  <s xml:id="echoid-s31243" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31244" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31245" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s31246" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s31247" xml:space="preserve">41. </s>
  <s xml:id="echoid-s31248" xml:space="preserve">noſtrorum triangulorum <lb/>ſphæricorum, vt ſinus anguli I, ad ſinum arcus B H, <lb/>complementi diſtantiæ Solis à proprio Meridiano da-<lb/>ti circuli, ita ſinus totus anguli recti H, ad ſinum arcus B I, qui quærendus proponitur. </s>
  <s xml:id="echoid-s31249" xml:space="preserve">Igi-<lb/>tur ſi fiat, vt ſinus totus ad ſinum diſtantiæ Solis à Meridiano proprio dati circuli, ita ſinus <lb/>complementi altitudinis poli ſupra circulum propoſitum ad aliud, inuenietur ſinus cuiuſdam ar <lb/>
<anchor type="note" xlink:label="note-0504-04a" xlink:href="note-0504-04"/>
cus, cuius complementum dabit angulum I. </s>
  <s xml:id="echoid-s31250" xml:space="preserve">Quod ſi rurſum fiat, vt ſinus anguli I, inuenti ad ſi-<lb/>num complementi diſtantię Solis à Meridiano proprio propoſiti circuli, ita ſinus totus ad aliud, <lb/>habebitur ſinus illius arcus circuli maximi propoſiti, qui inquiritur.</s>
  <s xml:id="echoid-s31251" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1617" type="float" level="2" n="1">
<note position="left" xlink:label="note-0504-01" xlink:href="note-0504-01a" xml:space="preserve">Qua arte ſuppu <lb/>te@ut<unsure/>arcus cu-<lb/>iusuis circuli <lb/>maximi per po <lb/>los mundi non <lb/>tran@euntis po-<lb/>ſitus inter circu <lb/>lum maximum <lb/>per polos mun-<lb/>di, cõmuneſq́; <lb/>ſectiones Æqua <lb/>toris, ac dati <lb/>circuli (i<unsure/>nſtar <lb/>circuli horæ 6. <lb/>à mer &amp; med. <lb/>noc. in Horizõ <lb/>@e) ductum, &amp; <lb/>quemuis alium <lb/>ho@arium circu <lb/>lum, qui per po <lb/>los mundi, &amp; <lb/>Solem ducitur.</note>
  <figure xlink:label="fig-0504-01" xlink:href="fig-0504-01a">
    <image file="0504-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0504-01"/>
  </figure>
<note position="left" xlink:label="note-0504-02" xlink:href="note-0504-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0504-03" xlink:href="note-0504-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0504-04" xlink:href="note-0504-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s31252" xml:space="preserve">QVOD ſi alius circulus horarius deſcribatur F K, ſecans Æquatorem in K, &amp; </s>
  <s xml:id="echoid-s31253" xml:space="preserve">propoſitum <lb/>circulum in L, ita vt arcus E K, diſtãtiæ Solis à proprio Meridiano dati circuli maior ſit quadran <lb/>te, ſeu ſex horis, eodem pacto arcus B L, inuenietur. </s>
  <s xml:id="echoid-s31254" xml:space="preserve">Erit enim, vt prius, in triangulo ſphærico <lb/>C F L, quemadmodum ſinus totus ad ſinũ anguli C F L, diſtantiæ Solis à proprio Meridiano dati <lb/>circuli (habent e<unsure/>nim anguli C F L, E F K, eundem ſinũ, cum æquales ſint duobus rectis) ita ſinus <lb/>complementi arcus C F, altitudinis poli ſupra circulum propoſitum, ad ſinum complementi an-<lb/>guli L, atque adeo angulus ipſe L, notus erit. </s>
  <s xml:id="echoid-s31255" xml:space="preserve">Rurſus in triangulo B K L, eſt, vt ſinus anguli L, ad <lb/>
<anchor type="note" xlink:label="note-0504-05a" xlink:href="note-0504-05"/>
ſinum arcus B K, complementi diſtantiæ Solis à Meridiano propoſiti circuli, ita ſinus totus an-<lb/>guli recti K, ad ſinum arcus B L, quęſiti.</s>
  <s xml:id="echoid-s31256" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1618" type="float" level="2" n="2">
<note position="left" xlink:label="note-0504-05" xlink:href="note-0504-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s31257" xml:space="preserve">ARCVS porro huiuſmodi, doctrinæ, &amp; </s>
  <s xml:id="echoid-s31258" xml:space="preserve">breuitatis cauſa, appellare poſſumus arcus horarios <lb/>
<anchor type="note" xlink:label="note-0504-06a" xlink:href="note-0504-06"/>
in propoſito circulo, eo quòd indicent, vt ex ſequentibus fiet perſpicuum, quantum in plano pro-<lb/>poſito inter ſe diſtare debeant lineæ horariæ, ſiue horaria ſpatia, hoc eſt, communes ſectiones pla <lb/>ni propoſiti, &amp; </s>
  <s xml:id="echoid-s31259" xml:space="preserve">horariorũ circulorum, qui per mundi polos ducuntur. </s>
  <s xml:id="echoid-s31260" xml:space="preserve">Diximus autem in propoſ. <lb/></s>
  <s xml:id="echoid-s31261" xml:space="preserve">hoſce arcus incluſos eſſe inter circulum maximum, qui per polos mundi ducitur per commu-<lb/>nes ſectiones Æquatoris, &amp; </s>
  <s xml:id="echoid-s31262" xml:space="preserve">dati circuli, inſtar circuli horæ 6. </s>
  <s xml:id="echoid-s31263" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31264" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31265" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31266" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31267" xml:space="preserve">in Horizõte, atq; </s>
  <s xml:id="echoid-s31268" xml:space="preserve"><lb/>alios circulos horarios, qui per mundi polos ducuntur, non autem inter cõmunes ſectiones Æqua <lb/>toris, datiq́; </s>
  <s xml:id="echoid-s31269" xml:space="preserve">circuli, &amp; </s>
  <s xml:id="echoid-s31270" xml:space="preserve">alios circulos horarios, quod tamen verum eſt; </s>
  <s xml:id="echoid-s31271" xml:space="preserve">vt facilius in propoſ. </s>
  <s xml:id="echoid-s31272" xml:space="preserve">ſequen <lb/>
<anchor type="note" xlink:label="note-0504-07a" xlink:href="note-0504-07"/>
ti demõſtremus, quo pacto ex hiſce arcubus horologia conficiantur in plano, quod propoſito cir-<lb/>culo maximo æquidiſtat.</s>
  <s xml:id="echoid-s31273" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1619" type="float" level="2" n="3">
<note position="left" xlink:label="note-0504-06" xlink:href="note-0504-06a" xml:space="preserve">Arcus horarij <lb/>in propoſito ci@ <lb/>cu@o qui dic<unsure/>an-<lb/>tur.</note>
<note position="left" xlink:label="note-0504-07" xlink:href="note-0504-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s31274" xml:space="preserve">IN Æquatore dicti arcus æquales ſunt diſtantiis Solis à Meridiano circulo, quales ſunt arcus <lb/>E H, E N, &amp;</s>
  <s xml:id="echoid-s31275" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31276" xml:space="preserve">Vnde neceſſe non eſt indagare arcus Æquatoris interiectos inter circulum, qui in-<lb/>ſtar circuli horæ 6. </s>
  <s xml:id="echoid-s31277" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31278" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31279" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31280" xml:space="preserve">in Horizonte ducitur, atque alios circulos horarios, qui <lb/>per polos mundi ducuntur. </s>
  <s xml:id="echoid-s31281" xml:space="preserve">Arcum ergo cuiuſuis circuli maximi per polos mundi non tranſeun-<lb/>
<anchor type="note" xlink:label="note-0504-08a" xlink:href="note-0504-08"/>
tis incluſum inter circulum maximum, &amp; </s>
  <s xml:id="echoid-s31282" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31283" xml:space="preserve">indagauimus. </s>
  <s xml:id="echoid-s31284" xml:space="preserve">Quod erat faciendum.</s>
  <s xml:id="echoid-s31285" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1620" type="float" level="2" n="4">
<note position="left" xlink:label="note-0504-08" xlink:href="note-0504-08a" xml:space="preserve">Quam in part@ <lb/>vergã<unsure/>t arcus ho <lb/>rarij in propoſi <lb/>to circulo, quo <lb/>pacto ex diſtan-<lb/>@ia Solis à Me-<lb/>ridiano proprio <lb/>cogn oſcatur.</note>
</div>
</div>
<div xml:id="echoid-div1622" type="section" level="1" n="411">
<head xml:id="echoid-head425" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s31286" xml:space="preserve">MANIFESTVM autem est, quando distantia Solis à Meridiano proprio dati circuli minor <lb/>eſt quadrante, ſeu ſex horis, dictos arcus tendere à communi ſectione circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s31287" xml:space="preserve">illius maxi-
<pb o="489" file="0505" n="505" rhead="LIBER QVINTVS."/>
mi, qui per polos mundi ducitur, inſtar circuli horæ 6. </s>
  <s xml:id="echoid-s31288" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31289" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31290" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31291" xml:space="preserve">noct. </s>
  <s xml:id="echoid-s31292" xml:space="preserve">in Horizonte, verſus polum <lb/>occultum, vt à puncto B, vel D, verſus A, in horologio autẽ vltra centrum horologĳ, &amp; </s>
  <s xml:id="echoid-s31293" xml:space="preserve">non verſus æqui-<lb/>noctialem lineam; </s>
  <s xml:id="echoid-s31294" xml:space="preserve">quia tunc circulus horarius ſecat quadr antem Aequatoris E B, vel E D, at que adco <lb/>&amp; </s>
  <s xml:id="echoid-s31295" xml:space="preserve">quadrantẽ circuli maximi propoſiti A B, vel A D: </s>
  <s xml:id="echoid-s31296" xml:space="preserve">Quando autem diſtantia Solis à Meridiano fuerit <lb/>quadranti æqualis, id eſt, cũ complectitur ſex horas, dictũ arcum nihil eſſe; </s>
  <s xml:id="echoid-s31297" xml:space="preserve">quod horarius circulus tunc <lb/>per punctum B, vel D, tranſeat. </s>
  <s xml:id="echoid-s31298" xml:space="preserve">Quando vero diſtantia Solis à Meridiano nihil eſt, arcum dictum eſſe <lb/>quadrantem: </s>
  <s xml:id="echoid-s31299" xml:space="preserve">Quando denique eadẽ distantia maior fuerit quadrante, aut ſex horis, dictos arcus tendere <lb/>à cõmuni ſectione circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s31300" xml:space="preserve">illius maximi, qui per polos mundi ducitur, inſtar circuli horæ 6. <lb/></s>
  <s xml:id="echoid-s31301" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31302" xml:space="preserve">et med. </s>
  <s xml:id="echoid-s31303" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31304" xml:space="preserve">in Horizonte, verſus polũ conſpicuũ, vt à puncto B, vel D, verſus C, &amp; </s>
  <s xml:id="echoid-s31305" xml:space="preserve">in horologio <lb/>verſus lineam æquinoctialem, hoc eſt, citra centrum horologĳ; </s>
  <s xml:id="echoid-s31306" xml:space="preserve">propterea quod tunc horarius circulus ca-<lb/>
<anchor type="note" xlink:label="note-0505-01a" xlink:href="note-0505-01"/>
dit vltra punctum B, vel D, in Aequatore, ac proinde quadrantem circuli propoſiti C B, vel C D, <lb/>interſecat.</s>
  <s xml:id="echoid-s31307" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1622" type="float" level="2" n="1">
<note position="left" xlink:label="note-0505-01" xlink:href="note-0505-01a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s31308" xml:space="preserve">IAM vero ſi Meridianus A E C, fuerit vnus ex circulis horarĳs, vel certe æqualiter à duabus ho-<lb/>
<anchor type="note" xlink:label="note-0505-02a" xlink:href="note-0505-02"/>
ris hinc inde poſitis æqualiter remotus, erunt arcus circuli maximi propoſiti binarum horarum æqua-<lb/>liter à Meridiano propoſiti circuli diſtantium, qui inter maximum illum circulum per polos mundi, inſtar <lb/>circuli hor. </s>
  <s xml:id="echoid-s31309" xml:space="preserve">6. </s>
  <s xml:id="echoid-s31310" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31311" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31312" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31313" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31314" xml:space="preserve">ductum, &amp; </s>
  <s xml:id="echoid-s31315" xml:space="preserve">circulos illarum horarũ ductos per polos mundi interĳ-<lb/>ciuntur, æquales, quorum vnus orient alis, &amp; </s>
  <s xml:id="echoid-s31316" xml:space="preserve">alter occident alis est. </s>
  <s xml:id="echoid-s31317" xml:space="preserve">Nam in triangulis ſphæricis A G I, <lb/>A G M, ſi circuli horarĳ F I G, F M G, ponantur æqualiter diſtare à Meridiano F A G, erunt angu-<lb/>li ad G, æquales, propter æqualitatem arcuum E H, E N; </s>
  <s xml:id="echoid-s31318" xml:space="preserve">ſunt autem &amp; </s>
  <s xml:id="echoid-s31319" xml:space="preserve">anguli ad A, recti, &amp; </s>
  <s xml:id="echoid-s31320" xml:space="preserve">latus <lb/>A G, commune, quod æqualibus adiacet angulis. </s>
  <s xml:id="echoid-s31321" xml:space="preserve">Quare per propoſ. </s>
  <s xml:id="echoid-s31322" xml:space="preserve">23. </s>
  <s xml:id="echoid-s31323" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31324" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31325" xml:space="preserve">Menelai, ex traditione <lb/>
<anchor type="note" xlink:label="note-0505-03a" xlink:href="note-0505-03"/>
Franciſci Maurolyci, vel per propoſ. </s>
  <s xml:id="echoid-s31326" xml:space="preserve">20. </s>
  <s xml:id="echoid-s31327" xml:space="preserve">noſtrorum triangulorum ſphæricorum, erunt quoque ar-<lb/>cus A I, A M, æquales, quib{us} ablatis ex quadrantibus A B, A D, ęquales erunt reliqui arcus <lb/>I B, M D.</s>
  <s xml:id="echoid-s31328" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1623" type="float" level="2" n="2">
<note position="right" xlink:label="note-0505-02" xlink:href="note-0505-02a" xml:space="preserve">Qui arcus hora <lb/>rij inter ſe ſint <lb/>æquales.</note>
<note position="left" xlink:label="note-0505-03" xlink:href="note-0505-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s31329" xml:space="preserve">RVRSVS arcus eiuſdem circuli maximi propoſiti reſ@ondentes duabus horis, quarũ vni{us} diſtan-<lb/>tia à Meridiano proprio tanto minor ſit quadrante, quanto altera maior est, æquales erunt. </s>
  <s xml:id="echoid-s31330" xml:space="preserve">Nam ſi duo <lb/>circuli horarĳ F K, F O, æqualiter diſtare ponantur à puncto B, ita vt arcus Aequator is B P, B K, <lb/>
<anchor type="note" xlink:label="note-0505-04a" xlink:href="note-0505-04"/>
æquales ſint, runt in triangulis ſphæricis B K L, B P O, anguli ad verticem B, æquales, &amp; </s>
  <s xml:id="echoid-s31331" xml:space="preserve">anguli K, P, <lb/>recti, &amp; </s>
  <s xml:id="echoid-s31332" xml:space="preserve">latera B k, B P, æqualia. </s>
  <s xml:id="echoid-s31333" xml:space="preserve">Quocirca vt prius, æquales erunt arcus B L, B O.</s>
  <s xml:id="echoid-s31334" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1624" type="float" level="2" n="3">
<note position="right" xlink:label="note-0505-04" xlink:href="note-0505-04a" xml:space="preserve">In Horizonte, <lb/>Verticaliq́ue <lb/>proprie dicto ſa <lb/>ti<unsure/>s eſt, ſi arcus <lb/>horarii ſu ppu-<lb/>tẽtur pro quin-<lb/>que hor is ante <lb/>vel poſt meri-<lb/>diem: In aliis <lb/>autem circulis <lb/>maximis pro il-<lb/>lis 12. horis à <lb/>mer. &amp; med. <lb/>noc. quæ minus <lb/>ſex horis a pro-<lb/>priis Meridia-<lb/>nis abſunt.</note>
</div>
<p style="it">
  <s xml:id="echoid-s31335" xml:space="preserve">EX his ſequitur, ſatis eſſe, ſi in Horizonte, &amp; </s>
  <s xml:id="echoid-s31336" xml:space="preserve">Verticali circulo proprie dicto (ſi de horis à mer. </s>
  <s xml:id="echoid-s31337" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31338" xml:space="preserve"><lb/>med. </s>
  <s xml:id="echoid-s31339" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31340" xml:space="preserve">loquamur) inueſtigentur hui@ſmodi ar cus pro quinque horis ante vel poſt meridiem. </s>
  <s xml:id="echoid-s31341" xml:space="preserve">Nam ar-<lb/>
<anchor type="note" xlink:label="note-0505-05a" xlink:href="note-0505-05"/>
c{us} hor. </s>
  <s xml:id="echoid-s31342" xml:space="preserve">6. </s>
  <s xml:id="echoid-s31343" xml:space="preserve">a mer. </s>
  <s xml:id="echoid-s31344" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31345" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31346" xml:space="preserve">nihil eſt; </s>
  <s xml:id="echoid-s31347" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31348" xml:space="preserve">arc{us} horæ 5. </s>
  <s xml:id="echoid-s31349" xml:space="preserve">poſt meridiem æqualis eſt arcui horæ 7. </s>
  <s xml:id="echoid-s31350" xml:space="preserve">poſt meri <lb/>diem, &amp; </s>
  <s xml:id="echoid-s31351" xml:space="preserve">arc{us} horæ 4 arcui horæ 8. </s>
  <s xml:id="echoid-s31352" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31353" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31354" xml:space="preserve">vt demõſtrauim{us}. </s>
  <s xml:id="echoid-s31355" xml:space="preserve">Immo in alĳs circulis maximis ſatis etiam <lb/>erit, ſi illarum duodecim horarum à mer. </s>
  <s xml:id="echoid-s31356" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31357" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31358" xml:space="preserve">arcus inueſtigentur, quæ min{us} diſtant à Meri-<lb/>diano proprio ipſi{us} circuli, quàm ſex horis, qui quidem omnes, vt ex dictis paret, exiſtũt vltra centrum <lb/>horologĳ, hoc eſt, verſ{us} polum occultũ. </s>
  <s xml:id="echoid-s31359" xml:space="preserve">Nam horum arcuum lineæ horariæ, quæ quidem æquinoctialem <lb/>lineam in horologio ſecabunt, productæ vltra centrum horologĳ dabunt etiam horas, quæ æquinoctialem <lb/>lineam non ſecant, maiorem{q́ue} diſtantiam à Meridiano proprio propoſiti circuli habent, quàm ſex hora-<lb/>rum. </s>
  <s xml:id="echoid-s31360" xml:space="preserve">Quæ omnia ex ſequenti propoſ. </s>
  <s xml:id="echoid-s31361" xml:space="preserve">fient perſpicua.</s>
  <s xml:id="echoid-s31362" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1625" type="float" level="2" n="4">
<note position="left" xlink:label="note-0505-05" xlink:href="note-0505-05a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Altitudo poli <lb/>ſupra Vertica-<lb/>lem proprie di-<lb/>ctum cuiuſque <lb/>regionis, com-<lb/>plemen@um eſt <lb/>altitudinis po-<lb/>li ſupra Horizõ <lb/>tem eiuſdem re <lb/>gionis.</note>
<p style="it">
  <s xml:id="echoid-s31363" xml:space="preserve">CAETERVM quoniã altitudo poli ſupra Verticalẽ circulũ proprie dictũ cuiuſ regionis cõple-<lb/>mentum eſt altitudinis poli ſupra Horizontem eiuſdem regionis; </s>
  <s xml:id="echoid-s31364" xml:space="preserve">cũ arcus Meridiani à vertice per polum <lb/>
<anchor type="note" xlink:label="note-0505-07a" xlink:href="note-0505-07"/>
mundi vſq; </s>
  <s xml:id="echoid-s31365" xml:space="preserve">ad Horizontẽ ductus, qui nimirũ altitudinẽ politam ſupra Verticalẽ, quam ſupra Horizontẽ <lb/>metitur, quadrans ſit, (Id quod etiã propoſ. </s>
  <s xml:id="echoid-s31366" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31367" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31368" xml:space="preserve">3. </s>
  <s xml:id="echoid-s31369" xml:space="preserve">docuimus) efficitur, vt arcus Horizontis cuiusli-<lb/>bet horæ à mer. </s>
  <s xml:id="echoid-s31370" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31371" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31372" xml:space="preserve">in aliqua regione per hanc propoſ. </s>
  <s xml:id="echoid-s31373" xml:space="preserve">ſupputatus, ſit arcus Verticalis eiuſdẽ <lb/>horæ in alia regione, cuius latitudo æqualis ſit complemento latitudinis prioris regionis: </s>
  <s xml:id="echoid-s31374" xml:space="preserve">quia in poſte-<lb/>riori regione eadem eſt altitudo poli ſupra Verticalem, quæ in priori ſupra Horizontem. </s>
  <s xml:id="echoid-s31375" xml:space="preserve">Nam vt ex di-<lb/>ctis conſtat, altitudo poli ſupra Verticalem illius regionis, cuius latitudo cum latitudine prioris regio-<lb/>nis quadrantem conficit, æqualis eſt complemento altitudinis poli ſupra Horizontem eiuſdem regionis, <lb/>hoc est, altitudini poli ſupra Horizontem regionis prioris. </s>
  <s xml:id="echoid-s31376" xml:space="preserve">Quapropter ſatis erit ſupputare dictos arc{us} <lb/>
<anchor type="note" xlink:label="note-0505-08a" xlink:href="note-0505-08"/>
Horizontum omnium latitudinum pro horis à mer. </s>
  <s xml:id="echoid-s31377" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31378" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31379" xml:space="preserve">Nam ĳdem accommodabuntur Ver-<lb/>ticalibus circulis, ſi pro latitudine loci ſumatur eius complementum. </s>
  <s xml:id="echoid-s31380" xml:space="preserve">Vt ſi ſupputati ſint dictiarcus Ho-<lb/>
<anchor type="note" xlink:label="note-0505-09a" xlink:href="note-0505-09"/>
rizontales ad omnes latitudines, erunt quidem arcus ad latitudinem grad. </s>
  <s xml:id="echoid-s31381" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31382" xml:space="preserve">horizontales in regione, <lb/>cuius latitudo grad. </s>
  <s xml:id="echoid-s31383" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31384" xml:space="preserve">complectatur, at arcus ad latitudinem grad. </s>
  <s xml:id="echoid-s31385" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31386" xml:space="preserve">ſupputati erunt Verticales <lb/>in eadem regione latitudinis grad. </s>
  <s xml:id="echoid-s31387" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31388" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31389" xml:space="preserve">c.</s>
  <s xml:id="echoid-s31390" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1626" type="float" level="2" n="5">
<note position="left" xlink:label="note-0505-07" xlink:href="note-0505-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0505-08" xlink:href="note-0505-08a" xml:space="preserve">Qua rarione ar<unsure/> <lb/>cus horarij o-<lb/>mnium Hori-<lb/>zont<unsure/>um ſint <lb/>etiam arcus ho-<lb/>rarij omnium <lb/>Verti calium <lb/>propri<unsure/>e dictorũ</note>
<note position="left" xlink:label="note-0505-09" xlink:href="note-0505-09a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s31391" xml:space="preserve">QVOD ſi arcuum horariorũ, qui per hanc propoſ. </s>
  <s xml:id="echoid-s31392" xml:space="preserve">ſupputantur, complementa accipiantur, habebũ-<lb/>
<anchor type="note" xlink:label="note-0505-10a" xlink:href="note-0505-10"/>
tur ĳdem arcus horarĳ initium habentes à Meridiano proprio circuli maximi propoſiti, quos multi ſcri-<lb/>ptores ſupputarunt. </s>
  <s xml:id="echoid-s31393" xml:space="preserve">Hos tamen ex propoſita figur a ita etiã indagabimus. </s>
  <s xml:id="echoid-s31394" xml:space="preserve">Poſtquam in triangulo A G I, <lb/>inuentus eſt angulus I, vt docuimus, quoniam in eodem triangulo, per propoſ. </s>
  <s xml:id="echoid-s31395" xml:space="preserve">16. </s>
  <s xml:id="echoid-s31396" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31397" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31398" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s31399" xml:space="preserve">Regiom. <lb/></s>
  <s xml:id="echoid-s31400" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s31401" xml:space="preserve">vei per propoſ. </s>
  <s xml:id="echoid-s31402" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31403" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31404" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31405" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s31406" xml:space="preserve">41. </s>
  <s xml:id="echoid-s31407" xml:space="preserve">nostrorum triang. </s>
  <s xml:id="echoid-s31408" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s31409" xml:space="preserve">eſt, vt ſinus <lb/>anguli I, ad ſinum arcus A G, altitudinis poli ſupra circulum propoſitum, ita ſinus anguli G, diſtantiæ <lb/>Solis à Meridiano ad ſinum arcus A I, qui quærendus proponitur: </s>
  <s xml:id="echoid-s31410" xml:space="preserve">Siſiat, vt ſinus totus ad ſinum diſtan <lb/>tię Solis à Meridiano proprio, ita ſinus complementi altitudinis poli ſupra circulũ propoſitum ad aliud,
<pb o="490" file="0506" n="506" rhead="GNOMONICES"/>
inuenietur, vt ſupra, ſi@us cuiuſdam arcus, cuius complementum dabit angulum I. </s>
  <s xml:id="echoid-s31411" xml:space="preserve">Quo<gap/>ſi rurſum fiat, <lb/>vt ſinus anguli I, inuenti ad ſinum altitudinis poli ſupra circulum propoſitum, ita ſinus distantiæ Solis <lb/>à Meridiano proprio ad aliud, habebitur ſinus illius arcus circuli maximi, qui inquiritur.</s>
  <s xml:id="echoid-s31412" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1627" type="float" level="2" n="6">
<note position="right" xlink:label="note-0505-10" xlink:href="note-0505-10a" xml:space="preserve">Quomodo ijdẽ <lb/>ar<unsure/>cus horarij à <lb/>Meridiano pro <lb/>prio initium <lb/>haben@es inue-<lb/>ſtigentur.</note>
</div>
<p style="it">
  <s xml:id="echoid-s31413" xml:space="preserve">TABELLAS porro aliquot arcuum horariorum in ſequenti propoſ. </s>
  <s xml:id="echoid-s31414" xml:space="preserve">exponemus.</s>
  <s xml:id="echoid-s31415" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1629" type="section" level="1" n="412">
<head xml:id="echoid-head426" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
<p>
  <s xml:id="echoid-s31416" xml:space="preserve">HOROLOGIA varia ex tabulis, quas in præcedentibus propo-<lb/>
<anchor type="note" xlink:label="note-0506-01a" xlink:href="note-0506-01"/>
ſitionibus ſupputare docuimus, componere.</s>
  <s xml:id="echoid-s31417" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1629" type="float" level="2" n="1">
<note position="left" xlink:label="note-0506-01" xlink:href="note-0506-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s31418" xml:space="preserve">VT planè, perfecteq́ue cognoſcatur, qua ratione ex tabulis, quas in propoſ. </s>
  <s xml:id="echoid-s31419" xml:space="preserve">præcedentibus <lb/>docuimus ſupputare, horologia conſiciantur, deſcribemus horologia in omnibus illis planis, in <lb/>quibus lib. </s>
  <s xml:id="echoid-s31420" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31421" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31422" xml:space="preserve">3. </s>
  <s xml:id="echoid-s31423" xml:space="preserve">horologia conſtruximus. </s>
  <s xml:id="echoid-s31424" xml:space="preserve">Ita enim fiet, vt omnis varietas, atque difficultas, quæ <lb/>ſubinde oriri poſſet, tollatur, Non deſcribemus autem in omnibus planis omnia quatuor genera <lb/>horarum, vt in 2. </s>
  <s xml:id="echoid-s31425" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31426" xml:space="preserve">3. </s>
  <s xml:id="echoid-s31427" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31428" xml:space="preserve">ſed in quibuſdam horas à mer. </s>
  <s xml:id="echoid-s31429" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31430" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31431" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31432" xml:space="preserve">ſimul ab occ. </s>
  <s xml:id="echoid-s31433" xml:space="preserve">dunta-<lb/>xat: </s>
  <s xml:id="echoid-s31434" xml:space="preserve">In quibuſdam horas tantum à mer. </s>
  <s xml:id="echoid-s31435" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31436" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31437" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31438" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s31439" xml:space="preserve">vel ab occ. </s>
  <s xml:id="echoid-s31440" xml:space="preserve">vel etiã horas inæquales-<lb/>Nam cũ omnes horæ, cuiuſcunque generis ſint, eodem modo deſcribantur, ſatis erit, ſi exempla <lb/>
<anchor type="note" xlink:label="note-0506-02a" xlink:href="note-0506-02"/>
in vno genere proponantur. </s>
  <s xml:id="echoid-s31441" xml:space="preserve">Pro quolibet ergo plano ſupputandæ erunt, per propoſ. </s>
  <s xml:id="echoid-s31442" xml:space="preserve">3. </s>
  <s xml:id="echoid-s31443" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s31444" xml:space="preserve">
<anchor type="note" xlink:label="note-0506-03a" xlink:href="note-0506-03"/>
latitudines vmbrarum pro illis horis, quas in horologio collocare optamus, Sole exiſtente in <lb/>principio ♋, ♈, vel ♎, &amp; </s>
  <s xml:id="echoid-s31445" xml:space="preserve">♑, ita tamen, vt diligenter notentur arcus latitudinum vmbrarum, <lb/>qui citra Verticalem proprium plani propoſiti reperiuntur, &amp; </s>
  <s xml:id="echoid-s31446" xml:space="preserve">qui vltra eundem exiſtunt. </s>
  <s xml:id="echoid-s31447" xml:space="preserve">Item <lb/>qui orientales ſint reſpectu proprij Meridiani, &amp; </s>
  <s xml:id="echoid-s31448" xml:space="preserve">qui occidentales. </s>
  <s xml:id="echoid-s31449" xml:space="preserve">Deinde ex tabula longitudinũ <lb/>vmbrarum, quas propoſ. </s>
  <s xml:id="echoid-s31450" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31451" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31452" xml:space="preserve">ſupputauimus, excerpendæ erunt longitudines vmbrarum <lb/>rectarũ conuenientes altitudinibus Solis, quas propoſ. </s>
  <s xml:id="echoid-s31453" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31454" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31455" xml:space="preserve">pro eiſdem horis inuenimus.</s>
  <s xml:id="echoid-s31456" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1630" type="float" level="2" n="2">
<note position="left" xlink:label="note-0506-02" xlink:href="note-0506-02a" xml:space="preserve">Quid pro quoli <lb/>bet plano ſuppu <lb/>t@dum ſit, vt ho <lb/>rologi<unsure/>a in eo cõ <lb/>ſ<unsure/>truantur.</note>
<note position="left" xlink:label="note-0506-03" xlink:href="note-0506-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s31457" xml:space="preserve">SIT ergo fabricandum horologium horizontale Aſtronomicum ex tabulis, in quibus dictæ <lb/>latitudines, &amp; </s>
  <s xml:id="echoid-s31458" xml:space="preserve">longitudines vmbrarum contineantur, ad latitudinem grad. </s>
  <s xml:id="echoid-s31459" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31460" xml:space="preserve">cuiuſmodi ſunt eæ, <lb/>quæ ſequuntur.</s>
  <s xml:id="echoid-s31461" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1632" type="section" level="1" n="413">
<head xml:id="echoid-head427" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio horizontali pro <lb/>horis à mer. &amp; med. noc. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head428" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim ſunt boreales, &amp; partim auſtrales, <lb/>vt hę ſyllabę [Bor. Auſtr.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ♋, à med. \\ nocte. # 5 \\ Bor. # 6 \\ Bor. # 7 \\ Bor. # 8 \\ Auſtr. # 9 \\ Auſtr. # 10 \\ Auſtr. # 11 \\ Auſtr. # 12 \\ Auſtr. # Oriẽta- \\ les. <lb/>Horæ ♋, à \\ meridie. # 7 \\ Bor. # 6 \\ Bor. # 5 \\ Bor. # 4 \\ Auſtr. # 3 \\ Auſtr. # 2 \\ Auſtr. # 1 \\ Auſtr. # 0 \\ Auſtr. # Occidẽ \\ tales. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 27. 12. # 17. 54. # 8. 48. # 0. 34. # 11. 57. # 27. 9. # 51. 19. # 90. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 132. 17 # 43. 19. # 24. 16. # 15. 41. # 10. 37. # 7. 13. # 4. 56. # 4. 1.
</note>
</div>
<div xml:id="echoid-div1633" type="section" level="1" n="414">
<head xml:id="echoid-head429" xml:space="preserve">In Aequatore omnes horæ, &amp; latitudines vmbrarum <lb/>ſunt auſtrales.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à me- \\ dia nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orienta- \\ les. <lb/>
Horæ ♈, &amp; ♎, à \\ meridie. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # occiden- \\ tales.
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 10. 10. # 21. 7. # 33. 47. # 49. 12. # 68. 11. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# I<unsure/>nſinita # 61. 16. # 29. 59. # 19. 26. # 14. 16. # 11. 39. # 10. 48.
</note>
<pb o="491" file="0507" n="507" rhead="LIBER QVINTVS."/>
<p>
  <s xml:id="echoid-s31462" xml:space="preserve">In tropico ♑, omnes horæ, &amp; </s>
  <s xml:id="echoid-s31463" xml:space="preserve">latitudines vmbrarum ſunt auſtrales.</s>
  <s xml:id="echoid-s31464" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à med. \\ nocte. # 8 # 9 # 10 # 11 # 12 # orientales. <lb/>Horæ ♑, à me- \\ ridie. # 4 # 3 # 2 # 1 # 0 # occidentales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 37. 13 # 48. 24. # 61. 1. # 75. 3. # 90. 0. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# 162. 8. # 54. 30. # 35. 7. # 28. 12. # 26. 20.
</note>
<p>
  <s xml:id="echoid-s31465" xml:space="preserve">FACILE autem diſcernuntur in his tabellis horæ, atque adeo latitudines vmbrarum <lb/>orientales ab occidentalibus. </s>
  <s xml:id="echoid-s31466" xml:space="preserve">Omnes enim horæ à med. </s>
  <s xml:id="echoid-s31467" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31468" xml:space="preserve">otientales ſunt; </s>
  <s xml:id="echoid-s31469" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31470" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31471" xml:space="preserve">occiden-<lb/>tales, vt in hiſce tabellis notatũ eſt. </s>
  <s xml:id="echoid-s31472" xml:space="preserve">Porro ſyllaba [ Bor. </s>
  <s xml:id="echoid-s31473" xml:space="preserve">] ſignificat horam illam, cui apponitur, <lb/>&amp; </s>
  <s xml:id="echoid-s31474" xml:space="preserve">latitudinem vinbræ ei reſpondentem, eſſe borealem in Horizonte, hoc eſt, citra Verticalem <lb/>circulum cadere: </s>
  <s xml:id="echoid-s31475" xml:space="preserve">ſyllaba vero [ Auſtr. </s>
  <s xml:id="echoid-s31476" xml:space="preserve">] indicat, horam illam, ad quam aſcripta eſt, &amp; </s>
  <s xml:id="echoid-s31477" xml:space="preserve">latitudiné <lb/>vinbræ illi reſpondentem, auſtralem eſſe, id eſt, cadere vltra circulum Verticalem.</s>
  <s xml:id="echoid-s31478" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s31479" xml:space="preserve">IN plano horologij deſcribatur circulus cuiuſuis magnitudinis A B C D, cuius centrum F, in <lb/>
<anchor type="note" xlink:label="note-0507-03a" xlink:href="note-0507-03"/>
<anchor type="note" xlink:label="note-0507-04a" xlink:href="note-0507-04"/>
quo ſtylus figendus eſtad angulos rectos; </s>
  <s xml:id="echoid-s31480" xml:space="preserve">ducãturq́; </s>
  <s xml:id="echoid-s31481" xml:space="preserve">duæ diametri A C, B D, ſeſe ad rectos angulos <lb/>ſecantes in centro, quarum A C, meridiana linea ſit, hoc eſt, communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s31482" xml:space="preserve">pla-<lb/>ni horologii<unsure/>, ac propterea B D, (quæ occulte ducenda eſt) communis ſectio Verticalis proprie d@-<lb/>cti, &amp; </s>
  <s xml:id="echoid-s31483" xml:space="preserve">eiuſdem plani horologii. </s>
  <s xml:id="echoid-s31484" xml:space="preserve">Quoniam enim tam Verticalis, quam Horizon, atque adeo &amp; </s>
  <s xml:id="echoid-s31485" xml:space="preserve">pla-<lb/>num horologij ei parallelum rectos angulos facit cum Meridiano, erit communis ſectio Vertica-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s31486" xml:space="preserve">plani horologij ad eundem Meridianum perpendicularis, ac proinde &amp; </s>
  <s xml:id="echoid-s31487" xml:space="preserve">ad meridianam li-<lb/>
<anchor type="note" xlink:label="note-0507-05a" xlink:href="note-0507-05"/>
neam A C, in Meridiano exiſtentem, ex deſin. </s>
  <s xml:id="echoid-s31488" xml:space="preserve">3. </s>
  <s xml:id="echoid-s31489" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31490" xml:space="preserve">11. </s>
  <s xml:id="echoid-s31491" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s31492" xml:space="preserve">Igitur cum tam Meridianus, quã <lb/>Verticalis per ſtylum ducatur, erit recta B D, quæ per E, locum ſtyli ducta eſt ad A C, perpendi-<lb/>cularis, communis ſectio Verticalis, ac plani horologij. </s>
  <s xml:id="echoid-s31493" xml:space="preserve">Hac eadem demonſtratione oſtendi <lb/>poteſt in omnibus horologijs, quæ ſequuntur, rectam, quæ in loco ſtyli lineam ſtyli, ſeu lineam <lb/>
<anchor type="note" xlink:label="note-0507-06a" xlink:href="note-0507-06"/>
meridianam propriam ſecat ad angulos rectos, communem eſſe ſectionem plani horologij, <lb/>&amp; </s>
  <s xml:id="echoid-s31494" xml:space="preserve">Verticalis proprie dicti ipſius. </s>
  <s xml:id="echoid-s31495" xml:space="preserve">Quod ſi planum horologij ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s31496" xml:space="preserve">Hoiizonti paral-<lb/>lelum, inuenienda eſt in eo, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s31497" xml:space="preserve">23. </s>
  <s xml:id="echoid-s31498" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31499" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31500" xml:space="preserve">demonſtrauimus, li-<lb/>nea meridiana A C, ex cuius puncto E, vbi ſtylus collocandus eſt, circulus deſoribendus A B-<lb/>C D, &amp; </s>
  <s xml:id="echoid-s31501" xml:space="preserve">diameter occulta B D, ad A C, perpendicularis ducenda pro communi ſectione Verti-<lb/>calis, ac plani horologij. </s>
  <s xml:id="echoid-s31502" xml:space="preserve">Statuantur autem partes meridionales, auſtralesve ad A, boreales vero <lb/>ad C, ac proinde orientales ad B, occidentaleſq́ue ad D. </s>
  <s xml:id="echoid-s31503" xml:space="preserve">Eligatur quoque longitudo ſtyli quæcũ-<lb/>que E F, cui ex linea recta G H, quantacunque abſcindantur quotuis partes æquales, &amp; </s>
  <s xml:id="echoid-s31504" xml:space="preserve">ad term<unsure/>inũ <lb/>primæ partis ponatur hic numerus 12. </s>
  <s xml:id="echoid-s31505" xml:space="preserve">ad finem ſecundæ hic numerus 24. </s>
  <s xml:id="echoid-s31506" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31507" xml:space="preserve">ſic dein@eps, add@n <lb/>do ſemper 12. </s>
  <s xml:id="echoid-s31508" xml:space="preserve">Item recta G H, ad partes G, producta, ſumatur adhuc recta G I, ſtylo æquali<unsure/>s, <lb/>
<anchor type="note" xlink:label="note-0507-07a" xlink:href="note-0507-07"/>
quæ in 12. </s>
  <s xml:id="echoid-s31509" xml:space="preserve">particulas æquales ſecetur. </s>
  <s xml:id="echoid-s31510" xml:space="preserve">Ita enim non cogemur ſingulas partes t<unsure/>ectæ G H, in 12. <lb/></s>
  <s xml:id="echoid-s31511" xml:space="preserve">partes diſtribuere, vt longitudines vmbrarum accipiamus, ſed eæ commodiſſime ex tota recta <lb/>I H, accipi poterunt, vt mox docebimus. </s>
  <s xml:id="echoid-s31512" xml:space="preserve">Poſt hæc, quoniam Sole exiſtente in Æ quatore, vmbra <lb/>
<anchor type="note" xlink:label="note-0507-08a" xlink:href="note-0507-08"/>
ſtyli in meridie, hoc eſt, hora 12. </s>
  <s xml:id="echoid-s31513" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31514" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31515" xml:space="preserve">proiicitur in boream, continetq́ue partes 10. <lb/></s>
  <s xml:id="echoid-s31516" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31517" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31518" xml:space="preserve">vt ex præcedentibus tabellis conſtat ſub hora 12. </s>
  <s xml:id="echoid-s31519" xml:space="preserve">♈, vel ♎, ſi hæc vmbra beneficio circi-<lb/>ni ex recta G I, ſumatur, &amp; </s>
  <s xml:id="echoid-s31520" xml:space="preserve">in lineam meridianam transferatur ex E, verſus partes boreales C, <lb/>vſque ad punctum K, cadet tempore æquinoctiorum in meridie extremitas vmbræ in K; </s>
  <s xml:id="echoid-s31521" xml:space="preserve">atque <lb/>adeo per K, linea æquinoctialis ducenda erit ad meridianam lineam perpendicularis, qualis eſt <lb/>K L. </s>
  <s xml:id="echoid-s31522" xml:space="preserve">Quam etiam ita ducemus. </s>
  <s xml:id="echoid-s31523" xml:space="preserve">Ducta recta E F, quæ ſtylo æqualis ſit, ad A C, perpendiculari, <lb/>conſtituatur in F, angulus E F K, altitudini poli æqualis, (Quod quidem facile ſiet, ſi ex F, ver-<lb/>
<anchor type="note" xlink:label="note-0507-09a" xlink:href="note-0507-09"/>
ſus D, circulus deſcribatur, in quo a recta F D, verſus C, altitudo poli numeretur, &amp;</s>
  <s xml:id="echoid-s31524" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s31525" xml:space="preserve">ita vt <lb/>recta F K, meridianam lineam verſus partes boreales ſecet in K. </s>
  <s xml:id="echoid-s31526" xml:space="preserve">Per punctum enim K, ducenda <lb/>erit æquinoctialis linea ad A C, perpendicularis, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s31527" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31528" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31529" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31530" xml:space="preserve">demonſtrauimus. <lb/></s>
  <s xml:id="echoid-s31531" xml:space="preserve">Quod ſi in F, alius angulus conſtituatur E F M, complemento altitudinis poli æqualis, ita vt re-<lb/>cta F M, meridianam lineam ſecet in M, erit M, centrum horologij, in quo omnes lineæ horarũ <lb/>
<anchor type="note" xlink:label="note-0507-10a" xlink:href="note-0507-10"/>
à mer. </s>
  <s xml:id="echoid-s31532" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31533" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31534" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31535" xml:space="preserve">conueniunt, vt in eodem ſcholio propoſ. </s>
  <s xml:id="echoid-s31536" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31537" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31538" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31539" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s31540" xml:space="preserve">Quod <lb/>etiam centrum hac ratione reperiemus. </s>
  <s xml:id="echoid-s31541" xml:space="preserve">In tabula longitudinum vmbrarum propoſ. </s>
  <s xml:id="echoid-s31542" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31543" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s31544" xml:space="preserve">ſumatur altitudo poli Grad. </s>
  <s xml:id="echoid-s31545" xml:space="preserve">42. </s>
  <s xml:id="echoid-s31546" xml:space="preserve">eiuſque vmbra P. </s>
  <s xml:id="echoid-s31547" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31548" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31549" xml:space="preserve">20. </s>
  <s xml:id="echoid-s31550" xml:space="preserve">Si namque beneſ<unsure/>icio circini hæc <lb/>vmbra ex recta I H, ſumatur, (ſtatuendo vnum pedem circini in numero 12. </s>
  <s xml:id="echoid-s31551" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31552" xml:space="preserve">alterum in P. </s>
  <s xml:id="echoid-s31553" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31554" xml:space="preserve"><lb/>M. </s>
  <s xml:id="echoid-s31555" xml:space="preserve">20. </s>
  <s xml:id="echoid-s31556" xml:space="preserve">rectæ G I, ita vt tota recta inter pedes circini poſita complectatur P. </s>
  <s xml:id="echoid-s31557" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31558" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31559" xml:space="preserve">20.) </s>
  <s xml:id="echoid-s31560" xml:space="preserve">transfera-<lb/>turq́ue ex E, in lineam meridianam verſus partes auſtrales A, vſque ad M, erit M, centrum ho-
<pb o="492" file="0508" n="508" rhead="GNOMONICES"/>
rologij. </s>
  <s xml:id="echoid-s31561" xml:space="preserve">Nam ſi Sol in polo arctico collocaretur, caderet vmbra ſtyli, atque adeo radius Solis, <lb/>id eſt, axis mundi, in punctum M, cum tunc altitudinem ſupra Horizontem haberet Grad. </s>
  <s xml:id="echoid-s31562" xml:space="preserve">42. <lb/></s>
  <s xml:id="echoid-s31563" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0508-01a" xlink:href="fig-0508-01"/>
<anchor type="note" xlink:label="note-0508-01a" xlink:href="note-0508-01"/>
<anchor type="note" xlink:label="note-0508-02a" xlink:href="note-0508-02"/>
Quare, vt in coro ll<unsure/>. </s>
  <s xml:id="echoid-s31564" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s31565" xml:space="preserve">21. </s>
  <s xml:id="echoid-s31566" xml:space="preserve">lib 1. </s>
  <s xml:id="echoid-s31567" xml:space="preserve">docuimus, punctum M, centrum erit horologii.</s>
  <s xml:id="echoid-s31568" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1633" type="float" level="2" n="1">
<note position="left" xlink:label="note-0507-03" xlink:href="note-0507-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0507-04" xlink:href="note-0507-04a" xml:space="preserve">Horizõtalis ho-<lb/>to og j<unsure/> Aſi@ono <lb/>m<gap/> <lb/>ex ta@uiis.</note>
<note position="right" xlink:label="note-0507-05" xlink:href="note-0507-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0507-06" xlink:href="note-0507-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0507-07" xlink:href="note-0507-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0507-08" xlink:href="note-0507-08a" xml:space="preserve">Quomodo li-<lb/>nea æquinoctia <lb/>lis duc@tur in <lb/>ho@olog@o hori-<lb/>zo<gap/>.</note>
<note position="left" xlink:label="note-0507-09" xlink:href="note-0507-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0507-10" xlink:href="note-0507-10a" xml:space="preserve">Centrum horo <lb/>logij hoi ta <lb/>@@ qua via repe-<lb/>riatur.</note>
  <figure xlink:label="fig-0508-01" xlink:href="fig-0508-01a">
    <image file="0508-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0508-01"/>
  </figure>
<note position="left" xlink:label="note-0508-01" xlink:href="note-0508-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0508-02" xlink:href="note-0508-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s31569" xml:space="preserve">IAM vero (vtad deſcriptionem horarum veniamus) deſcribenda ſit linea horæ 6. </s>
  <s xml:id="echoid-s31570" xml:space="preserve">à mer. <lb/></s>
  <s xml:id="echoid-s31571" xml:space="preserve">
<anchor type="note" xlink:label="note-0508-03a" xlink:href="note-0508-03"/>
Sub hora 6. </s>
  <s xml:id="echoid-s31572" xml:space="preserve">tropici ♋, quæ occidentalis eſt, &amp; </s>
  <s xml:id="echoid-s31573" xml:space="preserve">borealis, reperio arcum latitudinis vmbræ Gr. </s>
  <s xml:id="echoid-s31574" xml:space="preserve">17. <lb/></s>
  <s xml:id="echoid-s31575" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31576" xml:space="preserve">54. </s>
  <s xml:id="echoid-s31577" xml:space="preserve">Hunc ergo numero ex D, puncto occidentali verſus C, partes boreales v@que ad N, (Quod <lb/>
<anchor type="note" xlink:label="note-0508-04a" xlink:href="note-0508-04"/>
quidẽ beneficio illius quadrãtis, quẽ ad initiũ primi lib. </s>
  <s xml:id="echoid-s31578" xml:space="preserve">conſtruximus, efficio. </s>
  <s xml:id="echoid-s31579" xml:space="preserve">Per illũ enim facili <lb/>negotio omnes arcus in circulũ quemuis transferentur, vt illius vſus mirificus maxime hac in re <lb/>appareat) &amp; </s>
  <s xml:id="echoid-s31580" xml:space="preserve">ex N, per E, duco rectã occultã N E O, quæ cõmunis ſectio erit plani horologij, &amp; </s>
  <s xml:id="echoid-s31581" xml:space="preserve">Ver <lb/>ticalis per Solem tranſeuntis hora 6. </s>
  <s xml:id="echoid-s31582" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31583" xml:space="preserve">Cum enim circuli Verticales ſecẽt Horizontẽ, &amp; </s>
  <s xml:id="echoid-s31584" xml:space="preserve">circu <lb/>lũ A B C D, ei parallelum, per propoſ. </s>
  <s xml:id="echoid-s31585" xml:space="preserve">10. </s>
  <s xml:id="echoid-s31586" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31587" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31588" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s31589" xml:space="preserve">in partes ſimiles, ſit autem arcus D N, <lb/>ſimilis ei, qui in Horizonte intercipitur inter Verticalem primarium, &amp; </s>
  <s xml:id="echoid-s31590" xml:space="preserve">Verticalem illum, qui <lb/>
<anchor type="note" xlink:label="note-0508-05a" xlink:href="note-0508-05"/>
hora 6. </s>
  <s xml:id="echoid-s31591" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31592" xml:space="preserve">per Solem ducitur, tranſeatq́ue Verticalis primarius per D, tranſibit alius Verti-<lb/>calis per N, ac propterea recta N E O, communis ſectio erit illius Verticalis, &amp; </s>
  <s xml:id="echoid-s31593" xml:space="preserve">plani horologij. <lb/></s>
  <s xml:id="echoid-s31594" xml:space="preserve">
<anchor type="note" xlink:label="note-0508-06a" xlink:href="note-0508-06"/>
Igitur per propoſ. </s>
  <s xml:id="echoid-s31595" xml:space="preserve">11. </s>
  <s xml:id="echoid-s31596" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31597" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31598" xml:space="preserve">vmbra ſtyli in rectam E O, cadet; </s>
  <s xml:id="echoid-s31599" xml:space="preserve">vtpote in partem orientalem, au-<lb/>ſtralemq́ue, quæ parti occidentali, borealiq́ue, in qua Sol tunc eſt, opponitur. </s>
  <s xml:id="echoid-s31600" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s31601" xml:space="preserve">hac ratione ex <lb/>arcubus latitudinum vmbrarum latitudovmbrę inuenitur, hoc eſt, in quam partem vmbra proij-<lb/>ciatur, cognoſcitur, ſi dicti arcus recte ſupputentur à puncto D, vel B, verſus C, vel A, prout oc-<lb/>cidentales, oriẽtalesve fuerint, &amp; </s>
  <s xml:id="echoid-s31602" xml:space="preserve">boreales, auſtralesve. </s>
  <s xml:id="echoid-s31603" xml:space="preserve">Rurſus ſub eadẽ hora 6. </s>
  <s xml:id="echoid-s31604" xml:space="preserve">tropici ♋, inuenio <lb/>longitudinẽ vmbræ P. </s>
  <s xml:id="echoid-s31605" xml:space="preserve">43. </s>
  <s xml:id="echoid-s31606" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31607" xml:space="preserve">19 Hanc ergo beneficio circini ex recta I H, acceptã, (ſtatuendo vnũ <lb/>pedem circini in numero 36. </s>
  <s xml:id="echoid-s31608" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31609" xml:space="preserve">alterũ in P. </s>
  <s xml:id="echoid-s31610" xml:space="preserve">7. </s>
  <s xml:id="echoid-s31611" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31612" xml:space="preserve">19. </s>
  <s xml:id="echoid-s31613" xml:space="preserve">rectæ G I, ita vt tota recta inter circini pedes <lb/>interiecta cõplectatur P. </s>
  <s xml:id="echoid-s31614" xml:space="preserve">43. </s>
  <s xml:id="echoid-s31615" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s31616" xml:space="preserve">19.) </s>
  <s xml:id="echoid-s31617" xml:space="preserve">transfero ex E, in rectam occultam E O, vſq; </s>
  <s xml:id="echoid-s31618" xml:space="preserve">ad punctũ O. <lb/></s>
  <s xml:id="echoid-s31619" xml:space="preserve">In hoc enim punctum extremitas vmbræ cadet hora 6. </s>
  <s xml:id="echoid-s31620" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31621" xml:space="preserve">Sole exiſtẽte in principio ♋ Etquo <lb/>niam, vt propoſ. </s>
  <s xml:id="echoid-s31622" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31623" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31624" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31625" xml:space="preserve">oſtẽdimus, linea horæ 6. </s>
  <s xml:id="echoid-s31626" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31627" xml:space="preserve">parallela eſt lineæ æquinoctiali, &amp; </s>
  <s xml:id="echoid-s31628" xml:space="preserve">ad me <lb/>
<anchor type="note" xlink:label="note-0508-07a" xlink:href="note-0508-07"/>
ridianam lineã perpendicularis, ſi per O, ducatur recta ad A C, perpendicularis, vel lineæ æquino <lb/>ctiali æquidiſtans, deſcripta erit linea horæ 6. </s>
  <s xml:id="echoid-s31629" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31630" xml:space="preserve">Quod ſi arcui D N, ſumatur ęqualis arcus <lb/>B P, verſus C, &amp; </s>
  <s xml:id="echoid-s31631" xml:space="preserve">ex P, per E, recta occulta ducatur P E Q, &amp; </s>
  <s xml:id="echoid-s31632" xml:space="preserve">ex E Q, abſcindatur recta E Q, rectæ <lb/>E O, æqualis, cadet vmbræ extremũ in punctũ Q, hora 6. </s>
  <s xml:id="echoid-s31633" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31634" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31635" xml:space="preserve">Sole exiſtente in tropico ♋: <lb/></s>
  <s xml:id="echoid-s31636" xml:space="preserve">quia idem arcus eſt huius horæ, qui prioris, &amp; </s>
  <s xml:id="echoid-s31637" xml:space="preserve">eadem longitudo vmbrę, ſed arcus horæ 6 à med. </s>
  <s xml:id="echoid-s31638" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s31639" xml:space="preserve">orientalis eſt, quemadmodum arcus horæ 6. </s>
  <s xml:id="echoid-s31640" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31641" xml:space="preserve">occidentalis, vt ex tabella apparet. </s>
  <s xml:id="echoid-s31642" xml:space="preserve">Sit <lb/>rurſus deſcribenda hora 9. </s>
  <s xml:id="echoid-s31643" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31644" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31645" xml:space="preserve">Quoniam eius latitudo vmbræ in tabula, Sole exiſtente <lb/>in principio ♋, auſtralis eſt, &amp; </s>
  <s xml:id="echoid-s31646" xml:space="preserve">orientalis, continetq́ue gr. </s>
  <s xml:id="echoid-s31647" xml:space="preserve">11. </s>
  <s xml:id="echoid-s31648" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31649" xml:space="preserve">57. </s>
  <s xml:id="echoid-s31650" xml:space="preserve">ſupputo eam ex B, puncto <lb/>orientali verſus auſtrum vſque ad R, ducoq́ue rectam occultam R E S, &amp; </s>
  <s xml:id="echoid-s31651" xml:space="preserve">ex E S, abſcindo vm-<lb/>bram E S, Partium 10. </s>
  <s xml:id="echoid-s31652" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31653" xml:space="preserve">37. </s>
  <s xml:id="echoid-s31654" xml:space="preserve">quam in tabula reperio ſub hora 9. </s>
  <s xml:id="echoid-s31655" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31656" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31657" xml:space="preserve">Sole exiſtente in <lb/>tropico ♋. </s>
  <s xml:id="echoid-s31658" xml:space="preserve">Ita enim inuentum erit punctum S, in quod, Sole exiſtente in tropico ♋, extremitas
<pb o="493" file="0509" n="509" rhead="LIBER QVINTVS."/>
vmbræ cadet hora 9. </s>
  <s xml:id="echoid-s31659" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31660" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31661" xml:space="preserve">ac proinde per S, ducenda erit linea horæ 9. </s>
  <s xml:id="echoid-s31662" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31663" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31664" xml:space="preserve">Dein <lb/>de quia, Sole exiſtente in principio ♈, vel ♎, latitudo vmbræ eiuſdem horæ orientalis eſt, &amp; </s>
  <s xml:id="echoid-s31665" xml:space="preserve">au-<lb/>ſtralis, continetq́ue gr. </s>
  <s xml:id="echoid-s31666" xml:space="preserve">33. </s>
  <s xml:id="echoid-s31667" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31668" xml:space="preserve">47. </s>
  <s xml:id="echoid-s31669" xml:space="preserve">ſupputo illam ex B, verſus A, vſque ad punctum T. </s>
  <s xml:id="echoid-s31670" xml:space="preserve">Nam ſi oc <lb/>culta recta ducatur T E V, ſecans æquinoctialem lineam in V, cadet tempore æquinoctij hora 9. <lb/></s>
  <s xml:id="echoid-s31671" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31672" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31673" xml:space="preserve">extremũ vmbræ in punctum V, atque adeo per V, ducenda erit linea horæ 9. </s>
  <s xml:id="echoid-s31674" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31675" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s31676" xml:space="preserve">Quod quidẽ punctum V, per longitudinem vmbræ hac quoque ratione deprehẽdemus. </s>
  <s xml:id="echoid-s31677" xml:space="preserve">Sub <lb/>hora 9. </s>
  <s xml:id="echoid-s31678" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31679" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31680" xml:space="preserve">Sole exiſtente in principio ♈, vel ♎, ex tabula ſumatur longitudo vmbræ P. </s>
  <s xml:id="echoid-s31681" xml:space="preserve">19. </s>
  <s xml:id="echoid-s31682" xml:space="preserve"><lb/>M. </s>
  <s xml:id="echoid-s31683" xml:space="preserve">26. </s>
  <s xml:id="echoid-s31684" xml:space="preserve">Hac enim beneſicio circini accepta in recta I H, ſi ex E, arcus circuli occultus deſcriba-<lb/>tur, ſecabitur æquinoctialis linea in V, puncto. </s>
  <s xml:id="echoid-s31685" xml:space="preserve">Atque ita cuiuſque horæ punctum in æquinoctia <lb/>li linea reperiemus vel ex ſola latitudine vmbræ, vel ex ſola longitudine. </s>
  <s xml:id="echoid-s31686" xml:space="preserve">Præterea, Sole exiſtẽte in <lb/>
<anchor type="note" xlink:label="note-0509-01a" xlink:href="note-0509-01"/>
principio ♑, numero eiuſdem horæ latitudinem vmbræ orientalẽ, &amp; </s>
  <s xml:id="echoid-s31687" xml:space="preserve">auſtralem in tabella reper-<lb/>tam grad. </s>
  <s xml:id="echoid-s31688" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31689" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31690" xml:space="preserve">24. </s>
  <s xml:id="echoid-s31691" xml:space="preserve">ex B, verſus A, vſque ad X, ducoque occultam rectam X E Y. </s>
  <s xml:id="echoid-s31692" xml:space="preserve">Nam ſi ex E Y, <lb/>abſcindatur longitudo vmbræ. </s>
  <s xml:id="echoid-s31693" xml:space="preserve">P. </s>
  <s xml:id="echoid-s31694" xml:space="preserve">54. </s>
  <s xml:id="echoid-s31695" xml:space="preserve">M 30 eidem horæ debita, vt ex tabula patet, inuenietur pun <lb/>ctum Y, in quod, Sole exiſtente in principio ♑, extremitas vmbræ hora 9. </s>
  <s xml:id="echoid-s31696" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31697" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31698" xml:space="preserve">cadet, atque <lb/>idcirco per V, ducenda erit linea horę 9. </s>
  <s xml:id="echoid-s31699" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31700" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31701" xml:space="preserve">Itaq; </s>
  <s xml:id="echoid-s31702" xml:space="preserve">ſi ex S, ad Y, recta ducatur, quæ omnino <lb/>per V, tranſibit, ſi erratum non eſt, deſcripta erit linea horæ 9. </s>
  <s xml:id="echoid-s31703" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31704" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31705" xml:space="preserve">Hac ratione omnes <lb/>horariæ lineę ducentur, ſi pro ſingulis terna puncta reperiantur, vnum in tropico ♋, &amp; </s>
  <s xml:id="echoid-s31706" xml:space="preserve">al-<lb/>terum in linea æquinoctiali, tertiumq́ue in tropico ♑, vt in hora 9. </s>
  <s xml:id="echoid-s31707" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31708" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31709" xml:space="preserve">factum eſt. <lb/></s>
  <s xml:id="echoid-s31710" xml:space="preserve">Quod ſi forte in vno tropicorum punctum alicuius horæ inueniri nequeat, ducenda erit linea <lb/>horaria per duo puncta, quorum vnum in altero tropico, alterum vero in linea æquinoctiali <lb/>
<anchor type="note" xlink:label="note-0509-02a" xlink:href="note-0509-02"/>
<anchor type="note" xlink:label="note-0509-03a" xlink:href="note-0509-03"/>
inuentum ſit. </s>
  <s xml:id="echoid-s31711" xml:space="preserve">Ita vides ductam eſſe horam 7. </s>
  <s xml:id="echoid-s31712" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31713" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31714" xml:space="preserve">per punctum Z, in tropico ♋, inuen-<lb/>tum, &amp; </s>
  <s xml:id="echoid-s31715" xml:space="preserve">per punctum a, lineæ æquinoctialis. </s>
  <s xml:id="echoid-s31716" xml:space="preserve">Si autem aliquando contingat, horam aliquam <lb/>habere punctum in vno ſolo tropico, ducenda erit eius linea per illud punctum innentum, &amp; </s>
  <s xml:id="echoid-s31717" xml:space="preserve">per <lb/>M, centrum horologij, aut certe per illud punctum æquinoctialis lineæ, quod horæ oppoſitæ con <lb/>uenit. </s>
  <s xml:id="echoid-s31718" xml:space="preserve">Vt ſi hora 7. </s>
  <s xml:id="echoid-s31719" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31720" xml:space="preserve">ducenda ſit, reperietur punctum eius in ♋, duntaxat; </s>
  <s xml:id="echoid-s31721" xml:space="preserve">(quod tamen in <lb/>noſtro exemplo inuentum non eſt, propterea quò<unsure/>d longius, quam par eſt, à loco ſtyli E, abeſt.) <lb/></s>
  <s xml:id="echoid-s31722" xml:space="preserve">Per illud ergo, &amp; </s>
  <s xml:id="echoid-s31723" xml:space="preserve">per punctum a, lineæ æquinoctialis, quod horæ 7. </s>
  <s xml:id="echoid-s31724" xml:space="preserve">a med noc. </s>
  <s xml:id="echoid-s31725" xml:space="preserve">reſpondet, ducẽ-<lb/>da er it linea horæ 7. </s>
  <s xml:id="echoid-s31726" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31727" xml:space="preserve">Quia vero, vt ex propoſitis tabulis patet, binæ ſemper horæ eundem <lb/>arcum habent, &amp; </s>
  <s xml:id="echoid-s31728" xml:space="preserve">longitudinem vmbræ eandem, deſcribentur eæ vna eademq́ue opera, ſi arcus <lb/>ex tabula acceptus numeretur à B, &amp; </s>
  <s xml:id="echoid-s31729" xml:space="preserve">D, verſus A, vel C. </s>
  <s xml:id="echoid-s31730" xml:space="preserve">Nam ſi arcui B X, per quem inuenimus <lb/>
<anchor type="note" xlink:label="note-0509-04a" xlink:href="note-0509-04"/>
punctum Y, in tropico ♑, pro hora 9. </s>
  <s xml:id="echoid-s31731" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31732" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31733" xml:space="preserve">a qualem arcum accipiamus D b, &amp; </s>
  <s xml:id="echoid-s31734" xml:space="preserve">ex b, per <lb/>E, occultam rectam ducamus b E d, vmbramq́ue E d, æqualem vmbræ E Y, inuentum erit pun-<lb/>ctum d, in tropico ♑, pro hora 3. </s>
  <s xml:id="echoid-s31735" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31736" xml:space="preserve">quia hora 3. </s>
  <s xml:id="echoid-s31737" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31738" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31739" xml:space="preserve">hora 9. </s>
  <s xml:id="echoid-s31740" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31741" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31742" xml:space="preserve">æqualiter <lb/>diſtant à Meridiano, &amp;</s>
  <s xml:id="echoid-s31743" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31744" xml:space="preserve">Hac arte totum horologium Aſtronomicum deſcriptum eſt. </s>
  <s xml:id="echoid-s31745" xml:space="preserve">Quod ſi <lb/>
<anchor type="note" xlink:label="note-0509-05a" xlink:href="note-0509-05"/>
puncta in tropicis inuenta congruenter iungantur lineis inflexis, deſcripti erunt arcus ♋, &amp; </s>
  <s xml:id="echoid-s31746" xml:space="preserve">♑. <lb/></s>
  <s xml:id="echoid-s31747" xml:space="preserve">Et ſi pro alijs ſignis inueniantur altitudines Solis earundem horarum, &amp; </s>
  <s xml:id="echoid-s31748" xml:space="preserve">ex his longitudines vm-<lb/>brarum, quę ex E, loco ſtyli beneficio circini in lineas horarias transferantur, puncta in eis impri <lb/>mendo, deſcribentur quoque per ea aliorũ ſignorũ arcus. </s>
  <s xml:id="echoid-s31749" xml:space="preserve">Vel ſi inueniantur latitudines vmbrarũ <lb/>pro horis aliorum ſignorum, vbi earum lineæ occultæ per E, ductæ lineas horarias ſecabunt, per <lb/>ea puncta ijdem arcus ſignorum erunt delineandi. </s>
  <s xml:id="echoid-s31750" xml:space="preserve">Tranſibunt autem omnes lineæ horarũ à mer. </s>
  <s xml:id="echoid-s31751" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0509-06a" xlink:href="note-0509-06"/>
&amp; </s>
  <s xml:id="echoid-s31752" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31753" xml:space="preserve">nocte, ſi in deſcriptione nullus ſit error commiſſus, per M, centrum horologij, ſi produ-<lb/>cantur.</s>
  <s xml:id="echoid-s31754" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1634" type="float" level="2" n="2">
<note position="left" xlink:label="note-0508-03" xlink:href="note-0508-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0508-04" xlink:href="note-0508-04a" xml:space="preserve">@ſus illius qua <lb/>drãtis in princi <lb/>pio lib. 1. con-<lb/>@truct@.</note>
<note position="left" xlink:label="note-0508-05" xlink:href="note-0508-05a" xml:space="preserve">Qua arte ex at-<lb/>cubus latitudi-<lb/>num vmbtarũ <lb/>latitudo vmbræ <lb/>inquiratur.</note>
<note position="left" xlink:label="note-0508-06" xlink:href="note-0508-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0508-07" xlink:href="note-0508-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0509-01" xlink:href="note-0509-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0509-02" xlink:href="note-0509-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0509-03" xlink:href="note-0509-03a" xml:space="preserve">Quãdo in vno <lb/>tan ũtropico, &amp; <lb/>in linea æqui-<lb/>no ctiali punctũ <lb/>f<unsure/>e@ eritur, vel in <lb/>trop@@o tantum <lb/>quomodo linea <lb/>hora@@a ducen-<lb/>da ſit.</note>
<note position="left" xlink:label="note-0509-04" xlink:href="note-0509-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0509-05" xlink:href="note-0509-05a" xml:space="preserve">Arcus ſignorũ <lb/>quo pacto ex @a <lb/>bulis deſcriba@ <lb/>tur in horolo-<lb/>g@o.</note>
<note position="left" xlink:label="note-0509-06" xlink:href="note-0509-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s31755" xml:space="preserve">EADEM prorſus arte omnia alia horologia conficientnr, ſi recte ſumantur latitudines, lon-<lb/>gitudineſq́ue vmbrarum pro ſingulis horis, quæ deſcribendæ ſunt. </s>
  <s xml:id="echoid-s31756" xml:space="preserve">Pro horologio horizontali <lb/>Italico confectæ ſunt hæ ſequentes tabellæ continentes vmbrarum latitudines, longitudineſq́ue <lb/>pro horis ab occaſu Solis, ad latitudinem grad. </s>
  <s xml:id="echoid-s31757" xml:space="preserve">42.</s>
  <s xml:id="echoid-s31758" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1636" type="section" level="1" n="415">
<head xml:id="echoid-head430" xml:space="preserve">Latitudines, longitudineſq́ue vmbrarum in horologio horizontali pro horis <lb/>ab occaſu Solis ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1637" type="section" level="1" n="416">
<head xml:id="echoid-head431" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim ſunt Boreales, &amp; partim Auſtrales, vt <lb/>hæ ſyllabæ [ Bor. Auſtr. ] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 9 \\ Bor. # 10 \\ Bor. # 11 \\ Bor. # 12 \\ Bor. # 13 \\ Auſtr. # 14 \\ Auſtr. # 15 \\ Auſtr. # 16 \\ Auſtr. # Oriẽta- \\ les. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 31. 45. # 22. 11. # 13. 5. # 3. 49. # 6. 24. # 19. 21. # 38. 27. # 70. 20. <lb/>Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 1031. 45 # 64. 14. # 30. 56. # 19. 3. # 12. 43. # 8. 39 # 5. 51. # 4. 14 <lb/></note>
<pb o="494" file="0510" n="510" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 17 \\ Auſtr. # 18 \\ Auſtr. # 19 \\ Auſtr. # 20 \\ Auſtr. # 21 \\ Bor. # 22 \\ Bor. # 23 \\ Bor. # 24 \\ Bor. # Occidẽ- \\ tales. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 67. 43. # 36. 53. # 18. 21. # 5. 45. # 5. 52. # 13. 40. # 22. 48. # 32. 27. <lb/>Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 4. 17. # 6. 1. # 8. 53. # 13 3 # 19. 36. # 32. 8. # 68. 46 # Infinita <lb/></note>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1638" type="section" level="1" n="417">
<head xml:id="echoid-head432" xml:space="preserve">In Aequatore ſunt omnes horæ, &amp; latitudines vmbrarum auſtrales.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, ab \\ occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18 # orienta- \\ les. <lb/># 24 # 23 # 22 # 21 # 20 # 19 # 18 # occiden- \\ tales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 10. 10. # 21. 7. # 33. 47. # 49. 12. # 68. 11. # 90. 0. <lb/>
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# Inſinita # 61. 16. # 29. 59. # 19. 26 # 14. 16. # 11. 39 # 10. 48
</note>
</div>
<div xml:id="echoid-div1639" type="section" level="1" n="418">
<head xml:id="echoid-head433" xml:space="preserve">In tropico ♑, omnes horæ, &amp; vmbrarum latitudines auſtrales ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab \\ occaſu. # 16 \\ orient. # 17 \\ or. # 18 \\ or. # 19 \\ or. # 20 \\ occ. # 21 \\ occ. # 22 \\ occ. # 23 \\ occ. # 24 \\ occ. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 42. 16. # 54. 6. # 67. 25. # 81. 58. # 82. 58. # 68. 21. # 54. 56. # 43. 1. # 32. 27.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 82. 56 # 42. 44. # 31. 3. # 26. 51. # 26. 43. # 30. 36. # 41. 32. # 77. 40. # Inhnita
</note>
<p>
  <s xml:id="echoid-s31759" xml:space="preserve">Quemadmodum autem per has ſyllabas [Bor. </s>
  <s xml:id="echoid-s31760" xml:space="preserve">Auſtr.</s>
  <s xml:id="echoid-s31761" xml:space="preserve">] diſtinguimus latitudines vmbrarum <lb/>boreales ab auſtralibus, ita per has ſyllabas [or. </s>
  <s xml:id="echoid-s31762" xml:space="preserve">occ.</s>
  <s xml:id="echoid-s31763" xml:space="preserve">] orientales ab occidentalibus ſecer-<lb/>nimus.</s>
  <s xml:id="echoid-s31764" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s31765" xml:space="preserve">ITAQVE ſi deſcribenda ſit linea horæ 23. </s>
  <s xml:id="echoid-s31766" xml:space="preserve">abocc. </s>
  <s xml:id="echoid-s31767" xml:space="preserve">numerabimus eius latitudinem vmbræ <lb/>
<anchor type="note" xlink:label="note-0510-07a" xlink:href="note-0510-07"/>
grad. </s>
  <s xml:id="echoid-s31768" xml:space="preserve">22. </s>
  <s xml:id="echoid-s31769" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31770" xml:space="preserve">48. </s>
  <s xml:id="echoid-s31771" xml:space="preserve">quã in tropico ♋, habet occidentalẽ, borealemq́ue in antecedenti figura à D, <lb/>
<anchor type="note" xlink:label="note-0510-08a" xlink:href="note-0510-08"/>
verſus C, vſque ad e, lineamq́; </s>
  <s xml:id="echoid-s31772" xml:space="preserve">occultam ducemus e E f, ex qua ſi abſcindamus vmbram P. </s>
  <s xml:id="echoid-s31773" xml:space="preserve">68. <lb/></s>
  <s xml:id="echoid-s31774" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31775" xml:space="preserve">46. </s>
  <s xml:id="echoid-s31776" xml:space="preserve">nempe rectam E f, habebimus f, punctum horæ 23. </s>
  <s xml:id="echoid-s31777" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s31778" xml:space="preserve">Deinde eiuſdem horæ <lb/>23. </s>
  <s xml:id="echoid-s31779" xml:space="preserve">latitudinem vmbræ gr. </s>
  <s xml:id="echoid-s31780" xml:space="preserve">43. </s>
  <s xml:id="echoid-s31781" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31782" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31783" xml:space="preserve">quam in tropico ♑, habet occidentalem, &amp; </s>
  <s xml:id="echoid-s31784" xml:space="preserve">auſtralem ſup-<lb/>putabimus a D, verſus A, vſque ad g, rectamq́ue ducemus occultam g E h, ex qua ſi abſcinda-<lb/>mus vmbram P. </s>
  <s xml:id="echoid-s31785" xml:space="preserve">77. </s>
  <s xml:id="echoid-s31786" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31787" xml:space="preserve">40. </s>
  <s xml:id="echoid-s31788" xml:space="preserve">nimirum rectam E h, inuentum erit h, punctum horę 23. </s>
  <s xml:id="echoid-s31789" xml:space="preserve">in tropi-<lb/>co ♑. </s>
  <s xml:id="echoid-s31790" xml:space="preserve">Quare iuncta recta f h, dabit horam 23. </s>
  <s xml:id="echoid-s31791" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31792" xml:space="preserve">quæ omnino per punctum L, tranſibit in <lb/>linea æquinoctiali, per quod linea horæ 5. </s>
  <s xml:id="echoid-s31793" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31794" xml:space="preserve">ducta eſt. </s>
  <s xml:id="echoid-s31795" xml:space="preserve">Sunt enim eædem vmbrarum la-<lb/>titudines in horis ab occ. </s>
  <s xml:id="echoid-s31796" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s31797" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31798" xml:space="preserve">inæqualibus, quæ in horis à mer. </s>
  <s xml:id="echoid-s31799" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31800" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31801" xml:space="preserve">Vnde ſi ſe-<lb/>mel pro vno genere horarum inuenta ſint puncta in linea æquinoctiali, non opus eſt eadem pro <lb/>alijs horis inueſtigare. </s>
  <s xml:id="echoid-s31802" xml:space="preserve">Nõ aliter aliarum horarum ab occ. </s>
  <s xml:id="echoid-s31803" xml:space="preserve">lineas ducemus, dummodo memor ſis, <lb/>
<anchor type="note" xlink:label="note-0510-09a" xlink:href="note-0510-09"/>
horas illas, quæ nulla puncta habent in tropico ♑, quales ſunt hor. </s>
  <s xml:id="echoid-s31804" xml:space="preserve">15. </s>
  <s xml:id="echoid-s31805" xml:space="preserve">14. </s>
  <s xml:id="echoid-s31806" xml:space="preserve">13. </s>
  <s xml:id="echoid-s31807" xml:space="preserve">ducendas eſſe per <lb/>puncta earum reperta in tropico ♋, &amp; </s>
  <s xml:id="echoid-s31808" xml:space="preserve">in æquinoctiali linea. </s>
  <s xml:id="echoid-s31809" xml:space="preserve">Ita cernis lineam horæ 13. </s>
  <s xml:id="echoid-s31810" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s31811" xml:space="preserve">traiectam eſſe per punctum in tropico ♋, inuentum, &amp; </s>
  <s xml:id="echoid-s31812" xml:space="preserve">per a, punctum æquinoctialis lineæ, <lb/>per quod nimirum linea hor<unsure/>æ 7. </s>
  <s xml:id="echoid-s31813" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s31814" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31815" xml:space="preserve">ducta eſt. </s>
  <s xml:id="echoid-s31816" xml:space="preserve">Facile autem intelliges ex tabula propoſ. </s>
  <s xml:id="echoid-s31817" xml:space="preserve"><lb/>19. </s>
  <s xml:id="echoid-s31818" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31819" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31820" xml:space="preserve">quæ horæ à mer. </s>
  <s xml:id="echoid-s31821" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31822" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31823" xml:space="preserve">in æquinoctiali linea quibus horis ab or. </s>
  <s xml:id="echoid-s31824" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s31825" xml:space="preserve">re-<lb/>ſpondeant. </s>
  <s xml:id="echoid-s31826" xml:space="preserve">Linea horæ 12. </s>
  <s xml:id="echoid-s31827" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31828" xml:space="preserve">ducenda eſt per punctum in tropico ♋, inuentum parallela <lb/>lineæ æquinoctiali, vt propoſ. </s>
  <s xml:id="echoid-s31829" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31830" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31831" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31832" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s31833" xml:space="preserve">Reliquæ vero horæ ante horam 12. </s>
  <s xml:id="echoid-s31834" xml:space="preserve"><lb/>quæ æquinoctialem lineam nõ ſecant, ducendę ſunt per puncta in tropico ♋, inuenta per reſpon <lb/>dentes horas in linea æquinoctiali, vt ex tabula propoſ. </s>
  <s xml:id="echoid-s31835" xml:space="preserve">19. </s>
  <s xml:id="echoid-s31836" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31837" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31838" xml:space="preserve">conſtat: </s>
  <s xml:id="echoid-s31839" xml:space="preserve">Vt linea horæ 11. </s>
  <s xml:id="echoid-s31840" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s31841" xml:space="preserve">per horam 23. </s>
  <s xml:id="echoid-s31842" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31843" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s31844" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31845" xml:space="preserve">in linea æquinoctiali, &amp; </s>
  <s xml:id="echoid-s31846" xml:space="preserve">linea horæ 10. </s>
  <s xml:id="echoid-s31847" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31848" xml:space="preserve">per horã <lb/>22. </s>
  <s xml:id="echoid-s31849" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31850" xml:space="preserve">vel 4. </s>
  <s xml:id="echoid-s31851" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31852" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s31853" xml:space="preserve">c. </s>
  <s xml:id="echoid-s31854" xml:space="preserve">Vel certe pro eiſdem horis inueſtiganda ſunt alia puncta in paralle-
<pb o="495" file="0511" n="511" rhead="LIBER QVINTVS."/>
lo ♊, vel ♌, per earum latitudines vmbrarum, longitudineſq́ue in dicto parallelo inuentas.</s>
  <s xml:id="echoid-s31855" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1639" type="float" level="2" n="1">
<note position="left" xlink:label="note-0510-07" xlink:href="note-0510-07a" xml:space="preserve">Horizõtal is ho <lb/>rologij Italici <lb/>conſtructio ex <lb/>tabulis.</note>
<note position="left" xlink:label="note-0510-08" xlink:href="note-0510-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0510-09" xlink:href="note-0510-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s31856" xml:space="preserve">QVOD ſi tropici deſcripti ſint, facilius horologium Italicum deſcribemus vel per ſolas lon-<lb/>
<anchor type="note" xlink:label="note-0511-01a" xlink:href="note-0511-01"/>
gitudines vmbrarum, vel per ſolas latitudines. </s>
  <s xml:id="echoid-s31857" xml:space="preserve">Si enim beneficio circini longitudines vmbrarum <lb/>ex recta I H, accipiantur, &amp; </s>
  <s xml:id="echoid-s31858" xml:space="preserve">ex E, arcus occulti deſcribantur ſecantes tropicos; </s>
  <s xml:id="echoid-s31859" xml:space="preserve">vel ſi lineæ occultę <lb/>latitudinum vmbrarum ducantur ſecantes tropicos, habebuntur in vtroque tropico puncta ho-<lb/>rarum ab occ. </s>
  <s xml:id="echoid-s31860" xml:space="preserve">Si igitur reſpondentia puncta connectantur lineis rectis per horas à mer. </s>
  <s xml:id="echoid-s31861" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31862" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s31863" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31864" xml:space="preserve">in linea æquinoctiali tranſeuntibus, deſcriptum erit horologium Italicum.</s>
  <s xml:id="echoid-s31865" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1640" type="float" level="2" n="2">
<note position="right" xlink:label="note-0511-01" xlink:href="note-0511-01a" xml:space="preserve">Si deſcripti ſint <lb/>tropici, qua ra-<lb/>tione facilius <lb/>Italicum horo-<lb/>logium deſcri-<lb/>batur.</note>
</div>
<p>
  <s xml:id="echoid-s31866" xml:space="preserve">POSSVNT quoque longitudines vmbrarum ex altitudinibus Solis inueſtigari Geometrice, <lb/>
<anchor type="note" xlink:label="note-0511-02a" xlink:href="note-0511-02"/>
vt ad finem ſcholij propoſ. </s>
  <s xml:id="echoid-s31867" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31868" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31869" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s31870" xml:space="preserve">Sit enim circulus, vel potius (quod ſatis <lb/>
<anchor type="note" xlink:label="note-0511-03a" xlink:href="note-0511-03"/>
<anchor type="figure" xlink:label="fig-0511-01a" xlink:href="fig-0511-01"/>
<anchor type="note" xlink:label="note-0511-04a" xlink:href="note-0511-04"/>
eſt) ſemicirculus A B C, cuius centrum D, &amp; </s>
  <s xml:id="echoid-s31871" xml:space="preserve">in quo diameter B C, quam ad rectos angulos ſecet <lb/>ſemidiameter A D. </s>
  <s xml:id="echoid-s31872" xml:space="preserve">Accipiatur in A D, producta gnomoni horologij æqualis recta D E, &amp; </s>
  <s xml:id="echoid-s31873" xml:space="preserve">per E, <lb/>
<anchor type="note" xlink:label="note-0511-05a" xlink:href="note-0511-05"/>
diametro B C, parallela agatur I G. </s>
  <s xml:id="echoid-s31874" xml:space="preserve">Si igitur v. </s>
  <s xml:id="echoid-s31875" xml:space="preserve">g. </s>
  <s xml:id="echoid-s31876" xml:space="preserve">ſumatur arcus B F, æqualis altitudini Solis, quã <lb/>habet hora 16. </s>
  <s xml:id="echoid-s31877" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31878" xml:space="preserve">in tropico ♑, hoc eſt, gr. </s>
  <s xml:id="echoid-s31879" xml:space="preserve">8. </s>
  <s xml:id="echoid-s31880" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31881" xml:space="preserve">14. </s>
  <s xml:id="echoid-s31882" xml:space="preserve">ducaturq́ue recta F D G, ſecans rectã <lb/>I G, in G, erit E G, longitudo vmbræ à ſtvlo D E, proiectæ, vt ex ijs conſtat, quæ ad initium pro-<lb/>poſ. </s>
  <s xml:id="echoid-s31883" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31884" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31885" xml:space="preserve">ad ſinem ſcholij eiuſdem propoſ. </s>
  <s xml:id="echoid-s31886" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31887" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s31888" xml:space="preserve">Hac eadem arte inuenietur <lb/>E I, longitudo vmbræ pro hora 23. </s>
  <s xml:id="echoid-s31889" xml:space="preserve">in tropico ♑, ex C H, arcu altitudinis Solis eiuſdem horæ. <lb/></s>
  <s xml:id="echoid-s31890" xml:space="preserve">Item ex C K, arcu altitudinis Solis horæ 21. </s>
  <s xml:id="echoid-s31891" xml:space="preserve">in tropico ♑, reperietur longitudo vmbræ E L, pro <lb/>eadẽ hora 21. </s>
  <s xml:id="echoid-s31892" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31893" xml:space="preserve">Ita quoque B M, arcus altitudinis Solis horæ 18. </s>
  <s xml:id="echoid-s31894" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31895" xml:space="preserve">in tropico ♑, dabit <lb/>E N, longitudinem vmbræ eiuſdem horæ; </s>
  <s xml:id="echoid-s31896" xml:space="preserve">Et C O, arcus altitudinis. </s>
  <s xml:id="echoid-s31897" xml:space="preserve">Solis eiuſdem horæ in tro-<lb/>pico ♋, præbebit longitudinem vmbræ E P: </s>
  <s xml:id="echoid-s31898" xml:space="preserve">Denique ex B Q, arcu altitudinis Solis horæ 21. </s>
  <s xml:id="echoid-s31899" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s31900" xml:space="preserve">in tropico ♑, veniemus in cognitionem longitudinis vmbræ E R, &amp; </s>
  <s xml:id="echoid-s31901" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s31902" xml:space="preserve">Operæpre-<lb/>
<anchor type="note" xlink:label="note-0511-06a" xlink:href="note-0511-06"/>
tium autẽ erit longitudines vmbrarũ pro horis orientalibus inueſtigare ex vna parte ſtyli, ne@pe <lb/>dextra, ex altera vero, nimirum ſiniſtra, pro occidentalibus, vt in figura factum eſt. </s>
  <s xml:id="echoid-s31903" xml:space="preserve">Niſi enim ita <lb/>fiat, ſæpenumero inter ſe confundentur vmbræ, quæ ferè ſunt æquales, cuiuſmodi ſunt duæ vm-<lb/>bræ E P, E R, vel E L, E N, quæ ferme æquales inter ſe ſunt.</s>
  <s xml:id="echoid-s31904" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1641" type="float" level="2" n="3">
<note position="right" xlink:label="note-0511-02" xlink:href="note-0511-02a" xml:space="preserve">Longitudines <lb/>vmbrarũ quo <lb/>pacto Geometri <lb/>cæ inueniantur <lb/>ex datis altitu-<lb/>dinibus Solis <lb/>in horologio.</note>
<note position="left" xlink:label="note-0511-03" xlink:href="note-0511-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0511-01" xlink:href="fig-0511-01a">
    <image file="0511-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0511-01"/>
  </figure>
<note position="left" xlink:label="note-0511-04" xlink:href="note-0511-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0511-05" xlink:href="note-0511-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0511-06" xlink:href="note-0511-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s31905" xml:space="preserve">PRO vmbrarum latitudinibus vſurpare poſſumus commodiſſime arcubus horarijs, quos <lb/>
<anchor type="note" xlink:label="note-0511-07a" xlink:href="note-0511-07"/>
propoſ. </s>
  <s xml:id="echoid-s31906" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31907" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31908" xml:space="preserve">ſupputare docuimus, in ijs horologijs, in quibus commode centrum deſi-<lb/>gnari poteſt. </s>
  <s xml:id="echoid-s31909" xml:space="preserve">Quod in hunc modum fieri poteſt. </s>
  <s xml:id="echoid-s31910" xml:space="preserve">Ex centro horologij M, deſcribatur circulus <lb/>cuiuſcunque magnitudinis i p l m n, in quo diameter ducatur i m, ad meridianam lineam A C<emph style="sub">3</emph><emph style="super">1</emph>, <lb/>perpendicularis, quæ cõmunis ſectio erit plani horologij, &amp; </s>
  <s xml:id="echoid-s31911" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s31912" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31913" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31914" xml:space="preserve">med. </s>
  <s xml:id="echoid-s31915" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s31916" xml:space="preserve">vt propoſ. </s>
  <s xml:id="echoid-s31917" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31918" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31919" xml:space="preserve">2. </s>
  <s xml:id="echoid-s31920" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s31921" xml:space="preserve">Inueniaur iam, per propoſ. </s>
  <s xml:id="echoid-s31922" xml:space="preserve">4. </s>
  <s xml:id="echoid-s31923" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s31924" xml:space="preserve">arcus horarius <lb/>
<anchor type="note" xlink:label="note-0511-08a" xlink:href="note-0511-08"/>
v.</s>
  <s xml:id="echoid-s31925" xml:space="preserve">g. </s>
  <s xml:id="echoid-s31926" xml:space="preserve">pro hora 23. </s>
  <s xml:id="echoid-s31927" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31928" xml:space="preserve">in tropico ♋, inter circulum horæ 6. </s>
  <s xml:id="echoid-s31929" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31930" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31931" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31932" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31933" xml:space="preserve">alium cir-<lb/>culum maximum per polos mundi, &amp; </s>
  <s xml:id="echoid-s31934" xml:space="preserve">horam 23. </s>
  <s xml:id="echoid-s31935" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31936" xml:space="preserve">in tropico ♋, ductum incluſus, qui cõ-<lb/>tinet grad. </s>
  <s xml:id="echoid-s31937" xml:space="preserve">11. </s>
  <s xml:id="echoid-s31938" xml:space="preserve">M. </s>
  <s xml:id="echoid-s31939" xml:space="preserve">52. </s>
  <s xml:id="echoid-s31940" xml:space="preserve">eſtq́ue occidentalis, &amp; </s>
  <s xml:id="echoid-s31941" xml:space="preserve">borealis, propterea quod diſtantia Solis à Meri-<lb/>diano ſuperat quadrantem. </s>
  <s xml:id="echoid-s31942" xml:space="preserve">Hic autem arcus numeretur à puncto m, verſus partes boreales vſque <lb/>ad l, ducaturq́ue recta occulta l M f. </s>
  <s xml:id="echoid-s31943" xml:space="preserve">Nam ſi beneficio circini accipiatur longitudo vmbræ pro <lb/>hora 23. </s>
  <s xml:id="echoid-s31944" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31945" xml:space="preserve">in tropico ♋, &amp; </s>
  <s xml:id="echoid-s31946" xml:space="preserve">ex E, loco ſtyli transferatur verſus f, ſecabitur recta M f, in f, <lb/>puncto horæ 23. </s>
  <s xml:id="echoid-s31947" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31948" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s31949" xml:space="preserve">Quoniam enim circulus horæ 6. </s>
  <s xml:id="echoid-s31950" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31951" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31952" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31953" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31954" xml:space="preserve"><lb/>maximus ille circulus per polos mundi, &amp; </s>
  <s xml:id="echoid-s31955" xml:space="preserve">horã 23. </s>
  <s xml:id="echoid-s31956" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31957" xml:space="preserve">in tropico ♋, ductus, per axem mundi <lb/>ducuntur, occurruntq́ue Horizonti, cui horologium horizontale æquidiſtat, in centro mundi, <lb/>hoceſt, in F, vertice ſtyli ad p@anum horologij recti, fit vt cum Horizonte faciant communes <lb/>ſectiones, rectas lineas, quæ in mundi centro angulum conſtituant, cui ſubtenditur arcus Horizõ-<lb/>tis, qui inter circulum horæ 6 à mer. </s>
  <s xml:id="echoid-s31958" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31959" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31960" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31961" xml:space="preserve">alium illũ circulum maximũ interijcitur.</s>
  <s xml:id="echoid-s31962" xml:space="preserve">
<pb o="496" file="0512" n="512" rhead="GNOMONICES"/>
Quia vero hi duo circuli occurrunt plano horologij in M, vbi axis mundi eidẽ occurrit, faciuntq́; <lb/></s>
  <s xml:id="echoid-s31963" xml:space="preserve">cum @o ſectiones communes, lineas rectas, quæ illis in Horizonte æquidiſtant, comprehendent <lb/>
<anchor type="note" xlink:label="note-0512-01a" xlink:href="note-0512-01"/>
huiuſmodi lineæ in plano horologij angulum æqualem illi angulo, quẽ in Horizonte priores il-<lb/>
<anchor type="note" xlink:label="note-0512-02a" xlink:href="note-0512-02"/>
læ lineæ efficiunt. </s>
  <s xml:id="echoid-s31964" xml:space="preserve">Quare cum angulus M m l, ſit illi æqualis, quòd arcus m l, ſimilis ſit arcui Ho-<lb/>rizontis inter circulum horæ 6. </s>
  <s xml:id="echoid-s31965" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31966" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31967" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31968" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s31969" xml:space="preserve">alium illum circulum maximum interie-<lb/>cto, quia totidẽ gradus ac Minuta complectitur; </s>
  <s xml:id="echoid-s31970" xml:space="preserve">ſit autem M m, communis ſectio plani horolo-<lb/>gij, &amp; </s>
  <s xml:id="echoid-s31971" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s31972" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31973" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s31974" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s31975" xml:space="preserve">erit recta M l, communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s31976" xml:space="preserve"><lb/>alterius circuli maximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s31977" xml:space="preserve">horam 23. </s>
  <s xml:id="echoid-s31978" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31979" xml:space="preserve">in tropico ♋, tranſeuntis; </s>
  <s xml:id="echoid-s31980" xml:space="preserve">ac proin <lb/>de, Sole exiſtente in hoc circulo, puta in eo puncto, vbi tropicum ♋, interſecat, proijcietur, per <lb/>propoſ. </s>
  <s xml:id="echoid-s31981" xml:space="preserve">11. </s>
  <s xml:id="echoid-s31982" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s31983" xml:space="preserve">1. </s>
  <s xml:id="echoid-s31984" xml:space="preserve">vmbra ſtyli in rectam l M f. </s>
  <s xml:id="echoid-s31985" xml:space="preserve">Cum ergo interuallum E f, ſumptum ſit æquale <lb/>
<anchor type="note" xlink:label="note-0512-03a" xlink:href="note-0512-03"/>
longitudini vmbræ, cadet vmbra ſtyli hora 23. </s>
  <s xml:id="echoid-s31986" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s31987" xml:space="preserve">in tropico ♋, in punctum f. </s>
  <s xml:id="echoid-s31988" xml:space="preserve">Commo-<lb/>
<anchor type="note" xlink:label="note-0512-04a" xlink:href="note-0512-04"/>
dius fortaſſe res peragetur, ſi arcus horarius in oppoſita parte numeretur in circulo i p l m n, nẽ-<lb/>pe arcus m l, qui occidentalis eſt, &amp; </s>
  <s xml:id="echoid-s31989" xml:space="preserve">borealis, in parte orientali atque auſtrali, qualis eſt i n. </s>
  <s xml:id="echoid-s31990" xml:space="preserve">Ita e-<lb/>nim ſatis erit, ſi ducatur recta M n, in quam ex E, transferenda eſt longitudo vmbræ E f. </s>
  <s xml:id="echoid-s31991" xml:space="preserve">Idem <lb/>intelligendum eſt de arcubus latitudinum vmbrarum. </s>
  <s xml:id="echoid-s31992" xml:space="preserve">Nam ſi v.</s>
  <s xml:id="echoid-s31993" xml:space="preserve">g. </s>
  <s xml:id="echoid-s31994" xml:space="preserve">loco arcus D N, latitudinis <lb/>vmbræ horæ 6. </s>
  <s xml:id="echoid-s31995" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s31996" xml:space="preserve">in tropico ♋, qui occidentalis eſt, &amp; </s>
  <s xml:id="echoid-s31997" xml:space="preserve">borealis, accipiatur oppoſit@s B t, <lb/>orientalis, &amp; </s>
  <s xml:id="echoid-s31998" xml:space="preserve">auſtralis, ducenda tantu@ erit recta E t, ex qua longitudo vmbræ E O, abſcindi de <lb/>bet, &amp;</s>
  <s xml:id="echoid-s31999" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32000" xml:space="preserve">Rurſus inquiratur arcus horarius horæ eiuſdem 23. </s>
  <s xml:id="echoid-s32001" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32002" xml:space="preserve">in tropico ♑, nempe gr. </s>
  <s xml:id="echoid-s32003" xml:space="preserve">49. <lb/></s>
  <s xml:id="echoid-s32004" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32005" xml:space="preserve">26. </s>
  <s xml:id="echoid-s32006" xml:space="preserve">qui, quoniam occidentalis eſt, &amp; </s>
  <s xml:id="echoid-s32007" xml:space="preserve">auſtralis, numeretur in parte oppoſita ex i, verſus borea <lb/>les partes, vſque ad p, &amp; </s>
  <s xml:id="echoid-s32008" xml:space="preserve">occulta recta ducatur M p. </s>
  <s xml:id="echoid-s32009" xml:space="preserve">In hanc enim ſi ex E, transferatur longitudo <lb/>
<anchor type="note" xlink:label="note-0512-05a" xlink:href="note-0512-05"/>
vmbræ reſpondens horæ 23. </s>
  <s xml:id="echoid-s32010" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32011" xml:space="preserve">in tropico ♑, vſque ad punctum h, erit h, punctum horæ <lb/>23. </s>
  <s xml:id="echoid-s32012" xml:space="preserve">in tropico ♑. </s>
  <s xml:id="echoid-s32013" xml:space="preserve">Poſtremo inueniemus arcum horarium eiuſdem horæ 23. </s>
  <s xml:id="echoid-s32014" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32015" xml:space="preserve">Sole exiſten-<lb/>te in Æquatore, gr. </s>
  <s xml:id="echoid-s32016" xml:space="preserve">21. </s>
  <s xml:id="echoid-s32017" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32018" xml:space="preserve">49. </s>
  <s xml:id="echoid-s32019" xml:space="preserve">quem, quia occidentalis eſt, &amp; </s>
  <s xml:id="echoid-s32020" xml:space="preserve">auſtralis, ſi numeremus in parte <lb/>oppoſita à puncto i, vſque ad u, ducamuſq́ue rectam M u, ſecabitur æquinoctialis linea in L, pũ-<lb/>cto horæ 23. </s>
  <s xml:id="echoid-s32021" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32022" xml:space="preserve">Ducta igitur recta f L h, dabit horam 23. </s>
  <s xml:id="echoid-s32023" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32024" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32025" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s32026" xml:space="preserve">Eſt tamẽ <lb/>hic conſideratione dignum, quamlibet rectam occultam ex M, per extremum punctum cuiuſuis <lb/>lineæ horariæ in tropico ♋, ductam, ſi vltra centrum M, producatur, tranſire per extremum pun <lb/>ctum lineæ alterius horę in eodem tropico, quę a priore duodecim horis diſtar. </s>
  <s xml:id="echoid-s32027" xml:space="preserve">Ita vides rectam <lb/>f M, quæ per f, punctum extremũ horæ 23. </s>
  <s xml:id="echoid-s32028" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32029" xml:space="preserve">in tropico ♋, ducitur, productam vltra M, <lb/>trãſire per q, punctum extremum horæ 11. </s>
  <s xml:id="echoid-s32030" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32031" xml:space="preserve">in eodem tropico: </s>
  <s xml:id="echoid-s32032" xml:space="preserve">Item rectam r M ſ, duci <lb/>
<anchor type="note" xlink:label="note-0512-06a" xlink:href="note-0512-06"/>
per extrema puncta horarum 22. </s>
  <s xml:id="echoid-s32033" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32034" xml:space="preserve">10. </s>
  <s xml:id="echoid-s32035" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32036" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s32037" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32038" xml:space="preserve">Quocirca ſi duæ horæ ab or. </s>
  <s xml:id="echoid-s32039" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32040" xml:space="preserve">duode-<lb/>
<anchor type="note" xlink:label="note-0512-07a" xlink:href="note-0512-07"/>
cim horis inter ſe diſtantes, in vnum tropicum cadant, ſatis erit, ſi vnius duntaxat arcus hora-<lb/>rius inueſtigetur. </s>
  <s xml:id="echoid-s32041" xml:space="preserve">Ratio huius rei eſt, quod circulus maximus per polos mundi, &amp; </s>
  <s xml:id="echoid-s32042" xml:space="preserve">per quamlibet <lb/>horam ab occ. </s>
  <s xml:id="echoid-s32043" xml:space="preserve">in tropico ductus tranſeat quoque in eodem tropico per horam oppoſitam, quæ <lb/>nimirum ab ea duodecim horis abeſt, cum tropicum bifariã ſecet, ex propoſ. </s>
  <s xml:id="echoid-s32044" xml:space="preserve">15. </s>
  <s xml:id="echoid-s32045" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32046" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32047" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s32048" xml:space="preserve">Hinc enim fit, vt &amp; </s>
  <s xml:id="echoid-s32049" xml:space="preserve">communis eius, &amp; </s>
  <s xml:id="echoid-s32050" xml:space="preserve">plani horologij ſectio per M, ducta tranſeat in plano ho-<lb/>rologij per duas illas horas oppoſitas.</s>
  <s xml:id="echoid-s32051" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1642" type="float" level="2" n="4">
<note position="right" xlink:label="note-0511-07" xlink:href="note-0511-07a" xml:space="preserve">Deſcriptio horo <lb/>logij horizonta <lb/>lis ex tabulis ar <lb/>cuũ horario rũ, <lb/>qui per propoſ. <lb/>4. huius lib. ſup <lb/>putantur.</note>
<note position="left" xlink:label="note-0511-08" xlink:href="note-0511-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0512-01" xlink:href="note-0512-01a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0512-02" xlink:href="note-0512-02a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0512-03" xlink:href="note-0512-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0512-04" xlink:href="note-0512-04a" xml:space="preserve">Quomodo l@co <lb/>arcuũ horario-<lb/>rum, &amp; latitu-<lb/>dinum vmbra-<lb/>rum accipi poſ-<lb/>ſint arcus oppo-<lb/>ſiti in deſcriptio <lb/>nibus horologio <lb/>@um.</note>
<note position="left" xlink:label="note-0512-05" xlink:href="note-0512-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0512-06" xlink:href="note-0512-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0512-07" xlink:href="note-0512-07a" xml:space="preserve">Satis e@@, ſi pro <lb/>duabus horis <lb/>ab or. vel occ. <lb/>quarũ vna ab al <lb/>tera duodecim <lb/>horis abeſt, vnus <lb/>arcus horarius <lb/>inueſtigetur.</note>
</div>
<p>
  <s xml:id="echoid-s32052" xml:space="preserve">HÆC autem deſcriptio horologij per arcus horarios expeditiſſime fit in horis à mer. </s>
  <s xml:id="echoid-s32053" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32054" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s32055" xml:space="preserve">
<anchor type="note" xlink:label="note-0512-08a" xlink:href="note-0512-08"/>
noc. </s>
  <s xml:id="echoid-s32056" xml:space="preserve">propterea quod, cum omnes hiiuſmodi horæ per centrum M, tranſeant, neceſſe non ſit pro <lb/>ſingulis horis ternos arcus inquirere, vt in hora 23. </s>
  <s xml:id="echoid-s32057" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32058" xml:space="preserve">factum eſt, ſed ſatis fuerit, ſi ſinguli ar <lb/>
<anchor type="note" xlink:label="note-0512-09a" xlink:href="note-0512-09"/>
cus quærantur; </s>
  <s xml:id="echoid-s32059" xml:space="preserve">cuiuſmodi ſunt ſequentes pro ſingulis horis à mer. </s>
  <s xml:id="echoid-s32060" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32061" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32062" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32063" xml:space="preserve">horologij hori-<lb/>zontalis, ad latitudinem Grad. </s>
  <s xml:id="echoid-s32064" xml:space="preserve">42.</s>
  <s xml:id="echoid-s32065" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1643" type="float" level="2" n="5">
<note position="left" xlink:label="note-0512-08" xlink:href="note-0512-08a" xml:space="preserve">Deſc@iptio hora <lb/>rum à mer. &amp; <lb/>med. noc. per ar <lb/>cus horarios ex-<lb/>peditiſſima eſt.</note>
<note position="left" xlink:label="note-0512-09" xlink:href="note-0512-09a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1645" type="section" level="1" n="419">
<head xml:id="echoid-head434" xml:space="preserve">Arcus horarij in horologio horizontali pro horis à mer. <lb/>&amp; med. noc. ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horę à media \\ nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # Oriẽtales. <lb/>Horæ à meridie. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # Occidenta. <lb/>
Arcus ho- \\ rarij. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 21. 49. # 40. 48. # 56. 13. # 68. 53. # 79. 50. # 90. 0. # Auſtrales.
</note>
<p>
  <s xml:id="echoid-s32066" xml:space="preserve">Ex quibus arcubus, ſi numerentur à punctis i, m, verſus partes boreales, ſeu oppoſitas, cum ipſi <lb/>ſint auſtrales, &amp; </s>
  <s xml:id="echoid-s32067" xml:space="preserve">ex M, centro horologij per fines numerationum lineę rectæ ducantur, quæ ſi ab-<lb/>ſcindantur ſecundum interualla longitudinum vmbrarum, quas Sol habet, cum @ tropicis exi-<lb/>ſtit, deſcriptum erit horologium aſtronomicum. </s>
  <s xml:id="echoid-s32068" xml:space="preserve">Exemplum habes in hora 7. </s>
  <s xml:id="echoid-s32069" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32070" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32071" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32072" xml:space="preserve">5. <lb/></s>
  <s xml:id="echoid-s32073" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32074" xml:space="preserve">quarum vtraque arcum horarium habet auſtralem gr. </s>
  <s xml:id="echoid-s32075" xml:space="preserve">21. </s>
  <s xml:id="echoid-s32076" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32077" xml:space="preserve">49. </s>
  <s xml:id="echoid-s32078" xml:space="preserve">qui ſi numeretur à pun-<lb/>ctis i, &amp; </s>
  <s xml:id="echoid-s32079" xml:space="preserve">m, verſus partes oppoſitas, id eſt, boreales, vſque ad α, &amp; </s>
  <s xml:id="echoid-s32080" xml:space="preserve">u, ducanturq́ue rectæ M α, <lb/>M u, in quas interualla longitudinis vmbræ earundem horarum in tropico ♋, transferantur, de-<lb/>ſcriptæ erunt lineæ horarum 7. </s>
  <s xml:id="echoid-s32081" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32082" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32083" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32084" xml:space="preserve">5. </s>
  <s xml:id="echoid-s32085" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32086" xml:space="preserve">Idemq́ue de cæteris horis faciendum eſt.</s>
  <s xml:id="echoid-s32087" xml:space="preserve">
<pb o="497" file="0513" n="513" rhead="LIBER QVINTVS."/>
Sunt autem primum lineæ ex centro M, ducendæ occultę, donec in eis longitudines vmbrarum <lb/>notatę @uerint, quia partes earum extra tropicos ſuperuacaneę ſunt.</s>
  <s xml:id="echoid-s32088" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s32089" xml:space="preserve">PRO horologio Verticali auſtrali Aſtronomco, atque Italico ſupputatę ſunt inſequentes ta-<lb/>bellæ continentes latitudines, longitudineſq́ue vmbrarum pro horis tam à mer. </s>
  <s xml:id="echoid-s32090" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32091" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32092" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s32093" xml:space="preserve">quam ab occ. </s>
  <s xml:id="echoid-s32094" xml:space="preserve">nec non arcus horarios pro horis à mer. </s>
  <s xml:id="echoid-s32095" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32096" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32097" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32098" xml:space="preserve">Quia vero Horizon reſpectu <lb/>Verticalis circuli tamquam Horizontis, eſt Verticalis, appellauimus latitudines vmbrarum, quę <lb/>ſunt infra Horizontem, hoc eſt, citra Verticalem ipſius Verticalis, verſus polum conſpicuum, qui <lb/>videlicet ſupra Verticalem circulum eleuatur, qualis eſt polus antarcticus, inferiores, ſuperiores <lb/>aurem illas, quæ ſupra Horizontem, hoc eſt, vltra Verticalem Verticalis ſunt verſus polum occul-<lb/>tum, id eſt, verſus polum arcticum, ſiue verſus centrum horologij; </s>
  <s xml:id="echoid-s32099" xml:space="preserve">quia illæ infra horizontalem <lb/>
<anchor type="note" xlink:label="note-0513-01a" xlink:href="note-0513-01"/>
lineam, hæ vero ſupra eandem computandæ ſunt in horarum deſcriptione. </s>
  <s xml:id="echoid-s32100" xml:space="preserve">Illarum porro horarũ <lb/>latitudines vmbrarum infra Horizontem, hoc eſt, citra Verticalem Vetticalis, ſunt, quæ, minores <lb/>altitudines ſupra Verticalem circulum, tanquam Horizontem, habent illa, quam Sol habet in Ho <lb/>rizonte, tanquam Verticali ipſius Verticalis conſtitutus, ſupra eundem Verticalem, vt Hori-<lb/>zontem, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s32101" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32102" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s32103" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s32104" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1645" type="float" level="2" n="1">
<note position="left" xlink:label="note-0513-01" xlink:href="note-0513-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1647" type="section" level="1" n="420">
<head xml:id="echoid-head435" xml:space="preserve">Latitudines, longitudineſq́ue vmbrarum in horologio Verticali auſtrali pro horis à <lb/>mer. &amp; med. noc. ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1648" type="section" level="1" n="421">
<head xml:id="echoid-head436" xml:space="preserve">In tropico ♑, latitudines vmbrarum partim ſunt inferiores, &amp; partim ſuperiores, vt hę <lb/>ſyllabę [Infer. Super.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à me \\ dia nocte. # 5 \\ Infer. # 6 \\ Infer. # 7 \\ Infer. # 8 \\ Super # 9 \\ Super # 10 \\ Super. # 11 \\ Super. # 12 \\ Super. # orienta \\ les. <lb/>Horæ ♑, a \\ meridie. # 7 \\ Infer. # 6 \\ Infer. # 5 \\ Infer. # 4 \\ Super@ # 3 \\ Super. # 2 \\ Super. # 1 \\ Super. # 0 \\ Super. # occiden \\ tales. <lb/>Latitudines vm \\ brarum. # G. M # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 26. 35. # 16. 14 # 5. 47. # 5. 17. # 18. 22. # 35. 12. # 58. 47. # 90. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 86. 29. # 38. 41. # 23. 28. # 15. 52. # 11. 14. # 8. 8. # 6. 11. # 5. 28.
</note>
</div>
<div xml:id="echoid-div1649" type="section" level="1" n="422">
<head xml:id="echoid-head437" xml:space="preserve">In Aequatore omnes vmbrarum latitudines Superiores ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎ à \\ med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orienta \\ les. <lb/>
Horæ ♈, &amp; ♎, à mer. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # occidẽtales
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 11. 16. # 23. 13. # 36. 37. # 52. 9. # 70. 10. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# Infinita # 68. 17. # 33. 48 # 22. 21. # 16. 53. # 14. 10 # 13. 20.
</note>
</div>
<div xml:id="echoid-div1650" type="section" level="1" n="423">
<head xml:id="echoid-head438" xml:space="preserve">In tropico ♋, ſunt omnes latitudines vm- \\ brarum Superiores.</head>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. \\ nocte. # 8 # 9 # 10 # 11 # 12 # # orientales. <lb/>Horæ ♋, a meridie. # 4 # 3 # 2 # 1 # 0 # # occidentales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 37. 25. # 49. 6. # 61. 51. # 75. 37. # 90. 0. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 1146. 4. # 86. 29. # 49. 36. # 38. 41. # 35. 52. <lb/></note>
<pb o="498" file="0514" n="514" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1651" type="section" level="1" n="424">
<head xml:id="echoid-head439" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio Verticali Auſtrali pro \\ horis ab occ. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head440" xml:space="preserve">In tropico ♑, vmbrarum latitudines partim Inferiores ſunt, &amp; partim ſuperio- \\ res, vt hæ ſyllabæ [Infer. Super.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab \\ occaſu. # 12 \\ Infer. # 13 \\ Infer. # 14 \\ Infer. # 15 \\ Infer. # 16 \\ Super. # 17 \\ Super. # 18 \\ Super. # 19 \\ Super. # orientales. <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 32. 44. # 21. 43. # 11. 25. # 3. 48. # 11. 4. # 25. 34. # 45. 12. # 72. 38.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 211. 20 # 55. 35. # 30. 2. # 19. 24. # 13. 27. # 9. 38. # 7. 5. # 5. 41.
Horæ ♑, ab \\ occaſu. # 20 \\ Super. # 21 \\ Super. # 22 \\ Super. # 23 \\ Super. # 24 # # occidentales.
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M.
# 74. 44. # 46. 44. # 26. 41. # 11. 56. # 0. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M.
# 5. 38. # 6. 57. # 9. 26. # 13. 9. # 18. 52.
</note>
</div>
<div xml:id="echoid-div1652" type="section" level="1" n="425">
<head xml:id="echoid-head441" xml:space="preserve">In Æquatore latitudines vmbrarum omnes ſunt ſuperiores.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ ab occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18 # orientales. <lb/>
# 24 # 23 # 22 # 21 # 20 # 19 # 18 # occident.
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 0. 0. # 11. 16. # 23. 13. # 36. 37. # 52. 9. # 70. 10. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# Infinita # 68. 17. # 33. 48. # 22. 21. # 16. 53. # 14. 10. # 13. 20.
</note>
</div>
<div xml:id="echoid-div1653" type="section" level="1" n="426">
<head xml:id="echoid-head442" xml:space="preserve">In tropico ♋, latitudines vmbrarum omnes ſunt ſuperiores: orientales vero \\ ab occidentalibus per has ſyllabas [or. occ.] diſcernuntur.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 13 \\ or. # 14 \\ or. # 15 \\ or. # 16 \\ or. # 17 \\ occ. # 18 \\ occ. # 19 \\ occ. # 20 \\ occ. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 43. 32. # 55. 46. # 69. 5. # 83. 15. # 82. 17. # 68. 10. # 54. 54. # 42. 45. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 147. 1. # 60. 47. # 42. 22. # 36. 28. # 36. 39. # 43. 2. # 63. 0. # 163. 65 <lb/></note>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1654" type="section" level="1" n="427">
<head xml:id="echoid-head443" xml:space="preserve">Arcus horarij in horologio Verticali Auſtrali pro horis à mer. \\ &amp; med noc. ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horę à media \\ nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # Oriẽtales. <lb/>Horæ à meridie. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # Occidenta. <lb/>Arcus ho- \\ rarij. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 0. 0. # 19. 50. # 37. 51. # 53. 23. # 66. 47. # 78. 44. # 90. 0. # Superiores. <lb/></note>
<pb o="499" file="0515" n="515" rhead="LIBER QVINTVS."/>
<p>
  <s xml:id="echoid-s32105" xml:space="preserve">EX hiſce tabulis ita horologium Verticale Auſtrale pingemus. </s>
  <s xml:id="echoid-s32106" xml:space="preserve">In plano horologij deſcriba-<lb/>
<anchor type="note" xlink:label="note-0515-01a" xlink:href="note-0515-01"/>
tur circulus cuiuſuis magnitudinis A B C D, cuius centrum E, in quo ſtylus figendus eſt ad an-<lb/>gulos rectos; </s>
  <s xml:id="echoid-s32107" xml:space="preserve">ducanturq́ue duę diametri A C, B D, ſeſe ad rectos angulos in centro E, ſecantes <lb/>quarum A C, meridiana linea ſit, vtpote communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s32108" xml:space="preserve">plani horologij, ac <lb/>propterea reliqua B D, vt in horizontali horologio oſtendimus communis ſectio Verticalis pro-<lb/>priè dicti ipſius Verticalis, nempe Horizontis, &amp; </s>
  <s xml:id="echoid-s32109" xml:space="preserve">eiuſdem plani horologij, hoc eſt, linea hori-<lb/>zontalis, quæ inſtar eſt lineę Verticalis ipſius horologij Verticalis, à qua latitudines vmbra-<lb/>rum ſupputandæ erunt. </s>
  <s xml:id="echoid-s32110" xml:space="preserve">Quod ſi planum horologij ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s32111" xml:space="preserve">Verticali circulo paralle-<lb/>lum directo in meridiem ſpectans, ducenda eſt beneficio perpendiculi in eo recta A C, ad <lb/>Horizontem perpendicularis pro linea meridiana, ex cuius puncto E, vbi ſtylus collocandus eſt, <lb/>
<anchor type="note" xlink:label="note-0515-02a" xlink:href="note-0515-02"/>
circulus deſcribendus A B C D, diameterq́ue B D, ad A C, perpendicularis ducenda pro com-<lb/>muni ſectione Verticalis proprij ipſius Verticalis, qui ab Horizonte non differt, &amp; </s>
  <s xml:id="echoid-s32112" xml:space="preserve">plani horolo-<lb/>gij, id eſt, pro linea horizontali. </s>
  <s xml:id="echoid-s32113" xml:space="preserve">Vel primo loco in plano horologij beneficio perpendicu-<lb/>li ducenda eſt recta B D, Horizonti parallela pro linea horizontali, ex cuius puncto E, loco ſtyli <lb/>circulus deſcribendus A B C D, diameterq́ue A C, ad B D, perpendicularis ducenda pro linea <lb/>meridiana. </s>
  <s xml:id="echoid-s32114" xml:space="preserve">Statuantur autem partes ſuperiores ad A, inferiores vero ad C, ac proinde orientales <lb/>ad D, &amp; </s>
  <s xml:id="echoid-s32115" xml:space="preserve">occidentales ad B. </s>
  <s xml:id="echoid-s32116" xml:space="preserve">Eligatur quoque longitudo gnomonis quęcunque E F, cui quorcunq; <lb/></s>
  <s xml:id="echoid-s32117" xml:space="preserve">partes ęquales abſcindãtur ex recta G H, eique apponatur adhuc G I, eidem ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s32118" xml:space="preserve">in 12. </s>
  <s xml:id="echoid-s32119" xml:space="preserve"><lb/>particulas ęquales diuiſa, vt ex hac recta longitudines vmbrarum poſſint deſumi, vt in horizon-<lb/>tali horologio diximus.</s>
  <s xml:id="echoid-s32120" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1654" type="float" level="2" n="1">
<note position="right" xlink:label="note-0515-01" xlink:href="note-0515-01a" xml:space="preserve">Veriicalis horo <lb/>logii Auſtralis <lb/>deſcriptio ex ta-<lb/>bulis.</note>
<note position="left" xlink:label="note-0515-02" xlink:href="note-0515-02a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">20</note>
  <figure>
    <image file="0515-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0515-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s32121" xml:space="preserve">ITAQVE quoniam Sole exiſtente in Æquatore, vmbra ſtyli hora 12. </s>
  <s xml:id="echoid-s32122" xml:space="preserve">meridiei proiicitur in-<lb/>fra lineam horizontalem, ſicut &amp; </s>
  <s xml:id="echoid-s32123" xml:space="preserve">in omnibus alijs horis ſupra Horizontẽ extantibus, quæ, vt con <lb/>ſtat ex tabula horarum à mer. </s>
  <s xml:id="echoid-s32124" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32125" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32126" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32127" xml:space="preserve">continet Partes 13. </s>
  <s xml:id="echoid-s32128" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32129" xml:space="preserve">20. </s>
  <s xml:id="echoid-s32130" xml:space="preserve">ſi hanc vmbram beneficio <lb/>
<anchor type="note" xlink:label="note-0515-06a" xlink:href="note-0515-06"/>
circini ex recta I H, ſumptã in lineam meridianã transferamus ex E, deorſum verſus vſq; </s>
  <s xml:id="echoid-s32131" xml:space="preserve">ad K, du <lb/>
<anchor type="note" xlink:label="note-0515-07a" xlink:href="note-0515-07"/>
cemus per K, lineam ęqu@octialẽ K L, ad A C, perpendicularẽ. </s>
  <s xml:id="echoid-s32132" xml:space="preserve">Quam hac etiã ratione ducemus. <lb/></s>
  <s xml:id="echoid-s32133" xml:space="preserve">Sumpta in horizontali linea B D, recta E F, ſtylo ęquali, ſi conſtituatur in F, angulus E F K, altitu-<lb/>dinis poli ſupra Verticalẽ circulũ, hoc eſt, cõplementi altitudinis poli ſupra Horizontẽ, ita vt re-<lb/>cta F K, meridianam lineam infra ſtylũ ſecet in K, ducenda erit per K, ęquinoctialis linea. </s>
  <s xml:id="echoid-s32134" xml:space="preserve">Et ſi in <lb/>F, alius angulus cõſtituatur E F M, ęqualis cõplemento altitudinis poli ſupra circulũ Verticalẽ, hoc <lb/>
<anchor type="note" xlink:label="note-0515-08a" xlink:href="note-0515-08"/>
eſt, altitudini poli ſupra Horizontem ęqualis, ita vt recta F M, meridianam lineam ſecet in M, erit <lb/>M, centrum horologij. </s>
  <s xml:id="echoid-s32135" xml:space="preserve">Quod aliter hac arte reperiemus. </s>
  <s xml:id="echoid-s32136" xml:space="preserve">In tabula longitudinum vmbrarum <lb/>propoſ. </s>
  <s xml:id="echoid-s32137" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32138" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s32139" xml:space="preserve">accipiatur altitudo poli ſupra Verticalem circulum, nempe complementũ <lb/>altitudinis poli ſupra Horizontem, Grad. </s>
  <s xml:id="echoid-s32140" xml:space="preserve">48. </s>
  <s xml:id="echoid-s32141" xml:space="preserve">eiuſq́ue vmbra P. </s>
  <s xml:id="echoid-s32142" xml:space="preserve">10. </s>
  <s xml:id="echoid-s32143" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32144" xml:space="preserve">48. </s>
  <s xml:id="echoid-s32145" xml:space="preserve">Si enim hęc vmbra <lb/>beneficio circini transferatur ex E, in lineam meridianam ſurſum verſus vſque ad M, erit M, cẽ-<lb/>trum horologij. </s>
  <s xml:id="echoid-s32146" xml:space="preserve">Quod demonſtrabitur, vt in horologio horizontali. </s>
  <s xml:id="echoid-s32147" xml:space="preserve">Horę deſcribentur, vt in ho
<pb o="500" file="0516" n="516" rhead="GNOMONICES"/>
rizontali horologio, ſi latitudines vmbrarum ſupputentur ex B, vel D, ſurſum aut deorſum verſus, <lb/>prout tabulę indicant, &amp;</s>
  <s xml:id="echoid-s32148" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32149" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s32150" xml:space="preserve">Pro hora 13. </s>
  <s xml:id="echoid-s32151" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32152" xml:space="preserve">in tropico ♑, numero cius lati-<lb/>tudinem vmbrę Grad. </s>
  <s xml:id="echoid-s32153" xml:space="preserve">21. </s>
  <s xml:id="echoid-s32154" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32155" xml:space="preserve">43. </s>
  <s xml:id="echoid-s32156" xml:space="preserve">inferiorem &amp; </s>
  <s xml:id="echoid-s32157" xml:space="preserve">orientalem ex D, puncto orientali deorſum verſus <lb/>vſque ad N, vel in parte oppoſita, vt in horologio horizontali diximus, ex B, puncto occidenta-<lb/>li ſurſum verſus vſque ad N. </s>
  <s xml:id="echoid-s32158" xml:space="preserve">Si enim ex recta occulta E N, in parte oppoſita abſcindatur longi-<lb/>tudo vmbræ eiuſdem horę P. </s>
  <s xml:id="echoid-s32159" xml:space="preserve">55. </s>
  <s xml:id="echoid-s32160" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32161" xml:space="preserve">35. </s>
  <s xml:id="echoid-s32162" xml:space="preserve">inuenietur O, punctum horæ 13. </s>
  <s xml:id="echoid-s32163" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32164" xml:space="preserve">in tropico ♑. <lb/></s>
  <s xml:id="echoid-s32165" xml:space="preserve">Ita quoque ex D P, latitudine vmbrę orientali, &amp; </s>
  <s xml:id="echoid-s32166" xml:space="preserve">ſuperiori horę eiuſdem 13. </s>
  <s xml:id="echoid-s32167" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32168" xml:space="preserve">in Æquato-<lb/>re gr. </s>
  <s xml:id="echoid-s32169" xml:space="preserve">11. </s>
  <s xml:id="echoid-s32170" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32171" xml:space="preserve">16. </s>
  <s xml:id="echoid-s32172" xml:space="preserve">vel ex oppoſita latitudine B P, vel ex longitudine vmbrę eiuſdẽ horę P. </s>
  <s xml:id="echoid-s32173" xml:space="preserve">68. </s>
  <s xml:id="echoid-s32174" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32175" xml:space="preserve">17. </s>
  <s xml:id="echoid-s32176" xml:space="preserve"><lb/>inuentum eſt in linea æquinoctiali punctum L, pro hora 13. </s>
  <s xml:id="echoid-s32177" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32178" xml:space="preserve">Item ex D Q, latitudine vm <lb/>brę orientali, &amp; </s>
  <s xml:id="echoid-s32179" xml:space="preserve">ſuperiori horę 9. </s>
  <s xml:id="echoid-s32180" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32181" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32182" xml:space="preserve">in tropico ♋, gr. </s>
  <s xml:id="echoid-s32183" xml:space="preserve">49. </s>
  <s xml:id="echoid-s32184" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32185" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32186" xml:space="preserve">vel ex oppoſita latitu-<lb/>
<anchor type="note" xlink:label="note-0516-01a" xlink:href="note-0516-01"/>
dine B Q, longitudineq́ue vmbræ eiuſdem horę P. </s>
  <s xml:id="echoid-s32187" xml:space="preserve">86. </s>
  <s xml:id="echoid-s32188" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32189" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32190" xml:space="preserve">repertum eſt punctum R, horę 9. <lb/></s>
  <s xml:id="echoid-s32191" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32192" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32193" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s32194" xml:space="preserve">Et in eodem tropico ex eadem latitudine B S, occidentali, ſuperioriq́; </s>
  <s xml:id="echoid-s32195" xml:space="preserve"><lb/>horę 3. </s>
  <s xml:id="echoid-s32196" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32197" xml:space="preserve">vel ex oppoſita D S, eademq́; </s>
  <s xml:id="echoid-s32198" xml:space="preserve">longitudine vmbræ inuentum eſt punctum T, horę <lb/>3. </s>
  <s xml:id="echoid-s32199" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32200" xml:space="preserve">Quod ſi idem fiat in cęteris horis, abſolutum erit horologium Verticale Auſtrale. </s>
  <s xml:id="echoid-s32201" xml:space="preserve">Eadẽ <lb/>ratione ex arcu horario m V, occidentali, &amp; </s>
  <s xml:id="echoid-s32202" xml:space="preserve">ſuperiori gr. </s>
  <s xml:id="echoid-s32203" xml:space="preserve">19. </s>
  <s xml:id="echoid-s32204" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32205" xml:space="preserve">50. </s>
  <s xml:id="echoid-s32206" xml:space="preserve">horę 5. </s>
  <s xml:id="echoid-s32207" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32208" xml:space="preserve">vel ex oppoſi <lb/>to i X, in circulo i X Z m, ex M, deſcripto, inuentum eſt punctum X, per quod hora 5. </s>
  <s xml:id="echoid-s32209" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32210" xml:space="preserve"><lb/>ducitur. </s>
  <s xml:id="echoid-s32211" xml:space="preserve">Et ex eodem arcu horario i Y, orientali &amp; </s>
  <s xml:id="echoid-s32212" xml:space="preserve">ſuperiori horæ 7. </s>
  <s xml:id="echoid-s32213" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32214" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32215" xml:space="preserve">vel ex oppoſito <lb/>m Z, inuentum eſt in eodem circulo punctum Z, per quod hora 7. </s>
  <s xml:id="echoid-s32216" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32217" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32218" xml:space="preserve">ducenda eſt. </s>
  <s xml:id="echoid-s32219" xml:space="preserve">Quæ <lb/>
<anchor type="note" xlink:label="note-0516-02a" xlink:href="note-0516-02"/>
duæ horæ vltra centrum M, productæ dabunt horam 5. </s>
  <s xml:id="echoid-s32220" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32221" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32222" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32223" xml:space="preserve">7. </s>
  <s xml:id="echoid-s32224" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32225" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s32226" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32227" xml:space="preserve">Portio autẽ <lb/>ſupra lineam horizontalem dabit horologium Verticale Boreale, nempe in oppoſita facie plani <lb/>
<anchor type="note" xlink:label="note-0516-03a" xlink:href="note-0516-03"/>
collocandum, ſi inuertatur, vt ad propoſ. </s>
  <s xml:id="echoid-s32228" xml:space="preserve">13. </s>
  <s xml:id="echoid-s32229" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32230" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32231" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32232" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32233" xml:space="preserve">præcepimus. </s>
  <s xml:id="echoid-s32234" xml:space="preserve">Pro horis tamen ab occ. <lb/></s>
  <s xml:id="echoid-s32235" xml:space="preserve">ducendę erunt prius illæ ab or. </s>
  <s xml:id="echoid-s32236" xml:space="preserve">in Auſtrali horologio, quæ in Boreali mutantur in horas ab occ. </s>
  <s xml:id="echoid-s32237" xml:space="preserve">vt <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s32238" xml:space="preserve">23. </s>
  <s xml:id="echoid-s32239" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32240" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32241" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s32242" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s32243" xml:space="preserve">ratione ex ſequentibus horologijs abſcindentur <lb/>à linea horizontali horologia, quæ in oppoſitis faciebus planorum collocanda ſunt.</s>
  <s xml:id="echoid-s32244" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1655" type="float" level="2" n="2">
<note position="left" xlink:label="note-0515-06" xlink:href="note-0515-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0515-07" xlink:href="note-0515-07a" xml:space="preserve">Aequinoctialis <lb/>linea in Vetti-<lb/>cali horologio <lb/>quo pacto de-<lb/>ſcribatur.</note>
<note position="right" xlink:label="note-0515-08" xlink:href="note-0515-08a" xml:space="preserve">Centrum horo-<lb/>logii Verticalis <lb/>quo artificio in <lb/>ueniatur.</note>
<note position="left" xlink:label="note-0516-01" xlink:href="note-0516-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0516-02" xlink:href="note-0516-02a" xml:space="preserve">Qua arte ex ho-<lb/>@ologio conſtru <lb/>cto eruatur il-<lb/>lud, quod in fa <lb/>cie oppoſita pla <lb/>ni collocãdum <lb/>eſt, nempe Bo <lb/>reale ex Auſtra <lb/>li, &amp;c.</note>
<note position="left" xlink:label="note-0516-03" xlink:href="note-0516-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s32245" xml:space="preserve">AD horologium Meridianum vtrumque conſtruendum compoſitæ ſunt ſequentes tabellæ <lb/>latitudinum, longitudinumq́ue vmbrarum, tam pro horis à mer. </s>
  <s xml:id="echoid-s32246" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32247" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32248" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32249" xml:space="preserve">quam ab occ. <lb/></s>
  <s xml:id="echoid-s32250" xml:space="preserve">Quoniam autem circulus horæ 6. </s>
  <s xml:id="echoid-s32251" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32252" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32253" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32254" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32255" xml:space="preserve">incedens per polos mundi, &amp; </s>
  <s xml:id="echoid-s32256" xml:space="preserve">per po-<lb/>los Meridiani, nempe per communes ſectiones Æquatoris atque Horizontis, eſt veluti Meridia-<lb/>nus ipſius Meridiani, erit Æquator, cum rectus ſit &amp; </s>
  <s xml:id="echoid-s32257" xml:space="preserve">ad Meridianum, &amp; </s>
  <s xml:id="echoid-s32258" xml:space="preserve">ad circulum horæ 6. </s>
  <s xml:id="echoid-s32259" xml:space="preserve">à <lb/>mer. </s>
  <s xml:id="echoid-s32260" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32261" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32262" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32263" xml:space="preserve">inſtar Verticalis proprie dicti reſpectu Meridiani. </s>
  <s xml:id="echoid-s32264" xml:space="preserve">Ita enim &amp; </s>
  <s xml:id="echoid-s32265" xml:space="preserve">Verticalis Hori-<lb/>
<anchor type="note" xlink:label="note-0516-04a" xlink:href="note-0516-04"/>
zontis rectus eſt &amp; </s>
  <s xml:id="echoid-s32266" xml:space="preserve">ad Horizontem, &amp; </s>
  <s xml:id="echoid-s32267" xml:space="preserve">ad Meridianum Horizontis cum per vtriuſque polos duca-<lb/>tur. </s>
  <s xml:id="echoid-s32268" xml:space="preserve">Id quod in omni Verticali proprie dicto cuiuſque circuli maximi obſeruandum eſt, vt vide-<lb/>licet tranſeat &amp; </s>
  <s xml:id="echoid-s32269" xml:space="preserve">per polos ipſius circuli maximi, &amp; </s>
  <s xml:id="echoid-s32270" xml:space="preserve">per polos Meridiani proprij eiuſdem maximi <lb/>circuli. </s>
  <s xml:id="echoid-s32271" xml:space="preserve">Quare in horologio Meridiano computandæ erunt latitudines vmbrarum à linea æquino-<lb/>ctiali, nempe à communi ſectione plani horologij, &amp; </s>
  <s xml:id="echoid-s32272" xml:space="preserve">Verticalis proprie dicti ipſius Meridiani; <lb/></s>
  <s xml:id="echoid-s32273" xml:space="preserve">Sole quidẽ percurrente borealia ſigna, verſus partes horologij boreales, eodẽ autem in auſtralibus <lb/>gnis commorante, verſus auſtrales. </s>
  <s xml:id="echoid-s32274" xml:space="preserve">Rurſus quia inter Meridianum, &amp; </s>
  <s xml:id="echoid-s32275" xml:space="preserve">circulum horæ 6. </s>
  <s xml:id="echoid-s32276" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32277" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s32278" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32279" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32280" xml:space="preserve">interijcitur quadrans cuiuſque paralleli, latitudines vmbrarum, quæ illis horis de-<lb/>bentur, quæ minus à meridie diſtant, quàm ſex horis, ſupputandæ erunt à ſuperiori parte æqui-<lb/>noctialis lineæ; </s>
  <s xml:id="echoid-s32281" xml:space="preserve">latitudines vero horarum, quarum diſtantiæ à meridie quadrantem ſuperant, à <lb/>
<anchor type="note" xlink:label="note-0516-05a" xlink:href="note-0516-05"/>
parte inferiori. </s>
  <s xml:id="echoid-s32282" xml:space="preserve">Hinc factum eſt, vt in tabellis quædam horæ vtriuſque tropici, earumq́ue lati-<lb/>tudines, dictæ ſint Inferiores, quædam autem ſuperiores. </s>
  <s xml:id="echoid-s32283" xml:space="preserve">Poſtremo horarum antemeridianarũ, <lb/>ſiue orientalium latitudines in horologio orientali, pomeridianarum vero, ſiue occidentalium in <lb/>occidentali ſupputandæ ſunt.</s>
  <s xml:id="echoid-s32284" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1656" type="float" level="2" n="3">
<note position="left" xlink:label="note-0516-04" xlink:href="note-0516-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0516-05" xlink:href="note-0516-05a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1658" type="section" level="1" n="428">
<head xml:id="echoid-head444" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in vtroque horologio Meridiano pro horis à <lb/>mer. &amp; med. noc. ad quamcunque latitudinem.</head>
<head xml:id="echoid-head445" xml:space="preserve">In tropico ♋, latitudines vmbrarum omnes ſunt Boreales, &amp; in tropico ♑, Auſtrales. Ite@<unsure/> <lb/>in vtroque tropico latitudines vmbrarum partim ſunt Inferiores, &amp; par-<lb/>
tim ſuperiores, vt hæ ſyllabæ [Inf. Sup.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, &amp; ♑, a me- \\ dia nocte. # 0. 12. \\ inf. ſup # 1. 11. \\ inf. ſup # 2. 10. \\ inf. ſup # 3. 9. \\ inf. ſup # 4. 8. \\ inf. ſup # 5. 7. \\ inf. ſup # 6. 6. \\ inf. ſup # Ortenta- \\ les. <lb/>Horæ ♋, &amp; ♑, à \\ meridie. # 0. 12. \\ ſup. inf. # 1. 11. \\ ſup. inf. # 2. 10. \\ ſup. inf. # 3. 9. \\ ſup. inf. # 4. 8. \\ ſup. inf. # 5. 7. \\ ſup. inf. # 6. 6. \\ ſup. inf. # Occidẽ- \\ tales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 23. 30. # 24. 14. # 26. 40. # 32. 12. # 41. 1. # 59. 14. # 90. 1. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># Infinita # 49. 6. # 23. 15. # 14 5. # 9. 11. # 6. 17. # 5. 13. <lb/></note>
<pb o="501" file="0517" n="517" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1659" type="section" level="1" n="429">
<head xml:id="echoid-head446" xml:space="preserve">In Æquatore nullæ ſunt latitudines vmbrarum, quia tunc, per propoſ. 11. lib. 1. \\ perpetuo vmbra cadit in lineam æquinoctialem: ſed earum \\ longitudines hæ@ ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à me- \\ dia nocte. # 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. # Orientales. <lb/># 0. 12. # 1. 11. # 2. 10. # 3. 9. # 4. 8. # 5. 7. # 6. 6. # Occidental. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# Infinita # 44. 47. # 20. 47. # 12. 0. # 6. 56. # 3. 13. # 0. 0.
</note>
</div>
<div xml:id="echoid-div1660" type="section" level="1" n="430">
<head xml:id="echoid-head447" xml:space="preserve">Latitudines longitudinesq́ue vmbrarum in vtroque horologio Meridiano pro horis \\ ab occ. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head448" xml:space="preserve">In tropico ♋, omnes latitudines vmbrarum ſunt Boreales, quædam autem ex illis ſunt In- \\ feriores, &amp; quædam Superiores, vt hæ ſyllabæ [Infer. Super.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 9 \\ Infer. # 10 \\ Infer. # 11 \\ Super. # 12 \\ Super. # 13 \\ Super. # 14 \\ Super. # 15 \\ Super. # 16 \\ Super. # oriẽtales. <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 49. 16 # 74. 19. # 72. 16. # 48. 0. # 35. 14. # 28. 34. # 25. 8. # 23. 39.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 7. 26. # 5. 28. # 5. 32. # 7. 38. # 11. 29. # 18. 8. # 32. 48. # 106. 43.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 17 \\ Super. # 18 \\ Super. # 19 \\ Super. # 20 \\ Super. # 21 \\ Super. # 22 \\ Super. # 23 \\ Infer. # 24 \\ Infer. # occiden \\ tales. <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 23. 42. # 25. 17. # 28. 53. # 35. 51. # 49. 16. # 74. 19. # 72. 16. # 48. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 93. 15. # 31. 17. # 17. 33. # 11. 9. # 7. 26. # 5. 28. # 5. 32. # 7. 38.
</note>
</div>
<div xml:id="echoid-div1661" type="section" level="1" n="431">
<head xml:id="echoid-head449" xml:space="preserve">In Aequatore latitudines vmbrarum nullæ ſunt, ob cauſam dictam in tabella horarum \\ ♈, &amp; ♎, à mer. &amp; med. noc. ſed earum longitudines hæ ſunt.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, ab \\ occaſu. # 6. 18. # 7. 17. # 8. 16. # 9. 15. # 10. 14. # 11. 13. # 12 # orientales. <lb/># 6. 18. # 5. 19. # 4. 20. # 3. 21. # 2. 22. # 1. 23. # 24 # occident. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># Infinita # 44. 47. # 20. 47. # 12. 0. # 6. 56. # 3. 13. # 0. 0. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>########## In tropico ♑, omnes vmbrarum latitudines ſunt Auſtrales, &amp; omnes hic poſitæ ſunt \\ Superiores. Orientales autem ab occidentalibus diſtinguuntur \\ his ſyllabis [ or. occ.] <lb/>
Horæ ♑, ab \\ occaſu. # 16 \\ orient. # 17 \\ or. # 18 \\ or. # 19 \\ or. # 20 \\ occ. # 21 \\ occ. # 22 \\ occ. # 23 \\ occ. # 24 \\ occ.
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 35. 51. # 28. 53. # 25. 17. # 23. 42. # 23. 39. # 25. 8. # 28. 34. # 35. 14. # 48. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 11. 9. # 17. 33. # 31. 17. # 93. 15. # 106. 43 # 32. 48. # 18. 8. # 11. 29. # 7. 38.
</note>
<pb o="502" file="0518" n="518" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s32285" xml:space="preserve">POSVIMVS autem in iſtis tabellis omnes horas à mer. </s>
  <s xml:id="echoid-s32286" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32287" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32288" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32289" xml:space="preserve">ita vt omnes deſcribi <lb/>poſſint in vtroque Meridiano horologio, quamuis eæ, quæ ſupra lineam horizontalem cadunt, <lb/>ſint ſuperfluæ. </s>
  <s xml:id="echoid-s32290" xml:space="preserve">Idem fecimus in hoſis ab occ. </s>
  <s xml:id="echoid-s32291" xml:space="preserve">Sole Aequatorem percurrente: </s>
  <s xml:id="echoid-s32292" xml:space="preserve">Et ſi viſum fuerit, <lb/>idem fieri poterit in eiſdem horis ab occ. </s>
  <s xml:id="echoid-s32293" xml:space="preserve">Sole in tropicis exiſtente; </s>
  <s xml:id="echoid-s32294" xml:space="preserve">quod tamen non fecimus, ſed <lb/>eas duntaxat horas notauimus, quæ infra horizontalem lineam cadunt, cum eas ſolum vmbra ſty-<lb/>li indicet, Sole ſupra Horizontem extante.</s>
  <s xml:id="echoid-s32295" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s32296" xml:space="preserve">IGITVR, vt horologium Meridianum conſtruatur, in plano horologii ducatur recta A B, <lb/>
<anchor type="note" xlink:label="note-0518-01a" xlink:href="note-0518-01"/>
pro linea horizontali, quæ in plano ſtabili, ac firmo ducenda eſt beneficio perpendiculi Horizon-<lb/>ti parallela. </s>
  <s xml:id="echoid-s32297" xml:space="preserve">In haclocus ſtyli eligatur C, è quo circulus cuiuſq; </s>
  <s xml:id="echoid-s32298" xml:space="preserve">magnitudinis deſcribatur D E F. <lb/></s>
  <s xml:id="echoid-s32299" xml:space="preserve">Deinde in orientali horologio à puncto B, verſus boream exiſtente, quod nobis ad horologium <lb/>
<anchor type="note" xlink:label="note-0518-02a" xlink:href="note-0518-02"/>
conuerſis ad dextram poſitum eſt, in occidentali vero à puncto A, itidem boreali quod nobis ad <lb/>ſiniſtram ſtatuitur, ſi faciem ad horologium conuertamus, deorſum verſus numeretur cõplemen-<lb/>tum altitudinis poli vſque ad F, ducatur q́ue recta F C D, quam in centro C, ad angulos rectos ſe-<lb/>cet recta E C. </s>
  <s xml:id="echoid-s32300" xml:space="preserve">Erit ex ijs, quæ propoſ. </s>
  <s xml:id="echoid-s32301" xml:space="preserve">25. </s>
  <s xml:id="echoid-s32302" xml:space="preserve">lib 2. </s>
  <s xml:id="echoid-s32303" xml:space="preserve">demonſtrauimus, D F, linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s32304" xml:space="preserve">E C, <lb/>linea horæ 6. </s>
  <s xml:id="echoid-s32305" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32306" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32307" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32308" xml:space="preserve">Poſt hæc aſſumpta ſtyli longitudine, abſcindantur ei quotcun-<lb/>que partes æquales ex recta G H, vt in præcedentibus factum eſt. </s>
  <s xml:id="echoid-s32309" xml:space="preserve">Itaque ſi pro hora 11. </s>
  <s xml:id="echoid-s32310" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s32311" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32312" xml:space="preserve">ſumatur latitudo vmbræ grad. </s>
  <s xml:id="echoid-s32313" xml:space="preserve">24. </s>
  <s xml:id="echoid-s32314" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32315" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32316" xml:space="preserve">quæ ſuperior eſt, &amp; </s>
  <s xml:id="echoid-s32317" xml:space="preserve">in tropico ♋, borealis, numere-<lb/>
<anchor type="figure" xlink:label="fig-0518-01a" xlink:href="fig-0518-01"/>
<anchor type="note" xlink:label="note-0518-03a" xlink:href="note-0518-03"/>
<anchor type="note" xlink:label="note-0518-04a" xlink:href="note-0518-04"/>
<anchor type="note" xlink:label="note-0518-05a" xlink:href="note-0518-05"/>
turq́ue in orientali horologio à D, verſus Boreales partes, vel in parte oppoſita à puncto F, vſque <lb/>ad K, &amp; </s>
  <s xml:id="echoid-s32318" xml:space="preserve">in rectam occultam C K, in parte oppoſita transferatur ex C, eiuſdem horæ longitudo vm <lb/>bræ P 49. </s>
  <s xml:id="echoid-s32319" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32320" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32321" xml:space="preserve">vſque ad L, inuentum erit punctum L, pro hora 11. </s>
  <s xml:id="echoid-s32322" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32323" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32324" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s32325" xml:space="preserve">Sic <lb/>etiam reperiemus punctum L, in tropico ♑, pro eadem hora, ſi eadem latitudo vmbræ numere-<lb/>tur à D, verſus Auſtrum, vel in parte oppoſita ex puncto F, vſque ad K, eademq́ue longitudo vm-<lb/>
<anchor type="note" xlink:label="note-0518-06a" xlink:href="note-0518-06"/>
bræ ex recta occulta C K, abſcindatur. </s>
  <s xml:id="echoid-s32326" xml:space="preserve">Quòd ſi in linea æquinoctiali accipiatur recta C M, longi <lb/>tudini vmbræ eiuſdem horæ in Aequatore, quæ comprehendit P. </s>
  <s xml:id="echoid-s32327" xml:space="preserve">44. </s>
  <s xml:id="echoid-s32328" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32329" xml:space="preserve">47. </s>
  <s xml:id="echoid-s32330" xml:space="preserve">æqualis, dabit recta <lb/>L M L, horam 11. </s>
  <s xml:id="echoid-s32331" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32332" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32333" xml:space="preserve">in horblogio orientali. </s>
  <s xml:id="echoid-s32334" xml:space="preserve">Eadem ratione in occidentali horologio ex <lb/>eadem latitudine, &amp; </s>
  <s xml:id="echoid-s32335" xml:space="preserve">longitudine vmbræ horam 1. </s>
  <s xml:id="echoid-s32336" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32337" xml:space="preserve">deſcribemus, vt in figura patet. </s>
  <s xml:id="echoid-s32338" xml:space="preserve">Quòd ſi <lb/>eadem fiant in cæteris horis à med. </s>
  <s xml:id="echoid-s32339" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32340" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32341" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32342" xml:space="preserve">abſolutum erit vtrumque horologium Meridia-<lb/>num. </s>
  <s xml:id="echoid-s32343" xml:space="preserve">Quod tamen breuius ita perficiemus. </s>
  <s xml:id="echoid-s32344" xml:space="preserve">Transferantur in lineam æquinoctialem longitudi-<lb/>nes vmbrarum pro ſingulis horis in Aequatore, imprimendo puncta in linea æquinoctiali. </s>
  <s xml:id="echoid-s32345" xml:space="preserve">Per <lb/>hæc enim lineæ rectæ ad æquinoctialem lineam perpen diculares excitatæ dabunt horas à mer. </s>
  <s xml:id="echoid-s32346" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32347" xml:space="preserve"><lb/>med. </s>
  <s xml:id="echoid-s32348" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32349" xml:space="preserve">Quæ ſi ex C. </s>
  <s xml:id="echoid-s32350" xml:space="preserve">ſecundum longitudines vmbrarum, quas in tropicis horæ habent, vel cer-<lb/>te per lineas occultas latitudinum vmbrarum reſecentur, habebuntur puncta tropicorum. </s>
  <s xml:id="echoid-s32351" xml:space="preserve">In-<lb/>uenientur autem vna eademq́ue opera ex eadem latitudine vmbræ octo puncta in tropicis. </s>
  <s xml:id="echoid-s32352" xml:space="preserve">Ita vi-
<pb o="503" file="0519" n="519" rhead="LIBER QVINTVS."/>
des ex latitudine vmbræ grad. </s>
  <s xml:id="echoid-s32353" xml:space="preserve">32. </s>
  <s xml:id="echoid-s32354" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32355" xml:space="preserve">12. </s>
  <s xml:id="echoid-s32356" xml:space="preserve">quam in vtroque tropico habent horæ 9. </s>
  <s xml:id="echoid-s32357" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32358" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32359" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s32360" xml:space="preserve">
<anchor type="note" xlink:label="note-0519-01a" xlink:href="note-0519-01"/>
noc. </s>
  <s xml:id="echoid-s32361" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32362" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32363" xml:space="preserve">ac 9. </s>
  <s xml:id="echoid-s32364" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32365" xml:space="preserve">vtrinque ex punctis D, &amp; </s>
  <s xml:id="echoid-s32366" xml:space="preserve">F, in vtroque horologio ſupputata vſque ad N, in-<lb/>uenta eſſe earundem horarum octo puncta O, P, Q, R, S, T, V, X. </s>
  <s xml:id="echoid-s32367" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32368" xml:space="preserve">ſic de cæteris, ſi <lb/>diligenter in tabulis obſeruetur, quarum horarum laiitudines ſint Boreales, Auſtralesve, &amp; </s>
  <s xml:id="echoid-s32369" xml:space="preserve">quę <lb/>Superiores, aut Inferiores: </s>
  <s xml:id="echoid-s32370" xml:space="preserve">Item quæ in orientale horologium, &amp; </s>
  <s xml:id="echoid-s32371" xml:space="preserve">quæ in occidentale transfe-<lb/>rendæ ſint. </s>
  <s xml:id="echoid-s32372" xml:space="preserve">Ita quoque vna opera ex eadem longitudine vmbræ quatuor puncta reperientur in <lb/>linea æquinoctiali. </s>
  <s xml:id="echoid-s32373" xml:space="preserve">Sic vides ex longitudine vmbræ P. </s>
  <s xml:id="echoid-s32374" xml:space="preserve">12. </s>
  <s xml:id="echoid-s32375" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32376" xml:space="preserve">0. </s>
  <s xml:id="echoid-s32377" xml:space="preserve">quam in Aequatore habent <lb/>horæ 9. </s>
  <s xml:id="echoid-s32378" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32379" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32380" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32381" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32382" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32383" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32384" xml:space="preserve">ac 9. </s>
  <s xml:id="echoid-s32385" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32386" xml:space="preserve">Item 15. </s>
  <s xml:id="echoid-s32387" xml:space="preserve">9. </s>
  <s xml:id="echoid-s32388" xml:space="preserve">21. </s>
  <s xml:id="echoid-s32389" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32390" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32391" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32392" xml:space="preserve">inuenta eſſe quatuor puncta <lb/>Y, Z, a, b, in æquinoctiali linea pro dictis horis.</s>
  <s xml:id="echoid-s32393" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1661" type="float" level="2" n="1">
<note position="left" xlink:label="note-0518-01" xlink:href="note-0518-01a" xml:space="preserve">Conſtructio ho <lb/>rologij Meridia <lb/>ni ex tabulis.</note>
<note position="left" xlink:label="note-0518-02" xlink:href="note-0518-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0518-01" xlink:href="fig-0518-01a">
    <image file="0518-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0518-01"/>
  </figure>
<note position="left" xlink:label="note-0518-03" xlink:href="note-0518-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0518-04" xlink:href="note-0518-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0518-05" xlink:href="note-0518-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0518-06" xlink:href="note-0518-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0519-01" xlink:href="note-0519-01a" xml:space="preserve">Quo modo vna <lb/>opera in @@opi-<lb/>cis inuenian tur <lb/>octo puncta pro <lb/>horis à mer. &amp; <lb/>med. noc. In <lb/>æquinoctiali au <lb/>tẽ linea quatuor <lb/>euam pro horis <lb/>ab occ.</note>
</div>
<p>
  <s xml:id="echoid-s32394" xml:space="preserve">RVRSVS ſi pro hora 9. </s>
  <s xml:id="echoid-s32395" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32396" xml:space="preserve">in tropico ♋, quæ orientalis eſt, ſumatur latitudo vmbræ <lb/>
<anchor type="note" xlink:label="note-0519-02a" xlink:href="note-0519-02"/>
gr. </s>
  <s xml:id="echoid-s32397" xml:space="preserve">49. </s>
  <s xml:id="echoid-s32398" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32399" xml:space="preserve">16. </s>
  <s xml:id="echoid-s32400" xml:space="preserve">quæ inferior eſt, &amp; </s>
  <s xml:id="echoid-s32401" xml:space="preserve">borealis, ſupputeturq́ue à puncto F, verſus Boream vſque ad d, <lb/>in orientali horologio, &amp; </s>
  <s xml:id="echoid-s32402" xml:space="preserve">recta occulta d C, ducatur, inuenietur in hac per longitudinem vmbræ <lb/>punctum horæ 9. </s>
  <s xml:id="echoid-s32403" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32404" xml:space="preserve">in tropico ♋, quod linea recta connexum cum puncto z, horæ 3. </s>
  <s xml:id="echoid-s32405" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s32406" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32407" xml:space="preserve">in æquinoctialilinea dabit horam 9. </s>
  <s xml:id="echoid-s32408" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32409" xml:space="preserve">tranſit enim hora 9. </s>
  <s xml:id="echoid-s32410" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32411" xml:space="preserve">in linea æquinoctia-<lb/>li per horam 3. </s>
  <s xml:id="echoid-s32412" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32413" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32414" xml:space="preserve">vt conſtat ex tabula propoſ. </s>
  <s xml:id="echoid-s32415" xml:space="preserve">19. </s>
  <s xml:id="echoid-s32416" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32417" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32418" xml:space="preserve">Pari ratione, ſi pro hora 21. </s>
  <s xml:id="echoid-s32419" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s32420" xml:space="preserve">in tropico ♑, quæ occidentalis eſt, accipiatur latitudo vmbræ grad. </s>
  <s xml:id="echoid-s32421" xml:space="preserve">25. </s>
  <s xml:id="echoid-s32422" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32423" xml:space="preserve">8. </s>
  <s xml:id="echoid-s32424" xml:space="preserve">quæ ſuperior <lb/>eſt, &amp; </s>
  <s xml:id="echoid-s32425" xml:space="preserve">auſtralis, eaq́ue numeretur in occidentali horologio à D, verſus Auſtrum vſque ad e, repe-<lb/>riemus per longitudinem vmbræ in recta occulta e C, punctum f, horæ 21. </s>
  <s xml:id="echoid-s32426" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32427" xml:space="preserve">in tropico ♑, <lb/>&amp; </s>
  <s xml:id="echoid-s32428" xml:space="preserve">ſic reliquarum horarum puncta inueniemus. </s>
  <s xml:id="echoid-s32429" xml:space="preserve">Si igitur correſpondentia puncta tam in tropicis, <lb/>quàm in æquinoctiali linea inuenta lineis rectis iungantur, deſcriptũ erit horologium Italicum. </s>
  <s xml:id="echoid-s32430" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0519-03a" xlink:href="note-0519-03"/>
Solæ lineæ horarum S. </s>
  <s xml:id="echoid-s32431" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32432" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32433" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32434" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32435" xml:space="preserve">ducendæ ſunt æquinoctiali lineæ parallelæ per puncta, <lb/>quæ in tropico ♋, vtriuſque horologij inuenta ſunt, vt propoſ. </s>
  <s xml:id="echoid-s32436" xml:space="preserve">34. </s>
  <s xml:id="echoid-s32437" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32438" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32439" xml:space="preserve">demonſtratum eſt à no-<lb/>bis. </s>
  <s xml:id="echoid-s32440" xml:space="preserve">Facile autem ex tabula propoſ. </s>
  <s xml:id="echoid-s32441" xml:space="preserve">19. </s>
  <s xml:id="echoid-s32442" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32443" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32444" xml:space="preserve">percipitur, per quas horas à mer. </s>
  <s xml:id="echoid-s32445" xml:space="preserve">vel med noc. </s>
  <s xml:id="echoid-s32446" xml:space="preserve">in æqui <lb/>noctiali linea horæ ab occ. </s>
  <s xml:id="echoid-s32447" xml:space="preserve">ducendæ ſint.</s>
  <s xml:id="echoid-s32448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1662" type="float" level="2" n="2">
<note position="left" xlink:label="note-0519-02" xlink:href="note-0519-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0519-03" xlink:href="note-0519-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s32449" xml:space="preserve">HIC autem nullus vſus eſt horariorum arcuum, cum Meridianus, cui horologium æquidi-<lb/>
<anchor type="note" xlink:label="note-0519-04a" xlink:href="note-0519-04"/>
ſtat, per polos mundi tranſeat.</s>
  <s xml:id="echoid-s32450" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1663" type="float" level="2" n="3">
<note position="right" xlink:label="note-0519-04" xlink:href="note-0519-04a" xml:space="preserve">In Meridiano <lb/>horologio nul-<lb/>lus eſt v@us ho-<lb/>rarioruũ arcuũ.</note>
</div>
<p>
  <s xml:id="echoid-s32451" xml:space="preserve">PRO horologio polari ſuperiore, quod circulo horæ 6. </s>
  <s xml:id="echoid-s32452" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32453" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32454" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32455" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32456" xml:space="preserve">æquidiſtat, aſſu-<lb/>mendæ ſunt tabellæ ſequentes pro horis à mer. </s>
  <s xml:id="echoid-s32457" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32458" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32459" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32460" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32461" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32462" xml:space="preserve">ſupputatæ; </s>
  <s xml:id="echoid-s32463" xml:space="preserve">quas quidem <lb/>in ſolo horologio ſuperiori deſcribemus, cum ex hoc inferius ortum habeat, vt ſupra diximus de <lb/>Verticali horologio; </s>
  <s xml:id="echoid-s32464" xml:space="preserve">ſi tamen pro horis ab occ. </s>
  <s xml:id="echoid-s32465" xml:space="preserve">in ſuperiori horologio ducantur prius illæ horæ ab <lb/>
<anchor type="note" xlink:label="note-0519-05a" xlink:href="note-0519-05"/>
or quæ in inferiori mutãdæ ſunt in horas ab occ. </s>
  <s xml:id="echoid-s32466" xml:space="preserve">vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s32467" xml:space="preserve">23 lib. </s>
  <s xml:id="echoid-s32468" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32469" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s32470" xml:space="preserve">Hanc <lb/>ob cauſam in his tabellis ſolũ illas horas ſcripſimus, quæ in horologiũ ſuperius cadunt, hoc eſt, <lb/>quarũ diſtantia à meridie minor eſt quadrante, ſiue ſex horis. </s>
  <s xml:id="echoid-s32471" xml:space="preserve">Et quoniã Meridianus Horizontis <lb/>Meridianus etiã eſt circuli horæ 6. </s>
  <s xml:id="echoid-s32472" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32473" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32474" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32475" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32476" xml:space="preserve">erit Aequator rectus exiſtens &amp; </s>
  <s xml:id="echoid-s32477" xml:space="preserve">ad Meridia <lb/>nũ, &amp; </s>
  <s xml:id="echoid-s32478" xml:space="preserve">ad circulum horæ 6. </s>
  <s xml:id="echoid-s32479" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32480" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32481" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32482" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32483" xml:space="preserve">tanquam Verticalis eiuſdem circuli. </s>
  <s xml:id="echoid-s32484" xml:space="preserve">Quamobrem <lb/>in horologio polari cõputandæ eruntvmbrarũ latitudines à linea ęquinoctiali, vtpote à linea Ver <lb/>ticali ipſius horologij; </s>
  <s xml:id="echoid-s32485" xml:space="preserve">verſus quidem partes ſuperiores, ſiue boreales, Sole primum gradum ♋, <lb/>poſſidente, verſus autem partes inferiores auſtralesve, Sole exiſtente in principio ♑.</s>
  <s xml:id="echoid-s32486" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1664" type="float" level="2" n="4">
<note position="left" xlink:label="note-0519-05" xlink:href="note-0519-05a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1666" type="section" level="1" n="432">
<head xml:id="echoid-head450" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in ſuperiori horologio polari <lb/>pro horis à mer. &amp; med. noc. ad quam-<lb/>cunque latitudinem.</head>
<head xml:id="echoid-head451" xml:space="preserve">In tropico ♋, omnes vmbrarum latitudines ſunt Boreales, <lb/>ſuperioresve, in tropico autem ♑, Auſtra-<lb/>les, inferioresve.</head>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, &amp; ♑, à \\ med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orienta \\ les. <lb/>Horæ ♋, &amp; ♑, à mer. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # occidenta. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 23. 30 # 24. 14. # 26. 40. # 32. 12. # 41. 1 # 59. 14. # 90. 0. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># Infinita # 49. 6. # 23. 15. # 14. 5. # 9. 11. # 6. 17. # 5. 13. <lb/></note>
<pb o="504" file="0520" n="520" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1667" type="section" level="1" n="433">
<head xml:id="echoid-head452" xml:space="preserve">In Aequatore nullæ ſunt vmbrarum latitudines, cum tunc, per propoſ. 11. lib. 1. \\ vmbra ſtyli perpetuo cadat in lineam æquinoctialem: Earum \\ autem longitudines ita ſe habent.</head>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, à \\ med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orientales. <lb/>Horæ ♈, &amp; ♎, à mer # 6 # 5 # 4 # 3 # 2 # 1 # 0 # occident. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># Infinita # 44. 47. # 20. 47. # 12. 0. # 6. 56. # 3. 13. # 0. 0. <lb/></note>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1668" type="section" level="1" n="434">
<head xml:id="echoid-head453" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio polari Superiori pro horis \\ ab occ. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head454" xml:space="preserve">In tropico ♋ omnes latitudines vmbrarum Boreales ſunt, ſiue Superiores.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab occaſu. # 11 # 12 # 13 # 14 # 15 # 16 # # orientales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 23. 42. # 25. 17. # 28. 53. # 35. 51. # 49. 16. # 74. 19. <lb/>
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 93. 15. # 31. 16. # 17. 33. # 11. 9. # 7. 26. # 5. 28.
Horæ ♋, ab occaſu. # 17 # 18 # 19 # 20 # 21 # 22 # # occident.
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 72. 16. # 48. 3. # 35. 14. # 28. 30. # 25. 8. # 23. 39.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 5. 32. # 7. 37. # 11. 29. # 18. 8. # 32. 48. # 106. 43
</note>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1669" type="section" level="1" n="435">
<head xml:id="echoid-head455" xml:space="preserve">In Aequatore vmbrarum latitudines nullę ſint, quòd tunc perpetuo vmbra gnomo- \\ nis in æquinoctialem lineam pro@iciatur, vt propoſ. 11. lib. 1. oſten- \\ ſum eſt: Longitudines autem earum hæ ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ ab occaſu. # 12 # 13 # 14 # 15 # 16 # 17 # 18 # orienta- \\ les. <lb/># 24 # 23 # 22 # 21 # 20 # 19 # 18 # occident. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# Infinita # 44. 47. # 20. 47. # 12. 0. # 6. 56. # 3. 13. # 0. 0.
</note>
</div>
<div xml:id="echoid-div1670" type="section" level="1" n="436">
<head xml:id="echoid-head456" xml:space="preserve">In tropico ♑, latitudines vmbrarum omnes Auſtrales ſunt, inferioresve. Occi- \\ dentales porro ab orientalibus per has ſyllabas \\ [or. occ.] dignoſcuntur.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab \\ occaſu. # 16 \\ or. # 17 \\ or. # 18 \\ or. # 19 \\ or. # 20 \\ occ. # 21 \\ occ. # 22 \\ occ. # 23 \\ occ. # 24 \\ occ. <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 28. 30. # 35. 14. # 48. 3. # 72. 16. # 74. 19. # 49. 16. # 35. 51. # 28. 53. # 25. 17.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 18. 8. # 11. 29. # 7. 37. # 5. 32. # 5. 28. # 7. 26. # 11. 9. # 17. 33. # 31. 16.
</note>
<p>
  <s xml:id="echoid-s32487" xml:space="preserve">IN plano ergo horologii ducatur recta AB, pro linea æquinoctiali, quæ in plano ſtabili ac fir-<lb/>
<anchor type="note" xlink:label="note-0520-10a" xlink:href="note-0520-10"/>
mo, quod circnlo hora 6. </s>
  <s xml:id="echoid-s32488" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32489" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32490" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32491" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32492" xml:space="preserve">æquidiſtet, Horizonti beneficio perpendieuli paral-<lb/>lela ducenda eſt. </s>
  <s xml:id="echoid-s32493" xml:space="preserve">In hac aſſumpto C, loco ſtyli, deſcribatur ex eo cuiuſuis magnitudinis circulus
<pb o="505" file="0521" n="521" rhead="LIBER QVINTVS."/>
D E F, in quo ducatur diameter D C, ſecans A B, rectam ad angulos rectos, quæ meridiana linea <lb/>erit, vt propoſ. </s>
  <s xml:id="echoid-s32494" xml:space="preserve">37. </s>
  <s xml:id="echoid-s32495" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32496" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32497" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s32498" xml:space="preserve">Rurſus aſſumpto gnomone quantocunque, abſcindan-<lb/>tur ei partes quotlibet æquales ex recta G H, vt in ſuperioribus dictum eſt. </s>
  <s xml:id="echoid-s32499" xml:space="preserve">Itaque ſi latitudines <lb/>vmbrarum ſupputentur à puncto F, vel E, prout oriẽtales fuerint, aut occidẽtales, ver ſus Boream, <lb/>vel Auſtrum, prout Boreales fuerint, Auſtralesve, deſcribetur horologiũ polare, vt Meridianum, <lb/>vt in appoſita figura intueri licet, in qua ex quadruplici latitudine vmbræ F K, grad. </s>
  <s xml:id="echoid-s32500" xml:space="preserve">24. </s>
  <s xml:id="echoid-s32501" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32502" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32503" xml:space="preserve">quę <lb/>horæ 7. </s>
  <s xml:id="echoid-s32504" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32505" xml:space="preserve">noc &amp; </s>
  <s xml:id="echoid-s32506" xml:space="preserve">5. </s>
  <s xml:id="echoid-s32507" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32508" xml:space="preserve">debetur, ſupputata tam à puncto orientali F, quàm ab occidentali <lb/>E, in Boream, &amp; </s>
  <s xml:id="echoid-s32509" xml:space="preserve">Auſtrum, &amp; </s>
  <s xml:id="echoid-s32510" xml:space="preserve">ex eius longitudine vmbræ P. </s>
  <s xml:id="echoid-s32511" xml:space="preserve">49. </s>
  <s xml:id="echoid-s32512" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32513" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32514" xml:space="preserve">inuentum eſt quadruplex pun <lb/>ctum L, vna eademq; </s>
  <s xml:id="echoid-s32515" xml:space="preserve">opera, pro hora 7. </s>
  <s xml:id="echoid-s32516" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32517" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32518" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32519" xml:space="preserve">5. </s>
  <s xml:id="echoid-s32520" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32521" xml:space="preserve">in tropico ♋, &amp; </s>
  <s xml:id="echoid-s32522" xml:space="preserve">♑. </s>
  <s xml:id="echoid-s32523" xml:space="preserve">Ex vmbræ au-<lb/>tem longitudine earundem horarum in Aequatore, nempe P. </s>
  <s xml:id="echoid-s32524" xml:space="preserve">44. </s>
  <s xml:id="echoid-s32525" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32526" xml:space="preserve">47. </s>
  <s xml:id="echoid-s32527" xml:space="preserve">inuenta ſunt puncta A, &amp; </s>
  <s xml:id="echoid-s32528" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0521-01a" xlink:href="note-0521-01"/>
<anchor type="figure" xlink:label="fig-0521-01a" xlink:href="fig-0521-01"/>
<anchor type="note" xlink:label="note-0521-02a" xlink:href="note-0521-02"/>
<anchor type="note" xlink:label="note-0521-03a" xlink:href="note-0521-03"/>
B, pro eiſdem horis in linea ęquinoctiali, &amp;</s>
  <s xml:id="echoid-s32529" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32530" xml:space="preserve">Rurſus ex latitudine vmbræ E M, occidentali, atque <lb/>boreali grad. </s>
  <s xml:id="echoid-s32531" xml:space="preserve">72. </s>
  <s xml:id="echoid-s32532" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32533" xml:space="preserve">16. </s>
  <s xml:id="echoid-s32534" xml:space="preserve">vel eius oppoſita F M, quæ debetur horæ 17. </s>
  <s xml:id="echoid-s32535" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32536" xml:space="preserve">in tropico ♋, eiusq́; <lb/></s>
  <s xml:id="echoid-s32537" xml:space="preserve">longitudine vmbræ P. </s>
  <s xml:id="echoid-s32538" xml:space="preserve">5. </s>
  <s xml:id="echoid-s32539" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32540" xml:space="preserve">32. </s>
  <s xml:id="echoid-s32541" xml:space="preserve">inuentum eſt punctum N, pro hora 17. </s>
  <s xml:id="echoid-s32542" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32543" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s32544" xml:space="preserve">Item <lb/>
<anchor type="note" xlink:label="note-0521-04a" xlink:href="note-0521-04"/>
ex latitudine vmbræ F O, orientali, atque auſtrali gr. </s>
  <s xml:id="echoid-s32545" xml:space="preserve">35. </s>
  <s xml:id="echoid-s32546" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32547" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32548" xml:space="preserve">vel eius oppoſita E O, quæ reſpon-<lb/>det eidem horæ 17. </s>
  <s xml:id="echoid-s32549" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32550" xml:space="preserve">in tropico ♑, eiusq́ue longitudine vmbræ P. </s>
  <s xml:id="echoid-s32551" xml:space="preserve">11. </s>
  <s xml:id="echoid-s32552" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32553" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32554" xml:space="preserve">inuentum eſt <lb/>punctum P, pro hora 17. </s>
  <s xml:id="echoid-s32555" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32556" xml:space="preserve">in tropico ♑. </s>
  <s xml:id="echoid-s32557" xml:space="preserve">Denique ex longitudine vmbræ occidentali gr. </s>
  <s xml:id="echoid-s32558" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s32559" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32560" xml:space="preserve">13. </s>
  <s xml:id="echoid-s32561" xml:space="preserve">eiuſdem horę 17. </s>
  <s xml:id="echoid-s32562" xml:space="preserve">in Aequatore (cum enim hæc hora in Aequatore ſit orientalis, cadet eius <lb/>vmbra in partem occidentalem horologii, nempe in oppoſitam) repertũ eſt punctum a, eiuſdem <lb/>horæ 17. </s>
  <s xml:id="echoid-s32563" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32564" xml:space="preserve">in linea æquinoctiali, &amp;</s>
  <s xml:id="echoid-s32565" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32566" xml:space="preserve">Horæ autem 12. </s>
  <s xml:id="echoid-s32567" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32568" xml:space="preserve">24. </s>
  <s xml:id="echoid-s32569" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32570" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32571" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32572" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32573" xml:space="preserve">ducendæ ſunt <lb/>per puncta in tropicis inuenta lineæ æquinoctiali æquidiſtantes, vt propoſ. </s>
  <s xml:id="echoid-s32574" xml:space="preserve">46. </s>
  <s xml:id="echoid-s32575" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32576" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32577" xml:space="preserve">oſtenſum eſt. </s>
  <s xml:id="echoid-s32578" xml:space="preserve"><lb/>Linea porrò horæ 24. </s>
  <s xml:id="echoid-s32579" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32580" xml:space="preserve">producta dabit lineam horizontalem, cum ſit communis ſectio pla-<lb/>ni horologij, &amp; </s>
  <s xml:id="echoid-s32581" xml:space="preserve">circuli horæ 24. </s>
  <s xml:id="echoid-s32582" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32583" xml:space="preserve">hoc eſt, Horizontis. </s>
  <s xml:id="echoid-s32584" xml:space="preserve">Quam ita quoque ducemus. </s>
  <s xml:id="echoid-s32585" xml:space="preserve">Ex ta-<lb/>
<anchor type="note" xlink:label="note-0521-05a" xlink:href="note-0521-05"/>
bula longitudinum vmbrarum propoſ. </s>
  <s xml:id="echoid-s32586" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32587" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s32588" xml:space="preserve">ſumatur longitudo vmbræ reſpondens altitu-<lb/>
<anchor type="note" xlink:label="note-0521-06a" xlink:href="note-0521-06"/>
dini poli ſupra Horizontem, vt in noſtro exemplo reſpondens grad. </s>
  <s xml:id="echoid-s32589" xml:space="preserve">42. </s>
  <s xml:id="echoid-s32590" xml:space="preserve">quæ comprehendit P. </s>
  <s xml:id="echoid-s32591" xml:space="preserve">13. <lb/></s>
  <s xml:id="echoid-s32592" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32593" xml:space="preserve">20. </s>
  <s xml:id="echoid-s32594" xml:space="preserve">eaq́ue transferatur beneficio circini ex C, in lineam meridianam verſus Boream, vſque ad <lb/>punctum Q. </s>
  <s xml:id="echoid-s32595" xml:space="preserve">Per hoc enim ducenda eſt linea horizontalis, vel horæ 24. </s>
  <s xml:id="echoid-s32596" xml:space="preserve">lineæ æquinoctiali paral-<lb/>lela, vel ad C D, perpendicularis. </s>
  <s xml:id="echoid-s32597" xml:space="preserve">Quoniam enim arcus Meridiani inter circulum horæ 6. </s>
  <s xml:id="echoid-s32598" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32599" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s32600" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32601" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32602" xml:space="preserve">cui horologium æquidiſtat, atque Horizontem interpoſitus ex parte auſtrali metitur <lb/>altitudinem poli ſupra Horizontem, hoc eſt, in noſtro exemplo complectitur gr. </s>
  <s xml:id="echoid-s32603" xml:space="preserve">42. </s>
  <s xml:id="echoid-s32604" xml:space="preserve">ſi Sol ponere-<lb/>tur in eo puncto Horizontis ex parte auſtrali, vbi à Meridiano ſecatur, haberet ſupra circulum ho-<lb/>rę 6. </s>
  <s xml:id="echoid-s32605" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32606" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32607" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32608" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32609" xml:space="preserve">altitudinem grad. </s>
  <s xml:id="echoid-s32610" xml:space="preserve">42. </s>
  <s xml:id="echoid-s32611" xml:space="preserve">quanta nimirum eſt poli altitudo ſupra Horizontẽ. </s>
  <s xml:id="echoid-s32612" xml:space="preserve"><lb/>Igitur eius vmbra à ſtylo proiecta caderet in punctum Q, verſus Boreales partes, quæ Soli oppo-<lb/>nuntur, cum vmbra C Q, debeatur gradibus 42. </s>
  <s xml:id="echoid-s32613" xml:space="preserve">ſiue altitudini poli. </s>
  <s xml:id="echoid-s32614" xml:space="preserve">Et quoniam tantum ex alte-<lb/>ra parte diſtat linea horæ 12. </s>
  <s xml:id="echoid-s32615" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32616" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32617" xml:space="preserve">ab æquinoctiali linea, quantum horizontalis abeſt, ſi
<pb o="506" file="0522" n="522" rhead="GNOMONICES"/>
rectæ C Q, accipiatur æqualis C R, ducẽda erit hora 12. </s>
  <s xml:id="echoid-s32618" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32619" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32620" xml:space="preserve">per R, parallela lineæ æqui <lb/>noctiali, vel perpendicularis ad D C.</s>
  <s xml:id="echoid-s32621" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1670" type="float" level="2" n="1">
<note position="left" xlink:label="note-0520-10" xlink:href="note-0520-10a" xml:space="preserve">Polaris horolo-<lb/>gii cõpoſitio ex <lb/>tabulis.</note>
<note position="left" xlink:label="note-0521-01" xlink:href="note-0521-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0521-01" xlink:href="fig-0521-01a">
    <image file="0521-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0521-01"/>
  </figure>
<note position="left" xlink:label="note-0521-02" xlink:href="note-0521-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0521-03" xlink:href="note-0521-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0521-04" xlink:href="note-0521-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0521-05" xlink:href="note-0521-05a" xml:space="preserve">Linea horizon-<lb/>talis, atque hora <lb/>12. ab or. uel <lb/>occ. quomodo <lb/>ducenda.</note>
<note position="left" xlink:label="note-0521-06" xlink:href="note-0521-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s32622" xml:space="preserve">HIC quoque locum non habent horarij arcus, ſicut nec in Meridiano horologio, propterea <lb/>
<anchor type="note" xlink:label="note-0522-01a" xlink:href="note-0522-01"/>
quòd circulus horæ 6. </s>
  <s xml:id="echoid-s32623" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32624" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32625" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32626" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32627" xml:space="preserve">cui horologium æquidiſtat, per polos mundi incedit, <lb/>quemadmodum &amp; </s>
  <s xml:id="echoid-s32628" xml:space="preserve">Meridianus.</s>
  <s xml:id="echoid-s32629" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1671" type="float" level="2" n="2">
<note position="left" xlink:label="note-0522-01" xlink:href="note-0522-01a" xml:space="preserve">In polari horo-<lb/>logio vſum nul <lb/>lum habent ar-<lb/>cus horat@.</note>
</div>
<p>
  <s xml:id="echoid-s32630" xml:space="preserve">PORRO nullas tabulas compoſuimus pro conſtructione horologii æquinoctialis, quia mul <lb/>
<anchor type="note" xlink:label="note-0522-02a" xlink:href="note-0522-02"/>
to facilius æquinoctiale horologium conſtruitur eo modo, quem lib. </s>
  <s xml:id="echoid-s32631" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32632" xml:space="preserve">expoſuimus, quàm per vl-<lb/>las tabulas; </s>
  <s xml:id="echoid-s32633" xml:space="preserve">vt fruſtra ac temere tabulæ pro huiuſmodi horologij conſtructione componi videren <lb/>tur, præſertim cùm omnes latitudines vmbrarum, arcusq́ue horarij inter ſe æquales ſint in omni-<lb/>bus horis, &amp; </s>
  <s xml:id="echoid-s32634" xml:space="preserve">altitudo Solis in omnibus etiam horis cuiuſque paralleli, atque adeo &amp; </s>
  <s xml:id="echoid-s32635" xml:space="preserve">vmbrarum <lb/>
<anchor type="note" xlink:label="note-0522-03a" xlink:href="note-0522-03"/>
longitudo eadem ſemper, vt ex ſuperioribus perſpicuum eſſe poteſt.</s>
  <s xml:id="echoid-s32636" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1672" type="float" level="2" n="3">
<note position="left" xlink:label="note-0522-02" xlink:href="note-0522-02a" xml:space="preserve">Cur horologiũ <lb/>æquinoctiale nõ <lb/>conſtruatur per <lb/>tabulas.</note>
<note position="left" xlink:label="note-0522-03" xlink:href="note-0522-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s32637" xml:space="preserve">PRO horologio Verticali Auſtrali, quod à meridie in orrum declinat grad. </s>
  <s xml:id="echoid-s32638" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32639" xml:space="preserve">ſequentes ta-<lb/>bellæ conditæ ſunt pro horis à mer. </s>
  <s xml:id="echoid-s32640" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32641" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32642" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32643" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32644" xml:space="preserve">in quibus ſignum hoc *** denotat ho-<lb/>ram illam, quæ in Meridianum proprium horologii declinantis cadit, vt in tabellis altitudinum <lb/>Solis diximus propoſ. </s>
  <s xml:id="echoid-s32645" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32646" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s32647" xml:space="preserve">Appellamus autem in hiſce tabellis latitudines vmbrarum Su-<lb/>periores illas, quæ vltra Verticalem proprium horologij exiſtunt, nempe verſus centrum horolo-<lb/>gii; </s>
  <s xml:id="echoid-s32648" xml:space="preserve">Inferiores autem illas, quæ citra eundem Verticalem ſunt, hoc eſt, verſus lineam æquinoctia-<lb/>lem. </s>
  <s xml:id="echoid-s32649" xml:space="preserve">Arcus vero horarij ſuperiores illi dicuntur, qui vltra centrum horologii exiſtunt.</s>
  <s xml:id="echoid-s32650" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1674" type="section" level="1" n="437">
<head xml:id="echoid-head457" xml:space="preserve">Arcus horarii in horologio Verticali Auſtrali, quod à meridie in ortum declinat <lb/>grad. 30. pro horis à mer. &amp; med. noc. ad latitudinem Grad. 42.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ à media nocte. # 4 # 5 # 6 # 7 # 8 # 9 # *** # orientales. <lb/>Arcus horarii. # G. M. # G. M # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 16. 31. # 36. 55. # 53. 18. # 66. 23. # 77. 22. # 87. 18. # 90. 0. # Superiores. <lb/>
Horæ à med. nocte. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3 # occidenta- \\ les.
Arcus horarij. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M.
# 83. 0. # 72. 44. # 60. 57. # # 46. 34. # 28. 25. # 6. 31. # Superiores.
</note>
</div>
<div xml:id="echoid-div1675" type="section" level="1" n="438">
<head xml:id="echoid-head458" xml:space="preserve">Longitudines vmbrarum in horologio Verticali Auſtrali, quod à meridie in ortum declinat gr. 30. pro horis à mer. &amp; med. noc. ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, à med. nocte. # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # *** <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 468. 47 # 57. 16. # 28. 30. # 17. 39. # 11. 43. # 7. 50. # 5. 8. # 3. 39. # 3. 34. <lb/>Horę ♑, à med. nocte. # 10 # 11 # 12 # A meri- \\ die. # 1 # 2 # 3 # 4 <lb/>
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # # P. M. # P. M. # P. M. # P. M.
# 4. 6. # 6. 12. # 9. 23. # # 13. 59. # 21. 30. # 37. 5. # 95. 13.
</note>
<note position="right" xml:space="preserve"> <lb/>Hor. ♋, \\ à me<unsure/>d. \\ nocte. # 5 # 6 # 7 # 8 # 9 # *** # 10 # 11 # 12 # A meri- \\ die. # 1 <lb/>Longit. \\ vmbra. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # # P. M. <lb/># 245. 24 # 58. 7. # 35. 3. # 27. 1. # 24. 15. # 24. 7. # 24. 59. # 29. 38. # 41. 59. # # 85. 2. <lb/></note>
<pb o="507" file="0523" n="523" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1676" type="section" level="1" n="439">
<head xml:id="echoid-head459" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio declinante à Verticali à mer. in ortum grad. 30. pro horis ab occ. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head460" xml:space="preserve">In tropico ♑, latitudines vmbrarum partim ſunt Inferiores, &amp; partim Superiores, vt hæ ſyllabæ [Infer. Super.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab \\ occaſu. # 10 \\ Infer. # 11 \\ Infer. # 12 \\ Infer. # 13 \\ Super. # 14 \\ Super. # 15 \\ Super. # 16 \\ Super. # *** \\ Super. # oriẽtales, <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 25. 37. # 16. 47. # 8. 7. # 1. 21. # 12. 6. # 27. 40. # 54. 29. # 90. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 110. 10 # 39. 27. # 22. 28. # 14. 32. # 9. 44. # 6. 27. # 4. 15. # 3. 34.
Horæ ♑, ab \\ occaſu. # 17 \\ Super. # 18 \\ Super. # 19 \\ Super. # 20 \\ Super. # 21 \\ Infer. # 22 \\ Infer. # 23 \\ Infer. # 24 \\ Infer. # occiden \\ tales.
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 81. 2. # 42. 28. # 21. 0. # 7. 36. # 2. 35. # 11. 24. # 20. 2. # 29. 5.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 3. 36. # 4. 56. # 7. 33. # 11. 18. # 16. 58. # 27. 6 # 52. 36. # 286. 21
</note>
</div>
<div xml:id="echoid-div1677" type="section" level="1" n="440">
<head xml:id="echoid-head461" xml:space="preserve">In Aequatore omnes vmbrarum latitudines ſunt ſuperiores: orientales autem ab occidentalibus diſcernuntur his ſyllabis [or. occ.]</head>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve"> <lb/>Hor. ♈, \\ &amp; ♎, ab \\ occaſu. # 10 \\ or. # 11 \\ or. # 12 \\ or. # 13 \\ or. # 14 \\ or. # 15 \\ or. # 16 \\ occ. # 17 \\ occ. # 18 \\ occ. # 19 \\ occ. # 20 \\ occ. # 21 \\ occ. <lb/>Latitu. \\ vmbra. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 7. 0. # 17. 16. # 29. 3. # 43. 26. # 61. 35. # 83. 29. # 73. 29. # 53. 5. # 36. 42. # 23. 37. # 12. 38. # 2. 42. <lb/>Longit. \\ vmbra. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 82. 45. # 33. 57. # 20. 46. # 14. 40. # 11. 28. # 10. 9. # 10. 31. # 12. 37. # 16. 53. # 25. 11. # 46. 8. # 213. 32 <lb/></note>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1678" type="section" level="1" n="441">
<head xml:id="echoid-head462" xml:space="preserve">In tropico ♋, omnes latitudines vmbrarum ſuperiores ſunt; orientales vero ab occidentalibus his ſyllabis [or. occ.] diſtinguuntur.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 10 \\ or. # 11 \\ or. # 12 \\ or. # 13 \\ or. # *** # 14 \\ occ. # 15 \\ occ. # 16 \\ occ. # 17 \\ occ. # 18 \\ occ. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 39. 44. # 51. 7. # 64. 7. # 78. 36. # 90. 0. # 86. 7. # 71. 7. # 57. 20. # 45. 10. # 34. 31. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# 88. 45. # 42. 30. # 29. 50. # 25. 3. # 24. 7. # 24. 14. # 26. 51. # 34. 43. # 57. 2. # 225. 15
</note>
<p>
  <s xml:id="echoid-s32651" xml:space="preserve">SVPPVTAVIMVS autem pro horis à mer. </s>
  <s xml:id="echoid-s32652" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32653" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32654" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32655" xml:space="preserve">illarum duodecim tantummo-<lb/>do horarum arcus horarios, (ex quibus quidem, vna cum vmbrarum longitudinibus horologiũ <lb/>Aſtronomicum hic conficiemus) quæ minus à Meridiano proprio abſunt, quàm ſex horis, quod <lb/>in ſcholio præcedenti propoſ. </s>
  <s xml:id="echoid-s32656" xml:space="preserve">faciendum eſſe monuimus; </s>
  <s xml:id="echoid-s32657" xml:space="preserve">quia ex his integrum horologium de-<lb/>ſcribetur, vt patebit. </s>
  <s xml:id="echoid-s32658" xml:space="preserve">Illarum autem horarum longitudines vmbrarum notauimus, quæ ſupra fa-<lb/>ciem auſtralem horologii cadunt. </s>
  <s xml:id="echoid-s32659" xml:space="preserve">Idemq́ue fecimus in latitudinibus, longitudinibusq́ue vmbra-<lb/>rum pro horis ab occ. </s>
  <s xml:id="echoid-s32660" xml:space="preserve">Id quod in ſequentibus etiam obſeruabimus.</s>
  <s xml:id="echoid-s32661" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s32662" xml:space="preserve">DVCATVR iam in horologii plano recta A B, pro linea horizontali, quæ in plano ſtabi-
<pb o="508" file="0524" n="524" rhead="GNOMONICES"/>
li, firmoq́ue parallela ſit Horizonti, in qua locus ſtyli ſtatuatur in puncto C, è quo circulus quan-<lb/>
<anchor type="note" xlink:label="note-0524-01a" xlink:href="note-0524-01"/>
tæcunque magnitudinis D E F G, deſcribatur, atque in eo ex centro ad rectam A B, perpendicu-<lb/>laris occulta demittatur C H, quæ in plano ſtabili demitti poteſt beneficio perpendiculi ad Hori-<lb/>zontem recta. </s>
  <s xml:id="echoid-s32663" xml:space="preserve">Deinde per propoſ. </s>
  <s xml:id="echoid-s32664" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32665" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32666" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32667" xml:space="preserve">ſupputetur arcus circuli maximi, cui horologium de-<lb/>clinans æquidiſtat, inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s32668" xml:space="preserve">Meridianum proprium circuli eiuſdem ma-<lb/>ximi per polos mundi, &amp; </s>
  <s xml:id="echoid-s32669" xml:space="preserve">per polos ipſius circuli maximi ductum interpoſitus; </s>
  <s xml:id="echoid-s32670" xml:space="preserve">quem deprehen-<lb/>
<anchor type="figure" xlink:label="fig-0524-01a" xlink:href="fig-0524-01"/>
<anchor type="note" xlink:label="note-0524-02a" xlink:href="note-0524-02"/>
<anchor type="note" xlink:label="note-0524-03a" xlink:href="note-0524-03"/>
<anchor type="note" xlink:label="note-0524-04a" xlink:href="note-0524-04"/>
dimus complecti grad. </s>
  <s xml:id="echoid-s32671" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32672" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32673" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32674" xml:space="preserve">Hunc in circulo D E F G, ſupputabimus à puncto H, verſus <lb/>occaſum quidem, qui nobis ad horologium conuerſis ad ſiniſtram locatur, hoc eſt, verſus A, ſi <lb/>planum horologii à meridie in ortum declinet, verſus dextram autem, hoc eſt, verſus ortum, ſeu <lb/>
<anchor type="note" xlink:label="note-0524-05a" xlink:href="note-0524-05"/>
punctum B, ſi horologii planum à meridie deflectat in occaſum. </s>
  <s xml:id="echoid-s32675" xml:space="preserve">In noſtro exemplo, quoniam po-<lb/>nimus horologium declinare à mer. </s>
  <s xml:id="echoid-s32676" xml:space="preserve">in ortum grad. </s>
  <s xml:id="echoid-s32677" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32678" xml:space="preserve">dictum arcum numerauimus vſque ad F. <lb/></s>
  <s xml:id="echoid-s32679" xml:space="preserve">Recta enim ducta F C D, erit communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s32680" xml:space="preserve">Meridiani eius proprij, hoc <lb/>
<anchor type="note" xlink:label="note-0524-06a" xlink:href="note-0524-06"/>
eſt, linea ſtyli, inſtar propriæ lineæ meridianæ, quæ partem horologii orientalem ab occidentali <lb/>ſeparet, vt propoſ. </s>
  <s xml:id="echoid-s32681" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32682" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32683" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32684" xml:space="preserve">demonſtrauimus: </s>
  <s xml:id="echoid-s32685" xml:space="preserve">quia recta C H, æquidiſtans eſt lineæ meridianæ ho <lb/>rologii, quæ videlicet horam 12. </s>
  <s xml:id="echoid-s32686" xml:space="preserve">indicat, cum &amp; </s>
  <s xml:id="echoid-s32687" xml:space="preserve">hæc perpendicularis ſit ad horizontalẽ lineam <lb/>A B, &amp;</s>
  <s xml:id="echoid-s32688" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32689" xml:space="preserve">Hanc ad rectos angulos ſecet in centro recta E G, quæ communis ſectio erit plani horolo <lb/>gii, &amp; </s>
  <s xml:id="echoid-s32690" xml:space="preserve">Verticalis proprie dicti eiuſdem plani horologii, &amp; </s>
  <s xml:id="echoid-s32691" xml:space="preserve">à qua ſupputandæ erunt latitudines vm-<lb/>brarum. </s>
  <s xml:id="echoid-s32692" xml:space="preserve">In recta E G, ſumpto ſtylo C I, quantocunque, abſcindantur ei ex recta H I, quotcun-<lb/>que partes æquales, quarum G I, in 12. </s>
  <s xml:id="echoid-s32693" xml:space="preserve">particulas æquales ſubdiuidatur, vt in ſuperioribus factum <lb/>
<anchor type="note" xlink:label="note-0524-07a" xlink:href="note-0524-07"/>
eſt. </s>
  <s xml:id="echoid-s32694" xml:space="preserve">Poſt hæc, per propoſ. </s>
  <s xml:id="echoid-s32695" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32696" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32697" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32698" xml:space="preserve">ſupputetur altitudo poli ſupra circulum maximũ, cui horolo-<lb/>gium æquidiſtat, quam inuenimus eſſe gr. </s>
  <s xml:id="echoid-s32699" xml:space="preserve">40. </s>
  <s xml:id="echoid-s32700" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32701" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32702" xml:space="preserve">eiuſq́ue complementum propterea gr. </s>
  <s xml:id="echoid-s32703" xml:space="preserve">49. <lb/></s>
  <s xml:id="echoid-s32704" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32705" xml:space="preserve">57. </s>
  <s xml:id="echoid-s32706" xml:space="preserve">Si igitur ex tabula longitudinum vmbrarum propoſ. </s>
  <s xml:id="echoid-s32707" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32708" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s32709" xml:space="preserve">ſumatur vmbræ longi-<lb/>
<anchor type="note" xlink:label="note-0524-08a" xlink:href="note-0524-08"/>
tudo P. </s>
  <s xml:id="echoid-s32710" xml:space="preserve">10. </s>
  <s xml:id="echoid-s32711" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32712" xml:space="preserve">5. </s>
  <s xml:id="echoid-s32713" xml:space="preserve">reſpondens complemento dictæ altitudinis poli, hoc eſt, congruens altitudini <lb/>Solis in Aequatore, &amp; </s>
  <s xml:id="echoid-s32714" xml:space="preserve">Meridiano proprio horologii conſtituto, eaq́ue beneficio circini ex recta <lb/>H I, accepta in rectam C F, deorſum verſus transferatur vſque ad K, erit recta K L, ducta per K, <lb/>ad DF, perpendicularis, linea æquinoctialis ſecans neceſſario horizontalem lineam, ſi erratum <lb/>non fuerit, in puncto L, quod terminat vmbram horæ 6. </s>
  <s xml:id="echoid-s32715" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32716" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32717" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32718" xml:space="preserve">aut horæ 12. </s>
  <s xml:id="echoid-s32719" xml:space="preserve">ab or. <lb/></s>
  <s xml:id="echoid-s32720" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32721" xml:space="preserve">Sole in Aequatore exiſtente, quæ quidem vmbra, vt ex pręcedenti tabella horarum ♈, &amp; </s>
  <s xml:id="echoid-s32722" xml:space="preserve"><lb/>♎, ſub hora 12. </s>
  <s xml:id="echoid-s32723" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32724" xml:space="preserve">conſtat, continet P. </s>
  <s xml:id="echoid-s32725" xml:space="preserve">20. </s>
  <s xml:id="echoid-s32726" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32727" xml:space="preserve">46. </s>
  <s xml:id="echoid-s32728" xml:space="preserve">Si rurſus longitudo vmbræ P. </s>
  <s xml:id="echoid-s32729" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32730" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32731" xml:space="preserve">17. </s>
  <s xml:id="echoid-s32732" xml:space="preserve"><lb/>reſpondens altitudini poli ſupra circulum maximum, cui horologium ęquidiſtat, transferatur à
<pb o="509" file="0525" n="525" rhead="LIBER QVINTVS."/>
C, ſurſum verſus in rectam C D, vſque ad M, erit M, centrum horologii. </s>
  <s xml:id="echoid-s32733" xml:space="preserve">Quod tamen vnà cum <lb/>
<anchor type="note" xlink:label="note-0525-01a" xlink:href="note-0525-01"/>
K, puncto æquinoctialis lineæ reperiemus, ſi cum ſtylo C I, efficiamus angulum altitudinis poli <lb/>ſupra circulum maximum, cui horologium æquidiſtat, C I K, &amp; </s>
  <s xml:id="echoid-s32734" xml:space="preserve">alium angulum complementi al <lb/>titudinis poli C I M. </s>
  <s xml:id="echoid-s32735" xml:space="preserve">Ducatur per M, centrum horologir<unsure/>ad D F, perpendicularis N O, quæ erit <lb/>inſtar lineæ horæ 6. </s>
  <s xml:id="echoid-s32736" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32737" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32738" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32739" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32740" xml:space="preserve">ſi horologium foret horizontale, &amp; </s>
  <s xml:id="echoid-s32741" xml:space="preserve">à qua numerandi ſunt <lb/>arcus horari<unsure/>i in circulo N P O, ex M, deſcripto.</s>
  <s xml:id="echoid-s32742" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1678" type="float" level="2" n="1">
<note position="left" xlink:label="note-0524-01" xlink:href="note-0524-01a" xml:space="preserve">Conſtructio ho-<lb/>rologii à Verti-<lb/>cali declinantis <lb/>ex tabulis.</note>
  <figure xlink:label="fig-0524-01" xlink:href="fig-0524-01a">
    <image file="0524-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0524-01"/>
  </figure>
<note position="left" xlink:label="note-0524-02" xlink:href="note-0524-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0524-03" xlink:href="note-0524-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0524-04" xlink:href="note-0524-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0524-05" xlink:href="note-0524-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0524-06" xlink:href="note-0524-06a" xml:space="preserve">Linea ſtyli, ſeu <lb/>propria meridi<unsure/>a <lb/>na quæ in horo <lb/>logio declinan-<lb/>te.</note>
<note position="left" xlink:label="note-0524-07" xlink:href="note-0524-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0524-08" xlink:href="note-0524-08a" xml:space="preserve">Linea æquino-<lb/>ctialis quę in ho <lb/>rologio declinã <lb/>te.</note>
<note position="right" xlink:label="note-0525-01" xlink:href="note-0525-01a" xml:space="preserve">Centrum horo <lb/>logii declinan-<lb/>tis quod.</note>
</div>
<p>
  <s xml:id="echoid-s32743" xml:space="preserve">HORAS ita deſcribemus. </s>
  <s xml:id="echoid-s32744" xml:space="preserve">Ex N &amp; </s>
  <s xml:id="echoid-s32745" xml:space="preserve">O, computentur in circulo N P O, arcus horarij in parti-<lb/>bus oppoſitis, nempe omnes infra rectam N O, cum omnes ſint ſuperiores. </s>
  <s xml:id="echoid-s32746" xml:space="preserve">Item Orientales ex <lb/>N, &amp; </s>
  <s xml:id="echoid-s32747" xml:space="preserve">occidentales ex O. </s>
  <s xml:id="echoid-s32748" xml:space="preserve">Si enim ex M, per terminos iſtorum arcuum rectæ ductæ reſecentur be-<lb/>neficio circini ſecundum longitudines vmbrarum, quæ horis à mer. </s>
  <s xml:id="echoid-s32749" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32750" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32751" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32752" xml:space="preserve">debentur in <lb/>
<anchor type="note" xlink:label="note-0525-02a" xlink:href="note-0525-02"/>
tropicis, delineatum erit horologium Aſtronomicum. </s>
  <s xml:id="echoid-s32753" xml:space="preserve">Quod tamen per latitudines etiam vm <lb/>brarum, ſi eæ ſupputentur à recta E G, deſcribi poteſt. </s>
  <s xml:id="echoid-s32754" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s32755" xml:space="preserve">Quoniam arcus horæ 12. <lb/></s>
  <s xml:id="echoid-s32756" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32757" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32758" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s32759" xml:space="preserve">60. </s>
  <s xml:id="echoid-s32760" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32761" xml:space="preserve">57. </s>
  <s xml:id="echoid-s32762" xml:space="preserve">occidentalis eſt, ac ſuperior, numerabimus eum ex O, puncto oriẽ-<lb/>tali deorſum verſus vſque ad P; </s>
  <s xml:id="echoid-s32763" xml:space="preserve">Eritq́ue recta ducta M P, linea horæ 12, à med. </s>
  <s xml:id="echoid-s32764" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32765" xml:space="preserve">id eſt, linea <lb/>meridiana, quæ, ſi erratum nulla in re eſt, perpendicularis erit ad horizontalem lineam A B, &amp; </s>
  <s xml:id="echoid-s32766" xml:space="preserve">à <lb/>filo perpendiculi ex M, in plano ſtabili libere demiſſo non differet. </s>
  <s xml:id="echoid-s32767" xml:space="preserve">Sic etiam, quia arcus horæ 8. </s>
  <s xml:id="echoid-s32768" xml:space="preserve"><lb/>à med. </s>
  <s xml:id="echoid-s32769" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32770" xml:space="preserve">orientalis &amp; </s>
  <s xml:id="echoid-s32771" xml:space="preserve">ſuperior eſt, ſi is numeretur à puncto N, occidentali deorſum verſus vſq; </s>
  <s xml:id="echoid-s32772" xml:space="preserve"><lb/>ad Q, dabit recta M Q, horam 8. </s>
  <s xml:id="echoid-s32773" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32774" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32775" xml:space="preserve">quam in R, reſecabimus ſecundum longitudinem <lb/>vmbræ P. </s>
  <s xml:id="echoid-s32776" xml:space="preserve">27. </s>
  <s xml:id="echoid-s32777" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32778" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32779" xml:space="preserve">quæ eidem horæ 8. </s>
  <s xml:id="echoid-s32780" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32781" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32782" xml:space="preserve">debetur in parallelo ♋, vt habeamus R, pun-<lb/>ctum tropici ♋. </s>
  <s xml:id="echoid-s32783" xml:space="preserve">Atque ita de cæteris. </s>
  <s xml:id="echoid-s32784" xml:space="preserve">Rurſus ex latitudinibus vmbrarum, quæ pro horis ab occ. </s>
  <s xml:id="echoid-s32785" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0525-03a" xlink:href="note-0525-03"/>
ſupputatæ ſunt, à recta E G, ſupputatis, earumq́ue longitudinibus, horologium Italicum compo-<lb/>nemus, vt in præcedentibus. </s>
  <s xml:id="echoid-s32786" xml:space="preserve">Ita cernis, per latitudinem vmbræ G X, horæ 15. </s>
  <s xml:id="echoid-s32787" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32788" xml:space="preserve">in tropi-<lb/>co ♑, ſuperiorem, orientalemq́ue, quæ complectitur grad. </s>
  <s xml:id="echoid-s32789" xml:space="preserve">27. </s>
  <s xml:id="echoid-s32790" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32791" xml:space="preserve">40. </s>
  <s xml:id="echoid-s32792" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32793" xml:space="preserve">per eiuſdem vm-<lb/>bræ longitudinem P. </s>
  <s xml:id="echoid-s32794" xml:space="preserve">6. </s>
  <s xml:id="echoid-s32795" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32796" xml:space="preserve">27. </s>
  <s xml:id="echoid-s32797" xml:space="preserve">inuentum eſſe punctum S, pro hora 15. </s>
  <s xml:id="echoid-s32798" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32799" xml:space="preserve">in tropico ♑. <lb/></s>
  <s xml:id="echoid-s32800" xml:space="preserve">Pari ratione ex G Y, latitudine vmbræ orientali, ac ſuperiori, vel eius oppoſita E Z, P. </s>
  <s xml:id="echoid-s32801" xml:space="preserve">83. </s>
  <s xml:id="echoid-s32802" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32803" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32804" xml:space="preserve"><lb/>quæ eidem horæ 15. </s>
  <s xml:id="echoid-s32805" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32806" xml:space="preserve">in Aequatore cõuenit, vel certe ex longitudine vmbræ P. </s>
  <s xml:id="echoid-s32807" xml:space="preserve">10. </s>
  <s xml:id="echoid-s32808" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32809" xml:space="preserve">9. </s>
  <s xml:id="echoid-s32810" xml:space="preserve"><lb/>eiuſdem horæ in Aequatore, repertum eſt punctum T, in æquinoctiali linea pro hora 15. </s>
  <s xml:id="echoid-s32811" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32812" xml:space="preserve"><lb/>per quod omnino tranſibit, ſi nullum peccatum commiſſum eſt, per horam 9. </s>
  <s xml:id="echoid-s32813" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32814" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32815" xml:space="preserve"><lb/>in linea æquinoctiali. </s>
  <s xml:id="echoid-s32816" xml:space="preserve">Poſtremo ex E b, latitudine vmbræ gr. </s>
  <s xml:id="echoid-s32817" xml:space="preserve">71. </s>
  <s xml:id="echoid-s32818" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32819" xml:space="preserve">7. </s>
  <s xml:id="echoid-s32820" xml:space="preserve">occidentali, ſuperioriq́ue <lb/>eiuſdem horæ 15. </s>
  <s xml:id="echoid-s32821" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32822" xml:space="preserve">in tropico ♋, vel eius oppoſita G a, atque ex eiuſdem vmbræ longitudine <lb/>
<anchor type="note" xlink:label="note-0525-04a" xlink:href="note-0525-04"/>
P. </s>
  <s xml:id="echoid-s32823" xml:space="preserve">26. </s>
  <s xml:id="echoid-s32824" xml:space="preserve">Min 51. </s>
  <s xml:id="echoid-s32825" xml:space="preserve">inuentum eſt V, punctum horæ 15. </s>
  <s xml:id="echoid-s32826" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32827" xml:space="preserve">in tropico ♋, atque ita ducta eſt linea <lb/>S T V, horæ 15. </s>
  <s xml:id="echoid-s32828" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32829" xml:space="preserve">Eademq́ue ratio eſt in reliquis horis, Solum hoc aduertendum eſt, horã <lb/>23. </s>
  <s xml:id="echoid-s32830" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32831" xml:space="preserve">ductam eſſe per punctum in tropico ♑, inuentum, &amp; </s>
  <s xml:id="echoid-s32832" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s32833" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32834" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32835" xml:space="preserve">vel 11. <lb/></s>
  <s xml:id="echoid-s32836" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32837" xml:space="preserve">in æquinoctiali linea, vt in tabula propoſ. </s>
  <s xml:id="echoid-s32838" xml:space="preserve">19. </s>
  <s xml:id="echoid-s32839" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32840" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32841" xml:space="preserve">præcipitur: </s>
  <s xml:id="echoid-s32842" xml:space="preserve">Item per illud punctum, <lb/>vbi hora 6. </s>
  <s xml:id="echoid-s32843" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32844" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32845" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32846" xml:space="preserve">hora 13. </s>
  <s xml:id="echoid-s32847" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32848" xml:space="preserve">ſe interſecant, nempe per punctum d. </s>
  <s xml:id="echoid-s32849" xml:space="preserve">Sic quoque du-<lb/>cta eſt hora 22. </s>
  <s xml:id="echoid-s32850" xml:space="preserve">per punctum in tropico ♑, inuentum, &amp; </s>
  <s xml:id="echoid-s32851" xml:space="preserve">per punctum e, vbi hora 14. </s>
  <s xml:id="echoid-s32852" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32853" xml:space="preserve">ho-<lb/>ram 6. </s>
  <s xml:id="echoid-s32854" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32855" xml:space="preserve">noc interſ<unsure/>ecat; </s>
  <s xml:id="echoid-s32856" xml:space="preserve">quia nimis procul hora 4. </s>
  <s xml:id="echoid-s32857" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32858" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32859" xml:space="preserve">per quam duci deberet, æqui-<lb/>n<unsure/>octialem lineam ſecat. </s>
  <s xml:id="echoid-s32860" xml:space="preserve">Hora autem 21. </s>
  <s xml:id="echoid-s32861" xml:space="preserve">ducta eſt per punctum in tropico ♑, inuentum, &amp; </s>
  <s xml:id="echoid-s32862" xml:space="preserve">per <lb/>punctum f, vbi hora 15. </s>
  <s xml:id="echoid-s32863" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s32864" xml:space="preserve">horam 6. </s>
  <s xml:id="echoid-s32865" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s32866" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32867" xml:space="preserve">diuidit, &amp; </s>
  <s xml:id="echoid-s32868" xml:space="preserve">c. </s>
  <s xml:id="echoid-s32869" xml:space="preserve">Quæ omnia puncta horæ 6. </s>
  <s xml:id="echoid-s32870" xml:space="preserve">à <lb/>med. </s>
  <s xml:id="echoid-s32871" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32872" xml:space="preserve">eliciuntur ex tabula propoſ. </s>
  <s xml:id="echoid-s32873" xml:space="preserve">20. </s>
  <s xml:id="echoid-s32874" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32875" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32876" xml:space="preserve">cui titulus eſt. </s>
  <s xml:id="echoid-s32877" xml:space="preserve">Linea horæ 6. </s>
  <s xml:id="echoid-s32878" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32879" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32880" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32881" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0525-05a" xlink:href="note-0525-05"/>
ſunt tamen pro eiſdem horis alia puncta reperiri in parallelo ♐, vel ♒, ſi latitudines vmbrarum, <lb/>longitudinesq́ue reperiantur</s>
</p>
<div xml:id="echoid-div1679" type="float" level="2" n="2">
<note position="left" xlink:label="note-0525-02" xlink:href="note-0525-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0525-03" xlink:href="note-0525-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0525-04" xlink:href="note-0525-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0525-05" xlink:href="note-0525-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s32882" xml:space="preserve">PRO conſtructione horologii ſuperioris ab Horizonte declinantis, grad. </s>
  <s xml:id="echoid-s32883" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32884" xml:space="preserve">ſpectantisq́; </s>
  <s xml:id="echoid-s32885" xml:space="preserve">ad <lb/>occaſum, aſſumendæ ſunt tabellæ, quæ ſequuntur, pro horis ab ortu Solis computatæ. </s>
  <s xml:id="echoid-s32886" xml:space="preserve">In exem-<lb/>plum enim omnium ſolum horologium Babylonicum conficiemus. </s>
  <s xml:id="echoid-s32887" xml:space="preserve">Dicuntur autem in iſtis ta-<lb/>bellis latitudines vmbrarum Boreales illæ, quæ ſunt citra Verticalem proprium horologii, id eſt, <lb/>verſus æquinoctialem lineam; </s>
  <s xml:id="echoid-s32888" xml:space="preserve">Auſtrales vero illæ, quæ vltra eundem Verticalem exiſtunt, verſus <lb/>centrum horologij, vt in horizontali horologio.</s>
  <s xml:id="echoid-s32889" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s32890" xml:space="preserve">Latitudines longitudineſq; </s>
  <s xml:id="echoid-s32891" xml:space="preserve">vmbrarũ in horologio ſuperiore declinãte ab Horizõte ex parte orien <lb/>tali gr. </s>
  <s xml:id="echoid-s32892" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32893" xml:space="preserve">ad Verticalẽ autẽ proprie dictũ recto pro horis ab ortu Solis, ad latitudinẽ Gr. </s>
  <s xml:id="echoid-s32894" xml:space="preserve">42.</s>
  <s xml:id="echoid-s32895" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1681" type="section" level="1" n="442">
<head xml:id="echoid-head463" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim Boreales ſunt, &amp; partim Auſtrales, <lb/>vt hæ ſyllabæ [Bor. Auſtr.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ \\ ♋, ab \\ ortu. # 3 \\ Bor. # 4 \\ Bor. # 5 \\ Bor. # 6 \\ Bor. # 7 \\ Auſtr. # 8 \\ Auſtr. # 9 \\ Auſtr. # 10 \\ Auſtr. # *** # oriental. <lb/>Latitu. \\ vmbra. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 18. 2. # 19. 57. # 12. 23. # 4. 44. # 3. 54. # 15. 39. # 36. 42. # 86. 18. # 90. 0. <lb/>Longit \\ vmbra. # P M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 438. 45 # 53. 11. # 26. 24. # 16. 12. # 10. 31. # 6. 43. # 3. 56. # 2. 32. # 2. 32. <lb/></note>
<pb o="510" file="0526" n="526" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ ortu. # 11 \\ Auſtr. # 12 \\ Auſtr. # 13 \\ Auſtr. # 14 \\ Bor. # 15 \\ Bor. # # occidentales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 40. 18. # 16. 56. # 5. 13. # 3. 53. # 11. 32. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 3. 42. # 6. 21. # 10. 2. # 15. 25. # 24. 51. <lb/></note>
</div>
<div xml:id="echoid-div1682" type="section" level="1" n="443">
<head xml:id="echoid-head464" xml:space="preserve">In Æquatore omnes vmbrarum latitudines Auſtrales ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, ab ortu. # 3 # 4 # 5 # 6 # 7 # 8 # *** # orientales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 4. 10. # 13. 18. # 23. 43. # 36. 44. # 54. 0. # 76. 39. # 90. 0. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 117. 28 # 37. 9. # 21. 13. # 14. 16. # 10. 33. # 8. 46. # 8. 32. <lb/>Horæ ♈, &amp; ♎, ab ortu. # 9 # 10 # 11 # 12 # 13 # 14 # occidentales. <lb/>
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 77. 46. # 54. 54. # 37. 24. # 24. 13. # 13. 43. # 4. 35.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 8. 44. # 10. 26. # 14. 3. # 20. 47. # 36. 0. # 107. 33
</note>
</div>
<div xml:id="echoid-div1683" type="section" level="1" n="444">
<head xml:id="echoid-head465" xml:space="preserve">In tropico ♑, omnes vmbrarum latitudines Auſtrales ſunt, ſed ab orientalibus occidentales his ſyllabis [or. occ.] diſcernuntur.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ \\ ♑, ab \\ ortu. # 3 \\ or. # 4 \\ or. # 5 \\ or. # 6 \\ or. # *** # 7 \\ occ. # 8 \\ occ. # 9 \\ occ. # 10 \\ occ. # 11 \\ occ. <lb/>
Latitu. \\ vmbra. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 36. 45. # 47. 21. # 59. 52. # 74. 22. # 90. 0. # 89. 49. # 74. 1. # 59. 34. # 47. 6. # 36. 32.
Longit. \\ vmbra. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 82. 16. # 38. 18. # 26. 8. # 21. 16. # 19. 54. # 19. 54. # 21. 20. # 26. 19. # 38. 46. # 84. 30
</note>
<p>
  <s xml:id="echoid-s32896" xml:space="preserve">DVCATVR ergo in plano horologij recta A B, vtcunque, ſed in plano ſtabili ac firmo pa-<lb/>
<anchor type="note" xlink:label="note-0526-07a" xlink:href="note-0526-07"/>
<anchor type="note" xlink:label="note-0526-08a" xlink:href="note-0526-08"/>
rallela Horizonti, beneficio perpendiculi, atqueadeo &amp; </s>
  <s xml:id="echoid-s32897" xml:space="preserve">meridianæ lineæ in horologio ducendæ. <lb/></s>
  <s xml:id="echoid-s32898" xml:space="preserve">Sunt enim linea horizontalis, &amp; </s>
  <s xml:id="echoid-s32899" xml:space="preserve">linea meridiana in hoc horologio æquidiſtantes, vt propoſ. </s>
  <s xml:id="echoid-s32900" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32901" xml:space="preserve"><lb/>lib. </s>
  <s xml:id="echoid-s32902" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32903" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s32904" xml:space="preserve">In recta A B, aſſumpto loco ſtyli C, deſcribatur ex C, circulus A F D G, <lb/>cuiuſcunque magnitudinis, in quo numeretur à B, puncto boreali arcus circuli maximi, cui ho-<lb/>rologium ęquidiſtat, interceptus inter Meridianum Horizontis, &amp; </s>
  <s xml:id="echoid-s32905" xml:space="preserve">Meridianum proprium eiuſ-<lb/>dem circuli maximi, quem per propoſ. </s>
  <s xml:id="echoid-s32906" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32907" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32908" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32909" xml:space="preserve">reperimus centinere gr. </s>
  <s xml:id="echoid-s32910" xml:space="preserve">24. </s>
  <s xml:id="echoid-s32911" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32912" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32913" xml:space="preserve">verſus qui-<lb/>dem F, ſeu partes orientales, ſi horologium ſpectet ad occaſum, hoceſt, declinet ab Horizonte <lb/>ex parte orientali, verſus G, autem, ſiue partes occidentales, ſi horologium ad ortum ſpectet, id <lb/>eſt, ex parte occidentali declinet ab Horizonte. </s>
  <s xml:id="echoid-s32914" xml:space="preserve">In exemplo noſtro, quoniam ponimus horolo-<lb/>gium declinare ab Horizonte ex parte orientali grad. </s>
  <s xml:id="echoid-s32915" xml:space="preserve">30. </s>
  <s xml:id="echoid-s32916" xml:space="preserve">ita vt ad occaſum ſpectet, dictum arcum <lb/>
<anchor type="note" xlink:label="note-0526-09a" xlink:href="note-0526-09"/>
numerauimus vſque ad D. </s>
  <s xml:id="echoid-s32917" xml:space="preserve">Recta enim ducta D C E, erit communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s32918" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0526-10a" xlink:href="note-0526-10"/>
Meridiani eius proprij, id eſt, linea ſtyli, inſtar propriæ lineæ meridianæ, quæ partes orientales ho <lb/>rologii ab occidentalibus dirimat, vt propoſ. </s>
  <s xml:id="echoid-s32919" xml:space="preserve">14. </s>
  <s xml:id="echoid-s32920" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32921" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32922" xml:space="preserve">oſtendimus, cum recta A B, meridianæ li-<lb/>neæ ducendæ ponatur æquidiſtare. </s>
  <s xml:id="echoid-s32923" xml:space="preserve">Hancad angulos rectos ſecans F G, in centro C, communis <lb/>ſectio erit plani horologij, &amp; </s>
  <s xml:id="echoid-s32924" xml:space="preserve">Verticalis proprie dicti eiuſdem plani horologij, à qua computã-<lb/>dæ erunt vmbrarum latitudines. </s>
  <s xml:id="echoid-s32925" xml:space="preserve">In hac recta F G, ſumpto ſtylo C H, quantocunque, abſcindan-<lb/>tur ei ex recta H I, quotcumque partes æquales, quarum G I, in 12. </s>
  <s xml:id="echoid-s32926" xml:space="preserve">particulas æquales ſubdiuida-<lb/>tur, vt &amp; </s>
  <s xml:id="echoid-s32927" xml:space="preserve">in ſuperioribus factum eſt. </s>
  <s xml:id="echoid-s32928" xml:space="preserve">Deinde inuenta, per propoſ. </s>
  <s xml:id="echoid-s32929" xml:space="preserve">29. </s>
  <s xml:id="echoid-s32930" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32931" xml:space="preserve">1. </s>
  <s xml:id="echoid-s32932" xml:space="preserve">altitudine poli ſu-<lb/>pra circulum maximum, cui horologium æquidiſtat, quàm quidem deprehendimus eſſe gr. </s>
  <s xml:id="echoid-s32933" xml:space="preserve">35. <lb/></s>
  <s xml:id="echoid-s32934" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32935" xml:space="preserve">25. </s>
  <s xml:id="echoid-s32936" xml:space="preserve">atque adeo eius complementum gr. </s>
  <s xml:id="echoid-s32937" xml:space="preserve">54. </s>
  <s xml:id="echoid-s32938" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s32939" xml:space="preserve">35. </s>
  <s xml:id="echoid-s32940" xml:space="preserve">ſi ex tabula longitudinum vmbrarum <lb/>propoſ. </s>
  <s xml:id="echoid-s32941" xml:space="preserve">2. </s>
  <s xml:id="echoid-s32942" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32943" xml:space="preserve">ſumatur longitudo vmbræ Partium 8. </s>
  <s xml:id="echoid-s32944" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32945" xml:space="preserve">32. </s>
  <s xml:id="echoid-s32946" xml:space="preserve">reſpondens complemento dictæ al-
<pb o="511" file="0527" n="527" rhead="LIBER QVINTVS."/>
titudinis poli, hoc eſt, conueniens altitudini Solis in Æquatore, &amp; </s>
  <s xml:id="echoid-s32947" xml:space="preserve">proprio Meridiano horolo-<lb/>gij conſtituto, eàque beneficio circini ex recta H I, accepta in rectam C D, deorſum verſus tranſ-<lb/>feratur vſque ad I, erit recta I K, per I, ducta ad D E, perpendicularis, linea æquinoctialis; </s>
  <s xml:id="echoid-s32948" xml:space="preserve">quæ <lb/>
<anchor type="note" xlink:label="note-0527-01a" xlink:href="note-0527-01"/>
<anchor type="figure" xlink:label="fig-0527-01a" xlink:href="fig-0527-01"/>
<anchor type="note" xlink:label="note-0527-02a" xlink:href="note-0527-02"/>
<anchor type="note" xlink:label="note-0527-03a" xlink:href="note-0527-03"/>
neceſſario, ſi erratum non eſt, rectam C K, quæ ad A B, perpendicularis ducitur, eſtq́ue, vt propoſ. <lb/></s>
  <s xml:id="echoid-s32949" xml:space="preserve">
<anchor type="note" xlink:label="note-0527-04a" xlink:href="note-0527-04"/>
16. </s>
  <s xml:id="echoid-s32950" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s32951" xml:space="preserve">3. </s>
  <s xml:id="echoid-s32952" xml:space="preserve">oſtenſum eſt, communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s32953" xml:space="preserve">Verticalis proprie dicti ipſius Hori-<lb/>zontis, ſecat in puncto K, quod terminat vmbram horæ 6. </s>
  <s xml:id="echoid-s32954" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32955" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32956" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32957" xml:space="preserve">aut horæ 12. </s>
  <s xml:id="echoid-s32958" xml:space="preserve">ab or. <lb/></s>
  <s xml:id="echoid-s32959" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32960" xml:space="preserve">Sole exiſtente in Æquatore, quæ quidẽ vmbra in præcedẽti tabula continet P. </s>
  <s xml:id="echoid-s32961" xml:space="preserve">20. </s>
  <s xml:id="echoid-s32962" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32963" xml:space="preserve">47. </s>
  <s xml:id="echoid-s32964" xml:space="preserve"><lb/>Rurſus ſi longitudo vmbræ P. </s>
  <s xml:id="echoid-s32965" xml:space="preserve">16. </s>
  <s xml:id="echoid-s32966" xml:space="preserve">M. </s>
  <s xml:id="echoid-s32967" xml:space="preserve">53. </s>
  <s xml:id="echoid-s32968" xml:space="preserve">reſpondens altitudini poli ſupra circulum maximum, <lb/>cui horologium æquidiſtat, transferatur à C, ſurſum verſus in rectam C E, vſque ad L, erit L, <lb/>centrum horologij. </s>
  <s xml:id="echoid-s32969" xml:space="preserve">Quod tamen, vna cum I, puncto æquinoctialis lineæ inueniemus, vt in præ-<lb/>
<anchor type="note" xlink:label="note-0527-05a" xlink:href="note-0527-05"/>
cedentibus, ſi cum ſtylo C H, cõſtituamus angulum C H I, altitudinis poli ſupra circulum maxi-<lb/>mum, cui horologium æquidiſtat, &amp; </s>
  <s xml:id="echoid-s32970" xml:space="preserve">alium angulum C H L, cõplementi eiuſdẽ altitudinis poli. <lb/></s>
  <s xml:id="echoid-s32971" xml:space="preserve">Quòd ſi per M, ducatur ad D E, perpendicularis M N, erit hæc inſtar lineæ horæ 6. </s>
  <s xml:id="echoid-s32972" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32973" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s32974" xml:space="preserve">med. </s>
  <s xml:id="echoid-s32975" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s32976" xml:space="preserve">ſi ipſum horologiũ eſſet horizõtale, &amp; </s>
  <s xml:id="echoid-s32977" xml:space="preserve">à qua numerãdi forentarcus horarij in circulo MPN, <lb/>
<anchor type="note" xlink:label="note-0527-06a" xlink:href="note-0527-06"/>
ex L, deſcripto, ſi ſupputati eſſent. </s>
  <s xml:id="echoid-s32978" xml:space="preserve">Linea meridiana ducenda eſt ex L, ipſi A B, æquidiſtans, vel ad <lb/>
<anchor type="note" xlink:label="note-0527-07a" xlink:href="note-0527-07"/>
C K, perpendicularis, qualis eſt L O: </s>
  <s xml:id="echoid-s32979" xml:space="preserve">Similiter &amp; </s>
  <s xml:id="echoid-s32980" xml:space="preserve">linea horizõtalis per punctũ K, vbi æquinoctia-<lb/>
<anchor type="note" xlink:label="note-0527-08a" xlink:href="note-0527-08"/>
lis linea, &amp; </s>
  <s xml:id="echoid-s32981" xml:space="preserve">recta C K, ad A B, ducta perpendicularis ſeſe interſecant, quod quidẽ punctũ, vt dixi-<lb/>mus, terminus eſt, atq; </s>
  <s xml:id="echoid-s32982" xml:space="preserve">finis vmbræ horæ 6. </s>
  <s xml:id="echoid-s32983" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s32984" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s32985" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s32986" xml:space="preserve">aut horæ 12. </s>
  <s xml:id="echoid-s32987" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32988" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s32989" xml:space="preserve">Sole <lb/>exiſtente in Æquatore. </s>
  <s xml:id="echoid-s32990" xml:space="preserve">Quod tamen punctũ K, reperietur etiã hoc modo. </s>
  <s xml:id="echoid-s32991" xml:space="preserve">In recta A B, ſumpta re-<lb/>cta C a, ſtylo æquali, &amp; </s>
  <s xml:id="echoid-s32992" xml:space="preserve">in a, fiat angulus C a K, cõplemẽti declinationis ab Horizõte. </s>
  <s xml:id="echoid-s32993" xml:space="preserve">Recta enim <lb/>a K, ſecabit rectam C K, in puncto K, vbi hora 12. </s>
  <s xml:id="echoid-s32994" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s32995" xml:space="preserve">lineam æquinoctialem interſecat.</s>
  <s xml:id="echoid-s32996" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1683" type="float" level="2" n="1">
<note position="left" xlink:label="note-0526-07" xlink:href="note-0526-07a" xml:space="preserve">Horologii ab <lb/>Horizonte de-<lb/>clinantis d<unsure/>ſ ti <lb/>pt<unsure/>io ex tabulis.</note>
<note position="left" xlink:label="note-0526-08" xlink:href="note-0526-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0526-09" xlink:href="note-0526-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0526-10" xlink:href="note-0526-10a" xml:space="preserve">Linea ſtyli, ſiue <lb/>meridiana pro-<lb/>pria in horolo-<lb/>gio declinante <lb/>ab Horizonte <lb/>quæ.</note>
<note position="right" xlink:label="note-0527-01" xlink:href="note-0527-01a" xml:space="preserve">Aequinoctialis <lb/>linea quomodo <lb/>ducatur.</note>
  <figure xlink:label="fig-0527-01" xlink:href="fig-0527-01a">
    <image file="0527-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0527-01"/>
  </figure>
<note position="left" xlink:label="note-0527-02" xlink:href="note-0527-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0527-03" xlink:href="note-0527-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0527-04" xlink:href="note-0527-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0527-05" xlink:href="note-0527-05a" xml:space="preserve">Centrum horo-<lb/>logii.</note>
<note position="left" xlink:label="note-0527-06" xlink:href="note-0527-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0527-07" xlink:href="note-0527-07a" xml:space="preserve">Linea meridia-<lb/>na.</note>
<note position="right" xlink:label="note-0527-08" xlink:href="note-0527-08a" xml:space="preserve">Linea horizon-<lb/>talis.</note>
</div>
<p>
  <s xml:id="echoid-s32997" xml:space="preserve">IAM vero, ſi latitudines vmbrarũ in circulo A F D G, rite ſupputentur, oriẽtales quidẽ à pun <lb/>cto F, occidẽtales vero à puncto G, verſus boream B, aut verſus auſtrum A, prout tabellę indicant, <lb/>deſcribetur horologiũ hoc, ſicut &amp; </s>
  <s xml:id="echoid-s32998" xml:space="preserve">præcedẽtia. </s>
  <s xml:id="echoid-s32999" xml:space="preserve">Ita vides, ex latitudine vmbræ F Q, orientali, ac <lb/>
<anchor type="note" xlink:label="note-0527-09a" xlink:href="note-0527-09"/>
boreali, vel eius oppoſita G Q, gr. </s>
  <s xml:id="echoid-s33000" xml:space="preserve">19. </s>
  <s xml:id="echoid-s33001" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33002" xml:space="preserve">57. </s>
  <s xml:id="echoid-s33003" xml:space="preserve">quæ horæ 4. </s>
  <s xml:id="echoid-s33004" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33005" xml:space="preserve">in tropico ♋, debetur, atque ex lon-<lb/>gitudine vmbræ eiuſdẽ horæ P. </s>
  <s xml:id="echoid-s33006" xml:space="preserve">53. </s>
  <s xml:id="echoid-s33007" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33008" xml:space="preserve">11. </s>
  <s xml:id="echoid-s33009" xml:space="preserve">inuentum eſſe R, punctũ horæ 4. </s>
  <s xml:id="echoid-s33010" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33011" xml:space="preserve">in tropico ♋. <lb/></s>
  <s xml:id="echoid-s33012" xml:space="preserve">Item ex F S, latitudine vmbræ orientali, auſtraliq́ue, gr. </s>
  <s xml:id="echoid-s33013" xml:space="preserve">13. </s>
  <s xml:id="echoid-s33014" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33015" xml:space="preserve">18. </s>
  <s xml:id="echoid-s33016" xml:space="preserve">vel eius oppoſita G S, eiuſ-<lb/>dem horæ 4. </s>
  <s xml:id="echoid-s33017" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33018" xml:space="preserve">in Æquatore, vel certe ex longitudine vmbræ P. </s>
  <s xml:id="echoid-s33019" xml:space="preserve">37. </s>
  <s xml:id="echoid-s33020" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33021" xml:space="preserve">9. </s>
  <s xml:id="echoid-s33022" xml:space="preserve">quæ eidem horæ <lb/>cõgruit in Æquatore, repertũ eſſe T, pro dicta hora in linea ęquinoctiali. </s>
  <s xml:id="echoid-s33023" xml:space="preserve">Deniq; </s>
  <s xml:id="echoid-s33024" xml:space="preserve">ex FV, latitudine <lb/>vmbræ orientali, &amp; </s>
  <s xml:id="echoid-s33025" xml:space="preserve">auſtrali gr. </s>
  <s xml:id="echoid-s33026" xml:space="preserve">47. </s>
  <s xml:id="echoid-s33027" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33028" xml:space="preserve">21. </s>
  <s xml:id="echoid-s33029" xml:space="preserve">vel eius oppoſita G V, quæ eidẽ horæ 4. </s>
  <s xml:id="echoid-s33030" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33031" xml:space="preserve">reſpõdet <lb/>in tropico ♑; </s>
  <s xml:id="echoid-s33032" xml:space="preserve">atq; </s>
  <s xml:id="echoid-s33033" xml:space="preserve">ex eiuſdẽ horæ vmbra P. </s>
  <s xml:id="echoid-s33034" xml:space="preserve">38. </s>
  <s xml:id="echoid-s33035" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33036" xml:space="preserve">18. </s>
  <s xml:id="echoid-s33037" xml:space="preserve">deprehẽſum eſſe X, punctũ pro hora 4. </s>
  <s xml:id="echoid-s33038" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33039" xml:space="preserve"><lb/>in tropico ♑, &amp;</s>
  <s xml:id="echoid-s33040" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33041" xml:space="preserve">Tranſibit autẽ neceſſario hora 6. </s>
  <s xml:id="echoid-s33042" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33043" xml:space="preserve">per punctũ O, vbi linea meridiana æqui-<lb/>noctialem lineã ſecat. </s>
  <s xml:id="echoid-s33044" xml:space="preserve">Hora 14. </s>
  <s xml:id="echoid-s33045" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33046" xml:space="preserve">quia nimis procul æquinoctialem lineam ſecat, ducta eſt <lb/>per punctum in tropico ♋, inuentũ, &amp; </s>
  <s xml:id="echoid-s33047" xml:space="preserve">per punctum Y, in quo linea horæ 10. </s>
  <s xml:id="echoid-s33048" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33049" xml:space="preserve">meridianam <lb/>lineam ſecat: </s>
  <s xml:id="echoid-s33050" xml:space="preserve">Et hora 15. </s>
  <s xml:id="echoid-s33051" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33052" xml:space="preserve">ducta eſt per punctum in tropico ♋, inuentum, &amp; </s>
  <s xml:id="echoid-s33053" xml:space="preserve">per punctũ Z,
<pb o="512" file="0528" n="528" rhead="GNOMONICES"/>
in quo hora 9. </s>
  <s xml:id="echoid-s33054" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33055" xml:space="preserve">producta cum meridiana linea conuenit; </s>
  <s xml:id="echoid-s33056" xml:space="preserve">quemadmodum ex tabula propoſ. <lb/></s>
  <s xml:id="echoid-s33057" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33058" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33059" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33060" xml:space="preserve">cui titulus eſt, Linea horæ 12. </s>
  <s xml:id="echoid-s33061" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33062" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33063" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33064" xml:space="preserve">liquet. </s>
  <s xml:id="echoid-s33065" xml:space="preserve">Poſſnnt tamen pro eisdẽ <lb/>horis latitudines vmbrarum, longitudineſq́ue in parallelo ♊, vel ♌, inueſtigari, atque ex his alia <lb/>puncta in horologio reperiri.</s>
  <s xml:id="echoid-s33066" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1684" type="float" level="2" n="2">
<note position="left" xlink:label="note-0527-09" xlink:href="note-0527-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33067" xml:space="preserve">PRO horologio ſuperiori ad Horizontem ex parte auſtrali inclinato gr. </s>
  <s xml:id="echoid-s33068" xml:space="preserve">68. </s>
  <s xml:id="echoid-s33069" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33070" xml:space="preserve">ad Meridianũ <lb/>recto vſurpabimus ſequentes tabellas pro horis à mer. </s>
  <s xml:id="echoid-s33071" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33072" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33073" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33074" xml:space="preserve">ſupputatas. </s>
  <s xml:id="echoid-s33075" xml:space="preserve">Satis enim erit, <lb/>ſi exemplum in horis à mer. </s>
  <s xml:id="echoid-s33076" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33077" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33078" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33079" xml:space="preserve">proponamus. </s>
  <s xml:id="echoid-s33080" xml:space="preserve">Appellamus autem in iſtis tabellis ſupe-<lb/>riores vmbrarum latitudines illas, quæ ſunt citra Verticalem circulum horologij, hoc eſt, ver-<lb/>ſus polum, qui ſupra horologium conſpicitur; </s>
  <s xml:id="echoid-s33081" xml:space="preserve">Inferiores vero illas, quæ vltra Verticalem dictũ <lb/>exiſtunt, nempe verſus centrum horologij, aut ver ſus polum occultum.</s>
  <s xml:id="echoid-s33082" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1686" type="section" level="1" n="445">
<head xml:id="echoid-head466" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio Superiori ad Horizontem ex <lb/>parte auſtrali inclinato gr. 68. &amp; ad Meridianum recto, pro horis à mer. <lb/>&amp; med. noc. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head467" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim ſuperiores ſunt, &amp; partim inferiores, <lb/>vt his ſyllabis [Super. Infer.] indicatur.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. noct. # 0 # 1 # 2 # 3 # 4 # 5 # 6 # orientales. <lb/>Horæ ♋, à me- \\ ridie. # 12 \\ Infer. # 11 \\ Infer. # 10 \\ Infer. # 9 \\ Infer. # 8 \\ Infer. # 7 \\ Infer. # 6 \\ Super. # occiden- \\ tales. <lb/>
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 90. 0. # 71. 10. # 53. 4. # 36. 6. # 20. 20. # 5. 37. # 8. 28.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 12. 39. # 13. 1. # 14. 10. # 16. 9. # 19. 7. # 23. 26. # 29. 42.
Horæ ♋, à med. noct. # 7 # 8 # 9 # 10 # 11 # 12 # orientales.
Horę ♋, à me- \\ ridie. # 5 \\ Super. # 4 \\ Super. # 3 \\ Super. # 2 \\ Super. # 1 \\ Super. # 0 \\ Super. # occidentales.
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 22. 1. # 36. 2. # 48. 59. # 62. 33. # 76. 14. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 38. 53. # 53. 46. # 77. 31. # 115. 48 # 166. 45 # 196. 13
</note>
</div>
<div xml:id="echoid-div1687" type="section" level="1" n="446">
<head xml:id="echoid-head468" xml:space="preserve">In Aequatore omnes latitudines vmbrarum ſunt Inferiores.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ à med. nocte. # 0 # 1 # 2 # 3 # 4 # 5 # 6 # orientales. <lb/>
Hotæ ♈, &amp; ♎, à mer. # 12 # 11 # 10 # 9 # 8 # 7 # 6 # occident.
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 90. 0. # 74. 5. # 58. 26. # 43. 13. # 28. 29. # 14. 8. # 0. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 32. 58. # 34. 18. # 38. 41. # 48. 8. # 69. 7. # 134. 54 # Infinita
</note>
<p>
  <s xml:id="echoid-s33083" xml:space="preserve">OMNES horæ tropici ♑, cadunt in faciem horologii inferiore m, cum tropicus ♑, horolo-<lb/>
<anchor type="note" xlink:label="note-0528-07a" xlink:href="note-0528-07"/>
gii planum non ſecet, ſed totus ſupra faciem inferiorem extet, que mad modum &amp; </s>
  <s xml:id="echoid-s33084" xml:space="preserve">tropicus ♋, to-<lb/>tus ſupra faciem ſuperiorem exiſtit: </s>
  <s xml:id="echoid-s33085" xml:space="preserve">Vnde factum eſt, vt nullas vmbrarum latitudines pro horis <lb/>tropici ♑, ſupputauerimus. </s>
  <s xml:id="echoid-s33086" xml:space="preserve">Gnomonis autem vmbra, Sole exiſtente in principio ♋, deſcribit <lb/>in horologio ſuperiore Ellipſim, quæ tamen in exemplo integra, ob ſpatii anguſtias, deſcri-<lb/>pta non eſt.</s>
  <s xml:id="echoid-s33087" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1687" type="float" level="2" n="1">
<note position="left" xlink:label="note-0528-07" xlink:href="note-0528-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33088" xml:space="preserve">HOROLOGIVM autem ita delineabimus. </s>
  <s xml:id="echoid-s33089" xml:space="preserve">In plano horologii ducatur recta A B, pro <lb/>
<anchor type="note" xlink:label="note-0528-08a" xlink:href="note-0528-08"/>
communi ſectione plani horologij, &amp; </s>
  <s xml:id="echoid-s33090" xml:space="preserve">Verticalis proprii illius circuli maximi, cui horologiũ æqui <lb/>diſtat, quæ occulte ducenda eſt, &amp; </s>
  <s xml:id="echoid-s33091" xml:space="preserve">in plano firmo ac ſtabili æquidiſtans Horizonti, beneficio per-<lb/>pendiculi. </s>
  <s xml:id="echoid-s33092" xml:space="preserve">In hac aſſumpto loco ſtyli C, deſcribatur ex C, circulus cuiuslibet magnitudinis ADB, <lb/>in quo per centrum C, ducatur D E, ad A B, perpendicularis, quæ communis ſectio erit Meridia-<lb/>
<anchor type="note" xlink:label="note-0528-09a" xlink:href="note-0528-09"/>
ni plani horologii, vel Horizontis. </s>
  <s xml:id="echoid-s33093" xml:space="preserve">(Eſt enim idem Meridianus Horizontis, ac plani horologii) &amp;</s>
  <s xml:id="echoid-s33094" xml:space="preserve">
<pb o="513" file="0529" n="529" rhead="LIBER QVINTVS."/>
ipſius plani horologii, nempe linea meridiana, vt ex propoſ. </s>
  <s xml:id="echoid-s33095" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33096" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33097" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33098" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s33099" xml:space="preserve">Determinata autẽ <lb/>in recta A B, longitudine ſtyli C F, abſcindantur ei quotlibet partes æquales ex recta H I, &amp;</s>
  <s xml:id="echoid-s33100" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33101" xml:space="preserve">vt in <lb/>ſuperioribus factum quoque eſt. </s>
  <s xml:id="echoid-s33102" xml:space="preserve">Deinde inuenta altitudine poli ſupra circulum maximum, cui <lb/>horologium æquidiſtat, vt in eadem propoſ. </s>
  <s xml:id="echoid-s33103" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33104" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33105" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33106" xml:space="preserve">docuimus, quæ in dato exemplo comple-<lb/>ctitur grad. </s>
  <s xml:id="echoid-s33107" xml:space="preserve">70. </s>
  <s xml:id="echoid-s33108" xml:space="preserve">atque adeo eius complementum gr. </s>
  <s xml:id="echoid-s33109" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33110" xml:space="preserve">ſupputetur vmbra P. </s>
  <s xml:id="echoid-s33111" xml:space="preserve">32. </s>
  <s xml:id="echoid-s33112" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33113" xml:space="preserve">58. </s>
  <s xml:id="echoid-s33114" xml:space="preserve">conue-<lb/>niens complemento altitudinis poli inuentæ, hoc eſt, quæ debetur altitudini Solis in Aequatore <lb/>
<anchor type="figure" xlink:label="fig-0529-01a" xlink:href="fig-0529-01"/>
<anchor type="note" xlink:label="note-0529-01a" xlink:href="note-0529-01"/>
<anchor type="note" xlink:label="note-0529-02a" xlink:href="note-0529-02"/>
<anchor type="note" xlink:label="note-0529-03a" xlink:href="note-0529-03"/>
&amp; </s>
  <s xml:id="echoid-s33115" xml:space="preserve">Meridiano conſtituto, in linea meridiana à C, ſurſum verſus vſque ad E, ſi centrum horologij <lb/>infra locum ſtyli C, cadit, vt in noſtro exemplo contingit, deorſum autem verſus, ſi centrum ho-<lb/>rologii ſupra locum ſtyli cadit: </s>
  <s xml:id="echoid-s33116" xml:space="preserve">(Facile autem ex ijs, quæ propoſ. </s>
  <s xml:id="echoid-s33117" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33118" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33119" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33120" xml:space="preserve">tradidimus, percipie-<lb/>tur, an centrum horologii infra ſtylum, aut ſupra cadat.) </s>
  <s xml:id="echoid-s33121" xml:space="preserve">Recta enim E G, ducta per E, ad meri-<lb/>dianam lineam perpendicularis, erit linea æquinoctialis. </s>
  <s xml:id="echoid-s33122" xml:space="preserve">Si vero à C, in contrariam partem in li-<lb/>
<anchor type="note" xlink:label="note-0529-04a" xlink:href="note-0529-04"/>
nea meridiana numeretur longitudo vmbræ P. </s>
  <s xml:id="echoid-s33123" xml:space="preserve">4. </s>
  <s xml:id="echoid-s33124" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33125" xml:space="preserve">22. </s>
  <s xml:id="echoid-s33126" xml:space="preserve">quæ altitudini poli inuentę conuenit, <lb/>vſque ad H, erit H, centrum horologii. </s>
  <s xml:id="echoid-s33127" xml:space="preserve">Et ſi per H, ducatur ad meridianam lineam perpendicu-<lb/>
<anchor type="note" xlink:label="note-0529-05a" xlink:href="note-0529-05"/>
laris linea I K, erit hæc, linea horæ 6, à mer. </s>
  <s xml:id="echoid-s33128" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33129" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33130" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33131" xml:space="preserve">quemadmodum in horologio horizonta <lb/>li, à qua computandi eſſent arcus horarii in circulo ex H, deſcripto, ſi forent pro horis ſingulis in-<lb/>
<anchor type="note" xlink:label="note-0529-06a" xlink:href="note-0529-06"/>
uenti. </s>
  <s xml:id="echoid-s33132" xml:space="preserve">Inuenientur autem eadem hæc duo puncta E H, ſi cum ſtylo fiat angulus altitudinis poli <lb/>inuentę C F E, &amp; </s>
  <s xml:id="echoid-s33133" xml:space="preserve">angulus cõplementi eiuſdem altitudinis poli C F H, vt in ſuperioribus dictum <lb/>eſt. </s>
  <s xml:id="echoid-s33134" xml:space="preserve">Horizontalem lineam ita ducemus. </s>
  <s xml:id="echoid-s33135" xml:space="preserve">Ex C, ſurſum verſus in linea meridiana ſupputabimus <lb/>
<anchor type="note" xlink:label="note-0529-07a" xlink:href="note-0529-07"/>
vmbram P 4. </s>
  <s xml:id="echoid-s33136" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33137" xml:space="preserve">51. </s>
  <s xml:id="echoid-s33138" xml:space="preserve">quæ inclinationi plani horologii ad Horizontem conuenit, nempe gradibus <lb/>68. </s>
  <s xml:id="echoid-s33139" xml:space="preserve">in noſtro exemplo, vſque ad M, punctum: </s>
  <s xml:id="echoid-s33140" xml:space="preserve">Quod etiam comperiemus, ſi ad F, conſtituatur an <lb/>gulus complementi inclinationis C F M, ita vt recta F M, meridianam lineam ſecet in M. </s>
  <s xml:id="echoid-s33141" xml:space="preserve">Recta <lb/>cuim per M, ad meridianam lineam ducta perpendicularis, erit linea horizontalis, vt ex demon-<lb/>ſtratis in propoſ. </s>
  <s xml:id="echoid-s33142" xml:space="preserve">26. </s>
  <s xml:id="echoid-s33143" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33144" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33145" xml:space="preserve">manifeſtum eſt.</s>
  <s xml:id="echoid-s33146" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1688" type="float" level="2" n="2">
<note position="left" xlink:label="note-0528-08" xlink:href="note-0528-08a" xml:space="preserve">Deſctiptio ho-<lb/>rologii ad Ho-<lb/>rizontem incli-<lb/>nati ex tabulis.</note>
<note position="left" xlink:label="note-0528-09" xlink:href="note-0528-09a" xml:space="preserve">Linea meridia-<lb/>na.</note>
  <figure xlink:label="fig-0529-01" xlink:href="fig-0529-01a">
    <image file="0529-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0529-01"/>
  </figure>
<note position="left" xlink:label="note-0529-01" xlink:href="note-0529-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0529-02" xlink:href="note-0529-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0529-03" xlink:href="note-0529-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0529-04" xlink:href="note-0529-04a" xml:space="preserve">Linea æquínc@ <lb/>ctialis.</note>
<note position="right" xlink:label="note-0529-05" xlink:href="note-0529-05a" xml:space="preserve">Centrum horo-<lb/>logii.</note>
<note position="left" xlink:label="note-0529-06" xlink:href="note-0529-06a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0529-07" xlink:href="note-0529-07a" xml:space="preserve">Linea horizon-<lb/>talis.</note>
</div>
<p>
  <s xml:id="echoid-s33147" xml:space="preserve">SI iam à recta A B, in circulo A D B, numerentur latitudines vmbrarum, deſcribemus ex ea-<lb/>rundem longitudinibus ſingulas horas, vt in præcedentibus. </s>
  <s xml:id="echoid-s33148" xml:space="preserve">Ita namque vides, ex latitudine vm-<lb/>
<anchor type="note" xlink:label="note-0529-08a" xlink:href="note-0529-08"/>
bræ gr. </s>
  <s xml:id="echoid-s33149" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33150" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33151" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33152" xml:space="preserve">occidentali ac inferiori B L, quæ horæ 8. </s>
  <s xml:id="echoid-s33153" xml:space="preserve">à mer-conuenit in Aequatore, vel <lb/>ex longitudine eiuſdem vmbræ P. </s>
  <s xml:id="echoid-s33154" xml:space="preserve">69. </s>
  <s xml:id="echoid-s33155" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33156" xml:space="preserve">7. </s>
  <s xml:id="echoid-s33157" xml:space="preserve">inuentum eſſe in linea æquinoctiali punctum G, pro <lb/>hora 8. </s>
  <s xml:id="echoid-s33158" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33159" xml:space="preserve">Et ex eadem latitudine vmbræ orientali, inferioriq́ue A N, quæ etiam horæ 4. </s>
  <s xml:id="echoid-s33160" xml:space="preserve">à <lb/>med. </s>
  <s xml:id="echoid-s33161" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33162" xml:space="preserve">conuenit, vel ex eadem longitudine eiuſdem vmbræ, in linea æquinoctiali repertum eſſe <lb/>punctum O, pro hora 4. </s>
  <s xml:id="echoid-s33163" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33164" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33165" xml:space="preserve">Sic quoque êx A P, latitudine vmbræ gr. </s>
  <s xml:id="echoid-s33166" xml:space="preserve">22. </s>
  <s xml:id="echoid-s33167" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33168" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33169" xml:space="preserve">orientali, <lb/>&amp; </s>
  <s xml:id="echoid-s33170" xml:space="preserve">ſuperiori, quæ horæ 7. </s>
  <s xml:id="echoid-s33171" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33172" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33173" xml:space="preserve">in tropico ♋, conuenit, &amp; </s>
  <s xml:id="echoid-s33174" xml:space="preserve">ex longitudine eiuſdem vmbræ <lb/>P. </s>
  <s xml:id="echoid-s33175" xml:space="preserve">38. </s>
  <s xml:id="echoid-s33176" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33177" xml:space="preserve">53. </s>
  <s xml:id="echoid-s33178" xml:space="preserve">inuentum eſt punctum Q, pro hora 7. </s>
  <s xml:id="echoid-s33179" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33180" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33181" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s33182" xml:space="preserve">Et ex eadem latitu-<lb/>dine vmbræ occidentali, ſuperioriq́ue B R, &amp; </s>
  <s xml:id="echoid-s33183" xml:space="preserve">ex eadem longitudine repertum eſt punctum S, pro <lb/>hora 5. </s>
  <s xml:id="echoid-s33184" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33185" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s33186" xml:space="preserve">Et ſic de cæteris. </s>
  <s xml:id="echoid-s33187" xml:space="preserve">Solum hoc aduertendum eſt, latitudines vm brarũ <lb/>ſuperiores, quæ ſupra rectam A B, in circulo A D B, (qui ob anguſtiam loci integer deſcriptus nõ <lb/>eſt) commode numerari nequeunt, ſupputandas eſſe infra eandem rectam, in parte tamen oppo-
<pb o="514" file="0530" n="530" rhead="GNOMONICES"/>
ſita. </s>
  <s xml:id="echoid-s33188" xml:space="preserve">Vt quoniam latitudo vmbræ conueniens horæ 9. </s>
  <s xml:id="echoid-s33189" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33190" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33191" xml:space="preserve">in tropico ♋, orientalis eſt, ac <lb/>ſuperior, continens gr. </s>
  <s xml:id="echoid-s33192" xml:space="preserve">48. </s>
  <s xml:id="echoid-s33193" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33194" xml:space="preserve">59. </s>
  <s xml:id="echoid-s33195" xml:space="preserve">quæ ſupra rectam A B, numerari non poteſt, cõputabimus eam <lb/>infra rectam A B, à puncto B, occidentali vſque ad T. </s>
  <s xml:id="echoid-s33196" xml:space="preserve">Si enim ex recta occulta C T, abſcindatur <lb/>C V, longitudo vmbræ P. </s>
  <s xml:id="echoid-s33197" xml:space="preserve">77. </s>
  <s xml:id="echoid-s33198" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33199" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33200" xml:space="preserve">eidem horæ reſpondens, habebitur punctum V, pro hora 9. <lb/></s>
  <s xml:id="echoid-s33201" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33202" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33203" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s33204" xml:space="preserve">Eadem ratione inuentum eſt punctum Y, pro hora 3. </s>
  <s xml:id="echoid-s33205" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33206" xml:space="preserve">in tropico <lb/>♋, ex latitudine vmbræ eadem orientali, &amp; </s>
  <s xml:id="echoid-s33207" xml:space="preserve">inferiori, cum tamen latitudo vmbræ huius horæ in <lb/>tabula ſit occidentalis, &amp; </s>
  <s xml:id="echoid-s33208" xml:space="preserve">ſuperior.</s>
  <s xml:id="echoid-s33209" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1689" type="float" level="2" n="3">
<note position="left" xlink:label="note-0529-08" xlink:href="note-0529-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33210" xml:space="preserve">DVCVNTVR autem ferme ſingulæ horæ à mer. </s>
  <s xml:id="echoid-s33211" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33212" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33213" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33214" xml:space="preserve">per quaterna puncta, vt ho-<lb/>ra 9. </s>
  <s xml:id="echoid-s33215" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33216" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33217" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33218" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33219" xml:space="preserve">per puncta Z, a, H, V, vel ſaltem per terna, vt hora 7. </s>
  <s xml:id="echoid-s33220" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33221" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33222" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33223" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s33224" xml:space="preserve">per puncta e, H, Q; </s>
  <s xml:id="echoid-s33225" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33226" xml:space="preserve">hora 11. </s>
  <s xml:id="echoid-s33227" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33228" xml:space="preserve">per puncta d, b, H, &amp;</s>
  <s xml:id="echoid-s33229" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33230" xml:space="preserve">Omnes enim horæ à mer. </s>
  <s xml:id="echoid-s33231" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33232" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33233" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0530-01a" xlink:href="note-0530-01"/>
nocte per H, centrum horologii ducuntur.</s>
  <s xml:id="echoid-s33234" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1690" type="float" level="2" n="4">
<note position="left" xlink:label="note-0530-01" xlink:href="note-0530-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s33235" xml:space="preserve">PRO horologio ſuperiore declinante à mer. </s>
  <s xml:id="echoid-s33236" xml:space="preserve">in ortum gr. </s>
  <s xml:id="echoid-s33237" xml:space="preserve">40. </s>
  <s xml:id="echoid-s33238" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33239" xml:space="preserve">ad Horizontem inclinato <lb/>ex parte boreali gr. </s>
  <s xml:id="echoid-s33240" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33241" xml:space="preserve">ſupputarę ſunt tabellæ ſequentes pro horis à mer. </s>
  <s xml:id="echoid-s33242" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33243" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33244" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33245" xml:space="preserve">in quibus <lb/>ſolis exemplum hic proponemus. </s>
  <s xml:id="echoid-s33246" xml:space="preserve">Appellantur autem in his tabellis latitudines vmbrarum ſu-<lb/>periores illæ, quæ ſunt citra Verticalem proprium horologij verſus æquinoctialem lineam; </s>
  <s xml:id="echoid-s33247" xml:space="preserve">Infe-<lb/>riores autem illæ, quæ vltra Verticalem eundem exiſtunt verſus centrum horologij.</s>
  <s xml:id="echoid-s33248" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1692" type="section" level="1" n="447">
<head xml:id="echoid-head469" xml:space="preserve">Latitudines longitudineſq́ue vmbrarum in horlogio ſuperiore declinante à meridie <lb/>in ortum gr. 40. &amp; ad Horizontem inclinato ex parte boreali gr. 20. pro <lb/>
horis à mer. &amp; med. noc. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head470" xml:space="preserve">Intropico ♋, latitudines vmbrarum ſunt partim ſuperiores, &amp; partim inferiores, <lb/>vt hæ ſyllabæ [Super. Infer.] indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à me- \\ dia nocte. # 5 \\ Super. # 6 \\ Super. # 7 \\ Super. # 8 \\ Super. # 9 \\ Super. # 10 \\ Infer. # 11 \\ Infer. # *** # orienta \\ les. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 21. 42. # 16. 25. # 11. 39. # 7. 12. # 2. 32. # 5. 48. # 71. 34. # 90. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 73. 33. # 29. 39. # 17. 3. # 10. 38. # 6. 24. # 3. 7. # 0. 30. # 0. 28.
Horæ ♋, à med. \\ nocte. # 12 \\ Infer. # A meri \\ die. # 1 \\ Super. # 2 \\ Super. # 3 \\ Super. # 4 \\ Super. # 5 \\ Super. # occiden \\ tales.
Latirudines vm- \\ brarum. # G. M. # # G. M. # G. M. # G. M. # G. M. # G. M.
# 7. 28. # # 2. 6. # 2. 37. # 11. 10. # 15. 51. # 21. 5.
Longitudines vm- \\ brarum. # P. M. # # P. M. # P. M. # P. M. # P. M. # P. M.
# 2. 47. # # 6. 0. # 10. 5. # 16. 9. # 27. 37. # 63. 43.
</note>
</div>
<div xml:id="echoid-div1693" type="section" level="1" n="448">
<head xml:id="echoid-head471" xml:space="preserve">In Æquatore omnes latitudines vmbrarum Inferiores ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Hor. ♈, &amp; ♎, à med. no. # 6 # 7 # 8 # 9 # 10 # 11 # *** # orientales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>
# 6. 16. # 13. 36. # 22. 51. # 36. 1. # 56. 50. # 88. 5. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 53. 6. # 24. 33. # 14. 53. # 9. 50. # 6. 54. # 5. 47. # 5. 47.
Hor. ♈, &amp; ♎, à med. no. # 12 # A meri \\ die. # 1 # 2 # 3 # 4 # 5 # occidẽtales
Latitudines vm- \\ brarum. # G. M. # # G. M. # G. M. # G. M. # G. M. # G. M.
# 59. 49. # # 37. 52. # 24. 4. # 14. 32. # 7. 0. # 0. 20.
Longitudines vm- \\ brarum. # P. M. # # P. M. # P. M. # P. M. # P. M. # P. M.
# 6. 41. # # 9. 25. # 14. 10. # 23. 3. # @7. 18. # 917. 21
</note>
<pb o="515" file="0531" n="531" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1694" type="section" level="1" n="449">
<head xml:id="echoid-head472" xml:space="preserve">In tropico ♑, omnes latitudines vinbrarum inferiores ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horę ♑, a med. noc. # 6 # 7 # 8 # 9 # 10 # 11 # *** # orientales. <lb/>Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 27. 11 # 34. 38. # 44. 3. # 56. 9. # 71. 22. # 88. 59. # 90. 0. <lb/>Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 412. 29 # 50. 50. # 27. 16. # 18. 53. # 15. 7. # 13. 55. # 13. 55. <lb/>Horæ ♑, à med.noc. # 12 # A meri \\ die. # 1 # 2 # 3 # 4 # occidentales. <lb/>
Latitudines vm- \\ brarum. # G. M. # # G. M. # G. M. # G. M. # G. M.
# 72. 45. # # 57. 41. # 45. 15. # 35. 34. # 27. 56.
Longitudines vm- \\ brarum. # P. M. # # P. M. # P. M. # P. M. # P. M.
# 14. 52. # # 18. 17. # 25. 57. # 46. 24. # 229. 0.
</note>
<p>
  <s xml:id="echoid-s33249" xml:space="preserve">IN plano horologij ducatur recta A B, ita tamen, vt in plano ſtabili ac firmo parallela ſit Ho-<lb/>
<anchor type="note" xlink:label="note-0531-03a" xlink:href="note-0531-03"/>
rizonti, in qua aſſumpto loco ſtyli C, deſcribatur ex C, circulus A D B E, cuiuſuis magnitudinis <lb/>in quo per centrum C. </s>
  <s xml:id="echoid-s33250" xml:space="preserve">diameter excitetur D E, ad A B, perpendicularis, quæ communis ſectio <lb/>erit plani horologij &amp; </s>
  <s xml:id="echoid-s33251" xml:space="preserve">maximi circuli inclinationem ad Horizõtem metientis, vt perſpicuum eſt. <lb/></s>
  <s xml:id="echoid-s33252" xml:space="preserve">Inuento autem, per propoſ. </s>
  <s xml:id="echoid-s33253" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33254" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33255" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33256" xml:space="preserve">arcu circuli maximi, cui horologium æquidiſtat, inter cir <lb/>
<anchor type="note" xlink:label="note-0531-04a" xlink:href="note-0531-04"/>
culum maximum, qui inclinationem plani metitur, &amp; </s>
  <s xml:id="echoid-s33257" xml:space="preserve">Meridianum proprium horologii interie-<lb/>cto, quem in dato exemplo deprehendimus eſſe grad. </s>
  <s xml:id="echoid-s33258" xml:space="preserve">32. </s>
  <s xml:id="echoid-s33259" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33260" xml:space="preserve">7. </s>
  <s xml:id="echoid-s33261" xml:space="preserve">numerabimus eum in circu-<lb/>lo A D B E, à D, vſque ad F, versus ſiniſtram, hoc eſt, verſus occidentales partes A, quando ho-<lb/>rologium declinat à mer. </s>
  <s xml:id="echoid-s33262" xml:space="preserve">in ortum, inclinatumq́ue eſt ad Horizontem ex parte boreali, quale <lb/>noſtrum eſt; </s>
  <s xml:id="echoid-s33263" xml:space="preserve">verſus dextram autem, ſi planum ex eadem parte inclinatum à mer. </s>
  <s xml:id="echoid-s33264" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33265" xml:space="preserve">defle-<lb/>ctat: </s>
  <s xml:id="echoid-s33266" xml:space="preserve">ducaturq́ue recta F C G, quæ communis ſectio erit plani horologij, &amp; </s>
  <s xml:id="echoid-s33267" xml:space="preserve">proprij Meridia-<lb/>ni ipſius, id eſt, linea ſtyli. </s>
  <s xml:id="echoid-s33268" xml:space="preserve">Si enim planum horologii in proprio ſitu ſtatuatur, ſi quidem à me-<lb/>
<anchor type="note" xlink:label="note-0531-05a" xlink:href="note-0531-05"/>
ridie declinet in ortum, cadet punctum E, in quartam partem hemiſphærij ſuperi occidenta-<lb/>lem, ac borealem. </s>
  <s xml:id="echoid-s33269" xml:space="preserve">Si igitur circulus maximus inclinationem metiens per rectam D E, ductus, &amp; </s>
  <s xml:id="echoid-s33270" xml:space="preserve"><lb/>ad planum horologii rectus, concipiatur animo circa ſtylum in C, collocatum moueri, ita vt re-<lb/>
<anchor type="note" xlink:label="note-0531-06a" xlink:href="note-0531-06"/>
ctus ſemper maneat ad planum horologij, donec per polum mundi arcticum, qui nobis ad ho-<lb/>rologium conuerſis, ad dextram ipſius puncti E, exiſtit, ducatur, hoc eſt, deinde cum Meridia-<lb/>no proprio horologii coniungatur, faciet vtique in horologio ſectionem, quę in ſra ſtylum in-<lb/>ter puncta A, D, cadet, cuiuſmodi eſt F C G, vt conſtat. </s>
  <s xml:id="echoid-s33271" xml:space="preserve">Cum ergo D F, arcus ſimilis ei ſit, qui <lb/>intercipitur inter Meridianum proprium, &amp; </s>
  <s xml:id="echoid-s33272" xml:space="preserve">circulum maximum per D E, ductum, qui inclina-<lb/>tionem ad Horizontem metitur, erit recta F G, communis ſectio proprii Meridiani, &amp; </s>
  <s xml:id="echoid-s33273" xml:space="preserve">plani ho-<lb/>rologii, hoc eſt, linea ſtyli. </s>
  <s xml:id="echoid-s33274" xml:space="preserve">Si autem planum horologij à meridie in occaſum vergat, cadet <lb/>punctum E, in quartam partem hemiſphærij ſuperi orientalem, ac borealem, ita vt polus ar-<lb/>cticus ſit nobis conuerſis ad horologium verſus ſiniſtram puncti E, hoc eſt, verſus A. </s>
  <s xml:id="echoid-s33275" xml:space="preserve">Ergo ſi <lb/>circulus ille ad horologium rectus, qui per D E, ducitur, moueatur verſus A, donec per polum <lb/>
<anchor type="note" xlink:label="note-0531-07a" xlink:href="note-0531-07"/>
tranſeat, cadet eius ſectio, quam cum plano horologij facit, infra ſtylum inter puncta B, D, &amp;</s>
  <s xml:id="echoid-s33276" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s33277" xml:space="preserve">Quòd ſi per C, ad F G, ducatur perpendicularis H I, erit hæc, communis ſectio plani horologii, <lb/>&amp;</s>
  <s xml:id="echoid-s33278" xml:space="preserve">| Verticalis proprie dicti ipſius horologij, à qua ſupputandæ erunt omnes latitudines vmbra-<lb/>rum. </s>
  <s xml:id="echoid-s33279" xml:space="preserve">Parata autem linea H I, diuiſa in partes quotlibet ſtylo æquales, vt in præcedentibus, in-<lb/>uentaq́ue, per propoſ. </s>
  <s xml:id="echoid-s33280" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33281" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33282" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33283" xml:space="preserve">altitudine poli ſupra circulum maximum, cui horologium æqui-<lb/>diſtat, quæ in noſtro exemplo comprehendi@ grad. </s>
  <s xml:id="echoid-s33284" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33285" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33286" xml:space="preserve">43. </s>
  <s xml:id="echoid-s33287" xml:space="preserve">ac proinde eius complementum <lb/>grad. </s>
  <s xml:id="echoid-s33288" xml:space="preserve">64. </s>
  <s xml:id="echoid-s33289" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33290" xml:space="preserve">17. </s>
  <s xml:id="echoid-s33291" xml:space="preserve">ſi ex C, loco ſtyli ſurſum verſus in recta F G, quando centrum horologij ca-<lb/>dit infra ſtylum, vt contingit in planis ex parte boreali inclinatis ad Horizontem, cum arcus Me-<lb/>ridiani Horizontis inter planum, &amp; </s>
  <s xml:id="echoid-s33292" xml:space="preserve">Horizontem minor eſt altitudine poli ſupra Horizontem, <lb/>vt in noſtro exemplo, in quo dictus arcus continet grad. </s>
  <s xml:id="echoid-s33293" xml:space="preserve">15. </s>
  <s xml:id="echoid-s33294" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33295" xml:space="preserve">35. </s>
  <s xml:id="echoid-s33296" xml:space="preserve">(qui quidem ex propoſ. </s>
  <s xml:id="echoid-s33297" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33298" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0531-08a" xlink:href="note-0531-08"/>
lib. </s>
  <s xml:id="echoid-s33299" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33300" xml:space="preserve">inueſtigandus eſt) numeretur longitudo vmbræ P. </s>
  <s xml:id="echoid-s33301" xml:space="preserve">5. </s>
  <s xml:id="echoid-s33302" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33303" xml:space="preserve">47. </s>
  <s xml:id="echoid-s33304" xml:space="preserve">reſpondens complemento alti-<lb/>
<anchor type="note" xlink:label="note-0531-09a" xlink:href="note-0531-09"/>
tudinis poli inuentæ, vſq; </s>
  <s xml:id="echoid-s33305" xml:space="preserve">ad L, erit recta L M, ducta ad F G, perpendicularis, linea æquinoctia-<lb/>lis. </s>
  <s xml:id="echoid-s33306" xml:space="preserve">Hęc vmbra deorſum verſus ſupputanda erit, quando arcus Meridiani inter Horizontem, &amp; </s>
  <s xml:id="echoid-s33307" xml:space="preserve"><lb/>planum horologii maior eſt altitudine poli ſupra Horizontem, quia tunc centrum horologii ca-<lb/>dit ſupra ſtylum, vt in ſequenti horologio apparebit, in quo dictus arcus comprehendit grad. <lb/></s>
  <s xml:id="echoid-s33308" xml:space="preserve">68. </s>
  <s xml:id="echoid-s33309" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33310" xml:space="preserve">50. </s>
  <s xml:id="echoid-s33311" xml:space="preserve">Quòd ſi ex C, in oppoſitam partem in linea F G, vt hic deorſum verſus, compute-<lb/>tur longitudo vmbræ P. </s>
  <s xml:id="echoid-s33312" xml:space="preserve">24. </s>
  <s xml:id="echoid-s33313" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33314" xml:space="preserve">55. </s>
  <s xml:id="echoid-s33315" xml:space="preserve">conueniens inuentæ altitudini poli grad. </s>
  <s xml:id="echoid-s33316" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33317" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33318" xml:space="preserve">43. </s>
  <s xml:id="echoid-s33319" xml:space="preserve">in-<lb/>ucnietur N, centrum horologii. </s>
  <s xml:id="echoid-s33320" xml:space="preserve">Quæ duo puncta L, N, inuenientur quoque, vt ſupra di-<lb/>
<anchor type="note" xlink:label="note-0531-10a" xlink:href="note-0531-10"/>
ctum eſt in alijs horologijs, ſi pro puncto æquinoctialis lineæ ad verticem ſtyli K, qui perpen-<lb/>dicularis ſit ad rectam F G, conſtituatur angulus altitudinis poli inuentæ C K L, grad. </s>
  <s xml:id="echoid-s33321" xml:space="preserve">25. <lb/></s>
  <s xml:id="echoid-s33322" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33323" xml:space="preserve">43. </s>
  <s xml:id="echoid-s33324" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33325" xml:space="preserve">pro centro horologii angulus complementi eiuſdem altitudinis C K N, grad. </s>
  <s xml:id="echoid-s33326" xml:space="preserve">64.</s>
  <s xml:id="echoid-s33327" xml:space="preserve">
<pb o="516" file="0532" n="532" rhead="GNOMONICES"/>
Min. </s>
  <s xml:id="echoid-s33328" xml:space="preserve">17. </s>
  <s xml:id="echoid-s33329" xml:space="preserve">A recta autem Q R, quæ per centrum horologii ducitur perpendicularis ad F G, <lb/>numerandi erunt arcus horarij, (ſi fuerint pro horis ſingulis ſupputati) in circulo ex N, <lb/>deſcripto.</s>
  <s xml:id="echoid-s33330" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1694" type="float" level="2" n="1">
<note position="right" xlink:label="note-0531-03" xlink:href="note-0531-03a" xml:space="preserve">Deſcriptio hot@ <lb/>logii declinan-<lb/>tis à mer. in or-<lb/>tum gr. 40. &amp; ad <lb/>Horizoutem in <lb/>clinati gr. 20. ex <lb/>tabulis.</note>
<note position="left" xlink:label="note-0531-04" xlink:href="note-0531-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0531-05" xlink:href="note-0531-05a" xml:space="preserve">Linea ſtyli quę.</note>
<note position="left" xlink:label="note-0531-06" xlink:href="note-0531-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0531-07" xlink:href="note-0531-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0531-08" xlink:href="note-0531-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0531-09" xlink:href="note-0531-09a" xml:space="preserve">Linea xquin@-<lb/>ctia lis.</note>
<note position="right" xlink:label="note-0531-10" xlink:href="note-0531-10a" xml:space="preserve">Centrum horo-<lb/>logii.</note>
</div>
<p>
  <s xml:id="echoid-s33331" xml:space="preserve">HORÆ deſcribentur ex ſuprapoſitis tabellis, vt in prioribus, ſi à punctis H, I, ſupputentur <lb/>latitudines vmbrarum orientales, occidentaleſq́ue, obſeruando diligenter, quæ ſuperiores, &amp; </s>
  <s xml:id="echoid-s33332" xml:space="preserve"><lb/>quæ ſint inferiores &amp;</s>
  <s xml:id="echoid-s33333" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33334" xml:space="preserve">vt in appoſita figura apparet. </s>
  <s xml:id="echoid-s33335" xml:space="preserve">Tranſeunt autem omnes horæ à mer. </s>
  <s xml:id="echoid-s33336" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33337" xml:space="preserve"><lb/>med, noc. </s>
  <s xml:id="echoid-s33338" xml:space="preserve">per N, centrum horologij. </s>
  <s xml:id="echoid-s33339" xml:space="preserve">Quod ſi centrum horologij tam procul à ſtylo abeſſet, vt <lb/>
<anchor type="note" xlink:label="note-0532-01a" xlink:href="note-0532-01"/>
<anchor type="figure" xlink:label="fig-0532-01a" xlink:href="fig-0532-01"/>
<anchor type="note" xlink:label="note-0532-02a" xlink:href="note-0532-02"/>
<anchor type="note" xlink:label="note-0532-03a" xlink:href="note-0532-03"/>
commode in horologio notari non poſſet, inueſtiganda eſſent pro horis illis, quæ vnum tantum <lb/>punctum habent in altero tropicorum, nullum autem in reliquo tropico, aut linea æquinoctiali, <lb/>alia puncta in propinquo parallelo; </s>
  <s xml:id="echoid-s33340" xml:space="preserve">vt v. </s>
  <s xml:id="echoid-s33341" xml:space="preserve">g. </s>
  <s xml:id="echoid-s33342" xml:space="preserve">in noſtro exemplo in parallelo ♊, vel ♌. </s>
  <s xml:id="echoid-s33343" xml:space="preserve">Horizonta-<lb/>lis linea ducenda eſt per punctum M, vbi linea horæ 6. </s>
  <s xml:id="echoid-s33344" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33345" xml:space="preserve">vel med.</s>
  <s xml:id="echoid-s33346" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33347" xml:space="preserve">æquinoctialem lineã <lb/>
<anchor type="note" xlink:label="note-0532-04a" xlink:href="note-0532-04"/>
ſecat, perpendicularis ad rectã D E. </s>
  <s xml:id="echoid-s33348" xml:space="preserve">Vel ſumpta in recta A B, longitudinę ſtyli C O, ſi fiat ſurſum <lb/>
<anchor type="note" xlink:label="note-0532-05a" xlink:href="note-0532-05"/>
verſus angulus complementi inclinationis C O P, ſecabitur recta D E, in P, puncto, per quod ho-<lb/>rizontalis linea ducenda eſt ad D E, perpendicularis, quæ, ſi erratum non eſt, tranſibit neceſſario <lb/>per punctum M, horæ 6. </s>
  <s xml:id="echoid-s33349" xml:space="preserve">in ęquinoctiali linea. </s>
  <s xml:id="echoid-s33350" xml:space="preserve">Vel certe, ſi vmbra Par. </s>
  <s xml:id="echoid-s33351" xml:space="preserve">32. </s>
  <s xml:id="echoid-s33352" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33353" xml:space="preserve">58. </s>
  <s xml:id="echoid-s33354" xml:space="preserve">conueniens in-<lb/>clinationi plani ad Horizontem trãsfera tur à C, ſurſum verſus in recta D E, reperietur punctum <lb/>P, per quod ducenda eſt linea horizontalis ad D E, perpendicularis. </s>
  <s xml:id="echoid-s33355" xml:space="preserve">Lineam autem horæ 12. </s>
  <s xml:id="echoid-s33356" xml:space="preserve">quæ <lb/>eſt linea meridiana, ducemus etiam hac ratione. </s>
  <s xml:id="echoid-s33357" xml:space="preserve">Arcus horarius horæ 12. </s>
  <s xml:id="echoid-s33358" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33359" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33360" xml:space="preserve">quem hic <lb/>
<anchor type="note" xlink:label="note-0532-06a" xlink:href="note-0532-06"/>
inuenimus continere gr. </s>
  <s xml:id="echoid-s33361" xml:space="preserve">83. </s>
  <s xml:id="echoid-s33362" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33363" xml:space="preserve">44. </s>
  <s xml:id="echoid-s33364" xml:space="preserve">eſſeq́ue occidentalem, inferioremq́ue, (Quoniam enim ho <lb/>ra 12. </s>
  <s xml:id="echoid-s33365" xml:space="preserve">meridiei minorem habet diſtantiam à Meridiano proprio horologii, quàm 6. </s>
  <s xml:id="echoid-s33366" xml:space="preserve">horarũ, cum <lb/>diſtet duntaxat gr. </s>
  <s xml:id="echoid-s33367" xml:space="preserve">14. </s>
  <s xml:id="echoid-s33368" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33369" xml:space="preserve">10. </s>
  <s xml:id="echoid-s33370" xml:space="preserve">quanta nimirum eſt inclinatio Meridiani proprij ad Meridianũ Ho-<lb/>rizontis, erit arcus horarius horæ 12. </s>
  <s xml:id="echoid-s33371" xml:space="preserve">à med, noc. </s>
  <s xml:id="echoid-s33372" xml:space="preserve">inferior, id eſt, vltra centrum horologii exiſter, <lb/>
<anchor type="note" xlink:label="note-0532-07a" xlink:href="note-0532-07"/>
vt in ſcholio præcedentis propoſ. </s>
  <s xml:id="echoid-s33373" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s33374" xml:space="preserve">Rurſus quia planum horologii declinat à mer. </s>
  <s xml:id="echoid-s33375" xml:space="preserve">in or. <lb/></s>
  <s xml:id="echoid-s33376" xml:space="preserve">proiicietur vmbra ſtyli in meridie verſus ortum. </s>
  <s xml:id="echoid-s33377" xml:space="preserve">Quare arcus horarius tunc occidentalis erit, vt <lb/>eius vmbra in cõtrariam partem orientalem poſſit cadere, vt res poſtulat) ſupputetur in parte op-<lb/>poſita circuli Qa, ex N, deſcripti, nempe à puncto rectæ Q R, orientali ſurſum verſus vſque ad b. </s>
  <s xml:id="echoid-s33378" xml:space="preserve"><lb/>Nam recta N b, erit linea meridiana.</s>
  <s xml:id="echoid-s33379" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1695" type="float" level="2" n="2">
<note position="left" xlink:label="note-0532-01" xlink:href="note-0532-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0532-01" xlink:href="fig-0532-01a">
    <image file="0532-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0532-01"/>
  </figure>
<note position="left" xlink:label="note-0532-02" xlink:href="note-0532-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0532-03" xlink:href="note-0532-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0532-04" xlink:href="note-0532-04a" xml:space="preserve">Linea hotizon-<lb/>talis.</note>
<note position="left" xlink:label="note-0532-05" xlink:href="note-0532-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0532-06" xlink:href="note-0532-06a" xml:space="preserve">Linea meridia-<lb/>@a.</note>
<note position="left" xlink:label="note-0532-07" xlink:href="note-0532-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33380" xml:space="preserve">PRO ſuperiore horologio declinante à meridie in occaſum grad. </s>
  <s xml:id="echoid-s33381" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33382" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33383" xml:space="preserve">ad Horizontem in-<lb/>clinato ex parte boreali grad. </s>
  <s xml:id="echoid-s33384" xml:space="preserve">70. </s>
  <s xml:id="echoid-s33385" xml:space="preserve">tabellæ, quæ ſequuntur, compoſitæ ſunt prohoris inæqualibus, <lb/>in quibus ſolis exemplum exhibebimus. </s>
  <s xml:id="echoid-s33386" xml:space="preserve">Vocantur autem in hiſce tabellis latitudines vmbra-<lb/>rum Inferiores illæ, quæ ſunt citra Verticalem proprium horologii, hoc eſt, verſus lineam æqui-<lb/>noctialem; </s>
  <s xml:id="echoid-s33387" xml:space="preserve">ſuperiores autem illæ, quæ vltra eundem Verticalem verſus centrum horolo-<lb/>gij exiſtunt.</s>
  <s xml:id="echoid-s33388" xml:space="preserve"/>
</p>
<pb o="517" file="0533" n="533" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1697" type="section" level="1" n="450">
<head xml:id="echoid-head473" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in horologio ſuperiore declinante à mer. in \\ occ. grad. 20. &amp; ad Horizontem ex parte boreali inclinato grad. 70. \\ pro horis inæqualibus, ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head474" xml:space="preserve">In tropico ♑, latitudines vmbrarum partim Inferiores ſunt, &amp; partim Superiores, \\ vt hæ ſyllabæ [Infer. Super.] declarant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, in- \\ æquales. # 12 \\ Infer. # 1 \\ Infer. # 2 \\ Infer. # 3 \\ Infer. # 4 \\ Infer. # 5 \\ Infer. # 6 \\ Super. # 7. \\ Super. # *** # oriẽtales. <lb/>
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 20. 41. # 16. 52. # 13. 21. # 10. 4. # 6. 50. # 3. 33. # 0. 30. # 9. 38. # 90. 0.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 58. 22. # 31. 0. # 20. 2. # 13. 54. # 9. 48. # 6. 42. # 4. 9. # 1. 54. # 0. 23.
Horæ ♑, in- \\ ęquales. # 8 \\ Super. # 9 \\ Super. # 10 \\ Super. # 11 \\ Infer. # 12 \\ Infer. # occidentales. # Hora 1.♐, &amp;♒, \\ Inferior, &amp; oriẽ.
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M.
# 53. 17. # 6. 39. # 0. 1. # 4. 10. # 7. 42. # # 14. 36.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # # P. M.
# 0. 28. # 2. 28. # 4. 47. # 7. 26. # 10. 45. # # 38. 15.
</note>
<p>
  <s xml:id="echoid-s33389" xml:space="preserve">HIC appoſuimus latitudinem vmbræ, eiuſq́ue longitudinem, quam Sol efficit hora 1. </s>
  <s xml:id="echoid-s33390" xml:space="preserve">in-<lb/>æquali in parallelo ♐, &amp; </s>
  <s xml:id="echoid-s33391" xml:space="preserve">♒, quoniã ex ea deſcribenda eſt in horologio hora 1. </s>
  <s xml:id="echoid-s33392" xml:space="preserve">inæqualis, vt dice-<lb/>mus. </s>
  <s xml:id="echoid-s33393" xml:space="preserve">Longitudinem porro huius vmbræ exhibet altitudo Solis, quam in tabella 17. </s>
  <s xml:id="echoid-s33394" xml:space="preserve">altitudi-<lb/>num Solis notauimus.</s>
  <s xml:id="echoid-s33395" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1698" type="section" level="1" n="451">
<head xml:id="echoid-head475" xml:space="preserve">In Aequatore omnes latitudines vmbrarum ſuperiores ſunt, ſed orientales ab occi- dentalibus his ſyllabis [or.occ.] dignoſcuntur.</head>
<note position="right" xml:space="preserve"> <lb/>Hor. ♈, \\ &amp; ♎, in- \\ ęquales # 2 \\ or. # 3 \\ or. # 4 \\ or. # 5 \\ or. # 6 \\ or. # 7 \\ or. # *** # 8 \\ occ. # 9 \\ occ. # 10 \\ occ. # 11 \\ occ. # 12 \\ occ. <lb/>
Latitu. \\ vmbra. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 3. 56. # 10. 50. # 19. 11. # 30. 34. # 48. 16. # 76. 29. # 90. 0. # 69. 23. # 43. 38. # 27. 42. # 17. 17. # 9. 15.
Longit. \\ vmbra. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 82. 45. # 30. 9. # 17. 17. # 11. 9. # 7. 36. # 5. 50. # 5. 40. # 6. 4. # 8. 13. # 12. 12. # 19. 16. # 35. 17.
</note>
</div>
<div xml:id="echoid-div1699" type="section" level="1" n="452">
<head xml:id="echoid-head476" xml:space="preserve">In tropico ♋, omnes latitudines vmbrarum ſunt ſuperiores, ſed orientales ab occi- dentalibus hæ ſyllabæ [or. occ.] diſtinguunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, in- \\ æquales. # 3 \\ or. # 4 \\ or. # 5 \\ or. # 6 \\ or. # 7 \\ or. # *** # 8 \\ occ. # 9 \\ occ. # 10 \\ occ. # 11 \\ occ. <lb/>
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 26. 30 # 35. 51. # 48. 30. # 65. 48. # 87. 31. # 90. 0. # 70. 11. # 51. 48. # 38. 15. # 28. 18.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 1115. 1. # 44. 7. # 22. 42. # 15. 49. # 13. 43. # 13. 42. # 15. 3. # 20. 35. # 36. 36. # 176. 48
</note>
<p>
  <s xml:id="echoid-s33396" xml:space="preserve">IGITVR in plano horologii ducta recta A B, quæ in plano ſtabili, ac firmo æquidiſtans ſit <lb/>Horizonti, deſcribatur ex aſſumpto in ea loco ſtyli C, circulus cuiuſuis magnitudinis A D B E, <lb/>in quo diameter D E, ſecet rectam A B, ad angulos rectos, quæ communis ſectio erit plani ho-
<pb o="518" file="0534" n="534" rhead="GNOMONICES"/>
rologii, &amp; </s>
  <s xml:id="echoid-s33397" xml:space="preserve">circuli maximi inclinationem plani ad Horizontem metientis. </s>
  <s xml:id="echoid-s33398" xml:space="preserve">Inuento autẽ, per pro-<lb/>
<anchor type="note" xlink:label="note-0534-01a" xlink:href="note-0534-01"/>
poſ. </s>
  <s xml:id="echoid-s33399" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33400" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33401" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33402" xml:space="preserve">arcu circuli maximi, cui horologium æquidiſtat, inter circulum maximum, qui in-<lb/>clinationem plani metitur, &amp; </s>
  <s xml:id="echoid-s33403" xml:space="preserve">Meridianum proprium horologii interiecto, quem in propoſito ho <lb/>rologio reperimus eſſe gr. </s>
  <s xml:id="echoid-s33404" xml:space="preserve">16. </s>
  <s xml:id="echoid-s33405" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33406" xml:space="preserve">22. </s>
  <s xml:id="echoid-s33407" xml:space="preserve">computabimus eum à D, verſus ortum, ſiue punctum B, <lb/>vt in præcedenti horologio diximus, cum hoc horologium declinet à mer. </s>
  <s xml:id="echoid-s33408" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33409" xml:space="preserve">vſq; </s>
  <s xml:id="echoid-s33410" xml:space="preserve">ad F. </s>
  <s xml:id="echoid-s33411" xml:space="preserve">Nam <lb/>recta F C G, erit linea ſtyli, ſeu communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s33412" xml:space="preserve">Meridiani proprii ipſius ho-<lb/>
<anchor type="note" xlink:label="note-0534-02a" xlink:href="note-0534-02"/>
rologii. </s>
  <s xml:id="echoid-s33413" xml:space="preserve">A recta autem K L, rectam F G, ad rectos angulos ſecante numerandæ erunt latitudines <lb/>vmbrarum, cum ea ſit communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s33414" xml:space="preserve">Verticalis proprii eiuſdem horologii. <lb/></s>
  <s xml:id="echoid-s33415" xml:space="preserve">Diuiſa deinde recta H I, in partes quotcunque ſtylo æquales, vt in antecedentibus, inuentaq́ue al-<lb/>titudine poli ſupra circulum maximum, cui horologium æquidiſtat, quæ in dato horologio con-<lb/>
<anchor type="note" xlink:label="note-0534-03a" xlink:href="note-0534-03"/>
tinet gr. </s>
  <s xml:id="echoid-s33416" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33417" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33418" xml:space="preserve">18. </s>
  <s xml:id="echoid-s33419" xml:space="preserve">ac propterea eius complementum gr. </s>
  <s xml:id="echoid-s33420" xml:space="preserve">64. </s>
  <s xml:id="echoid-s33421" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33422" xml:space="preserve">42. </s>
  <s xml:id="echoid-s33423" xml:space="preserve">ſi ex C, loco ſtyli deorſum ver <lb/>ſus in recta C F, (vt in præcedenti horologio diximus) numeretur longitudo vmbræ P. </s>
  <s xml:id="echoid-s33424" xml:space="preserve">5. </s>
  <s xml:id="echoid-s33425" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33426" xml:space="preserve">40. <lb/></s>
  <s xml:id="echoid-s33427" xml:space="preserve">reſpondens inuentę altitudini poli, vſque ad H, erit recta H I, ducta ad F G, perpendicularis, linea <lb/>
<anchor type="note" xlink:label="note-0534-04a" xlink:href="note-0534-04"/>
æquinoctialis. </s>
  <s xml:id="echoid-s33428" xml:space="preserve">Quòd ſi ex C, in propoſito exemplo ſurſum verſus in linea F G, ſupputetur lon-<lb/>gitudo vmbræ P. </s>
  <s xml:id="echoid-s33429" xml:space="preserve">25. </s>
  <s xml:id="echoid-s33430" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33431" xml:space="preserve">23. </s>
  <s xml:id="echoid-s33432" xml:space="preserve">reſpondens altitudini poli inuentæ, reperietur M, centrum horolo-<lb/>
<anchor type="note" xlink:label="note-0534-05a" xlink:href="note-0534-05"/>
gii, ita vt recta N O, ſecans F G, in M, ad angulos rectos ſit inſtar lineæ horæ 6. </s>
  <s xml:id="echoid-s33433" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33434" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33435" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s33436" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33437" xml:space="preserve">à<unsure/> qua arcus horarii pro horis computati numerandi erunt. </s>
  <s xml:id="echoid-s33438" xml:space="preserve">Inuenientur autem eadem duo <lb/>puncta H, M, per angulum altitudinis poli inuentæ C P H, &amp; </s>
  <s xml:id="echoid-s33439" xml:space="preserve">complementi eiuſdem C P M, vt in <lb/>ſuperioribus, ſi C P, in recta K L, ſtylo accipiatur æqualis.</s>
  <s xml:id="echoid-s33440" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1699" type="float" level="2" n="1">
<note position="left" xlink:label="note-0534-01" xlink:href="note-0534-01a" xml:space="preserve">Deſcriptio horo <lb/>logii declinãtis <lb/>à mer. in occ.gr. <lb/>10. &amp; ad Horizõ <lb/>tẽ inclinati gr. <lb/>70. ex tabulis.</note>
<note position="left" xlink:label="note-0534-02" xlink:href="note-0534-02a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0534-03" xlink:href="note-0534-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0534-04" xlink:href="note-0534-04a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="left" xlink:label="note-0534-05" xlink:href="note-0534-05a" xml:space="preserve">Cen rum horo-<lb/>logii.</note>
</div>
<note position="left" xml:space="preserve">20</note>
  <figure>
    <image file="0534-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0534-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s33441" xml:space="preserve">LINEÆ horariæ ducentur hic, vt in præcedentibus, ſi à punctis K, L, numerentur latitudi-<lb/>nes vmbrarum, ſuperiores quidem verſus punctum G, &amp; </s>
  <s xml:id="echoid-s33442" xml:space="preserve">inferiores verſus F; </s>
  <s xml:id="echoid-s33443" xml:space="preserve">orientales item à <lb/>puncto L, &amp; </s>
  <s xml:id="echoid-s33444" xml:space="preserve">occidentales à puncto K, &amp;</s>
  <s xml:id="echoid-s33445" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33446" xml:space="preserve">vt in appoſita ſigura cernitur. </s>
  <s xml:id="echoid-s33447" xml:space="preserve">Pro hora autem 1. </s>
  <s xml:id="echoid-s33448" xml:space="preserve">in-<lb/>æquali, quod nullum punctum habet in tropico ♋, vel linea æquinoctiali, ſed ſolum punctum <lb/>Q, in tropico ♑, inueſtigauimus in parallelo ♐, &amp; </s>
  <s xml:id="echoid-s33449" xml:space="preserve">♒, ex eius latitudine vmbræ orientali L R, &amp; </s>
  <s xml:id="echoid-s33450" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0534-09a" xlink:href="note-0534-09"/>
inferiori, vel eius oppoſita K S; </s>
  <s xml:id="echoid-s33451" xml:space="preserve">Item ex longitudine eiuſdem vmbræ P. </s>
  <s xml:id="echoid-s33452" xml:space="preserve">38. </s>
  <s xml:id="echoid-s33453" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33454" xml:space="preserve">15. </s>
  <s xml:id="echoid-s33455" xml:space="preserve">punctum T, ita <lb/>vt recta QT, per puncta Q, &amp; </s>
  <s xml:id="echoid-s33456" xml:space="preserve">T, eiecta indicet horam 1. </s>
  <s xml:id="echoid-s33457" xml:space="preserve">inæqualem. </s>
  <s xml:id="echoid-s33458" xml:space="preserve">Horizontalis vero linea eſt <lb/>
<anchor type="note" xlink:label="note-0534-10a" xlink:href="note-0534-10"/>
ipſamet linea horæ 12. </s>
  <s xml:id="echoid-s33459" xml:space="preserve">inæqualis, cum hac hora Sol oriatur, ac occidat, hoc eſt, exiſtat in Hori-<lb/>zonte. </s>
  <s xml:id="echoid-s33460" xml:space="preserve">Pro qua hora matutina, cum in tropico ♑, Sol oritur, inuenimus punctum V, pro ve-<lb/>ſpertina vero, cum Sol in eodem tropico occidit, reperimus punctum X, necnon in linea æqui-<lb/>noctiali punctum I. </s>
  <s xml:id="echoid-s33461" xml:space="preserve">Hæcautem linea horizontalis, ſiue horæ 12. </s>
  <s xml:id="echoid-s33462" xml:space="preserve">inæqualis per tria inuenta pun-<lb/>cta V, X, I, ducta ſecabit neceſſario rectam D E, ad angulos rectos, ſi nuſquam erratum eſt. </s>
  <s xml:id="echoid-s33463" xml:space="preserve">In ho-<lb/>rologio Aſtronomico, vel Italico, Babylonicove tranſibit eadem linea per illud punctum, vbi hora <lb/>6. </s>
  <s xml:id="echoid-s33464" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33465" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33466" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33467" xml:space="preserve">aut hora 12. </s>
  <s xml:id="echoid-s33468" xml:space="preserve">abor vel occ. </s>
  <s xml:id="echoid-s33469" xml:space="preserve">æquinoctialem lineam interſecat: </s>
  <s xml:id="echoid-s33470" xml:space="preserve">quod quidem <lb/>ſemper erit punctum I. </s>
  <s xml:id="echoid-s33471" xml:space="preserve">Porro ſi longitudo vmbræ Par. </s>
  <s xml:id="echoid-s33472" xml:space="preserve">4. </s>
  <s xml:id="echoid-s33473" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33474" xml:space="preserve">22. </s>
  <s xml:id="echoid-s33475" xml:space="preserve">reſpondens inclinationi plani ad <lb/>Horizontem transferatur à C, ſurſum verſus in recta D E, vſque ad Z, ducenda eſt per Z, linea ho-
<pb o="519" file="0535" n="535" rhead="LIBER QVINTVS."/>
rizontalis ad D E, perpendicularis, Quòd ſi in recta A B, ſumatur C Y, ſtylo æqualis, conſtitua-<lb/>turq́ue angulus complementi inclinationis C Y Z, reperiemus quoque in recta D E, punctum Z, <lb/>per quod linea horizontalis ducenda eſt perpendicularis ad D E, &amp; </s>
  <s xml:id="echoid-s33476" xml:space="preserve">per puncta V, X, I, &amp;</s>
  <s xml:id="echoid-s33477" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s33478" xml:space="preserve">Linea quoque horæ 6. </s>
  <s xml:id="echoid-s33479" xml:space="preserve">inæqualis erit linea meridiana, ita vt producta tranſeat neceſſario per M, <lb/>
<anchor type="note" xlink:label="note-0535-01a" xlink:href="note-0535-01"/>
centrum horologii. </s>
  <s xml:id="echoid-s33480" xml:space="preserve">Quam lineam meridianam ducemus etiam, ſi arcum horarium horę 12. </s>
  <s xml:id="echoid-s33481" xml:space="preserve">à <lb/>med. </s>
  <s xml:id="echoid-s33482" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33483" xml:space="preserve">quem deprehendimus eſſe gr. </s>
  <s xml:id="echoid-s33484" xml:space="preserve">80. </s>
  <s xml:id="echoid-s33485" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33486" xml:space="preserve">45. </s>
  <s xml:id="echoid-s33487" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33488" xml:space="preserve">orientalem, ſuperioremq́ (Quoniam enim <lb/>hora 12. </s>
  <s xml:id="echoid-s33489" xml:space="preserve">meridiei minorem diſtantiam habet à proprio Meridiano horologii, quàm 6. </s>
  <s xml:id="echoid-s33490" xml:space="preserve">horarum, <lb/>cum diſtet tantum, quanta eſt inclinatio Meridiani proprii ad Meridianum Horizontis, nempe <lb/>gr. </s>
  <s xml:id="echoid-s33491" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33492" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33493" xml:space="preserve">52. </s>
  <s xml:id="echoid-s33494" xml:space="preserve">erit arcus horarius ſuperior, hoc eſt, vltra centrum horologii recedet, vt in ſcholio <lb/>præcedentis propoſ. </s>
  <s xml:id="echoid-s33495" xml:space="preserve">ſcripſimus. </s>
  <s xml:id="echoid-s33496" xml:space="preserve">Rurſus quia planum horologii declinat à mer. </s>
  <s xml:id="echoid-s33497" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33498" xml:space="preserve">proiicie-<lb/>
<anchor type="note" xlink:label="note-0535-02a" xlink:href="note-0535-02"/>
tur vinbra ſtyli in meridie verſus occaſum; </s>
  <s xml:id="echoid-s33499" xml:space="preserve">atque adeo arcus horarius horæ 12. </s>
  <s xml:id="echoid-s33500" xml:space="preserve">à med.</s>
  <s xml:id="echoid-s33501" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33502" xml:space="preserve">orien <lb/>talis erit, vt eius vmbra in oppoſitam partem occidentalem cadere poſſit, vt res poſtulat) ſuppute-<lb/>mus in oppoſita parte circuli Na O, ex M, deſcripti, nempe à puncto N, occidentali deorſum ver <lb/>ſus vſque ad b. </s>
  <s xml:id="echoid-s33503" xml:space="preserve">Recta enim M b, erit linea meridiana.</s>
  <s xml:id="echoid-s33504" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1700" type="float" level="2" n="2">
<note position="left" xlink:label="note-0534-09" xlink:href="note-0534-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0534-10" xlink:href="note-0534-10a" xml:space="preserve">Lineal horizon-<lb/>g<unsure/>alia.</note>
<note position="right" xlink:label="note-0535-01" xlink:href="note-0535-01a" xml:space="preserve">Linea meridia-<lb/>na.</note>
<note position="left" xlink:label="note-0535-02" xlink:href="note-0535-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s33505" xml:space="preserve">PRO horologio ſuperiore declinante à mer. </s>
  <s xml:id="echoid-s33506" xml:space="preserve">in ortum gr. </s>
  <s xml:id="echoid-s33507" xml:space="preserve">45. </s>
  <s xml:id="echoid-s33508" xml:space="preserve">ad Horizontem vero inclina-<lb/>to ex parte boreali gr. </s>
  <s xml:id="echoid-s33509" xml:space="preserve">51. </s>
  <s xml:id="echoid-s33510" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33511" xml:space="preserve">51. </s>
  <s xml:id="echoid-s33512" xml:space="preserve">conſectæ ſunt ſequentes tabellę pro horis à mer. </s>
  <s xml:id="echoid-s33513" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33514" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33515" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33516" xml:space="preserve">in <lb/>quibus ſolis exemplum afferemus. </s>
  <s xml:id="echoid-s33517" xml:space="preserve">Quoniam vero Aequator eſt Verticalis proprius huius horo-<lb/>logii, quemadmodum &amp; </s>
  <s xml:id="echoid-s33518" xml:space="preserve">horologii polaris, cõputandæ erunt latitudines vmbrarum à linea æqui-<lb/>noctiali ſurſum quidem verſus pro horis tropici ♋, verſus autem partes inferiores pro horis tro-<lb/>pici ♑, vt in polari horologio diximus: </s>
  <s xml:id="echoid-s33519" xml:space="preserve">quoniam &amp; </s>
  <s xml:id="echoid-s33520" xml:space="preserve">hoc horologium, vt illud, centro caret, cum <lb/>
<anchor type="note" xlink:label="note-0535-03a" xlink:href="note-0535-03"/>
maximus circulus, cui æquidiſtat, per polos mundi ducatur.</s>
  <s xml:id="echoid-s33521" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1701" type="float" level="2" n="3">
<note position="left" xlink:label="note-0535-03" xlink:href="note-0535-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1703" type="section" level="1" n="453">
<head xml:id="echoid-head477" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in ſuperiore horologio declinante à mer. in <lb/>or. grad. 45. &amp; ad Horizontem ex parte boreali inclinato gr. 51. M. 51. <lb/>pro horis à mer. &amp; med. noc. ad latitudinem Gr. 42.</head>
<head xml:id="echoid-head478" xml:space="preserve">In tropico ♋, omnes vmbrarum latitudines ſunt ſuperiores, <lb/>in tropico vero ♑, inferiores.</head>
<note position="right" xml:space="preserve"> <lb/>Hor. ♋, &amp; ♑, à med. no. # 4 # 5 # 6 # 7 # 8 # 9 # *** # orientales. <lb/>
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 23. 33. # 24. 40. # 27. 37. # 33. 25. # 44. 32. # 65. 54. # 90. 0.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 198. 7. # 38. 51. # 20. 14. # 12. 36. # 8. 18. # 5. 50. # 5. 13.
Hor.♋,&amp;♑, à med. no. # 10 # 11 # 12 # A meri \\ die. # 1 # 2 # 3 # occidẽtales
Latitudines vm- \\ brarum. # G. M. # G. M. # G. M. # # G. M. # G. M. # G. M. # G. M.
# 81. 24. # 53. 28. # 38. 2. # # 30. 2. # 25. 51. # 23. 54.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # # P. M. # P. M. # P. M.
# 5. 17. # 6. 52. # 10. 11. # # 15. 49. # 27. 5.<unsure/> # 66. 9.
</note>
</div>
<div xml:id="echoid-div1704" type="section" level="1" n="454">
<head xml:id="echoid-head479" xml:space="preserve">In Aequatore nullæ ſunt vmbrarum latitudines, cum tunc, per propoſ. 11. lib. 1. <lb/>vmbra ſtyli perpetuo cadat in lineam æquinoctialem: <lb/>Earum autem longitudines hæ ſunt.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à me- \\ dia nocte. # 4 # 5 # 6 # 7 # 8 # 9 # *** # orientales. <lb/>
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 181. 29 # 35. 17. # 17. 56. # 10. 31. # 5. 55. # 2. 23. # 0. 0.
Horę ♈, &amp; ♎, à me- \\ dia nocte. # 10 # 11 # 12 # A meri- \\ die. # 1 # 2 # 3 # occidenta.
Longitudines vm- \\ brarum. # P. M. # P. M. # P. M. # # P. M. # P. M. # P. M.
# 0. 48. # 4. 5. # 8. 2. # # 13. 42. # 24. 22. # 60. 31.
</note>
<pb o="520" file="0536" n="536" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s33522" xml:space="preserve">ITAQVE in horologii plano ducta recta A B, quæ in plano ſtabili ac firmo ſit æquidiſtans <lb/>
<anchor type="note" xlink:label="note-0536-01a" xlink:href="note-0536-01"/>
Horizonti, deſcribatur ex C,loco ſtyli aſſumpto circulus cuiuſuis magnitudinis A D B E, in quo <lb/>diameter D E, rectam A B,ſecetad rectos angulos, quæ communis ſectio erit plani horologii, &amp; </s>
  <s xml:id="echoid-s33523" xml:space="preserve"><lb/>maximi circuli inclinationem ad Horizontem metientis. </s>
  <s xml:id="echoid-s33524" xml:space="preserve">Inuento autem, per propoſ. </s>
  <s xml:id="echoid-s33525" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33526" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33527" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s33528" xml:space="preserve">arcu circuli maximi, cui horologium æquidiſtat, inter circulum maximum, qui inclinationem <lb/>metitur, &amp; </s>
  <s xml:id="echoid-s33529" xml:space="preserve">Meridianum proprium horologii interiecto, quem in propoſito exemplo reperimus <lb/>grad-31. </s>
  <s xml:id="echoid-s33530" xml:space="preserve">Min.</s>
  <s xml:id="echoid-s33531" xml:space="preserve">42 numerabimus eum à D, verſus A, ſiue occidentales partes, vſque ad F, quem-<lb/>admodum in in horologio declinante à mer. </s>
  <s xml:id="echoid-s33532" xml:space="preserve">in ortum grad 40. </s>
  <s xml:id="echoid-s33533" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33534" xml:space="preserve">ad Horizontem inclinato gr. </s>
  <s xml:id="echoid-s33535" xml:space="preserve"><lb/>20. </s>
  <s xml:id="echoid-s33536" xml:space="preserve">diximus, propterea quòd &amp; </s>
  <s xml:id="echoid-s33537" xml:space="preserve">hoc horologium declinat à mer. </s>
  <s xml:id="echoid-s33538" xml:space="preserve">in ortum, vt illud. </s>
  <s xml:id="echoid-s33539" xml:space="preserve">Re-<lb/>cta enim ducta F C G, erit linea ſtyli, ſeu communis ſectio horologii, &amp; </s>
  <s xml:id="echoid-s33540" xml:space="preserve">proprii Meridia-<lb/>
<anchor type="note" xlink:label="note-0536-02a" xlink:href="note-0536-02"/>
<anchor type="note" xlink:label="note-0536-03a" xlink:href="note-0536-03"/>
ni ipſius. </s>
  <s xml:id="echoid-s33541" xml:space="preserve">Recta autem K L, ſecans hanc ad angulos rectos erit linea æquinoctialis, hoc <lb/>eſt, communis ſectio plani horologii, atque Aequatoris, à qua latitudines vmbrarum ſuppu-<lb/>tandæ ſunt.</s>
  <s xml:id="echoid-s33542" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1704" type="float" level="2" n="1">
<note position="left" xlink:label="note-0536-01" xlink:href="note-0536-01a" xml:space="preserve">Deſcriptio horo <lb/>logii declinan-<lb/>tis à mer. in or. <lb/>gr. 45. &amp; ad Ho <lb/>rizontrm in@li-<lb/>nati gr. 51. M. <lb/>51.ex tabulis.</note>
<note position="left" xlink:label="note-0536-02" xlink:href="note-0536-02a" xml:space="preserve">Linea f@yli. <lb/>Linea ęquino-<lb/>noctialis.</note>
<note position="left" xlink:label="note-0536-03" xlink:href="note-0536-03a" xml:space="preserve">10</note>
</div>
  <figure>
    <image file="0536-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0536-01"/>
  </figure>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s33543" xml:space="preserve">HORAE deſcribentur ex latitudinibus vmbrarum à punctis K, L, ſupputatis, earumq́ue <lb/>longitudinibus, vt in Meridiano horologio, atque polari; </s>
  <s xml:id="echoid-s33544" xml:space="preserve">eruntq́ue horæ à mer. </s>
  <s xml:id="echoid-s33545" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33546" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33547" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s33548" xml:space="preserve">ad ęquinoctialem lineam perpendiculares, atque inter ſe parallelæ, vt in illis. </s>
  <s xml:id="echoid-s33549" xml:space="preserve">Horizontalis li-<lb/>nea ducenda eſt per punctum H, vbi hora 6. </s>
  <s xml:id="echoid-s33550" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33551" xml:space="preserve">vel med.</s>
  <s xml:id="echoid-s33552" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s33553" xml:space="preserve">ęquinoctialem lineam ſecat, ip-<lb/>
<anchor type="note" xlink:label="note-0536-07a" xlink:href="note-0536-07"/>
ſi A B, parallela, vel ad D E, perpendicularis. </s>
  <s xml:id="echoid-s33554" xml:space="preserve">Quòd ſi in recta D E, ſurſum verſus numeremus <lb/>vmbram P.</s>
  <s xml:id="echoid-s33555" xml:space="preserve">9.</s>
  <s xml:id="echoid-s33556" xml:space="preserve">M.</s>
  <s xml:id="echoid-s33557" xml:space="preserve">26. </s>
  <s xml:id="echoid-s33558" xml:space="preserve">quæ inclinationi planiad Horizontem reſpondet, vſque ad I, ducenda erit <lb/>horizontalis linea per I, &amp;</s>
  <s xml:id="echoid-s33559" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33560" xml:space="preserve">Vel ſi in recta A B, ſumatur C M,ſtylo æqualis, fiatq́ue angulus <lb/>
<anchor type="note" xlink:label="note-0536-08a" xlink:href="note-0536-08"/>
complementi inclinationis C M I, ſecabitur rurſus recta D E, in I, puncto, per quod linea ho-<lb/>tizontalis ducitur, &amp;</s>
  <s xml:id="echoid-s33561" xml:space="preserve">c.</s>
  <s xml:id="echoid-s33562" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1705" type="float" level="2" n="2">
<note position="left" xlink:label="note-0536-07" xlink:href="note-0536-07a" xml:space="preserve">Linea @otlzon-<lb/>@al@s.</note>
<note position="left" xlink:label="note-0536-08" xlink:href="note-0536-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33563" xml:space="preserve">PRO horologio ſuperiore declinante à Septentrionein occaſum grad. </s>
  <s xml:id="echoid-s33564" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33565" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33566" xml:space="preserve">ad Horizontem <lb/>ex parte auſtrali inclinato grad. </s>
  <s xml:id="echoid-s33567" xml:space="preserve">30. </s>
  <s xml:id="echoid-s33568" xml:space="preserve">accipiantur ſubſequentes tabellę pro horis à mer. </s>
  <s xml:id="echoid-s33569" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33570" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s33571" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33572" xml:space="preserve">ſupputatæ. </s>
  <s xml:id="echoid-s33573" xml:space="preserve">In quibus latitudines vmbrarum inferiores ſunt illę, quę citra Verticalem pro-<lb/>prium horologii exiſtunt verſus æquinoctialem lineam, ſuperiores autem illę, quæ vltra eundem <lb/>Verticalem verſus centrum horologii reperiuntur.</s>
  <s xml:id="echoid-s33574" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1707" type="section" level="1" n="455">
<head xml:id="echoid-head480" xml:space="preserve">SEQVVNTVR TABELLAE.</head>
<pb o="521" file="0537" n="537" rhead="LIBER QVINTVS."/>
</div>
<div xml:id="echoid-div1708" type="section" level="1" n="456">
<head xml:id="echoid-head481" xml:space="preserve">Latitudines, longitudinesq́ue vmbrarum in ſuperiore horologi<unsure/>o declinante à ſeptentr. <lb/>in occ. grad. 20. &amp; ad Horizontem ex parte auſtrali inclinato gr. 30. <lb/>pro horis à mer. &amp; med. noc. ad latitudinem Gr. 42.</head>
<head xml:id="echoid-head482" xml:space="preserve">In tropico ♋, ſunt latitudines vmbrarum partim Inferiores, &amp; partim <lb/>ſuperiores, vt tabellæ ipſæ declarant.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à med. nocte. # 2 # 3 # 4 # 5 # 6 # 7 # 8 # orientales \\ &amp; infer. <lb/>Latitudines vm- \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 87. 42. # 73. 59. # 60. 22. # 46. 56. # 33. 38. # 20. 22. # 6. 54. <lb/>
Longitudines vm- \\brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 396. 38 # 262. 36 # 143. 25 # 84. 40. # 55. 2. # 38. 39. # 28. 45.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, a med. nocte. # 9 # 10 # 11 # 12 # A meri \\ die. # 1 # *** # orientales \\ &amp; ſuper. <lb/>Latitudines vm- \\brarum. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M. <lb/># 7. 4. # 21. 49. # 37. 46. # 55. 7. # # 73. 48 # 90. 0. <lb/>Longitudines vm- \\brarum. # P. M. # P. M. # P. M. # P. M. # # P. M. # P. M. <lb/># 22. 23. # 18. 4. # 15. 8. # 13. 13. # # 12. 9. # 11. 53. <lb/></note>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à meridie. # 2 # 3 # 4 # 5 # 6 # 7 # occidentales, &amp; \\ ſuperiores. <lb/>Latitudines vm- \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 86. 46. # 67. 27. # 49. 10. # 32. 18. # 16. 46. # 2. 23. <lb/>Longitudines vm- \\brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 11. 54. # 12. 25. # 13. 45. # 16. 0. # 19. 20. # 24. 14. <lb/></note>
<note position="right" xml:space="preserve"> <lb/>Horę ♋, à mer. # 8 # 9 # 10 # 11 # 12 # A med. \\ nocte. # 1 # *** # occidenta. \\ &amp; inſer <lb/>
Latitudines vm \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M.
# 11. 26. # 24. 47. # 38. 3. # 51. 23. # 64. 53. # # 78. 33. # 90. 0.
Longitudines \\vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # # P. M. # P. M.
# 31. 34. # 43. 8. # 62. 54. # 99. 54. # 175. 17. # # 314. 49 # 400. 29
</note>
</div>
<div xml:id="echoid-div1709" type="section" level="1" n="457">
<head xml:id="echoid-head483" xml:space="preserve">In Aequatore omnes latitudines vmbrarum ſunt ſuperiores, vt tabellæ indicant.</head>
<note position="right" xml:space="preserve"> <lb/>Horę ♈, &amp; ♎, \\à med. nocte. # 8 # 9 # 10 # 11 # 12 # A meri- \\ die. # 1 # *** # orientales \\ &amp; ſuper. <lb/># G. M. # G. M. # G. M. # G. M. # G. M. # # G. M. # G. M. <lb/>
Latitu. vmbra. # 2. 24. # 16. 19. # 30. 36. # 45. 23. # 60. 44. # # 76. 34. # 90. 0.
Longitudines \\vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # # P. M. # P. M.
# 737. 0. # 106. 59 # 58. 59. # 42. 10. # 34. 26. # # 30. 53. # 30. 2.
</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, à mer. # 2 # 3 # 4 # 5 # 6 # 7 # occidenta. &amp; ſuper. <lb/>Latitudines vm- \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 87. 19. # 71. 15. # 55. 33. # 40. 24. # 25. 48. # 11. 38. <lb/>Longitudines vm- \\brarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# 30. 3. # 31. 42. # 36. 26. # 46. 21. # 69. 0. # 149. 10
</note>
<p>
  <s xml:id="echoid-s33575" xml:space="preserve">CADVNT in hoc horologio omnes horæ tropici ♑, in faciem in feriorem horologii, quia <lb/>tropicus ♋, totus ſupra faciem ſuperiorem extat, &amp; </s>
  <s xml:id="echoid-s33576" xml:space="preserve">tropicus ♑, infra. </s>
  <s xml:id="echoid-s33577" xml:space="preserve">Hanc ob cauſam nullas vi-<lb/>des latitudines vmbrarum pro horis tropici ♑, in tabellis poſitas. </s>
  <s xml:id="echoid-s33578" xml:space="preserve">Ex his ſequitur, vmbram gno-<lb/>monis, Sole exiſtente in principio ♋, deſcribere in ſuperiore horologio Ellipſim, quam tamen <lb/>ob locianguſtias integram non effecimus.</s>
  <s xml:id="echoid-s33579" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Deſcriptio horo <lb/>logii declinan-<lb/>tis à ſeptentr. in <lb/>occ.gr. 20. &amp; ad <lb/>Horizõtem in <lb/>clinati gr. 30. e@ <lb/>tabulis.</note>
<p>
  <s xml:id="echoid-s33580" xml:space="preserve">DVCTA ergo in plano horologij recta A B, quæ parallela ſit Horizonti in plano firmo, ac ſta <lb/>bili, deſcribatur ex C, aſſumpto loco ſtyli circulus cuiuſuis magnitudinis ADB, in quo recta DCE, <lb/>rectã A B, in centro ad rectos angulos ſecans ſit cõmunis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s33581" xml:space="preserve">circuli maximi <lb/>inclinationẽ planiad Horizontem metientis. </s>
  <s xml:id="echoid-s33582" xml:space="preserve">Inuento autem, per propoſ. </s>
  <s xml:id="echoid-s33583" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33584" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33585" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33586" xml:space="preserve">arcu circuli ma
<pb o="522" file="0538" n="538" rhead="GNOMONICES"/>
ximi, cui horologiũ parallelum eſt, inter circulũ maximum, qui inclinationem metitur, &amp; </s>
  <s xml:id="echoid-s33587" xml:space="preserve">Meridia <lb/>num horologii propriũ intercepto, quem in dato plano inuenimus eſſe gr. </s>
  <s xml:id="echoid-s33588" xml:space="preserve">43. </s>
  <s xml:id="echoid-s33589" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33590" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33591" xml:space="preserve">ſupputabi-<lb/>mus eum à D, verſus A, ſeu partes orientales horologii, vſq; </s>
  <s xml:id="echoid-s33592" xml:space="preserve">ad F; </s>
  <s xml:id="echoid-s33593" xml:space="preserve">propterea quòd horologiũ datũ <lb/>à ſeptentr. </s>
  <s xml:id="echoid-s33594" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33595" xml:space="preserve">deflectit, caditq́ eius centrũ ſupra lineã æquinoctialem: </s>
  <s xml:id="echoid-s33596" xml:space="preserve">(Vtrum autem centrũ <lb/>ſupra, vel infra lineã æquinoctialem cadat, cognoſcetur exiis, quæ propoſ. </s>
  <s xml:id="echoid-s33597" xml:space="preserve">37. </s>
  <s xml:id="echoid-s33598" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33599" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33600" xml:space="preserve">tradidimus. <lb/></s>
  <s xml:id="echoid-s33601" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0538-01a" xlink:href="fig-0538-01"/>
<anchor type="note" xlink:label="note-0538-01a" xlink:href="note-0538-01"/>
<anchor type="note" xlink:label="note-0538-02a" xlink:href="note-0538-02"/>
<anchor type="note" xlink:label="note-0538-03a" xlink:href="note-0538-03"/>
Quando enim arcus Meridiani inter Horizontem, &amp; </s>
  <s xml:id="echoid-s33602" xml:space="preserve">planũ ex parte auſtrali inclinatũ minor eſt <lb/>cõplemento altitudinis poli, vt in noſtro exẽplo cõtingit, cũ dictus arcus, ex propoſ. </s>
  <s xml:id="echoid-s33603" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33604" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33605" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33606" xml:space="preserve">inue-<lb/>ſtigatus cõtineat gr. </s>
  <s xml:id="echoid-s33607" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33608" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33609" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33610" xml:space="preserve">cadet centrũ horologii ſupra lineã æquinoctialem; </s>
  <s xml:id="echoid-s33611" xml:space="preserve">quãdo vero idẽ <lb/>arcus æqualis eſt, vel maior cõplemento altitudinis poli, infra, vt in dicta propoſ. </s>
  <s xml:id="echoid-s33612" xml:space="preserve">diximus in ſe-<lb/>cunda cõſtructione horologij declinantis ſimul &amp; </s>
  <s xml:id="echoid-s33613" xml:space="preserve">inclinati.) </s>
  <s xml:id="echoid-s33614" xml:space="preserve">Recta enim F C, erit linea ſtyli, id <lb/>
<anchor type="note" xlink:label="note-0538-04a" xlink:href="note-0538-04"/>
eſt, cõmunis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s33615" xml:space="preserve">Meridiani ipſius proprii. </s>
  <s xml:id="echoid-s33616" xml:space="preserve">Nã ſi horologium in proprio ſitu <lb/>collocetur, ſi quidé à ſeptentr. </s>
  <s xml:id="echoid-s33617" xml:space="preserve">declinet in occ. </s>
  <s xml:id="echoid-s33618" xml:space="preserve">cadet punctũ E, in quadrantem hemiſphærij ſuperi <lb/>auſtralẽ, orientalemq́;</s>
  <s xml:id="echoid-s33619" xml:space="preserve">, &amp; </s>
  <s xml:id="echoid-s33620" xml:space="preserve">punctũ D, in quadrantem in ſeri hemiſphærij borealem, &amp; </s>
  <s xml:id="echoid-s33621" xml:space="preserve">occidentalẽ, <lb/>ita vt, nobis ad horologiũ conuerſis, polus arcticus ſit ad ſiniſtrã puncti D. </s>
  <s xml:id="echoid-s33622" xml:space="preserve">Quare ſi circulus maxi-<lb/>
<anchor type="note" xlink:label="note-0538-05a" xlink:href="note-0538-05"/>
mus inclinationẽ metiens per rectam D E, &amp; </s>
  <s xml:id="echoid-s33623" xml:space="preserve">ſtylũ ductus intelligatur moueri circa ſtylum in C, <lb/>collocatũ donec per polum arcticũ tranſeat, hoc eſt, donec cum Meridiano proprio horologij cõ-<lb/>iungatur, faciet omnino cũ horologio ſectionem, quę infra ſtylum inter puncta A, D, cadet, qua-<lb/>lis eſt D C E, &amp;</s>
  <s xml:id="echoid-s33624" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33625" xml:space="preserve">Contrariũ accidet, ſi planum à ſeptentr. </s>
  <s xml:id="echoid-s33626" xml:space="preserve">in ortũ deflectat, &amp; </s>
  <s xml:id="echoid-s33627" xml:space="preserve">centrũ horologij ſit <lb/>ſupra ſtylum. </s>
  <s xml:id="echoid-s33628" xml:space="preserve">A recta igitur G H, rectã F C, in C, ad angulos rectos ſecante cõputandæ erunt lati-<lb/>tudines vmbrarum, tanquam à cõmuni ſectione plani horologii, &amp; </s>
  <s xml:id="echoid-s33629" xml:space="preserve">proprii Verticalis ipſius. </s>
  <s xml:id="echoid-s33630" xml:space="preserve">Parata <lb/>autem linea H I, in partes gnomoni æquales diuiſa, vtſupra, inuentaq́; </s>
  <s xml:id="echoid-s33631" xml:space="preserve">per propoſ. </s>
  <s xml:id="echoid-s33632" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33633" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33634" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33635" xml:space="preserve">altitu <lb/>dine poli ſupta planũ horologii, quã in noſtro exemplo deprehendimus eſſe gr. </s>
  <s xml:id="echoid-s33636" xml:space="preserve">68. </s>
  <s xml:id="echoid-s33637" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33638" xml:space="preserve">13. </s>
  <s xml:id="echoid-s33639" xml:space="preserve">eiusq́ue <lb/>cõplementum gr. </s>
  <s xml:id="echoid-s33640" xml:space="preserve">21. </s>
  <s xml:id="echoid-s33641" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33642" xml:space="preserve">47. </s>
  <s xml:id="echoid-s33643" xml:space="preserve">Si ex C, loco ſtyli deorſum verſus in linea ſtyli (quoniã centrũ horo-<lb/>logii, vt diximus, ſupra ſtylũ cadit, &amp; </s>
  <s xml:id="echoid-s33644" xml:space="preserve">æquinoctialis linea infra) numererur vmbra P. </s>
  <s xml:id="echoid-s33645" xml:space="preserve">30. </s>
  <s xml:id="echoid-s33646" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33647" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33648" xml:space="preserve">quã-<lb/>
<anchor type="note" xlink:label="note-0538-06a" xlink:href="note-0538-06"/>
tam requirit cõplementum altitudinis poli inuentæ, vſq; </s>
  <s xml:id="echoid-s33649" xml:space="preserve">ad I, erit recta I K, ducta per I, ad F C, <lb/>perpendicularis, linea æquinoctialis Et ſi ex C,ſurſum verſus vſq; </s>
  <s xml:id="echoid-s33650" xml:space="preserve">ad L, numeretur vmbra P. </s>
  <s xml:id="echoid-s33651" xml:space="preserve">4 M. <lb/></s>
  <s xml:id="echoid-s33652" xml:space="preserve">
<anchor type="note" xlink:label="note-0538-07a" xlink:href="note-0538-07"/>
48. </s>
  <s xml:id="echoid-s33653" xml:space="preserve">reſpondens altitudini poli inuentæ, inuenietur L, centrum horologii, ita vt à recta M L, ad FL, <lb/>
<anchor type="note" xlink:label="note-0538-08a" xlink:href="note-0538-08"/>
perpendiculari in circulo M N, ex L, deſcripto numerandi ſint arcus horarij, ſi pro ſingulis horis <lb/>ſupputẽtur. </s>
  <s xml:id="echoid-s33654" xml:space="preserve">Duo aũt puncta I, L, inuenientur quoq; </s>
  <s xml:id="echoid-s33655" xml:space="preserve">ex angulo C P I, altitudinis poli inuẽtę, &amp; </s>
  <s xml:id="echoid-s33656" xml:space="preserve">an-<lb/>gulo C P L, complementi eiuſdem altitudinis, ſi in recta G H, abſcindatur C P, ſtylo æqualis.</s>
  <s xml:id="echoid-s33657" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1709" type="float" level="2" n="1">
  <figure xlink:label="fig-0538-01" xlink:href="fig-0538-01a">
    <image file="0538-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0538-01"/>
  </figure>
<note position="left" xlink:label="note-0538-01" xlink:href="note-0538-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0538-02" xlink:href="note-0538-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0538-03" xlink:href="note-0538-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0538-04" xlink:href="note-0538-04a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0538-05" xlink:href="note-0538-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0538-06" xlink:href="note-0538-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0538-07" xlink:href="note-0538-07a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="left" xlink:label="note-0538-08" xlink:href="note-0538-08a" xml:space="preserve">Centrum horo <lb/>logii.</note>
</div>
<p>
  <s xml:id="echoid-s33658" xml:space="preserve">IN horarũ deſcriptione nulla difficultas eſt, ſi à punctis G, H, rectè ſupputentur latitudines vm <lb/>brarũ, &amp;</s>
  <s xml:id="echoid-s33659" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33660" xml:space="preserve">vt in appoſita figura manifeſtũ eſt, in qua, quia circulus A D B, integre nõ potuit deſcri <lb/>bi, numerauimus latitudines vmbrarũ ſuperiores, &amp; </s>
  <s xml:id="echoid-s33661" xml:space="preserve">orientales à puncto H, occidentali deorſum <lb/>verſus, occidentales autẽ à G, puncto oriẽtali. </s>
  <s xml:id="echoid-s33662" xml:space="preserve">Vt pro latitudine vmbræ horæ 10. </s>
  <s xml:id="echoid-s33663" xml:space="preserve">á med. </s>
  <s xml:id="echoid-s33664" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33665" xml:space="preserve">in tro-<lb/>pico ♋, quæ orientalis eſt, &amp; </s>
  <s xml:id="echoid-s33666" xml:space="preserve">ſuperior, cõtinetq́ gr. </s>
  <s xml:id="echoid-s33667" xml:space="preserve">21. </s>
  <s xml:id="echoid-s33668" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33669" xml:space="preserve">49. </s>
  <s xml:id="echoid-s33670" xml:space="preserve">accepimus occidentalem, &amp; </s>
  <s xml:id="echoid-s33671" xml:space="preserve">inferio-
<pb o="523" file="0539" n="539" rhead="LIBER QVINTVS."/>
rem<unsure/> H Q, &amp; </s>
  <s xml:id="echoid-s33672" xml:space="preserve">ex longitudine vmbræ P. </s>
  <s xml:id="echoid-s33673" xml:space="preserve">18. </s>
  <s xml:id="echoid-s33674" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33675" xml:space="preserve">4. </s>
  <s xml:id="echoid-s33676" xml:space="preserve">inuenimus punctũ R, pro hora 10. </s>
  <s xml:id="echoid-s33677" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s33678" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33679" xml:space="preserve">in <lb/>tropico ♋, &amp;</s>
  <s xml:id="echoid-s33680" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33681" xml:space="preserve">Horizontalis linea ducitur ex puncto k, vbi hora 6. </s>
  <s xml:id="echoid-s33682" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33683" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33684" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33685" xml:space="preserve">æquinoctia <lb/>
<anchor type="note" xlink:label="note-0539-01a" xlink:href="note-0539-01"/>
lem lineã ſecat, ipſi A B, parallela, vel ad D E, perpendicularis, quæ omnino trãſibit per E, punctũ, <lb/>quod in recta D E, terminat C E, longitudinẽ vmbræ P. </s>
  <s xml:id="echoid-s33686" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33687" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33688" xml:space="preserve">47. </s>
  <s xml:id="echoid-s33689" xml:space="preserve">quæ inclinationi plani ad Hori-<lb/>zontem reſpondet. </s>
  <s xml:id="echoid-s33690" xml:space="preserve">Quod punctũ inuenietur quoque, ſi in recta A B, ſumatur C S, ſtylo æqualis, <lb/>ſ<unsure/>iatq́; </s>
  <s xml:id="echoid-s33691" xml:space="preserve">angulus C S E, cõplementi inclinationis. </s>
  <s xml:id="echoid-s33692" xml:space="preserve">Hora porro 12. </s>
  <s xml:id="echoid-s33693" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33694" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33695" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33696" xml:space="preserve">dabit lineã me-<lb/>
<anchor type="note" xlink:label="note-0539-02a" xlink:href="note-0539-02"/>
ridianã quæ neceſſario trãſibit per punctũ O, quod in circulo M N, terminat arcũ horariũ M O, <lb/>gr. </s>
  <s xml:id="echoid-s33697" xml:space="preserve">64. </s>
  <s xml:id="echoid-s33698" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33699" xml:space="preserve">12. </s>
  <s xml:id="echoid-s33700" xml:space="preserve">qui horæ 12. </s>
  <s xml:id="echoid-s33701" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33702" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33703" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33704" xml:space="preserve">cõuenit: </s>
  <s xml:id="echoid-s33705" xml:space="preserve">quæ quidem linea meridiana in noſtro ho <lb/>rologio erit occidentalior, quàm linea ſtyli F C, propterea quòd planũ horologii in occaſum decli <lb/>nat. </s>
  <s xml:id="echoid-s33706" xml:space="preserve">Hinc enim fit, vt in meridie vmbra ſtyli proiiciatur verſus partes horologii occidentales.</s>
  <s xml:id="echoid-s33707" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1710" type="float" level="2" n="2">
<note position="right" xlink:label="note-0539-01" xlink:href="note-0539-01a" xml:space="preserve">Linea horizon-<lb/>talis.</note>
<note position="right" xlink:label="note-0539-02" xlink:href="note-0539-02a" xml:space="preserve">Linea meridiz-<lb/>na.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s33708" xml:space="preserve">PRO horologio Superiore declinante à ſeptentr. </s>
  <s xml:id="echoid-s33709" xml:space="preserve">in ortũ gr. </s>
  <s xml:id="echoid-s33710" xml:space="preserve">60. </s>
  <s xml:id="echoid-s33711" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33712" xml:space="preserve">ad Horizontẽ ex parte au-<lb/>ſtrali inclinato gr. </s>
  <s xml:id="echoid-s33713" xml:space="preserve">80. </s>
  <s xml:id="echoid-s33714" xml:space="preserve">ſubſequentes tabulæ cõſtructæ ſunt pro horis ab occ. </s>
  <s xml:id="echoid-s33715" xml:space="preserve">In quibus latitudines <lb/>vmbrarũ ſuperiores ſunt illæ, quæ citra Verticalẽ propriũ horologij, &amp; </s>
  <s xml:id="echoid-s33716" xml:space="preserve">verſus lineã æquinoctialẽ <lb/>exiſtũt, inferiores aũt illę, quę vltra eundẽ Verticalem, &amp; </s>
  <s xml:id="echoid-s33717" xml:space="preserve">verſus centrũ in horologio reperiuntur.</s>
  <s xml:id="echoid-s33718" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1712" type="section" level="1" n="458">
<head xml:id="echoid-head484" xml:space="preserve">Latitudines, longitudinesq́ vmbrarum in horologio ſuperiore declinante à ſeptentr. in <lb/>or. grad. 60. &amp; ad Horizontem ex parte auſtrali inclinato grad. 80. <lb/>pro horis ab occ. ad latitudinem Grad. 42.</head>
<head xml:id="echoid-head485" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim Superiores ſunt, &amp; partim Inferiores, <lb/>vt hæ ſyllabæ [Super, Infer.] declarant.</head>
<note position="left" xml:space="preserve">20</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 3 Super. # 4 \\ Super. # 5 \\ Super. # 6 \\ Super. # 7 \\ Super. # 8 \\ Infer. # 9 \\ Infer. # *** # occidentales. <lb/>Latitudines vm \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 24. 19. # 18. 11. # 12. 40. # 7. 17. # 1. 30. # 6. 39. # 30. 4. # 90. 0. <lb/>Longitudines \\vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 155. 58. # 39. 52. # 21. 11. # 13. 3. # 8. 9. # 4. 35. # 1. 44. # 0. 55. <lb/></note>
<note position="left" xml:space="preserve">30</note>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, ab \\ occaſu. # 10 \\ Infer. # 11 \\ Infer. # 12 \\ Super. # 13 \\ Super. # 14 \\ Super. # 15 \\ Super. # 16 \\ Super. # # orientales. <lb/>Latitudines vm \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 31. 54. # 7. 5. # 1. 33. # 7. 6. # 12. 28. # 17. 59. # 24. 4 <lb/>Longitudines \\vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 1. 39. # 4. 20. # 8. 0. # 12. 50. # 20. 47. # 38. 46. # 141. 5@. <lb/></note>
</div>
<div xml:id="echoid-div1713" type="section" level="1" n="459">
<head xml:id="echoid-head486" xml:space="preserve">In Aequatore omnes latitudines vmbrarum ſunt inferiores, occidentales vero <lb/>ab orientalibus diſtinguuntur his ſyllabis [or. occ.]</head>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>Hor. ♈, \\ &amp; ♎, ab \\ occaſu. # 6 \\ occ. # 7 \\ occ. # 8 \\ occ. # 9 \\ occ. # 10 \\ occ. # 11 \\ occ. # 12 \\ or. # 13 \\ or. # 14 \\ or. # 15 \\ or. # 16 \\ or. # 17 \\ or. <lb/>Latitu. \\vmbra. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 6. 46. # 14. 39. # 24. 27. # 38. 6. # 58. 51. # 88. 22. # 61. 29. # 9. 51. # 25. 37. # 15. 31. # 7. 31. # 0. 15. <lb/>Longit. \\vmbra. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 53. 54. # 25. 4. # 15. 19. # 10. 16. # 7. 24. # 6. 20. # 7. 13. # 9. 54. # 14. 39. # 23. 39. # 48. 29. # 1006. 38 <lb/></note>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1714" type="section" level="1" n="460">
<head xml:id="echoid-head487" xml:space="preserve">In tropico ♑, omnes vmbrarum latitudines ſunt inferiores, occidentales autem <lb/>ab orientalibus per has ſyllabas [or. occ.] ſegregantur.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♑, ab \\ occaſu. # 8 \\ occ. # 9 \\ occ. # 10 \\ occ. # 11 \\ occ. # 12 \\ occ. # *** # 13 \\ or. # 14 \\ or. # 15 \\ or. # 16 \\ or. # 17 \\ or. <lb/>Latitudines vm \\brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 30. 43. # 39. 19. # 50. 5. # 63. 36. # 79. 47. # 90. 0. # 82. 43. # 66. 10. # 52. 10. # 40. 58. # 32. 10. <lb/>Longitudines \\vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 111. 4. # 39. 48. # 24. 4. # 17. 56. # 15. 23. # 15. 0. # 15. 11. # 17. 19. # 22. 40. # 35. 19. # 84. 30. <lb/></note>
<pb o="524" file="0540" n="540" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s33719" xml:space="preserve">SIT igitur in plano horologii ducta recta A B, ita vt in plano ſtabili parallela ſit Horizõti, in <lb/>
<anchor type="note" xlink:label="note-0540-01a" xlink:href="note-0540-01"/>
qua ex aſſumpto loco ſtyli C, deſcribatur circulus cuiuſcunq; </s>
  <s xml:id="echoid-s33720" xml:space="preserve">magnitudinis A D B E, ſecetq́; </s>
  <s xml:id="echoid-s33721" xml:space="preserve">recta <lb/>DE, rectã A B, in centro ad angulos rectos, quæ cõmunis ſectio erit plani horologii, &amp; </s>
  <s xml:id="echoid-s33722" xml:space="preserve">circuli ma-<lb/>
<anchor type="figure" xlink:label="fig-0540-01a" xlink:href="fig-0540-01"/>
<anchor type="note" xlink:label="note-0540-02a" xlink:href="note-0540-02"/>
<anchor type="note" xlink:label="note-0540-03a" xlink:href="note-0540-03"/>
ximi inclinationẽ plani ad Horizontẽ metiẽtis. </s>
  <s xml:id="echoid-s33723" xml:space="preserve">Inuẽto autem, per propoſ. </s>
  <s xml:id="echoid-s33724" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33725" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33726" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33727" xml:space="preserve">arcu circuli ma <lb/>
<anchor type="note" xlink:label="note-0540-04a" xlink:href="note-0540-04"/>
ximi, cui horologiũ æquidiſtat, inter circulũ maximũ qui inclinationẽ metitur, &amp; </s>
  <s xml:id="echoid-s33728" xml:space="preserve">Meridianũ pro-<lb/>priũ horologii interpoſito, quẽ in dato exẽplo deprehẽdimus eſſe gr. </s>
  <s xml:id="echoid-s33729" xml:space="preserve">47, M. </s>
  <s xml:id="echoid-s33730" xml:space="preserve">0. </s>
  <s xml:id="echoid-s33731" xml:space="preserve">numerabimus eum <lb/>à D, nõ verſus occaſum B, vt in pręcedẽti horologio diximus, licet horologiũ à ſeptentr. </s>
  <s xml:id="echoid-s33732" xml:space="preserve">in ortum <lb/>declinet, quia centrũ horologii cadit infra ſtylũ cũ arcus Meridiani inter Horizontẽ &amp; </s>
  <s xml:id="echoid-s33733" xml:space="preserve">planũ ho-<lb/>rologii maior ſit cõplemẽto altitudinis poli, cõplectens nimirũ gr. </s>
  <s xml:id="echoid-s33734" xml:space="preserve">72. </s>
  <s xml:id="echoid-s33735" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33736" xml:space="preserve">57. </s>
  <s xml:id="echoid-s33737" xml:space="preserve">ſed à D, verſus ortũ <lb/>A, vſq; </s>
  <s xml:id="echoid-s33738" xml:space="preserve">ad F, &amp; </s>
  <s xml:id="echoid-s33739" xml:space="preserve">ſi horologiũ declinet à ſeptentr. </s>
  <s xml:id="echoid-s33740" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33741" xml:space="preserve">cuius centrũ ſit infra lineã ęquinoctialẽ, vel <lb/>ſtylum, à D, verſus occaſum B. </s>
  <s xml:id="echoid-s33742" xml:space="preserve">Recta enim ducta F C G, erit linea ſtyli, ſiue cõmunis ſectio plani <lb/>
<anchor type="note" xlink:label="note-0540-05a" xlink:href="note-0540-05"/>
horologii, &amp; </s>
  <s xml:id="echoid-s33743" xml:space="preserve">Meridiani proprii ipſius. </s>
  <s xml:id="echoid-s33744" xml:space="preserve">Nã cõſtituto horologio in proprio ſitu, ita vt punctũ E, ca-<lb/>dat in quadrantem hemiſphærii ſuperi occidentalẽ, &amp; </s>
  <s xml:id="echoid-s33745" xml:space="preserve">auſtralem, ſi horologiũ à ſeptentr. </s>
  <s xml:id="echoid-s33746" xml:space="preserve">in ortum <lb/>declinet, quoniã centrũ horologii infra ſtylũ cadit, erit omnino axis mũdi ad planũ horologii in-<lb/>clinatus inter puncta B, &amp; </s>
  <s xml:id="echoid-s33747" xml:space="preserve">E, quemadmodũ, quãdo centrũ ſupra ſtylũ cadit, &amp; </s>
  <s xml:id="echoid-s33748" xml:space="preserve">horologiũ à ſeptẽtr. <lb/></s>
  <s xml:id="echoid-s33749" xml:space="preserve">
<anchor type="note" xlink:label="note-0540-06a" xlink:href="note-0540-06"/>
in ortũ deflectit, inter puncta B, &amp; </s>
  <s xml:id="echoid-s33750" xml:space="preserve">E, inclinatus eſt ad planũ horologii, cũ neceſlario axis mundi <lb/>per verticẽ ſtyli incedat. </s>
  <s xml:id="echoid-s33751" xml:space="preserve">Id quod cuilibet, qui ſitũ horologii, centri ipſius, &amp; </s>
  <s xml:id="echoid-s33752" xml:space="preserve">axis mundi paulo at-<lb/>tentius inſpexerit, perſpicuũ eſſe poteſt. </s>
  <s xml:id="echoid-s33753" xml:space="preserve">Igitur ſi cogitetur circulus maximus inclinationem me-<lb/>tiens per rectã D E, ductus moueri circa ſtylũ rectũ ad horologiũ, donec per polos mundi, atque <lb/>adeo peraxem mundi trãſeat, habebit omnino eũ ſitũ, vt planũ horologii ſecet inter puncta B, &amp; </s>
  <s xml:id="echoid-s33754" xml:space="preserve"><lb/>E, atq; </s>
  <s xml:id="echoid-s33755" xml:space="preserve">adeo inter A, &amp; </s>
  <s xml:id="echoid-s33756" xml:space="preserve">D, propter inclinationem axis inter eadem puncta, vt dictũ eſt. </s>
  <s xml:id="echoid-s33757" xml:space="preserve">Cõtrarium <lb/>his fiet in plano declinante à ſeptentr. </s>
  <s xml:id="echoid-s33758" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s33759" xml:space="preserve">ſi centrũ horologii cadat infra ſtylũ, ſeulineã æquino <lb/>ctialem. </s>
  <s xml:id="echoid-s33760" xml:space="preserve">A recta autem H I, ſecãte rectã F G, in centro ad angulos rectos ſupputãdæ erunt vmbra-<lb/>rũ latitudines. </s>
  <s xml:id="echoid-s33761" xml:space="preserve">Præparata iam linea H I, diuiſa in partes gnomoni ęquales, vt ſupra dictum eſt, in-<lb/>uentaq́;</s>
  <s xml:id="echoid-s33762" xml:space="preserve">, per propoſ. </s>
  <s xml:id="echoid-s33763" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33764" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33765" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33766" xml:space="preserve">altitudine poli ſupra planũ horologii, quã in propoſito exẽplo repe <lb/>
<anchor type="note" xlink:label="note-0540-07a" xlink:href="note-0540-07"/>
rimus eſſe gr. </s>
  <s xml:id="echoid-s33767" xml:space="preserve">27. </s>
  <s xml:id="echoid-s33768" xml:space="preserve">M, 50. </s>
  <s xml:id="echoid-s33769" xml:space="preserve">ac propterea cõplementũ eiuſdẽ gr. </s>
  <s xml:id="echoid-s33770" xml:space="preserve">62. </s>
  <s xml:id="echoid-s33771" xml:space="preserve">M 10. </s>
  <s xml:id="echoid-s33772" xml:space="preserve">ſi ex C, loco ſtyli in lineã ſty <lb/>li ſursũ verſus (quoniã centrũ horologii, vt diximus, cadit infra ſtylũ, &amp; </s>
  <s xml:id="echoid-s33773" xml:space="preserve">ęquinoctialis linea ſupra) <lb/>cõputemus vmbrã P. </s>
  <s xml:id="echoid-s33774" xml:space="preserve">6. </s>
  <s xml:id="echoid-s33775" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33776" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33777" xml:space="preserve">cõgruentẽ cõplemento altitudinis poli inuentæ vſq; </s>
  <s xml:id="echoid-s33778" xml:space="preserve">ad K, dabit re-<lb/>cta K L, ad F G, perpendicularis lineã ęquinoctialem. </s>
  <s xml:id="echoid-s33779" xml:space="preserve">Et ſi deorſum verſus numeremus vmbrã P. <lb/></s>
  <s xml:id="echoid-s33780" xml:space="preserve">
<anchor type="note" xlink:label="note-0540-08a" xlink:href="note-0540-08"/>
22. </s>
  <s xml:id="echoid-s33781" xml:space="preserve">M 44. </s>
  <s xml:id="echoid-s33782" xml:space="preserve">offendemus M, centrũ horologii, ita vt à recta MN, ſecãte rectã F G, ad angulos rectos <lb/>
<anchor type="note" xlink:label="note-0540-09a" xlink:href="note-0540-09"/>
numerãdi ſint arcus horarii, ſi ſupputati ſint ad ſingulas horas, in circulo NO, ex M, deſcripto. </s>
  <s xml:id="echoid-s33783" xml:space="preserve">Ve-<lb/>rũ duo pũcta k, M, inueniẽtur etiã alio modo, ſi in recta HI, sũpta linea CP, ſtylo ęquali, cõſtituatur <lb/>angulus C P K, altitudinis poli inuentæ, &amp; </s>
  <s xml:id="echoid-s33784" xml:space="preserve">angulus C P M, cõplementi eiuſdem altitudinis poli.</s>
  <s xml:id="echoid-s33785" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1714" type="float" level="2" n="1">
<note position="left" xlink:label="note-0540-01" xlink:href="note-0540-01a" xml:space="preserve">Deſcriptio horo <lb/>logii declinan-<lb/>tis à ſeptentr. in <lb/>or. gr. 60. &amp; ad <lb/>Ho@ izõtem in-<lb/>clinati gr. 80. ex <lb/>tabulis.</note>
  <figure xlink:label="fig-0540-01" xlink:href="fig-0540-01a">
    <image file="0540-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0540-01"/>
  </figure>
<note position="left" xlink:label="note-0540-02" xlink:href="note-0540-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0540-03" xlink:href="note-0540-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0540-04" xlink:href="note-0540-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0540-05" xlink:href="note-0540-05a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0540-06" xlink:href="note-0540-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0540-07" xlink:href="note-0540-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0540-08" xlink:href="note-0540-08a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="left" xlink:label="note-0540-09" xlink:href="note-0540-09a" xml:space="preserve">Centrum horo <lb/>logii.</note>
</div>
<p>
  <s xml:id="echoid-s33786" xml:space="preserve">FACILIS autẽ eſt deſcriptio horarũ ex poſitis tabellis, ſi à punctis HI, cõputẽtur latitudines <lb/>vmbrarũ, obſeruãdo diligenter, quæ oriẽtales ſint, occidẽtalesve, &amp; </s>
  <s xml:id="echoid-s33787" xml:space="preserve">quæ ſuperiores, aut inferiores, <lb/>vt in appoſita figura cernitur. </s>
  <s xml:id="echoid-s33788" xml:space="preserve">Linea horizõtalis ducitur per punctũ R, vbi hora 12. </s>
  <s xml:id="echoid-s33789" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33790" xml:space="preserve">vel occ. <lb/></s>
  <s xml:id="echoid-s33791" xml:space="preserve">
<anchor type="note" xlink:label="note-0540-10a" xlink:href="note-0540-10"/>
<pb o="525" file="0541" n="541" rhead="LIBER QVINTVS."/>
vel hora 6. </s>
  <s xml:id="echoid-s33792" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33793" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33794" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33795" xml:space="preserve">ęquinoctialẽ lineã interſecat, parallela recta A B, vel ad D E, perpẽ-<lb/>dicularis, quæ neceſſario per punctũ a, trãſibit, quod in recta D E, terminat vmbrã P. </s>
  <s xml:id="echoid-s33796" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33797" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33798" xml:space="preserve">7. </s>
  <s xml:id="echoid-s33799" xml:space="preserve">incli-<lb/>nationi ad Horizontẽ congruentẽ. </s>
  <s xml:id="echoid-s33800" xml:space="preserve">Inueniemus autẽ idem punctũ a, ſi in A B, ſumpta recta C Q. <lb/></s>
  <s xml:id="echoid-s33801" xml:space="preserve">ſtylo æquali, conſtituamus angulum C Q a, cõplemento inclinationis ad Horizontẽ æqualẽ. </s>
  <s xml:id="echoid-s33802" xml:space="preserve">Meri-<lb/>diana quoque linea, ſi eã in horologio depingere lubeat, ducẽda eſt perM, centrũ horologii, &amp; </s>
  <s xml:id="echoid-s33803" xml:space="preserve">per <lb/>punctũ L, vbi hora 6. </s>
  <s xml:id="echoid-s33804" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s33805" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s33806" xml:space="preserve">æquinoctialẽ lineã diuidit. </s>
  <s xml:id="echoid-s33807" xml:space="preserve">Quod ſi forte punctũ L, ob angu-<lb/>ſtiam loci, haberi nõ poſſit, inquirendus erit arcus horarius horæ 12. </s>
  <s xml:id="echoid-s33808" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33809" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33810" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33811" xml:space="preserve">cuius di <lb/>ſtantia à Meridiano proprio eadẽ eſt, quæ inclinatio Meridiani proprij ad Meridianũ Horizõtis. </s>
  <s xml:id="echoid-s33812" xml:space="preserve"><lb/>Hunc inuenimus cõtinere gr. </s>
  <s xml:id="echoid-s33813" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33814" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33815" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33816" xml:space="preserve">Et quoniam planũ horologij ſecat quadrantem Æquato-<lb/>ris orientalem ſupra Horizontem, cũ arcus inter ipſum, &amp; </s>
  <s xml:id="echoid-s33817" xml:space="preserve">Horizontem maior ſit cõplemento alti <lb/>
<anchor type="note" xlink:label="note-0541-01a" xlink:href="note-0541-01"/>
tudinis poli, ac proinde quadrantem occidentalem ſub Horizõte, nõ illuminabit Sol faciem ſupe <lb/>riorem plani in Æquatore, ac Meridiano ſupra Horizontem conſtitutus, ſed cum infra Horizontẽ <lb/>exiſtet in Æ quatore, &amp; </s>
  <s xml:id="echoid-s33818" xml:space="preserve">Meridiano, niſi à terra impediretur, ac propterea vmbra ſtyli tũc cadet ver <lb/>ſus oriẽtales partes in linea æquinoctiali, puta verſus L. </s>
  <s xml:id="echoid-s33819" xml:space="preserve">Quare dictũ arcũ ſupputabimus ab N, vſq; <lb/></s>
  <s xml:id="echoid-s33820" xml:space="preserve">ad S, punctũ, per quod meridiana linea ducenda eſt. </s>
  <s xml:id="echoid-s33821" xml:space="preserve">Deſcripſimus autem illas etiam horas ab occ. </s>
  <s xml:id="echoid-s33822" xml:space="preserve"><lb/>quæ infra Horizontem ſunt, ſupra tamen planũ horologij, quales ſunt 8. </s>
  <s xml:id="echoid-s33823" xml:space="preserve">7. </s>
  <s xml:id="echoid-s33824" xml:space="preserve">6. </s>
  <s xml:id="echoid-s33825" xml:space="preserve">5. </s>
  <s xml:id="echoid-s33826" xml:space="preserve">4. </s>
  <s xml:id="echoid-s33827" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s33828" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33829" xml:space="preserve">vt earũ poſi-<lb/>tio conſideretur, duximusq́; </s>
  <s xml:id="echoid-s33830" xml:space="preserve">horã 5. </s>
  <s xml:id="echoid-s33831" xml:space="preserve">quæ nullũ punctũ habet in tropico ♑, vel linea æquinoctiali, <lb/>per punctũ in tropico ♋, inuentũ, &amp; </s>
  <s xml:id="echoid-s33832" xml:space="preserve">per punctũ e, vbi hora 7. </s>
  <s xml:id="echoid-s33833" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s33834" xml:space="preserve">lineã hora 6. </s>
  <s xml:id="echoid-s33835" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33836" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33837" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s33838" xml:space="preserve">ſecat per centrũ M, &amp; </s>
  <s xml:id="echoid-s33839" xml:space="preserve">per punctũ R, ductam, vt cõſtat ex tabula lineæ horæ 6. </s>
  <s xml:id="echoid-s33840" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33841" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33842" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s33843" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s33844" xml:space="preserve">20. </s>
  <s xml:id="echoid-s33845" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33846" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33847" xml:space="preserve">Sic etiam horam 4. </s>
  <s xml:id="echoid-s33848" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s33849" xml:space="preserve">ductam eſſe vides per punctũ in tropico ♋, inuẽ-<lb/>
<anchor type="note" xlink:label="note-0541-02a" xlink:href="note-0541-02"/>
tum, &amp; </s>
  <s xml:id="echoid-s33850" xml:space="preserve">per punctum f, in linea horæ 6. </s>
  <s xml:id="echoid-s33851" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33852" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33853" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33854" xml:space="preserve">per quod hora 8. </s>
  <s xml:id="echoid-s33855" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s33856" xml:space="preserve">tranſit, vt <lb/>ex eadem tabula manifeſtum eſt, vel certe per punctum T, æquinoctialis lineę, per quod hora 16. <lb/></s>
  <s xml:id="echoid-s33857" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s33858" xml:space="preserve">ducitur, vt ex tabula propoſ. </s>
  <s xml:id="echoid-s33859" xml:space="preserve">19. </s>
  <s xml:id="echoid-s33860" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33861" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33862" xml:space="preserve">perſpicue colligitur.</s>
  <s xml:id="echoid-s33863" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1715" type="float" level="2" n="2">
<note position="left" xlink:label="note-0540-10" xlink:href="note-0540-10a" xml:space="preserve">Linea horizon-<lb/>talic.</note>
<note position="left" xlink:label="note-0541-01" xlink:href="note-0541-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0541-02" xlink:href="note-0541-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s33864" xml:space="preserve">POSTREMO pro horologio ſuperiore declinãte à Septẽtr. </s>
  <s xml:id="echoid-s33865" xml:space="preserve">in ortũ gr. </s>
  <s xml:id="echoid-s33866" xml:space="preserve">30. </s>
  <s xml:id="echoid-s33867" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33868" xml:space="preserve">ad Horizontẽ in-<lb/>clinato ex parte auſtrali gr. </s>
  <s xml:id="echoid-s33869" xml:space="preserve">52. </s>
  <s xml:id="echoid-s33870" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33871" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33872" xml:space="preserve">cõfecimus ſequẽtes tabellas pro horis à mer. </s>
  <s xml:id="echoid-s33873" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s33874" xml:space="preserve">med. </s>
  <s xml:id="echoid-s33875" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33876" xml:space="preserve">In qui <lb/>bus latitudines vmbrarũ ſuperiores, inferioreſq́; </s>
  <s xml:id="echoid-s33877" xml:space="preserve">accipiẽdę ſunt, vt in proximo horologio diximus.</s>
  <s xml:id="echoid-s33878" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1717" type="section" level="1" n="461">
<head xml:id="echoid-head488" xml:space="preserve">Latitudines, longitudineſq́ue vmbrarũ in horologio ſuperiore declinante à Septentr. <lb/>in or. grad. 30. &amp; ad Horizontem ex parte inclinato gr. 52. M. 3. pro ho-<lb/>ris à mer. &amp; med. noe. ad latitudinem Grad. 42.</head>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div1718" type="section" level="1" n="462">
<head xml:id="echoid-head489" xml:space="preserve">In tropico ♋, latitudines vmbrarum partim ſunt ſuperiores, &amp; partim <lb/>inferiores: vt in tabellis apparet.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♋, à me- \\ ridie. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # Occidentales, &amp; \\ ſuperiores. <lb/># 6 # 5 # 4 # 3 # 2 # 1 # 0 # Oriẽta. &amp; ſuperio. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 90. 0. # 76. 16. # 62. 40. # 49. 16. # 36. 4. # 22. 58. # 9. 43. <lb/>Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/>
# 2429. 6. # 699. 12 # 224. 1. # 107. 33. # 63. 31. # 42. 19. # 30. 28.
Horę ♋, à me- \\ dia nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orientales, &amp; \\ inferiores.
# 6 # 5 # 4 # 3 # 2 # 1 # 0 # occidẽtales, &amp; in- \\ feriores, præter \\ vltimam.
Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
# 90. 0. # 70. 8. # 51. 19. # 34. 5. # 18. 23. # 3. 50. # 9. 43. # Hæc vltima ſu- \\ perior eſt.
Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M.
# 11. 18. # 11. 43. # 12. 58. # 15. 6. # 18. 21. # 23. 10 # 30. 28.
</note>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1719" type="section" level="1" n="463">
<head xml:id="echoid-head490" xml:space="preserve">In Æ quatore ſunt omnes vmbrarum latitudines inferiores.</head>
<note position="right" xml:space="preserve"> <lb/>Horæ ♈, &amp; ♎, \\ à med. nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # orientales. <lb/># 6 # 5 # 4 # 3 # 2 # 1 # 0 # occidentales. <lb/>Latitudines vm \\ brarum. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/># 90. 0. # 73. 45. # 57. 52. # 42. 35. # 27. 57. # 13. 50. # 0. 0. <lb/>Longitudines \\ vmbrarum. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. # P. M. <lb/># 27. 59. # 29. 8. # 33. 2. # 41. 21. # 59. 42. # 117. 8. # Infinita <lb/></note>
<pb o="526" file="0542" n="542" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s33879" xml:space="preserve">IN hoc horologio cadunt omnes horæ tropici ♑, ſupra faciem inferiorem plani propoſiti: <lb/></s>
  <s xml:id="echoid-s33880" xml:space="preserve">quia ab eo non ſecatur, ſed totus ſub ipſo occultatur, quemadmodum &amp; </s>
  <s xml:id="echoid-s33881" xml:space="preserve">tropicus ♋, totus ſupra <lb/>ipſum extat. </s>
  <s xml:id="echoid-s33882" xml:space="preserve">Hinc fit, vt nulla men@o fiat horarum tropici ♑, in iſtis tabellis. </s>
  <s xml:id="echoid-s33883" xml:space="preserve">Deſcribit autem <lb/>vmbra gnomonis, Sole exiſtente<gap/>incipio ♋, Ellipſim, licet in horologio, propter ſpatij an-<lb/>guſtias, integra non appareat.</s>
  <s xml:id="echoid-s33884" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s33885" xml:space="preserve">DVCTA ergo in plano horologij recta A B, quę in plano ſtabili ſit Horizonti æquidiſtans, <lb/>
<anchor type="note" xlink:label="note-0542-01a" xlink:href="note-0542-01"/>
aſſumptoq́ue in ea loco ſtyli C, deſcribatur ex C, circulus quicunque A D B E, in quo recta D E, <lb/>ſecet ipſam A B, ad angulos rectos in centro, tanquam communis ſectio plani horologij, &amp; </s>
  <s xml:id="echoid-s33886" xml:space="preserve">cir-<lb/>culi maximi inclinationem ad Horizontem metientis. </s>
  <s xml:id="echoid-s33887" xml:space="preserve">Inuento autem, per propoſ. </s>
  <s xml:id="echoid-s33888" xml:space="preserve">31. </s>
  <s xml:id="echoid-s33889" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33890" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33891" xml:space="preserve">ar-<lb/>cu circuli maximi, cui horologium æquidiſtat, inter maximum circulum, qui inclinationem me <lb/>
<anchor type="note" xlink:label="note-0542-02a" xlink:href="note-0542-02"/>
titur, &amp; </s>
  <s xml:id="echoid-s33892" xml:space="preserve">Meridianum proprium, quem in oblato horologio offendimus gr. </s>
  <s xml:id="echoid-s33893" xml:space="preserve">70. </s>
  <s xml:id="echoid-s33894" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33895" xml:space="preserve">28. </s>
  <s xml:id="echoid-s33896" xml:space="preserve">compu-<lb/>tabimus eum à D, verſus A, partes orientales, vt in proximo horologio diximus, (cadit enim &amp; </s>
  <s xml:id="echoid-s33897" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0542-01a" xlink:href="fig-0542-01"/>
<anchor type="note" xlink:label="note-0542-03a" xlink:href="note-0542-03"/>
<anchor type="note" xlink:label="note-0542-04a" xlink:href="note-0542-04"/>
in hoc horologio centrum inſra ſtylum, &amp; </s>
  <s xml:id="echoid-s33898" xml:space="preserve">æquinoctialis linea ſupra, cum arcus Meridiani in-<lb/>ter ipſum, &amp; </s>
  <s xml:id="echoid-s33899" xml:space="preserve">Horizontem ſit complemento altitudinis poli ſupra Horizontem æqualis, nempe gr. <lb/></s>
  <s xml:id="echoid-s33900" xml:space="preserve">
<anchor type="note" xlink:label="note-0542-05a" xlink:href="note-0542-05"/>
48. </s>
  <s xml:id="echoid-s33901" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33902" xml:space="preserve">o.) </s>
  <s xml:id="echoid-s33903" xml:space="preserve">vſque ad F. </s>
  <s xml:id="echoid-s33904" xml:space="preserve">Recta enim F C G, erit linea ſtyli, ſiue communis ſectio plani horologij, <lb/>
<anchor type="note" xlink:label="note-0542-06a" xlink:href="note-0542-06"/>
&amp; </s>
  <s xml:id="echoid-s33905" xml:space="preserve">Meridiani proprij ipſius: </s>
  <s xml:id="echoid-s33906" xml:space="preserve">Et à recta H I, ſecante rectam F G, ad angulos rectos in C, tanquam <lb/>communi ſectione plani horologij, &amp; </s>
  <s xml:id="echoid-s33907" xml:space="preserve">Verticalis proprij ipſius, numerandæ erunt latitudines <lb/>vmbrarum. </s>
  <s xml:id="echoid-s33908" xml:space="preserve">Diuiſa deinde recta H I, in partes ſtylo æquales, vt iam ſæpe factum eſt; </s>
  <s xml:id="echoid-s33909" xml:space="preserve">inuentaque <lb/>per propoſ. </s>
  <s xml:id="echoid-s33910" xml:space="preserve">29. </s>
  <s xml:id="echoid-s33911" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s33912" xml:space="preserve">1. </s>
  <s xml:id="echoid-s33913" xml:space="preserve">altitudine poli ſupra planum horologij, quam in noſtro exemplo reperi-<lb/>mus continere gr. </s>
  <s xml:id="echoid-s33914" xml:space="preserve">66. </s>
  <s xml:id="echoid-s33915" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33916" xml:space="preserve">47. </s>
  <s xml:id="echoid-s33917" xml:space="preserve">ac propterea complementum eiuſdem gr. </s>
  <s xml:id="echoid-s33918" xml:space="preserve">23. </s>
  <s xml:id="echoid-s33919" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33920" xml:space="preserve">13. </s>
  <s xml:id="echoid-s33921" xml:space="preserve">ſi à C, loco <lb/>ſtyli in linea ſtyli ſurſum verſus ſupputemus vmbram Par. </s>
  <s xml:id="echoid-s33922" xml:space="preserve">27. </s>
  <s xml:id="echoid-s33923" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33924" xml:space="preserve">59. </s>
  <s xml:id="echoid-s33925" xml:space="preserve">quæ complemento altitu-<lb/>dinis poli inuentæ debetur, inuen iemus punctum K, per quod linea æquinoctialis ad F G, ducẽ-<lb/>
<anchor type="note" xlink:label="note-0542-07a" xlink:href="note-0542-07"/>
da eſt perpendicularis: </s>
  <s xml:id="echoid-s33926" xml:space="preserve">Et ſi deorſum verſus accipiamus vmbram C L, Par. </s>
  <s xml:id="echoid-s33927" xml:space="preserve">5. </s>
  <s xml:id="echoid-s33928" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33929" xml:space="preserve">9. </s>
  <s xml:id="echoid-s33930" xml:space="preserve">altitudini <lb/>poli inuentæ reſpondentem, inuentum erit L, centrum horologij, per quod ſi ducamus ad F G, <lb/>
<anchor type="note" xlink:label="note-0542-08a" xlink:href="note-0542-08"/>
<anchor type="note" xlink:label="note-0542-09a" xlink:href="note-0542-09"/>
perpendicularem M N, computandi erunt arcus horarij, ſi pro ſingulis horis ſupputati fuerint à <lb/>punctis M, N, in circulo ex L, deſcripto. </s>
  <s xml:id="echoid-s33931" xml:space="preserve">Quæ duo puncta K, L, inueniri quoque poſſunt, ſi in <lb/>H I, accipiatur recta C O, gnomoni æqualis, fiatq́ue angulus C O K, altitudinis poli inuentæ, &amp; </s>
  <s xml:id="echoid-s33932" xml:space="preserve"><lb/>angulus C O L, complementi eiuſdem altitudinis.</s>
  <s xml:id="echoid-s33933" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1719" type="float" level="2" n="1">
<note position="left" xlink:label="note-0542-01" xlink:href="note-0542-01a" xml:space="preserve">Deſcriptio hoto <lb/>log@@ deci<unsure/> inãtis <lb/>à ſeptẽtr. in or. <lb/>g@. 30 &amp; ad H@ <lb/>@zontem incli-<lb/>nati gr. 52. M. 3. <lb/>@ tabulis.</note>
<note position="left" xlink:label="note-0542-02" xlink:href="note-0542-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0542-01" xlink:href="fig-0542-01a">
    <image file="0542-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0542-01"/>
  </figure>
<note position="left" xlink:label="note-0542-03" xlink:href="note-0542-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0542-04" xlink:href="note-0542-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0542-05" xlink:href="note-0542-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0542-06" xlink:href="note-0542-06a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0542-07" xlink:href="note-0542-07a" xml:space="preserve">Linea æquino <lb/>ctialis.</note>
<note position="left" xlink:label="note-0542-08" xlink:href="note-0542-08a" xml:space="preserve">Centrum horo <lb/>logii.</note>
<note position="left" xlink:label="note-0542-09" xlink:href="note-0542-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s33934" xml:space="preserve">SI iam à punctis H, I, ſupputentur, latitudines vmbrarũ, obſeruando diligenter, quæ orien-<lb/>tales ſint, occidentalesve, &amp; </s>
  <s xml:id="echoid-s33935" xml:space="preserve">quæ ſuperiores, in ferioresve, conſtruetur horologiũ, vt in præceden-<lb/>tibus. </s>
  <s xml:id="echoid-s33936" xml:space="preserve">Horizontalis autem linea ducenda eſt per punctum K, vbilinea ſtyli, quæ in dato plano <lb/>
<anchor type="note" xlink:label="note-0542-10a" xlink:href="note-0542-10"/>
horam 6. </s>
  <s xml:id="echoid-s33937" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33938" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33939" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33940" xml:space="preserve">indicat, æquinoctialem lineam ſecat, parallela rectę A B, vel per-<lb/>pendicularis ad D E, tranſiens omnino per punctum P, quod in recta C E terminat vmbram Par. <lb/></s>
  <s xml:id="echoid-s33941" xml:space="preserve">9. </s>
  <s xml:id="echoid-s33942" xml:space="preserve">M. </s>
  <s xml:id="echoid-s33943" xml:space="preserve">22. </s>
  <s xml:id="echoid-s33944" xml:space="preserve">congruentem inclinationi plani ad Horizontem. </s>
  <s xml:id="echoid-s33945" xml:space="preserve">Quod punctum P, inuenietur etiam, <lb/>ſi in recta AB, ſumatur C Q, ſtylo æqualis, conſtituaturq́ue angulus C Q P, complementi incli-
<pb o="527" file="0543" n="543" rhead="LIBER QVINTVS."/>
nationis, &amp;</s>
  <s xml:id="echoid-s33946" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33947" xml:space="preserve">Meridiana autem linea in hoc horologio perpendicularis eſt ad F G, ita vt à recta <lb/>
<anchor type="note" xlink:label="note-0543-01a" xlink:href="note-0543-01"/>
M N, non differat, propterea quòd arcus horarius horæ 12. </s>
  <s xml:id="echoid-s33948" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s33949" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s33950" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s33951" xml:space="preserve">continet grad. </s>
  <s xml:id="echoid-s33952" xml:space="preserve">o. <lb/></s>
  <s xml:id="echoid-s33953" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s33954" xml:space="preserve">o. </s>
  <s xml:id="echoid-s33955" xml:space="preserve">in dato exemplo.</s>
  <s xml:id="echoid-s33956" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1720" type="float" level="2" n="2">
<note position="left" xlink:label="note-0542-10" xlink:href="note-0542-10a" xml:space="preserve">Linea horizon <lb/>talis.</note>
<note position="right" xlink:label="note-0543-01" xlink:href="note-0543-01a" xml:space="preserve">Linea meridia-<lb/>na.</note>
</div>
<p>
  <s xml:id="echoid-s33957" xml:space="preserve">EX his facile arbitror percipi poſſe, qua ratione ex tabulis horologia conficiantur, cum in om <lb/>nibus horologijs, quæ in lib. </s>
  <s xml:id="echoid-s33958" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33959" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33960" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33961" xml:space="preserve">deſcripſimus, exempla poſuerimus, æquinoctiali horologio <lb/>excepto, ob rationem, quam ſupra diximus. </s>
  <s xml:id="echoid-s33962" xml:space="preserve">De collocatione autem iſtorum omnium horolo-<lb/>giorum nihil prorſus diximus, qua ita locanda ſunt, vt in lib. </s>
  <s xml:id="echoid-s33963" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33964" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33965" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33966" xml:space="preserve">præſcripſimus. </s>
  <s xml:id="echoid-s33967" xml:space="preserve">Atque hic <lb/>
<anchor type="note" xlink:label="note-0543-02a" xlink:href="note-0543-02"/>
modus deſcribendorum horologiorum, qui ex tabulis deſumitur, certiſſimus eſt, atque facilimus, <lb/>ſi tabulæ recte ſupputentur, vt hoc lib. </s>
  <s xml:id="echoid-s33968" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s33969" xml:space="preserve">In eo enim non opus eſt tot lineas perpendi-<lb/>culares, aut parallelas ducere, quot in aliis modis, ſed ſatis eſt, ſi lineæ latitudinum vmbrarum oc-<lb/>
<anchor type="note" xlink:label="note-0543-03a" xlink:href="note-0543-03"/>
cultæ ducantur, vt ex illis vmbrarum longitudines abſcindantur, quæ vel ex tabula vmbrarum <lb/>propoſ. </s>
  <s xml:id="echoid-s33970" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33971" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s33972" xml:space="preserve">eliciendæ ſunt, vel inueniendæ Geometrice ex altitudinibus Solis, vt in hac <lb/>propoſ. </s>
  <s xml:id="echoid-s33973" xml:space="preserve">cum horologium horizontale conſtrueremus, tradidimus, &amp;</s>
  <s xml:id="echoid-s33974" xml:space="preserve">c. </s>
  <s xml:id="echoid-s33975" xml:space="preserve">Ita enim inuenientur &amp; </s>
  <s xml:id="echoid-s33976" xml:space="preserve"><lb/>puncta tropicorum, &amp; </s>
  <s xml:id="echoid-s33977" xml:space="preserve">aliorum etiam, ſi placet, parallelorum. </s>
  <s xml:id="echoid-s33978" xml:space="preserve">Adde quòd hoc eodem modo in <lb/>muro quantumcunque horologium pingere licet, ad datam quamlibet longitudinem ſtyli, ita <lb/>vt opus non ſit, illud prius in charta deſcribere, vt poſtea ad maiorem formam in muro rediga-<lb/>tur. </s>
  <s xml:id="echoid-s33979" xml:space="preserve">Propoſueram ego ſane varias tabulas hoc loco pro variis latitudinibus ſupputare; </s>
  <s xml:id="echoid-s33980" xml:space="preserve">ſed quo-<lb/>niam liber in immenſum creſcebat, ſatius eſſe duxi, rationem, qua quilibet proprio Marte huiuſ-<lb/>modi tabulas condere poſſit, demonſtrare, &amp; </s>
  <s xml:id="echoid-s33981" xml:space="preserve">nonnullis exemplis, quibus omnis varietas, &amp; </s>
  <s xml:id="echoid-s33982" xml:space="preserve">dif-<lb/>ficultas explicetur, rem ipſam illuſtrare. </s>
  <s xml:id="echoid-s33983" xml:space="preserve">Id quod abunde me hoc lib. </s>
  <s xml:id="echoid-s33984" xml:space="preserve">præſtitiſſe exiſtimo. </s>
  <s xml:id="echoid-s33985" xml:space="preserve">Huc <lb/>
<anchor type="note" xlink:label="note-0543-04a" xlink:href="note-0543-04"/>
etiam accedit, quòd nullæ tabulæ ſatis eſſe poſſint pro omnibus eleuationibus poli, &amp; </s>
  <s xml:id="echoid-s33986" xml:space="preserve">declinatio-<lb/>nibus, inclinationibusq́ue planorum, niſi quis tabulas condere velit pro ſingulis Minutis eleua-<lb/>tionum, declinationum, inclinationumq́ue, quod infiniti propemodum eſſet laboris. </s>
  <s xml:id="echoid-s33987" xml:space="preserve">Alio for-<lb/>taſſis tempore, cum per otium licebit, aliquot tabulas in lucem edemus, præſertim pro horolo-<lb/>giis horizontalibus, Verticalibus, Meridianis, declinantibusq́ue à Verticali, quæ in muris ad Ho-<lb/>rizontem rectis deſcribuntur, cum hæc magis in vſu eſſe ſoleant.</s>
  <s xml:id="echoid-s33988" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1721" type="float" level="2" n="3">
<note position="right" xlink:label="note-0543-02" xlink:href="note-0543-02a" xml:space="preserve">Præſtantia de-<lb/>ſcriptionis horo <lb/>logiorum ex ta <lb/>bulus.</note>
<note position="left" xlink:label="note-0543-03" xlink:href="note-0543-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0543-04" xlink:href="note-0543-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s33989" xml:space="preserve">NEQVE ſilentio prætereundum eſt hoc loco, nos in horologio quccunque Aſtronomico <lb/>
<anchor type="note" xlink:label="note-0543-05a" xlink:href="note-0543-05"/>
per arcus horarios, qui per propoſ. </s>
  <s xml:id="echoid-s33990" xml:space="preserve">præcedentem huius lib. </s>
  <s xml:id="echoid-s33991" xml:space="preserve">ſupputantur, deſcripto delin eare poſ-<lb/>ſe parallelos, arcusve ſignorum, non ſecus ac in ſuperioribus libris, hoc eſt, per figuram, in qua ra-<lb/>dij ſignorum contineantur, vel etiam per Analemma, ſi diligenter habeatur ratio illius trianguli, <lb/>
<anchor type="note" xlink:label="note-0543-06a" xlink:href="note-0543-06"/>
quod in omnibus horologiis huius propoſ. </s>
  <s xml:id="echoid-s33992" xml:space="preserve">in quibus centrum notatum eſt, cõtinetur, cuius qui-<lb/>dem baſis eſt portio lineæ ſtyli inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s33993" xml:space="preserve">æquinoctialem lineam poſita, duo ve-<lb/>ro eius latera in vertice ſtyli coeunt, quorum illud, quod à vertice ſtyli in lineam æquinoctialem <lb/>cadit, eſt communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s33994" xml:space="preserve">Meridiani proprii ipſius horologii, (ſi nimirum trian-<lb/>gulum dictum circa lineam ſtyli circum duci in telligatur, donec rectum ſit ad planum horologii) <lb/>aliud vero inter verticem ſtyli, &amp; </s>
  <s xml:id="echoid-s33995" xml:space="preserve">centrum horologii incluſum, axem mundi refert, vt ex ijs, quæ <lb/>in lib. </s>
  <s xml:id="echoid-s33996" xml:space="preserve">2. </s>
  <s xml:id="echoid-s33997" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s33998" xml:space="preserve">3. </s>
  <s xml:id="echoid-s33999" xml:space="preserve">demonſtrauimus, perſpicuum eſt. </s>
  <s xml:id="echoid-s34000" xml:space="preserve">Exempli gratia, ſi horologium declinans à mer. <lb/></s>
  <s xml:id="echoid-s34001" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s34002" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s34003" xml:space="preserve">40. </s>
  <s xml:id="echoid-s34004" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34005" xml:space="preserve">inclinatum ad Horizontem grad. </s>
  <s xml:id="echoid-s34006" xml:space="preserve">20. </s>
  <s xml:id="echoid-s34007" xml:space="preserve">(quod quidem eſt primum inter ſex poſtre-<lb/>ma horologia huius propoſ.) </s>
  <s xml:id="echoid-s34008" xml:space="preserve">deſcriptum ſit per arcus horarios, accipienda erit in axe illius ſigu-<lb/>ræ, in qua radij ſignorum continentur, recta æqualis axi K N, in triangulo K L N, dicti horologii, <lb/>
<anchor type="note" xlink:label="note-0543-07a" xlink:href="note-0543-07"/>
&amp; </s>
  <s xml:id="echoid-s34009" xml:space="preserve">in radio Aequatoris, qui in extremo puncto K, ipſius axis ad axem perpendicularis eſt, abſcin-<lb/>denda recta æqualis rectæ K L, eiuſdem trianguli. </s>
  <s xml:id="echoid-s34010" xml:space="preserve">Deinde in linea ſtyli horologii ſumen-<lb/>da recta L S, ſiue ſurſum, ſiue deorſum verſus, æqualis eidem K L. </s>
  <s xml:id="echoid-s34011" xml:space="preserve">Poſtremo in-<lb/>terualla inter S, &amp; </s>
  <s xml:id="echoid-s34012" xml:space="preserve">puncta horarum in linea æquinoctiali in ra-<lb/>dium Aequatoris beneficio circini transferenda, &amp;</s>
  <s xml:id="echoid-s34013" xml:space="preserve">c. </s>
  <s xml:id="echoid-s34014" xml:space="preserve">Quod <lb/>vero attinet ad deſcriptionem ſignorum ex Analem-<lb/>mate, fabricandum erit Analemma, habita <lb/>ratione anguli K N L, altitu-<lb/>dinis poli, &amp;</s>
  <s xml:id="echoid-s34015" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s34016" xml:space="preserve">Horologia ergo varia ex tabulis, quas in præceden-<lb/>
<anchor type="note" xlink:label="note-0543-08a" xlink:href="note-0543-08"/>
tibus propoſitionibus ſupputare do-<lb/>cuimus, compoſuimus. </s>
  <s xml:id="echoid-s34017" xml:space="preserve">Quod <lb/>faciendum erat.</s>
  <s xml:id="echoid-s34018" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1722" type="float" level="2" n="4">
<note position="right" xlink:label="note-0543-05" xlink:href="note-0543-05a" xml:space="preserve">Qua ratione in <lb/>horologio Aſtro <lb/>nomico per ar-<lb/>cus horarios cõ-<lb/>ſtructo arcus ſi-<lb/>gnorum poſſins <lb/>deſcribi.</note>
<note position="left" xlink:label="note-0543-06" xlink:href="note-0543-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0543-07" xlink:href="note-0543-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0543-08" xlink:href="note-0543-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1724" type="section" level="1" n="464">
<head xml:id="echoid-head491" xml:space="preserve">FINIS QVINTI LIBRI.</head>
<pb o="528" file="0544" n="544"/>
</div>
<div xml:id="echoid-div1725" type="section" level="1" n="465">
<head xml:id="echoid-head492" xml:space="preserve">GNOMONICES</head>
<head xml:id="echoid-head493" xml:space="preserve">LIBER SEXTVS.</head>
  <figure>
    <image file="0544-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0544-01"/>
  </figure>
</div>
<div xml:id="echoid-div1726" type="section" level="1" n="466">
<head xml:id="echoid-head494" style="it" xml:space="preserve">AVCTORE</head>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1727" type="section" level="1" n="467">
<head xml:id="echoid-head495" xml:space="preserve">CHRISTOPHORO CLAVIO BAMBER GENSI</head>
<head xml:id="echoid-head496" xml:space="preserve">SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s34019" xml:space="preserve"><emph style="sc">EDidit</emph> Ptolemæus libellum acutiſſimum de Analemmate, <lb/>in quo &amp; </s>
  <s xml:id="echoid-s34020" xml:space="preserve">Geometrice, &amp; </s>
  <s xml:id="echoid-s34021" xml:space="preserve">per numeros arcus quoſdam circulo-<lb/>rum inueſtigat, per quos eadem ferme via, qua nos in proxi-<lb/>mo libro vſi ſumus, horologia omnis generis deſcribantur. <lb/></s>
  <s xml:id="echoid-s34022" xml:space="preserve">Id quod feliciter executus eſt Federicus Commandinus in li-<lb/>
<anchor type="note" xlink:label="note-0544-02a" xlink:href="note-0544-02"/>
bello de horologiorum deſcriptione, quem ad illud opus de <lb/>Analemmate adiunxit. </s>
  <s xml:id="echoid-s34023" xml:space="preserve">Quoniam vero quàm plurimi &amp; </s>
  <s xml:id="echoid-s34024" xml:space="preserve">Ana <lb/>lemma Ptolemæi, &amp; </s>
  <s xml:id="echoid-s34025" xml:space="preserve">deſcriptionem horologiorum à Federico <lb/>Commandino ex eo depromptam ſuſpiciunt quidem, &amp; </s>
  <s xml:id="echoid-s34026" xml:space="preserve">ad-<lb/>mirantur propter acumen ingenii, &amp; </s>
  <s xml:id="echoid-s34027" xml:space="preserve">ſubtilitatem demonſtrationum, ſed ſimul <lb/>vtrumque auctorem grauiſſime accuſant de affectata quadam obſcuritate, vt om-<lb/>nino diffidant, ſeſe fructum aliquem ex eorum ſeriptis capere poſſe: </s>
  <s xml:id="echoid-s34028" xml:space="preserve">faciendum <lb/>mihi omnino putaui, vt rationem illam deſcribendorum horologiorum, quam <lb/>Federicus Commandinus, vt diximus, ex Analemmate Ptolemæi deprompſit, &amp; </s>
  <s xml:id="echoid-s34029" xml:space="preserve"><lb/>quæ iucundiſſima eſt, ſubtiliſſimaq́;</s>
  <s xml:id="echoid-s34030" xml:space="preserve">, clarius, &amp;</s>
  <s xml:id="echoid-s34031" xml:space="preserve">, quoad eius ſieri poterit, breuius hoc <lb/>
<anchor type="note" xlink:label="note-0544-03a" xlink:href="note-0544-03"/>
libro explicem, vt à quouis, qui omnino rerum Geometricarum ignarus non ſit, in-<lb/>telligi poſſit, ac percipi. </s>
  <s xml:id="echoid-s34032" xml:space="preserve">Non ſequar autem verba Ptolemæi, ſed ſententiam, atque <lb/>rem ipſam, præſertim in arcubus, circumferentijsve inquirendis per numeros, vbi <lb/>multo breuiores ſupputationes, quam Ptolemæus, excogitauimus, vt facile quiuis <lb/>iudicabit, ſi hæc noſtra cum Ptolemæi ſcriptis contulerit.</s>
  <s xml:id="echoid-s34033" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1727" type="float" level="2" n="1">
<note position="left" xlink:label="note-0544-02" xlink:href="note-0544-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0544-03" xlink:href="note-0544-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1729" type="section" level="1" n="468">
<head xml:id="echoid-head497" style="it" xml:space="preserve">EXPLICATIO CIRCVLORVM, ET <lb/>circumferentiarum, quos præcipue in Analemmate <lb/>Ptolemæus conſiderat. CAPVTI.</head>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s34034" xml:space="preserve"><emph style="sc">PTolemaevs</emph> trium potiſſimum horologiorum, nempe Horizontalis, Verti-<lb/>calis, ac Meridiani, rationem habuiſſe videtur; </s>
  <s xml:id="echoid-s34035" xml:space="preserve">(Nos tamen eadem ratione, ad mo <lb/>
<anchor type="note" xlink:label="note-0544-05a" xlink:href="note-0544-05"/>
dum horizontalis horologii, omnia alia horologia, de quibus in ſuperioribus egi <lb/>mus, deſcribemus) propterea tres tantum circulos maximos præcipue in Analem-<lb/>mate conſiderat ſeſe in qualibet ſphæræ poſitione mutuo ad angulos rectos in-<lb/>terſecantes, puta Horizontem, Meridianum, &amp; </s>
  <s xml:id="echoid-s34036" xml:space="preserve">Verticalem circulum proprie di-<lb/>ctum, quibus dicta tria horologia æquidiſtant, vt ex ſuperioribus patet. </s>
  <s xml:id="echoid-s34037" xml:space="preserve">Quilibet enim horum <lb/>trium circulorum rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s34038" xml:space="preserve">15. </s>
  <s xml:id="echoid-s34039" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34040" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34041" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34042" xml:space="preserve">ad reliquos duos, cum per eorum po <lb/>los ducatur, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s34043" xml:space="preserve">Communes quoque eorundem circulorum ſectiones mutuo in-<lb/>ter ſe angulos rectos conſtituunt in centro mundi; </s>
  <s xml:id="echoid-s34044" xml:space="preserve">propterea quod quiliber duo horum circulo-<lb/>
<anchor type="note" xlink:label="note-0544-06a" xlink:href="note-0544-06"/>
<anchor type="note" xlink:label="note-0544-07a" xlink:href="note-0544-07"/>
rum ad reliquum recti ſunt, vt diximus, ac propterea &amp; </s>
  <s xml:id="echoid-s34045" xml:space="preserve">communis illorum ſectio ad eundem per-<lb/>pendicularis, &amp;</s>
  <s xml:id="echoid-s34046" xml:space="preserve">c. </s>
  <s xml:id="echoid-s34047" xml:space="preserve">Cõmunis autem ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s34048" xml:space="preserve">Meridiani appellatur à Ptolemęo linea <lb/>meridiana@ Sectio vero communis Horizontis, &amp; </s>
  <s xml:id="echoid-s34049" xml:space="preserve">Verticalis dicitur linea æquinoctialis, eo quod <lb/>
<anchor type="note" xlink:label="note-0544-08a" xlink:href="note-0544-08"/>
ſit communis etiam ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s34050" xml:space="preserve">æquinoctialis circuli: </s>
  <s xml:id="echoid-s34051" xml:space="preserve">Communis denique ſectio Me-<lb/>ridiani, &amp; </s>
  <s xml:id="echoid-s34052" xml:space="preserve">Verticalis Gnomon vocatur. </s>
  <s xml:id="echoid-s34053" xml:space="preserve">Quæ omnia in ſubiecta figura apparent, in qua circulus <lb/>A B C D, eſt Meridianus; </s>
  <s xml:id="echoid-s34054" xml:space="preserve">A F C G, Horizon ad Meridianum rectus, B F D G, Verticalis proprie <lb/>dictus ad vtrumque nominatum circulum rectus; </s>
  <s xml:id="echoid-s34055" xml:space="preserve">Linea meridiana recta A C, nempe communis <lb/>ſectio Horizontis, ac Meridian@; </s>
  <s xml:id="echoid-s34056" xml:space="preserve">Linea æquinoctialis recta F G, communis ſcilicet ſectio Horizõ-<lb/>tis, &amp; </s>
  <s xml:id="echoid-s34057" xml:space="preserve">Verticalis; </s>
  <s xml:id="echoid-s34058" xml:space="preserve">Linea denique recta D B, gnomon, nimirum ſectio communis Meridiani, &amp; </s>
  <s xml:id="echoid-s34059" xml:space="preserve"><lb/>Verticalis.</s>
  <s xml:id="echoid-s34060" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1729" type="float" level="2" n="1">
<note position="left" xlink:label="note-0544-05" xlink:href="note-0544-05a" xml:space="preserve">Quos cireulos <lb/>præcipue in A-<lb/>nalemmate Pto <lb/>lemæus conſi-<lb/>de@et.</note>
<note position="left" xlink:label="note-0544-06" xlink:href="note-0544-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0544-07" xlink:href="note-0544-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0544-08" xlink:href="note-0544-08a" xml:space="preserve">Linea meridia-<lb/>na, linea æqui-<lb/>noctialis, &amp; Gno <lb/>mon quid ſecũ-<lb/>du@ Ptolemęũ.</note>
</div>
<p>
  <s xml:id="echoid-s34061" xml:space="preserve">CVILIBET deinde horum trium circulorum motum quendam tribuit Ptolemæus.</s>
  <s xml:id="echoid-s34062" xml:space="preserve">
<pb o="529" file="0545" n="545" rhead="LIBER SEXTVS."/>
Debent enim omnes per centrum Solis tranſire, in quocunque loco, ſeu puncto cæli Sol exiſtat, <lb/>
<anchor type="note" xlink:label="note-0545-01a" xlink:href="note-0545-01"/>
ita vt quilibet tot poſitiones aſſumat in die, quot loca Sol pertranſit. </s>
  <s xml:id="echoid-s34063" xml:space="preserve">Mouetur autem Horizon <lb/>circa æquinoctialem diametrum, ſectionemve, tanquam ad id, quod ſupra terram, &amp; </s>
  <s xml:id="echoid-s34064" xml:space="preserve">ſub terra eſt, <lb/>vt ipſe ait, hoc eſt, ad verticem capitis, eiusq́ue oppoſitum: </s>
  <s xml:id="echoid-s34065" xml:space="preserve">quæ quidem duo puncta poli ſunt Ho <lb/>rizõtis immobilis, ab eoq́; <lb/></s>
  <s xml:id="echoid-s34066" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0545-01a" xlink:href="fig-0545-01"/>
æqualiter diſtant. </s>
  <s xml:id="echoid-s34067" xml:space="preserve">Itaque <lb/>circulus maximus, qui per <lb/>centrum Solis, vbicunq; <lb/></s>
  <s xml:id="echoid-s34068" xml:space="preserve">exiſtat, &amp; </s>
  <s xml:id="echoid-s34069" xml:space="preserve">per polos Meri-<lb/>diani, ſeu communes ſe-<lb/>
<anchor type="note" xlink:label="note-0545-02a" xlink:href="note-0545-02"/>
ctiones Horizontis, &amp; </s>
  <s xml:id="echoid-s34070" xml:space="preserve">Ae-<lb/>quatoris, Verticalisve du-<lb/>ci concipitur, appellatur <lb/>à Ptolemæo hoc loco Ho-<lb/>rizon mobilis. </s>
  <s xml:id="echoid-s34071" xml:space="preserve">Huic au-<lb/>
<anchor type="note" xlink:label="note-0545-03a" xlink:href="note-0545-03"/>
tem Horizonti mobili æ-<lb/>quidiſtat horologium ad <lb/>Horizontem inclinatum, <lb/>quod propoſ. </s>
  <s xml:id="echoid-s34072" xml:space="preserve">25. </s>
  <s xml:id="echoid-s34073" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34074" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34075" xml:space="preserve">de-<lb/>ſcripſimus. </s>
  <s xml:id="echoid-s34076" xml:space="preserve">Meridianus <lb/>
<anchor type="note" xlink:label="note-0545-04a" xlink:href="note-0545-04"/>
vero mouetur circa lineã <lb/>meridianam, tanquam ad <lb/>ortum, atque occaſum, vt <lb/>ipſe loquitur, hoc eſt, ad <lb/>punctũ ottus ęquinoctia-<lb/>lis, occaſusq́ue: </s>
  <s xml:id="echoid-s34077" xml:space="preserve">quæ qui-<lb/>dem duo puncta poli ſunt-<lb/>Meridiani immobilis, ab <lb/>eoq́ue ęqualitet diſtant. <lb/></s>
  <s xml:id="echoid-s34078" xml:space="preserve">Itaque circulus maximus <lb/>
<anchor type="note" xlink:label="note-0545-05a" xlink:href="note-0545-05"/>
per centrum Solis, vbi-<lb/>cunque exiſtat, &amp; </s>
  <s xml:id="echoid-s34079" xml:space="preserve">per polos Verticalis circuli, communesve ſectiones Horizontis, ac Meridiani <lb/>
<anchor type="note" xlink:label="note-0545-06a" xlink:href="note-0545-06"/>
ductus, à Ptolemæo Meridianus mobilis dicitur hoc loco. </s>
  <s xml:id="echoid-s34080" xml:space="preserve">Cui quidem Meridiano mobili paral-<lb/>lelum eſt horologium ab Horizõte declinans, quod propoſ. </s>
  <s xml:id="echoid-s34081" xml:space="preserve">13. </s>
  <s xml:id="echoid-s34082" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34083" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34084" xml:space="preserve">conſtruximus. </s>
  <s xml:id="echoid-s34085" xml:space="preserve">Verticalis de-<lb/>nique circa Gnomonem conuertitur, tanquam ad ſeptentrionem, &amp; </s>
  <s xml:id="echoid-s34086" xml:space="preserve">meridiem, vt ipſe ait, id eſt, <lb/>ad punctum Horizontis borealiſſimum, &amp; </s>
  <s xml:id="echoid-s34087" xml:space="preserve">auſtraliſſimum: </s>
  <s xml:id="echoid-s34088" xml:space="preserve">quæ quidem duo puncta poli ſunt Ver <lb/>ticalis immobilis, æqualiterq́ue ab eo recedunt. </s>
  <s xml:id="echoid-s34089" xml:space="preserve">Itaque circulus maximus per cen trum Solis, vbi-<lb/>cunque exiſtat, &amp; </s>
  <s xml:id="echoid-s34090" xml:space="preserve">per polos Horizõtis, ſectionesve Meridiani, ac Verticalis ductus, Verticalis mo-<lb/>bilis hoc loco intelligitur à Ptolemæo. </s>
  <s xml:id="echoid-s34091" xml:space="preserve">Vt autem mobiles hoſce circulos ab immobilibus diſtin-<lb/>
<anchor type="note" xlink:label="note-0545-07a" xlink:href="note-0545-07"/>
guat, imponit illis propria nomina. </s>
  <s xml:id="echoid-s34092" xml:space="preserve">Horizontẽ enim mobilem vocat ἑκτημ@ριον, propterea quòd, <lb/>
<anchor type="note" xlink:label="note-0545-08a" xlink:href="note-0545-08"/>
<anchor type="note" xlink:label="note-0545-09a" xlink:href="note-0545-09"/>
vt Olympiodorus in commentariis in tertium librum Meteororum Ariſtotelis ſcribit, ſex poſi-<lb/>tiones inter ſe diſtinctas in die aſſumit, ob ſex horas inæquales, quæ quolibet die ab ortu vſque ad <lb/>meridiem, &amp; </s>
  <s xml:id="echoid-s34093" xml:space="preserve">à meridie vſque ad occaſum numerabantur ab antiquis. </s>
  <s xml:id="echoid-s34094" xml:space="preserve">Meridianus vero mobilis <lb/>
<anchor type="note" xlink:label="note-0545-10a" xlink:href="note-0545-10"/>
dicitur circulus Horarius, quoniam ſingula ſpatia horaria comitatur ab ortu ad occaſum vſque. <lb/></s>
  <s xml:id="echoid-s34095" xml:space="preserve">
<anchor type="note" xlink:label="note-0545-11a" xlink:href="note-0545-11"/>
Verticalis denique mobilis appellatur καταβατικὸς, id eſt, Deſcenſiuus, quia oſtendit deſcenſum <lb/>Solis ab altiſſima partead humilimam, cùm in eo ſemper altitudo Solis ſupra Horizontem com-<lb/>putetur. </s>
  <s xml:id="echoid-s34096" xml:space="preserve">Vt in ſuperiori figura, ſi Sol ſtatuatur in H, pnncto, erit Horizon mobilis, ſiue Hectemo-<lb/>rion F H L G Q M, per centrum Solis ductus, qui quidem circa diametrum æquinoctialem F G, <lb/>verſus verticem capitis D, ſupra terram, eiusq́ue oppoſitum B, ſub terra conuertitur. </s>
  <s xml:id="echoid-s34097" xml:space="preserve">Meridianus <lb/>mobilis, ſiue circulus Horarius, erit A H K C Q O N, per idem centrum Solis incedens, qui cir-<lb/>
<anchor type="note" xlink:label="note-0545-12a" xlink:href="note-0545-12"/>
ca lineam meridianam A C, mouetur verſus ortum æquinoctialem F, occaſumq́ue G. </s>
  <s xml:id="echoid-s34098" xml:space="preserve">Verticalis <lb/>mobilis, hoc eſt, Deſcenſiuus circulus, erit D H N B Q P, per centrum etiam Solis tranſiens, qui <lb/>circa gnomonem D B, circumuoluitur verſus punctum auſtraliſſimum A, borealiſſimumq́ue C. <lb/></s>
  <s xml:id="echoid-s34099" xml:space="preserve">Supra terram igitur omnes tres circuli mobiles ſe interſecant in H, centro Solis, ſub terra vero in <lb/>puncto oppoſito Q; </s>
  <s xml:id="echoid-s34100" xml:space="preserve">communisq́ue eorum ſectio eſt recta H E Q: </s>
  <s xml:id="echoid-s34101" xml:space="preserve">Sectio deinde Hectemorii, &amp; </s>
  <s xml:id="echoid-s34102" xml:space="preserve"><lb/>Meridiani eſt recta L E M: </s>
  <s xml:id="echoid-s34103" xml:space="preserve">Sectio vero Horarii, ac Verticalis eſt recta K E O: </s>
  <s xml:id="echoid-s34104" xml:space="preserve">Sectio denique De-<lb/>ſcenſiui, atque Horizontis eſt recta N E P.</s>
  <s xml:id="echoid-s34105" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1730" type="float" level="2" n="2">
<note position="right" xlink:label="note-0545-01" xlink:href="note-0545-01a" xml:space="preserve">Quomodo tres <lb/>dicti circuli mo <lb/>ueri intelligan-<lb/>tur a Ptolemęo.</note>
  <figure xlink:label="fig-0545-01" xlink:href="fig-0545-01a">
    <image file="0545-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0545-01"/>
  </figure>
<note position="left" xlink:label="note-0545-02" xlink:href="note-0545-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0545-03" xlink:href="note-0545-03a" xml:space="preserve">Morizon mobi-<lb/>lis.</note>
<note position="left" xlink:label="note-0545-04" xlink:href="note-0545-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0545-05" xlink:href="note-0545-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0545-06" xlink:href="note-0545-06a" xml:space="preserve">Meridianus mo <lb/>bilis.</note>
<note position="right" xlink:label="note-0545-07" xlink:href="note-0545-07a" xml:space="preserve">Verticalis mo-<lb/>bilis.</note>
<note position="left" xlink:label="note-0545-08" xlink:href="note-0545-08a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0545-09" xlink:href="note-0545-09a" xml:space="preserve">Hectemorion <lb/>circulus.</note>
<note position="right" xlink:label="note-0545-10" xlink:href="note-0545-10a" xml:space="preserve">Horatius circu <lb/>lus.</note>
<note position="right" xlink:label="note-0545-11" xlink:href="note-0545-11a" xml:space="preserve">Deſcenſi uus cir <lb/>culus.</note>
<note position="left" xlink:label="note-0545-12" xlink:href="note-0545-12a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s34106" xml:space="preserve">QVONIAM vero inſtitutum eſt docere hoc lib. </s>
  <s xml:id="echoid-s34107" xml:space="preserve">qua ratione per arcus, circunferentiasve <lb/>quaſdam dictorum circulorum horologia deſcribantur, quæ Horizonti, Verticali circulo, &amp; </s>
  <s xml:id="echoid-s34108" xml:space="preserve">Me-<lb/>
<anchor type="note" xlink:label="note-0545-13a" xlink:href="note-0545-13"/>
ridiano æquidiſtent, conſiderandæ erunt cum Ptolemęo diligenter in ſex illis circulis, quorum <lb/>tres immobil es, &amp; </s>
  <s xml:id="echoid-s34109" xml:space="preserve">tres mobiles ſunt, vt diximus, ſex circunferentiæ pro qualibet hora, ſingulæ in
<pb o="530" file="0546" n="546" rhead="GNOMONICES"/>
ſingulis; </s>
  <s xml:id="echoid-s34110" xml:space="preserve">tres quidem in tribus circulis immobilibus, &amp; </s>
  <s xml:id="echoid-s34111" xml:space="preserve">in mobilibus totidem: </s>
  <s xml:id="echoid-s34112" xml:space="preserve">quæ omnes à cir-<lb/>culis, quorum ſunt partes, nomen accipiunt, ita vt ea, quæ in Horizonte ſumitur, dicatur circun-<lb/>ferentia horizontalis; </s>
  <s xml:id="echoid-s34113" xml:space="preserve">quæ in Deſcenſiuo, deſcenſiua; </s>
  <s xml:id="echoid-s34114" xml:space="preserve">quæ in Verticali, Verticalis; </s>
  <s xml:id="echoid-s34115" xml:space="preserve">quæ in Horario, <lb/>horatia; </s>
  <s xml:id="echoid-s34116" xml:space="preserve">quę in Meridiano, meridiana; </s>
  <s xml:id="echoid-s34117" xml:space="preserve">quæ denique in Hectemorio, hectemoria. </s>
  <s xml:id="echoid-s34118" xml:space="preserve">Horizontalis <lb/>
<anchor type="figure" xlink:label="fig-0546-01a" xlink:href="fig-0546-01"/>
circunferentia interiicitur <lb/>in Horizonte inter Verti-<lb/>calem circulum, &amp; </s>
  <s xml:id="echoid-s34119" xml:space="preserve">Deſcen <lb/>ſiuum, qualis eſt circunfe-<lb/>rentia Horizõtis F N: </s>
  <s xml:id="echoid-s34120" xml:space="preserve">De-<lb/>
<anchor type="note" xlink:label="note-0546-01a" xlink:href="note-0546-01"/>
ſcenſiua in Deſcenſiuo cir <lb/>
<anchor type="note" xlink:label="note-0546-02a" xlink:href="note-0546-02"/>
culo comprehenditur in-<lb/>ter centrum Solis, &amp; </s>
  <s xml:id="echoid-s34121" xml:space="preserve">verti-<lb/>cem capitis, cuiuſmodi eſt <lb/>circunferentia Deſcenſiui <lb/>
<anchor type="note" xlink:label="note-0546-03a" xlink:href="note-0546-03"/>
circuli D H: </s>
  <s xml:id="echoid-s34122" xml:space="preserve">Verticalis <lb/>clauditur inter Meridia-<lb/>num, &amp; </s>
  <s xml:id="echoid-s34123" xml:space="preserve">Horarium circu-<lb/>lum in circulo Verticali, <lb/>qualis eſt circunferentis <lb/>
<anchor type="note" xlink:label="note-0546-04a" xlink:href="note-0546-04"/>
circuli Verticalis D K: </s>
  <s xml:id="echoid-s34124" xml:space="preserve">Ho <lb/>
<anchor type="note" xlink:label="note-0546-05a" xlink:href="note-0546-05"/>
raria intercipitur in Hora-<lb/>rio circulo inter centrum <lb/>Solis, &amp; </s>
  <s xml:id="echoid-s34125" xml:space="preserve">alterutrum polo-<lb/>rũ Verticalis circuli, qua-<lb/>lis eſt circunſerentia cir-<lb/>culi Horarij A H: </s>
  <s xml:id="echoid-s34126" xml:space="preserve">Meri-<lb/>
<anchor type="note" xlink:label="note-0546-06a" xlink:href="note-0546-06"/>
diana cõtinetur inter Ho-<lb/>rizontem, atque Hectemo <lb/>rion in Meridiano circu-<lb/>lo, cuiuſmodi eſt circun-<lb/>
<anchor type="note" xlink:label="note-0546-07a" xlink:href="note-0546-07"/>
<anchor type="note" xlink:label="note-0546-08a" xlink:href="note-0546-08"/>
ferentia Meridiani A L: <lb/></s>
  <s xml:id="echoid-s34127" xml:space="preserve">Hectemoria denique in-<lb/>teriacet in Hectemorio circulo inter centrum Solis, &amp; </s>
  <s xml:id="echoid-s34128" xml:space="preserve">punctum ortus æquinoctialis, vel occaſus, <lb/>qualis eſt circunferentia Hectemorii F H. </s>
  <s xml:id="echoid-s34129" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0546-09a" xlink:href="note-0546-09"/>
</s>
</p>
<div xml:id="echoid-div1731" type="float" level="2" n="3">
<note position="right" xlink:label="note-0545-13" xlink:href="note-0545-13a" xml:space="preserve">Sex circunferen <lb/>tiæ in dictis ſex <lb/>circulis confi-<lb/>derandz ſunt.</note>
  <figure xlink:label="fig-0546-01" xlink:href="fig-0546-01a">
    <image file="0546-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0546-01"/>
  </figure>
<note position="left" xlink:label="note-0546-01" xlink:href="note-0546-01a" xml:space="preserve">Hurizõ@@lis cir-<lb/>cunfer@ntia.</note>
<note position="left" xlink:label="note-0546-02" xlink:href="note-0546-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0546-03" xlink:href="note-0546-03a" xml:space="preserve">Defcenſiuz.</note>
<note position="left" xlink:label="note-0546-04" xlink:href="note-0546-04a" xml:space="preserve">Ve@tieali@.</note>
<note position="left" xlink:label="note-0546-05" xlink:href="note-0546-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0546-06" xlink:href="note-0546-06a" xml:space="preserve">H@rati@.</note>
<note position="left" xlink:label="note-0546-07" xlink:href="note-0546-07a" xml:space="preserve">Meridiana.</note>
<note position="left" xlink:label="note-0546-08" xlink:href="note-0546-08a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0546-09" xlink:href="note-0546-09a" xml:space="preserve">Hectemoria.</note>
</div>
<p>
  <s xml:id="echoid-s34130" xml:space="preserve">CÆTERVM cùm dictæ circunferentiæ aliquando ſint quadrantes, interdum vero qua-<lb/>
<anchor type="note" xlink:label="note-0546-10a" xlink:href="note-0546-10"/>
drante maiores, minoresve; </s>
  <s xml:id="echoid-s34131" xml:space="preserve">quando quadrantem ſuperant, accipiendæ erunt eæ, quæ cum illis ſe-<lb/>micircuſum conſtituunt: </s>
  <s xml:id="echoid-s34132" xml:space="preserve">non quod omnino hoc ſit neceſſarium, ſed quòd expeditius hac ratio-<lb/>ne horologia deſcribantur. </s>
  <s xml:id="echoid-s34133" xml:space="preserve">Vt ſi v. </s>
  <s xml:id="echoid-s34134" xml:space="preserve">g. </s>
  <s xml:id="echoid-s34135" xml:space="preserve">Sol exiſtat poſt meridiem, non erit ſumenda illa circunfe-<lb/>rentia horizontalis, quæ inter Verticalem circulum ex parte orientis, &amp; </s>
  <s xml:id="echoid-s34136" xml:space="preserve">Deſcenſiuum ex parteoc-<lb/>cidentis poſita eſt, quoniam ea quadrantem ſuperat, ſed illa, quæ inter Verticalem ex parte occi-<lb/>
<anchor type="note" xlink:label="note-0546-11a" xlink:href="note-0546-11"/>
dentis, Deſcenſiuumq́ue interijcitur, quoniam hæc quadrante minor eſt. </s>
  <s xml:id="echoid-s34137" xml:space="preserve">atque ita de cæteris di-<lb/>cendum eſt. </s>
  <s xml:id="echoid-s34138" xml:space="preserve">Vnde quoniam omnes dictæ circunferentiæ initium ſumuntà tribus illis ſectioni-<lb/>
<anchor type="note" xlink:label="note-0546-12a" xlink:href="note-0546-12"/>
bus communibus trium circulorum immobilium, vt horizontalis, atque hectemoria à ſectione <lb/>æquinoctiali F G, quæ axis eſt Meridiani, cum per eius polos ducatur, Verticalis, &amp; </s>
  <s xml:id="echoid-s34139" xml:space="preserve">deſcenſiua <lb/>à gnomone D B, qui axis eſt Horizontis per illius polos incedens, meridiana denique, &amp; </s>
  <s xml:id="echoid-s34140" xml:space="preserve">horaria <lb/>à linea meridiana A B, quæ axis eſt Verticalis, cum per eius polos tranſeat: </s>
  <s xml:id="echoid-s34141" xml:space="preserve">fit, vt tempore anteme <lb/>ridiano tam horizontalis circunferentia, quàm hectemoria initium ſumat à diametro æquino-<lb/>ctiali ex parte orientis, puta ab ortu æquinoctiali; </s>
  <s xml:id="echoid-s34142" xml:space="preserve">pomeridiano vero tempore ex parte occidentis, <lb/>ſiue ab occaſu æquinoctiali. </s>
  <s xml:id="echoid-s34143" xml:space="preserve">Pari ratione efficitur, tam Verticalem circunferentiam, quàm deſcen <lb/>ſiuam principium habere in gnomone à vertice capitis, vbicunque Sol ſupra Horizontem exiſtat, <lb/>
<anchor type="note" xlink:label="note-0546-13a" xlink:href="note-0546-13"/>
quia femper minor eſt quadrante, alia vero inchoata ab oppoſito verticis, quadrãte maior. </s>
  <s xml:id="echoid-s34144" xml:space="preserve">Perſpi-<lb/>cuum denique eſt, Sole exiſtente in parte hemiſphærii auſtrali, quæ vergit à Verticali circulo ver-<lb/>ſus polum antarcticum, tam circunferentiam meridianam, quàm horariam initium habere à li-<lb/>nea meridiana ex parte auſtrali; </s>
  <s xml:id="echoid-s34145" xml:space="preserve">Sole vero exiſtente in parte hemiſphærii boreali, quæ à Verticali <lb/>circulo verſus polum arcticum porrigitur, ab eadem linea ex parte ſeptentrionali. </s>
  <s xml:id="echoid-s34146" xml:space="preserve">Quòd ſi quan <lb/>do circunferentia aliqua quadranti ſit æqualis, nihil intereſt, ab vtro ſectionis extremo initium <lb/>ſumatur,</s>
</p>
<div xml:id="echoid-div1732" type="float" level="2" n="4">
<note position="left" xlink:label="note-0546-10" xlink:href="note-0546-10a" xml:space="preserve">Nulla dictarú <lb/>circunferentia -<lb/>rum quadrani@ <lb/>ſuperare debet.</note>
<note position="left" xlink:label="note-0546-11" xlink:href="note-0546-11a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0546-12" xlink:href="note-0546-12a" xml:space="preserve">Vnde initium <lb/>habeant ſex di-<lb/>ctæ circunferen <lb/>tiæ.</note>
<note position="left" xlink:label="note-0546-13" xlink:href="note-0546-13a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s34147" xml:space="preserve">EX his autem ſex circunferentiis determinatur radii ſolaris poſitio in planis, quæ Horizon-<lb/>ti, Verticali, &amp; </s>
  <s xml:id="echoid-s34148" xml:space="preserve">Meridiano æquidiſtant, quam qualibet hora habet. </s>
  <s xml:id="echoid-s34149" xml:space="preserve">Nam horizontalis circunfe-<lb/>
<anchor type="note" xlink:label="note-0546-14a" xlink:href="note-0546-14"/>
rentia indicat vmbræ latitudinem in plano, quod Horizonti æquidiſtat, id eſt, demonſtrat, quan-<lb/>tum vmbra declinat à communi ſectione Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s34150" xml:space="preserve">illius plani, quæ ab ortu in occa-
<pb o="531" file="0547" n="547" rhead="LIBER SEXTVS."/>
ſum extenditur. </s>
  <s xml:id="echoid-s34151" xml:space="preserve">Cum enim horizontalis circunferentia eſt F N, initium habens à diametro æqui <lb/>noctiali F G, ita vt Deſcenſiuus circulus D H N, per centrum Solis H, ducatur, faciatq́ue in Hori-<lb/>zonte ſectionem N E P, cadet per propoſ. </s>
  <s xml:id="echoid-s34152" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34153" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34154" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34155" xml:space="preserve">vmbra ſtyli, cuius vertex in E, centro mundi <lb/>collocatur, vt propoſ. </s>
  <s xml:id="echoid-s34156" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34157" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34158" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34159" xml:space="preserve">oſten dimus, in communem ſectionem Deſcenſiui circuli D H N, &amp; </s>
  <s xml:id="echoid-s34160" xml:space="preserve"><lb/>plani horologii, quod Horizonti æquidiſtat. </s>
  <s xml:id="echoid-s34161" xml:space="preserve">Quoniam vero Deſcenſiuus circulus, &amp; </s>
  <s xml:id="echoid-s34162" xml:space="preserve">Verticalis <lb/>proprie dictus faciunt cum plano horologii horizontalis communes ſectiones rectis N E P, FEG, <lb/>
<anchor type="note" xlink:label="note-0547-01a" xlink:href="note-0547-01"/>
parallelas, comprehendent hæ ſectiones in plano horologii angulum æqualem angulo N E F; </s>
  <s xml:id="echoid-s34163" xml:space="preserve">at-<lb/>
<anchor type="note" xlink:label="note-0547-02a" xlink:href="note-0547-02"/>
que adeo ex circulo, quì in eodem plano deſcribitur ex loco ſtyli, vbi ille angulus efficitur, aufe-<lb/>rent arcum ſimilem circunferentiæ horizontali F N, ex iis, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s34164" xml:space="preserve">33. </s>
  <s xml:id="echoid-s34165" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34166" xml:space="preserve">6. </s>
  <s xml:id="echoid-s34167" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s34168" xml:space="preserve">demonſtrauimus. </s>
  <s xml:id="echoid-s34169" xml:space="preserve">Recte ergo horizontalis circunferentia F N, vel potius ei ſimilis in plano <lb/>
<anchor type="note" xlink:label="note-0547-03a" xlink:href="note-0547-03"/>
horologii indicare dicitur latitudinem vmbræ, cum oſtendat, quantum linea recta, in quam <lb/>vmbra cadit, diſtare debeat à com muni ſectione Verticalis, &amp; </s>
  <s xml:id="echoid-s34170" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s34171" xml:space="preserve">Complementum <lb/>vero circunferentiæ deſcenſiuæ D H, nempe circunferentia H N, oſtendit altitudinem Solis tunc <lb/>ſupra Horizontem. </s>
  <s xml:id="echoid-s34172" xml:space="preserve">Igitur, vt in præcedenti lib. </s>
  <s xml:id="echoid-s34173" xml:space="preserve">demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s34174" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34175" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34176" xml:space="preserve">5. </s>
  <s xml:id="echoid-s34177" xml:space="preserve">per eam via Geo <lb/>metrica longitudinem vmbræ cognoſcemus. </s>
  <s xml:id="echoid-s34178" xml:space="preserve">Quare determinata iam erit poſitio radij Solis, hoc <lb/>
<anchor type="note" xlink:label="note-0547-04a" xlink:href="note-0547-04"/>
eſt, extremitas vmbræ. </s>
  <s xml:id="echoid-s34179" xml:space="preserve">Atque hæ duæ circunferentiæ, hot izontalis ſcilicet, &amp; </s>
  <s xml:id="echoid-s34180" xml:space="preserve">deſcenſiua, requi-<lb/>runtur, &amp; </s>
  <s xml:id="echoid-s34181" xml:space="preserve">ſatis ſunt ad horologium horizontale conſtruendum, vt poſtea dicemus. </s>
  <s xml:id="echoid-s34182" xml:space="preserve">Rurſus Ver-<lb/>ticalis circunferentia D K, initium habens à gnomone D B, oſtendit latitudinem vmbræ in horo-<lb/>logio Verticali. </s>
  <s xml:id="echoid-s34183" xml:space="preserve">Nam vmbra ſtyli verticem in E, habentis cadet, per propoſ. </s>
  <s xml:id="echoid-s34184" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34185" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34186" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34187" xml:space="preserve">in commu-<lb/>nem ſectionem circuli horarii A K C O, &amp; </s>
  <s xml:id="echoid-s34188" xml:space="preserve">plani horologii, quod Verticali æquidiſtat. </s>
  <s xml:id="echoid-s34189" xml:space="preserve">Quia ve-<lb/>
<anchor type="note" xlink:label="note-0547-05a" xlink:href="note-0547-05"/>
ro Horarius circulus, &amp; </s>
  <s xml:id="echoid-s34190" xml:space="preserve">Meridianus faciunt cum plano horologii Verticalis communes ſectio-<lb/>
<anchor type="note" xlink:label="note-0547-06a" xlink:href="note-0547-06"/>
nes rectis K E O, D E B, parallelas, cõprehendent hæ ſectiones in plano horologij angulum æqua <lb/>
<anchor type="note" xlink:label="note-0547-07a" xlink:href="note-0547-07"/>
lem angulo K E D; </s>
  <s xml:id="echoid-s34191" xml:space="preserve">ac proinde auferent ex circulo, qui in eodem plano deſcribitur ex loco ſtyli, <lb/>vbi angulus ille efficitur, arcum ſimilem circunferentiæ Verticali D K, ex ijs, quæ in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s34192" xml:space="preserve">33. </s>
  <s xml:id="echoid-s34193" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34194" xml:space="preserve">6. </s>
  <s xml:id="echoid-s34195" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34196" xml:space="preserve">ſcripſimus. </s>
  <s xml:id="echoid-s34197" xml:space="preserve">Circunferentia ergo Verticalis D K, vel potius ei ſimilis in plano <lb/>horologii indicat latitudinem vmbræ, cum demonſtret, quantum linea recta, in quam vmbra ca-<lb/>dit, diſtare debeat à communi ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s34198" xml:space="preserve">plani horologii. </s>
  <s xml:id="echoid-s34199" xml:space="preserve">Complementum vero ho-<lb/>rariæ circunferentiæ A H, hoc eſt, circunferentia H K, manifeſtat altitudinem Solis tunc ſupra <lb/>Verticalem. </s>
  <s xml:id="echoid-s34200" xml:space="preserve">Quamobrem ex ea, vt propoſ. </s>
  <s xml:id="echoid-s34201" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34202" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34203" xml:space="preserve">5. </s>
  <s xml:id="echoid-s34204" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s34205" xml:space="preserve">oſtendimus, inueniemus via Geo-<lb/>metrica longitudinem vmbræ; </s>
  <s xml:id="echoid-s34206" xml:space="preserve">ac propterea determinata iam erit poſitio radij ſolaris, id eſt, ex-<lb/>
<anchor type="note" xlink:label="note-0547-08a" xlink:href="note-0547-08"/>
tremitas vmbræ. </s>
  <s xml:id="echoid-s34207" xml:space="preserve">Atque ita ex circunferentia Verticali, &amp; </s>
  <s xml:id="echoid-s34208" xml:space="preserve">horaria conficietur horologium Verti-<lb/>
<anchor type="note" xlink:label="note-0547-09a" xlink:href="note-0547-09"/>
cale, vt ſuo loco dicetur. </s>
  <s xml:id="echoid-s34209" xml:space="preserve">Poſtremo circunferentia meridiana A L, à linea meridiana A C, inchoa-<lb/>ta monſtrat in horologio Meridiano vmbræ latitudinem. </s>
  <s xml:id="echoid-s34210" xml:space="preserve">Eodem enim pacto vmbra ſtyli cadet in <lb/>communem ſectionem circuli hectemorij F L G M, &amp; </s>
  <s xml:id="echoid-s34211" xml:space="preserve">plani horologii, quod Meridiano æquidi-<lb/>ſtat. </s>
  <s xml:id="echoid-s34212" xml:space="preserve">Et quoniam circulus Hectemorion, &amp; </s>
  <s xml:id="echoid-s34213" xml:space="preserve">Horizon cum plano horologii faciunt communes ſe-<lb/>ctiones rectis L E O, A E C, parallelas, continebunt hæ ſectiones in plano horologii ad locum ſty-<lb/>
<anchor type="note" xlink:label="note-0547-10a" xlink:href="note-0547-10"/>
li angulum æqualem angulo L E A; </s>
  <s xml:id="echoid-s34214" xml:space="preserve">proptereaq́ue, per ea, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s34215" xml:space="preserve">33. </s>
  <s xml:id="echoid-s34216" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34217" xml:space="preserve">6. </s>
  <s xml:id="echoid-s34218" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s34219" xml:space="preserve">
<anchor type="note" xlink:label="note-0547-11a" xlink:href="note-0547-11"/>
demonſtrata ſunt à nobis, auferent ex circulo, qui in eodem plano ex loco ſtyli deſcribitur, arcum <lb/>ſimilem circunferentiæ meridianæ A L. </s>
  <s xml:id="echoid-s34220" xml:space="preserve">Quæ cum ita ſint, iure optimo dicitur meridiana circun-<lb/>ferentia, vel potius ei ſimilis in plano horologii indicare latitudinem vmbræ, cum oſtendat, quan <lb/>
<anchor type="note" xlink:label="note-0547-12a" xlink:href="note-0547-12"/>
tum linea recta, in quam vmbra cadit, diſtare debeat à communi ſectione Horizontis, &amp; </s>
  <s xml:id="echoid-s34221" xml:space="preserve">plani ho-<lb/>rologii. </s>
  <s xml:id="echoid-s34222" xml:space="preserve">Complementum autem hectemoriæ circunferentiæ F H, nimirum arcus H L, metitur al-<lb/>titudinem Solis tunc tem poris ſupra Meridianum circulum, per quam, ex ijs, quæ propoſ. </s>
  <s xml:id="echoid-s34223" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34224" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34225" xml:space="preserve">5. <lb/></s>
  <s xml:id="echoid-s34226" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s34227" xml:space="preserve">tradita ſunt, reperiemus via Geometrica longitudinem vmbræ, ideoq́ue determi-<lb/>
<anchor type="note" xlink:label="note-0547-13a" xlink:href="note-0547-13"/>
nata erit poſitio radii ſolaris, nempe extremitas vmbræ. </s>
  <s xml:id="echoid-s34228" xml:space="preserve">Atque hæ duæ circunferentiæ, meridia-<lb/>na &amp; </s>
  <s xml:id="echoid-s34229" xml:space="preserve">hectemoria, aſſumuntur ad horologij Meridiani compoſitionem, vt infra explicabimus. <lb/></s>
  <s xml:id="echoid-s34230" xml:space="preserve">Itaque totum artificium deſcribendorum horologiorum ex Analemmate Ptolemæi, conſiſtit in <lb/>inuentione dictarum circunferentiarum pro ſingulis horis, quas iamiam inueſtigare docebimus.</s>
  <s xml:id="echoid-s34231" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1733" type="float" level="2" n="5">
<note position="left" xlink:label="note-0546-14" xlink:href="note-0546-14a" xml:space="preserve">Oſſcia dictatũ <lb/>ſex circunferen-<lb/>tiarum.</note>
<note position="right" xlink:label="note-0547-01" xlink:href="note-0547-01a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0547-02" xlink:href="note-0547-02a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0547-03" xlink:href="note-0547-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0547-04" xlink:href="note-0547-04a" xml:space="preserve">Horizotalis cir <lb/>cunferentia, &amp; <lb/>deſcẽſiua requi-<lb/>runtur ad con-<lb/>ſtructionem ho <lb/>rologii horizon <lb/>talis.</note>
<note position="left" xlink:label="note-0547-05" xlink:href="note-0547-05a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0547-06" xlink:href="note-0547-06a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0547-07" xlink:href="note-0547-07a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0547-08" xlink:href="note-0547-08a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0547-09" xlink:href="note-0547-09a" xml:space="preserve">Vertica lis cir-<lb/>cunferentia. &amp; <lb/>horatia requirũ <lb/>tur ad conſtiu-<lb/>ctionem horolo <lb/>g@ Verticalis.</note>
<note position="right" xlink:label="note-0547-10" xlink:href="note-0547-10a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0547-11" xlink:href="note-0547-11a" xml:space="preserve">10. vndec.</note>
<note position="left" xlink:label="note-0547-12" xlink:href="note-0547-12a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0547-13" xlink:href="note-0547-13a" xml:space="preserve">Meridiana cir-<lb/>cunferentia, &amp; <lb/>hectemoria re-<lb/>quiruntur ad <lb/>compoſitionem <lb/>horologii Meri-<lb/>diani.</note>
</div>
</div>
<div xml:id="echoid-div1735" type="section" level="1" n="469">
<head xml:id="echoid-head498" style="it" xml:space="preserve">INVENTIO CIRCVNFERENTIÆ HECTEMORIÆ, <lb/>
horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, de
quibus in antecedenti cap. dictum eſt, ex Analemmate,
Sole exiſtente in Aequatore, ad quamcunque
latitudinem. CAP. II.</head>
<p>
  <s xml:id="echoid-s34232" xml:space="preserve">SIT Meridianus Analemmatis A B C D, in quo duæ diametri ſeſe ad angulos rectos ſecent <lb/>A C, B D, quarum illa ſit communis ſectio Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s34233" xml:space="preserve">Meridiani, hæc vero ſectio cõ-<lb/>munis eiuſdem Meridiani, &amp; </s>
  <s xml:id="echoid-s34234" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s34235" xml:space="preserve">Sit quoque axis mundi HI, ita vt arcus D H, comple-<lb/>ctatur grad. </s>
  <s xml:id="echoid-s34236" xml:space="preserve">42. </s>
  <s xml:id="echoid-s34237" xml:space="preserve">quanta videlicet eſt Romæ altitudo poli, ad quam omnia horologia in hoc opere <lb/>conſtruimus. </s>
  <s xml:id="echoid-s34238" xml:space="preserve">Aequatoris autem diameter ſit F G, ſecans axem ad angulos rectos in centro E. </s>
  <s xml:id="echoid-s34239" xml:space="preserve">Si <lb/>igitur cir ca diametrum FG, intelligatur deſcriptus ſemicirculus Aequatoris ad Meridianum re-
<pb o="532" file="0548" n="548" rhead="GNOMONICES"/>
ctus, &amp; </s>
  <s xml:id="echoid-s34240" xml:space="preserve">ad orientem vergens, (poſito Meridiano in proprio ſitu) erit is omnino æqualis ſemicir-<lb/>culo F H G, propter eandem diametrum F G, in vtroque ſemicirculo. </s>
  <s xml:id="echoid-s34241" xml:space="preserve">Quare recte poterit hic <lb/>pro illo accipi, ita vt F H G, fungatur officio ſemicirculi Aequatoris orientalis, quem videlicet <lb/>Meridianus ab occidentali reliquo ſeparat: </s>
  <s xml:id="echoid-s34242" xml:space="preserve">Eritq́ue F H, quadrans Aequatoris orientalis ſupra <lb/>
<anchor type="figure" xlink:label="fig-0548-01a" xlink:href="fig-0548-01"/>
terram, alter vero H G, quadrans <lb/>orientalis infra terram, ita vt re-<lb/>cta E H, communis ſectio ſit Ho-<lb/>rizontis, &amp; </s>
  <s xml:id="echoid-s34243" xml:space="preserve">ſemicirculi Acquato-<lb/>ris orientalis. </s>
  <s xml:id="echoid-s34244" xml:space="preserve">Quod facile perci-<lb/>pietur, ſi ſemicirculus Aequato-<lb/>
<anchor type="note" xlink:label="note-0548-01a" xlink:href="note-0548-01"/>
ris F H G, concipiatur conuerti <lb/>circa diametrum F G, donec re-<lb/>ctus inſiſtat plano Meridiani; </s>
  <s xml:id="echoid-s34245" xml:space="preserve">ſi-<lb/>militer &amp; </s>
  <s xml:id="echoid-s34246" xml:space="preserve">ſemicirculus Horizon <lb/>tis ſupra diametrum B D, poſitus <lb/>ad idem planum Meridiani re-<lb/>ctus. </s>
  <s xml:id="echoid-s34247" xml:space="preserve">Erit enim tunc communis <lb/>horum ſemicirculorum ſectio ad <lb/>idem planum Meridiani perpen-<lb/>dicularis; </s>
  <s xml:id="echoid-s34248" xml:space="preserve">atque adeo, per defin. <lb/></s>
  <s xml:id="echoid-s34249" xml:space="preserve">
<anchor type="note" xlink:label="note-0548-02a" xlink:href="note-0548-02"/>
<anchor type="note" xlink:label="note-0548-03a" xlink:href="note-0548-03"/>
3. </s>
  <s xml:id="echoid-s34250" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34251" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34252" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34253" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34254" xml:space="preserve">ad rectam F G. <lb/></s>
  <s xml:id="echoid-s34255" xml:space="preserve">Quocirca recta E H, ad F G, per-<lb/>pendicularis cõmunis ſectio erit <lb/>Aequatoris, &amp; </s>
  <s xml:id="echoid-s34256" xml:space="preserve">Horizontis. </s>
  <s xml:id="echoid-s34257" xml:space="preserve">Nulla <lb/>cnim alia recta in plano ſemicir-<lb/>culi Aequatoris F H G, ad F G, in <lb/>E, perpendicularis eſſe poteſt, <lb/>pręter E H; </s>
  <s xml:id="echoid-s34258" xml:space="preserve">quod tamen requiri-<lb/>tur ad communem ſectionem Horizontis, &amp; </s>
  <s xml:id="echoid-s34259" xml:space="preserve">Aequatoris, vt diximus. </s>
  <s xml:id="echoid-s34260" xml:space="preserve">Itaque cum quadrans Ae-<lb/>quatoris F H, tendat ab ortu, qui in H, vbi Horizon Aequatorem interſecat, ponitur, ad meridiem <lb/>
<anchor type="note" xlink:label="note-0548-04a" xlink:href="note-0548-04"/>
vſque, qui in F, ponitur, vbi Aequator Meridianum ſecat, poterit non incongrue idem quadrans <lb/>gerere vices alterius quadrantis, qui à meridie F, incipit, &amp; </s>
  <s xml:id="echoid-s34261" xml:space="preserve">in occaſu finitur, ita vt H, ſit etiam pun <lb/>ctum occaſus. </s>
  <s xml:id="echoid-s34262" xml:space="preserve">Habet enim quadrans Aequatoris occidentalis eandem prorſus poſitionem in ſphę <lb/>ra, quam orientalis: </s>
  <s xml:id="echoid-s34263" xml:space="preserve">Atque hac ratione quadrans F H, repręſentabit nobis totum ſemicirculum <lb/>Aequatoris ſupra terram.</s>
  <s xml:id="echoid-s34264" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1735" type="float" level="2" n="1">
  <figure xlink:label="fig-0548-01" xlink:href="fig-0548-01a">
    <image file="0548-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0548-01"/>
  </figure>
<note position="left" xlink:label="note-0548-01" xlink:href="note-0548-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0548-02" xlink:href="note-0548-02a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0548-03" xlink:href="note-0548-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0548-04" xlink:href="note-0548-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s34265" xml:space="preserve">STATVATVR igitur Sol in alterutro æquinoctiorum in puncto K, æquinoctialis circu-<lb/>
<anchor type="note" xlink:label="note-0548-05a" xlink:href="note-0548-05"/>
li, ſiue illud punctum terminet horam aliquam à mer. </s>
  <s xml:id="echoid-s34266" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s34267" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s34268" xml:space="preserve">ſiue ab or. </s>
  <s xml:id="echoid-s34269" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s34270" xml:space="preserve">aut certe <lb/>particulam aliquam horæ, ita vt H K, ſit arcus Aequatoris inter centrum Solis, atque Horizon-<lb/>tem ſiue ex parte orientis, ſiue occidentis interiectus; </s>
  <s xml:id="echoid-s34271" xml:space="preserve">arcus vero Aequatoris F K, poſitus ſit inter <lb/>Meridianum, &amp; </s>
  <s xml:id="echoid-s34272" xml:space="preserve">centrum Solis ſiue ex parte orientis, ſiue occidentis: </s>
  <s xml:id="echoid-s34273" xml:space="preserve">inquirendumq́ue ſit Geo-<lb/>
<anchor type="note" xlink:label="note-0548-06a" xlink:href="note-0548-06"/>
metrice ex Analem mate, quantæ ſint eo temp<unsure/>ore ſex expoſitæ circunferentiæ. </s>
  <s xml:id="echoid-s34274" xml:space="preserve">Ducatur ex K, pun <lb/>cto datæ horæ, vbi Sol ponitur, recta K L, ad F G, diametrum Aequatoris perpendicularis; </s>
  <s xml:id="echoid-s34275" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34276" xml:space="preserve">per <lb/>L, excitentur ad B E, A E, duæ perpendiculares N L M, O L P: </s>
  <s xml:id="echoid-s34277" xml:space="preserve">Ex quibus, quoniam maiores ſunt <lb/>recta k L, (Nam ductis rectis E K, E M, E P; </s>
  <s xml:id="echoid-s34278" xml:space="preserve">quoniam quadrata earum æqualia inter ſe ſunt, eſtq́; <lb/></s>
  <s xml:id="echoid-s34279" xml:space="preserve">quadratum ex E K, æquale duobus quadratis ſimul ex E L, L K, &amp; </s>
  <s xml:id="echoid-s34280" xml:space="preserve">quadratum ex E M, duobus <lb/>
<anchor type="note" xlink:label="note-0548-07a" xlink:href="note-0548-07"/>
quadratis ex E N, N M, &amp; </s>
  <s xml:id="echoid-s34281" xml:space="preserve">quadratum ex E P, duobus quadratis ex E O, O P; </s>
  <s xml:id="echoid-s34282" xml:space="preserve">erunt duo quadrata <lb/>ex E L, L K, æqualia tam duobus quadratis ex E N, N M, quàm duobus ex E O, O P. </s>
  <s xml:id="echoid-s34283" xml:space="preserve">Cum igitur <lb/>&amp; </s>
  <s xml:id="echoid-s34284" xml:space="preserve">quadratum ex E N, &amp; </s>
  <s xml:id="echoid-s34285" xml:space="preserve">ex E O, minus ſit quadrato ex E L, quòd tam linea E N, quàm E O, minor <lb/>
<anchor type="note" xlink:label="note-0548-08a" xlink:href="note-0548-08"/>
ſit in triangulis rectangulis E L N, E L O, recta E L; </s>
  <s xml:id="echoid-s34286" xml:space="preserve">erit tam reliquum quadratum rectæ N M, <lb/>quàm rectæ O P, maius quadrato reliquo rectę L K; </s>
  <s xml:id="echoid-s34287" xml:space="preserve">atque ob id vtrauis recta N M, O P, maior erit <lb/>
<anchor type="note" xlink:label="note-0548-09a" xlink:href="note-0548-09"/>
quàm recta L K) abſcindantur ipſi K L, duæ æquales N Q, O R; </s>
  <s xml:id="echoid-s34288" xml:space="preserve">atque per puncta Q, R, ex cen <lb/>tro E, duæ rectæ educantur E Q S, E R T, ſecantes circunferentiam Meridiani in S, &amp; </s>
  <s xml:id="echoid-s34289" xml:space="preserve">T. </s>
  <s xml:id="echoid-s34290" xml:space="preserve">Quibus <lb/>rite peractis, inuentæ erunt omnes dictæ ſex circun ferentiæ ad tempus propo ſitum, cum nimirum <lb/>Sol in puncto Aequatoris K, exiſtit. </s>
  <s xml:id="echoid-s34291" xml:space="preserve">Nam, vt in ſequenti cap. </s>
  <s xml:id="echoid-s34292" xml:space="preserve">demonſtrabimus, H K, erit circunfe-<lb/>rentia hectemoria; </s>
  <s xml:id="echoid-s34293" xml:space="preserve">B M, horaria; </s>
  <s xml:id="echoid-s34294" xml:space="preserve">A P, deſcenſiua; </s>
  <s xml:id="echoid-s34295" xml:space="preserve">B F, meridiana; </s>
  <s xml:id="echoid-s34296" xml:space="preserve">A T, Verticalis; </s>
  <s xml:id="echoid-s34297" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34298" xml:space="preserve">A S, hori-<lb/>zontalis. </s>
  <s xml:id="echoid-s34299" xml:space="preserve">Aliorum porro linea mentorum huius figuræ, cuiuſmodi ſunt lineæ F Y, S V, T X, F Z, <lb/>K N, K O, vſus apparebit in cap. </s>
  <s xml:id="echoid-s34300" xml:space="preserve">7. </s>
  <s xml:id="echoid-s34301" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s34302" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1736" type="float" level="2" n="2">
<note position="left" xlink:label="note-0548-05" xlink:href="note-0548-05a" xml:space="preserve">Inuentio ſex di <lb/>ctarum circun-<lb/>ferentiarum ex <lb/>Analemmate, <lb/>Sole exiſten te <lb/>in Aequatore.</note>
<note position="left" xlink:label="note-0548-06" xlink:href="note-0548-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0548-07" xlink:href="note-0548-07a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0548-08" xlink:href="note-0548-08a" xml:space="preserve">19. primi.</note>
<note position="left" xlink:label="note-0548-09" xlink:href="note-0548-09a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1738" type="section" level="1" n="470">
<head xml:id="echoid-head499" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s34303" xml:space="preserve">EX dictis patet ratio, qua, Sole exiſtente in Aequatore, ſeorſum inueſtigari poſſit quæcunque ex
<pb o="533" file="0549" n="549" rhead="LIBER SEXTVS."/>
dictis circunferentĳs, cum opus fuerit, nulla habita ratione aliarum. </s>
  <s xml:id="echoid-s34304" xml:space="preserve">Hactenus enim omnes ſex ſimul <lb/>
<anchor type="note" xlink:label="note-0549-01a" xlink:href="note-0549-01"/>
indagatæ ſunt, quibus non ſemper indigemus, ſed vna aut altera duntaxat: </s>
  <s xml:id="echoid-s34305" xml:space="preserve">quia vt in præcedenti cap. <lb/></s>
  <s xml:id="echoid-s34306" xml:space="preserve">dixim@s, ad conſtructionem horologĳ horizontalis neceſſariæ tantum ſunt circunferentia horizonta-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s34307" xml:space="preserve">deſcenſiua; </s>
  <s xml:id="echoid-s34308" xml:space="preserve">pro Verticali vero horologio indigemus circunferentia Verticali, &amp; </s>
  <s xml:id="echoid-s34309" xml:space="preserve">horaria; </s>
  <s xml:id="echoid-s34310" xml:space="preserve">pro <lb/>horologio denique Meridiano inueniendæ ſunt circunferentia meridiana, &amp; </s>
  <s xml:id="echoid-s34311" xml:space="preserve">hectemoria. </s>
  <s xml:id="echoid-s34312" xml:space="preserve">Pro qualibet <lb/>ergo inueſtiganda, ad diametrum Aequatoris F G, ex K, puncto horæ, vbi Sol conſtituitur, ducenda <lb/>est perpendicularis K L. </s>
  <s xml:id="echoid-s34313" xml:space="preserve">Deinde ſi quærenda proponitur circunferentia horizontalis, ducenda eſt <lb/>
<anchor type="note" xlink:label="note-0549-02a" xlink:href="note-0549-02"/>
per punctũ L, ad diametrũ Horizontis B D, perpendicularis M N, ex qua ſi abſcindatur recta N e, rectæ <lb/>K L, æqualis, ducatur{q́ue} ex centro E, per Q, recta E Q, ſecans circunferentiã Meridiani in S, erit A S, <lb/>circunferentia horizontalis ſumens in Analemmate initium à diametro Verticalis circuli, ſiue à gno-<lb/>
<anchor type="note" xlink:label="note-0549-03a" xlink:href="note-0549-03"/>
mone A E. </s>
  <s xml:id="echoid-s34314" xml:space="preserve">Si vero inuenienda ſit circunferentia deſcenſiua, ducenda eſt per punctum L, ad diametrũ <lb/>
<anchor type="note" xlink:label="note-0549-04a" xlink:href="note-0549-04"/>
Verticalis diametri A C, perpendicularis O P, ſecans circunferentiam Meridiani in P. </s>
  <s xml:id="echoid-s34315" xml:space="preserve">Nam A P, <lb/>erit circunferentia deſcenſiua à diametro Verticalis circuli A C, in Analemmate inchoata. </s>
  <s xml:id="echoid-s34316" xml:space="preserve">Quod ſi <lb/>cir cunfercntia Verticalis deſideretur, ducenda eſt per punctum L, ad diametrum Verticalis circuli <lb/>
<anchor type="note" xlink:label="note-0549-05a" xlink:href="note-0549-05"/>
A C, perpendicularis O P. </s>
  <s xml:id="echoid-s34317" xml:space="preserve">Si enim ex ea detrahatur recta O R, rectæ K L, æqualis, ducatur{q́ue} ex centro <lb/>E, per R, recta E R, ſecans circunferentiam Meridiani in T, erit A T, cir cunferentia Verticalis inci-<lb/>piens in Analemmate à V erticalis diametro A C. </s>
  <s xml:id="echoid-s34318" xml:space="preserve">Si autem quæratur circunferentia horaria, ducẽda <lb/>
<anchor type="note" xlink:label="note-0549-06a" xlink:href="note-0549-06"/>
eſt per L, ad Horizontis diametrum B D, perpendicularis M N, ſecans circunferentiam Meridiani <lb/>in M. </s>
  <s xml:id="echoid-s34319" xml:space="preserve">Nam B M, erit cir cunferentia horaria principium ſuum ſtatuens in Horizontis diametro <lb/>B D. </s>
  <s xml:id="echoid-s34320" xml:space="preserve">Pro meridiana cir cunferentia accipiatur arcus B F, inter Horizontem &amp; </s>
  <s xml:id="echoid-s34321" xml:space="preserve">Aequatorem, hoc eſt, <lb/>
<anchor type="note" xlink:label="note-0549-07a" xlink:href="note-0549-07"/>
<anchor type="note" xlink:label="note-0549-08a" xlink:href="note-0549-08"/>
complementum altitudinis poli ſupra Horizontem. </s>
  <s xml:id="echoid-s34322" xml:space="preserve">Pro cir cunferentia denique hectemoria ſumendus eſt <lb/>
<anchor type="note" xlink:label="note-0549-09a" xlink:href="note-0549-09"/>
ar cus H K, inter ortum vel occaſum, &amp; </s>
  <s xml:id="echoid-s34323" xml:space="preserve">locum Solis, hoc eſt, complementum diſtantiæ Solis à meridie.</s>
  <s xml:id="echoid-s34324" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1738" type="float" level="2" n="1">
<note position="right" xlink:label="note-0549-01" xlink:href="note-0549-01a" xml:space="preserve">Quo pacto, So-<lb/>le exiſtente in <lb/>Aequatore, quę <lb/>libet circunfe-<lb/>rentiarum in-<lb/>ueniatur, non <lb/>habita ratione <lb/>aliatum.</note>
<note position="right" xlink:label="note-0549-02" xlink:href="note-0549-02a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0549-03" xlink:href="note-0549-03a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0549-04" xlink:href="note-0549-04a" xml:space="preserve">Deſcenſiua<unsure/>.</note>
<note position="right" xlink:label="note-0549-05" xlink:href="note-0549-05a" xml:space="preserve">Vertioalis.</note>
<note position="right" xlink:label="note-0549-06" xlink:href="note-0549-06a" xml:space="preserve">Horaria.</note>
<note position="left" xlink:label="note-0549-07" xlink:href="note-0549-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0549-08" xlink:href="note-0549-08a" xml:space="preserve">Meridiana.</note>
<note position="right" xlink:label="note-0549-09" xlink:href="note-0549-09a" xml:space="preserve">Hectemoria.</note>
</div>
</div>
<div xml:id="echoid-div1740" type="section" level="1" n="471">
<head xml:id="echoid-head500" style="it" xml:space="preserve">DEMONSTRATIO EORVM, QV AE <lb/>dicta ſunt in antecedenti cap. de inuentione prædictarum <lb/>ſex circunferentiarum. CAP. III.</head>
<p>
  <s xml:id="echoid-s34325" xml:space="preserve">INTELLIGATVR circa diametrum Aequatoris F G, in figura præcedentis cap. </s>
  <s xml:id="echoid-s34326" xml:space="preserve">ſemi-<lb/>
<anchor type="note" xlink:label="note-0549-10a" xlink:href="note-0549-10"/>
circulus Aequatoris F K H G, conuerſus ad propriã poſitionem, hoc eſt, donec ad Meridianum <lb/>A B C D, rectus ſit, tranſeatq́ue per K, locum Solis. </s>
  <s xml:id="echoid-s34327" xml:space="preserve">Circa gnomonem vero A C, concipiatur ſe-<lb/>
<anchor type="note" xlink:label="note-0549-11a" xlink:href="note-0549-11"/>
micirculus Verticalis A X V H C, ad eundem Meridianum rectus: </s>
  <s xml:id="echoid-s34328" xml:space="preserve">Et circa eundem gnomonem <lb/>A C, per centrum Solis k, deſcriptus concipiatur Deſcenſiui ſemicirculus A K Y Z C. </s>
  <s xml:id="echoid-s34329" xml:space="preserve">Item cir-<lb/>ca Horizontis diametrum BD, eius ſemicirculus cogitetur deſcriptus B Y a H D, ad Meridianũ <lb/>rectus: </s>
  <s xml:id="echoid-s34330" xml:space="preserve">Et circa eandem ſemicirculus Horarij B K X b D, per centrum Solis K, ductus; </s>
  <s xml:id="echoid-s34331" xml:space="preserve">Hectemo-<lb/>
<anchor type="figure" xlink:label="fig-0549-01a" xlink:href="fig-0549-01"/>
rii porrò ſemicirculus idẽ pror-<lb/>ſus eſt, qui Aequatoris F K H G, <lb/>ad propriam poſitionem con-<lb/>uerſus, propterea quòd tam <lb/>Aequator, quàm Hectemorion <lb/>per centrum Solis k, tranſit, &amp; </s>
  <s xml:id="echoid-s34332" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0549-12a" xlink:href="note-0549-12"/>
vtriuſque eadem eſt diameter, <lb/>nempe communis ſectio Aequa <lb/>toris, &amp; </s>
  <s xml:id="echoid-s34333" xml:space="preserve">Horizontis, cuius me-<lb/>dietas eſt E H. </s>
  <s xml:id="echoid-s34334" xml:space="preserve">Deinde produ-<lb/>cta recta M N, vſque add, intel-<lb/>ligatur ex B, polo Verticalis cir-<lb/>culi, &amp; </s>
  <s xml:id="echoid-s34335" xml:space="preserve">interuallo B M, deſcri-<lb/>ptus in ſphæræ ſuperficie ſemi-<lb/>circulus M K a Z d, qui, per <lb/>propoſ. </s>
  <s xml:id="echoid-s34336" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34337" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34338" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34339" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34340" xml:space="preserve">paralle-<lb/>
<anchor type="note" xlink:label="note-0549-13a" xlink:href="note-0549-13"/>
lus erit Verticali circulo. </s>
  <s xml:id="echoid-s34341" xml:space="preserve">Et quo <lb/>niam communes ſectiones, quas <lb/>Verticalis, &amp; </s>
  <s xml:id="echoid-s34342" xml:space="preserve">hic ſemicirculus <lb/>cum Meridiano ſaciunt, paralle <lb/>
<anchor type="note" xlink:label="note-0549-14a" xlink:href="note-0549-14"/>
læ ſunt: </s>
  <s xml:id="echoid-s34343" xml:space="preserve">Sunt autem rectæ A C, <lb/>M d, inter ſe parallelæ, ob angu-<lb/>
<anchor type="note" xlink:label="note-0549-15a" xlink:href="note-0549-15"/>
los rectos A E N, M N E, eſtq́; <lb/></s>
  <s xml:id="echoid-s34344" xml:space="preserve">A C, communis ſectio Verticalis, ac Meridiani; </s>
  <s xml:id="echoid-s34345" xml:space="preserve">erit M d, cõmunis ſectio ſemicirculi M k a Z d, <lb/>&amp; </s>
  <s xml:id="echoid-s34346" xml:space="preserve">Meridiani. </s>
  <s xml:id="echoid-s34347" xml:space="preserve">Quia vero Aequatoris ſemicirculus F K H G, &amp; </s>
  <s xml:id="echoid-s34348" xml:space="preserve">ſemicirculus M K a Z d, ad Me-<lb/>ridianum recti ſunt, (Nam cum Meridianus per polos ſemicirculi M K a Z d, ducatur, rectus <lb/>erit, per propoſ. </s>
  <s xml:id="echoid-s34349" xml:space="preserve">15. </s>
  <s xml:id="echoid-s34350" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34351" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34352" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34353" xml:space="preserve">ad ipſum, at que adeo viciſſim &amp; </s>
  <s xml:id="echoid-s34354" xml:space="preserve">ipſe ſemicirculus ad Meridia-
<pb o="534" file="0550" n="550" rhead="GNOMONICES"/>
num rectus erit: </s>
  <s xml:id="echoid-s34355" xml:space="preserve">Aequator autem rectus poſitus eſt ad Meridianum in proprio ſitu) erit quoque <lb/>communis eorum ſectio ad eundem per pendicularis, ideoq́ue per defin. </s>
  <s xml:id="echoid-s34356" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34357" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34358" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34359" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34360" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34361" xml:space="preserve">ad re-<lb/>
<anchor type="note" xlink:label="note-0550-01a" xlink:href="note-0550-01"/>
ctam F G. </s>
  <s xml:id="echoid-s34362" xml:space="preserve">Cum ergo recta K L, per defin. </s>
  <s xml:id="echoid-s34363" xml:space="preserve">4. </s>
  <s xml:id="echoid-s34364" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34365" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34366" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34367" xml:space="preserve">perpendicularis ſit ad Meridiani planũ, <lb/>quòd ſit in plano Aequatoris ad Meridianum recto, perpendicularisq́ue ad F G, communem ſe-<lb/>ctionem Aequatoris, &amp; </s>
  <s xml:id="echoid-s34368" xml:space="preserve">Meridiani; </s>
  <s xml:id="echoid-s34369" xml:space="preserve">erit recta K L, communis ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s34370" xml:space="preserve">ſemicirculi <lb/>M K a Z d, cum horum circulorum plana ſe mutuo ſecent in puncto L; </s>
  <s xml:id="echoid-s34371" xml:space="preserve">ac propterea ſemicirculus <lb/>M K a Z d, per K, locum Solis tranſibit. </s>
  <s xml:id="echoid-s34372" xml:space="preserve">Recta autem a N, communis ſectio erit eiuſdem ſemi-<lb/>
<anchor type="figure" xlink:label="fig-0550-01a" xlink:href="fig-0550-01"/>
circuli, atque Horizontis. </s>
  <s xml:id="echoid-s34373" xml:space="preserve">Rur-<lb/>ſus producta recta P O, vſque ad <lb/>e, intelligatur in ſuperficie ſphę <lb/>
<anchor type="note" xlink:label="note-0550-02a" xlink:href="note-0550-02"/>
ræ ex A, polo Horizontis:</s>
  <s xml:id="echoid-s34374" xml:space="preserve">, &amp; </s>
  <s xml:id="echoid-s34375" xml:space="preserve">in-<lb/>teruallo A P, deſcriptus ſemicir <lb/>culus P K V b e, qui per propoſ. <lb/></s>
  <s xml:id="echoid-s34376" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34377" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34378" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34379" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34380" xml:space="preserve">Horizonti pa-<lb/>rallelus erit; </s>
  <s xml:id="echoid-s34381" xml:space="preserve">atque adeo ſectio-<lb/>nes, quas Horizon, &amp; </s>
  <s xml:id="echoid-s34382" xml:space="preserve">hic ſemi-<lb/>circulus cum Meridiano faciũt, <lb/>
<anchor type="note" xlink:label="note-0550-03a" xlink:href="note-0550-03"/>
parallelæ inter ſe erunt. </s>
  <s xml:id="echoid-s34383" xml:space="preserve">Cum er <lb/>
<anchor type="note" xlink:label="note-0550-04a" xlink:href="note-0550-04"/>
go rectæ B D, P e, ſint parallelæ <lb/>inter ſe, ob angulos rectos BEO, <lb/>
<anchor type="note" xlink:label="note-0550-05a" xlink:href="note-0550-05"/>
P O E, ſitq́ue BD, ſectio commu <lb/>nis Horizontis, ac Meridiani; <lb/></s>
  <s xml:id="echoid-s34384" xml:space="preserve">erit P e, communis ſectio ſemi <lb/>circuli P K V b e, &amp; </s>
  <s xml:id="echoid-s34385" xml:space="preserve">Meridiani. </s>
  <s xml:id="echoid-s34386" xml:space="preserve"><lb/>Quoniam vero tam Aequator, <lb/>quàm ſemicirculus hicad Me-<lb/>ridianum rectus eſt, (Aequator <lb/>enim in propria poſitione re-<lb/>ctus eſt ad Meridianum poſitus: </s>
  <s xml:id="echoid-s34387" xml:space="preserve"><lb/>Meridianus vero per polos dicti <lb/>
<anchor type="note" xlink:label="note-0550-06a" xlink:href="note-0550-06"/>
ſemicirculi P k V b e, ductus ad ipſum ſemicirculum rectus eſt, per propoſ. </s>
  <s xml:id="echoid-s34388" xml:space="preserve">15. </s>
  <s xml:id="echoid-s34389" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34390" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34391" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34392" xml:space="preserve">atq; <lb/></s>
  <s xml:id="echoid-s34393" xml:space="preserve">adeo &amp; </s>
  <s xml:id="echoid-s34394" xml:space="preserve">ſemicirculus viciſſim ad Meridianum rectus erit) erit quoque communis eorum ſectio <lb/>
<anchor type="note" xlink:label="note-0550-07a" xlink:href="note-0550-07"/>
ad Meridianum perpendicularis; </s>
  <s xml:id="echoid-s34395" xml:space="preserve">ac proinde, per defin. </s>
  <s xml:id="echoid-s34396" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34397" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34398" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34399" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34400" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34401" xml:space="preserve">ad rectam F G. </s>
  <s xml:id="echoid-s34402" xml:space="preserve">Quare <lb/>cum recta k L, per defin. </s>
  <s xml:id="echoid-s34403" xml:space="preserve">4. </s>
  <s xml:id="echoid-s34404" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34405" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34406" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34407" xml:space="preserve">perpendicularis ſit ad Meridiani planum, vt paulo ante <lb/>oſtendimus, erit recta <emph style="sc">K</emph> L, ſectio communis Aequatoris, &amp; </s>
  <s xml:id="echoid-s34408" xml:space="preserve">ſemicirculi P k V b e, cum plana ho-<lb/>rum circulorum ſe mutuo ſecent in L; </s>
  <s xml:id="echoid-s34409" xml:space="preserve">atque idcirco ſemicirculus P K V b e, per K, locum Solis <lb/>tranſibit. </s>
  <s xml:id="echoid-s34410" xml:space="preserve">Recta autem V O, communis ſectio erit eiuſdem ſemicirculi, &amp; </s>
  <s xml:id="echoid-s34411" xml:space="preserve">Verticalis. </s>
  <s xml:id="echoid-s34412" xml:space="preserve">Præterea <lb/>communis ſectio Deſcenſiui, &amp; </s>
  <s xml:id="echoid-s34413" xml:space="preserve">ſemicirculi M K a Z d, ſit recta K Z: </s>
  <s xml:id="echoid-s34414" xml:space="preserve">Et eiuſdem Deſcenſiui, at-<lb/>que Horizontis ſectio communis ſit recta Y E, quæ neceſſario tranſibit per punctum f, vbi rectæ <lb/>a N, K Z, ſe mutuo ſecant. </s>
  <s xml:id="echoid-s34415" xml:space="preserve">Quoniam enim vtraque recta a N, Y E, in plano Horizontis eſt, cum <lb/>
<anchor type="note" xlink:label="note-0550-08a" xlink:href="note-0550-08"/>
a N, communis ſectio ſit ipſius, &amp; </s>
  <s xml:id="echoid-s34416" xml:space="preserve">ſemicirculi M K a Z d, &amp; </s>
  <s xml:id="echoid-s34417" xml:space="preserve">Y E, com munis ſectio eiuſdem Ho-<lb/>rizontis, &amp; </s>
  <s xml:id="echoid-s34418" xml:space="preserve">Deſcenſiui; </s>
  <s xml:id="echoid-s34419" xml:space="preserve">eſtq́ue punctum Y, inter B, &amp; </s>
  <s xml:id="echoid-s34420" xml:space="preserve">a, quòd ſemicirculus M k a Z d, Deſcen-<lb/>ſiuum ſecet &amp; </s>
  <s xml:id="echoid-s34421" xml:space="preserve">ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s34422" xml:space="preserve">infra, vt facile intelligi poteſt, ſi dictus ſemicirculus, &amp; </s>
  <s xml:id="echoid-s34423" xml:space="preserve">De-<lb/>ſcenſiuus concipiantur in propriis poſitionibus, ſecabunt ſe mutuo rectæ a N, Y E, in plano Hori <lb/>zontis, in aliquo puncto, quod ſit f; </s>
  <s xml:id="echoid-s34424" xml:space="preserve">quod neceſſario erit in recta K Z. </s>
  <s xml:id="echoid-s34425" xml:space="preserve">Nam cum punctum f, vbi <lb/>ſe ſecant rectæ a N, Y E, ſit &amp; </s>
  <s xml:id="echoid-s34426" xml:space="preserve">in communi ſectione Deſcenſiui, &amp; </s>
  <s xml:id="echoid-s34427" xml:space="preserve">Horizontis, puta in recta Y E, <lb/>&amp; </s>
  <s xml:id="echoid-s34428" xml:space="preserve">in communi ſectione ſemicirculi M K a Z d, eiuſdemq́ue Horizontis, vt in recta a N, erit ne-<lb/>ceſſario &amp; </s>
  <s xml:id="echoid-s34429" xml:space="preserve">in plano Deſcenſiui, &amp; </s>
  <s xml:id="echoid-s34430" xml:space="preserve">in plano dicti ſemicirculi. </s>
  <s xml:id="echoid-s34431" xml:space="preserve">Quare in communi ſectione Deſcen-<lb/>ſiui, &amp; </s>
  <s xml:id="echoid-s34432" xml:space="preserve">dicti ſemicirculi, vt in recta K Z, erit. </s>
  <s xml:id="echoid-s34433" xml:space="preserve">Sit quoque recta K b, communis ſectio Horarii, &amp; </s>
  <s xml:id="echoid-s34434" xml:space="preserve">ſe-<lb/>micirculi P K V b e: </s>
  <s xml:id="echoid-s34435" xml:space="preserve">Eteiuſdem Horarii, &amp; </s>
  <s xml:id="echoid-s34436" xml:space="preserve">Verticalis communis ſectio ſit recta X E, quæ neceſſa-<lb/>
<anchor type="note" xlink:label="note-0550-09a" xlink:href="note-0550-09"/>
rio tranſibit per punctum I, vbi rectæ V O, K b, ſe interſecant. </s>
  <s xml:id="echoid-s34437" xml:space="preserve">Quoniam enim vtraque V O, X E, <lb/>in plano Verticalis eſt, cum illa ſectio communis ſit Verticalis, &amp; </s>
  <s xml:id="echoid-s34438" xml:space="preserve">ſemicirculi P K V b e, hæc vero <lb/>communis ſectio Verticalis, &amp; </s>
  <s xml:id="echoid-s34439" xml:space="preserve">Horarii; </s>
  <s xml:id="echoid-s34440" xml:space="preserve">eſtq́ue punctum X, inter A, &amp; </s>
  <s xml:id="echoid-s34441" xml:space="preserve">V, quòd ſemicirculus <lb/>P k V b e, Horarium ſecet &amp; </s>
  <s xml:id="echoid-s34442" xml:space="preserve">citra, &amp; </s>
  <s xml:id="echoid-s34443" xml:space="preserve">vltra Verticalem, vt manifeſtum eſt, ſi dictus ſemicirculus, <lb/>Horariusq́ue in propriis poſitionibus intelligantur; </s>
  <s xml:id="echoid-s34444" xml:space="preserve">ſecabunt ſe mutuo rectæ V O, X E, in plano <lb/>Verticalis in aliquo puncto, quod ſit I, quod omnino in recta K b, erit. </s>
  <s xml:id="echoid-s34445" xml:space="preserve">Cum enim punctum I, vbi <lb/>ſe ſecant rectæ V O, X E, ſit &amp; </s>
  <s xml:id="echoid-s34446" xml:space="preserve">in communi ſectione Horarij, Verticalisq́ue, puta in recta X E, &amp; </s>
  <s xml:id="echoid-s34447" xml:space="preserve"><lb/>in communi ſectione ſemicirculi P K V b e, eiuſdemq́ue Verticalis, nempe in recta V O, erit ne-<lb/>ceſſario &amp; </s>
  <s xml:id="echoid-s34448" xml:space="preserve">in plano Horarii, &amp; </s>
  <s xml:id="echoid-s34449" xml:space="preserve">in plano dicti ſemicirculi. </s>
  <s xml:id="echoid-s34450" xml:space="preserve">Quapropter in communi eorum ſectio-<lb/>ne exiſtet, hoc eſt, in recta K b. </s>
  <s xml:id="echoid-s34451" xml:space="preserve">Item communis ſectio Aequatoris, ſeu Hectemorii, Deſcenſiui, <lb/>atque Horarij, qui omnes per centrum Solis K, &amp; </s>
  <s xml:id="echoid-s34452" xml:space="preserve">per centrum mundi E, ducuntur, ſit recta k E:</s>
  <s xml:id="echoid-s34453" xml:space="preserve">
<pb o="535" file="0551" n="551" rhead="LIBER SEXTVS."/>
Sectio denique communis Horizontis, Verticalis, &amp; </s>
  <s xml:id="echoid-s34454" xml:space="preserve">Aequatoris, ſiue Hectemorii, qui omnes ſe <lb/>mutuo ſecant in ortu, occaſuve æquinoctiali, &amp; </s>
  <s xml:id="echoid-s34455" xml:space="preserve">per centrum mundi ducuntur, ſit recta E H. </s>
  <s xml:id="echoid-s34456" xml:space="preserve">His <lb/>omnibus recte perceptis, &amp; </s>
  <s xml:id="echoid-s34457" xml:space="preserve">demonſtratis, oſtendendum nunc eſt, arcum H K, in Meridiano æqua <lb/>lem eſſe circunferentiæ hectemoriæ H k, in Hectemorio, ſeu Aequatore propriam poſitionem ha-<lb/>bente; </s>
  <s xml:id="echoid-s34458" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34459" xml:space="preserve">arcum B M, in Meridiano æqualem circunferentiæ horariæ B K, in Horario; </s>
  <s xml:id="echoid-s34460" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34461" xml:space="preserve">arcum <lb/>A P, in Meridiano æqualem circunferentiæ deſcenſiuæ A K, in Deſcenſiuo: </s>
  <s xml:id="echoid-s34462" xml:space="preserve">Item arcum B F, æqua-<lb/>lem eſſe meridianæ circunferentiæ inter Horizontem, &amp; </s>
  <s xml:id="echoid-s34463" xml:space="preserve">Hectemorion; </s>
  <s xml:id="echoid-s34464" xml:space="preserve">arcum vero A T, in Meri-<lb/>diano circunferentiæ Verticali A X, in Verticali inter Meridianum, &amp; </s>
  <s xml:id="echoid-s34465" xml:space="preserve">Horarium; </s>
  <s xml:id="echoid-s34466" xml:space="preserve">arcum denique <lb/>A S, in Meridiano circunferentiæ horizõtali H Y, in Horizonte inter Verticalem, &amp; </s>
  <s xml:id="echoid-s34467" xml:space="preserve">Deſcenſiuũ. <lb/></s>
  <s xml:id="echoid-s34468" xml:space="preserve">Quod ita ferè cum Federico Commandino demonſtrabimus. </s>
</p>
<p>
  <s xml:id="echoid-s34469" xml:space="preserve">DVCTA recta E k, in plano Meridiani; </s>
  <s xml:id="echoid-s34470" xml:space="preserve">quoniam duo latera E K, K L, trianguli E K L, in <lb/>plano Meridiani, æqualia ſunt duobus lateribus E K, K L, in plano Hectemorii, (vtraque enim <lb/>
<anchor type="note" xlink:label="note-0551-02a" xlink:href="note-0551-02"/>
E K, à centro E, ad ſuperſiciem ſphæræ ducitur, proptereaq́ue vna alteri æqualis eſt: </s>
  <s xml:id="echoid-s34471" xml:space="preserve">recta autem <lb/>k L, in Meridiano congruet rectæ k L, communi ſectioni Hectemorii, &amp; </s>
  <s xml:id="echoid-s34472" xml:space="preserve">ſemicirculi M k a Z d, <lb/>ſi ſemicirculus Meridiani F H G, circa rectam F G, conuertatur, donec rectus ſit ad planum Me-<lb/>ridiani; </s>
  <s xml:id="echoid-s34473" xml:space="preserve">quòd vtraque | perpendicularis tunc ſit ad<unsure/> planum Meridiani; </s>
  <s xml:id="echoid-s34474" xml:space="preserve">recta quidem K L, quæ in <lb/>plano Meridiani eſt, ex defin. </s>
  <s xml:id="echoid-s34475" xml:space="preserve">4. </s>
  <s xml:id="echoid-s34476" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34477" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34478" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34479" xml:space="preserve">altera vero, quòd communis ſectio ſit duorum plano-<lb/>
<anchor type="note" xlink:label="note-0551-03a" xlink:href="note-0551-03"/>
rum ad Meridianum rectorum. </s>
  <s xml:id="echoid-s34480" xml:space="preserve">Hinc enim fit, vt perpendicularis ſit ad eundem Meridianum. <lb/></s>
  <s xml:id="echoid-s34481" xml:space="preserve">Cum ergo vtraque k L, in ſuperficie ſphæræ terminetur, vna alteri æqualis erit) eſtq́ue baſis E L, <lb/>communis; </s>
  <s xml:id="echoid-s34482" xml:space="preserve">erunt anguli K, illorum triangulorum æquales. </s>
  <s xml:id="echoid-s34483" xml:space="preserve">Sed ille in plano Meridiani æqualis <lb/>
<anchor type="note" xlink:label="note-0551-04a" xlink:href="note-0551-04"/>
<anchor type="note" xlink:label="note-0551-05a" xlink:href="note-0551-05"/>
eſt angulo alterno K E H, in eodem plano, propterea quòd rectæ K L, H E, parallelæ ſunt, ob an-<lb/>
<anchor type="note" xlink:label="note-0551-06a" xlink:href="note-0551-06"/>
gulos rectos k L E, H E L; </s>
  <s xml:id="echoid-s34484" xml:space="preserve">hic vero in Hectemorio, eandem ob cauſam, æqualis eſt angulo K E H, <lb/>
<anchor type="note" xlink:label="note-0551-07a" xlink:href="note-0551-07"/>
in eodem Hectemorio: </s>
  <s xml:id="echoid-s34485" xml:space="preserve">Rectæ enim k L, E H, parallelæ ſunt, cum ſint ſectiones factæ ab He-<lb/>
<anchor type="note" xlink:label="note-0551-08a" xlink:href="note-0551-08"/>
ctemorio in planis parallelis, nempe in Horizonte, &amp; </s>
  <s xml:id="echoid-s34486" xml:space="preserve">ſemicirculo P K V be. </s>
  <s xml:id="echoid-s34487" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34488" xml:space="preserve">angu-<lb/>lus K E H, in Meridiano æqualis erit angulo K E H, in Hectemorio, ideoq́ue arcus H K, in Me-<lb/>ridiano arcui H K, in Hectemorio æqualis. </s>
  <s xml:id="echoid-s34489" xml:space="preserve">Quod erat oſtendẽdum. </s>
  <s xml:id="echoid-s34490" xml:space="preserve">Quod etiam breuius ita colli-<lb/>
<anchor type="note" xlink:label="note-0551-09a" xlink:href="note-0551-09"/>
gi poteſt. </s>
  <s xml:id="echoid-s34491" xml:space="preserve">Quoniam tempore æquinoctij Hectemorion ab Aequatore non differt, erit arcus <lb/>H k, (ſi Meridianus pro Aequatore ſumatur) inter Horizontem, &amp; </s>
  <s xml:id="echoid-s34492" xml:space="preserve">centrum Solis, circunferentia <lb/>hectemoria.</s>
  <s xml:id="echoid-s34493" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1740" type="float" level="2" n="1">
<note position="right" xlink:label="note-0549-10" xlink:href="note-0549-10a" xml:space="preserve">Demonſtratio <lb/>in uentionis ſex <lb/>d ctatum circũ-<lb/>ferentiarum, So <lb/>le exiſtente in <lb/>Aequatoie.</note>
<note position="left" xlink:label="note-0549-11" xlink:href="note-0549-11a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0549-01" xlink:href="fig-0549-01a">
    <image file="0549-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0549-01"/>
  </figure>
<note position="left" xlink:label="note-0549-12" xlink:href="note-0549-12a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0549-13" xlink:href="note-0549-13a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0549-14" xlink:href="note-0549-14a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0549-15" xlink:href="note-0549-15a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0550-01" xlink:href="note-0550-01a" xml:space="preserve">19. vndec.</note>
  <figure xlink:label="fig-0550-01" xlink:href="fig-0550-01a">
    <image file="0550-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0550-01"/>
  </figure>
<note position="left" xlink:label="note-0550-02" xlink:href="note-0550-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0550-03" xlink:href="note-0550-03a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0550-04" xlink:href="note-0550-04a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0550-05" xlink:href="note-0550-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0550-06" xlink:href="note-0550-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0550-07" xlink:href="note-0550-07a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0550-08" xlink:href="note-0550-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0550-09" xlink:href="note-0550-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0551-02" xlink:href="note-0551-02a" xml:space="preserve">Demonſtratio <lb/>hectemoriæ cir <lb/>cunferentiæ.</note>
<note position="right" xlink:label="note-0551-03" xlink:href="note-0551-03a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0551-04" xlink:href="note-0551-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0551-05" xlink:href="note-0551-05a" xml:space="preserve">8. primi.</note>
<note position="right" xlink:label="note-0551-06" xlink:href="note-0551-06a" xml:space="preserve">29. primi.</note>
<note position="right" xlink:label="note-0551-07" xlink:href="note-0551-07a" xml:space="preserve">28. primi.</note>
<note position="right" xlink:label="note-0551-08" xlink:href="note-0551-08a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0551-09" xlink:href="note-0551-09a" xml:space="preserve">26. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34494" xml:space="preserve">DEINDE, quia Meridianus, &amp; </s>
  <s xml:id="echoid-s34495" xml:space="preserve">Horarius ducuntur per B D, polos Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s34496" xml:space="preserve">ſemicir <lb/>
<anchor type="note" xlink:label="note-0551-10a" xlink:href="note-0551-10"/>
<anchor type="note" xlink:label="note-0551-11a" xlink:href="note-0551-11"/>
culi M K a Z d, qui Verticali æquidiſtat, erũt, per propoſ. </s>
  <s xml:id="echoid-s34497" xml:space="preserve">10. </s>
  <s xml:id="echoid-s34498" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34499" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34500" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34501" xml:space="preserve">arcus Meridiani A M, <lb/>&amp; </s>
  <s xml:id="echoid-s34502" xml:space="preserve">arcus Horarij X K, cum inter parallelos circulos cõprehendantur, inter ſeæquales. </s>
  <s xml:id="echoid-s34503" xml:space="preserve">Cum igitur <lb/>A B, X B, quadrantes ſint, quod B, polus Verticalis quadrante abſit ab ipſo Verticali, ex coroll. <lb/></s>
  <s xml:id="echoid-s34504" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s34505" xml:space="preserve">16. </s>
  <s xml:id="echoid-s34506" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34507" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34508" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34509" xml:space="preserve">erit quoque arcus reliquus B M, in Meridiano æqualis reliquæ circun-<lb/>ferentiæ horariæ B K, in Horario. </s>
  <s xml:id="echoid-s34510" xml:space="preserve">Quod etiam breuius demonſtrabimus hoc modo. </s>
  <s xml:id="echoid-s34511" xml:space="preserve">Quoniam <lb/>B, polus eſt ſemicirculi M K a Z d, erunt, per defin. </s>
  <s xml:id="echoid-s34512" xml:space="preserve">poli, chordę B M, B K, æquales. </s>
  <s xml:id="echoid-s34513" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34514" xml:space="preserve">ar-<lb/>cus B M, B k, æquales erunt. </s>
  <s xml:id="echoid-s34515" xml:space="preserve">Quod eſt propoſitum. </s>
  <s xml:id="echoid-s34516" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0551-12a" xlink:href="note-0551-12"/>
</s>
</p>
<div xml:id="echoid-div1741" type="float" level="2" n="2">
<note position="left" xlink:label="note-0551-10" xlink:href="note-0551-10a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0551-11" xlink:href="note-0551-11a" xml:space="preserve">Demonſtratio <lb/>horariæ circun-<lb/>ferentiæ.</note>
<note position="right" xlink:label="note-0551-12" xlink:href="note-0551-12a" xml:space="preserve">28. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34517" xml:space="preserve">PARI ratione, quoniam Meridianus, &amp; </s>
  <s xml:id="echoid-s34518" xml:space="preserve">Deſcenſiuus ducuntur per A, C, polos Horizontis <lb/>
<anchor type="note" xlink:label="note-0551-13a" xlink:href="note-0551-13"/>
&amp; </s>
  <s xml:id="echoid-s34519" xml:space="preserve">ſemicirculi P K V b e, qui Horizonti æquidiſtat, erunt, per propoſ. </s>
  <s xml:id="echoid-s34520" xml:space="preserve">10. </s>
  <s xml:id="echoid-s34521" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34522" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34523" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34524" xml:space="preserve">arcus <lb/>Meridiani B P, &amp; </s>
  <s xml:id="echoid-s34525" xml:space="preserve">arcus Deſcenſiui Y K, cum inter parallelos circulos includantur, æquales inter <lb/>
<anchor type="note" xlink:label="note-0551-14a" xlink:href="note-0551-14"/>
ſe. </s>
  <s xml:id="echoid-s34526" xml:space="preserve">Cum igitur B A, Y A, quadrantes ſint, ex coroll. </s>
  <s xml:id="echoid-s34527" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s34528" xml:space="preserve">16. </s>
  <s xml:id="echoid-s34529" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34530" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34531" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34532" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s34533" xml:space="preserve">reliquus arcus <lb/>A P, in Meridiano æqualis reliquæ circunferentiæ deſcenſiuæ A K, in Deſcenſiuo. </s>
  <s xml:id="echoid-s34534" xml:space="preserve">Quod faci-<lb/>lius ita concludemus. </s>
  <s xml:id="echoid-s34535" xml:space="preserve">Quoniam A, polus eſt ſemicirculi P K V b e, erunt per defin. </s>
  <s xml:id="echoid-s34536" xml:space="preserve">poli chordæ <lb/>A P, A K, æquales. </s>
  <s xml:id="echoid-s34537" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34538" xml:space="preserve">arcus A P, A K, æquales erunt. </s>
  <s xml:id="echoid-s34539" xml:space="preserve">Quod eſt propoſitum. <lb/></s>
  <s xml:id="echoid-s34540" xml:space="preserve">
<anchor type="note" xlink:label="note-0551-15a" xlink:href="note-0551-15"/>
</s>
</p>
<div xml:id="echoid-div1742" type="float" level="2" n="3">
<note position="right" xlink:label="note-0551-13" xlink:href="note-0551-13a" xml:space="preserve">Demonſtratio <lb/>deſcenſiuæ cir-<lb/>cunfeientiæ.</note>
<note position="left" xlink:label="note-0551-14" xlink:href="note-0551-14a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0551-15" xlink:href="note-0551-15a" xml:space="preserve">28. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34541" xml:space="preserve">IAM vero B F, eſſe circunferentiam meridianam, perſpicuum eſt, cum inter lineam meridia <lb/>
<anchor type="note" xlink:label="note-0551-16a" xlink:href="note-0551-16"/>
nam B D, ſiue Horizontem, &amp; </s>
  <s xml:id="echoid-s34542" xml:space="preserve">Hectemorion F H G, interijciatur.</s>
  <s xml:id="echoid-s34543" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1743" type="float" level="2" n="4">
<note position="right" xlink:label="note-0551-16" xlink:href="note-0551-16a" xml:space="preserve">Demonſtratio <lb/>meridianę cir-<lb/>cunferentiæ.</note>
</div>
<p>
  <s xml:id="echoid-s34544" xml:space="preserve">RVRSVS, quia Horarius circulus B K X b D, ſecat duos circulos parallelos, nempe Hori-<lb/>
<anchor type="note" xlink:label="note-0551-17a" xlink:href="note-0551-17"/>
zontem, &amp; </s>
  <s xml:id="echoid-s34545" xml:space="preserve">ſemicirculum P K V b e, erunt ſectiones, quas in illis facit, hoc eſt, rectæ B D, K b, <lb/>inter ſe parallelæ: </s>
  <s xml:id="echoid-s34546" xml:space="preserve">Eſtautem, propter angulos rectos B E O, P O E, recta P e, ipſi B D, quoque pa-<lb/>
<anchor type="note" xlink:label="note-0551-18a" xlink:href="note-0551-18"/>
rallela. </s>
  <s xml:id="echoid-s34547" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34548" xml:space="preserve">rectæ K b, P e, parallelæ inter ſe erunt. </s>
  <s xml:id="echoid-s34549" xml:space="preserve">Item quia ſemicirculus P K V b e, ſecãs <lb/>
<anchor type="note" xlink:label="note-0551-19a" xlink:href="note-0551-19"/>
<anchor type="note" xlink:label="note-0551-20a" xlink:href="note-0551-20"/>
circulos parallelos, nimirum Verticalem, &amp; </s>
  <s xml:id="echoid-s34550" xml:space="preserve">ſemicirculum M K a Z d, facit communes ſectiones <lb/>
<anchor type="note" xlink:label="note-0551-21a" xlink:href="note-0551-21"/>
V O, K L, parallelas, parallelogrãmum erit K L O I, proptereaq́; </s>
  <s xml:id="echoid-s34551" xml:space="preserve">recta O I, rectę L K, æqualis, hoc <lb/>
<anchor type="note" xlink:label="note-0551-22a" xlink:href="note-0551-22"/>
eſt rectæ O R, cũ OR, ſumpta ſit æqualis, ipſi K L. </s>
  <s xml:id="echoid-s34552" xml:space="preserve">Cum igitur duo latera I O, O E, trianguli I O E, <lb/>
<anchor type="note" xlink:label="note-0551-23a" xlink:href="note-0551-23"/>
æqualia ſint duobus lateribus R O, O E, trianguli R O E, &amp; </s>
  <s xml:id="echoid-s34553" xml:space="preserve">anguli I O E, R O E, ſub ipſis contenti <lb/>recti. </s>
  <s xml:id="echoid-s34554" xml:space="preserve">(Quoniã enim tam Verticalis, quam ſemicirculus P K V b e, ad Meridianum rectus eſt, erit <lb/>&amp; </s>
  <s xml:id="echoid-s34555" xml:space="preserve">ipſorum cõmunis ſectio V O, ad eundẽ perpendicularis, atque adeo &amp; </s>
  <s xml:id="echoid-s34556" xml:space="preserve">ad rectam A C, ex defin. <lb/></s>
  <s xml:id="echoid-s34557" xml:space="preserve">
<anchor type="note" xlink:label="note-0551-24a" xlink:href="note-0551-24"/>
3. </s>
  <s xml:id="echoid-s34558" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34559" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34560" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34561" xml:space="preserve">Igitur angulus I O E, rectus eſt: </s>
  <s xml:id="echoid-s34562" xml:space="preserve">angulus autem R O E, per conſtructionem re-<lb/>ctus eſt:) </s>
  <s xml:id="echoid-s34563" xml:space="preserve">erit angulo I E O, angulus R E O, æqualis. </s>
  <s xml:id="echoid-s34564" xml:space="preserve">Quocirca &amp; </s>
  <s xml:id="echoid-s34565" xml:space="preserve">arcus A T, in Meridiano ſubten <lb/>
<anchor type="note" xlink:label="note-0551-25a" xlink:href="note-0551-25"/>
dens angulum T E A, in centro æqualis erit circunferentiæ Verticali A X, qui angulum X E A, <lb/>
<anchor type="note" xlink:label="note-0551-26a" xlink:href="note-0551-26"/>
in centro ſubtendit. <lb/></s>
  <s xml:id="echoid-s34566" xml:space="preserve">
<anchor type="note" xlink:label="note-0551-27a" xlink:href="note-0551-27"/>
</s>
</p>
<div xml:id="echoid-div1744" type="float" level="2" n="5">
<note position="right" xlink:label="note-0551-17" xlink:href="note-0551-17a" xml:space="preserve">Demonſtratio <lb/>Verticalis cir-<lb/>cunferenriæ.</note>
<note position="right" xlink:label="note-0551-18" xlink:href="note-0551-18a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0551-19" xlink:href="note-0551-19a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0551-20" xlink:href="note-0551-20a" xml:space="preserve">28. primi.</note>
<note position="right" xlink:label="note-0551-21" xlink:href="note-0551-21a" xml:space="preserve">9. vndec.</note>
<note position="right" xlink:label="note-0551-22" xlink:href="note-0551-22a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0551-23" xlink:href="note-0551-23a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0551-24" xlink:href="note-0551-24a" xml:space="preserve">19. vndec.</note>
<note position="right" xlink:label="note-0551-25" xlink:href="note-0551-25a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0551-26" xlink:href="note-0551-26a" xml:space="preserve">26. tertĳ.</note>
<note position="right" xlink:label="note-0551-27" xlink:href="note-0551-27a" xml:space="preserve">Demonſtratio <lb/>horizontalis cir <lb/>cunferentiæ.</note>
</div>
<p>
  <s xml:id="echoid-s34567" xml:space="preserve">POSTREMO, quoniam circulus Deſcenſiuus A K Y Z C, ſecat duos circulos parallelos,
<pb o="536" file="0552" n="552" rhead="GNOMONICES"/>
puta Verticalẽ, &amp; </s>
  <s xml:id="echoid-s34568" xml:space="preserve">ſemicirculũ M K a Z d, erũt ſectiones, quas in illis facit, nimitũ rectæ A C, K Z, <lb/>
<anchor type="note" xlink:label="note-0552-01a" xlink:href="note-0552-01"/>
inter ſe parallelę: </s>
  <s xml:id="echoid-s34569" xml:space="preserve">Eſt autẽ, propter angulos rectos A E N, M N E, recta M d, ipſi A C, quoque paral-<lb/>
<anchor type="note" xlink:label="note-0552-02a" xlink:href="note-0552-02"/>
lela. </s>
  <s xml:id="echoid-s34570" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34571" xml:space="preserve">rectæ K Z, M d, parallelæ inter ſe erunt. </s>
  <s xml:id="echoid-s34572" xml:space="preserve">Item quia ſemicirculus M K a Z d, ſecans <lb/>
<anchor type="note" xlink:label="note-0552-03a" xlink:href="note-0552-03"/>
parallelos circulos, nempe Horizontẽ, &amp; </s>
  <s xml:id="echoid-s34573" xml:space="preserve">ſemicirculum P K V b e, facit parallelas ſectiones com-<lb/>
<anchor type="note" xlink:label="note-0552-04a" xlink:href="note-0552-04"/>
munes a M, K L, parallelogrammum erit K L N f, ac proinde recta fN, rectæ K L, æqualis, id <lb/>
<anchor type="note" xlink:label="note-0552-05a" xlink:href="note-0552-05"/>
eſt, rectæ N Q, quæ ipſi k L, ſumpta eſt æqualis. </s>
  <s xml:id="echoid-s34574" xml:space="preserve">Quoniam igitur duo latera fN, N E, trianguli <lb/>fN E, duobus lateribus Q N, N E, trianguli Q N E, æqualia ſunt, continentq́ue angulos rectos, <lb/>(Quia enim tam Horizon, quam ſemicirculus M K a Z d, ad Meridianum rectus eſt, erit &amp; </s>
  <s xml:id="echoid-s34575" xml:space="preserve">ipſorũ <lb/>communis ſectio a N, ad eundem perpendicularis, atque ob id ad rectam quoque B D. </s>
  <s xml:id="echoid-s34576" xml:space="preserve">Rectus <lb/>
<anchor type="note" xlink:label="note-0552-06a" xlink:href="note-0552-06"/>
ergo eſt angulus f N E, angulus autem Q N E, ex conſtructione rectus eſt) erit angulus fE N, an-<lb/>
<anchor type="note" xlink:label="note-0552-07a" xlink:href="note-0552-07"/>
<anchor type="note" xlink:label="note-0552-08a" xlink:href="note-0552-08"/>
gulo Q E N, æqualis. </s>
  <s xml:id="echoid-s34577" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34578" xml:space="preserve">arcus B Y, B S, @ui hiſce angulis ſubijciuntur, æquales inter ſe <lb/>
<anchor type="note" xlink:label="note-0552-09a" xlink:href="note-0552-09"/>
erunt. </s>
  <s xml:id="echoid-s34579" xml:space="preserve">Cum ergo B H, B A, quadrantes ſint, quod B, polus Verticalis quadrante abſit à Verticali, <lb/>ex coroll, propoſ. </s>
  <s xml:id="echoid-s34580" xml:space="preserve">16. </s>
  <s xml:id="echoid-s34581" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34582" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34583" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34584" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s34585" xml:space="preserve">reliquus arcus A S, in Meridiano reliquæ circunferen-<lb/>tiæ horizontali H Y, in Horizonte æqualis. </s>
  <s xml:id="echoid-s34586" xml:space="preserve">Quæ omnia demonſtranda erant.</s>
  <s xml:id="echoid-s34587" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1745" type="float" level="2" n="6">
<note position="left" xlink:label="note-0552-01" xlink:href="note-0552-01a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0552-02" xlink:href="note-0552-02a" xml:space="preserve">28. primi.</note>
<note position="left" xlink:label="note-0552-03" xlink:href="note-0552-03a" xml:space="preserve">9. vndec.</note>
<note position="left" xlink:label="note-0552-04" xlink:href="note-0552-04a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0552-05" xlink:href="note-0552-05a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0552-06" xlink:href="note-0552-06a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0552-07" xlink:href="note-0552-07a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0552-08" xlink:href="note-0552-08a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0552-09" xlink:href="note-0552-09a" xml:space="preserve">26. tertĳ.</note>
</div>
</div>
<div xml:id="echoid-div1747" type="section" level="1" n="472">
<head xml:id="echoid-head501" style="it" xml:space="preserve">INVENTIO CIRCVNFERENTIAE HECTEMORIAE, <lb/>horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex <lb/>Analemmate, Sole exiſtente in quouis parallelo extra <lb/>æquinoctialem circulum, ad quamcunque <lb/>latitudinem. C A P. IIII.</head>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s34588" xml:space="preserve">SIT Meridianus Analemmatis A B C D, in quo duæ diametri ſeſead angulos rectos ſecent <lb/>A C, B D, quarum illa cõmunis ſectio ſit Verticalis circuli, &amp; </s>
  <s xml:id="echoid-s34589" xml:space="preserve">Meridiani, hæc vero ſectio com-<lb/>
<anchor type="figure" xlink:label="fig-0552-01a" xlink:href="fig-0552-01"/>
munis eiuſdem Meridiani &amp; </s>
  <s xml:id="echoid-s34590" xml:space="preserve"><lb/>Horizontis. </s>
  <s xml:id="echoid-s34591" xml:space="preserve">Sit quoque axis <lb/>mundi H I; </s>
  <s xml:id="echoid-s34592" xml:space="preserve">Aequatoris autem <lb/>diameter F G, ſecans axem ad <lb/>angulos rectos. </s>
  <s xml:id="echoid-s34593" xml:space="preserve">Diameter de-<lb/>nique cuiuſuis paralleli a b, ſi-<lb/>
<anchor type="note" xlink:label="note-0552-11a" xlink:href="note-0552-11"/>
ue ſeptentrionalis, ſiue auſtra-<lb/>
<anchor type="note" xlink:label="note-0552-12a" xlink:href="note-0552-12"/>
lis, circa quã deſcribatur ſemi-<lb/>circulus ipſius paralleli a K b, <lb/>&amp; </s>
  <s xml:id="echoid-s34594" xml:space="preserve">ex d, vbi diameter paralleli <lb/>diametrum Horizontis ſecat, <lb/>ducatur ad a b, diametrum pa-<lb/>ralleli perpendicularis d e, quæ <lb/>communis ſectio erit Horizon <lb/>tis, &amp; </s>
  <s xml:id="echoid-s34595" xml:space="preserve">paralleli. </s>
  <s xml:id="echoid-s34596" xml:space="preserve">Quoniã enim <lb/>tam Horizon, quàm parallelus <lb/>ad Meridianum rectus eſt, erit <lb/>
<anchor type="note" xlink:label="note-0552-13a" xlink:href="note-0552-13"/>
quoq; </s>
  <s xml:id="echoid-s34597" xml:space="preserve">eorũ cõmunis ſectio ad <lb/>eundem perpendicularis, atq; <lb/></s>
  <s xml:id="echoid-s34598" xml:space="preserve">
<anchor type="note" xlink:label="note-0552-14a" xlink:href="note-0552-14"/>
adeo, ex defin. </s>
  <s xml:id="echoid-s34599" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34600" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34601" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34602" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s34603" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34604" xml:space="preserve">ad rectam a b, in puncto d, <lb/>vbi in Meridiano ſe mutuo ſe-<lb/>cant Horizon, &amp; </s>
  <s xml:id="echoid-s34605" xml:space="preserve">parallelus. </s>
  <s xml:id="echoid-s34606" xml:space="preserve"><lb/>Cum igitur ex d, in plano paralleli vna ſola perpendicularis duci poſſitad a b, erit perpendicula-<lb/>ris d e, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s34607" xml:space="preserve">paralleli, ita vt a e, ſit ſegmẽtum paralleli ſupra terram, &amp; </s>
  <s xml:id="echoid-s34608" xml:space="preserve"><lb/>e b, ſegmentum eiuſdem ſub terra; </s>
  <s xml:id="echoid-s34609" xml:space="preserve">quorum illud referet nobis portionem paralleli ab ortu e, <lb/>v@quead meridiem a, &amp; </s>
  <s xml:id="echoid-s34610" xml:space="preserve">portionem à meridie a, vſque ad occaſum e; </s>
  <s xml:id="echoid-s34611" xml:space="preserve">hoc autem portionem ab <lb/>
<anchor type="note" xlink:label="note-0552-15a" xlink:href="note-0552-15"/>
occaſu e, vſque ad mediam noctem b, &amp; </s>
  <s xml:id="echoid-s34612" xml:space="preserve">portionem à media nocte b, vſque ad ortum e: </s>
  <s xml:id="echoid-s34613" xml:space="preserve">propte-<lb/>rea quod portio ante meridiem ſimilis ſit, &amp; </s>
  <s xml:id="echoid-s34614" xml:space="preserve">ęqualis portioni poſt meridiem: </s>
  <s xml:id="echoid-s34615" xml:space="preserve">Item portio ante <lb/>mediam noctem portioni poſt mediam noctem. </s>
  <s xml:id="echoid-s34616" xml:space="preserve">Atque hac ratione ſegmentum a e, repræſenta-<lb/>bit nobis totum arcum diurnum paralleli ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s34617" xml:space="preserve">ſegmentum e b, totum arcum <lb/>nocturnum ſub Horizonte.</s>
  <s xml:id="echoid-s34618" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1747" type="float" level="2" n="1">
  <figure xlink:label="fig-0552-01" xlink:href="fig-0552-01a">
    <image file="0552-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0552-01"/>
  </figure>
<note position="left" xlink:label="note-0552-11" xlink:href="note-0552-11a" xml:space="preserve">In his 6. fi-<lb/>guris hui{us} <lb/>cap produca-<lb/>tur recta YE, <lb/>vſque ad Z, vt <lb/>in 1. &amp; 6. fa-<lb/>ctum est. Item <lb/>in 2. figura <lb/>ducatur recta <lb/>K E, vt in <lb/>alĳs.</note>
<note position="left" xlink:label="note-0552-12" xlink:href="note-0552-12a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0552-13" xlink:href="note-0552-13a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0552-14" xlink:href="note-0552-14a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0552-15" xlink:href="note-0552-15a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s34619" xml:space="preserve">PONATVR igitur Sol in ſuo parallelo obtinere punctum k, quod terminet quamcunque <lb/>
<anchor type="note" xlink:label="note-0552-16a" xlink:href="note-0552-16"/>
horam, aut particulam horæ, ſiue illa æqualis ſit ab ortu, occaſuve, vel à mer. </s>
  <s xml:id="echoid-s34620" xml:space="preserve">aut med. </s>
  <s xml:id="echoid-s34621" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s34622" xml:space="preserve">ſiue in-<lb/>æqualis, ita vt e K, ſit arcus paralleli inter centrum Solis, &amp; </s>
  <s xml:id="echoid-s34623" xml:space="preserve">Horizontem ſiue ex parte orientis, ſiue <lb/>occidentis interceptus; </s>
  <s xml:id="echoid-s34624" xml:space="preserve">arcus vero paralleli a k, poſitus ſit inter Meridianum, &amp; </s>
  <s xml:id="echoid-s34625" xml:space="preserve">centrum Solis ſi-<lb/>ue ante meridiem, ſiue poſt: </s>
  <s xml:id="echoid-s34626" xml:space="preserve">inquirendumq́ue ſit Geometrice ex Analemmate, quantæ tunc tem-<lb/>poris ſint expoſitę ſex circunferentiæ. </s>
  <s xml:id="echoid-s34627" xml:space="preserve">Ex K, puncto horę datæ, vbi Sol ponitur, ducatur recta K L,
<pb o="537" file="0553" n="553" rhead="LIBER SEXTVS."/>
a d a b, diametrum paralle<unsure/>li propoſiti perpendicularis; </s>
  <s xml:id="echoid-s34628" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34629" xml:space="preserve">per L, excitentur ad B E, A E, duæ per-<lb/>p<unsure/>endiculares N L M, O L P. </s>
  <s xml:id="echoid-s34630" xml:space="preserve">Ex quibus, quoniam maiores ſunt recta K L, (Nam ſi concipiatur ſe-<lb/>inicirculus paralleli conuerſus ad propriam poſitionem, vt ad Meridianum ſit rectus, erit K L, per <lb/>
<anchor type="figure" xlink:label="fig-0553-01a" xlink:href="fig-0553-01"/>
defin. </s>
  <s xml:id="echoid-s34631" xml:space="preserve">4. </s>
  <s xml:id="echoid-s34632" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34633" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34634" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34635" xml:space="preserve">ad eundem <lb/>recta, atque adeo, per defin. </s>
  <s xml:id="echoid-s34636" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34637" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s34638" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34639" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34640" xml:space="preserve">perpendicularis ad om <lb/>nes in eo lineas per L, ductas. </s>
  <s xml:id="echoid-s34641" xml:space="preserve"><lb/>Ducta igitur recta E L Y, erit an-<lb/>gulus k L E, rectus. </s>
  <s xml:id="echoid-s34642" xml:space="preserve">Cum igitur <lb/>&amp; </s>
  <s xml:id="echoid-s34643" xml:space="preserve">anguli M N E, P O E, recti ſint; </s>
  <s xml:id="echoid-s34644" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0553-01a" xlink:href="note-0553-01"/>
ſi ducantur tres ſemidiametri <lb/>ſphęrę E k, E M, E P, quarū qua-<lb/>drata æqualia ſunt, erũt tam duo <lb/>quadrata rectarũ MN, NE, quàm <lb/>
<anchor type="note" xlink:label="note-0553-02a" xlink:href="note-0553-02"/>
duo quadrata rectarum P O, OE, <lb/>duobus quadratis rectarum K L, <lb/>L E, æqualia. </s>
  <s xml:id="echoid-s34645" xml:space="preserve">Quamobrem cum <lb/>tam quadratum ex N E, quàm ex <lb/>O E minus ſit quadrato ex L E, <lb/>quòd tam linea N E, quàm O E, <lb/>
<anchor type="note" xlink:label="note-0553-03a" xlink:href="note-0553-03"/>
in triangulis rectangulis N E L, <lb/>O E L, minor ſit quàm L E; </s>
  <s xml:id="echoid-s34646" xml:space="preserve">erit <lb/>
<anchor type="note" xlink:label="note-0553-04a" xlink:href="note-0553-04"/>
tam reliquum quadratum rectæ <lb/>M N, quàm reliquum quadratũ <lb/>rectæ P O, maius reliquo quadra <lb/>to rectæ K L: </s>
  <s xml:id="echoid-s34647" xml:space="preserve">atque idcirco vtra-<lb/>que recta M N, P O, maior erit <lb/>quàm K L. </s>
  <s xml:id="echoid-s34648" xml:space="preserve">Solum quando perpendicularis K L, cadit in punctum n, vbi diameter paralleli Verti <lb/>calis diametrum diuidit, vt in figura 3. </s>
  <s xml:id="echoid-s34649" xml:space="preserve">contingit, recta k L, æqualis eſt rectæ P O. </s>
  <s xml:id="echoid-s34650" xml:space="preserve">Quia enim tunc <lb/>
<anchor type="figure" xlink:label="fig-0553-02a" xlink:href="fig-0553-02"/>
duo quadrata ex K L, L E, duo-<lb/>
<anchor type="note" xlink:label="note-0553-05a" xlink:href="note-0553-05"/>
<anchor type="note" xlink:label="note-0553-06a" xlink:href="note-0553-06"/>
bus quadratis ex P O, O E, æqua <lb/>lia ſunt; </s>
  <s xml:id="echoid-s34651" xml:space="preserve">ſi auferatur commune <lb/>quadratum rectæ L E, æquale <lb/>erit reliquum quadratum rectæ <lb/>K L, reliquo quadrato rectę <lb/>P O; </s>
  <s xml:id="echoid-s34652" xml:space="preserve">ac proinde rectæ K L, PO, <lb/>æquales erunt. </s>
  <s xml:id="echoid-s34653" xml:space="preserve">Nihilominus <lb/>tunc etiam recta M N, rectam <lb/>K L, ſuperabit, quòd M N, ſit <lb/>tunc ſemidiameter ſphæræ, at <lb/>
<anchor type="note" xlink:label="note-0553-07a" xlink:href="note-0553-07"/>
K L, ſemidiametro minor) ab-<lb/>ſcindantur ipſi K L, duæ æqua-<lb/>les N Q, O R; </s>
  <s xml:id="echoid-s34654" xml:space="preserve">atque per pun-<lb/>cta Q, R, ex centro E, rectæ <lb/>emittantur E Q S, E R T, ſecan-<lb/>tes Meridiani circunferentiam <lb/>in S, T. </s>
  <s xml:id="echoid-s34655" xml:space="preserve">Poſtremo ad rectam <lb/>E Y, excitentur in E, &amp; </s>
  <s xml:id="echoid-s34656" xml:space="preserve">L, duæ <lb/>perpendiculares E g, L f. </s>
  <s xml:id="echoid-s34657" xml:space="preserve">His <lb/>enim rite peractis, inuentæ erũt <lb/>
<anchor type="note" xlink:label="note-0553-08a" xlink:href="note-0553-08"/>
omnes dictę ſex circunferentię <lb/>ad tempus propoſitum, cum ni-<lb/>mirum Sol in puncto K, paralleli a e b, exiſtit. </s>
  <s xml:id="echoid-s34658" xml:space="preserve">Nam, vt in ſequenti cap. </s>
  <s xml:id="echoid-s34659" xml:space="preserve">oſtendemus, g f, erit cir-<lb/>cunferentia hectemoria; </s>
  <s xml:id="echoid-s34660" xml:space="preserve">B M, horaria; </s>
  <s xml:id="echoid-s34661" xml:space="preserve">A P, deſcenſiua; </s>
  <s xml:id="echoid-s34662" xml:space="preserve">B Y, meridiana; </s>
  <s xml:id="echoid-s34663" xml:space="preserve">A T, Verticalis; </s>
  <s xml:id="echoid-s34664" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34665" xml:space="preserve">A S, <lb/>horizontalis.</s>
  <s xml:id="echoid-s34666" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1748" type="float" level="2" n="2">
<note position="left" xlink:label="note-0552-16" xlink:href="note-0552-16a" xml:space="preserve">Tnuentio dicta-<lb/>rum ſex circun-<lb/>ferentiarum ex <lb/>Analemmate, <lb/>Sole extra Ae-<lb/>quatotem exi-<lb/>@ent<unsure/>e.</note>
  <figure xlink:label="fig-0553-01" xlink:href="fig-0553-01a">
    <image file="0553-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553-01"/>
  </figure>
<note position="left" xlink:label="note-0553-01" xlink:href="note-0553-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0553-02" xlink:href="note-0553-02a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0553-03" xlink:href="note-0553-03a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0553-04" xlink:href="note-0553-04a" xml:space="preserve">19. primi.</note>
  <figure xlink:label="fig-0553-02" xlink:href="fig-0553-02a">
    <image file="0553-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553-02"/>
  </figure>
<note position="left" xlink:label="note-0553-05" xlink:href="note-0553-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0553-06" xlink:href="note-0553-06a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0553-07" xlink:href="note-0553-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0553-08" xlink:href="note-0553-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s34667" xml:space="preserve">POSSVNT autem tres circunferentiæ mobiles, vt hectemoria, horaria, ac deſcenſiua faci-<lb/>
<anchor type="note" xlink:label="note-0553-09a" xlink:href="note-0553-09"/>
lius reperiri, ſine tot lineis perpendicularibus, hac ratione. </s>
  <s xml:id="echoid-s34668" xml:space="preserve">Ducta ex K, loco Solis ad a b, diame-<lb/>trum paralleli perpendiculari K L, ducatur ex E, per L, recta E L Y, ad quam in E, excitetur per-<lb/>pendicularis E g. </s>
  <s xml:id="echoid-s34669" xml:space="preserve">Nam ſi ex L, vt centro, interuallo autem L K, ſumatur beneficio circini punctũ <lb/>f, in Meridiano, erit g f, circunferentia hectemoria. </s>
  <s xml:id="echoid-s34670" xml:space="preserve">Si vero ex puncto d, vbi paralleli diameter <lb/>ſecat diametrum Horizontis, vt cẽtro, interuallo autem d K, accipiatur in Meridiano punctũ M,
<pb o="538" file="0554" n="554" rhead="GNOMONICES"/>
erit B M, circunferentia horaria. </s>
  <s xml:id="echoid-s34671" xml:space="preserve">Si denique ex puncto n, vbi diameter paralleli diametrum Ver-<lb/>ticalis ſecat, vt centro, interuallo verò n K, in Meridiano ſumatur beneficio circini punctum P, <lb/>
<anchor type="figure" xlink:label="fig-0554-01a" xlink:href="fig-0554-01"/>
erit A P, circunferentia <lb/>deſcenſiua. </s>
  <s xml:id="echoid-s34672" xml:space="preserve">Ratio hu-<lb/>ius rei eſt, quòd ducta <lb/>recta f L, perpendicula <lb/>ris eſt ad rectam ELY: <lb/></s>
  <s xml:id="echoid-s34673" xml:space="preserve">ducta autẽ recta MLN, <lb/>ad B D, perpẽdicularis <lb/>eſt; </s>
  <s xml:id="echoid-s34674" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34675" xml:space="preserve">recta P L O, ad <lb/>
<anchor type="note" xlink:label="note-0554-01a" xlink:href="note-0554-01"/>
A C, vt mox demon-<lb/>ſtrabimus. </s>
  <s xml:id="echoid-s34676" xml:space="preserve">Cum ergo <lb/>prius per has perpendi <lb/>culares L f, M L N, <lb/>P L O, inuentę ſint tres <lb/>dictæ circunferentię, vt <lb/>in ſequenti cap. </s>
  <s xml:id="echoid-s34677" xml:space="preserve">oſten-<lb/>demus, eædem etiam <lb/>inuentæ erunt per pun-<lb/>cta f, M, P, in Meridia <lb/>
<anchor type="note" xlink:label="note-0554-02a" xlink:href="note-0554-02"/>
no accepta, vt diximus. <lb/></s>
  <s xml:id="echoid-s34678" xml:space="preserve">Rectam autem f L, ad <lb/>E L Y, perpendicularẽ <lb/>eſſe, ita probabimus. </s>
  <s xml:id="echoid-s34679" xml:space="preserve"><lb/>Ducta recta E f, quoniã <lb/>duo latera K L, L E, triã <lb/>guli K L E, ęqualia ſunt <lb/>duobus lateribus f L, <lb/>L E, trianguli f L E, (quòd interuallum L f, interuallo L K, ſumptum eſt æquale) eſtq́ue baſis k E, <lb/>baſi f E, ęqualis, (quòd vtraque ſit ſphęrę ſemidiameter) erit angulus k L E, angulo f L E, ęqualis. </s>
  <s xml:id="echoid-s34680" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0554-03a" xlink:href="note-0554-03"/>
<anchor type="note" xlink:label="note-0554-04a" xlink:href="note-0554-04"/>
<anchor type="figure" xlink:label="fig-0554-02a" xlink:href="fig-0554-02"/>
Cum ergo k L E, rectus ſit, vt <lb/>paulo ante oſtendimus, erit &amp; </s>
  <s xml:id="echoid-s34681" xml:space="preserve"><lb/>f L E, rectus, ideoq́; </s>
  <s xml:id="echoid-s34682" xml:space="preserve">fL.</s>
  <s xml:id="echoid-s34683" xml:space="preserve">, ad ELY, <lb/>perpendicularis erit. </s>
  <s xml:id="echoid-s34684" xml:space="preserve">Viciſſim <lb/>etiam probabimus, ſi ex L, duca <lb/>tur ad E L Y, perpendicularis <lb/>L f, eam æqualẽ eſſe rectæ L K. <lb/></s>
  <s xml:id="echoid-s34685" xml:space="preserve">Cũ enim duo quadrata ex E k, <lb/>
<anchor type="note" xlink:label="note-0554-05a" xlink:href="note-0554-05"/>
E f, æqualia ſint, erunt duo qua-<lb/>drata ex E L, L K, duobus qua-<lb/>
<anchor type="note" xlink:label="note-0554-06a" xlink:href="note-0554-06"/>
dratis ex E L, L f, æqualia Abla <lb/>to ergo communi quadrato re-<lb/>ctæ E L, reliqua erunt quadra-<lb/>ta rectarum L K, L f, æqualia, <lb/>proptereaq́ue &amp; </s>
  <s xml:id="echoid-s34686" xml:space="preserve">rectæ L K, L f, <lb/>æquales erunt. </s>
  <s xml:id="echoid-s34687" xml:space="preserve">Quod etiam ita <lb/>confirmabimus. </s>
  <s xml:id="echoid-s34688" xml:space="preserve">Extendatur re-<lb/>cta Y E, vſque ad Z. </s>
  <s xml:id="echoid-s34689" xml:space="preserve">Quoniam <lb/>igitur K L, ad diametrum paral <lb/>leli a b, perpendicularis media <lb/>
<anchor type="note" xlink:label="note-0554-07a" xlink:href="note-0554-07"/>
propottionalis eſt inter ſegmen <lb/>ta a L, Lb, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s34690" xml:space="preserve">13. <lb/></s>
  <s xml:id="echoid-s34691" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34692" xml:space="preserve">6. </s>
  <s xml:id="echoid-s34693" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34694" xml:space="preserve">erit quadratum ex <lb/>K L, æquale rectangulo ſub a L, <lb/>
<anchor type="note" xlink:label="note-0554-08a" xlink:href="note-0554-08"/>
Lb, contento. </s>
  <s xml:id="echoid-s34695" xml:space="preserve">Eodem modo, erit fL, perpendicularis ducta ad Y Z, media proportionalis inter <lb/>ſegmenta Y L, L Z, atque adeo quadratum ex fL, rectangulo ſub γ L, L Z, æquale. </s>
  <s xml:id="echoid-s34696" xml:space="preserve">Cum ergo re-<lb/>ctangula ſuba L, L b, &amp; </s>
  <s xml:id="echoid-s34697" xml:space="preserve">ſub γ L, L Z, æqualia ſint, erunt &amp; </s>
  <s xml:id="echoid-s34698" xml:space="preserve">quadrata ex K L, f L, æqualia, ideoq́ue <lb/>
<anchor type="note" xlink:label="note-0554-09a" xlink:href="note-0554-09"/>
&amp; </s>
  <s xml:id="echoid-s34699" xml:space="preserve">rectæ K L, f L, æquales.</s>
  <s xml:id="echoid-s34700" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1749" type="float" level="2" n="3">
<note position="right" xlink:label="note-0553-09" xlink:href="note-0553-09a" xml:space="preserve">Alia inuentio <lb/>circunferentiæ <lb/>hectemotiæ, ho-<lb/>rariæ, &amp; deſcen-<lb/>ſiuæ.</note>
  <figure xlink:label="fig-0554-01" xlink:href="fig-0554-01a">
    <image file="0554-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0554-01"/>
  </figure>
<note position="left" xlink:label="note-0554-01" xlink:href="note-0554-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0554-02" xlink:href="note-0554-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0554-03" xlink:href="note-0554-03a" xml:space="preserve">8. primi.</note>
<note position="left" xlink:label="note-0554-04" xlink:href="note-0554-04a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0554-02" xlink:href="fig-0554-02a">
    <image file="0554-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0554-02"/>
  </figure>
<note position="left" xlink:label="note-0554-05" xlink:href="note-0554-05a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0554-06" xlink:href="note-0554-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0554-07" xlink:href="note-0554-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0554-08" xlink:href="note-0554-08a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0554-09" xlink:href="note-0554-09a" xml:space="preserve">35. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34701" xml:space="preserve">AT vero rectas M L N, P L O, ad rectas B D, A C, perpendiculares eſſe, facile comprobabi-<lb/>mus, ſi prius demonſtremus, ſi per L, ducantur rectæ M L N, P L O, ad B D, A C, perpendicula-<lb/>res, coniungaturq́ue rectæ d M, d K, &amp; </s>
  <s xml:id="echoid-s34702" xml:space="preserve">n P, n K, rectam d M, rectæ d K, &amp; </s>
  <s xml:id="echoid-s34703" xml:space="preserve">rectam n P, rectæ
<pb o="539" file="0555" n="555" rhead="LIBER SEXTVS."/>
n K, æqualem eſſe. </s>
  <s xml:id="echoid-s34704" xml:space="preserve">Quod ita demonſtrabimus, &amp; </s>
  <s xml:id="echoid-s34705" xml:space="preserve">multo quidem breuius, quàm Federicus Com-<lb/>mandinus. </s>
  <s xml:id="echoid-s34706" xml:space="preserve">Producta recta M N, vſq; </s>
  <s xml:id="echoid-s34707" xml:space="preserve">ad α, quoniã recta M α, diuiſa eſt in N, bifariã, &amp; </s>
  <s xml:id="echoid-s34708" xml:space="preserve">in L, nõ bi-<lb/>
<anchor type="note" xlink:label="note-0555-01a" xlink:href="note-0555-01"/>
fariã, erit quadratũ ex M N, æquale rectangulo ſub M L, L α, vna cum quadrato ex L N. </s>
  <s xml:id="echoid-s34709" xml:space="preserve">Addito <lb/>
<anchor type="note" xlink:label="note-0555-02a" xlink:href="note-0555-02"/>
ergo cõmuni quadr@to ex N d, erunt quadrata ex M N, N d, æqualia rectangulo ſub M L, L α, vna <lb/>
<anchor type="figure" xlink:label="fig-0555-01a" xlink:href="fig-0555-01"/>
cum quadratis ex L N, N d. <lb/></s>
  <s xml:id="echoid-s34710" xml:space="preserve">Sunt autem quadrata ex M N, <lb/>N d, quadrato ex d M, &amp; </s>
  <s xml:id="echoid-s34711" xml:space="preserve">qua-<lb/>
<anchor type="note" xlink:label="note-0555-03a" xlink:href="note-0555-03"/>
drata ex L N, N d, quadrato ex <lb/>d L, æqualia. </s>
  <s xml:id="echoid-s34712" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34713" xml:space="preserve">quadra-<lb/>tum ex d M, æquale erit rectan <lb/>
<anchor type="note" xlink:label="note-0555-04a" xlink:href="note-0555-04"/>
gulo ſub M L, L α, vna cum <lb/>quadrato ex d L. </s>
  <s xml:id="echoid-s34714" xml:space="preserve">Sed rectangu-<lb/>lum ſub M L, L α, rectangulo <lb/>
<anchor type="note" xlink:label="note-0555-05a" xlink:href="note-0555-05"/>
ſub a L, L b, æquale eſt. </s>
  <s xml:id="echoid-s34715" xml:space="preserve">Erit er-<lb/>go &amp; </s>
  <s xml:id="echoid-s34716" xml:space="preserve">quadratum ex d M, æqua <lb/>le rectangulo ſub a L, L b, vna <lb/>cum quadrato ex d L. </s>
  <s xml:id="echoid-s34717" xml:space="preserve">Eſt autem <lb/>rectangulo ſub a L, L b, æquale <lb/>
<anchor type="note" xlink:label="note-0555-06a" xlink:href="note-0555-06"/>
quadratum ex K L, quòd recta <lb/>K L, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s34718" xml:space="preserve">13. </s>
  <s xml:id="echoid-s34719" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s34720" xml:space="preserve">
<anchor type="note" xlink:label="note-0555-07a" xlink:href="note-0555-07"/>
6. </s>
  <s xml:id="echoid-s34721" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34722" xml:space="preserve">media proportionalis <lb/>ſit inter a L, L b.</s>
  <s xml:id="echoid-s34723" xml:space="preserve">Igitur quadra-<lb/>tum ex d M, ęquale quoque erit <lb/>quadratis ex K L, L d. </s>
  <s xml:id="echoid-s34724" xml:space="preserve">Cum er-<lb/>go eiſdem quadratis ex KL Ld, <lb/>
<anchor type="note" xlink:label="note-0555-08a" xlink:href="note-0555-08"/>
æquale ſit etiam quadratum ex <lb/>d K, æqualia inter ſe erunt qua-<lb/>drata ex d M, d K, ac proinde &amp; </s>
  <s xml:id="echoid-s34725" xml:space="preserve"><lb/>recta d M, d K, æquales. </s>
  <s xml:id="echoid-s34726" xml:space="preserve">Rur-<lb/>ſus producta recta P O, vſque <lb/>
<anchor type="note" xlink:label="note-0555-09a" xlink:href="note-0555-09"/>
ad t, quoniam recta P t, ſecta eſt bifariam in O, &amp; </s>
  <s xml:id="echoid-s34727" xml:space="preserve">non bifariam in L, erit quadratum ex <lb/>
<anchor type="note" xlink:label="note-0555-10a" xlink:href="note-0555-10"/>
P O, æquale rectangulo ſub P L, L t, vna cum quadrato ex L O. </s>
  <s xml:id="echoid-s34728" xml:space="preserve">Addito ergo communi quadrato <lb/>
<anchor type="note" xlink:label="note-0555-11a" xlink:href="note-0555-11"/>
ex O n, erunt quadrata ex P O, O n, æqualia rectangulo ſub P L, L t, vna cum quadratis ex L O, <lb/>O n. </s>
  <s xml:id="echoid-s34729" xml:space="preserve">Sunt autem quadrata ex P O, O n, quadrato ex n P, &amp; </s>
  <s xml:id="echoid-s34730" xml:space="preserve">quadrata ex L O, O n, quadrato ex <lb/>
<anchor type="note" xlink:label="note-0555-12a" xlink:href="note-0555-12"/>
n L, æqualia. </s>
  <s xml:id="echoid-s34731" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34732" xml:space="preserve">quadratum ex n P, æquale erit rectangulo ſub P L, L t, vna cum quadrato <lb/>ex n L. </s>
  <s xml:id="echoid-s34733" xml:space="preserve">Sed rectangulum ſub P L, L t, rectangulo ſub a L, L b, æquale eſt. </s>
  <s xml:id="echoid-s34734" xml:space="preserve">Erit ergo &amp; </s>
  <s xml:id="echoid-s34735" xml:space="preserve">quadratum <lb/>
<anchor type="note" xlink:label="note-0555-13a" xlink:href="note-0555-13"/>
ex n P, æquale rectangulo ſub a L, L b, vna cum quadrato ex n L. </s>
  <s xml:id="echoid-s34736" xml:space="preserve">Eſt autem rectangulo ſub a L, <lb/>L b, æquale quadratum ex K L, quòd recta K L, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s34737" xml:space="preserve">13. </s>
  <s xml:id="echoid-s34738" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34739" xml:space="preserve">6. </s>
  <s xml:id="echoid-s34740" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34741" xml:space="preserve">media propor <lb/>
<anchor type="note" xlink:label="note-0555-14a" xlink:href="note-0555-14"/>
tionalis ſit inter a L, L b. </s>
  <s xml:id="echoid-s34742" xml:space="preserve">Igitur quadratum ex n P, æquale quoque erit quadratis ex K L, L n. <lb/></s>
  <s xml:id="echoid-s34743" xml:space="preserve">Cum ergo eiſdem quadratis ex K L, L n, æquale etiam ſit quadratum ex n K, æqualia inter ſe <lb/>
<anchor type="note" xlink:label="note-0555-15a" xlink:href="note-0555-15"/>
<anchor type="note" xlink:label="note-0555-16a" xlink:href="note-0555-16"/>
erunt quadrata ex n P, n K, proptereaq́ue &amp; </s>
  <s xml:id="echoid-s34744" xml:space="preserve">rectæ n P, n K, æquales. </s>
  <s xml:id="echoid-s34745" xml:space="preserve">Quod demonſtran-<lb/>dum erat.</s>
  <s xml:id="echoid-s34746" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1750" type="float" level="2" n="4">
<note position="right" xlink:label="note-0555-01" xlink:href="note-0555-01a" xml:space="preserve">3. tertĳ.</note>
<note position="right" xlink:label="note-0555-02" xlink:href="note-0555-02a" xml:space="preserve">5. ſecundi.</note>
  <figure xlink:label="fig-0555-01" xlink:href="fig-0555-01a">
    <image file="0555-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0555-01"/>
  </figure>
<note position="right" xlink:label="note-0555-03" xlink:href="note-0555-03a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0555-04" xlink:href="note-0555-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0555-05" xlink:href="note-0555-05a" xml:space="preserve">35. tertĳ.</note>
<note position="right" xlink:label="note-0555-06" xlink:href="note-0555-06a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0555-07" xlink:href="note-0555-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0555-08" xlink:href="note-0555-08a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0555-09" xlink:href="note-0555-09a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0555-10" xlink:href="note-0555-10a" xml:space="preserve">3. tertĳ.</note>
<note position="right" xlink:label="note-0555-11" xlink:href="note-0555-11a" xml:space="preserve">5. ſecundi.</note>
<note position="right" xlink:label="note-0555-12" xlink:href="note-0555-12a" xml:space="preserve">47. primi.</note>
<note position="right" xlink:label="note-0555-13" xlink:href="note-0555-13a" xml:space="preserve">35. tertĳ.</note>
<note position="right" xlink:label="note-0555-14" xlink:href="note-0555-14a" xml:space="preserve">17. ſexti.</note>
<note position="left" xlink:label="note-0555-15" xlink:href="note-0555-15a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0555-16" xlink:href="note-0555-16a" xml:space="preserve">47. primi</note>
</div>
<p>
  <s xml:id="echoid-s34747" xml:space="preserve">QVÆ cum ita ſint, perſpicuum eſt, ſi interuallum d M, interuallo d K, æquale ſumatur bene-<lb/>ficio circini, rectam M L N, ad B D, perpendicularem eſſe, hoc eſt, perpendicularemper L, ad <lb/>B D, excitatam cadere in punctum M. </s>
  <s xml:id="echoid-s34748" xml:space="preserve">Si enim aliò caderet, puta in S, eſſet ducta recta d S, ex ijs, <lb/>quæ proxime demonſtrauimus, æqualis rectæ d K, hoc eſt, rectæ d M, quæ eidem d K, ſumpta eſt <lb/>æqualis, quod abſurdũ eſt. </s>
  <s xml:id="echoid-s34749" xml:space="preserve">Eſt enim d M, maior, quàm d S. </s>
  <s xml:id="echoid-s34750" xml:space="preserve">Non ergo illa perpendicularis cadet <lb/>
<anchor type="note" xlink:label="note-0555-17a" xlink:href="note-0555-17"/>
in S; </s>
  <s xml:id="echoid-s34751" xml:space="preserve">eodemq́ue modo in nullum aliud punctum cadet, quam in M, atque adeo recta M L N, ad <lb/>B D, perpendicularis erit. </s>
  <s xml:id="echoid-s34752" xml:space="preserve">Non aliter oſtendemus, rectam P L O, ad A C, eſſe perpendicularem, <lb/>ſi interuallum n P, interuallo n K, æquale accipiatur. </s>
  <s xml:id="echoid-s34753" xml:space="preserve">Quæ omnia demonſtranda erant. </s>
  <s xml:id="echoid-s34754" xml:space="preserve">Alia li-<lb/>
<anchor type="note" xlink:label="note-0555-18a" xlink:href="note-0555-18"/>
neamenta porro harum figurarum, quorum hic non eſt facta mentio, cuiuſmodi ſunt linea a l h, <lb/>S V, Y ſ, T X, b p q, &amp; </s>
  <s xml:id="echoid-s34755" xml:space="preserve">in quinta figura recta H r, &amp; </s>
  <s xml:id="echoid-s34756" xml:space="preserve">in ſexta rectæ k N, K O, vſum habebunt in <lb/>cap. </s>
  <s xml:id="echoid-s34757" xml:space="preserve">7. </s>
  <s xml:id="echoid-s34758" xml:space="preserve">huius lib.</s>
  <s xml:id="echoid-s34759" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1751" type="float" level="2" n="5">
<note position="right" xlink:label="note-0555-17" xlink:href="note-0555-17a" xml:space="preserve">7. tertĳ.</note>
<note position="left" xlink:label="note-0555-18" xlink:href="note-0555-18a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1753" type="section" level="1" n="473">
<head xml:id="echoid-head502" style="it" xml:space="preserve">SCHOLIVM.</head>
<note position="right" xml:space="preserve">Qua ratione, <lb/>Sole exiſtente <lb/>in quouis paral <lb/>lelo, quælibet <lb/>circunferentia-<lb/>rũ inueniatur, <lb/>non habita ra-<lb/>tione aliarum.</note>
<p style="it">
  <s xml:id="echoid-s34760" xml:space="preserve">EX ĳs, quæ dicta ſunt, perſpicuum eſt, qua ratione, Sole exiſtente in quolibet par allelo, quæcunque <lb/>ex dictis circumferentĳs inueſtigari poſſit, cum opus fuerit, nulla habita ratione aliarum. </s>
  <s xml:id="echoid-s34761" xml:space="preserve">Pro quali-<lb/>bet enim indaganda ducenda eſt ex K, puncto horæ, vbi ponitur Sol, ad a b, diametrum paralleli perpẽ-<lb/>dicularis K L. </s>
  <s xml:id="echoid-s34762" xml:space="preserve">Deinde ſi quærenda eſt circumferentia horizontalis, ducenda eſt per L, ad diametrum <lb/>Horizontis B D, perpendicularis M N: </s>
  <s xml:id="echoid-s34763" xml:space="preserve">Vel (quod idẽ eſt) ex puncto d, vbi diameter paralleli diame-
<pb o="540" file="0556" n="556" rhead="GNOMONICES"/>
trum Horizontis ſecat, tanquam centro, interuallo vero d K, accipiendum eſt punctum M, be-<lb/>
<anchor type="note" xlink:label="note-0556-01a" xlink:href="note-0556-01"/>
neficio circini in Meridiano, &amp; </s>
  <s xml:id="echoid-s34764" xml:space="preserve">ex M, per L, recta ducenda M N, quæ, vt demonſtrauimus, ad B D, <lb/>perpendicularis eſt, Nam ſi ex M N, abſcindatur recta N Q, rectæ K L, æqualis, ducatur{q́ue} ex <lb/>centro E, per Q, recta ſecans circunferentiam Meridiani in S, erit A S, circunferentia borizon-<lb/>talis, initium habens in Analemmate à diametro Verticalis, ſeu gnomone A C, Si vero inuenien <lb/>
<anchor type="note" xlink:label="note-0556-02a" xlink:href="note-0556-02"/>
da ſit circunferentia deſcenſiua, ducenda eſt per L, ad diametrum Verticalis A C, perpendicularis <lb/>P O, ſecans Meridiani circunferentiam in P: </s>
  <s xml:id="echoid-s34765" xml:space="preserve">Vel (quod idem eſt) ex puncton, vbi diameter paralleli <lb/>diametrum Verticalis ſecat, veluti centro, interuallo autem n K, accipiendum eſt beneficio circini in <lb/>Meridiano punctum P. </s>
  <s xml:id="echoid-s34766" xml:space="preserve">Nam A P, erit circunferentia deſcenſiua, cuius principium in Analemma-<lb/>te ſumitur à gnomone, ſeu diametro Verticalis. </s>
  <s xml:id="echoid-s34767" xml:space="preserve">Quod ſi deſideretur circunferentia Verticalis, du-<lb/>
<anchor type="note" xlink:label="note-0556-03a" xlink:href="note-0556-03"/>
<anchor type="note" xlink:label="note-0556-04a" xlink:href="note-0556-04"/>
cenda<unsure/> est per L, ad diamctrum Verticalis A C, perpendicularis P O: </s>
  <s xml:id="echoid-s34768" xml:space="preserve">Vel (quod idem eſt,) ex puncto <lb/>n, vbi par alleli diameter diametrum Horizontis diuidit, vt centro, at interuallo n K, accipiendum est <lb/>beneficio circini in Meridiano punctum P, &amp; </s>
  <s xml:id="echoid-s34769" xml:space="preserve">ex P, per L, recta ducenda P O, quæ, vt demonstraui-<lb/>mus, ad A C, perpendicularis eſt, Nã ſiex O P, auferatur recta O R, rectæ K L, æqualis, ducatur{q́ue} <lb/>ex centro E, per R, recta ſecans Meridiani circunferentiam in T, erit A T, circunferentia Vertica-<lb/>lis, initiũ in Analemmate habens à gnomone, ſeu diametro Verticalis A C. </s>
  <s xml:id="echoid-s34770" xml:space="preserve">At voro ſi proponatur:</s>
  <s xml:id="echoid-s34771" xml:space="preserve"><unsure/> cir-<lb/>cunferentia horaria inueſtiganda, duccnda est per L, ad Horizontis diametrum B D, perpendicularis <lb/>
<anchor type="note" xlink:label="note-0556-05a" xlink:href="note-0556-05"/>
M N, ſecans circunferentiam Meridiani in M: </s>
  <s xml:id="echoid-s34772" xml:space="preserve">Vel (quod idem eſt) beneficio circini ex puncto d, vbi <lb/>diameter paralleli diametrum Horizontis ſecat, vt centro, interuallo vero d K, accipiendum eſt in Me-<lb/>ridiano punctum M. </s>
  <s xml:id="echoid-s34773" xml:space="preserve">Nam B M, erit circunferentia horaria, habens principium à diametro Horizon-<lb/>
<anchor type="note" xlink:label="note-0556-06a" xlink:href="note-0556-06"/>
tis B D, in Analemmate. </s>
  <s xml:id="echoid-s34774" xml:space="preserve">Vt autem habeatur circunferentia meridiana, ducenda eſt ex E, centro <lb/>
<anchor type="note" xlink:label="note-0556-07a" xlink:href="note-0556-07"/>
per L, recta ſecans circunferentiam Meridiani in γ. </s>
  <s xml:id="echoid-s34775" xml:space="preserve">Nam recta B γ, erit circunferentia meridiana. <lb/></s>
  <s xml:id="echoid-s34776" xml:space="preserve">Pro hectemoria denique circunferentia ducenda eſt ex centro E, per L, recta E γ, &amp; </s>
  <s xml:id="echoid-s34777" xml:space="preserve">ad eam ex E, <lb/>
<anchor type="note" xlink:label="note-0556-08a" xlink:href="note-0556-08"/>
&amp; </s>
  <s xml:id="echoid-s34778" xml:space="preserve">L, excitandæ duæ perpendiculares E g, L f: </s>
  <s xml:id="echoid-s34779" xml:space="preserve">ſecantes Meridiani circunferentiam in g, f: </s>
  <s xml:id="echoid-s34780" xml:space="preserve">Vel (quod <lb/>idem est) ducta E G, ad E γ, perpendiculari, ſumendum eſt ex L, vt centro, &amp; </s>
  <s xml:id="echoid-s34781" xml:space="preserve">interuallo L K, bene-<lb/>ficio circini in Meridiano punctum f. </s>
  <s xml:id="echoid-s34782" xml:space="preserve">Nam g f, erit circunferentia hecto<unsure/>moria.</s>
  <s xml:id="echoid-s34783" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1753" type="float" level="2" n="1">
<note position="left" xlink:label="note-0556-01" xlink:href="note-0556-01a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0556-02" xlink:href="note-0556-02a" xml:space="preserve">Deſcenſiua.</note>
<note position="left" xlink:label="note-0556-03" xlink:href="note-0556-03a" xml:space="preserve">Verticalis.</note>
<note position="left" xlink:label="note-0556-04" xlink:href="note-0556-04a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0556-05" xlink:href="note-0556-05a" xml:space="preserve">Heratia<unsure/>.</note>
<note position="left" xlink:label="note-0556-06" xlink:href="note-0556-06a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0556-07" xlink:href="note-0556-07a" xml:space="preserve">Meridiana.</note>
<note position="left" xlink:label="note-0556-08" xlink:href="note-0556-08a" xml:space="preserve">Hectemoria.</note>
</div>
<p style="it">
  <s xml:id="echoid-s34784" xml:space="preserve">PORRO confecimus pro parallelo boreali quinque figuras, vt omnis varietas, quæ accidere potest, <lb/>
<anchor type="note" xlink:label="note-0556-09a" xlink:href="note-0556-09"/>
explicaretur. </s>
  <s xml:id="echoid-s34785" xml:space="preserve">Nam in ſecunda figura huius cap. </s>
  <s xml:id="echoid-s34786" xml:space="preserve">exiſtit Sol vltra Verticalem circulum, propterea{q́ue} per-<lb/>pendicularis K L, vltra diametrum A C, Verticalis circuli verſus auſtrũ cadit: </s>
  <s xml:id="echoid-s34787" xml:space="preserve">In tertia vero ponitur <lb/>Sol in Verticali circulo; </s>
  <s xml:id="echoid-s34788" xml:space="preserve">vnde perpendicularis K L, cadit in punctũ n, vbi diameter Vertie<unsure/>alis à diame-<lb/>
<anchor type="note" xlink:label="note-0556-10a" xlink:href="note-0556-10"/>
tro paralleli ſecatur: </s>
  <s xml:id="echoid-s34789" xml:space="preserve">Deinde in quarta conſtituitur Sol citra Verticalem circulum, ita tamen, vt eius <lb/>diſtantia à Meridiano minor ſit quadrante, ſiue ſex horis; </s>
  <s xml:id="echoid-s34790" xml:space="preserve">ex quo fit vt perpendicularis K L, cadat <lb/>citra diametrum Verticalis, ſed ſupra centrum paralleli m: </s>
  <s xml:id="echoid-s34791" xml:space="preserve">Rurſus in quinta Sol abeſt ſex horis à Me-<lb/>ridiano, ac idcirco perpendicularis K L, in m, centrum paralleli cadit: </s>
  <s xml:id="echoid-s34792" xml:space="preserve">In ſexta denique Sol à Meridia-<lb/>no maiorem diſtantiam habet, quam ſex horarum, ideoque perpendicularis infra m, centrum paralleli <lb/>cadit. </s>
  <s xml:id="echoid-s34793" xml:space="preserve">In omnibus tamen iſtis figuris idem ſemper modus eſt inueſtigandi dictas circunferentias, vt pa-<lb/>tet. </s>
  <s xml:id="echoid-s34794" xml:space="preserve">Pro parallelo autem australi vnicam figuram, nempe primam, deſcripſimus, quia Sol tunc ſupra <lb/>Horizontem ſemper vltra Verticalem exiſtit, minorem{q́ue} diſtantiam babet à Meridiano, quam ſex ho-<lb/>rarum, vt patet.</s>
  <s xml:id="echoid-s34795" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1754" type="float" level="2" n="2">
<note position="left" xlink:label="note-0556-09" xlink:href="note-0556-09a" xml:space="preserve">Cur pro paralle <lb/>lo boreali con-<lb/>fectæ ſint quin-<lb/>que figuræ, pro <lb/>auſtrali vero <lb/>vnica.</note>
<note position="left" xlink:label="note-0556-10" xlink:href="note-0556-10a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
</div>
<div xml:id="echoid-div1756" type="section" level="1" n="474">
<head xml:id="echoid-head503" style="it" xml:space="preserve">DEMONSTR ATIO EORVM, QV AE IN ANTECEDENTI <lb/>cap. dicta ſunt de inuentione prædictarum ſex circun-<lb/>ferentiarum. CAP. V.</head>
<p>
  <s xml:id="echoid-s34796" xml:space="preserve">IN qualibet figura præcedentis cap. </s>
  <s xml:id="echoid-s34797" xml:space="preserve">(in qua tamen axis mundi, &amp; </s>
  <s xml:id="echoid-s34798" xml:space="preserve">diameter Aequatoris non du-<lb/>
<anchor type="note" xlink:label="note-0556-12a" xlink:href="note-0556-12"/>
cantur, ne multitudo linearum confuſionem pariat) intelligatur circa a b, diametrum paralleli <lb/>ſemicirculus paralleli a e b, ad propriam poſitionem conuerſus, ita vt rectus ſit ad Meridianum, <lb/>tranſeatq́ue per K, centrum Solis. </s>
  <s xml:id="echoid-s34799" xml:space="preserve">Et quoniam K L, per defin. </s>
  <s xml:id="echoid-s34800" xml:space="preserve">4 lib. </s>
  <s xml:id="echoid-s34801" xml:space="preserve">11. </s>
  <s xml:id="echoid-s34802" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s34803" xml:space="preserve">ad planum Meridia-<lb/>ni recta eſt in eo ſitu, extendatur recta Y E, vſque ad Z, ducaturq́ue per rectas Y Z, K L, planum <lb/>faciens in ſuperficie ſphæræ, per propoſ. </s>
  <s xml:id="echoid-s34804" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34805" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34806" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34807" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34808" xml:space="preserve">ſemicirculum Y K H Z, qui rectus erit <lb/>
<anchor type="note" xlink:label="note-0556-13a" xlink:href="note-0556-13"/>
<anchor type="note" xlink:label="note-0556-14a" xlink:href="note-0556-14"/>
ad planum Meridiani, atque adeo Hectemorion referet, cum hic etiã per centrum Solis ducatur, <lb/>rectusq́ue ſit ad Meridianum, per propoſ. </s>
  <s xml:id="echoid-s34809" xml:space="preserve">15. </s>
  <s xml:id="echoid-s34810" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34811" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34812" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34813" xml:space="preserve">vtpote qui per polos Meridiani tran-<lb/>ſeat, vt ſupra dictum eſt. </s>
  <s xml:id="echoid-s34814" xml:space="preserve">Reliqua in figura conſtruantur, vt in figura cap. </s>
  <s xml:id="echoid-s34815" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34816" xml:space="preserve">Quoniam igitur re-<lb/>
<anchor type="note" xlink:label="note-0556-15a" xlink:href="note-0556-15"/>
cta L f, æqualis eſt rectæ L K, ex conſtructione, vel ex demonſtratis in antecedenti cap. </s>
  <s xml:id="echoid-s34817" xml:space="preserve">(Dixi-<lb/>mus enim ad interuallum L K, ſumendum eſſe ex L, vt centro, punctum f, in Meridiano, pro in-<lb/>uentione circunferentiæ hectemoriæ. </s>
  <s xml:id="echoid-s34818" xml:space="preserve">Item ſi ex L, ducatur ad E L Y, perpendicularis L f, de-<lb/>monſtrauimus L f, rectæ L K, æqualem eſſe) erunt duo latera E f, f L, trianguli E f L, in plano <lb/>Meridiani duobus lateribus E <emph style="sc">K</emph>, <emph style="sc">K</emph> L, trianguli E K L, in plano Hectemorij æqualia: </s>
  <s xml:id="echoid-s34819" xml:space="preserve">Habent au-<lb/>tem &amp; </s>
  <s xml:id="echoid-s34820" xml:space="preserve">baſim E L, communem. </s>
  <s xml:id="echoid-s34821" xml:space="preserve">Igitur angulus E f L, angulo E K L, æqualis erit. </s>
  <s xml:id="echoid-s34822" xml:space="preserve">Eſtautem <lb/>
<anchor type="note" xlink:label="note-0556-16a" xlink:href="note-0556-16"/>
angulo E f L, æqualis alternus angulus f E g; </s>
  <s xml:id="echoid-s34823" xml:space="preserve">propterea quòd, cum anguli f L E, g E L, recti ſint, <lb/>
<anchor type="note" xlink:label="note-0556-17a" xlink:href="note-0556-17"/>
rectæ f L, g E, parallelæ ſunt. </s>
  <s xml:id="echoid-s34824" xml:space="preserve">Item angulo E K L, eadem ratione æqualis eſt angulus alternus <lb/>
<anchor type="note" xlink:label="note-0556-18a" xlink:href="note-0556-18"/>
<pb o="541" file="0557" n="557" rhead="LIBER SEXTVS."/>
K E H, propterea quòd rectæ K L, H E, parallelæ ſunt, cum ſint ſectiones factæ à plano Hectemo-<lb/>
<anchor type="note" xlink:label="note-0557-01a" xlink:href="note-0557-01"/>
lii in planis parallelis, nempe in Horizonte, &amp; </s>
  <s xml:id="echoid-s34825" xml:space="preserve">ſemicirculo P K V m l. </s>
  <s xml:id="echoid-s34826" xml:space="preserve">Anguli igitur f E g, <lb/>K E H, æquales quoque inter ſe erunt: </s>
  <s xml:id="echoid-s34827" xml:space="preserve">ac propterea arcus g f, in Meridiano æqualis erit circun-<lb/>
<anchor type="note" xlink:label="note-0557-02a" xlink:href="note-0557-02"/>
ferentiæ hectemoriæ H K, in Hectemorio.</s>
  <s xml:id="echoid-s34828" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1756" type="float" level="2" n="1">
<note position="left" xlink:label="note-0556-12" xlink:href="note-0556-12a" xml:space="preserve">Demonſtratio <lb/>iuuentionis ſex <lb/>dictarum circũ-<lb/>ferentiarum, So <lb/>le conſtituto in <lb/>qu@liber paral-<lb/>lelo.</note>
<note position="left" xlink:label="note-0556-13" xlink:href="note-0556-13a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0556-14" xlink:href="note-0556-14a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0556-15" xlink:href="note-0556-15a" xml:space="preserve">Demonſtratio <lb/>circunferentiæ <lb/>hectemoriæ.</note>
<note position="left" xlink:label="note-0556-16" xlink:href="note-0556-16a" xml:space="preserve">8. primi.</note>
<note position="left" xlink:label="note-0556-17" xlink:href="note-0556-17a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0556-18" xlink:href="note-0556-18a" xml:space="preserve">28. primi.</note>
<note position="right" xlink:label="note-0557-01" xlink:href="note-0557-01a" xml:space="preserve">16. vndec.</note>
<note position="right" xlink:label="note-0557-02" xlink:href="note-0557-02a" xml:space="preserve">26. tertĳ.</note>
</div>
  <figure>
    <image file="0557-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0557-01"/>
  </figure>
<p>
  <s xml:id="echoid-s34829" xml:space="preserve">ARCVM deinde B M, in <lb/>
<anchor type="note" xlink:label="note-0557-03a" xlink:href="note-0557-03"/>
Meridiano æqualem eſſe circun <lb/>ferentiæ horariæ B K, in Hora-<lb/>rio, oſtendetur, vt ſupra cap. </s>
  <s xml:id="echoid-s34830" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s34831" xml:space="preserve">Erunt enim rurſus, per propoſ. </s>
  <s xml:id="echoid-s34832" xml:space="preserve"><lb/>10. </s>
  <s xml:id="echoid-s34833" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34834" xml:space="preserve">2. </s>
  <s xml:id="echoid-s34835" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s34836" xml:space="preserve">arcus A M, <lb/>
<anchor type="note" xlink:label="note-0557-04a" xlink:href="note-0557-04"/>
X K, inter circulos parallelos <lb/>A X V H C, M k q G h, per <lb/>quorum polos tranſeunt, æqua-<lb/>les; </s>
  <s xml:id="echoid-s34837" xml:space="preserve">ac proinde &amp; </s>
  <s xml:id="echoid-s34838" xml:space="preserve">reliqui B M, <lb/>B K, ex quadrantibus B A, B X, <lb/>æquales erunt. </s>
  <s xml:id="echoid-s34839" xml:space="preserve">Vel certe, per <lb/>definitionem poli, erunt chor-<lb/>dæ B M, B K, æquales. </s>
  <s xml:id="echoid-s34840" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s34841" xml:space="preserve"><lb/>arcus B M, B K, æquales erunt. <lb/></s>
  <s xml:id="echoid-s34842" xml:space="preserve">
<anchor type="note" xlink:label="note-0557-05a" xlink:href="note-0557-05"/>
</s>
</p>
<div xml:id="echoid-div1757" type="float" level="2" n="2">
<note position="right" xlink:label="note-0557-03" xlink:href="note-0557-03a" xml:space="preserve">Demonſtratio <lb/>circunferentiæ <lb/>horari<unsure/>æ.</note>
<note position="left" xlink:label="note-0557-04" xlink:href="note-0557-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0557-05" xlink:href="note-0557-05a" xml:space="preserve">28. terĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34843" xml:space="preserve">PARI ratione demonſtra-<lb/>
<anchor type="note" xlink:label="note-0557-06a" xlink:href="note-0557-06"/>
bimus, vt ſupra cap. </s>
  <s xml:id="echoid-s34844" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34845" xml:space="preserve">arcum <lb/>
<anchor type="note" xlink:label="note-0557-07a" xlink:href="note-0557-07"/>
A P, in Meridiano æqualem eſ-<lb/>ſe circunferentiæ deſcenſiuæ <lb/>A K, in Deſcenſiuo. </s>
  <s xml:id="echoid-s34846" xml:space="preserve">Nam rur-<lb/>ſus erunt, per propoſ. </s>
  <s xml:id="echoid-s34847" xml:space="preserve">10. </s>
  <s xml:id="echoid-s34848" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s34849" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s34850" xml:space="preserve">Theod arcus B P, F K, inter pa-<lb/>rallelos circulos B q H e D, <lb/>P K V m l, æquales; </s>
  <s xml:id="echoid-s34851" xml:space="preserve">atque idcí<unsure/>rco &amp; </s>
  <s xml:id="echoid-s34852" xml:space="preserve">reliqui A P, A K, ex quadrantibus A B, A F, æquales erunt. </s>
  <s xml:id="echoid-s34853" xml:space="preserve"><lb/>Vel certe, per definitionem poli, erunt chordæ A P, A k, æquales. </s>
  <s xml:id="echoid-s34854" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s34855" xml:space="preserve">arcus A P, A k, <lb/>
<anchor type="note" xlink:label="note-0557-08a" xlink:href="note-0557-08"/>
æquales erunt.</s>
  <s xml:id="echoid-s34856" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1758" type="float" level="2" n="3">
<note position="left" xlink:label="note-0557-06" xlink:href="note-0557-06a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0557-07" xlink:href="note-0557-07a" xml:space="preserve">Demonſtratio <lb/>circunferentiæ <lb/>deſcenſiuæ.</note>
<note position="right" xlink:label="note-0557-08" xlink:href="note-0557-08a" xml:space="preserve">28. tertĳ.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s34857" xml:space="preserve">AT vero arcum B Y, eſſe circunferentiam meridianam, perſpicuum eſt, cum ſit portio Me-<lb/>
<anchor type="note" xlink:label="note-0557-10a" xlink:href="note-0557-10"/>
ridiani interiecta inter Horizontem, ſeu lineam meridianam B D, &amp; </s>
  <s xml:id="echoid-s34858" xml:space="preserve">Hectemorion Y K H Z.</s>
  <s xml:id="echoid-s34859" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1759" type="float" level="2" n="4">
<note position="right" xlink:label="note-0557-10" xlink:href="note-0557-10a" xml:space="preserve">Demonſtratio <lb/>circunferentiæ <lb/>meridianæ.</note>
</div>
<p>
  <s xml:id="echoid-s34860" xml:space="preserve">IAM vero oſtendemus, vt ſupra cap. </s>
  <s xml:id="echoid-s34861" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34862" xml:space="preserve">rectas X E, V O, ſe mutuo ſecare in puncto I, quod <lb/>
<anchor type="note" xlink:label="note-0557-11a" xlink:href="note-0557-11"/>
in recta K m, communi ſectione ſemicirculi Horarij B K X m D, &amp; </s>
  <s xml:id="echoid-s34863" xml:space="preserve">ſemicirculi P K V m l, exi-<lb/>ſtat. </s>
  <s xml:id="echoid-s34864" xml:space="preserve">Item K L O I, parallelogrãmum eſſe, ac propterea rectam I O, rectæ k L, hoc eſt, rectæ O R, <lb/>
<anchor type="note" xlink:label="note-0557-12a" xlink:href="note-0557-12"/>
quæ ipſi K L, æqualis ſumpta eſt, æqualem; </s>
  <s xml:id="echoid-s34865" xml:space="preserve">Et in triangulo R E O, angulum R E O, æqualem an-<lb/>
<anchor type="note" xlink:label="note-0557-13a" xlink:href="note-0557-13"/>
gulo I E O, in triangulo I E O, propterea quod duo latera illius O R, O E, duobus lateribus huius <lb/>O I, O E, æqualia ſint, anguloſq́ue comprehendant æquales, puta rectos. </s>
  <s xml:id="echoid-s34866" xml:space="preserve">Ex quo efficitur arcum <lb/>A T, in Meridiano æqualem eſſe circunferentiæ Verticali A X, in Verticali circulo. <lb/></s>
  <s xml:id="echoid-s34867" xml:space="preserve">
<anchor type="note" xlink:label="note-0557-14a" xlink:href="note-0557-14"/>
</s>
</p>
<div xml:id="echoid-div1760" type="float" level="2" n="5">
<note position="right" xlink:label="note-0557-11" xlink:href="note-0557-11a" xml:space="preserve">Demonſtratio <lb/>circunferentiæ <lb/>Verticalis.</note>
<note position="right" xlink:label="note-0557-12" xlink:href="note-0557-12a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0557-13" xlink:href="note-0557-13a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0557-14" xlink:href="note-0557-14a" xml:space="preserve">26. tertĳ.</note>
</div>
<p>
  <s xml:id="echoid-s34868" xml:space="preserve">DENIQVE eadem ratione concludemus, vt ſupra cap. </s>
  <s xml:id="echoid-s34869" xml:space="preserve">3. </s>
  <s xml:id="echoid-s34870" xml:space="preserve">rectas F E, q N, ſe mutuo ſecare <lb/>
<anchor type="note" xlink:label="note-0557-15a" xlink:href="note-0557-15"/>
<anchor type="note" xlink:label="note-0557-16a" xlink:href="note-0557-16"/>
in puncto p, quod in recta K G, communi ſectione ſemicirculi Deſcenſiui A K F G C, &amp; </s>
  <s xml:id="echoid-s34871" xml:space="preserve">ſemicir-<lb/>culi M K q G h, exiſtat. </s>
  <s xml:id="echoid-s34872" xml:space="preserve">Irem K L N p, parallelogrammum eſſe, atque idcirco rectam q N, rectæ <lb/>
<anchor type="note" xlink:label="note-0557-17a" xlink:href="note-0557-17"/>
K L, hoc eſt, rectæ N Q, quæ ipſi K L, æqualis ſumpta eſt, æqualem; </s>
  <s xml:id="echoid-s34873" xml:space="preserve">Et in triangulo Q E N, an-<lb/>gulum Q E N, angulo p E N, in triangulo p E N, æqualem, propterea quod duo illius latera <lb/>
<anchor type="note" xlink:label="note-0557-18a" xlink:href="note-0557-18"/>
Q N, N E, duobus lateribus huius N p, N E, æqualia ſint, anguloſq́ue contineant æquales, vtpo-<lb/>te rectos. </s>
  <s xml:id="echoid-s34874" xml:space="preserve">Quare arcus B S, in Meridiano arcui B F, in Horizonte æqualis erit; </s>
  <s xml:id="echoid-s34875" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s34876" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0557-19a" xlink:href="note-0557-19"/>
reliquus arcus A S, in Meridiano ex quadrante A B, reliquę circunferentiæ horizontali H F, ex <lb/>quadrante H B, æqualis erit. </s>
  <s xml:id="echoid-s34877" xml:space="preserve">Quæ omnia demonſtranda erant.</s>
  <s xml:id="echoid-s34878" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1761" type="float" level="2" n="6">
<note position="left" xlink:label="note-0557-15" xlink:href="note-0557-15a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0557-16" xlink:href="note-0557-16a" xml:space="preserve">Demonſtrati@ <lb/>circunferentiæ <lb/>horizontalis.</note>
<note position="right" xlink:label="note-0557-17" xlink:href="note-0557-17a" xml:space="preserve">34. primi</note>
<note position="right" xlink:label="note-0557-18" xlink:href="note-0557-18a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0557-19" xlink:href="note-0557-19a" xml:space="preserve">26. tertĳ.</note>
</div>
</div>
<div xml:id="echoid-div1763" type="section" level="1" n="475">
<head xml:id="echoid-head504" style="it" xml:space="preserve">DIVISIO ANALEMMATIS IN HORAS, <lb/>
pro quib{us} prædictę circunferentiæ ſunt inueſtigandæ, vt ex illis horo-
logium horizontale, Verticale, ac Meridianum con-
ſtruatur. CAP. VI.</head>
<p>
  <s xml:id="echoid-s34879" xml:space="preserve">QVATVOR ſunt genera horarum, vt in principio lib. </s>
  <s xml:id="echoid-s34880" xml:space="preserve">1. </s>
  <s xml:id="echoid-s34881" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s34882" xml:space="preserve">Quædam à mer. </s>
  <s xml:id="echoid-s34883" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s34884" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s34885" xml:space="preserve">initium ſumunt, dicunturq́; </s>
  <s xml:id="echoid-s34886" xml:space="preserve">Aſtronomicæ, ſiue vulgares, ex quibus horologium <lb/>Aſtronomicum conſtruitur: </s>
  <s xml:id="echoid-s34887" xml:space="preserve">Quædam autem ſuum principium habent ab occaſu Solis, &amp; </s>
  <s xml:id="echoid-s34888" xml:space="preserve">quędã <lb/>ab ortu, appellanturq́; </s>
  <s xml:id="echoid-s34889" xml:space="preserve">illæ Italicæ, &amp; </s>
  <s xml:id="echoid-s34890" xml:space="preserve">hæ Babylonicæ: </s>
  <s xml:id="echoid-s34891" xml:space="preserve">ex illis componitur horologium Italicum, <lb/>ex his vero Babylonicũ: </s>
  <s xml:id="echoid-s34892" xml:space="preserve">Atq; </s>
  <s xml:id="echoid-s34893" xml:space="preserve">omnes hæ horæ æquales ſunt, diuiduntq́; </s>
  <s xml:id="echoid-s34894" xml:space="preserve">ſingulos parallelos Solis in <lb/>24. </s>
  <s xml:id="echoid-s34895" xml:space="preserve">partes æquales, initio facto à meridie quidẽ vel media nocte in primo genere, in ſecundo autẽ <lb/>ab occaſu Solis, id eſt, ab eo puncto paralleli, vbi ex parte occidentis ab Horizonte ſecatur; </s>
  <s xml:id="echoid-s34896" xml:space="preserve">in ter-
<pb o="542" file="0558" n="558" rhead="GNOMONICES"/>
tio denique genere à Solis ortu, nempe ab illo puncto paralleli, vbi ab Horizonte ſecatur ex par-<lb/>teorientis. </s>
  <s xml:id="echoid-s34897" xml:space="preserve">Poſtremo aliæ horæ inæquales ſunt, quæ antiquæ dicuntur, ſecantes nimirum ſin-<lb/>gulos parallelos Solis, vno Æquatore excepto, in partes inæquales, ea tamen conditione, vt quẽ-<lb/>libet arcum diurnum, item &amp; </s>
  <s xml:id="echoid-s34898" xml:space="preserve">nocturnum in 12. </s>
  <s xml:id="echoid-s34899" xml:space="preserve">partes æquales partiantur. </s>
  <s xml:id="echoid-s34900" xml:space="preserve">Ex his horologium <lb/>Antiquum deſcribitur, vt latius in ſuperioribus, præſertim ad initium huius noſtræ Gnomonices <lb/>explicatum eſt. </s>
  <s xml:id="echoid-s34901" xml:space="preserve">Quoniam vero in quolibet plano omnes iſtæ horæ deſcribi poſſunt ex circunfe-<lb/>rentiis, de quibus ſupra egimus, exponendum eſt, qua ratione Analemma pro quolibet genere ho-<lb/>rarum diuidendum ſit, vt pro ſingulis horis dictas circunferentias inueſtigare poſſimus, Sole in <lb/>quocunque parallelo exiſtente; </s>
  <s xml:id="echoid-s34902" xml:space="preserve">hoc quidem cap. </s>
  <s xml:id="echoid-s34903" xml:space="preserve">quatenus ex eis horologium horizontale, Ver-<lb/>ticale ac Meridianum conſtruitur, quorum præcipue rationem habuiſſe Ptolemęum ſupra di-<lb/>
<anchor type="note" xlink:label="note-0558-01a" xlink:href="note-0558-01"/>
ximus: </s>
  <s xml:id="echoid-s34904" xml:space="preserve">De alijs vero horologijs cap. </s>
  <s xml:id="echoid-s34905" xml:space="preserve">10. </s>
  <s xml:id="echoid-s34906" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s34907" xml:space="preserve">agemus, vbi etiam Analemma pro quocunq; <lb/></s>
  <s xml:id="echoid-s34908" xml:space="preserve">genere horarum diuidemus.</s>
  <s xml:id="echoid-s34909" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1763" type="float" level="2" n="1">
<note position="left" xlink:label="note-0558-01" xlink:href="note-0558-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s34910" xml:space="preserve">SIT igitur Meridianus Analemmatis A B C D, cuius centrum E; </s>
  <s xml:id="echoid-s34911" xml:space="preserve">diameter Horizontis B D; <lb/></s>
  <s xml:id="echoid-s34912" xml:space="preserve">Verticalis diameter A C; </s>
  <s xml:id="echoid-s34913" xml:space="preserve">axis mundi H I; </s>
  <s xml:id="echoid-s34914" xml:space="preserve">Æquatoris diameter F G; </s>
  <s xml:id="echoid-s34915" xml:space="preserve">diameter paralleli ♋, M N; </s>
  <s xml:id="echoid-s34916" xml:space="preserve"><lb/>
<anchor type="figure" xlink:label="fig-0558-01a" xlink:href="fig-0558-01"/>
diameter paralleli ♉, <lb/>&amp; </s>
  <s xml:id="echoid-s34917" xml:space="preserve">♍, K L; </s>
  <s xml:id="echoid-s34918" xml:space="preserve">paralleli ♑, <lb/>diameter a b; </s>
  <s xml:id="echoid-s34919" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34920" xml:space="preserve">diame-<lb/>ter paralleli ♐, &amp; </s>
  <s xml:id="echoid-s34921" xml:space="preserve">♒, <lb/>S T. </s>
  <s xml:id="echoid-s34922" xml:space="preserve">Circa diametros <lb/>M N, K L, a b, deſcri-<lb/>
<anchor type="note" xlink:label="note-0558-02a" xlink:href="note-0558-02"/>
bantur ſemicirculi, &amp; </s>
  <s xml:id="echoid-s34923" xml:space="preserve"><lb/>ex punctis P, O, d, vbi <lb/>eædem diametri à dia-<lb/>metro Horizõtis ſecã-<lb/>tur, ad ipſas diametros <lb/>ducantur perpendicu-<lb/>lares PR, OQ, d e, quę, <lb/>vt ſupra oſtẽdimus, cõ-<lb/>munes ſectiones erunt <lb/>parallelorũ, arque Ho-<lb/>
<anchor type="note" xlink:label="note-0558-03a" xlink:href="note-0558-03"/>
rizontis, ita vt M R, <lb/>portio ſit paralleli ♋, <lb/>ſupra terram, &amp; </s>
  <s xml:id="echoid-s34924" xml:space="preserve">R N, <lb/>portio infra terrã: </s>
  <s xml:id="echoid-s34925" xml:space="preserve">Item <lb/>K Q, portio ♉, &amp; </s>
  <s xml:id="echoid-s34926" xml:space="preserve">♍, <lb/>ſupra terram, &amp; </s>
  <s xml:id="echoid-s34927" xml:space="preserve">Q L, <lb/>portio infra terrã: </s>
  <s xml:id="echoid-s34928" xml:space="preserve">De-<lb/>nique be, portio ♑, <lb/>ſupra terram, &amp; </s>
  <s xml:id="echoid-s34929" xml:space="preserve">ea, por <lb/>tio ſub terra. </s>
  <s xml:id="echoid-s34930" xml:space="preserve">Cur autẽ <lb/>
<anchor type="note" xlink:label="note-0558-04a" xlink:href="note-0558-04"/>
omiſerimus diametrũ paralleli ♊, &amp; </s>
  <s xml:id="echoid-s34931" xml:space="preserve">♌, itẽ diametrũ paralleli ♍, &amp; </s>
  <s xml:id="echoid-s34932" xml:space="preserve">♓, ratio in promptu eſt: </s>
  <s xml:id="echoid-s34933" xml:space="preserve">quo-<lb/>niam ſcilicet tres diametri M N, k L, S T, inſtar omnium eſſe poſſunt. </s>
  <s xml:id="echoid-s34934" xml:space="preserve">Nam M N, fungetur etiam <lb/>munere diametri paralleli ♑, ſi Analemma inuertatur, vt I, ſit polus arcticus, &amp; </s>
  <s xml:id="echoid-s34935" xml:space="preserve">H, antarcticus; </s>
  <s xml:id="echoid-s34936" xml:space="preserve">C, <lb/>vertex capitis, &amp; </s>
  <s xml:id="echoid-s34937" xml:space="preserve">A, eius oppoſitum; </s>
  <s xml:id="echoid-s34938" xml:space="preserve">ita vt N R, ſit portio ♑, ſupra terram, &amp; </s>
  <s xml:id="echoid-s34939" xml:space="preserve">R M, portio ſub <lb/>terra. </s>
  <s xml:id="echoid-s34940" xml:space="preserve">Eadem ratione K L, referet etiam diametrum paralleli ♏, &amp; </s>
  <s xml:id="echoid-s34941" xml:space="preserve">♓, ita vt L Q, ſit portio ♏, &amp; </s>
  <s xml:id="echoid-s34942" xml:space="preserve"><lb/>♓, ſupra terram, &amp; </s>
  <s xml:id="echoid-s34943" xml:space="preserve">Q K, portio ſub terra. </s>
  <s xml:id="echoid-s34944" xml:space="preserve">Denique S T, diametrum quoque paralleli ♊, &amp; </s>
  <s xml:id="echoid-s34945" xml:space="preserve">♌, <lb/>exprimet, portioq́ue ſemicirculi circa ST, deſcripti (quem tamen confuſionis vitandæ gratia non <lb/>deſcripſimus) reſpondens ſegmento diametri T V, erit portio ♊, &amp; </s>
  <s xml:id="echoid-s34946" xml:space="preserve">♌, ſupra terrã, &amp; </s>
  <s xml:id="echoid-s34947" xml:space="preserve">portio reſpon <lb/>dens ſegmento V S, infra terrã exiſter. </s>
  <s xml:id="echoid-s34948" xml:space="preserve">Ratio omniũ horum eſt, quod oppoſitorũ ſignorum paral-<lb/>leli æquales habeant declinationes. </s>
  <s xml:id="echoid-s34949" xml:space="preserve">Quæ cum ita ſint, ſuperuacanea eſſet a b, diameter paralleli ♑, <lb/>
<anchor type="note" xlink:label="note-0558-05a" xlink:href="note-0558-05"/>
vna cũ eius ſemicirculo, niſi eã pro diametro paralleli ♋, vſurpare vellemus, ſi inuertatur Analem-<lb/>ma, vt diximus, vt omnium horarum diuiſiones in propoſito Analemmate explicare poſſimus.</s>
  <s xml:id="echoid-s34950" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1764" type="float" level="2" n="2">
  <figure xlink:label="fig-0558-01" xlink:href="fig-0558-01a">
    <image file="0558-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0558-01"/>
  </figure>
<note position="left" xlink:label="note-0558-02" xlink:href="note-0558-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0558-03" xlink:href="note-0558-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0558-04" xlink:href="note-0558-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0558-05" xlink:href="note-0558-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s34951" xml:space="preserve">ITAQVE pro horis à mer. </s>
  <s xml:id="echoid-s34952" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34953" xml:space="preserve">med. </s>
  <s xml:id="echoid-s34954" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s34955" xml:space="preserve">diuidẽdi ſunt ſinguli ſemicirculi parallelorũ in 12. </s>
  <s xml:id="echoid-s34956" xml:space="preserve">par <lb/>
<anchor type="note" xlink:label="note-0558-06a" xlink:href="note-0558-06"/>
tes æquales, initio facto ab illis punctis, vbi eorũ diametri circunferentiã Meridiani ſecãt. </s>
  <s xml:id="echoid-s34957" xml:space="preserve">Vt factũ <lb/>eſſe cernis in M R N, ſemicirculo ♋, &amp; </s>
  <s xml:id="echoid-s34958" xml:space="preserve">♑, in quo numeri exteriores pertinẽt ad horas à med. </s>
  <s xml:id="echoid-s34959" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s34960" xml:space="preserve">interiores vero ad horas à mer. </s>
  <s xml:id="echoid-s34961" xml:space="preserve">Alios autem ſemicirculos nõ ita partiti ſumus, quia eos ſecabimus <lb/>in alias horas: </s>
  <s xml:id="echoid-s34962" xml:space="preserve">ſatis eſt, exemplũ in tropico ♋, &amp; </s>
  <s xml:id="echoid-s34963" xml:space="preserve">♑, poſuiſſe, ex quo facile quilibet intelliget, qua ra-<lb/>tione alij paralleli in horas à mer. </s>
  <s xml:id="echoid-s34964" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34965" xml:space="preserve">med. </s>
  <s xml:id="echoid-s34966" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s34967" xml:space="preserve">diſtribuendi ſint. </s>
  <s xml:id="echoid-s34968" xml:space="preserve">Cæterũ horæ portionis MR, arcui <lb/>diurno ♋, vel nocturno ♑, &amp; </s>
  <s xml:id="echoid-s34969" xml:space="preserve">horæ portionis N R, arcui nocturno ♋, vel diurno ♑, conueniunt. </s>
  <s xml:id="echoid-s34970" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0558-07a" xlink:href="note-0558-07"/>
</s>
</p>
<div xml:id="echoid-div1765" type="float" level="2" n="3">
<note position="left" xlink:label="note-0558-06" xlink:href="note-0558-06a" xml:space="preserve">Diuiſio Analẽ-<lb/>matis in horas <lb/>à mer. &amp; med. <lb/>noc.</note>
<note position="left" xlink:label="note-0558-07" xlink:href="note-0558-07a" xml:space="preserve">Diuiſio Analẽ-<lb/>matis in horas <lb/>ab ertu &amp; occa-<lb/>ſu Solis.</note>
</div>
<p>
  <s xml:id="echoid-s34971" xml:space="preserve">PRO horis autem ab ortu, &amp; </s>
  <s xml:id="echoid-s34972" xml:space="preserve">occaſu Solis, vt facilius in Analemmate reponantur, deſcriben-<lb/>di ſunt ſeorſum paralleli cum eorũ diametris, &amp; </s>
  <s xml:id="echoid-s34973" xml:space="preserve">communibus eorundem, &amp; </s>
  <s xml:id="echoid-s34974" xml:space="preserve">Horizontis ſectioni-
<pb o="543" file="0559" n="559" rhead="LIBER SEXTVS."/>
bus, diuidendiq́ue in 24. </s>
  <s xml:id="echoid-s34975" xml:space="preserve">partes æquales, facto initio à dictis communibus ſectionibus. </s>
  <s xml:id="echoid-s34976" xml:space="preserve">Exempli <lb/>gratia, circa a b, diametrum ♑, quæ nunc vices etiam gerat diametri ♋, ſeorſum expoſita deſcri-<lb/>bendus eſt circulus a e b e, ex centro m, vbi axis dictam diametrum ſecat, &amp; </s>
  <s xml:id="echoid-s34977" xml:space="preserve">per punctum d, quod <lb/>puncto d, in Analemmate reſpondeat, in vtramq; </s>
  <s xml:id="echoid-s34978" xml:space="preserve">partem excitanda ad a b, perpendicularis e b e, <lb/>
<anchor type="figure" xlink:label="fig-0559-01a" xlink:href="fig-0559-01"/>
quæ, vt demonſtrauimus, com-<lb/>munis ſectio eſt paralleli ♋, &amp; </s>
  <s xml:id="echoid-s34979" xml:space="preserve"><lb/>Horizontis; </s>
  <s xml:id="echoid-s34980" xml:space="preserve">ita vt e a e, ſit por-<lb/>tio ♋, ſupra Horizontem, ſiue <lb/>arcus diurnus ♋; </s>
  <s xml:id="echoid-s34981" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34982" xml:space="preserve">e b e, por-<lb/>tio ♋, ſub Horizonte, ſiue arcus <lb/>
<anchor type="note" xlink:label="note-0559-01a" xlink:href="note-0559-01"/>
nocturnus ♋. </s>
  <s xml:id="echoid-s34983" xml:space="preserve">Item e b e, por-<lb/>tio ♑, ſupra Horizontem, ſiue <lb/>arcus diurnus ♑; </s>
  <s xml:id="echoid-s34984" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s34985" xml:space="preserve">e a e, por-<lb/>tio ♑, infra Horizontem, ſiue <lb/>arcus nocturnus ♑. </s>
  <s xml:id="echoid-s34986" xml:space="preserve">Deinde di-<lb/>ctus circulus in 24. </s>
  <s xml:id="echoid-s34987" xml:space="preserve">partes æqua <lb/>les diuidendus, initio facto à <lb/>punctoe, vtrolibet, vt ab eo, <lb/>quod ad dextram ponitur in <lb/>noſtro exemplo. </s>
  <s xml:id="echoid-s34988" xml:space="preserve">Ita enim diui-<lb/>
<anchor type="note" xlink:label="note-0559-02a" xlink:href="note-0559-02"/>
ſus erit parallelus ♋, vel ♑, in <lb/>24. </s>
  <s xml:id="echoid-s34989" xml:space="preserve">horas æquales ab ortu, vel <lb/>occaſu Solis. </s>
  <s xml:id="echoid-s34990" xml:space="preserve">In tropico namq; <lb/></s>
  <s xml:id="echoid-s34991" xml:space="preserve">♋, dabũt numeri interiores ho-<lb/>ras ab ortuSolis, exteriores vero <lb/>numeri horas ab occaſu Solis <lb/>indicabunt. </s>
  <s xml:id="echoid-s34992" xml:space="preserve">In tropico autẽ ♑, contrariũ intelligatur. </s>
  <s xml:id="echoid-s34993" xml:space="preserve">Numeri enim exteriores ad horas ab ortu, <lb/>&amp; </s>
  <s xml:id="echoid-s34994" xml:space="preserve">interiores ad horas ab occaſu pertinent. </s>
  <s xml:id="echoid-s34995" xml:space="preserve">Ex quibus perſpicuũ eſt, qua ratione ex Analemmate, ſi <lb/>
<anchor type="note" xlink:label="note-0559-03a" xlink:href="note-0559-03"/>
circa diametros parallelorũ ipſi paralleli deſcribãtur, &amp; </s>
  <s xml:id="echoid-s34996" xml:space="preserve">in horas diuidãtur, cognoſci poſſit quanti <lb/>tas diei, &amp; </s>
  <s xml:id="echoid-s34997" xml:space="preserve">noctis cuiuſque paralleli. </s>
  <s xml:id="echoid-s34998" xml:space="preserve">Nam horæ in arcu e a e, deprehenſæ conficiunt arcũ diurnũ <lb/>
<anchor type="note" xlink:label="note-0559-04a" xlink:href="note-0559-04"/>
♋, vel nocturnũ ♑. </s>
  <s xml:id="echoid-s34999" xml:space="preserve">Horæ vero in arcu e b e, contentæ cõflantarcum nocturnũ ♋, vel diurnũ ♑, <lb/>Id quod in lib. </s>
  <s xml:id="echoid-s35000" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35001" xml:space="preserve">etiã docuimus. </s>
  <s xml:id="echoid-s35002" xml:space="preserve">Quòd ſi beneficio circini diuiſiones paralleli ♋, &amp; </s>
  <s xml:id="echoid-s35003" xml:space="preserve">♑, a e b e, trãſ-<lb/>ferantur in ſemicirculum ♋, &amp; </s>
  <s xml:id="echoid-s35004" xml:space="preserve">♑, in Analemmate, vt in figura apparet, idemq́ue fiat in omnibus <lb/>alijs parallelis (diuidendo videlicet ipſos circa proprias diametros deſcriptos in horas, facto ini-<lb/>tio à communibus ſectionibus eorum, &amp; </s>
  <s xml:id="echoid-s35005" xml:space="preserve">Horizontis, &amp;</s>
  <s xml:id="echoid-s35006" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35007" xml:space="preserve">vt in parallelo ♋, &amp; </s>
  <s xml:id="echoid-s35008" xml:space="preserve">♑, hic factũ eſt) <lb/>diuiſum erit Analemma in horas ab ortu, &amp; </s>
  <s xml:id="echoid-s35009" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s35010" xml:space="preserve">Solis. </s>
  <s xml:id="echoid-s35011" xml:space="preserve">Aſcripti tamen ſunt in Analemmate nu-<lb/>meri duntaxat horarum ab occaſu Solis. </s>
  <s xml:id="echoid-s35012" xml:space="preserve">Nam horum numerorum complementa vſquead 24. </s>
  <s xml:id="echoid-s35013" xml:space="preserve">da <lb/>bunt horas ab ortu. </s>
  <s xml:id="echoid-s35014" xml:space="preserve">Vt hora 23. </s>
  <s xml:id="echoid-s35015" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35016" xml:space="preserve">dabit horam 1. </s>
  <s xml:id="echoid-s35017" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s35018" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35019" xml:space="preserve">22. </s>
  <s xml:id="echoid-s35020" xml:space="preserve">dabit 2. </s>
  <s xml:id="echoid-s35021" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35022" xml:space="preserve">ſic de cæteris. <lb/></s>
  <s xml:id="echoid-s35023" xml:space="preserve">Meridianus autem circulus circa diametrum Æquatoris F G, deſcriptus, inſtar Æquatoris, diui-<lb/>dendus eſt in 24. </s>
  <s xml:id="echoid-s35024" xml:space="preserve">partes æquales, initio facto à diametro F G, vel axe H I. </s>
  <s xml:id="echoid-s35025" xml:space="preserve">Nam punctum F, erit <lb/>
<anchor type="note" xlink:label="note-0559-05a" xlink:href="note-0559-05"/>
hora 12. </s>
  <s xml:id="echoid-s35026" xml:space="preserve">aſtronomica, primum deinde punctum diuiſionis verſus H, hor. </s>
  <s xml:id="echoid-s35027" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35028" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s35029" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35030" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35031" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s35032" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35033" xml:space="preserve">ſequens autem punctum dabit horam 2. </s>
  <s xml:id="echoid-s35034" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s35035" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35036" xml:space="preserve">10. </s>
  <s xml:id="echoid-s35037" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s35038" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35039" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35040" xml:space="preserve">ita deinceps. </s>
  <s xml:id="echoid-s35041" xml:space="preserve">Sic etiã <lb/>punctum H, erit hora 24. </s>
  <s xml:id="echoid-s35042" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35043" xml:space="preserve">12. </s>
  <s xml:id="echoid-s35044" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35045" xml:space="preserve">primum deinde punctum diuiſionis verſus F, dabit ho-<lb/>ram 23. </s>
  <s xml:id="echoid-s35046" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35047" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35048" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35049" xml:space="preserve">ſequens autem punctum ad horam 22. </s>
  <s xml:id="echoid-s35050" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35051" xml:space="preserve">14. </s>
  <s xml:id="echoid-s35052" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35053" xml:space="preserve">pertinebit, &amp;</s>
  <s xml:id="echoid-s35054" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35055" xml:space="preserve">Idem <lb/>denique punctũ H, ſpectabit ad horam 24. </s>
  <s xml:id="echoid-s35056" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35057" xml:space="preserve">12. </s>
  <s xml:id="echoid-s35058" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s35059" xml:space="preserve">primum deinde punctum diuiſionis ver-<lb/>ſus F, ad horam 1. </s>
  <s xml:id="echoid-s35060" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35061" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35062" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s35063" xml:space="preserve">ſequens autem ad horam 2. </s>
  <s xml:id="echoid-s35064" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35065" xml:space="preserve">10. </s>
  <s xml:id="echoid-s35066" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s35067" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35068" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s35069" xml:space="preserve">Ita vt <lb/>tam hora 18. </s>
  <s xml:id="echoid-s35070" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35071" xml:space="preserve">quam 6. </s>
  <s xml:id="echoid-s35072" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s35073" xml:space="preserve">cadat in F, punctum meridiei, hora vero 6. </s>
  <s xml:id="echoid-s35074" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35075" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35076" xml:space="preserve">18. </s>
  <s xml:id="echoid-s35077" xml:space="preserve"><lb/>ab or. </s>
  <s xml:id="echoid-s35078" xml:space="preserve">in G, punctum mediæ noctis.</s>
  <s xml:id="echoid-s35079" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1766" type="float" level="2" n="4">
  <figure xlink:label="fig-0559-01" xlink:href="fig-0559-01a">
    <image file="0559-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0559-01"/>
  </figure>
<note position="left" xlink:label="note-0559-01" xlink:href="note-0559-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0559-02" xlink:href="note-0559-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0559-03" xlink:href="note-0559-03a" xml:space="preserve">Quantitas diei <lb/>&amp; noctis ex Ana <lb/>lemmate, quo <lb/>pacto cognoſca-<lb/>tur.</note>
<note position="left" xlink:label="note-0559-04" xlink:href="note-0559-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0559-05" xlink:href="note-0559-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s35080" xml:space="preserve">PRO horis denique inæqualibus, ſiue antiquis, diuidendæ ſunt ſingulæ portiones parallelo-<lb/>
<anchor type="note" xlink:label="note-0559-06a" xlink:href="note-0559-06"/>
rum inter communes eorum, atque Horizontis ſectiones, &amp; </s>
  <s xml:id="echoid-s35081" xml:space="preserve">Meridianum circulum poſitæ in <lb/>
<anchor type="note" xlink:label="note-0559-07a" xlink:href="note-0559-07"/>
ſenas partes æquales. </s>
  <s xml:id="echoid-s35082" xml:space="preserve">Punctum enim illud, vbi parallelus quicunque Meridianum ſecat, erit hora <lb/>6. </s>
  <s xml:id="echoid-s35083" xml:space="preserve">inæqualis, primum deinde diuiſionis punctum verſus communem ſectionem paralleli &amp; </s>
  <s xml:id="echoid-s35084" xml:space="preserve">Hori <lb/>zontis dabit horam 5. </s>
  <s xml:id="echoid-s35085" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35086" xml:space="preserve">7. </s>
  <s xml:id="echoid-s35087" xml:space="preserve">ſequens autem punctum horam 4. </s>
  <s xml:id="echoid-s35088" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35089" xml:space="preserve">8. </s>
  <s xml:id="echoid-s35090" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s35091" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35092" xml:space="preserve">Hac ratione diuiſus eſt <lb/>in Analem mate ſemicirculus ♉, &amp; </s>
  <s xml:id="echoid-s35093" xml:space="preserve">♍, qui ſemicirculum etiam ♏, &amp; </s>
  <s xml:id="echoid-s35094" xml:space="preserve">♓, refert: </s>
  <s xml:id="echoid-s35095" xml:space="preserve">Numeri autem <lb/>horarum inæqualium aſcripti ſunt punctis diametri k L, dicti paralleli, in quæ cadunt perpendi-<lb/>culares ex punctis diuiſionũ paralleli ad diametrum demiſſę. </s>
  <s xml:id="echoid-s35096" xml:space="preserve">Si enim punctis ſemicirculi K Q L, <lb/>appoſiti eſſent, confunderentur cum numeris horarum à mer. </s>
  <s xml:id="echoid-s35097" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35098" xml:space="preserve">med. </s>
  <s xml:id="echoid-s35099" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35100" xml:space="preserve">ſemicirculi M R N. <lb/></s>
  <s xml:id="echoid-s35101" xml:space="preserve">Eadem ratione alii paralleli diuidendi eruntin horas inæquales, quando res ita exiget. </s>
  <s xml:id="echoid-s35102" xml:space="preserve">Diuiſimus <lb/>porro tres ſemicirculos trium parallelorum, nempe M R N, in horas aſtronomicas, ſiue à mer. </s>
  <s xml:id="echoid-s35103" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35104" xml:space="preserve"><lb/>med. </s>
  <s xml:id="echoid-s35105" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35106" xml:space="preserve">Deinde a e b, in horas Babylonicas, Italicasq́ue, hoc eſt, ab or. </s>
  <s xml:id="echoid-s35107" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35108" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s35109" xml:space="preserve">Poſtremo K Q L, <lb/>in horas inæquales, vt in vno Analemmate diuiſiones omnium horarum continerentur. </s>
  <s xml:id="echoid-s35110" xml:space="preserve">Diuiſio-
<pb o="544" file="0560" n="560" rhead="GNOMONICES"/>
nes autem Meridiani, qui Aequatorem refert, omnibus horis accommodantur. </s>
  <s xml:id="echoid-s35111" xml:space="preserve">Nam punctum <lb/>H, erit hora 12. </s>
  <s xml:id="echoid-s35112" xml:space="preserve">inæqualis, prima autem diuiſio verſus F, exhibebit horam 1. </s>
  <s xml:id="echoid-s35113" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35114" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35115" xml:space="preserve">inæqualem, &amp; </s>
  <s xml:id="echoid-s35116" xml:space="preserve"><lb/>ſic deinceps, ita vt punctum F, det horam 6. </s>
  <s xml:id="echoid-s35117" xml:space="preserve">inæqualem. </s>
  <s xml:id="echoid-s35118" xml:space="preserve">Quo pacto autem eædem diuiſiones ho <lb/>ris æqualibus conueniant, ſiue hæ à mer. </s>
  <s xml:id="echoid-s35119" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35120" xml:space="preserve">med. </s>
  <s xml:id="echoid-s35121" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35122" xml:space="preserve">ſiue ab or. </s>
  <s xml:id="echoid-s35123" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35124" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s35125" xml:space="preserve">numerentur, paulo ante <lb/>expoſuimus.</s>
  <s xml:id="echoid-s35126" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1767" type="float" level="2" n="5">
<note position="right" xlink:label="note-0559-06" xlink:href="note-0559-06a" xml:space="preserve">Diuiſio Ana-<lb/>lemmatis in @o <lb/>ra<unsure/>. inæquale.</note>
<note position="left" xlink:label="note-0559-07" xlink:href="note-0559-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s35127" xml:space="preserve">DIVISIS vero hac ratione ſemicirculis parallelorum in horas ſiue æquales, ſiue inæquales, <lb/>
<anchor type="note" xlink:label="note-0560-01a" xlink:href="note-0560-01"/>
prout horologium horarum æqualium, puta Aſtronomicum, vel Italicum, Babylonicumve, aut <lb/>horarum inæqualium conſtruendum eſt, ducendæ ſunt à ſingulis horis cuiuſque ſemicirculi ad <lb/>propriam diametrum occultæ lineæ perpendiculares, punctaq́ue, vbi diametrum ſecant, diligen-<lb/>ter notanda: </s>
  <s xml:id="echoid-s35128" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35129" xml:space="preserve">ſi placet, ijdem numeri horarum dictis punctis apponendi, vt factum eſſe cernis <lb/>
<anchor type="note" xlink:label="note-0560-02a" xlink:href="note-0560-02"/>
in diametro <emph style="sc">K</emph> L, quæ habet numeros horarum inæqualium: </s>
  <s xml:id="echoid-s35130" xml:space="preserve">In alijs autem diametris numeros <lb/>horarum non ſcripſimus, vt confuſionem vitaremus; </s>
  <s xml:id="echoid-s35131" xml:space="preserve">eandemq́ue ob cauſam neque numeros ho <lb/>rarum inæqualium parallelo K Q L, aſcripſimus. </s>
  <s xml:id="echoid-s35132" xml:space="preserve">Ita enim paratum erit Analemma, vt ſine ma-<lb/>gno labore in ipſo per ſuperiora præcepta circunferentiæ ſupra dictæ inueniantur, vt mox dice-<lb/>mus. </s>
  <s xml:id="echoid-s35133" xml:space="preserve">Huiuſuſmodi autem perpendiculares facile ducentur, ſi integri circuli circa parallelorum <lb/>diametros deſcribantur, vt factum eſt circa diametrum a b; </s>
  <s xml:id="echoid-s35134" xml:space="preserve">poteſt tamen ſemicirculus intra Ana-<lb/>lemma cadens occulte delineari, ne confuſio inter lineas oriatur. </s>
  <s xml:id="echoid-s35135" xml:space="preserve">Nam ſi ſingulis arcubus ſemi-<lb/>circuli exterioris a e b, inter punctum a, vel b, &amp; </s>
  <s xml:id="echoid-s35136" xml:space="preserve">hora rum puncta accipiantur arcus æquales in re-<lb/>liquo ſemicirculo interiore, erunt rectæ correſpondentia puncta connectentes ad diametrum per-<lb/>
<anchor type="note" xlink:label="note-0560-03a" xlink:href="note-0560-03"/>
pendiculares. </s>
  <s xml:id="echoid-s35137" xml:space="preserve">Vt exempli gratia, ſi arcui inter a, &amp; </s>
  <s xml:id="echoid-s35138" xml:space="preserve">punctum horæ 11. </s>
  <s xml:id="echoid-s35139" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35140" xml:space="preserve">in ſemicirculo a e b, <lb/>
<anchor type="note" xlink:label="note-0560-04a" xlink:href="note-0560-04"/>
ſumatur in ſemicirculo reliq̃<unsure/>uo æqualis arcus a f, erit recta coniungens punctum horæ 11. </s>
  <s xml:id="echoid-s35141" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s35142" xml:space="preserve">cum puncto f, ad diametrum a b, perpendicularis ſecans eandem diametrum in puncto g, <lb/>quod notandum erit: </s>
  <s xml:id="echoid-s35143" xml:space="preserve">Et ſic de cæteris. </s>
  <s xml:id="echoid-s35144" xml:space="preserve">Immo ſi integri circuli deſcribantur, non opus erit pa-<lb/>rallelos ſeorſum deſcribere, vt in horas ab or. </s>
  <s xml:id="echoid-s35145" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s35146" xml:space="preserve">diſtribuantur, ſed in ipſomet Analemmate <lb/>diuiſio inſtitui poteſt, ſi d e, communis ſectio Horizontis &amp; </s>
  <s xml:id="echoid-s35147" xml:space="preserve">patalleli vſque ad punctum e, in al-<lb/>tero ſemicirculo extendatur, vt perſpicuum eſt. </s>
  <s xml:id="echoid-s35148" xml:space="preserve">Transferenda autem erunt puncta ſemicirculi <lb/>a f b, in ſemicirculum a e b, vt omnes horæ in exteriori ſemicirculo contineantur.</s>
  <s xml:id="echoid-s35149" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1768" type="float" level="2" n="6">
<note position="right" xlink:label="note-0560-01" xlink:href="note-0560-01a" xml:space="preserve">Quomodo dia-<lb/>@etri patallelo <lb/>rum in horas <lb/>ſecentur.</note>
<note position="left" xlink:label="note-0560-02" xlink:href="note-0560-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0560-03" xlink:href="note-0560-03a" xml:space="preserve">3. tertĳ.</note>
<note position="left" xlink:label="note-0560-04" xlink:href="note-0560-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s35150" xml:space="preserve">SATIS etiam eſt vt plurimum, ſi ſemicirculus ♋, &amp; </s>
  <s xml:id="echoid-s35151" xml:space="preserve">♑, in horas ſecetur, vt horologium <lb/>
<anchor type="note" xlink:label="note-0560-05a" xlink:href="note-0560-05"/>
quodcunque deſcribatur. </s>
  <s xml:id="echoid-s35152" xml:space="preserve">Quemadmodum enim in ſuperiore lib. </s>
  <s xml:id="echoid-s35153" xml:space="preserve">ex latitudinibus, longitudi-<lb/>nibusque vmbrarum, Sole exiſtente in principio ♋, &amp; </s>
  <s xml:id="echoid-s35154" xml:space="preserve">♑, horologia deſcripſimus, ita quoque hic <lb/>
<anchor type="note" xlink:label="note-0560-06a" xlink:href="note-0560-06"/>
ex circunferentiis ad quodcunque horologium requiſitis, ſi inueniantur pro horis ♋, &amp; </s>
  <s xml:id="echoid-s35155" xml:space="preserve">♑, horo-<lb/>logium quodcunque delineabimus: </s>
  <s xml:id="echoid-s35156" xml:space="preserve">excepto, quòd aliquando opus eſt inueſtigare vnam aut alte <lb/>ram circunferentiam pro nonnullis horis deſcribendis, Sole exiſtente in parallelo propinquo, vt <lb/>in parallelo ♊, &amp; </s>
  <s xml:id="echoid-s35157" xml:space="preserve">♌, aut ♐, &amp; </s>
  <s xml:id="echoid-s35158" xml:space="preserve">♒, vt in ſuperioris lib. </s>
  <s xml:id="echoid-s35159" xml:space="preserve">horologiis diximus.</s>
  <s xml:id="echoid-s35160" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1769" type="float" level="2" n="7">
<note position="left" xlink:label="note-0560-05" xlink:href="note-0560-05a" xml:space="preserve">Satis eſt ad ho-<lb/>rologia deſcti-<lb/>benda, ſi ſemi-<lb/>circulus cancri, <lb/>&amp; capri<unsure/>corni in <lb/>horas diſt@ibua <lb/>tur.</note>
<note position="left" xlink:label="note-0560-06" xlink:href="note-0560-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s35161" xml:space="preserve"><emph style="sc">H</emph>IS ita paratis, facili negotio circunferentiam quamcunque inueſtigabimus per præcepta, <lb/>
<anchor type="note" xlink:label="note-0560-07a" xlink:href="note-0560-07"/>
quæ in cap. </s>
  <s xml:id="echoid-s35162" xml:space="preserve">2. </s>
  <s xml:id="echoid-s35163" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35164" xml:space="preserve">4 eorumq́ue ſcholijs tradidimus. </s>
  <s xml:id="echoid-s35165" xml:space="preserve">Sit enim v. </s>
  <s xml:id="echoid-s35166" xml:space="preserve">g. </s>
  <s xml:id="echoid-s35167" xml:space="preserve">inuenienda circunferentia ho-<lb/>rizontalis, &amp; </s>
  <s xml:id="echoid-s35168" xml:space="preserve">deſcenſiua pro hora 23. </s>
  <s xml:id="echoid-s35169" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35170" xml:space="preserve">in parallelo ♋, &amp; </s>
  <s xml:id="echoid-s35171" xml:space="preserve">♑. </s>
  <s xml:id="echoid-s35172" xml:space="preserve">Per punctum in diametro a b, <lb/>paralleli ♋, &amp; </s>
  <s xml:id="echoid-s35173" xml:space="preserve">♑, reſpondens horæ 23. </s>
  <s xml:id="echoid-s35174" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35175" xml:space="preserve">in portione ♋, a e, ducatur ad <emph style="sc">H</emph>orizontis dtame-<lb/>trum B D, perpendicularis occulta h l, ex qua abſcindatur recta h n, æqualis interuallo inter ho-<lb/>ram 23. </s>
  <s xml:id="echoid-s35176" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35177" xml:space="preserve">punctum ei reſpondens in diametro a b. </s>
  <s xml:id="echoid-s35178" xml:space="preserve">ducaturq́ue ex centro E, per n, recta ſecans <lb/>
<anchor type="note" xlink:label="note-0560-08a" xlink:href="note-0560-08"/>
circunferentiam Meridiani in p. </s>
  <s xml:id="echoid-s35179" xml:space="preserve">Nam C p, erit circunferentia horizontalis. </s>
  <s xml:id="echoid-s35180" xml:space="preserve">Ducatur item per <lb/>idem punctum diametri a b, ad A C, diametrum Verticalis perpendiculatis q r, eritq́ue C r, cir-<lb/>cunferentia deſcenſiua. </s>
  <s xml:id="echoid-s35181" xml:space="preserve">Eadẽ ratione ex perpendicularibus occultis ſt, β α, &amp; </s>
  <s xml:id="echoid-s35182" xml:space="preserve">interuallo ſ δ<unsure/>, quod <lb/>interuallo inter horam 23. </s>
  <s xml:id="echoid-s35183" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s35184" xml:space="preserve">in portione ♑, b e, &amp; </s>
  <s xml:id="echoid-s35185" xml:space="preserve">punctum ei reſpondens in diametro <lb/>a b, æquale ſit, inuenietur circunferentia horizontalis A u, &amp; </s>
  <s xml:id="echoid-s35186" xml:space="preserve">deſcenſiua A α, pro hora 23. </s>
  <s xml:id="echoid-s35187" xml:space="preserve">tropi-<lb/>ci ♑. </s>
  <s xml:id="echoid-s35188" xml:space="preserve">Non aliter inueniemus aliarum horarum circunferentias horizontales, deſcẽſiuaſq́ue; </s>
  <s xml:id="echoid-s35189" xml:space="preserve">im-<lb/>mo &amp; </s>
  <s xml:id="echoid-s35190" xml:space="preserve">Verticales, horariaſq́ue, &amp; </s>
  <s xml:id="echoid-s35191" xml:space="preserve">meridianas, atque hectemorias, non solum in tropico ♋, &amp; </s>
  <s xml:id="echoid-s35192" xml:space="preserve">♑, <lb/>verum etiam in Aequatore, &amp; </s>
  <s xml:id="echoid-s35193" xml:space="preserve">alijs parallelis. </s>
  <s xml:id="echoid-s35194" xml:space="preserve">vt ex demonſtratis in cap. </s>
  <s xml:id="echoid-s35195" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35196" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35197" xml:space="preserve">5. </s>
  <s xml:id="echoid-s35198" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s35199" xml:space="preserve">mani-<lb/>feſtum eſt.</s>
  <s xml:id="echoid-s35200" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1770" type="float" level="2" n="8">
<note position="left" xlink:label="note-0560-07" xlink:href="note-0560-07a" xml:space="preserve">Quo pacto circũ <lb/>ferentiæ ſupra <lb/>dictę in Analem <lb/>mate hactenus <lb/>diuiſo inueſti-<lb/>gentur pro qua <lb/>hbet hora.</note>
<note position="left" xlink:label="note-0560-08" xlink:href="note-0560-08a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
</div>
<div xml:id="echoid-div1772" type="section" level="1" n="476">
<head xml:id="echoid-head505" style="it" xml:space="preserve">INVENTIO CIRCVNFERENTIAE HECTEMORIAE, <lb/>horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex <lb/>doctrina ſinuum, Sole exiſtente ſiue in Aequatore, ſiue <lb/>in alio quouis parallelo, ad quamcunque <lb/>latitudinem. CAP. VII.</head>
<p>
  <s xml:id="echoid-s35201" xml:space="preserve">INQVIRIT Ptolemæus ſupra dictas ſex circunferentias etiã per numeros, vtij, qui minus <lb/>exercitati ſunt in ducẽdis tot lineis perpendicularibus ſine errore, quæ requiruntur, vt recte in-<lb/>ueniantur dictæ circunferentiæ, facilius, &amp; </s>
  <s xml:id="echoid-s35202" xml:space="preserve">maiori cum delectatione eaſdẽ reperire poſſint per nu-<lb/>meros, cũ in his opus nõ ſit tot lineas pependiculares ducere, &amp; </s>
  <s xml:id="echoid-s35203" xml:space="preserve">parallelos in horas diuidere, in ea-<lb/>rumq́ue partes, quod non admodum facile eſt, ſed ſatis ſit cuiuslibet horæ, aut puncti, in quo
<pb o="545" file="0561" n="561" rhead="LIBER SEXTVS."/>
Sol ponitur, diſtantiam noſſe à meridie, vt ex ijs, quæ hoc cap. </s>
  <s xml:id="echoid-s35204" xml:space="preserve">demonſtrabimus, fiet perſpicuũ. <lb/></s>
  <s xml:id="echoid-s35205" xml:space="preserve">Nos enim Ptolemæi veſtigiis in ſiſtentes conabimur eaſdem circunferentias hoc cap. </s>
  <s xml:id="echoid-s35206" xml:space="preserve">per nume-<lb/>ros inueſtigare; </s>
  <s xml:id="echoid-s35207" xml:space="preserve">quod quidem multo facilius &amp; </s>
  <s xml:id="echoid-s35208" xml:space="preserve">breuius, meo iudicio, quàm Ptolemæus, effi-<lb/>ciemus, cum non tot multiplicationibus, diuiſionibusq́ue indigeamus, quot ipſe vſurpat. </s>
  <s xml:id="echoid-s35209" xml:space="preserve">Primũ <lb/>
<anchor type="figure" xlink:label="fig-0561-01a" xlink:href="fig-0561-01"/>
autem rem totam per triangu-<lb/>la tectilinea; </s>
  <s xml:id="echoid-s35210" xml:space="preserve">deinde candem <lb/>per triangula ſphærica exeque-<lb/>
<anchor type="note" xlink:label="note-0561-01a" xlink:href="note-0561-01"/>
mur: </s>
  <s xml:id="echoid-s35211" xml:space="preserve">atque hoc quidem pri-<lb/>mum, Sole extra Aequatorem <lb/>in quocunque parallelo exiſten <lb/>
<anchor type="note" xlink:label="note-0561-02a" xlink:href="note-0561-02"/>
te; </s>
  <s xml:id="echoid-s35212" xml:space="preserve">deinde vero, eodem conſtitu <lb/>to in Aequatote. </s>
  <s xml:id="echoid-s35213" xml:space="preserve">Ante omnia <lb/>igitur in omnibus ſex figuris <lb/>cap. </s>
  <s xml:id="echoid-s35214" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35215" xml:space="preserve">(quarum primam pro <lb/>parallelis auſtralibus, &amp; </s>
  <s xml:id="echoid-s35216" xml:space="preserve">ſolam <lb/>ſextam pro parallelis boreali-<lb/>bus hic in exemplum adduxi-<lb/>mus) in quibus demonſtraui-<lb/>mus, hectemoriam circunferen <lb/>tiam eſſe fg, horariam B M, de-<lb/>
<anchor type="note" xlink:label="note-0561-03a" xlink:href="note-0561-03"/>
ſcenſiuam A P, meridianam <lb/>B Y, Verticalem A T, &amp; </s>
  <s xml:id="echoid-s35217" xml:space="preserve">de-<lb/>ſcenſiuam A S, ducãtur ex pun-<lb/>ctis a, S, Y, ad B D, diametrum <lb/>Horizõtis perpendiculares a h, <lb/>S V, Y ſ, quarum a h, rectam <lb/>P t, ſecet in l: </s>
  <s xml:id="echoid-s35218" xml:space="preserve">Item ex punctis <lb/>T, b, ad A C, diametrum Ver-<lb/>ticalis perpendiculares T X, b q, quarum poſterior rectam M N, productam ſecet in p, puncto. <lb/></s>
  <s xml:id="echoid-s35219" xml:space="preserve">Poſtremo iungantur rectæ K N, K O, quæ tamen, vt confuſionem vitaremus, in ſola ſexta figura, <lb/>
<anchor type="note" xlink:label="note-0561-04a" xlink:href="note-0561-04"/>
quam hic poſuimus, ductæ ſunt à nobis: </s>
  <s xml:id="echoid-s35220" xml:space="preserve">In alijs autem animo concipiendæ ſunt duntaxat.</s>
  <s xml:id="echoid-s35221" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1772" type="float" level="2" n="1">
  <figure xlink:label="fig-0561-01" xlink:href="fig-0561-01a">
    <image file="0561-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0561-01"/>
  </figure>
<note position="right" xlink:label="note-0561-01" xlink:href="note-0561-01a" xml:space="preserve">Inhentio ſupra <lb/>dictarum circũ-<lb/>ferentiarum per <lb/>ſinus, ex trian-<lb/>gulis rectilineis, <lb/>Sole in quouis <lb/>parallelo extra <lb/>Aequator @ exi-<lb/>ftente.</note>
<note position="left" xlink:label="note-0561-02" xlink:href="note-0561-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0561-03" xlink:href="note-0561-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0561-04" xlink:href="note-0561-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s35222" xml:space="preserve">ITAQVE quoniam eſt vt a m, quatenus ſinus totus paralleli propoſiti, ad K L, quatenus ſi-<lb/>nus rectus eſt diſtantiæ Solis à meridie in eodem parallelo, ita a m, quatenus pars ſinus totius in <lb/>maximo circulo, puta in Meridiano, hoc eſt, quatenus ſinus complementi declinationis propoſiti <lb/>paralleli, ad K L, quatenus pars eſt eiuſdem ſinus totius in circulo maximo, hoc eſt, ad L f, quæ <lb/>ipſi K L, æqualis eſt, vt ex cap. </s>
  <s xml:id="echoid-s35223" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35224" xml:space="preserve">patet, eſtq́ue ſinus rectus arcus Y f, qui ex quadrante Y g, detra-<lb/>ctus relinquit hectemoriam circunferentiam fg: </s>
  <s xml:id="echoid-s35225" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum diſtantiæ Solis <lb/>
<anchor type="note" xlink:label="note-0561-05a" xlink:href="note-0561-05"/>
à meridie, ita ſinus complementi declinationis dati paralleli ad aliud, inuenietur ſinus comple-<lb/>menti hectemoriæ circunferentiæ atqueadeo complementum hoc notum erit, vnà cum ipſa <lb/>circunferentia hectemoria.</s>
  <s xml:id="echoid-s35226" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1773" type="float" level="2" n="2">
<note position="right" xlink:label="note-0561-05" xlink:href="note-0561-05a" xml:space="preserve">Hectemoria.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s35227" xml:space="preserve">DEINDE quia b n, ſinus verſus eſt arcus ſemidiurni illius loci, in quo Verticalis circulus <lb/>datæ regionis Horizon eſt, (voco datam regionem illam, pro qua circunferentiæ inueſtigantur) <lb/>hoc eſt, in quo altitudo poli ſupra Horizontem, id eſt, ſupra faciem borealem Verticalis datæ re-<lb/>gionis, complementum eſt altitudinis poli eiuſdem ſupra Horizontem datæ regionis, quemad-<lb/>modum a d, ſinus verſus eſt arcus ſemidiurni a e, in data regione. </s>
  <s xml:id="echoid-s35228" xml:space="preserve">Item b L, ſinus verſus eſt di-<lb/>ſtantiæ Solis à meridie illius loci, cum meridies ibi ſit in b, vel ſinus verſus diſtantiæ Solis à med. <lb/></s>
  <s xml:id="echoid-s35229" xml:space="preserve">noc-in data regione; </s>
  <s xml:id="echoid-s35230" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35231" xml:space="preserve">b q, ſinus rectus altitudinis meridianæ eiuſdem loci, ſeu ſinus comple-<lb/>menti depreſſionis meridianæ in data regione; </s>
  <s xml:id="echoid-s35232" xml:space="preserve">denique b p, differentia inter b q, ſinum dictæ alti <lb/>tudinis meridianæ, vel complementi depreſſionis meridianæ, &amp; </s>
  <s xml:id="echoid-s35233" xml:space="preserve">b q, ſinum arcus A M, cõplemen-<lb/>ti circunſerentiæ horariæ B M; </s>
  <s xml:id="echoid-s35234" xml:space="preserve">Eſt autem in triangulis n b q, L b p, vt n b, ad b q, ita b L, ita b L, <lb/>
<anchor type="note" xlink:label="note-0561-07a" xlink:href="note-0561-07"/>
<anchor type="note" xlink:label="note-0561-08a" xlink:href="note-0561-08"/>
ad b p: </s>
  <s xml:id="echoid-s35235" xml:space="preserve">Si ſiat, vt ſinus verſus arcus ſemidiurni illius loci, in quo altitudo poli arctici ſupra Hori-<lb/>
<anchor type="note" xlink:label="note-0561-09a" xlink:href="note-0561-09"/>
zontem complementum eſt altitudinis eiuſdem poli arctici ſupra Horizontem datæ regionis, <lb/>(qui arcus ſemidiurnus inuenietur per propoſ. </s>
  <s xml:id="echoid-s35236" xml:space="preserve">34. </s>
  <s xml:id="echoid-s35237" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35238" xml:space="preserve">1.) </s>
  <s xml:id="echoid-s35239" xml:space="preserve">ad ſinum rectum altitudinis meridia-<lb/>næ eiuſdem loci, vel complementi depreſſionis meridianæ in data regione, (quæ reperietur, vt <lb/>in ſcholio propoſ. </s>
  <s xml:id="echoid-s35240" xml:space="preserve">35. </s>
  <s xml:id="echoid-s35241" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35242" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35243" xml:space="preserve">docuimus) ita ſinus verſus diſtantiæ Solis à meridie iu eodem loco, <lb/>hoc eſt, ſinus verſus diſtantiæ Solis à med. </s>
  <s xml:id="echoid-s35244" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35245" xml:space="preserve">in data regione, (habebitur autem hic ſinus ver-<lb/>ſus b L, ſi ex tota diametro a b, ſeu ex ſinu toto duplicato, auferatur a L, ſinus verſus diſtantiæ So-<lb/>lis à meridie in data regione: </s>
  <s xml:id="echoid-s35246" xml:space="preserve">Vel certe, ſi a K, diſtantia Solis à meridie in data regione ex ſemicir-<lb/>culo a K b, dematur, remanebit b K, diſtantia Solis à meridie in illo loco, vbi Verticalis datæ re-<lb/>gionis Horizon eſt, vel diſtantia Solis à med. </s>
  <s xml:id="echoid-s35247" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35248" xml:space="preserve">in data regione; </s>
  <s xml:id="echoid-s35249" xml:space="preserve">ac propterea ſinus verſus hu-<lb/>ius diſtantiæ, laterenon poterit) ad aliud, inuenietur differentia inter ſinum altitudinis meridia-
<pb o="546" file="0562" n="562" rhead="GNOMONICES"/>
næ eiuſdem loci, vel complementi depreſſionis meridianæ in data regione, &amp; </s>
  <s xml:id="echoid-s35250" xml:space="preserve">ſinum complemen <lb/>ti circunferentiæ horariæ. </s>
  <s xml:id="echoid-s35251" xml:space="preserve">Si igitur ab hac differentia, cum Sol eſt vltta Verticalem datæ regio-<lb/>nis, (vt contingit in parallelis auſtralibus, &amp; </s>
  <s xml:id="echoid-s35252" xml:space="preserve">in ſecunda figura cap. </s>
  <s xml:id="echoid-s35253" xml:space="preserve">4.) </s>
  <s xml:id="echoid-s35254" xml:space="preserve">auferatur ſinus rectus alti-<lb/>tudinis meridianæ dicti illius loci, aut ſinus complementi depreſſionis meridianæ in data regio-<lb/>ne; </s>
  <s xml:id="echoid-s35255" xml:space="preserve">vel ſi hæc differentia, cum Sol in parallelis borealibus citra Verticalem datæ regionis exiſtit, <lb/>(vt in figura 4.</s>
  <s xml:id="echoid-s35256" xml:space="preserve">5. </s>
  <s xml:id="echoid-s35257" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35258" xml:space="preserve">6. </s>
  <s xml:id="echoid-s35259" xml:space="preserve">cap. </s>
  <s xml:id="echoid-s35260" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35261" xml:space="preserve">apparet) ex ſinu recto altitudinis meridianæ eiuſdem loci, vel ex ſinu <lb/>complementi depreſſionis meridianæ in data regione dematur, reliquus erit ſinus complementi <lb/>circunferentiæ horariæ. </s>
  <s xml:id="echoid-s35262" xml:space="preserve">Hoc ergo complementum, vnà cum ipſa horaria circunferentia, non <lb/>ignorabitur.</s>
  <s xml:id="echoid-s35263" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1774" type="float" level="2" n="3">
<note position="left" xlink:label="note-0561-07" xlink:href="note-0561-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0561-08" xlink:href="note-0561-08a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0561-09" xlink:href="note-0561-09a" xml:space="preserve">Horaria.</note>
</div>
  <figure>
    <image file="0562-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0562-01"/>
  </figure>
<p>
  <s xml:id="echoid-s35264" xml:space="preserve">EANDEM cir-<lb/>
<anchor type="note" xlink:label="note-0562-01a" xlink:href="note-0562-01"/>
<anchor type="note" xlink:label="note-0562-02a" xlink:href="note-0562-02"/>
cunferentiam horariã <lb/>inueniemus, etiamſi <lb/>Verticalem non pona-<lb/>mus eſſe Horizontem, <lb/>hoc modo. </s>
  <s xml:id="echoid-s35265" xml:space="preserve">Inueſtige-<lb/>tur per propoſ. </s>
  <s xml:id="echoid-s35266" xml:space="preserve">36. </s>
  <s xml:id="echoid-s35267" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s35268" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35269" xml:space="preserve">diſtantia Solis à me-<lb/>ridie, cum in Verticali <lb/>circulo exiſtit, (quod <lb/>quidem in parallelis <lb/>
<anchor type="note" xlink:label="note-0562-03a" xlink:href="note-0562-03"/>
auſtralibus infra Hori-<lb/>zontem contingit, ſed <lb/>in borealibus ſupra Ho <lb/>rizontem) &amp; </s>
  <s xml:id="echoid-s35270" xml:space="preserve">huius <lb/>diſtantiæ ſinus verſus <lb/>a n, ex diametro a b, <lb/>hoc eſt, ex ſinu toto du-<lb/>plicato, detrahatur, vt <lb/>nota relinquatur recta <lb/>n b. </s>
  <s xml:id="echoid-s35271" xml:space="preserve">Si enim fiat, vt <lb/>
<anchor type="note" xlink:label="note-0562-04a" xlink:href="note-0562-04"/>
hæc recta n b, inuenta <lb/>
<anchor type="note" xlink:label="note-0562-05a" xlink:href="note-0562-05"/>
ad b q, ſinum comple-<lb/>menti depreſſionis me <lb/>ridianæ (quam ex ſcho <lb/>lio propoſ. </s>
  <s xml:id="echoid-s35272" xml:space="preserve">35. </s>
  <s xml:id="echoid-s35273" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35274" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s35275" xml:space="preserve">inueniemus) ita L b, <lb/>ſinus verſus diſtantiæ Solis à media nocte ad aliud, inuenietur b p, differentia inter b q, ſinum cõ-<lb/>plementi depreſſionis meridianæ, &amp; </s>
  <s xml:id="echoid-s35276" xml:space="preserve">p q, ſinum complementi circunferentiæ horariæ, &amp;</s>
  <s xml:id="echoid-s35277" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35278" xml:space="preserve">Vel <lb/>inueniatur, per propoſ. </s>
  <s xml:id="echoid-s35279" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35280" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35281" xml:space="preserve">5. </s>
  <s xml:id="echoid-s35282" xml:space="preserve">altitudo Solis ſupra Verticalem circulum. </s>
  <s xml:id="echoid-s35283" xml:space="preserve">Nam eius complemen <lb/>tum dabit circunferentiam horariam, vt patet.</s>
  <s xml:id="echoid-s35284" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1775" type="float" level="2" n="4">
<note position="left" xlink:label="note-0562-01" xlink:href="note-0562-01a" xml:space="preserve">Alis innentio <lb/>h@rariæ, &amp; br@-<lb/>@io@.</note>
<note position="left" xlink:label="note-0562-02" xlink:href="note-0562-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0562-03" xlink:href="note-0562-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0562-04" xlink:href="note-0562-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0562-05" xlink:href="note-0562-05a" xml:space="preserve">4. ſexti.</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s35285" xml:space="preserve">RVRSVS quoniam in triangulis a h d, a l L, eſt vt a d, ſinus verſus arcus ſemidiurni a e, ad <lb/>
<anchor type="note" xlink:label="note-0562-07a" xlink:href="note-0562-07"/>
a h, ſinum rectum altitudinis meridianæ, ita a L, ſinus verſus diſtantiæ Solis à meridiead a l, dif-<lb/>ferentiam inter a h, ſinum altitudinis meridianæ, &amp; </s>
  <s xml:id="echoid-s35286" xml:space="preserve">l h, ſinum arcus B P, complementi circunfe-<lb/>rentiæ deſcenſiuæ A P: </s>
  <s xml:id="echoid-s35287" xml:space="preserve">Si fiat, vt ſinus verſus arcus ſemidiurni ad ſinum altitudinis meridianæ, <lb/>
<anchor type="note" xlink:label="note-0562-08a" xlink:href="note-0562-08"/>
ita ſinus verſus diſtantiæ Solis à meridie ad aliud, inuenietur numerus, qui ex ſinu altitudinis <lb/>meridianæ ſubductus relinquet ſinum complementi deſcenſiuæ circunferentiæ. </s>
  <s xml:id="echoid-s35288" xml:space="preserve">Hoc ergo com-<lb/>plementum, vna cum circunferentia deſcenſiua, cognitum erit. </s>
  <s xml:id="echoid-s35289" xml:space="preserve">Vel inueniatur, per vltimum mo <lb/>dum in propoſ. </s>
  <s xml:id="echoid-s35290" xml:space="preserve">36. </s>
  <s xml:id="echoid-s35291" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35292" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35293" xml:space="preserve">ante triangula ſphærica traditum, altitudo Solis ſupra Horizontem. </s>
  <s xml:id="echoid-s35294" xml:space="preserve">Eius <lb/>enim complementum deſcenſiuam circunferentiam exhibebit, vt perſpicuum eſt.</s>
  <s xml:id="echoid-s35295" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1776" type="float" level="2" n="5">
<note position="left" xlink:label="note-0562-07" xlink:href="note-0562-07a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0562-08" xlink:href="note-0562-08a" xml:space="preserve">Deſcenſiua.</note>
</div>
<p>
  <s xml:id="echoid-s35296" xml:space="preserve">PRAETEREA cum in triangulis E L N, E Y S, ſit, vt E L, ſinus circunferentiæ hectemo-<lb/>
<anchor type="note" xlink:label="note-0562-09a" xlink:href="note-0562-09"/>
<anchor type="note" xlink:label="note-0562-10a" xlink:href="note-0562-10"/>
riæ, hoceſt, ſinus complementi altitudinis Solis ſupra Meridianum, ad L N, ſinum complemen-<lb/>ti circunferentiæ deſcenſiuæ, hoc eſt, ad ſinum altitudinis Solis ſupra Horizontem, ita E Y, ſinus <lb/>totus ad Y ſ, ſinum meridianæ circunferentiæ B Y: </s>
  <s xml:id="echoid-s35297" xml:space="preserve">Si fiat vt ſinus circunferentiæ hectemoriæ <lb/>
<anchor type="note" xlink:label="note-0562-11a" xlink:href="note-0562-11"/>
inuentæ, hoc eſt, vt ſinus complementi altitudinis Solis ſupra Meridianum, ad ſinum comple-<lb/>menti circunferentiæ deſcenſiuæ, id eſt, ad ſinum altitudinis Solis ſupra Horizontem, ita ſinus <lb/>totus ad aliud, inuenietur ſinus circunferentię meridianæ; </s>
  <s xml:id="echoid-s35298" xml:space="preserve">atque adeo ipſa meridiana circunfe-<lb/>rentia nota fiet.</s>
  <s xml:id="echoid-s35299" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1777" type="float" level="2" n="6">
<note position="left" xlink:label="note-0562-09" xlink:href="note-0562-09a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0562-10" xlink:href="note-0562-10a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0562-11" xlink:href="note-0562-11a" xml:space="preserve">Meridiana.</note>
</div>
<p>
  <s xml:id="echoid-s35300" xml:space="preserve">AD hæc, quia in triangulo k L N, latera K L, L N, æqualia ſunt lateribus R O, O E, in trian-<lb/>gulo R O E, (ſumpta enim fuit in cap. </s>
  <s xml:id="echoid-s35301" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35302" xml:space="preserve">recta O R, rectæ K L. </s>
  <s xml:id="echoid-s35303" xml:space="preserve">ęqualis: </s>
  <s xml:id="echoid-s35304" xml:space="preserve">recta autem L N, rectæ <lb/>O E, æqualis eſt in parallelogrammo N O) continentq́ue angulos æquales, vtpote rectos; </s>
  <s xml:id="echoid-s35305" xml:space="preserve">(Nam, <lb/>
<anchor type="note" xlink:label="note-0562-12a" xlink:href="note-0562-12"/>
per deſin. </s>
  <s xml:id="echoid-s35306" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35307" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35308" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35309" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35310" xml:space="preserve">K L, ad planum Meridiani recta eſt, ſi ſemicirculus a K b, rectus ſtatua-
<pb o="547" file="0563" n="563" rhead="LIBER SEXTVS."/>
@ur ad idem planum Meridiani, propoterea quòd ad a b, communem ſectionem dicti ſemicirculi, <lb/>&amp; </s>
  <s xml:id="echoid-s35311" xml:space="preserve">Meridiani-perpendicularis eſt. </s>
  <s xml:id="echoid-s35312" xml:space="preserve">Igitur per deſin. </s>
  <s xml:id="echoid-s35313" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35314" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35315" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35316" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35317" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35318" xml:space="preserve">ad rectam M N, perpendicu-<lb/>laris erit.) </s>
  <s xml:id="echoid-s35319" xml:space="preserve">erunt baſes K N, R E, æquales. </s>
  <s xml:id="echoid-s35320" xml:space="preserve">Sed k N, æqualis eſt ipſi N M, ſinui circunferentiæ ho <lb/>
<anchor type="note" xlink:label="note-0563-01a" xlink:href="note-0563-01"/>
rariæ B M, propterea quòd tam N K, quàm N M, ſemidiameter eſt circuli in ſphæra ipſi vertica-<lb/>li æquidiſtantis, &amp; </s>
  <s xml:id="echoid-s35321" xml:space="preserve">per rectas M α, K L, nempe per Solem in puncto k, conſtitutum ducti, cu-<lb/>ius diameter M α; </s>
  <s xml:id="echoid-s35322" xml:space="preserve">vt conſtat, ſi ſemicirculus a Kb, ſtatuatur ad Meridianũ rectus. </s>
  <s xml:id="echoid-s35323" xml:space="preserve">Igitur erit quoq; <lb/></s>
  <s xml:id="echoid-s35324" xml:space="preserve">E R, ipſi N M, ſinui circunferentiæ horariæ æqualis. </s>
  <s xml:id="echoid-s35325" xml:space="preserve">Rurſus quia eſt, vt a m, quatenus ſinus to-<lb/>tus paralleli propoſiti, ad k L, quatenus ſinus rectus eſt diſtantię Solis à meridie in eodem paral-<lb/>lelo, ita a m, quatenus pars eſt ſinus totius in maximo circulo, vt in Meridiano, hoc eſt, quatenus <lb/>ſinus eſt complementi declinationis propoſiti paralleli, ad K L, quatenus pars eſt eiuſdem ſinus <lb/>
<anchor type="note" xlink:label="note-0563-02a" xlink:href="note-0563-02"/>
totius in circulo maximo, hoc eſt, ad R O, quæ in cap. </s>
  <s xml:id="echoid-s35326" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35327" xml:space="preserve">ipſi K L, ſumpta eſt æqualis: </s>
  <s xml:id="echoid-s35328" xml:space="preserve">Si fiat, vt ſi-<lb/>nus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complemẽti declinationis dati paralleli ad <lb/>aliud, nota euadet recta R O, in partibus ſinus totius in circulo maximo. </s>
  <s xml:id="echoid-s35329" xml:space="preserve">Quia vero eſt in triangu <lb/>lis E R O, E T X, vt E R, ſinus circunferentiæ horariæ, hoc eſt, ſinus complementi altitudinis So <lb/>
<anchor type="note" xlink:label="note-0563-03a" xlink:href="note-0563-03"/>
lis ſupra circulum Verticalem, (oſtendimus enim paulo ante, rectam E R, rectæ N M, eſſe æqua-<lb/>lem) ad R O, proxime cognitam in partibus ſinus totius in maximo circulo, ita E T, ſinus totus <lb/>ad T X, ſinum circunferentiæ Verticalis A T: </s>
  <s xml:id="echoid-s35330" xml:space="preserve">Si fiat, vt ſinus circunferentiæ horarię, hoc eſt, ſinus <lb/>
<anchor type="note" xlink:label="note-0563-04a" xlink:href="note-0563-04"/>
complementi altitudinis Solis ſupra Verticalem circulum, ad ſinum diſtantiæ Solis à meridie co <lb/>gnitũ in partibus ſinus totius in maximo circulo, (Nam R O, ipſi K L, æqualis ſumpta eſt) ita ſi-<lb/>nus totus ad aliud, reperietur ſinus circunferentiæ Verticalis; </s>
  <s xml:id="echoid-s35331" xml:space="preserve">ac proinde ipſa Verticalis circunfe-<lb/>
<anchor type="note" xlink:label="note-0563-05a" xlink:href="note-0563-05"/>
rentia nota erit;</s>
  <s xml:id="echoid-s35332" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1778" type="float" level="2" n="7">
<note position="left" xlink:label="note-0562-12" xlink:href="note-0562-12a" xml:space="preserve">14. primi</note>
<note position="right" xlink:label="note-0563-01" xlink:href="note-0563-01a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0563-02" xlink:href="note-0563-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0563-03" xlink:href="note-0563-03a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0563-04" xlink:href="note-0563-04a" xml:space="preserve">Verticalis.</note>
<note position="left" xlink:label="note-0563-05" xlink:href="note-0563-05a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s35333" xml:space="preserve">DENIQVE quoniam in triangulo k L O, latera k L, L O, æqualia ſuntlateribus Q N, NE, <lb/>trianguli Q N E, (Recta enim Q N, ipſi K L, ſumpta eſt æqualis in cap. </s>
  <s xml:id="echoid-s35334" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35335" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35336" xml:space="preserve">recta N E, ipſi L O, <lb/>æqualis eſt in parallelogrammo N O,) continentq́ue angulos æquales, vtpote rectos, (Eſt enim <lb/>
<anchor type="note" xlink:label="note-0563-06a" xlink:href="note-0563-06"/>
angulus K L O, rectus ex deſin. </s>
  <s xml:id="echoid-s35337" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35338" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35339" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35340" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35341" xml:space="preserve">propterea quòd k L, perpendicularis eſt ad planum <lb/>Meridiani, ex deſin. </s>
  <s xml:id="echoid-s35342" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35343" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35344" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35345" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35346" xml:space="preserve">ſi ſemicirculus a K b, ponatur ad Meridianum rectus) erunt <lb/>baſes K O, Q E, æquales. </s>
  <s xml:id="echoid-s35347" xml:space="preserve">Sed K O, ipſi O P, ſinui circunferentiæ deſcenſiuæ A P, æqualis eſt, <lb/>
<anchor type="note" xlink:label="note-0563-07a" xlink:href="note-0563-07"/>
quòd tam K O, quàm O P, ſemidiameter ſit circuli in ſphæra Horizonti æquidiſtantis, &amp; </s>
  <s xml:id="echoid-s35348" xml:space="preserve">per re-<lb/>ctas P t, K L, ducti, vt conſtat, ſi ſemicirculus a k b, ad Meridianum rectus ſtatuatur. </s>
  <s xml:id="echoid-s35349" xml:space="preserve">Igitur erit <lb/>quoque Q E, eidem O P, ſinui deſcenſiuæ circunferentiæ æqualis. </s>
  <s xml:id="echoid-s35350" xml:space="preserve">Rurſus quia in triangulis <lb/>
<anchor type="note" xlink:label="note-0563-08a" xlink:href="note-0563-08"/>
E Q N, E S V, eſt, vt E Q, ſinus circunferentię deſcenſiuę, hoc eſt, ſinus complementi altitudi-<lb/>
<anchor type="note" xlink:label="note-0563-09a" xlink:href="note-0563-09"/>
nis Solis ſupra Horizontem, (proxime namque oſtendimus, rectam E Q, rectæ O P, æqualem eſ-<lb/>ſe) ad Q N, ipſi K L, ſinui diſtantiæ Solis à meridie æqualem, quatenus cognita eſt in partibus ſi-<lb/>nus totius in maximo circulo, (cognoſcetur autem in hiſce partibus, vt paulo ante in Verticali <lb/>circunferentia demonſtrauimus) ita E S, ſinus totus ad S V, ſinum complementi circunferentiæ <lb/>
<anchor type="note" xlink:label="note-0563-10a" xlink:href="note-0563-10"/>
horizontalis A S: </s>
  <s xml:id="echoid-s35351" xml:space="preserve">Si fiat, vt ſinus circunferentiæ deſcenſiuæ, hoc eſt, ſinus complementi altitudi-<lb/>nis Solis ſupra Horizontem, ad ſinum diſtantiæ Solis à meridie cognitum in partibus ſinus to-<lb/>tius in circulo maximo, ita ſinus totus ad aliud, inuenietur ſinus complementi circunferentiæ <lb/>horizontalis. </s>
  <s xml:id="echoid-s35352" xml:space="preserve">Quocirca complementum hoc, vna cum circunferentia horizontali, cognita fiet.</s>
  <s xml:id="echoid-s35353" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1779" type="float" level="2" n="8">
<note position="right" xlink:label="note-0563-06" xlink:href="note-0563-06a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0563-07" xlink:href="note-0563-07a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0563-08" xlink:href="note-0563-08a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0563-09" xlink:href="note-0563-09a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0563-10" xlink:href="note-0563-10a" xml:space="preserve">Horizontalis.</note>
</div>
<p>
  <s xml:id="echoid-s35354" xml:space="preserve">CAETERVM quando Sol à meridie diſtat ſex horis, ſeu per quadrantem ſui paralleli, hoc <lb/>
<anchor type="note" xlink:label="note-0563-11a" xlink:href="note-0563-11"/>
<anchor type="note" xlink:label="note-0563-12a" xlink:href="note-0563-12"/>
eſt, cum in circulo horæ 6. </s>
  <s xml:id="echoid-s35355" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s35356" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s35357" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35358" xml:space="preserve">exiſtit, multo facilius prædictę ſex circunferentiæ <lb/>inueni@i poſſunt, hac ratione. </s>
  <s xml:id="echoid-s35359" xml:space="preserve">Quoniam tunc perpendicularis K L, cadit in m, centrum paralleli, <lb/>vt ex quinta ſigura cap. </s>
  <s xml:id="echoid-s35360" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35361" xml:space="preserve">quam hic repetiuimus, manifeſtum eſt, non differet recta E Y, ab axe <lb/>E H, cum vtraque hæc linea per m, ex E, ducatur; </s>
  <s xml:id="echoid-s35362" xml:space="preserve">ac proinde neque Eg, L f, perpendiculares ad <lb/>E Y, à ſemidiametris E G, m b, ad axem E H, perpendicularibus different. </s>
  <s xml:id="echoid-s35363" xml:space="preserve">Quare declinatio paral-<lb/>
<anchor type="note" xlink:label="note-0563-13a" xlink:href="note-0563-13"/>
leli, nempe arcus G b, erit tunc circunferentia hectemoria g f. <lb/></s>
  <s xml:id="echoid-s35364" xml:space="preserve">
<anchor type="note" xlink:label="note-0563-14a" xlink:href="note-0563-14"/>
</s>
</p>
<div xml:id="echoid-div1780" type="float" level="2" n="9">
<note position="left" xlink:label="note-0563-11" xlink:href="note-0563-11a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0563-12" xlink:href="note-0563-12a" xml:space="preserve">Quando Sol ſex <lb/>ho is abeſt à me <lb/>ridie, facilius <lb/>nominatæ cir-<lb/>cunferentiæ in-<lb/>ueniuntur.</note>
<note position="right" xlink:label="note-0563-13" xlink:href="note-0563-13a" xml:space="preserve">Hectemoria.</note>
<note position="right" xlink:label="note-0563-14" xlink:href="note-0563-14a" xml:space="preserve">4. ſexti.</note>
</div>
<p>
  <s xml:id="echoid-s35365" xml:space="preserve">DEINDE quia in triangulis E H r, E m O, eſt vt E H, ſinus totus ad H r, ſinum comple-<lb/>menti altitudinis poli, ita E m, ſinus declinationis paralleli propoſiti ad m O, ſinum arcus A M, <lb/>complementi circunferentiæ horariæ B M: </s>
  <s xml:id="echoid-s35366" xml:space="preserve">Si ſiat, vt ſinus totus ad ſinum complementi altitudi-<lb/>
<anchor type="note" xlink:label="note-0563-15a" xlink:href="note-0563-15"/>
nis poli, ita ſinus declinationis ad aliud, reperietur ſinus complementi horarię circunferentiæ; <lb/></s>
  <s xml:id="echoid-s35367" xml:space="preserve">
<anchor type="note" xlink:label="note-0563-16a" xlink:href="note-0563-16"/>
atque adeo complementum ipſum, vnà cum circunferentia horaria, notum erit.</s>
  <s xml:id="echoid-s35368" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1781" type="float" level="2" n="10">
<note position="right" xlink:label="note-0563-15" xlink:href="note-0563-15a" xml:space="preserve">Horaria.</note>
<note position="left" xlink:label="note-0563-16" xlink:href="note-0563-16a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s35369" xml:space="preserve">RVRSVS quia in triangulis E H ſ, E m N, eſt vt E H, ſinus totus ad H ſ, ſinum altitudinis <lb/>
<anchor type="note" xlink:label="note-0563-17a" xlink:href="note-0563-17"/>
poli, ita E m, ſinus declinationis paralleli propoſiti ad m N, ſinum arcus B R, complementi de-<lb/>
<anchor type="note" xlink:label="note-0563-18a" xlink:href="note-0563-18"/>
ſcenſiuæ circunferentiæ A P: </s>
  <s xml:id="echoid-s35370" xml:space="preserve">Si ſiat, vt ſinus totus ad ſinum altitudinis poli, ita ſinus declinatio-<lb/>nis ad aliud, inuenietur ſinus complementi circunferentiæ deſcenſiuæ. </s>
  <s xml:id="echoid-s35371" xml:space="preserve">Quamobrem ipſum com-<lb/>plementum, vna cum circunferentia deſcenſiua, notum euadet.</s>
  <s xml:id="echoid-s35372" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1782" type="float" level="2" n="11">
<note position="right" xlink:label="note-0563-17" xlink:href="note-0563-17a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0563-18" xlink:href="note-0563-18a" xml:space="preserve">Deſcenſiuæ.</note>
</div>
<p>
  <s xml:id="echoid-s35373" xml:space="preserve">MERIDIANA porro circunferentia eadem tunc eſt, quæ altitudo poli H B, propterea <lb/>
<anchor type="note" xlink:label="note-0563-19a" xlink:href="note-0563-19"/>
quod recta E Y, ab axe E H, non diſcrepat.</s>
  <s xml:id="echoid-s35374" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1783" type="float" level="2" n="12">
<note position="right" xlink:label="note-0563-19" xlink:href="note-0563-19a" xml:space="preserve">Meridiana.</note>
</div>
<p>
  <s xml:id="echoid-s35375" xml:space="preserve">AD hæc, cum in triangulis E R O, E T X, ſit vt E R, ſinus circunferentiæ horariæ, (oſten-<lb/>
<anchor type="note" xlink:label="note-0563-20a" xlink:href="note-0563-20"/>
ſum enim eſt ſupra in Verticali circunferentia, rectam E R, ipſi N M, ſinui horariæ circunferen-<lb/>tiæ æqualem eſſe) ad R O, quæ ipſi K L, hoc eſt, ipſi a m, ſinui complementi declinationis, ſum-
<pb o="548" file="0564" n="564" rhead="GNOMONICES"/>
pta eſt æqualis, ita E T, ſinus totus ad T X, ſinum Verticalis circunferentiæ A T: </s>
  <s xml:id="echoid-s35376" xml:space="preserve">Si fiat, vt ſinus ho <lb/>rariæ circunferentiæ, hoc eſt, vt ſinus complementi altitudinis Solis ſupra Verticalem circulum, <lb/>
<anchor type="note" xlink:label="note-0564-01a" xlink:href="note-0564-01"/>
<anchor type="figure" xlink:label="fig-0564-01a" xlink:href="fig-0564-01"/>
ad ſinum cõplementi declinatio-<lb/>nis, ita ſinus totus ad aliud, inue-<lb/>nietur ſinus circunferentiæ Ver-<lb/>ticalis; </s>
  <s xml:id="echoid-s35377" xml:space="preserve">ac propterea ipſa circũfe-<lb/>rentia Verticalis nota ſiet.</s>
  <s xml:id="echoid-s35378" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1784" type="float" level="2" n="13">
<note position="right" xlink:label="note-0563-20" xlink:href="note-0563-20a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0564-01" xlink:href="note-0564-01a" xml:space="preserve">Verticalis.</note>
  <figure xlink:label="fig-0564-01" xlink:href="fig-0564-01a">
    <image file="0564-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0564-01"/>
  </figure>
</div>
<p>
  <s xml:id="echoid-s35379" xml:space="preserve">POSTREMO, quoniam <lb/>in triangulis E Q N, E S V, eſt vt <lb/>
<anchor type="note" xlink:label="note-0564-02a" xlink:href="note-0564-02"/>
E Q, ſinus circunferentiæ de-<lb/>
<anchor type="note" xlink:label="note-0564-03a" xlink:href="note-0564-03"/>
ſcenſiuæ (Nam ſupra in horizon <lb/>tali circunferentia demonſtraui-<lb/>mus, rectam E Q, ipſi O P, ſinui <lb/>circunferentiæ deſcenſiuæ eſſe <lb/>æqualem) ad Q N, quæ ipſi k L, <lb/>hoc eſt, ipſi a m, ſinui | comple-<lb/>menti declinationis, ſumpta eſt <lb/>æqualis, ita E S, ſinus totus ad <lb/>S V, ſinum complementi circun <lb/>ferentiæ horizontalis A S; </s>
  <s xml:id="echoid-s35380" xml:space="preserve">Si <lb/>
<anchor type="note" xlink:label="note-0564-04a" xlink:href="note-0564-04"/>
fiat, vt ſinus @circunferentiæ de-<lb/>
<anchor type="note" xlink:label="note-0564-05a" xlink:href="note-0564-05"/>
ſcenſiuæ, id eſt, vt ſinus comple-<lb/>menti altitudinis Solis ſupra Ho <lb/>rizontem, ad ſinum complemen <lb/>ti declinationis, ita ſinus totus <lb/>ad aliud, inuenietur ſinus com-<lb/>plementi horizontalis circunferentiæ; </s>
  <s xml:id="echoid-s35381" xml:space="preserve">atque ob id complementum hoc, vnà cum circunferen-<lb/>tia horizontali, cognitum erit.</s>
  <s xml:id="echoid-s35382" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1785" type="float" level="2" n="14">
<note position="left" xlink:label="note-0564-02" xlink:href="note-0564-02a" xml:space="preserve">4. ſex@@.</note>
<note position="left" xlink:label="note-0564-03" xlink:href="note-0564-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0564-04" xlink:href="note-0564-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0564-05" xlink:href="note-0564-05a" xml:space="preserve">Horizontalis</note>
</div>
<p>
  <s xml:id="echoid-s35383" xml:space="preserve">EÆDEM circunferentiæ facilius adhuc reperiẽtur, Sole in Verticali circulo exiſtente. </s>
  <s xml:id="echoid-s35384" xml:space="preserve">Tunc <lb/>
<anchor type="note" xlink:label="note-0564-06a" xlink:href="note-0564-06"/>
<anchor type="figure" xlink:label="fig-0564-02a" xlink:href="fig-0564-02"/>
enim perpendicularis k L, ca-<lb/>
<anchor type="note" xlink:label="note-0564-07a" xlink:href="note-0564-07"/>
dit in punctum n, vbi paralleli <lb/>diameter diametrum Vertica-<lb/>lis interſecat, vt in tertia figura <lb/>cap 4. </s>
  <s xml:id="echoid-s35385" xml:space="preserve">quam hic repetiuimus, <lb/>apparet, &amp; </s>
  <s xml:id="echoid-s35386" xml:space="preserve">obid rectæ E Q S, <lb/>E Y, M N, à recta A E, nõ dif-<lb/>ferent: </s>
  <s xml:id="echoid-s35387" xml:space="preserve">Recta item O P, ipſi <lb/>k L, æqualis eſt, vt in cap. </s>
  <s xml:id="echoid-s35388" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s35389" xml:space="preserve">demonſtrauimus, atque adeo <lb/>recta E R T, in punctum P, ca-<lb/>
<anchor type="note" xlink:label="note-0564-08a" xlink:href="note-0564-08"/>
det: </s>
  <s xml:id="echoid-s35390" xml:space="preserve">Item L f, E g, perpendicu <lb/>lares ad E Y, à rectis O P, E B, <lb/>perpendicularibus ad A E, non <lb/>diſcrepabunt.</s>
  <s xml:id="echoid-s35391" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1786" type="float" level="2" n="15">
<note position="left" xlink:label="note-0564-06" xlink:href="note-0564-06a" xml:space="preserve">Quando Sol in <lb/>Verticali circu-<lb/>lo exiſtit, facili-<lb/>medictæ circu@ <lb/>feren@@æ re@@@ <lb/><gap/>.</note>
  <figure xlink:label="fig-0564-02" xlink:href="fig-0564-02a">
    <image file="0564-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0564-02"/>
  </figure>
<note position="left" xlink:label="note-0564-07" xlink:href="note-0564-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0564-08" xlink:href="note-0564-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s35392" xml:space="preserve">ITAQVE quoniam eſt, <lb/>vt a m, quatenus ſinus totus in <lb/>parallelo dato, ad K L, quate-<lb/>nus ſinus rectus eſt diſtantiæ <lb/>Solis à meridie in eodem pa-<lb/>rallelo, ita a m, quatenus ſinus <lb/>
<anchor type="note" xlink:label="note-0564-09a" xlink:href="note-0564-09"/>
eſt complementi declinationis <lb/>dati paralleli, nempe pars ſinus <lb/>totius in maximo circulo, puta in Meridiano, ad K L, quatenus pars eſt ſinus totius in eodem cir-<lb/>culo maximo, hoc eſt, ad O P, vel L f, ipſi K L, æqualem, quatenus ſinus eſt cõplementi circunfe-<lb/>rentiæ hectemoriæ f g, &amp; </s>
  <s xml:id="echoid-s35393" xml:space="preserve">ſinus rectus deſcenſiuæ circunferentiæ A P, &amp; </s>
  <s xml:id="echoid-s35394" xml:space="preserve">Verticalis A T: </s>
  <s xml:id="echoid-s35395" xml:space="preserve">Si fiat, vt <lb/>
<anchor type="note" xlink:label="note-0564-10a" xlink:href="note-0564-10"/>
ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis ad aliud, inue-<lb/>nietur ſinus O P, arcus A P, cuius complementum fg, dabit circunferentiam hectemoriam, ip-<lb/>ſemet vero arcus A P, erit circunferentia deſcenſiua, &amp; </s>
  <s xml:id="echoid-s35396" xml:space="preserve">Verticalis.</s>
  <s xml:id="echoid-s35397" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1787" type="float" level="2" n="16">
<note position="left" xlink:label="note-0564-09" xlink:href="note-0564-09a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0564-10" xlink:href="note-0564-10a" xml:space="preserve">Hectemoria. <lb/>Deſcenſiua, &amp; <lb/>Verticalis.</note>
</div>
<p>
  <s xml:id="echoid-s35398" xml:space="preserve">HORARIA autem circunferentia, &amp; </s>
  <s xml:id="echoid-s35399" xml:space="preserve">meridiana erit quadrans Meridiani B M, propterea <lb/>
<anchor type="note" xlink:label="note-0564-11a" xlink:href="note-0564-11"/>
quòd, vt diximus, rectæ N M, E Y, à recta A E, non differunt.</s>
  <s xml:id="echoid-s35400" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1788" type="float" level="2" n="17">
<note position="left" xlink:label="note-0564-11" xlink:href="note-0564-11a" xml:space="preserve">Horatia, &amp; Me-<lb/>ridiana.</note>
</div>
<p>
  <s xml:id="echoid-s35401" xml:space="preserve">HORIZONTALIS denique circunferentia A S, nihil tunc eſt. </s>
  <s xml:id="echoid-s35402" xml:space="preserve">Nam puncta A, &amp; </s>
  <s xml:id="echoid-s35403" xml:space="preserve">S, <lb/>
<anchor type="note" xlink:label="note-0564-12a" xlink:href="note-0564-12"/>
<pb o="549" file="0565" n="565" rhead="LIBER SEXTVS."/>
non differunt, cum Sol in Verticali circulo ponatur, atque adeo Verticalis circulus per centrum <lb/>Solis ductus idem ſit, qui Verticalis proprie dictus.</s>
  <s xml:id="echoid-s35404" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1789" type="float" level="2" n="18">
<note position="left" xlink:label="note-0564-12" xlink:href="note-0564-12a" xml:space="preserve">Horizontalis.</note>
</div>
<p>
  <s xml:id="echoid-s35405" xml:space="preserve">SED iam eaſdem ſex circunferentias inquiramus per triangula rectilinea, cum Sol in Aequa-<lb/>
<anchor type="note" xlink:label="note-0565-01a" xlink:href="note-0565-01"/>
tore exiſtit. </s>
  <s xml:id="echoid-s35406" xml:space="preserve">Repetatur ſigura cap. </s>
  <s xml:id="echoid-s35407" xml:space="preserve">2. </s>
  <s xml:id="echoid-s35408" xml:space="preserve">in qua ducantur F Y, S V, ad B D, diametrum Horizontis, &amp; </s>
  <s xml:id="echoid-s35409" xml:space="preserve"><lb/>F Z, T X, ad A C, diametrum Verticalis perpendiculares, iunganturq́ue rectæ k N, K O. </s>
  <s xml:id="echoid-s35410" xml:space="preserve">Eſt au-<lb/>tem ex demonſtratis in cap. </s>
  <s xml:id="echoid-s35411" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35412" xml:space="preserve">circunferentia hectemoria H K, horaria B M, deſcenſiua A P, me-<lb/>ridiana B F, Verticalis A T, &amp; </s>
  <s xml:id="echoid-s35413" xml:space="preserve">horizontalis A S: </s>
  <s xml:id="echoid-s35414" xml:space="preserve">quas omnes ex ſinubus inueniemus hac ratione.</s>
  <s xml:id="echoid-s35415" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1790" type="float" level="2" n="19">
<note position="right" xlink:label="note-0565-01" xlink:href="note-0565-01a" xml:space="preserve">Inuentio earun <lb/>dem ſex circun-<lb/>ferentiarum per <lb/>ſinus, ex trian-<lb/>gulis rectilineis, <lb/>dum Sol in Ae-<lb/>quatore exiſtit.</note>
</div>
<p>
  <s xml:id="echoid-s35416" xml:space="preserve">PRO hectemoria ſumatur complementum diſtantiæ Solis à meridie, tribuendo ſingulis <lb/>
<anchor type="note" xlink:label="note-0565-02a" xlink:href="note-0565-02"/>
horis grad. </s>
  <s xml:id="echoid-s35417" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35418" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s35419" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35420" xml:space="preserve">Eſt enim H K, complementum diſtantiæ Solis à meridie, nempe ipſius <lb/>arcus F K.</s>
  <s xml:id="echoid-s35421" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1791" type="float" level="2" n="20">
<note position="right" xlink:label="note-0565-02" xlink:href="note-0565-02a" xml:space="preserve">Hectemoria.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s35422" xml:space="preserve">QVONIAM vero eſt in triangulis E F Z, E L O, vt E F, ſinus totus ad F Z, ſinum altitudi-<lb/>
<anchor type="note" xlink:label="note-0565-04a" xlink:href="note-0565-04"/>
<anchor type="figure" xlink:label="fig-0565-01a" xlink:href="fig-0565-01"/>
nis poli, ita E L, ſinus complemẽ <lb/>ti diſtantiæ Solis à meridie ad <lb/>L O, ſinum arcus A M, comple-<lb/>mẽti circunferẽtiæ horariæ B M: <lb/></s>
  <s xml:id="echoid-s35423" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum al-<lb/>
<anchor type="note" xlink:label="note-0565-05a" xlink:href="note-0565-05"/>
titudinis poli, ita ſinus comple-<lb/>menti diſtantiæ Solis à meridie <lb/>ad aliud, producetur ſinus com-<lb/>plementi circunferentiæ hora-<lb/>
<anchor type="note" xlink:label="note-0565-06a" xlink:href="note-0565-06"/>
riæ. </s>
  <s xml:id="echoid-s35424" xml:space="preserve">Hoc ergo complementum, <lb/>vna cum circunferentia horaria, <lb/>non latebit.</s>
  <s xml:id="echoid-s35425" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1792" type="float" level="2" n="21">
<note position="right" xlink:label="note-0565-04" xlink:href="note-0565-04a" xml:space="preserve">4. ſexti.</note>
  <figure xlink:label="fig-0565-01" xlink:href="fig-0565-01a">
    <image file="0565-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0565-01"/>
  </figure>
<note position="right" xlink:label="note-0565-05" xlink:href="note-0565-05a" xml:space="preserve">Horatia.</note>
<note position="left" xlink:label="note-0565-06" xlink:href="note-0565-06a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s35426" xml:space="preserve">DEINDE quia in triangu-<lb/>
<anchor type="note" xlink:label="note-0565-07a" xlink:href="note-0565-07"/>
lis E F Y, E L N, eſt vt E F, ſinus <lb/>totus ad F Y, ſinum complemen <lb/>ti altitudinis poli, ita E L, ſinus <lb/>complementi diſtantiæ Solis à <lb/>meridie ad L N, ſinũ arcus B P, <lb/>complementi circunferentiæ de-<lb/>
<anchor type="note" xlink:label="note-0565-08a" xlink:href="note-0565-08"/>
ſcenſiuæ A P: </s>
  <s xml:id="echoid-s35427" xml:space="preserve">Si fiat, vt ſinus to-<lb/>
<anchor type="note" xlink:label="note-0565-09a" xlink:href="note-0565-09"/>
tus ad ſinum complementi alti-<lb/>tudinis poli, ita ſinus complement <lb/>ti diſtantiæ Solis à meridie ad <lb/>aliud, reperietur ſinus comple-<lb/>menti deſcenſiuæ circunferẽtiæ. <lb/></s>
  <s xml:id="echoid-s35428" xml:space="preserve">Quocirca complementum hoc, vna cum circunferentia deſcenſiua, notum fiet.</s>
  <s xml:id="echoid-s35429" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1793" type="float" level="2" n="22">
<note position="right" xlink:label="note-0565-07" xlink:href="note-0565-07a" xml:space="preserve">4. ſex@@.</note>
<note position="left" xlink:label="note-0565-08" xlink:href="note-0565-08a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0565-09" xlink:href="note-0565-09a" xml:space="preserve">Deſcen@@ua.</note>
</div>
<p>
  <s xml:id="echoid-s35430" xml:space="preserve">PRO circunferentia vero meridiana accipiendum eſt complementum altitudinis poli, vt ex <lb/>
<anchor type="note" xlink:label="note-0565-10a" xlink:href="note-0565-10"/>
figura perſpicuum eſt, nempearcus B F.</s>
  <s xml:id="echoid-s35431" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1794" type="float" level="2" n="23">
<note position="right" xlink:label="note-0565-10" xlink:href="note-0565-10a" xml:space="preserve">Meridiana.</note>
</div>
<p>
  <s xml:id="echoid-s35432" xml:space="preserve">RVRSVS, quia in triangulo K L N, latera K L, L N, æqualia ſunt lateribus R O, O E, trian-<lb/>
<anchor type="note" xlink:label="note-0565-11a" xlink:href="note-0565-11"/>
guli R O E, (ſumpta enim eſt in cap. </s>
  <s xml:id="echoid-s35433" xml:space="preserve">2. </s>
  <s xml:id="echoid-s35434" xml:space="preserve">recta O R, rectæ K L, æqualis: </s>
  <s xml:id="echoid-s35435" xml:space="preserve">at O E, ipſi L N, æqualis <lb/>eſt, ob parallelogrammum N O,) angulosq́ue continent æquales, puta rectos, (Nam angulus <lb/>
<anchor type="note" xlink:label="note-0565-12a" xlink:href="note-0565-12"/>
K L N, rectus eſt, ex deſin. </s>
  <s xml:id="echoid-s35436" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35437" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35438" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35439" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35440" xml:space="preserve">propterea quòd, ſi ſemicirculus F K G, rectus ſtatuatur <lb/>ad Meridianum, recta K L, perpendicularis eſt, per defin. </s>
  <s xml:id="echoid-s35441" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35442" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35443" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35444" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35445" xml:space="preserve">ad eundem Meridianũ, <lb/>cum ſit ad F G, communem ſectionem dicti ſemicirculi, &amp; </s>
  <s xml:id="echoid-s35446" xml:space="preserve">Meridiani perpendicularis) erunt ba-<lb/>ſes k N, E R, æquales. </s>
  <s xml:id="echoid-s35447" xml:space="preserve">Sed K N, æqualis eſt ipſi M N, ſinui circunferentiæ horarię B M, quòd <lb/>
<anchor type="note" xlink:label="note-0565-13a" xlink:href="note-0565-13"/>
tam K N, quàm M N, ſemidiameter ſit circuli æquidiſtantis Verticali, &amp; </s>
  <s xml:id="echoid-s35448" xml:space="preserve">per rectas K L, M N, du-<lb/>cti in ſphæra, vt patet, ſi ſemicirculus F K G, rectus ad Meridianum ponatur. </s>
  <s xml:id="echoid-s35449" xml:space="preserve">Igitur erit quoque <lb/>E R, eidem M N, ſinui circunferentiæ horariæ æqualis. </s>
  <s xml:id="echoid-s35450" xml:space="preserve">Quoniam vero in triangulis E R O, <lb/>E T X, eſt vt E R, ſinus horariæ circunferentiæ ad R O, hoc eſt, ad K L, illi æqualem, ſinum di-<lb/>
<anchor type="note" xlink:label="note-0565-14a" xlink:href="note-0565-14"/>
<anchor type="note" xlink:label="note-0565-15a" xlink:href="note-0565-15"/>
ſtantiæ Solis à meridie, ita E T, ſinus totus ad T X, ſinum circunſerentiæ Verticalis A T: </s>
  <s xml:id="echoid-s35451" xml:space="preserve">Si fiat, <lb/>vt ſinus circun ferentiæ horariæ, hoc eſt, ſinus complementi altitudinis Solis ſupra Verticalem <lb/>
<anchor type="note" xlink:label="note-0565-16a" xlink:href="note-0565-16"/>
circulum, ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad aliud, inuenietur ſinus circunfe-<lb/>rentiæ Verticalis; </s>
  <s xml:id="echoid-s35452" xml:space="preserve">ac proinde ipſa Verticalis circunferentia ignota non erit.</s>
  <s xml:id="echoid-s35453" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1795" type="float" level="2" n="24">
<note position="left" xlink:label="note-0565-11" xlink:href="note-0565-11a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0565-12" xlink:href="note-0565-12a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0565-13" xlink:href="note-0565-13a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0565-14" xlink:href="note-0565-14a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0565-15" xlink:href="note-0565-15a" xml:space="preserve">4. ſexti.</note>
<note position="right" xlink:label="note-0565-16" xlink:href="note-0565-16a" xml:space="preserve">Vertica@@@.</note>
</div>
<p>
  <s xml:id="echoid-s35454" xml:space="preserve">QVONIAM denique latera K L, L O, trianguli K L O, æqualia ſunt lateribus Q N, N E, <lb/>trianguli Q N E, (Recta namque Q N, rectæ K L, ſumpta eſt æqualis in cap. </s>
  <s xml:id="echoid-s35455" xml:space="preserve">2. </s>
  <s xml:id="echoid-s35456" xml:space="preserve">at N E, ipſi L O, <lb/>ęqualis eſt, ob parallelogrammum N O,) continentq́ueæquales angulos, nempe rectos, (Eſt enim <lb/>
<anchor type="note" xlink:label="note-0565-17a" xlink:href="note-0565-17"/>
K L O, rectus, ex deſin. </s>
  <s xml:id="echoid-s35457" xml:space="preserve">3. </s>
  <s xml:id="echoid-s35458" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35459" xml:space="preserve">11. </s>
  <s xml:id="echoid-s35460" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35461" xml:space="preserve">eò quòd K L, ad Meridianum recta eſt, ex defin. </s>
  <s xml:id="echoid-s35462" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35463" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35464" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s35465" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s35466" xml:space="preserve">vt ſupra etiam<unsure/> dictum eſt) erunt baſes K O, E Q, inter ſe æquales. </s>
  <s xml:id="echoid-s35467" xml:space="preserve">Eſt autem K O, ęqualis <lb/>
<anchor type="note" xlink:label="note-0565-18a" xlink:href="note-0565-18"/>
ipſi O P, ſinui circunferentiæ deſcenſiuæ A P, cum tam K O, quàm O P, ſemidiameter ſit circuli <lb/>æquidiſtantis Horizonti, &amp; </s>
  <s xml:id="echoid-s35468" xml:space="preserve">per rectas k L, O P, ducti in ſphæra, vt patet, ſi ſemicirculus F K G,
<pb o="550" file="0566" n="566" rhead="GNOMONICES"/>
ponatur rectus ad Meridianum. </s>
  <s xml:id="echoid-s35469" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s35470" xml:space="preserve">E Q, ipſi O P, ſinui circun ferentiæ deſcenſiuæ æqua-<lb/>lis erit. </s>
  <s xml:id="echoid-s35471" xml:space="preserve">Quia vero in triangulis E Q N, E S V, @ſt, vt E Q, ſinus circunferentiæ deſcenſiuæ, id eſt, <lb/>ſinus complementi altitudinis Solis ſupra Horizontem, ad Q N, hoc eſt, ad K L, illi æqualem, ſi-<lb/>num diſtantiæ Solis à meridie, ita E S, ſinus totus ad S V, ſinum complementi horizontalis cir-<lb/>
<anchor type="note" xlink:label="note-0566-01a" xlink:href="note-0566-01"/>
cunferentiæ A S; </s>
  <s xml:id="echoid-s35472" xml:space="preserve">Si fiat, vt ſinus circunferentiæ deſcenſiuæ, hoc eſt, vt ſinus complementi altitu-<lb/>dinis Solis ſupra Horizontem, ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad aliud, repe-<lb/>rietur ſinus complementi circunferentiæ horizontalis. </s>
  <s xml:id="echoid-s35473" xml:space="preserve">Hoc ergo complementum, vna cum cir-<lb/>cunferentia horizontali, cognitum erit.</s>
  <s xml:id="echoid-s35474" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1796" type="float" level="2" n="25">
<note position="right" xlink:label="note-0565-17" xlink:href="note-0565-17a" xml:space="preserve">34. primi</note>
<note position="right" xlink:label="note-0565-18" xlink:href="note-0565-18a" xml:space="preserve">4. primi.</note>
<note position="left" xlink:label="note-0566-01" xlink:href="note-0566-01a" xml:space="preserve">Horizontalis.</note>
</div>
<p>
  <s xml:id="echoid-s35475" xml:space="preserve">PER triangula ſphærica ita eaſdẽ ſex circunferentias inquiremus, Sole extra Aequatorẽ exiſtẽ <lb/>
<anchor type="note" xlink:label="note-0566-02a" xlink:href="note-0566-02"/>
<anchor type="figure" xlink:label="fig-0566-01a" xlink:href="fig-0566-01"/>
te in quouis parallelo. <lb/></s>
  <s xml:id="echoid-s35476" xml:space="preserve">
<anchor type="note" xlink:label="note-0566-03a" xlink:href="note-0566-03"/>
Sit Horizon A B C D; <lb/></s>
  <s xml:id="echoid-s35477" xml:space="preserve">Meridianus B E D; </s>
  <s xml:id="echoid-s35478" xml:space="preserve"><lb/>Aequator A F C; </s>
  <s xml:id="echoid-s35479" xml:space="preserve">Ver-<lb/>ticalis A E C; </s>
  <s xml:id="echoid-s35480" xml:space="preserve">Paralle-<lb/>lus Solis L M, ſiue au-<lb/>ſtralis, ſiue bore alis: </s>
  <s xml:id="echoid-s35481" xml:space="preserve"><lb/>ponaturq́ue primum <lb/>Sol in puncto G, vltra <lb/>Verticalem circulum, <lb/>vt contingit in omni-<lb/>
<anchor type="note" xlink:label="note-0566-04a" xlink:href="note-0566-04"/>
bus horis paralleli au-<lb/>ſtralis ſupra Horizon-<lb/>tem; </s>
  <s xml:id="echoid-s35482" xml:space="preserve">in illis autẽ dun-<lb/>taxat horis paralleli bo <lb/>realis, quę minorem <lb/>diſtantiam habent à <lb/>Meridiano, quàm cum Sol in Verticali exiſtit, ſi tamen parallelus Solis Verticalem interſecat; </s>
  <s xml:id="echoid-s35483" xml:space="preserve">quæ <lb/>quidem diſtantia Solis à meridie in Verticali exiſtentis inuenietur ex ijs, quæ in propoſ. </s>
  <s xml:id="echoid-s35484" xml:space="preserve">36. </s>
  <s xml:id="echoid-s35485" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35486" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s35487" xml:space="preserve">demonſtrata ſunt. </s>
  <s xml:id="echoid-s35488" xml:space="preserve">Ducatur ex E, vertice capitis per G, locum Solis Deſcenſiuus circulus E G H; </s>
  <s xml:id="echoid-s35489" xml:space="preserve"><lb/>&amp;</s>
  <s xml:id="echoid-s35490" xml:space="preserve">ex A, polo Meridiani per idem punctum G, Hectemorion A G I; </s>
  <s xml:id="echoid-s35491" xml:space="preserve">Ex polis tandem B, D, Verti-<lb/>
<anchor type="note" xlink:label="note-0566-05a" xlink:href="note-0566-05"/>
calis circuli per idem punctum G, Horarius circulus B G K D. </s>
  <s xml:id="echoid-s35492" xml:space="preserve">Erit igitur A G, circunferentia he-<lb/>ctemoria; </s>
  <s xml:id="echoid-s35493" xml:space="preserve">B G, horaria; </s>
  <s xml:id="echoid-s35494" xml:space="preserve">E G, deſcenſiua; </s>
  <s xml:id="echoid-s35495" xml:space="preserve">B I, meridiana; </s>
  <s xml:id="echoid-s35496" xml:space="preserve">E K, Verticalis; </s>
  <s xml:id="echoid-s35497" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35498" xml:space="preserve">A H, horizontalis, quas <lb/>omnes hoc pacto ſupputabimus, ducto prius ex polo mundi O, ſiue auſtrali, ſiue boreali per G, <lb/>circulo maximo O G P, qui declinationem paralleli dati metitur, &amp; </s>
  <s xml:id="echoid-s35499" xml:space="preserve">ex Aequatore abſcindit arcũ <lb/>F P, qui diſtantiam Solis à meridie metitur, cum per propoſ. </s>
  <s xml:id="echoid-s35500" xml:space="preserve">10. </s>
  <s xml:id="echoid-s35501" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35502" xml:space="preserve">2. </s>
  <s xml:id="echoid-s35503" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s35504" xml:space="preserve">ſimilis ſit arcui pa-<lb/>ralleli inter Meridianum, &amp; </s>
  <s xml:id="echoid-s35505" xml:space="preserve">punctum G, ſeu circulum O G P.</s>
  <s xml:id="echoid-s35506" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1797" type="float" level="2" n="26">
<note position="left" xlink:label="note-0566-02" xlink:href="note-0566-02a" xml:space="preserve">Inuentio earũ-<lb/>dem ſex circun-<lb/>ferentiarum per <lb/>triangula ſphæ-<lb/>rica, Sole exiſtẽ-<lb/>te in quouis pa-<lb/>rallelo extra <lb/>Aequatorem, <lb/>dummodo ſit <lb/>in parallelo bo-<lb/>reali vltra Ver-<lb/>@icalem ex par-<lb/>t<unsure/>e auſtrali.</note>
  <figure xlink:label="fig-0566-01" xlink:href="fig-0566-01a">
    <image file="0566-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0566-01"/>
  </figure>
<note position="left" xlink:label="note-0566-03" xlink:href="note-0566-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0566-04" xlink:href="note-0566-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0566-05" xlink:href="note-0566-05a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s35507" xml:space="preserve">QVONIAM in triangulo ſphærico A G P, angulus P, rectus eſt, erit, per propoſ. </s>
  <s xml:id="echoid-s35508" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35509" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35510" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s35511" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35512" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35513" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35514" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35515" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35516" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35517" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35518" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35519" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35520" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35521" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s35522" xml:space="preserve">vt ſinus complementi arcus A P, hoc eſt, vt ſinus arcus F P, diſtantiæ Solis à meridie, ad <lb/>ſinum totum, ita ſinus complementi hectemoriæ circunferentiæ A G, ad ſinum complementi ar-<lb/>
<anchor type="note" xlink:label="note-0566-06a" xlink:href="note-0566-06"/>
cus declinationis G P: </s>
  <s xml:id="echoid-s35523" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus <lb/>complementi declinationis ad ſinum complementi circunferentiæ hectemoriæ. </s>
  <s xml:id="echoid-s35524" xml:space="preserve">Quapropter ſi <lb/>fiat, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis ad <lb/>
<anchor type="note" xlink:label="note-0566-07a" xlink:href="note-0566-07"/>
aliud, inuenietur ſinus complementi hectemoriæ circunferentiæ; </s>
  <s xml:id="echoid-s35525" xml:space="preserve">ac proinde complementũ iſtud, <lb/>vna cum circunferentia hectemoria, ignotum non erit.</s>
  <s xml:id="echoid-s35526" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1798" type="float" level="2" n="27">
<note position="left" xlink:label="note-0566-06" xlink:href="note-0566-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0566-07" xlink:href="note-0566-07a" xml:space="preserve">Hectemoria.</note>
</div>
<p>
  <s xml:id="echoid-s35527" xml:space="preserve">DEINDE quia in triangulo O G I, angulus I, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35528" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35529" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35530" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35531" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35532" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s35533" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35534" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35535" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35536" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35537" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35538" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35539" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35540" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35541" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35542" xml:space="preserve">vt ſi-<lb/>nus complementi arcus O G, hoc eſt, vt ſinus arcus declinationis G P, ad ſinum complementi ar-<lb/>cus G I, hoc eſt, ad ſinum hectemoriæ circunferentiæ A G, ita ſinus complementi arcus O I, hoc <lb/>eſt, ſinus arcus F I, inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s35543" xml:space="preserve">Hectemorion, ad ſinum totum: </s>
  <s xml:id="echoid-s35544" xml:space="preserve">Et conuertendo,<unsure/> vt ſinus <lb/>
<anchor type="note" xlink:label="note-0566-08a" xlink:href="note-0566-08"/>
circunferentiæ hectemorię ad ſinum declinationis, ita ſinus totus ad arcum Meridiani inter Ae-<lb/>quatorem, &amp; </s>
  <s xml:id="echoid-s35545" xml:space="preserve">Hectemorion. </s>
  <s xml:id="echoid-s35546" xml:space="preserve">Si ergo fiat, vt ſinus circunferentię hectemoriæ ad ſinum declina-<lb/>
<anchor type="note" xlink:label="note-0566-09a" xlink:href="note-0566-09"/>
tionis, ita ſinus totus ad aliud, proueniet ſinusarcus Meridiani F I, inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s35547" xml:space="preserve">Hecte-<lb/>morion, qui in parallelis borealibus additus ad arcum B F, altitudinis Aequatoris, hoc eſt, ad com <lb/>plementum altitudinis poli, in auſtralibus vero parallelis ablatus ex eodem arcu B F, altitudinis <lb/>Aequatoris, hoc eſt, ex complemento altitudinis poli, dabit circunferentiam meridianam B I. <lb/></s>
  <s xml:id="echoid-s35548" xml:space="preserve">Itaque vt inueniatur circunferentia meridiana per triangula ſphęrica, inueſtiganda prius erit <lb/>hectemoria.</s>
  <s xml:id="echoid-s35549" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1799" type="float" level="2" n="28">
<note position="left" xlink:label="note-0566-08" xlink:href="note-0566-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0566-09" xlink:href="note-0566-09a" xml:space="preserve">Met<unsure/>idiana.</note>
</div>
<p>
  <s xml:id="echoid-s35550" xml:space="preserve">RVRSVS, cũ in triangulo E G I, angulus I, rectus ſit, erit per propoſ. </s>
  <s xml:id="echoid-s35551" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35552" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35553" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35554" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35555" xml:space="preserve">Regiom. <lb/></s>
  <s xml:id="echoid-s35556" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35557" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35558" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35559" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35560" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35561" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35562" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35563" xml:space="preserve">noſtrorũ triang. </s>
  <s xml:id="echoid-s35564" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35565" xml:space="preserve">vt ſinus cõple-<lb/>menti arcus GI, hoc eſt, vt ſinus circunferentię hectemorię A G, ad ſinũ totum, ita ſinus cõplemen
<pb o="551" file="0567" n="567" rhead="LIBER SEXTVS."/>
ti circunferentiæ deſcenſiuę E G, ad ſinum cõplementi arcus E I, hoc eſt, ad ſinum meridianæ cir-<lb/>cunferentiæ B I: </s>
  <s xml:id="echoid-s35566" xml:space="preserve">Et cõuertendo, vt ſinus totus ad ſinũ circunferentię hectemoriæ, ita ſinus circun-<lb/>ferentiæ meridianæ ad ſinum complementi circunferentiæ deſcenſiuę. </s>
  <s xml:id="echoid-s35567" xml:space="preserve">Quamobrem ſi fiat, vt <lb/>
<anchor type="note" xlink:label="note-0567-01a" xlink:href="note-0567-01"/>
ſinus totus ad ſinum circunferentię hectemorię, ita ſinus meridianę circunferentię ad aliud, pro-<lb/>ducetur ſinus complementi circunferentię deſcenſiuę; </s>
  <s xml:id="echoid-s35568" xml:space="preserve">proptereaq́ue complementum hoc, vna <lb/>cum deſcenſiua circunferentia, notum erit. </s>
  <s xml:id="echoid-s35569" xml:space="preserve">Itaque vt per triangula ſphęrica nota fiat deſcenſiua <lb/>circunferentia, inueſtigandę prius erunt hectemoria, ac meridiana. </s>
  <s xml:id="echoid-s35570" xml:space="preserve">Vnde facilius per triangula re-<lb/>ctilinea inueſtigabitur eadem circunferentia deſcenſiua per Solis altitudinem inuentam ex. </s>
  <s xml:id="echoid-s35571" xml:space="preserve">vlti-<lb/>mo modo, quem propoſ. </s>
  <s xml:id="echoid-s35572" xml:space="preserve">36. </s>
  <s xml:id="echoid-s35573" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35574" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35575" xml:space="preserve">ante triangula ſphęrica explicauimus. </s>
  <s xml:id="echoid-s35576" xml:space="preserve">Complementum enim <lb/>altitudinis Solis dabit circunferentiam deſcenſiuam.</s>
  <s xml:id="echoid-s35577" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1800" type="float" level="2" n="29">
<note position="right" xlink:label="note-0567-01" xlink:href="note-0567-01a" xml:space="preserve">Deſcenfiua.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s35578" xml:space="preserve">AD hęc, quoniam in triangulo E G O, per propoſ. </s>
  <s xml:id="echoid-s35579" xml:space="preserve">17. </s>
  <s xml:id="echoid-s35580" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35581" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35582" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35583" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35584" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35585" xml:space="preserve">vel per <lb/>propoſ. </s>
  <s xml:id="echoid-s35586" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35587" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35588" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35589" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35590" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35591" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35592" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35593" xml:space="preserve">eſt, vt ſinus circunferentię de-<lb/>ſcenſiuæ E G, ad ſinum anguli O, hoc eſt, ad ſinum diſtantię Solis à meridie, ita ſinus arcus O G, <lb/>complementi declinationis ad ſinum anguli D E H, vel B E H, cum hi duo anguli eundem ſinũ <lb/>habeant, hoc eſt, ad ſinum arcus B H, complementi horizontalis circunferentię A H: </s>
  <s xml:id="echoid-s35594" xml:space="preserve">Si fiat, vt <lb/>ſinus circunferentię deſcen ſiuę ad ſinum diſtantię Solis à meridie, ita ſinus complementi declina <lb/>
<anchor type="note" xlink:label="note-0567-03a" xlink:href="note-0567-03"/>
tionis ad aliud, reperietur ſinus complementi circunferentię horizontalis; </s>
  <s xml:id="echoid-s35595" xml:space="preserve">ac proinde cognitum <lb/>erit hoc complementum, vna cum hotizontali circunferentia. </s>
  <s xml:id="echoid-s35596" xml:space="preserve">Inueſtiganda ergo prius eſt circun-<lb/>ferentia deſcenſiua, antequam per triangula ſphærica horizontalis inquiratur.</s>
  <s xml:id="echoid-s35597" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1801" type="float" level="2" n="30">
<note position="right" xlink:label="note-0567-03" xlink:href="note-0567-03a" xml:space="preserve">Herizontalis.</note>
</div>
<p>
  <s xml:id="echoid-s35598" xml:space="preserve">PRAETEREA, quia in triangulo A G K, angulus K, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35599" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35600" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s35601" xml:space="preserve">
<anchor type="note" xlink:label="note-0567-04a" xlink:href="note-0567-04"/>
Regiom. </s>
  <s xml:id="echoid-s35602" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35603" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35604" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35605" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35606" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35607" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35608" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35609" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35610" xml:space="preserve">vt ſinus cir-<lb/>cunfercntię hectemorię A G, ad ſinum totum anguli recti K, ita ſinus arcus G K, hoc eſt, ita ſinus <lb/>complementi horarię circunferentię B G, ad ſinum anguli A, hoc eſt, ad ſinum arcus E I, com-<lb/>plementi circunfereutię meridianæ B I: </s>
  <s xml:id="echoid-s35611" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum circunferentię <lb/>hectemoriæ, ita ſinus complementi circunferentię meridianæ ad ſinum complementi circunfe-<lb/>rentię horarię. </s>
  <s xml:id="echoid-s35612" xml:space="preserve">Quocirca ſi fiat, vt ſinus totus ad ſinum circunferentię hectemorię, ita ſinus com <lb/>
<anchor type="note" xlink:label="note-0567-05a" xlink:href="note-0567-05"/>
plementi circunferentiæ meridianę ad aliud, inuenietur ſinus complementi circunferentię hora-<lb/>rię; </s>
  <s xml:id="echoid-s35613" xml:space="preserve">ac propterea notum fiet hoc complementum, vna cum circunferentia hectemoria. </s>
  <s xml:id="echoid-s35614" xml:space="preserve">Quam <lb/>etiam ita inueſtigabimus. </s>
  <s xml:id="echoid-s35615" xml:space="preserve">Quoniam in triangulo B G H, angulus H, rectus eſt, erit per propoſ. <lb/></s>
  <s xml:id="echoid-s35616" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35617" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35618" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35619" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35620" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35621" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35622" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35623" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35624" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35625" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35626" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35627" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35628" xml:space="preserve">noſtrorum <lb/>
<anchor type="note" xlink:label="note-0567-06a" xlink:href="note-0567-06"/>
triang. </s>
  <s xml:id="echoid-s35629" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35630" xml:space="preserve">vt ſinus complementi arcus B H, hoc eſt, vt ſinus circunferentię horizontalis A H, <lb/>ad ſinum totum, ita ſinus complementi circunferentiæ horarię B G, ad ſinum complementi ar-<lb/>cus G H, hoc eſt, ad ſinum deſcenſiuæ circunferentię E G: </s>
  <s xml:id="echoid-s35631" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſi-<lb/>num circunferentię horizontalis, ita ſinus circunferentię deſcenſiuæ ad ſinum complementi ho-<lb/>rarie circunferentię. </s>
  <s xml:id="echoid-s35632" xml:space="preserve">Quare ſi fiat, vt ſinus totus ad ſinum horizontalis circunferentiæ, ita ſinus <lb/>circunferentię deſcenſiuę ad aliud, reperietur ſinus complementi circunferentię horariæ; </s>
  <s xml:id="echoid-s35633" xml:space="preserve">ac pro-<lb/>pterea complementum hoc, vnà cum circunferentia horaria, notum erit. </s>
  <s xml:id="echoid-s35634" xml:space="preserve">Itaque vt ex triangulis <lb/>ſphęricis eliciatur circunferentia horaria, inueſtigandę prius erunt circunferentia hectemoria, <lb/>&amp; </s>
  <s xml:id="echoid-s35635" xml:space="preserve">meridiana, vel horizontalis, &amp; </s>
  <s xml:id="echoid-s35636" xml:space="preserve">deſcenſiua. </s>
  <s xml:id="echoid-s35637" xml:space="preserve">Vnde facilius per triangula rectilinea eandem ho-<lb/>rariam circunferentiam indagabimus, vt ſupra tradidimus, pręſertim per Solis altitudinem ſupra <lb/>
<anchor type="note" xlink:label="note-0567-07a" xlink:href="note-0567-07"/>
Verticalem circulum ex propoſ. </s>
  <s xml:id="echoid-s35638" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35639" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35640" xml:space="preserve">5. </s>
  <s xml:id="echoid-s35641" xml:space="preserve">inuentam.</s>
  <s xml:id="echoid-s35642" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1802" type="float" level="2" n="31">
<note position="left" xlink:label="note-0567-04" xlink:href="note-0567-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0567-05" xlink:href="note-0567-05a" xml:space="preserve">Horar@a.</note>
<note position="left" xlink:label="note-0567-06" xlink:href="note-0567-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0567-07" xlink:href="note-0567-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s35643" xml:space="preserve">QVIA denique in triangulo B G I, angulus I, rectus eſt, er<unsure/>it per propoſ. </s>
  <s xml:id="echoid-s35644" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35645" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35646" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35647" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35648" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s35649" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35650" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35651" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35652" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35653" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35654" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35655" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35656" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35657" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35658" xml:space="preserve">vt@ſi-<lb/>nus circunferentiæ horarię B G, ad ſinum totum anguli recti I, ita ſinus arcus G I, complementi <lb/>hectemoriæ circunferentię A G, ad ſinum anguli B, hoc eſt, ad ſinum circunferentiæ Verticalis <lb/>E K. </s>
  <s xml:id="echoid-s35659" xml:space="preserve">Quare fi fiat, vt ſinus circunferentiæ horariæ ad ſinum totum, ita ſinus complementi he-<lb/>
<anchor type="note" xlink:label="note-0567-08a" xlink:href="note-0567-08"/>
ctemoriæ circunferentię ad aliud, proueniet ſinus circunferentię Verticalis, atque adeo circunfe-<lb/>rentia ipſa Verticalis nota erit. </s>
  <s xml:id="echoid-s35660" xml:space="preserve">Quam hoc etiam artificio conſequemur. </s>
  <s xml:id="echoid-s35661" xml:space="preserve">Cum in triãgulo G E k, <lb/>angulus K, rectus ſit, erit per propoſ. </s>
  <s xml:id="echoid-s35662" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35663" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35664" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35665" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35666" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35667" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35668" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35669" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35670" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35671" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s35672" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35673" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35674" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35675" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35676" xml:space="preserve">vt ſinus complementi arcus G K, hoc eſt, vt <lb/>
<anchor type="note" xlink:label="note-0567-09a" xlink:href="note-0567-09"/>
ſinus horarię circunferentię B G, ad ſinum totum, ita ſinus complementi circunferentiæ deſcen-<lb/>ſiuæ E G, ad ſinum complementi circunferentiæ Verticalis E K. </s>
  <s xml:id="echoid-s35677" xml:space="preserve">Quapropter ſi fiat, vt ſinus ho-<lb/>rariæ circunferentię ad ſinum totum, ita ſinus complementi circunferentię deſcenſiuęad aliud, <lb/>producetur ſinus complementi circunferentię Verticalis; </s>
  <s xml:id="echoid-s35678" xml:space="preserve">ac proinde complementum hoc, vnà <lb/>cum circunferentia Verticali, notum erit. </s>
  <s xml:id="echoid-s35679" xml:space="preserve">Itaque vt per triangula ſphęrica inueniatur circunfe-<lb/>rentia Verticalis, quęrenda prius erit, pręter horariam circunferentiam, circunferentia hectemo-<lb/>ria, vel deſcenſiua.</s>
  <s xml:id="echoid-s35680" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1803" type="float" level="2" n="32">
<note position="right" xlink:label="note-0567-08" xlink:href="note-0567-08a" xml:space="preserve">Verticalis.</note>
<note position="left" xlink:label="note-0567-09" xlink:href="note-0567-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s35681" xml:space="preserve">STATVATVR rurſum Sol in parallelo boreali in ipſo puncto G, vbi Verticalem ſecat. <lb/></s>
  <s xml:id="echoid-s35682" xml:space="preserve">
<anchor type="note" xlink:label="note-0567-10a" xlink:href="note-0567-10"/>
Quo poſito, Hectemorion à Verticali non differet, cum vterque circulus per Solem, &amp; </s>
  <s xml:id="echoid-s35683" xml:space="preserve">polum Me <lb/>ridiani ducatur; </s>
  <s xml:id="echoid-s35684" xml:space="preserve">punctumq́ue k, vbi prius Horarius circulus Verticalem ſecabat, idem erit, quod <lb/>G; </s>
  <s xml:id="echoid-s35685" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35686" xml:space="preserve">punctum I, in quo Hectemorion Meridiano occurrebat, idem, quod E.</s>
  <s xml:id="echoid-s35687" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1804" type="float" level="2" n="33">
<note position="right" xlink:label="note-0567-10" xlink:href="note-0567-10a" xml:space="preserve">Inuentio earun <lb/>dem circunfe-<lb/>rentiarum, cum <lb/>Sol in Vertica-<lb/>li exiſtit.</note>
</div>
<pb o="552" file="0568" n="568" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s35688" xml:space="preserve">HECTEMORIA igitur circunferentia A G, inuenietur, vt prius, vt conſtat ex <lb/>
<anchor type="note" xlink:label="note-0568-01a" xlink:href="note-0568-01"/>
<anchor type="figure" xlink:label="fig-0568-01a" xlink:href="fig-0568-01"/>
triangulo A G P, quod idem hic eſt, quod ſu-<lb/>pra, &amp; </s>
  <s xml:id="echoid-s35689" xml:space="preserve">c.</s>
  <s xml:id="echoid-s35690" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1805" type="float" level="2" n="34">
<note position="left" xlink:label="note-0568-01" xlink:href="note-0568-01a" xml:space="preserve">Hect<unsure/>emoria.<unsure/></note>
  <figure xlink:label="fig-0568-01" xlink:href="fig-0568-01a">
    <image file="0568-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0568-01"/>
  </figure>
</div>
<p>
  <s xml:id="echoid-s35691" xml:space="preserve">MERIDIANA autem circunferentia tunc <lb/>
<anchor type="note" xlink:label="note-0568-02a" xlink:href="note-0568-02"/>
eſt quadrans circuli B I, vel D I.</s>
  <s xml:id="echoid-s35692" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1806" type="float" level="2" n="35">
<note position="left" xlink:label="note-0568-02" xlink:href="note-0568-02a" xml:space="preserve">Mendian@.</note>
</div>
<p>
  <s xml:id="echoid-s35693" xml:space="preserve">DESCENSIVA vero circunferentia eſt <lb/>
<anchor type="note" xlink:label="note-0568-03a" xlink:href="note-0568-03"/>
E G, complementum circunferentiæ hectemoriæ. <lb/></s>
  <s xml:id="echoid-s35694" xml:space="preserve">Itaque vt inueniatur circunferentia deſcenſiua, in-<lb/>uenienda eſt prius hectemoria, vt patet.</s>
  <s xml:id="echoid-s35695" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1807" type="float" level="2" n="36">
<note position="left" xlink:label="note-0568-03" xlink:href="note-0568-03a" xml:space="preserve">Deſcenſiua.</note>
</div>
<p>
  <s xml:id="echoid-s35696" xml:space="preserve">HORIZONTALIS porrò circunferen-<lb/>
<anchor type="note" xlink:label="note-0568-04a" xlink:href="note-0568-04"/>
<anchor type="note" xlink:label="note-0568-05a" xlink:href="note-0568-05"/>
tia nihil tunc eſt, cum Verticalis per Solem du-<lb/>ctus à Verticali primario non differat.</s>
  <s xml:id="echoid-s35697" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1808" type="float" level="2" n="37">
<note position="left" xlink:label="note-0568-04" xlink:href="note-0568-04a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0568-05" xlink:href="note-0568-05a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s35698" xml:space="preserve">HORARIA deinde circunferentia eſt tunc <lb/>
<anchor type="note" xlink:label="note-0568-06a" xlink:href="note-0568-06"/>
etiam quadrans circuli B G, vel D G.</s>
  <s xml:id="echoid-s35699" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1809" type="float" level="2" n="38">
<note position="left" xlink:label="note-0568-06" xlink:href="note-0568-06a" xml:space="preserve">Hotari@.</note>
</div>
<p>
  <s xml:id="echoid-s35700" xml:space="preserve">VERTICALIS denique circunferentia <lb/>
<anchor type="note" xlink:label="note-0568-07a" xlink:href="note-0568-07"/>
tunc eadem eſt, quæ deſcenſiua, ſiue complemen-<lb/>
<anchor type="note" xlink:label="note-0568-08a" xlink:href="note-0568-08"/>
tum hectemoriæ.</s>
  <s xml:id="echoid-s35701" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1810" type="float" level="2" n="39">
<note position="left" xlink:label="note-0568-07" xlink:href="note-0568-07a" xml:space="preserve">Verticalis.</note>
<note position="left" xlink:label="note-0568-08" xlink:href="note-0568-08a" xml:space="preserve">Inuentio eatun <lb/>dem circunte-<lb/>rentiatum, Sole <lb/>exiſtente citra <lb/>Verticalem, dũ-<lb/>modo minus, <lb/>aut plus abſit à <lb/>meridie, quàm <lb/>ſex horis.</note>
</div>
<p>
  <s xml:id="echoid-s35702" xml:space="preserve">SED ponatur iam Sol citra Verticalem verſus boream in puncto G, dummodo minus, aut <lb/>plus à meridie abſit, quàm ſex horis. </s>
  <s xml:id="echoid-s35703" xml:space="preserve">Quo poſito, cadet Hectemorion in quadrantem Meridia-<lb/>ni borealem D E.</s>
  <s xml:id="echoid-s35704" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s35705" xml:space="preserve">HECTEMORIA igitur circunferentia A G, inuenietur, vt prius, quando Sol ponebatur <lb/>vltra Verticalem verſus auſtrum; </s>
  <s xml:id="echoid-s35706" xml:space="preserve">vt ex triangulo A G P, manifeſtum eſt, quod idem hic eſt, <lb/>
<anchor type="note" xlink:label="note-0568-10a" xlink:href="note-0568-10"/>
quod ſupra, &amp; </s>
  <s xml:id="echoid-s35707" xml:space="preserve">c.</s>
  <s xml:id="echoid-s35708" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1811" type="float" level="2" n="40">
<note position="left" xlink:label="note-0568-10" xlink:href="note-0568-10a" xml:space="preserve">Hectemoria.</note>
</div>
  <figure>
    <image file="0568-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0568-02"/>
  </figure>
<p>
  <s xml:id="echoid-s35709" xml:space="preserve">QVONIAM ve-<lb/>ro in triangulo O G I, <lb/>angulus I, rectus eſt, <lb/>erit per propoſ. </s>
  <s xml:id="echoid-s35710" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35711" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s35712" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35713" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35714" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35715" xml:space="preserve">de <lb/>triang. </s>
  <s xml:id="echoid-s35716" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35717" xml:space="preserve"><lb/>15. </s>
  <s xml:id="echoid-s35718" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35719" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35720" xml:space="preserve">Gebri, vel per <lb/>
<anchor type="note" xlink:label="note-0568-11a" xlink:href="note-0568-11"/>
propoſ. </s>
  <s xml:id="echoid-s35721" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35722" xml:space="preserve">noſtrorum <lb/>triang. </s>
  <s xml:id="echoid-s35723" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35724" xml:space="preserve">vt ſinus <lb/>cõplementi arcus O G, <lb/>hoc eſt, vt ſinus arcus <lb/>declinationis G P, ad <lb/>ſinum complemẽti ar-<lb/>cus I G, hoc eſt, ad ſinũ <lb/>circunferentiæ hecte-<lb/>moriæ A G, ita ſinus <lb/>complementi arcus O I, ad ſinum totum: </s>
  <s xml:id="echoid-s35725" xml:space="preserve">Et conuertendo, vt ſinus circunferentiæ hectemoriæ <lb/>
<anchor type="note" xlink:label="note-0568-12a" xlink:href="note-0568-12"/>
ad ſinum declinationis, ita ſinus totus ad ſinum complementi arcus O I. </s>
  <s xml:id="echoid-s35726" xml:space="preserve">Quamobrem, ſi fiat, vt <lb/>ſinus circunferentiæ hectemoriæ ad ſinum declinationis, ita ſinus totus ad aliud, reperietur ſinus <lb/>
<anchor type="note" xlink:label="note-0568-13a" xlink:href="note-0568-13"/>
complementi arcus O I; </s>
  <s xml:id="echoid-s35727" xml:space="preserve">atqueadeo complementum hoc, vna cum arcu O I, notum erit. </s>
  <s xml:id="echoid-s35728" xml:space="preserve">Ex quo <lb/>arcu O I, qui inter polum, &amp; </s>
  <s xml:id="echoid-s35729" xml:space="preserve">Hectemorion interijcitur, ita meridianã circunferentiam D I, com-<lb/>periemus. </s>
  <s xml:id="echoid-s35730" xml:space="preserve">Quando diſtantia Solis à meridie minor eſt, quàm 6. </s>
  <s xml:id="echoid-s35731" xml:space="preserve">hor. </s>
  <s xml:id="echoid-s35732" xml:space="preserve">vt in priori figura, adden-<lb/>dus eſt arcus O I, inuentus altitudini poli O D, vt habeatur circunferentia meridiana D I. </s>
  <s xml:id="echoid-s35733" xml:space="preserve">Quia <lb/>enim diſtantia Solis à meridie minor eſt ſex horis, cadet circulus declinationis O G P, diſtantiam <lb/>Solis à meridie metiens in quadrantem Aequatoris A F, ſupra Horizontem, cum punctum A, ſex <lb/>horis abſit à meridie; </s>
  <s xml:id="echoid-s35734" xml:space="preserve">ac proinde Hectemorion ſecans dictum circulum in G, cadet in portionem <lb/>Meridiani O E, inter polum, &amp; </s>
  <s xml:id="echoid-s35735" xml:space="preserve">Verticalem. </s>
  <s xml:id="echoid-s35736" xml:space="preserve">Quando vero diſtantia Solis à meridie maior eſt, <lb/>
<anchor type="note" xlink:label="note-0568-14a" xlink:href="note-0568-14"/>
quàm 6 hor. </s>
  <s xml:id="echoid-s35737" xml:space="preserve">vt in poſteriori figura, auferendus eſt arcus O I, inuentus ex altitudine poli O D, vt <lb/>habeatur meridiana circunferentia D I. </s>
  <s xml:id="echoid-s35738" xml:space="preserve">Quia enim diſtantia Solis à meridie maior eſt ſex ho-<lb/>ris, ſecabit circulus declinationis OGP, diſtantiam Solis à meridie metiens Aequatorem infra Ho <lb/>rizontem vltra punctum A; </s>
  <s xml:id="echoid-s35739" xml:space="preserve">proptereaq́ue Hectemorion dictum circulum ſecans in G, ſupra Ho <lb/>rizontem cadet in arcum Meridiani O D, inter polum &amp; </s>
  <s xml:id="echoid-s35740" xml:space="preserve">Horizontem.</s>
  <s xml:id="echoid-s35741" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1812" type="float" level="2" n="41">
<note position="left" xlink:label="note-0568-11" xlink:href="note-0568-11a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0568-12" xlink:href="note-0568-12a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0568-13" xlink:href="note-0568-13a" xml:space="preserve">Meridiana.</note>
<note position="left" xlink:label="note-0568-14" xlink:href="note-0568-14a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s35742" xml:space="preserve">DESCENSIVA denique circunferentia E G, ex triangulo E G I; </s>
  <s xml:id="echoid-s35743" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35744" xml:space="preserve">Horizontalis A H, ex <lb/>
<anchor type="note" xlink:label="note-0568-15a" xlink:href="note-0568-15"/>
triangulo E G O; </s>
  <s xml:id="echoid-s35745" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35746" xml:space="preserve">Horaria D G, ex triangulo A G K, vel D G H; </s>
  <s xml:id="echoid-s35747" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35748" xml:space="preserve">Verticalis E K, ex triangu-<lb/>lo D G I, vel G E K, elicietur, vt ante demonſtratum eſt, quando Sol vltra Verticalem circulum <lb/>exiſtebat. </s>
  <s xml:id="echoid-s35749" xml:space="preserve">Solum in demonſtrationibus pro litera B, ad auſtrales partes aſſumenda eſt litera D, <lb/>ad partes boreales.</s>
  <s xml:id="echoid-s35750" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1813" type="float" level="2" n="42">
<note position="left" xlink:label="note-0568-15" xlink:href="note-0568-15a" xml:space="preserve">Deſcenſiua<unsure/>. <lb/>Horizontalis. <lb/>Horatia. <lb/>Verticalis.</note>
</div>
<p>
  <s xml:id="echoid-s35751" xml:space="preserve">AD extremum collocetur Sol in circulo horæ 6. </s>
  <s xml:id="echoid-s35752" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s35753" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s35754" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s35755" xml:space="preserve">in puncto G, ita vt eius
<pb o="553" file="0569" n="569" rhead="LIBER SEXTVS."/>
diſtantia à meridie complectatur 6. </s>
  <s xml:id="echoid-s35756" xml:space="preserve">horas. </s>
  <s xml:id="echoid-s35757" xml:space="preserve">Quo poſito, non differet Hectemorion A G I, ex A, per <lb/>
<anchor type="note" xlink:label="note-0569-01a" xlink:href="note-0569-01"/>
G, ductus à circulo horæ 6. </s>
  <s xml:id="echoid-s35758" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s35759" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s35760" xml:space="preserve">nocte O G A, angulos rectos ſaciente cum Meridiano <lb/>in polo mundi O, per propoſ. </s>
  <s xml:id="echoid-s35761" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35762" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35763" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35764" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s35765" xml:space="preserve">cum per eius polum A, ducatur.</s>
  <s xml:id="echoid-s35766" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1814" type="float" level="2" n="43">
<note position="right" xlink:label="note-0569-01" xlink:href="note-0569-01a" xml:space="preserve">Inuentio earun <lb/>dem circunfeiẽ <lb/>tiarum, quando <lb/>Solis diſtantia <lb/>à meridie ſex <lb/>horas complecti <lb/>tur.</note>
</div>
<p>
  <s xml:id="echoid-s35767" xml:space="preserve">HECTEMORIA ergo circunferentia A G, eadem eſt, quæ declinatio A G, paralleli pro-<lb/>poſiti L M. <lb/></s>
  <s xml:id="echoid-s35768" xml:space="preserve">
<anchor type="note" xlink:label="note-0569-02a" xlink:href="note-0569-02"/>
</s>
</p>
<div xml:id="echoid-div1815" type="float" level="2" n="44">
<note position="right" xlink:label="note-0569-02" xlink:href="note-0569-02a" xml:space="preserve">Hectemoria.</note>
</div>
<p>
  <s xml:id="echoid-s35769" xml:space="preserve">MERIDIANA autem circunferentia D I, eadem eſt, quæ altitudo poli D O.</s>
  <s xml:id="echoid-s35770" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Meridiana.</note>
<p>
  <s xml:id="echoid-s35771" xml:space="preserve">QVIA vero in triangulo E G O, angulus O, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35772" xml:space="preserve">19, lib. </s>
  <s xml:id="echoid-s35773" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35774" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35775" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s35776" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35777" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35778" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35779" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35780" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35781" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35782" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35783" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35784" xml:space="preserve">ſphæ4. </s>
  <s xml:id="echoid-s35785" xml:space="preserve">vt <lb/>
<anchor type="figure" xlink:label="fig-0569-01a" xlink:href="fig-0569-01"/>
ſinus complementi arcus E O, hoc eſt, vt ſinus altitudinis <lb/>poli O D, ad ſinum totum, ita ſinus complementi circun-<lb/>
<anchor type="note" xlink:label="note-0569-04a" xlink:href="note-0569-04"/>
ferentiæ deſcenſiuæ E G, ad ſinum cõplementi arcus O G, <lb/>hoc eſt, ad ſinum declinationis G A: </s>
  <s xml:id="echoid-s35786" xml:space="preserve">Et conuertendo, vt <lb/>ſinus totus ad ſinum altitudinis poli, ita ſinus declinationis <lb/>ad ſinum complementi circunferentiæ deſcenſiuæ. </s>
  <s xml:id="echoid-s35787" xml:space="preserve">Quare <lb/>ſi fiat, vt ſinus totus ad ſinum altitudinis poli, ita ſinus de-<lb/>
<anchor type="note" xlink:label="note-0569-05a" xlink:href="note-0569-05"/>
clinationis ad aliud, prodibit ſinus complementi circunfe-<lb/>rentiæ deſcenſiuę, atque ob id ipſum complementum, vna <lb/>cum deſcenſiua circunferentia, cognitum erit. </s>
  <s xml:id="echoid-s35788" xml:space="preserve">Quod etiam <lb/>ita perſpicuũ fiet. </s>
  <s xml:id="echoid-s35789" xml:space="preserve">Cum in triã gulo A G H, angulus H, re-<lb/>ctus ſit, erit per propoſ. </s>
  <s xml:id="echoid-s35790" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35791" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35792" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35793" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35794" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35795" xml:space="preserve">vel per pro-<lb/>
<anchor type="note" xlink:label="note-0569-06a" xlink:href="note-0569-06"/>
poſ. </s>
  <s xml:id="echoid-s35796" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35797" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35798" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35799" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35800" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35801" xml:space="preserve">noſtrorum triang. <lb/></s>
  <s xml:id="echoid-s35802" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35803" xml:space="preserve">vt ſinus arcus declinationis A G, ad ſinum totum an-<lb/>guli recti H, ita ſinus arcus G H, cõplementi deſcenſiuæ cir <lb/>cunferentię E G, ad ſinum anguli A, hoc eſt. </s>
  <s xml:id="echoid-s35804" xml:space="preserve">ad ſinum arcus <lb/>D O altitudinis poli: </s>
  <s xml:id="echoid-s35805" xml:space="preserve">Et conuertendo, vt ſinus t<unsure/>otus ad ſi-<lb/>num declinationis, ita ſinus altitudinis poli ad ſinum com-<lb/>plementi circunferentiæ deſcenſiuæ; </s>
  <s xml:id="echoid-s35806" xml:space="preserve">permutandoq́ue, vt ſinus totus ad ſinum altitudinis poli. </s>
  <s xml:id="echoid-s35807" xml:space="preserve"><lb/>ita ſinus declinationis ad ſinum complementi circunferentię deſcenſiuę, veluti prius, &amp;</s>
  <s xml:id="echoid-s35808" xml:space="preserve">c.</s>
  <s xml:id="echoid-s35809" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1816" type="float" level="2" n="45">
  <figure xlink:label="fig-0569-01" xlink:href="fig-0569-01a">
    <image file="0569-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0569-01"/>
  </figure>
<note position="left" xlink:label="note-0569-04" xlink:href="note-0569-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0569-05" xlink:href="note-0569-05a" xml:space="preserve">Deſcenf<unsure/>iua.</note>
<note position="left" xlink:label="note-0569-06" xlink:href="note-0569-06a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s35810" xml:space="preserve">DEINDE, quoniam in eodem triangulo E G O, angulus O, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35811" xml:space="preserve">16. <lb/></s>
  <s xml:id="echoid-s35812" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35813" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35814" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35815" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35816" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35817" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35818" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35819" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35820" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35821" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35822" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35823" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35824" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0569-07a" xlink:href="note-0569-07"/>
vt ſinus circunferentiæ deſcenſiuæ E G, ad ſinum totum anguli recti O, ita ſinus arcus O G, com <lb/>plementi declinationis ad ſinum anguli E, hoc eſt, ad ſinum arcus D H, complementi circun fe-<lb/>rentiæ horizontalis A H. </s>
  <s xml:id="echoid-s35825" xml:space="preserve">Quocirca ſi fiat, vt ſinus deſcenſiuæ circunferentiæ ad ſinum totum, ita <lb/>
<anchor type="note" xlink:label="note-0569-08a" xlink:href="note-0569-08"/>
ſinus complementi declinationis ad aliud, proueniet ſinus complementi circunferentiæ horizon-<lb/>talis; </s>
  <s xml:id="echoid-s35826" xml:space="preserve">atque ob id, complementum hoc, vna cum circunferentia horizontali, notum erit. </s>
  <s xml:id="echoid-s35827" xml:space="preserve">Quod <lb/>etiam hinc patere poteſt. </s>
  <s xml:id="echoid-s35828" xml:space="preserve">Quoniam in triangulo A G H, angulus H, rectus eſt, erit per propoſ. <lb/></s>
  <s xml:id="echoid-s35829" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35830" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35831" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35832" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35833" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35834" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35835" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35836" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35837" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35838" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35839" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35840" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35841" xml:space="preserve">noſtrorum <lb/>triang. </s>
  <s xml:id="echoid-s35842" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35843" xml:space="preserve">vt ſinus complementi arcus A G, declinationis ad ſinum complementi arcus G H, <lb/>hoc eſt, ad ſinum circunferentiæ deſcenſiuę E G, ita ſinus complementi hor izontalis circunferen <lb/>tiæ A H, ad ſinum totum: </s>
  <s xml:id="echoid-s35844" xml:space="preserve">Et conuertendo, vt ſinus circunferentiæ deſcenſiuæ ad ſinum comple-<lb/>
<anchor type="note" xlink:label="note-0569-09a" xlink:href="note-0569-09"/>
menti declinationis, ita ſinus to@ius ad ſinum complementi circunferentię horizontalis; </s>
  <s xml:id="echoid-s35845" xml:space="preserve">permu-<lb/>tandoq́ue, vt ſinus circunferentiæ deſcenſiuæ ad ſinum totum, ita ſinus complementi declinatio-<lb/>nis ad ſinum complementi circunferentiæ horizontalis, quemadmodum prius, &amp;</s>
  <s xml:id="echoid-s35846" xml:space="preserve">c. </s>
  <s xml:id="echoid-s35847" xml:space="preserve">Eandem au-<lb/>tem horizontalem circunferentiam ita quoque comperiemus. </s>
  <s xml:id="echoid-s35848" xml:space="preserve">Quoniam in triangulo A G E, <lb/>per propoſ. </s>
  <s xml:id="echoid-s35849" xml:space="preserve">17. </s>
  <s xml:id="echoid-s35850" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35851" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35852" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35853" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35854" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35855" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35856" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35857" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35858" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35859" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35860" xml:space="preserve">41. <lb/></s>
  <s xml:id="echoid-s35861" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35862" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35863" xml:space="preserve">eſt, vt ſinus deſcenſiuę circunferentiæ E G, ad ſinum anguli E A G, hoc <lb/>eſt, arcus O E, complementi altitudinis poli, ita ſinus arcus A G, declinationis ad ſinum anguli <lb/>A E G, hoc eſt, circunfereutiæ horizontalis A H: </s>
  <s xml:id="echoid-s35864" xml:space="preserve">Si fiat, vt ſinus circunferentiæ deſcenſiuę ad ſi-<lb/>num complementi altitudinis poli, ita ſinus declinationis ad aliud, inuenietur ſinus circunferentię <lb/>horizontalis, ac propterea circunferentia ipſa cognoſcetur, vt prius. </s>
  <s xml:id="echoid-s35865" xml:space="preserve">Sed prior modus expeditior <lb/>
<anchor type="note" xlink:label="note-0569-10a" xlink:href="note-0569-10"/>
eſt, cum ſinum totum vſurpet, vt patet.</s>
  <s xml:id="echoid-s35866" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1817" type="float" level="2" n="46">
<note position="left" xlink:label="note-0569-07" xlink:href="note-0569-07a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0569-08" xlink:href="note-0569-08a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0569-09" xlink:href="note-0569-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0569-10" xlink:href="note-0569-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s35867" xml:space="preserve">PRAETEREA quia in triangulo D G O, angulus O, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35868" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35869" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35870" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35871" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s35872" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35873" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35874" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35875" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35876" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35877" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35878" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35879" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35880" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35881" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35882" xml:space="preserve">vt <lb/>ſinus complementi arcus D O, altitudinis poli ad ſinum totum, ita ſinus complementi circunfe-<lb/>rentiæ horariæ D G, ad ſinum complementi arcus O G, hoc eſt, ad ſinum arcus declinationis <lb/>A G: </s>
  <s xml:id="echoid-s35883" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum complementi altitudinis poli, ita ſinus declinatio-<lb/>nis ad ſinum complementi circunferentię horariæ. </s>
  <s xml:id="echoid-s35884" xml:space="preserve">Quamobrem ſi fiat, vt ſinus totus ad ſinum <lb/>
<anchor type="note" xlink:label="note-0569-11a" xlink:href="note-0569-11"/>
complementi altitudinis poli, ita ſinus declinationis ad aliud, procreabitur ſinus complemẽti cir-<lb/>cunferentiæ horariæ, ac proinde complementum hoc notum erit, vna cum circunferentia hora-<lb/>ria. </s>
  <s xml:id="echoid-s35885" xml:space="preserve">Quod etiam ita manifeſtum erit. </s>
  <s xml:id="echoid-s35886" xml:space="preserve">Quoniam in triangulo A G K, angulus K, rectus eſt, erit <lb/>per propoſ. </s>
  <s xml:id="echoid-s35887" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35888" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35889" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35890" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35891" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35892" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35893" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35894" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35895" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35896" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35897" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35898" xml:space="preserve">41.</s>
  <s xml:id="echoid-s35899" xml:space="preserve">
<pb o="554" file="0570" n="570" rhead="GNOMONICES"/>
noſtrorum triang. </s>
  <s xml:id="echoid-s35900" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35901" xml:space="preserve">vt ſinus arcus declinationis A G, ad ſinum totum anguli recti k, ita ſi-<lb/>nus arcus G k, complementi horariæ circunferentiæ D G, ad ſinum anguli A, ſiue arcus O E, com <lb/>plementi altitudinis poli: </s>
  <s xml:id="echoid-s35902" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum declinationis, ita ſinus comple <lb/>menti altitudinis poli ad ſinum complementi circunferentiæ horarię; </s>
  <s xml:id="echoid-s35903" xml:space="preserve">permutandoq́ue, vt ſinus <lb/>totus ad ſinum complementi altitudinis poli, ita ſinus declinationis ad ſinum complementi ho-<lb/>rariæ circunferentiæ, veluti prius, &amp;</s>
  <s xml:id="echoid-s35904" xml:space="preserve">c.</s>
  <s xml:id="echoid-s35905" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1818" type="float" level="2" n="47">
<note position="right" xlink:label="note-0569-11" xlink:href="note-0569-11a" xml:space="preserve">Horaria<unsure/>.</note>
</div>
<p>
  <s xml:id="echoid-s35906" xml:space="preserve">DENIQVE, quia in triangulo D G O, angulus O, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35907" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35908" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35909" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s35910" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35911" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35912" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s35913" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35914" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35915" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35916" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35917" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35918" xml:space="preserve">41. </s>
  <s xml:id="echoid-s35919" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35920" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s35921" xml:space="preserve">vt ſinus circunferentię horariæ D G, ad ſinum totum anguli recti O, ita ſinus arcus O G, <lb/>complementi declinationis ad ſinum anguli G D O, hoc eſt, circunferentiæ Verticalis E K. </s>
  <s xml:id="echoid-s35922" xml:space="preserve">Igi-<lb/>
<anchor type="note" xlink:label="note-0570-01a" xlink:href="note-0570-01"/>
tur ſi fiat, vt ſinus circunferentię horarię ad ſinum totum, ita ſinus complementi declinationis <lb/>
<anchor type="note" xlink:label="note-0570-02a" xlink:href="note-0570-02"/>
ad aliud, reperietur ſinus circunferentię Verticalis; </s>
  <s xml:id="echoid-s35923" xml:space="preserve">atque adeo circunferentia ipſa latere non po-<lb/>terit. </s>
  <s xml:id="echoid-s35924" xml:space="preserve">Quod etiam ita faciemus perſpicuum. </s>
  <s xml:id="echoid-s35925" xml:space="preserve">Quoniam in triangulo A G K, angulus K, rectus eſt, <lb/>erit per propoſ. </s>
  <s xml:id="echoid-s35926" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35927" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35928" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35929" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35930" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35931" xml:space="preserve">detriang. </s>
  <s xml:id="echoid-s35932" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35933" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35934" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35935" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35936" xml:space="preserve">Gebri, vel per propoſ. <lb/></s>
  <s xml:id="echoid-s35937" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35938" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35939" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35940" xml:space="preserve">vt ſinus complementi arcus declinationis A G, ad ſinum comple-<lb/>menti arcus G K, hoc eſt, ad ſinum circunferentię horarię D G, ita ſinus complementi arcus A K, <lb/>id eſt, ſinus circunferentiæ Verticalis E K, ad ſinum totum, Et conuertendo, vt ſinus horariæ cir-<lb/>cunferentiæ ad ſinum complementi declinationis, ita ſinus totus ad ſinum Verticalis circunferen <lb/>tiæ; </s>
  <s xml:id="echoid-s35941" xml:space="preserve">permutandoq́ue vt ſinus circunferentiæ horariæ ad ſinum totum, ita ſinus complementi de-<lb/>clinationis ad ſinum circunferentiæ Verticalis, ſicut prius, &amp;</s>
  <s xml:id="echoid-s35942" xml:space="preserve">c.</s>
  <s xml:id="echoid-s35943" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1819" type="float" level="2" n="48">
<note position="left" xlink:label="note-0570-01" xlink:href="note-0570-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0570-02" xlink:href="note-0570-02a" xml:space="preserve">Verticalis.</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s35944" xml:space="preserve">IAM vero eaſdem ſex circunferentias per triangula ſphęrica inueſtigemus, cum Sol Aequato-<lb/>
<anchor type="note" xlink:label="note-0570-04a" xlink:href="note-0570-04"/>
rem percurrit, exiſtitq́ue in puncto G: </s>
  <s xml:id="echoid-s35945" xml:space="preserve">Quo poſito, Hectemorion A G I, ex A, per G, ductus ab <lb/>Aequatore A F C, non differet; </s>
  <s xml:id="echoid-s35946" xml:space="preserve">eritq́ue A G, circunferentia hectemoria; </s>
  <s xml:id="echoid-s35947" xml:space="preserve">B I, meridiana; </s>
  <s xml:id="echoid-s35948" xml:space="preserve">E G, de-<lb/>ſcenſiua; </s>
  <s xml:id="echoid-s35949" xml:space="preserve">A H, horizontalis; </s>
  <s xml:id="echoid-s35950" xml:space="preserve">B G, horaria; </s>
  <s xml:id="echoid-s35951" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s35952" xml:space="preserve">E k, Verticalis. </s>
  <s xml:id="echoid-s35953" xml:space="preserve">Quas omnes inueniemus, etiamſi <lb/>ex polo mundi O, per G, maximum circulum non ducamus.</s>
  <s xml:id="echoid-s35954" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1820" type="float" level="2" n="49">
<note position="left" xlink:label="note-0570-04" xlink:href="note-0570-04a" xml:space="preserve">Inuen<unsure/>tio earun <lb/>dem ſex circun-<lb/>fex<unsure/>entiarum ex <lb/>triangulis ſphæ <lb/>ricis. cum Sol <lb/>Aequatorẽ poſ-<lb/>ſidet.</note>
</div>
<p>
  <s xml:id="echoid-s35955" xml:space="preserve">NAM hectemoria circunferentia A G, à complemento diſtantię Solis à meridie A G, <lb/>
<anchor type="note" xlink:label="note-0570-05a" xlink:href="note-0570-05"/>
non differt.</s>
  <s xml:id="echoid-s35956" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1821" type="float" level="2" n="50">
<note position="left" xlink:label="note-0570-05" xlink:href="note-0570-05a" xml:space="preserve">Hectemoria.</note>
</div>
<p>
  <s xml:id="echoid-s35957" xml:space="preserve">MERIDIANA quoque circunferentia B I, eadem eſt, quæ circunferentia B F, altitudinis <lb/>
<anchor type="note" xlink:label="note-0570-06a" xlink:href="note-0570-06"/>
Aequa toris, ſiue complementi altitudinis poli.</s>
  <s xml:id="echoid-s35958" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1822" type="float" level="2" n="51">
<note position="left" xlink:label="note-0570-06" xlink:href="note-0570-06a" xml:space="preserve">Meridiana.</note>
</div>
  <figure>
    <image file="0570-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0570-01"/>
  </figure>
<p>
  <s xml:id="echoid-s35959" xml:space="preserve">QVONIAM vero in triangulo E G F, angulus F, re-<lb/>
<anchor type="note" xlink:label="note-0570-07a" xlink:href="note-0570-07"/>
ctus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s35960" xml:space="preserve">19. </s>
  <s xml:id="echoid-s35961" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35962" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35963" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35964" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35965" xml:space="preserve">de triang. <lb/></s>
  <s xml:id="echoid-s35966" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35967" xml:space="preserve">15. </s>
  <s xml:id="echoid-s35968" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35969" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35970" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35971" xml:space="preserve">43. </s>
  <s xml:id="echoid-s35972" xml:space="preserve">noſtrorũ <lb/>triang. </s>
  <s xml:id="echoid-s35973" xml:space="preserve">ſphęr. </s>
  <s xml:id="echoid-s35974" xml:space="preserve">vt ſinus complementi diſtantiæ Solis à meri-<lb/>die F G, ad ſinum totum, ita ſinus complementi circunfe-<lb/>rentiæ deſcenſiuę E G, ad ſinum complementi arcus E F, al-<lb/>titudinis poli; </s>
  <s xml:id="echoid-s35975" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum com <lb/>plementi diſtantię Solis à meridie, ita ſinus complementi al <lb/>titudinis poli ad ſinum complementi circunferentię deſcen <lb/>
<anchor type="note" xlink:label="note-0570-08a" xlink:href="note-0570-08"/>
ſiuę. </s>
  <s xml:id="echoid-s35976" xml:space="preserve">Si ergo fiat, vt ſinus totus ad ſinum complementi di-<lb/>ſtantiæ Solis à meridie, ita ſinus complementi altitudinis po <lb/>
<anchor type="note" xlink:label="note-0570-09a" xlink:href="note-0570-09"/>
li ad aliud, producetur ſinus complementi circunferentiæ <lb/>deſcenſiuæ; </s>
  <s xml:id="echoid-s35977" xml:space="preserve">proptereaq́ue complementum hoc, vna cum cir <lb/>cunferentia deſcenſiua, ex tabula ſinuum inuenietur.</s>
  <s xml:id="echoid-s35978" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1823" type="float" level="2" n="52">
<note position="left" xlink:label="note-0570-07" xlink:href="note-0570-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0570-08" xlink:href="note-0570-08a" xml:space="preserve">Deſcenfius<unsure/>.</note>
<note position="left" xlink:label="note-0570-09" xlink:href="note-0570-09a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s35979" xml:space="preserve">DEINDE in eodem triangulo E G F, cum angulus F, <lb/>rectus ſit, quoniam per propoſ. </s>
  <s xml:id="echoid-s35980" xml:space="preserve">16. </s>
  <s xml:id="echoid-s35981" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35982" xml:space="preserve">4. </s>
  <s xml:id="echoid-s35983" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s35984" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s35985" xml:space="preserve">de <lb/>triang. </s>
  <s xml:id="echoid-s35986" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s35987" xml:space="preserve">13. </s>
  <s xml:id="echoid-s35988" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s35989" xml:space="preserve">1. </s>
  <s xml:id="echoid-s35990" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s35991" xml:space="preserve">41. <lb/></s>
  <s xml:id="echoid-s35992" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s35993" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s35994" xml:space="preserve">eſt, vt ſinus circunferentię deſcenſiuæ E G, ad ſinum totum anguli re-<lb/>cti F, ita ſinus arcus F G, diſtantiæ Solis à meridie ad ſinum anguli E, hoc eſt, arcus B H, comple-<lb/>
<anchor type="note" xlink:label="note-0570-10a" xlink:href="note-0570-10"/>
menti circunferentiæ horizontalis A H: </s>
  <s xml:id="echoid-s35995" xml:space="preserve">Si fiat, vt ſinus circunferentię deſcenſiuæ ad ſinum totũ, <lb/>ita ſinus diſtantiæ Solis à meridie ad aliud, inuenietur ſinus complementi circunferentiæ hori-<lb/>
<anchor type="note" xlink:label="note-0570-11a" xlink:href="note-0570-11"/>
zontalis; </s>
  <s xml:id="echoid-s35996" xml:space="preserve">ac propterea complementum hoc, vna cum horizontali circunferentia, notum fiet. </s>
  <s xml:id="echoid-s35997" xml:space="preserve">Quod <lb/>etiam hac ratione perſpicuum erit. </s>
  <s xml:id="echoid-s35998" xml:space="preserve">Cum in triangulo A G H, angulus H, rectus ſit, erit per pro-<lb/>poſ. </s>
  <s xml:id="echoid-s35999" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36000" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36001" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36002" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36003" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36004" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36005" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36006" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36007" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36008" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36009" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36010" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36011" xml:space="preserve">noſtro-<lb/>rum triang. </s>
  <s xml:id="echoid-s36012" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36013" xml:space="preserve">vt ſinus complementi arcus G H, hoc eſt, vt ſinus circunferentiæ deſcenſiuæ, ad <lb/>ſinum totum, ita ſinus complementi arcus A G, hoc eſt, ſinus arcus F G, diſtantiæ Solis à meridie, <lb/>ad ſinum complementi circunferentiæ horizontalis A H, veluti prius, &amp;</s>
  <s xml:id="echoid-s36014" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36015" xml:space="preserve">Ita tamen etiam ean-<lb/>dem circunferentiam horizontalem conſequemur. </s>
  <s xml:id="echoid-s36016" xml:space="preserve">Quoniam in triangulo A G E, per propoſ. <lb/></s>
  <s xml:id="echoid-s36017" xml:space="preserve">17. </s>
  <s xml:id="echoid-s36018" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36019" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36020" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36021" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36022" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36023" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36024" xml:space="preserve">13. </s>
  <s xml:id="echoid-s36025" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36026" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36027" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36028" xml:space="preserve">41. </s>
  <s xml:id="echoid-s36029" xml:space="preserve">noſtrorum <lb/>triang. </s>
  <s xml:id="echoid-s36030" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36031" xml:space="preserve">eſt, vt ſinus circunferentiæ deſcenſiuæ E G, ad ſinum anguli A, ſeu arcus E F, alti-<lb/>tudinis poli, ita ſinus arcus A G, complementi diſtantiæ Solis à meridie ad ſinum anguli E, ſeu cir-<lb/>cunferentiæ horizontalis A H: </s>
  <s xml:id="echoid-s36032" xml:space="preserve">Si fiat, vt ſinus circunferentiæ deſcenſiuæ ad ſinum altitudinis po-
<pb o="555" file="0571" n="571" rhead="LIBER SEXTVS."/>
li, ita ſinus complementi diſtantiæ Solis à meridie ad aliud, inuenietur ſinus circunferentiæ hori-<lb/>zontalis; </s>
  <s xml:id="echoid-s36033" xml:space="preserve">atque adeo circunferentia horizontalis ignota non erit. </s>
  <s xml:id="echoid-s36034" xml:space="preserve">Sed prior modus videtur eſſe <lb/>commodior, cum vtatur ſinu toto, vt patet.</s>
  <s xml:id="echoid-s36035" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1824" type="float" level="2" n="53">
<note position="left" xlink:label="note-0570-10" xlink:href="note-0570-10a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0570-11" xlink:href="note-0570-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36036" xml:space="preserve">RVRSVS, quia in triangulo B F G, angulus F, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s36037" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36038" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36039" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36040" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36041" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s36042" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36043" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36044" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36045" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36046" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36047" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36048" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36049" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36050" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36051" xml:space="preserve">vt <lb/>ſinus complementi arcus F G, diſtantiæ Solis à meridie ad ſinum totum, ita ſinus complementi <lb/>circunferentiæ horariæ B G, ad ſinum complementi arcus B F, hoc eſt, ad ſinum arcus E F, altitu <lb/>dinis poli: </s>
  <s xml:id="echoid-s36052" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſi-<lb/>nus altitudinis poli ad ſinum complementi circunferentiæ horariæ. </s>
  <s xml:id="echoid-s36053" xml:space="preserve">Quare ſi fiat, vt ſinus totus ad <lb/>ſinum complementi diſtantiæ Solis à meridie, ita ſinus altitudinis poli ad aliud, reperietur ſinus <lb/>
<anchor type="note" xlink:label="note-0571-01a" xlink:href="note-0571-01"/>
<anchor type="note" xlink:label="note-0571-02a" xlink:href="note-0571-02"/>
complementi circunferentię horariæ; </s>
  <s xml:id="echoid-s36054" xml:space="preserve">ac proinde hoc complementum, vna cum horaria circun-<lb/>ferentia, notum erit.</s>
  <s xml:id="echoid-s36055" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1825" type="float" level="2" n="54">
<note position="left" xlink:label="note-0571-01" xlink:href="note-0571-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0571-02" xlink:href="note-0571-02a" xml:space="preserve">Horatia.</note>
</div>
<p>
  <s xml:id="echoid-s36056" xml:space="preserve">POSTREMO, quoniam in triangulo A G K, angulus K, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s36057" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36058" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s36059" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36060" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36061" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36062" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36063" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36064" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36065" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36066" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36067" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36068" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36069" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36070" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s36071" xml:space="preserve">vt ſinus complementi arcus A G, hoc eſt, vt ſinus arcus F G, diſtantiæ Solis à meridie, ad <lb/>ſinum complementi arcus G K, hoc eſt, ad ſinum circunferentiæ horariæ B G, ita ſinus comple-<lb/>menti arcus A K, id eſt, ſinus circunferentiæ Verticalis E K, ad ſinum totum: </s>
  <s xml:id="echoid-s36072" xml:space="preserve">Et conuertendo, vt <lb/>ſinus horatię circunferentiæ ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad ſinum circun-<lb/>ferentiæ Verticalis. </s>
  <s xml:id="echoid-s36073" xml:space="preserve">Quamobrem ſi fiat, vt ſinus circunferentiæ horariæ ad ſinum diſtantiæ Solis <lb/>
<anchor type="note" xlink:label="note-0571-03a" xlink:href="note-0571-03"/>
à meridie, ita ſinus totus ad aliud, inuenietur ſinus circunferentiæ Verticalis; </s>
  <s xml:id="echoid-s36074" xml:space="preserve">ideoq́ue circunfe-<lb/>
<anchor type="note" xlink:label="note-0571-04a" xlink:href="note-0571-04"/>
rentia Verticalis nota erit.</s>
  <s xml:id="echoid-s36075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1826" type="float" level="2" n="55">
<note position="right" xlink:label="note-0571-03" xlink:href="note-0571-03a" xml:space="preserve">Verticalis.</note>
<note position="left" xlink:label="note-0571-04" xlink:href="note-0571-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1828" type="section" level="1" n="477">
<head xml:id="echoid-head506" style="it" xml:space="preserve">INVENTIO SVPRADICT ARVM SEX CIRCVNFEREN-<lb/>tiarum in ſphæra recta tam Geometrice ex Analemmate, quàm per numeros <lb/>ex doctrina ſinuum, ſiue Sol exiſtat in Aequatore, ſiue in alio <lb/>quouis parallelo. CAP. VIII.</head>
<p>
  <s xml:id="echoid-s36076" xml:space="preserve">ETSI omnia præcepta, quæ hactenus pro inueſtigandis dictis ſex circunferentijs tradidimus, <lb/>
<anchor type="note" xlink:label="note-0571-05a" xlink:href="note-0571-05"/>
intelligenda ſunt in ſphæra obliqua, in qua polus arcticus ſupra Horizontem extollitur, cum <lb/>de hac Ptolemæus ſolum loquatur in ſuo Analemmate: </s>
  <s xml:id="echoid-s36077" xml:space="preserve">eadem tamen locum etiam habent in il-<lb/>
<anchor type="note" xlink:label="note-0571-06a" xlink:href="note-0571-06"/>
la ſphęrę obliquitate, vbi polus antarcticus ſupra Horizontem eſt eleuatus, ſi ea, quæ de paralle-<lb/>lis borealibus, &amp; </s>
  <s xml:id="echoid-s36078" xml:space="preserve">polo arctico dicta ſunt, accommodentur parallelis auſtralibus, &amp; </s>
  <s xml:id="echoid-s36079" xml:space="preserve">polo antarctico, <lb/>&amp; </s>
  <s xml:id="echoid-s36080" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s36081" xml:space="preserve">Immo vero eiſdem præceptis dictas ſex circunferentias indagabimus in ſphæra recta, <lb/>&amp; </s>
  <s xml:id="echoid-s36082" xml:space="preserve">multo quidem facilius, quàm in obliqua. </s>
  <s xml:id="echoid-s36083" xml:space="preserve">Quod vt planius fiat; </s>
  <s xml:id="echoid-s36084" xml:space="preserve">Sit Meridianus A B C D, cu-<lb/>ius centrum E; </s>
  <s xml:id="echoid-s36085" xml:space="preserve">communis ſectio ipſius, &amp; </s>
  <s xml:id="echoid-s36086" xml:space="preserve">Horizontis recti B D, quæ etiam axem mundi referet; <lb/></s>
  <s xml:id="echoid-s36087" xml:space="preserve">communis ſectio eiuſdem, ac Verticalis, Aequatorisve (Æquator enim &amp; </s>
  <s xml:id="echoid-s36088" xml:space="preserve">Verticalis in ſphęra re-<lb/>
<anchor type="figure" xlink:label="fig-0571-01a" xlink:href="fig-0571-01"/>
cta nõ differunt) recta A C, <lb/>ſecans B D, ad angulos re-<lb/>ctos; </s>
  <s xml:id="echoid-s36089" xml:space="preserve">communis ſectio deni <lb/>que eiuſdẽ, &amp; </s>
  <s xml:id="echoid-s36090" xml:space="preserve">paralleli ſiue <lb/>
<anchor type="note" xlink:label="note-0571-07a" xlink:href="note-0571-07"/>
borealis, ſiue auſtralis a b, <lb/>circa quam ſemicirculus <lb/>a e b, deſcribatur. </s>
  <s xml:id="echoid-s36091" xml:space="preserve">Quòd <lb/>ſi ſemicirculus A B C, circa <lb/>A C, moueri intelligatur, <lb/>donec rectus ſit ad Meridia-<lb/>num, repræſentabit is ſemi-<lb/>circulum Æquatoris orien-<lb/>talem, occidentalemve, ita <lb/>vt E B, ſit communis ſectio <lb/>
<anchor type="note" xlink:label="note-0571-08a" xlink:href="note-0571-08"/>
Æquatoris, &amp; </s>
  <s xml:id="echoid-s36092" xml:space="preserve">Horizontis <lb/>recti, &amp; </s>
  <s xml:id="echoid-s36093" xml:space="preserve">A B, portio Æquato <lb/>ris ſupra terram, &amp; </s>
  <s xml:id="echoid-s36094" xml:space="preserve">B C, por <lb/>tio infra terram, vt ſupra in <lb/>ſphęra obliqua oſtẽdimus. <lb/></s>
  <s xml:id="echoid-s36095" xml:space="preserve">Diuiſio Aequatoris in ho-<lb/>ras inchoanda eſt à puncto <lb/>A, vel B, ita vt in A, ſtatua-<lb/>tur hora 12. </s>
  <s xml:id="echoid-s36096" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s36097" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36098" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36099" xml:space="preserve">in B, hora 6. </s>
  <s xml:id="echoid-s36100" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36101" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s36102" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36103" xml:space="preserve">Item in A, hora 6. </s>
  <s xml:id="echoid-s36104" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s36105" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36106" xml:space="preserve">18. </s>
  <s xml:id="echoid-s36107" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36108" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s36109" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36110" xml:space="preserve">inæqualis: </s>
  <s xml:id="echoid-s36111" xml:space="preserve">In puncto autem B, hora 12. </s>
  <s xml:id="echoid-s36112" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36113" xml:space="preserve">24. </s>
  <s xml:id="echoid-s36114" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s36115" xml:space="preserve">Item 24. </s>
  <s xml:id="echoid-s36116" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36117" xml:space="preserve">12. </s>
  <s xml:id="echoid-s36118" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36119" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36120" xml:space="preserve">12. </s>
  <s xml:id="echoid-s36121" xml:space="preserve">inæqualis. </s>
  <s xml:id="echoid-s36122" xml:space="preserve"><lb/>Eodem modo erit d c, ad a b, perpendicularis, hoc eſt, d B, producta, communis ſectio Hori-
<pb o="556" file="0572" n="572" rhead="GNOMONICES"/>
zontis recti, &amp; </s>
  <s xml:id="echoid-s36123" xml:space="preserve">paralleli a e b, ita vt a e, ſit portio ſupra terram, &amp; </s>
  <s xml:id="echoid-s36124" xml:space="preserve">e b, ſub terra, diuiſioq́ue paral <lb/>leli in horas inchoanda erit à puncto a, vel e, vt in Æquatore à puncto A. </s>
  <s xml:id="echoid-s36125" xml:space="preserve">Sole enim exiſtente <lb/>in parallelo a e b, fit meridies in a, quemadmodum eodem exiſtente in Æquatore, meridies <lb/>fit in A.</s>
  <s xml:id="echoid-s36126" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1828" type="float" level="2" n="1">
<note position="right" xlink:label="note-0571-05" xlink:href="note-0571-05a" xml:space="preserve">Præcepta ſupe-<lb/>riota accommo <lb/>dantur etiam <lb/>ſphærę obliquę, <lb/>quę polum an-<lb/>t<unsure/>a@cticum con-<lb/>ſpicuum habet <lb/>ſupra Horizon-<lb/>tem.</note>
<note position="left" xlink:label="note-0571-06" xlink:href="note-0571-06a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0571-01" xlink:href="fig-0571-01a">
    <image file="0571-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0571-01"/>
  </figure>
<note position="left" xlink:label="note-0571-07" xlink:href="note-0571-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0571-08" xlink:href="note-0571-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36127" xml:space="preserve">STATVATVR ergo primum Sol in Aequatore, vt in puncto P, à quo ad diametrum <lb/>
<anchor type="note" xlink:label="note-0572-01a" xlink:href="note-0572-01"/>
Æquatoris A C, perpendicularis excitetur P O, quę etiam reſpondebit perpendiculari O P, quæ <lb/>in figura cap. </s>
  <s xml:id="echoid-s36128" xml:space="preserve">2. </s>
  <s xml:id="echoid-s36129" xml:space="preserve">ad diametrum Verticalis A C, ducebatur per punctum L, in diametro Æquato-<lb/>ris, in quod perpendicularis K L, à centro Solis cadebat: </s>
  <s xml:id="echoid-s36130" xml:space="preserve">Recta autem E A, reſpondebit perpen-<lb/>diculari M N, quæ in eadem figura per idem punctum L, ad Horizontis diametrum ducebatur; <lb/></s>
  <s xml:id="echoid-s36131" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0572-01a" xlink:href="fig-0572-01"/>
ac proinde ſi ex O P, abſcin-<lb/>
<anchor type="note" xlink:label="note-0572-02a" xlink:href="note-0572-02"/>
datur ipſi O P, æqualis O P, <lb/>immo eadem O P, ſumatur, <lb/>&amp; </s>
  <s xml:id="echoid-s36132" xml:space="preserve">ex E A, eidem O P, ęqua <lb/>lis E F, cadent rectę ductę <lb/>ex centro E, per puncta P, F, <lb/>quæ punctis R, &amp; </s>
  <s xml:id="echoid-s36133" xml:space="preserve">Q, reſpõ-<lb/>dent in dicta figura cap. </s>
  <s xml:id="echoid-s36134" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s36135" xml:space="preserve">in puncta P, &amp; </s>
  <s xml:id="echoid-s36136" xml:space="preserve">A. </s>
  <s xml:id="echoid-s36137" xml:space="preserve">Igitur ex <lb/>demonſtratis in cap. </s>
  <s xml:id="echoid-s36138" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36139" xml:space="preserve">erit <lb/>B P, circunferẽtia hectemo-<lb/>
<anchor type="note" xlink:label="note-0572-03a" xlink:href="note-0572-03"/>
ria; </s>
  <s xml:id="echoid-s36140" xml:space="preserve">B A, horaria; </s>
  <s xml:id="echoid-s36141" xml:space="preserve">A P, de-<lb/>ſcenſiua; </s>
  <s xml:id="echoid-s36142" xml:space="preserve">B A, meridiana <lb/>iuter Horizontem, &amp; </s>
  <s xml:id="echoid-s36143" xml:space="preserve">Hecte <lb/>morion, qui tunc ab Æqua-<lb/>tore non differt; </s>
  <s xml:id="echoid-s36144" xml:space="preserve">A P, Verti <lb/>calis; </s>
  <s xml:id="echoid-s36145" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36146" xml:space="preserve">horizontalis nihil <lb/>erit, cum Verticalis tũc per <lb/>Solem ductus idem ſit, qui <lb/>Verticalis proprie dictus, <lb/>aut Æquator. </s>
  <s xml:id="echoid-s36147" xml:space="preserve">Per vnicam <lb/>ergo perpendicularem P O, <lb/>
<anchor type="note" xlink:label="note-0572-04a" xlink:href="note-0572-04"/>
quæ ex loco Solis ad Æqua-<lb/>toris diametrum A C, duci <lb/>tur, inueniuntur circunferentia hectemoria B P, deſcenſiua A P, &amp; </s>
  <s xml:id="echoid-s36148" xml:space="preserve">Verticalis A P: </s>
  <s xml:id="echoid-s36149" xml:space="preserve">At quadrans <lb/>B A, exhibet &amp; </s>
  <s xml:id="echoid-s36150" xml:space="preserve">horariam, &amp; </s>
  <s xml:id="echoid-s36151" xml:space="preserve">meridianam; </s>
  <s xml:id="echoid-s36152" xml:space="preserve">horizontalis denique nihil eſt, cum Sol in Æquatore <lb/>
<anchor type="note" xlink:label="note-0572-05a" xlink:href="note-0572-05"/>
exiſtit in ſphæra recta.</s>
  <s xml:id="echoid-s36153" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1829" type="float" level="2" n="2">
<note position="left" xlink:label="note-0572-01" xlink:href="note-0572-01a" xml:space="preserve">Inuentio ſupra <lb/>dictarum circũ-<lb/>ferentiarum in <lb/>ſphæra recta ex <lb/>Analemmate, <lb/>cum Sol in Ae-<lb/>quatore exiſtit.</note>
  <figure xlink:label="fig-0572-01" xlink:href="fig-0572-01a">
    <image file="0572-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0572-01"/>
  </figure>
<note position="left" xlink:label="note-0572-02" xlink:href="note-0572-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0572-03" xlink:href="note-0572-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0572-04" xlink:href="note-0572-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0572-05" xlink:href="note-0572-05a" xml:space="preserve">Innentio eatun <lb/>dem circunfe-<lb/>rentia um in <lb/>ſphęra recta ex <lb/>Analemmate. <lb/>Sole exiſtente <lb/>in quouis paral <lb/>lelo extra Ae-<lb/>quatorem.</note>
</div>
<p>
  <s xml:id="echoid-s36154" xml:space="preserve">PONATVR deinde Sol in puncto k, paralleli a e b, ducaturq́ue ex K, ad a b, diametrum <lb/>paralleli perpendicularis K L; </s>
  <s xml:id="echoid-s36155" xml:space="preserve">eritq́ue ſemidiameter d a, eadem, quæ perpendicularis N M, quæ <lb/>in figuris cap. </s>
  <s xml:id="echoid-s36156" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36157" xml:space="preserve">duci iubebatur per L, ad Horizontis diametrum; </s>
  <s xml:id="echoid-s36158" xml:space="preserve">recta autem K L, producta ad <lb/>O, dabit O P, perpendicularem, quæ ibidem per L, ad diametrum Verticalis duci præcipiebatur. <lb/></s>
  <s xml:id="echoid-s36159" xml:space="preserve">
<anchor type="note" xlink:label="note-0572-06a" xlink:href="note-0572-06"/>
Poſt hæc, quoniam N M, O P, maiores ſunt, quàm K L, (Eſt enim N M, ſemidiameter paralleli, <lb/>&amp; </s>
  <s xml:id="echoid-s36160" xml:space="preserve">K L, ſemidiametro minor: </s>
  <s xml:id="echoid-s36161" xml:space="preserve">Deinde ductis rectis d K, E P, quoniam quadratum rectę d K, ęqua <lb/>le eſt quadratis rectarum k L, L d, &amp; </s>
  <s xml:id="echoid-s36162" xml:space="preserve">quadratum rectæ E P, quadratis rectarum P O, O E; </s>
  <s xml:id="echoid-s36163" xml:space="preserve">eſt autẽ <lb/>
<anchor type="note" xlink:label="note-0572-07a" xlink:href="note-0572-07"/>
quadratum ex E P, ſemidiametro circuli maximi maius quadrato ex d K, ſemidiametro circuli <lb/>non maximi; </s>
  <s xml:id="echoid-s36164" xml:space="preserve">erunt quoque quadrata rectarum P O, O E, maiora quadratis rectarum K L, L d. <lb/></s>
  <s xml:id="echoid-s36165" xml:space="preserve">Ablatis igitur quadratis ęqualibus rectarũ O E, L d, quę ęquales ſunt, maius erit reliquum qua-<lb/>
<anchor type="note" xlink:label="note-0572-08a" xlink:href="note-0572-08"/>
dratum rectę O P, reliquo quadrato rectę K L, proptereaq́ue &amp; </s>
  <s xml:id="echoid-s36166" xml:space="preserve">recta O P, maior erit, quàm re-<lb/>cta K L,) abſcindantur rectæ N Q, O R, ipſi K L, ęquales, ducanturq́ue rectę E Q S, E R T. <lb/></s>
  <s xml:id="echoid-s36167" xml:space="preserve">Poſtremo ducta per L, diametro Hcctemorij Y E Z, excitentur ad eam in E, &amp; </s>
  <s xml:id="echoid-s36168" xml:space="preserve">L, perpendicula-<lb/>res E g, L f; </s>
  <s xml:id="echoid-s36169" xml:space="preserve">eritq́ue L f, ipſi K L, ęqualis; </s>
  <s xml:id="echoid-s36170" xml:space="preserve">(Iunctis enim rectis E K, E f, quę ęquales inter ſe ſunt, <lb/>
<anchor type="note" xlink:label="note-0572-09a" xlink:href="note-0572-09"/>
<anchor type="note" xlink:label="note-0572-10a" xlink:href="note-0572-10"/>
cum vtraque ducatur à centto ſphęrę E, ad eius ſuperficiem, vt conſtat, ſi parallelus in proprio ſitu <lb/>ponatur, nempe ad Meridianum rectus; </s>
  <s xml:id="echoid-s36171" xml:space="preserve">ita vt in eo ſitu K L, ſit, per defin. </s>
  <s xml:id="echoid-s36172" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36173" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36174" xml:space="preserve">11. </s>
  <s xml:id="echoid-s36175" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s36176" xml:space="preserve">ad pla-<lb/>num Meridiani, atque adeo per defin. </s>
  <s xml:id="echoid-s36177" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36178" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s36179" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36180" xml:space="preserve">ad rectam E L, perpendicularis: </s>
  <s xml:id="echoid-s36181" xml:space="preserve">quoniã <lb/>tam quadratum rectæ E k, quadratis rectarum K L, L E, quàm quadratum rectę E f, quadratis re-<lb/>ctarum f L, L E, ęquale eſt, ſunt autem quadrata rectarum E k, E f, æqualium ęqualia, erunt quo-<lb/>que quadrata rectarum K L, L E, quadratis rectarum fL, L E, ęqualia. </s>
  <s xml:id="echoid-s36182" xml:space="preserve">Dempto ergo commu-<lb/>ni quadrato rectæ L E, ęqualia remanebunt quadrata rectarum K L, f L, ac ob id &amp; </s>
  <s xml:id="echoid-s36183" xml:space="preserve">rectę ipſę <lb/>ęquales erunt) ac proinde ſi beneficio circini ſumatur interuallum L f, ęquale rectę K L, erit ducta <lb/>L f, ad E Y, perpendicularis, &amp;</s>
  <s xml:id="echoid-s36184" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36185" xml:space="preserve">vt etiam in cap. </s>
  <s xml:id="echoid-s36186" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36187" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s36188" xml:space="preserve">His ita conſtitutis, erit ex ijs, quę <lb/>in cap. </s>
  <s xml:id="echoid-s36189" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36190" xml:space="preserve">oſtendimus, g f, circunferentia hectemoria; </s>
  <s xml:id="echoid-s36191" xml:space="preserve">B M, horaria; </s>
  <s xml:id="echoid-s36192" xml:space="preserve">A P, deſcenſiua; </s>
  <s xml:id="echoid-s36193" xml:space="preserve">B Y, meri-<lb/>diana; </s>
  <s xml:id="echoid-s36194" xml:space="preserve">A T, Verticalis; </s>
  <s xml:id="echoid-s36195" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36196" xml:space="preserve">A S, deſcenſiua.</s>
  <s xml:id="echoid-s36197" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1830" type="float" level="2" n="3">
<note position="left" xlink:label="note-0572-06" xlink:href="note-0572-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0572-07" xlink:href="note-0572-07a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0572-08" xlink:href="note-0572-08a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0572-09" xlink:href="note-0572-09a" xml:space="preserve">47. primi.</note>
<note position="left" xlink:label="note-0572-10" xlink:href="note-0572-10a" xml:space="preserve">50</note>
</div>
<pb o="557" file="0573" n="573" rhead="LIBER SEXTVS."/>
<p>
  <s xml:id="echoid-s36198" xml:space="preserve">IAM vero, ſi eaſdem circunferentias lubeat per ſinus inueſtigare ex triangulis rectilineis, <lb/>
<anchor type="note" xlink:label="note-0573-01a" xlink:href="note-0573-01"/>
res perfacilis erit, Sole Aequatotem percurrente.</s>
  <s xml:id="echoid-s36199" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1831" type="float" level="2" n="4">
<note position="right" xlink:label="note-0573-01" xlink:href="note-0573-01a" xml:space="preserve">Inuentio earun-<lb/>dem circunferẽ <lb/>tiar<unsure/>um in ſphæ <lb/>ra recta, ex ſinu <lb/>bus per triangu <lb/>la rectilinea, So <lb/>le exiſtente in <lb/>Aequatore. <lb/>Hectemoria. <lb/>Horaria. <lb/>Deſcenſiua. <lb/>Meridiana.</note>
</div>
<p>
  <s xml:id="echoid-s36200" xml:space="preserve">HECTEMORIA enim circunferentia æqualis eſt complemento diſtantiæ Solis à meri-<lb/>die, vel certe ipſi diſtantiæ ab Horizonte, qualis eſt circunferentia B P.</s>
  <s xml:id="echoid-s36201" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36202" xml:space="preserve">HORARIA autem circunferentia æqualis eſt quadranti Meridiani B A.</s>
  <s xml:id="echoid-s36203" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36204" xml:space="preserve">DESCENSIVA item circunferentia æqualis eſt diſtantiæ Solis à meridie, cuiuſmodi eſt <lb/>arcus A P.</s>
  <s xml:id="echoid-s36205" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36206" xml:space="preserve">MERIDIANA quoque circunferentia quadranti Meridiani B A, æqualis eſt.</s>
  <s xml:id="echoid-s36207" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36208" xml:space="preserve">VERTICALIS rurſum circunferentia æqualis eſt diſtantiæ Solis à meridie, quemadmo-<lb/>
<anchor type="note" xlink:label="note-0573-02a" xlink:href="note-0573-02"/>
dum &amp; </s>
  <s xml:id="echoid-s36209" xml:space="preserve">deſcenſiua, qualis eſt arcus A P.</s>
  <s xml:id="echoid-s36210" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1832" type="float" level="2" n="5">
<note position="right" xlink:label="note-0573-02" xlink:href="note-0573-02a" xml:space="preserve">Verticalis.</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s36211" xml:space="preserve">HORIZONTALIS denique nihil omnino eſt.</s>
  <s xml:id="echoid-s36212" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Horizontalis.</note>
<note position="right" xml:space="preserve">Inuentio earun <lb/>dem circunferẽ <lb/>tiarum in ſphæ <lb/>ra recta, per ſi-<lb/>nus, ex triangu <lb/>lis rectilineis, <lb/>Sole exiſtente <lb/>in quolibet pa-<lb/>rallelo.</note>
<p>
  <s xml:id="echoid-s36213" xml:space="preserve">SOLE vero exiſtente in parallelo quolibet, ita rem exequemur. </s>
  <s xml:id="echoid-s36214" xml:space="preserve">Quoniam eſt, vt a d@, quate-<lb/>nus ſinus totus paralleli a e b, ad K L, quatenus ſinus eſt diſtantiæ Solis à meridie in eodem paral <lb/>lelo, ita a d, quatenus pars eſt ſinus totius in circulo maximo, hoc eſt, quatenus ſinus eſt comple <lb/>menti declinationis dati paralleli, ad K L, quatenus pars eſt eiuſdem ſinus totius in circulo maxi-<lb/>mo, hoc eſt, ad L f, ipſi K L, ęqualem: </s>
  <s xml:id="echoid-s36215" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita <lb/>ſinus complementi declinationis ad aliud, inuenietur recta L f, nempe ſinus complementi hecte-<lb/>
<anchor type="note" xlink:label="note-0573-06a" xlink:href="note-0573-06"/>
moriæ circunferentiæ g f, ac proinde complementum hoc, vnà cum circunferentia hectemoria <lb/>g f, notum erit.</s>
  <s xml:id="echoid-s36216" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1833" type="float" level="2" n="6">
<note position="right" xlink:label="note-0573-06" xlink:href="note-0573-06a" xml:space="preserve">Hectemoria.</note>
</div>
<p>
  <s xml:id="echoid-s36217" xml:space="preserve">HORARIA porro circunferentia æqualis eſt complemento declinationis propoſiti paral-<lb/>
<anchor type="note" xlink:label="note-0573-07a" xlink:href="note-0573-07"/>
<anchor type="note" xlink:label="note-0573-08a" xlink:href="note-0573-08"/>
leli, cuiuſmodi eſt arcus B M.</s>
  <s xml:id="echoid-s36218" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1834" type="float" level="2" n="7">
<note position="left" xlink:label="note-0573-07" xlink:href="note-0573-07a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0573-08" xlink:href="note-0573-08a" xml:space="preserve">Horaria</note>
</div>
<p>
  <s xml:id="echoid-s36219" xml:space="preserve">DEINDE quia eſt, vt a d, quatenus ſinus totus paralleli propoſiti, ad L N, quatenus ſinus <lb/>eſt complementi diſtantiæ Solis à meridie, ita a d, quatenus pars eſt ſinus totius in circulo maxi-<lb/>mo, hoc eſt, quatenus eſt ſinus complementi declination is dati paralleli, ad L N, quatenus pars <lb/>eſt eiuſdem ſinus totius in circulo maximo, hoc eſt, quatenus ſinus eſt complementi circunferen <lb/>tiæ deſcenſiuæ: </s>
  <s xml:id="echoid-s36220" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus <lb/>
<anchor type="note" xlink:label="note-0573-09a" xlink:href="note-0573-09"/>
complementi declinationis ad aliud, reperietur ſinus complementi circunferentiæ deſcenſiuæ <lb/>A P; </s>
  <s xml:id="echoid-s36221" xml:space="preserve">atque ob id complementum hoc, vnà cum circunferentia deſcenſiua ignotum non erit.</s>
  <s xml:id="echoid-s36222" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1835" type="float" level="2" n="8">
<note position="right" xlink:label="note-0573-09" xlink:href="note-0573-09a" xml:space="preserve">Deſcenſiua.</note>
</div>
<p>
  <s xml:id="echoid-s36223" xml:space="preserve">MERIDIANA circunferentia B Y, inuenietur, vt in ſphæra obliqua, Sole in quouis paral-<lb/>
<anchor type="note" xlink:label="note-0573-10a" xlink:href="note-0573-10"/>
lelo exiſtente, veluti in præcedenti cap. </s>
  <s xml:id="echoid-s36224" xml:space="preserve">tradidimus.</s>
  <s xml:id="echoid-s36225" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1836" type="float" level="2" n="9">
<note position="right" xlink:label="note-0573-10" xlink:href="note-0573-10a" xml:space="preserve">Meridiana.</note>
</div>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s36226" xml:space="preserve">QVIA vero duo latera K L, L N, trianguli K L N, æqualia ſunt duobus lateribus R O, O E, <lb/>trianguli R O E, (ſumpta enim eſt R O, ipſi K L, æqualis; </s>
  <s xml:id="echoid-s36227" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36228" xml:space="preserve">L N, ipſi O E, æqualis eſt, ob paral-<lb/>
<anchor type="note" xlink:label="note-0573-12a" xlink:href="note-0573-12"/>
lelogrammum NO,) angulosq́ue continent æquales, puta rectos, erunt &amp; </s>
  <s xml:id="echoid-s36229" xml:space="preserve">baſes N K, E R, æqua-<lb/>
<anchor type="note" xlink:label="note-0573-13a" xlink:href="note-0573-13"/>
les. </s>
  <s xml:id="echoid-s36230" xml:space="preserve">Cum ergo N K, ſemidiameter paralleli æqualis ſit ſemidiametro M N, eiuſdem paralleli; </s>
  <s xml:id="echoid-s36231" xml:space="preserve">erit <lb/>quoque E R, ipſi M N, id eſt, ſinui circunferentię horariæ B M, ſiue ſinui complementi declinatio-<lb/>nis, æqualis. </s>
  <s xml:id="echoid-s36232" xml:space="preserve">Quare inueniemus circunferentiam Verticalem A T, vt in ſphæra obliqua, Sole exi-<lb/>
<anchor type="note" xlink:label="note-0573-14a" xlink:href="note-0573-14"/>
ſtente in quouis parallelo, quemadmodum in antecedenti cap. </s>
  <s xml:id="echoid-s36233" xml:space="preserve">docuimus; </s>
  <s xml:id="echoid-s36234" xml:space="preserve">vt conſtat in triangulis <lb/>E R O, E T X, ſi prius inueniatur R O, hoc eſt, K L, illi æqualis, nempe ſinus diſtãtiæ Solis à me-<lb/>ridie, in partibus ſinus totius in circulo maximo, vt in præcedenti cap. </s>
  <s xml:id="echoid-s36235" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s36236" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1837" type="float" level="2" n="10">
<note position="right" xlink:label="note-0573-12" xlink:href="note-0573-12a" xml:space="preserve">34. primi</note>
<note position="right" xlink:label="note-0573-13" xlink:href="note-0573-13a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0573-14" xlink:href="note-0573-14a" xml:space="preserve">Verticalis.</note>
</div>
<p>
  <s xml:id="echoid-s36237" xml:space="preserve">POSTREMO, poſito parallelo a e b, ad Meridianum recto, ita vt fiat angulus rectus <lb/>
<anchor type="note" xlink:label="note-0573-15a" xlink:href="note-0573-15"/>
K L O, concipiatur duci recta O K, ſubtenſa dicto angulo recto K L O. </s>
  <s xml:id="echoid-s36238" xml:space="preserve">Et quoniam duo latera <lb/>K L, L O, trianguli k L O, in eo ſitu, æqualia ſunt duobus lateribus Q N, N E, trianguli Q N E, <lb/>(ſumpta enim fuit Q N, ipſi K L, æqualis: </s>
  <s xml:id="echoid-s36239" xml:space="preserve">at L O, ipſi N E, æqualis eſt, ob parallelogrammum <lb/>
<anchor type="note" xlink:label="note-0573-16a" xlink:href="note-0573-16"/>
N O,) angulosq́ue continent æquales, nempe rectos, erunt &amp; </s>
  <s xml:id="echoid-s36240" xml:space="preserve">baſes O K, E Q, æquales. </s>
  <s xml:id="echoid-s36241" xml:space="preserve">Cum er-<lb/>
<anchor type="note" xlink:label="note-0573-17a" xlink:href="note-0573-17"/>
go O K, æqualis ſit ipſi O P; </s>
  <s xml:id="echoid-s36242" xml:space="preserve">quòd vtraque ſit ſemidiameter circuli in ſphæra Horizonti æquidi-<lb/>ſtantis, &amp; </s>
  <s xml:id="echoid-s36243" xml:space="preserve">per rectas K L, O P, ducti; </s>
  <s xml:id="echoid-s36244" xml:space="preserve">erit quoque E Q, eidem O P, id eſt, ſinui circunferentiæ <lb/>deſcenſiuæ A P, æqualis. </s>
  <s xml:id="echoid-s36245" xml:space="preserve">Quapropter inueniemus circunferentiam horizontalem A S, vt in ſphę <lb/>
<anchor type="note" xlink:label="note-0573-18a" xlink:href="note-0573-18"/>
ra obliqua, Sole exiſtente in quocunque parallelo, veluti in præcedenti cap. </s>
  <s xml:id="echoid-s36246" xml:space="preserve">docuimus; </s>
  <s xml:id="echoid-s36247" xml:space="preserve">vt patet <lb/>in triangulis E Q N, E S V, ſi prius inueniatur Q N, hoc eſt, K L, illi æqualis, nimirum ſinus di-<lb/>ſtantiæ Solis à meridie, in partibus ſinus totius in circulo maximo, veluti in antecedenti <lb/>
<anchor type="note" xlink:label="note-0573-19a" xlink:href="note-0573-19"/>
cap. </s>
  <s xml:id="echoid-s36248" xml:space="preserve">tradidimus.</s>
  <s xml:id="echoid-s36249" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1838" type="float" level="2" n="11">
<note position="left" xlink:label="note-0573-15" xlink:href="note-0573-15a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0573-16" xlink:href="note-0573-16a" xml:space="preserve">34. primi.</note>
<note position="right" xlink:label="note-0573-17" xlink:href="note-0573-17a" xml:space="preserve">4. primi.</note>
<note position="right" xlink:label="note-0573-18" xlink:href="note-0573-18a" xml:space="preserve">Hor<unsure/>izontalis.</note>
<note position="left" xlink:label="note-0573-19" xlink:href="note-0573-19a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Inuentio earun <lb/>dem circunfe-<lb/>rentiarum in <lb/>ſphæra recta ex <lb/>triangulis ſphæ <lb/>ricis, Sole exi-<lb/>ſtente in Aequa <lb/>tore.</note>
<p>
  <s xml:id="echoid-s36250" xml:space="preserve">VERVM iam eaſdem circunferentias in ſphæra recta per triangula ſphærica perſcrutemur. <lb/></s>
  <s xml:id="echoid-s36251" xml:space="preserve">Sit Horizon rectus A B C D; </s>
  <s xml:id="echoid-s36252" xml:space="preserve">Meridianus B E D; </s>
  <s xml:id="echoid-s36253" xml:space="preserve">Aequator A E C, idem qui Verticalis; </s>
  <s xml:id="echoid-s36254" xml:space="preserve">paralle-<lb/>lus quicunque ſiue auſtralis, ſiue borealis F G. </s>
  <s xml:id="echoid-s36255" xml:space="preserve">Ponatur primum Sol in Æquatore, in puncto H. </s>
  <s xml:id="echoid-s36256" xml:space="preserve"><lb/>Quo poſito, erit tam Hectemorion ex A, per H, ductus, quàm circulus Deſcenſiuus ex E, per H, <lb/>ductus, idem qui Æquator, ſeu Verticalis. </s>
  <s xml:id="echoid-s36257" xml:space="preserve">Ducto ergo Horario circulo B H D, inuentæ erunt <lb/>ſex dictæ circunferentiæ, vt paulo ante diximus. </s>
  <s xml:id="echoid-s36258" xml:space="preserve">Nam circunferentia hectemoria A H, eſt com-<lb/>plementũ diſtantiæ Solis à meridie, vel ipſa diſtantia Solis ab Horizonte: </s>
  <s xml:id="echoid-s36259" xml:space="preserve">Meridiana eſt quadrãs <lb/>Meridiani B E, vel D E: </s>
  <s xml:id="echoid-s36260" xml:space="preserve">Deſcenſiua, &amp; </s>
  <s xml:id="echoid-s36261" xml:space="preserve">Verticalis E H, eſt diſtantia Solis à meridie: </s>
  <s xml:id="echoid-s36262" xml:space="preserve">Horaria eſt <lb/>quadrans B H, vel D H: </s>
  <s xml:id="echoid-s36263" xml:space="preserve">Horizontalis denique nihil eſt.</s>
  <s xml:id="echoid-s36264" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36265" xml:space="preserve">COLLOCETVR deinde Sol in parallelo F G, in puncto I, per quod tres maximi circuli
<pb o="558" file="0574" n="574" rhead="GNOMONICES"/>
ducantur, nempe Hectemorion A I K, Deſcenſiuus E I L, &amp; </s>
  <s xml:id="echoid-s36266" xml:space="preserve">Horarius B I D. </s>
  <s xml:id="echoid-s36267" xml:space="preserve">Erit igitur A I, <lb/>
<anchor type="note" xlink:label="note-0574-01a" xlink:href="note-0574-01"/>
circunferentia hectemoria; </s>
  <s xml:id="echoid-s36268" xml:space="preserve">B K, vel D K, meridiana; </s>
  <s xml:id="echoid-s36269" xml:space="preserve">E I, deſcenſiua; </s>
  <s xml:id="echoid-s36270" xml:space="preserve">A L, horizontalis; </s>
  <s xml:id="echoid-s36271" xml:space="preserve">B I, <lb/>vel D I, horaria; </s>
  <s xml:id="echoid-s36272" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36273" xml:space="preserve">E H, Verticalis: </s>
  <s xml:id="echoid-s36274" xml:space="preserve">quas omnes hac ratione perueſtigabimus.</s>
  <s xml:id="echoid-s36275" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1839" type="float" level="2" n="12">
<note position="left" xlink:label="note-0574-01" xlink:href="note-0574-01a" xml:space="preserve">Inuentio earun <lb/>dem circunferẽ <lb/>tiarum in ſphæ <lb/>ra recta ex trian <lb/>gulis ſphęricis. <lb/>Sole conſtituto <lb/>in quouis paral <lb/>lelo extra Ae-<lb/>quatorem.</note>
</div>
<p>
  <s xml:id="echoid-s36276" xml:space="preserve">QVONIAM in triangulo B I K, vel D I K, angulus <lb/>
<anchor type="figure" xlink:label="fig-0574-01a" xlink:href="fig-0574-01"/>
K, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s36277" xml:space="preserve">16. </s>
  <s xml:id="echoid-s36278" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36279" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36280" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36281" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36282" xml:space="preserve">de <lb/>triang. </s>
  <s xml:id="echoid-s36283" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36284" xml:space="preserve">13. </s>
  <s xml:id="echoid-s36285" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36286" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36287" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36288" xml:space="preserve">41. <lb/></s>
  <s xml:id="echoid-s36289" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36290" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36291" xml:space="preserve">vt ſinus arcus B I, vel D I, com-<lb/>plementi declinationis paralleli dati F G; </s>
  <s xml:id="echoid-s36292" xml:space="preserve">(cum enim B, <lb/>D, ſint poli mundi, erit B I D, circulus declinationis) ad <lb/>ſinum totum anguli recti K, ita ſinus arcus I K, comple-<lb/>
<anchor type="note" xlink:label="note-0574-02a" xlink:href="note-0574-02"/>
menti circunferentiæ hectemoriæ A I, ad ſinum anguli B, <lb/>vel D, hoc eſt, ad ſinum arcus E H, diſtantiæ Solis à meri <lb/>die: </s>
  <s xml:id="echoid-s36293" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum complemen <lb/>ti declinationis, ita ſinus diſtantiæ Solis à meridie ad ſinũ <lb/>complementi circunferentię hectemoriæ. </s>
  <s xml:id="echoid-s36294" xml:space="preserve">Si igitur fiat, vt <lb/>ſinus totus ad ſinum complementi declinationis, ita ſinus <lb/>
<anchor type="note" xlink:label="note-0574-03a" xlink:href="note-0574-03"/>
diſtantiæ Solis à meridie ad aliud, producetur ſinus com-<lb/>plementi hectemoriæ circunferentiæ; </s>
  <s xml:id="echoid-s36295" xml:space="preserve">ac proinde comple <lb/>mentum hoc, vnà cum hectemoria circunferẽtia, notum <lb/>fiet. </s>
  <s xml:id="echoid-s36296" xml:space="preserve">Quod etiam ita perſpicuum faciemus. </s>
  <s xml:id="echoid-s36297" xml:space="preserve">Quoniam <lb/>
<anchor type="note" xlink:label="note-0574-04a" xlink:href="note-0574-04"/>
in triangulo A I H, angulus H, rectus eſt, erit per propoſ. <lb/></s>
  <s xml:id="echoid-s36298" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36299" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36300" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36301" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36302" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36303" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36304" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36305" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36306" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36307" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36308" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36309" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36310" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s36311" xml:space="preserve">vt ſinus complementi arcus H I, declinationis ad ſinum totum, ita ſinus complementi cir-<lb/>cunferentiæ hectemoriæ A I, ad ſinum complementi arcus A H, hoc eſt, ad ſinum arcus E H, di-<lb/>ſtantiæ Solis à meridie: </s>
  <s xml:id="echoid-s36312" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum complementi declinationis, ita <lb/>ſinus diſtantiæ Solis à meridie ad ſinum complementi circunferentiæ hectemoriæ, velu-<lb/>ti prius.</s>
  <s xml:id="echoid-s36313" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1840" type="float" level="2" n="13">
  <figure xlink:label="fig-0574-01" xlink:href="fig-0574-01a">
    <image file="0574-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0574-01"/>
  </figure>
<note position="left" xlink:label="note-0574-02" xlink:href="note-0574-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0574-03" xlink:href="note-0574-03a" xml:space="preserve">Hectemoria.</note>
<note position="left" xlink:label="note-0574-04" xlink:href="note-0574-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s36314" xml:space="preserve">DEINDE, quia in triangulo B I k, vel D I K, angulus K, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s36315" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36316" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s36317" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36318" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36319" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36320" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36321" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36322" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36323" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36324" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36325" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36326" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36327" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36328" xml:space="preserve"><lb/>ſphær. </s>
  <s xml:id="echoid-s36329" xml:space="preserve">vt ſinus complementi arcus I k, hoc eſt, vt ſinus circunferentiæ hectemoriæ A I, ad ſinum <lb/>
<anchor type="note" xlink:label="note-0574-05a" xlink:href="note-0574-05"/>
totum, ita ſinus complementi arcus B I, vel D I, hoc eſt, ita ſinus arcus declinationis H I, ad ſinum <lb/>complementi meridianæ circunferentiæ B K, vel D K. </s>
  <s xml:id="echoid-s36330" xml:space="preserve">Quocirca ſi fiat, vt ſinus circunferentiæ he <lb/>
<anchor type="note" xlink:label="note-0574-06a" xlink:href="note-0574-06"/>
ctemoriæ ad ſinum totum, ita ſinus declinationis ad aliud, inuenietur ſinus complementi cir-<lb/>cunferentiæ meridianæ; </s>
  <s xml:id="echoid-s36331" xml:space="preserve">ac propterea complementum hoc, vna cum circunferentia meridiana, <lb/>non latebit.</s>
  <s xml:id="echoid-s36332" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1841" type="float" level="2" n="14">
<note position="left" xlink:label="note-0574-05" xlink:href="note-0574-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0574-06" xlink:href="note-0574-06a" xml:space="preserve">Meridiana.</note>
</div>
<p>
  <s xml:id="echoid-s36333" xml:space="preserve">RVRSVS quia in triangulo E H I, angulus H, rectus eſt, erit per propoſ. </s>
  <s xml:id="echoid-s36334" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36335" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36336" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36337" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36338" xml:space="preserve">Re-<lb/>giom. </s>
  <s xml:id="echoid-s36339" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36340" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36341" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36342" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36343" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36344" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36345" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36346" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36347" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36348" xml:space="preserve">vt ſi-<lb/>nus complementi arcus declinationis H I, ad ſinum totum, ita ſinus complementi circunferen-<lb/>tiæ deſcenſiuæ E I, ad ſinum complementi arcus E H, diſtantiæ Solis à meridie: </s>
  <s xml:id="echoid-s36349" xml:space="preserve">Et conuertendo, <lb/>vt ſinus totus ad ſinum complementi declinationis, ita ſinus complementi diſtantiæ Solis à meri-<lb/>
<anchor type="note" xlink:label="note-0574-07a" xlink:href="note-0574-07"/>
die ad ſinum complementi circunferentię deſcenſiuæ. </s>
  <s xml:id="echoid-s36350" xml:space="preserve">Quamobrem, ſi fiat, vt finus totus ad ſi-<lb/>
<anchor type="note" xlink:label="note-0574-08a" xlink:href="note-0574-08"/>
num complementi declinationis, ita ſinus complementi diſtantiæ Solis à meridie ad aliud, pro-<lb/>creabitur ſinus complementi circunferentię deſcenſiuæ; </s>
  <s xml:id="echoid-s36351" xml:space="preserve">atque adeo complementum hoc redde-<lb/>tur no tum, vna cum deſcenſiua circunferentia.</s>
  <s xml:id="echoid-s36352" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1842" type="float" level="2" n="15">
<note position="left" xlink:label="note-0574-07" xlink:href="note-0574-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0574-08" xlink:href="note-0574-08a" xml:space="preserve">Deſcenſius<unsure/>.</note>
</div>
<p>
  <s xml:id="echoid-s36353" xml:space="preserve">PRÆTEREA, cum in triãgulo E H I, angulus H, ſit rectus, erit per propoſ. </s>
  <s xml:id="echoid-s36354" xml:space="preserve">16. </s>
  <s xml:id="echoid-s36355" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36356" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36357" xml:space="preserve">Ioan. <lb/></s>
  <s xml:id="echoid-s36358" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36359" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36360" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36361" xml:space="preserve">13, lib. </s>
  <s xml:id="echoid-s36362" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36363" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36364" xml:space="preserve">41. </s>
  <s xml:id="echoid-s36365" xml:space="preserve">noſtrorum triang. </s>
  <s xml:id="echoid-s36366" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36367" xml:space="preserve">vt <lb/>ſinus circunferentiæ deſcenſiuæ E I, ad ſinum totum anguli recti H, ita ſinus arcus declinationis <lb/>H I, ad ſinum anguli E, hoc eſt, ad ſinum circunferentiæ horizontalis A L. </s>
  <s xml:id="echoid-s36368" xml:space="preserve">Quare ſi fiat, vt ſinus <lb/>
<anchor type="note" xlink:label="note-0574-09a" xlink:href="note-0574-09"/>
deſcenſiuę circunferentię ad ſinum totum, ita ſinus declinationis ad aliud, producetur ſinus cir-<lb/>cunferentiæ horizontalis; </s>
  <s xml:id="echoid-s36369" xml:space="preserve">proptereaq́ue ipſa circunferentia horizontalis nota erit. </s>
  <s xml:id="echoid-s36370" xml:space="preserve">Quod etiam <lb/>
<anchor type="note" xlink:label="note-0574-10a" xlink:href="note-0574-10"/>
fiet hac ratione perſpicuum. </s>
  <s xml:id="echoid-s36371" xml:space="preserve">Quoniam in triangulo B I L, vel D I L, angulus L, rectus eſt, erit per <lb/>propoſ. </s>
  <s xml:id="echoid-s36372" xml:space="preserve">19. </s>
  <s xml:id="echoid-s36373" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36374" xml:space="preserve">4. </s>
  <s xml:id="echoid-s36375" xml:space="preserve">Ioan. </s>
  <s xml:id="echoid-s36376" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s36377" xml:space="preserve">de triang. </s>
  <s xml:id="echoid-s36378" xml:space="preserve">vel per propoſ. </s>
  <s xml:id="echoid-s36379" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36380" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36381" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36382" xml:space="preserve">Gebri, vel per propoſ. </s>
  <s xml:id="echoid-s36383" xml:space="preserve">43. </s>
  <s xml:id="echoid-s36384" xml:space="preserve">no-<lb/>ſtrorum triang. </s>
  <s xml:id="echoid-s36385" xml:space="preserve">ſphær. </s>
  <s xml:id="echoid-s36386" xml:space="preserve">vt ſinus complementi arcus I L, hoc eſt, vt ſinus deſcenſiuæ circunferen-<lb/>tię E I, ad ſinum totum, ita ſinus complementi arcus B I, vel D I, hoc eſt, ita ſinus arcus declina-<lb/>tionis H I, ad ſinum complementi arcus B L, vel D L, id eſt, ad ſinum circunferentiæ horizonta-<lb/>lis A L, vt prius.</s>
  <s xml:id="echoid-s36387" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1843" type="float" level="2" n="16">
<note position="left" xlink:label="note-0574-09" xlink:href="note-0574-09a" xml:space="preserve">Horizontalis.</note>
<note position="left" xlink:label="note-0574-10" xlink:href="note-0574-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36388" xml:space="preserve">DENIQVE circunferentia horaria B I, vel D I, complementum eſt declinationis dati pa-<lb/>
<anchor type="note" xlink:label="note-0574-11a" xlink:href="note-0574-11"/>
ralleli: </s>
  <s xml:id="echoid-s36389" xml:space="preserve">Et Verticalis E H, eſt diſtantia Solis à meridie, ac propterea vtraque ignota eſſe <lb/>non poterit.</s>
  <s xml:id="echoid-s36390" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1844" type="float" level="2" n="17">
<note position="left" xlink:label="note-0574-11" xlink:href="note-0574-11a" xml:space="preserve">Horaria. <lb/>Verticalis.</note>
</div>
<pb o="559" file="0575" n="575" rhead="LIBER SEXTVS."/>
</div>
<div xml:id="echoid-div1846" type="section" level="1" n="478">
<head xml:id="echoid-head507" style="it" xml:space="preserve">CONSTRVCTIO HOROLOGII HORIZONT ALIS, <lb/>Verticalis, ac Meridiani, ex ſupradictis ſex circun-<lb/>ferentĳs. CAP. IX.</head>
<p>
  <s xml:id="echoid-s36391" xml:space="preserve">HOROLOGIVM horizontale conſtruitur ex circunferentijs horizontalibus, &amp; </s>
  <s xml:id="echoid-s36392" xml:space="preserve">deſcen-<lb/>
<anchor type="note" xlink:label="note-0575-01a" xlink:href="note-0575-01"/>
ſiuis ad ſingulas horas inuentis pro data latitudine loci. </s>
  <s xml:id="echoid-s36393" xml:space="preserve">Nam horizontales indicant vm-<lb/>brarum latitudines, &amp; </s>
  <s xml:id="echoid-s36394" xml:space="preserve">deſcenſiuę earundem longitudines, quemadmodum in horologio horizon <lb/>tali ſuperioris lib. </s>
  <s xml:id="echoid-s36395" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s36396" xml:space="preserve">Horizontales enim circunferentiæ hic illos arcus referunt, quos ibi <lb/>latitudines vmbrarum nominauimus: </s>
  <s xml:id="echoid-s36397" xml:space="preserve">complementa autem circunferentiarum deſcenſiuarum <lb/>
<anchor type="note" xlink:label="note-0575-02a" xlink:href="note-0575-02"/>
altitudines Solis ſupra Horizontem metiuntur, vt in cap. </s>
  <s xml:id="echoid-s36398" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36399" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s36400" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s36401" xml:space="preserve">Quod vt pla-<lb/>
<anchor type="note" xlink:label="note-0575-03a" xlink:href="note-0575-03"/>
nius fiat, vnicum exemplum in medium afferemus. </s>
  <s xml:id="echoid-s36402" xml:space="preserve">In prima figura cap. </s>
  <s xml:id="echoid-s36403" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36404" xml:space="preserve">inuenta eſt circunfe-<lb/>rentia horizontalis C p, pro hora 23. </s>
  <s xml:id="echoid-s36405" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36406" xml:space="preserve">in tropico ♋, quæ borealis eſt, &amp; </s>
  <s xml:id="echoid-s36407" xml:space="preserve">occidentalis. </s>
  <s xml:id="echoid-s36408" xml:space="preserve">Om-<lb/>nes autem horę (vt intelligas, quę boreales ſint, &amp; </s>
  <s xml:id="echoid-s36409" xml:space="preserve">quę auſtrales) quarũ perpendiculares ad diame-<lb/>trum cuiuſque paralleli in Analemmate cap. </s>
  <s xml:id="echoid-s36410" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36411" xml:space="preserve">ductę cadunt in portionem diametri inter Hori-<lb/>zontis diametrum, &amp; </s>
  <s xml:id="echoid-s36412" xml:space="preserve">diametrum Verticalis, boreales ſunt, ſeptentrionalesve, reſpectu Verticalis <lb/>circuli, aliæ vero, quarum perpendiculares cadunt in portionem diametri paralleli inter circunfe <lb/>rentiam circuli Meridiani, &amp; </s>
  <s xml:id="echoid-s36413" xml:space="preserve">diametrum Verticalis, auſtrales ſunt. </s>
  <s xml:id="echoid-s36414" xml:space="preserve">Nam ſi Meridianus in pro-<lb/>prio ſitu collocetur, ita vt H, ad polum arcticum, &amp; </s>
  <s xml:id="echoid-s36415" xml:space="preserve">I, ad antarcticũ ſpectet, ſeparabit Verticalis dia <lb/>meter A C, portionem borealem A D C, ab auſtrali A B C. </s>
  <s xml:id="echoid-s36416" xml:space="preserve">Item ſi Analemma ita inuertatur, vt <lb/>
<anchor type="note" xlink:label="note-0575-04a" xlink:href="note-0575-04"/>
I, ad arcticum polum, &amp; </s>
  <s xml:id="echoid-s36417" xml:space="preserve">H, ad antarcticum ſpectet, rectaq́ue a b, ſit diameter tropici ♋, vt in diui <lb/>ſione Analemmatis in horas ab or. </s>
  <s xml:id="echoid-s36418" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36419" xml:space="preserve">occ factum eſt in cap. </s>
  <s xml:id="echoid-s36420" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36421" xml:space="preserve">ſeparabit eadem diameter Verticalis <lb/>C A, portionem borealem C B A, ab auſtrali C D A. </s>
  <s xml:id="echoid-s36422" xml:space="preserve">Cognoſci tamen etiam poſſunt horæ borea <lb/>les ab auſtralibus per doctrinam ſinuum. </s>
  <s xml:id="echoid-s36423" xml:space="preserve">Omnes enim horæ, quarum diſtantiæ à meridie maio-<lb/>res ſunt ea, quam Sol habet in Verticali circulo poſitus, quæ ex propoſ. </s>
  <s xml:id="echoid-s36424" xml:space="preserve">36. </s>
  <s xml:id="echoid-s36425" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36426" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36427" xml:space="preserve">elicitur, ſunt bo-<lb/>reales, reliquæ vero auſtrales. </s>
  <s xml:id="echoid-s36428" xml:space="preserve">Vel etiam hoc modo. </s>
  <s xml:id="echoid-s36429" xml:space="preserve">Horæ, quarum deſcenſiuæ circunferentiæ <lb/>maiores ſunt ea, quæ deprehenditur, Sole in Verticali conſtituto, ſunt boreales, auſtrales vero re-<lb/>liquæ. </s>
  <s xml:id="echoid-s36430" xml:space="preserve">Itaque circunferentiæ horizontali C p, inuentæ accipiemus in horologio horizontali ſu-<lb/>perioris lib. </s>
  <s xml:id="echoid-s36431" xml:space="preserve">à puncto D, occidentali verſus boream C, arcum ſimilem D e, (quod facile fiet, ſi ex <lb/>E, circulus deſcribatur æqualis Meridiano Analemmatis, in quo circunfeiẽtiæ ſunt inuentæ, &amp;</s>
  <s xml:id="echoid-s36432" xml:space="preserve">c.) <lb/></s>
  <s xml:id="echoid-s36433" xml:space="preserve">
<anchor type="note" xlink:label="note-0575-05a" xlink:href="note-0575-05"/>
In rectam enim e E f, occulte ductam proijcietur vmbra ſtyli. </s>
  <s xml:id="echoid-s36434" xml:space="preserve">Rurſus pro eadem hora 23. </s>
  <s xml:id="echoid-s36435" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s36436" xml:space="preserve">in tropico ♋, inuenta eſt in eodem Analemmate cap. </s>
  <s xml:id="echoid-s36437" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36438" xml:space="preserve">circunferentia deſcenſiua C r, ita vt ar-<lb/>cus r B, altitudinem Solis ſupra Horizontem metiatur. </s>
  <s xml:id="echoid-s36439" xml:space="preserve">Si igitur in ſecunda figura propoſ. </s>
  <s xml:id="echoid-s36440" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36441" xml:space="preserve">ſupe-<lb/>rioris lib. </s>
  <s xml:id="echoid-s36442" xml:space="preserve">quæ horologium horizontale ſequitur, ex D, circulus deſcribatur Meridiano Analem-<lb/>matis æqualis, &amp; </s>
  <s xml:id="echoid-s36443" xml:space="preserve">in eo à recta A D, ſumatur arcus æqualis circunferentiæ deſcenſiuæ C r, vel à re-<lb/>cta B C, arcus æqualis arcui altitudinis Solis r B, &amp; </s>
  <s xml:id="echoid-s36444" xml:space="preserve">à termino dicti arcus per D, centrum ducatur <lb/>recta, abſcindet hæc ex recta G I, longitudinem vmbræ, quam ſi transferamus beneficio circini in <lb/>rectam E f, in horologio vſque ad f, habebimus f, punctum horæ 23. </s>
  <s xml:id="echoid-s36445" xml:space="preserve">ab occ in tropico ♋. </s>
  <s xml:id="echoid-s36446" xml:space="preserve">Idem <lb/>punctum f, reperiemus, ſi ex cap. </s>
  <s xml:id="echoid-s36447" xml:space="preserve">7. </s>
  <s xml:id="echoid-s36448" xml:space="preserve">inuenta fuerit deſcenſiua circunferentia pro dicta hora 23. </s>
  <s xml:id="echoid-s36449" xml:space="preserve">per <lb/>ſinus. </s>
  <s xml:id="echoid-s36450" xml:space="preserve">Nam ex eius complemento, quod altitudinem Solis metitur ſupra Horizontem, inuenie-<lb/>
<anchor type="note" xlink:label="note-0575-06a" xlink:href="note-0575-06"/>
mus in tabula propoſ. </s>
  <s xml:id="echoid-s36451" xml:space="preserve">2. </s>
  <s xml:id="echoid-s36452" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s36453" xml:space="preserve">longitudinem vmbræ, quam ſi ex recta H I, iuxta horolo-<lb/>gium horizontale poſita accipiamus, transferamusq́ue in rectam E f, in horologio, inuentum erit <lb/>punctum f, vt prius. </s>
  <s xml:id="echoid-s36454" xml:space="preserve">Eodem modo de alijs horis omnibus iudicandum erit, vt earum puncta re-<lb/>periantur, &amp;</s>
  <s xml:id="echoid-s36455" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36456" xml:space="preserve">Totum autem horologium horizontale abſoluetur, vt in præcedenti lib. <lb/></s>
  <s xml:id="echoid-s36457" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s36458" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1846" type="float" level="2" n="1">
<note position="right" xlink:label="note-0575-01" xlink:href="note-0575-01a" xml:space="preserve">Quo pacto ho-<lb/>rizontale hoto-<lb/>logium cõſ<unsure/>trua <lb/>tur ex circunfe <lb/>ten@iis horizon <lb/>talibus, ac de <lb/>ſeenſiuis.</note>
<note position="left" xlink:label="note-0575-02" xlink:href="note-0575-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0575-03" xlink:href="note-0575-03a" xml:space="preserve">Qua ratione in <lb/>Analẽma@e ho-<lb/>ræ boreales ab <lb/>auſtralibus di-<lb/>ſcernantur.</note>
<note position="left" xlink:label="note-0575-04" xlink:href="note-0575-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0575-05" xlink:href="note-0575-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0575-06" xlink:href="note-0575-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s36459" xml:space="preserve">VERTICALE horologiũ eodem modo ex circunferentijs Verticalibus, horarijsq́; </s>
  <s xml:id="echoid-s36460" xml:space="preserve">inuen-<lb/>
<anchor type="note" xlink:label="note-0575-07a" xlink:href="note-0575-07"/>
tis pro ſingulis horis ad datam loci latitudinem cõponitur. </s>
  <s xml:id="echoid-s36461" xml:space="preserve">Verticales enim circunferẽtię latitudi <lb/>nes vmbrarum, &amp; </s>
  <s xml:id="echoid-s36462" xml:space="preserve">horariæ, quarum cõplementa altitudines Solis ſupra Verticalẽ circulum mon-<lb/>ſtrant, earundem longitudines exhibent, quemadmodum in horologio Verticali ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s36463" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s36464" xml:space="preserve">Solum hoc intereſt, Verticales circunferentias eſſe complementa illorum arcuum, quos <lb/>
<anchor type="note" xlink:label="note-0575-08a" xlink:href="note-0575-08"/>
in præcedenti lib. </s>
  <s xml:id="echoid-s36465" xml:space="preserve">latitudines vmbrarum in horologio Verticali appellauimus, cum in Verticali <lb/>circulo initium ſumant à communi ſectione Meridiani, &amp; </s>
  <s xml:id="echoid-s36466" xml:space="preserve">Verticalis, nempe à Zenith, non autẽ <lb/>à communi ſectione Horizontis, &amp; </s>
  <s xml:id="echoid-s36467" xml:space="preserve">Verticalis, vt latitudines vmbrarum ſuperioris lib. </s>
  <s xml:id="echoid-s36468" xml:space="preserve">Vnde in <lb/>horologio non erunt computandæ à recta B D, communi ſectione plani horologii, &amp; </s>
  <s xml:id="echoid-s36469" xml:space="preserve">Horizontis, <lb/>qui Verticalis eſt ipſius Verticalis, veluti latitudines vmbrarum, ſed à recta A C, communi ſectio <lb/>ne plani horologii, &amp; </s>
  <s xml:id="echoid-s36470" xml:space="preserve">Meridiani: </s>
  <s xml:id="echoid-s36471" xml:space="preserve">hac tamen lege, vt Verticales circunferentiæ illarum horarum, <lb/>quæ ſupra Horizontem exiſtunt, ſumantur in circulo ex E, loco ſtyli deſcripto, (qui Meridiano <lb/>Analemmatis ſit æqualis) à puncto A, verſus D, vel B, prout orientales fuerint, aut occidentales; <lb/></s>
  <s xml:id="echoid-s36472" xml:space="preserve">Verticales vero circunferentiæ horarum infra Horizontem exiſtentium, quales ſunt 5. </s>
  <s xml:id="echoid-s36473" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36474" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36475" xml:space="preserve">7. </s>
  <s xml:id="echoid-s36476" xml:space="preserve">à <lb/>mer. </s>
  <s xml:id="echoid-s36477" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36478" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36479" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36480" xml:space="preserve">in tropico ♑. </s>
  <s xml:id="echoid-s36481" xml:space="preserve">Item 13. </s>
  <s xml:id="echoid-s36482" xml:space="preserve">14. </s>
  <s xml:id="echoid-s36483" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36484" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36485" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36486" xml:space="preserve">in eodem tropico, &amp;</s>
  <s xml:id="echoid-s36487" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36488" xml:space="preserve">accipiantur in <lb/>eodem circulo à puncto C. </s>
  <s xml:id="echoid-s36489" xml:space="preserve">Reliqua omnia fiant, vt in Verticali horologio ad auſtrum ſpectante
<pb o="560" file="0576" n="576" rhead="GNOMONICES"/>
ſuperioris lib. </s>
  <s xml:id="echoid-s36490" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s36491" xml:space="preserve">Boreale autem horologium Verticale ex auſtrali conficietur, vt in ſupe-<lb/>rioribus lib. </s>
  <s xml:id="echoid-s36492" xml:space="preserve">non ſemel dictum eſt. </s>
  <s xml:id="echoid-s36493" xml:space="preserve">Quod tamen eodem modo ex propriis circunferentijs Verti <lb/>calibus horarijsq́ue in facie boreali Verticalis circuli inuentis deſcribi poteſt, ſi diligenter cõſide-<lb/>retur, quæ horæ in facie Verticalis boreali ſint orientales, &amp; </s>
  <s xml:id="echoid-s36494" xml:space="preserve">quæ occidentales, &amp;</s>
  <s xml:id="echoid-s36495" xml:space="preserve">c.</s>
  <s xml:id="echoid-s36496" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1847" type="float" level="2" n="2">
<note position="right" xlink:label="note-0575-07" xlink:href="note-0575-07a" xml:space="preserve">Qua ratione ho <lb/>rologium Verti <lb/>cale ex circun-<lb/>ferentijs Verti-<lb/>calibus, hora-<lb/>riisq́ue:<unsure/> compo-<lb/>natur.</note>
<note position="left" xlink:label="note-0575-08" xlink:href="note-0575-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36497" xml:space="preserve">MERIDIANVM denique horologium eadem ratione ex circunferentijs meridianis, &amp; </s>
  <s xml:id="echoid-s36498" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0576-01a" xlink:href="note-0576-01"/>
hectemoriis pro ſingulis horis ad datam loci latitudinem inuentis deſcribitur. </s>
  <s xml:id="echoid-s36499" xml:space="preserve">Nam circunferen-<lb/>tiæ meridianę indicant vmbrarum latitudines, hectemoriæ vero, quarum complementa altitudi-<lb/>nes Solis ſupra Meridianum metiuntur, longitudines earundem exhibent, quemadmodũ in ho-<lb/>rologio Meridiano ſuperioris lib. </s>
  <s xml:id="echoid-s36500" xml:space="preserve">declarauimus. </s>
  <s xml:id="echoid-s36501" xml:space="preserve">Hoc tantum intereſt, circunferentias meridia-<lb/>nas, quoniam in Analemmate initium ſumunt ab Horizontis diametro, non eſſe in horologio Me <lb/>
<anchor type="note" xlink:label="note-0576-02a" xlink:href="note-0576-02"/>
ridiano ſuperioris lib. </s>
  <s xml:id="echoid-s36502" xml:space="preserve">inchoandas in circulo ex C, loco ſtyli deſcripto à linea æquinoctiali D F, <lb/>quemadmodum latitudines vmbrarum in ſuperiori lib. </s>
  <s xml:id="echoid-s36503" xml:space="preserve">ſupputatæ, ſed à linea horizontali A B: <lb/></s>
  <s xml:id="echoid-s36504" xml:space="preserve">hac tamen lege, &amp; </s>
  <s xml:id="echoid-s36505" xml:space="preserve">conditione, vt circunferentiæ meridianę horarum illarum, quæ boreales ſunt, <lb/>(quas quidem cognoſcemus ex Analem mate, vt ſupra dictum eſt) ſumantur in dicto circulo, qui <lb/>Meridiano Analem matis ſit æqualis, à puncto boreali B, in horologio orientali, &amp; </s>
  <s xml:id="echoid-s36506" xml:space="preserve">à puncto A, in <lb/>occidentali, verſus partes ſuperiores, circunferentiæ vero meridianæ horarum auſtralium ab alte-<lb/>ro extremo lineæ horizontalis, nempe à puncto auſtrali. </s>
  <s xml:id="echoid-s36507" xml:space="preserve">Item vt horæ antemeridianæ in orien-<lb/>tali horologio, &amp; </s>
  <s xml:id="echoid-s36508" xml:space="preserve">pomeridianę in occidentali deſcribantur. </s>
  <s xml:id="echoid-s36509" xml:space="preserve">Quòd ſi puncta etiam illarum hora-<lb/>rum tropici ♑, quæ infra Horizontem exiſtunt, quales ſunt 5. </s>
  <s xml:id="echoid-s36510" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36511" xml:space="preserve">7. </s>
  <s xml:id="echoid-s36512" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36513" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36514" xml:space="preserve">med noc. </s>
  <s xml:id="echoid-s36515" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36516" xml:space="preserve">13. </s>
  <s xml:id="echoid-s36517" xml:space="preserve">14. </s>
  <s xml:id="echoid-s36518" xml:space="preserve"><lb/>15. </s>
  <s xml:id="echoid-s36519" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36520" xml:space="preserve">inuenienda ſint, ſumendæ erunt earum circunferentiæ meridianæ à termino Horizon <lb/>
<anchor type="note" xlink:label="note-0576-03a" xlink:href="note-0576-03"/>
talis lineæ auſtrali verſus partes inferiores. </s>
  <s xml:id="echoid-s36521" xml:space="preserve">Reliqua omnia perficienda erunt, vt in Meridiano ho <lb/>rologio ſuperioris lib. </s>
  <s xml:id="echoid-s36522" xml:space="preserve">dictum eſt.</s>
  <s xml:id="echoid-s36523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1848" type="float" level="2" n="3">
<note position="left" xlink:label="note-0576-01" xlink:href="note-0576-01a" xml:space="preserve">Quomodo @o-<lb/>rologium Meri <lb/>dianum ex ci@-<lb/>cunferentu<unsure/>s me <lb/>ridianis, hecte-<lb/>moriisq́ue de-<lb/>ſcribatur,</note>
<note position="left" xlink:label="note-0576-02" xlink:href="note-0576-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0576-03" xlink:href="note-0576-03a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1850" type="section" level="1" n="479">
<head xml:id="echoid-head508" style="it" xml:space="preserve">SCHOLIVW.</head>
<p style="it">
  <s xml:id="echoid-s36524" xml:space="preserve">CAETERVM ſi quis velit horologium Verticale, &amp; </s>
  <s xml:id="echoid-s36525" xml:space="preserve">Meridianum deſcribere, quemadmodum <lb/>
<anchor type="note" xlink:label="note-0576-04a" xlink:href="note-0576-04"/>
horizontale, non ſecus, ac ſi Verticalis, &amp; </s>
  <s xml:id="echoid-s36526" xml:space="preserve">Meridianus circulus eſſent Horizontes, inueſtigandæ erunt <lb/>circunferentię horizontales, deſcenſiuæ{q́ue} in Verticali circulo, &amp; </s>
  <s xml:id="echoid-s36527" xml:space="preserve">Meridiano, vt in Horizonte. </s>
  <s xml:id="echoid-s36528" xml:space="preserve">Nam ho-<lb/>rizontales cir cunferentiæ repræſentabunt arcus illos, quos in ſuperiori lib. </s>
  <s xml:id="echoid-s36529" xml:space="preserve">latitudines vmbrarum in ho-<lb/>rologio Verticali, &amp; </s>
  <s xml:id="echoid-s36530" xml:space="preserve">Meridiano nominauimus, deſcenſiuarum autem complementa erunt altitudines <lb/>
<anchor type="note" xlink:label="note-0576-05a" xlink:href="note-0576-05"/>
Solis ſupra Verticalem, ac Meridianum. </s>
  <s xml:id="echoid-s36531" xml:space="preserve">Vnde in Verticali horologio ſuperioris lib. </s>
  <s xml:id="echoid-s36532" xml:space="preserve">ſument horizon-<lb/>tales circunferentiæ initium à linca horizontali, quæ communis ſectio eſt plani horologĳ, &amp; </s>
  <s xml:id="echoid-s36533" xml:space="preserve">Horizontis, <lb/>qui Verticalis eſt ipſius Verticalis, quemadmodum &amp; </s>
  <s xml:id="echoid-s36534" xml:space="preserve">latitudines vmbrarum ab eadem horizontali li-<lb/>nea ſupputatæ ſunt: </s>
  <s xml:id="echoid-s36535" xml:space="preserve">non aliter, quàm in horizontali horologio factum eſt, in quo latitudines vmbrarũ, <lb/>ſiue circunferentiæ horizontales initium ſumpſerunt à recta B D, communi ſectione plani horologĳ, &amp; </s>
  <s xml:id="echoid-s36536" xml:space="preserve"><lb/>Verticalis circuli ipſius Horizontis. </s>
  <s xml:id="echoid-s36537" xml:space="preserve">Pari ratione in Meridiano horologio inchoandæ erunt circunferen-<lb/>tiæ horizontales à linea ęquinoctiali, quæ communis ſectio eſt plani horologĳ, &amp; </s>
  <s xml:id="echoid-s36538" xml:space="preserve">Aequatoris, qui Verti-<lb/>calis est ipſius Meridiani, quemadmodum &amp; </s>
  <s xml:id="echoid-s36539" xml:space="preserve">latitudincs vmbrarum ab eadem linea æquinoctiali nume-<lb/>ratæ ſunt in ſuperiori lib. </s>
  <s xml:id="echoid-s36540" xml:space="preserve">Obſeruandum autem diligenter eſt, vt dictæ circunſerentiæ horizontales in <lb/>Verticali horologio modo ſupra lineam horizontalem, modo infra eandem accipiantur, prout illarum ho <lb/>ræſupra Horizontem existunt, vel infra eundem, quemadmodum in Verticali horologio ſuperioris lib. <lb/></s>
  <s xml:id="echoid-s36541" xml:space="preserve">
<anchor type="note" xlink:label="note-0576-06a" xlink:href="note-0576-06"/>
explicauimns: </s>
  <s xml:id="echoid-s36542" xml:space="preserve">Item vt horizontales circunferentiæ in horologio Meridiano ſumantur modo ſupra lineã£ <lb/>æquinoctialem, hoc est, verſus ſeptentrionem, modo infra, id eſt, verſus auſtrum, prout illarum horę bo-<lb/>reales ſunt, auſtralesve, reſpectu Aequatoris: </s>
  <s xml:id="echoid-s36543" xml:space="preserve">Denique vt circunferentiæ horizontales illarum horarũ, <lb/>quæ minus abſunt à meridie, quàm 6. </s>
  <s xml:id="echoid-s36544" xml:space="preserve">horis, hoc est, quàm grad. </s>
  <s xml:id="echoid-s36545" xml:space="preserve">90. </s>
  <s xml:id="echoid-s36546" xml:space="preserve">incipiant à puncto D, ſuperiori li-<lb/>neæ æquinoctialis, illarum vero horarum circunferentiæ horizontales, quæ maiorem diſtantiam à meri-<lb/>die habent, quam 6. </s>
  <s xml:id="echoid-s36547" xml:space="preserve">hor. </s>
  <s xml:id="echoid-s36548" xml:space="preserve">id eſt, quàm grad. </s>
  <s xml:id="echoid-s36549" xml:space="preserve">90. </s>
  <s xml:id="echoid-s36550" xml:space="preserve">initium ſumant à puncto F, inferiori æquinoctialis lineæ, <lb/>vt in Meridiano horologio ſuperioris lib. </s>
  <s xml:id="echoid-s36551" xml:space="preserve">declaratum eſt. </s>
  <s xml:id="echoid-s36552" xml:space="preserve">Denique vt omnia, quæ in horologio Verticali, <lb/>Meridiano{q́ue} de latitudimbus vmbrarum dicta ſunt, hic de circunferentĳs horizontalibus intelligantur.</s>
  <s xml:id="echoid-s36553" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1850" type="float" level="2" n="1">
<note position="left" xlink:label="note-0576-04" xlink:href="note-0576-04a" xml:space="preserve">Quo pacto tam <lb/>Verticale horo <lb/>logium, quàm <lb/>Meridianú de <lb/>ſcribi poſſit ad <lb/>modum horolo <lb/>gii horizontalis.</note>
<note position="left" xlink:label="note-0576-05" xlink:href="note-0576-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0576-06" xlink:href="note-0576-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s36554" xml:space="preserve">HOC autem modo in Verticali circulo, tanquàm Horizonte, inquiremus circunferentias horizonta <lb/>
<anchor type="note" xlink:label="note-0576-07a" xlink:href="note-0576-07"/>
<anchor type="note" xlink:label="note-0576-08a" xlink:href="note-0576-08"/>
les, deſcenſiuas{q́ue}. </s>
  <s xml:id="echoid-s36555" xml:space="preserve">In Analemmate capitis 6. </s>
  <s xml:id="echoid-s36556" xml:space="preserve">intelligatur A C, diameter Verticalis pro diametro Ho-<lb/>rizontis, atque adeo B D, diameter Horizontis pro diametro Verticalis reſpectu Verticalis. </s>
  <s xml:id="echoid-s36557" xml:space="preserve">Et quoniã <lb/>ſupra faciem auſtralem Verticalis circuli polus antarcticus est eleuatus, ponitur autem I, eſſe polus <lb/>antar cticus, exiſtent omnes horæ, quarum perpendiculares in portiones diametrorum parallelorum in <lb/>ſemicirculo A B C, contentas cadunt, ſupra faciem auſtralem Verticalis circuli, earum{q́ue} circunferen-<lb/>tiæ deſcenſiuæ, ac horizontales inueſtigandæ erunt pro horologio auſtrali: </s>
  <s xml:id="echoid-s36558" xml:space="preserve">aliæ vero horæ ſupra faciem <lb/>borealem exiſtent, car@m{q́ue} circunfrrentiæ deſcenſiuæ, horizontales{q́ue} pro horologio borealierunt inda-<lb/>gandæ. </s>
  <s xml:id="echoid-s36559" xml:space="preserve">Itaque ſi per puncta horarum in diametris parallelorum ad B E, ſemidiametrum Verticalis, re-<lb/>ſpectu Verticalis, perpendiculares ducantur, abſcindent hæ ex circunferentia Meridiani circunferentias <lb/>deſcenſiuas initium ſumentes à puncto B, vertice capitis, ſeu polo Verticalis, tanquàm Horizontis, qua-<lb/>rum complementa altitudines Solis ſupra faciem auſtralem Verticalis, tanquàm ſupra Horizontem,
<pb o="561" file="0577" n="577" rhead="LIBER SEXTVS."/>
metiuntur, vt ex demonſtratis in cap. </s>
  <s xml:id="echoid-s36560" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36561" xml:space="preserve">perſpicuum eſt. </s>
  <s xml:id="echoid-s36562" xml:space="preserve">Si vero per eadem puncta horarum in paral-<lb/>lelorum diametris ad A C, diametrum Verticalis, tanquam Horizontis, perpendiculares ducantur, at-<lb/>que ex his abſcindantur rectæ æquales interuallis horarum inter diametros parallelorum, &amp; </s>
  <s xml:id="echoid-s36563" xml:space="preserve">circunfe-<lb/>rentias eorundem, imprimendo in dictis perpendicularibus puncta, per quæ ex centro E, rectæ emittan-<lb/>tur, auferent hæ ex circunferentia Meridiani circunferentias horizontales initium ſumentes à puncto B; <lb/></s>
  <s xml:id="echoid-s36564" xml:space="preserve">quæ nimirum in horologio Verticali, tanquam horizontali, latitudines vmbrarum manifeſtant, numeran <lb/>dę{q́ue} ſunt à linea horizontali horologĳ ſupra vel infra, prout puncta horarum in diametris parallelorum <lb/>ſupra Horizontis diametrum B D, exiſtunt, aut infra.</s>
  <s xml:id="echoid-s36565" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1851" type="float" level="2" n="2">
<note position="left" xlink:label="note-0576-07" xlink:href="note-0576-07a" xml:space="preserve">Inuentio circun <lb/>fetentiarum de-<lb/>ſcenſiuatum, &amp; <lb/>horizontalium, <lb/>ex Analemma-<lb/>te, in Verticali <lb/>@@ulo, tanquã <lb/>Horizonte.</note>
<note position="left" xlink:label="note-0576-08" xlink:href="note-0576-08a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s36566" xml:space="preserve">PER doctrinam quoque ſinuum commodiſſime deſcenſiuas circunferentias in Verticali circulo, ve-<lb/>
<anchor type="note" xlink:label="note-0577-01a" xlink:href="note-0577-01"/>
luti Horizonte, reperiemus, ſi per propoſ. </s>
  <s xml:id="echoid-s36567" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36568" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36569" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36570" xml:space="preserve">inuestigentur altitudines Solis ſupra Verticalem cir-<lb/>
<anchor type="note" xlink:label="note-0577-02a" xlink:href="note-0577-02"/>
culum, tanquam Horizontem. </s>
  <s xml:id="echoid-s36571" xml:space="preserve">Complementa enim harum altitudinum dabunt circunferentias deſcen-<lb/>ſiuas. </s>
  <s xml:id="echoid-s36572" xml:space="preserve">Horizontales vero circunferentiæ per propoſ. </s>
  <s xml:id="echoid-s36573" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36574" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36575" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36576" xml:space="preserve">inuenientur. </s>
  <s xml:id="echoid-s36577" xml:space="preserve">Arcus enim, qui ibi inueſti-<lb/>g<unsure/>antur, latitudines vmbrarum ſunt@, ſiue circunferentiæ horizontales reſpectu Verticalis circuli, tan-<lb/>quam Horizontis. </s>
  <s xml:id="echoid-s36578" xml:space="preserve">Vel certe huiuſmodi circunferentiæ inquirendæ erunt, vt in cap. </s>
  <s xml:id="echoid-s36579" xml:space="preserve">7. </s>
  <s xml:id="echoid-s36580" xml:space="preserve">ſumendo Vertica-<lb/>lem pro Horizonte, &amp; </s>
  <s xml:id="echoid-s36581" xml:space="preserve">Horizontem pro Verticali, &amp;</s>
  <s xml:id="echoid-s36582" xml:space="preserve">c.</s>
  <s xml:id="echoid-s36583" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1852" type="float" level="2" n="3">
<note position="right" xlink:label="note-0577-01" xlink:href="note-0577-01a" xml:space="preserve">Inuentio circun <lb/>ferẽtiarum de-<lb/>ſcenſiuatũ, hori <lb/>zontaliumque <lb/>in Verucali, @an <lb/>quam Horizon <lb/>te, per doctrinã <lb/>ſinuum.</note>
<note position="left" xlink:label="note-0577-02" xlink:href="note-0577-02a" xml:space="preserve">10</note>
</div>
<p style="it">
  <s xml:id="echoid-s36584" xml:space="preserve">AT vero in Meridiano, veluti Horizonte, indagabimus circunferentias deſcenſiuas, atque horizon-<lb/>
<anchor type="note" xlink:label="note-0577-03a" xlink:href="note-0577-03"/>
tales, hac ratione. </s>
  <s xml:id="echoid-s36585" xml:space="preserve">In eodem Analemmate capitis 6. </s>
  <s xml:id="echoid-s36586" xml:space="preserve">intelligatur circulus A B C D, eſſe circulus horæ <lb/>6. </s>
  <s xml:id="echoid-s36587" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36588" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36589" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36590" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36591" xml:space="preserve">tanquam Meridianus ipſius Meridiani, veluti Horizontis. </s>
  <s xml:id="echoid-s36592" xml:space="preserve">Et quoniam Meridia-<lb/>nus, tanquam Horizon, tranſit per polos mundi H, I, erit H I, communis ſectio Meridiani, tanquam Ho <lb/>rizontis, &amp; </s>
  <s xml:id="echoid-s36593" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s36594" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36595" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36596" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36597" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36598" xml:space="preserve">tanquam Meridiani reſpectu Meridiani: </s>
  <s xml:id="echoid-s36599" xml:space="preserve">atque adeo <lb/>
<anchor type="note" xlink:label="note-0577-04a" xlink:href="note-0577-04"/>
diameter Aequatoris F G, erit veluti diameter Verticalis ipſius Meridiani, tanquam Horizontis. </s>
  <s xml:id="echoid-s36600" xml:space="preserve">Si <lb/>igitur per puncta horarum in diametris parallelorum ad F E, ſemidiametrum A@quatoris, tanquam Ver <lb/>ticalis reſpectu Meridiani, veluti Horizontis, perpendiculares ducantur, auferent hæ ex circunferentia <lb/>circuli A B C D, deſcenſiuas circunferentias initium ſumentes à puncto F, vertice capitis, ſeu polo Me-<lb/>ridiani, vt Horizontis, quarum complementa altitudines Solis ſupra Meridianum, veluti Horizontem, <lb/>metiuntur, vt ex demonstratis liquet. </s>
  <s xml:id="echoid-s36601" xml:space="preserve">Rurſus ſi ex ſemidiametris parallelorum (quæ quidem perpendicu <lb/>lares ſunt per eadem puncta horarum in parallelorum ſemidiametris ad H I, diametrum Meridiani, tan <lb/>quam Horizontis, ductæ) abſcindantur rectæ æquales interuallis horarum inter diametros, &amp; </s>
  <s xml:id="echoid-s36602" xml:space="preserve">circunſe-<lb/>rentias parallelorum, imprimendo puncta in ipſis, per quæ ex centro E, emittantur rectæ, auferent hæ <lb/>ex circunferentia circuli A B C D, circunferentias horizontales initium ſumentes à puncto F; </s>
  <s xml:id="echoid-s36603" xml:space="preserve">quæ vide-<lb/>
<anchor type="note" xlink:label="note-0577-05a" xlink:href="note-0577-05"/>
licet in horologio Meridiano, velut horizontali, latitudines vmbrarum patefaciunt, numer andæ{q́ue} ſunt <lb/>à linea æquinoctiali horologĳ, vt de latitudinibus vmbrarum diximus in horologio Meridiano ſu-<lb/>perioris lib.</s>
  <s xml:id="echoid-s36604" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1853" type="float" level="2" n="4">
<note position="right" xlink:label="note-0577-03" xlink:href="note-0577-03a" xml:space="preserve">Inuentio circũ-<lb/>ferentiarum de-<lb/>ſcenſiuarum, ho <lb/>rizontaliumq́ue <lb/>@ Meridiano, <lb/>tanquam Hori-<lb/>zonte, ex Ana-<lb/>lemniate.</note>
<note position="left" xlink:label="note-0577-04" xlink:href="note-0577-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0577-05" xlink:href="note-0577-05a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s36605" xml:space="preserve">QVONIAM vero circulus Analemmatis A B C D, non refert Meridianum, ſed circulum ho-<lb/>
<anchor type="note" xlink:label="note-0577-06a" xlink:href="note-0577-06"/>
ræ 6. </s>
  <s xml:id="echoid-s36606" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36607" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36608" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36609" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36610" xml:space="preserve">qui Meridianus eſt reſpectu Meridiani, instituenda erit diuiſio parallelorum <lb/>in horas hoc modo. </s>
  <s xml:id="echoid-s36611" xml:space="preserve">Ex parallelo ♋, &amp; </s>
  <s xml:id="echoid-s36612" xml:space="preserve">♑, ſeorſum deſcripto in cap. </s>
  <s xml:id="echoid-s36613" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36614" xml:space="preserve">transferantur omnes horæ, ini-<lb/>tio facto à puncto meridiei a, in parallelum ♋, Analemmatis, initio facto à puncto, vbi recta I H, pro-<lb/>ducta parallelum ſecat, tanquam communis ſectio paralleli, ac Meridiani, veluti Horizontis, &amp; </s>
  <s xml:id="echoid-s36615" xml:space="preserve">in quo <lb/>puncto meridies fit: </s>
  <s xml:id="echoid-s36616" xml:space="preserve">ita tamen, vt earum horarum interualla, quæ plus diſtant, quàm 6. </s>
  <s xml:id="echoid-s36617" xml:space="preserve">horis, aut quàm <lb/>quadrante, à puncto a, ſumantur à puncto b, in parallelo ſeorſum deſcripto. </s>
  <s xml:id="echoid-s36618" xml:space="preserve">Ita enim diuiſus erit paral-<lb/>
<anchor type="note" xlink:label="note-0577-07a" xlink:href="note-0577-07"/>
lelus ♋, in Analemmate in horas. </s>
  <s xml:id="echoid-s36619" xml:space="preserve">Eodem modo alĳ paralleli diuidentur, ſi ſeorſum prius deſcriban-<lb/>tur, &amp; </s>
  <s xml:id="echoid-s36620" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36621" xml:space="preserve">Quod intelligendum eſt de horis æqualibus ab or. </s>
  <s xml:id="echoid-s36622" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s36623" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36624" xml:space="preserve">de horis inæqualibus. </s>
  <s xml:id="echoid-s36625" xml:space="preserve">Nam quod ad <lb/>horas à mer. </s>
  <s xml:id="echoid-s36626" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36627" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36628" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36629" xml:space="preserve">attinet, diuiſio initium habebit à punctis, in quibus circulus A B C D, à pa-<lb/>rallelis diuiditur, vt in ſuperioribus, itatamen, vt illa puncta non pertineant ad horam 12. </s>
  <s xml:id="echoid-s36630" xml:space="preserve">meridiei, vel <lb/>mediæ noctis, vt antea, ſed ad horam 6. </s>
  <s xml:id="echoid-s36631" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36632" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s36633" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36634" xml:space="preserve">puncta vero, vbi recta I H, producta pa-<lb/>rallelos ſecat, pertineant ad horam 12. </s>
  <s xml:id="echoid-s36635" xml:space="preserve">meridiei, vel mediæ noctis, non autem ad horam 6. </s>
  <s xml:id="echoid-s36636" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36637" xml:space="preserve">vel med. <lb/></s>
  <s xml:id="echoid-s36638" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36639" xml:space="preserve">vt prius.</s>
  <s xml:id="echoid-s36640" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1854" type="float" level="2" n="5">
<note position="right" xlink:label="note-0577-06" xlink:href="note-0577-06a" xml:space="preserve">Qua ratione <lb/>Analemma di-<lb/>u@datur in ho-<lb/>ras, vt circunfe-<lb/>rentiæ deſcen@i-<lb/>uæ, horizonta-<lb/>le@q́ue in Meri <lb/>diano, veluti <lb/>Horizonte, re-<lb/>periantur.</note>
<note position="left" xlink:label="note-0577-07" xlink:href="note-0577-07a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Inuentio circũ-<lb/>ferentiarum de <lb/>ſcenſiuarũ, ho-<lb/>rizontaliumque <lb/>in Meridiano, <lb/>tanquam Hori <lb/>zonte, ex doct@@ <lb/>na ſinuum.</note>
<p style="it">
  <s xml:id="echoid-s36641" xml:space="preserve">CIRCVNFERENTIAE deſcenſiuæ in Meridiano, tanquam Horizonte, inuenientur per ſi-<lb/>nus, ſi ex ĳs, quæ propoſ. </s>
  <s xml:id="echoid-s36642" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36643" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s36644" xml:space="preserve">ſcripſimus, altitudines Solis ſupra Meridianum, vcluti Hori-<lb/>zontem, inuestigentur. </s>
  <s xml:id="echoid-s36645" xml:space="preserve">Harum enim altitudinum complementa dabunt circunferentias deſcenſiuas. <lb/></s>
  <s xml:id="echoid-s36646" xml:space="preserve">
<anchor type="note" xlink:label="note-0577-09a" xlink:href="note-0577-09"/>
Horizontales vero circunferentiæ in eodem Meridiano, veluti Horizonte, reperientur, vt propoſ. </s>
  <s xml:id="echoid-s36647" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36648" xml:space="preserve">ſu-<lb/>perioris lib. </s>
  <s xml:id="echoid-s36649" xml:space="preserve">demonſtratum eſt, cum arcus ibi inueſtigati ſint latitudines vmbrarum, ſiue circunferentiæ <lb/>horizontales, reſpectu Meridiani, tanquam Horizontis. </s>
  <s xml:id="echoid-s36650" xml:space="preserve">Poſſunt tamen tam deſcenſiuæ circunferentiæ, <lb/>quàm horizontales inuestigari, vt in cap. </s>
  <s xml:id="echoid-s36651" xml:space="preserve">7. </s>
  <s xml:id="echoid-s36652" xml:space="preserve">ſi Meridianus pro Horizonte, &amp; </s>
  <s xml:id="echoid-s36653" xml:space="preserve">Aequator pro Vertica-<lb/>
<anchor type="note" xlink:label="note-0577-10a" xlink:href="note-0577-10"/>
li accipiatur.</s>
  <s xml:id="echoid-s36654" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1855" type="float" level="2" n="6">
<note position="left" xlink:label="note-0577-09" xlink:href="note-0577-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0577-10" xlink:href="note-0577-10a" xml:space="preserve">Inuentio circun <lb/>ferent@arum de <lb/>ſcenſiuar<gap/>, a<unsure/> <lb/>horizontalium <lb/>in circulo horæ <lb/>6. a mer. &amp; med. <lb/>noc. tanquam <lb/>Horizonte, ex <lb/>Analemmate, <lb/>pro conſtructio-<lb/>ne horologii po <lb/>laris.</note>
</div>
<p style="it">
  <s xml:id="echoid-s36655" xml:space="preserve">EADEM ratione pro conſtructione horologĳ polaris inuenientur circunferentię deſcenſiuæ, hori-<lb/>zontales{q́ue} in circulo horæ 6. </s>
  <s xml:id="echoid-s36656" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36657" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36658" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36659" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36660" xml:space="preserve">tanquam Horizonte. </s>
  <s xml:id="echoid-s36661" xml:space="preserve">In Analemmate enim eodem cap. <lb/></s>
  <s xml:id="echoid-s36662" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36663" xml:space="preserve">deſcripto recta H I, est communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s36664" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s36665" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36666" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s36667" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36668" xml:space="preserve">veluti Ho-<lb/>rizontis; </s>
  <s xml:id="echoid-s36669" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36670" xml:space="preserve">propterea F G, diameter Aequatoris, communis ſectio eiuſdem Meridiani, &amp; </s>
  <s xml:id="echoid-s36671" xml:space="preserve">Verticalis <lb/>proprii ipſius circuli horę 6. </s>
  <s xml:id="echoid-s36672" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36673" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36674" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36675" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36676" xml:space="preserve">tanquam Horizontis. </s>
  <s xml:id="echoid-s36677" xml:space="preserve">Diuiſio tamen parallelorum in ho <lb/>ras inſtituenda eſt, vt cap. </s>
  <s xml:id="echoid-s36678" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36679" xml:space="preserve">docuimus, quia circulus Analemmatis A B C D, eſt Meridianus reſpectu
<pb o="562" file="0578" n="578" rhead="GNOMONICES"/>
circuli horæ 6. </s>
  <s xml:id="echoid-s36680" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36681" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36682" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36683" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36684" xml:space="preserve">tan<unsure/>quam Horizontis.</s>
  <s xml:id="echoid-s36685" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s36686" xml:space="preserve">PER ſinus reperientur eædem circunferentiæ deſcenſiuæ, horizontales{q́ue} in circulo horæ 6. </s>
  <s xml:id="echoid-s36687" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36688" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36689" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0578-01a" xlink:href="note-0578-01"/>
med. </s>
  <s xml:id="echoid-s36690" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36691" xml:space="preserve">tanquam Horizonte, quemadmodum in Meridiano, ſi circulus horæ 6. </s>
  <s xml:id="echoid-s36692" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36693" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36694" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36695" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36696" xml:space="preserve">ſuma-<lb/>tur pro Horizonte, &amp; </s>
  <s xml:id="echoid-s36697" xml:space="preserve">Aequator pro Verticali. </s>
  <s xml:id="echoid-s36698" xml:space="preserve">Horologium autem ipſum polare ex circunferentĳs de-<lb/>ſcenſiuis, horizontalibus{q́ue} in circulo horæ 6. </s>
  <s xml:id="echoid-s36699" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36700" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36701" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36702" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36703" xml:space="preserve">tanquam Horizonte, inuentis deſcribe-<lb/>tur, vt propoſ, 5. </s>
  <s xml:id="echoid-s36704" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s36705" xml:space="preserve">præcepimus. </s>
  <s xml:id="echoid-s36706" xml:space="preserve">Horizontales enim circunferentiæ ſunt, quas ibi latitudi-<lb/>nes vmbr arum diximus: </s>
  <s xml:id="echoid-s36707" xml:space="preserve">complementa vero deſcenſiuarum ſunt altitudines Solis, ex quibus longitudines <lb/>vmbrarum elicientur, vt propoſ. </s>
  <s xml:id="echoid-s36708" xml:space="preserve">2. </s>
  <s xml:id="echoid-s36709" xml:space="preserve">eiuſdem ſuperioris lib. </s>
  <s xml:id="echoid-s36710" xml:space="preserve">docuimus.</s>
  <s xml:id="echoid-s36711" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1856" type="float" level="2" n="7">
<note position="left" xlink:label="note-0578-01" xlink:href="note-0578-01a" xml:space="preserve">Inuentio earun <lb/>dem circun e-<lb/>@en@@arũ in eo-<lb/>dem circulo per <lb/>finus.</note>
</div>
<p style="it">
  <s xml:id="echoid-s36712" xml:space="preserve">VT autem horologium æquinoctiale componamus, non indigemus circunferentĳs horizontalibus, de-<lb/>
<anchor type="note" xlink:label="note-0578-02a" xlink:href="note-0578-02"/>
ſcenſiuisq́, in Aequatore, tanquam Horizonte, inuentis; </s>
  <s xml:id="echoid-s36713" xml:space="preserve">quoniam horæ æquales diuidunt integros circu-<lb/>
<anchor type="note" xlink:label="note-0578-03a" xlink:href="note-0578-03"/>
los ex loco ſtyli deſcriptos, &amp; </s>
  <s xml:id="echoid-s36714" xml:space="preserve">horæ inæquales eorundem circulorum portiones, quæ arcubus diurnis, no-<lb/>cturnis{q́ue} reſpondent, in partes æquales, vt ex ĳs conſtat, quæ lib. </s>
  <s xml:id="echoid-s36715" xml:space="preserve">2. </s>
  <s xml:id="echoid-s36716" xml:space="preserve">demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s36717" xml:space="preserve">49. </s>
  <s xml:id="echoid-s36718" xml:space="preserve">50. </s>
  <s xml:id="echoid-s36719" xml:space="preserve">58. <lb/></s>
  <s xml:id="echoid-s36720" xml:space="preserve">59. </s>
  <s xml:id="echoid-s36721" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36722" xml:space="preserve">60. </s>
  <s xml:id="echoid-s36723" xml:space="preserve">Item altitudines Solis ſupra Aequatorem in omnibus horis cuiuſcunque paralleli æquales <lb/>ſunt, cum parallelus quilibet ſit Almucantarath Solis, hoc est, circulus non maximus Aequatori, velu-<lb/>ti Horizonti, æquidiſtans. </s>
  <s xml:id="echoid-s36724" xml:space="preserve">Vnde facile in æquinoctiali horologio omnes horæ deſcribẽtur, ſine circunferen <lb/>tĳs horizontalibus, deſcenſiuis{q́ue}, diuidendo circulos ex loco ſtyli deſcriptos, vel eorum portiones arcu-<lb/>bus diurnis, nocturnis{q́ue} reſpondentes in partes æquales, vt in prædictis propoſitionibus tradidimus. </s>
  <s xml:id="echoid-s36725" xml:space="preserve"><lb/>Qui tamen eaſdem beneficio illarum circunferentiarum potius deſcribere volet, deprehendet omnes cir-<lb/>cunferentias horizontales ab eo inuentas, Sole in quolibet parallelo exiſtente, ſecare Meridianum Ana-<lb/>
<anchor type="note" xlink:label="note-0578-04a" xlink:href="note-0578-04"/>
lemmatis in partes æquales; </s>
  <s xml:id="echoid-s36726" xml:space="preserve">Vnam autem eandem{q́ue} deſcenſiuam circunfer entiam eſſe omnium horarum <lb/>
<anchor type="note" xlink:label="note-0578-05a" xlink:href="note-0578-05"/>
eiuſdem par alleli. </s>
  <s xml:id="echoid-s36727" xml:space="preserve">Quod ita demonſtrabimus. </s>
  <s xml:id="echoid-s36728" xml:space="preserve">In Analemmate cap. </s>
  <s xml:id="echoid-s36729" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36730" xml:space="preserve">ſi F G, diameter Aequatoris in-<lb/>telligatur eſſe diameter Horizontis cuiuſpiam, erit axis mundi H I, diameter circuli Verticalis reſpectu <lb/>Aequatoris, tanquam Horizontis, nempe communis ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s36731" xml:space="preserve">circuli horæ 6. </s>
  <s xml:id="echoid-s36732" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36733" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36734" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s36735" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36736" xml:space="preserve">qui Verticalis est ipſius Aequatoris, tanquam Horizontis. </s>
  <s xml:id="echoid-s36737" xml:space="preserve">Itaque ſi exempli gratia, per puncta ho-<lb/>rarum in diametro paralleli ♋, in quæ nimirum cadunt perpendiculares ex horis in parallelo ♋, ad di-<lb/>ctam diametrum demiſſæ, ducantur ad H I, diametrum Verticalis ipſius Aequatoris, tanquam Hori-<lb/>zontis, lineæ perpendiculares, non different hæ à diametro M N, paralleli ♋. </s>
  <s xml:id="echoid-s36738" xml:space="preserve">Quare ex demonſtratis, <lb/>in omnibus horis dicti paralleli circunferentia deſcenſiua erit H M, vel H N. </s>
  <s xml:id="echoid-s36739" xml:space="preserve">Rurſus ſi per d, punctum <lb/>horæ 24. </s>
  <s xml:id="echoid-s36740" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36741" xml:space="preserve">in diametro paralleli ♋, ad F G, diametrum Aequatoris, tanquam Horizontis, perpen-<lb/>
<anchor type="note" xlink:label="note-0578-06a" xlink:href="note-0578-06"/>
dicularis ducatur θ ε, ſecans circunferentiam Meridiani in ε, (quæ à perpendiculari ed, ducta ex hora <lb/>
<anchor type="note" xlink:label="note-0578-07a" xlink:href="note-0578-07"/>
24. </s>
  <s xml:id="echoid-s36742" xml:space="preserve">tropici ♋, ad eiuſdem tropici diametrum non differt) auferatur{q́ue} recta θ μ, rectæ d e, æqualis, &amp; </s>
  <s xml:id="echoid-s36743" xml:space="preserve"><lb/>per μ, ex centro E, recta emittatur E μ, ſecans Meridiani circunferentiam in π, erit, ex demonſtratis, <lb/>I π, circunferentia horizontalis prohora 24. </s>
  <s xml:id="echoid-s36744" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36745" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s36746" xml:space="preserve">Quoniam vero θ μ, ipſi d e, æqualis <lb/>eſt; </s>
  <s xml:id="echoid-s36747" xml:space="preserve">ſi dematur communis d μ, erit quoque reliqua θ d, reliquæ μ e, æqualis; </s>
  <s xml:id="echoid-s36748" xml:space="preserve">Vel certe quando punctum <lb/>μ, cadit in rectam θ d, (quod accidit in horis prope puncta M, &amp; </s>
  <s xml:id="echoid-s36749" xml:space="preserve">N, vbi interualla horarum inter dia-<lb/>metrum paralleli, &amp; </s>
  <s xml:id="echoid-s36750" xml:space="preserve">eiuſdem circunferentiam minora ſunt, quàm recta θ d.) </s>
  <s xml:id="echoid-s36751" xml:space="preserve">ſi addatur recta d μ, fiet <lb/>θ d, ipſi μ e, ęqualis: </s>
  <s xml:id="echoid-s36752" xml:space="preserve">Eſt autem θ d, ipſi E m, ęqualis, ob parallelogrammum θ m. </s>
  <s xml:id="echoid-s36753" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s36754" xml:space="preserve">μ e, eidem <lb/>
<anchor type="note" xlink:label="note-0578-08a" xlink:href="note-0578-08"/>
E m, æqualis erit. </s>
  <s xml:id="echoid-s36755" xml:space="preserve">Cum ergo μ e, E m, parallelæ etiam ſint; </s>
  <s xml:id="echoid-s36756" xml:space="preserve">fit vt ſi ducatur ex m, centro paralleli ad <lb/>horam 24. </s>
  <s xml:id="echoid-s36757" xml:space="preserve">in parallelo recta me, rectæ E μ, me, parallelæ quoque ſint. </s>
  <s xml:id="echoid-s36758" xml:space="preserve">Quare &amp; </s>
  <s xml:id="echoid-s36759" xml:space="preserve">anguli π E I, e m I, <lb/>
<anchor type="note" xlink:label="note-0578-09a" xlink:href="note-0578-09"/>
æquales erunt. </s>
  <s xml:id="echoid-s36760" xml:space="preserve">Non aliter demonſtrabim{us}, rect{as}, quę ex m, centro paralleli ad alias horas paralleli <lb/>
<anchor type="note" xlink:label="note-0578-10a" xlink:href="note-0578-10"/>
<anchor type="note" xlink:label="note-0578-11a" xlink:href="note-0578-11"/>
ducuntur, parallelas eſſe rectis, quæ ex centro E, ductæ terminant in circunferentia Meridiani circunfe-<lb/>rentias horizontales earundem horarum; </s>
  <s xml:id="echoid-s36761" xml:space="preserve">ac propterea &amp; </s>
  <s xml:id="echoid-s36762" xml:space="preserve">angulos ad m, angulis ad E, æquales eſſe. </s>
  <s xml:id="echoid-s36763" xml:space="preserve">Quam <lb/>
<anchor type="note" xlink:label="note-0578-12a" xlink:href="note-0578-12"/>
ob rem cum anguli ad m, omnes ſint æquales, quòd æqualibus peripherĳs inſiſtant ad centrum m, erunt <lb/>
<anchor type="note" xlink:label="note-0578-13a" xlink:href="note-0578-13"/>
quoque omnes anguli ad E, æquales; </s>
  <s xml:id="echoid-s36764" xml:space="preserve">atque idcirco peripheriæ Meridiani, quibus inſiſtunt, ęquales inter ſe <lb/>erunt: </s>
  <s xml:id="echoid-s36765" xml:space="preserve">hoc eſt, circunferentiæ horizontales ſecabunt Meridiani circunferentiam in partes æquales. </s>
  <s xml:id="echoid-s36766" xml:space="preserve">quod <lb/>demonſtr andum ſuſcepimus.</s>
  <s xml:id="echoid-s36767" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1857" type="float" level="2" n="8">
<note position="left" xlink:label="note-0578-02" xlink:href="note-0578-02a" xml:space="preserve">Horologium <lb/>æquinoctia@e fa <lb/>cilius de@eribi-<lb/>tur ſine circun-<lb/>ferenuis hori-<lb/>z<unsure/>ontalibus, de-<lb/>ſcenſiuisque, vt <lb/>in lib 2. @radi-<lb/>tum eſt.</note>
<note position="left" xlink:label="note-0578-03" xlink:href="note-0578-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0578-04" xlink:href="note-0578-04a" xml:space="preserve">In Aequatore, <lb/>tanquam Hori-<lb/>zonte, circunfe <lb/>rentiæ horizon-<lb/>ta@es ſecant Me <lb/>ridianum Ana-<lb/>lemmatis in par <lb/>tes ęquale@, Sole <lb/>exi@tente in quo <lb/>uis parallelo; in <lb/>omnibus autem <lb/>horis eiuſdem <lb/>patalleli vna ea <lb/>demque eſt cir-<lb/>cunferentia de-<lb/>ſcenſiua.</note>
<note position="left" xlink:label="note-0578-05" xlink:href="note-0578-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0578-06" xlink:href="note-0578-06a" xml:space="preserve">Inuen@@o circũ-<lb/>ferentiarum de-<lb/>ſcenſiuarum, &amp; <lb/>horizontalium <lb/>in Aequatore <lb/>tanquam Ho@i <lb/>zonte, ex Ana-<lb/>lemm<unsure/>ate, pro <lb/>conitructione <lb/>horologii æqui <lb/>noctialis.</note>
<note position="left" xlink:label="note-0578-07" xlink:href="note-0578-07a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0578-08" xlink:href="note-0578-08a" xml:space="preserve">34. primi</note>
<note position="left" xlink:label="note-0578-09" xlink:href="note-0578-09a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0578-10" xlink:href="note-0578-10a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0578-11" xlink:href="note-0578-11a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0578-12" xlink:href="note-0578-12a" xml:space="preserve">27. tertĳ.</note>
<note position="left" xlink:label="note-0578-13" xlink:href="note-0578-13a" xml:space="preserve">26. tertĳ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s36768" xml:space="preserve">EX his ef@icitur, ſiex centro paralleli ad ſingulas horas in circunferentia paralleli rectæ ducantur, <lb/>rect{as} ex centro E, emiſſ{as}, quæ illis æquidiſtent, auferre ex Meridiano Analemmatis circunferenti{as} <lb/>horizontales, quæ nimirum in horologio æquinoctiali latitudines vmbrarum indicant, quarum principiũ <lb/>in axe H I, ſtatuitur: </s>
  <s xml:id="echoid-s36769" xml:space="preserve">quemadmodum recta E π, ipſi m e, parallela aufert horizontalem circunferen-<lb/>
<anchor type="note" xlink:label="note-0578-14a" xlink:href="note-0578-14"/>
tiam I π, pro hora 24. </s>
  <s xml:id="echoid-s36770" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36771" xml:space="preserve">vt oſtendimus. </s>
  <s xml:id="echoid-s36772" xml:space="preserve">Quæ cum ita ſint, recte lib. </s>
  <s xml:id="echoid-s36773" xml:space="preserve">2. </s>
  <s xml:id="echoid-s36774" xml:space="preserve">pręcepimus, horologium <lb/>æquinoctiale deſcribendum eſſe per diuiſionem circulorum in 24. </s>
  <s xml:id="echoid-s36775" xml:space="preserve">partes æquales, initio facto vel à linea <lb/>meridiana, vel ab horizontali, prout horæ à mer. </s>
  <s xml:id="echoid-s36776" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36777" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36778" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36779" xml:space="preserve">aut ab or. </s>
  <s xml:id="echoid-s36780" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s36781" xml:space="preserve">delineandæ proponun-<lb/>tur: </s>
  <s xml:id="echoid-s36782" xml:space="preserve">Vel certe per diuiſionem arcnum diurnorum in 12. </s>
  <s xml:id="echoid-s36783" xml:space="preserve">partes æquales, ſi horæ inæquales ſint deſcriben-<lb/>dæ; </s>
  <s xml:id="echoid-s36784" xml:space="preserve">vt opus non ſit, circunferentias horizontales inquirere: </s>
  <s xml:id="echoid-s36785" xml:space="preserve">quandoquidem ſpatia horaria inter ſe æqua-<lb/>lia ſunt, vt demonſtrauimus.</s>
  <s xml:id="echoid-s36786" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1858" type="float" level="2" n="9">
<note position="left" xlink:label="note-0578-14" xlink:href="note-0578-14a" xml:space="preserve">50</note>
</div>
<p style="it">
  <s xml:id="echoid-s36787" xml:space="preserve">QVONIAM vero E μ, ęqualis est ſemidiametro paralleli me, hoc eſt, ſinui complementi de-<lb/>clinationis, &amp; </s>
  <s xml:id="echoid-s36788" xml:space="preserve">recta θ μ, rectæ de, hoc est, ſinui diſtantiæ Solis à meridie, est{q́ue} vt E μ, ad μ θ, ita E π, <lb/>
<anchor type="note" xlink:label="note-0578-15a" xlink:href="note-0578-15"/>
ſinus totus ad rectam, quæ ex π, æquidiſtans duceretur ipſi θ @, hoc eſt, ad ſinum complementi circunfe-<lb/>
<anchor type="note" xlink:label="note-0578-16a" xlink:href="note-0578-16"/>
rentiæ horizontalis I π: </s>
  <s xml:id="echoid-s36789" xml:space="preserve">Si fiat, vt ſinus declinationis ad ſinum diſtantiæ Solis à meridie cognitum in <lb/>partibus ſinus totius maximi circuli, (cognoſcetur autem hic ſinus in dictis partibus, vt ſupra oſtendi-
<pb o="563" file="0579" n="579" rhead="LIBER SEXTVS."/>
mus) ita ſinus totus ad aliud, inuenietur ſinus complementi circunferentiæ horizontalis: </s>
  <s xml:id="echoid-s36790" xml:space="preserve">ac propterea <lb/>
<anchor type="note" xlink:label="note-0579-01a" xlink:href="note-0579-01"/>
complementum hoc, vna cum circunferentia horizontali, notum erit. </s>
  <s xml:id="echoid-s36791" xml:space="preserve">Pro deſcenſiua autem circunfe-<lb/>rentia cuiuſcunque horæ accipienda est declinatio paralleli, vt patet.</s>
  <s xml:id="echoid-s36792" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1859" type="float" level="2" n="10">
<note position="left" xlink:label="note-0578-15" xlink:href="note-0578-15a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0578-16" xlink:href="note-0578-16a" xml:space="preserve">Inuen@o circun <lb/>feren@@arum h o <lb/>rizontalium de-<lb/>ſcenſiuarumq́ue</note>
<note position="right" xlink:label="note-0579-01" xlink:href="note-0579-01a" xml:space="preserve">in Aequatore, <lb/>ex doctrina ſi-<lb/>nuum.</note>
</div>
<p style="it">
  <s xml:id="echoid-s36793" xml:space="preserve">INVENTIS autem circunferentĳs horizontalibus, ſupput abim{us} ill{as} in circulo ex loco ſtyli <lb/>
<anchor type="note" xlink:label="note-0579-02a" xlink:href="note-0579-02"/>
deſcripto à linea horę 6. </s>
  <s xml:id="echoid-s36794" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s36795" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36796" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36797" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36798" xml:space="preserve">quæ lineam meridianam in loco ſtyli ad angulos rectos ſecat, <lb/>eſt{q́ue} inſtar lineæ Verticalis ipſi{us} æquinoctialis horologĳ, vt horologium æquinoctiale componamus, ſur-<lb/>ſum quidem verſus in ſuperiorihorologio æquinoctiali pro horis, quę maiorem diſtantiam habent à meri-<lb/>die, quàm 6. </s>
  <s xml:id="echoid-s36799" xml:space="preserve">horar@m, deorſum vero, ſi minorem: </s>
  <s xml:id="echoid-s36800" xml:space="preserve">Contra vero in inferiori. </s>
  <s xml:id="echoid-s36801" xml:space="preserve">Per puncta enim hoc modo <lb/>inuenta ducendæ ſunt lineæ horariæ ex centro, ſeulocoſtyli.</s>
  <s xml:id="echoid-s36802" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1860" type="float" level="2" n="11">
<note position="right" xlink:label="note-0579-02" xlink:href="note-0579-02a" xml:space="preserve">Deſcriptio horo <lb/>logii æquino-<lb/>ctialis ex circun <lb/>ferentijs hori-<lb/>zon@alibus de-<lb/>ſcenſiuisq́ue in <lb/>Aequatore, tan-<lb/>quam Horizon <lb/>te, inuentis.</note>
</div>
<p style="it">
  <s xml:id="echoid-s36803" xml:space="preserve">CAETERVM omnia, quæ in hoc cap. </s>
  <s xml:id="echoid-s36804" xml:space="preserve">eius{q́ue} ſcholio de horologiorum deſcriptione ex circunferen <lb/>
<anchor type="note" xlink:label="note-0579-03a" xlink:href="note-0579-03"/>
tĳs horizontalib{us}, deſcenſiuis diximus, meli{us} intelligentur, ſi in memoriam renocentur ea, quæ in ſu-<lb/>periori lib. </s>
  <s xml:id="echoid-s36805" xml:space="preserve">de eorundem horologiorum deſcriptione tradidimus. </s>
  <s xml:id="echoid-s36806" xml:space="preserve">Horizontales enim circunferentiæ eæ-<lb/>dem hic ſunt, quæ ibi latitudines vmbrarum, &amp; </s>
  <s xml:id="echoid-s36807" xml:space="preserve">deſcenſiuæ eædem, quę complementa altitud inum So-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s36808" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36809" xml:space="preserve">Quamobrem ſi quid minus recte hic intelligetur, recurrendum erit ad ſuperiorem lib. </s>
  <s xml:id="echoid-s36810" xml:space="preserve">Superua-<lb/>caneum enim duximus, ea, quæ ibi ſcripſimus, hoc loco repetere.</s>
  <s xml:id="echoid-s36811" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1861" type="float" level="2" n="12">
<note position="left" xlink:label="note-0579-03" xlink:href="note-0579-03a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1863" type="section" level="1" n="480">
<head xml:id="echoid-head509" style="it" xml:space="preserve">DE HOROLOGIIS DECLINANTIBVS VEL AVERTICALI, <lb/>vel ab Horizonte, &amp; inclinatis ad Horizontem, &amp; ĳs, quæ à Ver-<lb/>ticali declinant, &amp; ſimul ad Horizontem ſunt <lb/>
inclinata. CAP. X.</head>
<p>
  <s xml:id="echoid-s36812" xml:space="preserve">VT TANDEM per Analemma horologium declinans à Verticali, aut ab Horizonte; </s>
  <s xml:id="echoid-s36813" xml:space="preserve">Itẽ <lb/>inclinatum ad Horizontem, vel declinans à Verticali, &amp; </s>
  <s xml:id="echoid-s36814" xml:space="preserve">inclinatum ſimul ad Horizontem <lb/>deſcribatur, inueſtiganda primum erit, per propoſ. </s>
  <s xml:id="echoid-s36815" xml:space="preserve">29. </s>
  <s xml:id="echoid-s36816" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36817" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36818" xml:space="preserve">altitudo poli ſupra circulum maxi-<lb/>mum, cui horologium deſcribendum ęquidiſtat, &amp; </s>
  <s xml:id="echoid-s36819" xml:space="preserve">ad hanc altitudinem Analemma fabricãdum, <lb/>obſeruando diligenter, num polus arcticus, antarcticusve eleuetur ſupra faciem illam circuli ma-<lb/>ximi, cui horologium æquidiſtat: </s>
  <s xml:id="echoid-s36820" xml:space="preserve">quod quidem cognoſcemus ex ijs, quæ ad initium ſcholij pro-<lb/>poſ. </s>
  <s xml:id="echoid-s36821" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36822" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s36823" xml:space="preserve">ſcripſimus. </s>
  <s xml:id="echoid-s36824" xml:space="preserve">In exemplum ſit propoſitum hoc Analemma circulo illi maxi-<lb/>mo congruens, cui ho-<lb/>
<anchor type="figure" xlink:label="fig-0579-01a" xlink:href="fig-0579-01"/>
rologium declinans à <lb/>
<anchor type="note" xlink:label="note-0579-05a" xlink:href="note-0579-05"/>
Verticali circulo gr. </s>
  <s xml:id="echoid-s36825" xml:space="preserve">30. <lb/></s>
  <s xml:id="echoid-s36826" xml:space="preserve">æquidiſtat, quod &amp; </s>
  <s xml:id="echoid-s36827" xml:space="preserve">pro-<lb/>poſ. </s>
  <s xml:id="echoid-s36828" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36829" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36830" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36831" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36832" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s36833" xml:space="preserve"><lb/>5. </s>
  <s xml:id="echoid-s36834" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36835" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36836" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s36837" xml:space="preserve"><lb/>Nam altitudo poli DH, <lb/>complectitur grad. </s>
  <s xml:id="echoid-s36838" xml:space="preserve">40. </s>
  <s xml:id="echoid-s36839" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s36840" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36841" xml:space="preserve">quantam videli-<lb/>cer ſupra dictum circu-<lb/>lum inuenimus, vt ex ſu <lb/>perioribus conſtat. </s>
  <s xml:id="echoid-s36842" xml:space="preserve">Et <lb/>
<anchor type="note" xlink:label="note-0579-06a" xlink:href="note-0579-06"/>
quoniam polus antarcti <lb/>cus ſupra illius circuli <lb/>faciem auſtralem eleua-<lb/>tur, ſi ponamus H, po-<lb/>lum antarcticum, erit <lb/>k L, diameter paralleli <lb/>♑, &amp; </s>
  <s xml:id="echoid-s36843" xml:space="preserve">M N, diameter <lb/>paralleli ♋; </s>
  <s xml:id="echoid-s36844" xml:space="preserve">ita vt K R, <lb/>ſit arcus ſemidiurnus <lb/>♑, &amp; </s>
  <s xml:id="echoid-s36845" xml:space="preserve">L R, arcus ſemino <lb/>
<anchor type="note" xlink:label="note-0579-07a" xlink:href="note-0579-07"/>
cturnus, at M P, arcus <lb/>ſemidiurnus ♋, &amp; </s>
  <s xml:id="echoid-s36846" xml:space="preserve">N P, <lb/>ſeminocturnus, ſi præ-<lb/>dictus circulus maxi-<lb/>mus eſſet Horizon, in <lb/>quo polus antarcticus <lb/>conſpicuus ſit. </s>
  <s xml:id="echoid-s36847" xml:space="preserve">E contrario vero, quia polus arcticus ſupra eiuſdem circuli faciem borealem ele-<lb/>uatur, ſi ponatur H, polus arcticus, erit k L, diameter paralleli ♋, &amp; </s>
  <s xml:id="echoid-s36848" xml:space="preserve">M N, diameter paralleli ♑; </s>
  <s xml:id="echoid-s36849" xml:space="preserve">ita <lb/>vt k R, ſit arcus ſemidiurnus ♋, &amp; </s>
  <s xml:id="echoid-s36850" xml:space="preserve">L R, arcus ſeminocturnus, at M P, arcus ſemidiurnus ♑, &amp; </s>
  <s xml:id="echoid-s36851" xml:space="preserve"><lb/>N P, arcus ſeminocturnus. </s>
  <s xml:id="echoid-s36852" xml:space="preserve">Circulus autem A B C D, non refert Meridianum eius loci, in quo <lb/>horologium conſtruitur, ſed Meridianum illius loci, in quo dictus circulus maximus eſſet Hori-
<pb o="564" file="0580" n="580" rhead="GNOMONICES"/>
zon, tranſiens nimirum per polos mundi, &amp; </s>
  <s xml:id="echoid-s36853" xml:space="preserve">per polos illius circuli maximi: </s>
  <s xml:id="echoid-s36854" xml:space="preserve">Cuius circuli maxi-<lb/>mi, veluti Horizontis, &amp; </s>
  <s xml:id="echoid-s36855" xml:space="preserve">dicti Meridiani communis ſectio eſt B D; </s>
  <s xml:id="echoid-s36856" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36857" xml:space="preserve">eiuſdem Meridiani, ac Ver-<lb/>ticalis proprii illius circuli maximi communis ſectio A C.</s>
  <s xml:id="echoid-s36858" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1863" type="float" level="2" n="1">
  <figure xlink:label="fig-0579-01" xlink:href="fig-0579-01a">
    <image file="0579-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0579-01"/>
  </figure>
<note position="left" xlink:label="note-0579-05" xlink:href="note-0579-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0579-06" xlink:href="note-0579-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0579-07" xlink:href="note-0579-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36859" xml:space="preserve">DEINDE Analemma ita conſtructum diuidendum eſt in horas, vt circunferentiæ horizon-<lb/>tales, deſcenſiuæq́ue ad ſingulas horas poſſint inueniri. </s>
  <s xml:id="echoid-s36860" xml:space="preserve">Quæ diuiſio (quoniam ab ea, quam cap. <lb/></s>
  <s xml:id="echoid-s36861" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36862" xml:space="preserve">expoſuimus, differt, cum circulus A B C D, non ſit Meridianus illius loci, in quo horæ deſcri-<lb/>bendæ ſunt) ita inſtituenda erit.</s>
  <s xml:id="echoid-s36863" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s36864" xml:space="preserve">CIRCA diametrum K L, v. </s>
  <s xml:id="echoid-s36865" xml:space="preserve">g. </s>
  <s xml:id="echoid-s36866" xml:space="preserve">paralleli ♑, ſeorſum expoſitam deſcribatur parallelus ♑, <lb/>
<anchor type="note" xlink:label="note-0580-01a" xlink:href="note-0580-01"/>
K R L R, vna cum R Q R, communi ſectione circuli maximi propoſiti, tanquam Horizontis, &amp; </s>
  <s xml:id="echoid-s36867" xml:space="preserve"><lb/>Meridiani proprii eiuſdem circuli maximi, vt in Analemmate; </s>
  <s xml:id="echoid-s36868" xml:space="preserve">ita vt R K R, ſit portio ♑, ſupra <lb/>
<anchor type="note" xlink:label="note-0580-02a" xlink:href="note-0580-02"/>
faciem auſtralem dicti maximi circuli, tanquam ſupra Horizontem, &amp; </s>
  <s xml:id="echoid-s36869" xml:space="preserve">R L R, portio ♑, ſupra fa-<lb/>ciem borealem oppoſitam, hoc eſt, infra faciem auſtralem: </s>
  <s xml:id="echoid-s36870" xml:space="preserve">Inuenta autem, per propoſ. </s>
  <s xml:id="echoid-s36871" xml:space="preserve">30. </s>
  <s xml:id="echoid-s36872" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36873" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s36874" xml:space="preserve">inclinatione Meridiani proprij circuli maximi propoſiti ad Meridianum Horizontis illius loci, <lb/>in quo horologium fabricandum eſt, quam inuenimus continere grad. </s>
  <s xml:id="echoid-s36875" xml:space="preserve">40. </s>
  <s xml:id="echoid-s36876" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s36877" xml:space="preserve">48. </s>
  <s xml:id="echoid-s36878" xml:space="preserve">vt propoſ. </s>
  <s xml:id="echoid-s36879" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36880" xml:space="preserve"><lb/>lib. </s>
  <s xml:id="echoid-s36881" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36882" xml:space="preserve">diximus, numerabimus eam à puncto K, dextrorſum, aut ſiniſtrorſum, vſque ad S, duce-<lb/>musq́ue ex S, per centrum paralleli rectam S T, pro communi ſectione paralleli, &amp; </s>
  <s xml:id="echoid-s36883" xml:space="preserve">Meridiani Ho-<lb/>rizontis, vna cum X V X, communi ſectione paralleli, &amp; </s>
  <s xml:id="echoid-s36884" xml:space="preserve">Horizontis; </s>
  <s xml:id="echoid-s36885" xml:space="preserve">ita vt S V, æqualis ſit ſegmen <lb/>to N P, diametri ♑, in Analemmate cap. </s>
  <s xml:id="echoid-s36886" xml:space="preserve">6. </s>
  <s xml:id="echoid-s36887" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36888" xml:space="preserve">X S X, ſit arcus diurnus ♑, &amp; </s>
  <s xml:id="echoid-s36889" xml:space="preserve">X T X, nocturnus. </s>
  <s xml:id="echoid-s36890" xml:space="preserve"><lb/>Quoniam vero Meridianus Horizontis occidentalior eſt in Aequatore, ac proinde in omnibus pa <lb/>rallelis, quàm Meridianus proprius propoſiti maximi circuli, cui horologium æquidiſtat, vt pro-<lb/>poſ. </s>
  <s xml:id="echoid-s36891" xml:space="preserve">1. </s>
  <s xml:id="echoid-s36892" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36893" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36894" xml:space="preserve">ſcripſimus; </s>
  <s xml:id="echoid-s36895" xml:space="preserve">Eſt autem K, punctum, in quo Meridianus proprius dati circuli paralle-<lb/>
<anchor type="note" xlink:label="note-0580-03a" xlink:href="note-0580-03"/>
lum ♑, ſecat, &amp; </s>
  <s xml:id="echoid-s36896" xml:space="preserve">S, punctum, vbi Meridianus Horizontis eundem parallelum diuidit; </s>
  <s xml:id="echoid-s36897" xml:space="preserve">erit punctũ <lb/>X, ad dexteram ipſius S, occidentale, aliud vero punctum X, ad ſiniſtram eiuſdem S, orientale. <lb/></s>
  <s xml:id="echoid-s36898" xml:space="preserve">Pro horis igitur inæqualibus diurnis ſecandus eſt arcus diurnus ♑, X K S X, in 12. </s>
  <s xml:id="echoid-s36899" xml:space="preserve">partes æqua-<lb/>les, initio facto à puncto X, orientali, quòd nimirum ad ſiniſtram ipſius S, collocatum eſt. </s>
  <s xml:id="echoid-s36900" xml:space="preserve">Simili-<lb/>ter arcus nocturnus ♑, X R L T R X, ſecandus eſt in 12. </s>
  <s xml:id="echoid-s36901" xml:space="preserve">partes æquales pro horis inæqualibus no <lb/>cturnis, initio facto à puncto X, ad dextram ipſius S, poſito, quod nimirum occidentale eſt. </s>
  <s xml:id="echoid-s36902" xml:space="preserve">Pro <lb/>horis vero à mer. </s>
  <s xml:id="echoid-s36903" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36904" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36905" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36906" xml:space="preserve">totus circulus in 24. </s>
  <s xml:id="echoid-s36907" xml:space="preserve">partes æquales eſt diuidendus, initio facto à <lb/>puncto S, meridiei, ita vt horæ pomeridianæ tendantab S, verſus dextram per X, R, L, vſque ad <lb/>D, antemeridianæ vero, ſiue poſt med. </s>
  <s xml:id="echoid-s36908" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36909" xml:space="preserve">à puncto T, verſus ſiniſtram per R, X, K, vſque ad S. </s>
  <s xml:id="echoid-s36910" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0580-04a" xlink:href="note-0580-04"/>
Pro horis deinde ab ortu idem circulus in 24. </s>
  <s xml:id="echoid-s36911" xml:space="preserve">partes æquales diſtribuendus eſt, facto initio à pun <lb/>cto X, orientali, quod videlicet ad ſiniſtram ipſius S, exiſtit, ita vt punctum X, indicet horam 24. <lb/></s>
  <s xml:id="echoid-s36912" xml:space="preserve">ab ortu, primum autem punctum diuiſionis verſus S, pertineat ad horam 1. </s>
  <s xml:id="echoid-s36913" xml:space="preserve">ab ortu, ſequens ad <lb/>2. </s>
  <s xml:id="echoid-s36914" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s36915" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36916" xml:space="preserve">Pro horis denique ab occaſu diuidendus eſt idem circulus in partes 24. </s>
  <s xml:id="echoid-s36917" xml:space="preserve">æquales, ſumpto <lb/>initio à puncto X, occidentali, quod nimirum ipſi S, ad dexteram collocatur, ita vt punctum X, <lb/>denotet horam 24. </s>
  <s xml:id="echoid-s36918" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36919" xml:space="preserve">primum autem punctum diuiſionis verſus S, pertineat ad horam 23. </s>
  <s xml:id="echoid-s36920" xml:space="preserve"><lb/>ab occ. </s>
  <s xml:id="echoid-s36921" xml:space="preserve">ſequens ad 22. </s>
  <s xml:id="echoid-s36922" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s36923" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36924" xml:space="preserve">Exemplum poſuimus in horis ab occaſu, &amp; </s>
  <s xml:id="echoid-s36925" xml:space="preserve">ortu, vt ex ſigura manife-<lb/>ſtum eſt, in qua numeri exteriores ad horas ♑, ab occ. </s>
  <s xml:id="echoid-s36926" xml:space="preserve">interiores vero ad horas ♑, ab ortu pertinẽt.</s>
  <s xml:id="echoid-s36927" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1864" type="float" level="2" n="2">
<note position="left" xlink:label="note-0580-01" xlink:href="note-0580-01a" xml:space="preserve">Diuiſio Analẽ-<lb/>matis in horas <lb/>pro conſtructio-<lb/>ne horologiorũ <lb/>declinantium, <lb/>&amp; inclinatorũ.</note>
<note position="left" xlink:label="note-0580-02" xlink:href="note-0580-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0580-03" xlink:href="note-0580-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0580-04" xlink:href="note-0580-04a" xml:space="preserve">30</note>
</div>
  <figure>
    <image file="0580-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0580-01"/>
  </figure>
<p>
  <s xml:id="echoid-s36928" xml:space="preserve">OMNES autem horæ, quæ <lb/>
<anchor type="note" xlink:label="note-0580-05a" xlink:href="note-0580-05"/>
in portione R k R, comprehendun <lb/>
<anchor type="note" xlink:label="note-0580-06a" xlink:href="note-0580-06"/>
tur, cadunt ſupra faciem auſtralem <lb/>propoſiti circuli maximi, quæ vero <lb/>in portione R L R, continentur, in <lb/>dictam faciem non cadunt, ſed in <lb/>oppoſitam borealem, ſole exiſtenre <lb/>in principio ♑. </s>
  <s xml:id="echoid-s36929" xml:space="preserve">Igitur omnes ho-<lb/>ræ arcus diurni ♑, in horologio <lb/>propoſito, quod ad auſtrum ſpe-<lb/>ctat, deſcribi poterunt; </s>
  <s xml:id="echoid-s36930" xml:space="preserve">ex horis au-<lb/>tem arcus nocturni ♑, deſcribi po-<lb/>
<anchor type="note" xlink:label="note-0580-07a" xlink:href="note-0580-07"/>
terunt horæ cõprehenſæ inter duas <lb/>rectas X V X, R Q R, quales ſunt <lb/>10. </s>
  <s xml:id="echoid-s36931" xml:space="preserve">11. </s>
  <s xml:id="echoid-s36932" xml:space="preserve">12. </s>
  <s xml:id="echoid-s36933" xml:space="preserve">13. </s>
  <s xml:id="echoid-s36934" xml:space="preserve">14. </s>
  <s xml:id="echoid-s36935" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36936" xml:space="preserve">15. </s>
  <s xml:id="echoid-s36937" xml:space="preserve">quæ quidẽ <lb/>omnes continentur in tropico ♑, <lb/>horologij propoſ. </s>
  <s xml:id="echoid-s36938" xml:space="preserve">10. </s>
  <s xml:id="echoid-s36939" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36940" xml:space="preserve">3. </s>
  <s xml:id="echoid-s36941" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36942" xml:space="preserve">horo <lb/>logij declinantis propoſ. </s>
  <s xml:id="echoid-s36943" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36944" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s36945" xml:space="preserve">5. </s>
  <s xml:id="echoid-s36946" xml:space="preserve">ho <lb/>ra 10. </s>
  <s xml:id="echoid-s36947" xml:space="preserve">excepta, quæ propter ſpatij an <lb/>guſtiam poni non potuit, cum ni-<lb/>mis procul excurrat. </s>
  <s xml:id="echoid-s36948" xml:space="preserve">Ex hac figura <lb/>ita conſtructa facile cognoſcemus, <lb/>quantus ſit arcus diurnus ♑, ſupra faciem auſtralem propoſiti circuli, &amp; </s>
  <s xml:id="echoid-s36949" xml:space="preserve">quantus nocturnus: </s>
  <s xml:id="echoid-s36950" xml:space="preserve">Itẽ
<pb o="565" file="0581" n="581" rhead="LIBER SEXTVS."/>
qua hora eandem faciem Sol in principio ♑, exiſtens illuminare incipiat, aut deſinat, ſi à terra non <lb/>impediatur. </s>
  <s xml:id="echoid-s36951" xml:space="preserve">Ita enim vides Solem ſupra faciem auſtralem oriri paulo ante hor. </s>
  <s xml:id="echoid-s36952" xml:space="preserve">9 {1/2}. </s>
  <s xml:id="echoid-s36953" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36954" xml:space="preserve">occi-<lb/>dere vero, hoc eſt, oriri ſupra oppoſitam faciem borealem aliquanto poſt hor. </s>
  <s xml:id="echoid-s36955" xml:space="preserve">24. </s>
  <s xml:id="echoid-s36956" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36957" xml:space="preserve">Idem ex-<lb/>periri licebit in alijs horis.</s>
  <s xml:id="echoid-s36958" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1865" type="float" level="2" n="3">
<note position="left" xlink:label="note-0580-05" xlink:href="note-0580-05a" xml:space="preserve">Quæ horæ ca-<lb/>dant in faciem <lb/>auſtralem circu <lb/>li maximi pro-<lb/>poſiti, &amp; quæ in <lb/>borealem, quo-<lb/>modo ex figura <lb/>proxima cogno <lb/>ſcatur.</note>
<note position="left" xlink:label="note-0580-06" xlink:href="note-0580-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0580-07" xlink:href="note-0580-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s36959" xml:space="preserve">SI iam circulus K R L R, pro parallelo ♋, accipiatur, erit R L R, portio ♋, ſupra faciem au-<lb/>ſtralem propoſiti circuli maximi, &amp; </s>
  <s xml:id="echoid-s36960" xml:space="preserve">R k R, portio ſupra faciem oppoſitam borealem, vt ex proxi-<lb/>mo Analemmate conſtat: </s>
  <s xml:id="echoid-s36961" xml:space="preserve">At X T X, erit arcus diurnus ♋, &amp; </s>
  <s xml:id="echoid-s36962" xml:space="preserve">X S X, nocturnus. </s>
  <s xml:id="echoid-s36963" xml:space="preserve">Quia vero Meri-<lb/>dianus Horizontis occidentalior eſt in parallelo ♋, quàm Meridianus proprius circuli maximi <lb/>propoſiti, ſicut &amp; </s>
  <s xml:id="echoid-s36964" xml:space="preserve">in alijs, vt ſupra diximus; </s>
  <s xml:id="echoid-s36965" xml:space="preserve">Eſt autem L, punctum, in quo Meridianus proprius <lb/>circuli maximi propoſiti, tanquam Horizontis, parallelum ♋, ſupra Horizontem ſecat, (Nam hic <lb/>
<anchor type="note" xlink:label="note-0581-01a" xlink:href="note-0581-01"/>
Meridianus ſecat maiorem portionem paralleli ♋, infra Horizontem, vt ex ſphæra materiali con <lb/>ſtat) &amp; </s>
  <s xml:id="echoid-s36966" xml:space="preserve">T, punctum meridiei ſupra Horizontem illius loci, in quo horologium deſcribendum eſt; <lb/></s>
  <s xml:id="echoid-s36967" xml:space="preserve">erit X, ad ſiniſtram ipſius T, occidentale, aliud vero punctum X, ad dextram ipſius T, orientale, <lb/>Pro horis igitur inæqualibus diurnis ſecandus eſt arcus diurnus ♋, X L T X, in 12. </s>
  <s xml:id="echoid-s36968" xml:space="preserve">partes æquales, <lb/>initio facto à puncto X, orientali, quod ad dexteram ipſius T, collocatur. </s>
  <s xml:id="echoid-s36969" xml:space="preserve">Similiter arcus noctur-<lb/>nus ♋, X k S X, pro horis inæqualibus nocturnis diuidendus eſt in 12. </s>
  <s xml:id="echoid-s36970" xml:space="preserve">partes æquales, facto ini-<lb/>tio à puncto occidentali X, quod ad ſiniſtram ipſius T, eſt poſitum. </s>
  <s xml:id="echoid-s36971" xml:space="preserve">Pro horis vero à mer. </s>
  <s xml:id="echoid-s36972" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36973" xml:space="preserve">med. </s>
  <s xml:id="echoid-s36974" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s36975" xml:space="preserve">totus circulus in 24. </s>
  <s xml:id="echoid-s36976" xml:space="preserve">partes æquales ſecandus eſt, ſumpto initio à puncto T, meridiei, ita vt <lb/>horę pomeridianę tendant à T, verſus ſiniſtram per R, X, K, vſque ad S, antemeridianę vero, ſiue <lb/>poſt med. </s>
  <s xml:id="echoid-s36977" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s36978" xml:space="preserve">ab S, verſus dextram per X, R, L, vſque ad T. </s>
  <s xml:id="echoid-s36979" xml:space="preserve">Pro horis deinde ab ortu idem cir-<lb/>
<anchor type="note" xlink:label="note-0581-02a" xlink:href="note-0581-02"/>
culus in partes 24. </s>
  <s xml:id="echoid-s36980" xml:space="preserve">æquales diſtribuendus eſt, initio ſumpto à puncto X, orientali, quod videlicet <lb/>ad dexteram eſt ipſius T, ita vt punctum X, ſignificet horam 24. </s>
  <s xml:id="echoid-s36981" xml:space="preserve">ab ortu, primum autem punctũ <lb/>diuiſionis verſus T, pertineat ad horam 1. </s>
  <s xml:id="echoid-s36982" xml:space="preserve">ab ortu, ſequens ad 2 &amp;</s>
  <s xml:id="echoid-s36983" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36984" xml:space="preserve">Pro horis denique ab occ. </s>
  <s xml:id="echoid-s36985" xml:space="preserve">ſe-<lb/>candus eſt idem circulus in partes 24. </s>
  <s xml:id="echoid-s36986" xml:space="preserve">æquales, initio facto à puncto X, occidentali, q uod nimirũ <lb/>ipſi T, eſt ad ſiniſtram, ita vt punctum X, indicet horam 24. </s>
  <s xml:id="echoid-s36987" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36988" xml:space="preserve">primum autem punctum di-<lb/>uiſionis verſus T, pertineat ad horam 23. </s>
  <s xml:id="echoid-s36989" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s36990" xml:space="preserve">ſequens ad 22. </s>
  <s xml:id="echoid-s36991" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s36992" xml:space="preserve">c. </s>
  <s xml:id="echoid-s36993" xml:space="preserve">In his horis ab occ. </s>
  <s xml:id="echoid-s36994" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s36995" xml:space="preserve">or. <lb/></s>
  <s xml:id="echoid-s36996" xml:space="preserve">exemplum in figura proxima poſuimus. </s>
  <s xml:id="echoid-s36997" xml:space="preserve">Nam interiores numeri ad horas ♋, ab occ. </s>
  <s xml:id="echoid-s36998" xml:space="preserve">exteriores <lb/>vero ad horas ♋, ab ortu pertinent.</s>
  <s xml:id="echoid-s36999" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1866" type="float" level="2" n="4">
<note position="left" xlink:label="note-0581-01" xlink:href="note-0581-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0581-02" xlink:href="note-0581-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s37000" xml:space="preserve">HORAE autem omnes, quæ in portione ♋, RLR, continentur, cadunt ſupra faciem au-<lb/>ſtralem circuli maximi propoſiti, quæ vero in portione R K R, comprehenduntur, in dictam fa-<lb/>
<anchor type="note" xlink:label="note-0581-03a" xlink:href="note-0581-03"/>
ciem non cadunt, ſed in oppoſitam borealem, Sole exiſtente in principio ♋. </s>
  <s xml:id="echoid-s37001" xml:space="preserve">Itaque non omnes <lb/>horæ arcus diurni ♋, in propoſito horologio ad auſtrum ſpectante deſcribi poterunt, ſed illæ ſo-<lb/>lum, quæ in portione R L R, continentur, quales ſunt 10. </s>
  <s xml:id="echoid-s37002" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37003" xml:space="preserve">12. </s>
  <s xml:id="echoid-s37004" xml:space="preserve">13. </s>
  <s xml:id="echoid-s37005" xml:space="preserve">14. </s>
  <s xml:id="echoid-s37006" xml:space="preserve">15. </s>
  <s xml:id="echoid-s37007" xml:space="preserve">16. </s>
  <s xml:id="echoid-s37008" xml:space="preserve">17. </s>
  <s xml:id="echoid-s37009" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37010" xml:space="preserve">18. </s>
  <s xml:id="echoid-s37011" xml:space="preserve">quæ om-<lb/>nes in tropico ♋, deſcriptæ ſunt in horologio propoſ. </s>
  <s xml:id="echoid-s37012" xml:space="preserve">10. </s>
  <s xml:id="echoid-s37013" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37014" xml:space="preserve">3. </s>
  <s xml:id="echoid-s37015" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37016" xml:space="preserve">in horologio declinante pro-<lb/>poſ. </s>
  <s xml:id="echoid-s37017" xml:space="preserve">5. </s>
  <s xml:id="echoid-s37018" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s37019" xml:space="preserve">exceptis horis 10. </s>
  <s xml:id="echoid-s37020" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37021" xml:space="preserve">18. </s>
  <s xml:id="echoid-s37022" xml:space="preserve">quatum puncta notari non potuerunt, cum nimis <lb/>procul excurrant. </s>
  <s xml:id="echoid-s37023" xml:space="preserve">Hinc etiam cognoſcemus, quan tus ſit arcus diutnus ♋, ſupra faciem auſtralem <lb/>circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s37024" xml:space="preserve">quantus nocturnus: </s>
  <s xml:id="echoid-s37025" xml:space="preserve">Item qua hora eandem faciem Sol in principio ♋, exi-<lb/>ſtens illuminare incipiat, aut deſinat. </s>
  <s xml:id="echoid-s37026" xml:space="preserve">Ita enim yides Solem ſupra faciem auſtralem oriri paulo <lb/>poſt horam 9. </s>
  <s xml:id="echoid-s37027" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37028" xml:space="preserve">occidere vero, hoc eſt, oriri ſupra faciem oppoſitam borealem paulo poſt <lb/>horam 18. </s>
  <s xml:id="echoid-s37029" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37030" xml:space="preserve">Idem experiri licebit in alijs horis.</s>
  <s xml:id="echoid-s37031" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1867" type="float" level="2" n="5">
<note position="left" xlink:label="note-0581-03" xlink:href="note-0581-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s37032" xml:space="preserve">POSTREMO transferendæ ſunt diuiſiones huius circuli beneficio circini incipiendo à <lb/>punctis K, L, vel R, in K R L, parallelum ♑, Analemmatis, ſi de horis ♑, agatur, initio facto etiã <lb/>à punctis k; </s>
  <s xml:id="echoid-s37033" xml:space="preserve">L, vel R, quæ illis reſpondent; </s>
  <s xml:id="echoid-s37034" xml:space="preserve">aut, ſi de horis ♋, ſit ſermo, in parallelum ♋, M P N, <lb/>initio ſumpto à punctis M, N, vel P, quæ punctis L, K, R, prædicti circuli reſpondent. </s>
  <s xml:id="echoid-s37035" xml:space="preserve">Si enim <lb/>ex diuiſionibus parallelorum KRL, MPN, ad proprias diametros ducantur perpendiculares; <lb/></s>
  <s xml:id="echoid-s37036" xml:space="preserve">idemq́ue fiat in alijs omnibus parallelis, etiam in Aequatore, quem circunferentia Meridiani <lb/>Analemmatis refert, diuiſum erit Analemma in horas pro conſtructione horologii declinantis à <lb/>meridie in ortum grad. </s>
  <s xml:id="echoid-s37037" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37038" xml:space="preserve">Ad has autem horas inueniendæ ſunt circunferentiæ horizontales, <lb/>deſcenſiuæq́ue, vt ſupra docuimus, perinde ac ſi B D, eſſet diameter Horizontis cuiuſpiam, ſupra <lb/>quem polus antarcticus eleuatur, &amp; </s>
  <s xml:id="echoid-s37039" xml:space="preserve">A C, diameter Verticalis reſpectu illius Horizontis. </s>
  <s xml:id="echoid-s37040" xml:space="preserve">His <lb/>
<anchor type="note" xlink:label="note-0581-05a" xlink:href="note-0581-05"/>
etenim circunferentijs inuentis, deſcribetur horologium, vt propoſ. </s>
  <s xml:id="echoid-s37041" xml:space="preserve">5. </s>
  <s xml:id="echoid-s37042" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s37043" xml:space="preserve">docuimus. <lb/></s>
  <s xml:id="echoid-s37044" xml:space="preserve">
<anchor type="note" xlink:label="note-0581-06a" xlink:href="note-0581-06"/>
Nam circunferentię horizontales hic inuentæ ſunt arcus, quos ibi latitudines vmbrarum nomi-<lb/>nauimus: </s>
  <s xml:id="echoid-s37045" xml:space="preserve">Ex complementis autem deſcen ſiuarum altitudines Solis ſupra planum propoſitum, <lb/>ac proinde &amp; </s>
  <s xml:id="echoid-s37046" xml:space="preserve">longitudines vmbrarum pro ſingulis horis cognoſcemus. </s>
  <s xml:id="echoid-s37047" xml:space="preserve">Horæ porrò, quæ citra, <lb/>aut vltra Verticalem proprium circuli maximi propoſiti, tanquàm Horizontis, exiſtunt, cogno-<lb/>ſcentur hic ex Analemmate, vt ſupra. </s>
  <s xml:id="echoid-s37048" xml:space="preserve">Nam illæ, quarum perpendiculares cadunt in ſegmenta <lb/>diametrorum inter diametrum Verticalis A C, &amp; </s>
  <s xml:id="echoid-s37049" xml:space="preserve">ſemicirculum Meridiani A D C, in quo polus <lb/>conſpicuus ſupra datum planum continetur, ſunt citra Verticalem, ac ptopterea earum horizon-<lb/>tales circunferentiæ in horologio numerandæ erunt à linea Verticali, quæ per locum ſtyli ad li-<lb/>neam ſtyli perpendicularis ducitur, verſus lineam æquinoctialem; </s>
  <s xml:id="echoid-s37050" xml:space="preserve">quarum vero perpendiculares <lb/>cadunt in diametrorum ſegmenta inter diametrum Verticalis A C, &amp; </s>
  <s xml:id="echoid-s37051" xml:space="preserve">ſemicirculum Meridiani
<pb o="566" file="0582" n="582" rhead="GNOMONICES"/>
ABC, in quo polus occultus continetur, illæ vltra Verticalem exiſtunt, earumq́ue circunferen-<lb/>tiæ horizontales in horologio numerandæ ſunt ab eadem linea Verticali verſus centrum horolo-<lb/>gii. </s>
  <s xml:id="echoid-s37052" xml:space="preserve">Ex horologio autem declinante à mer. </s>
  <s xml:id="echoid-s37053" xml:space="preserve">in ortum conficiemus etiam aliud, quod à ſeptentrio-<lb/>ne in occ. </s>
  <s xml:id="echoid-s37054" xml:space="preserve">declinat, veluti ſupra explicauimus.</s>
  <s xml:id="echoid-s37055" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1868" type="float" level="2" n="6">
<note position="left" xlink:label="note-0581-05" xlink:href="note-0581-05a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0581-06" xlink:href="note-0581-06a" xml:space="preserve">Deſcriptio ho-<lb/>rologii declinã-<lb/>tis ex circunt@. <lb/>ren tiis horizon-<lb/>tal bus, atque <lb/>deſcenſ<unsure/>iuis.</note>
</div>
<p>
  <s xml:id="echoid-s37056" xml:space="preserve">QVOD ſi quis horologium in oppoſita facie boreali deſcribere velit ex proprijs circunfe-<lb/>
<anchor type="note" xlink:label="note-0582-01a" xlink:href="note-0582-01"/>
rentijs horizontalibus, deſcenſiuisq́ue, diuidendus erit idem circuius KRLR, ſeorſum deſcri-<lb/>ptus circa diametrum paralleli in horas eadem ferme ratione, vt paulo ante tradidimus. </s>
  <s xml:id="echoid-s37057" xml:space="preserve">Nam <lb/>RkR, erit portio ♋, ſupra faciẽ borealẽ circuli maximi propoſiti, &amp; </s>
  <s xml:id="echoid-s37058" xml:space="preserve">RLR, portio ſupra faciẽ au-<lb/>ſtralem oppoſitam, vt ex Analemmate patet, ſi H, ſumatur pro polo arctico, qui ſupra faciẽ borea-<lb/>lem circuli propoſiti eleuatur. </s>
  <s xml:id="echoid-s37059" xml:space="preserve">Quoniam vero punctum L, vbi parallelus ♋, à proprio Meridia-<lb/>
<anchor type="note" xlink:label="note-0582-02a" xlink:href="note-0582-02"/>
no circuli maximi propoſiti ſecatur, eſt ſupra Horizontem, quemadmodum &amp; </s>
  <s xml:id="echoid-s37060" xml:space="preserve">punctum T, vbi ar <lb/>cum diurnum XTX, eiuſdem paralleli Meridianus Horizontis ſecat, ſupra Horizontem exiſtit, <lb/>cum in eo fiat meridies, Sole exiſtente in principio ♋; </s>
  <s xml:id="echoid-s37061" xml:space="preserve">erit punctum K, vbi idem parallelus à <lb/>proprio Meridiano maximi circuli propoſiti ſecatur, infra Horizontem. </s>
  <s xml:id="echoid-s37062" xml:space="preserve">Id quod facile percipie-<lb/>tur, ſi parallelus ♋, ſeorſum proxime deſcriptus in tali ſitu collocetur, vt recta XVX, Horizonti <lb/>æquidiſtet, punctumq́ue S, deorſum, &amp; </s>
  <s xml:id="echoid-s37063" xml:space="preserve">T, ſurſum vergat, recta item ST, communem ſectio-<lb/>nem Meridiani Horizontis, &amp; </s>
  <s xml:id="echoid-s37064" xml:space="preserve">paralleli ♋, referat, &amp; </s>
  <s xml:id="echoid-s37065" xml:space="preserve">ſemicirculus SKT, in occaſum vergat, &amp; </s>
  <s xml:id="echoid-s37066" xml:space="preserve"><lb/>ſemicirculus SLT, in ortum. </s>
  <s xml:id="echoid-s37067" xml:space="preserve">Hac enim ratione ſecabit Meridianus Horizontis arcum diurnũ <lb/>♋, XTX, ſupra Horizontem in T, &amp; </s>
  <s xml:id="echoid-s37068" xml:space="preserve">minorem portionem ♋, RLR, quam circulus maximus <lb/>propoſitus ex tropico ♋, verſus auſtrum abſcindit, in puncto L, ſupra Horizontem vergente ver-<lb/>
<anchor type="note" xlink:label="note-0582-03a" xlink:href="note-0582-03"/>
ſus ortum, vt res poſtulat. </s>
  <s xml:id="echoid-s37069" xml:space="preserve">Itaque pro horis inæqualibus portio ♋, XTX. </s>
  <s xml:id="echoid-s37070" xml:space="preserve">ſupra Horizontem di-<lb/>nidenda eſt in 12. </s>
  <s xml:id="echoid-s37071" xml:space="preserve">partes ęquales, initio facto à puncto orientali X, quod nobis ad circulum con-<lb/>uerſis in eo ſitu, de quo proxime diximus, ad ſiniſtram exiſtit. </s>
  <s xml:id="echoid-s37072" xml:space="preserve">Pro horis vero æqualibus à mer. </s>
  <s xml:id="echoid-s37073" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37074" xml:space="preserve"><lb/>med. </s>
  <s xml:id="echoid-s37075" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37076" xml:space="preserve">totus circulus in 24. </s>
  <s xml:id="echoid-s37077" xml:space="preserve">partes æquales ſecandus eſt, initio facto à punctis T, &amp; </s>
  <s xml:id="echoid-s37078" xml:space="preserve">S, ita vt ho <lb/>ræ pomeridianæ comprehendantur in ſemicirculo occidentali TKS, antemeridianæ vero, ſiue <lb/>poſt med. </s>
  <s xml:id="echoid-s37079" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37080" xml:space="preserve">in ſemicirculo orientali SLT. </s>
  <s xml:id="echoid-s37081" xml:space="preserve">Pro horis deinde ab ortu idem circulus in 24. </s>
  <s xml:id="echoid-s37082" xml:space="preserve">par <lb/>tes æquales diſtribuendus eſt, initio facto à puncto X, orientali per L, verſus T, progrediendo. </s>
  <s xml:id="echoid-s37083" xml:space="preserve">Pro <lb/>horis denique ab occ. </s>
  <s xml:id="echoid-s37084" xml:space="preserve">principiũ diuiſionis eiuſdẽ circuli in 24. </s>
  <s xml:id="echoid-s37085" xml:space="preserve">partes ęquales fieri debet à puncto <lb/>X, occidentali. </s>
  <s xml:id="echoid-s37086" xml:space="preserve">In figura numeri interiores ad horas ab occ. </s>
  <s xml:id="echoid-s37087" xml:space="preserve">exteriores vero ad lioras ab ortu ſpe-<lb/>ctant. </s>
  <s xml:id="echoid-s37088" xml:space="preserve">Solæ autem horæ diurnæ in parallelo ♋, comprehenſæ inter rectas XVX, RQR, in fa-<lb/>
<anchor type="note" xlink:label="note-0582-04a" xlink:href="note-0582-04"/>
ciem borealem plani propoſiti cadunt, quales ſunt horæ ab occ. </s>
  <s xml:id="echoid-s37089" xml:space="preserve">9. </s>
  <s xml:id="echoid-s37090" xml:space="preserve">19. </s>
  <s xml:id="echoid-s37091" xml:space="preserve">20. </s>
  <s xml:id="echoid-s37092" xml:space="preserve">21. </s>
  <s xml:id="echoid-s37093" xml:space="preserve">22. </s>
  <s xml:id="echoid-s37094" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37095" xml:space="preserve">24. </s>
  <s xml:id="echoid-s37096" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37097" xml:space="preserve">horæ <lb/>ab ortu 10. </s>
  <s xml:id="echoid-s37098" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37099" xml:space="preserve">12. </s>
  <s xml:id="echoid-s37100" xml:space="preserve">13. </s>
  <s xml:id="echoid-s37101" xml:space="preserve">14. </s>
  <s xml:id="echoid-s37102" xml:space="preserve">15. </s>
  <s xml:id="echoid-s37103" xml:space="preserve">omnesq́ue nocturnæ, vt ex proxima figura perſpicuum eſt. </s>
  <s xml:id="echoid-s37104" xml:space="preserve">Quod <lb/>ſi circulus KRLR, ſumatur pro tropico ♑, erit, vt dictum eſt, RKR, portio ♑, ſupra faciem <lb/>auſtralem circuli propoſiti, &amp; </s>
  <s xml:id="echoid-s37105" xml:space="preserve">RLR. </s>
  <s xml:id="echoid-s37106" xml:space="preserve">portio ſupra faciem oppoſitam borealem. </s>
  <s xml:id="echoid-s37107" xml:space="preserve">Item XSX, ar-<lb/>cus diurnus ♑, &amp; </s>
  <s xml:id="echoid-s37108" xml:space="preserve">XTX, arcus nocturnus. </s>
  <s xml:id="echoid-s37109" xml:space="preserve">Nulla autem hora arcus diurni ♑, XSX, cadit in por <lb/>tionem ♑, RLR, quæ ſupra faciem borealem circuli propoſiti extat, ſed ſolæ horęarcus noctur <lb/>ni ♑, XTX, quæ in portione RLR, continentur, vt patet.</s>
  <s xml:id="echoid-s37110" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1869" type="float" level="2" n="7">
<note position="left" xlink:label="note-0582-01" xlink:href="note-0582-01a" xml:space="preserve">Horologium in <lb/>facie oppoſita <lb/>p'ani dati quo <lb/>modo deſcriba <lb/>tur ex <unsure/>propriis <lb/>circunferentiis <lb/>hotizontalibus <lb/>deſcenſiuis{q́ue}.</note>
<note position="left" xlink:label="note-0582-02" xlink:href="note-0582-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0582-03" xlink:href="note-0582-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0582-04" xlink:href="note-0582-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s37111" xml:space="preserve">ITAQVE ſi horæ ſupra faciem borealem plani dati exiſtentes ex circulo kRLR, transfe-<lb/>rantur in Analemma, vt prius, ducanturq́ue ex horis ad diametros parallelorum perpendiculares, <lb/>idemq́ue fiat in alijs parallelis, etiam in Aequatore, diuiſum erit Analemma in horas pro con-<lb/>
<anchor type="note" xlink:label="note-0582-05a" xlink:href="note-0582-05"/>
ſtructione horologii declinantis à ſeptentrione in occaſum grad. </s>
  <s xml:id="echoid-s37112" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37113" xml:space="preserve">Ad has autem horas inue-<lb/>ſtigandæ ſunt circunferentiæ horizontales, atque deſcenſiuæ, vt prius, non ſecus, ac ſi BD, diame-<lb/>ter eſſet cuiuſpiam Horizontis, ſupra quem polus arcticus I, eleuatur.</s>
  <s xml:id="echoid-s37114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1870" type="float" level="2" n="8">
<note position="left" xlink:label="note-0582-05" xlink:href="note-0582-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s37115" xml:space="preserve">QVONIAM vero numeri exteriores in parallelo ſeorſum deſcripto, dum pro tropico ♑, <lb/>
<anchor type="note" xlink:label="note-0582-06a" xlink:href="note-0582-06"/>
ſumitur, ſpectant in facie auſtrali ad horas ab occaſu, in boreali vero, dum idem parallelus pro <lb/>tropico ♋, ſumitur, ad horas ab ortu: </s>
  <s xml:id="echoid-s37116" xml:space="preserve">Item interiores in auſtrali facie, dum idem parallelus pro <lb/>tropico ♑, accipitur, ad horas ab ortu, in boreali vero, dum pro tropico ♋, parallelus ſumitur, <lb/>ad horas ab occaſu pertinent, vt ex dictis eſt manifeſtum: </s>
  <s xml:id="echoid-s37117" xml:space="preserve">efficitur, vt circunferentiæ horizonta-<lb/>les, deſcenſiuæq́ue pro horis ♑, ab occ. </s>
  <s xml:id="echoid-s37118" xml:space="preserve">inuentæ in facie auſtrali plani propoſiti, ſint etiam circun-<lb/>ferentiæ pro horis ♋, ab or. </s>
  <s xml:id="echoid-s37119" xml:space="preserve">in facie oppoſita boreali eiuſdem plani; </s>
  <s xml:id="echoid-s37120" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37121" xml:space="preserve">quę ibi pro horis ab or. <lb/></s>
  <s xml:id="echoid-s37122" xml:space="preserve">
<anchor type="note" xlink:label="note-0582-07a" xlink:href="note-0582-07"/>
inuentæ fuerint, ſint hic circunferentiæ pro horis ab occ. </s>
  <s xml:id="echoid-s37123" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37124" xml:space="preserve">contra; </s>
  <s xml:id="echoid-s37125" xml:space="preserve">quandoquidem eodem mo-<lb/>do parallelus ♑, diuiditur in horas ab occ. </s>
  <s xml:id="echoid-s37126" xml:space="preserve">ſupra faciem auſtralem circuli maximi propoſiti, quo <lb/>parallelus ♋, in horas ab or. </s>
  <s xml:id="echoid-s37127" xml:space="preserve">diuiditur, ſupra faciem borealem, &amp;</s>
  <s xml:id="echoid-s37128" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37129" xml:space="preserve">Idem dicendum eſt de horis <lb/>à mer. </s>
  <s xml:id="echoid-s37130" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37131" xml:space="preserve">med. </s>
  <s xml:id="echoid-s37132" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37133" xml:space="preserve">Nam circunferentiæ pro horis à mer. </s>
  <s xml:id="echoid-s37134" xml:space="preserve">inuentæ in tropico ♑, ſupra vnam faciẽ <lb/>plani, erunt circunferentiæ pro horis à med. </s>
  <s xml:id="echoid-s37135" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37136" xml:space="preserve">in oppoſito tropico ♋, ſupra alteram faciem pla <lb/>ni oppoſitam. </s>
  <s xml:id="echoid-s37137" xml:space="preserve">Quocirca cum complementa circunferentiarum deſcenſiuarum metiantur altitu-<lb/>dines Solis ſupra datum planum, erunt eædem altitudines Solis earundem horarum ſupra vtram-<lb/>que faciem plani propoſiti, dummodo horæ, quæ ſupra vnam faciem plani ſumuntur in vno pa-<lb/>rallelo á<unsure/> mer. </s>
  <s xml:id="echoid-s37138" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s37139" xml:space="preserve">aut occ. </s>
  <s xml:id="echoid-s37140" xml:space="preserve">ſupra alteram faciem plani oppoſitam in oppoſito parallelo acci-<lb/>piantur à med. </s>
  <s xml:id="echoid-s37141" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37142" xml:space="preserve">vel ab occ. </s>
  <s xml:id="echoid-s37143" xml:space="preserve">aut or. </s>
  <s xml:id="echoid-s37144" xml:space="preserve">Id quod propoſ. </s>
  <s xml:id="echoid-s37145" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37146" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s37147" xml:space="preserve">quoque oſtendimus. <lb/></s>
  <s xml:id="echoid-s37148" xml:space="preserve">Idemq́ue dicendum eſt de alijs planis, quæ non ſolum declinant, ſed etiam ſimul inclinata ſunt,
<pb o="567" file="0583" n="583" rhead="LIBER SEXTVS."/>
vel quæ ſolum inclinata ſunt ad Horizontem.</s>
  <s xml:id="echoid-s37149" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1871" type="float" level="2" n="9">
<note position="left" xlink:label="note-0582-06" xlink:href="note-0582-06a" xml:space="preserve">Circunſerentiæ <lb/>pro horis à mer. <lb/>vel ab or. aut ab <lb/>occ. in quolibet <lb/>parallelo i@uen <lb/>tæ ſupra unam <lb/>faciẽ plani pro <lb/>poſiti, ſunt e iã <lb/>circunferenriæ <lb/>ꝓ horis à med. <lb/>noc. vel ab ote. <lb/>autab or. in op <lb/>poſito patallelo <lb/>ſupra alteram <lb/>faciem plani op <lb/>poſitam.</note>
<note position="left" xlink:label="note-0582-07" xlink:href="note-0582-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s37150" xml:space="preserve">IAM vero ſi in horologio contrario modo ducatur linea ſtyli, quàm in ſuperiori lib. </s>
  <s xml:id="echoid-s37151" xml:space="preserve">præce-<lb/>pimus, &amp; </s>
  <s xml:id="echoid-s37152" xml:space="preserve">centrum item horologii in oppoſita parte inueſtigetur, delineabitur ex inuentis circun-<lb/>ferentijs horologium declinans boreale, hoc eſt, in oppoſita facie plani, quemadmodum au-<lb/>ſtrale, dummodo circunferentiæ horizontales horarum orientalium à linea Verticali, quæ lineã <lb/>ſtyli ad angulos rectos ſecat in loco ſtyli, numerentur ex parte orientali, occidentalium vero ex <lb/>parte occidentali, vltra vel citra Verticalẽ lineam, id eſt, verſus centrum horologij, vel verſus li-<lb/>neam æquinoctialem, prout horæ fuerint vltra, vel citra Verticalem circulum plani propoſiti: <lb/></s>
  <s xml:id="echoid-s37153" xml:space="preserve">quæ horæ facile ex Analemmate huius cap. </s>
  <s xml:id="echoid-s37154" xml:space="preserve">cognoſcẽtur. </s>
  <s xml:id="echoid-s37155" xml:space="preserve">Quoniam enim alter polus I, nempe ar-<lb/>cticus in dato exemplo, ſupra faciem oppoſitam plani eleuatur, erunt omnes illæ horæ, quarum <lb/>
<anchor type="note" xlink:label="note-0583-01a" xlink:href="note-0583-01"/>
perpendiculares cadunt in ſegmenta diametrorum inter diametrum Verticalis AC, &amp; </s>
  <s xml:id="echoid-s37156" xml:space="preserve">ſemicir-<lb/>culum ABC, in quo polus conſpicuus ſupra faciem datam plani propoſiti continetur, poſitæ ci-<lb/>tra Verticalem, aliæ vero vltra, &amp;</s>
  <s xml:id="echoid-s37157" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37158" xml:space="preserve">vt in ſuperioribus quoque dictum eſt, vt pater, ſi Analemma <lb/>huius cap. </s>
  <s xml:id="echoid-s37159" xml:space="preserve">inuertatur, ita vt C, ſit vertex capitis, &amp; </s>
  <s xml:id="echoid-s37160" xml:space="preserve">A, verticis oppoſitum.</s>
  <s xml:id="echoid-s37161" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1872" type="float" level="2" n="10">
<note position="left" xlink:label="note-0583-01" xlink:href="note-0583-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s37162" xml:space="preserve">DIVISO autem Analemmate in horas, vt dictum eſt, cognitaq́ue diſtantia cuiuslibet <lb/>
<anchor type="note" xlink:label="note-0583-02a" xlink:href="note-0583-02"/>
horæ à Meridiano proprio plani declinantis, (quæ quidem ex inclinatione huius Meridiani ad <lb/>Meridianum Horizontis cognoſcetur, vt propoſ. </s>
  <s xml:id="echoid-s37163" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37164" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s37165" xml:space="preserve">tradidimus) inueſtigari pote-<lb/>runt circunferentiæ horizontales, deſcenſiuæq́ue ex doctrina ſinuum, tam per triangula rectili-<lb/>nea, quam per ſphærica, vt ſupra docuimus, ſi circulus maximus propoſitus accipiatur pro Ho-<lb/>rizonte quopiam. </s>
  <s xml:id="echoid-s37166" xml:space="preserve">Vel ſi ex propoſ. </s>
  <s xml:id="echoid-s37167" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37168" xml:space="preserve">ſuperioris lib. </s>
  <s xml:id="echoid-s37169" xml:space="preserve">inueniantur altitudines Solis ſupra propoſi-<lb/>
<anchor type="note" xlink:label="note-0583-03a" xlink:href="note-0583-03"/>
tum circulum maximum pro ſingulis horis, erunt earum complementa circunferentiæ deſcenſi-<lb/>uæ: </s>
  <s xml:id="echoid-s37170" xml:space="preserve">Latitudines autem vmbrarum per propoſ. </s>
  <s xml:id="echoid-s37171" xml:space="preserve">3. </s>
  <s xml:id="echoid-s37172" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s37173" xml:space="preserve">ſuperioris inuentæ, erunt horiz on-<lb/>tales circunferentiæ.</s>
  <s xml:id="echoid-s37174" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1873" type="float" level="2" n="11">
<note position="right" xlink:label="note-0583-02" xlink:href="note-0583-02a" xml:space="preserve">Inuentio circũ-<lb/>ſerentiarum ho <lb/>rizõtalium, de-<lb/>fcẽſiuarumque <lb/>per finus in pla <lb/>nis declinanti-<lb/>bus.</note>
<note position="left" xlink:label="note-0583-03" xlink:href="note-0583-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s37175" xml:space="preserve">QVEMADMODVM autem Analemma diuiſimus in horas pro circulo maximo, qui <lb/>à Verticali declinat, &amp; </s>
  <s xml:id="echoid-s37176" xml:space="preserve">ad Horizontem rectus eſt, ita quoque idem diuidemus pro circulo maxi-<lb/>mo, qui ad Horizontem eſt inclinatus, ſiue is à Verticali declinet, ſiue non ſi diligenter perpen-<lb/>datur, an Meridianus proprius dati circuli maximi ſecet in ſphæra parallelum, quem ſeorſum de-<lb/>ſcripſimus, ſupra Horizõtem, nec ne, &amp; </s>
  <s xml:id="echoid-s37177" xml:space="preserve">quantam habeat idem Meridianus inclinationem ad Me-<lb/>ridianum Horizontis. </s>
  <s xml:id="echoid-s37178" xml:space="preserve">Eodemq́ue pacto horologium Superius depingemus, vt in ſuperiori lib. <lb/></s>
  <s xml:id="echoid-s37179" xml:space="preserve">traditum eſt, ex quo Inferius deducetur, vt ſæpius diximus. </s>
  <s xml:id="echoid-s37180" xml:space="preserve">Vel certe Inferius ex propriis circunfe <lb/>
<anchor type="note" xlink:label="note-0583-04a" xlink:href="note-0583-04"/>
rentijs horizontalibus, deſcenſiuisq́ue deſcribemus, vt ſuperius, dummodo lineam ſtyli contrario <lb/>modo ducamus, &amp; </s>
  <s xml:id="echoid-s37181" xml:space="preserve">horizontalem lineam infra ſtylum deſcribamus, non autem ſupra, vt in ſupe-<lb/>riori horologio, &amp;</s>
  <s xml:id="echoid-s37182" xml:space="preserve">c.</s>
  <s xml:id="echoid-s37183" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1874" type="float" level="2" n="12">
<note position="left" xlink:label="note-0583-04" xlink:href="note-0583-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s37184" xml:space="preserve">EXAMINARI quoque poteſt diuiſio paralleli ſeorſum deſcripti, ſi ex inclinatione Meri-<lb/>
<anchor type="note" xlink:label="note-0583-05a" xlink:href="note-0583-05"/>
diani proprii dati circuli maximi ad Meridianum Horizontis inueniatur hora, aut illa particula <lb/>horæ, quæ in illo parallelo cadit in proprium Meridianum plani propoſiti. </s>
  <s xml:id="echoid-s37185" xml:space="preserve">Si enim illa hora, aut <lb/>horæ particula congruat puncto K, vel L, in parallelo ſecundum diuiſionem factam, recte inſtitu-<lb/>ta fuit diuiſio, ſin minus, nequaquam. </s>
  <s xml:id="echoid-s37186" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s37187" xml:space="preserve">Meridianus proprius circuli maximi de-<lb/>clinantis à meridie in ortum grad. </s>
  <s xml:id="echoid-s37188" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37189" xml:space="preserve">recedit à Meridiano Horizontis ſupra Horizontem verſus <lb/>ortum grad. </s>
  <s xml:id="echoid-s37190" xml:space="preserve">40. </s>
  <s xml:id="echoid-s37191" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37192" xml:space="preserve">48. </s>
  <s xml:id="echoid-s37193" xml:space="preserve">hoc eſt, horis 2. </s>
  <s xml:id="echoid-s37194" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37195" xml:space="preserve">43. </s>
  <s xml:id="echoid-s37196" xml:space="preserve">fere: </s>
  <s xml:id="echoid-s37197" xml:space="preserve">Item Meridianus Horizontis arcum <lb/>
<anchor type="note" xlink:label="note-0583-06a" xlink:href="note-0583-06"/>
diurnũ ♑, ſecat in hora 19. </s>
  <s xml:id="echoid-s37198" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37199" xml:space="preserve">32. </s>
  <s xml:id="echoid-s37200" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37201" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37202" xml:space="preserve">in hora 4. </s>
  <s xml:id="echoid-s37203" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37204" xml:space="preserve">28. </s>
  <s xml:id="echoid-s37205" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s37206" xml:space="preserve">Si igitur ex hiſce horis <lb/>detrahamus horas 2. </s>
  <s xml:id="echoid-s37207" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37208" xml:space="preserve">43. </s>
  <s xml:id="echoid-s37209" xml:space="preserve">remanebunt hor. </s>
  <s xml:id="echoid-s37210" xml:space="preserve">16. </s>
  <s xml:id="echoid-s37211" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37212" xml:space="preserve">49. </s>
  <s xml:id="echoid-s37213" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37214" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37215" xml:space="preserve">hora 1. </s>
  <s xml:id="echoid-s37216" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37217" xml:space="preserve">45. </s>
  <s xml:id="echoid-s37218" xml:space="preserve">ab or-<lb/>tu. </s>
  <s xml:id="echoid-s37219" xml:space="preserve">His ergo horis reſpondere debet punctum K, in parallelo. </s>
  <s xml:id="echoid-s37220" xml:space="preserve">Quòd ſi Meridianus proprius à <lb/>Meridiano Horizontis recederet in occaſum, adijcienda eſſet inclinatio Meridianorum ad hor. <lb/></s>
  <s xml:id="echoid-s37221" xml:space="preserve">19. </s>
  <s xml:id="echoid-s37222" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37223" xml:space="preserve">32. </s>
  <s xml:id="echoid-s37224" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37225" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37226" xml:space="preserve">Rurſus quoniam Meridianus Horizontis ſecat arcum diurnum ♋, in hora 16. </s>
  <s xml:id="echoid-s37227" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s37228" xml:space="preserve">28. </s>
  <s xml:id="echoid-s37229" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37230" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37231" xml:space="preserve">in hora 7. </s>
  <s xml:id="echoid-s37232" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37233" xml:space="preserve">32. </s>
  <s xml:id="echoid-s37234" xml:space="preserve">ab ortu; </s>
  <s xml:id="echoid-s37235" xml:space="preserve">ſi ab iſtis horis auferantur horæ 2. </s>
  <s xml:id="echoid-s37236" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37237" xml:space="preserve">43. </s>
  <s xml:id="echoid-s37238" xml:space="preserve">quæ <lb/>inclinationi Meridianorum debentur, reliquæ erunt horæ 13. </s>
  <s xml:id="echoid-s37239" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37240" xml:space="preserve">45. </s>
  <s xml:id="echoid-s37241" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37242" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37243" xml:space="preserve">hor. </s>
  <s xml:id="echoid-s37244" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37245" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37246" xml:space="preserve">49. </s>
  <s xml:id="echoid-s37247" xml:space="preserve"><lb/>ab ortu, quibus reſpondere debet punctum L, in eodem parallelo, &amp; </s>
  <s xml:id="echoid-s37248" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s37249" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1875" type="float" level="2" n="13">
<note position="right" xlink:label="note-0583-05" xlink:href="note-0583-05a" xml:space="preserve">Examen diuiſio <lb/>nis factæ @@ pa-<lb/>tallelo ſeorſu@@ <lb/>deſcripto in h@@ <lb/>cap.</note>
<note position="left" xlink:label="note-0583-06" xlink:href="note-0583-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s37250" xml:space="preserve">AD hæc, ſi in Analemmate ſcholij propoſ. </s>
  <s xml:id="echoid-s37251" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37252" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37253" xml:space="preserve">5. </s>
  <s xml:id="echoid-s37254" xml:space="preserve">Ellipſis γ ε {δι}<unsure/> θ, deſcripta ſit, habita ra-<lb/>tione inclinationis circuli maximipropoſiti ad Meridianum Horizontis, diuiſusq́ue v. </s>
  <s xml:id="echoid-s37255" xml:space="preserve">g. </s>
  <s xml:id="echoid-s37256" xml:space="preserve">ſemi-<lb/>
<anchor type="note" xlink:label="note-0583-07a" xlink:href="note-0583-07"/>
circulus ♋, &amp; </s>
  <s xml:id="echoid-s37257" xml:space="preserve">♑, FRG, in horas, vt cap. </s>
  <s xml:id="echoid-s37258" xml:space="preserve">6. </s>
  <s xml:id="echoid-s37259" xml:space="preserve">præſcripſimus, illico apparebit, quãto interuallo quæ-<lb/>libet hora in portione ♑, RG, abſit à puncto 4. </s>
  <s xml:id="echoid-s37260" xml:space="preserve">vbi planum propoſitum ſecat parallelum ♑: <lb/></s>
  <s xml:id="echoid-s37261" xml:space="preserve">Item quanta ſit diſtantia cuiuslibet horæ in portione ♋, RF, à puncto 3. </s>
  <s xml:id="echoid-s37262" xml:space="preserve">vbi parallelus ♋, ab eo-<lb/>dem plano ſecatur. </s>
  <s xml:id="echoid-s37263" xml:space="preserve">Si igitur huiuſmodi diſtantiæ congruant diſtantijs hora@um in parallelo ſe-<lb/>orſum deſcripto in hoc cap. </s>
  <s xml:id="echoid-s37264" xml:space="preserve">quas à recta RQR, communi ſectione propoſiti plani, &amp; </s>
  <s xml:id="echoid-s37265" xml:space="preserve">paralleli <lb/>habent, recte inſtituta erit diuiſio, &amp;</s>
  <s xml:id="echoid-s37266" xml:space="preserve">c.</s>
  <s xml:id="echoid-s37267" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1876" type="float" level="2" n="14">
<note position="left" xlink:label="note-0583-07" xlink:href="note-0583-07a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1878" type="section" level="1" n="481">
<head xml:id="echoid-head510" style="it" xml:space="preserve">SCHOLIVM.</head>
<p style="it">
  <s xml:id="echoid-s37268" xml:space="preserve">ANTEQVAM finem huic ſexto lib. </s>
  <s xml:id="echoid-s37269" xml:space="preserve">imponamus, viſum est paucis demonſtrare, quaratione ex <lb/>ſolo horologio horizontali accuratè deſcripto, mira &amp; </s>
  <s xml:id="echoid-s37270" xml:space="preserve">facilitate, &amp; </s>
  <s xml:id="echoid-s37271" xml:space="preserve">iucunditate delineari poſſint omnia
<pb o="568" file="0584" n="584" rhead="GNOMONICES"/>
horologia ad Horizontem recta, quale eſt Verticale vtrumque, vtrumque Meridianum, &amp; </s>
  <s xml:id="echoid-s37272" xml:space="preserve">omnia decli-<lb/>
<anchor type="note" xlink:label="note-0584-01a" xlink:href="note-0584-01"/>
nantia à Verticali proprie dicto, cuiuſmodi ſunt illa, quæ in muris ædificiorum depingi ſolent, habent{q́ue} <lb/>frequentiorem vſum, quàm alia, quœ ad Horizontem inclinata ſunt. </s>
  <s xml:id="echoid-s37273" xml:space="preserve">Sit igitur horologium horizontale <lb/>Italicum, in quo ſtylus A B, eiuſ{q́ue} locus in A; </s>
  <s xml:id="echoid-s37274" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37275" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37276" xml:space="preserve">Propoſitum autem ſit ex eo deſcribere horologium <lb/>declinans à meridie in ortum grad. </s>
  <s xml:id="echoid-s37277" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37278" xml:space="preserve">Constituatur in A, angulus B A C, complemento declinationis <lb/>æqualis, qualem nimirum circulus maximus, cui horologium œquidistat, cum Meridiano facit, ita vt re-<lb/>cta C AD, ſit communis ſectio plani horologĳ horizont alis, &amp; </s>
  <s xml:id="echoid-s37279" xml:space="preserve">illius verticalis declinantis, cui horolo-<lb/>gium æquidiſtat, cuius facies australis à meridie in ortum, &amp; </s>
  <s xml:id="echoid-s37280" xml:space="preserve">borealis à ſeptentrione in occaſum vergit. <lb/></s>
  <s xml:id="echoid-s37281" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0584-01a" xlink:href="fig-0584-01"/>
<anchor type="note" xlink:label="note-0584-02a" xlink:href="note-0584-02"/>
<anchor type="note" xlink:label="note-0584-03a" xlink:href="note-0584-03"/>
<anchor type="note" xlink:label="note-0584-04a" xlink:href="note-0584-04"/>
Ducatur ex A, ad C@D, perpendicularis AE, ex qua verſus ſeptentrionem abſcindatur recta AE, ſty-<lb/>lo futuri horologĳ æqualis, cuiuſcunque is magnitudinis proponatur: </s>
  <s xml:id="echoid-s37282" xml:space="preserve">ſumatur autem &amp; </s>
  <s xml:id="echoid-s37283" xml:space="preserve">E F, ſtylo A B, <lb/>horizontalis horologĳ æqualis, &amp; </s>
  <s xml:id="echoid-s37284" xml:space="preserve">per E, F, ipſi C D, parallelæ agantur E G, F H. </s>
  <s xml:id="echoid-s37285" xml:space="preserve">Si deſcribendum ſit <lb/>horologium verticale non declinans, ſumenda erit in meridiana linea, initio facto à puncto A, recta <lb/>æqualis stylo futuri horologĳ ſiue uerſus ſeptent. </s>
  <s xml:id="echoid-s37286" xml:space="preserve">ſiue verſus meridiem, prout horologium deſcribendum <lb/>
<anchor type="note" xlink:label="note-0584-05a" xlink:href="note-0584-05"/>
Australe est, aut Boreale, &amp; </s>
  <s xml:id="echoid-s37287" xml:space="preserve">per extremitatem ſtyli ducenda recta ad meridianam lineam perpendi-<lb/>cularis, &amp; </s>
  <s xml:id="echoid-s37288" xml:space="preserve">huic vna parallela tanto interuallo ab ea diſtans, quantus eſt gnomon horologĳ horizontalis: <lb/></s>
  <s xml:id="echoid-s37289" xml:space="preserve">quemad@nodum &amp; </s>
  <s xml:id="echoid-s37290" xml:space="preserve">in dato exemplo recta F H, ipſi E G, œquidist at ſecundum interuallum ſtyli E F. </s>
  <s xml:id="echoid-s37291" xml:space="preserve">Si <lb/>autem horologium Meridianum ſit deſcribendum, accipienda erit ex recta ad meridianã lineam perpen-<lb/>diculari in A, longitudo styli, &amp; </s>
  <s xml:id="echoid-s37292" xml:space="preserve">per extremum huius ſtyli aſſumpti linea ducenda ipſi meridianę lineę <lb/>parallela, ex parte quidem occaſus, ſi horologium orientale deſideretur, ex parte vero ortus, ſi occiden <lb/>tale deſcribendum ſit: </s>
  <s xml:id="echoid-s37293" xml:space="preserve">Huic autem parallelæ ducenda alia parallela ſecundum interuallum ſiyli horolo-<lb/>gĳ horizont alis. </s>
  <s xml:id="echoid-s37294" xml:space="preserve">Sed ad exemplum propoſitum reuertamur. </s>
  <s xml:id="echoid-s37295" xml:space="preserve">Planum per rectas E F, E G, F H, du-<lb/>ctum intelligatur circa rectam E G, circumuerti, donec rectum ſit ad planum horologĳ horizontalis: </s>
  <s xml:id="echoid-s37296" xml:space="preserve"><lb/>Quo poſito, erit, per defin. </s>
  <s xml:id="echoid-s37297" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37298" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37299" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37300" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37301" xml:space="preserve">F E, ad idem planum horologĳ horizontalis recta: </s>
  <s xml:id="echoid-s37302" xml:space="preserve">Est autem <lb/>
<anchor type="note" xlink:label="note-0584-06a" xlink:href="note-0584-06"/>
&amp; </s>
  <s xml:id="echoid-s37303" xml:space="preserve">ſtylus B A, ad idem planum rectus. </s>
  <s xml:id="echoid-s37304" xml:space="preserve">Igitur parallelæ inter ſe erunt rectæ A B, E F: </s>
  <s xml:id="echoid-s37305" xml:space="preserve">quæ cum æqua-<lb/>
<anchor type="note" xlink:label="note-0584-07a" xlink:href="note-0584-07"/>
les ſint poſitę, erit &amp; </s>
  <s xml:id="echoid-s37306" xml:space="preserve">recta connectens puncta B, &amp; </s>
  <s xml:id="echoid-s37307" xml:space="preserve">F, ipſi A E, parallela, &amp; </s>
  <s xml:id="echoid-s37308" xml:space="preserve">æqualis. </s>
  <s xml:id="echoid-s37309" xml:space="preserve">Et quoniã A E, <lb/>
<anchor type="note" xlink:label="note-0584-08a" xlink:href="note-0584-08"/>
ex defin. </s>
  <s xml:id="echoid-s37310" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37311" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37312" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37313" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37314" xml:space="preserve">perpendicularis est ad planum per rectas EF, EG, FH, ductum, erit quoque <lb/>recta BF, ad idem planum perpendicularis. </s>
  <s xml:id="echoid-s37315" xml:space="preserve">Quamobrem planum per rectas EF, EG, FH, ductum <lb/>
<anchor type="note" xlink:label="note-0584-09a" xlink:href="note-0584-09"/>
erit planum horologĳ declinantis à mer. </s>
  <s xml:id="echoid-s37316" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s37317" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s37318" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37319" xml:space="preserve">cum rectum ſit ad planum horologĳ horizonta-<lb/>lis, recta{q́ue} BF, ſtylo aſſumpto AE, æqualis ad idem illud planum perpendicularis ſit, atque adeo gno-<lb/>mon exiſtat futuri horologĳ declinantis, cuius locus in F, cum vertex eius B, in centro mundi, nempe in <lb/>vertice ſtyli in horologio horizontali, ſtatuatur: </s>
  <s xml:id="echoid-s37320" xml:space="preserve">Recta ergo EG, communis ſectio est plani horologĳ <lb/>
<anchor type="note" xlink:label="note-0584-10a" xlink:href="note-0584-10"/>
declinantis, &amp; </s>
  <s xml:id="echoid-s37321" xml:space="preserve">plani horologĳ horizontalis: </s>
  <s xml:id="echoid-s37322" xml:space="preserve">Recta autem FH, erit linea horizontalis, hoc est, commu <lb/>nis ſectio plani horologĳ declinantis, &amp; </s>
  <s xml:id="echoid-s37323" xml:space="preserve">Horizontis, cum planum per centrum mundi B, &amp; </s>
  <s xml:id="echoid-s37324" xml:space="preserve">per rectas <lb/>BF, FH, (quæ rectis AE, EG, parallelæ ſunt) ductum ęquidiſtet plano horologĳ horizontalis per
<pb o="569" file="0585" n="585" rhead="LIBER SEXTVS."/>
rectas AE, EG, ducto, atque adeo ab Horizonte non differat, propterea quòd Horizon per centrũ mun <lb/>
<anchor type="note" xlink:label="note-0585-01a" xlink:href="note-0585-01"/>
di B, ductus horologio horizontali æquidiſtat.</s>
  <s xml:id="echoid-s37325" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1878" type="float" level="2" n="1">
<note position="left" xlink:label="note-0584-01" xlink:href="note-0584-01a" xml:space="preserve">Quaratione ex <lb/>horologio hori-<lb/>zontali deſcribi <lb/>poſſint horolo-<lb/>gia ad Horizon <lb/>tẽ recta, quale eſt <lb/>Verticale vtrũ-<lb/>que, vtrumque <lb/>Meridianum, &amp; <lb/>omnia declinan <lb/>tia à Verticali <lb/>proprie dicto.</note>
  <figure xlink:label="fig-0584-01" xlink:href="fig-0584-01a">
    <image file="0584-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0584-01"/>
  </figure>
<note position="left" xlink:label="note-0584-02" xlink:href="note-0584-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0584-03" xlink:href="note-0584-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0584-04" xlink:href="note-0584-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0584-05" xlink:href="note-0584-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0584-06" xlink:href="note-0584-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0584-07" xlink:href="note-0584-07a" xml:space="preserve">6. vndec.</note>
<note position="left" xlink:label="note-0584-08" xlink:href="note-0584-08a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0584-09" xlink:href="note-0584-09a" xml:space="preserve">8. vndec.</note>
<note position="left" xlink:label="note-0584-10" xlink:href="note-0584-10a" xml:space="preserve">Linea horizon-<lb/>@alis in hoiolo-<lb/>gio quæ.</note>
<note position="right" xlink:label="note-0585-01" xlink:href="note-0585-01a" xml:space="preserve">15. vndec.</note>
</div>
<p style="it">
  <s xml:id="echoid-s37326" xml:space="preserve">LINEAM itaque meridianam ita in horologio declinante ducemus. </s>
  <s xml:id="echoid-s37327" xml:space="preserve">Ex puncto I, vbi meridia-<lb/>
<anchor type="note" xlink:label="note-0585-02a" xlink:href="note-0585-02"/>
na linea horologĳ horizontalis rectam EG, ſecat, ducatur ad EG, perpendicularis IK: </s>
  <s xml:id="echoid-s37328" xml:space="preserve">quam dico eſ-<lb/>ſe lineam meridianam. </s>
  <s xml:id="echoid-s37329" xml:space="preserve">Quoniam enim planum horologĳ declinantis ad planum horologĳ horizontalis <lb/>rectum eſt, erit, per defin. </s>
  <s xml:id="echoid-s37330" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37331" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37332" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37333" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37334" xml:space="preserve">recta KI, ad idem planum perpendicularis; </s>
  <s xml:id="echoid-s37335" xml:space="preserve">ac proinde planũ <lb/>per rectas K I, I A, ductum ad idem planum erit rectum. </s>
  <s xml:id="echoid-s37336" xml:space="preserve">Cum ergo Meridianus ad idem planum horo-<lb/>
<anchor type="note" xlink:label="note-0585-03a" xlink:href="note-0585-03"/>
logĳ horizontalis ſit rectus, ducatur{q́ue} per meridianam lineam A I, non differet Meridianus à plano <lb/>per rectas A I, I K, ducto; </s>
  <s xml:id="echoid-s37337" xml:space="preserve">propterea{q́ue} I K, communis erit ſectio Meridiani, &amp; </s>
  <s xml:id="echoid-s37338" xml:space="preserve">plani horologĳ de-<lb/>clinantis, hoc eſt, linea meridiana in horologio declinante. </s>
  <s xml:id="echoid-s37339" xml:space="preserve">In hac linea meridiana reperiemus centrum <lb/>
<anchor type="note" xlink:label="note-0585-04a" xlink:href="note-0585-04"/>
horologĳ hoc modo. </s>
  <s xml:id="echoid-s37340" xml:space="preserve">Ex I, ad meridianam lineam horologĳ horizontalis A I, excitetur perpendicula-<lb/>ris I L. </s>
  <s xml:id="echoid-s37341" xml:space="preserve">Deſcripto autem ex A, loco styli in horologio horizontali, ad interuallũ longitudinis ſtyli A B, <lb/>
<anchor type="note" xlink:label="note-0585-05a" xlink:href="note-0585-05"/>
circulo B M, ad cum finem, vt omnes lineæ ex A, ad circunferentiam huius circuli ductœ (quœ non rarò <lb/>ducendœ erunt) ſtylo A B, ſint œquales, ducatur ex A, ad AI, perpendicularis A M, vſque ad cir-<lb/>cunferentiam dicti circuli, &amp; </s>
  <s xml:id="echoid-s37342" xml:space="preserve">ad eaſdem partes, ad quas recta I L, ducta est. </s>
  <s xml:id="echoid-s37343" xml:space="preserve">Ex N, autem centro horo-<lb/>logĳ horizontalis per M, ductarecta ſecet rectam I L, in L, &amp; </s>
  <s xml:id="echoid-s37344" xml:space="preserve">ipſi I L, in linea meridiana horologĳ de-<lb/>clinantis abſcindatur æqualis I K, verſus lineam horizontalem F H. </s>
  <s xml:id="echoid-s37345" xml:space="preserve">Dico K, centrum eſſe horologĳ <lb/>declinantis à meridie. </s>
  <s xml:id="echoid-s37346" xml:space="preserve">Si enim triangulum NLI, circa NI, con@ertatur, donec ad planum horologĳ <lb/>horizontalis ſit rectum, ita vt puncta M, L, ſtatuantur ſupra horologium, non autem infra, erunt rectę <lb/>L I, M A, ad idem planum, ex defin. </s>
  <s xml:id="echoid-s37347" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37348" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37349" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37350" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37351" xml:space="preserve">perpendiculares. </s>
  <s xml:id="echoid-s37352" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s37353" xml:space="preserve">I K, ad idem planum <lb/>
<anchor type="note" xlink:label="note-0585-06a" xlink:href="note-0585-06"/>
ſit perpendicularis, eadem erit I L, quæ I K, &amp; </s>
  <s xml:id="echoid-s37354" xml:space="preserve">punctum L, idem, quod K. </s>
  <s xml:id="echoid-s37355" xml:space="preserve">Quia vero A M, ſtyl{us} est <lb/>horologĳ horizontalis, erit N M L, axis mundi. </s>
  <s xml:id="echoid-s37356" xml:space="preserve">Axis enim mundi per M, verticem ſtyli duct{us} occur-<lb/>rit plano horologĳ in centro horologĳ. </s>
  <s xml:id="echoid-s37357" xml:space="preserve">Igitur axis mundi plano horologĳ declinantis occurret in K; </s>
  <s xml:id="echoid-s37358" xml:space="preserve">ac <lb/>proinde K, centrum erit eiuſdem horologĳ, vt ex coroll. </s>
  <s xml:id="echoid-s37359" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s37360" xml:space="preserve">21. </s>
  <s xml:id="echoid-s37361" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37362" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37363" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s37364" xml:space="preserve">Ex K, centro horologĳ <lb/>
<anchor type="note" xlink:label="note-0585-07a" xlink:href="note-0585-07"/>
recta K F, ducta per F, locum ſtyli erit linea ſtyli, ſiue communis ſectio horologĳ declinantis, &amp; </s>
  <s xml:id="echoid-s37365" xml:space="preserve">Me-<lb/>ridiani proprĳ eiuſdem horologii: </s>
  <s xml:id="echoid-s37366" xml:space="preserve">quę licet in dato exemplo parallela ſit lineæ meridianæ A I, in horo-<lb/>logio horizontali, ſecet{q́ue} lineam æquinoctialem eiuſdem horologii ad angulos rectos, non tamen idcirco <lb/>putes, neceſſario ita debere contingere in omnib{us} horologĳs declinantib{us}, quia caſu id in noſtro exem-<lb/>plo accidit; </s>
  <s xml:id="echoid-s37367" xml:space="preserve">in alĳs autem horologiis declinantibus contrarium experieris.</s>
  <s xml:id="echoid-s37368" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1879" type="float" level="2" n="2">
<note position="right" xlink:label="note-0585-02" xlink:href="note-0585-02a" xml:space="preserve">Linea me@idia-<lb/>na quomode <lb/>ducatur.</note>
<note position="right" xlink:label="note-0585-03" xlink:href="note-0585-03a" xml:space="preserve">18. vndec.</note>
<note position="left" xlink:label="note-0585-04" xlink:href="note-0585-04a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0585-05" xlink:href="note-0585-05a" xml:space="preserve">Centrum hore <lb/>logii quo pact@ <lb/>reperiatur.</note>
<note position="left" xlink:label="note-0585-06" xlink:href="note-0585-06a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0585-07" xlink:href="note-0585-07a" xml:space="preserve">Linea ſtyli quæ.</note>
</div>
<p style="it">
  <s xml:id="echoid-s37369" xml:space="preserve">QVONIAM autem linea æquinoctialis lineam@ ſtyli ad angulos rectos ſecat, vt propoſ. </s>
  <s xml:id="echoid-s37370" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37371" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37372" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s37373" xml:space="preserve">
<anchor type="note" xlink:label="note-0585-08a" xlink:href="note-0585-08"/>
<anchor type="note" xlink:label="note-0585-09a" xlink:href="note-0585-09"/>
demonſtr auimus, ducenda eſt autem æquinoctialis linea in horologio declinante per punctum O, vbi Ae-<lb/>quator per æquinoctialem lineam horologii horizont alis ductus plano horologii declinantis occurrit, erit <lb/>recta O P, ducta ex O, ad lineam ſtyli perpendicularis, linea æquinoctialis, quœ in noſtro exemplo ab æqui <lb/>noctiali linea horizontalis horologĳ non differt; </s>
  <s xml:id="echoid-s37374" xml:space="preserve">propterea quód, vt dixim{us}, linea ſtyli æquinoctialem li-<lb/>neam horologĳ horizont alis ſecat ad rectos angulos: </s>
  <s xml:id="echoid-s37375" xml:space="preserve">quod tamen in alĳs horologĳs declinantib{us} non <lb/>continget. </s>
  <s xml:id="echoid-s37376" xml:space="preserve">Inueniem{us} autem in K I, linea meridiana horologĳ declinantis producta punctum P, per <lb/>quod linea æquino ctialis ducenda eſt, hoc modo. </s>
  <s xml:id="echoid-s37377" xml:space="preserve">Ex A, ad meridianam lineam A I, horologĳ horizon-<lb/>talis excitetur linea perpendicularis AQ, vſque ad circumferentiam circuli BMQ, non ad e{as}dem <lb/>partes, ad qu{as} recta I L, ducta eſt, ſed ad contrari{as}, ducatur{q́ue} ex Q, per punctum R, vbi linea meri-<lb/>diana, &amp; </s>
  <s xml:id="echoid-s37378" xml:space="preserve">æquinoctialis ſe interſecant in horologio horizontali, linea recta, donec rectam IL, quæ ex <lb/>
<anchor type="note" xlink:label="note-0585-10a" xlink:href="note-0585-10"/>
puncto I, vbimeridiana linea horologĳ horizontalis plano horelogĳ declinantis occurrit, ad eandem <lb/>meridianam lineam perpendicularis ducta eſt, ſecet in puncto S. </s>
  <s xml:id="echoid-s37379" xml:space="preserve">Si enim rectæ I S, ex K I, producta <lb/>verſ{us} centrum A, auferatur æqualis I P, ducenda erit linea æquinoctialis in horologio declinante ex <lb/>O, per P. </s>
  <s xml:id="echoid-s37380" xml:space="preserve">Intelligatur enim planum, in quo triangula AQR, RSI, existunt, conuerti circa meridia-<lb/>nam lineam A I, donec rectum ſit ad horologium horizontale, ita vt punctum Q, existat ſupra horolo-<lb/>gium, &amp; </s>
  <s xml:id="echoid-s37381" xml:space="preserve">S, infra; </s>
  <s xml:id="echoid-s37382" xml:space="preserve">quo poſito, erit tam AQ, quam IS, ad planum horologĳ horizontalis recta, ex <lb/>defin. </s>
  <s xml:id="echoid-s37383" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37384" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37385" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37386" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37387" xml:space="preserve">Eſt autem per eandem defin. </s>
  <s xml:id="echoid-s37388" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37389" xml:space="preserve">meridiana linea I P, in horologio declinante ad <lb/>idem planum recta. </s>
  <s xml:id="echoid-s37390" xml:space="preserve">Igitur congruet recta IS, rectæ I P, punctum{q́ue} S, puncto P. </s>
  <s xml:id="echoid-s37391" xml:space="preserve">Quoniam vero radius <lb/>Solis in meridie per Q, verticem styli tranſiens, Sole exiſtente in Aequatore, cadit in punctum R, pro-<lb/>duct{us} autem infra planum horologĳ horizontalis cadit in punctum S, vel P, in horologio declinante, <lb/>
<anchor type="note" xlink:label="note-0585-11a" xlink:href="note-0585-11"/>
occurret Aequator plano horologĳ declinantis in P, quandoquidem radi{us} Solis per centrum mundi <lb/>tranſiens tunc à plano Aequatoris nonrecedit. </s>
  <s xml:id="echoid-s37392" xml:space="preserve">Igitur per P, ducenda eſt æquinoctialis linea. </s>
  <s xml:id="echoid-s37393" xml:space="preserve">Aliud <lb/>adhuc punctum H, reperiem{us} in linea horizontali F H, per quod eadem linea æquinoctialis ducenda <lb/>eſt, hac ratione. </s>
  <s xml:id="echoid-s37394" xml:space="preserve">Ex A, ducatur AV, æquinoctiali lineæ par allela ſecans rectam E G, in V: </s>
  <s xml:id="echoid-s37395" xml:space="preserve">(Hæc au-<lb/>tem facile ducetur, ſirectœ T A, æqualis ſumatur O V. </s>
  <s xml:id="echoid-s37396" xml:space="preserve">Ita enim fiet, vt rectæ A V, T O, connecten-<lb/>tes extrema puncta rectarum T A, O V, æqualium, &amp; </s>
  <s xml:id="echoid-s37397" xml:space="preserve">parallelarum, æquales inter ſe ſint, ac parallelę.) <lb/></s>
  <s xml:id="echoid-s37398" xml:space="preserve">
<anchor type="note" xlink:label="note-0585-12a" xlink:href="note-0585-12"/>
Et ex V, ad E V, excitetur perpendicularis V H, ſecans horizontalem lineam in H, puncto, per quod <lb/>æquinoctialis linea ducenda eſt. </s>
  <s xml:id="echoid-s37399" xml:space="preserve">Cum enim planum horologĳ declinantis rectum ſit ad planum horologĳ <lb/>horizontalis, erit recta H V, ex defin. </s>
  <s xml:id="echoid-s37400" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37401" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37402" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37403" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37404" xml:space="preserve">ad idem horologium horizontale perpendicularis. <lb/></s>
  <s xml:id="echoid-s37405" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s37406" xml:space="preserve">ſtyl{us} B A, ad idem ſit rect{us}, parallelæ inter ſe erunt B A, H V: </s>
  <s xml:id="echoid-s37407" xml:space="preserve">Sunt autem &amp; </s>
  <s xml:id="echoid-s37408" xml:space="preserve">inter ſe <lb/>
<anchor type="note" xlink:label="note-0585-13a" xlink:href="note-0585-13"/>
æquales. </s>
  <s xml:id="echoid-s37409" xml:space="preserve">(Nam E F, cui recta H V, in parallelogrammo F V, æqualis eſt, ſumpta est æqualis ſtylo A B.) <lb/></s>
  <s xml:id="echoid-s37410" xml:space="preserve">
<anchor type="note" xlink:label="note-0585-14a" xlink:href="note-0585-14"/>
<pb o="570" file="0586" n="586" rhead="GNOMONICES"/>
Igitur recta coniungens extrema puncta B, H, ipſi A V, æqualis erit, ac parallela. </s>
  <s xml:id="echoid-s37411" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s37412" xml:space="preserve">T O, <lb/>
<anchor type="note" xlink:label="note-0586-01a" xlink:href="note-0586-01"/>
<anchor type="note" xlink:label="note-0586-02a" xlink:href="note-0586-02"/>
eidem A V, ſit parallela, ex conſtructione; </s>
  <s xml:id="echoid-s37413" xml:space="preserve">erit &amp; </s>
  <s xml:id="echoid-s37414" xml:space="preserve">recta B H, eidem T O, parallela; </s>
  <s xml:id="echoid-s37415" xml:space="preserve">ac proinde B H, <lb/>T O, in vno eodem{q́ue} plano erunt, nempe in plano Aequatoris, quod per rectam T O, nempe per lineam <lb/>æquinoctialem horologĳ horizontalis, &amp; </s>
  <s xml:id="echoid-s37416" xml:space="preserve">per verticem ſtyli B, ducitur. </s>
  <s xml:id="echoid-s37417" xml:space="preserve">Quare Aequator plano horolo-<lb/>gĳ declinantis occurret in puncto H, propterea{q́ue} per H, ducenda erit linea æquinoctialis. </s>
  <s xml:id="echoid-s37418" xml:space="preserve">Itaque ſi <lb/>
<anchor type="figure" xlink:label="fig-0586-01a" xlink:href="fig-0586-01"/>
<anchor type="note" xlink:label="note-0586-03a" xlink:href="note-0586-03"/>
<anchor type="note" xlink:label="note-0586-04a" xlink:href="note-0586-04"/>
<anchor type="note" xlink:label="note-0586-05a" xlink:href="note-0586-05"/>
tria puncta H, O, P, in recta linea existant, quæ ad lineam styli K F, perpendicularis ſit, recte duce-<lb/>tur linea æquinoctialis per puncta H, O, P. </s>
  <s xml:id="echoid-s37419" xml:space="preserve">Punctum tamen H, in linea horizontali facili{us} reperie-<lb/>tur hoc modo. </s>
  <s xml:id="echoid-s37420" xml:space="preserve">Ex N, centro horologĳ horizontalis excitetur ad meridianam lineam N I, perpendi-<lb/>cularis N X, pro linea horæ 6. </s>
  <s xml:id="echoid-s37421" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s37422" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37423" xml:space="preserve">med. </s>
  <s xml:id="echoid-s37424" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37425" xml:space="preserve">ſecans rectam E G, in X. </s>
  <s xml:id="echoid-s37426" xml:space="preserve">Nam recta ex K, centro <lb/>horologĳ declinantis ad X, ducta, erit linea horæ 6. </s>
  <s xml:id="echoid-s37427" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s37428" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s37429" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37430" xml:space="preserve">in horologio declinante, cum <lb/>circul{us} horæ 6. </s>
  <s xml:id="echoid-s37431" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s37432" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s37433" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37434" xml:space="preserve">occurrat huic horologio in puncto X, &amp; </s>
  <s xml:id="echoid-s37435" xml:space="preserve">in centro horologii. </s>
  <s xml:id="echoid-s37436" xml:space="preserve">Hæc <lb/>
<anchor type="note" xlink:label="note-0586-06a" xlink:href="note-0586-06"/>
ergo recta K X, ſecabit lineam horizontalem in puncto H, per quod linea æquinoctialis ducenda eſt. <lb/></s>
  <s xml:id="echoid-s37437" xml:space="preserve">Semper enim linea æquinoctialis, linea horæ 6. </s>
  <s xml:id="echoid-s37438" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s37439" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s37440" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37441" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37442" xml:space="preserve">linea horizontalis ſe mutuo in <lb/>vno eodem{q́ue} puncto interſecant, vt ex demonſtratis in lib. </s>
  <s xml:id="echoid-s37443" xml:space="preserve">3. </s>
  <s xml:id="echoid-s37444" xml:space="preserve">perſpicuum eſt.</s>
  <s xml:id="echoid-s37445" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1880" type="float" level="2" n="3">
<note position="left" xlink:label="note-0585-08" xlink:href="note-0585-08a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0585-09" xlink:href="note-0585-09a" xml:space="preserve">Linea æquino-<lb/>ctialis, qua ra-<lb/>tione ducatur.</note>
<note position="left" xlink:label="note-0585-10" xlink:href="note-0585-10a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0585-11" xlink:href="note-0585-11a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0585-12" xlink:href="note-0585-12a" xml:space="preserve">33. primi.</note>
<note position="right" xlink:label="note-0585-13" xlink:href="note-0585-13a" xml:space="preserve">6. vndec.</note>
<note position="right" xlink:label="note-0585-14" xlink:href="note-0585-14a" xml:space="preserve">34. primi.</note>
<note position="left" xlink:label="note-0586-01" xlink:href="note-0586-01a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0586-02" xlink:href="note-0586-02a" xml:space="preserve">9. vndec.</note>
  <figure xlink:label="fig-0586-01" xlink:href="fig-0586-01a">
    <image file="0586-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0586-01"/>
  </figure>
<note position="left" xlink:label="note-0586-03" xlink:href="note-0586-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0586-04" xlink:href="note-0586-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0586-05" xlink:href="note-0586-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0586-06" xlink:href="note-0586-06a" xml:space="preserve">40</note>
</div>
<p style="it">
  <s xml:id="echoid-s37446" xml:space="preserve">EODEM artificio, quo lineam æquinoctialem in horologio declinante deſcripſim{us}, depingem{us} <lb/>omnes line{as} horari{as} vnà cum punctis tropicorum, &amp; </s>
  <s xml:id="echoid-s37447" xml:space="preserve">aliorum parallelorum. </s>
  <s xml:id="echoid-s37448" xml:space="preserve">Quod vt planius fiat, <lb/>rem vno aut a<unsure/>ltero exemplo illuſtrabimus. </s>
  <s xml:id="echoid-s37449" xml:space="preserve">Sit v. </s>
  <s xml:id="echoid-s37450" xml:space="preserve">g. </s>
  <s xml:id="echoid-s37451" xml:space="preserve">delineanda hora 23. </s>
  <s xml:id="echoid-s37452" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37453" xml:space="preserve">Quoniam linea horæ <lb/>
<anchor type="note" xlink:label="note-0586-07a" xlink:href="note-0586-07"/>
23. </s>
  <s xml:id="echoid-s37454" xml:space="preserve">in horologio horizontali rectam E G, non ſecat, producemus illam, donec ipſam E G, ſecet in G, pun <lb/>cto, per quod in horologio declinante neceſſario ducenda erit hora 23. </s>
  <s xml:id="echoid-s37455" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37456" xml:space="preserve">cum in eo puncto circulus <lb/>horæ 23. </s>
  <s xml:id="echoid-s37457" xml:space="preserve">per lineam eiuſdem horæ ductus occurrat plano horologii declinantis. </s>
  <s xml:id="echoid-s37458" xml:space="preserve">Atque ita omnes horæ <lb/>per illa puncta rectæ E G, in horologio declinante ducendæ erunt, in quib{us} lineæ horariæ in horologio <lb/>
<anchor type="note" xlink:label="note-0586-08a" xlink:href="note-0586-08"/>
horizontali rectam E G, ſecant. </s>
  <s xml:id="echoid-s37459" xml:space="preserve">Deinde rectæ D A, inter lineam horæ 23. </s>
  <s xml:id="echoid-s37460" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37461" xml:space="preserve">locum ſtyli A, inhorolo-<lb/>gio horizontali ſumemus in recta E G, æqualem G a, &amp; </s>
  <s xml:id="echoid-s37462" xml:space="preserve">ex a, ad E G, perpendicularem ducemus a Y, <lb/>quæ horizontalem lineam F H, ſecet in Y, puncto, per quod ducenda quoque eſt linea horæ 23. </s>
  <s xml:id="echoid-s37463" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s37464" xml:space="preserve">ita vt recta Y G, producta indicet horam 23. </s>
  <s xml:id="echoid-s37465" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37466" xml:space="preserve">in horologio declinante. </s>
  <s xml:id="echoid-s37467" xml:space="preserve">Quia enim planum horo-<lb/>logii declinantis ad planum horizontalis horologii rectum est, erit Y a, ad idem planum, ex defin. </s>
  <s xml:id="echoid-s37468" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37469" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37470" xml:space="preserve"><lb/>11. </s>
  <s xml:id="echoid-s37471" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37472" xml:space="preserve">perpendicularis: </s>
  <s xml:id="echoid-s37473" xml:space="preserve">Eſt autem &amp; </s>
  <s xml:id="echoid-s37474" xml:space="preserve">ſtyl{us} A B, ad idem planum rectus. </s>
  <s xml:id="echoid-s37475" xml:space="preserve">Igitur a Y, A B, paralle-<lb/>
<anchor type="note" xlink:label="note-0586-09a" xlink:href="note-0586-09"/>
læ inter ſe erunt. </s>
  <s xml:id="echoid-s37476" xml:space="preserve">Cum ergo &amp; </s>
  <s xml:id="echoid-s37477" xml:space="preserve">æquales inter ſe ſint, quòd E F, cui a Y, in parallelogrammo a F, ęqua-<lb/>
<anchor type="note" xlink:label="note-0586-10a" xlink:href="note-0586-10"/>
lis eſt, ſumpta ſit æqualis ſtylo A B, erit quoque recta connectens puncta B, Y, rectæ A a, connecten-<lb/>ti extrema A, a, æqualis, ac parallela. </s>
  <s xml:id="echoid-s37478" xml:space="preserve">Eſt autem rectæ A a, puncta A, a, coniungenti parallela quo-<lb/>
<anchor type="note" xlink:label="note-0586-11a" xlink:href="note-0586-11"/>
que D G, quòd rectę D A, G A, ęquales ſint, &amp; </s>
  <s xml:id="echoid-s37479" xml:space="preserve">parallelæ, per conſtructionem. </s>
  <s xml:id="echoid-s37480" xml:space="preserve">Igitur &amp; </s>
  <s xml:id="echoid-s37481" xml:space="preserve">recta conne-<lb/>ctens puncta B, Y, eidem D G, parallela erit, ac propterea rectæ B Y, D G, in vno eodem{q́ue} plano exi-<lb/>
<anchor type="note" xlink:label="note-0586-12a" xlink:href="note-0586-12"/>
<pb o="571" file="0587" n="587" rhead="LIBER SEXTVS."/>
ſtent, nimirum in plano circuli horæ 23. </s>
  <s xml:id="echoid-s37482" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37483" xml:space="preserve">quod per rectam D G, &amp; </s>
  <s xml:id="echoid-s37484" xml:space="preserve">per B, verticem ſtyli ducitur. <lb/></s>
  <s xml:id="echoid-s37485" xml:space="preserve">Quocirca circulus horæ 23 occurret plano horologii declinantis in puncto Y. </s>
  <s xml:id="echoid-s37486" xml:space="preserve">Eadem ratione linea horæ <lb/>22. </s>
  <s xml:id="echoid-s37487" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37488" xml:space="preserve">per puncta b, d, ducenda erit, ſi rectæ e A, inter horam 22. </s>
  <s xml:id="echoid-s37489" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37490" xml:space="preserve">locum ſtyli in horologio ho-<lb/>rizontali ſumatur ęqualis b f, hoc eſt, lineæ horæ 22. </s>
  <s xml:id="echoid-s37491" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37492" xml:space="preserve">agatur per A, parallela A f, occulta, du-<lb/>catur{q́ue} f d, ad E G, perpendicularis ſecans horizontalem lineã in d. </s>
  <s xml:id="echoid-s37493" xml:space="preserve">Sic quoque linea horæ 15. </s>
  <s xml:id="echoid-s37494" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37495" xml:space="preserve">per <lb/>puncta i, g, ducẽda erit, ſiquide<unsure/>m linea horæ 15. </s>
  <s xml:id="echoid-s37496" xml:space="preserve">in horologio horizontali ſecat rectã E G, in i, &amp; </s>
  <s xml:id="echoid-s37497" xml:space="preserve">A h, pa <lb/>rallela lineæ horæ 15. </s>
  <s xml:id="echoid-s37498" xml:space="preserve">eandem E G, ſecat in h, ducta{q́ue} eſt h g, ad E G, perpendicularis ſecans lineam ho-<lb/>rizontalem in g. </s>
  <s xml:id="echoid-s37499" xml:space="preserve">Non aliter quamcunque lineam in horologio horizontali deſcriptam, (ſiue ea ex nume-<lb/>
<anchor type="note" xlink:label="note-0587-01a" xlink:href="note-0587-01"/>
ro horariarum linearum ſit, ſiue aliqua ex Verticalibus, Meridianisve, aut vna ex domibus cæleſtibus, <lb/>ſeu ſignis aſcendentibus) ſi tamen producta rectam E G, ſecet, in horologio declinante ducemus per il-<lb/>
<anchor type="note" xlink:label="note-0587-02a" xlink:href="note-0587-02"/>
lud punctum, in quo ipſa linea horologĳ horizontalis in declinante horologio deſcribenda rectam E G, <lb/>interſecat, &amp; </s>
  <s xml:id="echoid-s37500" xml:space="preserve">per illud punctum lineæ horizontalis, in quod cadit linea perpendicularis ad E G, ex eo <lb/>puncto ducta, in quod cadit linea per A, ducta propoſitę lineæ in horologio horizontali parallela, vt ex <lb/>demonſtratis manifeſtum est. </s>
  <s xml:id="echoid-s37501" xml:space="preserve">Lineæ autem horarum à mer. </s>
  <s xml:id="echoid-s37502" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37503" xml:space="preserve">med. </s>
  <s xml:id="echoid-s37504" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37505" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37506" xml:space="preserve">communes ſectiones Meri-<lb/>dianorum, circulorumve longitudinum, &amp; </s>
  <s xml:id="echoid-s37507" xml:space="preserve">plani horologii, tranſibunt omnes per K, centrum horologii. <lb/></s>
  <s xml:id="echoid-s37508" xml:space="preserve">Vnde ſatis est, ſi inueniatur centrum horologĳ K. </s>
  <s xml:id="echoid-s37509" xml:space="preserve">Rectæ enim ductæ per centrum horologii K, &amp; </s>
  <s xml:id="echoid-s37510" xml:space="preserve">per pun <lb/>cta, in quibus recta E G, à lineis horarum à mer. </s>
  <s xml:id="echoid-s37511" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37512" xml:space="preserve">med. </s>
  <s xml:id="echoid-s37513" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37514" xml:space="preserve">vel à communibus ſectionibus Meridiano-<lb/>rum, &amp; </s>
  <s xml:id="echoid-s37515" xml:space="preserve">plani horologii horizontalis ſecatur, dabunt horas à mer. </s>
  <s xml:id="echoid-s37516" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37517" xml:space="preserve">med. </s>
  <s xml:id="echoid-s37518" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37519" xml:space="preserve">vel communes ſectiones <lb/>Meridianorum, &amp; </s>
  <s xml:id="echoid-s37520" xml:space="preserve">plani horologii declinantis. </s>
  <s xml:id="echoid-s37521" xml:space="preserve">Accuratius tamen ducentur, ſi pro linea quacunque ter <lb/>tium adhuc punctum in linea horizontali inucniatur. </s>
  <s xml:id="echoid-s37522" xml:space="preserve">Rurſus quia lineę Verticales in horologio declinan <lb/>
<anchor type="note" xlink:label="note-0587-03a" xlink:href="note-0587-03"/>
te omnes parallelæ ſunt, &amp; </s>
  <s xml:id="echoid-s37523" xml:space="preserve">ad horizontalem lineam perpendiculares, vt propoſ. </s>
  <s xml:id="echoid-s37524" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37525" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37526" xml:space="preserve">3. </s>
  <s xml:id="echoid-s37527" xml:space="preserve">oſtendimus, du-<lb/>cendæ erunt lineæ V erticales in horologio declinante per ea puncta rectæ E G, in quibus à lineis Verti-<lb/>calibus horologii horizontalis ſecatur, ad ipſam rectam E G, vel ad lineam horizontalem perpendicula <lb/>res. </s>
  <s xml:id="echoid-s37528" xml:space="preserve">Denique quoniam lineæ domorum cæleſtium ducuntur in horologio declinante per punctum, vbi me <lb/>vidiana linea lineam horizontalem ſecat, ducendæ erunt huiuſmodi lineæ in præcedenti figur a per pun-<lb/>ctum Z, &amp; </s>
  <s xml:id="echoid-s37529" xml:space="preserve">per illa puncta rectæ E G, in quibus eædem lineæ in horologio horizontali rectæ E G, <lb/>occurrunt.</s>
  <s xml:id="echoid-s37530" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1881" type="float" level="2" n="4">
<note position="left" xlink:label="note-0586-07" xlink:href="note-0586-07a" xml:space="preserve">Lineæ horariæ <lb/>quo pacto deli-<lb/>@e@ntur,</note>
<note position="left" xlink:label="note-0586-08" xlink:href="note-0586-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0586-09" xlink:href="note-0586-09a" xml:space="preserve">@. vndec.</note>
<note position="left" xlink:label="note-0586-10" xlink:href="note-0586-10a" xml:space="preserve">34. primi</note>
<note position="left" xlink:label="note-0586-11" xlink:href="note-0586-11a" xml:space="preserve">33. primi.</note>
<note position="left" xlink:label="note-0586-12" xlink:href="note-0586-12a" xml:space="preserve">9. vndec.</note>
<note position="right" xlink:label="note-0587-01" xlink:href="note-0587-01a" xml:space="preserve">Linea quæcun-<lb/>que horologii <lb/>horizõtalis qua <lb/>ratione in horo <lb/>logio declinan-<lb/>te depingatur,</note>
<note position="left" xlink:label="note-0587-02" xlink:href="note-0587-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0587-03" xlink:href="note-0587-03a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s37531" xml:space="preserve">POSTREMO in lineis ex horologio horizontali in declinante horologio deſcriptis inueniemus <lb/>
<anchor type="note" xlink:label="note-0587-04a" xlink:href="note-0587-04"/>
puncta, per quæ arcus ſignorum ducendi ſunt, hac ratione. </s>
  <s xml:id="echoid-s37532" xml:space="preserve">Sit v. </s>
  <s xml:id="echoid-s37533" xml:space="preserve">g. </s>
  <s xml:id="echoid-s37534" xml:space="preserve">in linea d b, horæ 22. </s>
  <s xml:id="echoid-s37535" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37536" xml:space="preserve">inue-<lb/>niendum punctum, per quod tropicus ♑, ducendus ſit. </s>
  <s xml:id="echoid-s37537" xml:space="preserve">Ex A, loco ſtyli in horizontali horologio per <lb/>
<anchor type="note" xlink:label="note-0587-05a" xlink:href="note-0587-05"/>
punctum horæ 22. </s>
  <s xml:id="echoid-s37538" xml:space="preserve">in tropico ♑, ducatur recta occulta A 22. </s>
  <s xml:id="echoid-s37539" xml:space="preserve">ſecans producta rectam E G, in puncto <lb/>m, per quod ad rectas A m, E G, per pendiculares ducantur m n, m l: </s>
  <s xml:id="echoid-s37540" xml:space="preserve">Item ex A, ad eandem A m, in <lb/>contrariam partem ei, in quam m n, ducta eſt, ducatur perpendicularis A p, vſque ad circunferentiam <lb/>circuli B M. </s>
  <s xml:id="echoid-s37541" xml:space="preserve">Deinde ducta recta occulta ex p, per idem punctum horæ 22. </s>
  <s xml:id="echoid-s37542" xml:space="preserve">in tropico ♑, quæ perpendi-<lb/>cularem m n, ſecet in n, ſi rectæ m n, abſcindatur ex m l, ęqualis m l, erit per punctum l, in horologio <lb/>declinante ducendus parallelus ♑, hoc eſt, Sole exiſtente in principio ♑, vmbra gnomonis hora 22. </s>
  <s xml:id="echoid-s37543" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s37544" xml:space="preserve">cadet in punctum l, ita vt neceſſario linea d b, horæ 22. </s>
  <s xml:id="echoid-s37545" xml:space="preserve">iam pridem ducta tranſeat per punctum <lb/>l, ſi erratum non est. </s>
  <s xml:id="echoid-s37546" xml:space="preserve">Vnde ſatis eſſet, ſi ex puncto m, in quod cadit recta occulta ex A, per horam 22. <lb/></s>
  <s xml:id="echoid-s37547" xml:space="preserve">in tropico ♑, ducta, duceretur ad E G, perpendicularis m l. </s>
  <s xml:id="echoid-s37548" xml:space="preserve">V bi enim hæc lineam horę 22. </s>
  <s xml:id="echoid-s37549" xml:space="preserve">d b, ſecabit, <lb/>ibi erit punctum tropici ♑. </s>
  <s xml:id="echoid-s37550" xml:space="preserve">Sed magis exquiſite linea horaria deſcribetur, ſi punctum l, reperiatur, vt <lb/>
<anchor type="note" xlink:label="note-0587-06a" xlink:href="note-0587-06"/>
docuimus. </s>
  <s xml:id="echoid-s37551" xml:space="preserve">Si enim recta m l, rectæ m n, ſumpta fuerit æqualis, atque tria puncta l, b, d, in recta linea <lb/>iaceant, exquiſitiſſime ducetur per tria hæc puncta linea horæ 22. </s>
  <s xml:id="echoid-s37552" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37553" xml:space="preserve">Quòd ſi reperiatur etiam pun <lb/>ctum tropici ♋, habebuntur quatuor puncta, per quæ duccnda erit linea horaria propoſita. </s>
  <s xml:id="echoid-s37554" xml:space="preserve">In hora 22. <lb/></s>
  <s xml:id="echoid-s37555" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37556" xml:space="preserve">noſtri exempli quartum hoc punctum reperiri non potest, quia recta ex A, ducta per punctum <lb/>♋, in dicta hora non ſecat rectam E G. </s>
  <s xml:id="echoid-s37557" xml:space="preserve">Vnde Sol in principio ♋, exiſtens hora 22. </s>
  <s xml:id="echoid-s37558" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37559" xml:space="preserve">planum ho-<lb/>rologii declinantis à mer. </s>
  <s xml:id="echoid-s37560" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s37561" xml:space="preserve">non illuminat. </s>
  <s xml:id="echoid-s37562" xml:space="preserve">Extremum autem vmbræ gnomonis cadere hora 22. </s>
  <s xml:id="echoid-s37563" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s37564" xml:space="preserve">Sole exiſtente in principio ♑, in punctum l, demonſtr abim{us} eo modo, quo paulo ante oſtendimus, <lb/>vmbræ extremum in meridie, Sole exiſtente in æquinoctiis, cadere in punctum P, lineæ meridianæ K I. </s>
  <s xml:id="echoid-s37565" xml:space="preserve"><lb/>Si enim planum, in quo triangula A p 22, 22 n m, exiſtunt, circa rectam A m, intelligatur conuerti, <lb/>donec rectum ſit ad horologium horizontale, ita vt punctum p, ſupra horologium horizontale existat, <lb/>
<anchor type="note" xlink:label="note-0587-07a" xlink:href="note-0587-07"/>
&amp; </s>
  <s xml:id="echoid-s37566" xml:space="preserve">n, infra, erit ex defin. </s>
  <s xml:id="echoid-s37567" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37568" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37569" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37570" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37571" xml:space="preserve">tam A p, quam m n, ad idem horologium recta: </s>
  <s xml:id="echoid-s37572" xml:space="preserve">Eſt autem, per <lb/>eandem defin. </s>
  <s xml:id="echoid-s37573" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37574" xml:space="preserve">m l, ad idem perpendicularis in plano horologii declinantis ad horologium horizon-<lb/>tale recto. </s>
  <s xml:id="echoid-s37575" xml:space="preserve">Recta ergo m n, rectę m l, &amp; </s>
  <s xml:id="echoid-s37576" xml:space="preserve">punctum n, puncto l, congruet, ob æqualitatem rectarum m n, <lb/>m l. </s>
  <s xml:id="echoid-s37577" xml:space="preserve">Quoniam vero radius Solis per p, verticẽ ſtyli incedens hora 22. </s>
  <s xml:id="echoid-s37578" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37579" xml:space="preserve">in tropico ♑, cadit in pun-<lb/>ctum 22. </s>
  <s xml:id="echoid-s37580" xml:space="preserve">cadet idem productus infra planum horologii horizontalis in punctam n, vel l, in horologio de-<lb/>clinante; </s>
  <s xml:id="echoid-s37581" xml:space="preserve">ac proinde occurret circulus horæ 22. </s>
  <s xml:id="echoid-s37582" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37583" xml:space="preserve">plano horologii declinantis in l, puncto, quando-<lb/>quidem radi{us} Solis per centrum munditranſiens à plano dicti circuli tunc non recedit. </s>
  <s xml:id="echoid-s37584" xml:space="preserve">Eadem ratione <lb/>
<anchor type="note" xlink:label="note-0587-08a" xlink:href="note-0587-08"/>
omnia alia puncta horologii horizontalis in horologium declinans transferentur, ſi per ipſa ducantur ex <lb/>A, rectę occultæ, (qualis fuit in hora 22. </s>
  <s xml:id="echoid-s37585" xml:space="preserve">♑, recta A m,) &amp; </s>
  <s xml:id="echoid-s37586" xml:space="preserve">per puncta, in quibus recta E G, à dictis re-<lb/>ctis occultis ſecatur, (quale eſt punctũm.) </s>
  <s xml:id="echoid-s37587" xml:space="preserve">tam ad rect{as} ill{as} occult{as}, quàm ad rectã E G, ducãtur per-<lb/>pendiculares, (cuiuſmodi ſunt perpendiculares m n, m l.) </s>
  <s xml:id="echoid-s37588" xml:space="preserve">in quib{us} puncta reperiantur, in quæ vmbra
<pb o="572" file="0588" n="588" rhead="GNOMONICES"/>
proiicitur, ductis prius ex A, ad eaſdem occultas lineis perpendicularibus vſq; </s>
  <s xml:id="echoid-s37589" xml:space="preserve">ad circulũ B M, &amp; </s>
  <s xml:id="echoid-s37590" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37591" xml:space="preserve">Solũ <lb/>hoc obſeruandum eſt, quòd, quando punctum ex horologio horizontali transferendum exiſtit inter A, &amp; </s>
  <s xml:id="echoid-s37592" xml:space="preserve"><lb/>rectam E G, quemadmodum fuit punctum horæ 22. </s>
  <s xml:id="echoid-s37593" xml:space="preserve">♑, in nostro exemplo, perpendicularis ad E G, qua-<lb/>lis eſt m l, ducenda eſt verſ{us} A, nempe infra rectam E G, in horologio declinante; </s>
  <s xml:id="echoid-s37594" xml:space="preserve">quia tunc radius <lb/>Solis ſecat in dato puncto planum horologĳ horizontalis, antequam plano horologĳ declinantis ad pla-<lb/>num horologĳ horizontalis recto occurrat; </s>
  <s xml:id="echoid-s37595" xml:space="preserve">atque adeo horologio declinanti occurret infra rectam E G: <lb/></s>
  <s xml:id="echoid-s37596" xml:space="preserve">quando autem recta E G, eſt inter A, &amp; </s>
  <s xml:id="echoid-s37597" xml:space="preserve">punctum trãsferendum, cuiuſmodi ſunt in noſtro exemplo pun-<lb/>cta horarum 18. </s>
  <s xml:id="echoid-s37598" xml:space="preserve">17. </s>
  <s xml:id="echoid-s37599" xml:space="preserve">16. </s>
  <s xml:id="echoid-s37600" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37601" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37602" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37603" xml:space="preserve">in tropico ♑, perpendicularis ad E G, ducenda eſt verſus lineam <lb/>horizontalem, nimirum ſupra rectam E G, in horologio declinante; </s>
  <s xml:id="echoid-s37604" xml:space="preserve">quia tunc radius Solis occurrit ho-<lb/>rologio declinanti ſupra rectam E G, antequam in dato puncto planum horologĳ horizontalis ſecet, vt <lb/>
<anchor type="note" xlink:label="note-0588-01a" xlink:href="note-0588-01"/>
perſpicuum eſt. </s>
  <s xml:id="echoid-s37605" xml:space="preserve">Verum in qoam partem perpendiculares ad E G, ducendæ ſint, ipſæmet lineæ horariæ <lb/>prius ductæ pulchre indicant. </s>
  <s xml:id="echoid-s37606" xml:space="preserve">Debent enim dictæ perpendiculares ad E G, verſus eam partem erigi, <lb/>vbi hor arias lineas poſſint ſecare. </s>
  <s xml:id="echoid-s37607" xml:space="preserve">Nihil autem intereſt, in vtram partem ducatur perpendicularis ad <lb/>rectam occultam ductam ex A, per punctum, quod in horologium declinans ex horizontali horologio <lb/>transferendum eſt, dummodo alia perpendicularis ex A, ad eandem occultam rectam in contrariam <lb/>partem ducatur, vt in exemplo factum eſt. </s>
  <s xml:id="echoid-s37608" xml:space="preserve">Hac ratione in ſingulis lineis horarĳs, quæ æquinoctialem <lb/>lineam in horologio declinante ſecant, (quales ſunt illæ, per quarum puncta in æquinoctiali linea horolo-<lb/>gĳ horizontalis rectæ ex A, emiſſæ rectam E G, interſecant.) </s>
  <s xml:id="echoid-s37609" xml:space="preserve">puncta inueniri poſſunt, per quæ linea <lb/>æquinoctialis ducenda eſt. </s>
  <s xml:id="echoid-s37610" xml:space="preserve">In eodem noſtro exemplo duximus ex A, per punctum horæ 15. </s>
  <s xml:id="echoid-s37611" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37612" xml:space="preserve">in <lb/>tropico ♋, rectam A q, quæ rectam E G, ſecat in q, &amp; </s>
  <s xml:id="echoid-s37613" xml:space="preserve">per q, ad A q, perpendicularem excitauimus <lb/>
<anchor type="note" xlink:label="note-0588-02a" xlink:href="note-0588-02"/>
q r, quam in r, ſecat recta t r, ducta ab extremo ſtyli A t, (qui ad A q, perpendicularis eſt.) </s>
  <s xml:id="echoid-s37614" xml:space="preserve">per pun-<lb/>ctum horæ 15. </s>
  <s xml:id="echoid-s37615" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37616" xml:space="preserve">in tropico ♋; </s>
  <s xml:id="echoid-s37617" xml:space="preserve">rectæque q r, ex q ſ, ad E G, perpendiculari æqualem abſcidimus <lb/>q ſ, in puncto ſ, vbi hæc perpendicularis lineam g h, horæ 15. </s>
  <s xml:id="echoid-s37618" xml:space="preserve">iam pridem ductam interſecat. </s>
  <s xml:id="echoid-s37619" xml:space="preserve">Nam per <lb/>ſ, tranſibit tropicus ♋. </s>
  <s xml:id="echoid-s37620" xml:space="preserve">in linea horæ 15 ab occ. </s>
  <s xml:id="echoid-s37621" xml:space="preserve">Pro tropico autem ♑, nullum puuctum inuenimus in ho-<lb/>ra 15. </s>
  <s xml:id="echoid-s37622" xml:space="preserve">ſed eam in horizontali linea terminauimus, quia hæc hora in horologio horizontali nullum pun-<lb/>ctum habet in tropico ♑.</s>
  <s xml:id="echoid-s37623" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1882" type="float" level="2" n="5">
<note position="right" xlink:label="note-0587-04" xlink:href="note-0587-04a" xml:space="preserve">Quomodoar-<lb/>cus ſignorũ ex <lb/>hori<unsure/>zontali ho-<lb/>rologio in horo <lb/>logiũ declinans <lb/>transferantur.</note>
<note position="left" xlink:label="note-0587-05" xlink:href="note-0587-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0587-06" xlink:href="note-0587-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0587-07" xlink:href="note-0587-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0587-08" xlink:href="note-0587-08a" xml:space="preserve">Qua ratione<unsure/> <lb/>omnia puncta <lb/>puncta horolo@ <lb/>gii horizontalis <lb/>in horologium <lb/>declinãs tranſ-<lb/>ferantur.</note>
<note position="left" xlink:label="note-0588-01" xlink:href="note-0588-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0588-02" xlink:href="note-0588-02a" xml:space="preserve">20</note>
</div>
<p style="it">
  <s xml:id="echoid-s37624" xml:space="preserve">SI horologium declinans à Septentrione in occ. </s>
  <s xml:id="echoid-s37625" xml:space="preserve">deſcribendum ſit, ſumenda eſt in recta A E, verſus <lb/>
<anchor type="note" xlink:label="note-0588-03a" xlink:href="note-0588-03"/>
meridiem recta A E, æqualis ſtylo futuri horologĳ declinantis, &amp; </s>
  <s xml:id="echoid-s37626" xml:space="preserve">recta E F, ſtylo horologĳ horizonta-<lb/>lis æqualis: </s>
  <s xml:id="echoid-s37627" xml:space="preserve">Deinde per E, F, ipſi A D, parallelæ ducendæ E G, F H, quarum E G, communis ſectio <lb/>erit horologii horizontalis, &amp; </s>
  <s xml:id="echoid-s37628" xml:space="preserve">horologii declinantis, recta vero F H, linea horizontalis. </s>
  <s xml:id="echoid-s37629" xml:space="preserve">Reliqua autem <lb/>
<anchor type="note" xlink:label="note-0588-04a" xlink:href="note-0588-04"/>
abſoluenda erunt, vt in horologio declinante à mer. </s>
  <s xml:id="echoid-s37630" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s37631" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s37632" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1883" type="float" level="2" n="6">
<note position="left" xlink:label="note-0588-03" xlink:href="note-0588-03a" xml:space="preserve">Horologium @ <lb/>Sept. declinans <lb/>quo pacto ex ho <lb/>rizontali deſcri <lb/>batur.</note>
<note position="left" xlink:label="note-0588-04" xlink:href="note-0588-04a" xml:space="preserve">30</note>
</div>
<p style="it">
  <s xml:id="echoid-s37633" xml:space="preserve">QVOD ſi in horizontali horologio deſcriptus eſſet parallelus omnium ſemper apparentium maxi-<lb/>mus, ſtatim diſcerneremus in horologio declinante à Septentr. </s>
  <s xml:id="echoid-s37634" xml:space="preserve">horas ab or. </s>
  <s xml:id="echoid-s37635" xml:space="preserve">ab horis ab occ. </s>
  <s xml:id="echoid-s37636" xml:space="preserve">Nam il-<lb/>læ horæ, quę in horologio Italico horizontali tangunt dictum parallelum, antequam rectæ E G, occur-<lb/>rant, pertinent in horologio declinante ad horas ab ortu, vt ex ĳs, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s37637" xml:space="preserve">10. </s>
  <s xml:id="echoid-s37638" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37639" xml:space="preserve">2. </s>
  <s xml:id="echoid-s37640" xml:space="preserve">ſcri-<lb/>pſimus, manifeſtum eſt.</s>
  <s xml:id="echoid-s37641" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s37642" xml:space="preserve">CAETERVM inuentum hoc nostrum non multum differt ab artificio, quod Guid{us} Vbaldus <lb/>
<anchor type="note" xlink:label="note-0588-05a" xlink:href="note-0588-05"/>
è Marchionibus Montis, vir in rebus Mathematicis præſtantiſſimus, excogitau<unsure/>it, atque humaniſſime ad <lb/>me miſit: </s>
  <s xml:id="echoid-s37643" xml:space="preserve">quo quidem artificio ex Solis circunferentiis horizontalibus, deſcenſiuis{q́ue} in Horizonte in-<lb/>uentis conficiemus eadem horologia ad Horizontem recta. </s>
  <s xml:id="echoid-s37644" xml:space="preserve">Quamuis autem ipſe in plano Horizontis <lb/>
<anchor type="note" xlink:label="note-0588-06a" xlink:href="note-0588-06"/>
deſcribat prius Ellipſes, quas perpendiculares ex horis omnium parallelorum in planum Horizontis ca-<lb/>dentes in plano Horizontis efficiunt, vt propoſ. </s>
  <s xml:id="echoid-s37645" xml:space="preserve">24. </s>
  <s xml:id="echoid-s37646" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37647" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37648" xml:space="preserve">demonstrauim{us}, nos tamen rem ipſam ex ſo-<lb/>lis circunferentiis horizontalibus, ac deſcenſiuis facilius explicabimus hocmodo. </s>
  <s xml:id="echoid-s37649" xml:space="preserve">Sit Horizon A B-<lb/>C D, cuius centrum E; </s>
  <s xml:id="echoid-s37650" xml:space="preserve">communis ſectio ipſi{us} &amp; </s>
  <s xml:id="echoid-s37651" xml:space="preserve">Verticalis proprie dicti, ſiue Aequatoris B D; </s>
  <s xml:id="echoid-s37652" xml:space="preserve">eiuſ-<lb/>dem vero, &amp; </s>
  <s xml:id="echoid-s37653" xml:space="preserve">Meridiani communis ſectio A C: </s>
  <s xml:id="echoid-s37654" xml:space="preserve">ſit{q́ue} deſcribendum horologium declinans tam à mer. <lb/></s>
  <s xml:id="echoid-s37655" xml:space="preserve">in ortum, quàm à Septentr. </s>
  <s xml:id="echoid-s37656" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s37657" xml:space="preserve">Ducta diametro F G, quę communis ſectio ſit Horizontis, &amp; </s>
  <s xml:id="echoid-s37658" xml:space="preserve">circu-<lb/>limaximi, cui horologium deſcribendum æquidiſtat, ita vt D G, B F, ſint arcus declinationis, facies{q́ue} <lb/>auſtralis dicti circuli maximi declinet à mer. </s>
  <s xml:id="echoid-s37659" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s37660" xml:space="preserve">ſeptentrionalis autem à ſeptentr. </s>
  <s xml:id="echoid-s37661" xml:space="preserve">in occaſum, du-<lb/>catur ad F G, per centrum E, perpendicularis H I, ex qua vtrinque abſcindantur rectæ E H, E I, ſty-<lb/>lo futuri horologĳ æquales: </s>
  <s xml:id="echoid-s37662" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37663" xml:space="preserve">per H, I, ipſi F G, parallelæ agantur H K, I K; </s>
  <s xml:id="echoid-s37664" xml:space="preserve">erit{q́ue} H K, commu-<lb/>
<anchor type="note" xlink:label="note-0588-07a" xlink:href="note-0588-07"/>
nis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s37665" xml:space="preserve">plani horologii declinantis à mer, in or. </s>
  <s xml:id="echoid-s37666" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37667" xml:space="preserve">I K, communis ſectio Horizontis, &amp; </s>
  <s xml:id="echoid-s37668" xml:space="preserve"><lb/>plani horologĳ declinantis à ſeptentr. </s>
  <s xml:id="echoid-s37669" xml:space="preserve">in occ. </s>
  <s xml:id="echoid-s37670" xml:space="preserve">Supputemus à D, puncto occidentali horizontalem cir-<lb/>cunferentiam horæ 24. </s>
  <s xml:id="echoid-s37671" xml:space="preserve">♋, ab occ. </s>
  <s xml:id="echoid-s37672" xml:space="preserve">vſque ad L, verſus boream, quia hæc hora pomeridiana eſt, &amp; </s>
  <s xml:id="echoid-s37673" xml:space="preserve">borea-<lb/>lis in tropico ♋, vt ex Analemmate constat: </s>
  <s xml:id="echoid-s37674" xml:space="preserve">quę quidem circunferentia @latitudo eſt occidua Solis in <lb/>principio ♋, existentis, ducatur{q́ue} ex L, per centrum E, recta occulta ſecans I K, in M, puncto, in quod <lb/>radius Solis per centrum E, hoc est, per verticem styli E I, ductus tunc cadit, Sole exiſtente in puncto <lb/>L, in Horizonte, vt perſpicuum eſt; </s>
  <s xml:id="echoid-s37675" xml:space="preserve">atque adeo M, punctum erit horæ 24. </s>
  <s xml:id="echoid-s37676" xml:space="preserve">♋, ab occ. </s>
  <s xml:id="echoid-s37677" xml:space="preserve">in horologio bo-<lb/>reali. </s>
  <s xml:id="echoid-s37678" xml:space="preserve">Rurſus D N, ſit circunferentia horizontalis horæ 23. </s>
  <s xml:id="echoid-s37679" xml:space="preserve">♋, ab occ. </s>
  <s xml:id="echoid-s37680" xml:space="preserve">quæ etiam horealis est, &amp; </s>
  <s xml:id="echoid-s37681" xml:space="preserve">occi-<lb/>dentalis, pomeridianave, ducaturq́, recta occulta ex N, per E, ſecans E K, in O, puncto, ex quo excite-<lb/>tur tam O P, ad N O, quàm O R, ad I K, perpendicularis: </s>
  <s xml:id="echoid-s37682" xml:space="preserve">Complementum vero deſcenſiuæ circunfe-<lb/>rentiæ eiuſdem horæ 23. </s>
  <s xml:id="echoid-s37683" xml:space="preserve">ſit N Q, &amp; </s>
  <s xml:id="echoid-s37684" xml:space="preserve">ex Q, per E, emittatur recta occulta ſecans O P, in P, rectæ{q́ue}<unsure/>
<pb o="573" file="0589" n="589" rhead="LIBER SEXTVS."/>
O P, in O R, ſumatur æqualis O R; </s>
  <s xml:id="echoid-s37685" xml:space="preserve">erit{q́ue} R, punctum horæ 23. </s>
  <s xml:id="echoid-s37686" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37687" xml:space="preserve">in tropico ♋. </s>
  <s xml:id="echoid-s37688" xml:space="preserve">Si enim circulus <lb/>A B C D, circa N O, conuertatur, donec ad Horizontem rectus ſit, atque adeo efficiatur Verticalis <lb/>per Solem tunc tranſiens, ita vt punctum Q, ſupra Horizontem exiſtat, erit arcus N Q, altitudo So-<lb/>
<anchor type="figure" xlink:label="fig-0589-01a" xlink:href="fig-0589-01"/>
<anchor type="note" xlink:label="note-0589-01a" xlink:href="note-0589-01"/>
<anchor type="note" xlink:label="note-0589-02a" xlink:href="note-0589-02"/>
<anchor type="note" xlink:label="note-0589-03a" xlink:href="note-0589-03"/>
lis, &amp; </s>
  <s xml:id="echoid-s37689" xml:space="preserve">recta O P, ex defin. </s>
  <s xml:id="echoid-s37690" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37691" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37692" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37693" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s37694" xml:space="preserve">ad Horizontem perpendicularis erit: </s>
  <s xml:id="echoid-s37695" xml:space="preserve">Eſt autem, per ean-<lb/>dem defin. </s>
  <s xml:id="echoid-s37696" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37697" xml:space="preserve">O R, in plano horologii declinantis (Intelligimus enim nunc planum horologĳ declinan-<lb/>tis per rectas I K, O R, duci, &amp; </s>
  <s xml:id="echoid-s37698" xml:space="preserve">ad Horizontem eſſe rectum) ad Horizontem recta. </s>
  <s xml:id="echoid-s37699" xml:space="preserve">Igitur recta O P, <lb/>rectæ O R, congruet, &amp; </s>
  <s xml:id="echoid-s37700" xml:space="preserve">punctum P, puncto R. </s>
  <s xml:id="echoid-s37701" xml:space="preserve">Radius ergo Solis Q E P, per centrum E, ductus in pun-<lb/>ctum P, ſeu R, cadet. </s>
  <s xml:id="echoid-s37702" xml:space="preserve">Simili ratione ex horizontali circunferentia D S, horę 22. </s>
  <s xml:id="echoid-s37703" xml:space="preserve">♋, ab occ. </s>
  <s xml:id="echoid-s37704" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37705" xml:space="preserve">deſcen <lb/>ſiuę complemento S X, reperietur punctum V, horę 22. </s>
  <s xml:id="echoid-s37706" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37707" xml:space="preserve">in tropico ♋, ſi ducatur recta S E K, &amp; </s>
  <s xml:id="echoid-s37708" xml:space="preserve"><lb/>K T, ad S K, perpendicularis, &amp; </s>
  <s xml:id="echoid-s37709" xml:space="preserve">K V, ad I K, punctum{q́ue} T, in quo recta X E, rectam K T, ſecat, tranſ-<lb/>
<anchor type="note" xlink:label="note-0589-04a" xlink:href="note-0589-04"/>
feratur in rectam K V, vſque ad V; </s>
  <s xml:id="echoid-s37710" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37711" xml:space="preserve">ſic de cęteris. </s>
  <s xml:id="echoid-s37712" xml:space="preserve">Eadem arte ex circunferentia horizontali D Y, <lb/>horæ 24. </s>
  <s xml:id="echoid-s37713" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s37714" xml:space="preserve">quę auſtralis est, &amp; </s>
  <s xml:id="echoid-s37715" xml:space="preserve">occidentalis, inuenietur in linea horizontali H K, horologii de-<lb/>clinantis à mer. </s>
  <s xml:id="echoid-s37716" xml:space="preserve">in or. </s>
  <s xml:id="echoid-s37717" xml:space="preserve">punctum horę 24. </s>
  <s xml:id="echoid-s37718" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37719" xml:space="preserve">in tropico ♑, in quo nimirum recta Y E, horizontalem li-<lb/>neam H K, ſecat: </s>
  <s xml:id="echoid-s37720" xml:space="preserve">quod tamen punctum in nostro exemplo, ob ſpatii anguſtiam, non continetur. </s>
  <s xml:id="echoid-s37721" xml:space="preserve">Item ex <lb/>circunferentia horizontali D Z, horæ 23. </s>
  <s xml:id="echoid-s37722" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s37723" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37724" xml:space="preserve">deſcenſiuæ cõplemento Z a, inuentum eſt punctum <lb/>b, prohora 23. </s>
  <s xml:id="echoid-s37725" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37726" xml:space="preserve">in tropico ♑. </s>
  <s xml:id="echoid-s37727" xml:space="preserve">Et ex circunferentia horizontali D e, deſcenſiuæ{q́ue} complemento <lb/>
<anchor type="note" xlink:label="note-0589-05a" xlink:href="note-0589-05"/>
ef, horę 22. </s>
  <s xml:id="echoid-s37728" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s37729" xml:space="preserve">inuentum eſt punctum d, pro hora 22. </s>
  <s xml:id="echoid-s37730" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37731" xml:space="preserve">in tropico ♑. </s>
  <s xml:id="echoid-s37732" xml:space="preserve">Atque ita pro qua-<lb/>libet hora punctum reperiemus in quolibet parallelo, ſi à D, vel B, horizontalem circunferentiam com-<lb/>putemus verſus A, vel C, prout circunferentia occidentalis, orientalisve fuerit, &amp; </s>
  <s xml:id="echoid-s37733" xml:space="preserve">auſtralis, borea-<lb/>lisve; </s>
  <s xml:id="echoid-s37734" xml:space="preserve">atque ex termino huius circunferentię per centrum E, rectam occultam ducamus, quę horizonta-<lb/>
<anchor type="note" xlink:label="note-0589-06a" xlink:href="note-0589-06"/>
lem lineam ſecet in puncto, è quo duę perpendiculares excitandę ſunt, vna ad hanc occultam proxime <lb/>ductam, &amp; </s>
  <s xml:id="echoid-s37735" xml:space="preserve">altera ad horizontalem lineam; </s>
  <s xml:id="echoid-s37736" xml:space="preserve">poſtremo à termino horizontalis circunferentię in quam-<lb/>cunque partem numeremus complementum circunferentię deſcenſiuę, &amp; </s>
  <s xml:id="echoid-s37737" xml:space="preserve">ex eius termino per centrum <lb/>E, rectam ducamus, quæ occultam @illam perpendicularem, quę ad rectam occultam à termino circun-<lb/>ferentiæ horizontalis ductam erigitur, ſecet in puncto, quod in perpendicularem ductam ad horizon-<lb/>talem lineam transferatur. </s>
  <s xml:id="echoid-s37738" xml:space="preserve">Hoc enim erit punctum horę propoſitæ pro illo parallelo, pro quo cir-<lb/>cunferentia horizontalis fuit inuenta, &amp; </s>
  <s xml:id="echoid-s37739" xml:space="preserve">complementum deſcenſiuæ. </s>
  <s xml:id="echoid-s37740" xml:space="preserve">Eſt autem perpendicula-<lb/>ris ad lineam horizontalem ſemper ducenda ad partes centri in vtroque horologio: </s>
  <s xml:id="echoid-s37741" xml:space="preserve">alia autem <lb/>perpendicularis ad occultam illam lineam à termino horizontalis circunferentię ductam educenda <lb/>in quamcunque partem, dummodo complementum circunferentiæ deſcenſiuę numeretur à termino cir-<lb/>cunferentiæ horizontalis in contrariam partem, vt recta occulta à termino huius complementi per
<pb o="574" file="0590" n="590" rhead="GNOMONICES"/>
centrũ ducta ſecare poſſit hanc perpendicularem, vt in exemplis fac@um eſſe cernis. </s>
  <s xml:id="echoid-s37742" xml:space="preserve">Illæ porrò ſolę horę <lb/>
<anchor type="note" xlink:label="note-0590-01a" xlink:href="note-0590-01"/>
in horologio australi deſcribi poſſunt, quarum circunferentiæ horizontales talem ſitum in Horizonte ha-<lb/>bent, vt rectæ ab earũ extremis vltra centrũ E, productę horizontalẽ lineã H K, ſecent, alię vero non. <lb/></s>
  <s xml:id="echoid-s37743" xml:space="preserve">Idem{q́ue} dicendum eſt de boreali horologio. </s>
  <s xml:id="echoid-s37744" xml:space="preserve">Hinc factũ eſt, vt horæ 24. </s>
  <s xml:id="echoid-s37745" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37746" xml:space="preserve">22. </s>
  <s xml:id="echoid-s37747" xml:space="preserve">♋, ab occ. </s>
  <s xml:id="echoid-s37748" xml:space="preserve">in horeali horolo <lb/>gio deſcriptę ſint, non autem in auſtrali: </s>
  <s xml:id="echoid-s37749" xml:space="preserve">Itẽ horę 24. </s>
  <s xml:id="echoid-s37750" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37751" xml:space="preserve">22. </s>
  <s xml:id="echoid-s37752" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s37753" xml:space="preserve">in auſtrali, nõ autẽ in boreali, &amp;</s>
  <s xml:id="echoid-s37754" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37755" xml:space="preserve"><lb/>Vt autem exemplum habeas alicuius lineæ horariæ, quæ punctum habeat &amp; </s>
  <s xml:id="echoid-s37756" xml:space="preserve">in tropico ♋, &amp; </s>
  <s xml:id="echoid-s37757" xml:space="preserve">in tropico <lb/>♑, inuenimus punctum g, pro hora 16. </s>
  <s xml:id="echoid-s37758" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37759" xml:space="preserve">in tropico ♋, ex circunferentia horizontali eiuſdem ho-<lb/>re 16. </s>
  <s xml:id="echoid-s37760" xml:space="preserve">Bh, quę auſtralis eſt, orientalis{q́ue}, &amp; </s>
  <s xml:id="echoid-s37761" xml:space="preserve">ex deſcenſiuę circunferentiæ complemento h l. </s>
  <s xml:id="echoid-s37762" xml:space="preserve">quamuis enim <lb/>recta l E, producta in exemplo non ſecet perpendicularem, quæ ad h m, ducta eſt, punctum tamen, vbi <lb/>eam ſecaret, tranſtulimus in perpendicularem m g, vſque ad g. </s>
  <s xml:id="echoid-s37763" xml:space="preserve">Item ex B p, circunferentia horizonta-<lb/>
<anchor type="note" xlink:label="note-0590-02a" xlink:href="note-0590-02"/>
li eiuſdem horę 16. </s>
  <s xml:id="echoid-s37764" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s37765" xml:space="preserve">quæ etiam auſtralis eſt, oriẽtalis{q́ue}, &amp; </s>
  <s xml:id="echoid-s37766" xml:space="preserve">ex deſcenſiuæ circunferentiæ comple <lb/>mento p q, reperim{us} punctum r, pro hora 16. </s>
  <s xml:id="echoid-s37767" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37768" xml:space="preserve">in tropico ♑, ita vt r g, ſit linea horæ 16. </s>
  <s xml:id="echoid-s37769" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s37770" xml:space="preserve">Poſtremo vt linea æquinoctialis ducatur, inueſtiganda erunt duo, aut tria, aut plura puncta pro dua-<lb/>
<anchor type="note" xlink:label="note-0590-03a" xlink:href="note-0590-03"/>
b{us}, aut tribus, aut pluribus horis, Sole existente in Aequatore. </s>
  <s xml:id="echoid-s37771" xml:space="preserve">Per ea enim ducenda erit æquinoctia-<lb/>lis linea. </s>
  <s xml:id="echoid-s37772" xml:space="preserve">Ita vides, inuentum eſſepunctum ſ, in linea r g, horę 16. </s>
  <s xml:id="echoid-s37773" xml:space="preserve">pro hora 16. </s>
  <s xml:id="echoid-s37774" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37775" xml:space="preserve">Sole exiſtente in <lb/>Aequatore, ex circunferentia horizontali B t, eiuſdem horę, quæ orientalis eſt, &amp; </s>
  <s xml:id="echoid-s37776" xml:space="preserve">auſtralis, &amp; </s>
  <s xml:id="echoid-s37777" xml:space="preserve">ex comple <lb/>mento t u, circunferentię deſcenſiuę. </s>
  <s xml:id="echoid-s37778" xml:space="preserve">Ad rectam enim t E α, ducta eſt perpendicularis α β, quam in <lb/>β, ſecat rectau E β, punctum{q́ue} β, translatum eſt in α ſ, perpendicularem ad H K; </s>
  <s xml:id="echoid-s37779" xml:space="preserve">quod quidem pun-<lb/>ctum ſ, neceſſario in rectam r g, cadet, ſi erratum non eſt. </s>
  <s xml:id="echoid-s37780" xml:space="preserve">Hoc artificio totum horologium abſoluetur, <lb/>quod ad hor{as}, &amp; </s>
  <s xml:id="echoid-s37781" xml:space="preserve">arcus ſignorum attinet. </s>
  <s xml:id="echoid-s37782" xml:space="preserve">Alia enim, quæ in horologĳs lib. </s>
  <s xml:id="echoid-s37783" xml:space="preserve">2. </s>
  <s xml:id="echoid-s37784" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37785" xml:space="preserve">3. </s>
  <s xml:id="echoid-s37786" xml:space="preserve">deſcripſimus, hac <lb/>
<anchor type="note" xlink:label="note-0590-04a" xlink:href="note-0590-04"/>
ratione delineari non poſſunt, niſi quis circunferenti{as} horizontales, deſcẽſiuas{q́ue} pro illis alĳs etiam de-<lb/>ſcriptionibus in horologio horizontali prius inueniret: </s>
  <s xml:id="echoid-s37787" xml:space="preserve">quod neq; </s>
  <s xml:id="echoid-s37788" xml:space="preserve">à Ptolemęo, neque à quouis alio factum <lb/>eſt; </s>
  <s xml:id="echoid-s37789" xml:space="preserve">propterea quòd prius inueſtigandum eſſet, quo pacto paralleli Solis à Verticalibus circulis, paralle-<lb/>
<anchor type="note" xlink:label="note-0590-05a" xlink:href="note-0590-05"/>
lis Horizontis, circulis domorum cęleſtium, &amp;</s>
  <s xml:id="echoid-s37790" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37791" xml:space="preserve">diuidantur; </s>
  <s xml:id="echoid-s37792" xml:space="preserve">quod arduũ nimis eſt, ac difficile. </s>
  <s xml:id="echoid-s37793" xml:space="preserve">Vt enim <lb/>pro ſingulis horis huiuſmodi circunferentiæ inueſtigentur, neceſſe eſt prius noſſe, vbi horę parallelos So-<lb/>lis interſecent, &amp; </s>
  <s xml:id="echoid-s37794" xml:space="preserve">quantum à meridie, vel ab ortu, occaſuve Solis abſint in propriis parallelis. </s>
  <s xml:id="echoid-s37795" xml:space="preserve">Etenim <lb/>ob hanc cauſam parallelos in horas ſecare in præcedentibus docuimus. </s>
  <s xml:id="echoid-s37796" xml:space="preserve">Quę cum ita ſint, perſpicuum eſt, <lb/>inuentum noſtrum, quo ex horologio horizontali declinans horologium deſcribitur, multo vniuerſalius <lb/>eſſe hoc artificio, quo ex circunferentiis horizontalibus, deſcenſiuis{q́ue} horologium declinans depingitur, <lb/>cùm per illud omnia puncta horologii horizontalis, etiamſi ad hor{as} non pertineant, in horologium de-<lb/>
<anchor type="note" xlink:label="note-0590-06a" xlink:href="note-0590-06"/>
clinans transferantur; </s>
  <s xml:id="echoid-s37797" xml:space="preserve">quod per hoc aliud artificium efficere nonlicet, propterea quòd, quaratione pro <lb/>omnibus punctis ad hor{as} non pertinentibus circunferentię horizontales, ac deſcenſiuę inquirendę ſint, <lb/>à nemine traditum eſt. </s>
  <s xml:id="echoid-s37798" xml:space="preserve">Immo hoc etiam nomine priorem rationem à nobis explicatam anteponendam <lb/>poſteriori cenſeo, quòd omnes line{as} horarias, vel etiam alias quaſcunque ex horologio horizontali in ho-<lb/>rologium declinans transfert, etiamſi pro ipſis puncta, per quę paralleli ſignorum ducendi ſunt, inuenta <lb/>non ſint. </s>
  <s xml:id="echoid-s37799" xml:space="preserve">Vnde ibi duci poteſt linea horę 22. </s>
  <s xml:id="echoid-s37800" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37801" xml:space="preserve">per. </s>
  <s xml:id="echoid-s37802" xml:space="preserve">punctum l, in tropico ♑, inuentum, hic au-<lb/>tem per punctum d, eiuſdem horę inuentum in eodem tropico ♑, non poteſt, niſi prius aliud punctum <lb/>eiuſdem horæ, Sole exiſtente in alio ſigno, vt in principio ♐, vel ♒, reperiatur. </s>
  <s xml:id="echoid-s37803" xml:space="preserve">Hac tamen vnare poste-<lb/>rior ratio priori pręſtare videtur, quòd ex circunferentiis horizontalibus, deſcenſiuis{q́ue} deſcribi poſſint <lb/>in horologio declinante illę etiam horæ, quę parum ab ortu, vel occaſu Solis diſtant, puta hora 23 {1/4}. <lb/></s>
  <s xml:id="echoid-s37804" xml:space="preserve">
<anchor type="note" xlink:label="note-0590-07a" xlink:href="note-0590-07"/>
23 {1/2}. </s>
  <s xml:id="echoid-s37805" xml:space="preserve">23 {3/4}. </s>
  <s xml:id="echoid-s37806" xml:space="preserve">9. </s>
  <s xml:id="echoid-s37807" xml:space="preserve">9 {1/4}. </s>
  <s xml:id="echoid-s37808" xml:space="preserve">9 {1/2}. </s>
  <s xml:id="echoid-s37809" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37810" xml:space="preserve">9 {3/4}. </s>
  <s xml:id="echoid-s37811" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s37812" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37813" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37814" xml:space="preserve">quod priori nostra via vix fieri poteſt, propterea quòd hu-<lb/>iuſmodi horæ, cum in illis vmbra gnomonis in horologio horizontali nimis longa ſit, difficile <lb/>admodum in horologio horizontali poſſint deſcribi: </s>
  <s xml:id="echoid-s37815" xml:space="preserve">adeo vt ad abſolutam <lb/>atque perfectam horarum deſcriptionem in horologiis <lb/>declinantibus vtraque via ac ratio adbi-<lb/>benda eſſe videatur.</s>
  <s xml:id="echoid-s37816" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1884" type="float" level="2" n="7">
<note position="left" xlink:label="note-0588-05" xlink:href="note-0588-05a" xml:space="preserve">Qua ratione ex<unsure/> <lb/>circunferentiis <lb/>horizontalibus, <lb/>deſcenſiuisque <lb/>in Horizonte <lb/>in uentis eadem <lb/>horologia ad <lb/>Horizontem r<unsure/>e <lb/>@a cõponantur.</note>
<note position="left" xlink:label="note-0588-06" xlink:href="note-0588-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0588-07" xlink:href="note-0588-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0589-01" xlink:href="fig-0589-01a">
    <image file="0589-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0589-01"/>
  </figure>
<note position="left" xlink:label="note-0589-01" xlink:href="note-0589-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0589-02" xlink:href="note-0589-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0589-03" xlink:href="note-0589-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0589-04" xlink:href="note-0589-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0589-05" xlink:href="note-0589-05a" xml:space="preserve">Quo pacto prò<unsure/> <lb/>qualibet hora <lb/>in quouis paral <lb/>lelo punctum <lb/>reperiatur in ho <lb/>rologio decli-<lb/>nante.</note>
<note position="left" xlink:label="note-0589-06" xlink:href="note-0589-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0590-01" xlink:href="note-0590-01a" xml:space="preserve">Quomodo co-<lb/>gnoſcatur ex cir <lb/>cunferentiis ho <lb/>rizõtalibus, quæ <lb/>horæ in propo-<lb/>ſito horologio <lb/>deſcribi poſſint.</note>
<note position="left" xlink:label="note-0590-02" xlink:href="note-0590-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0590-03" xlink:href="note-0590-03a" xml:space="preserve">Aequinoctialis <lb/>linea quo pacto <lb/>ducatur,</note>
<note position="left" xlink:label="note-0590-04" xlink:href="note-0590-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0590-05" xlink:href="note-0590-05a" xml:space="preserve">Comparatio in <lb/>ter duos modos <lb/>quibus in hoc <lb/>ſcholio horolo-<lb/>gia declinantia <lb/>conſtructa ſunt.</note>
<note position="left" xlink:label="note-0590-06" xlink:href="note-0590-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0590-07" xlink:href="note-0590-07a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1886" type="section" level="1" n="482">
<head xml:id="echoid-head511" style="it" xml:space="preserve">FINIS SEXTI LIBRI.</head>
<pb o="575" file="0591" n="591"/>
</div>
<div xml:id="echoid-div1887" type="section" level="1" n="483">
<head xml:id="echoid-head512" xml:space="preserve">GNOMONICES <lb/>LIBER SEPTIMVS.</head>
  <figure>
    <image file="0591-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0591-01"/>
  </figure>
</div>
<div xml:id="echoid-div1888" type="section" level="1" n="484">
<head xml:id="echoid-head513" style="it" xml:space="preserve">AVCTORE</head>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div1889" type="section" level="1" n="485">
<head xml:id="echoid-head514" xml:space="preserve">CHRISTOPHORO CLAVIO BAMBERGENSI <lb/>SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s37817" xml:space="preserve">QVONIAM Superioribus libris demonſtrationes cum horo-<lb/>logiorum deſcriptionibus plerunque permiſtæ ſunt, vt pluri-<lb/>bus verbis, quàm par ſit, res ipſa tractata nonnullis poſſit vide-<lb/>ri: </s>
  <s xml:id="echoid-s37818" xml:space="preserve">operæpretium mefacturum exiſtimo, ſi hoc ſeptimo libro <lb/>in gratiam eorum, qui vel Geometricis demonſtrationibus mi <lb/>
<anchor type="note" xlink:label="note-0591-02a" xlink:href="note-0591-02"/>
nus delectantur, vel in rebus Mathematicis nõ tantum ſe exer-<lb/>cuerunt, vt eas poſſint aſſequi, vel denique regulas deſcriben-<lb/>dorum horologiorum in vnum locum ſine demonſtrationi-<lb/>bus congregatas habere volunt, ſeorſum proponam, atq; </s>
  <s xml:id="echoid-s37819" xml:space="preserve">bre-<lb/>uiſſimè capita præcipua, quibus omnia genera horarum, de quibus copioſiſſimè <lb/>in ſuperioribus libris diſſeruimus, in quauis plana ſuperſicie ad datam ſtyli magni-<lb/>tudinem deſcribi poſſint. </s>
  <s xml:id="echoid-s37820" xml:space="preserve">Ita enim fiet, vt cum præcepta deſcriptionum à demon-<lb/>ſtrationibus ſint ſeiuncta, ſeparatimque perſcripta, ac diſtinctè, nullum prorſus im-<lb/>pedimentum, aut mora horologiographum in horis deſcribendis poſſit retardare. <lb/></s>
  <s xml:id="echoid-s37821" xml:space="preserve">Nam in antecedentibus libris ſępenumero curſus deſcriptionis horologiorum in-<lb/>
<anchor type="note" xlink:label="note-0591-03a" xlink:href="note-0591-03"/>
terrumpatur neceſſe eſt, ob multitudinem demonſtrationum, quæ paſſim cum prę-<lb/>ceptis inuolutæ ſunt; </s>
  <s xml:id="echoid-s37822" xml:space="preserve">adeo vt vix ſine moleſtia horologium vllum deſcribi queat. <lb/></s>
  <s xml:id="echoid-s37823" xml:space="preserve">Atque hac in re morem etiam geram quàm plurimis, qui enixe hoc à me efflagita-<lb/>runt. </s>
  <s xml:id="echoid-s37824" xml:space="preserve">Modus autem, quem in hac præceptorum breuitate tradenda ſequemur, ta-<lb/>lis erit. </s>
  <s xml:id="echoid-s37825" xml:space="preserve">Præcepta illa, quæ omnino ad horas deſcribendas neceſſaria ſunt, hoc loco <lb/>repetemus, vt opus non ſit quicquam ex ijs, quæ ſuperioribus libris ſcripta ſunt, huc <lb/>ad cuiuſuis horologii deſcriptionem transferre, exceptis quibuſdam, quæ ad vbe-<lb/>riorem doctrinam faciunt, vel ad horas non pertinent, in quibus lector ad ſuperio-<lb/>res libros remittendus erit. </s>
  <s xml:id="echoid-s37826" xml:space="preserve">Neque vero hoc loco diuiſionem horarum, atque ho-<lb/>rologiorum, neque naturam circulorum horariorum, aut eorum poſitionẽ in cælo <lb/>
<anchor type="note" xlink:label="note-0591-04a" xlink:href="note-0591-04"/>
repetere neceſſarium videtur, cum omnia hæc copioſe lib. </s>
  <s xml:id="echoid-s37827" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37828" xml:space="preserve">explicata ſint à nobis; <lb/></s>
  <s xml:id="echoid-s37829" xml:space="preserve">diuiſio quidem horarum, atque horologiorum ad initium, poſitio vero circulorum <lb/>horariorum propoſ. </s>
  <s xml:id="echoid-s37830" xml:space="preserve">9. </s>
  <s xml:id="echoid-s37831" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37832" xml:space="preserve">10. </s>
  <s xml:id="echoid-s37833" xml:space="preserve">Quare ad horologiorum deſcriptionem aggrediemur.</s>
  <s xml:id="echoid-s37834" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1889" type="float" level="2" n="1">
<note position="left" xlink:label="note-0591-02" xlink:href="note-0591-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0591-03" xlink:href="note-0591-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0591-04" xlink:href="note-0591-04a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1891" type="section" level="1" n="486">
<head xml:id="echoid-head515" style="it" xml:space="preserve">DE HOROLOGIO HORIZONTALI <lb/>Aſtronomico. CAP. I.</head>
<p>
  <s xml:id="echoid-s37835" xml:space="preserve">HOROLOGIVM horizontale Aſtronomicum hac ratione deſcribemus. </s>
  <s xml:id="echoid-s37836" xml:space="preserve">In <lb/>
<anchor type="note" xlink:label="note-0591-05a" xlink:href="note-0591-05"/>
plano horologii ducatur recta vtcunque H N, pro linea meridiana; </s>
  <s xml:id="echoid-s37837" xml:space="preserve">vel, ſi planum <lb/>ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s37838" xml:space="preserve">Horizonti æquidiſtans, inueniatur in eo linea meridiana H N, per <lb/>
<anchor type="note" xlink:label="note-0591-06a" xlink:href="note-0591-06"/>
ea, quæ in commentarijs in ſphæram ſcripſimus, cum Meridiani circuli officia <lb/>explicaremus, vel certè, vt docuimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s37839" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37840" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37841" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37842" xml:space="preserve">huius Gno-<lb/>monices. </s>
  <s xml:id="echoid-s37843" xml:space="preserve">Deinde electo loco ſtyli in puncto G, ductaq́ue recta G D, ad H N, <lb/>perpendiculari, ſumatur G D, propoſito ſtylo cuiuſcunque magnitudinis æqualis. </s>
  <s xml:id="echoid-s37844" xml:space="preserve">Facto autem <lb/>D, centro, deſcribatur arcus circuli A B C, in quo à recta D G, producta verſus partes auſtrales, <lb/>hoc eſt, verſus A, numeretur complementum altitudinis poli B A, &amp; </s>
  <s xml:id="echoid-s37845" xml:space="preserve">verſus C, ipſa altitudo poli <lb/>B C, ducanturq́ue rectæ D A, D C, (quarum illa axem mundi, hæc vero communem ſectionẽ <lb/>Aequatoris ac Meridiani reſert) ſecantes meridianam lineam in punctis H, &amp; </s>
  <s xml:id="echoid-s37846" xml:space="preserve">I: </s>
  <s xml:id="echoid-s37847" xml:space="preserve">per punctum <lb/>
<anchor type="note" xlink:label="note-0591-07a" xlink:href="note-0591-07"/>
autem I, excitetur ad lineam meridianam perpendicularis F K. </s>
  <s xml:id="echoid-s37848" xml:space="preserve">Erit H, centrum horologii, in <lb/>quo nimirum omnes lineæ horariæ ſe interſecant; </s>
  <s xml:id="echoid-s37849" xml:space="preserve">recta autem F K, erit linea æquinoctialis, cõmu <lb/>
<anchor type="note" xlink:label="note-0591-08a" xlink:href="note-0591-08"/>
nis videlicet ſectio Aequatoris, &amp; </s>
  <s xml:id="echoid-s37850" xml:space="preserve">plani horologij<unsure/>, in quam, Sole in ęquinoctiis exiſtẽte, vmbra ſtyli
<pb o="576" file="0592" n="592" rhead="GNOMONICES"/>
ſingulis horis, &amp; </s>
  <s xml:id="echoid-s37851" xml:space="preserve">horarum momentis cadit. </s>
  <s xml:id="echoid-s37852" xml:space="preserve">Sumpta quoque recta I E, æquali ipſi I D, deſcriba-<lb/>tur ex E, circulus ad quodcunque interuallum, quo diuiſo in 24. </s>
  <s xml:id="echoid-s37853" xml:space="preserve">partes æquales, initio ſacto à li-<lb/>nea meridiana H N, ducantur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s37854" xml:space="preserve">centrum E, lineæ rectæ occultæ ſecantes <lb/>
<anchor type="figure" xlink:label="fig-0592-01a" xlink:href="fig-0592-01"/>
<anchor type="note" xlink:label="note-0592-01a" xlink:href="note-0592-01"/>
<anchor type="note" xlink:label="note-0592-02a" xlink:href="note-0592-02"/>
<anchor type="note" xlink:label="note-0592-03a" xlink:href="note-0592-03"/>
æquinoctialem lineam F k, in punctis, per quę, &amp; </s>
  <s xml:id="echoid-s37855" xml:space="preserve">punctum H, emiſſæ lineæ rectæ dabunt lineas <lb/>
<anchor type="note" xlink:label="note-0592-04a" xlink:href="note-0592-04"/>
horarum à mer. </s>
  <s xml:id="echoid-s37856" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s37857" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s37858" xml:space="preserve">in plano, quod Horizonti æquidiſtat. </s>
  <s xml:id="echoid-s37859" xml:space="preserve">Pro hora verò ſexta eſt per <lb/>H, ducenda linea C L, ad H N, perpendicularis, vel æquidiſtans ipſi F K. </s>
  <s xml:id="echoid-s37860" xml:space="preserve">Poſſunt autem dictæ li-<lb/>neæ horariæ per punctum H, produci in vtramque partem inſinite, licet nos eas ornatus gratia <lb/>terminauerimus in circunſerentia circuli ex centro H, ad quodcunque interuallum deſcripti. </s>
  <s xml:id="echoid-s37861" xml:space="preserve">De-<lb/>monſtrationem huius deſcriptionis reperies in ſcholio propoſ. </s>
  <s xml:id="echoid-s37862" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37863" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37864" xml:space="preserve">2.</s>
  <s xml:id="echoid-s37865" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1891" type="float" level="2" n="1">
<note position="right" xlink:label="note-0591-05" xlink:href="note-0591-05a" xml:space="preserve">Horizentalis <lb/>horologii Aſtro <lb/>nomici deſcri-<lb/>ptio.</note>
<note position="left" xlink:label="note-0591-06" xlink:href="note-0591-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0591-07" xlink:href="note-0591-07a" xml:space="preserve">Centrum horo <lb/>logii.</note>
<note position="right" xlink:label="note-0591-08" xlink:href="note-0591-08a" xml:space="preserve">Linca æquino-<lb/>ctialis<unsure/>.</note>
  <figure xlink:label="fig-0592-01" xlink:href="fig-0592-01a">
    <image file="0592-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0592-01"/>
  </figure>
<note position="left" xlink:label="note-0592-01" xlink:href="note-0592-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0592-02" xlink:href="note-0592-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0592-03" xlink:href="note-0592-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0592-04" xlink:href="note-0592-04a" xml:space="preserve">Lia@@ horatiæ.</note>
</div>
<p>
  <s xml:id="echoid-s37866" xml:space="preserve">PORTIO autem lineæ meridianæ à centro H, verſus lineam æquinoctialem excurrens in-<lb/>
<anchor type="note" xlink:label="note-0592-05a" xlink:href="note-0592-05"/>
dicat horam 12. </s>
  <s xml:id="echoid-s37867" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s37868" xml:space="preserve">reliqua portio ab eodem centro H, inchoata horam 12. </s>
  <s xml:id="echoid-s37869" xml:space="preserve">mediæ no-<lb/>ctis. </s>
  <s xml:id="echoid-s37870" xml:space="preserve">Horæ autem ad dextram ipſius lineæ meridianæ collocatæ, hoc eſt, verſus punctum L, ſunt <lb/>antemeridianæ, pomeridianæ vero ad ſiniſtram eiuſdem meridianæ lineæ, id eſt, verſus punctum <lb/>
<anchor type="note" xlink:label="note-0592-06a" xlink:href="note-0592-06"/>
C, ſitæ ſunt: </s>
  <s xml:id="echoid-s37871" xml:space="preserve">ita vt proxima hora horæ 12. </s>
  <s xml:id="echoid-s37872" xml:space="preserve">meridiei verſus C, ſit hora 1. </s>
  <s xml:id="echoid-s37873" xml:space="preserve">poſt meridiem, ſequens <lb/>2. </s>
  <s xml:id="echoid-s37874" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37875" xml:space="preserve">ſic de cæteris, vt figura indicat.</s>
  <s xml:id="echoid-s37876" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1892" type="float" level="2" n="2">
<note position="left" xlink:label="note-0592-05" xlink:href="note-0592-05a" xml:space="preserve">Quæ horæ ante <lb/>meridianæ ſint, <lb/>&amp; quę pometi-<lb/>dianæ.</note>
<note position="left" xlink:label="note-0592-06" xlink:href="note-0592-06a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s37877" xml:space="preserve">ERVNT autem, ſi erratum non eſt, interualla horarum in portione æquinoctialis lineæ I F, <lb/>æqualia interuallis horarum in altera portione I k, ſingula ſingulis: </s>
  <s xml:id="echoid-s37878" xml:space="preserve">Item arcus circuli ex H, de-<lb/>ſcripti inter meridianam lineam H N, &amp; </s>
  <s xml:id="echoid-s37879" xml:space="preserve">horas ex parte ſiniſtra poſiti æquales arcubus eiuſdem <lb/>circuli inter lineam meridianam, &amp; </s>
  <s xml:id="echoid-s37880" xml:space="preserve">horas ex parte dextra interceptis, ſinguli ſingulis. </s>
  <s xml:id="echoid-s37881" xml:space="preserve">Quocirca <lb/>danda opera erit, vt huiuſmodi interualla æqualia inter ſe ſint, ſi accurata horarum deſcriptio de-<lb/>ſideretur.</s>
  <s xml:id="echoid-s37882" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s37883" xml:space="preserve">QVOD ſi dimidiatas etiam horas, &amp; </s>
  <s xml:id="echoid-s37884" xml:space="preserve">horarum quadrantes, immò &amp; </s>
  <s xml:id="echoid-s37885" xml:space="preserve">octauas partes, &amp;</s>
  <s xml:id="echoid-s37886" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37887" xml:space="preserve">in <lb/>
<anchor type="note" xlink:label="note-0592-07a" xlink:href="note-0592-07"/>
horologio deſcribere quis velit, diuidendæ erunt ſingulæ partes circuli ex E, deſcripti in duas par <lb/>
<anchor type="note" xlink:label="note-0592-08a" xlink:href="note-0592-08"/>
tes æquales, quatuor, vel octo, &amp;</s>
  <s xml:id="echoid-s37888" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37889" xml:space="preserve">reliqua autẽ perſicienda, vt prius. </s>
  <s xml:id="echoid-s37890" xml:space="preserve">Quod in alijs quoque horolo <lb/>giis, quæ ſequuntur, obſeruandum erit.</s>
  <s xml:id="echoid-s37891" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1893" type="float" level="2" n="3">
<note position="left" xlink:label="note-0592-07" xlink:href="note-0592-07a" xml:space="preserve">Dimidiatæ ho-<lb/>ræ, &amp; quadran-<lb/>tes hotatum in <lb/>horologio qua <lb/>ratione deſcri-<lb/>ban@ur.</note>
<note position="left" xlink:label="note-0592-08" xlink:href="note-0592-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s37892" xml:space="preserve">STYLVS, ſeu gnomon G D, erigendus eſt ſupra horologium ad angulos rectos ex puncto <lb/>
<anchor type="note" xlink:label="note-0592-09a" xlink:href="note-0592-09"/>
G, vt propoſ. </s>
  <s xml:id="echoid-s37893" xml:space="preserve">12. </s>
  <s xml:id="echoid-s37894" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37895" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37896" xml:space="preserve">oſtendimus. </s>
  <s xml:id="echoid-s37897" xml:space="preserve">Ita enim extremitas vmbræ in lineas horarias cadens horas <lb/>indicabit, tangetq́ue vertex ipſius ſtyli axem mundi ex H, per polum arcticum extenſum in pun-<lb/>cto D, ita vt H D, axem mundi reſerat. </s>
  <s xml:id="echoid-s37898" xml:space="preserve">Quòd ſi triangulum H D I, in linea meridiana H N, eri-<lb/>gatur ad rectos angulos ſupra planum horologii, indicabit quoque vmbra axis H D, eaſdem ho-<lb/>ras: </s>
  <s xml:id="echoid-s37899" xml:space="preserve">ſi tamen horologium in plano, quod Horizonti æquidiſtat, ita ſtatuatur, vt recta H N, lineam <lb/>
<anchor type="note" xlink:label="note-0592-10a" xlink:href="note-0592-10"/>
meridianam reſerat, punctumq́ue H, ad auſtrum, &amp; </s>
  <s xml:id="echoid-s37900" xml:space="preserve">I, ad boream vergat.</s>
  <s xml:id="echoid-s37901" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1894" type="float" level="2" n="4">
<note position="left" xlink:label="note-0592-09" xlink:href="note-0592-09a" xml:space="preserve">Stylus quomo-<lb/>do collocandus <lb/>@t.</note>
<note position="left" xlink:label="note-0592-10" xlink:href="note-0592-10a" xml:space="preserve">Horologiũ ho-<lb/>rizontale quo <lb/>pacto collocan-<lb/>dum ſit, vt ho-<lb/>@a@ indicet.</note>
</div>
<p>
  <s xml:id="echoid-s37902" xml:space="preserve">QVO autem artiſicio altitudo poli inueſtiganda ſit, (Nam vt horologium rectè deſcribatur <lb/>in propoſita regione, neceſſe eſt, noſſe altitudinem poli ſupra Horizontem illius loci, atque eiuſ-
<pb o="577" file="0593" n="593" rhead="LIBER SEPTIMVS."/>
dem complementum, vt ex conſtructione tradita conſtat) docuimus in vſu Aſtrolabij, in Coſmo <lb/>graphia, in commentariis in ſphæram, cum de oſſiciis Meridiani circuli ageremus, &amp; </s>
  <s xml:id="echoid-s37903" xml:space="preserve">in 2. </s>
  <s xml:id="echoid-s37904" xml:space="preserve">ſcho-<lb/>lio propoſ. </s>
  <s xml:id="echoid-s37905" xml:space="preserve">28. </s>
  <s xml:id="echoid-s37906" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s37907" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37908" xml:space="preserve">huius Gnomonices.</s>
  <s xml:id="echoid-s37909" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1896" type="section" level="1" n="487">
<head xml:id="echoid-head516" style="it" xml:space="preserve">DE ARCVBVS SIGNORVM IN HOROLOGIO <lb/>horizontali deſcribendis. CAP. II.</head>
<p>
  <s xml:id="echoid-s37910" xml:space="preserve">RADIVS Solis in æquinoctiali circulo exiſtentis deſcribit motu diurno circa centrum mun <lb/>di circulum, nempe ipſummet Aequatorem: </s>
  <s xml:id="echoid-s37911" xml:space="preserve">Sole verò in quouis alio parallelo citra, vltrave <lb/>æquinoctialem circulum commorante, idem radius per centrum mundi eductus deſcribit duas <lb/>
<anchor type="note" xlink:label="note-0593-01a" xlink:href="note-0593-01"/>
ſuperſicies conicas ad centrum mundi, tanquàm ad verticem, connexas, quarum baſes ſunt duo <lb/>paralleli poſiti, &amp; </s>
  <s xml:id="echoid-s37912" xml:space="preserve">æquales; </s>
  <s xml:id="echoid-s37913" xml:space="preserve">Vt cum Sol eſt in initio ♋, vel ♑, baſes dictarum, ſuperſicierum <lb/>conicarum ſunt tropicus ♋, &amp; </s>
  <s xml:id="echoid-s37914" xml:space="preserve">tropicus ♑: </s>
  <s xml:id="echoid-s37915" xml:space="preserve">quæ omnia à nobis demonſtrata ſunt lib, 1. </s>
  <s xml:id="echoid-s37916" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s37917" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s37918" xml:space="preserve">Et quoniam planum horologii cuiuſcunque ſecans has ſuperſicies conicas ſacit vel circulum, vel <lb/>Parabolam, vel Hyperbolam, vel Ellipſim, cum non tranſeat per verticem illarum, hoc eſt, per <lb/>centrum mundi, vt conſtat ex conicis elementis Apollonii, &amp; </s>
  <s xml:id="echoid-s37919" xml:space="preserve">vt in eodem lib. </s>
  <s xml:id="echoid-s37920" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37921" xml:space="preserve">oſtendimus, pro-<lb/>poſ. </s>
  <s xml:id="echoid-s37922" xml:space="preserve">4. </s>
  <s xml:id="echoid-s37923" xml:space="preserve">5. </s>
  <s xml:id="echoid-s37924" xml:space="preserve">6. </s>
  <s xml:id="echoid-s37925" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37926" xml:space="preserve">7. </s>
  <s xml:id="echoid-s37927" xml:space="preserve">à quibus quidem ſectionibus vmbra gnomonis non recedit, Sole exiſtente in <lb/>illo parallello, qui baſis eſt ſuperſiciei conicę, vt in eodem lib. </s>
  <s xml:id="echoid-s37928" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37929" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s37930" xml:space="preserve">12. </s>
  <s xml:id="echoid-s37931" xml:space="preserve">demonſtrauimus; </s>
  <s xml:id="echoid-s37932" xml:space="preserve">ſit <lb/>vt arcus ſignorum, quos nimirum vmbra gnomonis deſcribit in horologio, Sole in ſignorum ini-<lb/>tijs exiſtente, ſint vel circuli, vel Parabolæ, vel Hyperbolæ, vel Ellipſes, præterquam cum Sol in <lb/>
<anchor type="note" xlink:label="note-0593-02a" xlink:href="note-0593-02"/>
æquinoctiali circulo exiſtit: </s>
  <s xml:id="echoid-s37933" xml:space="preserve">tunc enim gnomonis vmbra rectam lineam deſcribit, vt ex coroll. </s>
  <s xml:id="echoid-s37934" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s37935" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s37936" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37937" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s37938" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37939" xml:space="preserve">perſpicuum eſt. </s>
  <s xml:id="echoid-s37940" xml:space="preserve">In quonam autem horologio arcus hi ſignorum ſint <lb/>vel circnli, vel Parabolæ, vel Hyperbolæ, vel Ellipſes, abunde demonſtrauimus in lib. </s>
  <s xml:id="echoid-s37941" xml:space="preserve">1. </s>
  <s xml:id="echoid-s37942" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s37943" xml:space="preserve">4-<lb/>5. </s>
  <s xml:id="echoid-s37944" xml:space="preserve">6. </s>
  <s xml:id="echoid-s37945" xml:space="preserve">7. </s>
  <s xml:id="echoid-s37946" xml:space="preserve">in earumq́ue ſcholijs: </s>
  <s xml:id="echoid-s37947" xml:space="preserve">Nunc certum ſit, huiuſmodi arcus in horologio ęquinoctiali vbi-<lb/>uis gentium eſſe circulos; </s>
  <s xml:id="echoid-s37948" xml:space="preserve">in horologio verò horizontali minoris latitudinis quàm grad. </s>
  <s xml:id="echoid-s37949" xml:space="preserve">66. </s>
  <s xml:id="echoid-s37950" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s37951" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37952" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37953" xml:space="preserve">tam in Meridiano, quàm in Polari horologio cuiuſcunque regionis, atque in Vertica-<lb/>li illius loci, vbi poli eleuatio ſupra Horizontem maior eſt, quàm grad. </s>
  <s xml:id="echoid-s37954" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37955" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37956" xml:space="preserve">30. </s>
  <s xml:id="echoid-s37957" xml:space="preserve">eſſe <lb/>hyperbolas.</s>
  <s xml:id="echoid-s37958" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1896" type="float" level="2" n="1">
<note position="left" xlink:label="note-0593-01" xlink:href="note-0593-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0593-02" xlink:href="note-0593-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s37959" xml:space="preserve">IGITVR vt hoſce arcus, cuiuſcunque ſint ſiguræ, deſignemus, præparanda eſt prius figura <lb/>
<anchor type="note" xlink:label="note-0593-03a" xlink:href="note-0593-03"/>
radiorum Zodiaci vna cum lineis horarijs, hunc in modum. </s>
  <s xml:id="echoid-s37960" xml:space="preserve">Ducatur in tranſuerſum linea vt <lb/>
<anchor type="note" xlink:label="note-0593-04a" xlink:href="note-0593-04"/>
cunque A H, quæ axẽ <lb/>
<anchor type="figure" xlink:label="fig-0593-01a" xlink:href="fig-0593-01"/>
mundi reſerat, &amp; </s>
  <s xml:id="echoid-s37961" xml:space="preserve">ad <lb/>eam perpendicularis <lb/>excitetur D C, pro ra-<lb/>dio æquinoctiali. </s>
  <s xml:id="echoid-s37962" xml:space="preserve">De-<lb/>inde ex D, deſcribatur <lb/>arcus circuli N O, in <lb/>quo ſupputata maxi-<lb/>ma declinatione So-<lb/>lis grad. </s>
  <s xml:id="echoid-s37963" xml:space="preserve">23. </s>
  <s xml:id="echoid-s37964" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s37965" xml:space="preserve">30. <lb/></s>
  <s xml:id="echoid-s37966" xml:space="preserve">
<anchor type="note" xlink:label="note-0593-05a" xlink:href="note-0593-05"/>
ad vtraſque partes ra-<lb/>
<anchor type="note" xlink:label="note-0593-06a" xlink:href="note-0593-06"/>
dii Aequatoris D C, <lb/>vſque ad puncta N, O, <lb/>ducatur recta N O, ſe-<lb/>cans D C, in R, pun-<lb/>cto, è quo, vt centro, <lb/>circa diametrum NO, <lb/>circulus deſcribatur, <lb/>qui in partes 12. </s>
  <s xml:id="echoid-s37967" xml:space="preserve">æqua <lb/>les ſecetur, initio facto <lb/>
<anchor type="note" xlink:label="note-0593-07a" xlink:href="note-0593-07"/>
à recta N O, vel à ra-<lb/>dio Aequatoris D C, <lb/>Poſt hæc bina quæli-<lb/>bet puncta æqualiter <lb/>à puncto N, vel O, di-<lb/>ſtantia iungantur re-<lb/>ctis lineis ſecãtibus ar-<lb/>cum N O, in punctis, per quæ ex D, rectæ emiſſæ dabunt radios omnium ſignorum Zodiaci, vt <lb/>in figura apparet.</s>
  <s xml:id="echoid-s37968" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1897" type="float" level="2" n="2">
<note position="right" xlink:label="note-0593-03" xlink:href="note-0593-03a" xml:space="preserve">Conſtr@ctio ſi-<lb/>guræ @adiorum <lb/>Zodiaci, ex qua <lb/>arcus ſignorum <lb/>in horologio ho <lb/>rizontali deſ@r@ <lb/>banta<unsure/>r.</note>
<note position="left" xlink:label="note-0593-04" xlink:href="note-0593-04a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0593-01" xlink:href="fig-0593-01a">
    <image file="0593-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0593-01"/>
  </figure>
<note position="left" xlink:label="note-0593-05" xlink:href="note-0593-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0593-06" xlink:href="note-0593-06a" xml:space="preserve">Deſcri@tio ra-<lb/>diorum ſigno-<lb/>rum in figura <lb/>radiorum Zo-<lb/>diaci.</note>
<note position="left" xlink:label="note-0593-07" xlink:href="note-0593-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio line@ <lb/>rum horariarũ <lb/>in figura radio <lb/>rum Zodia@i.</note>
<p>
  <s xml:id="echoid-s37969" xml:space="preserve">POST hæc ex triangulo H D I, ſiguræ capitis præcedentis transferatur in axem A H, ſigurę <lb/>proxime conſtructæ ex D, ſiniſtram verſus recta D H, &amp; </s>
  <s xml:id="echoid-s37970" xml:space="preserve">in radium Aequatoris D C, deorſum ver-
<pb o="578" file="0594" n="594" rhead="GNOMONICES"/>
ſus recta D I, &amp; </s>
  <s xml:id="echoid-s37971" xml:space="preserve">ex H, per I, recta educatur H I, quantacunque pro hora 12. </s>
  <s xml:id="echoid-s37972" xml:space="preserve">quam commodius ſor-<lb/>taſſe ita ducemus. </s>
  <s xml:id="echoid-s37973" xml:space="preserve">Ex H, deſcribatur verſus D, arcus circuli A B, ad quouis interuallum, ex quo <lb/>abſcindatur arcus A B, altitudini poli æqualis. </s>
  <s xml:id="echoid-s37974" xml:space="preserve">Recta enim H B, ducta erit linea horæ 12. </s>
  <s xml:id="echoid-s37975" xml:space="preserve">tranſi-<lb/>bitq́ue per I@. </s>
  <s xml:id="echoid-s37976" xml:space="preserve">Deinde ex centro E, illius circuli in figura pręcedẽtis capitis, beneſicio cuius in <lb/>linea æquinoctiali F K, puncta horarum inuenimus, accipiantur interualla vſque ad puncta, vbi <lb/>æquinoctialis linea F K, à lineis horariis ſecatur, &amp; </s>
  <s xml:id="echoid-s37977" xml:space="preserve">ex puncto D, ſiguræ proxime conſtructæ in <lb/>radiũ Aequatoris D C, transſerantur, imprimendo puncta in ipſo radio Aequatoris, per quæ ex <lb/>H, rectæ educantur. </s>
  <s xml:id="echoid-s37978" xml:space="preserve">Poſtremo per H, agatur H V, radio Aequatoris D C, parallela; </s>
  <s xml:id="echoid-s37979" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37980" xml:space="preserve">, ſi opus <lb/>fuerit, lineæ ex H, prodeuntes, &amp; </s>
  <s xml:id="echoid-s37981" xml:space="preserve">radium Aequatoris D C, ſecantes, beneſicio circini ad ſiniſtrã pa-<lb/>rallelæ A V, traducantur: </s>
  <s xml:id="echoid-s37982" xml:space="preserve">quod ſacile ſiet, ſi ex centro H, arcus circuli deſcribatur L Q, ſecans paral <lb/>
<anchor type="note" xlink:label="note-0594-01a" xlink:href="note-0594-01"/>
lelã H V, in P, ſi enim diſtantiam P L, ex P, ad Q, transſeramus, habebit recta ex H, per Q, du-<lb/>cta eandem diſtantiam à recta H V, quam ab eadem habet recta H L, &amp;</s>
  <s xml:id="echoid-s37983" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37984" xml:space="preserve">Nam rectæ ex H, <lb/>prodeuntes erunt lineæ aliarum horarum poſt horam 12. </s>
  <s xml:id="echoid-s37985" xml:space="preserve">quarum numerus reſpondet numeris <lb/>illorum interuallorum, quę in radium Aequatoris ex centro E, ſiguræ antecedentis cap. </s>
  <s xml:id="echoid-s37986" xml:space="preserve">ſunt trãſ-<lb/>lata, ita vt proxima linea ipſi H B, det horam 1. </s>
  <s xml:id="echoid-s37987" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37988" xml:space="preserve">11. </s>
  <s xml:id="echoid-s37989" xml:space="preserve">ſequens verò 2. </s>
  <s xml:id="echoid-s37990" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s37991" xml:space="preserve">10. </s>
  <s xml:id="echoid-s37992" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s37993" xml:space="preserve">c. </s>
  <s xml:id="echoid-s37994" xml:space="preserve">Quod ſi lineas <lb/>
<anchor type="note" xlink:label="note-0594-02a" xlink:href="note-0594-02"/>
horarias inter H, centrum horologii præcedentis capitis, &amp; </s>
  <s xml:id="echoid-s37995" xml:space="preserve">æquinoctialem lineam F K, in radiũ <lb/>Aequatoris D C, in proxima figura ex H, transſeramus, imprimendo puncta in radio Aequatoris <lb/>D C, &amp; </s>
  <s xml:id="echoid-s37996" xml:space="preserve">per hæc ex H, rectas lineas producamus, habebimus eaſdem lineas horarias.</s>
  <s xml:id="echoid-s37997" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1898" type="float" level="2" n="3">
<note position="left" xlink:label="note-0594-01" xlink:href="note-0594-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0594-02" xlink:href="note-0594-02a" xml:space="preserve">Alia deſcriptio <lb/>li<unsure/>nea@um hora-<lb/>riarum in figu-<lb/>ra radiorum Zo <lb/>diaci.</note>
</div>
<p>
  <s xml:id="echoid-s37998" xml:space="preserve">HAS etiam lineas horarias ex H, procedentes commodiſſime deſcribemus ſine translatione <lb/>
<anchor type="note" xlink:label="note-0594-03a" xlink:href="note-0594-03"/>
interuallorum horariorum inter centrum E, vel H, &amp; </s>
  <s xml:id="echoid-s37999" xml:space="preserve">æquinoctialem lineam F K, horologij ante-<lb/>
<anchor type="note" xlink:label="note-0594-04a" xlink:href="note-0594-04"/>
cedentis cap. </s>
  <s xml:id="echoid-s38000" xml:space="preserve">poſitorum, in radium Aequatoris D C, hac ratione. </s>
  <s xml:id="echoid-s38001" xml:space="preserve">In linea H I, protracta aſſume-<lb/>mus punctum quodcunque φ, per quod lineam φ V, ipſi A H, parallelam agemus, perq́ue H, ipſi <lb/>D C, aliam parallelam H V, quæ ipſam φ V, ſecet in V. </s>
  <s xml:id="echoid-s38002" xml:space="preserve">Deinde centro V, &amp; </s>
  <s xml:id="echoid-s38003" xml:space="preserve">interuallo V φ, circu-<lb/>lum deſcribemus, eumq́ue partiemur in 24. </s>
  <s xml:id="echoid-s38004" xml:space="preserve">partes æquales, initio facto à puncto φ. </s>
  <s xml:id="echoid-s38005" xml:space="preserve">Si namque <lb/>bina quæuis puncta à φ, æqualiter remota rectis lineis occultis coniungamus ſecantibus rectam <lb/>φ V, in punctis, dabunt rectæ ex H, per hæc puncta emiſſæ lineas horarias, vt prius. </s>
  <s xml:id="echoid-s38006" xml:space="preserve">Quòd <lb/>ſi ſinguli arcus circuli ex V, deſcripti ſecentur bifariam, &amp; </s>
  <s xml:id="echoid-s38007" xml:space="preserve">in quatuor partes æquales, ducemus ea-<lb/>dem ratione in figura radiorum Zodiaci lineas horarias, quæ ad horas dimidiatas, earumq́ue <lb/>quadrantes ſpectent.</s>
  <s xml:id="echoid-s38008" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1899" type="float" level="2" n="4">
<note position="left" xlink:label="note-0594-03" xlink:href="note-0594-03a" xml:space="preserve">Alia adhu@ de-<lb/>ſcriptio linearũ <lb/>horariarum pul <lb/>ch@trima in fi-<lb/>gura radiorum <lb/>Zodiaci.</note>
<note position="left" xlink:label="note-0594-04" xlink:href="note-0594-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s38009" xml:space="preserve">EX hac autem figura radiorũ Zodiaci facile intelligemus, qui arcus ſignorũ in horologio de-<lb/>
<anchor type="note" xlink:label="note-0594-05a" xlink:href="note-0594-05"/>
<anchor type="note" xlink:label="note-0594-06a" xlink:href="note-0594-06"/>
ſcribẽdi ſint hyperbolę &amp; </s>
  <s xml:id="echoid-s38010" xml:space="preserve">qui parabolæ, vel Ellipſes. </s>
  <s xml:id="echoid-s38011" xml:space="preserve">Nam quotieſcunque recta H B, ſecat duos ra-<lb/>dios ſignorum oppoſitorum, vt ♋, &amp; </s>
  <s xml:id="echoid-s38012" xml:space="preserve">♑; </s>
  <s xml:id="echoid-s38013" xml:space="preserve">♊, &amp; </s>
  <s xml:id="echoid-s38014" xml:space="preserve">♐; </s>
  <s xml:id="echoid-s38015" xml:space="preserve">♉, &amp; </s>
  <s xml:id="echoid-s38016" xml:space="preserve">♏, &amp;</s>
  <s xml:id="echoid-s38017" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38018" xml:space="preserve">arcus illorum oppoſitorum ſigno <lb/>rum ſunt hyperbolæ oppoſitæ, &amp; </s>
  <s xml:id="echoid-s38019" xml:space="preserve">æquales: </s>
  <s xml:id="echoid-s38020" xml:space="preserve">Quando verò eadem recta H B, ſecat quidem radium <lb/>cuiuſuis ſigni inter rectas H V, &amp; </s>
  <s xml:id="echoid-s38021" xml:space="preserve">D C, radio verò ſigni oppoſiti eſt parallela, arcus illius ſigni, <lb/>cuius radius ſecatur, eſt parabola, alterius autem ſigni oppoſiti arcus deſcribi non poteſt: </s>
  <s xml:id="echoid-s38022" xml:space="preserve">Quando <lb/>denique recta H B, ſecat vnum radium inter rectas H V, D C, radio vero ſigni oppoſiti neque æqui <lb/>diſtat, neque eum ſecat, niſi vltra punctum D, productum, arcus illius ſigni, cuius radius ſecatur, eſt <lb/>Ellipſis, alterius verò ſigni oppoſiti arcus deſcribi non poteſt. </s>
  <s xml:id="echoid-s38023" xml:space="preserve">Quæ omnia lib. </s>
  <s xml:id="echoid-s38024" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38025" xml:space="preserve">demonſtrauimus. <lb/></s>
  <s xml:id="echoid-s38026" xml:space="preserve">Idem in aliis horologiis cognoſcemus, ſi pro linea meridiana ſumamus lineam ſtyli in horologiis <lb/>declinantibus, &amp; </s>
  <s xml:id="echoid-s38027" xml:space="preserve">in figura radiorum Zodiaci lineam indicis pro linea horæ 12. </s>
  <s xml:id="echoid-s38028" xml:space="preserve">vt ex ſequentibus <lb/>
<anchor type="note" xlink:label="note-0594-07a" xlink:href="note-0594-07"/>
maniſeſtum erit. </s>
  <s xml:id="echoid-s38029" xml:space="preserve">T unc autem recta H B, (quæ in horizontali horologio eſt linea horæ 12. </s>
  <s xml:id="echoid-s38030" xml:space="preserve">in de-<lb/>clinantibus vero linea ſtyli) radios parallelorum oppoſitorum ſecabit, quando angulus D H I, al-<lb/>titudinis poli ſupra planum horologij, quem recta H B, facit cum axe A H, minor eſt angulo <lb/>A D N, oppoſito &amp; </s>
  <s xml:id="echoid-s38031" xml:space="preserve">externo, quem facit radius D N, ſigni oppoſiti cum eodem axe A H, qualis <lb/>eſt angulus complementi declinationis ſigni oppſiti: </s>
  <s xml:id="echoid-s38032" xml:space="preserve">Quando autem dicti duo anguli fuerint <lb/>æquales, erit recta H B, parallela radio ſigni oppoſiti: </s>
  <s xml:id="echoid-s38033" xml:space="preserve">Quando denique ille hoc maior fuerit, re-<lb/>cta H B, radium ſigni oppoſiti neque ſecabit, neque ei parallela erit, vt conſtat ex propoſ. </s>
  <s xml:id="echoid-s38034" xml:space="preserve">28. <lb/></s>
  <s xml:id="echoid-s38035" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38036" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38037" xml:space="preserve">Euclidis.</s>
  <s xml:id="echoid-s38038" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1900" type="float" level="2" n="5">
<note position="left" xlink:label="note-0594-05" xlink:href="note-0594-05a" xml:space="preserve">Qui a@cu@ ſigno <lb/>rum in horolo-<lb/>gio deſcribendi <lb/>ſint hyperbolæ, <lb/>aut parabolæ, <lb/>au@ ellipſe@, quo <lb/>pacto ex figura <lb/>radiorum Zo-<lb/>diaci cognoſca-<lb/>@ur.</note>
<note position="left" xlink:label="note-0594-06" xlink:href="note-0594-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0594-07" xlink:href="note-0594-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s38039" xml:space="preserve">HIS ita peractis, hoc modo arcus ſignorum deſcribemus. </s>
  <s xml:id="echoid-s38040" xml:space="preserve">Ex figura radiorum Zodiaci hacte <lb/>
<anchor type="note" xlink:label="note-0594-08a" xlink:href="note-0594-08"/>
nus conſtructa ſumemus portionem lineæ H B, horæ 12. </s>
  <s xml:id="echoid-s38041" xml:space="preserve">inter punctum H, &amp; </s>
  <s xml:id="echoid-s38042" xml:space="preserve">radium ♋, interce-<lb/>
<anchor type="note" xlink:label="note-0594-09a" xlink:href="note-0594-09"/>
ptam, eamq́ue transferemus in horologium (quod in hunc vſum deſcriptum eſſe debet lineis oc-<lb/>cultis, vt poſtea ſolum illæ lineæ, quæ inter arcum ♋, &amp; </s>
  <s xml:id="echoid-s38043" xml:space="preserve">arcum ♑, exiſtunt, perſpicuæ fiant, cum <lb/>omnes alię ſint ſuperuacaneæ, quippe in quas vmbra ſtyli cadere non poſſit) ex centro H, in lineã <lb/>meridianam verſus lineam æquinoctialem, ſignando punctum in linea meridiana. </s>
  <s xml:id="echoid-s38044" xml:space="preserve">Deinde eodẽ <lb/>modo accipiemus portionem lineæ horæ 1. </s>
  <s xml:id="echoid-s38045" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38046" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38047" xml:space="preserve">inter idem punctum H, &amp; </s>
  <s xml:id="echoid-s38048" xml:space="preserve">radium ♋, poſitam, <lb/>eamq́ue in horologium traducemus ex centro H, in lineas hor. </s>
  <s xml:id="echoid-s38049" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38050" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38051" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38052" xml:space="preserve">verſus lineam æquinoctia <lb/>lem, ſignando rurſus duo puncta in hiſce lineis horarijs, &amp; </s>
  <s xml:id="echoid-s38053" xml:space="preserve">ſic in reliquis horarijs lineis radium <lb/>♋, ſecantibus procedemus, transferentes ſemper interualla earum inter H, &amp; </s>
  <s xml:id="echoid-s38054" xml:space="preserve">radium ♋, incluſa, <lb/>in horologium ex centro H, in lineas horarias reſpondentes, puncta in illis notando. </s>
  <s xml:id="echoid-s38055" xml:space="preserve">Obſeruandũ <lb/>tamen erit hic, &amp; </s>
  <s xml:id="echoid-s38056" xml:space="preserve">in ſequentibus, vt interualla linearum ex H, cadentium verſus radium Aequato <lb/>tis D C, transferantur ex centro horologij H, in eas lineas horarias, quæ ex H, verſus lineam æqui
<pb o="579" file="0595" n="595" rhead="LIBER SEPTIMVS."/>
noctialem F k, tendunt, vt à nobis factum eſt in lineis horarum 12. </s>
  <s xml:id="echoid-s38057" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38058" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38059" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38060" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38061" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38062" xml:space="preserve">Interualla verò li-<lb/>nearum ex H, cadentium in alteram partem rectæ H V, ita vt radium Aequatoris D C, ſecare non <lb/>poſſint, transferantur in lineas horologii ex H, in eas lineas, quæ vltra centrum horologii ſemper <lb/>
<anchor type="figure" xlink:label="fig-0595-01a" xlink:href="fig-0595-01"/>
<anchor type="note" xlink:label="note-0595-01a" xlink:href="note-0595-01"/>
<anchor type="note" xlink:label="note-0595-02a" xlink:href="note-0595-02"/>
magis magisq́; </s>
  <s xml:id="echoid-s38063" xml:space="preserve">à linea æquinoctiali recedũt. </s>
  <s xml:id="echoid-s38064" xml:space="preserve">Vt hic in lineas horarias ſupra lineam horæ 6. </s>
  <s xml:id="echoid-s38065" xml:space="preserve">caden <lb/>tes, &amp; </s>
  <s xml:id="echoid-s38066" xml:space="preserve">lineam æquinoctialem non ſecantes: </s>
  <s xml:id="echoid-s38067" xml:space="preserve">quales in exemplo ſunt linea horæ 7. </s>
  <s xml:id="echoid-s38068" xml:space="preserve">poſt meridiem, <lb/>&amp; </s>
  <s xml:id="echoid-s38069" xml:space="preserve">linea horæ 4. </s>
  <s xml:id="echoid-s38070" xml:space="preserve">poſt mediam noctem, &amp;</s>
  <s xml:id="echoid-s38071" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38072" xml:space="preserve">Harum tamen puncta in horologio noſtro, propter ſpa-<lb/>tii anguſtias, notata non ſunt. </s>
  <s xml:id="echoid-s38073" xml:space="preserve">Punctis hoc modo in lineis horarum notatis, ſi per ea rite lineam <lb/>inſlexam, ita vt nullibi faciat angulos, duxerimus, deſcriptus erit arcus ♋, quem extremitas vmbræ <lb/>
<anchor type="note" xlink:label="note-0595-03a" xlink:href="note-0595-03"/>
gnomonis deſcribit, Sole in principio ♋, exiſtente. </s>
  <s xml:id="echoid-s38074" xml:space="preserve">Non aliter aliorum ſignorum arcus deſcribe-<lb/>mus, ſi interualla horaria inter H, &amp; </s>
  <s xml:id="echoid-s38075" xml:space="preserve">radios ſignorum interiecta in horologium transſeramus ex <lb/>centro H, in correſpondentes lineas horarias, &amp;</s>
  <s xml:id="echoid-s38076" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38077" xml:space="preserve">Eoſdem arcus ſignorum delineabimus, ſi in-<lb/>
<anchor type="note" xlink:label="note-0595-04a" xlink:href="note-0595-04"/>
terualla horarum inter radium Aequatoris, &amp; </s>
  <s xml:id="echoid-s38078" xml:space="preserve">radios aliorum ſignorum comprehenſa transfera-<lb/>mus in lineas horarias reſpondentes in horologio, à linea àquinoctiali inchoando, &amp;</s>
  <s xml:id="echoid-s38079" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38080" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1901" type="float" level="2" n="6">
<note position="left" xlink:label="note-0594-08" xlink:href="note-0594-08a" xml:space="preserve">Deſcriptio a@-<lb/>@uum ſignorum <lb/>in horologio ho <lb/><gap/>tali.</note>
<note position="left" xlink:label="note-0594-09" xlink:href="note-0594-09a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0595-01" xlink:href="fig-0595-01a">
    <image file="0595-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0595-01"/>
  </figure>
<note position="left" xlink:label="note-0595-01" xlink:href="note-0595-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0595-02" xlink:href="note-0595-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0595-03" xlink:href="note-0595-03a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0595-04" xlink:href="note-0595-04a" xml:space="preserve">Alia deſcriptio <lb/>arcuum ſigno-<lb/>rum.</note>
</div>
<p>
  <s xml:id="echoid-s38081" xml:space="preserve">IAM verò ſi ex lineamentis hactenus deſcriptis maius, aut minus horologium ſit delinean-<lb/>
<anchor type="note" xlink:label="note-0595-05a" xlink:href="note-0595-05"/>
dum, prout maior, aut minor gnomon, quàm D G, datus fuerit, fiet id in hunc modum. </s>
  <s xml:id="echoid-s38082" xml:space="preserve">Deſcri-<lb/>batur ſeorſum triangulum H D I, in horologio pręcedentis cap. </s>
  <s xml:id="echoid-s38083" xml:space="preserve">vel in figura radiorum ſignorum <lb/>huius cap. </s>
  <s xml:id="echoid-s38084" xml:space="preserve">contentum, vna cum ſtylo D G, atque ex recta D G, producta abſcindatur recta D K, <lb/>minori, aut maiori ſtylo propoſito æqualis, &amp; </s>
  <s xml:id="echoid-s38085" xml:space="preserve">per K, ipſi H I, parallela agatur L M, ſecans D H, <lb/>
<anchor type="note" xlink:label="note-0595-06a" xlink:href="note-0595-06"/>
D I, productas in L, &amp; </s>
  <s xml:id="echoid-s38086" xml:space="preserve">M. </s>
  <s xml:id="echoid-s38087" xml:space="preserve">Deinde ex triangulo D L M, ſumatur axis D L, transferaturq́ue in fi-<lb/>guram radiorum Zodiaci huius cap. </s>
  <s xml:id="echoid-s38088" xml:space="preserve">ex H, vſque ad D, ita vt H D, æqualis ſit axi D L, dicti trian-<lb/>guli. </s>
  <s xml:id="echoid-s38089" xml:space="preserve">Si igitur ex D, demittatur ad H D, perpendicularis linea D M, pro radio Aequatoris, &amp; </s>
  <s xml:id="echoid-s38090" xml:space="preserve">ex <lb/>D, radii aliorum ſignorum educantur, vt in hoc cap. </s>
  <s xml:id="echoid-s38091" xml:space="preserve">docuimus (qui tamen vt confuſio linearum <lb/>vitaretur, in figura non ſunt educti) deſcribentur pro ratione dati ſtyli D K, arcus ſignorum, vt <lb/>prius, ſi interualla linearum horariarum ex H, prodeuntium inter H, &amp; </s>
  <s xml:id="echoid-s38092" xml:space="preserve">radios ſignorum nunc <lb/>deſcriptorum interiecta (quæ quidem lineæ horariæ mutari non debent, etiam ſi maius, minusve <lb/>horologium deſcribendum ſit, in eadem eleuatione poli) in lineas horarias horologii occulte du <lb/>ctas (quæ etiam in eadem poli altitudine permanent) ex puncto H, &amp;</s>
  <s xml:id="echoid-s38093" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38094" xml:space="preserve">Aequinoctialis autem li-<lb/>nea ducenda eſt in horologio ad meridianam lineam perpendicularis per punctum, quod tanto <lb/>
<anchor type="note" xlink:label="note-0595-07a" xlink:href="note-0595-07"/>
ſpatio à centro horologii H, abeſt, quanta eſt in figura radiorum Zodiaci recta H M, inter H, &amp; </s>
  <s xml:id="echoid-s38095" xml:space="preserve"><lb/>radium Aequatoris nuper ductum intercepta: </s>
  <s xml:id="echoid-s38096" xml:space="preserve">quemadmodum etiam in horologio recta H I, in-<lb/>ter centrum horologii, &amp; </s>
  <s xml:id="echoid-s38097" xml:space="preserve">lineam æquinoctialem æqualis eſt rectæ H I, in figura radiorum Zodia-<lb/>ci inter H, &amp; </s>
  <s xml:id="echoid-s38098" xml:space="preserve">radium Aequatoris. </s>
  <s xml:id="echoid-s38099" xml:space="preserve">Triangulũ H D I, deſcriptum eſt prope ſigurã radiorũ Zodiaci.</s>
  <s xml:id="echoid-s38100" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1902" type="float" level="2" n="7">
<note position="right" xlink:label="note-0595-05" xlink:href="note-0595-05a" xml:space="preserve">Qua ratione ad <lb/>maiorem, mino <lb/>remve ſiylum <lb/>maiu@, aut mi-<lb/>nus horologiũ <lb/>ex figura radio <lb/>rum Zodiaci @@ <lb/>ſcribatur.</note>
<note position="left" xlink:label="note-0595-06" xlink:href="note-0595-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0595-07" xlink:href="note-0595-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s38101" xml:space="preserve">QVO pacto autem arcus ſignorum auſtralium ex arcubus ſignorum borealium accuratius <lb/>deſcribantur; </s>
  <s xml:id="echoid-s38102" xml:space="preserve">Vel etiam qua ratione duo arcus duorum ſignorum oppoſitorum (quando nimirũ <lb/>
<anchor type="note" xlink:label="note-0595-08a" xlink:href="note-0595-08"/>
in figura radiorum Zodiaci recta H B, radios oppoſitorum ſignorum ſecat) vna eademq́ue ope-<lb/>ra depingantur, (quod quidem ſcitu periucundum, atque perutile eſt) explicatum reperies <lb/>lib. </s>
  <s xml:id="echoid-s38103" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38104" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s38105" xml:space="preserve">2.</s>
  <s xml:id="echoid-s38106" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1903" type="float" level="2" n="8">
<note position="right" xlink:label="note-0595-08" xlink:href="note-0595-08a" xml:space="preserve">Deſcriptio ar-<lb/>cuum, quos vm <lb/>bra percurrit, <lb/>Sole exrra i@i-<lb/>tia ſignorum in <lb/>in aliis pu@ctis <lb/>Zodia@i exiſte@ <lb/>te.</note>
</div>
<p>
  <s xml:id="echoid-s38107" xml:space="preserve">QVOD ſi accipiamus declinationes aliorum punctorum Zodiaci in arcu N O, figuræ radio-<lb/>rum Zodiaci, eorumq́ue radios ex puncto D, emittamus, deſcribemus illorum arcus in horolo-
<pb o="580" file="0596" n="596" rhead="GNOMONICES"/>
gio, quos nimirum vmbrę extremitas percurrit, cum Sol in illis punctis Zodiaci exiſtit, eadem <lb/>arte, qua arcus ſignorum deſcripſimus. </s>
  <s xml:id="echoid-s38108" xml:space="preserve">Immo propoſito die primo cuiuſque menſis, vel alio <lb/>
<anchor type="note" xlink:label="note-0596-01a" xlink:href="note-0596-01"/>
quouis, ſi quæratur locus Solis illo die in Zodiaco, eiuſq́ue declinatio, ducatur autem &amp; </s>
  <s xml:id="echoid-s38109" xml:space="preserve">radius <lb/>illius puncti Zodiaci, quem Sol occupat, habita ratione declinationis dicti puncti, ex puncto D, <lb/>prædictę figuræ radiorum Zodiaci, deſcribetur eadem ratione in horologio linea quædam infle-<lb/>xa, quam vmbræ extremitas percurrit die illo propoſito. </s>
  <s xml:id="echoid-s38110" xml:space="preserve">Hac via deſcribi poterunt in eodem ho-<lb/>
<anchor type="note" xlink:label="note-0596-02a" xlink:href="note-0596-02"/>
rologio dies feſti ſanctorũ, hoc eſt, lineæ quædam in flexæ, quas vmbra ſtyli illis diebus percurrit: <lb/></s>
  <s xml:id="echoid-s38111" xml:space="preserve">Immo &amp; </s>
  <s xml:id="echoid-s38112" xml:space="preserve">paralleli ciuitatum intra duos tropicos poſitarum eadem ratione deſcribentur, ſi eorum <lb/>radii ducantur, &amp;</s>
  <s xml:id="echoid-s38113" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38114" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1904" type="float" level="2" n="9">
<note position="left" xlink:label="note-0596-01" xlink:href="note-0596-01a" xml:space="preserve">Deſcriptio at-<lb/>cuum, quos<unsure/> vm <lb/>bra percur@it <lb/>quolibet die <lb/>Menſis propo-<lb/>ſito.</note>
<note position="left" xlink:label="note-0596-02" xlink:href="note-0596-02a" xml:space="preserve">Deſcriptio die-<lb/>rum feſtorum <lb/>in horologio.</note>
</div>
<p>
  <s xml:id="echoid-s38115" xml:space="preserve">HIS autem omnibus arcubus, ſiue lineis inflexis, aſcribi poſſunt characteres ſignorum, dies <lb/>
<anchor type="note" xlink:label="note-0596-03a" xlink:href="note-0596-03"/>
<anchor type="note" xlink:label="note-0596-04a" xlink:href="note-0596-04"/>
menſium, in quibus vmbræ extremitas illos percurrit, necnon tempus ortus Solis; </s>
  <s xml:id="echoid-s38116" xml:space="preserve">dierum, &amp; </s>
  <s xml:id="echoid-s38117" xml:space="preserve"><lb/>crepuſculorum magnitudines, &amp; </s>
  <s xml:id="echoid-s38118" xml:space="preserve">alia huiuſmodi; </s>
  <s xml:id="echoid-s38119" xml:space="preserve">Vt in horologiis Italico, &amp; </s>
  <s xml:id="echoid-s38120" xml:space="preserve">Babylonico, de qui-<lb/>bus paulo infra agemus, tempus meridiei, &amp;</s>
  <s xml:id="echoid-s38121" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38122" xml:space="preserve">In huius verò rei gratiam ducendæ ſunt quædam <lb/>lineæ parallelæ ipſi lineæ meridianæ tam ad ſiniſtram partem, quàm ad dexteram: </s>
  <s xml:id="echoid-s38123" xml:space="preserve">quæ quo remo <lb/>tiores erunt à meridiana linea, eo maiori temporis ſpatio vmbra gnomonis in horologio excipie-<lb/>tur, vt in horologio huius cap apparet.</s>
  <s xml:id="echoid-s38124" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1905" type="float" level="2" n="10">
<note position="left" xlink:label="note-0596-03" xlink:href="note-0596-03a" xml:space="preserve">Quid aſcribi <lb/>poſſit<unsure/> arcubus <lb/>ſ<unsure/>ignorum in ho <lb/>@ologio delinea <lb/>tu@.</note>
<note position="left" xlink:label="note-0596-04" xlink:href="note-0596-04a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s38125" xml:space="preserve">TANDEM quoniam Sol à ♑, per ♈, aſcendit vſq; </s>
  <s xml:id="echoid-s38126" xml:space="preserve">ad ♋; </s>
  <s xml:id="echoid-s38127" xml:space="preserve">à ♋, vero per ♎, vſque ad ♑, de-<lb/>ſcendit, apponi poterunt prope ſex priora ſigna, hęc verba, ASCENSVS SOLIS; </s>
  <s xml:id="echoid-s38128" xml:space="preserve">iuxta ve-<lb/>rò poſteriora, hæc, DESCENSVS SOLIS.</s>
  <s xml:id="echoid-s38129" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1907" type="section" level="1" n="488">
<head xml:id="echoid-head517" style="it" xml:space="preserve">DE ARCVBVS LONGITVDINVM DIERVM <lb/>in eodem horologio horizontali deſcribendis. CAP. III.</head>
<p>
  <s xml:id="echoid-s38130" xml:space="preserve">SICVT in præcedenti capite arcus deſcripſimus, quos extremitas vmbræ ſtyli percurrit, Sole <lb/>in ſignorum initijs, vel in alio quouis puncto Zodiaci exiſtente, ita nunc alios arcus delineabi-<lb/>mus, quos eadem vmbra deſcribit, cum dies artificialis cõtinet numerum horarum propoſitum, <lb/>
<anchor type="figure" xlink:label="fig-0596-01a" xlink:href="fig-0596-01"/>
vt 10. </s>
  <s xml:id="echoid-s38131" xml:space="preserve">vel 11. </s>
  <s xml:id="echoid-s38132" xml:space="preserve">vel 13. </s>
  <s xml:id="echoid-s38133" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38134" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38135" xml:space="preserve">Hi autem <lb/>arcus deſcribuntur non aliter, atq; <lb/></s>
  <s xml:id="echoid-s38136" xml:space="preserve">arcus ſignorum, dummodo loco <lb/>radiorum ſignorum in figura radio <lb/>
<anchor type="note" xlink:label="note-0596-06a" xlink:href="note-0596-06"/>
rum Zodiaci cap. </s>
  <s xml:id="echoid-s38137" xml:space="preserve">antecedentis du-<lb/>cantur radii longitudinum dierum <lb/>ex puncto D. </s>
  <s xml:id="echoid-s38138" xml:space="preserve">Qui quidẽ radij lon-<lb/>gitudinum dierum ducentur hoc <lb/>artificio. </s>
  <s xml:id="echoid-s38139" xml:space="preserve">Ducta recta A B, deſcri-<lb/>
<anchor type="note" xlink:label="note-0596-07a" xlink:href="note-0596-07"/>
batur ex A, arcus circuli C B D, in <lb/>quo à puncto B, vtrinque numere-<lb/>tur arcus complementi altitudinis <lb/>poli vſquead puncta C, &amp; </s>
  <s xml:id="echoid-s38140" xml:space="preserve">D. </s>
  <s xml:id="echoid-s38141" xml:space="preserve">Du-<lb/>cta deinde recta C D, rectam A B, <lb/>
<anchor type="note" xlink:label="note-0596-08a" xlink:href="note-0596-08"/>
ſecante in E, deſcribatur ex centro <lb/>E, &amp; </s>
  <s xml:id="echoid-s38142" xml:space="preserve">interuallo E C, vel E D, circu-<lb/>lus, quo diuiſo in 48. </s>
  <s xml:id="echoid-s38143" xml:space="preserve">partes æqua-<lb/>les, coniungantur quælibet duo <lb/>puncta à C, vel D, æqualiter remo-<lb/>ta lineis rectis ſecantibus rectam <lb/>C D, in punctis, per quæ ex A, rectæ emiſſæ erunt radij longitudinum dierum, indicabuntq́ue de-<lb/>clina tiones illorum parallelorum, quorum arcus diurni dictas dierum longitudines comprehen-<lb/>dunt: </s>
  <s xml:id="echoid-s38144" xml:space="preserve">ita vt recta A D, ſit radius arcus diurninullius horæ, hoc eſt, radius illius paralleli, qui ſem <lb/>per occultorum eſt maximus, proximè ſequens linea ſit radius arcus diurni horæ vnius, inſequens <lb/>
<anchor type="note" xlink:label="note-0596-09a" xlink:href="note-0596-09"/>
horarum duarum, &amp;</s>
  <s xml:id="echoid-s38145" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38146" xml:space="preserve">adeò vt radius Aequatoris A B, ſit horarum 12. </s>
  <s xml:id="echoid-s38147" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38148" xml:space="preserve">A C, horarũ 24. </s>
  <s xml:id="echoid-s38149" xml:space="preserve">hoc eſt, <lb/>radius paralleli illius, qui ſemper apparentium maximus eſt. </s>
  <s xml:id="echoid-s38150" xml:space="preserve">Deſcripſimus hoſce radios longitu-<lb/>dinum dierum hic ſeorſum, &amp; </s>
  <s xml:id="echoid-s38151" xml:space="preserve">non in figura radiorum Zodiaci antecedentis cap. </s>
  <s xml:id="echoid-s38152" xml:space="preserve">ne multitudo <lb/>linearum confuſionem pareret. </s>
  <s xml:id="echoid-s38153" xml:space="preserve">Vt igitur arcum longitudinis cuiuſcunque diei deſcribamus, ſu-<lb/>mendus eſt arcus in hac figura inter B, &amp; </s>
  <s xml:id="echoid-s38154" xml:space="preserve">radium propoſitum, eiq́ue ſimilis abſcindendus ex arcu <lb/>N O, in figura radiorum Zodiaci cap. </s>
  <s xml:id="echoid-s38155" xml:space="preserve">præcedentis, initio facto à radio Aequatoris. </s>
  <s xml:id="echoid-s38156" xml:space="preserve">Quod facile<unsure/> <lb/>@i<unsure/>et, ſi in figura radiorum Zodiaci deſcribatur arcus ex D, puncto ad interuallum ſemidiametri <lb/>A B, arcus C B D, figuræ huius cap. </s>
  <s xml:id="echoid-s38157" xml:space="preserve">Tunc enim arcui inter B, &amp; </s>
  <s xml:id="echoid-s38158" xml:space="preserve">radium propoſitum ſumendus <lb/>eſt in arcu deſcripto in figura radiorum Zodiaci arcus æqualis, &amp; </s>
  <s xml:id="echoid-s38159" xml:space="preserve">per finem huius arcus ex D, li-<lb/>nea ducenda occultè pro radio illius diei. </s>
  <s xml:id="echoid-s38160" xml:space="preserve">Hæc enim linea auferet ex arcu N O, arcum ſimi-<lb/>lem, &amp;</s>
  <s xml:id="echoid-s38161" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38162" xml:space="preserve">Ex hoc autem radio deſcribetur arcus illius diei, ſicut ex radijs ſignorum arcus ſignorum
<pb o="581" file="0597" n="597" rhead="LIBER SEPTIMVS."/>
ſunt deſcripti, &amp;</s>
  <s xml:id="echoid-s38163" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38164" xml:space="preserve">In figuram radiorum Zodiaci cap. </s>
  <s xml:id="echoid-s38165" xml:space="preserve">præcedentis tranſportauimus radios longi-<lb/>
<anchor type="note" xlink:label="note-0597-01a" xlink:href="note-0597-01"/>
tudinum dierum horarum 14. </s>
  <s xml:id="echoid-s38166" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38167" xml:space="preserve">10. </s>
  <s xml:id="echoid-s38168" xml:space="preserve">Item horarum 18. </s>
  <s xml:id="echoid-s38169" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38170" xml:space="preserve">6. </s>
  <s xml:id="echoid-s38171" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38172" xml:space="preserve">horarum 24. </s>
  <s xml:id="echoid-s38173" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38174" xml:space="preserve">0. </s>
  <s xml:id="echoid-s38175" xml:space="preserve">punctis quibuſ-<lb/>dam inſignitos, ne cum radijs ſignorum confundantur. </s>
  <s xml:id="echoid-s38176" xml:space="preserve">His enim maxime in ijs, quæ ſequuntur <lb/>indigemus. </s>
  <s xml:id="echoid-s38177" xml:space="preserve">Facile autem ex ijs, quæ in præcedenti cap. </s>
  <s xml:id="echoid-s38178" xml:space="preserve">ſcripſimus, iudicabimus, quinam arcus <lb/>diurni ſint hyperbolæ, &amp; </s>
  <s xml:id="echoid-s38179" xml:space="preserve">qui parabolæ, vel Ellipſes, ſi pro radiis ſignorum oppoſitorum ex pun-<lb/>cto D, in figura radiorum Zodiaci dicti capitis ducantur duo radii diurni oppoſiti, hoc eſt, æqua-<lb/>liter à radio Aequatoris diſtantes.</s>
  <s xml:id="echoid-s38180" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1907" type="float" level="2" n="1">
  <figure xlink:label="fig-0596-01" xlink:href="fig-0596-01a">
    <image file="0596-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0596-01"/>
  </figure>
<note position="left" xlink:label="note-0596-06" xlink:href="note-0596-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0596-07" xlink:href="note-0596-07a" xml:space="preserve">Quo pact<unsure/>oradij <lb/>lo @gitudinum <lb/>dierum deſcri-<lb/>bantur.</note>
<note position="left" xlink:label="note-0596-08" xlink:href="note-0596-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0596-09" xlink:href="note-0596-09a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0597-01" xlink:href="note-0597-01a" xml:space="preserve">Deſcriptio at-<lb/>cuum longitu-<lb/>dinum dierum <lb/>in horologio ho <lb/>rizontali.</note>
</div>
</div>
<div xml:id="echoid-div1909" type="section" level="1" n="489">
<head xml:id="echoid-head518" style="it" xml:space="preserve">DE HOROLOGIO HORIZONTALI <lb/>Italico, &amp; Babylonico. CAP. IIII.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s38181" xml:space="preserve">CIRCVLVS ex E, deſcriptus cap. </s>
  <s xml:id="echoid-s38182" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38183" xml:space="preserve">ſecetur in horas 24. </s>
  <s xml:id="echoid-s38184" xml:space="preserve">æquales, initio facto à puncto <lb/>
<anchor type="note" xlink:label="note-0597-03a" xlink:href="note-0597-03"/>
N, numereturq́ue ad vtraſque partes N, arcus ſemidiurnus paralleli ♋, nempe ad latitu <lb/>dinem grad. </s>
  <s xml:id="echoid-s38185" xml:space="preserve">42. </s>
  <s xml:id="echoid-s38186" xml:space="preserve">horæ 7. </s>
  <s xml:id="echoid-s38187" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s38188" xml:space="preserve">32. </s>
  <s xml:id="echoid-s38189" xml:space="preserve">vſque ad puncta a, &amp; </s>
  <s xml:id="echoid-s38190" xml:space="preserve">b, ducaturq́ue recta a b, ita vt, poſito cir <lb/>culo N a M b, parallelo ♋, arcus a N b, ſit portio illius ſupra terram, &amp; </s>
  <s xml:id="echoid-s38191" xml:space="preserve">a M b, portio infra terrã. <lb/></s>
  <s xml:id="echoid-s38192" xml:space="preserve">Supputetur rurí<unsure/>us ad vtraſque partes N, arcus ſemidiurnus paralleli ♑, nempe ad eandem latitu <lb/>dinem grad. </s>
  <s xml:id="echoid-s38193" xml:space="preserve">42. </s>
  <s xml:id="echoid-s38194" xml:space="preserve">horæ 4. </s>
  <s xml:id="echoid-s38195" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s38196" xml:space="preserve">28. </s>
  <s xml:id="echoid-s38197" xml:space="preserve">vſque ad puncta d, &amp; </s>
  <s xml:id="echoid-s38198" xml:space="preserve">e, ducaturq́ue recta de, ita vt, poſito eo-<lb/>dem circulo N d M e, parallelo ♑, arcus d N e, ſit portio illius ſupra terram, &amp; </s>
  <s xml:id="echoid-s38199" xml:space="preserve">d M e, portio in-<lb/>fra terram. </s>
  <s xml:id="echoid-s38200" xml:space="preserve">Idem circulus M a d N e b, alio modo diuidi poteſt in arcum diurnum ♋, &amp; </s>
  <s xml:id="echoid-s38201" xml:space="preserve">♑, vt do <lb/>cuimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s38202" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38203" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38204" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38205" xml:space="preserve">Beneficio huius circuli hac ratione horologium Italicum con-<lb/>
<anchor type="note" xlink:label="note-0597-04a" xlink:href="note-0597-04"/>
ſtruemus. </s>
  <s xml:id="echoid-s38206" xml:space="preserve">Circulus dictus diſtribuatur in 24. </s>
  <s xml:id="echoid-s38207" xml:space="preserve">horas æquales, initio facto à puncto b, quod nimi <lb/>rum, horologio proprium ſitum habente, ad occaſum vergit, ac per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s38208" xml:space="preserve">cen-<lb/>
<anchor type="figure" xlink:label="fig-0597-01a" xlink:href="fig-0597-01"/>
<anchor type="note" xlink:label="note-0597-05a" xlink:href="note-0597-05"/>
<anchor type="note" xlink:label="note-0597-06a" xlink:href="note-0597-06"/>
trum E, rectæ ducantur occultæ ſecantes æquinoctialem lineam in punctis, per quæ ſi alię occul-<lb/>tæ rectæ ducantur ex H, centro horologii, ſecabitur tropicus ♋, in punctis, per quæ ducendæ ſunt <lb/>
<anchor type="note" xlink:label="note-0597-07a" xlink:href="note-0597-07"/>
horæ ab occaſu Solis, quę diligenter notentur. </s>
  <s xml:id="echoid-s38209" xml:space="preserve">Vt exempli gratia, per punctum f, horæ 18. </s>
  <s xml:id="echoid-s38210" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s38211" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38212" xml:space="preserve">centrum E, ducta recta f E, ſecat lineam æquinoctialem in g; </s>
  <s xml:id="echoid-s38213" xml:space="preserve">recta autem H g, ducta ſecatar-<lb/>cum ♋, in h, puncto, per quod linea horæ 18. </s>
  <s xml:id="echoid-s38214" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38215" xml:space="preserve">in horologio ducenda eſt. </s>
  <s xml:id="echoid-s38216" xml:space="preserve">Eademq́ue ratio <lb/>habenda eſt de cæteris. </s>
  <s xml:id="echoid-s38217" xml:space="preserve">Sed puncta horarum, quæ inter b, &amp; </s>
  <s xml:id="echoid-s38218" xml:space="preserve">u, necnon inter a, &amp; </s>
  <s xml:id="echoid-s38219" xml:space="preserve">t, continentur, <lb/>quales in noſtro exemplo ſunt hora 23. </s>
  <s xml:id="echoid-s38220" xml:space="preserve">9. </s>
  <s xml:id="echoid-s38221" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38222" xml:space="preserve">10. </s>
  <s xml:id="echoid-s38223" xml:space="preserve">hoc modo inuenientur in tropico ♋. </s>
  <s xml:id="echoid-s38224" xml:space="preserve">Ex horis, <lb/>quæ per diametrum opponuntur iſtis horis in circulo ex E, deſcripto (habentur autem horæ op-<lb/>poſitę ex additione horarum 12. </s>
  <s xml:id="echoid-s38225" xml:space="preserve">ad horas illas, reiectis tamen 24. </s>
  <s xml:id="echoid-s38226" xml:space="preserve">ſi numerus ex additione colle-<lb/>ctus maior fuerit, quàm 24. </s>
  <s xml:id="echoid-s38227" xml:space="preserve">Vt horæ 9. </s>
  <s xml:id="echoid-s38228" xml:space="preserve">opponitur hora 21. </s>
  <s xml:id="echoid-s38229" xml:space="preserve">quia ex 9. </s>
  <s xml:id="echoid-s38230" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38231" xml:space="preserve">12. </s>
  <s xml:id="echoid-s38232" xml:space="preserve">fiunt 21. </s>
  <s xml:id="echoid-s38233" xml:space="preserve">Ita etiam ho <lb/>ræ 23. </s>
  <s xml:id="echoid-s38234" xml:space="preserve">opponitur hora 11. </s>
  <s xml:id="echoid-s38235" xml:space="preserve">propterea quod ex 23. </s>
  <s xml:id="echoid-s38236" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38237" xml:space="preserve">12. </s>
  <s xml:id="echoid-s38238" xml:space="preserve">fiunt 35. </s>
  <s xml:id="echoid-s38239" xml:space="preserve">à quibus ſi abiiciantur 24. </s>
  <s xml:id="echoid-s38240" xml:space="preserve">rema-<lb/>nent 11. </s>
  <s xml:id="echoid-s38241" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38242" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s38243" xml:space="preserve">ducendæ erunt per centrum E, rectæ ſecantes æquinoctialem lineam in punctis, per <lb/>quæ, ſi ex H, ducantur rectæ, ſecabitur quidem tropicus ♋, in punctis, quæ horis iſtis oppoſitis re-
<pb o="582" file="0598" n="598" rhead="GNOMONICES"/>
ſpondent: </s>
  <s xml:id="echoid-s38244" xml:space="preserve">at verò ſi eædem illæ rectæ vltra centrum producantur, ſecabitur idem arcus ♋, in pun <lb/>ctis, quæ illis horis reſpondent, quæ in arcubus b u, &amp; </s>
  <s xml:id="echoid-s38245" xml:space="preserve">a t, comprehenduntur. </s>
  <s xml:id="echoid-s38246" xml:space="preserve">Vt ex m, puncto ho-<lb/>ræ 11. </s>
  <s xml:id="echoid-s38247" xml:space="preserve">quæ per diametrum opponitur horæ 23. </s>
  <s xml:id="echoid-s38248" xml:space="preserve">ducta recta per centrum E, ſecat ęquinoctialem li-<lb/>neam in n; </s>
  <s xml:id="echoid-s38249" xml:space="preserve">ducta autem recta H n, ſecat tropicum ♋, in q, puncto horæ 11. </s>
  <s xml:id="echoid-s38250" xml:space="preserve">producta denique re-<lb/>cta n H, vltra H, ſecat tropicum eundem in puncto p, per quod linea horæ 23. </s>
  <s xml:id="echoid-s38251" xml:space="preserve">ducenda eſt. </s>
  <s xml:id="echoid-s38252" xml:space="preserve">Eodẽ <lb/>artificio inueſtigabimus in eodem tropico puncta pro horis 9. </s>
  <s xml:id="echoid-s38253" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38254" xml:space="preserve">10. </s>
  <s xml:id="echoid-s38255" xml:space="preserve">ſi ex horis 21. </s>
  <s xml:id="echoid-s38256" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38257" xml:space="preserve">22. </s>
  <s xml:id="echoid-s38258" xml:space="preserve">quæ illis <lb/>opponuntur, per centrum E, rectas educamus, &amp;</s>
  <s xml:id="echoid-s38259" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38260" xml:space="preserve">Cauſa autem huius rei eſt, quod in tropico in-<lb/>ueniuntur primo loco puncta reſpondentia illis punctis circuli M a N b, ex quibus rectæ per E, <lb/>ductæ prius per E, tranſeunt, quàm æquinoctialem lineam ſecent. </s>
  <s xml:id="echoid-s38261" xml:space="preserve">Vnde cum rectæ ex punctis ar-<lb/>cuum b u, &amp; </s>
  <s xml:id="echoid-s38262" xml:space="preserve">a t, per E, ductæ, non prius per E, tranſeant, quàm lineam<unsure/> æquinoctialem ſecent, in-<lb/>
<anchor type="note" xlink:label="note-0598-01a" xlink:href="note-0598-01"/>
uenientur primo loco in tropico puncta reſpondentia punctis illis oppoſitis. </s>
  <s xml:id="echoid-s38263" xml:space="preserve">Deinde verò ſi pro-<lb/>ducantur illæ rectæ occultæ per H, reperientur puncta etiam reſpondentia dictis punctis, vt lib. </s>
  <s xml:id="echoid-s38264" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s38265" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s38266" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1909" type="float" level="2" n="1">
<note position="right" xlink:label="note-0597-03" xlink:href="note-0597-03a" xml:space="preserve">Deſcriptio ho-<lb/>rologii @alici <lb/>&amp; Babyl<unsure/>enici <lb/>horizontalis.</note>
<note position="left" xlink:label="note-0597-04" xlink:href="note-0597-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0597-01" xlink:href="fig-0597-01a">
    <image file="0597-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0597-01"/>
  </figure>
<note position="left" xlink:label="note-0597-05" xlink:href="note-0597-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0597-06" xlink:href="note-0597-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0597-07" xlink:href="note-0597-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0598-01" xlink:href="note-0598-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s38267" xml:space="preserve">QVOD ſi idem circulus ex E, deſcriptus ſecetur in 24 horas æquales, initio facto à puncto <lb/>e, quod eriam ad occaſum vergit, ſi horologium proprium ſitum adipiſcatur, &amp; </s>
  <s xml:id="echoid-s38268" xml:space="preserve">per puncta diui-<lb/>ſionum, ac centrum E, rectæ emittantur, ſecabitur æquinoctialis linea in punctis, per quæ ſi rurſus <lb/>ducantur ex H, rectæ, ſecabitur tropicus ♑, in punctis, per quæ horæ ab occaſu Solis ducendæ <lb/>erunt. </s>
  <s xml:id="echoid-s38269" xml:space="preserve">Vt ſi ex puncto {δι}<unsure/>, horæ 23. </s>
  <s xml:id="echoid-s38270" xml:space="preserve">tropici ♑, per centrum E, recta ducatur ſecans æquinoctialem <lb/>lineam in ε, inueniemus per rectam H ε, productam in arcu ♑, punctũ λ, pro hora 23. </s>
  <s xml:id="echoid-s38271" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38272" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38273" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s38274" xml:space="preserve">Iraque ſi puncta horarum correſpondentia in tropicis inuenta connectantur lineis rectis, deſcri-<lb/>
<anchor type="note" xlink:label="note-0598-02a" xlink:href="note-0598-02"/>
ptum erit horologium Italicum.</s>
  <s xml:id="echoid-s38275" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1910" type="float" level="2" n="2">
<note position="left" xlink:label="note-0598-02" xlink:href="note-0598-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s38276" xml:space="preserve">PORRO in circulo M a N b, ſi diuiſio in partes 24. </s>
  <s xml:id="echoid-s38277" xml:space="preserve">incipiat à puncto b, punctum b, perti-<lb/>netad horam 24. </s>
  <s xml:id="echoid-s38278" xml:space="preserve">♋. </s>
  <s xml:id="echoid-s38279" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38280" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38281" xml:space="preserve">ſequens punctum verſus N. </s>
  <s xml:id="echoid-s38282" xml:space="preserve">ad horam 23. </s>
  <s xml:id="echoid-s38283" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38284" xml:space="preserve">inſequensad 22. </s>
  <s xml:id="echoid-s38285" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38286" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s38287" xml:space="preserve">Item ſi diuiſio initium ſumat à puncto e, punctum e, ſpectatad horam 24. </s>
  <s xml:id="echoid-s38288" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s38289" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38290" xml:space="preserve">ſequens <lb/>verſus N, ad 23. </s>
  <s xml:id="echoid-s38291" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38292" xml:space="preserve">ſubſequens ad 22. </s>
  <s xml:id="echoid-s38293" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38294" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38295" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s38296" xml:space="preserve">TRANSIBVNT autem neceſſario lineæ horarum ab occaſu per puncta lineæ æquino-<lb/>ctialis, vbi à lineis horarum à meridie, vel media nocte ſecatur. </s>
  <s xml:id="echoid-s38297" xml:space="preserve">Vt linea horæ 23. </s>
  <s xml:id="echoid-s38298" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38299" xml:space="preserve">per pun-<lb/>ctum horæ 5. </s>
  <s xml:id="echoid-s38300" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38301" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38302" xml:space="preserve">linea horæ 22. </s>
  <s xml:id="echoid-s38303" xml:space="preserve">per punctum horæ 4 &amp; </s>
  <s xml:id="echoid-s38304" xml:space="preserve">ſic deinceps, vt ex tabula conſtat, <lb/>quam in ſcholio propoſ. </s>
  <s xml:id="echoid-s38305" xml:space="preserve">19. </s>
  <s xml:id="echoid-s38306" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38307" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38308" xml:space="preserve">deſcripſimus, &amp; </s>
  <s xml:id="echoid-s38309" xml:space="preserve">cuius tir<unsure/>ulus eſt. </s>
  <s xml:id="echoid-s38310" xml:space="preserve">[ÆQVINOCTIALIS <lb/>LINEA] quam hic, quoad horas integras, repetiuimus, vt videas, quæ horæ ab or. </s>
  <s xml:id="echoid-s38311" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38312" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38313" xml:space="preserve">à <lb/>
<anchor type="note" xlink:label="note-0598-03a" xlink:href="note-0598-03"/>
mer. </s>
  <s xml:id="echoid-s38314" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38315" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38316" xml:space="preserve">ſe mutuo interſecent in linea æquinoctiali cuiuſcunque horologii, atque adeo <lb/>quæ horæ ab or. </s>
  <s xml:id="echoid-s38317" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38318" xml:space="preserve">per quas horas à mer. </s>
  <s xml:id="echoid-s38319" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38320" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38321" xml:space="preserve">ducendæ ſint in æquinoctiali linea. <lb/></s>
  <s xml:id="echoid-s38322" xml:space="preserve">Ternæ enim horæ huius tabellæ per vnum idemq́ue punctum lineæ æquinoctialis tranſeunt. </s>
  <s xml:id="echoid-s38323" xml:space="preserve"><lb/>Quod idem de partibus horarum intelligendum eſt,</s>
</p>
<div xml:id="echoid-div1911" type="float" level="2" n="3">
<note position="left" xlink:label="note-0598-03" xlink:href="note-0598-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div1913" type="section" level="1" n="490">
<head xml:id="echoid-head519" xml:space="preserve">Horæ ab or. vel occ. &amp; à mer. vel med. noc. ſe mutuo ſecantes in vno \\ eodem puncto lineæ æquinoctialis.</head>
<note position="right" xml:space="preserve"> <lb/>
Horæ ab \\ or. vel \\ occ. # 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 # 10 # 11 # 12
Horæ a \\ mer. vel \\ med. no. # VII # VIII # IX # X # XI # XII # I # II # III # IIII # V # VI
Ho. ab or. \\ vel occ. # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24
</note>
<p>
  <s xml:id="echoid-s38324" xml:space="preserve">QVOD ſi puncta horarum in tropico ♋, non habeant in tropico ♑, puncta reſpondentia, <lb/>
<anchor type="note" xlink:label="note-0598-06a" xlink:href="note-0598-06"/>
cuiu@modi ſuntin noſtro exemplo omnes horæ ante horam 16. </s>
  <s xml:id="echoid-s38325" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38326" xml:space="preserve">ducendæ erun t lineę ho-<lb/>rariæ per puncta in tropico ♋, inuenta, &amp; </s>
  <s xml:id="echoid-s38327" xml:space="preserve">per puncta reſpondentia in æquinoctiali linea: </s>
  <s xml:id="echoid-s38328" xml:space="preserve">quæ <lb/>quidem puncta ex dicta tabula in ſcholio propoſ. </s>
  <s xml:id="echoid-s38329" xml:space="preserve">19. </s>
  <s xml:id="echoid-s38330" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38331" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38332" xml:space="preserve">poſita inueniuntur, vel ex proxima ta-<lb/>bella hic poſita. </s>
  <s xml:id="echoid-s38333" xml:space="preserve">Vt linea horæ 11. </s>
  <s xml:id="echoid-s38334" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38335" xml:space="preserve">ducenda eſt per horam 23. </s>
  <s xml:id="echoid-s38336" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38337" xml:space="preserve">in linea æquinoctia. <lb/></s>
  <s xml:id="echoid-s38338" xml:space="preserve">li, à qua nimirum illa abeſt horis 12. </s>
  <s xml:id="echoid-s38339" xml:space="preserve">Item hora 10. </s>
  <s xml:id="echoid-s38340" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38341" xml:space="preserve">ducenda eſt per horam 22. </s>
  <s xml:id="echoid-s38342" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38343" xml:space="preserve">hora 9. </s>
  <s xml:id="echoid-s38344" xml:space="preserve"><lb/>per horam 21. </s>
  <s xml:id="echoid-s38345" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38346" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38347" xml:space="preserve">Linea vero horæ 12. </s>
  <s xml:id="echoid-s38348" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38349" xml:space="preserve">ducenda erit per punctum in tropico ♋, inuen-<lb/>tum parallela lineæ æquinoctiali, vel lineæ horæ 6. </s>
  <s xml:id="echoid-s38350" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38351" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38352" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s38353" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1913" type="float" level="2" n="1">
<note position="left" xlink:label="note-0598-06" xlink:href="note-0598-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s38354" xml:space="preserve">NON diſſimili arte horologium Babylonicum conficiemus, ſi diuiſionem circuli ex E, de-<lb/>
<anchor type="note" xlink:label="note-0598-07a" xlink:href="note-0598-07"/>
ſcripti in 24. </s>
  <s xml:id="echoid-s38355" xml:space="preserve">horas æquales inchoemus à punctis a, &amp; </s>
  <s xml:id="echoid-s38356" xml:space="preserve">d, quæ horologio poſito in proprio ſitu, <lb/>orientalia ſunt; </s>
  <s xml:id="echoid-s38357" xml:space="preserve">ita vt punctum a, pertineat ad horam 24. </s>
  <s xml:id="echoid-s38358" xml:space="preserve">ab ortu in tropico ♋, &amp; </s>
  <s xml:id="echoid-s38359" xml:space="preserve">ſequens pun-<lb/>ctum verſus N, ad horam 1. </s>
  <s xml:id="echoid-s38360" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s38361" xml:space="preserve">inſequens ad 2. </s>
  <s xml:id="echoid-s38362" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38363" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38364" xml:space="preserve">Item punctum d, referat horam 24.</s>
  <s xml:id="echoid-s38365" xml:space="preserve">
<pb o="583" file="0599" n="599" rhead="LIBER SEPTIMVS."/>
ab ortu in tropico ♑, &amp; </s>
  <s xml:id="echoid-s38366" xml:space="preserve">proximum punctum verſus N, horam 1. </s>
  <s xml:id="echoid-s38367" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38368" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38369" xml:space="preserve">Per hæc enim puncta diui-<lb/>ſionum inueniemus in vtroque tropico horologii puncta horarum ab ortu Solis, vt proximè de <lb/>punctis horarum ab occaſu diximus, horologiumq́ue Babylonicum conficiemus.</s>
  <s xml:id="echoid-s38370" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1914" type="float" level="2" n="2">
<note position="left" xlink:label="note-0598-07" xlink:href="note-0598-07a" xml:space="preserve">Conſtructio ho-<lb/>rologii Babylo-<lb/>nici horizonta-<lb/>lis.</note>
</div>
<p>
  <s xml:id="echoid-s38371" xml:space="preserve">DESCRIBETVR alio modo vtrumque horologium ex tabellis arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s38372" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0599-01a" xlink:href="note-0599-01"/>
nocturnorum, quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s38373" xml:space="preserve">33. </s>
  <s xml:id="echoid-s38374" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38375" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38376" xml:space="preserve">compoſuimus. </s>
  <s xml:id="echoid-s38377" xml:space="preserve">Ex his enim dicto citius intellige-<lb/>tur, quæ horæ ab or. </s>
  <s xml:id="echoid-s38378" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38379" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38380" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38381" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38382" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38383" xml:space="preserve">ſe mutuo ſecent in vno eodemq́ue puncto di-<lb/>ctorum arcuum diurnorum, nocturnorumq́ue. </s>
  <s xml:id="echoid-s38384" xml:space="preserve">Superuacaneum autem duximus hoc loco eas ta-<lb/>bulas repetere, cum facile ex dicto ſcholio ſumi poſſint.</s>
  <s xml:id="echoid-s38385" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1915" type="float" level="2" n="3">
<note position="right" xlink:label="note-0599-01" xlink:href="note-0599-01a" xml:space="preserve">Deſcriptio eiuſ-<lb/>dem horologii <lb/>Italici, &amp; Baby-<lb/>lonici perarcu @ <lb/>diut<unsure/>nos.</note>
</div>
<p>
  <s xml:id="echoid-s38386" xml:space="preserve">ITAQVE deſcribantur in horologio Aſtronomico duo arcus diurni, vnus horarum 14. </s>
  <s xml:id="echoid-s38387" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38388" xml:space="preserve"><lb/>horarum 10. </s>
  <s xml:id="echoid-s38389" xml:space="preserve">alter, vt in præcedenti capite docuimus. </s>
  <s xml:id="echoid-s38390" xml:space="preserve">Satis autem erit, ſi in horis à meridie, vel <lb/>
<anchor type="note" xlink:label="note-0599-02a" xlink:href="note-0599-02"/>
media nocte ſignentur puncta, per quę prædicti arcus tranſire debent, etiamſi arcus ipſi non deli-<lb/>neentur. </s>
  <s xml:id="echoid-s38391" xml:space="preserve">Deinde diligenter conſiderentur tabellæ arcuum diurnorum horarum 10. </s>
  <s xml:id="echoid-s38392" xml:space="preserve">12. </s>
  <s xml:id="echoid-s38393" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38394" xml:space="preserve">14. <lb/></s>
  <s xml:id="echoid-s38395" xml:space="preserve">quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s38396" xml:space="preserve">33. </s>
  <s xml:id="echoid-s38397" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38398" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38399" xml:space="preserve">propoſuimus. </s>
  <s xml:id="echoid-s38400" xml:space="preserve">Ex illis enim confeſtim diſces, per quaſnam horas <lb/>à meridie, vel media nocte dictorum arcuũ ducendæ ſint horæ ab ortu, &amp; </s>
  <s xml:id="echoid-s38401" xml:space="preserve">occaſu Solis. </s>
  <s xml:id="echoid-s38402" xml:space="preserve">Ita nam-<lb/>que vides horam 1. </s>
  <s xml:id="echoid-s38403" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38404" xml:space="preserve">ducendam eſſe per horam 6. </s>
  <s xml:id="echoid-s38405" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38406" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38407" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38408" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38409" xml:space="preserve">per <lb/>horam 7. </s>
  <s xml:id="echoid-s38410" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38411" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38412" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38413" xml:space="preserve">qui in horologio à linea æquinoctiali non differt, &amp; </s>
  <s xml:id="echoid-s38414" xml:space="preserve"><lb/>per horam 8. </s>
  <s xml:id="echoid-s38415" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38416" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38417" xml:space="preserve">in arcu horarum 10. </s>
  <s xml:id="echoid-s38418" xml:space="preserve">Item horam 23. </s>
  <s xml:id="echoid-s38419" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38420" xml:space="preserve">duci debere per horam 6. </s>
  <s xml:id="echoid-s38421" xml:space="preserve"><lb/>à mer. </s>
  <s xml:id="echoid-s38422" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38423" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38424" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s38425" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38426" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38427" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38428" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s38429" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38430" xml:space="preserve">in <lb/>arcu horarum 10. </s>
  <s xml:id="echoid-s38431" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38432" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s38433" xml:space="preserve">Horæ autem, quæ in arcu horarum 10. </s>
  <s xml:id="echoid-s38434" xml:space="preserve">non habent puncta re-<lb/>ſpondentia, quales ſunt in noſtro exemplo omnes horæ ab ortu poſt horam 9. </s>
  <s xml:id="echoid-s38435" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s38436" xml:space="preserve">omnes <lb/>
<anchor type="note" xlink:label="note-0599-03a" xlink:href="note-0599-03"/>
horæ ab occ. </s>
  <s xml:id="echoid-s38437" xml:space="preserve">ante horam 15. </s>
  <s xml:id="echoid-s38438" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38439" xml:space="preserve">ducendæ ſunt per puncta in arcubus horarum 14. </s>
  <s xml:id="echoid-s38440" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38441" xml:space="preserve">12. </s>
  <s xml:id="echoid-s38442" xml:space="preserve">Ho-<lb/>ra verò 12. </s>
  <s xml:id="echoid-s38443" xml:space="preserve">ab ortu, vel occaſu ducenda eſt parallela lineæ æquinoctiali per horam 5. </s>
  <s xml:id="echoid-s38444" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38445" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38446" xml:space="preserve">per <lb/>horam 7. </s>
  <s xml:id="echoid-s38447" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38448" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38449" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38450" xml:space="preserve">vt ex tabella dicti arcus conſtat.</s>
  <s xml:id="echoid-s38451" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1916" type="float" level="2" n="4">
<note position="left" xlink:label="note-0599-02" xlink:href="note-0599-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0599-03" xlink:href="note-0599-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s38452" xml:space="preserve">QVOD ſi quando contingat, vt in dictis tabellis arcuum diurnorum inueniatur vnum dun-<lb/>taxat punctum, vel nullum pro hora aliqua ab or. </s>
  <s xml:id="echoid-s38453" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38454" xml:space="preserve">ducenda, ducemus per eaſdem tabellas <lb/>alterius nominis horam, eiuſdem tamen numeri, vtpote ab occaſu, vel ortu. </s>
  <s xml:id="echoid-s38455" xml:space="preserve">Hæc enim producta <lb/>ad alteram partem tropici dabit quæſitam horam ab ortu, vel occaſu. </s>
  <s xml:id="echoid-s38456" xml:space="preserve">Exempli gratia, quoniam <lb/>hora 13. </s>
  <s xml:id="echoid-s38457" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38458" xml:space="preserve">ſolum in arcu horarum 14. </s>
  <s xml:id="echoid-s38459" xml:space="preserve">punctum habet, nempe horam 6. </s>
  <s xml:id="echoid-s38460" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38461" xml:space="preserve">ducemus <lb/>horam 13.</s>
  <s xml:id="echoid-s38462" xml:space="preserve"><unsure/> ab occ. </s>
  <s xml:id="echoid-s38463" xml:space="preserve">per horam 8. </s>
  <s xml:id="echoid-s38464" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38465" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38466" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38467" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38468" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s38469" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38470" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38471" xml:space="preserve">in ar-<lb/>cu horarum 12. </s>
  <s xml:id="echoid-s38472" xml:space="preserve">vt ex dictorum arcuum tabellis conſtat. </s>
  <s xml:id="echoid-s38473" xml:space="preserve">Hæc enim producta@ ad alteram partem <lb/>
<anchor type="note" xlink:label="note-0599-04a" xlink:href="note-0599-04"/>
tropici dabit horam 13. </s>
  <s xml:id="echoid-s38474" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38475" xml:space="preserve">Tranſibit autem neceſſario hora hæc 13. </s>
  <s xml:id="echoid-s38476" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38477" xml:space="preserve">producta per ho-<lb/>ram 6. </s>
  <s xml:id="echoid-s38478" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38479" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38480" xml:space="preserve">per quam nimirum ducenda eſt hora 13. </s>
  <s xml:id="echoid-s38481" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38482" xml:space="preserve">vt tabella arcus <lb/>horarum 14. </s>
  <s xml:id="echoid-s38483" xml:space="preserve">indicat. </s>
  <s xml:id="echoid-s38484" xml:space="preserve">Sic etiam quia hora 14. </s>
  <s xml:id="echoid-s38485" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38486" xml:space="preserve">nullum habet punctum in prædictis arcubus <lb/>diurnis, ducemus horam 14. </s>
  <s xml:id="echoid-s38487" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38488" xml:space="preserve">per horam 9. </s>
  <s xml:id="echoid-s38489" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38490" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38491" xml:space="preserve">in arcu horarũ 14. </s>
  <s xml:id="echoid-s38492" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38493" xml:space="preserve">per horã 8. </s>
  <s xml:id="echoid-s38494" xml:space="preserve">à <lb/>med. </s>
  <s xml:id="echoid-s38495" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38496" xml:space="preserve">in arcu horarũ 12. </s>
  <s xml:id="echoid-s38497" xml:space="preserve">vt ex horum arcuum tabellis colligitur. </s>
  <s xml:id="echoid-s38498" xml:space="preserve">Rurſus quia hora 11. </s>
  <s xml:id="echoid-s38499" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s38500" xml:space="preserve">in arcu horarum 14. </s>
  <s xml:id="echoid-s38501" xml:space="preserve">ſolum punctum habet, nempe horam 6. </s>
  <s xml:id="echoid-s38502" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38503" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38504" xml:space="preserve">ducemus horam 11. </s>
  <s xml:id="echoid-s38505" xml:space="preserve">ab <lb/>or. </s>
  <s xml:id="echoid-s38506" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s38507" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38508" xml:space="preserve">in arcu horarũ 14. </s>
  <s xml:id="echoid-s38509" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38510" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s38511" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38512" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38513" xml:space="preserve">vt ex dicto-<lb/>rum arcuum tabellis elicitur. </s>
  <s xml:id="echoid-s38514" xml:space="preserve">Nam hæc producta ad alteram partem tropici ♋, exhibebit horam <lb/>11. </s>
  <s xml:id="echoid-s38515" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38516" xml:space="preserve">tranſibitq́ue neceſſario perhoram 6. </s>
  <s xml:id="echoid-s38517" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38518" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38519" xml:space="preserve">per quam videlicet hora 11. </s>
  <s xml:id="echoid-s38520" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38521" xml:space="preserve"><lb/>ducenda eſt, ſecundum tabellam arcus horarum 14. </s>
  <s xml:id="echoid-s38522" xml:space="preserve">Eademq́ue ratio de cæteris habenda eſt.</s>
  <s xml:id="echoid-s38523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1917" type="float" level="2" n="5">
<note position="left" xlink:label="note-0599-04" xlink:href="note-0599-04a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s38524" xml:space="preserve">IAM verò commodiſſime etiam deſcribi poterunt horæ ab or. </s>
  <s xml:id="echoid-s38525" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38526" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s38527" xml:space="preserve">ſi deſcribatur arcus <lb/>
<anchor type="note" xlink:label="note-0599-06a" xlink:href="note-0599-06"/>
diurnus horarum 24. </s>
  <s xml:id="echoid-s38528" xml:space="preserve">Nam rectę ductæ per horas à mer. </s>
  <s xml:id="echoid-s38529" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38530" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38531" xml:space="preserve">in dicto arcu ſecundum <lb/>tabellam arcus diurni horarum 24. </s>
  <s xml:id="echoid-s38532" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38533" xml:space="preserve">per horas à mer. </s>
  <s xml:id="echoid-s38534" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38535" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38536" xml:space="preserve">in arcu diurno horarum 12. <lb/></s>
  <s xml:id="echoid-s38537" xml:space="preserve">dabunt horas ab ortu, &amp; </s>
  <s xml:id="echoid-s38538" xml:space="preserve">occaſu. </s>
  <s xml:id="echoid-s38539" xml:space="preserve">Tranſit enim hora 23. </s>
  <s xml:id="echoid-s38540" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38541" xml:space="preserve">per horam 11. </s>
  <s xml:id="echoid-s38542" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38543" xml:space="preserve">arcus diurni <lb/>horarum 24. </s>
  <s xml:id="echoid-s38544" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38545" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s38546" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38547" xml:space="preserve">arcus diurni horarum 12. </s>
  <s xml:id="echoid-s38548" xml:space="preserve">ſeu lineæ æquinoctialis. </s>
  <s xml:id="echoid-s38549" xml:space="preserve">Hora verò <lb/>22. </s>
  <s xml:id="echoid-s38550" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38551" xml:space="preserve">per horam 10. </s>
  <s xml:id="echoid-s38552" xml:space="preserve">à<unsure/> mer. </s>
  <s xml:id="echoid-s38553" xml:space="preserve">in arcu horarum 24. </s>
  <s xml:id="echoid-s38554" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38555" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s38556" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38557" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38558" xml:space="preserve"><lb/>Item hora 1. </s>
  <s xml:id="echoid-s38559" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38560" xml:space="preserve">ducitur per horam 1. </s>
  <s xml:id="echoid-s38561" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38562" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38563" xml:space="preserve">in arcu horarum 24. </s>
  <s xml:id="echoid-s38564" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38565" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s38566" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38567" xml:space="preserve"><lb/>noc. </s>
  <s xml:id="echoid-s38568" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38569" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38570" xml:space="preserve">ita deinceps, vt liquido conſtat ex dictorum arcuum tabellis. </s>
  <s xml:id="echoid-s38571" xml:space="preserve">Hora <lb/>autem 12. </s>
  <s xml:id="echoid-s38572" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38573" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38574" xml:space="preserve">ducitur parallela lineę æquinoctiali, vel horæ 6. </s>
  <s xml:id="echoid-s38575" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38576" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38577" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38578" xml:space="preserve">per <lb/>punctum, vbi arcus horarum 24. </s>
  <s xml:id="echoid-s38579" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38580" xml:space="preserve">linea meridiana ſe mutuo interſecant, vt ex eadem tabella <lb/>
<anchor type="note" xlink:label="note-0599-07a" xlink:href="note-0599-07"/>
arcus diurni horarum 24. </s>
  <s xml:id="echoid-s38581" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s38582" xml:space="preserve">Immò verò omnes lineæ horarum ab or. </s>
  <s xml:id="echoid-s38583" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38584" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s38585" xml:space="preserve">tangunt ar-<lb/>cum diurnum horarum 24. </s>
  <s xml:id="echoid-s38586" xml:space="preserve">in punctis, vbi ſecatur à lineis horarum à mer. </s>
  <s xml:id="echoid-s38587" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38588" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38589" xml:space="preserve">quæ <lb/>horis ab or. </s>
  <s xml:id="echoid-s38590" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38591" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s38592" xml:space="preserve">ſecundum tabellam eiuſdem arcus reſpondent, vt conſtat ex iis, quæ demon-<lb/>ſtrauimus propoſ. </s>
  <s xml:id="echoid-s38593" xml:space="preserve">14. </s>
  <s xml:id="echoid-s38594" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38595" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38596" xml:space="preserve">Cæterum ducta vna aliqua hora ab or. </s>
  <s xml:id="echoid-s38597" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38598" xml:space="preserve">ſecundum tabellas ar-<lb/>cuum diurnorum, ducemus alias ſine magno labore per ſequentia puncta, quæ inter ſe reſpondẽt, <lb/>nulla amplius habita conſideratione tabellarum arcuum diurnorum. </s>
  <s xml:id="echoid-s38599" xml:space="preserve">Vt ducta v. </s>
  <s xml:id="echoid-s38600" xml:space="preserve">g. </s>
  <s xml:id="echoid-s38601" xml:space="preserve">hora 23. </s>
  <s xml:id="echoid-s38602" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s38603" xml:space="preserve">ducemus 22. </s>
  <s xml:id="echoid-s38604" xml:space="preserve">per proximum punctum in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s38605" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38606" xml:space="preserve">per proximum in arcu <lb/>horarum 12. </s>
  <s xml:id="echoid-s38607" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38608" xml:space="preserve">per proximum in arcu horarum 10. </s>
  <s xml:id="echoid-s38609" xml:space="preserve">Item 21. </s>
  <s xml:id="echoid-s38610" xml:space="preserve">per alia proxime inſequentia pun-<lb/>cta, vt in exemplo ſuprapoſito apparet.</s>
  <s xml:id="echoid-s38611" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1918" type="float" level="2" n="6">
<note position="right" xlink:label="note-0599-06" xlink:href="note-0599-06a" xml:space="preserve">Deſcriptio eiuſ-<lb/>dem horologii <lb/>Italici &amp; Babylo <lb/>nici horizõtalis <lb/>ex arcu diurno <lb/>horarum 24.</note>
<note position="left" xlink:label="note-0599-07" xlink:href="note-0599-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s38612" xml:space="preserve">PORRO ex ipſa deſcriptione horologii Italici &amp; </s>
  <s xml:id="echoid-s38613" xml:space="preserve">Babylonici perſpicuum eſt, duo hæc horo <lb/>logia inter ſe non differre, niſi ſitu, &amp; </s>
  <s xml:id="echoid-s38614" xml:space="preserve">ordine horarum: </s>
  <s xml:id="echoid-s38615" xml:space="preserve">ita vt horologium Italicum inſeruire etiã
<pb o="584" file="0600" n="600" rhead="GNOMONICES"/>
nobis poſſit pro Babylonico, ſi modo inuertatur, vt pars ſiniſtra fiat dextra, &amp; </s>
  <s xml:id="echoid-s38616" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s38617" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38618" xml:space="preserve">ex linea <lb/>horæ 23. </s>
  <s xml:id="echoid-s38619" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38620" xml:space="preserve">fiat hora 1. </s>
  <s xml:id="echoid-s38621" xml:space="preserve">ab ortu: </s>
  <s xml:id="echoid-s38622" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38623" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38624" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s38625" xml:space="preserve">fiat ex 22. </s>
  <s xml:id="echoid-s38626" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38627" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38628" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38629" xml:space="preserve">In exemplo ſuprapoſito <lb/>continentur &amp; </s>
  <s xml:id="echoid-s38630" xml:space="preserve">horæ Aſtronomicæ, &amp; </s>
  <s xml:id="echoid-s38631" xml:space="preserve">Italicæ, vna cum Babylonicis. </s>
  <s xml:id="echoid-s38632" xml:space="preserve">Aſtronomicæ ſunt occultæ <lb/>punctis tantummodo notatæ: </s>
  <s xml:id="echoid-s38633" xml:space="preserve">Italicæ ſunt 23. </s>
  <s xml:id="echoid-s38634" xml:space="preserve">22. </s>
  <s xml:id="echoid-s38635" xml:space="preserve">21. </s>
  <s xml:id="echoid-s38636" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38637" xml:space="preserve">ita deinceps, Babylonicæ denique 1. <lb/></s>
  <s xml:id="echoid-s38638" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38639" xml:space="preserve">3. </s>
  <s xml:id="echoid-s38640" xml:space="preserve">4. </s>
  <s xml:id="echoid-s38641" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38642" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38643" xml:space="preserve">Vbietiam vides, horas Italicas productas dare eaſdem numero horas Babylonicas, <lb/>&amp; </s>
  <s xml:id="echoid-s38644" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s38645" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s38646" xml:space="preserve">PLVRIMVM etiam conferent ad rectam deſcriptionem horolog@i Italici, &amp; </s>
  <s xml:id="echoid-s38647" xml:space="preserve">Babylonici <lb/>ea, quæ lib. </s>
  <s xml:id="echoid-s38648" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38649" xml:space="preserve">diximus de mutua ſectione linearum horarum à mer. </s>
  <s xml:id="echoid-s38650" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38651" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38652" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38653" xml:space="preserve">horarum ab <lb/>or. </s>
  <s xml:id="echoid-s38654" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s38655" xml:space="preserve">inter ſe. </s>
  <s xml:id="echoid-s38656" xml:space="preserve">Pro qua re varias etiam tabulas conſtruximus in ſcholiis propoſ. </s>
  <s xml:id="echoid-s38657" xml:space="preserve">19. </s>
  <s xml:id="echoid-s38658" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38659" xml:space="preserve">20. <lb/></s>
  <s xml:id="echoid-s38660" xml:space="preserve">eiuſdem lib. </s>
  <s xml:id="echoid-s38661" xml:space="preserve">Quo pacto autem ex hiſce tabulis tam horæ ab or. </s>
  <s xml:id="echoid-s38662" xml:space="preserve">quàm ab occ deſcribantur, vel de-<lb/>
<anchor type="note" xlink:label="note-0600-01a" xlink:href="note-0600-01"/>
ſcriptæ examinentur, abunde declarauimus propoſ. </s>
  <s xml:id="echoid-s38663" xml:space="preserve">10. </s>
  <s xml:id="echoid-s38664" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38665" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38666" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38667" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38668" xml:space="preserve">Vtopus non ſit ea, quæ ibi hac <lb/>de re ſcripſimus, iterum hic inculcare.</s>
  <s xml:id="echoid-s38669" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1919" type="float" level="2" n="7">
<note position="left" xlink:label="note-0600-01" xlink:href="note-0600-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1921" type="section" level="1" n="491">
<head xml:id="echoid-head520" style="it" xml:space="preserve">DE HOROLOGIO HORIZONT ALI <lb/>Antiquo. CAP. V.</head>
<p>
  <s xml:id="echoid-s38670" xml:space="preserve">SECETVR circulus ex E, deſcriptus in arcum diurnum tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s38671" xml:space="preserve">in arcum diur-<lb/>
<anchor type="note" xlink:label="note-0600-02a" xlink:href="note-0600-02"/>
num tropici ♑, d N e, vt ad initium præcedentis capitis docuimus. </s>
  <s xml:id="echoid-s38672" xml:space="preserve">Deinde arcus diurnus ♋, <lb/>a N b, in 12. </s>
  <s xml:id="echoid-s38673" xml:space="preserve">partes æquales diſtribuatur, initio facto à puncto a, orientali. </s>
  <s xml:id="echoid-s38674" xml:space="preserve">Nam ſi per diuiſionũ <lb/>puncta, &amp; </s>
  <s xml:id="echoid-s38675" xml:space="preserve">centrum E, rectas occultas ducamus, ſecabitur ęquinoctialis linea in punctis, per quæ ſi <lb/>
<anchor type="note" xlink:label="note-0600-03a" xlink:href="note-0600-03"/>
rurſus ex H, centro horologii aliæ rectę occultæ emittantur ſecantes tropicum ♋, inuenta erunt <lb/>
<anchor type="figure" xlink:label="fig-0600-01a" xlink:href="fig-0600-01"/>
<anchor type="note" xlink:label="note-0600-04a" xlink:href="note-0600-04"/>
<anchor type="note" xlink:label="note-0600-05a" xlink:href="note-0600-05"/>
puncta, per quæ ducendæ eruntlineæ horarum inæqualium, non aliter atque in antecedenti capi-<lb/>te inuenimus in eodem tropico puncta horarum ab or. </s>
  <s xml:id="echoid-s38676" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38677" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s38678" xml:space="preserve">Quod ſi arcus diurnus ♑, d N e, <lb/>
<anchor type="note" xlink:label="note-0600-06a" xlink:href="note-0600-06"/>
in 12. </s>
  <s xml:id="echoid-s38679" xml:space="preserve">quoque æquales partes diuidatur initio facto à puncto d, orientali, reperiemus eodem mo-<lb/>do in tropico ♑, puncta horarum inæqualium. </s>
  <s xml:id="echoid-s38680" xml:space="preserve">Siigitur reſpondentia puncta lineis rectis con-<lb/>iungantur, deſcriptum erit horologium Antiquum. </s>
  <s xml:id="echoid-s38681" xml:space="preserve">Tranſibunt autem omnes lineæ horarum <lb/>inęqualium per horas à mer. </s>
  <s xml:id="echoid-s38682" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38683" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38684" xml:space="preserve">in linea æquinoctiali. </s>
  <s xml:id="echoid-s38685" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s38686" xml:space="preserve">Ex f, puncto ho-<lb/>ræ 3. </s>
  <s xml:id="echoid-s38687" xml:space="preserve">inæqualis tropici ♑, per E, ducta recta ſecat æquinoctialem lineam in g, recta autem ex H, <lb/>per g, emiſſa ſecat tropicum ♑, in h, puncto, per quod linea horæ 3. </s>
  <s xml:id="echoid-s38688" xml:space="preserve">inæqualis ducenda eſt. </s>
  <s xml:id="echoid-s38689" xml:space="preserve">Rur-<lb/>ſus ex puncto m, quod opponitur horæ 11. </s>
  <s xml:id="echoid-s38690" xml:space="preserve">inæquali tropici ♋, (Nam hora 11. </s>
  <s xml:id="echoid-s38691" xml:space="preserve">inæqualis tropici <lb/>♋, in arcu b u, continetur; </s>
  <s xml:id="echoid-s38692" xml:space="preserve">atque ita eius punctum in tropico ♋, inueſtigandum eſt per punctũ <lb/>oppoſitum, vt de horisab or. </s>
  <s xml:id="echoid-s38693" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38694" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s38695" xml:space="preserve">in arcubus bu, at, contentis diximus in pręcedẽti cap.) </s>
  <s xml:id="echoid-s38696" xml:space="preserve">recta <lb/>emiſſa per E, ſecat lineam æquinoctialẽ in puncto n, (quod tamen in exemplo propter anguſtiam <lb/>ſpatij non continetur) at recta H n, ſecat tropicũ ♋, in puncto p, quod puncto aſſumpto m, debe-
<pb o="585" file="0601" n="601" rhead="LIBER SEPTIMVS."/>
tur: </s>
  <s xml:id="echoid-s38697" xml:space="preserve">producta autem n H, vltra centrum horologii H, ſecat eundem tropicum ♋, in q, puncto ho <lb/>ræ 11, inæqualis, &amp;</s>
  <s xml:id="echoid-s38698" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38699" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1921" type="float" level="2" n="1">
<note position="left" xlink:label="note-0600-02" xlink:href="note-0600-02a" xml:space="preserve">Deſcriptio ho-<lb/>rologij Antiqui <lb/>hor@zo@talis.</note>
<note position="left" xlink:label="note-0600-03" xlink:href="note-0600-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0600-01" xlink:href="fig-0600-01a">
    <image file="0600-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0600-01"/>
  </figure>
<note position="left" xlink:label="note-0600-04" xlink:href="note-0600-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0600-05" xlink:href="note-0600-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0600-06" xlink:href="note-0600-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s38700" xml:space="preserve">IAM verò ſi attente conſiderentur ſex tabulæ arcuum diurnorum, nocturnorumq́ue hora-<lb/>rum 18. </s>
  <s xml:id="echoid-s38701" xml:space="preserve">6. </s>
  <s xml:id="echoid-s38702" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38703" xml:space="preserve">12. </s>
  <s xml:id="echoid-s38704" xml:space="preserve">pro horis inæqualibus in ſcholio propoſ. </s>
  <s xml:id="echoid-s38705" xml:space="preserve">33. </s>
  <s xml:id="echoid-s38706" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38707" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38708" xml:space="preserve">conſtructę, ex quibus cogno-<lb/>
<anchor type="note" xlink:label="note-0601-01a" xlink:href="note-0601-01"/>
ſcitur, quænam horæ à mer. </s>
  <s xml:id="echoid-s38709" xml:space="preserve">vel med.</s>
  <s xml:id="echoid-s38710" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38711" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38712" xml:space="preserve">inæquales ſe mutuo ſecent in vno, eodemq́ue puncto <lb/>dictorum arcuum, vt latius explicauimus in dicto ſcholio propoſ. </s>
  <s xml:id="echoid-s38713" xml:space="preserve">33. </s>
  <s xml:id="echoid-s38714" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38715" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38716" xml:space="preserve">facili etiam negotio <lb/>horologium Antiquum componemus, ſi prius arcum horarum 18. </s>
  <s xml:id="echoid-s38717" xml:space="preserve">deſcribamus. </s>
  <s xml:id="echoid-s38718" xml:space="preserve">Nam hora 1. <lb/></s>
  <s xml:id="echoid-s38719" xml:space="preserve">inæqualis ducenda eſt per horam 4 {1/2}. </s>
  <s xml:id="echoid-s38720" xml:space="preserve">à med.</s>
  <s xml:id="echoid-s38721" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38722" xml:space="preserve">in arcu diurno horarum 18. </s>
  <s xml:id="echoid-s38723" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38724" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s38725" xml:space="preserve">à <lb/>med.</s>
  <s xml:id="echoid-s38726" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38727" xml:space="preserve">in arcu horarum 12. </s>
  <s xml:id="echoid-s38728" xml:space="preserve">vt ex tabulis dictorum arcuum manifeſtum eſt. </s>
  <s xml:id="echoid-s38729" xml:space="preserve">Hora autem 2. </s>
  <s xml:id="echoid-s38730" xml:space="preserve">in-<lb/>æqualis ducenda eſt per horam 6. </s>
  <s xml:id="echoid-s38731" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38732" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38733" xml:space="preserve">in arcu horarum 18. </s>
  <s xml:id="echoid-s38734" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38735" xml:space="preserve">per 8. </s>
  <s xml:id="echoid-s38736" xml:space="preserve">à media nocte in <lb/>
<anchor type="note" xlink:label="note-0601-02a" xlink:href="note-0601-02"/>
arcu horarum 12. </s>
  <s xml:id="echoid-s38737" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38738" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38739" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1922" type="float" level="2" n="2">
<note position="right" xlink:label="note-0601-01" xlink:href="note-0601-01a" xml:space="preserve">Deſcriptio horo <lb/>legii Antiqui <lb/>horizontalis per <lb/>arcus diurnos <lb/>horarũ 18. &amp; 6.</note>
<note position="left" xlink:label="note-0601-02" xlink:href="note-0601-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1924" type="section" level="1" n="492">
<head xml:id="echoid-head521" style="it" xml:space="preserve">DE HOROLOGIO VERTICALI <lb/>Aſtronomico. CAP. VI.</head>
<p>
  <s xml:id="echoid-s38740" xml:space="preserve">IN plano horologii aſſumpto vtcunque loco ſtyli in G, ducatur per G, recta vtcunque H N, pro <lb/>
<anchor type="note" xlink:label="note-0601-03a" xlink:href="note-0601-03"/>
linea meridiana; </s>
  <s xml:id="echoid-s38741" xml:space="preserve">vel, ſi planum ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s38742" xml:space="preserve">Verticali circulo æquidiſtans, ducatur beneficio <lb/>perpendiculi in eodem plano per G, recta H N, ad Horizontem perpendicularis. </s>
  <s xml:id="echoid-s38743" xml:space="preserve">hæc enim erit <lb/>meridiana linea. </s>
  <s xml:id="echoid-s38744" xml:space="preserve">Deinde per aſſumptum locum ſtyli G, ducta recta G D, ad H N, perpendicu-<lb/>lari, ſumatur G D, propoſito ſtylo æqualis. </s>
  <s xml:id="echoid-s38745" xml:space="preserve">Facto autem D, cẽtro, deſcribatur arcus circuli A B C, <lb/>
<anchor type="note" xlink:label="note-0601-04a" xlink:href="note-0601-04"/>
<anchor type="figure" xlink:label="fig-0601-01a" xlink:href="fig-0601-01"/>
<anchor type="note" xlink:label="note-0601-05a" xlink:href="note-0601-05"/>
<anchor type="note" xlink:label="note-0601-06a" xlink:href="note-0601-06"/>
in quo verſus A, hoc eſt, verſus partes ſuperiores, ſi horologium ad meridiem ſpectet, (quale eſt <lb/>horologium, quod in exemplum adducimus) à recta D G, producta numeretur altitudo poli B A, <lb/>&amp; </s>
  <s xml:id="echoid-s38746" xml:space="preserve">verſus C, ſeu verſus partes inferiores, complementum eiuſdem altitudinis poli B C. </s>
  <s xml:id="echoid-s38747" xml:space="preserve">Quòd ſi <lb/>horologium ad ſeptentrionem ſpectet, ſumendus erit arcus altitudinis poli b A, deorſum verſus, <lb/>
<anchor type="note" xlink:label="note-0601-07a" xlink:href="note-0601-07"/>
&amp; </s>
  <s xml:id="echoid-s38748" xml:space="preserve">arcus complementi eiuſdem altitudinis poli B C, ſurſum verſus. </s>
  <s xml:id="echoid-s38749" xml:space="preserve">Ductis verò rectis D A, D C, <lb/>(quarum illa axem mundi, hæc verò communem ſectionem Aequatoris, &amp; </s>
  <s xml:id="echoid-s38750" xml:space="preserve">Meridiani refert) ſeca-<lb/>bitur meridiana linea in punctis H, &amp; </s>
  <s xml:id="echoid-s38751" xml:space="preserve">I, quorum H, centrum eſt horologii, at per I, ducenda eſt ad <lb/>
<anchor type="note" xlink:label="note-0601-08a" xlink:href="note-0601-08"/>
HI, perpendicularis F K, pro linea æquinoctiali. </s>
  <s xml:id="echoid-s38752" xml:space="preserve">Sumpta quoque recta I E, ipſi I D, æquali, <lb/>
<anchor type="note" xlink:label="note-0601-09a" xlink:href="note-0601-09"/>
deſcribatur ex E, circulus ad quodcunque interuallum, quo diuiſo in 24. </s>
  <s xml:id="echoid-s38753" xml:space="preserve">partes æquales, initio fa-<lb/>cto à linea meridiana H N, ducantur per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s38754" xml:space="preserve">centrum E, lineæ rectæ occultæ <lb/>ſecantes lineam æquinoctialem in punctis, per quæ, &amp; </s>
  <s xml:id="echoid-s38755" xml:space="preserve">punctum H, rectæ emiſſæ dabunt lineas ho <lb/>
<anchor type="note" xlink:label="note-0601-10a" xlink:href="note-0601-10"/>
rarum à mer. </s>
  <s xml:id="echoid-s38756" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s38757" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38758" xml:space="preserve">in plano, quod Verticali circulo æquidiſtat. </s>
  <s xml:id="echoid-s38759" xml:space="preserve">Pro hora vero 6. </s>
  <s xml:id="echoid-s38760" xml:space="preserve">ducen-<lb/>da eſt per H, linea perpendicularis ad H N, vel æquidiſtans rectæ F K.</s>
  <s xml:id="echoid-s38761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1924" type="float" level="2" n="1">
<note position="right" xlink:label="note-0601-03" xlink:href="note-0601-03a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Aſtrono <lb/>mi@i Verticalis.</note>
<note position="left" xlink:label="note-0601-04" xlink:href="note-0601-04a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0601-01" xlink:href="fig-0601-01a">
    <image file="0601-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0601-01"/>
  </figure>
<note position="left" xlink:label="note-0601-05" xlink:href="note-0601-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0601-06" xlink:href="note-0601-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0601-07" xlink:href="note-0601-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0601-08" xlink:href="note-0601-08a" xml:space="preserve">Cen@@um horo<unsure/> <lb/>logii.</note>
<note position="right" xlink:label="note-0601-09" xlink:href="note-0601-09a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="right" xlink:label="note-0601-10" xlink:href="note-0601-10a" xml:space="preserve">Lineæ hor@ri@@</note>
</div>
<p>
  <s xml:id="echoid-s38762" xml:space="preserve">INTERVALLA autem horarum in portione æquinoctialis lineæ I F, hic quoque, ſi erra-<lb/>tum non eſt, æqualia ſunt interuallis horarum in altera portione I K, ſingula ſingulis: </s>
  <s xml:id="echoid-s38763" xml:space="preserve">Item arcus
<pb o="586" file="0602" n="602" rhead="GNOMONICES"/>
circuli ex H, deſcripti inter meridianam lineam H N, &amp; </s>
  <s xml:id="echoid-s38764" xml:space="preserve">horas ex parte ſiniſtra poſiti æquales arcu-<lb/>bus eiuſdem circuli inter meridianam lineam, &amp; </s>
  <s xml:id="echoid-s38765" xml:space="preserve">horas ex parte dextra interiectis, ſinguli ſingu-<lb/>lis. </s>
  <s xml:id="echoid-s38766" xml:space="preserve">Quare, vt accurata ſit horarum deſcriptio, danda erit opera, vt huiuſmodi interualla inter ſe <lb/>ſint æqualia.</s>
  <s xml:id="echoid-s38767" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s38768" xml:space="preserve">COLLOCANDVM autem eſt horologium, ſi quidem in Auſtrum vergit. </s>
  <s xml:id="echoid-s38769" xml:space="preserve">ita vt <emph style="sc">H</emph> N, ad <lb/>ad Horizontem ſit perpendicularis, rectaq́ue F k, eidem <emph style="sc">H</emph>orizonti æquidiſtet, atque infra punctũ <lb/>
<anchor type="note" xlink:label="note-0602-01a" xlink:href="note-0602-01"/>
H, exiſtat; </s>
  <s xml:id="echoid-s38770" xml:space="preserve">ſi verò ad Boream ſpectat, ita collocandum eſt, vt N H, perpendicularis ſit ad Horizon-<lb/>tem, eidemq́ue Horizonti æquidiſtet recta F K, &amp; </s>
  <s xml:id="echoid-s38771" xml:space="preserve">ſupra punctum H, exiſtat. </s>
  <s xml:id="echoid-s38772" xml:space="preserve">Itaque in Horolo-<lb/>gio auſtrali punctum F, nobis erit ad ſiniſtram, ſi faciem ad horologium conuertamus, &amp; </s>
  <s xml:id="echoid-s38773" xml:space="preserve">in occi-<lb/>
<anchor type="note" xlink:label="note-0602-02a" xlink:href="note-0602-02"/>
dentem verget, &amp; </s>
  <s xml:id="echoid-s38774" xml:space="preserve">punctum K, ad dexteram ſitum erit, orientemq́ue Solem reſpiciet. </s>
  <s xml:id="echoid-s38775" xml:space="preserve">Ex quo fit, <lb/>
<anchor type="note" xlink:label="note-0602-03a" xlink:href="note-0602-03"/>
horas ad ſiniſtram lineæ meridianæ poſitas eſſe antemeridianas, quæ verò ad dextram eiuſdem <lb/>ſunt collocatæ, pomeridianas. </s>
  <s xml:id="echoid-s38776" xml:space="preserve">Portio autem ipſius lineæ meridianæ à centro <emph style="sc">H</emph>, verſus æquino-<lb/>ctialem lineam producta oſtendet horam 12. </s>
  <s xml:id="echoid-s38777" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s38778" xml:space="preserve">reliqua portio ab eodem centro inci-<lb/>piens horam 12. </s>
  <s xml:id="echoid-s38779" xml:space="preserve">mediæ noctis: </s>
  <s xml:id="echoid-s38780" xml:space="preserve">Ita vt hora proxima horę 12. </s>
  <s xml:id="echoid-s38781" xml:space="preserve">meridiei ad dexteram ſit hora 1. <lb/></s>
  <s xml:id="echoid-s38782" xml:space="preserve">poſt meridiem, &amp; </s>
  <s xml:id="echoid-s38783" xml:space="preserve">ſequens 2. </s>
  <s xml:id="echoid-s38784" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38785" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38786" xml:space="preserve">Item hora proxima horę 12. </s>
  <s xml:id="echoid-s38787" xml:space="preserve">mediæ noctis ad ſiniſtram ſit hora <lb/>1. </s>
  <s xml:id="echoid-s38788" xml:space="preserve">poſt mediam noctem, &amp; </s>
  <s xml:id="echoid-s38789" xml:space="preserve">ſequens 2. </s>
  <s xml:id="echoid-s38790" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38791" xml:space="preserve">ita deinceps. </s>
  <s xml:id="echoid-s38792" xml:space="preserve">In horologio autem Boreali erit punctum <lb/>F, nobis ad dextram, reſpicietq́ue occidentem, &amp; </s>
  <s xml:id="echoid-s38793" xml:space="preserve">k, erit ad ſiniſtram, ſpectabitq́ue ad orientem: </s>
  <s xml:id="echoid-s38794" xml:space="preserve">ita <lb/>vt horæ ad dexteram lineę meridianæ ſint antemeridianæ, ad ſiniſtram verò pomeridianæ. </s>
  <s xml:id="echoid-s38795" xml:space="preserve">Portio <lb/>autem ipſius lineæ meridianæ à centro H, verſus lineam æquinoctialem educta ſignificabit ho-<lb/>ram 12. </s>
  <s xml:id="echoid-s38796" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s38797" xml:space="preserve">portio reliqua ab eodem centro H, inchoata horam 12. </s>
  <s xml:id="echoid-s38798" xml:space="preserve">meridiei: </s>
  <s xml:id="echoid-s38799" xml:space="preserve">Ita vt <lb/>
<anchor type="note" xlink:label="note-0602-04a" xlink:href="note-0602-04"/>
hora proxima horæ 12. </s>
  <s xml:id="echoid-s38800" xml:space="preserve">mediæ noctis ad dexteram ſit hora 1. </s>
  <s xml:id="echoid-s38801" xml:space="preserve">poſt mediam noctem, ſequens 2. </s>
  <s xml:id="echoid-s38802" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38803" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s38804" xml:space="preserve">Item hora proxima horæ 12. </s>
  <s xml:id="echoid-s38805" xml:space="preserve">meridiei ad ſiniſtram ſit hora 1. </s>
  <s xml:id="echoid-s38806" xml:space="preserve">poſt meridiem, ſequens 2. </s>
  <s xml:id="echoid-s38807" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38808" xml:space="preserve">ſic de <lb/>cæteris, vt ex ipſa figura apparet. </s>
  <s xml:id="echoid-s38809" xml:space="preserve">Hinc fit ſingulas horas in Boreali horologio eſſe complementa <lb/>12. </s>
  <s xml:id="echoid-s38810" xml:space="preserve">horatum, ſi cum horis horologii auſtralis conſerantur.</s>
  <s xml:id="echoid-s38811" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1925" type="float" level="2" n="2">
<note position="left" xlink:label="note-0602-01" xlink:href="note-0602-01a" xml:space="preserve">Quomodo vtrũ <lb/>que horologiu <lb/>Verticale collo <lb/>candum ſit, vt <lb/>horas indicet.</note>
<note position="left" xlink:label="note-0602-02" xlink:href="note-0602-02a" xml:space="preserve">Horę antemeri-<lb/>dianæ quo pa-<lb/>cto à pomeridia <lb/>nis diſcernan-<lb/>tur.</note>
<note position="left" xlink:label="note-0602-03" xlink:href="note-0602-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0602-04" xlink:href="note-0602-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s38812" xml:space="preserve">STYLVS denique D G, erigendus eſt ſupra planum horologii ad angulos rectos in puncto <lb/>
<anchor type="note" xlink:label="note-0602-05a" xlink:href="note-0602-05"/>
G. </s>
  <s xml:id="echoid-s38813" xml:space="preserve">Velloco gnomonis ſtatuendum eſt triangulum D H I, ſupra rectam H I, ad angulos rectos ipſi <lb/>plano horologii. </s>
  <s xml:id="echoid-s38814" xml:space="preserve">Nã axis D H, horas ſua vmbra indicabit, vt de horologio horizontali dictũ eſt.</s>
  <s xml:id="echoid-s38815" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1926" type="float" level="2" n="3">
<note position="left" xlink:label="note-0602-05" xlink:href="note-0602-05a" xml:space="preserve">Stylus quc pa-<lb/>cto ſit coll@@an-<lb/>d<unsure/>us.</note>
</div>
</div>
<div xml:id="echoid-div1928" type="section" level="1" n="493">
<head xml:id="echoid-head522" style="it" xml:space="preserve">DE ARCVBVS SIGNORVM IN HOROLOGIO <lb/>Verticali. CAP. VII.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s38816" xml:space="preserve">VT arcus ſignorum deſcribantur, præpatanda erit figura radiorum Zodiaci, vna cum ho-<lb/>ratiis lineis, hunc in modum. </s>
  <s xml:id="echoid-s38817" xml:space="preserve">Ducatur in tranſuerſum linea vtcunque A <emph style="sc">H</emph>, axem mundi re-<lb/>
<anchor type="note" xlink:label="note-0602-07a" xlink:href="note-0602-07"/>
ferens, ad quam perpendicularis ducatur D C, pro radio æquinoctiali. </s>
  <s xml:id="echoid-s38818" xml:space="preserve">Deinde hinc inde aliorum <lb/>
<anchor type="figure" xlink:label="fig-0602-01a" xlink:href="fig-0602-01"/>
ſignorum radii ducã-<lb/>tur, vt in cap. </s>
  <s xml:id="echoid-s38819" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38820" xml:space="preserve">præ-<lb/>cepimus. </s>
  <s xml:id="echoid-s38821" xml:space="preserve">Poſt hæc <lb/>ex triangulo D <emph style="sc">H</emph> I, <lb/>
<anchor type="note" xlink:label="note-0602-08a" xlink:href="note-0602-08"/>
figuræ capitis præce-<lb/>dentis transferatur in <lb/>
<anchor type="note" xlink:label="note-0602-09a" xlink:href="note-0602-09"/>
axem AH, figurę pro-<lb/>xime cõſtructæ ex D, <lb/>dextram verſus recta <lb/>D H, &amp; </s>
  <s xml:id="echoid-s38822" xml:space="preserve">in radiũ Ae-<lb/>quatoris deorſum ver <lb/>ſus recta D I; </s>
  <s xml:id="echoid-s38823" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38824" xml:space="preserve">ex H, <lb/>per I, educatur recta <lb/>H I, quantũlibet, pro <lb/>hora 12. </s>
  <s xml:id="echoid-s38825" xml:space="preserve">quam fortaſ-<lb/>ſe commodius ita du <lb/>
<anchor type="note" xlink:label="note-0602-10a" xlink:href="note-0602-10"/>
cemus. </s>
  <s xml:id="echoid-s38826" xml:space="preserve">Ex H, arcus <lb/>circuli A B, verſus D, <lb/>ad quoduis interual-<lb/>lum deſcribatur, ex <lb/>quo abſcindatur ar-<lb/>cus A B, complemen <lb/>to altitudinis poliæ-<lb/>qualis. </s>
  <s xml:id="echoid-s38827" xml:space="preserve">Nam recta <lb/>H B, ducta erit linea horæ 12. </s>
  <s xml:id="echoid-s38828" xml:space="preserve">tranſibitq́ue per I. </s>
  <s xml:id="echoid-s38829" xml:space="preserve">Quod ſi ex centro E, illius circuli, beneſi-<lb/>cio cuius in capite antecedenti puncta horarum in linea æquinoctiali inuenimus, accipiantur <lb/>interualla vſque ad puncta, vbi linea æquinoctialis F K, à lineis horariis ſecatur, &amp; </s>
  <s xml:id="echoid-s38830" xml:space="preserve">ex pun-
<pb o="587" file="0603" n="603" rhead="LIBER SEPTIMVS."/>
cto D, ſiguræ proximè conſtructę transſerantur in radium Aequatoris D C, imprimendo pun-<lb/>cta in ipſo radio Aequatoris, atque ex H, per hęc puncta rectæ lineæ emittantur, habebimus <lb/>lineas aliarum horarum ante, &amp; </s>
  <s xml:id="echoid-s38831" xml:space="preserve">poſt 12. </s>
  <s xml:id="echoid-s38832" xml:space="preserve">horam: </s>
  <s xml:id="echoid-s38833" xml:space="preserve">ſi tamen pro hora 6. </s>
  <s xml:id="echoid-s38834" xml:space="preserve">ex H, ducatur H V, <lb/>parallela radio Aequatoris D C, &amp; </s>
  <s xml:id="echoid-s38835" xml:space="preserve">aliæ lineæ ad dexteram parallelæ H V, ſi opus fuerit, traducan <lb/>tur, vt cap. </s>
  <s xml:id="echoid-s38836" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38837" xml:space="preserve">ſcripſimus, cum de horizontali horologio agermus. </s>
  <s xml:id="echoid-s38838" xml:space="preserve">Has etiam horarias lineas ob-<lb/>
<anchor type="note" xlink:label="note-0603-01a" xlink:href="note-0603-01"/>
tinebimus, ſi ex horologio præcedentis capitis interualla horaria inter centrum H, &amp; </s>
  <s xml:id="echoid-s38839" xml:space="preserve">lineam ęqui <lb/>noctialem F k, poſita transferamus ex H, ſiguræ nuper præparatæ in radium Aequatoris D C, im <lb/>primendo puncta in ipſo radio Aequatoris, &amp; </s>
  <s xml:id="echoid-s38840" xml:space="preserve">per hęc rectas ex H, educamus, &amp;</s>
  <s xml:id="echoid-s38841" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38842" xml:space="preserve">Vel certè, ſi in <lb/>
<anchor type="note" xlink:label="note-0603-02a" xlink:href="note-0603-02"/>
linea H I, producta ſumamus punctum φ, vtcunque, &amp; </s>
  <s xml:id="echoid-s38843" xml:space="preserve">per hoc lineam φ V, ipſi A H, parallelam <lb/>agamus, atque reliqua perficiamus, vt in horologio horizontali dictum eſt. </s>
  <s xml:id="echoid-s38844" xml:space="preserve">Id quod figura ipſa <lb/>
<anchor type="note" xlink:label="note-0603-03a" xlink:href="note-0603-03"/>
ſatis indicat. </s>
  <s xml:id="echoid-s38845" xml:space="preserve">Cognoſcemus autem ex hac figura, quorumnam ſignorum arcus ſint Hyperbolæ, &amp; </s>
  <s xml:id="echoid-s38846" xml:space="preserve"><lb/>quorum Parabolæ, vel Ellipſes, quemadmodum in horizontali horologio, vt cap. </s>
  <s xml:id="echoid-s38847" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38848" xml:space="preserve">tradidimus.</s>
  <s xml:id="echoid-s38849" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1928" type="float" level="2" n="1">
<note position="left" xlink:label="note-0602-07" xlink:href="note-0602-07a" xml:space="preserve">Conſtructio fi-<lb/>guræ radiorum <lb/>Zodiaci, ex qua <lb/>arous ſignorum <lb/>in Ver@@@cali ho <lb/>rologio deſcti-<lb/>@an@@t.</note>
  <figure xlink:label="fig-0602-01" xlink:href="fig-0602-01a">
    <image file="0602-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0602-01"/>
  </figure>
<note position="left" xlink:label="note-0602-08" xlink:href="note-0602-08a" xml:space="preserve">Qua ratione li-<lb/>neæ horatiæ in <lb/>ſiguta radi@rũ <lb/>Zodiaci duca@-<lb/>@ur.</note>
<note position="left" xlink:label="note-0602-09" xlink:href="note-0602-09a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0602-10" xlink:href="note-0602-10a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0603-01" xlink:href="note-0603-01a" xml:space="preserve">Alia deſcriptio<unsure/> <lb/>linearum hora-<lb/>riatum in figu-<lb/>ra radiorum Zo <lb/>diaci.</note>
<note position="right" xlink:label="note-0603-02" xlink:href="note-0603-02a" xml:space="preserve">Alia adhuc de-<lb/>ſcriptio linearũ <lb/>horariarum in <lb/>fi gura radiorũ <lb/>Zodiaci pulcher <lb/>rima.</note>
<note position="left" xlink:label="note-0603-03" xlink:href="note-0603-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s38850" xml:space="preserve">EX hac ergo ſigura radiorum Zodiaci non ſecus, ac in horologio horizontali, arcus ſignorũ <lb/>
<anchor type="note" xlink:label="note-0603-04a" xlink:href="note-0603-04"/>
deſcribemus, transferendo ſci-<lb/>
<anchor type="figure" xlink:label="fig-0603-01a" xlink:href="fig-0603-01"/>
licet interualla horarum huius <lb/>ſiguræ intercepta inter H, &amp; </s>
  <s xml:id="echoid-s38851" xml:space="preserve"><lb/>radios ſignorum in horas horo <lb/>
<anchor type="note" xlink:label="note-0603-05a" xlink:href="note-0603-05"/>
logii reſpondentes ex centro <lb/>H, &amp;</s>
  <s xml:id="echoid-s38852" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38853" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1929" type="float" level="2" n="2">
<note position="right" xlink:label="note-0603-04" xlink:href="note-0603-04a" xml:space="preserve">Qui arcus ſigno <lb/>rum in horolo-<lb/>gio deſcribendi <lb/>hyperbolæ ſint, <lb/>aut parabolæ, <lb/>aut ellipſes.</note>
  <figure xlink:label="fig-0603-01" xlink:href="fig-0603-01a">
    <image file="0603-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0603-01"/>
  </figure>
<note position="right" xlink:label="note-0603-05" xlink:href="note-0603-05a" xml:space="preserve">Deſ@riptio at-<lb/>cuum ſignorũ <lb/>in horologio <lb/>Vert@@cali.</note>
</div>
<note position="right" xml:space="preserve">Horizontalis li <lb/>nea.</note>
<p>
  <s xml:id="echoid-s38854" xml:space="preserve">QVONIAM verò Sole <lb/>
<anchor type="note" xlink:label="note-0603-07a" xlink:href="note-0603-07"/>
exiſtente in Horizonte, cum vi-<lb/>delicet oritur, occiditve, vm-<lb/>bra ſtyli proiicitur in commu-<lb/>nem ſectionem Horizontis, ac <lb/>plani horologii, vt propoſ. </s>
  <s xml:id="echoid-s38855" xml:space="preserve">11. <lb/></s>
  <s xml:id="echoid-s38856" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38857" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38858" xml:space="preserve">oſtendimus, quæ quidem <lb/>linea horizontalis ſolet appella-<lb/>ri; </s>
  <s xml:id="echoid-s38859" xml:space="preserve">ſi per G, locum ſtyli duca-<lb/>mus æquinoctiali lineæ F k, pa <lb/>rallelam, vel perpendicularem <lb/>
<anchor type="note" xlink:label="note-0603-08a" xlink:href="note-0603-08"/>
ad lineam meridianam, erit <lb/>hæc ipſa horizontalis linea.</s>
  <s xml:id="echoid-s38860" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1930" type="float" level="2" n="3">
<note position="left" xlink:label="note-0603-07" xlink:href="note-0603-07a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0603-08" xlink:href="note-0603-08a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Hora ortus, &amp; <lb/>occaſus Solis <lb/>quo pacto ex li-<lb/>nea horizonta-<lb/>li cognoſcatur.</note>
<p>
  <s xml:id="echoid-s38861" xml:space="preserve">PVLCHRE autem linea <lb/>horizontalis demonſtrat, qua-<lb/>nam hora Sol in quolibet paral <lb/>lelo exiſtens oriatur, vel occi-<lb/>dat. </s>
  <s xml:id="echoid-s38862" xml:space="preserve">Nam vbi arcus ſignorum <lb/>lineam horizontalem interſe-<lb/>cant, ibi Sol oritur, &amp; </s>
  <s xml:id="echoid-s38863" xml:space="preserve">occidit, <lb/>cum in illis ſignis exiſtit, quę <lb/>
<anchor type="note" xlink:label="note-0603-10a" xlink:href="note-0603-10"/>
per dictos arcus repreſentãtur. <lb/></s>
  <s xml:id="echoid-s38864" xml:space="preserve">Si igitur per illa puncta, vbi ſe <lb/>mutuo ſecant linea horizonta-<lb/>lis, &amp; </s>
  <s xml:id="echoid-s38865" xml:space="preserve">arcus ſignorum, ducan-<lb/>tur lineæ horariæ, indicabunt <lb/>hæ tempus ortus Solis, &amp; </s>
  <s xml:id="echoid-s38866" xml:space="preserve">occaſus. </s>
  <s xml:id="echoid-s38867" xml:space="preserve">Ita vides, Solem exiſtentem in principio ♑, oriri cirea <lb/>horam 7 {1/2}. </s>
  <s xml:id="echoid-s38868" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38869" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38870" xml:space="preserve">occidere autem fermè hora 4 {1/2}. </s>
  <s xml:id="echoid-s38871" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38872" xml:space="preserve">In ♒, verò &amp; </s>
  <s xml:id="echoid-s38873" xml:space="preserve">♐, oriri paulo an-<lb/>te horam 7 {1/2}. </s>
  <s xml:id="echoid-s38874" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38875" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38876" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38877" xml:space="preserve">occidere paulo poſt horam 4 {1/2}. </s>
  <s xml:id="echoid-s38878" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38879" xml:space="preserve">In ♓, denique &amp; </s>
  <s xml:id="echoid-s38880" xml:space="preserve">♏, oriri an <lb/>te horam 7. </s>
  <s xml:id="echoid-s38881" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38882" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38883" xml:space="preserve">occidere verò poſt horam 5. </s>
  <s xml:id="echoid-s38884" xml:space="preserve">à mer.</s>
  <s xml:id="echoid-s38885" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1931" type="float" level="2" n="4">
<note position="left" xlink:label="note-0603-10" xlink:href="note-0603-10a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s38886" xml:space="preserve">EADEM hæc linea horizontalis totum horologium diſtinguit in duo, quorum maius, in <lb/>
<anchor type="note" xlink:label="note-0603-11a" xlink:href="note-0603-11"/>
<anchor type="note" xlink:label="note-0603-12a" xlink:href="note-0603-12"/>
quo linea æquinoctialis comprehenditur, auſtrale, alterum verò boreale dicitur. </s>
  <s xml:id="echoid-s38887" xml:space="preserve">Vtrumque autẽ <lb/>ita collocandum eſt, vt linea horizontalis æquidiſtet Horizonti, atque ſuperiorem occupet lo-<lb/>cum: </s>
  <s xml:id="echoid-s38888" xml:space="preserve">In boreali tamen mutantur numeri horarum in complementa earum vſque ad 12. </s>
  <s xml:id="echoid-s38889" xml:space="preserve">vt ſupra <lb/>diximus; </s>
  <s xml:id="echoid-s38890" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38891" xml:space="preserve">arcus ſignorum auſtralium vertuntur in arcus ſignorum borealium oppoſitorum. </s>
  <s xml:id="echoid-s38892" xml:space="preserve">Vt <lb/>ex arcu ♑, fit arcus ♋, &amp; </s>
  <s xml:id="echoid-s38893" xml:space="preserve">ex arcu ♒, &amp; </s>
  <s xml:id="echoid-s38894" xml:space="preserve">♐, fit arcus ♌, &amp; </s>
  <s xml:id="echoid-s38895" xml:space="preserve">♊, &amp; </s>
  <s xml:id="echoid-s38896" xml:space="preserve">ex arcu ♓, &amp; </s>
  <s xml:id="echoid-s38897" xml:space="preserve">♏, fit arcus ♍, &amp; </s>
  <s xml:id="echoid-s38898" xml:space="preserve"><lb/>♉, &amp;</s>
  <s xml:id="echoid-s38899" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38900" xml:space="preserve">Vbi etiam indicat linea horizontalis, qua hora Sol oriatur, &amp; </s>
  <s xml:id="echoid-s38901" xml:space="preserve">occidat. </s>
  <s xml:id="echoid-s38902" xml:space="preserve">Nam ortus Solis <lb/>in principio ♋, exiſtentis eſt paulo ante horam 4 {1/2}. </s>
  <s xml:id="echoid-s38903" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s38904" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s38905" xml:space="preserve">occaſus verò paulo poſt horã 7 {1/2}. <lb/></s>
  <s xml:id="echoid-s38906" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s38907" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38908" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38909" xml:space="preserve">Idem officium habet linea horizontalis in omnibus aliis horologiis, excepto horizon <lb/>
<anchor type="note" xlink:label="note-0603-13a" xlink:href="note-0603-13"/>
tali, in quo linea horizontalis duci non poteſt, vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s38910" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38911" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s38912" xml:space="preserve">1. </s>
  <s xml:id="echoid-s38913" xml:space="preserve">demonſtrauimus.</s>
  <s xml:id="echoid-s38914" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1932" type="float" level="2" n="5">
<note position="left" xlink:label="note-0603-11" xlink:href="note-0603-11a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0603-12" xlink:href="note-0603-12a" xml:space="preserve">Linea horizon-<lb/>talis totum ho-<lb/>rologium ſecat <lb/>in Auſtiale, a@ <lb/>Boreale.</note>
<note position="right" xlink:label="note-0603-13" xlink:href="note-0603-13a" xml:space="preserve">Horizontalis @-<lb/>nea diuidit to <lb/>tũ horologiũ in <lb/>D@urnũ, &amp; No <lb/>cturnum.</note>
</div>
<p>
  <s xml:id="echoid-s38915" xml:space="preserve">RVRSVS linea horizontalis partitur totum horologium in eaſdem duas partes, quarum <lb/>ea, quæ inſra ipſam eſt, interdiu horas demonſtrat, ideoq́ue horologium diurnum appellari po-
<pb o="588" file="0604" n="604" rhead="GNOMONICES"/>
teſt: </s>
  <s xml:id="echoid-s38916" xml:space="preserve">altera verò pars noctu horas oſtenderet, ſi radii Solis terram penetrare poſſent, ita vt planum <lb/>horologii illuſtrarent: </s>
  <s xml:id="echoid-s38917" xml:space="preserve">qua de cauſa horologium nocturnum dicere poſſumus. </s>
  <s xml:id="echoid-s38918" xml:space="preserve">Vnde portiones <lb/>arcuum ſignorum in diurno horologio arcus diurni, portio verò eorundem in horologio noctur <lb/>no nocturni non incongrue nominari poſſunt: </s>
  <s xml:id="echoid-s38919" xml:space="preserve">Sed hoc modo numeri horarum in horologio <lb/>nocturno mutari non debent in complementa earum vſque ad 12. </s>
  <s xml:id="echoid-s38920" xml:space="preserve">veluti antea factum eſt in bo-<lb/>reali horologio. </s>
  <s xml:id="echoid-s38921" xml:space="preserve">Idem in ſequentibus intelligendum eſt. </s>
  <s xml:id="echoid-s38922" xml:space="preserve">Nocturnum porro horologiũ, tanquam <lb/>ſuperuacaneum, reſcindendum erit, cum interdiu à Sole non illuminetur.</s>
  <s xml:id="echoid-s38923" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s38924" xml:space="preserve">QVOD ſi maius, aut minus horologium ex lineamentis hactenus ductis deſcribendum ſit, <lb/>
<anchor type="note" xlink:label="note-0604-01a" xlink:href="note-0604-01"/>
pro maiore, aut minore ſtylo propoſito, efficiemus id non aliter, atque in horizontali horologio <lb/>tradidimus cap. </s>
  <s xml:id="echoid-s38925" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38926" xml:space="preserve">deſcribendo videlicet triangulum D H I, horologii pręcedentis cap. </s>
  <s xml:id="echoid-s38927" xml:space="preserve">ſeorſum, <lb/>
<anchor type="note" xlink:label="note-0604-02a" xlink:href="note-0604-02"/>
vnà cum ſtylo D G, &amp; </s>
  <s xml:id="echoid-s38928" xml:space="preserve">ſumendo in ſtylo D G, producto rectam D K, æqualem dato gnomoni, &amp; </s>
  <s xml:id="echoid-s38929" xml:space="preserve"><lb/>per K, ipſi H I, agendo parallelam, vel perpendicularem ad D G, quæ rectas D <emph style="sc">H</emph>, D I, productas <lb/>ſecet in L, &amp; </s>
  <s xml:id="echoid-s38930" xml:space="preserve">M. </s>
  <s xml:id="echoid-s38931" xml:space="preserve">Si enim axis D L, transſeratur ex puncto H, figuræ radiorum Zodiaci vſque ad <lb/>D, punctum, ex quo radii ſignorum educantur, &amp; </s>
  <s xml:id="echoid-s38932" xml:space="preserve">reliqua ſiant, vt prius, deſcribentur arcus ſigno <lb/>rum, pro ratione dati ſtyli D k, &amp;</s>
  <s xml:id="echoid-s38933" xml:space="preserve">c.</s>
  <s xml:id="echoid-s38934" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1933" type="float" level="2" n="6">
<note position="left" xlink:label="note-0604-01" xlink:href="note-0604-01a" xml:space="preserve">Qua ratione ad <lb/>maiorem, mino <lb/>remve ſtylum <lb/>maius, aut mi-<lb/>nus horologiũ <lb/>deſcribatur ex <lb/>ſigura radiorũ <lb/>Zodiaci.</note>
<note position="left" xlink:label="note-0604-02" xlink:href="note-0604-02a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1935" type="section" level="1" n="494">
<head xml:id="echoid-head523" style="it" xml:space="preserve">DE ARCVBVS LONGITVDINVM DIERVM <lb/>in eodem Verticali horologio. CAP. VIII.</head>
<p>
  <s xml:id="echoid-s38935" xml:space="preserve">HOS arcus eodem modo deſcribemus, quo arcus ſignorum deſcripti ſunt, dummodo loco <lb/>
<anchor type="note" xlink:label="note-0604-03a" xlink:href="note-0604-03"/>
<anchor type="note" xlink:label="note-0604-04a" xlink:href="note-0604-04"/>
radiorum ſignorum accipiamus radios longitudinũ dierum, quos in cap. </s>
  <s xml:id="echoid-s38936" xml:space="preserve">3. </s>
  <s xml:id="echoid-s38937" xml:space="preserve">delineauimus; <lb/></s>
  <s xml:id="echoid-s38938" xml:space="preserve">ex quibus in figuram radiorum Zodiaci præcedentis cap. </s>
  <s xml:id="echoid-s38939" xml:space="preserve">translati ſunt radii longitudinum die-<lb/>rum horarum 14. </s>
  <s xml:id="echoid-s38940" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38941" xml:space="preserve">10. </s>
  <s xml:id="echoid-s38942" xml:space="preserve">Item horarum 18. </s>
  <s xml:id="echoid-s38943" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38944" xml:space="preserve">6. </s>
  <s xml:id="echoid-s38945" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38946" xml:space="preserve">horarum 24. </s>
  <s xml:id="echoid-s38947" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s38948" xml:space="preserve">0. </s>
  <s xml:id="echoid-s38949" xml:space="preserve">obſeruandum tamen eſt, in <lb/>horologio boreali, &amp; </s>
  <s xml:id="echoid-s38950" xml:space="preserve">nocturno, hoſce arcus commutari in complementa vſque ad 24. </s>
  <s xml:id="echoid-s38951" xml:space="preserve">hoc eſt, ar-<lb/>cum horarum 10. </s>
  <s xml:id="echoid-s38952" xml:space="preserve">mutari in arcum horarum 14 &amp; </s>
  <s xml:id="echoid-s38953" xml:space="preserve">arcum horarum 6. </s>
  <s xml:id="echoid-s38954" xml:space="preserve">in arcum horarum 18. </s>
  <s xml:id="echoid-s38955" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38956" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38957" xml:space="preserve"><lb/>Non difficile etiam erit iudicare, quinam arcus diurni ſint hyperbolę, &amp; </s>
  <s xml:id="echoid-s38958" xml:space="preserve">qui parabolæ, vel Elli-<lb/>pſes, ſi loco radiorum ſignorum oppoſitorum accipiantur radii diurni oppoſiti ex D, educti, hoc <lb/>eſt, æqualiter à radio Aequatoris diſtantes, quemadmodum in cap. </s>
  <s xml:id="echoid-s38959" xml:space="preserve">2. </s>
  <s xml:id="echoid-s38960" xml:space="preserve">expoſuimus.</s>
  <s xml:id="echoid-s38961" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1935" type="float" level="2" n="1">
<note position="left" xlink:label="note-0604-03" xlink:href="note-0604-03a" xml:space="preserve">Deſcriptio ar-<lb/>cuum diurnorũ <lb/>in horol ogie <lb/>Vertieali.</note>
<note position="left" xlink:label="note-0604-04" xlink:href="note-0604-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1937" type="section" level="1" n="495">
<head xml:id="echoid-head524" style="it" xml:space="preserve">DE HOROLOGIO VERTIC ALI IT ALICO, <lb/>&amp; Babylonico. CAP. IX</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s38962" xml:space="preserve">DESCRIBETVR vtrumque hoc horologium non ſecus ac horizontale, vt in cap. </s>
  <s xml:id="echoid-s38963" xml:space="preserve">4. </s>
  <s xml:id="echoid-s38964" xml:space="preserve">do-<lb/>
<anchor type="note" xlink:label="note-0604-06a" xlink:href="note-0604-06"/>
cuimus. </s>
  <s xml:id="echoid-s38965" xml:space="preserve">Nam ſi primo modo inſtituenda ſit deſcriptio, ſumendus erit pro horologio auſtra-<lb/>li arcus diurnus paralleli ♋, in circulo ex E, deſcripto a N b, arcus autem diurnus paralleli ♑, <lb/>d N e, diuiſioq́ue circuli inchoanda à punctis b, &amp; </s>
  <s xml:id="echoid-s38966" xml:space="preserve">e, occidentalibus, ſi horologium Italicum de-<lb/>ſcribendum fuerit, vel ſi Babylonicum proponatur delineandum, à punctis a, &amp; </s>
  <s xml:id="echoid-s38967" xml:space="preserve">d, orientalibus, <lb/>verſus N, procedendo. </s>
  <s xml:id="echoid-s38968" xml:space="preserve">Aſſumendus autem erit etiam arcus nocturnus ♑, in horologio ſupra li-<lb/>neam horizontalem, vt in eo reperiantur puncta horarum 15. </s>
  <s xml:id="echoid-s38969" xml:space="preserve">14. </s>
  <s xml:id="echoid-s38970" xml:space="preserve">13. </s>
  <s xml:id="echoid-s38971" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38972" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38973" xml:space="preserve">ab occaſu, &amp; </s>
  <s xml:id="echoid-s38974" xml:space="preserve">9. </s>
  <s xml:id="echoid-s38975" xml:space="preserve">10. <lb/></s>
  <s xml:id="echoid-s38976" xml:space="preserve">11. </s>
  <s xml:id="echoid-s38977" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s38978" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38979" xml:space="preserve">ab ortu, quæ in arcu nocturno ♑, in circulo ex E, deſcripto continentur. </s>
  <s xml:id="echoid-s38980" xml:space="preserve">Pro horologio <lb/>
<anchor type="note" xlink:label="note-0604-07a" xlink:href="note-0604-07"/>
autem boreali arcus diurnus tropici ♋, in circulo M a N b, erit d M e, tropici verò ♑, a M b; </s>
  <s xml:id="echoid-s38981" xml:space="preserve">atque <lb/>diuiſio circuli à punctis e, b, d, a, initium habebit, &amp; </s>
  <s xml:id="echoid-s38982" xml:space="preserve">verſus M, progredietur. </s>
  <s xml:id="echoid-s38983" xml:space="preserve">Tropicus quoque <lb/>♋, in horologio boreali eſt ille, qui inter centrum horologii H, &amp; </s>
  <s xml:id="echoid-s38984" xml:space="preserve">lineam æquinoctialem compre-<lb/>henditur, fungiturq́ue munere tropici ♋, in auſtrali horologio. </s>
  <s xml:id="echoid-s38985" xml:space="preserve">Sed aſferamus vnum, aut alte-<lb/>rum exemplum. </s>
  <s xml:id="echoid-s38986" xml:space="preserve">Ex f, puncto horæ 14. </s>
  <s xml:id="echoid-s38987" xml:space="preserve">ab occaſu in tropico ♋, ducta recta per E, centrum ſecat <lb/>æquinoctialem lineam in puncto quodam, per quod recta ex centro H, ducta ſecabit tropicum <lb/>♋, in auſtrali horologio in puncto h, per quod hora 14. </s>
  <s xml:id="echoid-s38988" xml:space="preserve">ducenda eſt, Sic etiam ſi ex hora 14. </s>
  <s xml:id="echoid-s38989" xml:space="preserve">tro-<lb/>pici ♑, quæ in arcu nocturno ♑, d M e, reperitur, per E, recta ducatur, &amp;</s>
  <s xml:id="echoid-s38990" xml:space="preserve">c. </s>
  <s xml:id="echoid-s38991" xml:space="preserve">inuenietur in arcu no-<lb/>cturno ♑, punctum eiuſdem horæ 14. </s>
  <s xml:id="echoid-s38992" xml:space="preserve">ab occaſu, quod cum puncto h, coniunctum dabit horam <lb/>14. </s>
  <s xml:id="echoid-s38993" xml:space="preserve">Rurſus recta ex m, puncto horæ 1. </s>
  <s xml:id="echoid-s38994" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s38995" xml:space="preserve">quæ horæ 13. </s>
  <s xml:id="echoid-s38996" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s38997" xml:space="preserve">opponitur, ducta per E, <lb/>
<anchor type="note" xlink:label="note-0604-08a" xlink:href="note-0604-08"/>
occurrit lineæ æquinoctiali in n. </s>
  <s xml:id="echoid-s38998" xml:space="preserve">Et quia recta m E, tranſit per centrum E, antequam æquinoctia-<lb/>li lineæ occurrat, idcirco recta H n, dabit in tropico ♑, punctum q, pro hora 1. </s>
  <s xml:id="echoid-s38999" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39000" xml:space="preserve">producta <lb/>verò vltra H, offeret in eodem tropico punctum p, pro hora 13. </s>
  <s xml:id="echoid-s39001" xml:space="preserve">vt in cap. </s>
  <s xml:id="echoid-s39002" xml:space="preserve">4. </s>
  <s xml:id="echoid-s39003" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s39004" xml:space="preserve">Eadem <lb/>ratione puncta aliarum horarum &amp; </s>
  <s xml:id="echoid-s39005" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39006" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39007" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39008" xml:space="preserve">reperientur in vtroque tropico. </s>
  <s xml:id="echoid-s39009" xml:space="preserve">In horologio <lb/>boreali exemplum nullum ponimus, ne multitudo linearum confuſionem pariat: </s>
  <s xml:id="echoid-s39010" xml:space="preserve">præſertim quia <lb/>ex auſtrali horologio deſcripto facili negotio boreale elicitur hoc modo. </s>
  <s xml:id="echoid-s39011" xml:space="preserve">Producantur omnes li-<lb/>neæ horarum ab or. </s>
  <s xml:id="echoid-s39012" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39013" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39014" xml:space="preserve">vltra lineam horizontalem, aſcriptis eiſdem numeris, qui in horolo-<lb/>
<anchor type="note" xlink:label="note-0604-09a" xlink:href="note-0604-09"/>
gio auſtrali ſcripti ſunt. </s>
  <s xml:id="echoid-s39015" xml:space="preserve">Nam portio horologii à linea horizontali abſciſſa erit horologium bo-<lb/>reale, ſi omnes eius partes ita permutentur, vt ſuperior vertatur in inferiorem, hoc eſt, linea ho-<lb/>rizontalis occupet ſuperiorem locum, &amp; </s>
  <s xml:id="echoid-s39016" xml:space="preserve">pars, quæ in eo ſitu nobis ad horologium conuerſis dex-<lb/>tra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s39017" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s39018" xml:space="preserve">Sed quæ lineæ productæ ad horas ab or. </s>
  <s xml:id="echoid-s39019" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39020" xml:space="preserve">quæ ad horas ab occ.</s>
  <s xml:id="echoid-s39021" xml:space="preserve">
<pb o="589" file="0605" n="605" rhead="LIBER SEPTIMVS."/>
pertineant, ita percipietur. </s>
  <s xml:id="echoid-s39022" xml:space="preserve">Conſiderentur in portione horologii auſtralis nocturna (quam dixi-<lb/>inus eſſe horologium boreale, ſi illa partium permutatio fiat) horæ ab or. </s>
  <s xml:id="echoid-s39023" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39024" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39025" xml:space="preserve">ſunt autem om <lb/>nes horæ ab ortu productæ vltra lineam horizontalem, antequam lineam meridianam ſecent, nu-<lb/>
<anchor type="figure" xlink:label="fig-0605-01a" xlink:href="fig-0605-01"/>
<anchor type="note" xlink:label="note-0605-01a" xlink:href="note-0605-01"/>
<anchor type="note" xlink:label="note-0605-02a" xlink:href="note-0605-02"/>
merandæ etiam ab ortu in portione horologii nocturna, poſtquam autem meridianam lineam, a@-<lb/>que adeò rurſus tropicum ſecuerint, ſupputandæ erunt ab occ. </s>
  <s xml:id="echoid-s39026" xml:space="preserve">Sic etiam horæ ab occ. </s>
  <s xml:id="echoid-s39027" xml:space="preserve">productæ <lb/>
<anchor type="note" xlink:label="note-0605-03a" xlink:href="note-0605-03"/>
ſunt numerandæ in eadem portione nocturna ab occ. </s>
  <s xml:id="echoid-s39028" xml:space="preserve">ante lineam meridianam, poſt verò ab or-<lb/>tu: </s>
  <s xml:id="echoid-s39029" xml:space="preserve">Ita vt in portione nocturna ſequentes horę 23. </s>
  <s xml:id="echoid-s39030" xml:space="preserve">22. </s>
  <s xml:id="echoid-s39031" xml:space="preserve">9. </s>
  <s xml:id="echoid-s39032" xml:space="preserve">10. </s>
  <s xml:id="echoid-s39033" xml:space="preserve">11. </s>
  <s xml:id="echoid-s39034" xml:space="preserve">numerandæ ſint ab ortu: </s>
  <s xml:id="echoid-s39035" xml:space="preserve">hæ <lb/>verò 1. </s>
  <s xml:id="echoid-s39036" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39037" xml:space="preserve">13. </s>
  <s xml:id="echoid-s39038" xml:space="preserve">14. </s>
  <s xml:id="echoid-s39039" xml:space="preserve">15. </s>
  <s xml:id="echoid-s39040" xml:space="preserve">ab occaſu. </s>
  <s xml:id="echoid-s39041" xml:space="preserve">Idem dicendum eſt in ſequentibus horologiis, ſi pro linea meri-<lb/>diana ſumatur linea indicis, ſeu ſtyli, quæ quidẽ in horologiis meridianis eſt linea horæ 6. </s>
  <s xml:id="echoid-s39042" xml:space="preserve">à mer. <lb/></s>
  <s xml:id="echoid-s39043" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39044" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39045" xml:space="preserve">in polaribus verò, &amp; </s>
  <s xml:id="echoid-s39046" xml:space="preserve">æquinoctialibus, linea etiam meridiana, vt propriis in locis per-<lb/>ſpicuum erit. </s>
  <s xml:id="echoid-s39047" xml:space="preserve">His rectè conſideratis, facile ſecernemus horas ab or. </s>
  <s xml:id="echoid-s39048" xml:space="preserve">ab horis ab occ. </s>
  <s xml:id="echoid-s39049" xml:space="preserve">in horolo-<lb/>gio Boteali. </s>
  <s xml:id="echoid-s39050" xml:space="preserve">Omnes enim horæ, quæ in portione nocturna ſupputantur ab or. </s>
  <s xml:id="echoid-s39051" xml:space="preserve">numerandæ ſunt <lb/>in Boreali ab occ. </s>
  <s xml:id="echoid-s39052" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39053" xml:space="preserve">quæ ibi ab occ. </s>
  <s xml:id="echoid-s39054" xml:space="preserve">numerantur, hic ſumendę ſunt ab or. </s>
  <s xml:id="echoid-s39055" xml:space="preserve">vt in ſcholio propoſ. </s>
  <s xml:id="echoid-s39056" xml:space="preserve"><lb/>22. </s>
  <s xml:id="echoid-s39057" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39058" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39059" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s39060" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1937" type="float" level="2" n="1">
<note position="left" xlink:label="note-0604-06" xlink:href="note-0604-06a" xml:space="preserve">Deſcriptio ho-<lb/>rologii Vertica <lb/>lis Italici ac Ba <lb/>bylonici.</note>
<note position="left" xlink:label="note-0604-07" xlink:href="note-0604-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0604-08" xlink:href="note-0604-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0604-09" xlink:href="note-0604-09a" xml:space="preserve">Quo pàcto ho-<lb/>rologium borea <lb/>le ex auſtrali eli <lb/>@@atur.</note>
  <figure xlink:label="fig-0605-01" xlink:href="fig-0605-01a">
    <image file="0605-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0605-01"/>
  </figure>
<note position="left" xlink:label="note-0605-01" xlink:href="note-0605-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0605-02" xlink:href="note-0605-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0605-03" xlink:href="note-0605-03a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Alia deſctiptio <lb/>horologii Ver-<lb/>tiealis italioi, ac<unsure/> <lb/>Babylonici ex <lb/>arcubus diurnis <lb/>atq; @octurnis.</note>
<p>
  <s xml:id="echoid-s39061" xml:space="preserve">QVOD ad alteram rationem attinet, quæ ex arcubus diurnis, nocturnisq́ue ſumitur, nulla eſt <lb/>
<anchor type="note" xlink:label="note-0605-05a" xlink:href="note-0605-05"/>
diſficultas, ſi rectè conſiderentur tabellæ arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s39062" xml:space="preserve">nocturnorum, quas in ſcholio <lb/>propoſ. </s>
  <s xml:id="echoid-s39063" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39064" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39065" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39066" xml:space="preserve">poſuimus. </s>
  <s xml:id="echoid-s39067" xml:space="preserve">Ducitur enim hora 24. </s>
  <s xml:id="echoid-s39068" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39069" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s39070" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39071" xml:space="preserve">in arcu diurno <lb/>horarum 10. </s>
  <s xml:id="echoid-s39072" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39073" xml:space="preserve">per horam 12. </s>
  <s xml:id="echoid-s39074" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39075" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39076" xml:space="preserve">quæ eſt hora meridiei, in arcu nocturno horarum 24. <lb/></s>
  <s xml:id="echoid-s39077" xml:space="preserve">qui lineam meridianam ſecat in G, loco ſtyli, atque hæc linea horæ 24. </s>
  <s xml:id="echoid-s39078" xml:space="preserve">parallela eſt lineę ęquino-<lb/>ctiali, immo eadem eſt, quæ horizontalis linea. </s>
  <s xml:id="echoid-s39079" xml:space="preserve">Hora verò 23. </s>
  <s xml:id="echoid-s39080" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39081" xml:space="preserve">tranſit per horam 4. </s>
  <s xml:id="echoid-s39082" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39083" xml:space="preserve"><lb/>in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s39084" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39085" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s39086" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39087" xml:space="preserve">in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s39088" xml:space="preserve">qui in hoc horo <lb/>logio ab ęquinoctiali linea non diſcrepat. </s>
  <s xml:id="echoid-s39089" xml:space="preserve">et ſic de cęteris. </s>
  <s xml:id="echoid-s39090" xml:space="preserve">Hora autem 13. </s>
  <s xml:id="echoid-s39091" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39092" xml:space="preserve">quia non ha-<lb/>bet punctum reſpondens in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s39093" xml:space="preserve">ducenda eſt per horam 6. </s>
  <s xml:id="echoid-s39094" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39095" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39096" xml:space="preserve">in ar-<lb/>cu nocturno horarum 14. </s>
  <s xml:id="echoid-s39097" xml:space="preserve">vt ex tabella huius arcus patet. </s>
  <s xml:id="echoid-s39098" xml:space="preserve">Vbi aduertendum eſt, horas à mer. </s>
  <s xml:id="echoid-s39099" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s39100" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39101" xml:space="preserve">nunc non eſſe mutandas in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s39102" xml:space="preserve">in portione nocturna <lb/>
<anchor type="note" xlink:label="note-0605-06a" xlink:href="note-0605-06"/>
vltra horizontalem lineam, vt ſupra factum eſt, ſed manere eaſdem numero. </s>
  <s xml:id="echoid-s39103" xml:space="preserve">Non aliter horas ab <lb/>ortu ducemus, vt ex tabellis arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s39104" xml:space="preserve">nocturnorum apparet, Pro horologio Boreali <lb/>non opus eſt exemplum adducere, propterea quod eodem modo deſcribatur ex prædictis arcu-<lb/>bus, maximè cum ipſum ex auſtrali habeatur, vt paulo ante ſcripſimus.</s>
  <s xml:id="echoid-s39105" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1938" type="float" level="2" n="2">
<note position="left" xlink:label="note-0605-05" xlink:href="note-0605-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0605-06" xlink:href="note-0605-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s39106" xml:space="preserve">HIC etiam magnam vtilitatem habent ca, quæ lib. </s>
  <s xml:id="echoid-s39107" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39108" xml:space="preserve">ſcripſimus de mutuis interſectionibus <lb/>horarum à mer. </s>
  <s xml:id="echoid-s39109" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39110" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39111" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39112" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39113" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39114" xml:space="preserve">inter ſeſe. </s>
  <s xml:id="echoid-s39115" xml:space="preserve">Qua de re conſule propoſ. </s>
  <s xml:id="echoid-s39116" xml:space="preserve">22. </s>
  <s xml:id="echoid-s39117" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39118" xml:space="preserve">2.</s>
  <s xml:id="echoid-s39119" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1940" type="section" level="1" n="496">
<head xml:id="echoid-head525" style="it" xml:space="preserve">DE HOROLOGIO VERTICALI <lb/>Antiquo. CAP. X.</head>
<note position="right" xml:space="preserve">Deſcriptio horo <lb/>logii Verticalis <lb/>Antiqui.</note>
<p>
  <s xml:id="echoid-s39120" xml:space="preserve">EADEM fiant, quæ in cap. </s>
  <s xml:id="echoid-s39121" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39122" xml:space="preserve">hac tamen lege, vt diuiſio arcus diurni tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s39123" xml:space="preserve">tro-<lb/>pici ♑, d N e, in 12. </s>
  <s xml:id="echoid-s39124" xml:space="preserve">partes æquales incipiat à punctis a, &amp; </s>
  <s xml:id="echoid-s39125" xml:space="preserve">d, orientalibus. </s>
  <s xml:id="echoid-s39126" xml:space="preserve">Ex punctis enim di <lb/>uiſionum inueniemus puncta horarum inæqualium in vtroque tropico, horologiumq́ue Anti-
<pb o="590" file="0606" n="606" rhead="GNOMONICES"/>
quum abſoluemus, vt cap. </s>
  <s xml:id="echoid-s39127" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39128" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s39129" xml:space="preserve">Vtv. </s>
  <s xml:id="echoid-s39130" xml:space="preserve">g. </s>
  <s xml:id="echoid-s39131" xml:space="preserve">in auſtrali horologio linea recta ex f, puncto <lb/>horæ 4. </s>
  <s xml:id="echoid-s39132" xml:space="preserve">inęqualis tropici ♋, per E, ducta ſecat lineam ęquinoctialem in g. </s>
  <s xml:id="echoid-s39133" xml:space="preserve">Recta verò ex H, per <lb/>g, ducta ſecat tropicum ♋, in h, puncto horæ 4. </s>
  <s xml:id="echoid-s39134" xml:space="preserve">inæqualis. </s>
  <s xml:id="echoid-s39135" xml:space="preserve">Sic etiam recta ex m, puncto horę 4. <lb/></s>
  <s xml:id="echoid-s39136" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0606-01a" xlink:href="fig-0606-01"/>
<anchor type="note" xlink:label="note-0606-01a" xlink:href="note-0606-01"/>
<anchor type="note" xlink:label="note-0606-02a" xlink:href="note-0606-02"/>
inæqualis tropici ♑, per E, ducta ſecat æquinoctialem lineam in n, &amp; </s>
  <s xml:id="echoid-s39137" xml:space="preserve">recta H n, tropicum ♑, ſecat <lb/>in p, puncto horæ 4- inæqualis. </s>
  <s xml:id="echoid-s39138" xml:space="preserve">Recta igitur coniuncta p h, dabit horam 4. </s>
  <s xml:id="echoid-s39139" xml:space="preserve">inęqualem, &amp;</s>
  <s xml:id="echoid-s39140" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39141" xml:space="preserve">Pro <lb/>
<anchor type="note" xlink:label="note-0606-03a" xlink:href="note-0606-03"/>
horologio Boreali exemplum non damus, tum quia ex dictis facile deſcribetur; </s>
  <s xml:id="echoid-s39142" xml:space="preserve">tum etiam quia <lb/>horæ inæquales in horologio auſtrali productæ vltra lineam horizontalem efficiunt horologium <lb/>boreale, ſi fiat illa permutatio partium, de qua in præcedenti capite diximus.</s>
  <s xml:id="echoid-s39143" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1940" type="float" level="2" n="1">
  <figure xlink:label="fig-0606-01" xlink:href="fig-0606-01a">
    <image file="0606-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0606-01"/>
  </figure>
<note position="left" xlink:label="note-0606-01" xlink:href="note-0606-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0606-02" xlink:href="note-0606-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0606-03" xlink:href="note-0606-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">Deſcriptio alla <lb/>Verticalis horo <lb/>logii Antiqui ex <lb/>taoulis diurnis.</note>
<p>
  <s xml:id="echoid-s39144" xml:space="preserve">QVOD ſi deſcribatur arcus diurnus horarum 6. </s>
  <s xml:id="echoid-s39145" xml:space="preserve">qui in horologio Boreali erit horarum 18. <lb/></s>
  <s xml:id="echoid-s39146" xml:space="preserve">conficiemus idem horologium per tabellas arcuum diurnorum nocturnorumq́ue horarum 6. </s>
  <s xml:id="echoid-s39147" xml:space="preserve"><lb/>12. </s>
  <s xml:id="echoid-s39148" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39149" xml:space="preserve">18. </s>
  <s xml:id="echoid-s39150" xml:space="preserve">quas in ſcholio propoſ. </s>
  <s xml:id="echoid-s39151" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39152" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39153" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39154" xml:space="preserve">compoſuimus, vt de horizontali dictum eſt.</s>
  <s xml:id="echoid-s39155" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1942" type="section" level="1" n="497">
<head xml:id="echoid-head526" style="it" xml:space="preserve">DE HOROLOGIO MERIDIANO <lb/>Aſtronomico. CAP. XI.</head>
<p>
  <s xml:id="echoid-s39156" xml:space="preserve">DVCTA recta <lb/>
<anchor type="note" xlink:label="note-0606-05a" xlink:href="note-0606-05"/>
<anchor type="figure" xlink:label="fig-0606-02a" xlink:href="fig-0606-02"/>
linea A B, vtcũ-<lb/>
<anchor type="note" xlink:label="note-0606-06a" xlink:href="note-0606-06"/>
que, (Hæc ſi planum <lb/>horologii ſtabile eſt, <lb/>&amp; </s>
  <s xml:id="echoid-s39157" xml:space="preserve">Meridiano paral-<lb/>lelum, Horizonti du <lb/>cẽda eſt parallela, be <lb/>neficio perpẽdiculi) <lb/>in qua delecto loco <lb/>gnomonis in A, pun <lb/>cto, deſcribatur ex A, <lb/>cẽtro, &amp; </s>
  <s xml:id="echoid-s39158" xml:space="preserve">ad quoduis <lb/>
<anchor type="note" xlink:label="note-0606-07a" xlink:href="note-0606-07"/>
interuallum, arcus <lb/>circuli B C, ad par-<lb/>tem quidem ſiniſtrã <lb/>pro horologio, quod <lb/>ad orientem, ad par <lb/>tem verò dextrã pro <lb/>eo, quod ad occiden-<lb/>tem ſpectat. </s>
  <s xml:id="echoid-s39159" xml:space="preserve">In hoc <lb/>arcu numerata altitu <lb/>dine Aequatoris, ſi-<lb/>ue complemento al-
<pb o="591" file="0607" n="607" rhead="LIBER SEPTIMVS."/>
titudinis poli B C, ducatur per A, &amp; </s>
  <s xml:id="echoid-s39160" xml:space="preserve">C, recta A C, pro linea æquinoctiali, quam in A, ſecet ad an-<lb/>gulos rectos recta D E. </s>
  <s xml:id="echoid-s39161" xml:space="preserve">Sumpta deinde recta A E, quæ longitudini gnomonis cuiuslibet magnitu <lb/>dinis ſit æqualis, deſcribatur ex E, centro, ad quodcunque interuallum, circulus F G H I, qui in <lb/>24. </s>
  <s xml:id="echoid-s39162" xml:space="preserve">horas æquales ſecetur, initio ſumpto à recta F H, vel à recta G I, ipſam F H, ad angulos rectos <lb/>
<anchor type="figure" xlink:label="fig-0607-01a" xlink:href="fig-0607-01"/>
ſecante. </s>
  <s xml:id="echoid-s39163" xml:space="preserve">Poſt hęc per <lb/>puncta diuiſionum, <lb/>&amp; </s>
  <s xml:id="echoid-s39164" xml:space="preserve">per centrum E, du <lb/>ctis rectis occultis, <lb/>ſecabitur æquinoctia <lb/>lis linea A C, in pun <lb/>
<anchor type="note" xlink:label="note-0607-01a" xlink:href="note-0607-01"/>
ctis, per quæ lineę <lb/>ductæ parallelæ ipſi <lb/>D E, vel perpendicu-<lb/>lares ad lineam æqui <lb/>noctialem, dabunt <lb/>lineas horarũ à mer. <lb/></s>
  <s xml:id="echoid-s39165" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39166" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39167" xml:space="preserve">Hæ au-<lb/>tem parallelæ, ſiue <lb/>perpendiculares, fa-<lb/>cile ducentur, ſi per <lb/>
<anchor type="note" xlink:label="note-0607-02a" xlink:href="note-0607-02"/>
quodcunque punctũ <lb/>rectæ A D, vt per D, <lb/>ipſi A C, agatur pa-<lb/>rallela. </s>
  <s xml:id="echoid-s39168" xml:space="preserve">In hanc enim <lb/>ſi à puncto D, omnia <lb/>puncta lineæ A C, <lb/>transferantur, ſumen <lb/>do eorum interualla <lb/>à puncto A, erunt re <lb/>ctæ connectentes bi-<lb/>
<anchor type="note" xlink:label="note-0607-03a" xlink:href="note-0607-03"/>
na puncta æqualiter à recta D E, remota, &amp; </s>
  <s xml:id="echoid-s39169" xml:space="preserve">ipſi D E, &amp; </s>
  <s xml:id="echoid-s39170" xml:space="preserve">inter ſeſe parallelæ. </s>
  <s xml:id="echoid-s39171" xml:space="preserve">Ordo horarum hic eſt. <lb/></s>
  <s xml:id="echoid-s39172" xml:space="preserve">Recta D E, dat horam 6. </s>
  <s xml:id="echoid-s39173" xml:space="preserve">in vtroque horologio. </s>
  <s xml:id="echoid-s39174" xml:space="preserve">Proxima infra ipſam in orientali quidem horolo <lb/>gio indicat 7. </s>
  <s xml:id="echoid-s39175" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39176" xml:space="preserve">ſubſequens 8. </s>
  <s xml:id="echoid-s39177" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39178" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39179" xml:space="preserve">In occidentali verò proxima infra D E, exhibet quintam, &amp; </s>
  <s xml:id="echoid-s39180" xml:space="preserve">ſub-<lb/>ſequens 4. </s>
  <s xml:id="echoid-s39181" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39182" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39183" xml:space="preserve">vt in ſiguris manifeſtum eſt. </s>
  <s xml:id="echoid-s39184" xml:space="preserve">Sola hora 12. </s>
  <s xml:id="echoid-s39185" xml:space="preserve">deſcribi nequit, cum Meridianus circu-<lb/>lus planum horologii non ſecet, ſed ei ſit parallelum.</s>
  <s xml:id="echoid-s39186" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1942" type="float" level="2" n="1">
<note position="left" xlink:label="note-0606-05" xlink:href="note-0606-05a" xml:space="preserve">Deſcriptio horo <lb/>logii Meridiani <lb/>Attronomici.</note>
  <figure xlink:label="fig-0606-02" xlink:href="fig-0606-02a">
    <image file="0606-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0606-02"/>
  </figure>
<note position="left" xlink:label="note-0606-06" xlink:href="note-0606-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0606-07" xlink:href="note-0606-07a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0607-01" xlink:href="fig-0607-01a">
    <image file="0607-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0607-01"/>
  </figure>
<note position="left" xlink:label="note-0607-01" xlink:href="note-0607-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0607-02" xlink:href="note-0607-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0607-03" xlink:href="note-0607-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s39187" xml:space="preserve">SATIS etiam eſt ad deſcriptionem horologii Meridiani, vnum quadrantem circuli ex E, <lb/>deſcripti in ſex æquales partes diſtribuere, qualis eſt quadrans F G. </s>
  <s xml:id="echoid-s39188" xml:space="preserve">Nam ductis rectis occultis <lb/>per puncta diuiſionum, &amp; </s>
  <s xml:id="echoid-s39189" xml:space="preserve">centrum E, quæ rectam A S, ſecent in punctis, per quæ horariæ lineæ <lb/>ſunt ducendæ parallelæ ipſi D E, ſi hæc puncta ex A, transferantur ex altera parte in rectam A C, <lb/>habebimus alia puncta, per quæ ducendæ ſunt lineę horariæ; </s>
  <s xml:id="echoid-s39190" xml:space="preserve">propterea quod ſingula ſegmenta <lb/>
<anchor type="note" xlink:label="note-0607-04a" xlink:href="note-0607-04"/>
rectæ A S, ſingulis ſegmentis rectæ A C, æqualia ſunt.</s>
  <s xml:id="echoid-s39191" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1943" type="float" level="2" n="2">
<note position="left" xlink:label="note-0607-04" xlink:href="note-0607-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s39192" xml:space="preserve">IAM verò ſi horologium orientale in plano, quod Meridiano æquidiſtet, ſpectetq́ue ad orien <lb/>
<anchor type="note" xlink:label="note-0607-05a" xlink:href="note-0607-05"/>
tem, occidentale autem in eodem plano occidentem reſpiciente collocetur, ita vt A B, recta Hori-<lb/>zonti ſit æquidiſtans, &amp; </s>
  <s xml:id="echoid-s39193" xml:space="preserve">punctum A, ad Boream, punctum verò B, ad Auſtrum pertineat, hoc eſt, <lb/>angulus B A C, complemẽti altitudinis poli perpetuo verſus auſtrum ſtatuatur, indica buntur ho-<lb/>ræ à gnomone A E, ad angulos rectos inſiſtente plano horologii in puncto A. </s>
  <s xml:id="echoid-s39194" xml:space="preserve">Quod ſi ex duobus <lb/>quibuslibet punctis rectę D E, vt ex D, &amp; </s>
  <s xml:id="echoid-s39195" xml:space="preserve">E, erigantur ad planum horologii duæ perpendiculares <lb/>
<anchor type="figure" xlink:label="fig-0607-02a" xlink:href="fig-0607-02"/>
E O, D P, gnomoni A E, æquales, ipſisq́ue ſuper-<lb/>ponatur recta O P, vel certè ſilum extendatur ex <lb/>O, ad P, fungetur illa recta, vel hoc filum, mune-<lb/>
<anchor type="note" xlink:label="note-0607-06a" xlink:href="note-0607-06"/>
re axis, cuius vmbra in lineas horarias proiecta <lb/>indicabit quoque horas à meridie vel media no-<lb/>cte. </s>
  <s xml:id="echoid-s39196" xml:space="preserve">Gnomon itidem A E, ſi in deſcriptione <lb/>horologii erratum non fuerit, perpetuo æqualis <lb/>eſt illi ſegmento æquinoctialis lineæ, quod inter <lb/>punctum A, &amp; </s>
  <s xml:id="echoid-s39197" xml:space="preserve">horam 3. </s>
  <s xml:id="echoid-s39198" xml:space="preserve">vel 9. </s>
  <s xml:id="echoid-s39199" xml:space="preserve">interiicitur.</s>
  <s xml:id="echoid-s39200" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1944" type="float" level="2" n="3">
<note position="right" xlink:label="note-0607-05" xlink:href="note-0607-05a" xml:space="preserve">Quomodo vtru <lb/>que horologiũ <lb/>Meridianum <lb/>collocandũ ſit, <lb/>vt horas indi-<lb/>cet.</note>
  <figure xlink:label="fig-0607-02" xlink:href="fig-0607-02a">
    <image file="0607-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0607-02"/>
  </figure>
<note position="left" xlink:label="note-0607-06" xlink:href="note-0607-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div1946" type="section" level="1" n="498">
<head xml:id="echoid-head527" style="it" xml:space="preserve">DE ARCVBVS SIGNORVM IN ME-<lb/>
ridiano horologio. CAP. XII.</head>
<note position="right" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſignorum <lb/>in vttoque ho-<lb/>rologio Meridia <lb/>no.</note>
<p>
  <s xml:id="echoid-s39201" xml:space="preserve">DVCTA recta D C, vtcunque pro radio Aequatoris, &amp; </s>
  <s xml:id="echoid-s39202" xml:space="preserve">hinc inde radiis aliorum ſignorum <lb/>deſcriptis, vt cap. </s>
  <s xml:id="echoid-s39203" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39204" xml:space="preserve">docuimus, ductoq́ue axe D G, ad æquinoctialem radium D C, perpendi-
<pb o="592" file="0608" n="608" rhead="GNOMONICES"/>
culari, transferantur in radium Aequatoris D C, ex D, omnia horaria interualla intercepta inter <lb/>E, centrum circuli F G <emph style="sc">H</emph> I, in præcedenti capite, &amp; </s>
  <s xml:id="echoid-s39205" xml:space="preserve">lineam æquinoctialem A C, imprimendo in <lb/>
<anchor type="figure" xlink:label="fig-0608-01a" xlink:href="fig-0608-01"/>
ipſo radio Aequa <lb/>toris puncta, per <lb/>quæ axi D G, pa-<lb/>rallelæ agãtur, qui <lb/>bus numeri hora-<lb/>rum ſpatijs hora-<lb/>riis translatis re-<lb/>ſpondentes aſcri-<lb/>
<anchor type="note" xlink:label="note-0608-01a" xlink:href="note-0608-01"/>
bantur. </s>
  <s xml:id="echoid-s39206" xml:space="preserve">Si enim <lb/>ſegmenta harum <lb/>parallelarũ inter-<lb/>cepta inter radiũ <lb/>Aequatoris D C, <lb/>&amp; </s>
  <s xml:id="echoid-s39207" xml:space="preserve">radios aliorum <lb/>ſignorum transfe-<lb/>rantur in reſpon-<lb/>dentes horarias li <lb/>neas horologii à <lb/>
<anchor type="note" xlink:label="note-0608-02a" xlink:href="note-0608-02"/>
linea æquinoctia-<lb/>li A C, vtrinque, <lb/>imprimendo in li <lb/>neis horariis pun-<lb/>cta, &amp; </s>
  <s xml:id="echoid-s39208" xml:space="preserve">per hęc pũ-<lb/>cta lineę curuę du <lb/>cantur, deſcripti <lb/>erunt arcus ſigno-<lb/>rum, quorum ſuperiores Auſtrales, inferiores vero Boreales ſunt. </s>
  <s xml:id="echoid-s39209" xml:space="preserve">Recta <emph style="sub">v</emph>erò A B, eſt linea hori <lb/>@ontalis. </s>
  <s xml:id="echoid-s39210" xml:space="preserve">Vnde omnia lineamenta, quæ ſupra illam reperiuntur, reſecand<emph style="sub">a</emph> ſunt, tanquam ſuper-<lb/>
<anchor type="note" xlink:label="note-0608-03a" xlink:href="note-0608-03"/>
<anchor type="figure" xlink:label="fig-0608-02a" xlink:href="fig-0608-02"/>
<anchor type="note" xlink:label="note-0608-04a" xlink:href="note-0608-04"/>
<anchor type="note" xlink:label="note-0608-05a" xlink:href="note-0608-05"/>
uacanea. </s>
  <s xml:id="echoid-s39211" xml:space="preserve">Facile autem per puncta impreſſa in radio Aequatoris D C, axi D G, parallelæ agentur, <lb/>ſi omnia eorum interualla a puncto D, accepta transferantur in rectam G F, ipſi D C, vtcunque <lb/>ductam parallelam. </s>
  <s xml:id="echoid-s39212" xml:space="preserve">Nam rectæ iungentes bina puncta rectarum D C, G F, à punctis D, G, æqua <lb/>liter remota parallelę erunt. </s>
  <s xml:id="echoid-s39213" xml:space="preserve">Numeri autem hiſce parallelis lineis appoſiti ad dexteram pertinent
<pb o="593" file="0609" n="609" rhead="LIBER SEPTIMVS."/>
ad horas horologii Meridiani vtriuſque, qui verò ad ſiniſtram ſunt, ad horas vtriuſque horologii <lb/>polaris, de quo paulo poſt. </s>
  <s xml:id="echoid-s39214" xml:space="preserve">Sunt autem hic omnes arcus ſignorum hyperbolę, vt cap. </s>
  <s xml:id="echoid-s39215" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39216" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s39217" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1946" type="float" level="2" n="1">
  <figure xlink:label="fig-0608-01" xlink:href="fig-0608-01a">
    <image file="0608-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0608-01"/>
  </figure>
<note position="left" xlink:label="note-0608-01" xlink:href="note-0608-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0608-02" xlink:href="note-0608-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0608-03" xlink:href="note-0608-03a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0608-02" xlink:href="fig-0608-02a">
    <image file="0608-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0608-02"/>
  </figure>
<note position="left" xlink:label="note-0608-04" xlink:href="note-0608-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0608-05" xlink:href="note-0608-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s39218" xml:space="preserve">CAETERVM portio vtriuſque horologii ſuperior, quam horizontalis linea abſcindit, ex-<lb/>hibet horologium in facie plani horologii oppoſita collocandum, dummodo inuertatur, vt pars, <lb/>quæ nunc ſuperior eſt, fiat inferior, &amp; </s>
  <s xml:id="echoid-s39219" xml:space="preserve">contra, &amp; </s>
  <s xml:id="echoid-s39220" xml:space="preserve">quæ dextra eſt in eo ſitu, mutetur in ſiniſtram, <lb/>horæq́ue, quę à meridie computabantur, numerentur à media nocte, &amp; </s>
  <s xml:id="echoid-s39221" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s39222" xml:space="preserve">ſigna denique <lb/>borealia mutentur in auſtralia, &amp; </s>
  <s xml:id="echoid-s39223" xml:space="preserve">auſtralia in borealia, vt propoſ. </s>
  <s xml:id="echoid-s39224" xml:space="preserve">26. </s>
  <s xml:id="echoid-s39225" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39226" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39227" xml:space="preserve">demonſtrauimus.</s>
  <s xml:id="echoid-s39228" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s39229" xml:space="preserve">RVRSVS portio ſuperior horologii vtriuslibet mõſtraret horas nocturno tẽpore, ſi in eam <lb/>radii Solis inciderent, vt ſupra de Verticali horologio dictum eſt. </s>
  <s xml:id="echoid-s39230" xml:space="preserve">Nam in parte ſuperiori orien-<lb/>talis horologii comprehenduntur horæ à media nocte vſque ad ortum Solis: </s>
  <s xml:id="echoid-s39231" xml:space="preserve">In ſuperiori verò <lb/>
<anchor type="note" xlink:label="note-0609-01a" xlink:href="note-0609-01"/>
parte horologii occidentalis horæ ab occaſu Solis vſque ad mediam noctem continentur.</s>
  <s xml:id="echoid-s39232" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1947" type="float" level="2" n="2">
<note position="left" xlink:label="note-0609-01" xlink:href="note-0609-01a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div1949" type="section" level="1" n="499">
<head xml:id="echoid-head528" style="it" xml:space="preserve">DE ARCVBVS LONGITVDINVM DIERVM <lb/>in horologio Meridiano. CAP. XIII.</head>
<p>
  <s xml:id="echoid-s39233" xml:space="preserve">HI arcus, qui etiam omnes ſunt hyperbolę, deſcribentur, vt arcus ſignorum, ſi pro radiis ſi-<lb/>
<anchor type="note" xlink:label="note-0609-02a" xlink:href="note-0609-02"/>
gnorum radii longitudinum dierum accipiantur, vt in pręcedentibus dictum eſt. </s>
  <s xml:id="echoid-s39234" xml:space="preserve">In ſigura <lb/>radiorum Zodiaci præcedentis cap. </s>
  <s xml:id="echoid-s39235" xml:space="preserve">duximus radios diurnos horarum 0. </s>
  <s xml:id="echoid-s39236" xml:space="preserve">24. </s>
  <s xml:id="echoid-s39237" xml:space="preserve">6. </s>
  <s xml:id="echoid-s39238" xml:space="preserve">18. </s>
  <s xml:id="echoid-s39239" xml:space="preserve">10. </s>
  <s xml:id="echoid-s39240" xml:space="preserve">14. </s>
  <s xml:id="echoid-s39241" xml:space="preserve">quales <lb/>ſunt rectæ ex D, emiſſæ, punctisq́ue ſunt notatæ.</s>
  <s xml:id="echoid-s39242" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1949" type="float" level="2" n="1">
<note position="right" xlink:label="note-0609-02" xlink:href="note-0609-02a" xml:space="preserve">Deſcriptio ar-<lb/>cuum diurnorũ <lb/>in vtroque ho-<lb/>rologio Meti-<lb/>diano.</note>
</div>
</div>
<div xml:id="echoid-div1951" type="section" level="1" n="500">
<head xml:id="echoid-head529" style="it" xml:space="preserve">DE HOROLOGIO MERIDIANO ITALICO, <lb/>
&amp; Babylonico. CAP. XIIII.</head>
<p>
  <s xml:id="echoid-s39243" xml:space="preserve">SVMATVR in circulo FGHI, beneficio cuius cap. </s>
  <s xml:id="echoid-s39244" xml:space="preserve">11. </s>
  <s xml:id="echoid-s39245" xml:space="preserve">puncta in linea æquinoctiali inue-<lb/>
<anchor type="note" xlink:label="note-0609-04a" xlink:href="note-0609-04"/>
nimus, vt horologium Meridianum Aſtronomicum deſcriberemus, arcus diurnus ♋, BGC, <lb/>
<anchor type="figure" xlink:label="fig-0609-01a" xlink:href="fig-0609-01"/>
<anchor type="note" xlink:label="note-0609-05a" xlink:href="note-0609-05"/>
<anchor type="note" xlink:label="note-0609-06a" xlink:href="note-0609-06"/>
<anchor type="note" xlink:label="note-0609-07a" xlink:href="note-0609-07"/>
&amp; </s>
  <s xml:id="echoid-s39246" xml:space="preserve">arcus diurnus ♑, DGE: </s>
  <s xml:id="echoid-s39247" xml:space="preserve">quod facile fiet, ſi in dicto circulo à puncto G, ex vtraque parte nume <lb/>retur arcus ſemidiurnus ♋, &amp; </s>
  <s xml:id="echoid-s39248" xml:space="preserve">♑, vſque ad puncta B, C, &amp; </s>
  <s xml:id="echoid-s39249" xml:space="preserve">D, E. </s>
  <s xml:id="echoid-s39250" xml:space="preserve">Deinde idem circulus in partes <lb/>24. </s>
  <s xml:id="echoid-s39251" xml:space="preserve">æquales ſecetur, initio facto pro horologio Italico orientali à puncto C, &amp; </s>
  <s xml:id="echoid-s39252" xml:space="preserve">pro occidentali à
<pb o="594" file="0610" n="610" rhead="GNOMONICES"/>
puncto B, ita vt tam C, quàm B, ſit hora 24. </s>
  <s xml:id="echoid-s39253" xml:space="preserve">ab occaſu, proximum verò punctum verſus G, ho-<lb/>ra 23. </s>
  <s xml:id="echoid-s39254" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39255" xml:space="preserve">ita deinceps. </s>
  <s xml:id="echoid-s39256" xml:space="preserve">Contrarium fiat pro horologio Babylonico, hoc eſt, in orientali diuiſio <lb/>inchoetur à puncto b, in occidentali verò à puncto C, ita vt tam punctum B, quàm punctum C, <lb/>det horam 24. </s>
  <s xml:id="echoid-s39257" xml:space="preserve">ab ortu, &amp; </s>
  <s xml:id="echoid-s39258" xml:space="preserve">proximum punctum verſus G, horam 1. </s>
  <s xml:id="echoid-s39259" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39260" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39261" xml:space="preserve">Nam ſi pro horologio Ita-<lb/>lico in vtroque horologio ex horis inter puncta B, G, poſitis per centrum circuli rectę occultæ <lb/>ducantur, ſecabitur æquinoctialis linea in punctis, per quæ, ſi ad eandem perpendiculares erigan-<lb/>tur, ſecabitur tropicus ♋, in punctis horarum ab occaſu Solis. </s>
  <s xml:id="echoid-s39262" xml:space="preserve">Si autem pro vtroque horo-<lb/>logio Babylonico ex horis inter puncta C, &amp; </s>
  <s xml:id="echoid-s39263" xml:space="preserve">G, interiectis per centrum circuli egrediantur re-<lb/>ctæ occultæ, diuidetur linea æquinoctialis in punctis, per quæ ſi ad eandem educantur lineæ <lb/>perpendiculares ſecantes tropicum ♋, habebimus puncta horarum ab ortu Solis in dicto tro-<lb/>
<anchor type="note" xlink:label="note-0610-01a" xlink:href="note-0610-01"/>
pico. </s>
  <s xml:id="echoid-s39264" xml:space="preserve">Non aliter in tropico ♑, earundem horarum puncta inueſtigabimus, ſi diuiſio circu-<lb/>li F G H I, principium ſumat in orientali horologio Italico à puncto E, &amp; </s>
  <s xml:id="echoid-s39265" xml:space="preserve">in occidentali à pun-<lb/>cto D: </s>
  <s xml:id="echoid-s39266" xml:space="preserve">In horologio verò Babylonico orientali à puncto D, &amp; </s>
  <s xml:id="echoid-s39267" xml:space="preserve">in occidentali à puncto E, verſus <lb/>punctum G, ſemper progrediendo. </s>
  <s xml:id="echoid-s39268" xml:space="preserve">Itaque ſi horæ inter ſe reſpondentes in tropicis iungantur <lb/>lineis rectis, deſcriptum erit horologium tam Italicum, quàm Babylonicum. </s>
  <s xml:id="echoid-s39269" xml:space="preserve">Tranſibunt autem <lb/>horæ ab or. </s>
  <s xml:id="echoid-s39270" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39271" xml:space="preserve">occ neceſſario per puncta horarum à mer. </s>
  <s xml:id="echoid-s39272" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39273" xml:space="preserve">med. </s>
  <s xml:id="echoid-s39274" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39275" xml:space="preserve">in linea æquinoctiali, vt in <lb/>ſuperioribus dictum eſt, &amp; </s>
  <s xml:id="echoid-s39276" xml:space="preserve">manifeſtè ex tabella, quam in cap. </s>
  <s xml:id="echoid-s39277" xml:space="preserve">4. </s>
  <s xml:id="echoid-s39278" xml:space="preserve">reperies, colligitur. </s>
  <s xml:id="echoid-s39279" xml:space="preserve">Quòd ſi horæ <lb/>nonnullę ab or. </s>
  <s xml:id="echoid-s39280" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39281" xml:space="preserve">in alterutro tropicorum non habeant puncta reſpõdentia, ducendæ erunt <lb/>illæ per horas reſpondentes in linea æquinoctiali. </s>
  <s xml:id="echoid-s39282" xml:space="preserve">Vt in horologio orientali hor. </s>
  <s xml:id="echoid-s39283" xml:space="preserve">16. </s>
  <s xml:id="echoid-s39284" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39285" xml:space="preserve">17. </s>
  <s xml:id="echoid-s39286" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s39287" xml:space="preserve">Item 4. </s>
  <s xml:id="echoid-s39288" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39289" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39290" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39291" xml:space="preserve">ductę ſunt per hor. </s>
  <s xml:id="echoid-s39292" xml:space="preserve">10. </s>
  <s xml:id="echoid-s39293" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39294" xml:space="preserve">11. </s>
  <s xml:id="echoid-s39295" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39296" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39297" xml:space="preserve">in linea ęquinoctiali: </s>
  <s xml:id="echoid-s39298" xml:space="preserve">In occi-<lb/>
<anchor type="note" xlink:label="note-0610-02a" xlink:href="note-0610-02"/>
dentali vero hor. </s>
  <s xml:id="echoid-s39299" xml:space="preserve">19. </s>
  <s xml:id="echoid-s39300" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39301" xml:space="preserve">20. </s>
  <s xml:id="echoid-s39302" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39303" xml:space="preserve">Item 7. </s>
  <s xml:id="echoid-s39304" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39305" xml:space="preserve">8. </s>
  <s xml:id="echoid-s39306" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39307" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s39308" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39309" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39310" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39311" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39312" xml:space="preserve">Lineæ autem horæ 6. <lb/></s>
  <s xml:id="echoid-s39313" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39314" xml:space="preserve">18. </s>
  <s xml:id="echoid-s39315" xml:space="preserve">ducendæ ſunt æquidiſtantes lineæ æquinoctiali, vt lib. </s>
  <s xml:id="echoid-s39316" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39317" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s39318" xml:space="preserve">34 oſtendimus, per puncta <lb/>in tropicis vtriuſque horologii inuenta.</s>
  <s xml:id="echoid-s39319" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1951" type="float" level="2" n="1">
<note position="right" xlink:label="note-0609-04" xlink:href="note-0609-04a" xml:space="preserve">Conſtructio ho <lb/>rologii Meridia <lb/>ni Italici &amp; Ba-<lb/>bylonici.</note>
  <figure xlink:label="fig-0609-01" xlink:href="fig-0609-01a">
    <image file="0609-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0609-01"/>
  </figure>
<note position="left" xlink:label="note-0609-05" xlink:href="note-0609-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0609-06" xlink:href="note-0609-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0609-07" xlink:href="note-0609-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0610-01" xlink:href="note-0610-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0610-02" xlink:href="note-0610-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s39320" xml:space="preserve">PER arcus diurnos, nocturnosq́ue horarum 14. </s>
  <s xml:id="echoid-s39321" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39322" xml:space="preserve">10. </s>
  <s xml:id="echoid-s39323" xml:space="preserve">deſcribemus quoque vtrumque horo-<lb/>
<anchor type="note" xlink:label="note-0610-03a" xlink:href="note-0610-03"/>
logium, vtin horizontali, Verticaliq́ue declarauimus. </s>
  <s xml:id="echoid-s39324" xml:space="preserve">Idem fiet beneſicio arcus diurni, &amp; </s>
  <s xml:id="echoid-s39325" xml:space="preserve">noctur <lb/>ni horarum 24. </s>
  <s xml:id="echoid-s39326" xml:space="preserve">Verum obſeruandum eſt, vt ex arcubus diurnis, atque nocturnis in ſcholio pro-<lb/>poſ. </s>
  <s xml:id="echoid-s39327" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39328" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39329" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39330" xml:space="preserve">poſitis ſumantur illæ duntaxat horæ ab or. </s>
  <s xml:id="echoid-s39331" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39332" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39333" xml:space="preserve">pro horologio orientali, quibus in <lb/>eiſdem tabulis reſpondent horæ à med. </s>
  <s xml:id="echoid-s39334" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39335" xml:space="preserve">non autem à meridie, quia hæ non continentur in eo <lb/>horologio. </s>
  <s xml:id="echoid-s39336" xml:space="preserve">Pro horologio verò occidentali illę quibus reſpondent horæ à mer. </s>
  <s xml:id="echoid-s39337" xml:space="preserve">non autem à med. <lb/></s>
  <s xml:id="echoid-s39338" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39339" xml:space="preserve">Vt horam 14. </s>
  <s xml:id="echoid-s39340" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39341" xml:space="preserve">in orientali horologio ducemus per horam 2. </s>
  <s xml:id="echoid-s39342" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39343" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39344" xml:space="preserve">in arcu no-<lb/>
<anchor type="note" xlink:label="note-0610-04a" xlink:href="note-0610-04"/>
cturno horarum 24. </s>
  <s xml:id="echoid-s39345" xml:space="preserve">non autem per horam 2. </s>
  <s xml:id="echoid-s39346" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39347" xml:space="preserve">in arcu diurno horarum 24. </s>
  <s xml:id="echoid-s39348" xml:space="preserve">Item horam 14. <lb/></s>
  <s xml:id="echoid-s39349" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39350" xml:space="preserve">in occidentali horologio ducemus per horam 2. </s>
  <s xml:id="echoid-s39351" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39352" xml:space="preserve">in arcu diurno horarum 24. </s>
  <s xml:id="echoid-s39353" xml:space="preserve">non au <lb/>tem per horam 2. </s>
  <s xml:id="echoid-s39354" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39355" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39356" xml:space="preserve">in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s39357" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39358" xml:space="preserve">c.</s>
  <s xml:id="echoid-s39359" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1952" type="float" level="2" n="2">
<note position="left" xlink:label="note-0610-03" xlink:href="note-0610-03a" xml:space="preserve">Alia deſcriptio <lb/>horologii Meri <lb/>diani &amp; Baby-<lb/>lonici per arcus <lb/>diurnos, ac no-<lb/>cturnos.</note>
<note position="left" xlink:label="note-0610-04" xlink:href="note-0610-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s39360" xml:space="preserve">QVOD ad ſectiones mutuas horarum à mer. </s>
  <s xml:id="echoid-s39361" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39362" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39363" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39364" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39365" xml:space="preserve">vel occaſu in linea horę <lb/>12. </s>
  <s xml:id="echoid-s39366" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39367" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39368" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39369" xml:space="preserve">in linea horizontali attinet, conſideranda ſunt ea, quę propoſ. </s>
  <s xml:id="echoid-s39370" xml:space="preserve">34. </s>
  <s xml:id="echoid-s39371" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39372" xml:space="preserve">35. </s>
  <s xml:id="echoid-s39373" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39374" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s39375" xml:space="preserve">ſcripſimus.</s>
  <s xml:id="echoid-s39376" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s39377" xml:space="preserve">MANIFESTVM porrò eſt ex ſigura huius cap. </s>
  <s xml:id="echoid-s39378" xml:space="preserve">lineas horarum ab occ. </s>
  <s xml:id="echoid-s39379" xml:space="preserve">in horologio <lb/>
<anchor type="note" xlink:label="note-0610-05a" xlink:href="note-0610-05"/>
orientali eundem ſitum habere, quem lineæ horarum ab or. </s>
  <s xml:id="echoid-s39380" xml:space="preserve">ſeruant in horologio occidenta-<lb/>li. </s>
  <s xml:id="echoid-s39381" xml:space="preserve">Quod etiam verum eſt de horis ab or. </s>
  <s xml:id="echoid-s39382" xml:space="preserve">in orientali, &amp; </s>
  <s xml:id="echoid-s39383" xml:space="preserve">de horis ab occ. </s>
  <s xml:id="echoid-s39384" xml:space="preserve">in occidentali. </s>
  <s xml:id="echoid-s39385" xml:space="preserve">Vnde ho-<lb/>rologium Italicum orientale in facie oppoſita plani horologii deſcriptum, ita vt lineæ lineis re-<lb/>ſpondeant, erit Babylonicum occidentale: </s>
  <s xml:id="echoid-s39386" xml:space="preserve">Et Italicum occidentale erit Babylonicum orientale, &amp; </s>
  <s xml:id="echoid-s39387" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0610-06a" xlink:href="note-0610-06"/>
contra: </s>
  <s xml:id="echoid-s39388" xml:space="preserve">dummodo numeri ſinguli horarum mutentur in earundem complementa vſque ad 24. <lb/></s>
  <s xml:id="echoid-s39389" xml:space="preserve">vt 9. </s>
  <s xml:id="echoid-s39390" xml:space="preserve">in 15. </s>
  <s xml:id="echoid-s39391" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39392" xml:space="preserve">3. </s>
  <s xml:id="echoid-s39393" xml:space="preserve">in 21. </s>
  <s xml:id="echoid-s39394" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39395" xml:space="preserve">c.</s>
  <s xml:id="echoid-s39396" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1953" type="float" level="2" n="3">
<note position="left" xlink:label="note-0610-05" xlink:href="note-0610-05a" xml:space="preserve">Qua ratione ex <lb/>horologio Itali <lb/>co ſiat Babylo-<lb/>nicum, &amp; cõtra, <lb/>ta ſaci@ oppoli-<lb/>ta plani @orolo <lb/>gu Mcridiani <lb/>delineandum.</note>
<note position="left" xlink:label="note-0610-06" xlink:href="note-0610-06a" xml:space="preserve">40</note>
</div>
</div>
<div xml:id="echoid-div1955" type="section" level="1" n="501">
<head xml:id="echoid-head530" style="it" xml:space="preserve">DE HOROLOGIO MERIDIANO <lb/>Antiquo. CAP. XV.</head>
<p>
  <s xml:id="echoid-s39397" xml:space="preserve">TAM arcus diurnus ♋, B G C, quàm ♑, D G E, in circulo F G H I, vtriuſque horologii ſe-<lb/>
<anchor type="note" xlink:label="note-0610-07a" xlink:href="note-0610-07"/>
cetur in 12. </s>
  <s xml:id="echoid-s39398" xml:space="preserve">æquales partes. </s>
  <s xml:id="echoid-s39399" xml:space="preserve">Harum enim beneſicio inueniemus in vtroque tropico puncta, <lb/>per quæ ducendæ ſunt horæ inæquales, non ſecus, atque in præcedenti cap. </s>
  <s xml:id="echoid-s39400" xml:space="preserve">puncta horarum ab <lb/>
<anchor type="note" xlink:label="note-0610-08a" xlink:href="note-0610-08"/>
or. </s>
  <s xml:id="echoid-s39401" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39402" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39403" xml:space="preserve">in eiſdem tropicis indagauimus. </s>
  <s xml:id="echoid-s39404" xml:space="preserve">Tranſibunt autem horæ inæquales per horas à me-<lb/>ridie vel media nocte in æquinoctiali linea, vt in horologio horizontali, ac Verticali do-<lb/>cuimus.</s>
  <s xml:id="echoid-s39405" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1955" type="float" level="2" n="1">
<note position="left" xlink:label="note-0610-07" xlink:href="note-0610-07a" xml:space="preserve">Deſcriptio horo <lb/>logii Meridiani <lb/>Antiqui.</note>
<note position="left" xlink:label="note-0610-08" xlink:href="note-0610-08a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">Coſtructio eiuſ <lb/>dem horologii <lb/>Merid@ani Anti <lb/>qui ex arcubus <lb/>diurnis.</note>
<p>
  <s xml:id="echoid-s39406" xml:space="preserve">QVOD ſi duo arcus diurni deſcribantur, vnus horarum 18. </s>
  <s xml:id="echoid-s39407" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39408" xml:space="preserve">horarum 6. </s>
  <s xml:id="echoid-s39409" xml:space="preserve">alter, conſtrue-<lb/>mus idem horologi<unsure/>um Antiquum, quemadmodum ſupra factum eſt in horizontali horologio, <lb/>&amp; </s>
  <s xml:id="echoid-s39410" xml:space="preserve">Verticali, ex tabellis in ſcholio propoſ. </s>
  <s xml:id="echoid-s39411" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39412" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39413" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39414" xml:space="preserve">deſcriptis.</s>
  <s xml:id="echoid-s39415" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s39416" xml:space="preserve">CONSTAT autem ex ſiguta, &amp; </s>
  <s xml:id="echoid-s39417" xml:space="preserve">deſcriptione vtriuſque horologii, lineas horarum inęqua-<lb/>
<anchor type="note" xlink:label="note-0610-10a" xlink:href="note-0610-10"/>
lium eandem habere poſitionem, &amp; </s>
  <s xml:id="echoid-s39418" xml:space="preserve">ſitum in vtroque horologio. </s>
  <s xml:id="echoid-s39419" xml:space="preserve">Quapropter vno deſcripto, ſi in <lb/>oppoſita facie eædem lineę depingantur prioribus lineis ad vnguem reſpondentes, habebitur etiã <lb/>alterum horologium: </s>
  <s xml:id="echoid-s39420" xml:space="preserve">Numeri tainen horarum in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s39421" xml:space="preserve">commutan <lb/>di ſunt, vt 1. </s>
  <s xml:id="echoid-s39422" xml:space="preserve">in 11. </s>
  <s xml:id="echoid-s39423" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39424" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39425" xml:space="preserve">in 10. </s>
  <s xml:id="echoid-s39426" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39427" xml:space="preserve">c.</s>
  <s xml:id="echoid-s39428" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1956" type="float" level="2" n="2">
<note position="left" xlink:label="note-0610-10" xlink:href="note-0610-10a" xml:space="preserve">Quo pacto ex <lb/>horologio Anti <lb/>quo orientali <lb/>fiatoccidentale, <lb/>&amp; contra.</note>
</div>
<pb o="595" file="0611" n="611" rhead="LIBER SEPTIMVS."/>
  <figure>
    <image file="0611-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0611-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1958" type="section" level="1" n="502">
<head xml:id="echoid-head531" style="it" xml:space="preserve">DE HOROLOGIO POLARI <lb/>Astronomico. CAP. XVI.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s39429" xml:space="preserve">POLARE horologium à Meridiano, quod cap. </s>
  <s xml:id="echoid-s39430" xml:space="preserve">13. </s>
  <s xml:id="echoid-s39431" xml:space="preserve">deſcripſimus, non differt, excepto nume <lb/>
<anchor type="note" xlink:label="note-0611-04a" xlink:href="note-0611-04"/>
ro horarum, &amp; </s>
  <s xml:id="echoid-s39432" xml:space="preserve">ordine. </s>
  <s xml:id="echoid-s39433" xml:space="preserve">In hoc enim ex vtraque parte rectæ D E, ſumendæ ſunt omnes horæ, <lb/>
<anchor type="figure" xlink:label="fig-0611-02a" xlink:href="fig-0611-02"/>
quæ in planum <lb/>horologii cadere <lb/>poſſunt, &amp; </s>
  <s xml:id="echoid-s39434" xml:space="preserve">ipſa <lb/>recta D E, non eſt <lb/>amplius hora 6, <lb/>aſtron. </s>
  <s xml:id="echoid-s39435" xml:space="preserve">ſed 12. </s>
  <s xml:id="echoid-s39436" xml:space="preserve">vt <lb/>in appoſito horo <lb/>
<anchor type="note" xlink:label="note-0611-05a" xlink:href="note-0611-05"/>
logio apparet. <lb/></s>
  <s xml:id="echoid-s39437" xml:space="preserve">Nam ſi horolo-<lb/>gium hoc ita col <lb/>locetur, vt recta <lb/>
<anchor type="note" xlink:label="note-0611-06a" xlink:href="note-0611-06"/>
C S, Horizonti <lb/>æquidiſter, re-<lb/>ctaq́ue D E, in <lb/>plano circuliMe <lb/>ridiani ſita ſit, <lb/>punctumq́; </s>
  <s xml:id="echoid-s39438" xml:space="preserve">E, ad <lb/>
<anchor type="note" xlink:label="note-0611-07a" xlink:href="note-0611-07"/>
auſtrũ, &amp; </s>
  <s xml:id="echoid-s39439" xml:space="preserve">D, ad <lb/>boream vergat, punctum denique D, ex parte ſeptentrionis eleuetur ſecundum altitudinem poli, <lb/>hoc eſt, recta D E, cum linea meridiana in plano Horizontis conſtituat ad partes puncti D, angu-<lb/>lum altitudinis poli, indicabit ſtylus A E, in puncto A, ad rectos angulos inſiſtens plano horolo-<lb/>gii, vel certe recta O P, vt in cap. </s>
  <s xml:id="echoid-s39440" xml:space="preserve">13. </s>
  <s xml:id="echoid-s39441" xml:space="preserve">docuimus, horas à mer. </s>
  <s xml:id="echoid-s39442" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39443" xml:space="preserve">med. </s>
  <s xml:id="echoid-s39444" xml:space="preserve">noc, hoc ordine ſeruato, vt <lb/>horę inter D E, lineam meridianam, quæ indicat horam 12. </s>
  <s xml:id="echoid-s39445" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s39446" xml:space="preserve">punctum C, ſiniſtram <lb/>verſus, ſint à med. </s>
  <s xml:id="echoid-s39447" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39448" xml:space="preserve">quæ verò verſus punctum S, deſcriptę ſunt, computentur à meridie. </s>
  <s xml:id="echoid-s39449" xml:space="preserve">Sed <lb/>ſola hora 6. </s>
  <s xml:id="echoid-s39450" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39451" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39452" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39453" xml:space="preserve">in hoc horologio deſcribi non poteſt, cum circulus horę 6. </s>
  <s xml:id="echoid-s39454" xml:space="preserve">pla-<lb/>num horologii non ſecet, ſed ei ſit ęquidiſtans.</s>
  <s xml:id="echoid-s39455" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1958" type="float" level="2" n="1">
<note position="right" xlink:label="note-0611-04" xlink:href="note-0611-04a" xml:space="preserve">Qua ratiene ex <lb/>horologio Me-<lb/>ridiano Polare <lb/>efficîatur.</note>
  <figure xlink:label="fig-0611-02" xlink:href="fig-0611-02a">
    <image file="0611-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0611-02"/>
  </figure>
<note position="left" xlink:label="note-0611-05" xlink:href="note-0611-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0611-06" xlink:href="note-0611-06a" xml:space="preserve">Quo pacto col-<lb/>locãdum ſit ho <lb/>rologium Pola-<lb/>re, vt horas mon <lb/>ſt@et.</note>
<note position="left" xlink:label="note-0611-07" xlink:href="note-0611-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio he@o <lb/>logii Polaris A-<lb/>ſtronomici.</note>
<p>
  <s xml:id="echoid-s39456" xml:space="preserve">ITAQVE ſi deſcriben dum ſit horologium Polare aſtronomicum, ducendę erunt in plano <lb/>propoſito duæ rectę lineę C S, D E, ſe ſe ad angulos rectos ſecantes in A, quarum D E, meridianã
<pb o="596" file="0612" n="612" rhead="GNOMONICES"/>
lineam referat, adeò vt, ſi planum ſit firmum, ae<unsure/> ſtabile, &amp; </s>
  <s xml:id="echoid-s39457" xml:space="preserve">ęquidiſtans circulo horæ 6. </s>
  <s xml:id="echoid-s39458" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39459" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s39460" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39461" xml:space="preserve">ducenda ſit prius, beneficio libellę, ac perpendiculi, in dato plano recta C S, Horizonti <lb/>ęquidiſtans, &amp; </s>
  <s xml:id="echoid-s39462" xml:space="preserve">ad hanc excitanda perpendicularis D E, pro linea meridiana, quæ priorem ſecet <lb/>in A. </s>
  <s xml:id="echoid-s39463" xml:space="preserve">Deinde in recta D E, ſumenda recta A E, propoſito ſtylo ęqualis: </s>
  <s xml:id="echoid-s39464" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39465" xml:space="preserve">deſcripto circulo cuiuſ-<lb/>uis magnitudinis ex E, reliqua perficienda, vt in Meridiano horologio cap. </s>
  <s xml:id="echoid-s39466" xml:space="preserve">11. </s>
  <s xml:id="echoid-s39467" xml:space="preserve">diximus, &amp;</s>
  <s xml:id="echoid-s39468" xml:space="preserve">c.</s>
  <s xml:id="echoid-s39469" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1960" type="section" level="1" n="503">
<head xml:id="echoid-head532" style="it" xml:space="preserve">DE ARCVBVS SIGNORVM, ET LON-<lb/>gitudinum dierum in horologio Polari. CAP. XVII.</head>
<p>
  <s xml:id="echoid-s39470" xml:space="preserve">ARCVS ſignorum, &amp; </s>
  <s xml:id="echoid-s39471" xml:space="preserve">longitudinum dierum, qui omnes ſunt hyperbolæ, deſcribentur hic, <lb/>
<anchor type="note" xlink:label="note-0612-01a" xlink:href="note-0612-01"/>
vt in Meridiano horologio, ex figura radiorum Zodiaci cap. </s>
  <s xml:id="echoid-s39472" xml:space="preserve">12. </s>
  <s xml:id="echoid-s39473" xml:space="preserve">dummodo memor ſis, li-<lb/>neam, quę ibi ſextę horę deputabatur, hic horam 12. </s>
  <s xml:id="echoid-s39474" xml:space="preserve">referre, &amp;</s>
  <s xml:id="echoid-s39475" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39476" xml:space="preserve">vt ibidem monuimus. </s>
  <s xml:id="echoid-s39477" xml:space="preserve">Horizon <lb/>
<anchor type="note" xlink:label="note-0612-02a" xlink:href="note-0612-02"/>
talis linea ita ducetur. </s>
  <s xml:id="echoid-s39478" xml:space="preserve">Ex B, puncto, vbi hora 9. </s>
  <s xml:id="echoid-s39479" xml:space="preserve">vel 3. </s>
  <s xml:id="echoid-s39480" xml:space="preserve">æquinoctialem lineam interſecat, arcus cir <lb/>culi verſus meridianam lineam deſcribatur, ſurſum verſus, (voco partem ſuperiorem illam, <lb/>quæ ſupra lineam æquinoctialem eſt, poſito horologio in proprio ſitu, ita vt horę à med. <lb/></s>
  <s xml:id="echoid-s39481" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39482" xml:space="preserve">ſint nobis ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s39483" xml:space="preserve">pomeridianę ad dexteram) in quo ſumpto arcu, qui comple-<lb/>mento altitudinis poli ęqualis ſit, ducatur ex fine ipſius ad 9. </s>
  <s xml:id="echoid-s39484" xml:space="preserve">horam, vel 3. </s>
  <s xml:id="echoid-s39485" xml:space="preserve">in linea equino-<lb/>ctiali linea recta, quę lineam horę 12. </s>
  <s xml:id="echoid-s39486" xml:space="preserve">ſecabit in puncto D, per quod recta æquinoctiali lineę pa-<lb/>rallela acta erit Horizontalis diſtribuens totum horologium in duo, quorum maius, in quo <lb/>
<anchor type="note" xlink:label="note-0612-03a" xlink:href="note-0612-03"/>
linea æquinoctialis comprehenditur, ſuperius, vel diurnum, alterum verò inferius noctur-<lb/>num ve appellatur. </s>
  <s xml:id="echoid-s39487" xml:space="preserve">In inferiori tamen mutantur numeri horarum in earum complementa vſque <lb/>ad 12. </s>
  <s xml:id="echoid-s39488" xml:space="preserve">linea meridiana ſignificante horam 12. </s>
  <s xml:id="echoid-s39489" xml:space="preserve">medię noctis, &amp; </s>
  <s xml:id="echoid-s39490" xml:space="preserve">arcus ſignorum auſtralium fiunt <lb/>
<anchor type="note" xlink:label="note-0612-04a" xlink:href="note-0612-04"/>
arcus borealium ſignorum, &amp;</s>
  <s xml:id="echoid-s39491" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39492" xml:space="preserve">Sed ſi idem horologium pro nocturno accipiatur, mutatio hæc <lb/>facienda non eſt. </s>
  <s xml:id="echoid-s39493" xml:space="preserve">Sunt autem arcus ſignorum auſtralium illi, qui exiſtunt ſupra lineam æqui-<lb/>noctialem, verſus horizontalem lineam procedendo: </s>
  <s xml:id="echoid-s39494" xml:space="preserve">borealium verò illi, qui infra ęquino-<lb/>ctialem lineam ſunt deſcripti. </s>
  <s xml:id="echoid-s39495" xml:space="preserve">Exemplum poſitum eſt in pręcedenti capite.</s>
  <s xml:id="echoid-s39496" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1960" type="float" level="2" n="1">
<note position="left" xlink:label="note-0612-01" xlink:href="note-0612-01a" xml:space="preserve">Deſe@i@ti@ ar-<lb/>cuum ſignorũ, <lb/>&amp; longitudinũ <lb/>dierum in Po-<lb/>@arii horologio. <lb/>Hotizontalis li <lb/>mea in horolo-<lb/>gio Polari, quo <lb/>m@do deſcriba <lb/>tur.</note>
<note position="left" xlink:label="note-0612-02" xlink:href="note-0612-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0612-03" xlink:href="note-0612-03a" xml:space="preserve">Horoiogiũ Po-<lb/>late Superius, &amp; <lb/>inferius. Item <lb/>Diurnum, &amp; no <lb/>@ursum quod.</note>
<note position="left" xlink:label="note-0612-04" xlink:href="note-0612-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div1962" type="section" level="1" n="504">
<head xml:id="echoid-head533" style="it" xml:space="preserve">DE HOROLOGIO POLARI ITALICO, <lb/>&amp; Babylonico. CAP. XVIII.</head>
  <figure>
    <image file="0612-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0612-01"/>
  </figure>
<note position="left" xml:space="preserve">30</note>
<note position="left" xml:space="preserve">40</note>
<note position="left" xml:space="preserve">50</note>
<pb o="597" file="0613" n="613" rhead="LIBER SEPTIMVS."/>
<p>
  <s xml:id="echoid-s39497" xml:space="preserve">SECETVR arcus diurnus ♋, a F b, in circulo F G H I, &amp; </s>
  <s xml:id="echoid-s39498" xml:space="preserve">arcus diurnus ♑, d F e, (quorum <lb/>
<anchor type="note" xlink:label="note-0613-01a" xlink:href="note-0613-01"/>
vterque habetur, ſi a puncto F, vtrinque numeretur arcus ſemidiurnus ♋, &amp; </s>
  <s xml:id="echoid-s39499" xml:space="preserve">♑, vſquead pun <lb/>ct<unsure/>a a, b, &amp; </s>
  <s xml:id="echoid-s39500" xml:space="preserve">d, e,) in 24. </s>
  <s xml:id="echoid-s39501" xml:space="preserve">partes ęquales, initio ſumpto à punctis a, d, occidentalibus pro horologio <lb/>Italico, pro Babylonico verò à punctis b, e, orientalibus verſus F, ſemper progrediendo. </s>
  <s xml:id="echoid-s39502" xml:space="preserve">Si enim <lb/>ex punctis diuifionum per centrum rectę occultę ducantur, ſecabitur linea ęquinoctialis in pun-<lb/>ctis, per quę ad ipſam perpendiculares lineę eductę in dicabunt in vtroque tropico puncta hora-<lb/>rum ab occ. </s>
  <s xml:id="echoid-s39503" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39504" xml:space="preserve">or. </s>
  <s xml:id="echoid-s39505" xml:space="preserve">vt in Meridiano horologio factum eſt. </s>
  <s xml:id="echoid-s39506" xml:space="preserve">Quòd ſi aliquę horę non habeant pun-<lb/>cta in alterutro tropicorum, vt ſunt illę, quę in arcubus a G, b I, comprehenduntur, ducendæ <lb/>ſunt illæ per puncta horarum à mer. </s>
  <s xml:id="echoid-s39507" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39508" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39509" xml:space="preserve">in linea ęquinoctiali. </s>
  <s xml:id="echoid-s39510" xml:space="preserve">Omnes enim horę ab or. <lb/></s>
  <s xml:id="echoid-s39511" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39512" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39513" xml:space="preserve">per dictas horas tranſeunt, vt ex tabella cap. </s>
  <s xml:id="echoid-s39514" xml:space="preserve">4. </s>
  <s xml:id="echoid-s39515" xml:space="preserve">manifeſtum eſt. </s>
  <s xml:id="echoid-s39516" xml:space="preserve">Linea autem horæ 12. </s>
  <s xml:id="echoid-s39517" xml:space="preserve">tam <lb/>
<anchor type="note" xlink:label="note-0613-02a" xlink:href="note-0613-02"/>
ab or. </s>
  <s xml:id="echoid-s39518" xml:space="preserve">quam ab occ. </s>
  <s xml:id="echoid-s39519" xml:space="preserve">ducenda eſt parallela lineę ęquinoctiali per punctum in tropico ♋, inuentũ, <lb/>quod quidem ad horam 12. </s>
  <s xml:id="echoid-s39520" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39521" xml:space="preserve">pertinens reperitur ad dexteram lineę meridianę, horam verò <lb/>12. </s>
  <s xml:id="echoid-s39522" xml:space="preserve">ab occ, indicans, ad ſiniſtram.</s>
  <s xml:id="echoid-s39523" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1962" type="float" level="2" n="1">
<note position="right" xlink:label="note-0613-01" xlink:href="note-0613-01a" xml:space="preserve">Compoſitio ho <lb/>rologii Polaris <lb/>Italici<unsure/>, ac Baby <lb/>lonici.</note>
<note position="left" xlink:label="note-0613-02" xlink:href="note-0613-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s39524" xml:space="preserve">HAE autem lineæ horarum ab or. </s>
  <s xml:id="echoid-s39525" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39526" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39527" xml:space="preserve">vltra lineam horizontalem productæ exhibent eaſ-<lb/>
<anchor type="note" xlink:label="note-0613-03a" xlink:href="note-0613-03"/>
dem horas in inferiori horologio Polari, ſi portio illa horologii abſciſſa à linea horizontali in-<lb/>uertatur ſecundum omnes ſui partes, vt in cap. </s>
  <s xml:id="echoid-s39528" xml:space="preserve">9. </s>
  <s xml:id="echoid-s39529" xml:space="preserve">de Verticali horologio diximus.</s>
  <s xml:id="echoid-s39530" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1963" type="float" level="2" n="2">
<note position="right" xlink:label="note-0613-03" xlink:href="note-0613-03a" xml:space="preserve">Quomodo ex <lb/>Polari horolo-<lb/>gio Superiori ef <lb/>ficiatur Polare <lb/>infcrius.</note>
</div>
<p>
  <s xml:id="echoid-s39531" xml:space="preserve">IDEM horologium conſtruemus per arcus diurnos nocturnosq́ue horarum 10. </s>
  <s xml:id="echoid-s39532" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39533" xml:space="preserve">14. </s>
  <s xml:id="echoid-s39534" xml:space="preserve">atque <lb/>
<anchor type="note" xlink:label="note-0613-04a" xlink:href="note-0613-04"/>
etiam 24. </s>
  <s xml:id="echoid-s39535" xml:space="preserve">beneficio tabellarum ad illos arcus pertinentium, vt in ſuperioribus horologiis factum <lb/>eſt. </s>
  <s xml:id="echoid-s39536" xml:space="preserve">Vbi hoc ſolum notandum eſt, lineas horæ 6. </s>
  <s xml:id="echoid-s39537" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39538" xml:space="preserve">18. </s>
  <s xml:id="echoid-s39539" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39540" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39541" xml:space="preserve">cum arcu diurno horarum <lb/>24. </s>
  <s xml:id="echoid-s39542" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39543" xml:space="preserve">nocturno non conuenire, ſed eſſe ἀτυμπτότους, vt ex coroll. </s>
  <s xml:id="echoid-s39544" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s39545" xml:space="preserve">15. </s>
  <s xml:id="echoid-s39546" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39547" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39548" xml:space="preserve">perſpicuum eſt. <lb/></s>
  <s xml:id="echoid-s39549" xml:space="preserve">
<anchor type="note" xlink:label="note-0613-05a" xlink:href="note-0613-05"/>
Quod etiam cap. </s>
  <s xml:id="echoid-s39550" xml:space="preserve">14. </s>
  <s xml:id="echoid-s39551" xml:space="preserve">de horis 12. </s>
  <s xml:id="echoid-s39552" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39553" xml:space="preserve">24. </s>
  <s xml:id="echoid-s39554" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39555" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39556" xml:space="preserve">diximus in Meridiano horologio.</s>
  <s xml:id="echoid-s39557" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1964" type="float" level="2" n="3">
<note position="right" xlink:label="note-0613-04" xlink:href="note-0613-04a" xml:space="preserve">Cõſtruc@o eiuſ-<lb/>dem horologii <lb/>Polaris Italici <lb/>ac Babylonici <lb/>ex arcubus diur <lb/>nis, nocturnisq́;</note>
<note position="left" xlink:label="note-0613-05" xlink:href="note-0613-05a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s39558" xml:space="preserve">QVA ratione autem idem horologium deſcribatur, beneficio lineæ horæ 12. </s>
  <s xml:id="echoid-s39559" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39560" xml:space="preserve">vel occ. <lb/></s>
  <s xml:id="echoid-s39561" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39562" xml:space="preserve">lineæ horizontalis, ſeu horæ 24. </s>
  <s xml:id="echoid-s39563" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39564" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39565" xml:space="preserve">petatur ex propoſ. </s>
  <s xml:id="echoid-s39566" xml:space="preserve">46. </s>
  <s xml:id="echoid-s39567" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39568" xml:space="preserve">47. </s>
  <s xml:id="echoid-s39569" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39570" xml:space="preserve">2.</s>
  <s xml:id="echoid-s39571" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1966" type="section" level="1" n="505">
<head xml:id="echoid-head534" style="it" xml:space="preserve">DE HOROLOGIO POLARI <lb/>Antiquo. CAP. XIX.</head>
<p>
  <s xml:id="echoid-s39572" xml:space="preserve">QVEMADMODVM in præcedentibus, ita &amp; </s>
  <s xml:id="echoid-s39573" xml:space="preserve">hic deſcribemus horas inæquales, ſi arcũ <lb/>
<anchor type="note" xlink:label="note-0613-06a" xlink:href="note-0613-06"/>
diurnum tam ♋, a F b, quàm ♑, d F e, in circulo F G H I, ſecemus in 12. </s>
  <s xml:id="echoid-s39574" xml:space="preserve">partes æquales, <lb/>ex quibus puncta horarum inæqualium in vtroque tropico inquiramus. </s>
  <s xml:id="echoid-s39575" xml:space="preserve">Quod etiam perficie-<lb/>
<anchor type="note" xlink:label="note-0613-07a" xlink:href="note-0613-07"/>
<anchor type="figure" xlink:label="fig-0613-01a" xlink:href="fig-0613-01"/>
<anchor type="note" xlink:label="note-0613-08a" xlink:href="note-0613-08"/>
<anchor type="note" xlink:label="note-0613-09a" xlink:href="note-0613-09"/>
mus beneficio arcuum diurnorum, &amp; </s>
  <s xml:id="echoid-s39576" xml:space="preserve">nocturnorum horarum 18. </s>
  <s xml:id="echoid-s39577" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39578" xml:space="preserve">6. </s>
  <s xml:id="echoid-s39579" xml:space="preserve">Id quod appoſita figura <lb/>perſpicue declarat. </s>
  <s xml:id="echoid-s39580" xml:space="preserve">Vbi etiam lineæ horarum inæqualium vltra horizontalem lineam productæ <lb/>exhibent earundem horarum lineas in inferiori horologio, dummodo portio horologii abſciſſa à <lb/>linea horizontali inuertatur ſecundum omnes ſui partes, vt in cap. </s>
  <s xml:id="echoid-s39581" xml:space="preserve">9. </s>
  <s xml:id="echoid-s39582" xml:space="preserve">tradidimus.</s>
  <s xml:id="echoid-s39583" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1966" type="float" level="2" n="1">
<note position="right" xlink:label="note-0613-06" xlink:href="note-0613-06a" xml:space="preserve">Conſtructio @o <lb/>rologii Polatis <lb/>Antiqui.</note>
<note position="left" xlink:label="note-0613-07" xlink:href="note-0613-07a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0613-01" xlink:href="fig-0613-01a">
    <image file="0613-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0613-01"/>
  </figure>
<note position="left" xlink:label="note-0613-08" xlink:href="note-0613-08a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0613-09" xlink:href="note-0613-09a" xml:space="preserve">50</note>
</div>
<pb o="598" file="0614" n="614" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div1968" type="section" level="1" n="506">
<head xml:id="echoid-head535" style="it" xml:space="preserve">DE HOROLOGIO AEQVINOCTIALI ASTRONOMICO, <lb/>arcubus ſignorum, &amp; longitudinum dierum. CAP. XX.</head>
<p>
  <s xml:id="echoid-s39584" xml:space="preserve">DVCTA recta linea A B, vtcunque pro linea meridiana, vel horæ 12. </s>
  <s xml:id="echoid-s39585" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39586" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39587" xml:space="preserve">noc. <lb/></s>
  <s xml:id="echoid-s39588" xml:space="preserve">
<anchor type="note" xlink:label="note-0614-01a" xlink:href="note-0614-01"/>
quam ad angulos rectos ſecet alia recta C D, in E, pro hora 6. </s>
  <s xml:id="echoid-s39589" xml:space="preserve">ante, &amp; </s>
  <s xml:id="echoid-s39590" xml:space="preserve">poſt meridiem; </s>
  <s xml:id="echoid-s39591" xml:space="preserve">ex E, <lb/>circulus cuiuslibet magnitudinis deſcribatur, isq́ue in 24. </s>
  <s xml:id="echoid-s39592" xml:space="preserve">partes ęquales diuidatur. </s>
  <s xml:id="echoid-s39593" xml:space="preserve">Si enim per <lb/>centrum E, &amp; </s>
  <s xml:id="echoid-s39594" xml:space="preserve">per puncta diuiſionum rectæ lineæ emittantur, deſcriptum erit horologium ęquino <lb/>
<anchor type="note" xlink:label="note-0614-02a" xlink:href="note-0614-02"/>
<anchor type="figure" xlink:label="fig-0614-01a" xlink:href="fig-0614-01"/>
<anchor type="note" xlink:label="note-0614-03a" xlink:href="note-0614-03"/>
<anchor type="note" xlink:label="note-0614-04a" xlink:href="note-0614-04"/>
ctiale. </s>
  <s xml:id="echoid-s39595" xml:space="preserve">Nam ſi in E, figatur ſtylus E F, cuiuſcunque magnitudinis rectus ad planum horologii, ip-<lb/>
<anchor type="note" xlink:label="note-0614-05a" xlink:href="note-0614-05"/>
ſumq́ue horologium ita collocetur, vt recta C D, Horizonti æquidiſtet, &amp; </s>
  <s xml:id="echoid-s39596" xml:space="preserve">recta A B, in plano cir-<lb/>culi Meridiani ſtatuatur, tanquam communis ſectio plani horologii, &amp; </s>
  <s xml:id="echoid-s39597" xml:space="preserve">Meridiani, punctum de-<lb/>nique A, ex parte meridiei (puncto B, ad Boream vergente; </s>
  <s xml:id="echoid-s39598" xml:space="preserve">C, ad ortum, &amp; </s>
  <s xml:id="echoid-s39599" xml:space="preserve">D, ad occaſum) eleue-<lb/>uetur ſecundum complementum altitudinis poli ſupra Horizontem, hoc eſt, recta A B, cum li-<lb/>nea meridiana in plano Horizontis conſtituat ad partes B, angulum complementi altitudinis po-<lb/>li, oſtendet ſtylus E F, horas à meridie, vel media nocte, hoc ordine inter eas ſeruato, vt horę ad <lb/>dexteram lineæ meridianæ A B, à media nocte, ad ſiniſtram verò à meridie numerentur.</s>
  <s xml:id="echoid-s39600" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1968" type="float" level="2" n="1">
<note position="left" xlink:label="note-0614-01" xlink:href="note-0614-01a" xml:space="preserve">Compoſitio ho-<lb/>rologii Aequi-<lb/>nocti<unsure/>alis Aſtro-<lb/>nomico.</note>
<note position="left" xlink:label="note-0614-02" xlink:href="note-0614-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0614-01" xlink:href="fig-0614-01a">
    <image file="0614-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0614-01"/>
  </figure>
<note position="left" xlink:label="note-0614-03" xlink:href="note-0614-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0614-04" xlink:href="note-0614-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0614-05" xlink:href="note-0614-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s39601" xml:space="preserve">ARCVS ſignorum, &amp; </s>
  <s xml:id="echoid-s39602" xml:space="preserve">longitudinum dierum, qui in hoc horologio omnes circuli ſunt, ita <lb/>
<anchor type="note" xlink:label="note-0614-06a" xlink:href="note-0614-06"/>
deſcribentur. </s>
  <s xml:id="echoid-s39603" xml:space="preserve">In figura radiorũ Zodiaci cap. </s>
  <s xml:id="echoid-s39604" xml:space="preserve">12. </s>
  <s xml:id="echoid-s39605" xml:space="preserve">ſumatur in axe D G, recta D q, ſiniſtrorſum, vel <lb/>D h, dextrorſum, ſtylo horologij æqualis, &amp; </s>
  <s xml:id="echoid-s39606" xml:space="preserve">per q, vel h, radio Aequatoris D C, parallela agatur <lb/>
<anchor type="note" xlink:label="note-0614-07a" xlink:href="note-0614-07"/>
q n, vel h l, ſecans radios ſignorum, &amp; </s>
  <s xml:id="echoid-s39607" xml:space="preserve">longitudinum dierum in punctis p, o, n, &amp;</s>
  <s xml:id="echoid-s39608" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39609" xml:space="preserve">Nam ſi ex cen-<lb/>tro horologii E, deſcribantur circuli ſecundum in terualla q p, q o, q n, &amp;</s>
  <s xml:id="echoid-s39610" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39611" xml:space="preserve">deſcripti erunt arcus <lb/>ſignorum, ac longitudinum dierum, ita vt in horologio ſuperiori omnes arcus ſint boreales, &amp; </s>
  <s xml:id="echoid-s39612" xml:space="preserve"><lb/>maxime borealis is, qui centro E, proximus eſt. </s>
  <s xml:id="echoid-s39613" xml:space="preserve">In inferiori verò omnes auſtrales, &amp; </s>
  <s xml:id="echoid-s39614" xml:space="preserve">proximus cen <lb/>tro E, maxime auſtralis. </s>
  <s xml:id="echoid-s39615" xml:space="preserve">Itaque in illo circulus ſecundum ſemidiametrum q p, deſcriptus erit ar-<lb/>cus ♋, ſequens ♊, &amp; </s>
  <s xml:id="echoid-s39616" xml:space="preserve">♌, &amp; </s>
  <s xml:id="echoid-s39617" xml:space="preserve">tertius ♉, &amp; </s>
  <s xml:id="echoid-s39618" xml:space="preserve">♍; </s>
  <s xml:id="echoid-s39619" xml:space="preserve">In hoc verò primus erit ♑, ſequens ♐, &amp; </s>
  <s xml:id="echoid-s39620" xml:space="preserve">♒, tertius <lb/>♏, &amp; </s>
  <s xml:id="echoid-s39621" xml:space="preserve">♓; </s>
  <s xml:id="echoid-s39622" xml:space="preserve">ſed quonam pacto inferius à ſuperiori ortum habet, linea horizontalis patefaciet, quam <lb/>ſic delineabimus.</s>
  <s xml:id="echoid-s39623" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1969" type="float" level="2" n="2">
<note position="left" xlink:label="note-0614-06" xlink:href="note-0614-06a" xml:space="preserve">Deſcriotio at-<lb/>cuum ſignorũ, <lb/>&amp; longitudiũ <lb/>dierum in horo <lb/>logio æquino-<lb/>cti<unsure/>ali.</note>
<note position="left" xlink:label="note-0614-07" xlink:href="note-0614-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s39624" xml:space="preserve">IN linea horæ 6. </s>
  <s xml:id="echoid-s39625" xml:space="preserve">C D, ſumatur recta E l, longitudini ſtyli E F, æqualis, &amp; </s>
  <s xml:id="echoid-s39626" xml:space="preserve">ex l, arcus circuli <lb/>
<anchor type="note" xlink:label="note-0614-08a" xlink:href="note-0614-08"/>
deſcribatur verſus meridianam lineam, in quo ſi accipiatur arcus altitudini poli æqualis, &amp; </s>
  <s xml:id="echoid-s39627" xml:space="preserve">ex ſi-<lb/>ne illius ad l, recta ducatur, ſecabitur linea meridiana A B, in puncto m, per quod recta lineam
<pb o="599" file="0615" n="615" rhead="LIBER SEPTIMVS."/>
meridianam ſecans ad angulos rectos ducta erit horizontalis diſtinguens totum horologium in <lb/>duo, quorum maius, in quo centrum E, exiſtit, ſuperius aut diurnum, alterum verò inferius <lb/>nocturnum ve nuncupatur. </s>
  <s xml:id="echoid-s39628" xml:space="preserve">In inferiori tamen mutantur numeri horarum in complementa vſq; <lb/></s>
  <s xml:id="echoid-s39629" xml:space="preserve">ad 12. </s>
  <s xml:id="echoid-s39630" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39631" xml:space="preserve">arcus ſignorum borealium commutantur in arcus ſignorum auſtralium: </s>
  <s xml:id="echoid-s39632" xml:space="preserve">in nocturno <lb/>autem non item. </s>
  <s xml:id="echoid-s39633" xml:space="preserve">Aequinoctialis circulus in hoc horologio deſignari nõ poteſt, quia planum ho-<lb/>rologii non ſecat, ſed ei æquidiſtat. </s>
  <s xml:id="echoid-s39634" xml:space="preserve">Vnde eius communis ſectio cum plano horologii, quæ debe-<lb/>ret ei<unsure/>ſe linea recta, euaneſcit, vt propoſ. </s>
  <s xml:id="echoid-s39635" xml:space="preserve">11. </s>
  <s xml:id="echoid-s39636" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39637" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39638" xml:space="preserve">demonſtrauimus.</s>
  <s xml:id="echoid-s39639" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1970" type="float" level="2" n="3">
<note position="left" xlink:label="note-0614-08" xlink:href="note-0614-08a" xml:space="preserve">Hotizontalis li <lb/>neæ deſcriptio <lb/>in horologio æ-<lb/>quinoctiali.</note>
</div>
<p>
  <s xml:id="echoid-s39640" xml:space="preserve">QVONIAM verò, Sole exiſtente in Aequatote, vmbra ſtyli infinita eſt, &amp; </s>
  <s xml:id="echoid-s39641" xml:space="preserve">paulo ante, &amp; </s>
  <s xml:id="echoid-s39642" xml:space="preserve">poſt <lb/>
<anchor type="note" xlink:label="note-0615-01a" xlink:href="note-0615-01"/>
æquinoctia propemodum etiam infinita, producendæ erunt lineæ horariæ in horologio ſuperiori <lb/>vltra circulum ♉, &amp; </s>
  <s xml:id="echoid-s39643" xml:space="preserve">♍, quantum magnitudo plani, in quo horologium deſcribitur, patitur, vt il-<lb/>
<anchor type="note" xlink:label="note-0615-02a" xlink:href="note-0615-02"/>
lis diebus ante, &amp; </s>
  <s xml:id="echoid-s39644" xml:space="preserve">poſt æquinoctia horas gnomon demonſtrare poſſit. </s>
  <s xml:id="echoid-s39645" xml:space="preserve">Vel certè deſcribendus erit <lb/>circulus alicuius gradus prope æquinoctialem circulum, nempe grad. </s>
  <s xml:id="echoid-s39646" xml:space="preserve">25. </s>
  <s xml:id="echoid-s39647" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s39648" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39649" xml:space="preserve">♉, vel 20. </s>
  <s xml:id="echoid-s39650" xml:space="preserve">♍, &amp; </s>
  <s xml:id="echoid-s39651" xml:space="preserve"><lb/>10. </s>
  <s xml:id="echoid-s39652" xml:space="preserve">♍, &amp;</s>
  <s xml:id="echoid-s39653" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39654" xml:space="preserve">Idem intelligatur in horologio inferiori debere fieri in ſignis auſtralibus, habita ſem-<lb/>per ratione magnitudinis plani horologij. </s>
  <s xml:id="echoid-s39655" xml:space="preserve">Hoc etiam de horis Italicis, ac Babylonicis intel-<lb/>ligendum eſt.</s>
  <s xml:id="echoid-s39656" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1971" type="float" level="2" n="4">
<note position="right" xlink:label="note-0615-01" xlink:href="note-0615-01a" xml:space="preserve">Quid agendum <lb/>ſit, vt vmbra ſty <lb/>li horas indicet <lb/>prope tempus <lb/>ęquinoctiorum.</note>
<note position="left" xlink:label="note-0615-02" xlink:href="note-0615-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s39657" xml:space="preserve">CAETERVM in horologio ſuperiori portio lineæ meridianæ E B, indicat horam 12. </s>
  <s xml:id="echoid-s39658" xml:space="preserve">me-<lb/>ridiei, &amp; </s>
  <s xml:id="echoid-s39659" xml:space="preserve">reliqua portio E A, horam 12. </s>
  <s xml:id="echoid-s39660" xml:space="preserve">mediæ noctis. </s>
  <s xml:id="echoid-s39661" xml:space="preserve">In inferiori autem horologio cõtrario mo-<lb/>do res ſe habet. </s>
  <s xml:id="echoid-s39662" xml:space="preserve">Nam portio E B, horam 12. </s>
  <s xml:id="echoid-s39663" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s39664" xml:space="preserve">portio reliqua E A, horam 12. </s>
  <s xml:id="echoid-s39665" xml:space="preserve">me-<lb/>ridiei ſignificat.</s>
  <s xml:id="echoid-s39666" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">20</note>
</div>
<div xml:id="echoid-div1973" type="section" level="1" n="507">
<head xml:id="echoid-head536" style="it" xml:space="preserve">DE HOROLOGIO AEQVINOCTIALI, <lb/>Italico, &amp; Babylonico. CAP. XXI.</head>
<p>
  <s xml:id="echoid-s39667" xml:space="preserve">DIVIDANTVR ſinguli arcus ſignorum, vel duo ſaltem, (quod ſatis eſt) interior, &amp; </s>
  <s xml:id="echoid-s39668" xml:space="preserve">exte-<lb/>
<anchor type="note" xlink:label="note-0615-04a" xlink:href="note-0615-04"/>
rior, in 24. </s>
  <s xml:id="echoid-s39669" xml:space="preserve">partes æquaìes, initio facto à linea horizontali ex parte ſiniſtra pro horologio Ita <lb/>lico, ex dextra verò pro Babylonico. </s>
  <s xml:id="echoid-s39670" xml:space="preserve">Deinde per proxima puncta horum arcuum ſupra, vel infra <lb/>lineam horizontalem linea recta ducatur, necnon per proximè ſequentia puncta, &amp; </s>
  <s xml:id="echoid-s39671" xml:space="preserve">ita deinceps, <lb/>donec per omnia puncta lineæ rectæ ductæ ſint. </s>
  <s xml:id="echoid-s39672" xml:space="preserve">Hæ enim rectæ horas ab or. </s>
  <s xml:id="echoid-s39673" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39674" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s39675" xml:space="preserve">indicabunt in <lb/>horologio ſuperiori, ac propterea horologium æquinoctiale Italicum, &amp; </s>
  <s xml:id="echoid-s39676" xml:space="preserve">Babylonicum ſuperius <lb/>deſcriptum erit, in quo horarum numerus, &amp; </s>
  <s xml:id="echoid-s39677" xml:space="preserve">ordo hic eſt. </s>
  <s xml:id="echoid-s39678" xml:space="preserve">Proxima linea ſupra horizontalem li-<lb/>
<anchor type="note" xlink:label="note-0615-05a" xlink:href="note-0615-05"/>
neam, quæ horam 24. </s>
  <s xml:id="echoid-s39679" xml:space="preserve">indicat, hoc eſt, in horologio nocturno (quod à linea horizontali abſcindi-<lb/>tur) ad ſiniſtram monſtrat horam 1. </s>
  <s xml:id="echoid-s39680" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39681" xml:space="preserve">ſequens 2. </s>
  <s xml:id="echoid-s39682" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39683" xml:space="preserve">ſic deinceps, ita vt proxima linea infra <lb/>horizontalem lineam ex eadem parte ſiniſtra indicet horam 23. </s>
  <s xml:id="echoid-s39684" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39685" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39686" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39687" xml:space="preserve">Rurſus prima linea <lb/>infra lineam horizontalem ex parte dextra oſtendit horam 1. </s>
  <s xml:id="echoid-s39688" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39689" xml:space="preserve">ſequens 2. </s>
  <s xml:id="echoid-s39690" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s39691" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39692" xml:space="preserve">vt ex figura con <lb/>ſtat. </s>
  <s xml:id="echoid-s39693" xml:space="preserve">Hæautem lineæ productæ, vltra horizontalem lineam efficiunt horologium Italicum, &amp; </s>
  <s xml:id="echoid-s39694" xml:space="preserve"><lb/>Babylonicum inferius, ſi inuertantur omnes partes inferioris horologii, vt de Verticali boreali, &amp; </s>
  <s xml:id="echoid-s39695" xml:space="preserve"><lb/>polari inferiori diximus. <lb/></s>
  <s xml:id="echoid-s39696" xml:space="preserve">
<anchor type="note" xlink:label="note-0615-06a" xlink:href="note-0615-06"/>
</s>
</p>
<div xml:id="echoid-div1973" type="float" level="2" n="1">
<note position="right" xlink:label="note-0615-04" xlink:href="note-0615-04a" xml:space="preserve">Conſtructio ho <lb/>rologii Aequi-<lb/>noctiali<unsure/>s Italici <lb/>ac Babyloniei.</note>
<note position="left" xlink:label="note-0615-05" xlink:href="note-0615-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0615-06" xlink:href="note-0615-06a" xml:space="preserve">Alia deſcriptio <lb/>horologii Ae <lb/>quinoctialis Ita <lb/>lici &amp; Babyloni <lb/>ci per arcus diur <lb/>nos, &amp; noctur-<lb/>nos.</note>
</div>
<p>
  <s xml:id="echoid-s39697" xml:space="preserve">VTRVMQVE horologium deſcribi etiam poterit per arcus diurnos, nocturnosq́ue hora-<lb/>rum 10. </s>
  <s xml:id="echoid-s39698" xml:space="preserve">14. </s>
  <s xml:id="echoid-s39699" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39700" xml:space="preserve">24. </s>
  <s xml:id="echoid-s39701" xml:space="preserve">vt in præcedentibus factum eſt. </s>
  <s xml:id="echoid-s39702" xml:space="preserve">Nam hora 23. </s>
  <s xml:id="echoid-s39703" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39704" xml:space="preserve">v.</s>
  <s xml:id="echoid-s39705" xml:space="preserve">g. </s>
  <s xml:id="echoid-s39706" xml:space="preserve">ducitur per horam <lb/>6. </s>
  <s xml:id="echoid-s39707" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39708" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39709" xml:space="preserve">Et quia eadem vltra arcum diurnum horarum 24. </s>
  <s xml:id="echoid-s39710" xml:space="preserve">qui hori <lb/>
<anchor type="note" xlink:label="note-0615-07a" xlink:href="note-0615-07"/>
zontalem lineam in puncto m, tangit, producta indicat horam 23. </s>
  <s xml:id="echoid-s39711" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39712" xml:space="preserve">vt lib. </s>
  <s xml:id="echoid-s39713" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39714" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s39715" xml:space="preserve">10. </s>
  <s xml:id="echoid-s39716" xml:space="preserve">de-<lb/>monſtratum eſt à nobis, tranſit autem hora 23. </s>
  <s xml:id="echoid-s39717" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39718" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s39719" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39720" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39721" xml:space="preserve">in arcu nocturno <lb/>horarum 10. </s>
  <s xml:id="echoid-s39722" xml:space="preserve">idcirco, vt rectè ducatur hora 23. </s>
  <s xml:id="echoid-s39723" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39724" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s39725" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39726" xml:space="preserve">in arcu diurno hora-<lb/>rum 14. </s>
  <s xml:id="echoid-s39727" xml:space="preserve">accipienda etiam erit hora 4. </s>
  <s xml:id="echoid-s39728" xml:space="preserve">à media nocte reſpondens horæ 23. </s>
  <s xml:id="echoid-s39729" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39730" xml:space="preserve">in arcu noctur-<lb/>no horarum 10. </s>
  <s xml:id="echoid-s39731" xml:space="preserve">Eadem ratione hora 22. </s>
  <s xml:id="echoid-s39732" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39733" xml:space="preserve">ducitur per horam 5. </s>
  <s xml:id="echoid-s39734" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39735" xml:space="preserve">in arcu diurno ho-<lb/>rarum 14. </s>
  <s xml:id="echoid-s39736" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39737" xml:space="preserve">per horam 3. </s>
  <s xml:id="echoid-s39738" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39739" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39740" xml:space="preserve">arcus nocturni horarum 10. </s>
  <s xml:id="echoid-s39741" xml:space="preserve">quæ horæ 22. </s>
  <s xml:id="echoid-s39742" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39743" xml:space="preserve">reſpõdet. <lb/></s>
  <s xml:id="echoid-s39744" xml:space="preserve">Atque ita deinceps, accipiẽdo ſemper in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39745" xml:space="preserve">vnum punctum pro hora qua-<lb/>libet ab occ. </s>
  <s xml:id="echoid-s39746" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39747" xml:space="preserve">alterum in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s39748" xml:space="preserve">vel etiam diurno horarum 14. </s>
  <s xml:id="echoid-s39749" xml:space="preserve">pro eadem <lb/>hora ab ortu, prout tabellæ ſcholii propoſ. </s>
  <s xml:id="echoid-s39750" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39751" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39752" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39753" xml:space="preserve">indicabunt. </s>
  <s xml:id="echoid-s39754" xml:space="preserve">Ita vides horam 11. </s>
  <s xml:id="echoid-s39755" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39756" xml:space="preserve">ductã <lb/>eſſe per horam 6. </s>
  <s xml:id="echoid-s39757" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39758" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39759" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39760" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39761" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s39762" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39763" xml:space="preserve">in eodem arcu, <lb/>
<anchor type="note" xlink:label="note-0615-08a" xlink:href="note-0615-08"/>
quæ conuenit horæ 11. </s>
  <s xml:id="echoid-s39764" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s39765" xml:space="preserve">Hac enim ratione facile horologium Italicum componetur. </s>
  <s xml:id="echoid-s39766" xml:space="preserve">Eo-<lb/>demq́ue modo Babylonicum conficietur, ſi pro qualibet hora ab ortu ſumatur vnum punctum <lb/>in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39767" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39768" xml:space="preserve">alterum in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s39769" xml:space="preserve">vel etiam diurno hora-<lb/>rum 14. </s>
  <s xml:id="echoid-s39770" xml:space="preserve">pro eadem hora ab occ. </s>
  <s xml:id="echoid-s39771" xml:space="preserve">Ita cernis horam 1. </s>
  <s xml:id="echoid-s39772" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39773" xml:space="preserve">tranſire per horam 6. </s>
  <s xml:id="echoid-s39774" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39775" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39776" xml:space="preserve">in <lb/>arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39777" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39778" xml:space="preserve">horam 1. </s>
  <s xml:id="echoid-s39779" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39780" xml:space="preserve">per horam 8. </s>
  <s xml:id="echoid-s39781" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39782" xml:space="preserve">in arcu nocturno horarum 10. <lb/></s>
  <s xml:id="echoid-s39783" xml:space="preserve">Item horam 13. </s>
  <s xml:id="echoid-s39784" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39785" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s39786" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39787" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s39788" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39789" xml:space="preserve">horam 13. </s>
  <s xml:id="echoid-s39790" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39791" xml:space="preserve">per <lb/>horam 8. </s>
  <s xml:id="echoid-s39792" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39793" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39794" xml:space="preserve">in eodem arcu, &amp; </s>
  <s xml:id="echoid-s39795" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s39796" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0615-09a" xlink:href="note-0615-09"/>
</s>
</p>
<div xml:id="echoid-div1974" type="float" level="2" n="2">
<note position="left" xlink:label="note-0615-07" xlink:href="note-0615-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0615-08" xlink:href="note-0615-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0615-09" xlink:href="note-0615-09a" xml:space="preserve">Alia adhuc de-<lb/>ſcripto horolo-<lb/>gii Aequinoctia <lb/>lis Italici, &amp; Ba <lb/>byloniei per ar-<lb/>cus diurnos no-<lb/>cturno@que.</note>
</div>
<p>
  <s xml:id="echoid-s39797" xml:space="preserve">SED multo facilius vtrumque horologium delineabitur beneficio arcus diurni horarum 14. <lb/></s>
  <s xml:id="echoid-s39798" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39799" xml:space="preserve">arcus diurni horarum 24. </s>
  <s xml:id="echoid-s39800" xml:space="preserve">Nam v.</s>
  <s xml:id="echoid-s39801" xml:space="preserve">g. </s>
  <s xml:id="echoid-s39802" xml:space="preserve">hora 23. </s>
  <s xml:id="echoid-s39803" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39804" xml:space="preserve">tranſit per horam 6. </s>
  <s xml:id="echoid-s39805" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39806" xml:space="preserve">in arcu diurno <lb/>horarum 14. </s>
  <s xml:id="echoid-s39807" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39808" xml:space="preserve">per horam 11. </s>
  <s xml:id="echoid-s39809" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39810" xml:space="preserve">in arcu diurno horarum 24. </s>
  <s xml:id="echoid-s39811" xml:space="preserve">Item hora 8. </s>
  <s xml:id="echoid-s39812" xml:space="preserve">ab ortu ducitur <lb/>per horam 1. </s>
  <s xml:id="echoid-s39813" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39814" xml:space="preserve">in priori arcu, &amp; </s>
  <s xml:id="echoid-s39815" xml:space="preserve">in poſteriori per horam 8. </s>
  <s xml:id="echoid-s39816" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39817" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39818" xml:space="preserve">Denique in inferiori
<pb o="600" file="0616" n="616" rhead="GNOMONICES"/>
horologio hora 17. </s>
  <s xml:id="echoid-s39819" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s39820" xml:space="preserve">ducitur per horam 10. </s>
  <s xml:id="echoid-s39821" xml:space="preserve">à media nocte in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s39822" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39823" xml:space="preserve"><lb/>per horam 5. </s>
  <s xml:id="echoid-s39824" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s39825" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39826" xml:space="preserve">in arcu nocturno horarum 24. </s>
  <s xml:id="echoid-s39827" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39828" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39829" xml:space="preserve">vt horum arcuum tabellæ in ſcho-<lb/>lio propoſ. </s>
  <s xml:id="echoid-s39830" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39831" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39832" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39833" xml:space="preserve">deſcriptæ docent: </s>
  <s xml:id="echoid-s39834" xml:space="preserve">aduertendum tamen eſt, horas à mer. </s>
  <s xml:id="echoid-s39835" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39836" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39837" xml:space="preserve">in ſup@ <lb/>
<anchor type="figure" xlink:label="fig-0616-01a" xlink:href="fig-0616-01"/>
<anchor type="note" xlink:label="note-0616-01a" xlink:href="note-0616-01"/>
<anchor type="note" xlink:label="note-0616-02a" xlink:href="note-0616-02"/>
<anchor type="note" xlink:label="note-0616-03a" xlink:href="note-0616-03"/>
riori horologio, &amp; </s>
  <s xml:id="echoid-s39838" xml:space="preserve">inferiori eaſdem eſſe, dummodo quæ in ſuperiori à mer. </s>
  <s xml:id="echoid-s39839" xml:space="preserve">numerantur, in infe-<lb/>riori ſupputentur à med. </s>
  <s xml:id="echoid-s39840" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39841" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39842" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s39843" xml:space="preserve">Quod quidem fit propter inuerſionem omnium partiũ <lb/>inferioris horologii, quæ inuerſio omnino neceſſaria eſt in horologio Italico, &amp; </s>
  <s xml:id="echoid-s39844" xml:space="preserve">Babylonico. </s>
  <s xml:id="echoid-s39845" xml:space="preserve">Vn-<lb/>de cum ſupra in cap. </s>
  <s xml:id="echoid-s39846" xml:space="preserve">20. </s>
  <s xml:id="echoid-s39847" xml:space="preserve">docuimus horas à mer. </s>
  <s xml:id="echoid-s39848" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39849" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39850" xml:space="preserve">in inferiori horologio mutandas <lb/>eſſe in earum complementa vſque ad 12. </s>
  <s xml:id="echoid-s39851" xml:space="preserve">intelligendum eſt, ſi non fiat prædicta partium inuerſio. <lb/></s>
  <s xml:id="echoid-s39852" xml:space="preserve">Sed ſatius erit inferius horologium Italicum, &amp; </s>
  <s xml:id="echoid-s39853" xml:space="preserve">Babylonicum ex ſuperiori deducere, veluti paulo <lb/>ante tradidimus.</s>
  <s xml:id="echoid-s39854" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1975" type="float" level="2" n="3">
  <figure xlink:label="fig-0616-01" xlink:href="fig-0616-01a">
    <image file="0616-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0616-01"/>
  </figure>
<note position="left" xlink:label="note-0616-01" xlink:href="note-0616-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0616-02" xlink:href="note-0616-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0616-03" xlink:href="note-0616-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s39855" xml:space="preserve">NON eſt autem hic prętereundum, lineas horarum ab or. </s>
  <s xml:id="echoid-s39856" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39857" xml:space="preserve">tangere circulum horarũ <lb/>
<anchor type="note" xlink:label="note-0616-04a" xlink:href="note-0616-04"/>
<anchor type="note" xlink:label="note-0616-05a" xlink:href="note-0616-05"/>
24. </s>
  <s xml:id="echoid-s39858" xml:space="preserve">in punctis, vbi à lineis horarum aſtronomicarum ſecatur, atque adeo has ab illis ibidem ſe-<lb/>cari ad angulos rectos, vt lib. </s>
  <s xml:id="echoid-s39859" xml:space="preserve">2. </s>
  <s xml:id="echoid-s39860" xml:space="preserve">demonſtrauimus propoſ. </s>
  <s xml:id="echoid-s39861" xml:space="preserve">58. </s>
  <s xml:id="echoid-s39862" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39863" xml:space="preserve">59.</s>
  <s xml:id="echoid-s39864" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1976" type="float" level="2" n="4">
<note position="left" xlink:label="note-0616-04" xlink:href="note-0616-04a" xml:space="preserve">Lineæ horarum <lb/>ab or. &amp; occ.@ <lb/>tangunt circu-<lb/>lum horatũ 24. <lb/>in horis à mer. <lb/>&amp; med.noc.</note>
<note position="left" xlink:label="note-0616-05" xlink:href="note-0616-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s39865" xml:space="preserve">SED &amp; </s>
  <s xml:id="echoid-s39866" xml:space="preserve">hic intueri licet communes interſectiones horarum à mer. </s>
  <s xml:id="echoid-s39867" xml:space="preserve">vel med.</s>
  <s xml:id="echoid-s39868" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39869" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39870" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39871" xml:space="preserve">vel <lb/>occ. </s>
  <s xml:id="echoid-s39872" xml:space="preserve">quas faciunt in linea horizontali ſeu horæ 24. </s>
  <s xml:id="echoid-s39873" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39874" xml:space="preserve">in linea horę 12. </s>
  <s xml:id="echoid-s39875" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s39876" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39877" xml:space="preserve">necnon inter-<lb/>ſectiones mutuas, quas faciunt horæ ab or. </s>
  <s xml:id="echoid-s39878" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s39879" xml:space="preserve">in linea hor. </s>
  <s xml:id="echoid-s39880" xml:space="preserve">6. </s>
  <s xml:id="echoid-s39881" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s39882" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s39883" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39884" xml:space="preserve">vt ex tabu-<lb/>lis in ſcholio propoſ. </s>
  <s xml:id="echoid-s39885" xml:space="preserve">20. </s>
  <s xml:id="echoid-s39886" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39887" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39888" xml:space="preserve">poſitis perſpicuum eſt.</s>
  <s xml:id="echoid-s39889" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div1978" type="section" level="1" n="508">
<head xml:id="echoid-head537" style="it" xml:space="preserve">DE HOROLOGIO AEQVINOCTIALI <lb/>Antiquo. CAP. XXII.</head>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s39890" xml:space="preserve">DIVIDANTVR ſingulæ portiones arcuum ſignorum, quas horizontalis linea abſcindit, <lb/>
<anchor type="note" xlink:label="note-0616-07a" xlink:href="note-0616-07"/>
in vtroque horologio tam ſuperiori, quàm inferiori, in 12. </s>
  <s xml:id="echoid-s39891" xml:space="preserve">partes æquales: </s>
  <s xml:id="echoid-s39892" xml:space="preserve">ſatis autem eſt, <lb/>hoc præſtare in circulo interiori, &amp; </s>
  <s xml:id="echoid-s39893" xml:space="preserve">exteriori. </s>
  <s xml:id="echoid-s39894" xml:space="preserve">Deinde per puncta proxima infra lineam horizon-<lb/>talem linea recta ducatur, idemq́ue fiat in ſequentibus deinceps punctis ſibi reſpondentibus. </s>
  <s xml:id="echoid-s39895" xml:space="preserve">Hoc <lb/>enim facto, deſcriptum erit horologium Antiquum. </s>
  <s xml:id="echoid-s39896" xml:space="preserve">Nam proxima linea infra lineam horizon-<lb/>talem, ex parte quidem dextra in ſuperiori horologio, ex ſiniſtra verò in inferiori, dabit horam 1. <lb/></s>
  <s xml:id="echoid-s39897" xml:space="preserve">inæqualem, ſequens 2. </s>
  <s xml:id="echoid-s39898" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39899" xml:space="preserve">c. </s>
  <s xml:id="echoid-s39900" xml:space="preserve">Verum &amp; </s>
  <s xml:id="echoid-s39901" xml:space="preserve">hic horæ in ſuperiori horologio protractæ vltra lineam ho <lb/>rizontalem dant eiuſdem horas in inferiori, ſi omnes eius partes inuertantur, vt ſupra dictum eſt. </s>
  <s xml:id="echoid-s39902" xml:space="preserve"><lb/>Itaque ſingulæ lineæ horarum inæqualium tranſeunt per ſena puncta diuiſionum arcuum ſigno-<lb/>rum, quorum terna in horologio ſuperiori, &amp; </s>
  <s xml:id="echoid-s39903" xml:space="preserve">terna in inferiori exiſtunt.</s>
  <s xml:id="echoid-s39904" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1978" type="float" level="2" n="1">
<note position="left" xlink:label="note-0616-07" xlink:href="note-0616-07a" xml:space="preserve">Deſctiptio ho-<lb/>rologii Aequi-<lb/>noctialis Anti-<lb/>qui.</note>
</div>
<pb o="601" file="0617" n="617" rhead="LIBER SEPTIMVS."/>
  <figure>
    <image file="0617-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0617-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s39905" xml:space="preserve">ANTIQVVM quoque horologium facili negotio deſcribi poteſt per areum diurnum ho-<lb/>
<anchor type="note" xlink:label="note-0617-04a" xlink:href="note-0617-04"/>
rarum 18. </s>
  <s xml:id="echoid-s39906" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39907" xml:space="preserve">nocturnum horarum 6. </s>
  <s xml:id="echoid-s39908" xml:space="preserve">vt in ſuperioribus factum eſt, &amp; </s>
  <s xml:id="echoid-s39909" xml:space="preserve">ex tabellis in hunc vſum <lb/>confectis in ſcholio propoſ. </s>
  <s xml:id="echoid-s39910" xml:space="preserve">33. </s>
  <s xml:id="echoid-s39911" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39912" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39913" xml:space="preserve">colligitur, perſpicueq́ue in appoſita figura apparet.</s>
  <s xml:id="echoid-s39914" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1979" type="float" level="2" n="2">
<note position="right" xlink:label="note-0617-04" xlink:href="note-0617-04a" xml:space="preserve">Alia deſeripti@ <lb/>horologii Aequi <lb/>noctialis Anti-<lb/>qui per arcum <lb/>diurnum hora <lb/>rũ 18. &amp; noctur <lb/>nũ horarum 6.</note>
</div>
</div>
<div xml:id="echoid-div1981" type="section" level="1" n="509">
<head xml:id="echoid-head538" style="it" xml:space="preserve">DE HOROLOGIO ASTRONOMICO, QVOD <lb/>à Verticali circulo declinat. CAP. XXIII.</head>
<p>
  <s xml:id="echoid-s39915" xml:space="preserve">ANTE omnia inueſtiganda eſt declinatio plani, in quo horologium deſcribendum eſt, vt <lb/>
<anchor type="note" xlink:label="note-0617-05a" xlink:href="note-0617-05"/>
propoſ. </s>
  <s xml:id="echoid-s39916" xml:space="preserve">23. </s>
  <s xml:id="echoid-s39917" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39918" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39919" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39920" xml:space="preserve">in ſcholio eiuſdem tradidimus. </s>
  <s xml:id="echoid-s39921" xml:space="preserve">Quoniam enim ibi copiose de declina-<lb/>
<anchor type="note" xlink:label="note-0617-06a" xlink:href="note-0617-06"/>
tione, inclinationeq́ue planorum diſſeruimus, nihil prorſus hoc loco ea de re dicendum eſſe vi-<lb/>detur. </s>
  <s xml:id="echoid-s39922" xml:space="preserve">Inuenta autem declinatione, ad deſcriptionem horologii à Verticali declinantis aggredie-<lb/>mur, hoc modo. </s>
  <s xml:id="echoid-s39923" xml:space="preserve">In plano horologii, aſſumpto loco ſtyli vtcunque in K, ducantur per K, duæ re-<lb/>ctæ A B, D F, ſeſe in k, ad angulos rectos ſecantes, vel ſi planum ſtabile ſit, &amp; </s>
  <s xml:id="echoid-s39924" xml:space="preserve">ad Horizontem re-<lb/>ctum, ducatur per K, recta A B, <emph style="sc">H</emph>orizonti æquidiſtans beneficio libellæ, &amp; </s>
  <s xml:id="echoid-s39925" xml:space="preserve">perpendiculi, quam <lb/>ad rectos angulos ſecet D F, perpendicularis ad Horizontem: </s>
  <s xml:id="echoid-s39926" xml:space="preserve">Vel certe primo loco ducatur be-<lb/>neficio perpendiculi recta F D, ad Horizontem perpendicularis, quam in K, ſecet ad rectos angu-<lb/>los recta A B, Horizonti æquidiſtans. </s>
  <s xml:id="echoid-s39927" xml:space="preserve">In F D, autẽ ſumpta longitudine ſtyli quacunque <emph style="sc">K</emph> F, ſiue <lb/>ſurſum, ſiue deorſum verſus, deſcribatur ex F, verſus A B, arcus D H, verſus B, quidẽ, ſi murus, pla-<lb/>numve horologii à meridie in ortum, vel à ſeptentrione in occaſum declinet, verſus A, verò, ſi de-<lb/>
<anchor type="note" xlink:label="note-0617-07a" xlink:href="note-0617-07"/>
flectat à meridie in occaſum, aut à Borea in ortum. </s>
  <s xml:id="echoid-s39928" xml:space="preserve">Numerata autem declinatione muri D H, <lb/>(quam in noſtro exemplo ponimus eſſe grad. </s>
  <s xml:id="echoid-s39929" xml:space="preserve">30. </s>
  <s xml:id="echoid-s39930" xml:space="preserve">à meridie in ortum) ductaq́ue F H, ſecante ip-<lb/>ſam A B, in E, agatur per E, recta C E, ipſi F D, parallela, ſeu ad A B, perpendicularis. </s>
  <s xml:id="echoid-s39931" xml:space="preserve">Nam C E, <lb/>erit linea meridiana, ſiue horæ 12. </s>
  <s xml:id="echoid-s39932" xml:space="preserve">Deinde in arcu D H, ex altera parte rectæ F D, producto, ſup-<lb/>
<anchor type="note" xlink:label="note-0617-08a" xlink:href="note-0617-08"/>
putato complemento declinationis D N, ducatur recta F N; </s>
  <s xml:id="echoid-s39933" xml:space="preserve">vel certè ducatur recta F α, ad F E, <lb/>perpendicularis, ſecans A B, in α Per α, enim ducenda eſt &amp; </s>
  <s xml:id="echoid-s39934" xml:space="preserve">linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s39935" xml:space="preserve">linea horæ 6. <lb/></s>
  <s xml:id="echoid-s39936" xml:space="preserve">Sumpta quoque in A B, recta E β, ſiue ad dexteram, ſiue ad ſiniſtram meridianæ lineæ C E, quæ <lb/>ipſi E F, æqualis ſit deſcribatur ex β, verſus C E, arcus circuli, ſurſum quidem verſus in horologio <lb/>declinante à meridie, deorſum autem in eo, quod à ſeptentrione deflectit; </s>
  <s xml:id="echoid-s39937" xml:space="preserve">in quo numerata alti-<lb/>tudine poli, initio facto à recta A B, ducatur ex β, ad finem ſupputationis recta ſecans C E, in C, <lb/>
<anchor type="note" xlink:label="note-0617-09a" xlink:href="note-0617-09"/>
puncto, quod centrum erit horologii, in quo omnes lineæ horariæ conuenient. </s>
  <s xml:id="echoid-s39938" xml:space="preserve">Ducta igitur ex
<pb o="602" file="0618" n="618" rhead="GNOMONICES"/>
C, per K, locum ſtyli recta C k, quæ linea ſtyli dici poteſt, quam recta ex α, ducta ſecet ad angulos <lb/>
<anchor type="note" xlink:label="note-0618-01a" xlink:href="note-0618-01"/>
rectos in G, erit recta α G, linea æquinoctialis. </s>
  <s xml:id="echoid-s39939" xml:space="preserve">Poſt hęc excitetur ex K, recta K I, ad C K, perpen <lb/>
<anchor type="note" xlink:label="note-0618-02a" xlink:href="note-0618-02"/>
dicularis, &amp; </s>
  <s xml:id="echoid-s39940" xml:space="preserve">ſtylo K F, æqualis. </s>
  <s xml:id="echoid-s39941" xml:space="preserve">Recta enim ducta C I, dabit axem mundi, quem coniuncta recta <lb/>
<anchor type="note" xlink:label="note-0618-03a" xlink:href="note-0618-03"/>
<anchor type="figure" xlink:label="fig-0618-01a" xlink:href="fig-0618-01"/>
<anchor type="note" xlink:label="note-0618-04a" xlink:href="note-0618-04"/>
<anchor type="note" xlink:label="note-0618-05a" xlink:href="note-0618-05"/>
G I, ad angulos rectos ſecabit, ſi erratum non eſt. </s>
  <s xml:id="echoid-s39942" xml:space="preserve">Iam vero in linea ſtyli C K, ſumpta recta G L, <lb/>
<anchor type="note" xlink:label="note-0618-06a" xlink:href="note-0618-06"/>
ipſi G I, æquali, deſcribatur ex L, circulus cuiuſcunque magnitudinis, qui in partes 24. </s>
  <s xml:id="echoid-s39943" xml:space="preserve">æquales <lb/>diſtribuatur, initio facto à recta L M, quæ ex L, ducitur per punctum M, vbi æquinoctialis linea <lb/>meridianam interſecat, quæ quidem recta L M, neceſſario ductain rectam L α, ad angulos rectos <lb/>ſecabit, ſi erratum non fuerit Si enim per centrum L, &amp; </s>
  <s xml:id="echoid-s39944" xml:space="preserve">puncta diuiſionum rectæ occultæ egre-<lb/>diantur, ſecabitur linea æquinoctialis in punctis, per quæ rectæ emiſſæ ex C, dabunt horas à mer. <lb/></s>
  <s xml:id="echoid-s39945" xml:space="preserve">
<anchor type="note" xlink:label="note-0618-07a" xlink:href="note-0618-07"/>
&amp; </s>
  <s xml:id="echoid-s39946" xml:space="preserve">med. </s>
  <s xml:id="echoid-s39947" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39948" xml:space="preserve">hoc ordine. </s>
  <s xml:id="echoid-s39949" xml:space="preserve">In horologio, quod ad meridiem ſpectat, portio lineæ meridianæ à cen-<lb/>tro C, verſus æquinoctialem lineam monſtrat hora@m 12. </s>
  <s xml:id="echoid-s39950" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s39951" xml:space="preserve">reliqua portio incipiens <lb/>ab eodem centro C, horam 12. </s>
  <s xml:id="echoid-s39952" xml:space="preserve">mediæ noctis. </s>
  <s xml:id="echoid-s39953" xml:space="preserve">Lineæ verò præcedentes meridianam lineam ad <lb/>ſiniſtram, hoc eſt, ad partes A, indicant horas poſt mediam noctem, vel ante meridiem, ſequen-<lb/>res denique eandem ad dexteram, id eſt, ad partes B, horas poſt meridiem demonſtrant: </s>
  <s xml:id="echoid-s39954" xml:space="preserve">qua-<lb/>
<anchor type="note" xlink:label="note-0618-08a" xlink:href="note-0618-08"/>
rum ordo, &amp; </s>
  <s xml:id="echoid-s39955" xml:space="preserve">numerus progreditur in recta A B, vel linea æquinoctiali à ſiniſtra ad dexteram. </s>
  <s xml:id="echoid-s39956" xml:space="preserve">In <lb/>horologo autem, quod ad ſeptentrionem vergit, portio lineæ meridianæ à centro C, verſus lineã <lb/>æquinoctialem indicat horam 12. </s>
  <s xml:id="echoid-s39957" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s39958" xml:space="preserve">reliqua portio horam 12. </s>
  <s xml:id="echoid-s39959" xml:space="preserve">meridiei. </s>
  <s xml:id="echoid-s39960" xml:space="preserve">Lineæ <lb/>autem meridianam lineam præcedentes in recta A B, vel linea æquinoctiali ad ſiniſtram oſten-<lb/>dunt horas à meridie, &amp; </s>
  <s xml:id="echoid-s39961" xml:space="preserve">quæ ad dextram ſunt, horas à media nocte: </s>
  <s xml:id="echoid-s39962" xml:space="preserve">quarum ordo, &amp; </s>
  <s xml:id="echoid-s39963" xml:space="preserve">numerus <lb/>progreditur quoque à ſiniſtra ad dexteram in linea ęquinoctiali, vel recta A B.</s>
  <s xml:id="echoid-s39964" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1981" type="float" level="2" n="1">
<note position="right" xlink:label="note-0617-05" xlink:href="note-0617-05a" xml:space="preserve">Deſcriptio horo <lb/>logii Aſtrono-<lb/>mici à Verticali <lb/>declinantis.</note>
<note position="left" xlink:label="note-0617-06" xlink:href="note-0617-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0617-07" xlink:href="note-0617-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0617-08" xlink:href="note-0617-08a" xml:space="preserve">Linea meridia-<lb/>na.</note>
<note position="right" xlink:label="note-0617-09" xlink:href="note-0617-09a" xml:space="preserve">Centrum<unsure/> horo-<lb/>logii.</note>
<note position="left" xlink:label="note-0618-01" xlink:href="note-0618-01a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0618-02" xlink:href="note-0618-02a" xml:space="preserve">Linea æquino-<lb/>ctialis.</note>
<note position="left" xlink:label="note-0618-03" xlink:href="note-0618-03a" xml:space="preserve">Axis mundi.</note>
  <figure xlink:label="fig-0618-01" xlink:href="fig-0618-01a">
    <image file="0618-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0618-01"/>
  </figure>
<note position="left" xlink:label="note-0618-04" xlink:href="note-0618-04a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0618-05" xlink:href="note-0618-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0618-06" xlink:href="note-0618-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0618-07" xlink:href="note-0618-07a" xml:space="preserve">Lineæ horarum <lb/>@ mer. &amp; med. <lb/>n<unsure/>oc.</note>
<note position="left" xlink:label="note-0618-08" xlink:href="note-0618-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s39965" xml:space="preserve">CAETERVM eędem lineæ horariæ commodiſſimè ducentur hac ratione. </s>
  <s xml:id="echoid-s39966" xml:space="preserve">Ex puncto F, <lb/>
<anchor type="note" xlink:label="note-0618-09a" xlink:href="note-0618-09"/>
egrediantur rectæ efficientes cum F E, eoſdem angulos, quos in horizontali horologio lineæ ho-<lb/>rariæ cum linea meridiana conſtituunt, nempe linea horæ 6. </s>
  <s xml:id="echoid-s39967" xml:space="preserve">qualis eſt F α, angulum rectum, &amp; </s>
  <s xml:id="echoid-s39968" xml:space="preserve">c. <lb/></s>
  <s xml:id="echoid-s39969" xml:space="preserve">quod facile fiet, ſi ex centro horologii horizontalis deſcribatur arcus circuli omnes horarias lineas <lb/>
<anchor type="note" xlink:label="note-0618-10a" xlink:href="note-0618-10"/>
ſecans, &amp; </s>
  <s xml:id="echoid-s39970" xml:space="preserve">ei æqualis ex F, verſus rectam A B. </s>
  <s xml:id="echoid-s39971" xml:space="preserve">Si enim ex illo arcu omnia horaria interualla, initio <lb/>facto à linea meridiana, transferantur in hunc, initio facto á recta F E, erunt rectæ ex F, per pun-<lb/>cta huius arcus emiſſæ lineæ horariæ reſpondentes lineis horariis in horologio horizontali. </s>
  <s xml:id="echoid-s39972" xml:space="preserve">Vbi <lb/>ergo hæ lineæ rectam A B, interſecant, per illa puncta rectæ ex centro C, eductæ dabunt horarias <lb/>lineas, vt prius. </s>
  <s xml:id="echoid-s39973" xml:space="preserve">Arque hoc modo facile prior deſcriptio poterit examinari, &amp; </s>
  <s xml:id="echoid-s39974" xml:space="preserve">corrigi, ſi error for <lb/>tè aliquis in ea commiſſus fuerit. </s>
  <s xml:id="echoid-s39975" xml:space="preserve">Immo poſterior hæc ratio hotariarum linearum ducendarum <lb/>perutilis eſt ad illas lineas ducendas, quæ vel nullo modo, vel vix, niſi in punctis remotiſſimis li-<lb/>neam ęquinoctialem interſecant, qualis eſt in propoſito exemplo linea horæ 4 &amp; </s>
  <s xml:id="echoid-s39976" xml:space="preserve">3.</s>
  <s xml:id="echoid-s39977" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1982" type="float" level="2" n="2">
<note position="left" xlink:label="note-0618-09" xlink:href="note-0618-09a" xml:space="preserve">Qua ratione li-<lb/>neæ horariæ ex <lb/>horologio hori <lb/>zont<unsure/>ali deſcri-<lb/>bantur.</note>
<note position="left" xlink:label="note-0618-10" xlink:href="note-0618-10a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s39978" xml:space="preserve">QVOD ſi quis dubiter, an recte hac ratione lineæ horariæ ducantur, demonſtrabimus id bre <lb/>uiter, hoc modo. </s>
  <s xml:id="echoid-s39979" xml:space="preserve">Intelligatur triangulum α F E, moueri circa rectam α E, donec rectum ſit ad <lb/>planum horologii, atque adeo F, vertex ſtyli idem ſit, quod centrũ mundi, ipſumq́ triangulum
<pb o="603" file="0619" n="619" rhead="LIBER SEPTIMVS."/>
in plano Horizontis iaceat. </s>
  <s xml:id="echoid-s39980" xml:space="preserve">Quo poſito, ducentur omnes circuli horarii à mer. </s>
  <s xml:id="echoid-s39981" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39982" xml:space="preserve">med. </s>
  <s xml:id="echoid-s39983" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s39984" xml:space="preserve">per <lb/>F, centrum mundi. </s>
  <s xml:id="echoid-s39985" xml:space="preserve">Cum ergo Meridianus per rectam F E, ducatur, ducetur circulus horæ 6. <lb/></s>
  <s xml:id="echoid-s39986" xml:space="preserve">per rectam F α. </s>
  <s xml:id="echoid-s39987" xml:space="preserve">Et quoniam communes ſectiones circulorum horariorum, atque Horizontis in <lb/>centro Horizontis conſtituunt angulos æquales illis, quos communes ſectiones eorundem circu-<lb/>lorum &amp; </s>
  <s xml:id="echoid-s39988" xml:space="preserve">plani horologii horizontalis efficiunt in centro horologii, in quod axis mundi cadit, vt <lb/>conſtat ex iis, quæ ad finem propoſ. </s>
  <s xml:id="echoid-s39989" xml:space="preserve">1. </s>
  <s xml:id="echoid-s39990" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39991" xml:space="preserve">3. </s>
  <s xml:id="echoid-s39992" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s39993" xml:space="preserve">ex iis, quæ propoſ. </s>
  <s xml:id="echoid-s39994" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39995" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s39996" xml:space="preserve">5. </s>
  <s xml:id="echoid-s39997" xml:space="preserve">cum horizontale horolo-<lb/>gium per arcus horarios deſcriberemus, demonſtrauimus; </s>
  <s xml:id="echoid-s39998" xml:space="preserve">perſpicuum eſt, circulos horarios oc-<lb/>currere horologio declinante in punctis rectæ A B, in quæ cadunt rectæ efficientes in F, eoſdem <lb/>angulos, quos horariæ lineę in horizontali horologio faciunt in centro horologii, &amp; </s>
  <s xml:id="echoid-s39999" xml:space="preserve">c.</s>
  <s xml:id="echoid-s40000" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40001" xml:space="preserve">RVRSVS quoniam puncta L, &amp; </s>
  <s xml:id="echoid-s40002" xml:space="preserve">M, aliquando tam parum inter ſe diſtant, vt vix ſine erro-<lb/>
<anchor type="note" xlink:label="note-0619-01a" xlink:href="note-0619-01"/>
<anchor type="note" xlink:label="note-0619-02a" xlink:href="note-0619-02"/>
re per ipſa duci poſſit linea, à qua diuiſio circuli ex L, deſcripti inchoanda eſt, (Facile enim in <lb/>vnam, aut alteram partem deflectere poteſt: </s>
  <s xml:id="echoid-s40003" xml:space="preserve">Vnde error in lineis horariis ducendis continget in-<lb/>terdum non paruus) rectius fecerimus, ſi prius ex α, per centrum L, rectam ducamus. </s>
  <s xml:id="echoid-s40004" xml:space="preserve">Hanc <lb/>enim neceſſario ad angulos rectos ſecabit recta L M, ſi erratum non fuerit. </s>
  <s xml:id="echoid-s40005" xml:space="preserve">Idem quoque in ſe-<lb/>quentibus horologiis declinantibus, &amp; </s>
  <s xml:id="echoid-s40006" xml:space="preserve">inclinatis obſeruandum erit. </s>
  <s xml:id="echoid-s40007" xml:space="preserve">Hac enim ratione fiet, vt ac-<lb/>curatiſſime lineæ horarię ducantur, ſi dictæ duæ lineæ ſeſe ad angulos rectos ſecuerint. </s>
  <s xml:id="echoid-s40008" xml:space="preserve">Qua-<lb/>re diligenter examinanda erit hæc operatio, antequam vlterius in deſcriptione horologij pro-<lb/>grediamur.</s>
  <s xml:id="echoid-s40009" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1983" type="float" level="2" n="3">
<note position="left" xlink:label="note-0619-01" xlink:href="note-0619-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0619-02" xlink:href="note-0619-02a" xml:space="preserve">Quando pun-<lb/>cta L, M, præce<unsure/>-<lb/>dẽtis horologii <lb/>parum inter ſe <lb/>diſtant, quid a-<lb/>gendum, vt ac-<lb/>cura@è hot<unsure/>æ de-<lb/>pingantur.</note>
</div>
<p>
  <s xml:id="echoid-s40010" xml:space="preserve">EADEM ratione, ſi fortè recta F α, nimis procul à puncto E, rectam A B, ſecat, ducere poteri <lb/>
<anchor type="note" xlink:label="note-0619-03a" xlink:href="note-0619-03"/>
mus ex F, quamcunque aliam lineam horariam præter lineam horæ 6. </s>
  <s xml:id="echoid-s40011" xml:space="preserve">quæ nimirum cum F E, <lb/>
<anchor type="note" xlink:label="note-0619-04a" xlink:href="note-0619-04"/>
eum angulum faciat, quem illa hora in horologio horizontali cum meridiana linea facit, commo <lb/>deq́ue rectam A B, ſecet. </s>
  <s xml:id="echoid-s40012" xml:space="preserve">Si enim per punctum, vbi rectam A B, ſecat, ad C, centrum horologii <lb/>rectam duxerimus, &amp; </s>
  <s xml:id="echoid-s40013" xml:space="preserve">aliam rectam per punctum, vbi hæc linea æquinoctialem ſecat, &amp; </s>
  <s xml:id="echoid-s40014" xml:space="preserve">per cen-<lb/>trum L, habebimus aliam rectam, a qua diuiſionem circuli ex L, deſcripti inchoare commodiſſi-<lb/>mè poterimus. </s>
  <s xml:id="echoid-s40015" xml:space="preserve">Si igitur tunc vnum punctum diuiſionis cadit præcisè in rectam per L, &amp; </s>
  <s xml:id="echoid-s40016" xml:space="preserve">M, du-<lb/>ctam, rectè inſtituta erit operatio, ſin minus, error aliquis commiſſus erit, quem corrigas, neceſſe <lb/>eſt, antequàm ad alia pergas.</s>
  <s xml:id="echoid-s40017" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1984" type="float" level="2" n="4">
<note position="right" xlink:label="note-0619-03" xlink:href="note-0619-03a" xml:space="preserve">Qua ratione di-<lb/>utſio<unsure/> circuli ex <lb/>@, deſeripti anũ <lb/>de poſſit inchoa <lb/>r@. quàm à recta <lb/>L M.</note>
<note position="left" xlink:label="note-0619-04" xlink:href="note-0619-04a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s40018" xml:space="preserve">ITAQVE ſi horologium hoc in muro, qui à meridie in ortum declinet grad. </s>
  <s xml:id="echoid-s40019" xml:space="preserve">30. </s>
  <s xml:id="echoid-s40020" xml:space="preserve">collocetur, <lb/>
<anchor type="note" xlink:label="note-0619-05a" xlink:href="note-0619-05"/>
ita vt recta A B, Horizonti æquidiſtet, &amp; </s>
  <s xml:id="echoid-s40021" xml:space="preserve">recta F D, ad eundem ſit perpendicularis, atque in pun-<lb/>cto K, inſigatur ſtylus ad murum rectus, æqualisq́ue rectæ K F, vel K I, vel triangulum C I G, ſu-<lb/>
<anchor type="note" xlink:label="note-0619-06a" xlink:href="note-0619-06"/>
per lineam ſtyli C K, erigatur ad angulos rectos, indicabit extremum vmbræ à vertice ſtyli proie-<lb/>ctæ, vel vmbra axis C I, horas à mer. </s>
  <s xml:id="echoid-s40022" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s40023" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s40024" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1985" type="float" level="2" n="5">
<note position="right" xlink:label="note-0619-05" xlink:href="note-0619-05a" xml:space="preserve">Quomodo ho-<lb/>rologium decli-<lb/>nans à Verzica-<lb/>li collocan dum <lb/>ſit. vt horas in-<lb/>dicet.</note>
<note position="left" xlink:label="note-0619-06" xlink:href="note-0619-06a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s40025" xml:space="preserve">QVO pacto autem in muris, quæ parum à Meridiano circulo abſunt, horologium ſit deli-<lb/>
<anchor type="note" xlink:label="note-0619-07a" xlink:href="note-0619-07"/>
neandum, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s40026" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40027" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40028" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40029" xml:space="preserve">petatur.</s>
  <s xml:id="echoid-s40030" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1986" type="float" level="2" n="6">
<note position="right" xlink:label="note-0619-07" xlink:href="note-0619-07a" xml:space="preserve">Quando mutus <lb/>par<unsure/>urr à Meri-<lb/>diano abeſt.</note>
</div>
<p>
  <s xml:id="echoid-s40031" xml:space="preserve">SEMPER in his horologiis, &amp; </s>
  <s xml:id="echoid-s40032" xml:space="preserve">in omnibus aliis ſequentibus, angulus contentus ſub axe, &amp; </s>
  <s xml:id="echoid-s40033" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0619-08a" xlink:href="note-0619-08"/>
linea ſtyli, cuiuſmodi hic eſt angulus I C K, eſt quantitas altitudinis poli ſupra planum horologii <lb/>vt in lib. </s>
  <s xml:id="echoid-s40034" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40035" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40036" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40037" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s40038" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1987" type="float" level="2" n="7">
<note position="right" xlink:label="note-0619-08" xlink:href="note-0619-08a" xml:space="preserve">Altitudo poli <lb/>ſupra planum <lb/>declinans.</note>
</div>
<p>
  <s xml:id="echoid-s40039" xml:space="preserve">IAM verò idem hoc horologium à meridie declinans in ortum monſtrabit horas etiam in <lb/>facie muri oppoſita, hoc eſt, in muro, qui à ſeptentrione in occaſum declinet grad. </s>
  <s xml:id="echoid-s40040" xml:space="preserve">30. </s>
  <s xml:id="echoid-s40041" xml:space="preserve">ſi ita collo <lb/>cetur, vt recta A B, Horizonti æquidiſtet, centrumq́ue C, ſit in fra ipſam poſitum, &amp; </s>
  <s xml:id="echoid-s40042" xml:space="preserve">quæ in eo ſi-<lb/>
<anchor type="note" xlink:label="note-0619-09a" xlink:href="note-0619-09"/>
tu dextra nobis ſunt, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s40043" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s40044" xml:space="preserve">Sed tunc linea C E M, indicabit horam 12. </s>
  <s xml:id="echoid-s40045" xml:space="preserve">mediæ <lb/>noctis, non autem meridiei, ſicut in horologio ad auſtrum vergente, vt paulo ante diximus. </s>
  <s xml:id="echoid-s40046" xml:space="preserve">Itaque <lb/>conuerſo ad nos horologio declinante à meridie in ortum, quod hactenus deſcripſimus, ita vt ſu <lb/>perior pars fiat inferior, &amp; </s>
  <s xml:id="echoid-s40047" xml:space="preserve">contra, hoc eſt, punctum A, ſit nobis ad dexteram, &amp; </s>
  <s xml:id="echoid-s40048" xml:space="preserve">B, ad ſiniſtram, <lb/>ſi in facie horologii oppoſita omnia lineamenta deſcribantur, ita vt ſingulæ lineæ ſingulis lineis ad <lb/>vnguem reſpondeant, &amp; </s>
  <s xml:id="echoid-s40049" xml:space="preserve">rurſus punctum A, fiat nobis ad ſiniſtram, &amp; </s>
  <s xml:id="echoid-s40050" xml:space="preserve">B, ad dexteram, deſcriptum <lb/>erit horologium declinans à ſeptentrione in occaſum totidem gradibus, quot prius deſcriptum à <lb/>meridie in ortum declinat, collocandum in muro, vt iacet. </s>
  <s xml:id="echoid-s40051" xml:space="preserve">Hac enim ratione erit centrum C, in-<lb/>fra rectam A B, &amp; </s>
  <s xml:id="echoid-s40052" xml:space="preserve">quæ prius erant nobis ſiniſtra, (conuerſo nimirum ad nos horologio, vt A, ad <lb/>dexteram, &amp; </s>
  <s xml:id="echoid-s40053" xml:space="preserve">B, ad ſiniſtram vergeret) facta erunt dextra, &amp; </s>
  <s xml:id="echoid-s40054" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s40055" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1988" type="float" level="2" n="8">
<note position="left" xlink:label="note-0619-09" xlink:href="note-0619-09a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Quid agendum <lb/>ſit, quando ho <lb/>rologium decli-<lb/>nans à Septen-<lb/>trione deſcribẽ-<lb/>dũ proponitur.</note>
<p>
  <s xml:id="echoid-s40056" xml:space="preserve">CONSTRVCTVRI igitur horologium à ſeptentrione declinans in ortum, occaſumve, <lb/>deſcribemus horologium declinans à meridie in partem oppoſitam totidem gradibus, quot de-<lb/>ſcribendum declinat: </s>
  <s xml:id="echoid-s40057" xml:space="preserve">(Semper enim eadem declinatio eſt horologii ad Boream ſpectantis, quæ <lb/>vergentis ad auſtrum, quamuis non ad eaſdem partes ambo declinent: </s>
  <s xml:id="echoid-s40058" xml:space="preserve">propterea quod vno de-<lb/>clinante in ortum, alterum in occaſum declinet, &amp; </s>
  <s xml:id="echoid-s40059" xml:space="preserve">contra, ęqualibus tamen numero gradibus.) </s>
  <s xml:id="echoid-s40060" xml:space="preserve">Vt <lb/>ſi deſcribendum ſit horologium declinans à ſeptentrione in occaſum, deſcribemus, declinans à <lb/>
<anchor type="note" xlink:label="note-0619-12a" xlink:href="note-0619-12"/>
meridie in ortum: </s>
  <s xml:id="echoid-s40061" xml:space="preserve">Si verò declinans à ſeptentrione in ortum, deſcribemus declinans à meridie <lb/>in occaſum. </s>
  <s xml:id="echoid-s40062" xml:space="preserve">Ex hoc enim colligemus id, quod proponitur, ſi omnes eius partes inuertantur, <lb/>vt dictum eſt.</s>
  <s xml:id="echoid-s40063" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1989" type="float" level="2" n="9">
<note position="right" xlink:label="note-0619-12" xlink:href="note-0619-12a" xml:space="preserve">Qua ratione ex <lb/>horologio decli <lb/>nante à mer. vel <lb/>Sept. in ortum, <lb/>vel occ. fiat de-<lb/>clinans à mer. <lb/>vel Sept. in oc-<lb/>caſum, vel ortũ, <lb/>&amp; contra.</note>
</div>
<p>
  <s xml:id="echoid-s40064" xml:space="preserve">CONSTRVCTO autem quocunque horologio à meridie, ſeptentrioneve in ortum, vel <lb/>occaſum declinante, ſi omnia eius lineamenta in alio quopiam plano deſcribantur, ita vt quæ ſunt
<pb o="604" file="0620" n="620" rhead="GNOMONICES"/>
ad dexteram ipſius lineæ meridianæ ſita, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s40065" xml:space="preserve">quæ ſunt ad ſiniſtram, dextra euadant, <lb/>confectum erit horologium à meridie quoque vel ſeptentrione declinans in partem contrariam, <lb/>vt ſi illud in ortum declinat, hoc vergat in occaſum, &amp; </s>
  <s xml:id="echoid-s40066" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s40067" xml:space="preserve">Huiuſmodi ſunt lineamenta cui<unsure/>us-<lb/>libet horologii in parte oppoſita plani deſcripta, vt ſingulæ lineæ ſingulis lineis reſpondeant. </s>
  <s xml:id="echoid-s40068" xml:space="preserve">Hac <lb/>arte vides hic factũ eſſe horologium declinans à meridie in occaſum grad. </s>
  <s xml:id="echoid-s40069" xml:space="preserve">30. </s>
  <s xml:id="echoid-s40070" xml:space="preserve">ex horologio decli-<lb/>nante totidem gradibus à meridie in ortum.</s>
  <s xml:id="echoid-s40071" xml:space="preserve"/>
</p>
  <figure>
    <image file="0620-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0620-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s40072" xml:space="preserve">VIDES igitur vna ferè opera quatuor horologia deſcribi, vnum declinans à meridie in or-<lb/>
<anchor type="note" xlink:label="note-0620-04a" xlink:href="note-0620-04"/>
tum, alterum à meridie in occaſum, ſi prioris lineamenta ita permutentur, vt dextra fiant ſiniſtra, <lb/>&amp; </s>
  <s xml:id="echoid-s40073" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s40074" xml:space="preserve">tertium à ſeptentrione in occaſum, ſi primum ita inuertatur, vt ſuperiora fiant inferio-<lb/>ra, &amp; </s>
  <s xml:id="echoid-s40075" xml:space="preserve">quæ poſt hanc inuerſionem dextra ſunt, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s40076" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s40077" xml:space="preserve">quartũ à ſeptentrione in or-<lb/>tum, ſi ſecundum inuertatur ſecundum omnes ſui partes, vt proxime diximus de primo. </s>
  <s xml:id="echoid-s40078" xml:space="preserve">In his <lb/>autem omnibus eadem ſemper eſt declinationis quantitas.</s>
  <s xml:id="echoid-s40079" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1990" type="float" level="2" n="10">
<note position="left" xlink:label="note-0620-04" xlink:href="note-0620-04a" xml:space="preserve">Quo p@@o vna <lb/>opera ferme <lb/>quatuor horolo <lb/>gia declinantia <lb/>a Verticali de-<lb/>ſcriban@.</note>
</div>
</div>
<div xml:id="echoid-div1992" type="section" level="1" n="510">
<head xml:id="echoid-head539" style="it" xml:space="preserve">DE ARCVBVS SIGNORVM, ET LONGITVDINVM DIERVM <lb/>in horologio, quod à Verticali circulo declinat. CAP. XXIIII.</head>
<p>
  <s xml:id="echoid-s40080" xml:space="preserve">DVCTA recta C I, pro axe mundi, excitetur in I, ad C I, perpendicularis I G, pro radio <lb/>
<anchor type="note" xlink:label="note-0620-05a" xlink:href="note-0620-05"/>
<anchor type="note" xlink:label="note-0620-06a" xlink:href="note-0620-06"/>
Aequatoris, ex cuius vtraque parte radii aliorum ſignorum ducantur, vt in ſuperioribus, ſu-<lb/>maturq́ue I C, æqualis rectæ I C, in axe horologii præcedentis cap. </s>
  <s xml:id="echoid-s40081" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40082" xml:space="preserve">recta I G, ęqualis rectæ I G, <lb/>vel G L, in eodem horologio; </s>
  <s xml:id="echoid-s40083" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40084" xml:space="preserve">ex C, per G, educatur recta C G, pro linea ſtyli. </s>
  <s xml:id="echoid-s40085" xml:space="preserve">quam commo-<lb/>dius fortaſſe ducemus, ſi ex C, ducatur recta C G, faciens cum I C, angulum I C G, æqualem an-<lb/>gulo I C k, quem in horologio axis C I, cum linea ſtyli CG, conſtituit. </s>
  <s xml:id="echoid-s40086" xml:space="preserve">Deinde ex centro L, illius <lb/>circuli, beneficio cuius in horologio puncta horarum in linea æquinoctiali inuenimus, accipian-<lb/>tur omnia interualla vſque ad illa puncta æquinoctialis lineæ, vbi à lineis horariis ſecatur, eaq́ue <lb/>ex I, in radium Aequatoris I G, transferantur, ſignando puncta in radio Aequatoris. </s>
  <s xml:id="echoid-s40087" xml:space="preserve">Si enim ex C, <lb/>per hæc puncta rectæ lineæ ducantur, erunt hæ omnium horarum lineæ citra &amp; </s>
  <s xml:id="echoid-s40088" xml:space="preserve">vltra lin eam ſty-<lb/>li, quæ æquinoctialem lineam interſecant. </s>
  <s xml:id="echoid-s40089" xml:space="preserve">His igitur apponantur numeri horarum reſponden-<lb/>
<anchor type="note" xlink:label="note-0620-07a" xlink:href="note-0620-07"/>
tes horis, quarum interualla translata ſunt, notando diligenter, quæ lineæ reſpondeant horis ad <lb/>ſiniſtram lineæ ſtyli poſitis, &amp; </s>
  <s xml:id="echoid-s40090" xml:space="preserve">quæ horis ad dexteram eiuſdem collocatis. </s>
  <s xml:id="echoid-s40091" xml:space="preserve">Id quod numeri lineis <lb/>appoſiti vel facile indicant, correſpondentes numeris linearum horariarum horologii, quæ ęqui-<lb/>noctialem lineam interſecaut. </s>
  <s xml:id="echoid-s40092" xml:space="preserve">Has enim lineas duntaxat referunt lineæ hactenus ex puncto C, per <lb/>puncta radii Aequatoris emiſſæ. </s>
  <s xml:id="echoid-s40093" xml:space="preserve">Eaſdem has lineas obtinebimus, ſi ex horologio ſumamus in-<lb/>terualla horaria inter centrum C, &amp; </s>
  <s xml:id="echoid-s40094" xml:space="preserve">lineam æquinoctialem α M, eaq́ue in figura radiorum Zodia-<lb/>ci ex C, transferamus in radium Aequatoris I G, puncta in eo ſignando, per quæ horarum lineæ <lb/>ductæ ex C, tranſire debent, &amp; </s>
  <s xml:id="echoid-s40095" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40096" xml:space="preserve">Quod ſi quando linea aliqua horaria in horologio lineam æqui-<lb/>noctialem non ſecet, ſed ei æquidiſtet, ducenda erit ex C, linea C A, radio Aequatoris I G, paral-<lb/>lela. </s>
  <s xml:id="echoid-s40097" xml:space="preserve">Hæc enim illi horę reſpondebit, quemadmodum in horologio horizõtali, &amp; </s>
  <s xml:id="echoid-s40098" xml:space="preserve">Verticali, quia <lb/>linea horę 6. </s>
  <s xml:id="echoid-s40099" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40100" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s40101" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40102" xml:space="preserve">æquinoctiali lineæ æquidiſtat, ducta eſt in figura radiorum Zo-
<pb o="605" file="0621" n="621" rhead="LIBER SEPTIMVS."/>
diaci ex H, recta H V, radio Aequatoris parallela pro ſexta hora, vt conſtat ex cap.</s>
  <s xml:id="echoid-s40103" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40104" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40105" xml:space="preserve">7. </s>
  <s xml:id="echoid-s40106" xml:space="preserve">Vtautem <lb/>lineas habeamus aliarum horarum, quæ æquinoctialem lineam neque ſecant, neque ei parallelæ <lb/>
<anchor type="note" xlink:label="note-0621-01a" xlink:href="note-0621-01"/>
ſunt, cuiuſmodi ſunt illæ, quæ poſtquam lineam æquinoctialem ſecuerunt, vltra centrum C, ſunt <lb/>productæ, vt in noſtro exemplo hor. </s>
  <s xml:id="echoid-s40107" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40108" xml:space="preserve">5. </s>
  <s xml:id="echoid-s40109" xml:space="preserve">6. </s>
  <s xml:id="echoid-s40110" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40111" xml:space="preserve">cæteræ poſt meridiem, &amp; </s>
  <s xml:id="echoid-s40112" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40113" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40114" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40115" xml:space="preserve">ante meridiem, <lb/>(hæ etenim omnes vltra centrum C, productæ ſunt) hanc viam ſequemur. </s>
  <s xml:id="echoid-s40116" xml:space="preserve">Per C, centrum ho-<lb/>rologii ducemus rectam lineam lineæ æquinoctiali parallelam, (Hanc in noſtro exemplo tantum-<lb/>modo animo concipere oportebit, cum non ſit ducta) &amp; </s>
  <s xml:id="echoid-s40117" xml:space="preserve">per C, in figura radiorum Zodiaci rectã <lb/>C A, radio Acquatoris I G, parallelam, quæ illi reſpondebit. </s>
  <s xml:id="echoid-s40118" xml:space="preserve">Poſt hæc quoniam quælibet linea <lb/>horaria cum recta illa, quæ in horologio per centrum C, ducitur lineæ æquinoctiali æquidiſtans, <lb/>ad verticem C, æquales angulos facit, transferemus lineas in figura radiorum Zodiaci ex C, pro-<lb/>
<anchor type="note" xlink:label="note-0621-02a" xlink:href="note-0621-02"/>
<anchor type="note" xlink:label="note-0621-03a" xlink:href="note-0621-03"/>
deuntes, radiumq́ue Aequatoris ſecantes, ad alteram partem rectæ C A, beneſicio arcus circuli <lb/>ex C, deſcripti, in figura radiorum Zodiaci, vt in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s40119" xml:space="preserve">Verticali fecimus cap. <lb/></s>
  <s xml:id="echoid-s40120" xml:space="preserve">2.</s>
  <s xml:id="echoid-s40121" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40122" xml:space="preserve">7. </s>
  <s xml:id="echoid-s40123" xml:space="preserve">ita vt lineæ hinc inde æqualiter à C A, diſtantes æquales arcus illius circuli ex C, deſcri-<lb/>pti, &amp; </s>
  <s xml:id="echoid-s40124" xml:space="preserve">angulos æquales ad C, comprehendant cum recta C A. </s>
  <s xml:id="echoid-s40125" xml:space="preserve">Nam hæ lineæ translatæ hoc mo-<lb/>do reſpondebunt illis horis, quæ æquinoctialem lineam non ſecant, ſed vltra centrum C, excur-<lb/>runt, ita vt binæ lineæ æquali interuallo à recta C A, diſtantes pertineant ad binas horas eiuſdem <lb/>numeri, quarum illa, quæ radium Aequatoris ſecat, hoc eſt, à C, ducitur verſus radium Aequato-<lb/>ris, reſerat horam, quæ lineam æquinoctialem interſecat, alia verò translata in alteram partem re-<lb/>præſentet eandem horam vltra centrum C, productam, quæ lineam æquinoctialem non ſecat: </s>
  <s xml:id="echoid-s40126" xml:space="preserve"><lb/>non ſecus ac in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s40127" xml:space="preserve">Verticali factum eſt. </s>
  <s xml:id="echoid-s40128" xml:space="preserve">Nam &amp; </s>
  <s xml:id="echoid-s40129" xml:space="preserve">ibi lineæ vltra rectã H V, <lb/>
<anchor type="note" xlink:label="note-0621-04a" xlink:href="note-0621-04"/>
translatæ referunt eaſdem horas numero, quæ tamen æquinoctialem lineam non ſecant: </s>
  <s xml:id="echoid-s40130" xml:space="preserve">quia ni-<lb/>mirum quæuis linea horaria cum linea horæ 6. </s>
  <s xml:id="echoid-s40131" xml:space="preserve">conſtituit ad verticem, hoc eſt, ad centrum H, <lb/>angulos æquales, quemadmodum hic cum linea illa, quę per C, centrũ horologii ducitur æqui-<lb/>noctiali lineę parallela, cui reſpõdet recta C A, in figura radiorum Zodiaci, ſicut &amp; </s>
  <s xml:id="echoid-s40132" xml:space="preserve">ibi recta H V, <lb/>horæ 6. </s>
  <s xml:id="echoid-s40133" xml:space="preserve">reſpondet, quæ lineæ æquinoctiali parallela eſt in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s40134" xml:space="preserve">Verticali. </s>
  <s xml:id="echoid-s40135" xml:space="preserve">Ita <lb/>vides hic translatam eſſe vltra rectam C A, lineam horæ 3. </s>
  <s xml:id="echoid-s40136" xml:space="preserve">poſt med. </s>
  <s xml:id="echoid-s40137" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s40138" xml:space="preserve">quia hora 3. </s>
  <s xml:id="echoid-s40139" xml:space="preserve">poſt mer. <lb/></s>
  <s xml:id="echoid-s40140" xml:space="preserve">æquinoctialem lineam ſecat, necnon lineam horæ 4. </s>
  <s xml:id="echoid-s40141" xml:space="preserve">poſt meridiem, quia hora 4. </s>
  <s xml:id="echoid-s40142" xml:space="preserve">poſt med. </s>
  <s xml:id="echoid-s40143" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40144" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0621-05a" xlink:href="note-0621-05"/>
ſecat lineam æquinoctialem. </s>
  <s xml:id="echoid-s40145" xml:space="preserve">Eademq́ue ratio habenda eſt in alijs.</s>
  <s xml:id="echoid-s40146" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1992" type="float" level="2" n="1">
<note position="left" xlink:label="note-0620-05" xlink:href="note-0620-05a" xml:space="preserve">Conſtructio fi-<lb/>guræ radiorum <lb/>Zodiaci pro at-<lb/>@u bus ſiguorũ, <lb/>&amp; longitudinũ <lb/>dierum deſcri-<lb/>bendis in horo-<lb/>logio declinan-<lb/>@@ a Verticali.</note>
<note position="left" xlink:label="note-0620-06" xlink:href="note-0620-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0620-07" xlink:href="note-0620-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0621-01" xlink:href="note-0621-01a" xml:space="preserve">Qua arte lineæ <lb/>horatiæ, quæ in <lb/>horologio lineã <lb/>æquinoctialem <lb/>non ſecant, du <lb/>cendæ ſint in <lb/>figura radiorũ <lb/>Zodiaci.</note>
<note position="left" xlink:label="note-0621-02" xlink:href="note-0621-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0621-03" xlink:href="note-0621-03a" xml:space="preserve">15. primi.</note>
<note position="left" xlink:label="note-0621-04" xlink:href="note-0621-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0621-05" xlink:href="note-0621-05a" xml:space="preserve">Quando linea <lb/>ſtyli una eſt ex <lb/>horariis lineis, <lb/>vel æqualiter à <lb/>duabus hinc in-<lb/>de diſtat, perti-<lb/>net quælibet li-<lb/>nea horatia in <lb/>figuta radio<unsure/>rũ <lb/>Zodiaci ad du-<lb/>as horas.</note>
</div>
<p>
  <s xml:id="echoid-s40147" xml:space="preserve">QVOD ſi quando linea ſtyli ſit etiam linea horatia, vel æqualiter à duabus horariis lineis in <lb/>medio earum poſita diſtet, (quod aliquando contingere ſolet) inſeruiet quęlibet linea horaria ex <lb/>
<anchor type="note" xlink:label="note-0621-06a" xlink:href="note-0621-06"/>
C, in figura radiorũ Zodiaci ducta duabus horis æqualiter à linea ſtyli hinc inde remotis, quem-<lb/>admodum in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s40148" xml:space="preserve">Verticali. </s>
  <s xml:id="echoid-s40149" xml:space="preserve">Vnde ſingulis lineis bini numeri aſcribendi <lb/>erunt reſpondentes binis illis horis à linea ſtyli æquali ſpatio diſtantibus, vt &amp; </s>
  <s xml:id="echoid-s40150" xml:space="preserve">in horizontali ho-<lb/>rologio, ac Verticali factum eſt. <lb/></s>
  <s xml:id="echoid-s40151" xml:space="preserve">
<anchor type="note" xlink:label="note-0621-07a" xlink:href="note-0621-07"/>
</s>
</p>
<div xml:id="echoid-div1993" type="float" level="2" n="2">
<note position="left" xlink:label="note-0621-06" xlink:href="note-0621-06a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0621-07" xlink:href="note-0621-07a" xml:space="preserve">Quando linea <lb/>ſtyli inæquali-<lb/>ter diſtat à dua-<lb/>bus proximis <lb/>horis, conſtruen <lb/>dæ eſſent duæ <lb/>figuræ radiorũ, <lb/>vt cõfuſio linea <lb/>rum tolleretur.</note>
</div>
<p>
  <s xml:id="echoid-s40152" xml:space="preserve">NON eſſet autem pręter rem, quando linea ſtyli inæqualiter à duabus proximis horis diſtat, <lb/>immo vero expediret, ſi conſtruerentur duæ figuræ radiorum Zodiaci, in quarum vna ducerentur <lb/>horarię lineæ ex C, reſpondentes illis lineis horariis in horologio, quæ ex vna parte, nempe ſini-<lb/>ſtra lineæ ſtyli continentur, in alia vero horariæ lineæ reſpondentes lineis horarijs horologii ex <lb/>altera parte lineę ſtyli. </s>
  <s xml:id="echoid-s40153" xml:space="preserve">Ita enim omnis linearum confuſio tolleretur, quę neceſſario ſequitur, quan <lb/>do linea ſtyli ferè æqualiter à lineis hinc inde poſitis diſtat, quia tunc puncta in radio Aequatoris <lb/>
<anchor type="note" xlink:label="note-0621-08a" xlink:href="note-0621-08"/>
inuenta vix inter ſe diſcernuntur, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s40154" xml:space="preserve">Hac ratione in noſtro exemplo in vna figu-<lb/>rarum ducerentur lineę ex C, reſpondentes hiſce horis 1. </s>
  <s xml:id="echoid-s40155" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40156" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40157" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40158" xml:space="preserve">5. </s>
  <s xml:id="echoid-s40159" xml:space="preserve">6. </s>
  <s xml:id="echoid-s40160" xml:space="preserve">7. </s>
  <s xml:id="echoid-s40161" xml:space="preserve">8. </s>
  <s xml:id="echoid-s40162" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40163" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40164" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40165" xml:space="preserve">quę <lb/>ſunt ad ſiniſtram lineę ſtyli: </s>
  <s xml:id="echoid-s40166" xml:space="preserve">In altera vero continerentur lineę reſpondentes horis ad dexteram <lb/>eiuſdem lineę ſtyli, quales ſunt, 10. </s>
  <s xml:id="echoid-s40167" xml:space="preserve">11. </s>
  <s xml:id="echoid-s40168" xml:space="preserve">12. </s>
  <s xml:id="echoid-s40169" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40170" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40171" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40172" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40173" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40174" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40175" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40176" xml:space="preserve">5. </s>
  <s xml:id="echoid-s40177" xml:space="preserve">6. </s>
  <s xml:id="echoid-s40178" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40179" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40180" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40181" xml:space="preserve">In qualibet <lb/>tamen figura ducenda eſſet C G, pro linea ſtyli. </s>
  <s xml:id="echoid-s40182" xml:space="preserve"><emph style="sc">H</emph>uius rei exemplum poſitum eſſe videbis in cap. <lb/></s>
  <s xml:id="echoid-s40183" xml:space="preserve">29. </s>
  <s xml:id="echoid-s40184" xml:space="preserve">cum de horologiis declinantibus, &amp; </s>
  <s xml:id="echoid-s40185" xml:space="preserve">ſimul inclinatis agemus.</s>
  <s xml:id="echoid-s40186" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1994" type="float" level="2" n="3">
<note position="left" xlink:label="note-0621-08" xlink:href="note-0621-08a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s40187" xml:space="preserve">COMMODISSIME quoque eaſdem lineas horarias ex C, prodeuntes ducemus hac ra-<lb/>
<anchor type="note" xlink:label="note-0621-09a" xlink:href="note-0621-09"/>
tione. </s>
  <s xml:id="echoid-s40188" xml:space="preserve">Ducta recta C G, vt prius, ſumemus in ea producta punctum quodcunque B, per quod <lb/>lineam B A, ipſi I C, parallelam agemus, perq́ue C, radio Aequatoris aliam parallelam C A, quæ <lb/>priorem ſecet in A. </s>
  <s xml:id="echoid-s40189" xml:space="preserve">Deinde centro A, &amp; </s>
  <s xml:id="echoid-s40190" xml:space="preserve">interuallo A B, circulo deſcripto, ſecabimus eum in par-<lb/>
<anchor type="note" xlink:label="note-0621-10a" xlink:href="note-0621-10"/>
tes 24. </s>
  <s xml:id="echoid-s40191" xml:space="preserve">ęquales initio facto à puncto, quod iam iam inuenire docebimus hoc modo. </s>
  <s xml:id="echoid-s40192" xml:space="preserve">Recta L M, <lb/>in horologio accepta transferatur in radium Acquatoris ex I, vſque ad E, &amp; </s>
  <s xml:id="echoid-s40193" xml:space="preserve">per E, ex C, ducatur <lb/>recta C E, pro linea horę 12. </s>
  <s xml:id="echoid-s40194" xml:space="preserve">ſecans rectam B A, in D, atque ex D, ad rectam B A, perpendicula-<lb/>ris excitetur D F, ſecans circunferentiam circuli in F, puncto, quod initium diuiſionis circuli erit. <lb/></s>
  <s xml:id="echoid-s40195" xml:space="preserve">Vel certè interuallum inter centrum L, &amp; </s>
  <s xml:id="echoid-s40196" xml:space="preserve">horam quamcunque in ęquinoctiali linea, quę commo <lb/>dior viſa fuerit, transferatur ex I, in radium Aequatoris, imprimendo punctum in ipſo, perq́; </s>
  <s xml:id="echoid-s40197" xml:space="preserve">hoc <lb/>punctum ex C, recta ducatur pro illa hora ſecans rectam B A, in puncto, per quod ſi ad B A, per-<lb/>pendicularis ducatur, ſurſum quidem, ſi hora aſſumpta fuerit ex ea parte lineę ſtyli, vbi eſt hora <lb/>12. </s>
  <s xml:id="echoid-s40198" xml:space="preserve">deorſum autem, ſi ex altera parte, habebimus iterum in circunferentia punctum, à quo diuiſio <lb/>circuli principium poteſt habere. </s>
  <s xml:id="echoid-s40199" xml:space="preserve">Immo perutile aliquando erit, vt inueſtigetur hoc alterum pun <lb/>ctum. </s>
  <s xml:id="echoid-s40200" xml:space="preserve">Nam ſi vnum punctum diuiſionis ab eo inchoatę cadat in punctum F, quod primo loco in-
<pb o="606" file="0622" n="622" rhead="GNOMONICES"/>
uentum fuerat, ex ſententia res ſuccedet, ſin minus, corrigendus erit error, qui alicubi commiſſus <lb/>eſt. </s>
  <s xml:id="echoid-s40201" xml:space="preserve">Præſtat etiam potius incipere diuiſionem circuli à poſteriori hoc puncto inuento, quàm à <lb/>puncto F, quando linea horæ 12. </s>
  <s xml:id="echoid-s40202" xml:space="preserve">valde propinqua eſt lineę ſtyli. </s>
  <s xml:id="echoid-s40203" xml:space="preserve">Tunc enim perpendicularis D F, <lb/>
<anchor type="figure" xlink:label="fig-0622-01a" xlink:href="fig-0622-01"/>
<anchor type="note" xlink:label="note-0622-01a" xlink:href="note-0622-01"/>
<anchor type="note" xlink:label="note-0622-02a" xlink:href="note-0622-02"/>
<anchor type="note" xlink:label="note-0622-03a" xlink:href="note-0622-03"/>
nimis obliquè ſecat circunferentiam, vt vix punctum F, ſine errore poſſit accipi. </s>
  <s xml:id="echoid-s40204" xml:space="preserve">Hocidem intel-<lb/>
<anchor type="note" xlink:label="note-0622-04a" xlink:href="note-0622-04"/>
ligi volo in ſequentibus omnibus horologiis, quæ declinant, &amp; </s>
  <s xml:id="echoid-s40205" xml:space="preserve">inclinata ſunt. </s>
  <s xml:id="echoid-s40206" xml:space="preserve">Si igitur ex pun-<lb/>ctis diuiſionum circuli ad rectam B A, deducantur perpendiculares, vel ipſi C A, parallelæ, ſecan-<lb/>tes rectam B A, in punctis, dabunt rectę ex C, per hæc puncta emiſſę horarias lineas, vt prius. <lb/></s>
  <s xml:id="echoid-s40207" xml:space="preserve">Facile autem erit iudicare, quæ lineæ quibuſnam horis in horologio reſpondeant, ex punctis di-<lb/>uiſionum circuli. </s>
  <s xml:id="echoid-s40208" xml:space="preserve">Nam ſemper puncta ab F, verſus B, procedendo, illas horas referunt, quæ in <lb/>horologio horam 12. </s>
  <s xml:id="echoid-s40209" xml:space="preserve">ſequuntur verſus lineam ſtyli, vt ex figura patet. </s>
  <s xml:id="echoid-s40210" xml:space="preserve">Cęterum lineas illas ad <lb/>rectam B A, perpendiculares ex punctis diuiſionum circuli facile hoc modo ducemus. </s>
  <s xml:id="echoid-s40211" xml:space="preserve">Si fortè <lb/>duo puncta puncto B, proxima ab eo æqualiter diſtent, (quod quidem tunc eueniet, cum linea <lb/>ſtyli fuerit etiam linea horaria, vel à duabus horariis lineis æqualiter receſſerit) erunt rectæ lineæ <lb/>coniungentes bina puncta à puncto B, æqualiter diſtantia ad B A, perpendiculares; </s>
  <s xml:id="echoid-s40212" xml:space="preserve">Sin minus, <lb/>
<anchor type="note" xlink:label="note-0622-05a" xlink:href="note-0622-05"/>
ſumptum cuiuſuis puncti interuallum ex B, in ſemicirculo ſuperiori transferatur in inferiorem <lb/>ſemicirculum ex eodem puncto B. </s>
  <s xml:id="echoid-s40213" xml:space="preserve">Recta enim hæc duo puncta connectens perpendicularis erit <lb/>ad B A. </s>
  <s xml:id="echoid-s40214" xml:space="preserve">Idem fiet, ſi interualla punctorum à recta B A, in inferiori ſemicirculo transferantur in <lb/>ſuperiorem ſemicirculum ab eadem recta B A, vt factum eſſe vides in noſtro exemplo.</s>
  <s xml:id="echoid-s40215" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1995" type="float" level="2" n="4">
<note position="right" xlink:label="note-0621-09" xlink:href="note-0621-09a" xml:space="preserve">Que artificio a-<lb/>liter horariæ li-<lb/>neæ in figura <lb/>ra diorum Zo-<lb/>dia@i ducantur.</note>
<note position="left" xlink:label="note-0621-10" xlink:href="note-0621-10a" xml:space="preserve">50</note>
  <figure xlink:label="fig-0622-01" xlink:href="fig-0622-01a">
    <image file="0622-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0622-01"/>
  </figure>
<note position="left" xlink:label="note-0622-01" xlink:href="note-0622-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0622-02" xlink:href="note-0622-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0622-03" xlink:href="note-0622-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0622-04" xlink:href="note-0622-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0622-05" xlink:href="note-0622-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s40216" xml:space="preserve">EX his hoc modo paratis deſcribentur arcus ſignorum, vt in horizontali horologio, &amp; </s>
  <s xml:id="echoid-s40217" xml:space="preserve">Verti-<lb/>
<anchor type="note" xlink:label="note-0622-06a" xlink:href="note-0622-06"/>
cali, transferendo nimirum interualla horarum intercepta inter C, &amp; </s>
  <s xml:id="echoid-s40218" xml:space="preserve">radios ſignorum in horas <lb/>horologii reſpondentes ex centro C; </s>
  <s xml:id="echoid-s40219" xml:space="preserve">vel etiam transferendo horaria interualla inter radium Ae-<lb/>quatoris, &amp; </s>
  <s xml:id="echoid-s40220" xml:space="preserve">ſignorum radios poſita in lineas horarias horologii reſpondentes, initio facto à linea <lb/>æquinoctiali, &amp;</s>
  <s xml:id="echoid-s40221" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40222" xml:space="preserve">Si linea ſtyli eadem fuerit, quæ linea quæpiam horaria, vel æqualiter à duabus <lb/>horis hinc inde poſitis receſſerit, transferenda erunt ſingula interualla prædicta in binas lineas <lb/>horarias ęqualiter à linea ſtyli diſtantes, veluti in horologio horizontali, &amp; </s>
  <s xml:id="echoid-s40223" xml:space="preserve">Verticali factum eſt.</s>
  <s xml:id="echoid-s40224" xml:space="preserve">
<pb o="607" file="0623" n="623" rhead="LIBER SEPTIMVS."/>
Si verò linea ſtyli inæqualiter à lineis duabus horarijs hinc inde collocatis remota fuerit, vt accu-<lb/>
<anchor type="note" xlink:label="note-0623-01a" xlink:href="note-0623-01"/>
ratius ſignorum arcus poſſint deſcribi, transferri poterunt omnia puncta horaria lineę ęquino-<lb/>ctialis ex vna parte (ex ea ſcilicet, in qua plura extiterint, vt in noſtro exemplo ex parte ſiniſtra) in <lb/>alteram, initio ſemper facto à linea indicis, ſeu ſtyli, vt in horologio noſtro fecimus. </s>
  <s xml:id="echoid-s40225" xml:space="preserve">Si enim per <lb/>
<anchor type="figure" xlink:label="fig-0623-01a" xlink:href="fig-0623-01"/>
<anchor type="note" xlink:label="note-0623-02a" xlink:href="note-0623-02"/>
<anchor type="note" xlink:label="note-0623-03a" xlink:href="note-0623-03"/>
<anchor type="note" xlink:label="note-0623-04a" xlink:href="note-0623-04"/>
<anchor type="note" xlink:label="note-0623-05a" xlink:href="note-0623-05"/>
hęc puncta ex C, lineas occultas duxerimus, quales ſunt illæ, quæ minutis illis lineis diſtinctæ <lb/>ſunt in horologio, habebimus ſemper binas lineas ęqualiter à linea indicis remotas, vt in eas idẽ <lb/>horarium interuallum ex figura radiorum Zodiaci acceptum transferri poſſit. </s>
  <s xml:id="echoid-s40226" xml:space="preserve">Immo ſi in horolo <lb/>gio per C, ducatur linea recta lineæ ęquinoctiali parallela, &amp; </s>
  <s xml:id="echoid-s40227" xml:space="preserve">in eam transferantur ex C, centro <lb/>horologii ad vtramque partem portiones rectæ C A, in figura radiorum Zodiaci inter C, &amp; </s>
  <s xml:id="echoid-s40228" xml:space="preserve">ra-<lb/>dios ſignorum interceptæ, habebuntur in ea puncta, per quę arcus ſignorum ducendi ſunt, vt in <lb/>horologio horizontali, &amp; </s>
  <s xml:id="echoid-s40229" xml:space="preserve">Verticali in linea horę 6.</s>
  <s xml:id="echoid-s40230" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1996" type="float" level="2" n="5">
<note position="left" xlink:label="note-0622-06" xlink:href="note-0622-06a" xml:space="preserve">Deſetiptio ar-<lb/>cuum ſignotum <lb/>in horologio de <lb/>clinante à Ver-<lb/>ticali.</note>
<note position="right" xlink:label="note-0623-01" xlink:href="note-0623-01a" xml:space="preserve">Quando linea <lb/>ſtyli inæquali-<lb/>ter à duabus ho <lb/>ris hinc inde di <lb/>ſtat, quid facien <lb/>dum, vt accura-<lb/>tius arcus ſigno-<lb/>sunt<unsure/> deſcriban-<lb/>t@r.</note>
  <figure xlink:label="fig-0623-01" xlink:href="fig-0623-01a">
    <image file="0623-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0623-01"/>
  </figure>
<note position="left" xlink:label="note-0623-02" xlink:href="note-0623-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0623-03" xlink:href="note-0623-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0623-04" xlink:href="note-0623-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0623-05" xlink:href="note-0623-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s40231" xml:space="preserve">HIC etiam arcus ſupra lineam ęquinoctialem pertinent ad ſigna auſtralia, reliqui verò ad bo-<lb/>
<anchor type="note" xlink:label="note-0623-06a" xlink:href="note-0623-06"/>
realia, quemadmodum in Verticali horologio. </s>
  <s xml:id="echoid-s40232" xml:space="preserve">Porrò ex iis, quę cap.</s>
  <s xml:id="echoid-s40233" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40234" xml:space="preserve">ſcripſimus, facile cogno-<lb/>ſcemus, quorum ſignorum arcus ſint hyperbolæ, &amp; </s>
  <s xml:id="echoid-s40235" xml:space="preserve">quorum parabolæ, vel Ellipſes, prout nimirũ <lb/>
<anchor type="note" xlink:label="note-0623-07a" xlink:href="note-0623-07"/>
linea ſtyli C B, radios ſignorum oppoſitorum ſecat, vel non. <lb/></s>
  <s xml:id="echoid-s40236" xml:space="preserve">
<anchor type="note" xlink:label="note-0623-08a" xlink:href="note-0623-08"/>
</s>
</p>
<div xml:id="echoid-div1997" type="float" level="2" n="6">
<note position="right" xlink:label="note-0623-06" xlink:href="note-0623-06a" xml:space="preserve">Qui arcus ad ſi-<lb/>gna auſtralia, &amp; <lb/>qui ad borealia <lb/>ſpectent.</note>
<note position="left" xlink:label="note-0623-07" xlink:href="note-0623-07a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0623-08" xlink:href="note-0623-08a" xml:space="preserve">Plura ſcripta <lb/>ſunt propoſ. 2. <lb/>lib. 3. &amp; in ſcho <lb/>lio eiuſdẽ pro-<lb/>poſ. de deſcri-<lb/>ptione arcuum <lb/>ſign orum.</note>
</div>
<p>
  <s xml:id="echoid-s40237" xml:space="preserve">PLVRA ad accuratam arcuum ſignorum deſcriptionem attinentia reperies explicata à no-<lb/>bis lib. </s>
  <s xml:id="echoid-s40238" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40239" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40240" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40241" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40242" xml:space="preserve">ln ſcholio eiuſdem propof.</s>
  <s xml:id="echoid-s40243" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40244" xml:space="preserve"><emph style="sc">H</emph>ORIZONTALIS linea eſt ipſa recta A B, quæ per locum ſtyli ducitur ad lineam meri <lb/>dianam perpendicularis. </s>
  <s xml:id="echoid-s40245" xml:space="preserve"><emph style="sc">H</emph>ęc autem linea horizontalis totum horologium dirimit in duo, quo-<lb/>
<anchor type="note" xlink:label="note-0623-09a" xlink:href="note-0623-09"/>
rum illud, quod infra ipſam eſt, ad meridiem ſpectat, aliud verò ad Boream. </s>
  <s xml:id="echoid-s40246" xml:space="preserve">Vtrumque autem <lb/>
<anchor type="note" xlink:label="note-0623-10a" xlink:href="note-0623-10"/>
in muro ita collocandum eſt, vt linea horizontalis Horizonti ſit parallela, ſuperioremq́ue occu-<lb/>pet locum. </s>
  <s xml:id="echoid-s40247" xml:space="preserve">In boreali tamen arcus ſignorum auſtralium mutantur in arcus ſignorum borealium <lb/>oppoſitorum, velut in Verticali horologio, &amp; </s>
  <s xml:id="echoid-s40248" xml:space="preserve">lineamenta, quæ ſunt ad ſiniſtram, deſcribenda ſunt <lb/>in parte dextra, &amp; </s>
  <s xml:id="echoid-s40249" xml:space="preserve">è contrario, vt in pręcedenti cap. </s>
  <s xml:id="echoid-s40250" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s40251" xml:space="preserve">Quando autem arcus ♑, in auſtra-<lb/>li horologio lineam horizontalem etiam ex altera parte ſecat, vt contingit, cum planum horologii
<pb o="608" file="0624" n="624" rhead="GMOMONICES"/>
exiguam habet declinationem à Vertícali, deſcribendum erit quoque altera ex parte portio borea-<lb/>lis horologii, quam horizontalis linea abſcindit, que madmodum &amp; </s>
  <s xml:id="echoid-s40252" xml:space="preserve">in Verticali horologio Borea-<lb/>le deſcriptum eſt ex vtraque parte: </s>
  <s xml:id="echoid-s40253" xml:space="preserve">Alioquin in horologio Boreali, quod in ortum declinat, non <lb/>monſtrarentur horæ, cum Sol oritur: </s>
  <s xml:id="echoid-s40254" xml:space="preserve">neque in eo, quod in occaíum vergit, cum Sol occidit.</s>
  <s xml:id="echoid-s40255" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1998" type="float" level="2" n="7">
<note position="right" xlink:label="note-0623-09" xlink:href="note-0623-09a" xml:space="preserve">Linea horizon-<lb/>talis.</note>
<note position="right" xlink:label="note-0623-10" xlink:href="note-0623-10a" xml:space="preserve">Horizontalis li <lb/>nea diuidit to-<lb/>tum horologiũ <lb/>in auſtrale, &amp; <lb/>boreale.</note>
</div>
<p>
  <s xml:id="echoid-s40256" xml:space="preserve">PRIVS quoque horologium appellari poteſt Diurnum, &amp; </s>
  <s xml:id="echoid-s40257" xml:space="preserve">poſterius Nocturnum, vt in Ver-<lb/>
<anchor type="note" xlink:label="note-0624-01a" xlink:href="note-0624-01"/>
ticali horologio docuimus.</s>
  <s xml:id="echoid-s40258" xml:space="preserve"/>
</p>
<div xml:id="echoid-div1999" type="float" level="2" n="8">
<note position="left" xlink:label="note-0624-01" xlink:href="note-0624-01a" xml:space="preserve">Horologium de <lb/>clinans diurnũ, <lb/>ac nocturnum.</note>
</div>
<p>
  <s xml:id="echoid-s40259" xml:space="preserve">IAM verò arcus longitudinum dierum eodem prorſus modo deſcribentur, ſi pro radiis ſi-<lb/>
<anchor type="note" xlink:label="note-0624-02a" xlink:href="note-0624-02"/>
gnorum aſſumantur radii longitudinum dierum, dummodo obſeruetur, hoſce arcus in ho-<lb/>rologio, quod ad Boream vergit, conuerti in complementa vſque ad 24. </s>
  <s xml:id="echoid-s40260" xml:space="preserve">vt in Verticali horo-<lb/>logio ſcripſimus cap.</s>
  <s xml:id="echoid-s40261" xml:space="preserve">8. </s>
  <s xml:id="echoid-s40262" xml:space="preserve">In figura radiorum Zodiaci duximus radios horarum 0. </s>
  <s xml:id="echoid-s40263" xml:space="preserve">6. </s>
  <s xml:id="echoid-s40264" xml:space="preserve">8. </s>
  <s xml:id="echoid-s40265" xml:space="preserve">10. <lb/></s>
  <s xml:id="echoid-s40266" xml:space="preserve">
<anchor type="note" xlink:label="note-0624-03a" xlink:href="note-0624-03"/>
14. </s>
  <s xml:id="echoid-s40267" xml:space="preserve">16. </s>
  <s xml:id="echoid-s40268" xml:space="preserve">18. </s>
  <s xml:id="echoid-s40269" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40270" xml:space="preserve">24.</s>
  <s xml:id="echoid-s40271" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2000" type="float" level="2" n="9">
<note position="left" xlink:label="note-0624-02" xlink:href="note-0624-02a" xml:space="preserve">Arcus longitu-<lb/>dinum dierum <lb/>quo pacto de-<lb/>ſctibantur.</note>
<note position="left" xlink:label="note-0624-03" xlink:href="note-0624-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s40272" xml:space="preserve">QVOD ſi ex lineamentis hactenus deſcriptis maius aut minus horologium pro data ſtyli ma-<lb/>gnitudine deſcribendum ſit, efficiemus id hoc modo. </s>
  <s xml:id="echoid-s40273" xml:space="preserve">Deſcribatur ſeorſum (vt prope figuram <lb/>radiorum Zodiaci factum eſt) triangulum I C G, ex horologio cap. </s>
  <s xml:id="echoid-s40274" xml:space="preserve">præcedentis, vel ex figura ra-<lb/>diorum Zodiaei huius cap. </s>
  <s xml:id="echoid-s40275" xml:space="preserve">deſumptum, in quo I C, axis mundi eſt; </s>
  <s xml:id="echoid-s40276" xml:space="preserve">I G, Aequator; </s>
  <s xml:id="echoid-s40277" xml:space="preserve">C G, linea <lb/>ſtyli; </s>
  <s xml:id="echoid-s40278" xml:space="preserve">gnomon verò I K, rectos angulos faciens cum linea indicis C G. </s>
  <s xml:id="echoid-s40279" xml:space="preserve">Sumendo igitur in ſtylo <lb/>I K, producto rectam I A, dato gnomoni ęqualem, &amp; </s>
  <s xml:id="echoid-s40280" xml:space="preserve">ducendo per A, rectam B D, rectæ C G, pa-<lb/>rallelam, ſi axis B I, transferatur ex C, in figura radiorum Zodiaci vſque ad punctum B, verſus <lb/>I, &amp; </s>
  <s xml:id="echoid-s40281" xml:space="preserve">ex B, radii ſignorum educantur, ac reliqua omnia fiant, vt prius, deſcribentur arcus ſignorũ <lb/>pro magnitudine dati ſtyli I A, ſicuti antea deſcripti ſunt ad datum ſtylum I K. </s>
  <s xml:id="echoid-s40282" xml:space="preserve">Nam lineę hora-<lb/>
<anchor type="note" xlink:label="note-0624-04a" xlink:href="note-0624-04"/>
riæ ex C, prodeuntes in figura radiorum Zodiaci, &amp; </s>
  <s xml:id="echoid-s40283" xml:space="preserve">in horologio, quod in cap. </s>
  <s xml:id="echoid-s40284" xml:space="preserve">pręcedente deſcri-<lb/>pſimus, eędem omnino permanent in eadem altitudine poli, &amp; </s>
  <s xml:id="echoid-s40285" xml:space="preserve">declinatione plani eadem. </s>
  <s xml:id="echoid-s40286" xml:space="preserve">Aequi <lb/>noctialis autem linea ducenda eſt ad lineam ſtyli perpendicularis, tanto interuallo à centro horo-<lb/>logii diſtans, quanta eſt recta B D.</s>
  <s xml:id="echoid-s40287" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2001" type="float" level="2" n="10">
<note position="left" xlink:label="note-0624-04" xlink:href="note-0624-04a" xml:space="preserve">20</note>
</div>
</div>
<div xml:id="echoid-div2003" type="section" level="1" n="511">
<head xml:id="echoid-head540" style="it" xml:space="preserve">DE HOROLOGIO ITALICO, ET BABYLONICO, <lb/>quod à Verticali circulo declinat. CAP. XXV.</head>
<p>
  <s xml:id="echoid-s40288" xml:space="preserve">SECETVR circulus ex L, deſcriptus, beneficio cuius in linea æquinoctiali puncta horarum <lb/>
<anchor type="note" xlink:label="note-0624-05a" xlink:href="note-0624-05"/>
offendi mus, in arcum diurnnm tropici ♋, a N b, &amp; </s>
  <s xml:id="echoid-s40289" xml:space="preserve">arcum diurnum tropici ♑, d N e, ita vt <lb/>
<anchor type="note" xlink:label="note-0624-06a" xlink:href="note-0624-06"/>
rectę a b, d e, ſecent rectam M N, ad angulos rectos, numerenturq́ue arcus ſemidiurni ♋, &amp; </s>
  <s xml:id="echoid-s40290" xml:space="preserve">♑, <lb/>vtrinque à puncto N, in circulo M a N b, vt integri arcus diurni habeantur, veluti cap.</s>
  <s xml:id="echoid-s40291" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40292" xml:space="preserve">tradi-<lb/>dimus. </s>
  <s xml:id="echoid-s40293" xml:space="preserve">Deinde pro horologio Italico diſtribuatur ſemel, atque iterum circulus Ma N b, in 24. <lb/></s>
  <s xml:id="echoid-s40294" xml:space="preserve">partes æquales, primum facto initio à puncto a, ſecundo à puncto d, ita vt a, ſit hora 24. </s>
  <s xml:id="echoid-s40295" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40296" xml:space="preserve"><lb/>in tropico ♋, &amp; </s>
  <s xml:id="echoid-s40297" xml:space="preserve">proximum punctum verſus N, hora 23. </s>
  <s xml:id="echoid-s40298" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40299" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40300" xml:space="preserve">At vero d, ſit hora 24. </s>
  <s xml:id="echoid-s40301" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40302" xml:space="preserve">in <lb/>tropico ♑, &amp; </s>
  <s xml:id="echoid-s40303" xml:space="preserve">proximum punctum verſus N, hora 23. </s>
  <s xml:id="echoid-s40304" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40305" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40306" xml:space="preserve">Rurſus idem circulus diuidatur ſemel <lb/>in 24. </s>
  <s xml:id="echoid-s40307" xml:space="preserve">partes æquales, initio ſumpto à puncto b, &amp; </s>
  <s xml:id="echoid-s40308" xml:space="preserve">iterum in 24. </s>
  <s xml:id="echoid-s40309" xml:space="preserve">partes æquales, initio facto à pun <lb/>cto e, ita vt b, ſit 24. </s>
  <s xml:id="echoid-s40310" xml:space="preserve">hora ab or. </s>
  <s xml:id="echoid-s40311" xml:space="preserve">in tropico ♋, &amp; </s>
  <s xml:id="echoid-s40312" xml:space="preserve">proximum punctum verſus N, hora 1. </s>
  <s xml:id="echoid-s40313" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40314" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40315" xml:space="preserve">pun-<lb/>ctum vero e, hora 24. </s>
  <s xml:id="echoid-s40316" xml:space="preserve">♑, ab or. </s>
  <s xml:id="echoid-s40317" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40318" xml:space="preserve">proximum punctum verſus N, hora 1. </s>
  <s xml:id="echoid-s40319" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40320" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40321" xml:space="preserve">Inueniemus enim <lb/>per hęc puncta diuiſionũ in vtroque tropico puncta horarum ab occ. </s>
  <s xml:id="echoid-s40322" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40323" xml:space="preserve">or. </s>
  <s xml:id="echoid-s40324" xml:space="preserve">horologiumq́ue Ita-<lb/>
<anchor type="note" xlink:label="note-0624-07a" xlink:href="note-0624-07"/>
licum, &amp; </s>
  <s xml:id="echoid-s40325" xml:space="preserve">Babylonicum perficiemus, non aliter, atque horizontale conſtruximus cap. </s>
  <s xml:id="echoid-s40326" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40327" xml:space="preserve">Exempli <lb/>gratia. </s>
  <s xml:id="echoid-s40328" xml:space="preserve">Ex f, puncto horæ 16. </s>
  <s xml:id="echoid-s40329" xml:space="preserve">♋. </s>
  <s xml:id="echoid-s40330" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40331" xml:space="preserve">ducta recta per centrum L, ſecat ęquinoctialem lineam <lb/>in g, puncto, per quod ſi ex C, centro horologii recta emittatur, ſecabitur tropicus ♋, in h, puncto <lb/>horę 16. </s>
  <s xml:id="echoid-s40332" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40333" xml:space="preserve">Sic etiam recta ex m, puncto horę 21. </s>
  <s xml:id="echoid-s40334" xml:space="preserve">♑, ab occ. </s>
  <s xml:id="echoid-s40335" xml:space="preserve">per L, educta ſecat lineam æqui-<lb/>noctialem in puncton, per quod recta ducta ex C, ſecat tropicum ♑, in p, puncto horæ 21. </s>
  <s xml:id="echoid-s40336" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s40337" xml:space="preserve">Pari ratione linea recta ex q, horæ 14. </s>
  <s xml:id="echoid-s40338" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40339" xml:space="preserve">in tropico ♑, quæ quidem in arcu nocturno <lb/>♑, d M e, continetur, ducta per L, ſecat lineam ęquinoctialem in r, puncto, per quod recta du-<lb/>cta ex C, ſecat tropicum ♑, in arcu nocturno in t, puncto horæ 14. </s>
  <s xml:id="echoid-s40340" xml:space="preserve">ab occ.</s>
  <s xml:id="echoid-s40341" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2003" type="float" level="2" n="1">
<note position="left" xlink:label="note-0624-05" xlink:href="note-0624-05a" xml:space="preserve">Compoſitio ho <lb/>rologii Italici, <lb/>ac Babyolnici à <lb/>Verticali decli-<lb/>@anti@.</note>
<note position="left" xlink:label="note-0624-06" xlink:href="note-0624-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0624-07" xlink:href="note-0624-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s40342" xml:space="preserve">HAC ratione inueniemus ſolum puncta illarum horarum, quę in ſemicirculo A N B, cuius <lb/>diameter A B, ęquinoctiali lineæ ęquidiſtat, continentur: </s>
  <s xml:id="echoid-s40343" xml:space="preserve">propterea quòd rectę ex ipſis per L, <lb/>
<anchor type="note" xlink:label="note-0624-08a" xlink:href="note-0624-08"/>
ductæ tranſeunt per centrum L, priuſquam ęquinoctialem lineam ſecant. </s>
  <s xml:id="echoid-s40344" xml:space="preserve">Vnde aliarum hora-<lb/>rum puncta inueniemus, vt de horizontali horologio diximus cap. </s>
  <s xml:id="echoid-s40345" xml:space="preserve">4. </s>
  <s xml:id="echoid-s40346" xml:space="preserve">per horas è regione illis op-<lb/>poſitas. </s>
  <s xml:id="echoid-s40347" xml:space="preserve">Vt ſi velimus reperire punctum horæ 23. </s>
  <s xml:id="echoid-s40348" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40349" xml:space="preserve">in tropico ♑, cui in circulo reſpon-<lb/>det punctum D, extra ſemicirculum A N B, ducemus ex E, puncto oppoſito, nempe ex hora 11. <lb/></s>
  <s xml:id="echoid-s40350" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40351" xml:space="preserve">in tropico ♑, in arcu nocturno ♑, comprehenſa, rectam per L, &amp; </s>
  <s xml:id="echoid-s40352" xml:space="preserve">D, quæ ſecabit æquino-<lb/>ctialem lineam in puncto R, (quod quia valde remotum eſt, in exemplo non continetur) per <lb/>quod ſi ducatur recta ex C, ſecabitur tropicus ♑, in arcu nocturno in puncto F, horæ 11. </s>
  <s xml:id="echoid-s40353" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40354" xml:space="preserve"><lb/>producta verò recta R C, vltra centrum C, ſecabit eundem tropicum ♑, in P, puncto horæ 23. </s>
  <s xml:id="echoid-s40355" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40356" xml:space="preserve"><lb/>ſic de cæteris.</s>
  <s xml:id="echoid-s40357" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2004" type="float" level="2" n="2">
<note position="left" xlink:label="note-0624-08" xlink:href="note-0624-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s40358" xml:space="preserve">EODEM modo puncta horarum ab ortu Solis in vtroque tropico deprehendemus. </s>
  <s xml:id="echoid-s40359" xml:space="preserve">Pro ho <lb/>rologio porro Boreali nullum exemplum afferimus, quia lineæ horarum ab or. </s>
  <s xml:id="echoid-s40360" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40361" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s40362" xml:space="preserve">productæ
<pb o="609" file="0625" n="625" rhead="LIBER SEPTIMVS."/>
vltra lineam horizontalem efficiunt horologium Boreale, vt de Verticali horologio dixi-<lb/>mus cap. </s>
  <s xml:id="echoid-s40363" xml:space="preserve">9.</s>
  <s xml:id="echoid-s40364" xml:space="preserve"/>
</p>
  <figure>
    <image file="0625-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0625-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s40365" xml:space="preserve">QVOD attinet ad eorundem horologiorũ deſcriptionem ex arcubus diurnis, nocturnisq́ue <lb/>
<anchor type="note" xlink:label="note-0625-04a" xlink:href="note-0625-04"/>
deſumptam, nulla prorſus difficultas apparet, ſi diligenter tabulæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s40366" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40367" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40368" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40369" xml:space="preserve">de-<lb/>ſcriptæ conſiderentur. </s>
  <s xml:id="echoid-s40370" xml:space="preserve">Nam v.</s>
  <s xml:id="echoid-s40371" xml:space="preserve">g. </s>
  <s xml:id="echoid-s40372" xml:space="preserve">hora 11. </s>
  <s xml:id="echoid-s40373" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40374" xml:space="preserve">ducitur per horam 6. </s>
  <s xml:id="echoid-s40375" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40376" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40377" xml:space="preserve">in arcu diur-<lb/>
<anchor type="note" xlink:label="note-0625-05a" xlink:href="note-0625-05"/>
no horarum 14. </s>
  <s xml:id="echoid-s40378" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40379" xml:space="preserve">per 5. </s>
  <s xml:id="echoid-s40380" xml:space="preserve">à med.</s>
  <s xml:id="echoid-s40381" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40382" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40383" xml:space="preserve">nec non per horam 4. </s>
  <s xml:id="echoid-s40384" xml:space="preserve">à med. <lb/></s>
  <s xml:id="echoid-s40385" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40386" xml:space="preserve">in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s40387" xml:space="preserve">Ita quoque hora 20. </s>
  <s xml:id="echoid-s40388" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40389" xml:space="preserve">tranſit per horam 1. </s>
  <s xml:id="echoid-s40390" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40391" xml:space="preserve">in ar-<lb/>cu diurno horarum 10. </s>
  <s xml:id="echoid-s40392" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40393" xml:space="preserve">per horam 2. </s>
  <s xml:id="echoid-s40394" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40395" xml:space="preserve">in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s40396" xml:space="preserve">Hora verò 21.</s>
  <s xml:id="echoid-s40397" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40398" xml:space="preserve"><lb/>quæ vnum duntaxat punctum habet in noſtro exemplo, nempe horam 2. </s>
  <s xml:id="echoid-s40399" xml:space="preserve">à mer.</s>
  <s xml:id="echoid-s40400" xml:space="preserve">in arcu diurno <lb/>horarum 10. </s>
  <s xml:id="echoid-s40401" xml:space="preserve">deſcribetur, ſi hora 21. </s>
  <s xml:id="echoid-s40402" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40403" xml:space="preserve">ducatur per horam 4. </s>
  <s xml:id="echoid-s40404" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40405" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40406" xml:space="preserve">in arcu nocturno <lb/>horarum 14. </s>
  <s xml:id="echoid-s40407" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40408" xml:space="preserve">per horam 2. </s>
  <s xml:id="echoid-s40409" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40410" xml:space="preserve">in arcu diurno horarum 10. </s>
  <s xml:id="echoid-s40411" xml:space="preserve">extendatur. </s>
  <s xml:id="echoid-s40412" xml:space="preserve">Sic etiam pro hora <lb/>22. </s>
  <s xml:id="echoid-s40413" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40414" xml:space="preserve">ducenda erit hora 22. </s>
  <s xml:id="echoid-s40415" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40416" xml:space="preserve">per horam 5. </s>
  <s xml:id="echoid-s40417" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40418" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40419" xml:space="preserve">in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s40420" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s40421" xml:space="preserve">per horam 4. </s>
  <s xml:id="echoid-s40422" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40423" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40424" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40425" xml:space="preserve">Hęc enim producta dabit horam 22. </s>
  <s xml:id="echoid-s40426" xml:space="preserve"><lb/>ab occ. </s>
  <s xml:id="echoid-s40427" xml:space="preserve">Eadem denique ratione pro hora 23. </s>
  <s xml:id="echoid-s40428" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40429" xml:space="preserve">ducenda erit hora 23. </s>
  <s xml:id="echoid-s40430" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40431" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s40432" xml:space="preserve"><lb/>à med. </s>
  <s xml:id="echoid-s40433" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40434" xml:space="preserve">in a@cu nocturno horarum 14. </s>
  <s xml:id="echoid-s40435" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40436" xml:space="preserve">per horam quintam à med. </s>
  <s xml:id="echoid-s40437" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40438" xml:space="preserve">in arcu noctur-<lb/>
<anchor type="note" xlink:label="note-0625-06a" xlink:href="note-0625-06"/>
no horarum 12. </s>
  <s xml:id="echoid-s40439" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40440" xml:space="preserve">c.</s>
  <s xml:id="echoid-s40441" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2005" type="float" level="2" n="3">
<note position="right" xlink:label="note-0625-04" xlink:href="note-0625-04a" xml:space="preserve">Alia deſcriptio <lb/>horologii. Itali-<lb/>ci, ac Babyloni-<lb/>ci à Verticali <lb/>declinantis, per <lb/>arcus diurnos, <lb/>&amp; nocturnos.</note>
<note position="left" xlink:label="note-0625-05" xlink:href="note-0625-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0625-06" xlink:href="note-0625-06a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div2007" type="section" level="1" n="512">
<head xml:id="echoid-head541" style="it" xml:space="preserve">DE HOROLOGIO ANTIQVO, QVOD <lb/>à circulo Verticali declinat. CAP. XXVI.</head>
<p>
  <s xml:id="echoid-s40442" xml:space="preserve">TAM arcus diurnus ♋, a N b, quàm ♑, d N e, ſecetur in 12. </s>
  <s xml:id="echoid-s40443" xml:space="preserve">partes æquales in circulo <lb/>
<anchor type="note" xlink:label="note-0625-07a" xlink:href="note-0625-07"/>
M a N b, ita vt puncta proxima, quæ ſequũtur puncta b, e, verſus N, pertineant ad horã 1. </s>
  <s xml:id="echoid-s40444" xml:space="preserve">in-<lb/>æqualem, &amp; </s>
  <s xml:id="echoid-s40445" xml:space="preserve">ſequentia ad 2. </s>
  <s xml:id="echoid-s40446" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40447" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40448" xml:space="preserve">Ex punctis enim diuiſionum inueniemus in vtroque tropico pun <lb/>cta horarum inæqualium, vt in horologio Verticali docuimus cap. </s>
  <s xml:id="echoid-s40449" xml:space="preserve">10. </s>
  <s xml:id="echoid-s40450" xml:space="preserve">Nam recta ex f, puncto ho <lb/>ræ 2. </s>
  <s xml:id="echoid-s40451" xml:space="preserve">inæqualis tropici ♋, per centrum L, eiecta ſecat æquinoctialẽ lineam in g, puncto, per quod <lb/>recta ex C, emiſſa ſecat tropicum ♋, in h, puncto horæ 2. </s>
  <s xml:id="echoid-s40452" xml:space="preserve">inęqualis. </s>
  <s xml:id="echoid-s40453" xml:space="preserve">Item recta ex m, puncto ho-
<pb o="610" file="0626" n="626" rhead="GNOMONICES"/>
ræ 9. </s>
  <s xml:id="echoid-s40454" xml:space="preserve">inæqualis tropici ♑, per L, ducta ſecat lineam æquinoctialem in puncto n, &amp; </s>
  <s xml:id="echoid-s40455" xml:space="preserve">recta ex C, per <lb/>n, ducta ſecat tropicum ♑, in p, puncto horę 9. </s>
  <s xml:id="echoid-s40456" xml:space="preserve">inæqualis, &amp; </s>
  <s xml:id="echoid-s40457" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s40458" xml:space="preserve">Pro hora 11. </s>
  <s xml:id="echoid-s40459" xml:space="preserve">inæquali <lb/>tropici ♑, quoniam non continetur in ſemicirculo A N B, cuius ſolum puncta in tropicis repe-<lb/>riuntur, vt ſupra dictum eſt, accipiemus punctum D, ei oppoſitum, quod cadit in horam 11. </s>
  <s xml:id="echoid-s40460" xml:space="preserve">in-<lb/>
<anchor type="figure" xlink:label="fig-0626-01a" xlink:href="fig-0626-01"/>
<anchor type="note" xlink:label="note-0626-01a" xlink:href="note-0626-01"/>
<anchor type="note" xlink:label="note-0626-02a" xlink:href="note-0626-02"/>
<anchor type="note" xlink:label="note-0626-03a" xlink:href="note-0626-03"/>
<anchor type="note" xlink:label="note-0626-04a" xlink:href="note-0626-04"/>
æqualem arcus nocturni tropici ♋, vt lib. </s>
  <s xml:id="echoid-s40461" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40462" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40463" xml:space="preserve">12. </s>
  <s xml:id="echoid-s40464" xml:space="preserve">oſtendimus, ex quo ſi per L, ducamus re-<lb/>ctam, ſecabitur æquinoctialis linea in puncto quodam, (quod in noſtro exemplo ob ſpatij angu-<lb/>ſtiam non continetur) per quod recta ex C, emiſſa dabit in arcu nocturno ♋, punctum reſpon-<lb/>dens puncto D, eadem verò recta vltra centrum C, eiecta offeret in arcu diurno ♑, punctum <lb/>aliud pro hora 11. </s>
  <s xml:id="echoid-s40465" xml:space="preserve">diurna inæquali tropici ♑. </s>
  <s xml:id="echoid-s40466" xml:space="preserve">Eadem ratione pro horis 11. </s>
  <s xml:id="echoid-s40467" xml:space="preserve">10. </s>
  <s xml:id="echoid-s40468" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40469" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40470" xml:space="preserve">inæqualibus <lb/>tropici ♋, qui etiam extra ſemicirculum A N B, cadunt, accipiemus puncta ipſis oppoſita E, F, G, <lb/>quæ cadunt in horas inæquales 11. </s>
  <s xml:id="echoid-s40471" xml:space="preserve">10. </s>
  <s xml:id="echoid-s40472" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40473" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40474" xml:space="preserve">arcus nocturni ♑, &amp; </s>
  <s xml:id="echoid-s40475" xml:space="preserve">ex ipſis rectas per L, ducemus, <lb/>vt inueniamus in arcu nocturno ♑, puncta K, P, Q, reſpondentia punctis E, F, G, arcus nocturni <lb/>tropici ♑, in circulo M a N b. </s>
  <s xml:id="echoid-s40476" xml:space="preserve">Quod ſi quando hora aliqua cadat præciſe in punctum A, vel B, <lb/>tum ducta recta per C, æquinoctiali lineæ parallela, indicabit in tropico ♑, duo puncta, quorum <lb/>
<anchor type="note" xlink:label="note-0626-05a" xlink:href="note-0626-05"/>
illud, quod ad dexteram ipſius C L, exiſtet, ad horam, quæ cadit in punctum A, alterum verò, <lb/>quod ad ſiniſtram ipſius C L, ſtatuetur, ad horam, quæ in punctum B, cadit, pertinebit. </s>
  <s xml:id="echoid-s40477" xml:space="preserve">Si igitur <lb/>reſpondentia puncta in tropicis iungantur lineis rectis, deſcriptum erit horologium Antiquum, <lb/>iranſibuntq́ue omnes horę inęquales per horas à mer. </s>
  <s xml:id="echoid-s40478" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s40479" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40480" xml:space="preserve">in linea æquinoctiali, vt in ſu-<lb/>perioribus ſcripſimus. </s>
  <s xml:id="echoid-s40481" xml:space="preserve">Quoniam verò puncta horarum 11. </s>
  <s xml:id="echoid-s40482" xml:space="preserve">10. </s>
  <s xml:id="echoid-s40483" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40484" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40485" xml:space="preserve">arcus ♑, non habent puncta <lb/>reſpondentia in tropico ♋, iungemus ea cum punctis earundem horarum arcus nocturni ♑, in-<lb/>uentis beneficio punctorum E, F, G, quæ illis horis in arcu diurno ♋, opponuntur, caduntq́ue in <lb/>horas inęquales 11. </s>
  <s xml:id="echoid-s40486" xml:space="preserve">10. </s>
  <s xml:id="echoid-s40487" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40488" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40489" xml:space="preserve">arcus nocturni ♑. <lb/></s>
  <s xml:id="echoid-s40490" xml:space="preserve">
<anchor type="note" xlink:label="note-0626-06a" xlink:href="note-0626-06"/>
</s>
</p>
<div xml:id="echoid-div2007" type="float" level="2" n="1">
<note position="right" xlink:label="note-0625-07" xlink:href="note-0625-07a" xml:space="preserve">Deſcriptio hor@ <lb/>logii Antiqui à <lb/>Verticali decli-<lb/>nantis.</note>
  <figure xlink:label="fig-0626-01" xlink:href="fig-0626-01a">
    <image file="0626-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0626-01"/>
  </figure>
<note position="left" xlink:label="note-0626-01" xlink:href="note-0626-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0626-02" xlink:href="note-0626-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0626-03" xlink:href="note-0626-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0626-04" xlink:href="note-0626-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0626-05" xlink:href="note-0626-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0626-06" xlink:href="note-0626-06a" xml:space="preserve">Cõſtructio eiuſ <lb/>dem @orologii <lb/>An tiqui ex arcu <lb/>bus diurnis at-<lb/>que nocturnis.</note>
</div>
<p>
  <s xml:id="echoid-s40491" xml:space="preserve">IAM verò ſi arcus diurnus horarum 6. </s>
  <s xml:id="echoid-s40492" xml:space="preserve">qui ſupra lineam horizontalem eſt arcus nocturnus <lb/>horarum 18. </s>
  <s xml:id="echoid-s40493" xml:space="preserve">deſcribatur, conſtruetur idem horologium. </s>
  <s xml:id="echoid-s40494" xml:space="preserve">Antiquum ex tabulis horatum inæqua <lb/>lium in ſcholio propoſ. </s>
  <s xml:id="echoid-s40495" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40496" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40497" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40498" xml:space="preserve">expoſitis.</s>
  <s xml:id="echoid-s40499" xml:space="preserve"/>
</p>
<pb o="611" file="0627" n="627" rhead="LIBER SEPTIMVS."/>
<p>
  <s xml:id="echoid-s40500" xml:space="preserve">PORRO lineæ horarum inæqualium productæ vltra lineam horizontalem exhibẽt eaſdem <lb/>
<anchor type="note" xlink:label="note-0627-01a" xlink:href="note-0627-01"/>
horas in horologio Boreali, ſi omnes partes immutentur, vt ſupradictum eſt.</s>
  <s xml:id="echoid-s40501" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2008" type="float" level="2" n="2">
<note position="right" xlink:label="note-0627-01" xlink:href="note-0627-01a" xml:space="preserve">Qua ratione Bo <lb/>reale hotologiũ <lb/>Ant@quum ex <lb/>Auſtrali ortum <lb/>habeat.</note>
</div>
</div>
<div xml:id="echoid-div2010" type="section" level="1" n="513">
<head xml:id="echoid-head542" style="it" xml:space="preserve">DE HOROLOGIIS AE HORIZONTE <lb/>declinantib{us}. CAP. XXVII.</head>
<p>
  <s xml:id="echoid-s40502" xml:space="preserve">HOROLOGIVM ab Horizonte declinans appellauimus ad initium lib. </s>
  <s xml:id="echoid-s40503" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40504" xml:space="preserve">illud, cuius <lb/>plana ſuperficies, in qua deſcribitur, ęquidiſtat circulo maximo ad Verticalẽ circulum pro-<lb/>priè dictum recto, &amp; </s>
  <s xml:id="echoid-s40505" xml:space="preserve">per communes ſectiones Horizontis, &amp; </s>
  <s xml:id="echoid-s40506" xml:space="preserve">meridiani tranſeunti, ita vt commu-<lb/>nis ſectio illius &amp; </s>
  <s xml:id="echoid-s40507" xml:space="preserve">Horizontis ſit linea meridiana. </s>
  <s xml:id="echoid-s40508" xml:space="preserve">Hoc autem quadruplex eſt. </s>
  <s xml:id="echoid-s40509" xml:space="preserve">Aut enim reſpi-<lb/>
<anchor type="note" xlink:label="note-0627-02a" xlink:href="note-0627-02"/>
<anchor type="note" xlink:label="note-0627-03a" xlink:href="note-0627-03"/>
cit Zenith, &amp; </s>
  <s xml:id="echoid-s40510" xml:space="preserve">orientem Solem, vel ſpectat ad Nadir, &amp; </s>
  <s xml:id="echoid-s40511" xml:space="preserve">ad Solem occidentem, ita vt angulus incli-<lb/>nationis, quem cum Horizonte conſtituit, vergat ad occaſum: </s>
  <s xml:id="echoid-s40512" xml:space="preserve">Aut reſpicit Zenith, &amp; </s>
  <s xml:id="echoid-s40513" xml:space="preserve">Solem occi <lb/>dentem, vel ad Nadir, &amp; </s>
  <s xml:id="echoid-s40514" xml:space="preserve">ad orientem Solem pertinet, ita vt angulus inclinationis verſus ortũ con-<lb/>ſtituatur. </s>
  <s xml:id="echoid-s40515" xml:space="preserve">Primum dici poteſt horologium ſuperius orientale; </s>
  <s xml:id="echoid-s40516" xml:space="preserve">quia Sole oriente ſtatim horas de-<lb/>monſtrat, deſcribiturq́ue in parte plani ſuperiori. </s>
  <s xml:id="echoid-s40517" xml:space="preserve">Secundum inferius occidentale; </s>
  <s xml:id="echoid-s40518" xml:space="preserve">quia in parte <lb/>inferiori plani deſctibitur, horasq́ue oſtendit vſque ad occaſum Solis. </s>
  <s xml:id="echoid-s40519" xml:space="preserve">Tertium ſuperius occi-<lb/>dentale, &amp; </s>
  <s xml:id="echoid-s40520" xml:space="preserve">quartum inferius orientale; </s>
  <s xml:id="echoid-s40521" xml:space="preserve">quoniam illud in ſuperiori parte plani conſtruitur indi-<lb/>catq́ue horas vſque ad Solis occaſum, hoc verò in inferiori parte plani delineatur, horasq́ue ſta-<lb/>tim ab ortu Solis manifeſtat.</s>
  <s xml:id="echoid-s40522" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2010" type="float" level="2" n="1">
<note position="left" xlink:label="note-0627-02" xlink:href="note-0627-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0627-03" xlink:href="note-0627-03a" xml:space="preserve">Horologium <lb/>ab Horizon@e <lb/>declinans qua-<lb/>druplex.</note>
</div>
<p>
  <s xml:id="echoid-s40523" xml:space="preserve">HOROLOGIVM igitur ſuperius ab Horizonte declinans deſcribitur, vt horologium <lb/>
<anchor type="note" xlink:label="note-0627-04a" xlink:href="note-0627-04"/>
<anchor type="note" xlink:label="note-0627-05a" xlink:href="note-0627-05"/>
auſtrale à Verticali declinans, &amp; </s>
  <s xml:id="echoid-s40524" xml:space="preserve">inferius, vt ſeptentrionale, his exceptis, quæ ſequuntur. </s>
  <s xml:id="echoid-s40525" xml:space="preserve">Loco <lb/>declinationis à Verticali circulo ſupputetur inclinatio ad Horizontem, quam inueniemus per <lb/>
<anchor type="figure" xlink:label="fig-0627-01a" xlink:href="fig-0627-01"/>
<anchor type="note" xlink:label="note-0627-06a" xlink:href="note-0627-06"/>
<anchor type="note" xlink:label="note-0627-07a" xlink:href="note-0627-07"/>
propoſ. </s>
  <s xml:id="echoid-s40526" xml:space="preserve">23. </s>
  <s xml:id="echoid-s40527" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40528" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40529" xml:space="preserve">à D, quidem ad dexteram verſus B, ſi planum horologii occaſum reſpicit, eſtq́; <lb/></s>
  <s xml:id="echoid-s40530" xml:space="preserve">ſuperius; </s>
  <s xml:id="echoid-s40531" xml:space="preserve">ad ſiniſtram verò verſus A, ſi planum horologii ſuperius eſt, ſpectatq́ue ad ortum. </s>
  <s xml:id="echoid-s40532" xml:space="preserve">At ſi <lb/>
<anchor type="note" xlink:label="note-0627-08a" xlink:href="note-0627-08"/>
horologium inferius eſt, reſpicitq́ue occaſum, numeranda eſt inclinatio à D, ad ſiniſtram verſus <lb/>A; </s>
  <s xml:id="echoid-s40533" xml:space="preserve">ſi denique inferius eſt horologiũ, &amp; </s>
  <s xml:id="echoid-s40534" xml:space="preserve">ad ortum pertinet, ſupputanda eſt inclinatio à D, ad dex-<lb/>teram verſus B. </s>
  <s xml:id="echoid-s40535" xml:space="preserve">Deinde in arcu circuli ex β, deſcripto numerandum eſt à recta A B, complemen <lb/>tum altitudinis poli, non autem ipſa altitudo poli, vt in horologiis à Verticali declinantibus prius <lb/>fiebat, ſupra quidem rectam A B, ſi ſuperius eſt horologium, infra verò, ſi inferius. </s>
  <s xml:id="echoid-s40536" xml:space="preserve">Reliqua omnia <lb/>fiant, vt in horologiis declinantibus à Verticali, vt figura ipſa indicat, in qua ponitur horologium <lb/>ſuperius ad occaſum ſpectans, declinatio vero ab Horizonte grad. </s>
  <s xml:id="echoid-s40537" xml:space="preserve">30. </s>
  <s xml:id="echoid-s40538" xml:space="preserve">Ordo in horis hic eſt. </s>
  <s xml:id="echoid-s40539" xml:space="preserve">Re-<lb/>cta C E, ſemper eſt linea horæ 12. </s>
  <s xml:id="echoid-s40540" xml:space="preserve">meridiei, præcedentes verò eam ad ſiniſtram verſus A, oſtendũt <lb/>horas pomeridianas, ſequentes verò eandem verſus dexteram B, pertinent ad horas antemeridia-<lb/>
<anchor type="note" xlink:label="note-0627-09a" xlink:href="note-0627-09"/>
nas, in horologio ſuperioritam ad ortum, quàm ad occaſum ſpectante. </s>
  <s xml:id="echoid-s40541" xml:space="preserve">In inferiori autem horo-<lb/>logio occaſum reſpiciente, vel ortum recta C E, eſt linea horæ 12. </s>
  <s xml:id="echoid-s40542" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s40543" xml:space="preserve">non meridiei,
<pb o="612" file="0628" n="628" rhead="GNOMONICES"/>
præcedentes verò eam verſus A, monſtrant horas antemeridianas, ſeu poſt mediam noctem, ſe-<lb/>quentes autem eandem verſus B, ſignificant horas pomeridianas. <lb/></s>
  <s xml:id="echoid-s40544" xml:space="preserve">
<anchor type="note" xlink:label="note-0628-01a" xlink:href="note-0628-01"/>
</s>
</p>
<div xml:id="echoid-div2011" type="float" level="2" n="2">
<note position="left" xlink:label="note-0627-04" xlink:href="note-0627-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0627-05" xlink:href="note-0627-05a" xml:space="preserve">Deſcri@tio horo <lb/>logii ab Hori-<lb/>zonte declinan-<lb/>@is.</note>
  <figure xlink:label="fig-0627-01" xlink:href="fig-0627-01a">
    <image file="0627-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0627-01"/>
  </figure>
<note position="left" xlink:label="note-0627-06" xlink:href="note-0627-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0627-07" xlink:href="note-0627-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0627-08" xlink:href="note-0627-08a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0627-09" xlink:href="note-0627-09a" xml:space="preserve">Ordo horarum <lb/>in horologio de <lb/>clinante ab Ho <lb/>rizonte.</note>
<note position="left" xlink:label="note-0628-01" xlink:href="note-0628-01a" xml:space="preserve">Deſcriptio eiuſ-<lb/>dem horologii <lb/>ab Hotizonte <lb/>declinantis ex <lb/>horologio Ver-<lb/>ticali.</note>
</div>
<p>
  <s xml:id="echoid-s40545" xml:space="preserve">QVOD verò attinet ad poſteriorem rationem ducendarum linearum horariarum, qua vide-<lb/>licet cap. </s>
  <s xml:id="echoid-s40546" xml:space="preserve">24. </s>
  <s xml:id="echoid-s40547" xml:space="preserve">inuenimus puncta in recta A B, per quæ tranſeunt horæ ex centro C, emiſſæ, obſer-<lb/>uandum eſt, lineas horarias ex F, egredientes, rectamq́ue A B ſecantes non eſſe ſumendas ex horo-<lb/>logio horizontali, ſed ex Verticali, vt lib. </s>
  <s xml:id="echoid-s40548" xml:space="preserve">2. </s>
  <s xml:id="echoid-s40549" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40550" xml:space="preserve">13. </s>
  <s xml:id="echoid-s40551" xml:space="preserve">oſtendimus.</s>
  <s xml:id="echoid-s40552" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40553" xml:space="preserve">ANGVLVS autem G C I, eſt hic quoque quantitas altitudinis poli ſupra planum horolo-<lb/>
<anchor type="note" xlink:label="note-0628-02a" xlink:href="note-0628-02"/>
gii, ſicut in horologiis declinantibus à Verticali, vt cap. </s>
  <s xml:id="echoid-s40554" xml:space="preserve">24. </s>
  <s xml:id="echoid-s40555" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s40556" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2012" type="float" level="2" n="3">
<note position="left" xlink:label="note-0628-02" xlink:href="note-0628-02a" xml:space="preserve">Altitudo poli ſu <lb/>pra planum ab <lb/>Horizonte de <lb/>clinans.</note>
</div>
<p>
  <s xml:id="echoid-s40557" xml:space="preserve">ARCVS ſignorum, &amp; </s>
  <s xml:id="echoid-s40558" xml:space="preserve">longitudinum dietum deſcribentur hic, vt in horologio declinante à <lb/>Verticali. </s>
  <s xml:id="echoid-s40559" xml:space="preserve">Id quod ex ſequentibus duabus figuris perſpicuum eſt. <lb/></s>
  <s xml:id="echoid-s40560" xml:space="preserve">
<anchor type="note" xlink:label="note-0628-03a" xlink:href="note-0628-03"/>
<anchor type="note" xlink:label="note-0628-04a" xlink:href="note-0628-04"/>
<anchor type="figure" xlink:label="fig-0628-01a" xlink:href="fig-0628-01"/>
<anchor type="note" xlink:label="note-0628-05a" xlink:href="note-0628-05"/>
<anchor type="note" xlink:label="note-0628-06a" xlink:href="note-0628-06"/>
</s>
</p>
<p>
  <s xml:id="echoid-s40561" xml:space="preserve">LINEA horizontalis ducitur hic parallela rectæ C E, per punctum, vbi linea hòræ 6. </s>
  <s xml:id="echoid-s40562" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40563" xml:space="preserve">ęqui <lb/>
<anchor type="note" xlink:label="note-0628-08a" xlink:href="note-0628-08"/>
noctialis ſe mutuo interſecant, vt in figura cernitur. </s>
  <s xml:id="echoid-s40564" xml:space="preserve">Hæc autem horizontalis linea diſpertit to-<lb/>tum horologium in duo, quorum maius, in quo nimirum includitur linea horæ 12. </s>
  <s xml:id="echoid-s40565" xml:space="preserve">ad Zenith <lb/>
<anchor type="note" xlink:label="note-0628-09a" xlink:href="note-0628-09"/>
ſpectat, eſtq́ue ſuperius, aliud verò inferius eſt, dum modo, conuerſis nobis ad horologium verſus <lb/>ortum, occaſumve, prout horologium ad occaſum, aut ortum ſpectat, ſuperiora omnia fiant in-<lb/>feriora, &amp; </s>
  <s xml:id="echoid-s40566" xml:space="preserve">quæ tunc nobis dextra ſunt, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s40567" xml:space="preserve">contra: </s>
  <s xml:id="echoid-s40568" xml:space="preserve">cuiuſmodi eſſent lineamenta, quæ <lb/>in parte oppoſita ſuperioris horologii (poſtquam pars ſuperior facta eſt inferior) deſcriberentur <lb/>
<anchor type="note" xlink:label="note-0628-10a" xlink:href="note-0628-10"/>
reſpondentia ad vnguem lineamentis vltra lineam horizontalem. </s>
  <s xml:id="echoid-s40569" xml:space="preserve">Vtrumque portò horologium <lb/>tam ſupertius, quàm inferius ita collo candum eſt, vt linea horizontalis &amp; </s>
  <s xml:id="echoid-s40570" xml:space="preserve">Horizonti, &amp; </s>
  <s xml:id="echoid-s40571" xml:space="preserve">lineæ me-<lb/>ridianę in plano Horizonti parallelo inuentæ æquidiſtet, atque recta A B, in plano circuli Vertica-<lb/>
<anchor type="note" xlink:label="note-0628-11a" xlink:href="note-0628-11"/>
lis propriè dicti ſita ſit, hac tamen lege, vt linea horizontalis in ſuperiori quocunque horologio <lb/>ſit ſupra lineam meridianam, in inferiori autem infra. </s>
  <s xml:id="echoid-s40572" xml:space="preserve">Denique vt, ſi ſuperuacanea reſcindantur, <lb/>horizontalis linea ſuperiorem ſemper occupet locum, &amp; </s>
  <s xml:id="echoid-s40573" xml:space="preserve">centrum C, in ſuperiori vergat in au-<lb/>ſtrum, in Boream verò in Inferiori, nec non recta A B, cum linea, quæ meridianam lineam ad re-<lb/>ctos angulos ſecat, angulum cõſtituat inclinationis planiad Horizontem, &amp; </s>
  <s xml:id="echoid-s40574" xml:space="preserve">communis ſectio pla-<lb/>
<anchor type="note" xlink:label="note-0628-12a" xlink:href="note-0628-12"/>
ni horologii, &amp; </s>
  <s xml:id="echoid-s40575" xml:space="preserve">plani Horizonti æquidiſtantis ſit ipſa linea meridiana in plano Horizonti pa-<lb/>rallelo, vel ei æquidiſtans.</s>
  <s xml:id="echoid-s40576" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2013" type="float" level="2" n="4">
<note position="left" xlink:label="note-0628-03" xlink:href="note-0628-03a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſig norũ, <lb/>&amp; longitudinu <lb/>d@e@um in horo <lb/>logio declinan-<lb/>te ab Horizon-<lb/>te.</note>
<note position="left" xlink:label="note-0628-04" xlink:href="note-0628-04a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0628-01" xlink:href="fig-0628-01a">
    <image file="0628-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0628-01"/>
  </figure>
<note position="left" xlink:label="note-0628-05" xlink:href="note-0628-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0628-06" xlink:href="note-0628-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0628-08" xlink:href="note-0628-08a" xml:space="preserve">Horizontalis li <lb/>neæ deſcriptio.</note>
<note position="left" xlink:label="note-0628-09" xlink:href="note-0628-09a" xml:space="preserve">Horologium ſu <lb/>perius. &amp; Infe-<lb/>rius.</note>
<note position="left" xlink:label="note-0628-10" xlink:href="note-0628-10a" xml:space="preserve">Quomodo ho-<lb/>rologium collo <lb/>eandum ſit, vt <lb/>horas indicet.</note>
<note position="left" xlink:label="note-0628-11" xlink:href="note-0628-11a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0628-12" xlink:href="note-0628-12a" xml:space="preserve">Horologiũ diur <lb/>nũ &amp; nocturnũ.</note>
</div>
<note position="left" xml:space="preserve">Qui arcus in ho <lb/>rologio declinã <lb/>te ab Horizon-<lb/>te pertineant ad <lb/>ſigna borealia, <lb/>&amp; qui ad auſtra <lb/>lia.</note>
<p>
  <s xml:id="echoid-s40577" xml:space="preserve">RVRSVS eadem linea horizontalis dirimit totum horologium in diurnum, &amp; </s>
  <s xml:id="echoid-s40578" xml:space="preserve">nocturnum, <lb/>vt in Verticali horologio dictum eſt.</s>
  <s xml:id="echoid-s40579" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40580" xml:space="preserve">IN omni autem horologio declinante ab Horizonte arcus ſignorum borealium ſunt verſus <lb/>auſtrum, &amp; </s>
  <s xml:id="echoid-s40581" xml:space="preserve">auſtralium verſus Boream, hoc eſt, in ſuperiori horologio arcus borealium ſignorum
<pb o="613" file="0629" n="629" rhead="LIBER SEPTIMVS."/>
continentur inter æquinoctialem lineam, &amp; </s>
  <s xml:id="echoid-s40582" xml:space="preserve">cẽtrum: </s>
  <s xml:id="echoid-s40583" xml:space="preserve">in inferiori vero arcus ſignorum auſtralium <lb/>verſus centrum deſcripti ſunt, &amp;</s>
  <s xml:id="echoid-s40584" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40585" xml:space="preserve">Eodem quoque modo hic iudicabimus, qui arcus ſignorum <lb/>
<anchor type="figure" xlink:label="fig-0629-01a" xlink:href="fig-0629-01"/>
<anchor type="note" xlink:label="note-0629-01a" xlink:href="note-0629-01"/>
<anchor type="note" xlink:label="note-0629-02a" xlink:href="note-0629-02"/>
<anchor type="note" xlink:label="note-0629-03a" xlink:href="note-0629-03"/>
ſint hyperbolæ, &amp; </s>
  <s xml:id="echoid-s40586" xml:space="preserve">qui parabolæ, &amp; </s>
  <s xml:id="echoid-s40587" xml:space="preserve">qui Ellipſes, vt in horologio declinante à Verticali cap. </s>
  <s xml:id="echoid-s40588" xml:space="preserve">24. <lb/></s>
  <s xml:id="echoid-s40589" xml:space="preserve">diximus.</s>
  <s xml:id="echoid-s40590" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2014" type="float" level="2" n="5">
  <figure xlink:label="fig-0629-01" xlink:href="fig-0629-01a">
    <image file="0629-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0629-01"/>
  </figure>
<note position="left" xlink:label="note-0629-01" xlink:href="note-0629-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0629-02" xlink:href="note-0629-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0629-03" xlink:href="note-0629-03a" xml:space="preserve">30</note>
</div>
<note position="left" xml:space="preserve">40</note>
<p>
  <s xml:id="echoid-s40591" xml:space="preserve">QVOD ſi omnia lineamenta horologii ſuperioris ad occaſum ſpectantis deſcribantur in alio <lb/>
<anchor type="note" xlink:label="note-0629-05a" xlink:href="note-0629-05"/>
plano, ita vt, quæ ſunt ad dexteram ipſius lineæ meridianæ ſita, fiant ſiniſtra, &amp; </s>
  <s xml:id="echoid-s40592" xml:space="preserve">è contrario, con-<lb/>ſtructum erit horologium ſuperius ad ortum ſpectans, commutatis horarum numeris in earum <lb/>complementa vſque ad 12. </s>
  <s xml:id="echoid-s40593" xml:space="preserve">Huiuſmodi ſunt lineamenta horologii, quod ad occaſum ſpectat, in <lb/>parte oppoſita deſcripta, vt ſingulæ ſingulis lineis ad vnguem reſpondeant. </s>
  <s xml:id="echoid-s40594" xml:space="preserve">Eodem modo <lb/>horologium quod ad ortum ſpectat, mutari poterit in aliud, quod ad occaſum ſpectet, ſi illa per-<lb/>mutatio linearum &amp; </s>
  <s xml:id="echoid-s40595" xml:space="preserve">numerorum fiat. </s>
  <s xml:id="echoid-s40596" xml:space="preserve">Immo &amp; </s>
  <s xml:id="echoid-s40597" xml:space="preserve">inferius orientale eadem ratione mutabitur in <lb/>inferius occidentale, &amp; </s>
  <s xml:id="echoid-s40598" xml:space="preserve">contra. <lb/></s>
  <s xml:id="echoid-s40599" xml:space="preserve">
<anchor type="note" xlink:label="note-0629-06a" xlink:href="note-0629-06"/>
</s>
</p>
<div xml:id="echoid-div2015" type="float" level="2" n="6">
<note position="right" xlink:label="note-0629-05" xlink:href="note-0629-05a" xml:space="preserve">Qua ratione ex <lb/>horologio ad <lb/>occaſum ſpe-<lb/>ctante fiat horo <lb/>logium ſpectans <lb/>ad orum &amp; cõ-<lb/>tra.</note>
<note position="right" xlink:label="note-0629-06" xlink:href="note-0629-06a" xml:space="preserve">Conſtructio ho <lb/>rologii Italici, <lb/>&amp; Babylonici <lb/>ab Horizont@ <lb/>de@iinantis.</note>
</div>
<p>
  <s xml:id="echoid-s40600" xml:space="preserve">HOROLOGIVM tam Italicum, quàm Babylonicum deſcribetur, vt ſupra diximus, ſi ni-<lb/>mirum circulus ex L, deſcriptus ſecetur in arcum diurnum ♋, a N b, &amp; </s>
  <s xml:id="echoid-s40601" xml:space="preserve">diurnum ♑, d N e, vt an-<lb/>
<anchor type="note" xlink:label="note-0629-07a" xlink:href="note-0629-07"/>
te docuimus, diuiſioq́ue eiuſdem circuli initium ſumat pro horologio Italico à punctis b, e, oc-<lb/>cidentalibus, pro Babylonico vero à punctis a, d, orientalibus. </s>
  <s xml:id="echoid-s40602" xml:space="preserve">Exemplum habes in hora 21. </s>
  <s xml:id="echoid-s40603" xml:space="preserve">ab <lb/>occ. </s>
  <s xml:id="echoid-s40604" xml:space="preserve">Nam exm, puncto horę 21. </s>
  <s xml:id="echoid-s40605" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40606" xml:space="preserve">in tropico ♑, ducta recta per L, ſecat æquinoctialem li-<lb/>neam in n; </s>
  <s xml:id="echoid-s40607" xml:space="preserve">recta autem ex C, per n, ducta ſecat tropicum ♑, in p, puncto horæ 21. </s>
  <s xml:id="echoid-s40608" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40609" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40610" xml:space="preserve">c.</s>
  <s xml:id="echoid-s40611" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2016" type="float" level="2" n="7">
<note position="left" xlink:label="note-0629-07" xlink:href="note-0629-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s40612" xml:space="preserve">QVOD ad deſcriptionem ex arcubus diurnis, nocturnisq́ue depromptam attinet, nulla eſt <lb/>
<anchor type="note" xlink:label="note-0629-08a" xlink:href="note-0629-08"/>
difficultas, ſi tamen, quotieſcunque hora aliqua ab or. </s>
  <s xml:id="echoid-s40613" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s40614" xml:space="preserve">non habet punctum in arcubus <lb/>diurnis, nocturnisve, accipiatur eiuſdem numeri hora ab occ. </s>
  <s xml:id="echoid-s40615" xml:space="preserve">vel or. </s>
  <s xml:id="echoid-s40616" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s40617" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40618" xml:space="preserve">vt in ſuperioribus di-<lb/>ctum eſt. </s>
  <s xml:id="echoid-s40619" xml:space="preserve">Verbi gratia, quia hora 12. </s>
  <s xml:id="echoid-s40620" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40621" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40622" xml:space="preserve">nullum punctum habet, <lb/>vt conſtat ex tabella 3. </s>
  <s xml:id="echoid-s40623" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40624" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40625" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40626" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40627" xml:space="preserve">accipiemus horam 12. </s>
  <s xml:id="echoid-s40628" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40629" xml:space="preserve">eamq́ue, vt vult dicta tabella <lb/>3. </s>
  <s xml:id="echoid-s40630" xml:space="preserve">ducemus per horam 5. </s>
  <s xml:id="echoid-s40631" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40632" xml:space="preserve">in arcu diurno horar ũ 14. </s>
  <s xml:id="echoid-s40633" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40634" xml:space="preserve">per horã 6. </s>
  <s xml:id="echoid-s40635" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40636" xml:space="preserve">(vt vult tabella 6. <lb/></s>
  <s xml:id="echoid-s40637" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40638" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40639" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40640" xml:space="preserve">1.) </s>
  <s xml:id="echoid-s40641" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40642" xml:space="preserve">Hæc enim producta dabit etiam horam 12. </s>
  <s xml:id="echoid-s40643" xml:space="preserve">ab
<pb o="614" file="0630" n="630" rhead="GNOMONICES"/>
occ. </s>
  <s xml:id="echoid-s40644" xml:space="preserve">Pari ratione pro hora 13. </s>
  <s xml:id="echoid-s40645" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40646" xml:space="preserve">ducta eſt hora 13. </s>
  <s xml:id="echoid-s40647" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40648" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s40649" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40650" xml:space="preserve">in arcu diurno <lb/>horarum 14. </s>
  <s xml:id="echoid-s40651" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40652" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s40653" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40654" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40655" xml:space="preserve">Item pro hora 14. </s>
  <s xml:id="echoid-s40656" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40657" xml:space="preserve">quæ <lb/>
<anchor type="figure" xlink:label="fig-0630-01a" xlink:href="fig-0630-01"/>
<anchor type="note" xlink:label="note-0630-01a" xlink:href="note-0630-01"/>
<anchor type="note" xlink:label="note-0630-02a" xlink:href="note-0630-02"/>
<anchor type="note" xlink:label="note-0630-03a" xlink:href="note-0630-03"/>
<anchor type="note" xlink:label="note-0630-04a" xlink:href="note-0630-04"/>
vnicum punctum habet, nempe horam 9. </s>
  <s xml:id="echoid-s40658" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40659" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40660" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40661" xml:space="preserve">accepimus ho-<lb/>tam 14. </s>
  <s xml:id="echoid-s40662" xml:space="preserve">abor. </s>
  <s xml:id="echoid-s40663" xml:space="preserve">quæ ducenda eſt per horam 7. </s>
  <s xml:id="echoid-s40664" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40665" xml:space="preserve">in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s40666" xml:space="preserve">Recta enim <lb/>ducta per hæc duo puncta, nimirum per horam 9. </s>
  <s xml:id="echoid-s40667" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40668" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40669" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40670" xml:space="preserve">per horam 7. </s>
  <s xml:id="echoid-s40671" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40672" xml:space="preserve">dabit in ar-<lb/>cu diurno horarum 14. </s>
  <s xml:id="echoid-s40673" xml:space="preserve">horam 14. </s>
  <s xml:id="echoid-s40674" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40675" xml:space="preserve">in arcu vero nocturno horarum 10. </s>
  <s xml:id="echoid-s40676" xml:space="preserve">horam 10. </s>
  <s xml:id="echoid-s40677" xml:space="preserve">ab or. <lb/></s>
  <s xml:id="echoid-s40678" xml:space="preserve">Denique pro hora 1. </s>
  <s xml:id="echoid-s40679" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40680" xml:space="preserve">in horologio Inferiori ducta eſt hora 1. </s>
  <s xml:id="echoid-s40681" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40682" xml:space="preserve">in horologio nocturno <lb/>per horam 7. </s>
  <s xml:id="echoid-s40683" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40684" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40685" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40686" xml:space="preserve">per horam 8. </s>
  <s xml:id="echoid-s40687" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40688" xml:space="preserve">in arcu nocturno hora-<lb/>rum 10. </s>
  <s xml:id="echoid-s40689" xml:space="preserve">nec non per horam ♉. </s>
  <s xml:id="echoid-s40690" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40691" xml:space="preserve">in arcu nocturno horarum 14. </s>
  <s xml:id="echoid-s40692" xml:space="preserve">Hæc enim in inferiori horo-<lb/>logio dat horam 1. </s>
  <s xml:id="echoid-s40693" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s40694" xml:space="preserve">vt oſtendimus in ſcholio propoſ. </s>
  <s xml:id="echoid-s40695" xml:space="preserve">23. </s>
  <s xml:id="echoid-s40696" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40697" xml:space="preserve">2.</s>
  <s xml:id="echoid-s40698" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2017" type="float" level="2" n="8">
<note position="right" xlink:label="note-0629-08" xlink:href="note-0629-08a" xml:space="preserve">Alia deſcriptio <lb/>horologii Itali-<lb/>ci, &amp; Babylonſ-<lb/>ci ab Horizonte <lb/>declinantis, ex <lb/>arcubus d@ut-<lb/>nis, nocturnis.</note>
  <figure xlink:label="fig-0630-01" xlink:href="fig-0630-01a">
    <image file="0630-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0630-01"/>
  </figure>
<note position="left" xlink:label="note-0630-01" xlink:href="note-0630-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0630-02" xlink:href="note-0630-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0630-03" xlink:href="note-0630-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0630-04" xlink:href="note-0630-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s40699" xml:space="preserve">HORAE autem productæ vltra lineam horizontalem dant in inferiori quoque horologio <lb/>horas ab or. </s>
  <s xml:id="echoid-s40700" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40701" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s40702" xml:space="preserve">vt in Verticali horologio explicauimus.</s>
  <s xml:id="echoid-s40703" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s40704" xml:space="preserve">ANTIQVVM horologium conſtruitur, vt declinans à Verticali. </s>
  <s xml:id="echoid-s40705" xml:space="preserve">Nam v. </s>
  <s xml:id="echoid-s40706" xml:space="preserve">g. </s>
  <s xml:id="echoid-s40707" xml:space="preserve">ex f, puncto <lb/>
<anchor type="note" xlink:label="note-0630-06a" xlink:href="note-0630-06"/>
horę 4. </s>
  <s xml:id="echoid-s40708" xml:space="preserve">inęqualis tropici ♋, ducta recta per L, ſecat æquinoctialem lineam in g, &amp; </s>
  <s xml:id="echoid-s40709" xml:space="preserve">recta C g, tro-<lb/>picum ♋, ſecat in h, puncto horæ 4. </s>
  <s xml:id="echoid-s40710" xml:space="preserve">inæqualis, &amp; </s>
  <s xml:id="echoid-s40711" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s40712" xml:space="preserve">Pro hora autem 1. </s>
  <s xml:id="echoid-s40713" xml:space="preserve">in horologio <lb/>inferiori duximus ex in, puncto horæ 1. </s>
  <s xml:id="echoid-s40714" xml:space="preserve">nocturnæ tropici ♑, per L, rectam, quæ lineam ęquino-<lb/>ctialem ſecat in n. </s>
  <s xml:id="echoid-s40715" xml:space="preserve">Recta enim C n, ſecat tropicum ♑, in p, puncto horæ 1. </s>
  <s xml:id="echoid-s40716" xml:space="preserve">inæqualis nocturnæ. <lb/></s>
  <s xml:id="echoid-s40717" xml:space="preserve">Quapropter recta ex p, per horam 7. </s>
  <s xml:id="echoid-s40718" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40719" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40720" xml:space="preserve">ducta dabit horam 1. </s>
  <s xml:id="echoid-s40721" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0630-07a" xlink:href="note-0630-07"/>
nocturnam inęqualem in portione horologii nocturna: </s>
  <s xml:id="echoid-s40722" xml:space="preserve">hęc autem in horologio inferiori erit <lb/>hora 1. </s>
  <s xml:id="echoid-s40723" xml:space="preserve">inæqualis diurna, &amp;</s>
  <s xml:id="echoid-s40724" xml:space="preserve">c.</s>
  <s xml:id="echoid-s40725" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2018" type="float" level="2" n="9">
<note position="left" xlink:label="note-0630-06" xlink:href="note-0630-06a" xml:space="preserve">Conſtructio ho <lb/>rolegii Antiqui <lb/>ab Horizonte <lb/>decliuantis.</note>
<note position="left" xlink:label="note-0630-07" xlink:href="note-0630-07a" xml:space="preserve">Deſcriptio eiuſ-<lb/>dem horologii <lb/>An@qui ab Ho <lb/>rizonte decli-<lb/>nantis, ex arcu <lb/>diutno hora-<lb/>rum 18.</note>
</div>
<p>
  <s xml:id="echoid-s40726" xml:space="preserve">SECVNDVM autem poſteriorem rationem notauimus in horis à media nocte 9. </s>
  <s xml:id="echoid-s40727" xml:space="preserve">10 {1/2}. <lb/></s>
  <s xml:id="echoid-s40728" xml:space="preserve">12. </s>
  <s xml:id="echoid-s40729" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40730" xml:space="preserve">in horis à meridie 1 {1/2}. </s>
  <s xml:id="echoid-s40731" xml:space="preserve">3. </s>
  <s xml:id="echoid-s40732" xml:space="preserve">4 {1/2}. </s>
  <s xml:id="echoid-s40733" xml:space="preserve">6. </s>
  <s xml:id="echoid-s40734" xml:space="preserve">7 {1/2}. </s>
  <s xml:id="echoid-s40735" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40736" xml:space="preserve">puncta arcus diurni horarum 18. </s>
  <s xml:id="echoid-s40737" xml:space="preserve">per quæ ducendæ <lb/>ſunt horæ inæquales, vt ex tabulis ſcholii propoſ. </s>
  <s xml:id="echoid-s40738" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40739" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40740" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40741" xml:space="preserve">manifeſtum eſt.</s>
  <s xml:id="echoid-s40742" xml:space="preserve"/>
</p>
<pb o="615" file="0631" n="631" rhead="LIBER SEPTIMVS."/>
  <figure>
    <image file="0631-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0631-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div2020" type="section" level="1" n="514">
<head xml:id="echoid-head543" style="it" xml:space="preserve">DE HOROLOGIIS AD HORIZONTEM <lb/>inclinatis. CAP. XXVIII.</head>
<p>
  <s xml:id="echoid-s40743" xml:space="preserve">DIXIMVS in principio huius Gnomonices, illud horologium dici inclinatum ad Horizon <lb/>tem, quod æquidiſtat circulo maximo ad Meridianum recto, &amp; </s>
  <s xml:id="echoid-s40744" xml:space="preserve">per communes ſectiones <lb/>
<anchor type="note" xlink:label="note-0631-04a" xlink:href="note-0631-04"/>
Horizontis, Aequatoris, &amp; </s>
  <s xml:id="echoid-s40745" xml:space="preserve">Verticalis circuli ducto, ita vt communis ſectio illius, ac Horizontis <lb/>
<anchor type="note" xlink:label="note-0631-05a" xlink:href="note-0631-05"/>
perpendicularis ſit ad lineam meridianam. </s>
  <s xml:id="echoid-s40746" xml:space="preserve">Hoc autem quadruplex eſt. </s>
  <s xml:id="echoid-s40747" xml:space="preserve">Aut enim ſpectat ad Ze-<lb/>nith, &amp; </s>
  <s xml:id="echoid-s40748" xml:space="preserve">auſtrum, vel ad Nadir, &amp; </s>
  <s xml:id="echoid-s40749" xml:space="preserve">Boream, ita vt lineæ angulum inclinationis, quem cum Horizon <lb/>te efficit, conſtituentes vergant in Boream: </s>
  <s xml:id="echoid-s40750" xml:space="preserve">Aut reſpicit Zenith &amp; </s>
  <s xml:id="echoid-s40751" xml:space="preserve">boreã, vel Nadir, &amp; </s>
  <s xml:id="echoid-s40752" xml:space="preserve">auſtrum, <lb/>
<anchor type="note" xlink:label="note-0631-06a" xlink:href="note-0631-06"/>
ita vt lineæ angulum inclinationis conſtituentes auſtrum verſus protendantur. </s>
  <s xml:id="echoid-s40753" xml:space="preserve">Primum appel-<lb/>lari poteſt ſuperius auſtrale: </s>
  <s xml:id="echoid-s40754" xml:space="preserve">alterum Inferius boreale: </s>
  <s xml:id="echoid-s40755" xml:space="preserve">Tertium ſuperius boreale: </s>
  <s xml:id="echoid-s40756" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40757" xml:space="preserve">poſtremum <lb/>Inferius auſtrale. </s>
  <s xml:id="echoid-s40758" xml:space="preserve">Vt autem facilius omnia hæc horologia deſcribantur, diligenter memoriæ man <lb/>danda ſunt ſex præcepta, quæ ſequuntur.</s>
  <s xml:id="echoid-s40759" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2020" type="float" level="2" n="1">
<note position="left" xlink:label="note-0631-04" xlink:href="note-0631-04a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0631-05" xlink:href="note-0631-05a" xml:space="preserve">Horologium ad <lb/>Horizõtem in-<lb/>clinatum qua-<lb/>druplex.</note>
<note position="right" xlink:label="note-0631-06" xlink:href="note-0631-06a" xml:space="preserve">Horologiũ Su-<lb/>perius auſtrale: <lb/>Inferius borea-<lb/>le: Superius bo-<lb/>reale: &amp; Inferius <lb/>auſtrale, quod <lb/>dicatur.</note>
</div>
</div>
<div xml:id="echoid-div2022" type="section" level="1" n="515">
<head xml:id="echoid-head544" style="it" xml:space="preserve">PRAECEPTVM I.</head>
<note position="left" xml:space="preserve">50</note>
<note position="right" xml:space="preserve">Sex præcepta <lb/>pro conſtructio-<lb/>ne horologior@ <lb/>ad Horizontem <lb/>inclinat<unsure/>orum.</note>
<p>
  <s xml:id="echoid-s40760" xml:space="preserve">QVANDO planum horologii ſuperioris auſtralis, vel inferioris Borealis, cuius ſcilicet in-<lb/>clinationis angulus in Boream vergit, inclinationem habet æqualem altitudini poli, non differet <lb/>eius horologium à Polari ſuperiori, &amp; </s>
  <s xml:id="echoid-s40761" xml:space="preserve">inferiori, de quo cap. </s>
  <s xml:id="echoid-s40762" xml:space="preserve">16. </s>
  <s xml:id="echoid-s40763" xml:space="preserve">egimus.</s>
  <s xml:id="echoid-s40764" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2023" type="section" level="1" n="516">
<head xml:id="echoid-head545" style="it" xml:space="preserve">PRAECEPTVM II.</head>
<p>
  <s xml:id="echoid-s40765" xml:space="preserve">CVM verò idem planum inclinationem habuerit altitudine poli minorem, ſi detrahatur in-<lb/>clinatio ab altitudine poli, relinquetur altitudo poli ſupra planum propoſitum; </s>
  <s xml:id="echoid-s40766" xml:space="preserve">ad quam horolo-<lb/>gium horizontale deſcribendum eſt, vt cap. </s>
  <s xml:id="echoid-s40767" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40768" xml:space="preserve">tradidimus. </s>
  <s xml:id="echoid-s40769" xml:space="preserve">Hoc autem ita collocandum erit, vt li-<lb/>nea æquinoctialis æquidiſtet lineæ rectæ, quæ in plano, quod Horizonti æquidiſtat, lineam meri-<lb/>dianam ſecatad rectos angulos; </s>
  <s xml:id="echoid-s40770" xml:space="preserve">(Quod facile fiet, ſi recra quępiam linea meridianam lineam ho-<lb/>rologii ad rectos angulos ſecans ſtatuatur in plano, quod Horizonti parallelum eſt, perpendicula-
<pb o="616" file="0632" n="632" rhead="GNOMONICES"/>
ris ad lineam meridianam in eo inuentam) &amp; </s>
  <s xml:id="echoid-s40771" xml:space="preserve">horologium ipſum eleuetur ex parte boreali ſecun <lb/>dum inclinationem plani, ita vt eius linea meridiana cum meridiana linea in plano, quod Hori-<lb/>zonti æquidiſtat, inuenta ad partes ſeptentrionis contineat angulum inclinationis: </s>
  <s xml:id="echoid-s40772" xml:space="preserve">hac tamen le-<lb/>ge, vt in ſuperiori facie plani, quæ ad Zenith, &amp; </s>
  <s xml:id="echoid-s40773" xml:space="preserve">meridiem conuertitur, centrum horologii infra <lb/>lineam æquinoctialem exiſtat, in inferiori verò, &amp; </s>
  <s xml:id="echoid-s40774" xml:space="preserve">boreali ſupra eandem. </s>
  <s xml:id="echoid-s40775" xml:space="preserve">Ordo horarum hic erit. <lb/></s>
  <s xml:id="echoid-s40776" xml:space="preserve">In ſuperiori horologio horæ poſt med. </s>
  <s xml:id="echoid-s40777" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40778" xml:space="preserve">ſunt nobis ad horologium verſus boream conuerſis <lb/>ad ſiniſtram lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s40779" xml:space="preserve">pomeridianæ ad dexteram eiuſdem, ita vt portio lineæ meridia-<lb/>næ à centro verſus æquinoctialem lineam ſignificet horam 12. </s>
  <s xml:id="echoid-s40780" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s40781" xml:space="preserve">reliqua portio à cen-<lb/>tro etiam inchoata horam 12. </s>
  <s xml:id="echoid-s40782" xml:space="preserve">mediæ noctis, quemadmodum in horologio horizontali. </s>
  <s xml:id="echoid-s40783" xml:space="preserve">In infe-<lb/>riori autem cõtrario modo ſe res habet: </s>
  <s xml:id="echoid-s40784" xml:space="preserve">quia horæ poſt med. </s>
  <s xml:id="echoid-s40785" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40786" xml:space="preserve">ſunt nobis ad horologium ver-<lb/>
<anchor type="note" xlink:label="note-0632-01a" xlink:href="note-0632-01"/>
ſus auſtrum conuerſis ad dexteram ipſius lineę meridianæ, &amp; </s>
  <s xml:id="echoid-s40787" xml:space="preserve">pomeridianæ ad ſiniſtram, ita vt por <lb/>tio lineæ meridianæ à centro verſus lineam æquinoctialem indicet horam 12. </s>
  <s xml:id="echoid-s40788" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s40789" xml:space="preserve">re-<lb/>liqua portio à centro quoque inchoata horam 12. </s>
  <s xml:id="echoid-s40790" xml:space="preserve">meridiei, vt in Verticali horologio ad bo-<lb/>ream ſpectante.</s>
  <s xml:id="echoid-s40791" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2023" type="float" level="2" n="1">
<note position="left" xlink:label="note-0632-01" xlink:href="note-0632-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s40792" xml:space="preserve">ARCVS præterea ſignorum borealium exiſtunt inter centrum, &amp; </s>
  <s xml:id="echoid-s40793" xml:space="preserve">æquinoctialem lineam in <lb/>horologio ſuperiori, &amp; </s>
  <s xml:id="echoid-s40794" xml:space="preserve">auſtralium vltra lineam æquinoctialem: </s>
  <s xml:id="echoid-s40795" xml:space="preserve">In inferiori autem contrario <lb/>ſe modo habent.</s>
  <s xml:id="echoid-s40796" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2025" type="section" level="1" n="517">
<head xml:id="echoid-head546" style="it" xml:space="preserve">PRAECEPTVM III.</head>
<p>
  <s xml:id="echoid-s40797" xml:space="preserve">INCLINATIONE denique plani ſuperante poli altitudinem, ſi altitudo poli ab incli-<lb/>
<anchor type="note" xlink:label="note-0632-02a" xlink:href="note-0632-02"/>
natione auferatur, remanebit altitudo poli ſupra planum propoſitum; </s>
  <s xml:id="echoid-s40798" xml:space="preserve">ad quam horologium ho-<lb/>zontale fabricandum eſt, ex doctrina cap. </s>
  <s xml:id="echoid-s40799" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40800" xml:space="preserve">quod locandum erit, vt pręcedens, hoc excepto, quod <lb/>hic in ſuperiori, &amp; </s>
  <s xml:id="echoid-s40801" xml:space="preserve">auſtrali facie plani centrum horologij ſtatuendum eſt ſupra lineam æquino-<lb/>ctialem, in inferiori verò, &amp; </s>
  <s xml:id="echoid-s40802" xml:space="preserve">boreali infra eandem, veluti in Verticalibus horologiis fit. </s>
  <s xml:id="echoid-s40803" xml:space="preserve">Ordo <lb/>horarum idem hic eſt omnino, qui in 2. </s>
  <s xml:id="echoid-s40804" xml:space="preserve">pręcepto declaratus eſt.</s>
  <s xml:id="echoid-s40805" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2025" type="float" level="2" n="1">
<note position="left" xlink:label="note-0632-02" xlink:href="note-0632-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s40806" xml:space="preserve">ARCVS autem ſignorum auſtralium includuntur inter centrum, &amp; </s>
  <s xml:id="echoid-s40807" xml:space="preserve">æquinoctialem lineam <lb/>in ſuperiori horologio, &amp; </s>
  <s xml:id="echoid-s40808" xml:space="preserve">Borealium vltra lineam æquinoctialem: </s>
  <s xml:id="echoid-s40809" xml:space="preserve">At in inferiori oppoſito ſe <lb/>modo habent.</s>
  <s xml:id="echoid-s40810" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2027" type="section" level="1" n="518">
<head xml:id="echoid-head547" style="it" xml:space="preserve">PRAECEPTVM IIII.</head>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s40811" xml:space="preserve">RVRSVS quando planum horologii ſuperioris borealis, vel inferioris auſtralis, cuius ni-<lb/>mirum inclinationis angulus in auſtrum vergit, inclinationem æqualem habet complemento al-<lb/>titudinis poli, idem erit eius horologium, quod Aequinoctiale ſuperius, ac inferius cap. </s>
  <s xml:id="echoid-s40812" xml:space="preserve">20. </s>
  <s xml:id="echoid-s40813" xml:space="preserve">de-<lb/>ſcriptum.</s>
  <s xml:id="echoid-s40814" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2028" type="section" level="1" n="519">
<head xml:id="echoid-head548" style="it" xml:space="preserve">PRAECEPTVM V.</head>
<p>
  <s xml:id="echoid-s40815" xml:space="preserve">QVANDO verò eius inclinatio minor eſt cõplemento altitudinis poli, ſi addatur inclinatio <lb/>altitudini poli, conflabitur altitudo poli ſupra ipſum planum; </s>
  <s xml:id="echoid-s40816" xml:space="preserve">ad quam ſecundum doctrinã cap. </s>
  <s xml:id="echoid-s40817" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s40818" xml:space="preserve">horologium horizontale conſtruendum eſt; </s>
  <s xml:id="echoid-s40819" xml:space="preserve">quod collocandum erit, vt in 2. </s>
  <s xml:id="echoid-s40820" xml:space="preserve">præcepto diximus, <lb/>niſi quòd hoc horologium eleuandum eſt ex parte auſtrali ſecundum inclinationem plani, ita vt <lb/>
<anchor type="note" xlink:label="note-0632-04a" xlink:href="note-0632-04"/>
eius meridiana linea cum linea meridiana in plano, quod Horizonti æquidiſtat, inuenta con-<lb/>ſtituat angulum inclinationis ad partes auſtrales, hac inſuper adiecta conditione, vt in ſuperiori, <lb/>&amp; </s>
  <s xml:id="echoid-s40821" xml:space="preserve">boreali facie plani centrum horologii ſedem habeat ſupra lineam æquinoctialem, at verò in <lb/>inferiori, &amp; </s>
  <s xml:id="echoid-s40822" xml:space="preserve">auſtrali infra eandem. </s>
  <s xml:id="echoid-s40823" xml:space="preserve">Ordo horarum hic erit. </s>
  <s xml:id="echoid-s40824" xml:space="preserve">In horologio ſuperiori, nobis ad <lb/>horologium conuerſis, horæ ad dexteram lineæ meridianæ exiſtentes ſunt poſt med. </s>
  <s xml:id="echoid-s40825" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40826" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40827" xml:space="preserve">quæ <lb/>ad eiuſdem ſiniſtram, pomeridianæ; </s>
  <s xml:id="echoid-s40828" xml:space="preserve">hac tamen lege, vt portio lineę meridianæ à centro verſus <lb/>æquinoctialem lineam notet horam 12. </s>
  <s xml:id="echoid-s40829" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s40830" xml:space="preserve">reliqua portio à centro etiam inchoata horã <lb/>12. </s>
  <s xml:id="echoid-s40831" xml:space="preserve">mediæ noctis. </s>
  <s xml:id="echoid-s40832" xml:space="preserve">In inferiori verò, nobis ad horologium conuerſis, horæ à med. </s>
  <s xml:id="echoid-s40833" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40834" xml:space="preserve">reperiun-<lb/>tur ad ſiniſtram lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s40835" xml:space="preserve">pomeridianæ ad dexteram, ita tamen vt portio lineæ meri-<lb/>dianæ à centro verſus æquinoctialem lineam pertineat ad horam 12. </s>
  <s xml:id="echoid-s40836" xml:space="preserve">medię noctis, &amp; </s>
  <s xml:id="echoid-s40837" xml:space="preserve">portio reli-<lb/>
<anchor type="note" xlink:label="note-0632-05a" xlink:href="note-0632-05"/>
qua à centro initium quoque ſumens horam 12. </s>
  <s xml:id="echoid-s40838" xml:space="preserve">meridiei indicet.</s>
  <s xml:id="echoid-s40839" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2028" type="float" level="2" n="1">
<note position="left" xlink:label="note-0632-04" xlink:href="note-0632-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0632-05" xlink:href="note-0632-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s40840" xml:space="preserve">ARCVS porrò ſignorum borealium ſunt illi, qui continentur in horologio ſuperiori inter <lb/>centrum, &amp; </s>
  <s xml:id="echoid-s40841" xml:space="preserve">lineam æquinoctialem, qui verò vltra dictam lineam ſunt, ad ſigna auſtralia perti-<lb/>nent, vt in horizontali horologio. </s>
  <s xml:id="echoid-s40842" xml:space="preserve">In inferiori autem contrario modo res ſe ſe habet.</s>
  <s xml:id="echoid-s40843" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2030" type="section" level="1" n="520">
<head xml:id="echoid-head549" style="it" xml:space="preserve">PRAECEPTVM VI.</head>
<p>
  <s xml:id="echoid-s40844" xml:space="preserve">SI denique inclinatio plani maior fuerit complemento altitudinis poli, addendum erit incli-<lb/>nationis complementum complemento altitudinis poli. </s>
  <s xml:id="echoid-s40845" xml:space="preserve">Hac enim ratione coficietur altitudo <lb/>poli ſupra planum propoſitum; </s>
  <s xml:id="echoid-s40846" xml:space="preserve">ad quam, vt cap. </s>
  <s xml:id="echoid-s40847" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40848" xml:space="preserve">docuimus, horologium horizontale compo <lb/>nendum eſt; </s>
  <s xml:id="echoid-s40849" xml:space="preserve">quod locari debet, vt in antecedenti præcepto docuimus, hac tamen cõditione, vt in <lb/>ſuperiori, &amp; </s>
  <s xml:id="echoid-s40850" xml:space="preserve">boreali facie plani centrum horologii ſtatuatur infra lineam æquinoctialem, quem-
<pb o="617" file="0633" n="633" rhead="LIBER SEPTIMVS."/>
admodum in horologio Verticali ad boream vergente: </s>
  <s xml:id="echoid-s40851" xml:space="preserve">at in inferiori, auſtraliq́; </s>
  <s xml:id="echoid-s40852" xml:space="preserve">ſupra eandem, <lb/>vt in horologio Verticali auſtrali. </s>
  <s xml:id="echoid-s40853" xml:space="preserve">Ordo horarum idem hic eſt, qui in præcepto antecedenti, hoc <lb/>dempto, quòd hic in ſuperiori horologio portio lineę meridianæ à centro verſus lineam æqui-<lb/>noctialem indicat horam 12. </s>
  <s xml:id="echoid-s40854" xml:space="preserve">mediæ noctis, &amp; </s>
  <s xml:id="echoid-s40855" xml:space="preserve">reliqua portio à centro etiam incipiẽs horam 12. <lb/></s>
  <s xml:id="echoid-s40856" xml:space="preserve">meridiei: </s>
  <s xml:id="echoid-s40857" xml:space="preserve">In inferiori verò contrarium fit.</s>
  <s xml:id="echoid-s40858" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40859" xml:space="preserve">ARCVS præterea ſignorum borealium continentur inter centrum, &amp; </s>
  <s xml:id="echoid-s40860" xml:space="preserve">æquinoctialem li-<lb/>neam in horologio ſuperiori, &amp; </s>
  <s xml:id="echoid-s40861" xml:space="preserve">auſtralium vltra dictam lineam: </s>
  <s xml:id="echoid-s40862" xml:space="preserve">at in inferiori contra.</s>
  <s xml:id="echoid-s40863" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40864" xml:space="preserve">EXEMPLVM omnium hoc ſit. </s>
  <s xml:id="echoid-s40865" xml:space="preserve">Proponatur planum ſpectans ad Zenith, &amp; </s>
  <s xml:id="echoid-s40866" xml:space="preserve">Boream ad <lb/>
<anchor type="note" xlink:label="note-0633-01a" xlink:href="note-0633-01"/>
Horizõtem inclinatum gr. </s>
  <s xml:id="echoid-s40867" xml:space="preserve">68. </s>
  <s xml:id="echoid-s40868" xml:space="preserve">Quoniam igitur inclinatio complemento altitudinis poli maior <lb/>eſt, cum in Horizõte Romano, pro quo omnia horologia in noſtra hac Gnomonica deſcribimus, <lb/>
<anchor type="note" xlink:label="note-0633-02a" xlink:href="note-0633-02"/>
<anchor type="figure" xlink:label="fig-0633-01a" xlink:href="fig-0633-01"/>
<anchor type="note" xlink:label="note-0633-03a" xlink:href="note-0633-03"/>
<anchor type="note" xlink:label="note-0633-04a" xlink:href="note-0633-04"/>
complementum altitudinis poli com <lb/>
<anchor type="figure" xlink:label="fig-0633-02a" xlink:href="fig-0633-02"/>
plectatur grad. </s>
  <s xml:id="echoid-s40869" xml:space="preserve">48. </s>
  <s xml:id="echoid-s40870" xml:space="preserve">addemus comple-<lb/>mentum inclinationis nempe grad. <lb/></s>
  <s xml:id="echoid-s40871" xml:space="preserve">22. </s>
  <s xml:id="echoid-s40872" xml:space="preserve">complemento altitudinis poli, <lb/>
<anchor type="note" xlink:label="note-0633-05a" xlink:href="note-0633-05"/>
efficiemusq́; </s>
  <s xml:id="echoid-s40873" xml:space="preserve">altitudinem poli ſupra <lb/>planum propoſitum grad. </s>
  <s xml:id="echoid-s40874" xml:space="preserve">70. </s>
  <s xml:id="echoid-s40875" xml:space="preserve">vt in <lb/>6. </s>
  <s xml:id="echoid-s40876" xml:space="preserve">præcepto tradidimus. </s>
  <s xml:id="echoid-s40877" xml:space="preserve">Ad hanc igi <lb/>tur altitudinem gr. </s>
  <s xml:id="echoid-s40878" xml:space="preserve">70. </s>
  <s xml:id="echoid-s40879" xml:space="preserve">horologium <lb/>inclinatum deſcribemus, quemad-<lb/>modum horizontale, vt in ſubiecta <lb/>
<anchor type="note" xlink:label="note-0633-06a" xlink:href="note-0633-06"/>
figura apparet.</s>
  <s xml:id="echoid-s40880" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2030" type="float" level="2" n="1">
<note position="right" xlink:label="note-0633-01" xlink:href="note-0633-01a" xml:space="preserve">Deſcriptio horo<unsure/> <lb/>logii Aſtrono-<lb/>mici ad Hor<unsure/>i-<lb/>zontem inclina <lb/>ti.</note>
<note position="left" xlink:label="note-0633-02" xlink:href="note-0633-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0633-01" xlink:href="fig-0633-01a">
    <image file="0633-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0633-01"/>
  </figure>
<note position="left" xlink:label="note-0633-03" xlink:href="note-0633-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0633-04" xlink:href="note-0633-04a" xml:space="preserve">30</note>
  <figure xlink:label="fig-0633-02" xlink:href="fig-0633-02a">
    <image file="0633-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0633-02"/>
  </figure>
<note position="left" xlink:label="note-0633-05" xlink:href="note-0633-05a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0633-06" xlink:href="note-0633-06a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſignorũ. <lb/>&amp; longitudinũ <lb/>dierum, una cũ <lb/>figura radiorũ <lb/>Zodiaci.</note>
</div>
<p>
  <s xml:id="echoid-s40881" xml:space="preserve">FIGVRA radiorum Zodiaci, <lb/>&amp; </s>
  <s xml:id="echoid-s40882" xml:space="preserve">longitudinum dierum conſtrue-<lb/>tur, vt in horologio horizontali oſten <lb/>
<anchor type="note" xlink:label="note-0633-07a" xlink:href="note-0633-07"/>
dimus; </s>
  <s xml:id="echoid-s40883" xml:space="preserve">atque ex ea eodem modo &amp; </s>
  <s xml:id="echoid-s40884" xml:space="preserve"><lb/>arcus ſignorum, &amp; </s>
  <s xml:id="echoid-s40885" xml:space="preserve">arcus diurni de-<lb/>ſcribentur. </s>
  <s xml:id="echoid-s40886" xml:space="preserve">Id quod appoſita figu-<lb/>ra cum ſequenti indicat.</s>
  <s xml:id="echoid-s40887" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2031" type="float" level="2" n="2">
<note position="left" xlink:label="note-0633-07" xlink:href="note-0633-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Horizontalis li <lb/>nea quo pacto <lb/>in horologiis ad <lb/>Horizõtem in-<lb/>clinaus deſcri-<lb/>ba@ur.</note>
<p>
  <s xml:id="echoid-s40888" xml:space="preserve">HORIZONTALIS linea in <lb/>omnibus hoc modo ducetur. </s>
  <s xml:id="echoid-s40889" xml:space="preserve">Per lo-<lb/>cum ſtyli G, ducatur ad meridianam <lb/>lineam perpendicularis G A, in qua <lb/>ſumpta recta G A, ſtylo æquali, de-<lb/>ſcribatur ex A, ad quoduis interuallũ <lb/>verſus meridianam lineam acceptum
<pb o="618" file="0634" n="634" rhead="GNOMONICES"/>
arcus circuli, in quo ſupputetur à recta A G, complementum inclinationis plani horologii ad <lb/>Horizontem, ſuríum quidem in ſuperioribus horologiis, deorſum verò in inferioribus. </s>
  <s xml:id="echoid-s40890" xml:space="preserve">Nam re-<lb/>cta ex A, per finem ſupputationis ducta ſecabit meridianam lineam in puncto, per quod recta ad <lb/>
<anchor type="figure" xlink:label="fig-0634-01a" xlink:href="fig-0634-01"/>
<anchor type="note" xlink:label="note-0634-01a" xlink:href="note-0634-01"/>
<anchor type="note" xlink:label="note-0634-02a" xlink:href="note-0634-02"/>
<anchor type="figure" xlink:label="fig-0634-02a" xlink:href="fig-0634-02"/>
<anchor type="note" xlink:label="note-0634-03a" xlink:href="note-0634-03"/>
<anchor type="note" xlink:label="note-0634-04a" xlink:href="note-0634-04"/>
<anchor type="note" xlink:label="note-0634-05a" xlink:href="note-0634-05"/>
<pb o="619" file="0635" n="635" rhead="LIBER SEPTIMVS."/>
lineam meridianam perpendicularis, vel lineæ æquinoctiali parallela ducta dabit lineam horizon <lb/>talem. </s>
  <s xml:id="echoid-s40891" xml:space="preserve">Quam etiam hoc modo ducemus. </s>
  <s xml:id="echoid-s40892" xml:space="preserve">In ſuperiori horologio inueniatur in linea meridia-<lb/>na punctum mediæ noctis, per quod tranſit arcus diurnus horarum 24. </s>
  <s xml:id="echoid-s40893" xml:space="preserve">In inferiori autem pun-<lb/>ctum meridiei, per quod arcus nocturnus horarum 24. </s>
  <s xml:id="echoid-s40894" xml:space="preserve">incedit. </s>
  <s xml:id="echoid-s40895" xml:space="preserve">Per hoc namque punctum linea <lb/>recta ducta ad meridianam perpendicularis erit horizontalis, vt prius.</s>
  <s xml:id="echoid-s40896" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2032" type="float" level="2" n="3">
  <figure xlink:label="fig-0634-01" xlink:href="fig-0634-01a">
    <image file="0634-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0634-01"/>
  </figure>
<note position="left" xlink:label="note-0634-01" xlink:href="note-0634-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0634-02" xlink:href="note-0634-02a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0634-02" xlink:href="fig-0634-02a">
    <image file="0634-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0634-02"/>
  </figure>
<note position="left" xlink:label="note-0634-03" xlink:href="note-0634-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0634-04" xlink:href="note-0634-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0634-05" xlink:href="note-0634-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s40897" xml:space="preserve">HAEC autem linea horizontalis totum horologium in duo diſtinguit, ſuperius, ac inferius, <lb/>nec non in diurnum &amp; </s>
  <s xml:id="echoid-s40898" xml:space="preserve">nocturnum, vt in Verticali horologio dictum eſt cap. </s>
  <s xml:id="echoid-s40899" xml:space="preserve">7. </s>
  <s xml:id="echoid-s40900" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40901" xml:space="preserve">9. </s>
  <s xml:id="echoid-s40902" xml:space="preserve">ita tamen, vt <lb/>in inferiori omnes partes immutentur, vt in præcedentibus dictum eſt, &amp; </s>
  <s xml:id="echoid-s40903" xml:space="preserve">arcus ſignorum Borea-<lb/>lium in arcus auſtralium ſignorum vertantur, &amp; </s>
  <s xml:id="echoid-s40904" xml:space="preserve">è contrario. </s>
  <s xml:id="echoid-s40905" xml:space="preserve">Itaque ſi deſcriptum fuerit horolo-<lb/>gium ſuperius, abſcindet linea horizontalis inferius, &amp; </s>
  <s xml:id="echoid-s40906" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s40907" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s40908" xml:space="preserve">DESCRIPTIO horarum ab or. </s>
  <s xml:id="echoid-s40909" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s40910" xml:space="preserve">fit, vt in præcedentibus dictum eſt. </s>
  <s xml:id="echoid-s40911" xml:space="preserve">Commodiſ-<lb/>
<anchor type="note" xlink:label="note-0635-02a" xlink:href="note-0635-02"/>
ſime vero, quod ad ſecundam rationem attinet, deſcribentur ex ſolo arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40912" xml:space="preserve">in <lb/>noſtro exemplo, qui in portione nocturna eſt arcus nocturnus horarum 10. </s>
  <s xml:id="echoid-s40913" xml:space="preserve">ſi pro ſingulis horis <lb/>ab occ. </s>
  <s xml:id="echoid-s40914" xml:space="preserve">quæ ſingula puncta duntaxat haben t in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40915" xml:space="preserve">accipiantur pro eiſdem <lb/>numero horis ab ortu alia puncta ſiue in eodem arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40916" xml:space="preserve">ſiue in nocturno hora-<lb/>rum 10. </s>
  <s xml:id="echoid-s40917" xml:space="preserve">Ita vides horam 23. </s>
  <s xml:id="echoid-s40918" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40919" xml:space="preserve">tranſire per horam 6. </s>
  <s xml:id="echoid-s40920" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s40921" xml:space="preserve">in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s40922" xml:space="preserve">at <lb/>verò horam 23. </s>
  <s xml:id="echoid-s40923" xml:space="preserve">ab ortu per horam 4. </s>
  <s xml:id="echoid-s40924" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40925" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40926" xml:space="preserve">in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s40927" xml:space="preserve">Si igitur duo hæc <lb/>puncta connectantur per lineam rectam, habebitut quidem in ſuperiori horologio diurno hora <lb/>23. </s>
  <s xml:id="echoid-s40928" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40929" xml:space="preserve">in nocturno verò hora 23. </s>
  <s xml:id="echoid-s40930" xml:space="preserve">ab ortu. </s>
  <s xml:id="echoid-s40931" xml:space="preserve">Sic etiam pro hora 20. </s>
  <s xml:id="echoid-s40932" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s40933" xml:space="preserve">ducta eſt hora 20. </s>
  <s xml:id="echoid-s40934" xml:space="preserve">ab <lb/>ortu per horam 1. </s>
  <s xml:id="echoid-s40935" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40936" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40937" xml:space="preserve">in arcu nocturno horarum 10. </s>
  <s xml:id="echoid-s40938" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40939" xml:space="preserve">per horam 2. </s>
  <s xml:id="echoid-s40940" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40941" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40942" xml:space="preserve">in ar-<lb/>
<anchor type="note" xlink:label="note-0635-03a" xlink:href="note-0635-03"/>
cu nocturno horarum 12. </s>
  <s xml:id="echoid-s40943" xml:space="preserve">Hæc enim producta exhibet horam 20. </s>
  <s xml:id="echoid-s40944" xml:space="preserve">ab occaſu, &amp;</s>
  <s xml:id="echoid-s40945" xml:space="preserve">c.</s>
  <s xml:id="echoid-s40946" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2033" type="float" level="2" n="4">
<note position="right" xlink:label="note-0635-02" xlink:href="note-0635-02a" xml:space="preserve">Compoſitio ho-<lb/>rologii Italici &amp; <lb/>Babylonici ad <lb/>Horizõtem in-<lb/>@linati.</note>
<note position="left" xlink:label="note-0635-03" xlink:href="note-0635-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s40947" xml:space="preserve">PERCOMMODE etiam eædem horæ delineabuntur per arcum diurnum horarum 24. <lb/></s>
  <s xml:id="echoid-s40948" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40949" xml:space="preserve">nocturnũ horarum 12. </s>
  <s xml:id="echoid-s40950" xml:space="preserve">vt ex ſuperioribus patet. </s>
  <s xml:id="echoid-s40951" xml:space="preserve">Exemplũ habes in proxima figura pręcedente.</s>
  <s xml:id="echoid-s40952" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s40953" xml:space="preserve">LINEA horæ 12. </s>
  <s xml:id="echoid-s40954" xml:space="preserve">ab ortu, vel occaſu ducitur per punctum D, inuentum in linea horę 12. <lb/></s>
  <s xml:id="echoid-s40955" xml:space="preserve">meridiei, per quod tranſire debet arcus paralleli ſemper apparentium maximi, nempe horarum <lb/>24. </s>
  <s xml:id="echoid-s40956" xml:space="preserve">ad lineam meridianam perpendicularis, vel lineæ æquinoctiali parallela.</s>
  <s xml:id="echoid-s40957" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">Con@tructio ho <lb/>rologii Antiqui <lb/>ad Horizontem <lb/>inclinati.</note>
<p>
  <s xml:id="echoid-s40958" xml:space="preserve">HOROLOGIVM Antiquum denique conſtrui, vt in præcedentibus dictum eſt, ipſa figu-<lb/>
<anchor type="figure" xlink:label="fig-0635-01a" xlink:href="fig-0635-01"/>
<anchor type="note" xlink:label="note-0635-05a" xlink:href="note-0635-05"/>
<anchor type="note" xlink:label="note-0635-06a" xlink:href="note-0635-06"/>
<anchor type="note" xlink:label="note-0635-07a" xlink:href="note-0635-07"/>
<pb o="620" file="0636" n="636" rhead="GNOMONICES"/>
ra ſatis perſpicuè declarat. </s>
  <s xml:id="echoid-s40959" xml:space="preserve">Nam verbi gratia, puncto A, horæ 3. </s>
  <s xml:id="echoid-s40960" xml:space="preserve">inæqualis in circulo ex E, deſcri-<lb/>pto accepimus punctum oppoſitum C, duximusq́ue rectam C E A, quæ lineam æquinoctialem <lb/>ſecat in D, puncto, per quod recta per <emph style="sc">H</emph>, centrum horologii extenſa ſecat quidem tropicum ♋, in <lb/>arcu nocturno in puncto quodam, quod puncto C, dicti circuli in arcu nocturno debetur, vltra <lb/>autem H, ſecat eundem tropicum in arcu diurno in F, puncto horæ 3. </s>
  <s xml:id="echoid-s40961" xml:space="preserve">inæqualis, &amp;</s>
  <s xml:id="echoid-s40962" xml:space="preserve">c. </s>
  <s xml:id="echoid-s40963" xml:space="preserve">Sed idem ho <lb/>rologium aptiſſime delineabitur beneſicio ſolius arcus nocturni tropici ♋, in noſtro exemplo. <lb/></s>
  <s xml:id="echoid-s40964" xml:space="preserve">Ita enim vides rectam ex I, puncto horæ 11. </s>
  <s xml:id="echoid-s40965" xml:space="preserve">in arcu nocturno tropici ♋, per E, ductã ſecare æqui-<lb/>noctialem lineam in L, rectam autem L H, ſecare arcũ nocturnum ♋, in M, puncto horæ 11. </s>
  <s xml:id="echoid-s40966" xml:space="preserve">no-<lb/>cturnæ. </s>
  <s xml:id="echoid-s40967" xml:space="preserve">Si igitur ex M, per horam 5. </s>
  <s xml:id="echoid-s40968" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s40969" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s40970" xml:space="preserve">in arcu nocturno horarum 12. </s>
  <s xml:id="echoid-s40971" xml:space="preserve">vt conſtat ex ta-<lb/>bula 14. </s>
  <s xml:id="echoid-s40972" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s40973" xml:space="preserve">33. </s>
  <s xml:id="echoid-s40974" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s40975" xml:space="preserve">1. </s>
  <s xml:id="echoid-s40976" xml:space="preserve">ducamus rectam lineam, habebimus horam 11. </s>
  <s xml:id="echoid-s40977" xml:space="preserve">inęqualem nocturnam, <lb/>
<anchor type="note" xlink:label="note-0636-01a" xlink:href="note-0636-01"/>
quæ producta vltra lineam horizontalem dabit etiam horam 11. </s>
  <s xml:id="echoid-s40978" xml:space="preserve">diurnam. </s>
  <s xml:id="echoid-s40979" xml:space="preserve">Eodemq́ue modo re-<lb/>liquas horas ducemus.</s>
  <s xml:id="echoid-s40980" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2034" type="float" level="2" n="5">
  <figure xlink:label="fig-0635-01" xlink:href="fig-0635-01a">
    <image file="0635-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0635-01"/>
  </figure>
<note position="left" xlink:label="note-0635-05" xlink:href="note-0635-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0635-06" xlink:href="note-0635-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0635-07" xlink:href="note-0635-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0636-01" xlink:href="note-0636-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s40981" xml:space="preserve">QVOD ad alteram deſcriptionem attinet, quæ per arcum diurnum horarum 18. </s>
  <s xml:id="echoid-s40982" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s40983" xml:space="preserve">noctur-<lb/>num horarum 6. </s>
  <s xml:id="echoid-s40984" xml:space="preserve">conficitur, res perſpicua eſt ex ipſa figura.</s>
  <s xml:id="echoid-s40985" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2036" type="section" level="1" n="521">
<head xml:id="echoid-head550" style="it" xml:space="preserve">DE HOROLOGIIS AVERTICALI DECLINANTIBVS, <lb/>&amp; ad Horizontem inclinatis. CAP. XXIX.</head>
<p>
  <s xml:id="echoid-s40986" xml:space="preserve">ILLVD horologium appellauimus initio huius noſtræ Gnomonices à Verticali circulo decli-<lb/>nans, &amp; </s>
  <s xml:id="echoid-s40987" xml:space="preserve">inclinatum ad Horizontem, quod æquidiſtat circulo maximo, qui nec ad Horizontem, <lb/>
<anchor type="note" xlink:label="note-0636-02a" xlink:href="note-0636-02"/>
nec ad Verticalem, nec ad Meridianum rectus eſt, ſed ad omnes hos circulos inclinatus, ita vt per <lb/>nullius polos tranſeat, cuiuſmodi ſunt pleraque tecta domorum. </s>
  <s xml:id="echoid-s40988" xml:space="preserve">Hoc autem in octo genera di-<lb/>ſtribuitur. </s>
  <s xml:id="echoid-s40989" xml:space="preserve">Aut enim declinat à meridie in ortum, vel occaſum, ſpectatque ad Zenith, &amp; </s>
  <s xml:id="echoid-s40990" xml:space="preserve">auſtrũ; <lb/></s>
  <s xml:id="echoid-s40991" xml:space="preserve">
<anchor type="note" xlink:label="note-0636-03a" xlink:href="note-0636-03"/>
vel declinat à ſeptentrione in ortum, vel occaſum, intueturq́ue Nadir, &amp; </s>
  <s xml:id="echoid-s40992" xml:space="preserve">Boream, ita vt lineæ an-<lb/>gulum inclinationis, quem cum Horizonte conſtituit, efficientes vergant in Boream verſus occa-<lb/>ſum, aut ortum: </s>
  <s xml:id="echoid-s40993" xml:space="preserve">Aut declinat à ſeptentrione in ortum, vel occaſum, ſpectatq́ue ad Zenith, &amp; </s>
  <s xml:id="echoid-s40994" xml:space="preserve">Bo-<lb/>ream; </s>
  <s xml:id="echoid-s40995" xml:space="preserve">vel declinat à meridie in ortum, vel occaſum, reſpicitq́ue Nadir, &amp; </s>
  <s xml:id="echoid-s40996" xml:space="preserve">auſtrum, ita vt lineæ <lb/>conſtituentes angulum inclinationis, quem efficit cum <emph style="sc">H</emph>orizonte, vergant in auſtrum verſus oc-<lb/>caſum, aut ortum: </s>
  <s xml:id="echoid-s40997" xml:space="preserve">Quę quidem octo horologia ita nominari poterunt: </s>
  <s xml:id="echoid-s40998" xml:space="preserve">Superius auſtrale ver-<lb/>
<anchor type="note" xlink:label="note-0636-04a" xlink:href="note-0636-04"/>
gens in ortum: </s>
  <s xml:id="echoid-s40999" xml:space="preserve">Inferius Boreale declinans in occaſum: </s>
  <s xml:id="echoid-s41000" xml:space="preserve">Superius auſtrale declinans in occaſum: <lb/></s>
  <s xml:id="echoid-s41001" xml:space="preserve">
<anchor type="note" xlink:label="note-0636-05a" xlink:href="note-0636-05"/>
Inferius boreale declinans in ortum: </s>
  <s xml:id="echoid-s41002" xml:space="preserve">Superius boreale declinans in ortum: </s>
  <s xml:id="echoid-s41003" xml:space="preserve">Inferius auſtrale in <lb/>occaſum declinans: </s>
  <s xml:id="echoid-s41004" xml:space="preserve">ſuperius boreale in occaſum declinans: </s>
  <s xml:id="echoid-s41005" xml:space="preserve">Inferius auſtrale declinans in ortum. <lb/></s>
  <s xml:id="echoid-s41006" xml:space="preserve">Sunt ergo quatuor ſuperiora, quorum duo priora declinant à meridie in ortum, vel occaſum, ſpe <lb/>ctantq́ue ad Zenith, &amp; </s>
  <s xml:id="echoid-s41007" xml:space="preserve">auſtrum: </s>
  <s xml:id="echoid-s41008" xml:space="preserve">poſteriora verò duo à ſeptentrione declinant in ortum, vel oc-<lb/>caſum, ſpectantq́ue ad Zenith, &amp; </s>
  <s xml:id="echoid-s41009" xml:space="preserve">Boream: </s>
  <s xml:id="echoid-s41010" xml:space="preserve">Item quatuor inferiora, quorum priora duo à ſepten-<lb/>trione declinant in ortum, vel occaſum, ſpectantq́ue ad Nadir, &amp; </s>
  <s xml:id="echoid-s41011" xml:space="preserve">Boream: </s>
  <s xml:id="echoid-s41012" xml:space="preserve">duo verò poſteriora <lb/>declinant à meridie in ortum, vel occaſum, intuenturq́ue Nadir, &amp; </s>
  <s xml:id="echoid-s41013" xml:space="preserve">auſtrum. </s>
  <s xml:id="echoid-s41014" xml:space="preserve">Atque hæc inferio-<lb/>ra deſcribuntur in eiſdem planis, in quibus ſuperiora deſcribuntur, licet in partibus oppoſitis om <lb/>nino. </s>
  <s xml:id="echoid-s41015" xml:space="preserve">Nam in parte oppoſita plani ſuperioris, quod à meridie v. </s>
  <s xml:id="echoid-s41016" xml:space="preserve">g. </s>
  <s xml:id="echoid-s41017" xml:space="preserve">in ortum declinat grad. </s>
  <s xml:id="echoid-s41018" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41019" xml:space="preserve"><lb/>reſpicitq́ue Zenith, &amp; </s>
  <s xml:id="echoid-s41020" xml:space="preserve">auſtrum, &amp; </s>
  <s xml:id="echoid-s41021" xml:space="preserve">inclinat ad <emph style="sc">H</emph>orizontem grad. </s>
  <s xml:id="echoid-s41022" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41023" xml:space="preserve">deſcribitur horologium in-<lb/>
<anchor type="note" xlink:label="note-0636-06a" xlink:href="note-0636-06"/>
ferius, quod à ſeptentrione in occaſum declinat grad. </s>
  <s xml:id="echoid-s41024" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41025" xml:space="preserve">reſpicitq́ue Nadir, &amp; </s>
  <s xml:id="echoid-s41026" xml:space="preserve">boream, &amp; </s>
  <s xml:id="echoid-s41027" xml:space="preserve">incli-<lb/>nat ad Horizontem grad. </s>
  <s xml:id="echoid-s41028" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41029" xml:space="preserve">Idemq́ue de aliis iudicium erit. </s>
  <s xml:id="echoid-s41030" xml:space="preserve">Semper enim eadem eſt declinatio <lb/>inferioris horologii, quæ ſuperioris, quamuis non ad eaſdem partes, cum ſuperiore declinante à <lb/>meridie in ortum, ſpectanteq́ue ad Zenith, &amp; </s>
  <s xml:id="echoid-s41031" xml:space="preserve">auſtrum, inferius declinet à ſeptentrione in occa-<lb/>ſum, ſpectetq́ue ad Nadir, &amp; </s>
  <s xml:id="echoid-s41032" xml:space="preserve">Boream, &amp; </s>
  <s xml:id="echoid-s41033" xml:space="preserve">ſic de aliis. </s>
  <s xml:id="echoid-s41034" xml:space="preserve">Angulus tamen inclinationis horologii in-<lb/>ferioris, &amp; </s>
  <s xml:id="echoid-s41035" xml:space="preserve">ſuperioris conſtituitur ſemper verſus eandem partem. </s>
  <s xml:id="echoid-s41036" xml:space="preserve">Nos, vt facilius omnia hæc ho-<lb/>rologia deſcribamus, præcepta tantummodo trademus de ſuperioribus deſcribendis. </s>
  <s xml:id="echoid-s41037" xml:space="preserve">Ita enim <lb/>fiet, vt res tota, quæ aliquantulum difficilis eſt, &amp; </s>
  <s xml:id="echoid-s41038" xml:space="preserve">obſcura, planius percipiatur. </s>
  <s xml:id="echoid-s41039" xml:space="preserve">Deſcriptis autem <lb/>horologiis ſuperioribus, nullo negotio ex ipſis inferiora fabricabimus, quemadmodum in Decli-<lb/>nantibus à Verticali borealia ex auſtralibus cap. </s>
  <s xml:id="echoid-s41040" xml:space="preserve">23. </s>
  <s xml:id="echoid-s41041" xml:space="preserve">24. </s>
  <s xml:id="echoid-s41042" xml:space="preserve">25. </s>
  <s xml:id="echoid-s41043" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41044" xml:space="preserve">26. </s>
  <s xml:id="echoid-s41045" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41046" xml:space="preserve">in Declinantibus ab Hori-<lb/>
<anchor type="note" xlink:label="note-0636-07a" xlink:href="note-0636-07"/>
zonte inferiora ex ſuperioribus cap. </s>
  <s xml:id="echoid-s41047" xml:space="preserve">27. </s>
  <s xml:id="echoid-s41048" xml:space="preserve">deſcripta ſunt. </s>
  <s xml:id="echoid-s41049" xml:space="preserve">Id quod ex figuris ſequentibus perſpi-<lb/>cuum fiet.</s>
  <s xml:id="echoid-s41050" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2036" type="float" level="2" n="1">
<note position="left" xlink:label="note-0636-02" xlink:href="note-0636-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0636-03" xlink:href="note-0636-03a" xml:space="preserve">Horologium à <lb/>Verticali dccli-<lb/>nans, &amp; ad Ho-<lb/>rizontem incli <lb/>@atũ, octuplex.</note>
<note position="left" xlink:label="note-0636-04" xlink:href="note-0636-04a" xml:space="preserve">Nomina octo <lb/>horologiotum <lb/>à Verticali de-<lb/>clinantium, &amp; <lb/>ad Horizontem <lb/>inclinatorum.</note>
<note position="left" xlink:label="note-0636-05" xlink:href="note-0636-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0636-06" xlink:href="note-0636-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0636-07" xlink:href="note-0636-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41051" xml:space="preserve">ITA igitur rem exequemur. </s>
  <s xml:id="echoid-s41052" xml:space="preserve">In plano horologii aſſumpto vtcunque loco ſtyli in K, ducantur <lb/>
<anchor type="note" xlink:label="note-0636-08a" xlink:href="note-0636-08"/>
per K, duæ rectæ A B, C D, ſeſe in K, ſecantes ad angulos rectos: </s>
  <s xml:id="echoid-s41053" xml:space="preserve">vel ſi planum ſtabile ſit à Verti-<lb/>cali declinans, &amp; </s>
  <s xml:id="echoid-s41054" xml:space="preserve">ad Horizontem inclinatum, ducatur beneficio libellæ, &amp; </s>
  <s xml:id="echoid-s41055" xml:space="preserve">perpendiculi per K, re-<lb/>cta A B, Horizonti æquidiſtans, quam C D, in K, ſecet ad rectos angulos. </s>
  <s xml:id="echoid-s41056" xml:space="preserve">Sumpta autem in A B, <lb/>longitudine gnomonis quacunque K β, ſiue ad dextram rectæ C D, ſiue ad ſiniſtram, deſcribatur <lb/>ex β, verſus C D, arcus circuli, in quo numerata inclinatione plani ad Horizontem, (quam in pri <lb/>ma figura ponimus eſſe grad. </s>
  <s xml:id="echoid-s41057" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41058" xml:space="preserve">In ſecunda grad. </s>
  <s xml:id="echoid-s41059" xml:space="preserve">70. </s>
  <s xml:id="echoid-s41060" xml:space="preserve">In tertia grad. </s>
  <s xml:id="echoid-s41061" xml:space="preserve">51. </s>
  <s xml:id="echoid-s41062" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s41063" xml:space="preserve">51. </s>
  <s xml:id="echoid-s41064" xml:space="preserve">In quarta gr. </s>
  <s xml:id="echoid-s41065" xml:space="preserve">30. <lb/></s>
  <s xml:id="echoid-s41066" xml:space="preserve">In quinta gr. </s>
  <s xml:id="echoid-s41067" xml:space="preserve">80. </s>
  <s xml:id="echoid-s41068" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41069" xml:space="preserve">in ſexta gr. </s>
  <s xml:id="echoid-s41070" xml:space="preserve">52. </s>
  <s xml:id="echoid-s41071" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s41072" xml:space="preserve">3.) </s>
  <s xml:id="echoid-s41073" xml:space="preserve">initio facto à recta A B, deorſum verſus, ducatur per fi-<lb/>nem numerationis ex β, recta ſecans C D, in D, puncto, per quod meridiana linea ducenda erit.</s>
  <s xml:id="echoid-s41074" xml:space="preserve">
<pb o="621" file="0637" n="637" rhead="LIBER SEPTIMVS."/>
Supputato quoque in eodem arcu ſurſum verſus complemento inclinationis, ducatur ex β, per fi-<lb/>nem ſupputationis recta (quę perpendicularis erit ad β D,) ſecans C D, in C, puncto, per quod <lb/>recta C E, ducta ad C D, perpendicularis erit linea horizontalis.</s>
  <s xml:id="echoid-s41075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2037" type="float" level="2" n="2">
<note position="left" xlink:label="note-0636-08" xlink:href="note-0636-08a" xml:space="preserve">Conſtructio ho <lb/>rologii Aſtrono <lb/>mici à Verticali <lb/>declinantis, &amp; <lb/>ad Horizontem <lb/>fimul inclinati.</note>
</div>
<note position="right" xml:space="preserve">Horizontalis li-<lb/>nea.</note>
<p>
  <s xml:id="echoid-s41076" xml:space="preserve">DEINDE in recta C D, <lb/>ſumpta recta C F, ſurſum, aut <lb/>deorſum verſus, æquali ipſi <lb/>
<anchor type="figure" xlink:label="fig-0637-01a" xlink:href="fig-0637-01"/>
C β, deſcribatur ex F, verſus <lb/>C E, arcus circuli, in quo nu-<lb/>merata à recta C D, declina-<lb/>tione plani à Verticali circu-<lb/>
<anchor type="note" xlink:label="note-0637-02a" xlink:href="note-0637-02"/>
lo, (quam in prima figura po-<lb/>nimus eſſe à mer. </s>
  <s xml:id="echoid-s41077" xml:space="preserve">in ortum <lb/>gr. </s>
  <s xml:id="echoid-s41078" xml:space="preserve">40. </s>
  <s xml:id="echoid-s41079" xml:space="preserve">In ſecunda à mer. </s>
  <s xml:id="echoid-s41080" xml:space="preserve">in <lb/>occaſum grad. </s>
  <s xml:id="echoid-s41081" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41082" xml:space="preserve">In tertia à <lb/>mer. </s>
  <s xml:id="echoid-s41083" xml:space="preserve">in ortum gr. </s>
  <s xml:id="echoid-s41084" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41085" xml:space="preserve">In quar-<lb/>ta à Sept. </s>
  <s xml:id="echoid-s41086" xml:space="preserve">in occaſum gr. </s>
  <s xml:id="echoid-s41087" xml:space="preserve">20. <lb/></s>
  <s xml:id="echoid-s41088" xml:space="preserve">In quinta à Sept. </s>
  <s xml:id="echoid-s41089" xml:space="preserve">in ortum gr. </s>
  <s xml:id="echoid-s41090" xml:space="preserve"><lb/>60. </s>
  <s xml:id="echoid-s41091" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41092" xml:space="preserve">in ſexta à Sept. </s>
  <s xml:id="echoid-s41093" xml:space="preserve">in ortũ <lb/>gr. </s>
  <s xml:id="echoid-s41094" xml:space="preserve">30.) </s>
  <s xml:id="echoid-s41095" xml:space="preserve">ad dexteram quidẽ, <lb/>ſi planum à meridie in ortum <lb/>
<anchor type="note" xlink:label="note-0637-03a" xlink:href="note-0637-03"/>
deflectit, vt in figura 1. </s>
  <s xml:id="echoid-s41096" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41097" xml:space="preserve">3. <lb/></s>
  <s xml:id="echoid-s41098" xml:space="preserve">vel à Septentr. </s>
  <s xml:id="echoid-s41099" xml:space="preserve">in occaſum, vt <lb/>in quarta figura, ad ſiniſtram <lb/>autem, ſi planum declinat à <lb/>meridie in occaſum, vt in ſe-<lb/>cunda figura, vel à Septent. </s>
  <s xml:id="echoid-s41100" xml:space="preserve">in <lb/>ortum, vt in 5. </s>
  <s xml:id="echoid-s41101" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41102" xml:space="preserve">6. </s>
  <s xml:id="echoid-s41103" xml:space="preserve">figura, du-<lb/>catur ex F, per finem numera-<lb/>tionis recta ſecans horizonta-<lb/>lem lineam C E, in E. </s>
  <s xml:id="echoid-s41104" xml:space="preserve">Nam <lb/>
<anchor type="note" xlink:label="note-0637-04a" xlink:href="note-0637-04"/>
recta D E, per D, &amp; </s>
  <s xml:id="echoid-s41105" xml:space="preserve">E, in vtrã-<lb/>que partem eiecta dabit lineã <lb/>
<anchor type="note" xlink:label="note-0637-05a" xlink:href="note-0637-05"/>
meridianam, ſeu horam 12. <lb/></s>
  <s xml:id="echoid-s41106" xml:space="preserve">
<anchor type="figure" xlink:label="fig-0637-02a" xlink:href="fig-0637-02"/>
<anchor type="note" xlink:label="note-0637-06a" xlink:href="note-0637-06"/>
<anchor type="figure" xlink:label="fig-0637-03a" xlink:href="fig-0637-03"/>
<anchor type="note" xlink:label="note-0637-07a" xlink:href="note-0637-07"/>
à mer. </s>
  <s xml:id="echoid-s41107" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41108" xml:space="preserve">noc Supputato quoque in eodem arcu à recta C D, in contrariam partem comple <lb/>mento declinationis, ducatur ex F, per finẽ ſupputationis recta (quæ ad F E, perpendicularis erit)
<pb o="622" file="0638" n="638" rhead="GNOMONICES"/>
ſecans lineam horizontalem in α, puncto, per quod linea æquinoctialis, &amp; </s>
  <s xml:id="echoid-s41109" xml:space="preserve">linea horę 6. </s>
  <s xml:id="echoid-s41110" xml:space="preserve">à mer. <lb/></s>
  <s xml:id="echoid-s41111" xml:space="preserve">vel med noc. </s>
  <s xml:id="echoid-s41112" xml:space="preserve">ducenda eſt. </s>
  <s xml:id="echoid-s41113" xml:space="preserve">Ducta autem recta α K, quæ neceſſario ad meridianam lineam perpen-<lb/>dicularis eſt, ſi erratum non fuerit, deſcribantur ex D, &amp; </s>
  <s xml:id="echoid-s41114" xml:space="preserve">E, duo arcus ad interualla rectarum D β, <lb/>E F, ſecantes ſeſe neceſſario, ſi error commiſſus nõ ſit, in recta α k, vt in puncto H, ſiue autem hoc <lb/>fiat ex parte dextra, ſiue ex ſiniſtra, nihil intere ſt.</s>
  <s xml:id="echoid-s41115" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2038" type="float" level="2" n="3">
  <figure xlink:label="fig-0637-01" xlink:href="fig-0637-01a">
    <image file="0637-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0637-01"/>
  </figure>
<note position="left" xlink:label="note-0637-02" xlink:href="note-0637-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0637-03" xlink:href="note-0637-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0637-04" xlink:href="note-0637-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0637-05" xlink:href="note-0637-05a" xml:space="preserve">Linea meridia-<lb/>@a.</note>
  <figure xlink:label="fig-0637-02" xlink:href="fig-0637-02a">
    <image file="0637-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0637-02"/>
  </figure>
<note position="left" xlink:label="note-0637-06" xlink:href="note-0637-06a" xml:space="preserve">40</note>
  <figure xlink:label="fig-0637-03" xlink:href="fig-0637-03a">
    <image file="0637-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0637-03"/>
  </figure>
<note position="left" xlink:label="note-0637-07" xlink:href="note-0637-07a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41116" xml:space="preserve">IAM verò ducta recta <lb/>H E, deſcribatur ex H, arcus <lb/>
<anchor type="figure" xlink:label="fig-0638-01a" xlink:href="fig-0638-01"/>
circuli, in quo à recta H E, <lb/>numeretur complementum <lb/>altitudinis poli, verſus rectã <lb/>
<anchor type="note" xlink:label="note-0638-01a" xlink:href="note-0638-01"/>
H D, ſi planum horologii à <lb/>meridie declinat, vt in prio-<lb/>ribus tribus figuris, &amp; </s>
  <s xml:id="echoid-s41117" xml:space="preserve">per fi-<lb/>nem numerationis ex H, du-<lb/>catur recta H b, ſecans meri-<lb/>dianam lineam in M, pun-<lb/>cto, per quod æquinoctialis <lb/>
<anchor type="note" xlink:label="note-0638-02a" xlink:href="note-0638-02"/>
linea ducenda eſt ex puncto <lb/>α, iampridem inuento. </s>
  <s xml:id="echoid-s41118" xml:space="preserve">Et <lb/>ſi in eodem arcu in contra-<lb/>
<anchor type="note" xlink:label="note-0638-03a" xlink:href="note-0638-03"/>
riam partem à recta H E, nu-<lb/>meretur altitudo poli, &amp; </s>
  <s xml:id="echoid-s41119" xml:space="preserve">ex <lb/>fine numerationis pei H, re-<lb/>cta H d, ducatur, quæ ad <lb/><emph style="sc">H</emph> M, perpendicularis neceſ-<lb/>ſario erit, niſi ſit erratum, ſe-<lb/>cabitur eadem linea meridia <lb/>na in puncto ρ, quod centrũ <lb/>
<anchor type="note" xlink:label="note-0638-04a" xlink:href="note-0638-04"/>
erit horologii. </s>
  <s xml:id="echoid-s41120" xml:space="preserve">Quòd ſi quã-<lb/>do accidat, rectam hanc Hd, <lb/>
<anchor type="note" xlink:label="note-0638-05a" xlink:href="note-0638-05"/>
vltimo loco per H, ductam <lb/>parallelam eſſe lineę meri-<lb/>dianæ, vt contingit in tertia <lb/>figura, carebit horologium centro, eruntq́ue omnes lineę horariæ inter ſe æquidiſtãtes; </s>
  <s xml:id="echoid-s41121" xml:space="preserve">quia tunc <lb/>circulus maximus, cui horologium ęquidiſtat, per polos mundi ducitur. </s>
  <s xml:id="echoid-s41122" xml:space="preserve">Si verò horologii planũ <lb/>declinat à Septentrione, vt in tribus figuris poſterioribus, numeranda erit altitudo poli in dicto <lb/>arcu circuli ex H, deſcripto, à recta H E, verſus lineam H D. </s>
  <s xml:id="echoid-s41123" xml:space="preserve">Recta enim H d, ducta ex H, per finẽ <lb/>numerationis ſecabit meridianam lineam in ρ, centro horologij: </s>
  <s xml:id="echoid-s41124" xml:space="preserve">Et ſi in eodem arcu in partem <lb/>contrariam à recta H E, ſupputetur complementum altitudinis poli, atque ex fine numerationis <lb/>per H, traijciatur recta H b, quæ ad H d, perpendicularis erit, ſecabitur linea meridiana in puncto <lb/>
<anchor type="note" xlink:label="note-0638-06a" xlink:href="note-0638-06"/>
M, per quod linea æquinoctialis ex α, ducenda eſt. </s>
  <s xml:id="echoid-s41125" xml:space="preserve">Quòd ſi quando contingat hanc rectam <emph style="sc">H</emph> b, <lb/>vltimo loco ductam, parallelam eſſe meridianæ lineæ, veluti in ſexta figura, ducenda erit linea <lb/>æquinoctialis per α, ipſi lineæ meridianę parallela. </s>
  <s xml:id="echoid-s41126" xml:space="preserve">Si igitur ex centro horologii ρ, per K, locum <lb/>ſtyli, recta ducatur, habebimus lineam ſtyli, quam neceſſario linea æquinoctialis ex α, ducta ad <lb/>
<anchor type="note" xlink:label="note-0638-07a" xlink:href="note-0638-07"/>
angulos rectos ſecabit. </s>
  <s xml:id="echoid-s41127" xml:space="preserve">Sed vbi centrum nõ habetur, vt in tertia figura, ducenda erit linea ſtyli per <lb/>K, locum ſtyli parallela lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s41128" xml:space="preserve">ad æquinoctialem lineam perpendicularis. </s>
  <s xml:id="echoid-s41129" xml:space="preserve">Item vbi <lb/>æquinoctialis linea meridianæ lineæ ęquidiſtat, vt in ſexta figura, erit linea ſtyli ρ K, non ſolum ad <lb/>ęquinoctialem lineam, ſed etiam ad lineam meridianam perpendicularis. </s>
  <s xml:id="echoid-s41130" xml:space="preserve">Itaque ſi prius linea <lb/>æquinoctialis ducatur, ducenda erit linea ſtyli ad ipſam perpendicularis ex centro ρ, vel ex loco <lb/>ſtyli K: </s>
  <s xml:id="echoid-s41131" xml:space="preserve">Si verò prius linea ſtyli ducatur ex centro ρ, per K, vel vbi centrum non eſt, per K, lineæ <lb/>
<anchor type="note" xlink:label="note-0638-08a" xlink:href="note-0638-08"/>
meridianæ æquidiſtans, ducenda erit linea æquinoctialis ad ipſam perpendicularis ex α.</s>
  <s xml:id="echoid-s41132" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2039" type="float" level="2" n="4">
  <figure xlink:label="fig-0638-01" xlink:href="fig-0638-01a">
    <image file="0638-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0638-01"/>
  </figure>
<note position="left" xlink:label="note-0638-01" xlink:href="note-0638-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0638-02" xlink:href="note-0638-02a" xml:space="preserve">Linea æqaine<unsure/>-<lb/>ct<unsure/>ialis.</note>
<note position="left" xlink:label="note-0638-03" xlink:href="note-0638-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0638-04" xlink:href="note-0638-04a" xml:space="preserve">Ce@trum horo<unsure/>-<lb/>logii.</note>
<note position="left" xlink:label="note-0638-05" xlink:href="note-0638-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0638-06" xlink:href="note-0638-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0638-07" xlink:href="note-0638-07a" xml:space="preserve">Linea ſtyli.</note>
<note position="left" xlink:label="note-0638-08" xlink:href="note-0638-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41133" xml:space="preserve">POST hæc ex loco ſtyli K, excitetur ad lineam ſtyli recta perpendicularis k I, ſtylo æqualis, <lb/>&amp; </s>
  <s xml:id="echoid-s41134" xml:space="preserve">ex centro ρ, per I, recta emittatur ρ I, pro axe mundi. </s>
  <s xml:id="echoid-s41135" xml:space="preserve">At vbi centrum non eſt, vt in tertia figu-<lb/>
<anchor type="note" xlink:label="note-0638-09a" xlink:href="note-0638-09"/>
ra, ducendus erit axis per I, lineę ſtyli, vel meridianæ æquidiſtans. </s>
  <s xml:id="echoid-s41136" xml:space="preserve">Quod ſi ex I, ad axem perpen <lb/>dicularis demittatur, ſecabit ea lineam ſtyli in puncto G, per quod æquinoctialis linea ducitur, <lb/>niſi errorem commiſerimus. </s>
  <s xml:id="echoid-s41137" xml:space="preserve">Vnde vbi horologium centro caret, atque adeo axis lineæ ſtyli ęqui <lb/>diſtat, vt in tertia figura, cadet dicta perpendicularis in K, locum ſtyli, lineaq́ue ęquinoctialis per <lb/>eundem locum ſtyli ducenda erit. </s>
  <s xml:id="echoid-s41138" xml:space="preserve">Itaque ſi ductus fuerit axis mundi per I, inueniemus per lineã <lb/>perpendicularem I G, in linea ſtyli aliud punctum G, per quod æquinoctialis linea ex puncto α, <lb/>ducenda eſt, quæ neceſſario cum linea ſtyli angulos rectos efficiet.</s>
  <s xml:id="echoid-s41139" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2040" type="float" level="2" n="5">
<note position="left" xlink:label="note-0638-09" xlink:href="note-0638-09a" xml:space="preserve">Axis mundi.</note>
</div>
<p>
  <s xml:id="echoid-s41140" xml:space="preserve">AD extremum ſumpta recta G L, in linea indicis, quæ æqualis ſit ipſi G I, deſcribatur ex L,
<pb o="623" file="0639" n="639" rhead="LIBER SEPTIMVS."/>
circulus cuiuslibet magnitudinis, qui in 24. </s>
  <s xml:id="echoid-s41141" xml:space="preserve">partes æquales diſtribuatur, initio facto à recta L M, <lb/>quæ ex centro L, ducitur per punctum M, vbi æquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s41142" xml:space="preserve">meridiana ſe interſecant, <lb/>vel à recta L α, ducta ex eodem centro L, per punctum α, vbi coeunt horizontalis linea, &amp; </s>
  <s xml:id="echoid-s41143" xml:space="preserve">æqui-<lb/>
<anchor type="figure" xlink:label="fig-0639-01a" xlink:href="fig-0639-01"/>
noctialis, ſen linea horę 6. <lb/></s>
  <s xml:id="echoid-s41144" xml:space="preserve">Neceſſe eſt autem duas re-<lb/>ctas L M, L α, ſe ſe in L, <lb/>ad rectos angulos interſe-<lb/>care, ſi nulla in re commiſ-<lb/>ſus fuerit error. </s>
  <s xml:id="echoid-s41145" xml:space="preserve">Quòd ſi <lb/>ęquinoctialis linea paral-<lb/>
<anchor type="note" xlink:label="note-0639-01a" xlink:href="note-0639-01"/>
lela ſit meridianæ lineæ, <lb/>vt in ſexta figura, ducenda <lb/>erit loco rectæ L M, recta <lb/>eidem meridianę paralle-<lb/>la, quæ rectam L α, ad an-<lb/>gulos rectos ſecet. </s>
  <s xml:id="echoid-s41146" xml:space="preserve">Iam ſi <lb/>ex L, per diuiſionum pun-<lb/>cta rectæ occultæ ducan-<lb/>tur, ſecabitur æquinoctia-<lb/>lis linea in pũctis, per quæ <lb/>
<anchor type="note" xlink:label="note-0639-02a" xlink:href="note-0639-02"/>
ex centro ρ, ducendæ ſunt <lb/>
<anchor type="note" xlink:label="note-0639-03a" xlink:href="note-0639-03"/>
lineæ horarum à mer. </s>
  <s xml:id="echoid-s41147" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41148" xml:space="preserve"><lb/>med. </s>
  <s xml:id="echoid-s41149" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41150" xml:space="preserve">vel quando cen <lb/>tro caret horologium, vt <lb/>in tertia figura, per quę ip-<lb/>ſi lineæ meridianæ, vel li-<lb/>neæ ſtyli, axive ducendę <lb/>ſunt parallelæ, &amp; </s>
  <s xml:id="echoid-s41151" xml:space="preserve">ad ęqui-<lb/>noctialem lineam perpen-<lb/>diculares pro horis à mer. <lb/></s>
  <s xml:id="echoid-s41152" xml:space="preserve">
<anchor type="note" xlink:label="note-0639-04a" xlink:href="note-0639-04"/>
vel med. </s>
  <s xml:id="echoid-s41153" xml:space="preserve">nocte.</s>
  <s xml:id="echoid-s41154" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2041" type="float" level="2" n="6">
  <figure xlink:label="fig-0639-01" xlink:href="fig-0639-01a">
    <image file="0639-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0639-01"/>
  </figure>
<note position="left" xlink:label="note-0639-01" xlink:href="note-0639-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0639-02" xlink:href="note-0639-02a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0639-03" xlink:href="note-0639-03a" xml:space="preserve">Lineæ horarun@ <lb/>à mer. &amp; med. <lb/>no<unsure/>c,</note>
<note position="left" xlink:label="note-0639-04" xlink:href="note-0639-04a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Horar@or@@.</note>
<p>
  <s xml:id="echoid-s41155" xml:space="preserve">ORDO horarum hic <lb/>eſt. </s>
  <s xml:id="echoid-s41156" xml:space="preserve">In planis, quæ ad au-<lb/>ſtrum ſpectant, portio li-<lb/>neæ meridianæ a centro <lb/>horologii ρ, verſus æqui-<lb/>noctialem lineam extenſa, <lb/>vt in prioribus duabus fi-<lb/>guris, vel tota linea meri-<lb/>diana, vbi centrum deeſt, vt in tertia figura, demonſtrat horam 12. </s>
  <s xml:id="echoid-s41157" xml:space="preserve">meridiei; </s>
  <s xml:id="echoid-s41158" xml:space="preserve">quæ verò ei ſunt <lb/>
<anchor type="note" xlink:label="note-0639-06a" xlink:href="note-0639-06"/>
ad dexteram in linea æquinoctiali, (nobis ad horologium verſus boream conuerſis) horas pome-<lb/>ridianas, &amp; </s>
  <s xml:id="echoid-s41159" xml:space="preserve">quæ ad ſiniſtram, antemeridianas ſignificant: </s>
  <s xml:id="echoid-s41160" xml:space="preserve">reliqua vero portio meridianæ lineæ à <lb/>centro inchoata oſtendit horam 12. </s>
  <s xml:id="echoid-s41161" xml:space="preserve">mediæ noctis; </s>
  <s xml:id="echoid-s41162" xml:space="preserve">quemadmodum in Verticali horologio au-<lb/>ſtrali. </s>
  <s xml:id="echoid-s41163" xml:space="preserve">In planis autem ad boream ſpectantibus, exiſtente quidem linea æquinoctiali infra centrum <lb/>horologii ρ, in linea indicis, vt in quarta figura, portio lineæ meridianæ à centro ρ, verſus æquino <lb/>ctialem lineam porrecta indicat horam 12. </s>
  <s xml:id="echoid-s41164" xml:space="preserve">meridiei; </s>
  <s xml:id="echoid-s41165" xml:space="preserve">quę vero (nobis ad horologium verſus au-<lb/>ſtrum conuerſis) ei ſunt ad dexteram in linea æquinoctiali, horas antemeridianas, &amp; </s>
  <s xml:id="echoid-s41166" xml:space="preserve">quæ ad ſini-<lb/>ſtram, pomeridianas demonſtrant: </s>
  <s xml:id="echoid-s41167" xml:space="preserve">reliqua autem portio lineæ meridianæ vltra centrum verſus <lb/>partes ſuperiores extenſa, ad horam 12. </s>
  <s xml:id="echoid-s41168" xml:space="preserve">medię noctis pertinet; </s>
  <s xml:id="echoid-s41169" xml:space="preserve">non ſecus, atque in horologio <lb/>horizontali. </s>
  <s xml:id="echoid-s41170" xml:space="preserve">Exiſtente vero æquinoctiali linea ſupra horologii centrum ρ, in linea ſtyli, vt in po-<lb/>
<anchor type="note" xlink:label="note-0639-07a" xlink:href="note-0639-07"/>
ſtremis duabus figuris, portio lineę meridianæ à centro ρ, verſus lineam æquinoctialem produ-<lb/>cta, vel certe, vbi parallelæ ſunt ęquinoctialis linea, &amp; </s>
  <s xml:id="echoid-s41171" xml:space="preserve">meridiana, vt in ſexta figura, portio ad par-<lb/>tes ſuperiores tendens, denotat horam 12. </s>
  <s xml:id="echoid-s41172" xml:space="preserve">medię noctis; </s>
  <s xml:id="echoid-s41173" xml:space="preserve">horæ vero ad dexteram lineæ meridia-<lb/>nę in æquinoctiali linea deſcendentes (nobis ad horologium verſus auſtrum conuerſis) ſunt ante-<lb/>meridianæ, &amp; </s>
  <s xml:id="echoid-s41174" xml:space="preserve">pomeridianę ad ſiniſtram: </s>
  <s xml:id="echoid-s41175" xml:space="preserve">reliqua vero portio meridianæ lineæ infra centrum ho-<lb/>rologii ρ, ad horam 12. </s>
  <s xml:id="echoid-s41176" xml:space="preserve">meridiei ſpectat; </s>
  <s xml:id="echoid-s41177" xml:space="preserve">non ſecus, ac in Verticali horologio boreali.</s>
  <s xml:id="echoid-s41178" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2042" type="float" level="2" n="7">
<note position="left" xlink:label="note-0639-06" xlink:href="note-0639-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0639-07" xlink:href="note-0639-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Qua ratione li-<lb/>neæ horariæ in <lb/>plano declinan <lb/>te, ſi mu@q̃ue in-<lb/>clina@o ex hori-<lb/>zontali horolo-<lb/>gio deſcriban-<lb/>t<unsure/>ur.</note>
<p>
  <s xml:id="echoid-s41179" xml:space="preserve">QVOD ſi ex puncto F, egrediantur rectæ efficientes cum recta F E, eoſdem angulos, quos <lb/>cum linea meridiana conſtituunt lineæ horariæ in horologio Aſtronomico horizõ tali, vt cap. </s>
  <s xml:id="echoid-s41180" xml:space="preserve">23. <lb/></s>
  <s xml:id="echoid-s41181" xml:space="preserve">docuimus in horologio declinante à Verticali, ſecabitur horizõtalis linea α E, in punctis, per quę <lb/>rectę emiſſæ ex centro ρ, vel vbi centrum non habetur, ipſi meridianæ lineæ ęquidiſtantes lineæ <lb/>rectæ ductæ dabunt lineas horarum à mer. </s>
  <s xml:id="echoid-s41182" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41183" xml:space="preserve">med. </s>
  <s xml:id="echoid-s41184" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41185" xml:space="preserve">vt prius.</s>
  <s xml:id="echoid-s41186" xml:space="preserve"/>
</p>
<pb o="624" file="0640" n="640" rhead="GNOMONICES"/>
<p>
  <s xml:id="echoid-s41187" xml:space="preserve">HOROLOGIVM declinans, &amp; </s>
  <s xml:id="echoid-s41188" xml:space="preserve">inclinatum ſimul ita in proprio ſitu collocabitur. </s>
  <s xml:id="echoid-s41189" xml:space="preserve">Linea <lb/>
<anchor type="note" xlink:label="note-0640-01a" xlink:href="note-0640-01"/>
horizontalis ſtatuatur Horizonti æquidiſtans, communisq́ue ſectio horologii, &amp; </s>
  <s xml:id="echoid-s41190" xml:space="preserve">plani <emph style="sc">H</emph>orizonti <lb/>æquidiſtantis cum linea meridiana in plano, quod Horizonti æquidiſtat, inuenta conſtituat angu-<lb/>lum complementi declinationis, ad auſtrum quidem &amp; </s>
  <s xml:id="echoid-s41191" xml:space="preserve">occaſum, ſi horologium à meridie in or-<lb/>tum declinat, ad auſtrum vero &amp; </s>
  <s xml:id="echoid-s41192" xml:space="preserve">ortum, ſi à meridie in occaſum; </s>
  <s xml:id="echoid-s41193" xml:space="preserve">at vero ad boream &amp; </s>
  <s xml:id="echoid-s41194" xml:space="preserve">occaſum, ſi <lb/>
<anchor type="figure" xlink:label="fig-0640-01a" xlink:href="fig-0640-01"/>
<anchor type="note" xlink:label="note-0640-02a" xlink:href="note-0640-02"/>
<anchor type="note" xlink:label="note-0640-03a" xlink:href="note-0640-03"/>
<anchor type="note" xlink:label="note-0640-04a" xlink:href="note-0640-04"/>
horologium à Septentr. </s>
  <s xml:id="echoid-s41195" xml:space="preserve">in ortum, ad boream autem &amp; </s>
  <s xml:id="echoid-s41196" xml:space="preserve">ortum, ſi à Septentr. </s>
  <s xml:id="echoid-s41197" xml:space="preserve">in occaſum defle-<lb/>
<anchor type="note" xlink:label="note-0640-05a" xlink:href="note-0640-05"/>
ctit. </s>
  <s xml:id="echoid-s41198" xml:space="preserve">Ita enim debitam declinationem habebit horologium. </s>
  <s xml:id="echoid-s41199" xml:space="preserve">Deinde recta C D, horizontalem li-<lb/>neam ad angulos rectos diuidens cum recta in plano horizontali communem ſectionem horolo-<lb/>gii, &amp; </s>
  <s xml:id="echoid-s41200" xml:space="preserve">plani horizontalis ad rectos angulos ſecante conſtituat angulum inclinationis, ad partes <lb/>quidem boreales, ſi horologium ad auſtrum ſpec@at, ad auſtrales vero, ſi ad boream. </s>
  <s xml:id="echoid-s41201" xml:space="preserve">Hac etenim <lb/>ratione collocato horologio, ſi axis ρ I, in triangulo ρ I G, ad planum horologii recto intelligatur <lb/>filum extenſum, vel ferrum aliquod ſubtile, indicabit eius vmbra ſingulas horas à mer. </s>
  <s xml:id="echoid-s41202" xml:space="preserve">vel med. <lb/></s>
  <s xml:id="echoid-s41203" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41204" xml:space="preserve">quamdiu Sol ipſum horologium illuminabit: </s>
  <s xml:id="echoid-s41205" xml:space="preserve">Vel certe vertex I, ſtyli I k, recti ad horolo-<lb/>gii planum in puncto K, idem præſtabit, vt in horologio horizontali diximus. </s>
  <s xml:id="echoid-s41206" xml:space="preserve">Quando horolo-<lb/>gium centro caret, vt in 3. </s>
  <s xml:id="echoid-s41207" xml:space="preserve">figura, ducendus erit axis per I, verticem ſtyli æquidiſtans lineæ <lb/>ſtyli G L.</s>
  <s xml:id="echoid-s41208" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2043" type="float" level="2" n="8">
<note position="left" xlink:label="note-0640-01" xlink:href="note-0640-01a" xml:space="preserve">Quomodo ho-<lb/>rologium decli <lb/>nans, &amp; ſimul <lb/>inclinatum in <lb/>proprio ſitu lo-<lb/>candum ſit.</note>
  <figure xlink:label="fig-0640-01" xlink:href="fig-0640-01a">
    <image file="0640-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0640-01"/>
  </figure>
<note position="left" xlink:label="note-0640-02" xlink:href="note-0640-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0640-03" xlink:href="note-0640-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0640-04" xlink:href="note-0640-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0640-05" xlink:href="note-0640-05a" xml:space="preserve">40</note>
</div>
<note position="left" xml:space="preserve">50</note>
<p>
  <s xml:id="echoid-s41209" xml:space="preserve">TOTAM autem hanc deſcriptionem horologii declinantis, ſimulq́ue inclinati ſex figuris <lb/>abſoluimus, vt omnis varietas in huiuſcemodi horologiis patefieret: </s>
  <s xml:id="echoid-s41210" xml:space="preserve">quarum priores tres ad ea <lb/>horologia ſuperiora pertinent, quę auſtrum reſpiciunt, in quibus centrum horologii vel eſt in-<lb/>fra æquinoctialem lineam, vel ſupra eandem, vel certe horologium centro caret, omnesq́ue li-<lb/>neę horariæ ſunt parallelæ ſecãtes lineam æquinoctialem ad angulos rectos; </s>
  <s xml:id="echoid-s41211" xml:space="preserve">poſteriores vero tres <lb/>referunt ea horologia ſuperiora, quæ ad boream ſpectant, in quibus linea meridiana æquino-<lb/>ctialem lineam ſecat vel infra centrum horologii, vel ſupra, vel certe ipſi æquinoctiali lineæ pa-<lb/>rallela eſt. </s>
  <s xml:id="echoid-s41212" xml:space="preserve">Cæterum in ſola ſexta figura omnes lineas horarias duximus, in alijs autem ea dun-<lb/>taxat lineamenta expreſſa ſunt, quæ ad cognitionem deſcriptionis requiruntur, omiſſis lineis ho-<lb/>rariis, vt cõfuſionem linearum vitaremus. </s>
  <s xml:id="echoid-s41213" xml:space="preserve">Facile enim quiuis in his, vt in illo, lineas horarias du-<lb/>cere poterit, ſi pręcepta, quæ à nobis tradita ſunt, diligenter conſideret.</s>
  <s xml:id="echoid-s41214" xml:space="preserve"/>
</p>
<pb o="625" file="0641" n="641" rhead="LIBER SEPTIMVS."/>
<p>
  <s xml:id="echoid-s41215" xml:space="preserve">IAM vero ſi horologium quodcunque Superius inuertatur, ita vt ſuperior pars euadat inſe-<lb/>
<anchor type="note" xlink:label="note-0641-01a" xlink:href="note-0641-01"/>
rior, &amp; </s>
  <s xml:id="echoid-s41216" xml:space="preserve">quæ poſt hanc inuerſionem nobis dextra eſt, fiat ſiniſtra, &amp; </s>
  <s xml:id="echoid-s41217" xml:space="preserve">contra, vt in præcedentibus <lb/>declaratum eſt, habebimus horologium Inferius: </s>
  <s xml:id="echoid-s41218" xml:space="preserve">Sed lineæ horarum, quæ prius in ſuperiori ho-<lb/>rologio indicabant horas à meridie, oſtendent in inferiori horas à med. </s>
  <s xml:id="echoid-s41219" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41220" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41221" xml:space="preserve">contra. </s>
  <s xml:id="echoid-s41222" xml:space="preserve">Pulchrè <lb/>autem hic, vt &amp; </s>
  <s xml:id="echoid-s41223" xml:space="preserve">in antecedentibus, inuerſionem hanc declarant lineamenta horologii Superioris <lb/>deſcripta in facie oppoſita, ita vt ſingula ſingulis reſpondeant ad vnguem, dummodo pars ſupe-<lb/>rior faciei oppoſitę fiat inferior, &amp; </s>
  <s xml:id="echoid-s41224" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s41225" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2044" type="float" level="2" n="9">
<note position="right" xlink:label="note-0641-01" xlink:href="note-0641-01a" xml:space="preserve">Quo pacto ex <lb/>horologio Su <lb/>periore genere-<lb/>tur Inferius.</note>
</div>
<p>
  <s xml:id="echoid-s41226" xml:space="preserve">ARCVS ſignorum, longitudinumq́ue dierum deſcribuntur hic, vt in antecedentibus. </s>
  <s xml:id="echoid-s41227" xml:space="preserve">Du-<lb/>
<anchor type="note" xlink:label="note-0641-02a" xlink:href="note-0641-02"/>
cta enim recta ρ I, pro axe mundi, erigatur ad eam in I, perpendicularis I G, pro radio Aequato-<lb/>ris, ad cuius vtramque partem radii aliorum ſignorum, &amp; </s>
  <s xml:id="echoid-s41228" xml:space="preserve">longitudinum dierum educantur, vt <lb/>
<anchor type="note" xlink:label="note-0641-03a" xlink:href="note-0641-03"/>
in ſuperioribus factum eſt. </s>
  <s xml:id="echoid-s41229" xml:space="preserve">Deinde ſit I ρ, ęqualis portioni axis ρ I, in horologio, &amp; </s>
  <s xml:id="echoid-s41230" xml:space="preserve">recta I G, re-<lb/>ctę I G, vel L G, in eodem horologio; </s>
  <s xml:id="echoid-s41231" xml:space="preserve">atque ex ρ, per G, emittatur recta ρ G: </s>
  <s xml:id="echoid-s41232" xml:space="preserve">quam commodius <lb/>
<anchor type="figure" xlink:label="fig-0641-01a" xlink:href="fig-0641-01"/>
<anchor type="note" xlink:label="note-0641-04a" xlink:href="note-0641-04"/>
<anchor type="note" xlink:label="note-0641-05a" xlink:href="note-0641-05"/>
<anchor type="note" xlink:label="note-0641-06a" xlink:href="note-0641-06"/>
<anchor type="note" xlink:label="note-0641-07a" xlink:href="note-0641-07"/>
fortaſſe ducemus, ſi ex ρ, ducamus rectam ρ G, quę cum axe ρ I, conſtituat angulum G ρ I, ęqua-<lb/>lem angulo G ρ I, quem in horologio conſtituunt axis ρ I, &amp; </s>
  <s xml:id="echoid-s41233" xml:space="preserve">linea ſtyli ρ G, nempe angulo altitu-<lb/>dinis poli ſupra planum horologii. </s>
  <s xml:id="echoid-s41234" xml:space="preserve">Poſtremo reliqua omnia fiant, vt cap. </s>
  <s xml:id="echoid-s41235" xml:space="preserve">24. </s>
  <s xml:id="echoid-s41236" xml:space="preserve">tradidimus, cum <lb/>de horologio declinante à Verticali ageremus. </s>
  <s xml:id="echoid-s41237" xml:space="preserve">Ita enim conſtructa erit figura radiorum Zodia-<lb/>ci, ex qua arcus ſignorum deſcribentur, vt in horologio declinante à Verticali. </s>
  <s xml:id="echoid-s41238" xml:space="preserve">Exemplum <lb/>ſubiecimus reſpondens vltimo horologio Superiori ex illis ſex, quæ paulo ante deſcripſimus. <lb/></s>
  <s xml:id="echoid-s41239" xml:space="preserve">Vbi quoniam linea ſtyli eadem eſt, quæ linea horæ 6. </s>
  <s xml:id="echoid-s41240" xml:space="preserve">appoſiti ſunt ſingulis lineis horarijs ex pun-<lb/>cto ρ, ſiguræ radiorum Zodiaci egredientibus bini numeri horarum ęqualiter hinc inde à linea <lb/>horę 6. </s>
  <s xml:id="echoid-s41241" xml:space="preserve">hoc eſt, à linea ſtyli diſtantium, vt cap. </s>
  <s xml:id="echoid-s41242" xml:space="preserve">24. </s>
  <s xml:id="echoid-s41243" xml:space="preserve">monuimus. </s>
  <s xml:id="echoid-s41244" xml:space="preserve">Rurſus hic recta ρ V, radio <lb/>Aequatoris ęquidiſtans exhibet horam 12. </s>
  <s xml:id="echoid-s41245" xml:space="preserve">quoniam huius horę linea in horologio ęquidiſtat
<pb o="626" file="0642" n="642" rhead="GNOMONICES"/>
ęquinoctiali lineę: </s>
  <s xml:id="echoid-s41246" xml:space="preserve">quemadmodum in horizontali horologio recta H V, radio Aequatoris ęqui-<lb/>diſtans in figura radiorum Zodici cap. </s>
  <s xml:id="echoid-s41247" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41248" xml:space="preserve">deſcripta refert horam 6. </s>
  <s xml:id="echoid-s41249" xml:space="preserve">quia huius linea etiam ęqui-<lb/>noctiali lineę ęquidiſta t in horologio.</s>
  <s xml:id="echoid-s41250" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2045" type="float" level="2" n="10">
<note position="right" xlink:label="note-0641-02" xlink:href="note-0641-02a" xml:space="preserve">Deſcriptio ar-<lb/>cuum ſignorũ, <lb/>&amp; longitudinũ <lb/>dierum in ho-<lb/>rologio declinã <lb/>te, &amp; ſimul in-<lb/>elinato.</note>
<note position="left" xlink:label="note-0641-03" xlink:href="note-0641-03a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0641-01" xlink:href="fig-0641-01a">
    <image file="0641-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0641-01"/>
  </figure>
<note position="left" xlink:label="note-0641-04" xlink:href="note-0641-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0641-05" xlink:href="note-0641-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0641-06" xlink:href="note-0641-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0641-07" xlink:href="note-0641-07a" xml:space="preserve">50</note>
</div>
  <figure>
    <image file="0642-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0642-01"/>
  </figure>
<note position="left" xml:space="preserve">10</note>
<note position="left" xml:space="preserve">20</note>
<note position="left" xml:space="preserve">30</note>
<p>
  <s xml:id="echoid-s41251" xml:space="preserve">ADDIDIMVS quoque aliam figuram radiorum Zodiaci, cum lineis horariis ex ρ, egre-<lb/>
<anchor type="figure" xlink:label="fig-0642-02a" xlink:href="fig-0642-02"/>
<anchor type="note" xlink:label="note-0642-04a" xlink:href="note-0642-04"/>
<anchor type="note" xlink:label="note-0642-05a" xlink:href="note-0642-05"/>
dientibus, reſpondentem primo horologio huius cap. </s>
  <s xml:id="echoid-s41252" xml:space="preserve">in quo linea ſtyli neque vna eſt ex lineisho<unsure/>
<pb o="627" file="0643" n="643" rhead="LIBER SEPTIMVS."/>
rariis, neque æqualiter à duabus hinc inde poſitis diſtat. </s>
  <s xml:id="echoid-s41253" xml:space="preserve">Vndeſit, vt ſingulæ lineæ ex ρ, emiſſæ ſin <lb/>gulos quoque numeros habeant affixos. </s>
  <s xml:id="echoid-s41254" xml:space="preserve">Ex hac igitur ſigura in dicto horologio (ſi prius in eo <lb/>omnes lineæ horariæ ducantur) arcus ſignorum deſcribere licebit, cum res tulerit. </s>
  <s xml:id="echoid-s41255" xml:space="preserve">Partiti autem <lb/>ſumus ſiguram hanc, vt cernis, in duas, quia alioquin nimis inter ſe conſunderentur lineæ, pro-<lb/>pterea quòd linea ſtyli primi horologii parum diſtat à linea horæ 11, vt conſtat ex ſigura prima <lb/>propoſ. </s>
  <s xml:id="echoid-s41256" xml:space="preserve">37. </s>
  <s xml:id="echoid-s41257" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41258" xml:space="preserve">3. </s>
  <s xml:id="echoid-s41259" xml:space="preserve">in qua lineæ horariæ deſcriptæ ſunt. </s>
  <s xml:id="echoid-s41260" xml:space="preserve">In priore harum ſigurarum continentur <lb/>lineæ horarum, quæ in horologio poſitæ ſunt ad ſiniſtram lineæ ſtyli in prima ſigura propoſ. </s>
  <s xml:id="echoid-s41261" xml:space="preserve">37. <lb/></s>
  <s xml:id="echoid-s41262" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41263" xml:space="preserve">3. </s>
  <s xml:id="echoid-s41264" xml:space="preserve">aut quæ in prima figura huius cap. </s>
  <s xml:id="echoid-s41265" xml:space="preserve">ad ſiniſtram collocarentur, ſi deſcriptæ eſſent; </s>
  <s xml:id="echoid-s41266" xml:space="preserve">quales <lb/>ſunt 5. </s>
  <s xml:id="echoid-s41267" xml:space="preserve">6. </s>
  <s xml:id="echoid-s41268" xml:space="preserve">7. </s>
  <s xml:id="echoid-s41269" xml:space="preserve">8. </s>
  <s xml:id="echoid-s41270" xml:space="preserve">9. </s>
  <s xml:id="echoid-s41271" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41272" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41273" xml:space="preserve">11. </s>
  <s xml:id="echoid-s41274" xml:space="preserve">In poſteriori vero reliquæ horæ ad dextram eiuſdem lineę ſtyli ſitæ, <lb/>nempe 12. </s>
  <s xml:id="echoid-s41275" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41276" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41277" xml:space="preserve">3. </s>
  <s xml:id="echoid-s41278" xml:space="preserve">4. </s>
  <s xml:id="echoid-s41279" xml:space="preserve">5. </s>
  <s xml:id="echoid-s41280" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s41281" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41282" xml:space="preserve">Id quod in cap. </s>
  <s xml:id="echoid-s41283" xml:space="preserve">24. </s>
  <s xml:id="echoid-s41284" xml:space="preserve">monuimus faciendum eſſe in horologiis decli-<lb/>
<anchor type="note" xlink:label="note-0643-01a" xlink:href="note-0643-01"/>
nantibus, atque adeo &amp; </s>
  <s xml:id="echoid-s41285" xml:space="preserve">in inclinatis, in quibus huiuſmodi confuſio linearum reperitur.</s>
  <s xml:id="echoid-s41286" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2046" type="float" level="2" n="11">
  <figure xlink:label="fig-0642-02" xlink:href="fig-0642-02a">
    <image file="0642-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0642-02"/>
  </figure>
<note position="left" xlink:label="note-0642-04" xlink:href="note-0642-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0642-05" xlink:href="note-0642-05a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0643-01" xlink:href="note-0643-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41287" xml:space="preserve">POSTREMO, vt videas, quid agendum ſit in tertio horologio huius cap. </s>
  <s xml:id="echoid-s41288" xml:space="preserve">in quo lineæ <lb/>
<anchor type="figure" xlink:label="fig-0643-01a" xlink:href="fig-0643-01"/>
<anchor type="note" xlink:label="note-0643-02a" xlink:href="note-0643-02"/>
<anchor type="note" xlink:label="note-0643-03a" xlink:href="note-0643-03"/>
horariæ ſunt æquidiſtantes, quæ quidem in tertia ſigura propoſ. </s>
  <s xml:id="echoid-s41289" xml:space="preserve">37. </s>
  <s xml:id="echoid-s41290" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41291" xml:space="preserve">3. </s>
  <s xml:id="echoid-s41292" xml:space="preserve">ductæ ſunt, deſcripſi-<lb/>mus etiam in eo arcus ſignorum: </s>
  <s xml:id="echoid-s41293" xml:space="preserve">qui quidem deſcribuntur, vt in Meridiano horologio, vel pola-<lb/>ri, hoc excepto, quòd hic lineæ horarię in figura radiorum radium Aequatoris ad angulos rectos <lb/>
<anchor type="note" xlink:label="note-0643-04a" xlink:href="note-0643-04"/>
ſecantes habent ſingulę ſingulos numeros, non autem binos, vt ibi, niſi cum linea ſtyli vna eſt ex <lb/>lineis horariis, vel certe à duabus proximis hinc inde poſitis æqualiter diſtat, quemadmodum in <lb/>aliis horologiis declinantibus contingere ſolet.</s>
  <s xml:id="echoid-s41294" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2047" type="float" level="2" n="12">
  <figure xlink:label="fig-0643-01" xlink:href="fig-0643-01a">
    <image file="0643-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0643-01"/>
  </figure>
<note position="left" xlink:label="note-0643-02" xlink:href="note-0643-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0643-03" xlink:href="note-0643-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0643-04" xlink:href="note-0643-04a" xml:space="preserve">40</note>
</div>
<note position="right" xml:space="preserve">Horizontalis li-<lb/>nea partitur ho <lb/>rologium in Su <lb/>perius, Infe-<lb/>riusq́ue. Et in <lb/>Diurnum, No-<lb/>cturnumque.</note>
<p>
  <s xml:id="echoid-s41295" xml:space="preserve">LINEA horizontalis totum horologium diuidit, vt in præcedentibus dictum eſt, in Supe-<lb/>rius atque Inferius, quorum Superius eſt pars illa, quæ infra lineam horizontalem continetur: <lb/></s>
  <s xml:id="echoid-s41296" xml:space="preserve">Reliqua autem pars dabit Inferius, ſi tamen omnes partes inuertantur, vt ſupra dictum eſt, &amp; </s>
  <s xml:id="echoid-s41297" xml:space="preserve">ho-<lb/>ræ, quæ prius à med. </s>
  <s xml:id="echoid-s41298" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41299" xml:space="preserve">computabantur, nunc à mer. </s>
  <s xml:id="echoid-s41300" xml:space="preserve">numerentur, &amp;</s>
  <s xml:id="echoid-s41301" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41302" xml:space="preserve">Eadem horizonta-<lb/>lis linea dirimit totum horologium in Diurnum, ac Nocturnum, vt in pręcedentibus explica-<lb/>tum eſt.</s>
  <s xml:id="echoid-s41303" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s41304" xml:space="preserve">PORRO arcus ſignorum borealium continentur inter centrum horologii, &amp; </s>
  <s xml:id="echoid-s41305" xml:space="preserve">æquinoctia-<lb/>
<anchor type="note" xlink:label="note-0643-06a" xlink:href="note-0643-06"/>
<anchor type="note" xlink:label="note-0643-07a" xlink:href="note-0643-07"/>
lem lineam in horologiis ſuperioribus à ſeptentrione declinantibus, &amp; </s>
  <s xml:id="echoid-s41306" xml:space="preserve">in iis etiam, quæ à meri-<lb/>die declinant, ſi tamen centrum habeant infra æquinoctialem lineam, quemadmodum in hori-<lb/>zontalibus horologiis: </s>
  <s xml:id="echoid-s41307" xml:space="preserve">Si autem hæc horologia à meridie declinantia centrum habeant ſupra li-<lb/>neam æquin octialem, pertinebunt arcus inter centrum, &amp; </s>
  <s xml:id="echoid-s41308" xml:space="preserve">æquinoctialem lineam ad ſigna auſtra-<lb/>lia, veluti in Verticalibus horologiis ad auſtrum ſpectantibus. </s>
  <s xml:id="echoid-s41309" xml:space="preserve">Quòd ſi huiuſmodi horologia cen <lb/>tro careant, exiſtent arcus ſignorum auſtralium ſupra lineam æquinoctialem, ſicuti in polaribus <lb/>horologijs, &amp;</s>
  <s xml:id="echoid-s41310" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41311" xml:space="preserve">In horologiis Inferioribus contrarium prorſus eſt intelligendum.</s>
  <s xml:id="echoid-s41312" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2048" type="float" level="2" n="13">
<note position="left" xlink:label="note-0643-06" xlink:href="note-0643-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0643-07" xlink:href="note-0643-07a" xml:space="preserve">Qui arc<unsure/>us ſi-<lb/>gnorum ad bo-<lb/>realia ſigna, &amp; <lb/>qui ad auſtralia <lb/>pertineant.</note>
</div>
<note position="right" xml:space="preserve">Qua ratione ex <lb/>figura radiorũ <lb/>ad datam ſtyli <lb/>longitudinem <lb/>maius aut mi-<lb/>nus horologiũ <lb/>deſcribatur.</note>
<p>
  <s xml:id="echoid-s41313" xml:space="preserve">QVOD ſi ex ſigura radiorum Zodiaci huius cap. </s>
  <s xml:id="echoid-s41314" xml:space="preserve">maius, aut minus horologium deſcriben-<lb/>dum ſit, pro data ſtyli magnitudine, fiet id hunc in modum. </s>
  <s xml:id="echoid-s41315" xml:space="preserve">Deſcribatur ſeorſum, veluti iuxta ſi-<lb/>guram radiorum huius propoſ. </s>
  <s xml:id="echoid-s41316" xml:space="preserve">vides, triangulum ρ I G, ex horologio hoc cap. </s>
  <s xml:id="echoid-s41317" xml:space="preserve">conſtructo, vel ex <lb/>ipſa ſigura radiorum deſumptum, in quo axis mundi eſt ρ I; </s>
  <s xml:id="echoid-s41318" xml:space="preserve">Aequator I G; </s>
  <s xml:id="echoid-s41319" xml:space="preserve">linea ſtyli ρ G, in quã
<pb o="628" file="0644" n="644" rhead="GNOMONICES"/>
ſtylus I K, ad angulos rectos cadit. </s>
  <s xml:id="echoid-s41320" xml:space="preserve">Deinde productis rectis I ρ, I G, I K, ſi ſumatur in I K, recta <lb/>I A, dato gnomoni æqualis, ſiue is maior exiſtat ſtylo I K, ſiue minor, &amp; </s>
  <s xml:id="echoid-s41321" xml:space="preserve">per A, ipſi ρ G, parallela <lb/>agatur B D, erit triangulum B I D, triangulo ρ I G, ſimile. </s>
  <s xml:id="echoid-s41322" xml:space="preserve">Quare ſi axis I B, transferatur in figu-<lb/>ram radiorum ex ρ, vſque ad B, verſus I, atque ex B, egrediantur radij ſignorum, &amp; </s>
  <s xml:id="echoid-s41323" xml:space="preserve">reliqua omnia <lb/>fiant, vt in præcedentibus expoſitum eſt, deſcribentur arcus ſignorum pro magnitudine ſtyli <lb/>I A, &amp;</s>
  <s xml:id="echoid-s41324" xml:space="preserve">c.</s>
  <s xml:id="echoid-s41325" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s41326" xml:space="preserve">HOROLOGIVM Italicum &amp; </s>
  <s xml:id="echoid-s41327" xml:space="preserve">Babylonicum conficietur, vt in antecedentibus dictum eſt. <lb/></s>
  <s xml:id="echoid-s41328" xml:space="preserve">
<anchor type="note" xlink:label="note-0644-01a" xlink:href="note-0644-01"/>
Nam ſi circulus ex L, deſcriptus ſecetur in arcum diurnum ♋, a M b, &amp; </s>
  <s xml:id="echoid-s41329" xml:space="preserve">in arcum diurnum ♑, <lb/>d M e, ita vt rectæ a b, d e, ſecent rectam L M, quæ per centrum L, meridianæ lineæ parallela du-<lb/>citur, ad angulos rectos, hoc eſt, arcus ſemidiurni à puncto M, numerentur vſque ad puncta a, b, <lb/>
<anchor type="note" xlink:label="note-0644-02a" xlink:href="note-0644-02"/>
<anchor type="figure" xlink:label="fig-0644-01a" xlink:href="fig-0644-01"/>
<anchor type="note" xlink:label="note-0644-03a" xlink:href="note-0644-03"/>
<anchor type="note" xlink:label="note-0644-04a" xlink:href="note-0644-04"/>
<anchor type="note" xlink:label="note-0644-05a" xlink:href="note-0644-05"/>
<anchor type="note" xlink:label="note-0644-06a" xlink:href="note-0644-06"/>
d, e, diuiſioq́ue eiuſdem circuli in 24. </s>
  <s xml:id="echoid-s41330" xml:space="preserve">partes æquales initium ſumat à punctis occidentalibus b, e, <lb/>pro horologio Italico, &amp; </s>
  <s xml:id="echoid-s41331" xml:space="preserve">à punctis orientalibus a, d, pro Babylonico, inueniemus in tropicis pun-<lb/>cta horarum ab or. </s>
  <s xml:id="echoid-s41332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41333" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41334" xml:space="preserve">vt in præcedentibus. </s>
  <s xml:id="echoid-s41335" xml:space="preserve">Sed quoniam in noſtro exemplo tropicus ♑, de-<lb/>ſcribi non poteſt, ſatis erit, ſi inueniantur puncta horarum ab or. </s>
  <s xml:id="echoid-s41336" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41337" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41338" xml:space="preserve">in tropico ♋, beneficio ar-<lb/>cus diurni a M b, eiuſdem tropici. </s>
  <s xml:id="echoid-s41339" xml:space="preserve">Hæc enim lineis rectis coniuncta cum horis reſpondentibus <lb/>in linea æquinoctiali, vt in præcedentibus, dabunt horas ab or. </s>
  <s xml:id="echoid-s41340" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41341" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41342" xml:space="preserve">Reperiemus autem in Su-<lb/>periori horologio noſtri exempli, hoc eſt, in portione infra horizontalem lineam contenta, pun-<lb/>cta duntaxat horarum ab occ. </s>
  <s xml:id="echoid-s41343" xml:space="preserve">à 9. </s>
  <s xml:id="echoid-s41344" xml:space="preserve">vſque ad 16. </s>
  <s xml:id="echoid-s41345" xml:space="preserve">incluſiue; </s>
  <s xml:id="echoid-s41346" xml:space="preserve">Item puncta horarum ab or. </s>
  <s xml:id="echoid-s41347" xml:space="preserve">à 1. </s>
  <s xml:id="echoid-s41348" xml:space="preserve">vſque
<pb o="629" file="0645" n="645" rhead="LIBER SEPTIMVS."/>
ad 7. </s>
  <s xml:id="echoid-s41349" xml:space="preserve">incluſiue: </s>
  <s xml:id="echoid-s41350" xml:space="preserve">quia hæ omnes horæ continentur in arcu circuli a M, ex cuius punctis lineæ rectę <lb/>ductæ per centrum L, occurrunt lineæ æquinoctiali, poſtquam per centrum L, ductę ſunt. </s>
  <s xml:id="echoid-s41351" xml:space="preserve">Pun-<lb/>cta vero horarum 17. </s>
  <s xml:id="echoid-s41352" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41353" xml:space="preserve">18. </s>
  <s xml:id="echoid-s41354" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41355" xml:space="preserve">ita inueniemus in tropico ♋. </s>
  <s xml:id="echoid-s41356" xml:space="preserve">Ex punctis hor. </s>
  <s xml:id="echoid-s41357" xml:space="preserve">5. </s>
  <s xml:id="echoid-s41358" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41359" xml:space="preserve">6. </s>
  <s xml:id="echoid-s41360" xml:space="preserve">ab occ. <lb/></s>
  <s xml:id="echoid-s41361" xml:space="preserve">quæ continentur in arcu a N, opponunturq́ue dictis horis 17. </s>
  <s xml:id="echoid-s41362" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41363" xml:space="preserve">18. </s>
  <s xml:id="echoid-s41364" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41365" xml:space="preserve">ducemus lineas oc-<lb/>cultas per centrum L. </s>
  <s xml:id="echoid-s41366" xml:space="preserve">Beneficio enim earum reperiemus in tropico ♋, in portione nocturna pun-<lb/>cta pro hor. </s>
  <s xml:id="echoid-s41367" xml:space="preserve">5. </s>
  <s xml:id="echoid-s41368" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41369" xml:space="preserve">6. </s>
  <s xml:id="echoid-s41370" xml:space="preserve">à quibus rectæ occultæ per ρ, centrum horologii ductæ dabunt in eodem tro-<lb/>pico ♋, puncta horarum 17. </s>
  <s xml:id="echoid-s41371" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41372" xml:space="preserve">18. </s>
  <s xml:id="echoid-s41373" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41374" xml:space="preserve">Ducenda eſt autem hora 18. </s>
  <s xml:id="echoid-s41375" xml:space="preserve">parallela lineæ meridianę, <lb/>ſeu ęquinoctiali: </s>
  <s xml:id="echoid-s41376" xml:space="preserve">Hora vero 17. </s>
  <s xml:id="echoid-s41377" xml:space="preserve">per horam 11. </s>
  <s xml:id="echoid-s41378" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s41379" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41380" xml:space="preserve">in linea ęquinoctiali ducenda eſt. </s>
  <s xml:id="echoid-s41381" xml:space="preserve">At <lb/>vero puncta horarum 8. </s>
  <s xml:id="echoid-s41382" xml:space="preserve">9. </s>
  <s xml:id="echoid-s41383" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41384" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41385" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41386" xml:space="preserve">in tropico ♋, inueniemus hoc pacto. </s>
  <s xml:id="echoid-s41387" xml:space="preserve">Ex punctis hor. </s>
  <s xml:id="echoid-s41388" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41389" xml:space="preserve"><lb/>21. </s>
  <s xml:id="echoid-s41390" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41391" xml:space="preserve">22. </s>
  <s xml:id="echoid-s41392" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41393" xml:space="preserve">quæ continentur in arcu a N, opponunturq́ue dictis horis 8. </s>
  <s xml:id="echoid-s41394" xml:space="preserve">9. </s>
  <s xml:id="echoid-s41395" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41396" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41397" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41398" xml:space="preserve">du-<lb/>
<anchor type="note" xlink:label="note-0645-01a" xlink:href="note-0645-01"/>
cemus lineas occultas per centrum L. </s>
  <s xml:id="echoid-s41399" xml:space="preserve">Harum enim beneficio deprehendemus in tropico ♋, in <lb/>portione nocturna puncta pro hor. </s>
  <s xml:id="echoid-s41400" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41401" xml:space="preserve">21. </s>
  <s xml:id="echoid-s41402" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41403" xml:space="preserve">22. </s>
  <s xml:id="echoid-s41404" xml:space="preserve">à quibus rectæ occultæ per ρ, centrum horologii <lb/>ductæ dabunt in eodem tropico ♋, puncta horarum 8. </s>
  <s xml:id="echoid-s41405" xml:space="preserve">9. </s>
  <s xml:id="echoid-s41406" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41407" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41408" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41409" xml:space="preserve">Porro hora 6. </s>
  <s xml:id="echoid-s41410" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41411" xml:space="preserve">ducen <lb/>da eſt parallela lineæ meridianæ, vel æquinoctiali. </s>
  <s xml:id="echoid-s41412" xml:space="preserve">Hora vero 7. </s>
  <s xml:id="echoid-s41413" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41414" xml:space="preserve">ducenda eſt per hor. </s>
  <s xml:id="echoid-s41415" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41416" xml:space="preserve">à <lb/>mer. </s>
  <s xml:id="echoid-s41417" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41418" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41419" xml:space="preserve">in linea æquinoetiali, &amp; </s>
  <s xml:id="echoid-s41420" xml:space="preserve">hora 8. </s>
  <s xml:id="echoid-s41421" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s41422" xml:space="preserve">per hor. </s>
  <s xml:id="echoid-s41423" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41424" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41425" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41426" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41427" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s41428" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41429" xml:space="preserve">vt ex <lb/>tabula propoſ. </s>
  <s xml:id="echoid-s41430" xml:space="preserve">19. </s>
  <s xml:id="echoid-s41431" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41432" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41433" xml:space="preserve">conſtat.</s>
  <s xml:id="echoid-s41434" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2049" type="float" level="2" n="14">
<note position="left" xlink:label="note-0644-01" xlink:href="note-0644-01a" xml:space="preserve">Conſtructio ho <lb/>@ologii Italici <lb/>&amp; Babylonici <lb/>declinantis, &amp; <lb/>ſimul inclinati.</note>
<note position="left" xlink:label="note-0644-02" xlink:href="note-0644-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0644-01" xlink:href="fig-0644-01a">
    <image file="0644-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0644-01"/>
  </figure>
<note position="left" xlink:label="note-0644-03" xlink:href="note-0644-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0644-04" xlink:href="note-0644-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0644-05" xlink:href="note-0644-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0644-06" xlink:href="note-0644-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0645-01" xlink:href="note-0645-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41435" xml:space="preserve">VTRVMQVE vero horologium commodiſſime componetur per arcum diurnum hora-<lb/>rum 24. </s>
  <s xml:id="echoid-s41436" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41437" xml:space="preserve">per arcum diurnum horarum 14. </s>
  <s xml:id="echoid-s41438" xml:space="preserve">qui in portione nocturna horologii mutatur in ar-<lb/>cum nocturnum horarum 10. </s>
  <s xml:id="echoid-s41439" xml:space="preserve">Omnes enim lineæ horarum ab or. </s>
  <s xml:id="echoid-s41440" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41441" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41442" xml:space="preserve">tangunt arcum diurnũ <lb/>horarum 24. </s>
  <s xml:id="echoid-s41443" xml:space="preserve">in punctis horarum à mer. </s>
  <s xml:id="echoid-s41444" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41445" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41446" xml:space="preserve">Vnde fere ſemper in deſcriptione hora-<lb/>
<anchor type="note" xlink:label="note-0645-02a" xlink:href="note-0645-02"/>
rum ab or. </s>
  <s xml:id="echoid-s41447" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41448" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41449" xml:space="preserve">habebimus pro ſingulis horis terna puncta, vnum videlicet in arcu diurno ho-<lb/>rarum 24. </s>
  <s xml:id="echoid-s41450" xml:space="preserve">alterum in arcu diurno horarum 14. </s>
  <s xml:id="echoid-s41451" xml:space="preserve">vel nocturno horarum 10. </s>
  <s xml:id="echoid-s41452" xml:space="preserve">tertium denique in <lb/>linea æquinoctiali, ſeu arcu diurno, nocturnove horarum 12. </s>
  <s xml:id="echoid-s41453" xml:space="preserve">vt ex ſigura manifeſtum eſt.</s>
  <s xml:id="echoid-s41454" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2050" type="float" level="2" n="15">
<note position="left" xlink:label="note-0645-02" xlink:href="note-0645-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s41455" xml:space="preserve">AD extremum horologium Antiquum declinans, ſimulq́ue inclinatum conſtruetur, vt in <lb/>
<anchor type="note" xlink:label="note-0645-03a" xlink:href="note-0645-03"/>
<anchor type="figure" xlink:label="fig-0645-01a" xlink:href="fig-0645-01"/>
<anchor type="note" xlink:label="note-0645-04a" xlink:href="note-0645-04"/>
<anchor type="note" xlink:label="note-0645-05a" xlink:href="note-0645-05"/>
<anchor type="note" xlink:label="note-0645-06a" xlink:href="note-0645-06"/>
præcedentibus. </s>
  <s xml:id="echoid-s41456" xml:space="preserve">Id quod figura ipſa indicat, in qua arcum diurnum horarum 18. </s>
  <s xml:id="echoid-s41457" xml:space="preserve">delineauimus, <lb/>qui in portione nocturna horologij inarcum nocturnum horarum 6. </s>
  <s xml:id="echoid-s41458" xml:space="preserve">commutatur.</s>
  <s xml:id="echoid-s41459" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2051" type="float" level="2" n="16">
<note position="right" xlink:label="note-0645-03" xlink:href="note-0645-03a" xml:space="preserve">Conſtructio he <lb/>rologii Antiqul <lb/>declinantis, ſi-<lb/>mulque incli@a <lb/>@@.</note>
  <figure xlink:label="fig-0645-01" xlink:href="fig-0645-01a">
    <image file="0645-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0645-01"/>
  </figure>
<note position="left" xlink:label="note-0645-04" xlink:href="note-0645-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0645-05" xlink:href="note-0645-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0645-06" xlink:href="note-0645-06a" xml:space="preserve">50</note>
</div>
<pb o="630" file="0646" n="646" rhead="GNOMONICES"/>
</div>
<div xml:id="echoid-div2053" type="section" level="1" n="522">
<head xml:id="echoid-head551" style="it" xml:space="preserve">DE HOROLOGIORVM DESCRIPTIONE IN QVOCVNQVE <lb/>plano, &amp; ad quamuis latitudinem loci, per instrumentum in hunc <lb/>vſum conſtructum. CAP. XXX.</head>
<p>
  <s xml:id="echoid-s41460" xml:space="preserve">EX cupro, vel orichalco, ſiue ex alia materia dura paretur quadrangulũ A B, in quo recta C D, <lb/>
<anchor type="note" xlink:label="note-0646-01a" xlink:href="note-0646-01"/>
meridianam lineam referat, cui ad angulos rectos inſiſtat planum C D E, in quo ex centro F, <lb/>deſcriptus ſit quadrans F G H, ita vt ſemidiameter F G, rectæ C D, æquidiſtet, ſemidiameter au-<lb/>tem F H, ad planum A B, recta ſit, ipſeq́ue quadrans in 90. </s>
  <s xml:id="echoid-s41461" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s41462" xml:space="preserve">diſtributus ſit, initio facto à G, <lb/>verſus H, procedendo. </s>
  <s xml:id="echoid-s41463" xml:space="preserve">Deinde fiat axis I k, mediocris longitudinis, cuius portio I M, ſemidiame-<lb/>
<anchor type="note" xlink:label="note-0646-02a" xlink:href="note-0646-02"/>
tro quadrantis F G H, æqualis, quadrata ſit, id eſt, habeat formam parallelepipedi, reliqua autem <lb/>portio M K, rotunda exiſtat, ad modum cylindri. </s>
  <s xml:id="echoid-s41464" xml:space="preserve">In extremitate I, firmetur ad angulos rectos ipſi <lb/>
<anchor type="figure" xlink:label="fig-0646-01a" xlink:href="fig-0646-01"/>
axi clauus teres I L, vt <lb/>imponi poſſit centro <lb/>F, perforato, &amp; </s>
  <s xml:id="echoid-s41465" xml:space="preserve">axis ip-<lb/>ſe cochleola L, aſtringi, <lb/>in eum finem, vt libe-<lb/>re eleuari, deprimiq́ue <lb/>poſſit circa centrum I; <lb/></s>
  <s xml:id="echoid-s41466" xml:space="preserve">dummodo in M, pro-<lb/>
<anchor type="note" xlink:label="note-0646-03a" xlink:href="note-0646-03"/>
mineat fruſtum M N, <lb/>excauatum, ad hoc, vt <lb/>axis eleuatus, aut de-<lb/>preſſus perpetuo qua-<lb/>drãti F G H, adhęreat, <lb/>aſtringiq́ue poſſit co-<lb/>chleola O, vt nimirum <lb/>axis firmari poſſit in <lb/>quadrante ad datã la-<lb/>titudinẽ loci: </s>
  <s xml:id="echoid-s41467" xml:space="preserve">Habeat <lb/>
<anchor type="note" xlink:label="note-0646-04a" xlink:href="note-0646-04"/>
quoque parallelipipedum I M, in medio è regione fruſti M N, foramen quadrangulare P, vt per <lb/>illud inſpici poſſint gradus quadrantis, in quibus axis firmandus eſt. </s>
  <s xml:id="echoid-s41468" xml:space="preserve">Neque enim axis extremi-<lb/>tas ad gradus latitudin is firmanda eſt, ſed eius medium reſpondens centro claui I L, vel quadran <lb/>tis F G H. </s>
  <s xml:id="echoid-s41469" xml:space="preserve">Tandem axi circumponatur annulus ſurſum, ac deorſum mobilis Q R, qui in quo-<lb/>cunque loco axis ſiſti poſſit beneficio cochleolæ S.</s>
  <s xml:id="echoid-s41470" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2053" type="float" level="2" n="1">
<note position="left" xlink:label="note-0646-01" xlink:href="note-0646-01a" xml:space="preserve">Conſtructio in-<lb/>ſtrumenti, quo <lb/>horologia in <lb/>quocunque pla <lb/>no, &amp; ad quam-<lb/>uis latitudinem <lb/>loci deſcriban-<lb/>tur.</note>
<note position="left" xlink:label="note-0646-02" xlink:href="note-0646-02a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0646-01" xlink:href="fig-0646-01a">
    <image file="0646-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0646-01"/>
  </figure>
<note position="left" xlink:label="note-0646-03" xlink:href="note-0646-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0646-04" xlink:href="note-0646-04a" xml:space="preserve">30</note>
</div>
  <figure>
    <image file="0646-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0646-02"/>
  </figure>
<p>
  <s xml:id="echoid-s41471" xml:space="preserve">POST hæc ex <lb/>eadem materia fiat <lb/>circulus A B C D, <lb/>circa centrum E, <lb/>diuiſus in 24. </s>
  <s xml:id="echoid-s41472" xml:space="preserve">ho-<lb/>
<anchor type="note" xlink:label="note-0646-05a" xlink:href="note-0646-05"/>
ras æquales, initio <lb/>facto à puncto C, <lb/>ſiniſtrorſum pro-<lb/>grediendo. </s>
  <s xml:id="echoid-s41473" xml:space="preserve">Dein-<lb/>de ad vtramq; </s>
  <s xml:id="echoid-s41474" xml:space="preserve">par <lb/>tem rectæ E D, du-<lb/>cantur ẽx E, centro <lb/>radii ſignorum, vt <lb/>cap. </s>
  <s xml:id="echoid-s41475" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41476" xml:space="preserve">huius lib. <lb/></s>
  <s xml:id="echoid-s41477" xml:space="preserve">docuimus, ita vt <lb/>
<anchor type="note" xlink:label="note-0646-06a" xlink:href="note-0646-06"/>
E D, ſit radius Ae-<lb/>quatoris, &amp; </s>
  <s xml:id="echoid-s41478" xml:space="preserve">radii <lb/>ſignorum borealiũ <lb/>ſint inter E D, &amp; </s>
  <s xml:id="echoid-s41479" xml:space="preserve"><lb/>E C, auſtraliũ ve-<lb/>ro inter E D, &amp; </s>
  <s xml:id="echoid-s41480" xml:space="preserve"><lb/>E A. </s>
  <s xml:id="echoid-s41481" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s41482" xml:space="preserve">ra-<lb/>tione radii longitu <lb/>dinum dierum du <lb/>ci poterunt, vt cap. <lb/></s>
  <s xml:id="echoid-s41483" xml:space="preserve">3. </s>
  <s xml:id="echoid-s41484" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s41485" xml:space="preserve">tradi-
<pb o="631" file="0647" n="647" rhead="LIBER SEPTIMVS."/>
tum eſt, quando res exiget. </s>
  <s xml:id="echoid-s41486" xml:space="preserve">In figura nulli ducti ſunt, quia non eodem modo ſe habent in omni-<lb/>bus regionibus. </s>
  <s xml:id="echoid-s41487" xml:space="preserve">Vnde ſatis eſt, ſi occultè ducantur pro data latitudine loci. </s>
  <s xml:id="echoid-s41488" xml:space="preserve">Supputata quoque à <lb/>recta A E, verſus D, altitudine poli vſque ad F, ducatur recta E F, cui aſcribatur [Horizon]: </s>
  <s xml:id="echoid-s41489" xml:space="preserve">Eo-<lb/>demq́ue modo à recta E D, verſus C, numerata eadem poli altitudine vſque ad G, ducatur recta <lb/>E G, cui [Verticalis] aſcribatur. </s>
  <s xml:id="echoid-s41490" xml:space="preserve">Poſtremo in oppoſita facie circuli A B C D, affigatur ad angulos <lb/>rectos in centro cylindrus perforatus E H, vt axis I K, ei imponi poſſit. </s>
  <s xml:id="echoid-s41491" xml:space="preserve">Eodem modo in eadem <lb/>facie oppoſita in diametro A C, ſtatuantur duo arcus circulorum perforati I, k, vt idem axis per <lb/>ea commode tranſire poſſit, facto prius ſimili etiam foramine in cylindro E H. </s>
  <s xml:id="echoid-s41492" xml:space="preserve">Hac ratione con <lb/>ſtructum erit inſtrumentum ad deſcribenda horologia in quocunque plano ad quamlibet latitu-<lb/>dinem loci, hoc modo.</s>
  <s xml:id="echoid-s41493" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2054" type="float" level="2" n="2">
<note position="left" xlink:label="note-0646-05" xlink:href="note-0646-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0646-06" xlink:href="note-0646-06a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s41494" xml:space="preserve">PROPE murum, in quo horologium deſcribendum eſt, ſiue is ad Horizontem rectus ſit, ſi-<lb/>
<anchor type="note" xlink:label="note-0647-02a" xlink:href="note-0647-02"/>
ue non, ſtatuatur planum aliquod firmum Horizonti parallelum, tanto interuallo, plus minus, <lb/>à muro diſtans, quantus futurus eſt gnomon horologii deſcribendi. </s>
  <s xml:id="echoid-s41495" xml:space="preserve">Hoc autem planum, ne <lb/>impedimento nobis ſit in horis delineandis, commodiſſime collocabitur in ligno quopiam, aut <lb/>ferro in muro infixo, ita vt Horizonti æquidiſtans ſit. </s>
  <s xml:id="echoid-s41496" xml:space="preserve">In hoc plano inuenta linea meridiana, <lb/>firmandum erit inſtrumentum A B, ita vt recta C D, lineæ meridianæ congruat, punctumq́; </s>
  <s xml:id="echoid-s41497" xml:space="preserve">D, ad <lb/>boreã, &amp; </s>
  <s xml:id="echoid-s41498" xml:space="preserve">C, ad auſtrum vergat. </s>
  <s xml:id="echoid-s41499" xml:space="preserve">Quo firmato, imponendus erit clauus I L, qui in axe I K, eſt, cen-<lb/>tro F, &amp; </s>
  <s xml:id="echoid-s41500" xml:space="preserve">axis ipſe cochleola L, aſtringendus, circumducendusq́ue circa centrum F, donec per fo-<lb/>ramen P, gradus altitudinis poli illius loci, pro quo horologium deſcribitur, in quadrante <lb/>conſpiciatur: </s>
  <s xml:id="echoid-s41501" xml:space="preserve">Hoc enim perſpecto, aſtringendus erit axis cochleola O, vt amplius neque ſurſum, <lb/>
<anchor type="note" xlink:label="note-0647-03a" xlink:href="note-0647-03"/>
neque deorſum moueri poſſit, ſed permaneat in proprio ſuo ſitu, vſque ad finem deſcriptionis.</s>
  <s xml:id="echoid-s41502" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2055" type="float" level="2" n="3">
<note position="right" xlink:label="note-0647-02" xlink:href="note-0647-02a" xml:space="preserve">Vſus prædicti <lb/>inſtrumenti.</note>
<note position="left" xlink:label="note-0647-03" xlink:href="note-0647-03a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s41503" xml:space="preserve">DEINDE circulus A B C D, axi imponatur per foramina K, E, I, ita vt I, polum arcticum, <lb/>&amp; </s>
  <s xml:id="echoid-s41504" xml:space="preserve">K, antarcticum reſpiciat, circumuertaturq́ue, donec filum perpendiculi ex centro E, libere de-<lb/>miſſi ſuperficiem circuli radat, atque adeo lineæ E G, Verticalis circuli congruat, quandoqui-<lb/>dem Verticalis circulus per centrum E, tranſiens ad Horizontem, vt &amp; </s>
  <s xml:id="echoid-s41505" xml:space="preserve">perpendiculum, rectus <lb/>eſt, facitq́ue cum axe verſus polum antarcticum angulum complementi altitudinis poli, qualis <lb/>eſt angulus G E C. </s>
  <s xml:id="echoid-s41506" xml:space="preserve">Aſtringatur autem circulus ad axem cochleolis I, &amp; </s>
  <s xml:id="echoid-s41507" xml:space="preserve">K, vt hinc inde dimoue-<lb/>ri nequeat, noteturq́ue diligenter punctum axis, cui congtuit centrum huius circuli, quod ver-<lb/>tex ſtyli appellari poteſt. </s>
  <s xml:id="echoid-s41508" xml:space="preserve">Circulus autem ipſe in Meridiani plano collocatus tunc erit. </s>
  <s xml:id="echoid-s41509" xml:space="preserve">Stabili-<lb/>to ita circulo, extendatur ex centro E, filum radens circuli ſuperficiem vſq; </s>
  <s xml:id="echoid-s41510" xml:space="preserve">ad planum horologii, <lb/>
<anchor type="note" xlink:label="note-0647-04a" xlink:href="note-0647-04"/>
ſigneturq́; </s>
  <s xml:id="echoid-s41511" xml:space="preserve">punctum, in quod filum cadit: </s>
  <s xml:id="echoid-s41512" xml:space="preserve">Eodemq́; </s>
  <s xml:id="echoid-s41513" xml:space="preserve">filo circulum radente notetur alterum pun-<lb/>ctum in muro, vel etiam plura ſiue ſurſum, ſiue deorſum. </s>
  <s xml:id="echoid-s41514" xml:space="preserve">Nam recta coniungens hæc puncta erit <lb/>
<anchor type="note" xlink:label="note-0647-05a" xlink:href="note-0647-05"/>
linea meridiana, quæ in muris ad Horizontem rectis recta erit ad Horizontẽ, &amp; </s>
  <s xml:id="echoid-s41515" xml:space="preserve">in omnibus trã-<lb/>
<anchor type="note" xlink:label="note-0647-06a" xlink:href="note-0647-06"/>
ſibit per centrum horologii, quod indicabitur à filo ex centro E, egrediente, axemq́ue radente. <lb/></s>
  <s xml:id="echoid-s41516" xml:space="preserve">Hocautem centrum accuratius inuenietur, ſi duo fila ex cẽtro E, egrediẽtia axẽ in partibus oppoſi <lb/>tis radant, ſignenturq́; </s>
  <s xml:id="echoid-s41517" xml:space="preserve">duo puncta in plano horologii. </s>
  <s xml:id="echoid-s41518" xml:space="preserve">Mediũ enim punctũ inter hæc erit horo-<lb/>logii centrum. </s>
  <s xml:id="echoid-s41519" xml:space="preserve">Quod ſi linea@meridiana vel non cõmode, vel nullo modo in plano horologii du-<lb/>ci poſſit, vt fit in muris parum à Meridiano deflectentibus, firmanda erit tabula aliqua ad mu-<lb/>rum verſus boream, ita vt auſtrum reſpiciat, &amp; </s>
  <s xml:id="echoid-s41520" xml:space="preserve">in ea, vt prius, linea meridiana inueſtiganda.</s>
  <s xml:id="echoid-s41521" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2056" type="float" level="2" n="4">
<note position="left" xlink:label="note-0647-04" xlink:href="note-0647-04a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0647-05" xlink:href="note-0647-05a" xml:space="preserve">Linea meridia-<lb/>na.</note>
<note position="right" xlink:label="note-0647-06" xlink:href="note-0647-06a" xml:space="preserve">Centrum horo-<lb/>logii.</note>
</div>
<p>
  <s xml:id="echoid-s41522" xml:space="preserve">ALIAE horæ à mer. </s>
  <s xml:id="echoid-s41523" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41524" xml:space="preserve">med. </s>
  <s xml:id="echoid-s41525" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41526" xml:space="preserve">ita depingentur. </s>
  <s xml:id="echoid-s41527" xml:space="preserve">Amoueatur circulus A B C D, &amp; </s>
  <s xml:id="echoid-s41528" xml:space="preserve">per ca-<lb/>
<anchor type="note" xlink:label="note-0647-07a" xlink:href="note-0647-07"/>
<anchor type="note" xlink:label="note-0647-08a" xlink:href="note-0647-08"/>
nalem E H, axi imponatur, ita vt centrum E, rurſus congruat illi puncto prius notato in axe, quod <lb/>verticem ſtyli appellauimus, &amp; </s>
  <s xml:id="echoid-s41529" xml:space="preserve">canalis ad polum antarcticum vergat: </s>
  <s xml:id="echoid-s41530" xml:space="preserve">admoueaturq́ue annulus <lb/>Q R, ad extremitatem canalis, &amp; </s>
  <s xml:id="echoid-s41531" xml:space="preserve">cochleola S, ita aſtringatur ad axem, vt circulus deorſum moueri <lb/>non poſſit. </s>
  <s xml:id="echoid-s41532" xml:space="preserve">Circumuoluatur autem circulus circa axem, donec punctum A, ſurſum vergat, &amp; </s>
  <s xml:id="echoid-s41533" xml:space="preserve">C, <lb/>deorſum, punctum vero B, ad ortum, &amp; </s>
  <s xml:id="echoid-s41534" xml:space="preserve">D, ad occaſum ſpectet, ac filum ex centro E, egrediens, <lb/>radensq́ue circulum pertingat ad lineam meridianam inuentam: </s>
  <s xml:id="echoid-s41535" xml:space="preserve">ac denique in hoc ſitu circulus <lb/>ita firmetur cocheolis in canali E H, poſitis, vt hinc inde non poſſit moueri. </s>
  <s xml:id="echoid-s41536" xml:space="preserve">Manente enim cir-<lb/>culo in hoc ſitu, nempe in plano Aequatoris, ſi filum ècentro emiſſum, &amp; </s>
  <s xml:id="echoid-s41537" xml:space="preserve">circulum radens ſin-<lb/>gulis horis cõgruat, punctaq́ue in plano horologii notentur, inuenta erunt puncta, quæ lineis re-<lb/>ctis cum centro horologij inuento connexa dabunt lineas horarum à mer. </s>
  <s xml:id="echoid-s41538" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41539" xml:space="preserve">med. </s>
  <s xml:id="echoid-s41540" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41541" xml:space="preserve">Quòd ſi <lb/>
<anchor type="note" xlink:label="note-0647-09a" xlink:href="note-0647-09"/>
forte centrum horologij non habeatur, ducemus eaſdem lineas hoc modo. </s>
  <s xml:id="echoid-s41542" xml:space="preserve">Imponatur rurſum <lb/>circulus axi per foramina K, E, I, vt E, centrum vertici gnomonis congruat, firmeturq́ue annulo <lb/>Q R, vt deorſum moueri nequeat. </s>
  <s xml:id="echoid-s41543" xml:space="preserve">Deinde circumuoluatur toties circulus, donec filum ex cen-<lb/>tro emiſſum, &amp; </s>
  <s xml:id="echoid-s41544" xml:space="preserve">circulum radens ad ſingula puncta horarum inuenta in plano horologii applicari <lb/>poſſit, ita vt circulus cum planis ſingulorum horariorum circulorũ coniungatur in illa circum-<lb/>uolutione. </s>
  <s xml:id="echoid-s41545" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41546" xml:space="preserve">beneficio fili alia puncta ſiue ſurſum, ſiue deorſum pro ſingulis horis inquirantur, <lb/>vt de linea meridiana diximus. </s>
  <s xml:id="echoid-s41547" xml:space="preserve">Si enim puncta hęc pro qualibet hora inuenta coniungantur li-<lb/>neis rectis, deſcriptæ erunt rurſum lineæ horariæ. </s>
  <s xml:id="echoid-s41548" xml:space="preserve">Verum poſteriora hæc puncta commodius <lb/>fortaſſis inuenientur lumine aliquo, vel radio viſuali. </s>
  <s xml:id="echoid-s41549" xml:space="preserve">Nam ſi lumen, vel oculus circulo ita appli-<lb/>cetur, vt circulus ipſe in plano horologii linea recta appareat tranſiens per puncta horarum prius <lb/>inuenta, notenturq́ue in illa linea aliquot puncta, tranſibunt per ea lineæ horariæ, vt prius. </s>
  <s xml:id="echoid-s41550" xml:space="preserve">Eadem
<pb o="632" file="0648" n="648" rhead="GNOMONICES"/>
quoque puncta reperientur ſine circulo per ſolum axem. </s>
  <s xml:id="echoid-s41551" xml:space="preserve">Si namque lumen, vel oculus axi ita ap-<lb/>plicetur, vt axis in plano horologii per puncta horarum prius inuenta tranſire videatur, noten-<lb/>turq́ue rurſum puncta aliquot in plano horologii, per quæ axis tranſire conſpicitur, ducendæ <lb/>erunt per hæclineæ horariæ, vt prius. </s>
  <s xml:id="echoid-s41552" xml:space="preserve">Quòd ſi quando filum per aliquam horam extenſum in <lb/>circulo, dum in plano Aequatoris iacet, æquidiſtet plano horologii, vel cum eo non conueniat, <lb/>ducenda erit illa hora per centrum horologii ad meridianam lineam perpendicularis: </s>
  <s xml:id="echoid-s41553" xml:space="preserve">qualis eſt <lb/>hora 6. </s>
  <s xml:id="echoid-s41554" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41555" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41556" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41557" xml:space="preserve">in horologio horizontali, Verticali, Æquinocti<unsure/>ali, &amp; </s>
  <s xml:id="echoid-s41558" xml:space="preserve">inclinato ad <lb/>Horizontem. </s>
  <s xml:id="echoid-s41559" xml:space="preserve">Vel certe, vbi horologium centro caret, illa hora deſcribi nequit, cuiuſmodi eſt ho-<lb/>ra 6. </s>
  <s xml:id="echoid-s41560" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41561" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41562" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41563" xml:space="preserve">in horologio polari.</s>
  <s xml:id="echoid-s41564" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2057" type="float" level="2" n="5">
<note position="left" xlink:label="note-0647-07" xlink:href="note-0647-07a" xml:space="preserve">40</note>
<note position="right" xlink:label="note-0647-08" xlink:href="note-0647-08a" xml:space="preserve">Horæ à mer. &amp; <lb/>med. noc.</note>
<note position="left" xlink:label="note-0647-09" xlink:href="note-0647-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41565" xml:space="preserve">ARCVS ſignorum ita delineabuntur. </s>
  <s xml:id="echoid-s41566" xml:space="preserve">Firmato circulo, vt proxime dictum eſt, applicetur <lb/>
<anchor type="note" xlink:label="note-0648-01a" xlink:href="note-0648-01"/>
<anchor type="note" xlink:label="note-0648-02a" xlink:href="note-0648-02"/>
filum ex centro E, egrediens ſingulis radijs ſignorum, ita vt radat circulum, &amp; </s>
  <s xml:id="echoid-s41567" xml:space="preserve">circumducto cir-<lb/>culo puncta in plano horologii, etiam in ipſis lineis horariis, ſignentur. </s>
  <s xml:id="echoid-s41568" xml:space="preserve">Per hæc enim arcus ſi-<lb/>gnorum deſcribendi erunt. </s>
  <s xml:id="echoid-s41569" xml:space="preserve">Pro ęquinoctiali vero linea inuenientur per radium Aequatoris pun-<lb/>cta in recta linea iacentia, quę quidem per puncta horarum per circulum, dum in plano Aequato-<lb/>ris collocabatur, inuenta tranſibit.</s>
  <s xml:id="echoid-s41570" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2058" type="float" level="2" n="6">
<note position="left" xlink:label="note-0648-01" xlink:href="note-0648-01a" xml:space="preserve">Ar@@s ſ<unsure/>ignorũ.</note>
<note position="left" xlink:label="note-0648-02" xlink:href="note-0648-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41571" xml:space="preserve">EADEM ratione arcus longitudinum dierum deſcribentur, ſi ex centro E, radii longitudi-<lb/>
<anchor type="note" xlink:label="note-0648-03a" xlink:href="note-0648-03"/>
num dierum emittantur, &amp;</s>
  <s xml:id="echoid-s41572" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41573" xml:space="preserve">Sed ſatis erit, ſi puncta arcuum diurnorum, qui ad deſcriptionem <lb/>horarum ab or. </s>
  <s xml:id="echoid-s41574" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41575" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41576" xml:space="preserve">inæqualiumq́ue requiruntur, in lineis horarũ à mer. </s>
  <s xml:id="echoid-s41577" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41578" xml:space="preserve">med. </s>
  <s xml:id="echoid-s41579" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41580" xml:space="preserve">notentur.</s>
  <s xml:id="echoid-s41581" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2059" type="float" level="2" n="7">
<note position="left" xlink:label="note-0648-03" xlink:href="note-0648-03a" xml:space="preserve">Arcus longitu-<lb/>dinum dierum.</note>
</div>
<p>
  <s xml:id="echoid-s41582" xml:space="preserve">HORAE ab or. </s>
  <s xml:id="echoid-s41583" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41584" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41585" xml:space="preserve">atque inæquales deſcribentur per arcus diurnos, vt in præcedentibus <lb/>
<anchor type="note" xlink:label="note-0648-04a" xlink:href="note-0648-04"/>
explicatum eſt.</s>
  <s xml:id="echoid-s41586" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2060" type="float" level="2" n="8">
<note position="left" xlink:label="note-0648-04" xlink:href="note-0648-04a" xml:space="preserve">Horæ ab or. &amp; <lb/>occ. atque in-<lb/>æquales.</note>
</div>
<note position="left" xml:space="preserve">20</note>
<p>
  <s xml:id="echoid-s41587" xml:space="preserve">LINEA horizontalis ita ducetur. </s>
  <s xml:id="echoid-s41588" xml:space="preserve">Firmato circulo A B C D, vt diximus, cum meridiana <lb/>
<anchor type="note" xlink:label="note-0648-06a" xlink:href="note-0648-06"/>
linea deſcribebatur, vt nimirum in Meridiano circulo collocatus ſit, applicetur filum ex centro <lb/>E, egrediens ad lineam Horizontis E F, ita vt circulum radat, noteturq́ue punctum, vbi plano ho <lb/>rologii occurrit, quod neceſſario in linea meridiana exiſtet; </s>
  <s xml:id="echoid-s41589" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41590" xml:space="preserve">per illud punctum linea recta du-<lb/>catur Horizonti æquidiſtans, quæ in horologiis ad Horizontem rectis lineam meridianam ad an-<lb/>gulos rectos ſecabit, tranſibitq́ue per locum ſtyli, &amp; </s>
  <s xml:id="echoid-s41591" xml:space="preserve">per horam 6. </s>
  <s xml:id="echoid-s41592" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41593" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41594" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41595" xml:space="preserve">in linea <lb/>æquinoctiali. </s>
  <s xml:id="echoid-s41596" xml:space="preserve">Hæc enim erit linea horizontalis. </s>
  <s xml:id="echoid-s41597" xml:space="preserve">Vbi autem centrum horologii non habetur, vel <lb/>linea meridiana cõmode haberi nequit, ducenda erit linea horizontalis per horam 6. </s>
  <s xml:id="echoid-s41598" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41599" xml:space="preserve">vel <lb/>med. </s>
  <s xml:id="echoid-s41600" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41601" xml:space="preserve">in linea æquinoctiali æquidiſtans Horizonti.</s>
  <s xml:id="echoid-s41602" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2061" type="float" level="2" n="9">
<note position="left" xlink:label="note-0648-06" xlink:href="note-0648-06a" xml:space="preserve">Horizontalis li <lb/>mea.</note>
</div>
<p>
  <s xml:id="echoid-s41603" xml:space="preserve">LOCVS gnomonis erit punctum illud horologii, in quod perpendicularis ex illo puncto <lb/>
<anchor type="note" xlink:label="note-0648-07a" xlink:href="note-0648-07"/>
<anchor type="note" xlink:label="note-0648-08a" xlink:href="note-0648-08"/>
axis, vbi centrum circuli A B C D, firmatum eſt, ad planum horologii demiſſa cadit. </s>
  <s xml:id="echoid-s41604" xml:space="preserve">Quod qui-<lb/>dem punctum facile inuenietur, ſi ex dicto puncto axis, tanquam polo, in plano horologii circu-<lb/>lus deſcribatur. </s>
  <s xml:id="echoid-s41605" xml:space="preserve">Centrum enim huius circuli erit locus ſtyli: </s>
  <s xml:id="echoid-s41606" xml:space="preserve">Cuius longitudo eſt ipſamet per-<lb/>pendicularis ex dicto puncto axis in planum horologii, nempe in centrum circuli proxime de-<lb/>ſcripti, cadens.</s>
  <s xml:id="echoid-s41607" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2062" type="float" level="2" n="10">
<note position="left" xlink:label="note-0648-07" xlink:href="note-0648-07a" xml:space="preserve">Locus, &amp; longi-<lb/>tudo ſtyli.</note>
<note position="left" xlink:label="note-0648-08" xlink:href="note-0648-08a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s41608" xml:space="preserve">NON aliter horologium horizontale per prædictum inſtrumentum conſtruetur, præſertim <lb/>cum ingens aliquod horologium deſcribendum proponatur. </s>
  <s xml:id="echoid-s41609" xml:space="preserve">Nam in paruis non commode id <lb/>fieri poterit, quòd difficulter tunc circulus A B C D, circa axem circumducatur, vt perſpicuũ eſt.</s>
  <s xml:id="echoid-s41610" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2064" type="section" level="1" n="523">
<head xml:id="echoid-head552" style="it" xml:space="preserve">DEHOROLOGIORVM DESCRIPTIONE IN QVOCVNQVE <lb/>
plano per vmbram ſtyli horologĳ alicuius horizontalis, vel alterius
cuiuſpiam. CAP. XXXI.</head>
<p>
  <s xml:id="echoid-s41611" xml:space="preserve">NON videtur omittendus hoc loco modus deſcribendorum horologiorum facilimus, ac <lb/>
<anchor type="note" xlink:label="note-0648-10a" xlink:href="note-0648-10"/>
ſimpliciſſimus, traditus à Ioan. </s>
  <s xml:id="echoid-s41612" xml:space="preserve">Bapt. </s>
  <s xml:id="echoid-s41613" xml:space="preserve">Vimercato in libello de horologiorum deſcriptione, <lb/>qui ferè eſt eiuſmodi. </s>
  <s xml:id="echoid-s41614" xml:space="preserve">Firmato horologio horizontali accurate deſcripto in tabella aliqua plana, <lb/>in qua ſit ducta recta linea reſpondens lineę meridianę horologii horizõtalis, firmetur in eadem <lb/>tabella planum aliud, quod vel illi adhæreat, ſi horologium aliud horizontale deſcribendum ſit; <lb/></s>
  <s xml:id="echoid-s41615" xml:space="preserve">vel ad ipſam rectum ſit, aut inclinatum, ita vt lineam meridianam tabellæ ad angulos rectos ſecet, <lb/>ſi deſcribendum ſit horologium Verticale, aut Aequinoctiale, aut@ polare, inclinatumve ad Hori-<lb/>
<anchor type="note" xlink:label="note-0648-11a" xlink:href="note-0648-11"/>
zontem; </s>
  <s xml:id="echoid-s41616" xml:space="preserve">vel meridianam lineam ſecet ad angulos inæquales, ſi declinans horologium à Vertica-<lb/>li proponatur delineandum, ſiue illud inclinatum ſit ad Horizontem, ſiue non; </s>
  <s xml:id="echoid-s41617" xml:space="preserve">vel denique li-<lb/>neam meridianam nullo modo ſecet, ſed in tabella faciat lineam ei parallelam, ſi horologium Me <lb/>ridianum, aut ab Horizonte declinans conſtruendum ſit, habita ſemper ratione declinationis, in-<lb/>clinationisq́ue horologii deſcribendi. </s>
  <s xml:id="echoid-s41618" xml:space="preserve">Deinde in aſſumpto loco ſtyli in plano horologij deſcri-<lb/>bendi figatur gnomon cuiuſcunque magnitudinis rectus ad horologii planum: </s>
  <s xml:id="echoid-s41619" xml:space="preserve">Mota autem ta-<lb/>bella in loco, vbi à Sole illuſtretur, hinc inde, donec extremitas vmbræ ſtyli in horologio hori-<lb/>zontali cadat in ſingulas horas tropici ♋, notentur ſingulæ extremitates vmbrarum ſtyli in futu-<lb/>ro horologio. </s>
  <s xml:id="echoid-s41620" xml:space="preserve">Ita enim inuenta erunt puncta horarum tropici ♋, in horologio futuro. </s>
  <s xml:id="echoid-s41621" xml:space="preserve">Quòd ſi <lb/>idem fiat in tropico ♑, &amp; </s>
  <s xml:id="echoid-s41622" xml:space="preserve">in linea æquinoctiali, vel in quocunque alio arcu ſignorum, vel deniq; <lb/></s>
  <s xml:id="echoid-s41623" xml:space="preserve">in quacunque alia linea horologii, etiamſi horaria non ſit, &amp; </s>
  <s xml:id="echoid-s41624" xml:space="preserve">puncta reſpondentia in futuro ho-
<pb o="633" file="0649" n="649" rhead="LIBER SEPTIMVS."/>
rologio iungantur vel lineis rectis, vel curuis, deſcriptum erit horologium in plano propoſito. <lb/></s>
  <s xml:id="echoid-s41625" xml:space="preserve">Hac ratione omnia puncta horologii horizontalis in futurum horologium transferri poterunt, ſi <lb/>circumuoluatur tabella, donec vmbrę extremum in datum punctum cadat in horologio horizon <lb/>tali, &amp; </s>
  <s xml:id="echoid-s41626" xml:space="preserve">tunc in futuro horologio extremum etiam punctum vmbræ notetur. </s>
  <s xml:id="echoid-s41627" xml:space="preserve">Horologium autem <lb/>ita deſcriptum in muro augendum erit, pro data longitudine ſtyli, vt propoſ. </s>
  <s xml:id="echoid-s41628" xml:space="preserve">vltima lib. </s>
  <s xml:id="echoid-s41629" xml:space="preserve">4. </s>
  <s xml:id="echoid-s41630" xml:space="preserve">oſten-<lb/>dimus. </s>
  <s xml:id="echoid-s41631" xml:space="preserve">Neque enim in tabella circumduci poterit tantum planum, quantum requirit horolo-<lb/>gium in muro delineandum.</s>
  <s xml:id="echoid-s41632" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2064" type="float" level="2" n="1">
<note position="left" xlink:label="note-0648-10" xlink:href="note-0648-10a" xml:space="preserve">Qua ratione <lb/>in quouis pla-<lb/>no per vmbrã <lb/>ſtyli horologii <lb/>alicuius hotizõ-<lb/>talis horologiũ <lb/>deſcribatur.</note>
<note position="left" xlink:label="note-0648-11" xlink:href="note-0648-11a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41633" xml:space="preserve">FACILE hac arte ex horologio horizontali deſcribi poterit aliud horizontale ad datam ſty-<lb/>lilongitudinem, etiam minimam, quod vix per præcepta alia abſolui poteſt. </s>
  <s xml:id="echoid-s41634" xml:space="preserve">Immo eodem arti-<lb/>ficio deſcribetur horologium in ſuperficie non plana@, ſed concaua, ſi plura puncta pro ſingulis <lb/>
<anchor type="note" xlink:label="note-0649-01a" xlink:href="note-0649-01"/>
horis notentur, quæ deinde congruenter lineis connectantur, quę angulos non faciant. </s>
  <s xml:id="echoid-s41635" xml:space="preserve">Adde <lb/>quòd etiam in cylindro ad Horizontem recto horæ deſignari hac ratione poſſunt, vt in ſequenti <lb/>lib. </s>
  <s xml:id="echoid-s41636" xml:space="preserve">dicemus.</s>
  <s xml:id="echoid-s41637" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2065" type="float" level="2" n="2">
<note position="left" xlink:label="note-0649-01" xlink:href="note-0649-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41638" xml:space="preserve">LOCO horizontalis horologii vti poterimus horologio ſphærico concauo, quod <lb/>in lib. </s>
  <s xml:id="echoid-s41639" xml:space="preserve">ſequenti conſtruemus. </s>
  <s xml:id="echoid-s41640" xml:space="preserve">Nam in hoc multo accuratius <lb/>vmbrarum extremitates notari poſſunt, <lb/>quàm in horizontali.</s>
  <s xml:id="echoid-s41641" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2067" type="section" level="1" n="524">
<head xml:id="echoid-head553" xml:space="preserve">FINIS SEPTIMI LIBRI.</head>
<note position="left" xml:space="preserve">20</note>
<pb o="634" file="0650" n="650"/>
</div>
<div xml:id="echoid-div2068" type="section" level="1" n="525">
<head xml:id="echoid-head554" xml:space="preserve">GNOMONICES <lb/>LIBER OCTAVVS.</head>
  <figure>
    <image file="0650-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0650-01"/>
  </figure>
</div>
<div xml:id="echoid-div2069" type="section" level="1" n="526">
<head xml:id="echoid-head555" xml:space="preserve">AVCTORE <lb/>
CHRISTOPHORO CLAVIO BAMBERGENSI
SOCIETATIS IESV.</head>
<p>
  <s xml:id="echoid-s41642" xml:space="preserve">EXTREMO hoc libro, ne quid eorum, quæ ad horologio-<lb/>rum deſcriptionẽ pertinent, omittere videamur, paucis com-<lb/>plectemur ea horologia, quæ non in plano aliquo ſtabili ac <lb/>firmo deſcribuntur, cuiuſmodi ſunt illa, de quibus in præce-<lb/>dentibus egimus, ſed quæ deloco ad locum circunferuntur, <lb/>
<anchor type="note" xlink:label="note-0650-02a" xlink:href="note-0650-02"/>
atque Viatoria nuncupari ſolent, quòd maxime iis, qui iter <lb/>agunt, aut peregre proficiſcuntur, vſui eſſe conſueuerunt. </s>
  <s xml:id="echoid-s41643" xml:space="preserve">Ex <lb/>quibus quidem non omnia, ſed quæ præcipua eſſe, maio-<lb/>remq́ue vſum habere iudicamus, deſcribemus. </s>
  <s xml:id="echoid-s41644" xml:space="preserve">Neque verò <lb/>hactenus omnia excogitata ſunt, ſed quotidie noua in lucem ab artificibus varijs <lb/>inuenta prodeunt, vt fruſtra quis omnium eiuſmodi horologiorum deſcriptionem <lb/>polliceatur, cum quilibet proprio Marte noua ac varia in proprium vſum excogi-<lb/>tare adhuc poſſit. </s>
  <s xml:id="echoid-s41645" xml:space="preserve">Exordium autem ſumemus ab ijs, quæ ad quam cunque latitudi-<lb/>num loci accommodantur, quæque ob id vniuerſalia à pleriſque nominantur: <lb/></s>
  <s xml:id="echoid-s41646" xml:space="preserve">Deinde ea tractabimus, quæ ad propoſitam poli altitudinem conficiuntur.</s>
  <s xml:id="echoid-s41647" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2069" type="float" level="2" n="1">
<note position="left" xlink:label="note-0650-02" xlink:href="note-0650-02a" xml:space="preserve">20</note>
</div>
<note position="left" xml:space="preserve">30</note>
</div>
<div xml:id="echoid-div2071" type="section" level="1" n="527">
<head xml:id="echoid-head556" style="it" xml:space="preserve">DE HOROLOGIO AEQVINOCTIALI <lb/>vniuerſali. CAP. I.</head>
  <figure>
    <image file="0650-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0650-02"/>
  </figure>
<p>
  <s xml:id="echoid-s41648" xml:space="preserve"><emph style="sc">PAren</emph> <lb/>
<anchor type="note" xlink:label="note-0650-04a" xlink:href="note-0650-04"/>
<emph style="sc">TVR</emph> <lb/>ex ori-<lb/>chalco, <lb/>vel ex <lb/>alia ma <lb/>
<anchor type="note" xlink:label="note-0650-05a" xlink:href="note-0650-05"/>
teria ſolida, duo qua-<lb/>drata æqualia ABCD, <lb/>A E F G, &amp; </s>
  <s xml:id="echoid-s41649" xml:space="preserve">prioris la-<lb/>teribus bifariam ſectis <lb/>in A, B, C, D, iungan <lb/>tur rectæ A C, B D, <lb/>ſeſe ad angulos rectos <lb/>ſecantes, &amp; </s>
  <s xml:id="echoid-s41650" xml:space="preserve">ex puncto <lb/>interſectionis in vtra-<lb/>que facie plani circu-<lb/>
<anchor type="note" xlink:label="note-0650-06a" xlink:href="note-0650-06"/>
lus deſcriptus in 24. <lb/></s>
  <s xml:id="echoid-s41651" xml:space="preserve">horas æquales ſecetur, <lb/>initio facto à recta <lb/>A C, quarum anteme-<lb/>ridianæ, ſeu poſt me-<lb/>diam noctem, progre-<lb/>diantur à C, per B, vſ-<lb/>que ad A, pomeridia-<lb/>næ vero ab A, per D, <lb/>vſque ad C. </s>
  <s xml:id="echoid-s41652" xml:space="preserve">Deind@ <lb/>hæc quadrata ita inter
<pb o="635" file="0651" n="651" rhead="LIBER OCTAVVS."/>
ſe coaptentur ad commune latus per A, ductum, vt A B C D, circa illud latus moueri poſſit, ſeu <lb/>eleuari, &amp; </s>
  <s xml:id="echoid-s41653" xml:space="preserve">deprimi ad altitudinem Aequatoris, ſeu ad cõplementũ altitudinis poli, in quadrante <lb/>H I K, qui in H, ita accommodetur, vt, cum claudendum eſt horologiũ, inclinari poſſit, &amp; </s>
  <s xml:id="echoid-s41654" xml:space="preserve">poni <lb/>ſuper planum A E F G. </s>
  <s xml:id="echoid-s41655" xml:space="preserve">Poſtreḿo centrum circuli perforetur, vt axis æneus cuiuſcunque longitu <lb/>dinis per foramen im mitti poſſit ad angulos rectos ipſi plano: </s>
  <s xml:id="echoid-s41656" xml:space="preserve">atque in plano A E F G, ſtatuatur <lb/>acus Magnete illita, vt beneficio ipſius horologium ita collocari poſſit in plano, quod Horizonti <lb/>æquidiſtet, vt A, ad boream, &amp; </s>
  <s xml:id="echoid-s41657" xml:space="preserve">F, ad auſtrum vergat, lateraq́ue per E, &amp; </s>
  <s xml:id="echoid-s41658" xml:space="preserve">G, ducta meridianam li-<lb/>neam referant. </s>
  <s xml:id="echoid-s41659" xml:space="preserve">Hunc enim ſitum obtinente horologio, ſi planum A B C D, firmetur in quadran <lb/>te H I K, ad altitudinem Aequatoris, indicabit axis horas à mer. </s>
  <s xml:id="echoid-s41660" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41661" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41662" xml:space="preserve">in exteriori quidem <lb/>facie plani A B C D, Sole exiſtente in ſemicirculo Eclipticæ boreali, in interiori vero, eodem exi-<lb/>
<anchor type="note" xlink:label="note-0651-01a" xlink:href="note-0651-01"/>
ſtente in auſtrali ſemicirculo Eclipticæ. </s>
  <s xml:id="echoid-s41663" xml:space="preserve">Si autem excindatur pars intra circulum, relicta tantum <lb/>portione L M, vt cẽtrum cum axe ſuſtineat, apparebit vmbra axis in horis faciei exterioris, etiamſi <lb/>Sol in ſignis auſtralibus exiſtat. </s>
  <s xml:id="echoid-s41664" xml:space="preserve">Quòd ſi imponatur alius circulus mobilis intra priorem, diui-<lb/>ſus in 24. </s>
  <s xml:id="echoid-s41665" xml:space="preserve">horas æquales ab or. </s>
  <s xml:id="echoid-s41666" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s41667" xml:space="preserve">ponaturq́; </s>
  <s xml:id="echoid-s41668" xml:space="preserve">hora meridiei, more Italorum, vel Babylonio-<lb/>rum, ſupra rectam A C, verſus punctum A, indicabit eiuſdem axis vmbra horas ab or. </s>
  <s xml:id="echoid-s41669" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s41670" xml:space="preserve">in <lb/>hoc poſteriori circulo.</s>
  <s xml:id="echoid-s41671" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2071" type="float" level="2" n="1">
<note position="left" xlink:label="note-0650-04" xlink:href="note-0650-04a" xml:space="preserve">Conſtructio <lb/>Ae<unsure/>quinoctialis <lb/>horologii vai-<lb/>@erſalis.</note>
<note position="left" xlink:label="note-0650-05" xlink:href="note-0650-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0650-06" xlink:href="note-0650-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0651-01" xlink:href="note-0651-01a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41672" xml:space="preserve">LOCO quadrantis H I K, confici poterit ſcala latitudinum regionum hoc modo. </s>
  <s xml:id="echoid-s41673" xml:space="preserve">Deſcripto <lb/>
<anchor type="note" xlink:label="note-0651-02a" xlink:href="note-0651-02"/>
ſemicirculo ex centro A, cuius ſemidiameter A B, diametrum ad rectos angulos ſecans æqualis <lb/>ſit vni lateri quadrati A B C D, eoq́ue diuiſo in 180. </s>
  <s xml:id="echoid-s41674" xml:space="preserve">partes æquales, (Nos in. </s>
  <s xml:id="echoid-s41675" xml:space="preserve">18. </s>
  <s xml:id="echoid-s41676" xml:space="preserve">diuiſimus, vt <lb/>
<anchor type="note" xlink:label="note-0651-03a" xlink:href="note-0651-03"/>
<anchor type="figure" xlink:label="fig-0651-01a" xlink:href="fig-0651-01"/>
<anchor type="note" xlink:label="note-0651-04a" xlink:href="note-0651-04"/>
<anchor type="note" xlink:label="note-0651-05a" xlink:href="note-0651-05"/>
ſingulæ partes complectantur grad. </s>
  <s xml:id="echoid-s41677" xml:space="preserve">10.) </s>
  <s xml:id="echoid-s41678" xml:space="preserve">ſi bina puncta à puncto B, æqualiter remota rectis linei@ <lb/>occultis iungantur, ſecabitur recta A B, in 90@ partes inæquales pro 90. </s>
  <s xml:id="echoid-s41679" xml:space="preserve">gradibus altitudinum poli, <lb/>
<anchor type="note" xlink:label="note-0651-06a" xlink:href="note-0651-06"/>
quorum numerus à puncto A, incipit. </s>
  <s xml:id="echoid-s41680" xml:space="preserve">Si igitur partes rectæ A B, transferantur in quadratum <lb/>A E F G, prope latus per E, ductum, facto initio à communi ſectione quadratorum A B C D, <lb/>A E F G, &amp; </s>
  <s xml:id="echoid-s41681" xml:space="preserve">in diametro B D, prope punctum B, ſtylus annectatur volubilis, qui dimidio vnius <lb/>lateris quadrati ſit æqualis, parata erit ſcala latitudinum regionum. </s>
  <s xml:id="echoid-s41682" xml:space="preserve">Si enim extremum illius ſty-<lb/>li ſtatuatur in eo numero graduum, qui altitudinem poli (non Aequatoris) indicat, eleuatum erit <lb/>quadratum A B C D, ſecundum altitudinem Aequatoris, ac proinde Aequatorem referet, ſicut <lb/>
<anchor type="note" xlink:label="note-0651-07a" xlink:href="note-0651-07"/>
prius, cum in quadrante H I K, eleuabatur ſecundum altitudinem Aequatoris, aut ſecundum com <lb/>plementum altitudinis poli.</s>
  <s xml:id="echoid-s41683" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2072" type="float" level="2" n="2">
<note position="right" xlink:label="note-0651-02" xlink:href="note-0651-02a" xml:space="preserve">Con@tructio ſea <lb/>læ latitudinum <lb/>regionum.</note>
<note position="left" xlink:label="note-0651-03" xlink:href="note-0651-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0651-01" xlink:href="fig-0651-01a">
    <image file="0651-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0651-01"/>
  </figure>
<note position="left" xlink:label="note-0651-04" xlink:href="note-0651-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0651-05" xlink:href="note-0651-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0651-06" xlink:href="note-0651-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0651-07" xlink:href="note-0651-07a" xml:space="preserve">Compofitio dio <lb/>ptræ, per quam <lb/>ſine acu Magne <lb/>te illita horolo-<lb/>gium proprium <lb/>ſitum habeat, &amp; <lb/>hora indicetur <lb/>ſine axe.</note>
</div>
<p>
  <s xml:id="echoid-s41684" xml:space="preserve">QVOD ſi vti nolimus acu Magnete illita, paranda erit dioptra cum linea fiduciæ, quæ nos <lb/>in cognitionem lineæ meridianæ, &amp; </s>
  <s xml:id="echoid-s41685" xml:space="preserve">horæ ſine axe per centrum quadrati A B C D, immiſſo, ducet, <lb/>hac ratione. </s>
  <s xml:id="echoid-s41686" xml:space="preserve">Linea fiduciæ C D, æqualis ſit diametro quadrati A B C D, ita vt circa claui@@lum
<pb o="636" file="0652" n="652" rhead="GNOMONICES"/>
in centro infixum moueri poſſit, tranſeatq́ue per centrum, vt in Aſtrolabio fieri ſolet, in cuius <lb/>extremitatibus duæ tabellæ C E, D F, ad angulos rectos erigantur, ita vt deprimi poſſint, &amp; </s>
  <s xml:id="echoid-s41687" xml:space="preserve">erigi: <lb/></s>
  <s xml:id="echoid-s41688" xml:space="preserve">quarum altitudines ita explorabimus. </s>
  <s xml:id="echoid-s41689" xml:space="preserve">Sumpta in recta G H, diametro quadrati A B C D, æquali, <lb/>ducatur H I, ad G H, perpendicularis; </s>
  <s xml:id="echoid-s41690" xml:space="preserve">deſcriptoq́ue ex G, vt centro, arcu circuli, ſupputentur in <lb/>@o declinationes ſignorum, &amp; </s>
  <s xml:id="echoid-s41691" xml:space="preserve">aliorum graduum Eclipticæ, (Nos integrorum tantum ſignorum <lb/>declinationes in exemplum adduximus) per quas rectæ ex G, emiſſę ſecent rectam H I, in K, L, <lb/>M. </s>
  <s xml:id="echoid-s41692" xml:space="preserve">Deinde in dioptra ſiant in recta C E, quæ ipſam dioptram bifariam ſecet, duo foramina par-<lb/>ua, vt per illa radius Solis tranſire poſſit, tanto interuallo inter ſe diſtantia, quanta eſt recta H K, <lb/>quibus reſpondentia puncta in recta D F, quæ alteram tabellam bifariam ſecet, notentur, tanto <lb/>ſpatio à puncto D, remota, quanto foramina à puncto C, abſunt. </s>
  <s xml:id="echoid-s41693" xml:space="preserve">Si enim puncta K, L, M, trans-<lb/>
<anchor type="note" xlink:label="note-0652-01a" xlink:href="note-0652-01"/>
ferantur in rectam D F, inter dicta duo puncta interiectam. </s>
  <s xml:id="echoid-s41694" xml:space="preserve">initio facto à puncto prope D, &amp; </s>
  <s xml:id="echoid-s41695" xml:space="preserve">ite-<lb/>rum initio facto ab altero puncto prope F, imprimendo puncta in recta D F, per quæ parallelæ li-<lb/>neę ducantur, inter quas 12. </s>
  <s xml:id="echoid-s41696" xml:space="preserve">ſigna Zodiaci deſcribantur, vt in figura apparet, perfecta erit dio-<lb/>ptra, cuius hic vſus eſt. </s>
  <s xml:id="echoid-s41697" xml:space="preserve">Poſito quadrato horologii A B C D, in propria altitudine, ita vt Aequato-<lb/>riæquidiſtet, vertatur ipſum horologium, &amp; </s>
  <s xml:id="echoid-s41698" xml:space="preserve">dioptra hinc inde, donec radius Solis per foramen <lb/>prope C, Sole in ſignis auſtralibus exiſtente, vel per foramen prope E, Sole in borealibus ſignis <lb/>commorante, incidens cadat in locum Solis in recta D F, hoc ſolo notato, quòd antemeridiano <lb/>tempore (quod cognoſcetur ex vmbra cuiuſcunque rei in plano Horizonti æquidiſtante. </s>
  <s xml:id="echoid-s41699" xml:space="preserve">Hæc <lb/>enim ſi decreſcit, Sol nondum ad Meridianum peruenit, ſi vero creſcit, ipſum iam pertranſijt) <lb/>dioptra dirigenda eſt verſus ortum, pomeridiano vero verſus occaſum. </s>
  <s xml:id="echoid-s41700" xml:space="preserve">Hac etenim ratione ho-<lb/>
<anchor type="note" xlink:label="note-0652-02a" xlink:href="note-0652-02"/>
rologium proprium ſitum obtinebit, &amp; </s>
  <s xml:id="echoid-s41701" xml:space="preserve">linea fiduciæ vltra centrum verſus tabellam dioptræ op-<lb/>poſitam indicabit horam præſentem, ſiue Sol exiſtat in borealibus ſignis, ſiue in auſtralibus.</s>
  <s xml:id="echoid-s41702" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2073" type="float" level="2" n="3">
<note position="left" xlink:label="note-0652-01" xlink:href="note-0652-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0652-02" xlink:href="note-0652-02a" xml:space="preserve">20</note>
</div>
<p>
  <s xml:id="echoid-s41703" xml:space="preserve">COLLOCATO horologio ſiue per acum Magnete illitam, ſiue per lineam meridianam <lb/>inuentam, in proprio ſitu, inuenietur hora multo facilius ex dioptra. </s>
  <s xml:id="echoid-s41704" xml:space="preserve">Tunc enim dioptra ſolum <lb/>circumducenda eſt, donec radius Solis cadat in rectam D F, etiamſi in tabella non ſint deſcripta <lb/>ſigna. </s>
  <s xml:id="echoid-s41705" xml:space="preserve">Quòd ſi deſcripta ſint ſigna, indicabit idem radius, in quonam ſigno Sol exiſtat.</s>
  <s xml:id="echoid-s41706" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s41707" xml:space="preserve">IAM vero ſi horologium in plano Horizonti æquidiſtante verſus Solem dirigatur, ita vt vm-<lb/>bra axis cadat in lineam meridianam, vel radius Solis per dioptram incidens in rectam D F, &amp; </s>
  <s xml:id="echoid-s41708" xml:space="preserve"><lb/>quadratum A B C D, eleuetur, donec à Sole non amplius illuminetur, ſed productum per Solem <lb/>tranſeat, vel donec radius Solis in duo puncta rectæ D F, quæ foraminibus dioptræ oppoſita <lb/>
<anchor type="note" xlink:label="note-0652-03a" xlink:href="note-0652-03"/>
ſunt, cadat, indicabit quadratum ipſum in quadrante altitudinem Solis ſupra Horizontem. </s>
  <s xml:id="echoid-s41709" xml:space="preserve">Ex <lb/>qua, ſi meridiana fuerit, id eſt, maxima illo die, &amp; </s>
  <s xml:id="echoid-s41710" xml:space="preserve">ex declinatione Solis altitudo poli elicietur, vt <lb/>in commentariis in ſphæram docuimus.</s>
  <s xml:id="echoid-s41711" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2074" type="float" level="2" n="4">
<note position="left" xlink:label="note-0652-03" xlink:href="note-0652-03a" xml:space="preserve">30</note>
</div>
</div>
<div xml:id="echoid-div2076" type="section" level="1" n="528">
<head xml:id="echoid-head557" style="it" xml:space="preserve">DE HOROLOGIO VNIVERS ALI IN FORMAM <lb/>crucis conſtructo. CAP. II.</head>
<p>
  <s xml:id="echoid-s41712" xml:space="preserve">FIAT ex eadem materia crux plana A B C D, &amp; </s>
  <s xml:id="echoid-s41713" xml:space="preserve">alia ſolida, concaua tamen, A E F G, quæ <lb/>
<anchor type="note" xlink:label="note-0652-04a" xlink:href="note-0652-04"/>
cum priori ita coniungatur, vt libere poſſit erigi &amp; </s>
  <s xml:id="echoid-s41714" xml:space="preserve">deprimi; </s>
  <s xml:id="echoid-s41715" xml:space="preserve">ſintq́ue tria brachia E, F, G, inter <lb/>
<anchor type="figure" xlink:label="fig-0652-01a" xlink:href="fig-0652-01"/>
ſe prorſus æqualia. </s>
  <s xml:id="echoid-s41716" xml:space="preserve">Deinde ad longitudi-<lb/>
<anchor type="note" xlink:label="note-0652-05a" xlink:href="note-0652-05"/>
nem ſtyli vni brachiorum æqualis deſcri <lb/>batur tam horologium Meridianum, <lb/>quàm Polare: </s>
  <s xml:id="echoid-s41717" xml:space="preserve">Et Meridianum qui-<lb/>dem orientale in latere crucis A F, depin-<lb/>gatur, ductis lineis ad rectam E K, per-<lb/>pendic ularibus; </s>
  <s xml:id="echoid-s41718" xml:space="preserve">occidentale autem in <lb/>oppoſito latere, vt numeri indi cant: </s>
  <s xml:id="echoid-s41719" xml:space="preserve">Po-<lb/>lare vero in ſuperiore parte brachiorum <lb/>E, H, hoc eſt, in plano crucis ad planum <lb/>E G, recto, horę quidem antemeridianæ <lb/>
<anchor type="note" xlink:label="note-0652-06a" xlink:href="note-0652-06"/>
ad partes H, pomeridianæ vero ad par-<lb/>tes E, vt numeri oſtendunt, ductis lineis <lb/>ad rectam E H, perpendicularibus. </s>
  <s xml:id="echoid-s41720" xml:space="preserve">In <lb/>cruce denique A B C D, acus Magnete <lb/>illita ſtatuatur, vt beneficio ipſius horolo <lb/>gium ita poſſit collocari in plano, quod <lb/>Horizonti ęquidiſtet, vt A, ad Boream, &amp; </s>
  <s xml:id="echoid-s41721" xml:space="preserve"><lb/>C, ad Auſtrum vergat, latusq́ue A C, me-<lb/>ridianam lineam referat. </s>
  <s xml:id="echoid-s41722" xml:space="preserve">Poſito enim ho <lb/>rologio in tali ſitu, ſi beneficio quadrantis crux A E F G, ita eleuetur, vt angulus C A L, ſit angulus <lb/>con@@lementi altitudinis poli, iacebit planum F M, in Aequatore, &amp; </s>
  <s xml:id="echoid-s41723" xml:space="preserve">brachia E, H, I, G, L, F, &amp;</s>
  <s xml:id="echoid-s41724" xml:space="preserve">c.</s>
  <s xml:id="echoid-s41725" xml:space="preserve">
<pb o="637" file="0653" n="653" rhead="LIBER OCTAVVS."/>
horas à mer. </s>
  <s xml:id="echoid-s41726" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s41727" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41728" xml:space="preserve">indicabunt. </s>
  <s xml:id="echoid-s41729" xml:space="preserve">Poteſt etiam prope latus A C, inferioris crucis ſcala lati-<lb/>tudinum regionum depingi, vt in pręcedenti cap. </s>
  <s xml:id="echoid-s41730" xml:space="preserve">docuimus. </s>
  <s xml:id="echoid-s41731" xml:space="preserve">Si enim in medio lateris A L, ſty-<lb/>lus volubilis annectatur dimidiato lateri A L, æqualis, &amp; </s>
  <s xml:id="echoid-s41732" xml:space="preserve">ſtatuatur in ſcala latitudinum regionum <lb/>ad gradum altitudinis poli, habebit rurſus horologium proprium ſitum.</s>
  <s xml:id="echoid-s41733" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2076" type="float" level="2" n="1">
<note position="left" xlink:label="note-0652-04" xlink:href="note-0652-04a" xml:space="preserve">Compo@itio ho-<lb/>rologii vniuer-<lb/>ſalis in formam <lb/>@@cis,</note>
  <figure xlink:label="fig-0652-01" xlink:href="fig-0652-01a">
    <image file="0652-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0652-01"/>
  </figure>
<note position="left" xlink:label="note-0652-05" xlink:href="note-0652-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0652-06" xlink:href="note-0652-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41734" xml:space="preserve">POSSVNT quoque in cruce depingi arcus ſignorum, vt in horologio Meridiano, &amp; </s>
  <s xml:id="echoid-s41735" xml:space="preserve">pola-<lb/>ri, habita ratione ſtyli F 12. </s>
  <s xml:id="echoid-s41736" xml:space="preserve">vel 9 12. </s>
  <s xml:id="echoid-s41737" xml:space="preserve">ita vt latus E H, ſit linea æquinoctialis in horologio polari, <lb/>&amp; </s>
  <s xml:id="echoid-s41738" xml:space="preserve">ſigna borealia tendant deorſum verſus, &amp; </s>
  <s xml:id="echoid-s41739" xml:space="preserve">auſtralia ſurſum verſus, &amp;</s>
  <s xml:id="echoid-s41740" xml:space="preserve">c. </s>
  <s xml:id="echoid-s41741" xml:space="preserve">Item habita ratione alio-<lb/>rum laterum brachii G H, E I, tanquàm ſtylorum, ita vt tam latus F K, quàm 9 M, ſit linea æqui-<lb/>noctialis in Meridiano horologio, &amp; </s>
  <s xml:id="echoid-s41742" xml:space="preserve">ſigna borealia deorſum verſus tendant, &amp; </s>
  <s xml:id="echoid-s41743" xml:space="preserve">auſtralia ſur-<lb/>ſum verſus, &amp;</s>
  <s xml:id="echoid-s41744" xml:space="preserve">c.</s>
  <s xml:id="echoid-s41745" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">10</note>
</div>
<div xml:id="echoid-div2078" type="section" level="1" n="529">
<head xml:id="echoid-head558" style="it" xml:space="preserve">DE ALIO HOROLOGIO VNIVERSALI IN PLANA <lb/>ſuperficie deſcripto, &amp; ad quamcunque latitudinem loci, quę <lb/>complementum maximę declinationis Solis <lb/>non excedat, accommodato. <lb/>CAP. III.</head>
<p>
  <s xml:id="echoid-s41746" xml:space="preserve">IN plano aliquo ductis duabus rectis B C, A D, ſeſe in A, ad angulos rectos ſecantibus, deſcri-<lb/>
<anchor type="note" xlink:label="note-0653-02a" xlink:href="note-0653-02"/>
batur ex centro A, arcus circuli occultus E D F, in quo vtrinque à D, maxima Solis declinatio <lb/>numeretur vſque ad E, &amp; </s>
  <s xml:id="echoid-s41747" xml:space="preserve">F: </s>
  <s xml:id="echoid-s41748" xml:space="preserve">ductaq́ue recta E F, ſecante rectam A D, in G, deſcribatur ex G, cen-<lb/>
<anchor type="note" xlink:label="note-0653-03a" xlink:href="note-0653-03"/>
tro, interuallo autem G E, vel G F, circulus occultus, quo diuſo in 12. </s>
  <s xml:id="echoid-s41749" xml:space="preserve">partes æquales pro 12. </s>
  <s xml:id="echoid-s41750" xml:space="preserve">ſignis <lb/>Zodiaci, vel in plures, pro partibus etiam ſignorum, (Nos eum partiti ſumus in 36. </s>
  <s xml:id="echoid-s41751" xml:space="preserve">partes, vt quæ-<lb/>libet comprehendat grad. </s>
  <s xml:id="echoid-s41752" xml:space="preserve">10.) </s>
  <s xml:id="echoid-s41753" xml:space="preserve">iungantur quælibet bina puncta à recta A D, ęqualiter di-<lb/>ſtantia lineis rectis occultis ſecantibus arcum E D F, in punctis, ad quæ ſi rectæ ducantur ex A, <lb/>(quæ tamen vltra rectam E F, produci non debent) deſcripti erunt radij ſignorum Zodia-<lb/>ci, ita vt A G, ſit radius principii ♈, &amp; </s>
  <s xml:id="echoid-s41754" xml:space="preserve">♎, radii vero verſus E, ſignis borealibus, &amp; </s>
  <s xml:id="echoid-s41755" xml:space="preserve">radii ver-<lb/>ſus F, auſtralibus ſignis tribuantur, vt ſignorum characteres indicant. </s>
  <s xml:id="echoid-s41756" xml:space="preserve">Si lubet, poterunt <lb/>prope initia ſignorum, eorumq́ue partes aſcribi dies menſium, in quibus Sol illa puncta Eclipticæ <lb/>poſſidet, vt in dorſo Aſtrolabij fieri ſolet. </s>
  <s xml:id="echoid-s41757" xml:space="preserve">In hoc triangulo radiorum Zodiaci accommodandæ <lb/>erunt latitudines omnium locorum, quæ complementum maximæ declinationis Solis non exce-<lb/>
<anchor type="note" xlink:label="note-0653-04a" xlink:href="note-0653-04"/>
dunt, hoc modo. </s>
  <s xml:id="echoid-s41758" xml:space="preserve">Ex E, &amp; </s>
  <s xml:id="echoid-s41759" xml:space="preserve">F, ducantur rectæ E O, F L, ipſi A G, parallelę, (quod facile fiet, ſi ſu-<lb/>mantur A O, A L, rectis G E, G F, æquales) &amp; </s>
  <s xml:id="echoid-s41760" xml:space="preserve">ex A, circulus deſcribatur occultus B H C, cuius <lb/>quadrans B H, in grad. </s>
  <s xml:id="echoid-s41761" xml:space="preserve">90. </s>
  <s xml:id="echoid-s41762" xml:space="preserve">diſtribuatur. </s>
  <s xml:id="echoid-s41763" xml:space="preserve">Nos eum partiti ſumus in 18. </s>
  <s xml:id="echoid-s41764" xml:space="preserve">partes æquales, vt ſingn-<lb/>læ quinos gradus complectantur. </s>
  <s xml:id="echoid-s41765" xml:space="preserve">Deinde ex A, per puncta diuiſionum rectæ occultæ emiſſæ ſe-<lb/>cent rectam E O, in punctis, per quę ſi ipſi O L, parallelæ agantur (quod facile fiet, ſi omnia pun-<lb/>cta rectæ E O, in rectam F L, transferantur) deſcriptæ erunt latitudines locorum, vt figu-<lb/>ra indicat.</s>
  <s xml:id="echoid-s41766" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2078" type="float" level="2" n="1">
<note position="right" xlink:label="note-0653-02" xlink:href="note-0653-02a" xml:space="preserve">Deſcriptio alte-<lb/>rius horologii <lb/>vniuerſalis in <lb/>ſuperfieieplana.</note>
<note position="left" xlink:label="note-0653-03" xlink:href="note-0653-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0653-04" xlink:href="note-0653-04a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s41767" xml:space="preserve">POST hæc conſtruendus erit ad rectam F L, alius Zodiacus hac ratione. </s>
  <s xml:id="echoid-s41768" xml:space="preserve">In circulo B H C, <lb/>numeretur vtrinque à C, maxima Solis declinatio vſque ad I, &amp; </s>
  <s xml:id="echoid-s41769" xml:space="preserve">K, ductisq́ue rectis A I, A K, ſe-<lb/>cantibus rectam F L, in duobus punctis, deſcribatur ex L, circa rectam inter duo illa puncta in-<lb/>
<anchor type="note" xlink:label="note-0653-05a" xlink:href="note-0653-05"/>
teriectam circulus occultus, quo diuiſo in 12. </s>
  <s xml:id="echoid-s41770" xml:space="preserve">partes æquales, vel in plures, prout ſigna integra, <lb/>vel eorum partes deſiderantur, (Nos eum diuiſimus in 24. </s>
  <s xml:id="echoid-s41771" xml:space="preserve">par tes ęquales, vt quodlibet ſignum <lb/>bifariam diuidatur) ducantur per quęuis bina puncta à recta A C, æqualiter remota rectæ occul-<lb/>tæ ſecantes arcum a d b, occulte deſcriptum ex A, tranſeuntemq́ue per puncta illa, vbi recta F L, <lb/>à rectis A I, A K, ſecatur. </s>
  <s xml:id="echoid-s41772" xml:space="preserve">Nam ſi per puncta huius arcus ex A, rectæ occultæ egrediantut, ſecabi-<lb/>tur portio rectæ F L, inter rectas A I, A K, comprehenſa in ſigna Zodiaci, ita vt punctum L, prin-<lb/>cipio ♈, &amp; </s>
  <s xml:id="echoid-s41773" xml:space="preserve">♎, tribuatur, ſigna autem borealia verſus F, progrediantur, &amp; </s>
  <s xml:id="echoid-s41774" xml:space="preserve">auſtralia deorſum ver-<lb/>ſus, hoc eſt, vt borealia ſigna huius poſterioris Zodiaci propinquiora ſint ſignis auſtrali-<lb/>bus prioris Zodiaci, quàm auſtralia. </s>
  <s xml:id="echoid-s41775" xml:space="preserve">Quod ſi poſterior hic Zodiacus ad rectam E O, eſſet de-<lb/>ſcriptus, tenderent ſigna auſtralia ſurſum verſus, &amp; </s>
  <s xml:id="echoid-s41776" xml:space="preserve">borealia deorſum verſus, ita vt auſtralia ſigna <lb/>huius Zodiaci propinquiora eſſent borealibus ſignis illius Zodiaci, quàm borealia. </s>
  <s xml:id="echoid-s41777" xml:space="preserve">In conſtru-<lb/>
<anchor type="note" xlink:label="note-0653-06a" xlink:href="note-0653-06"/>
ctione porrò poſterioris huius Zodiaci hallucinatus eſt Orontius, quem ferè omnes @equuntur. <lb/></s>
  <s xml:id="echoid-s41778" xml:space="preserve">
<anchor type="note" xlink:label="note-0653-07a" xlink:href="note-0653-07"/>
Vult enim rectas ex A, educẽdas eſſe per puncta rectæ F L, in quibus à rectis per bina puncta quæ-<lb/>uis circuli ex L, deſcripti ſecatur. </s>
  <s xml:id="echoid-s41779" xml:space="preserve">quod omnino falſum eſt. </s>
  <s xml:id="echoid-s41780" xml:space="preserve">Ducendę enim ſunt per puncta arcus <lb/>a d b, vt propoſ. </s>
  <s xml:id="echoid-s41781" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41782" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41783" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41784" xml:space="preserve">oſtendimus, quemadmodum &amp; </s>
  <s xml:id="echoid-s41785" xml:space="preserve">radij ſignorum prioris Zodiaci ducti <lb/>ſunt per puncta arcus E D F, non autem per puncta rectę E F. </s>
  <s xml:id="echoid-s41786" xml:space="preserve">Immo ſecum pugnat Orontius, <lb/>cum dicat, puncta ſignorum in recta F L, ęqualia eſſe debere punctis ſignorum prioris Zodiaci <lb/>in recta, quæ gradum 45. </s>
  <s xml:id="echoid-s41787" xml:space="preserve">latitudinis indicat. </s>
  <s xml:id="echoid-s41788" xml:space="preserve">quod ſecun dum eius deſcriptionem verum eſſe nõ <lb/>poteſt, niſi rectæ ex A, per puncta arcus a d b, ducantur, &amp;</s>
  <s xml:id="echoid-s41789" xml:space="preserve">c.</s>
  <s xml:id="echoid-s41790" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2079" type="float" level="2" n="2">
<note position="left" xlink:label="note-0653-05" xlink:href="note-0653-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0653-06" xlink:href="note-0653-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0653-07" xlink:href="note-0653-07a" xml:space="preserve">Error Orontii.</note>
</div>
<p>
  <s xml:id="echoid-s41791" xml:space="preserve">HORAE ita deſcribentur. </s>
  <s xml:id="echoid-s41792" xml:space="preserve">Ex A, centro ad interuallum A L, vel A O, vel A M, vſque ad li-<lb/>neam latitudinis grad. </s>
  <s xml:id="echoid-s41793" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41794" xml:space="preserve">(Hæ enim tres rectæ, ſi erratum non eſt, æquales inter ſe erunt) de-
<pb o="638" file="0654" n="654" rhead="GNOMONICES"/>
ſcriptus circulus in 24. </s>
  <s xml:id="echoid-s41795" xml:space="preserve">horas ęquales diuidatur, quæ rurſus, ſi placet, in ſemihoras, &amp; </s>
  <s xml:id="echoid-s41796" xml:space="preserve">in quadrã<unsure/>-<lb/>tes horarum ſubdiuidantur. </s>
  <s xml:id="echoid-s41797" xml:space="preserve">Rectæ enim ductæ per bina quęuis puncta æqualiter à punctis L, O, <lb/>
<anchor type="figure" xlink:label="fig-0654-01a" xlink:href="fig-0654-01"/>
<anchor type="note" xlink:label="note-0654-01a" xlink:href="note-0654-01"/>
<anchor type="note" xlink:label="note-0654-02a" xlink:href="note-0654-02"/>
<anchor type="note" xlink:label="note-0654-03a" xlink:href="note-0654-03"/>
<anchor type="note" xlink:label="note-0654-04a" xlink:href="note-0654-04"/>
<anchor type="note" xlink:label="note-0654-05a" xlink:href="note-0654-05"/>
remota dabunt 12. </s>
  <s xml:id="echoid-s41798" xml:space="preserve">horas à meridie, &amp; </s>
  <s xml:id="echoid-s41799" xml:space="preserve">12. </s>
  <s xml:id="echoid-s41800" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s41801" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41802" xml:space="preserve">quarum M A, ſextam horam dabit, ante-<lb/>meridianę vero horæ à recta E O, verſus F L, &amp; </s>
  <s xml:id="echoid-s41803" xml:space="preserve">pomeridianæ à recta F L, verſus E O, numeran-<lb/>tur. </s>
  <s xml:id="echoid-s41804" xml:space="preserve">Term inabuntur autem hæ lineæ horarum, in ſuperiore quidem parte, in circunferentia cir-<lb/>culi ex M, ad interuallum M A, deſcripti, in inferiori autem in linea ipſi L O, parallela tanto ſal-<lb/>tem interuallo diſtante à recta L O, quanta eſt portio rectæ A I, vel A K, inter A, &amp; </s>
  <s xml:id="echoid-s41805" xml:space="preserve">rectam F L.</s>
  <s xml:id="echoid-s41806" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2080" type="float" level="2" n="3">
  <figure xlink:label="fig-0654-01" xlink:href="fig-0654-01a">
    <image file="0654-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0654-01"/>
  </figure>
<note position="left" xlink:label="note-0654-01" xlink:href="note-0654-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0654-02" xlink:href="note-0654-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0654-03" xlink:href="note-0654-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0654-04" xlink:href="note-0654-04a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0654-05" xlink:href="note-0654-05a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41807" xml:space="preserve">RVRSVS fabricandum erit brachiolum ex dura aliqua, &amp; </s>
  <s xml:id="echoid-s41808" xml:space="preserve">ſolida materia, conſtans tribus <lb/>volubilibus ſegmentis Q R, R S, S T, quæ in longum extenſa longitudinem efficiant rectæ G A, <lb/>æqualem. </s>
  <s xml:id="echoid-s41809" xml:space="preserve">Huius brachioli extremum punctum Q, figendum eſt in puncto G, ita vt alterum extre <lb/>mum T, liberæ per omnia loca trianguli A, E F, diſcurrere poſſit, &amp; </s>
  <s xml:id="echoid-s41810" xml:space="preserve">in quocunque loco firmari, ne
<pb o="639" file="0655" n="655" rhead="LIBER OCTAVVS."/>
facile dimoueatur: </s>
  <s xml:id="echoid-s41811" xml:space="preserve">atque in hoc extremo appendendum eſt filum tenuiſſimum, vna cum perpen <lb/>diculo, &amp; </s>
  <s xml:id="echoid-s41812" xml:space="preserve">ipſi filo nodulus mobilis N, circumponendus loco indicis.</s>
  <s xml:id="echoid-s41813" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s41814" xml:space="preserve">POSTREMO reſectis omnibus ſuperuacaneis, ita vt horologium ad formam quadrangu-<lb/>larem redigatur, cuius extrema latera ſint E F, &amp; </s>
  <s xml:id="echoid-s41815" xml:space="preserve">proxime ducta parallela in lineis horariis; </s>
  <s xml:id="echoid-s41816" xml:space="preserve">Item <lb/>E O, F L, vſque ad eandem parallelam producta: </s>
  <s xml:id="echoid-s41817" xml:space="preserve">Relicto quoque tanto ſpatio ad partes L, vt ſi-<lb/>gnorum characteres deſcribi poſſint, conficienda erunt duo pinnacidia ſubtiliter perforata, atq; <lb/></s>
  <s xml:id="echoid-s41818" xml:space="preserve">lateri E F, ad angulos rectos adaptanda. </s>
  <s xml:id="echoid-s41819" xml:space="preserve">Ita enim completa erit horologij deſcriptio.</s>
  <s xml:id="echoid-s41820" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s41821" xml:space="preserve">VSVS huius horologij hic eſt. </s>
  <s xml:id="echoid-s41822" xml:space="preserve">Firmato extremo puncto T, brachioli in communi ſectione <lb/>
<anchor type="note" xlink:label="note-0655-01a" xlink:href="note-0655-01"/>
radij illius gradus Eclipticæ, in quo Sol exiſtit, &amp; </s>
  <s xml:id="echoid-s41823" xml:space="preserve">lineæ latitudinis loci propoſitæ, extendatur fi-<lb/>lum perpendiculi verſus Zodiacum ad rectam F L, deſcriptum, ponaturq́ue nodulus mobilis N, <lb/>
<anchor type="note" xlink:label="note-0655-02a" xlink:href="note-0655-02"/>
in recta F L, in eodem gradu Zodiaci. </s>
  <s xml:id="echoid-s41824" xml:space="preserve">Nam ſi tunc, filo perpendiculi planum horologii radente, <lb/>eleuetur pinnacidium prope E, donec radius Solis per eius foramen tranſiens cadat in foramen <lb/>alterius pinnacidij prope F, indicabit nodulus mobilis N, inter lineas horarias horam præſentem. <lb/></s>
  <s xml:id="echoid-s41825" xml:space="preserve">Loco pinnacidiorum vti poteris clauiculo ad angulos rectos in recta E F, prope E, affixo. </s>
  <s xml:id="echoid-s41826" xml:space="preserve">Si enim <lb/>inſtrumentum eleuetur, donec vmbra clauiculi in rectam E F, cadat, indicabit idem nodu-<lb/>lus horam.</s>
  <s xml:id="echoid-s41827" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2081" type="float" level="2" n="4">
<note position="right" xlink:label="note-0655-01" xlink:href="note-0655-01a" xml:space="preserve">Vſus huius ho-<lb/>rologii vni@er-<lb/>ſalis.</note>
<note position="left" xlink:label="note-0655-02" xlink:href="note-0655-02a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s41828" xml:space="preserve">QVOD ſi ex puncto, vbi ſe mutuo interſecant radius Zodiaci illius gradus, in quo Sol exi-<lb/>
<anchor type="note" xlink:label="note-0655-03a" xlink:href="note-0655-03"/>
ſtit, &amp; </s>
  <s xml:id="echoid-s41829" xml:space="preserve">lineæ latitudinis loci propoſitæ, ducatur rectæ G A, linea occulta parallela, dabunt horæ <lb/>inter hanc parallelã, &amp; </s>
  <s xml:id="echoid-s41830" xml:space="preserve">rectã F L, arcum ſemidiurnũ, horæ vero inter eandẽ parallelam, &amp; </s>
  <s xml:id="echoid-s41831" xml:space="preserve">rectam <lb/>E O, arcũ ſeminocturnum. </s>
  <s xml:id="echoid-s41832" xml:space="preserve">Vnde in illa parallela orietur Sol, &amp; </s>
  <s xml:id="echoid-s41833" xml:space="preserve">occidet. </s>
  <s xml:id="echoid-s41834" xml:space="preserve">Ex quo fit, vt facile horæ à <lb/>
<anchor type="note" xlink:label="note-0655-04a" xlink:href="note-0655-04"/>
mer. </s>
  <s xml:id="echoid-s41835" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41836" xml:space="preserve">med. </s>
  <s xml:id="echoid-s41837" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41838" xml:space="preserve">ad horas ab or. </s>
  <s xml:id="echoid-s41839" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41840" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s41841" xml:space="preserve">reducantur. </s>
  <s xml:id="echoid-s41842" xml:space="preserve">Si enim ab illa parallela numerẽtur verſus re-<lb/>ctã F L, horæ integræ vſque ad horã, quam nodulus mobilis indicat, redeundo tamen à recta F L, <lb/>
<anchor type="note" xlink:label="note-0655-05a" xlink:href="note-0655-05"/>
verſus dictam parallelam, vſque ad nodulum, ſi tempus eſt pomeridianũ, habebitur hora ab ortu <lb/>Solis: </s>
  <s xml:id="echoid-s41843" xml:space="preserve">Si vero ab eadem parallela horæ integræ ſupputentur verſus rectam E O, vſque ad nodu-<lb/>lum, redeundo tamen à recta E O, verſus dictam parallelam vſque ad nodulum N, ſi tem pus an-<lb/>temeridianum eſt, vel ſi pomeridianum, redeundo etiam à recta F L, verſus eandem parallelam, <lb/>habebitur hora ab occaſu Solis. </s>
  <s xml:id="echoid-s41844" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s41845" xml:space="preserve">Ponatur nodulum N, cadere in horam 10. </s>
  <s xml:id="echoid-s41846" xml:space="preserve">ante-<lb/>meridianam in latitudine grad. </s>
  <s xml:id="echoid-s41847" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41848" xml:space="preserve">Sole exiſtente in grad. </s>
  <s xml:id="echoid-s41849" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41850" xml:space="preserve">♈, vel grad. </s>
  <s xml:id="echoid-s41851" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41852" xml:space="preserve">♍. </s>
  <s xml:id="echoid-s41853" xml:space="preserve">Quoniam igi-<lb/>tur ex puncto, vbi linea latitudinis grad. </s>
  <s xml:id="echoid-s41854" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41855" xml:space="preserve">radium grad. </s>
  <s xml:id="echoid-s41856" xml:space="preserve">20. </s>
  <s xml:id="echoid-s41857" xml:space="preserve">♈, vel grad. </s>
  <s xml:id="echoid-s41858" xml:space="preserve">10. </s>
  <s xml:id="echoid-s41859" xml:space="preserve">♍, ſecat, ducta ipſi <lb/>G A, parallela cadit fere in medium ſpatium inter horam 5. </s>
  <s xml:id="echoid-s41860" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41861" xml:space="preserve">6. </s>
  <s xml:id="echoid-s41862" xml:space="preserve">antemeridianam, &amp; </s>
  <s xml:id="echoid-s41863" xml:space="preserve">inter ho-<lb/>
<anchor type="note" xlink:label="note-0655-06a" xlink:href="note-0655-06"/>
ram 6. </s>
  <s xml:id="echoid-s41864" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41865" xml:space="preserve">7. </s>
  <s xml:id="echoid-s41866" xml:space="preserve">pomeridianam, continebit arcus ſemidiurnus horas 6 {1/2}. </s>
  <s xml:id="echoid-s41867" xml:space="preserve">fere. </s>
  <s xml:id="echoid-s41868" xml:space="preserve">ſeminocturnus autem <lb/>horas 5 {1/2}. </s>
  <s xml:id="echoid-s41869" xml:space="preserve">ferè; </s>
  <s xml:id="echoid-s41870" xml:space="preserve">orieturq́ue Sol hora 5 {1/2}. </s>
  <s xml:id="echoid-s41871" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s41872" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s41873" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s41874" xml:space="preserve">occidet hora 6 {1/2}. </s>
  <s xml:id="echoid-s41875" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41876" xml:space="preserve">Quia vero ab ho <lb/>ra 5 {1/2}. </s>
  <s xml:id="echoid-s41877" xml:space="preserve">antemeridiana vſque ad horam 10. </s>
  <s xml:id="echoid-s41878" xml:space="preserve">antemeridianam, verſus rectam F L, progrediendo, <lb/>numerantur horæ 4 {1/2}. </s>
  <s xml:id="echoid-s41879" xml:space="preserve">inſtabit tunc hora 4 {1/2}. </s>
  <s xml:id="echoid-s41880" xml:space="preserve">ab ortu Solis. </s>
  <s xml:id="echoid-s41881" xml:space="preserve">Si autem tunc tempus fuerit pome <lb/>ridianum, atque adeo nodulus N, in horam 2. </s>
  <s xml:id="echoid-s41882" xml:space="preserve">à mer@ cadat, numerabuntur ab hora 5 {1/2}. </s>
  <s xml:id="echoid-s41883" xml:space="preserve">antemeri-<lb/>diana verſus rectam F L, progrediendo, redeundoq́ue ad horam 2. </s>
  <s xml:id="echoid-s41884" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41885" xml:space="preserve">horæ 8 {1/2}. </s>
  <s xml:id="echoid-s41886" xml:space="preserve">Inſtabit er-<lb/>go tunc hora 8 {1/2}. </s>
  <s xml:id="echoid-s41887" xml:space="preserve">ab ortu Solis. </s>
  <s xml:id="echoid-s41888" xml:space="preserve">Rurſus quia ab hora eadem 5 {1/2}. </s>
  <s xml:id="echoid-s41889" xml:space="preserve">antemeridiana vſque ad horam <lb/>10. </s>
  <s xml:id="echoid-s41890" xml:space="preserve">antemeridianam, verſus rectam E O, progrediendo, ab eaq́; </s>
  <s xml:id="echoid-s41891" xml:space="preserve">redeundo, reperiuntur horæ 15 {1/2}. <lb/></s>
  <s xml:id="echoid-s41892" xml:space="preserve">erit tunc hora 15 {1/2}. </s>
  <s xml:id="echoid-s41893" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41894" xml:space="preserve">Item quoniã ab eadem hora 5 {1/2}. </s>
  <s xml:id="echoid-s41895" xml:space="preserve">antemeridiana vſque ad horam 2. </s>
  <s xml:id="echoid-s41896" xml:space="preserve"><lb/>pomeridianam, progrediendo verſus rectam E O, ab eaq́ue regrediendo verſus rectam F L, &amp; </s>
  <s xml:id="echoid-s41897" xml:space="preserve">ab <lb/>
<anchor type="note" xlink:label="note-0655-07a" xlink:href="note-0655-07"/>
hac rurſus regrediendo verſus horam 2. </s>
  <s xml:id="echoid-s41898" xml:space="preserve">pomeridianam, numerantur horæ 19 {1/2}. </s>
  <s xml:id="echoid-s41899" xml:space="preserve">inſtabit tunc ho-<lb/>ra 19 {1/2}. </s>
  <s xml:id="echoid-s41900" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41901" xml:space="preserve">Vel certe, quia ab hora 2. </s>
  <s xml:id="echoid-s41902" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41903" xml:space="preserve">vſque ad horam 6 {1/2}. </s>
  <s xml:id="echoid-s41904" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s41905" xml:space="preserve">qua Sol occidit, nu-<lb/>merantur horę 4 {1/2}. </s>
  <s xml:id="echoid-s41906" xml:space="preserve">ſi hæ detrahantur ex 24. </s>
  <s xml:id="echoid-s41907" xml:space="preserve">hoc eſt, ex hora, qua Sol occidit, remanebunt horæ <lb/>19 {1/2}. </s>
  <s xml:id="echoid-s41908" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s41909" xml:space="preserve">vt prius. </s>
  <s xml:id="echoid-s41910" xml:space="preserve">Eadem ratio eſt de cæteris habenda.</s>
  <s xml:id="echoid-s41911" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2082" type="float" level="2" n="5">
<note position="right" xlink:label="note-0655-03" xlink:href="note-0655-03a" xml:space="preserve">Inuentio arcus <lb/>ſemidiurni, &amp; <lb/>ſeminocturni: <lb/>Item hora or-<lb/>tus &amp; occaſus <lb/>Solis. ex hoc ho <lb/>rologio.</note>
<note position="left" xlink:label="note-0655-04" xlink:href="note-0655-04a" xml:space="preserve">20</note>
<note position="right" xlink:label="note-0655-05" xlink:href="note-0655-05a" xml:space="preserve">Reductio hora-<lb/>rum à mer. &amp; <lb/>med noc. ad ho <lb/>ras ab or. &amp; occ. <lb/>ex eodem hoc <lb/>horologio.</note>
<note position="left" xlink:label="note-0655-06" xlink:href="note-0655-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0655-07" xlink:href="note-0655-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s41912" xml:space="preserve">AD hæc, ſi quadrans L V, ex A, deſcriptus ſecetur in 90. </s>
  <s xml:id="echoid-s41913" xml:space="preserve">gradus, &amp; </s>
  <s xml:id="echoid-s41914" xml:space="preserve">extremum punctum T, <lb/>
<anchor type="note" xlink:label="note-0655-08a" xlink:href="note-0655-08"/>
brachioli in centro A, collocetur, eleueturq́ue inſtrumentum, donec radius Solis foramini-<lb/>bus pinnacidiorum reſpondeat, indicabit filum perpendiculi in quadrante L V, altitudinem So-<lb/>lis ſupra Horizontem. </s>
  <s xml:id="echoid-s41915" xml:space="preserve">Progredietur autem numerus graduum in quadrante L V, à puncto V, <lb/>verſus L.</s>
  <s xml:id="echoid-s41916" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2083" type="float" level="2" n="6">
<note position="right" xlink:label="note-0655-08" xlink:href="note-0655-08a" xml:space="preserve">Altitudo Soli@ <lb/>quo pacto de-<lb/>prehendatur ex <lb/>hoc horologio.</note>
</div>
<p>
  <s xml:id="echoid-s41917" xml:space="preserve">IAM vero ſi tota longitudo horologij bifariam ſecetur in P, diuidaturq́; </s>
  <s xml:id="echoid-s41918" xml:space="preserve">horologium ipſum <lb/>
<anchor type="note" xlink:label="note-0655-09a" xlink:href="note-0655-09"/>
per rectam, quæ per P, ipſi L O, parallela ducitur; </s>
  <s xml:id="echoid-s41919" xml:space="preserve">atque hæ partes horologii iuncturis, &amp; </s>
  <s xml:id="echoid-s41920" xml:space="preserve">clauicu-<lb/>lis ita inter ſe colligentur, vt vna alteri ſuperimponi poſſit, veluti de quadratis horologii æquino-<lb/>ctialis diximus cap. </s>
  <s xml:id="echoid-s41921" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41922" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s41923" xml:space="preserve">redactum erit horologium ad commodiſſimam formam, ita vt <lb/>facile de loco ad locum poſſit circunferri. </s>
  <s xml:id="echoid-s41924" xml:space="preserve">In vſu autem aperiendum erit, vt ex duabus illis parti-<lb/>bus vna plana ſuperficies efficiatur. </s>
  <s xml:id="echoid-s41925" xml:space="preserve">Immo ſi in exteriore facie tabellæ, in qua eſt recta L O, ex pun <lb/>cto reſpondente cẽtro A, circulus reſpondens circulo L M O V, deſcribatur, &amp; </s>
  <s xml:id="echoid-s41926" xml:space="preserve">in 24. </s>
  <s xml:id="echoid-s41927" xml:space="preserve">partes æqua-<lb/>les diuidatur, figaturq́ue in centro ſtylus ad angulos rectos; </s>
  <s xml:id="echoid-s41928" xml:space="preserve">atque hæc tabella eleuetur ſecundũ <lb/>@leuationem Aequatoris, beneficio quadrantis, vel ſcalæ latitudinum regionum, vt de horologio <lb/>æquinoctiali diximus cap. </s>
  <s xml:id="echoid-s41929" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41930" xml:space="preserve">huius lib. </s>
  <s xml:id="echoid-s41931" xml:space="preserve">ipſum denique horologium dirigatur ad lineam meridia-<lb/>nam, beneficio acus illitæ Magnete poſitæ in altera tabella, in qua recta P G, exiſtit, confectum <lb/>erit etiam horologium æquinoctiale vniuerſale, cuius ſemicirculus interior L M O, horas mon-
<pb o="640" file="0656" n="656" rhead="GNOMONICES"/>
ſtrabit, Sole in ſignis auſtralibus exiſtente: </s>
  <s xml:id="echoid-s41932" xml:space="preserve">niſi portionem inter duos ſemicirculos L M O, X Y Z, <lb/>comprehenſam excindere velis, (relicto tamen denticulo M Y, ne tabella nimis debilis reddatur) <lb/>vt vmbra ſtyli interioris appareat in facie exteriori per illam portionem excauatam. </s>
  <s xml:id="echoid-s41933" xml:space="preserve">Poteri s etiam <lb/>loco ſtyli vti dioptra in facie exteriori, vt cap. </s>
  <s xml:id="echoid-s41934" xml:space="preserve">1. </s>
  <s xml:id="echoid-s41935" xml:space="preserve">diximus. </s>
  <s xml:id="echoid-s41936" xml:space="preserve">Tunc enim ſemper horæ monſtrabun-<lb/>tur à linea fiducię in exteriori facie, etiamſi Sol in auſtralibus ſignis exiſtat, ſi dioptra circumuol-<lb/>uatur, donec radius Solis per foramen vnius pinnacidij intrans cadat in lineam foramini oppoſi-<lb/>tam in altero pinnacidio.</s>
  <s xml:id="echoid-s41937" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2084" type="float" level="2" n="7">
<note position="left" xlink:label="note-0655-09" xlink:href="note-0655-09a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div2086" type="section" level="1" n="530">
<head xml:id="echoid-head559" style="it" xml:space="preserve">DE HOROLOGIO HEMISPHAERICO <lb/>concauo. CAP. IIII.</head>
<note position="left" xml:space="preserve">10</note>
<p>
  <s xml:id="echoid-s41938" xml:space="preserve">SIT hemiſphærium concauum torno accurate fabricatum ex ligno, vel orichalco, vel alia <lb/>
<anchor type="note" xlink:label="note-0656-02a" xlink:href="note-0656-02"/>
materia ſolida &amp; </s>
  <s xml:id="echoid-s41939" xml:space="preserve">dura, A B C D, quod diligenter, antequam horæ deſcribantur, examinandum <lb/>erit ſemicirculo ferreo, aut ligneo, cuius ſemidiameter æqualis ſit ſemidiametro orificij A B C D. <lb/></s>
  <s xml:id="echoid-s41940" xml:space="preserve">Si enim ſemicirculus hic concauo hemiſphærio impoſitus, &amp; </s>
  <s xml:id="echoid-s41941" xml:space="preserve">circumductus ſuperficiem conca-<lb/>uam ſemper radat, ita vt nihil emineat, aut depreſſum ſit, dubitandum non erit, hemiſphærium <lb/>perfecte concauum eſſe. </s>
  <s xml:id="echoid-s41942" xml:space="preserve">Diuidatur circulus orificii A B C D, beneficio circini, qui crura habeat <lb/>recurua, in quatuor quadrãtes A B, B C, C D, D A: </s>
  <s xml:id="echoid-s41943" xml:space="preserve">Et ex A, vel C, tanquã polo, ad interuallũ A B, <lb/>vel A D, vel C B, vel C D, circulus maximus deſcribatur B E D, &amp; </s>
  <s xml:id="echoid-s41944" xml:space="preserve">eodem interuallo ex polo B, vel <lb/>
<anchor type="figure" xlink:label="fig-0656-01a" xlink:href="fig-0656-01"/>
D, alius circulus maximus <lb/>
<anchor type="note" xlink:label="note-0656-03a" xlink:href="note-0656-03"/>
A E C, ſecans priorem in E. <lb/></s>
  <s xml:id="echoid-s41945" xml:space="preserve">Hi duo circuli repreſentan-<lb/>tur per lineas rectas A C, <lb/>B D, in noſtra figura, ſeſe <lb/>ad angulos rectos in centro <lb/>E, ſecantes. </s>
  <s xml:id="echoid-s41946" xml:space="preserve">Itaque A B C D, <lb/>erit Horizon; </s>
  <s xml:id="echoid-s41947" xml:space="preserve">A E C, ſemi-<lb/>circulus Meridiani infra Ho <lb/>rizontẽ; </s>
  <s xml:id="echoid-s41948" xml:space="preserve">B E D, ſemicircu-<lb/>lus Verticalis primarij ſub <lb/>
<anchor type="note" xlink:label="note-0656-04a" xlink:href="note-0656-04"/>
Horizonte; </s>
  <s xml:id="echoid-s41949" xml:space="preserve">atque adeo E, <lb/>Nadir, ſeu punctum Verti-<lb/>ci oppoſitum. </s>
  <s xml:id="echoid-s41950" xml:space="preserve">Ponatur au-<lb/>tem in A, meridies; </s>
  <s xml:id="echoid-s41951" xml:space="preserve">in C, <lb/>ſeptentrio; </s>
  <s xml:id="echoid-s41952" xml:space="preserve">in B, ortus, &amp; </s>
  <s xml:id="echoid-s41953" xml:space="preserve">in <lb/>D, occaſus. </s>
  <s xml:id="echoid-s41954" xml:space="preserve">Deinde in ſe-<lb/>micirculo Meridiani AEC, <lb/>numerata ab A, altitudine <lb/>poli vſque ad F, &amp; </s>
  <s xml:id="echoid-s41955" xml:space="preserve">ab E, vſq; <lb/></s>
  <s xml:id="echoid-s41956" xml:space="preserve">ad G, erit F, polus antarcti-<lb/>
<anchor type="note" xlink:label="note-0656-05a" xlink:href="note-0656-05"/>
cus, &amp; </s>
  <s xml:id="echoid-s41957" xml:space="preserve">G, punctũ, per quod <lb/>ſub Horizonte Aequator in-<lb/>cedit. </s>
  <s xml:id="echoid-s41958" xml:space="preserve">Ex polo autem F, ad <lb/>interuallum F E, deſcribatur parallelus O E P , per Nadir ductus, qui ſi integer non deſcribitur, <lb/>(vt in noſtro exemplo, &amp; </s>
  <s xml:id="echoid-s41959" xml:space="preserve">in omni alio loco, vbi altitudo poli ſupra Horizontem minor eſt, quàm <lb/>grad. </s>
  <s xml:id="echoid-s41960" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41961" xml:space="preserve">Tunc enim ſemper arcus F E, complementi altitudinis poli maior eſt arcu F A. </s>
  <s xml:id="echoid-s41962" xml:space="preserve">Si vero <lb/>altitudo poli contineat grad. </s>
  <s xml:id="echoid-s41963" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41964" xml:space="preserve">tanget dictus parallelus Horizontem in A, quia tunc arcus F E, <lb/>F A, æquales ſunt. </s>
  <s xml:id="echoid-s41965" xml:space="preserve">Si denique altitudo poli ſuperet grad. </s>
  <s xml:id="echoid-s41966" xml:space="preserve">45. </s>
  <s xml:id="echoid-s41967" xml:space="preserve">ſecabit idem parallelus Meridianum <lb/>infra punctum A; </s>
  <s xml:id="echoid-s41968" xml:space="preserve">quòd maior tunc ſit arcus F A, arcu F E, complementi altitudinis poli, vt patet) <lb/>ſumendus erit arcus G S, arcui G E, æqualis, &amp; </s>
  <s xml:id="echoid-s41969" xml:space="preserve">ex polo eodem F, ad interuallum F S, portio circu-<lb/>
<anchor type="note" xlink:label="note-0656-06a" xlink:href="note-0656-06"/>
li deſcribenda Q S R, quæ portio eſt paralleli per verticem loci deſcripti, &amp; </s>
  <s xml:id="echoid-s41970" xml:space="preserve">parallelo O E P, op-<lb/>poſiti, eſtq́ue æqualis portioni paralleli O E P, quæ deeſt; </s>
  <s xml:id="echoid-s41971" xml:space="preserve">propterea quòd, declinationibus G E, <lb/>G S, æqualibus exiſtentibus, æquales ſint paralleli per E, &amp; </s>
  <s xml:id="echoid-s41972" xml:space="preserve">S, deſcripti, habeantq́ue, ex propoſ. </s>
  <s xml:id="echoid-s41973" xml:space="preserve">19. <lb/></s>
  <s xml:id="echoid-s41974" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41975" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41976" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s41977" xml:space="preserve">ſegmenta alterna æqualia, nempe ſegmentum Q S R, infra Horizontem, &amp; </s>
  <s xml:id="echoid-s41978" xml:space="preserve">illud, <lb/>quod parallelo O E P, ſupra Horizontem deeſt. </s>
  <s xml:id="echoid-s41979" xml:space="preserve">Erunt autem &amp; </s>
  <s xml:id="echoid-s41980" xml:space="preserve">arcus Horizontis C Q, C R, ar-<lb/>cubus A O, A P, æquales, propter æquales latitudines ortiuas B P, B R, &amp; </s>
  <s xml:id="echoid-s41981" xml:space="preserve">occiduas D O, D Q. </s>
  <s xml:id="echoid-s41982" xml:space="preserve"><lb/>Rurſus ex polo F, ad interuallum quadrantis F G, (Eſt enim F G, arcus compoſitus ex E G, altitu-<lb/>dine poli, &amp; </s>
  <s xml:id="echoid-s41983" xml:space="preserve">ex F E, complemento eiuſdem altitudinis quadrans) vel quadrantis A B, deſcriba-<lb/>tur ſemicirculus Aequatoris B G D, infra Horizontem tranſiens neceſſario per puncta B, D, vbi <lb/>Horizontem Verticalis ſecat: </s>
  <s xml:id="echoid-s41984" xml:space="preserve">Supputata quoque vtrinque à G, maxima declinatione Solis vſque <lb/>ad H, L, deſcribatur ex polo F, ad interuallum F H, portio tropici ♑, infra Horizontem K H I,
<pb o="641" file="0657" n="657" rhead="LIBER OCTAVVS."/>
&amp; </s>
  <s xml:id="echoid-s41985" xml:space="preserve">ad inter@allum F L, portio tropici ♋, infra Horizontem. </s>
  <s xml:id="echoid-s41986" xml:space="preserve">Et quoniam, Sole exiſtente ſupra Ho <lb/>rizontem in principio ♋, eius radius per centrum ſphæræ tranſiens cadit in parallelum oppoſitũ, <lb/>nempe in tropicum ♑, ſub Horizonte; </s>
  <s xml:id="echoid-s41987" xml:space="preserve">in tropicum vero ♋, ſub Horizonte, eodem exiſtente in <lb/>principio ♑, ſupra Horizontem, appellabitur K H I, tropicus ♋, &amp; </s>
  <s xml:id="echoid-s41988" xml:space="preserve">N L M, tropicus ♑, quòd <lb/>vmbra centri ſphæræ in eos cadat, Sole in dictis tropicis exiſtente. </s>
  <s xml:id="echoid-s41989" xml:space="preserve">Eodemq́ue modo alii paralleli <lb/>inter duos tropicos deſcribentur ex polo F, ſi eorum declinationes à G, in vtramque partem <lb/>ſupputentur.</s>
  <s xml:id="echoid-s41990" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2086" type="float" level="2" n="1">
<note position="left" xlink:label="note-0656-02" xlink:href="note-0656-02a" xml:space="preserve">Conſtructio ho <lb/>rologii hemi-<lb/>ſphærici conca-<lb/>ui.</note>
  <figure xlink:label="fig-0656-01" xlink:href="fig-0656-01a">
    <image file="0656-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0656-01"/>
  </figure>
<note position="left" xlink:label="note-0656-03" xlink:href="note-0656-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0656-04" xlink:href="note-0656-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0656-05" xlink:href="note-0656-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0656-06" xlink:href="note-0656-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s41991" xml:space="preserve">IAM vero diuiſo vtroque quadrante Aequatoris G B, G D, in ſex partes æquales, vel etiam <lb/>in plures, ſi horarum partes deſiderentur, (Eſſe autem G B, G D, quadrantes, ita planum fiet. <lb/></s>
  <s xml:id="echoid-s41992" xml:space="preserve">Quoniam Meridianus A C, per polos Verticalis A, C, &amp; </s>
  <s xml:id="echoid-s41993" xml:space="preserve">per F, polum Aequatoris ductus ſecat, <lb/>
<anchor type="note" xlink:label="note-0657-01a" xlink:href="note-0657-01"/>
per propoſ. </s>
  <s xml:id="echoid-s41994" xml:space="preserve">9. </s>
  <s xml:id="echoid-s41995" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s41996" xml:space="preserve">2. </s>
  <s xml:id="echoid-s41997" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s41998" xml:space="preserve">ſegmenta Verticalis, &amp; </s>
  <s xml:id="echoid-s41999" xml:space="preserve">Aequatoris B E D, B G D, quæ quidem, per <lb/>propoſ. </s>
  <s xml:id="echoid-s42000" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42001" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42002" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42003" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42004" xml:space="preserve">ſemicirculi ſunt, bifariam, erunt ſegmenta E B, E D, G B, G D, quadran <lb/>tes) deſcribemus horas æquales tam à mer. </s>
  <s xml:id="echoid-s42005" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42006" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42007" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42008" xml:space="preserve">quàm ab or. </s>
  <s xml:id="echoid-s42009" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42010" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s42011" xml:space="preserve">vnica apertura cir-<lb/>
<anchor type="note" xlink:label="note-0657-02a" xlink:href="note-0657-02"/>
cini hoc modo. </s>
  <s xml:id="echoid-s42012" xml:space="preserve">Quoniam circuli horarij à mer. </s>
  <s xml:id="echoid-s42013" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42014" xml:space="preserve">med.</s>
  <s xml:id="echoid-s42015" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s42016" xml:space="preserve">per F, polum Aequatoris ducuntur, <lb/>vt propoſ. </s>
  <s xml:id="echoid-s42017" xml:space="preserve">9. </s>
  <s xml:id="echoid-s42018" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42019" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42020" xml:space="preserve">demonſtrauimus, tranſibit viciſſim, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s42021" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42022" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42023" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42024" xml:space="preserve">Theod. <lb/></s>
  <s xml:id="echoid-s42025" xml:space="preserve">Aequator per eorum polos. </s>
  <s xml:id="echoid-s42026" xml:space="preserve">Omnes ergo polos habent in Aequatore. </s>
  <s xml:id="echoid-s42027" xml:space="preserve">Quare diſtentis circini <lb/>cruribus ad interuallum quadrantis A B, vel G B, vel F G, circuli maximi, ſi alter pes ſtatuatur in <lb/>ſingulis punctis diuiſionum Aequatoris B G D, &amp; </s>
  <s xml:id="echoid-s42028" xml:space="preserve">alter in Aequatote firmetur, nem pe in punctis, <lb/>quæ ſex horis, vel quadrante à prioribus abſunt, deſcribentur omnes circuli horarii ab hora 6. </s>
  <s xml:id="echoid-s42029" xml:space="preserve">à <lb/>med. </s>
  <s xml:id="echoid-s42030" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42031" xml:space="preserve">vſque ad horam 6. </s>
  <s xml:id="echoid-s42032" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42033" xml:space="preserve">inter tropicos contenti. </s>
  <s xml:id="echoid-s42034" xml:space="preserve">Inter hos enim circuli horarii dun-<lb/>
<anchor type="note" xlink:label="note-0657-03a" xlink:href="note-0657-03"/>
taxat erunt delineandi: </s>
  <s xml:id="echoid-s42035" xml:space="preserve">Si tamen producerentur, tranſirent omnes per polum F. </s>
  <s xml:id="echoid-s42036" xml:space="preserve">Exempli gra-<lb/>tia, ex G, tanquam polo, ad interuallum G D, vel G B, vel G F, (quod interuallum mutari non de-<lb/>bet, donec omnes horarii circuli, vel quicunque alii maximi deſcripti ſint) deſcribentur arcus cir <lb/>culi horæ 6. </s>
  <s xml:id="echoid-s42037" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42038" xml:space="preserve">noc &amp; </s>
  <s xml:id="echoid-s42039" xml:space="preserve">mer. </s>
  <s xml:id="echoid-s42040" xml:space="preserve">terminati inter Aequatorem, &amp; </s>
  <s xml:id="echoid-s42041" xml:space="preserve">tropicum ♋. </s>
  <s xml:id="echoid-s42042" xml:space="preserve">Ponendo poſtea cir <lb/>cini pedem vnum in proximo puncto Aequatoris à G, verſus B, deſcribentur altero pede arcus cir <lb/>culi horæ 7. </s>
  <s xml:id="echoid-s42043" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42044" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42045" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42046" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42047" xml:space="preserve">quorum prior tranſibit per proximum punctum Aequatoris in-<lb/>fra D, poſterior vero tranſiret per proximum punctum Aequatoris ſupra B, ſi integra ſphæra eſſet. <lb/></s>
  <s xml:id="echoid-s42048" xml:space="preserve">Sic etiam ſtatuendo vnum pedem circini in ſecundo puncto à G, verſus B, deſcribetur altero ho-<lb/>ra 8. </s>
  <s xml:id="echoid-s42049" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42050" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42051" xml:space="preserve">tranſiens per ſecundum punctum infra D, &amp; </s>
  <s xml:id="echoid-s42052" xml:space="preserve">ita deinceps, ſtatuendo polos circu-<lb/>lorum per puncta quadrantis G D, tranſeuntium in quadrante G B, aliorum autem in quadrante <lb/>
<anchor type="note" xlink:label="note-0657-04a" xlink:href="note-0657-04"/>
G D, ita vt deſcribantur eadem circini apertura etiam arcus inter Horizontem, &amp; </s>
  <s xml:id="echoid-s42053" xml:space="preserve">tropicum ♋, <lb/>licet Aequatorem non ſecent in hemiſphærio, vt contingit in hora 5. </s>
  <s xml:id="echoid-s42054" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42055" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42056" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42057" xml:space="preserve">7. </s>
  <s xml:id="echoid-s42058" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42059" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s42060" xml:space="preserve">c.</s>
  <s xml:id="echoid-s42061" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2087" type="float" level="2" n="2">
<note position="left" xlink:label="note-0657-01" xlink:href="note-0657-01a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0657-02" xlink:href="note-0657-02a" xml:space="preserve">Deſcripiio ho-<lb/>rarum à mer. <lb/>&amp; med. noc. in <lb/>hemiſphærio <lb/>concauo.</note>
<note position="left" xlink:label="note-0657-03" xlink:href="note-0657-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0657-04" xlink:href="note-0657-04a" xml:space="preserve">30</note>
</div>
<note position="right" xml:space="preserve">Deſeript@@ h@-<lb/>rarum ab occ. <lb/>&amp; or. in h@mi@ <lb/>ſphærio conca-<lb/>uo.</note>
<p>
  <s xml:id="echoid-s42062" xml:space="preserve">RVRSVS quia circuli horarum ab occ. </s>
  <s xml:id="echoid-s42063" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42064" xml:space="preserve">or. </s>
  <s xml:id="echoid-s42065" xml:space="preserve">polos habent in parallelo R S Q, per verticem <lb/>loci ducto, vt propoſ. </s>
  <s xml:id="echoid-s42066" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42067" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42068" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42069" xml:space="preserve">demonſtrauimus, atque adeo &amp; </s>
  <s xml:id="echoid-s42070" xml:space="preserve">in parallelo O E P, oppoſito, cum <lb/>huius puncta ſingula ſingulis punctis illius opponantur; </s>
  <s xml:id="echoid-s42071" xml:space="preserve">ſi eadem circini apertura manente, vnus <lb/>pes in ſingulis punctis Aequatoris ſtatuatur, &amp; </s>
  <s xml:id="echoid-s42072" xml:space="preserve">alter pes in parallelo O E P, vel in R S Q , quando <lb/>non poteſt ſtatui in O E P, deſcribentur per puncta Aequatoris arcus circulorum horarum ab occ. <lb/></s>
  <s xml:id="echoid-s42073" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42074" xml:space="preserve">or. </s>
  <s xml:id="echoid-s42075" xml:space="preserve">Diuident autem poli horum circulorum parallelos O E P, Q S R, in partes æquales, exi-<lb/>ſtentq́ue in illis punctis, vbi à circulis horarum à mer. </s>
  <s xml:id="echoid-s42076" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42077" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42078" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42079" xml:space="preserve">diuiduntur in ſpatia horaria <lb/>æqualia, vt propoſ. </s>
  <s xml:id="echoid-s42080" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42081" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42082" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42083" xml:space="preserve">oſtendimus: </s>
  <s xml:id="echoid-s42084" xml:space="preserve">propterea quòd cum circuli horarum ab or. </s>
  <s xml:id="echoid-s42085" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42086" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0657-06a" xlink:href="note-0657-06"/>
tranſeant in Aequatore per polos circulorum horarum à mer. </s>
  <s xml:id="echoid-s42087" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42088" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42089" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42090" xml:space="preserve">hi viciſſim per illo-<lb/>rum polos ducantur, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s42091" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42092" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42093" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42094" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42095" xml:space="preserve">Cum ergo illorum poli in parallelis <lb/>O E P, Q S R, exiſtant, erunt omnino poli illa puncta, vbi dicti paralleli à circulis horarum à <lb/>mer. </s>
  <s xml:id="echoid-s42096" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42097" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42098" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42099" xml:space="preserve">ſecantur, ita vt polus cuiuslibet circuli horarii ab or. </s>
  <s xml:id="echoid-s42100" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42101" xml:space="preserve">ſit in eo puncto <lb/>paralleli O E P, vel Q S R, per quod circulus horarius à mer. </s>
  <s xml:id="echoid-s42102" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42103" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42104" xml:space="preserve">ab illo ſex horis in <lb/>Aequatore diſtans tranſit. </s>
  <s xml:id="echoid-s42105" xml:space="preserve">Vnde vt hi poli expedite habeantur, producendi erunt circuli hora-<lb/>rum à mer. </s>
  <s xml:id="echoid-s42106" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42107" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42108" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42109" xml:space="preserve">vſque ad parallelos O E P, Q S R, occultè tamen. </s>
  <s xml:id="echoid-s42110" xml:space="preserve">Vel certe ex G, ad in-<lb/>teruallum quadrantis G F, arcus circuli horæ 6@ à mer. </s>
  <s xml:id="echoid-s42111" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42112" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42113" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42114" xml:space="preserve">deſcribendus, atque vterq; <lb/></s>
  <s xml:id="echoid-s42115" xml:space="preserve">quadrans E T, E V, in ſex partes æquales diuidendus pro polis circulorum horarum ab or. </s>
  <s xml:id="echoid-s42116" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42117" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s42118" xml:space="preserve"><lb/>ac denique hæc puncta beneficio circini ex E, accepta transferenda in parallelum Q S R, ex S, <lb/>
<anchor type="note" xlink:label="note-0657-07a" xlink:href="note-0657-07"/>
pro polis aliorum circulorum, qui polos non habent in portione O E P. </s>
  <s xml:id="echoid-s42119" xml:space="preserve">Exempli gratia, E, polus <lb/>eſt Horizontis, ſiue circuli horæ 24. </s>
  <s xml:id="echoid-s42120" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s42121" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42122" xml:space="preserve">proximum deinde punctũ in parallelo O E P, <lb/>ab E, verſus O, polus eſt circuli horæ 23. </s>
  <s xml:id="echoid-s42123" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42124" xml:space="preserve">proximum vero punctum ab E, verſus P, polus <lb/>eſt circuli horæ 1. </s>
  <s xml:id="echoid-s42125" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s42126" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42127" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s42128" xml:space="preserve">In exemplo deſcriptæ ſunt tantum horæ à mer. </s>
  <s xml:id="echoid-s42129" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42130" xml:space="preserve">med. <lb/></s>
  <s xml:id="echoid-s42131" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42132" xml:space="preserve">atque horæ ab occ.</s>
  <s xml:id="echoid-s42133" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2088" type="float" level="2" n="3">
<note position="left" xlink:label="note-0657-06" xlink:href="note-0657-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0657-07" xlink:href="note-0657-07a" xml:space="preserve">50</note>
</div>
<note position="right" xml:space="preserve">Deſcriptio ho-<lb/>rarum inæqua-<lb/>lium in hemi-<lb/>ſphærio couca-<lb/>uo.</note>
<p>
  <s xml:id="echoid-s42134" xml:space="preserve">PRO deſcriptione denique horarum inæqualium, diuidendæ ſunt ſingulæ portiones tropi-<lb/>corum H I, H K, L M, L N, in ſenas partes æquales, &amp; </s>
  <s xml:id="echoid-s42135" xml:space="preserve">per terna puncta, (quorum vnum eſt in tro <lb/>pico ♋, alterum in Aequatore, &amp; </s>
  <s xml:id="echoid-s42136" xml:space="preserve">tertium in tropico ♑,) æqualiter à Meridiano remota circuli <lb/>horarum inæqualium deſcribendi. </s>
  <s xml:id="echoid-s42137" xml:space="preserve">Erit autem polus cuiuslibet circuli in circulo horario à mer. <lb/></s>
  <s xml:id="echoid-s42138" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42139" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42140" xml:space="preserve">qui ſex horis ab eo abeſt in Aequatore. </s>
  <s xml:id="echoid-s42141" xml:space="preserve">Quoniam enim quilibet circulus horarum <lb/>inæqualium tranſit in Aequatore per polum circuli horarii à mer. </s>
  <s xml:id="echoid-s42142" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42143" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42144" xml:space="preserve">ſex horis ab eo
<pb o="642" file="0658" n="658" rhead="GNOMONICES"/>
diſtantis, tranſibit hic, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s42145" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42146" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42147" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42148" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42149" xml:space="preserve">viciſſim per illius polũ. </s>
  <s xml:id="echoid-s42150" xml:space="preserve">Vnde ſi eadem <lb/>
<anchor type="note" xlink:label="note-0658-01a" xlink:href="note-0658-01"/>
circini apertura manente, vnus pes ſtatuatur in quolibet puncto tropici ♋, vel ♑, &amp; </s>
  <s xml:id="echoid-s42151" xml:space="preserve">alter pona-<lb/>tur in circulo illius horæ à mer. </s>
  <s xml:id="echoid-s42152" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42153" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42154" xml:space="preserve">occulte producti, qui ſex horis in Aequatore ab-<lb/>eſt à puncto, quod puncto accepto in tropico reſpondet, habebitur polus illius circuli horarum <lb/>inæqualium. </s>
  <s xml:id="echoid-s42155" xml:space="preserve">Verbi gratia. </s>
  <s xml:id="echoid-s42156" xml:space="preserve">Quoniam circulus horæ 1. </s>
  <s xml:id="echoid-s42157" xml:space="preserve">inæqualis ducendus eſt per primum pun-<lb/>ctum Aequatoris infra D, &amp; </s>
  <s xml:id="echoid-s42158" xml:space="preserve">per prima puncta tropicorum infra I, &amp; </s>
  <s xml:id="echoid-s42159" xml:space="preserve">M; </s>
  <s xml:id="echoid-s42160" xml:space="preserve">abeſt autem circulus ho-<lb/>ræ 1. </s>
  <s xml:id="echoid-s42161" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42162" xml:space="preserve">in Aequatore ſex horis à primo puncto infra D. </s>
  <s xml:id="echoid-s42163" xml:space="preserve">Igitur ſi vnus pes circini ſtatuatur in <lb/>primo puncto tropici infra I, vel M, &amp; </s>
  <s xml:id="echoid-s42164" xml:space="preserve">alter extendatur vſque ad circulum horæ 1. </s>
  <s xml:id="echoid-s42165" xml:space="preserve">à mei<unsure/>. </s>
  <s xml:id="echoid-s42166" xml:space="preserve">occultè <lb/>productum, habebitur in hoc circulo polus illius circuli, &amp; </s>
  <s xml:id="echoid-s42167" xml:space="preserve">ſic de cæteris.</s>
  <s xml:id="echoid-s42168" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2089" type="float" level="2" n="4">
<note position="left" xlink:label="note-0658-01" xlink:href="note-0658-01a" xml:space="preserve">Tacilis inuen-<lb/>tio polorum, ex <lb/>quibus circuli <lb/>horatum in-<lb/>æqualium de-<lb/>ſcribuntur.</note>
</div>
<p>
  <s xml:id="echoid-s42169" xml:space="preserve">STYLVS horas indicans erit axis mundi æqualis ſemidiametro hemiſphærij, qui ita in F, <lb/>
<anchor type="note" xlink:label="note-0658-02a" xlink:href="note-0658-02"/>
<anchor type="note" xlink:label="note-0658-03a" xlink:href="note-0658-03"/>
polo figendus eſt, vt eius punctum extremum centrum hemiſphærij occupet. </s>
  <s xml:id="echoid-s42170" xml:space="preserve">quod tum demum <lb/>factum erit, cum extenſis in orificio hemiſphærii duobus filis ab A, in C, &amp; </s>
  <s xml:id="echoid-s42171" xml:space="preserve">á B, in D, extremum <lb/>punctum in communi interſectione filorum collocatum erit. </s>
  <s xml:id="echoid-s42172" xml:space="preserve">Poteſt idem ſtylus in quouis pun-<lb/>cto figi, ſed tunc non erit axis mundi. </s>
  <s xml:id="echoid-s42173" xml:space="preserve">Accommodandum quoque erit inſtrumentum in circulo <lb/>Meridiano vna cum acu Magnete illita, ita tamen, vt planum inſtrumenti Horizonti æquidiſtet.</s>
  <s xml:id="echoid-s42174" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2090" type="float" level="2" n="5">
<note position="left" xlink:label="note-0658-02" xlink:href="note-0658-02a" xml:space="preserve">Stylus horas <lb/>monſtrans.</note>
<note position="left" xlink:label="note-0658-03" xlink:href="note-0658-03a" xml:space="preserve">10</note>
</div>
<p>
  <s xml:id="echoid-s42175" xml:space="preserve">SI LVBET, poterunt quoque in hoc hemiſphærio deſcribi omnia illa, quæ in planis ho-<lb/>
<anchor type="note" xlink:label="note-0658-04a" xlink:href="note-0658-04"/>
rologiis lib. </s>
  <s xml:id="echoid-s42176" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42177" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42178" xml:space="preserve">3. </s>
  <s xml:id="echoid-s42179" xml:space="preserve">deſcripſimus. </s>
  <s xml:id="echoid-s42180" xml:space="preserve">Nam paralleli longitudinum dierum, &amp; </s>
  <s xml:id="echoid-s42181" xml:space="preserve">latitudinum ciuita-<lb/>tum delineabuntur ex polo F, vt paralleli ſignorum, ſi eorum declinationes à G, ſupputentur in <lb/>Meridiano, verſus H, quidem, ſi fuerint boreales, at verſus L, ſi auſtrales. </s>
  <s xml:id="echoid-s42182" xml:space="preserve">Verticales autem cir-<lb/>culi deſcribentur per E, ex ſingulis gradibus Horizontis A B C D, qui per eorum polos tranſit, <lb/>
<anchor type="note" xlink:label="note-0658-05a" xlink:href="note-0658-05"/>
ex ſcholio propoſ. </s>
  <s xml:id="echoid-s42183" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42184" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42185" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42186" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42187" xml:space="preserve">cum viciſſim Verticales per Horizontis polum E, tranſeant. <lb/></s>
  <s xml:id="echoid-s42188" xml:space="preserve">Paralleli vero Horizontis deſcribentur ex E, polo Horizõtis per ſingulos gradus Meridiani A C, <lb/>vel Verticalis B D. </s>
  <s xml:id="echoid-s42189" xml:space="preserve">Meridiani, hoc eſt, circuli longitudinum ciuitatum, ducentur per ſingulos <lb/>gradus Aequatoris, veluti circuli horarum à mer. </s>
  <s xml:id="echoid-s42190" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42191" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42192" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42193" xml:space="preserve">ſi diuiſio Aequatoris in gradus ini-<lb/>tium ſumat ab eo puncto, quod terminat longitudinem loci à G, verſus B, computatam. </s>
  <s xml:id="echoid-s42194" xml:space="preserve">Circuli <lb/>domorum cæleſtium ſecundum ſententiam loan. </s>
  <s xml:id="echoid-s42195" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s42196" xml:space="preserve">deſcribentur per diuiſiones Aequa-<lb/>toris, ſtatuendo pro polis ipſorum pedem circini immobilem in Verticali B D, ita vt omnes tran-<lb/>ſeant per puncta A, C, vbi Meridianus Horizontem interſecat: </s>
  <s xml:id="echoid-s42197" xml:space="preserve">Ex ſententia vero Campani per <lb/>diuiſiones Verticalis, ſtatuendo quoque pro polis ipſorum pedem circini immobilem in Vertica-<lb/>li circulo, ita vt rurſus tranſeant per puncta A, C. </s>
  <s xml:id="echoid-s42198" xml:space="preserve">Hi enim circuli ſecundum Ioan. </s>
  <s xml:id="echoid-s42199" xml:space="preserve">Regiom. </s>
  <s xml:id="echoid-s42200" xml:space="preserve">di-<lb/>
<anchor type="note" xlink:label="note-0658-06a" xlink:href="note-0658-06"/>
uidunt Aequatorem in 12. </s>
  <s xml:id="echoid-s42201" xml:space="preserve">partes æquales, ſecundum vero Campanum Verticalis circulus ab eiſ-<lb/>dem in 12. </s>
  <s xml:id="echoid-s42202" xml:space="preserve">æquales partes ſecatur. </s>
  <s xml:id="echoid-s42203" xml:space="preserve">Signa denique aſcendentia, id eſt, Eclipticæ poſitiones variæ, <lb/>initijs ſignorum orientibus, depingentur hac ratione. </s>
  <s xml:id="echoid-s42204" xml:space="preserve">Ex tabulis 3. </s>
  <s xml:id="echoid-s42205" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42206" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42207" xml:space="preserve">poſitis in propoſ. </s>
  <s xml:id="echoid-s42208" xml:space="preserve">9. </s>
  <s xml:id="echoid-s42209" xml:space="preserve">lib. <lb/></s>
  <s xml:id="echoid-s42210" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42211" xml:space="preserve">aut aliis ſimilibus ex doctrina dictæ propoſ. </s>
  <s xml:id="echoid-s42212" xml:space="preserve">ad datam loci latitudinem ſupputatis, accipiatur <lb/>hora, qua quoduis ſignum oritur, Sole exiſtente in principio ♋, vel ♑, prout illa hora in tropico <lb/>♋, aut ♑, continebitur in hemiſphærio concauo, eaq́ue in Aequatore numeretur à G, verſus qui-<lb/>dem D, ſi antemeridiana eſt, ſi vero pomeridiana, verſus B: </s>
  <s xml:id="echoid-s42213" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42214" xml:space="preserve">per finem numerationis (poſito <lb/>pede circini immobili in puncto Aequatoris, quod quadrante abeſt à fine numerationis) deſcriba-<lb/>tur circulus maximus occultus ſecans tropicum ♋, aut ♑, (prout hora ſumpta eſt, Sole in ♋, exi-<lb/>ſtente, aut in ♑.) </s>
  <s xml:id="echoid-s42215" xml:space="preserve">in puncto, per quod ad interuallum quadrantis in illo circulo occulto acceptũ <lb/>
<anchor type="note" xlink:label="note-0658-07a" xlink:href="note-0658-07"/>
circulus maximus deſcribatur, referet is Eclipticæ ſitum, dum propoſitum ſignum<unsure/> oritur, adeo <lb/>vt, extremitate vmbræ in hunc circulum cadente, ſignum illud ſupra Horizontem incipiat oriri. <lb/></s>
  <s xml:id="echoid-s42216" xml:space="preserve">Quoniam enim, vmbra cadente in illud punctum notatum in tropico ♋, vel ♑, monſtratur ho-<lb/>ra, qua datum ſignum oritur, exiſtit autem radius Solis per centrum tranſiens in plano Eclipticæ, <lb/>tranſibit neceſſario Ecliptica per illud punctum tropici ♋, vel ♑; </s>
  <s xml:id="echoid-s42217" xml:space="preserve">atque adeo in eo puncto tropi-<lb/>cum tanget, quemadmodum &amp; </s>
  <s xml:id="echoid-s42218" xml:space="preserve">in cælo. </s>
  <s xml:id="echoid-s42219" xml:space="preserve">Cum ergo, per propoſ. </s>
  <s xml:id="echoid-s42220" xml:space="preserve">3. </s>
  <s xml:id="echoid-s42221" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42222" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42223" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42224" xml:space="preserve">circulus vltimo <lb/>deſcriptus tropicum in eo puncto tangat, propterea quòd tam ipſe, quàm tropicus eo in puncto <lb/>ſecet circulum illum maximum occultum, in quo vtriuſque polus exiſtit, erit omnino circulus <lb/>hic Ecliptica. </s>
  <s xml:id="echoid-s42225" xml:space="preserve">Hoc artificio omia ſigna aſcendentia deſcribentur. </s>
  <s xml:id="echoid-s42226" xml:space="preserve">Signum ♈, tanget tropicum <lb/>♑, in L, habebitq́ue polum in Meridiano diſtantem quadrante à puncto L. </s>
  <s xml:id="echoid-s42227" xml:space="preserve">Signum vero ♎, tro-<lb/>
<anchor type="note" xlink:label="note-0658-08a" xlink:href="note-0658-08"/>
picum ♋, tanget in H, &amp; </s>
  <s xml:id="echoid-s42228" xml:space="preserve">vtrumque per puncta B, &amp; </s>
  <s xml:id="echoid-s42229" xml:space="preserve">D, tranſibit. </s>
  <s xml:id="echoid-s42230" xml:space="preserve">Signum autem ♋, tanget tropi-<lb/>cum ♋, in I, &amp; </s>
  <s xml:id="echoid-s42231" xml:space="preserve">tropicum ♑, in N. </s>
  <s xml:id="echoid-s42232" xml:space="preserve">Signum denique ♑, tropicum ♋, tanget in K, &amp; </s>
  <s xml:id="echoid-s42233" xml:space="preserve">tropicum ♑, <lb/>in M, vt ex dictis tabellis colligitur.</s>
  <s xml:id="echoid-s42234" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2091" type="float" level="2" n="6">
<note position="left" xlink:label="note-0658-04" xlink:href="note-0658-04a" xml:space="preserve">Deſcriptio pa@ <lb/>rallelorum lon <lb/>gitudinum die-<lb/>rum, &amp; latitu-<lb/>dinum ciui-<lb/>tatum, Ve@tica <lb/>lium circulorũ, <lb/>&amp; parallelorum <lb/>Horizon is; Me <lb/>ridianorũ; Do-<lb/>morum cæle <lb/>ſtium, &amp; aſcen-<lb/>dentium ſigno-<lb/>rum in hemi-<lb/>ſphærio conca-<lb/>uo.</note>
<note position="left" xlink:label="note-0658-05" xlink:href="note-0658-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0658-06" xlink:href="note-0658-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0658-07" xlink:href="note-0658-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0658-08" xlink:href="note-0658-08a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s42235" xml:space="preserve">ITAQVE, vt vides, facili negotio omnia illa, quæ in horologiis planis lib. </s>
  <s xml:id="echoid-s42236" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42237" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42238" xml:space="preserve">3. </s>
  <s xml:id="echoid-s42239" xml:space="preserve">deſcripſi-<lb/>mus, in hemiſphærio cõcauo delineantur. </s>
  <s xml:id="echoid-s42240" xml:space="preserve">Vnde ſi in aliqua tabula plana hemiſphæriũ concauũ, <lb/>
<anchor type="note" xlink:label="note-0658-09a" xlink:href="note-0658-09"/>
in quo omnia ſint deſcripta, affigatur, ducaturq́ue in ea linea meridiana, reſpondens Meridiano <lb/>hemiſphærii, (quod facile fiet, ſi tabula Soli expoſita vna cum hemiſphærio circumuertatur, do-<lb/>nec vmbra ſtyli in Meridianum circulum cadat. </s>
  <s xml:id="echoid-s42241" xml:space="preserve">Si enim tunc obſeruetur in tabula vmbra alicuius <lb/>ſtyli ad angulos rectos in fixi, in cuius medio duo puncta notentur, erit recta per hæc puncta du-<lb/>cta linea meridiana) deſcribetur ex vmbra ſtyli horologium quodcunque (ſi habeatur ratio ſitus <lb/>eius proprij, quod ad inclinationem ad Horizontem, &amp; </s>
  <s xml:id="echoid-s42242" xml:space="preserve">ad declinationem à Verticali attinet, vt
<pb o="643" file="0659" n="659" rhead="LIBER OCTAVVS."/>
cap. </s>
  <s xml:id="echoid-s42243" xml:space="preserve">vltimo præcedentis lib. </s>
  <s xml:id="echoid-s42244" xml:space="preserve">diximus) multò commodius, &amp; </s>
  <s xml:id="echoid-s42245" xml:space="preserve">fortaſſe accuratius, quàm ex horo-<lb/>logio horizontali, tum quia clarius, ac diſtinctius vmbræ extremum diſcernitur in hemiſphærio <lb/>concauo, quàm in horologio plano, tum etiam quia facilius, &amp; </s>
  <s xml:id="echoid-s42246" xml:space="preserve">accuratius omnia in hemiſphærio <lb/>concauo deſcribuntur, quàm in plano horologio, vt manifeſtum eſt.</s>
  <s xml:id="echoid-s42247" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2092" type="float" level="2" n="7">
<note position="left" xlink:label="note-0658-09" xlink:href="note-0658-09a" xml:space="preserve">Quomedo be-<lb/>neficio horolo-<lb/>gii hemiſphæri-<lb/>ci@concaui ex <lb/>vmbra in quo-<lb/>uis plano hoto <lb/>logia deſcriban <lb/>tur.</note>
</div>
</div>
<div xml:id="echoid-div2094" type="section" level="1" n="531">
<head xml:id="echoid-head560" style="it" xml:space="preserve">DE HOROLOGII CONSTRVCTIONE IN CYLINDRO <lb/>conucxo. CAP. V.</head>
<p>
  <s xml:id="echoid-s42248" xml:space="preserve">VT planior fiat horarum deſcriptio in cylindro conuexo, (quæ quidem per vmbras verſas, <lb/>
<anchor type="note" xlink:label="note-0659-01a" xlink:href="note-0659-01"/>
altitudinesve Solis tota perficitur) deſcribemus horas in plano aliquo, vt poſtea eas in cylin <lb/>drum transferamus. </s>
  <s xml:id="echoid-s42249" xml:space="preserve">Sed ante omnia inueſtigandę ſunt altitudines Solis ſupra Horizontem pro <lb/>ſingulis horis, Sole in initijs ſignorum exiſtente. </s>
  <s xml:id="echoid-s42250" xml:space="preserve">quæ ita ſe habent, ad latitudinem grad. </s>
  <s xml:id="echoid-s42251" xml:space="preserve">42. <lb/></s>
  <s xml:id="echoid-s42252" xml:space="preserve">ſupputatæ pro horis à mer. </s>
  <s xml:id="echoid-s42253" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42254" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42255" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s42256" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2094" type="float" level="2" n="1">
<note position="left" xlink:label="note-0659-01" xlink:href="note-0659-01a" xml:space="preserve">10</note>
</div>
<note position="right" xml:space="preserve"> <lb/>Horæ # 12 # 1 # 2 # 3 # 4 # 5 # 6 # 7 # poſt meridiem. <lb/>Horæ # # 11 # 10 # 9 # 8 # 7 # 6 # 5 # poſt med. noc. <lb/>########## Altitudines Solis ſupra Horizontem in ſignorum initĳs. <lb/>Signa. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # Signa. <lb/>♋ # 71. 30. # 67. 41 # 58. 59 # 48. 29 # 37. 25 # 26. 19 # 15. 29 # 5. 11 # ♋ <lb/>♌ # 68. 12. # 64. 47 # 56. 37 # 46 24 # 35. 26 # 24. 18 # 13. 22 # 2. 54 # ♊ <lb/>♍ # 59. 30. # 56. 48 # 49. 49 # 40. 25 # 29. 50 # 18. 46 # 7. 40 # # ♉ <lb/>♎ # 48. 0. # 45. 52 # 40. 4 # 31. 42 # 21. 49 # 11. 5 # 0. 0 # # ♈ <lb/>♏ # 36. 30. # 34. 45 # 29. 49 # 22. 26 # 13. 20 # 3. 10 # # # ♓ <lb/>
♐ # 27. 48 # 26. 16 # 21. 54 # 15. 12 # 6. 45 # # # # ♒
♑ # 24 30 # 23. 3 # 18. 52 # 12. 25 # 4. 14 # # # # ♑
</note>
<p>
  <s xml:id="echoid-s42257" xml:space="preserve">ALTITVDINES autem Solis ſupra Horizontẽ inuentę pro horis ab occ. </s>
  <s xml:id="echoid-s42258" xml:space="preserve">Sole non in ini-<lb/>tijs ſignorum, excepto ♋, &amp; </s>
  <s xml:id="echoid-s42259" xml:space="preserve">♑, Item ♈, &amp; </s>
  <s xml:id="echoid-s42260" xml:space="preserve">♎, exiſtente, ſed in parallelis, quorum arcus diurni <lb/>complectuntur determinatum numerum horarum, nempe 15. </s>
  <s xml:id="echoid-s42261" xml:space="preserve">14. </s>
  <s xml:id="echoid-s42262" xml:space="preserve">13. </s>
  <s xml:id="echoid-s42263" xml:space="preserve">12. </s>
  <s xml:id="echoid-s42264" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42265" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42266" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42267" xml:space="preserve">9. </s>
  <s xml:id="echoid-s42268" xml:space="preserve">vna cum <lb/>declinationibus illorum parallelorum, ex doctrina propoſ. </s>
  <s xml:id="echoid-s42269" xml:space="preserve">33. </s>
  <s xml:id="echoid-s42270" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42271" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42272" xml:space="preserve">ad latitudinem grad. </s>
  <s xml:id="echoid-s42273" xml:space="preserve">42. <lb/></s>
  <s xml:id="echoid-s42274" xml:space="preserve">ſupputatis, ita ſe habent.</s>
  <s xml:id="echoid-s42275" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">40</note>
<note position="right" xml:space="preserve"> <lb/>########### Altitudin@s Solis ſupra Horizontem pro horis ab occ. in arcu horarum 15. \\ qui declinat in Boream Grad. 23. Min. 2. <lb/>Horæ # 24 # 23. # 22. # 21. # 20. # 19. # 18. # 17. # 16 {1/2}. # pomeridianæ. <lb/>Horæ # 9 # 10 # 11. # 12. # 13. # 14. # 15. # 16. # 16 {1/2}. # antemeridianę<unsure/>. <lb/># G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>Alti<unsure/>tu # 0. 0. # 9. 56 # 20. 33. # 31. 34. # 42. 42. # 53. @3. # 63. 20. # 70. 2. # 71. 2. # dines Solis. <lb/>
########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu horarum 14. \\ qui declinat in Boream Grad. 16. Min. 2.
Horæ # 24. # 23. # 22. # 21. # 20. # 19. # 18. # 17. # # pomeridianę.
Horæ # 10. # 11. # 12. # 13. # 14. # 15. # 16. # 17. # # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu- # 0 0. # 10. 39 # 21. 42. # 32. 49. # 43. 37. # 53. 27. # 61. 1. # 64. 2. # # dines Solis.
</note>
<pb o="644" file="0660" n="660" rhead="GNOMONICES"/>
<note position="right" xml:space="preserve"> <lb/>########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu horarum 13. \\ qui in Boream declinat Grad. 8. Min. 15. <lb/>Horæ # 24. # 23. # 22. # 21. # 20. # 19. # 18. # 17 {1/2}. # # pomeridianæ. <lb/>Horæ # 11. # 12. # 13. # 14. # 15. # 16. # 17. # 17 {1/2}. # # antemeridianę. <lb/># G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. <lb/>Allttu- # 0. 0. # 11. 4. # 22. 11. # 32. 56. # 42. 48. # 50. 51. # 55. 36. # 56. 15. # # dines Solis. <lb/>########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu \\ horarum 12. hoc eſt, in Aequatore. <lb/>
Horæ # 24. # 23. # 22. # 21. # 20. # 19. # 18. # # # pomeridianæ.
Horæ # 12. # 13. # 14. # 15. # 16. # 17. # 18. # # # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu- # 0. 0. # 11. 5. # 21. 49. # 31. 42. # 40. 4. # 45. 52. # 48. 0 # # # dines Solis.
########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu horarum 11. \\ qui in Auſtrum declinat Grad. 8. Min. 15.
Horæ # 24. # 23. # 22. # 21. # 20. # 19. # 18 {1/2}. # # # pomeridianæ.
Horæ # 13. # 14. # 15. # 16. # 17. # 18. # 18 {1/2}. # # # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu # 0. 0. # 10. 41. # 20. 30. # 29. 10. # 35. 42. # 39. 17. # 39. 45. # # # dines Solis.
########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu horarum 10. \\ qui declinat in Anſtrum Grad. 16. Min. 2.
Horæ # 24. # 23. # 22. # 21. # 20. # 19. # # # # pomeridianæ.
Horæ # 14. # 15. # 16. # 17. # 18. # 19. # # # # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu # 0. 0. # 9. 55 # 18. 41. # 25. 42. # 30. 20 # 31. 58 # # # # dines Solis.
########### Altitudines Solis ſupra Horizontem pro horis ab occ. in arcu horarum 9. \\ qui in Auſtrum d@clinat Grad. 23. Min. 2.
Horæ # 24. # 23. # 22. # 21. # 20. # 19 {1/2} # # # # pomeridianæ.
Horæ # 15. # 16. # 17. # 18. # 19. # 19 {1/2}. # # # # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu- # 0. 0. # 8. 53. # 16. 18. # 21. 43. # 24. 36 # 24. 58. # # # # dines Solis.
########### Altitudines Solis ſupra Horizontem pro horis ab occ. in tropico ♋.
Horæ # 24. # 23. # 22. # 21. # 20. # 19. # 18. # 17. # 16 {28/60}. # pomeridianæ.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu- # 0. 0. # 9. 54. # 20. 29. # 31. 28 # 42. 36. # 53. 30. # 63. 24. # 70. 20. # 71. 30. # dines Solis.
Horæ # 9. # 10. # 11. # 12. # 13. # 14. # 15. # 16. # 16 {28/60}. # antemeridianę.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitu # 0. 40. # 10. 35. # 21. 12. # 32. 13. # 43. 21. # 54. 12. # 63. 59 # 70. 36. # 71. 30. # dines Solis
########### Altitudines Solis ſupra Horizontem prohoris ab occ. in tropico ♑.
Horæ # 24. # 23. # 22. # 21. # 20. # 19 {32/60}. # 19 # 18. # 17. # 16.
# G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M.
Altitudines. # 0. 0 # 8. 47. # 16. 7. # 21. 25. # 24. 11. # 24. 30. # 24. 5. # 21. 8. # 15. 41. # 8. 14
</note>
<pb o="645" file="0661" n="661" rhead="LIBER OCTAVVS."/>
<p>
  <s xml:id="echoid-s42276" xml:space="preserve">SIT ergo plana ſuperficies A B, in qua horæ depingendæ ſunt: </s>
  <s xml:id="echoid-s42277" xml:space="preserve">Et quoniam vmbræ verſæ, So-<lb/>le exiſtente in ♋, longiſſimæ ſunt, &amp; </s>
  <s xml:id="echoid-s42278" xml:space="preserve">in ♑, breuiſſimæ, non abs re erit, ſi duo ſtyli eligantur <lb/>inæquales, quorum minor horas indicet, Sole in borealibus ſignis exiſtente, maior vero horas <lb/>monſtret, Sole exiſtente in ſignis auſtralibus. </s>
  <s xml:id="echoid-s42279" xml:space="preserve">Itaque pro ſignis borealibus conſtruatur parallelo-<lb/>grammum rectangulum A C, &amp; </s>
  <s xml:id="echoid-s42280" xml:space="preserve">pro auſtralibus D B; </s>
  <s xml:id="echoid-s42281" xml:space="preserve">diuidaturq́ue A@C, in tria parallelogramma <lb/>vtcunque E I, M K, N C, pro ſex ſignis borealibus: </s>
  <s xml:id="echoid-s42282" xml:space="preserve">ſed vt habeant proportionatam diſtantiam <lb/>
<anchor type="figure" xlink:label="fig-0661-01a" xlink:href="fig-0661-01"/>
<anchor type="note" xlink:label="note-0661-01a" xlink:href="note-0661-01"/>
<anchor type="note" xlink:label="note-0661-02a" xlink:href="note-0661-02"/>
<anchor type="note" xlink:label="note-0661-03a" xlink:href="note-0661-03"/>
inter ſe, deſcribendus erit ex G, quadrans E F, diuidendusq́ue in tres partes æquales, &amp; </s>
  <s xml:id="echoid-s42283" xml:space="preserve">per pun-<lb/>cta diuiſionum rectæ M I, N K, rectis A H, L C, ducendæ parallellæ. </s>
  <s xml:id="echoid-s42284" xml:space="preserve">Spatium enim ab E, vſque <lb/>ad M, cancro, ſpatia vero ab M, vſque ad N, &amp; </s>
  <s xml:id="echoid-s42285" xml:space="preserve">ab N, vſque ad G, ſignis ♌, &amp; </s>
  <s xml:id="echoid-s42286" xml:space="preserve">♍, ſpatia denique <lb/>à G, vſque ad N, &amp; </s>
  <s xml:id="echoid-s42287" xml:space="preserve">ab N, vſque ad M, &amp; </s>
  <s xml:id="echoid-s42288" xml:space="preserve">ab M, vſque ad E, ſignis ♈, ♉, &amp; </s>
  <s xml:id="echoid-s42289" xml:space="preserve">♊, accõmodandum <lb/>erit. </s>
  <s xml:id="echoid-s42290" xml:space="preserve">Eodem modo parallelogrammum D B, in ſigna auſtralia diuidetur, quod tamen nos in arcus <lb/>
<anchor type="note" xlink:label="note-0661-04a" xlink:href="note-0661-04"/>
diurnos, non autem in ſignorum initia diſtribuimus, vt facilius horæ ab occ. </s>
  <s xml:id="echoid-s42291" xml:space="preserve">deſcribi poſſint. <lb/></s>
  <s xml:id="echoid-s42292" xml:space="preserve">Recta enim P Q, arcui diurno horarum 12. </s>
  <s xml:id="echoid-s42293" xml:space="preserve">hoc eſt, Æ quatori, &amp; </s>
  <s xml:id="echoid-s42294" xml:space="preserve">recta R S, arcui horarum 11. </s>
  <s xml:id="echoid-s42295" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s42296" xml:space="preserve">T V, arcui horarum 10. </s>
  <s xml:id="echoid-s42297" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42298" xml:space="preserve">X Y, arcui horarum 9. </s>
  <s xml:id="echoid-s42299" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42300" xml:space="preserve">Z B, tropico ♑, accommodabitur. </s>
  <s xml:id="echoid-s42301" xml:space="preserve"><lb/>Quæ quidem rectæ ducendæ ſunt ipſis D Q, O B, parallelæ ad quamcunque diſtantiam, quamuis <lb/>nos eas commoditatis gratia æqualibus fere ſpatijs inter ſe diſtantes duxerimus, excepta linea <lb/>♑, Z B, quæ rectæ X Y, propinqua eſt, ſicut &amp; </s>
  <s xml:id="echoid-s42302" xml:space="preserve">in cælo tropicus ♑, propinquus eſt parallelo, cu-<lb/>ius arcus diurnus horas 9. </s>
  <s xml:id="echoid-s42303" xml:space="preserve">complectitur, in latitudine gr. </s>
  <s xml:id="echoid-s42304" xml:space="preserve">42.</s>
  <s xml:id="echoid-s42305" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2095" type="float" level="2" n="2">
  <figure xlink:label="fig-0661-01" xlink:href="fig-0661-01a">
    <image file="0661-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0661-01"/>
  </figure>
<note position="left" xlink:label="note-0661-01" xlink:href="note-0661-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0661-02" xlink:href="note-0661-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0661-03" xlink:href="note-0661-03a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0661-04" xlink:href="note-0661-04a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s42306" xml:space="preserve">VT igitur horas ab occ. </s>
  <s xml:id="echoid-s42307" xml:space="preserve">deſcribamus in poſteriori parallelogrammo D B, producatur D O, <lb/>
<anchor type="note" xlink:label="note-0661-05a" xlink:href="note-0661-05"/>
ſumatnrq́ue O a, ſtylo cuiuſcumque magnitudinis æqualis, &amp; </s>
  <s xml:id="echoid-s42308" xml:space="preserve">ex a, deſcribatur quadrans O b, <lb/>qui in 90. </s>
  <s xml:id="echoid-s42309" xml:space="preserve">gradus diſtribuatur, initio facto à recta O a, &amp; </s>
  <s xml:id="echoid-s42310" xml:space="preserve">ex a, per gradus rectæ occultæ <lb/>emittantur ſecantes O b, in punctis vmbrarum verſarum altitudinibus Solis debitarum. </s>
  <s xml:id="echoid-s42311" xml:space="preserve">Nam ſi <lb/>O a, ponatur Horizonti æquidiſtans, &amp; </s>
  <s xml:id="echoid-s42312" xml:space="preserve">O B, ad Horizontem perpendicularis, cadent radij So-<lb/>
<anchor type="note" xlink:label="note-0661-06a" xlink:href="note-0661-06"/>
lis per centrum mundi a, &amp; </s>
  <s xml:id="echoid-s42313" xml:space="preserve">ſingulos gradus altitudinis incedentes (qui quidem gradibus qua-<lb/>drantis O b, opponerentur, exiſterentq́; </s>
  <s xml:id="echoid-s42314" xml:space="preserve">ſupra Horizontem O a, ſi integer circulus ex a, centro <lb/>eſſet deſcriptus.) </s>
  <s xml:id="echoid-s42315" xml:space="preserve">in puncta vmbrarum verſarum in recta O B, vt manifeſtum eſt. </s>
  <s xml:id="echoid-s42316" xml:space="preserve">Quod ſi vmbris <lb/>verſis ex tabula vmbrarũ, quam in propoſ. </s>
  <s xml:id="echoid-s42317" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42318" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42319" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42320" xml:space="preserve">confecimus, erutis, loco altitudinum Solis, <lb/>vti malueris, ſumenda erit in recta D Q, recta D f, ſtylo O a, æqualis, ſecandaque in 12. </s>
  <s xml:id="echoid-s42321" xml:space="preserve">partes <lb/>vmbræ verſæ æquales, &amp; </s>
  <s xml:id="echoid-s42322" xml:space="preserve">ſi opus erit, alia infra f, ſumenda eidem ſtylo æqualis, &amp; </s>
  <s xml:id="echoid-s42323" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42324" xml:space="preserve">In noſtro <lb/>exemplo ſatis eſt, ſi infra f, ſumantur duæ particulæ vmbræ verſæ. </s>
  <s xml:id="echoid-s42325" xml:space="preserve">Iam vero lineam meridianam <lb/>ita ducemus. </s>
  <s xml:id="echoid-s42326" xml:space="preserve">Sumantur ex proximis tabellis altitudines meridianæ in Æquatore, &amp; </s>
  <s xml:id="echoid-s42327" xml:space="preserve">in arcubus <lb/>diurnis horarum 11. </s>
  <s xml:id="echoid-s42328" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42329" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42330" xml:space="preserve">9. </s>
  <s xml:id="echoid-s42331" xml:space="preserve">Item in tropico ♑; </s>
  <s xml:id="echoid-s42332" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42333" xml:space="preserve">beneficio circini in recta O B, accipiantur
<pb o="646" file="0662" n="662" rhead="GNOMONICES"/>
longitudines vmbrarum illis altitudinibus debitarum, vel certe ex recta D Q, vmbræ verſæ eiſdẽ <lb/>altitudinibus, prout tabula propoſ. </s>
  <s xml:id="echoid-s42334" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42335" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42336" xml:space="preserve">5 indicat, debitæ, transferanturq́ue in rectas D Q, <lb/>R S, T V, X Y, O B, initio ſemper facto à recta D O, puncta imprimendo in hiſce rectis. </s>
  <s xml:id="echoid-s42337" xml:space="preserve">Linea <lb/>enim inflexa congruenter ducta per hæc puncta erit linea meridiana. </s>
  <s xml:id="echoid-s42338" xml:space="preserve">Eodem modo lineas hora-<lb/>rum ab occ. </s>
  <s xml:id="echoid-s42339" xml:space="preserve">ducemus, ſi habita ratione altitudinum Solis pro ſingulis horis, &amp; </s>
  <s xml:id="echoid-s42340" xml:space="preserve">vmbrarum ver-<lb/>ſarum illis debitarum, puncta imprimamus in rectis arcuum diurnorum. </s>
  <s xml:id="echoid-s42341" xml:space="preserve">Exempli gratia. </s>
  <s xml:id="echoid-s42342" xml:space="preserve">Hora <lb/>16. </s>
  <s xml:id="echoid-s42343" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42344" xml:space="preserve">in Æquatore habet altitudinem grad. </s>
  <s xml:id="echoid-s42345" xml:space="preserve">40. </s>
  <s xml:id="echoid-s42346" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42347" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42348" xml:space="preserve">Si igitur beneficio circini in recta <lb/>O B, ſumatur portio inter O, &amp; </s>
  <s xml:id="echoid-s42349" xml:space="preserve">grad. </s>
  <s xml:id="echoid-s42350" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42351" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42352" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42353" xml:space="preserve">transferaturq́ue ex D, vſque ad g, quod quidem <lb/>punctum g, terminat vmbram verſam partium 10. </s>
  <s xml:id="echoid-s42354" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42355" xml:space="preserve">6. </s>
  <s xml:id="echoid-s42356" xml:space="preserve">quæ in tabula propoſ. </s>
  <s xml:id="echoid-s42357" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42358" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42359" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42360" xml:space="preserve">di-<lb/>ctæ altitudini reſpondet, ducenda erit hora 16. </s>
  <s xml:id="echoid-s42361" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42362" xml:space="preserve">per g. </s>
  <s xml:id="echoid-s42363" xml:space="preserve">Rurſus eadem hora 16. </s>
  <s xml:id="echoid-s42364" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42365" xml:space="preserve">in <lb/>
<anchor type="note" xlink:label="note-0662-01a" xlink:href="note-0662-01"/>
arcu diurno horarum 11. </s>
  <s xml:id="echoid-s42366" xml:space="preserve">altitudinem habet gr. </s>
  <s xml:id="echoid-s42367" xml:space="preserve">29. </s>
  <s xml:id="echoid-s42368" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42369" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42370" xml:space="preserve">Igitur ſi beneficio circini in recta <lb/>O B, ſumatur portio inter O, &amp; </s>
  <s xml:id="echoid-s42371" xml:space="preserve">dictam altitudinem, vel in recta D Q, ſumatur vmbra verſa par-<lb/>tium 6. </s>
  <s xml:id="echoid-s42372" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42373" xml:space="preserve">42. </s>
  <s xml:id="echoid-s42374" xml:space="preserve">eidem altitudini reſpondens in tabula propoſ. </s>
  <s xml:id="echoid-s42375" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42376" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42377" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42378" xml:space="preserve">transferaturq́ue à re-<lb/>cta D O, in rectam R S, vſquead h, ducenda erit eadem hora 16. </s>
  <s xml:id="echoid-s42379" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42380" xml:space="preserve">per punctum h, atque <lb/>ita de ceteris. </s>
  <s xml:id="echoid-s42381" xml:space="preserve">Vides igitur per ſingula puncta rectarum P Q, R S, T V, X Y, tranſire binas horas <lb/>ab occ. </s>
  <s xml:id="echoid-s42382" xml:space="preserve">quod non cõtingeret, ſi hæ rectæ initijs ſignorum, non autem arcubus diurnis integrarũ <lb/>horarum eſſent deputatæ. </s>
  <s xml:id="echoid-s42383" xml:space="preserve">Et quoniam prope lineam meridianam horæ inter ſe confunduntur, <lb/>inſigniuimus lineam horæ 19. </s>
  <s xml:id="echoid-s42384" xml:space="preserve">punctis quibuſdam, vt facilius ab alijs diſtinguatur. </s>
  <s xml:id="echoid-s42385" xml:space="preserve">Eadem ratio-<lb/>ne horæ ab ortu Solis, inæquales, &amp; </s>
  <s xml:id="echoid-s42386" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42387" xml:space="preserve">ac med. </s>
  <s xml:id="echoid-s42388" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42389" xml:space="preserve">deſcribentur, ſi earum altitudines ſup-<lb/>putentur. </s>
  <s xml:id="echoid-s42390" xml:space="preserve">Ita cernis in parallelogrammo A C, horas à mer. </s>
  <s xml:id="echoid-s42391" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42392" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42393" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42394" xml:space="preserve">eſſe deſcriptas ex vm-<lb/>
<anchor type="note" xlink:label="note-0662-02a" xlink:href="note-0662-02"/>
bris verſis rectæ A H, in qua ſumptæ ſunt tres partes ſtylo æquales, quarum A m, diuiſa eſt in 12. <lb/></s>
  <s xml:id="echoid-s42395" xml:space="preserve">partes æquales, quæ quidem vmbræ verſæ ſumendæ ſunt ex tabula propoſ. </s>
  <s xml:id="echoid-s42396" xml:space="preserve">2. </s>
  <s xml:id="echoid-s42397" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42398" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42399" xml:space="preserve">reſpondentes <lb/>altitudinibus Solis; </s>
  <s xml:id="echoid-s42400" xml:space="preserve">vel certe ex vmbris verſis rectæ n l, quas offeruntrectæ occultæ ex centro a, <lb/>per gradus quadrantis O b, emiſſæ, dummodo a n, æqualis ſit ſtylo A m, &amp; </s>
  <s xml:id="echoid-s42401" xml:space="preserve">recta n l, ad a O, per-<lb/>pendicularis ducatur. </s>
  <s xml:id="echoid-s42402" xml:space="preserve">Solum hoc notandum eſt: </s>
  <s xml:id="echoid-s42403" xml:space="preserve">quando hora aliqua duci non poteſt per omnia <lb/>initia ſignorum, vt fit in hora 5. </s>
  <s xml:id="echoid-s42404" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42405" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42406" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42407" xml:space="preserve">7. </s>
  <s xml:id="echoid-s42408" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42409" xml:space="preserve">quæ nullam altitudinem habet in prin-<lb/>cipio ♉, &amp; </s>
  <s xml:id="echoid-s42410" xml:space="preserve">♍, atque adeo nullum punctum in recta N K, ſumendum erit in hacrecta N K, ſupra <lb/>A L, punctum pro hora oppoſita, hoc eſt, pro hora 5. </s>
  <s xml:id="echoid-s42411" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42412" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42413" xml:space="preserve">7. </s>
  <s xml:id="echoid-s42414" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42415" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42416" xml:space="preserve">ex altitudine, quam <lb/>habet in ſigno oppoſito, puta in principio ♏, &amp; </s>
  <s xml:id="echoid-s42417" xml:space="preserve">♓: </s>
  <s xml:id="echoid-s42418" xml:space="preserve">quia hæc altitudo ſupra Horizontem æqualis <lb/>eſt depreſſioni prioris horæ (quæ nullum punctum habebat) infra Horizontem, vt ex ſphæra ma-<lb/>
<anchor type="note" xlink:label="note-0662-03a" xlink:href="note-0662-03"/>
teriali conſtat; </s>
  <s xml:id="echoid-s42419" xml:space="preserve">propterea quod prior illa hora eſt ſupra Horizontem Antipodum, numeraturq́ue <lb/>à mer. </s>
  <s xml:id="echoid-s42420" xml:space="preserve">ſi prius à med. </s>
  <s xml:id="echoid-s42421" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42422" xml:space="preserve">numerabatur, &amp; </s>
  <s xml:id="echoid-s42423" xml:space="preserve">contra, parallelusq́ue borealis ſe habebit apud illos, <lb/>vt apud nos oppoſitus auſtralis, &amp;</s>
  <s xml:id="echoid-s42424" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42425" xml:space="preserve">Eadem ratione, ſi hora aliqua ab or. </s>
  <s xml:id="echoid-s42426" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42427" xml:space="preserve">punctum non <lb/>habet in aliquo parallelo, aut arcu diurno, ſumenda erit eadem hora in parallelo, arcuve oppoſi-<lb/>to, ita tamen, vt ab or. </s>
  <s xml:id="echoid-s42428" xml:space="preserve">numeretur, ſi prius ab occ. </s>
  <s xml:id="echoid-s42429" xml:space="preserve">ſupputabatur, &amp; </s>
  <s xml:id="echoid-s42430" xml:space="preserve">contra.</s>
  <s xml:id="echoid-s42431" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2096" type="float" level="2" n="3">
<note position="right" xlink:label="note-0661-05" xlink:href="note-0661-05a" xml:space="preserve">Deſcriptio ho-<lb/>tarum ab occ. <lb/>in cylindro con <lb/>uexo.</note>
<note position="left" xlink:label="note-0661-06" xlink:href="note-0661-06a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0662-01" xlink:href="note-0662-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0662-02" xlink:href="note-0662-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0662-03" xlink:href="note-0662-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s42432" xml:space="preserve">HOC eodẽ artificio delineabuntur horæ in cylindro conuexo, ſi in eo ducantur pro lineis ſi-<lb/>gnorum, ſiue arcuum diurnorum lineæ parallelæ, vt diximus, quæ, cylindro libere pendente, ad <lb/>Horizontem rectæ ſint. </s>
  <s xml:id="echoid-s42433" xml:space="preserve">Stylus autem ita accommodandus erit, vt facile circumduci poſſit ad lo-<lb/>cum Solis, vel diem menſis, quo horam obſeruare volumus, hac tamen lege, vt linea fiduciæ ſtyli, <lb/>qualis eſt recta O a, in ſtylo O a, perpetuo rectos angulos cum recta D O, vel A L, conſtituat.</s>
  <s xml:id="echoid-s42434" xml:space="preserve"/>
</p>
<note position="left" xml:space="preserve">Horologiũ pla-<lb/>num initar cy-<lb/>lindri commo-<lb/>diſſimum.</note>
<p>
  <s xml:id="echoid-s42435" xml:space="preserve">VERVM percommode quoque horas cognoſcemus ex duobus parallelogrammis A C, DB, <lb/>
<anchor type="note" xlink:label="note-0662-05a" xlink:href="note-0662-05"/>
in lamina aliqua ænea deſcriptis, vna nimirum in vna facie laminæ deſcripto, &amp; </s>
  <s xml:id="echoid-s42436" xml:space="preserve">in oppoſita facie <lb/>altero, vt in minorem formam redigatur horologium. </s>
  <s xml:id="echoid-s42437" xml:space="preserve">Si enim in lamina fiat canalis p q, in quo <lb/>ſtylus poſitus (cuius forma ad pedem figuræ præcedentis poſita eſt) hinc inde poſſit diſcurrere, <lb/>ita vt linea fiduciæ ſtyli perpendicularis ſit ad rectas A L, D O, ſtylusq́ue ipſe in oppoſita parte <lb/>laminę cochleola poſſit aſtringi, cum poſitus fuerit in loco Solis, aut in die menſis propoſito, vt <lb/>amplius dimoueri nequeat; </s>
  <s xml:id="echoid-s42438" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42439" xml:space="preserve">lamina verſus Solem dirigatur, ita vt filum, cui perpendiculum <lb/>annexum ſit, congruat vni ex lineis rectis, quę initiis ſignorum, aut arcubus diurnis deputan-<lb/>tur, vmbraq́; </s>
  <s xml:id="echoid-s42440" xml:space="preserve">ſtyli ęquidiſtet lineis ſignorum, arcuum ve diurnorum, indicabit extremitas vm-<lb/>bræ horam pręſentem, antemeridianam, aut pomeridianam, prout obſeruatio ante, aut poſt <lb/>
<anchor type="note" xlink:label="note-0662-06a" xlink:href="note-0662-06"/>
meridiem fit. </s>
  <s xml:id="echoid-s42441" xml:space="preserve">Atque hoc horologium planum multo, præſtantius iudicarem, quàm ſi in cy-<lb/>lindro deſcriptum eſſet, propterea quòd difficile admodum ſit, cylindrum ita fabricare, vt li-<lb/>bere pendens non deflectat in aliquam partem. </s>
  <s xml:id="echoid-s42442" xml:space="preserve">quod incommodum in plano noſtro horologio <lb/>locum non habet, cum à perpendiculo regatur. </s>
  <s xml:id="echoid-s42443" xml:space="preserve">Eodem modo horæ in cylindro cognoſcentur, <lb/>ſi ſtylus in gradu Solis, vel die menſis ſtatuatur, &amp; </s>
  <s xml:id="echoid-s42444" xml:space="preserve">vmbra ſtyli lineis ſignorum, arcuumve diur-<lb/>norum æqnidiſtet, &amp;</s>
  <s xml:id="echoid-s42445" xml:space="preserve">c.</s>
  <s xml:id="echoid-s42446" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2097" type="float" level="2" n="4">
<note position="left" xlink:label="note-0662-05" xlink:href="note-0662-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0662-06" xlink:href="note-0662-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s42447" xml:space="preserve">QVINETIAM ſi conſtruatur regula quępiã ſolida, qualis eſt n l, in qua deſcribantur par-<lb/>
<anchor type="note" xlink:label="note-0662-07a" xlink:href="note-0662-07"/>
tes vmbrę verſæ, quas exhibent rectæ ex centro a, per gradus quadrantis O b, emiſſæ, &amp; </s>
  <s xml:id="echoid-s42448" xml:space="preserve">in n, affi-<lb/>gatur ſtylus n a, perpendicularis ad n l, tantæ longitudinis, quanta eſt diſtantia regulæ n l, in quã <lb/>traductę ſunt vmbræ verſæ altitudinum quadrantis O b, erit nobis hæc regula inſtar horologii. <lb/></s>
  <s xml:id="echoid-s42449" xml:space="preserve">Nam ſi beneficio perpendiculi regula hæc Soli obuerſa ita libere pendeat, vt perpendicularis ſit
<pb o="647" file="0663" n="663" rhead="LIBER OCTAVVS."/>
ad Horizontem, vmbraque ſtyli lateribus regulæ æquidiſtet, indicabit vmbræ extremitas altitudi-<lb/>
<anchor type="note" xlink:label="note-0663-01a" xlink:href="note-0663-01"/>
nem Solis, atque adeo ex proximis tabellis altitudinum Solis præſentem horam facile cognoſce-<lb/>mus. </s>
  <s xml:id="echoid-s42450" xml:space="preserve">Quam horam deprehendemus etiam ex eiſdem tabellis, ſi quadrante, aut alio inſtrumento <lb/>altitudinem Solis inquira m<unsure/>us.</s>
  <s xml:id="echoid-s42451" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2098" type="float" level="2" n="5">
<note position="left" xlink:label="note-0662-07" xlink:href="note-0662-07a" xml:space="preserve">Hotæ quo pa-<lb/>cto ex r<unsure/>egula ſo <lb/>lida per altitu-<lb/>dines Solis co <lb/>gnoſcantur.</note>
<note position="right" xlink:label="note-0663-01" xlink:href="note-0663-01a" xml:space="preserve">Horæ cognitio <lb/>ex alri@ud@ne <lb/>Sol@s quadran-<lb/>te, vt alio inſtru <lb/>mento inuẽta.</note>
</div>
<p>
  <s xml:id="echoid-s42452" xml:space="preserve">QVOD ſi cylindrus in plano collocetur rectus, in quo horologiũ horizontale deſcriptũ ſit, <lb/>
<anchor type="note" xlink:label="note-0663-02a" xlink:href="note-0663-02"/>
aut horologium hemiſphęricum concauũ firmatum, deſcribentur horæ in cylindro ex vmbra, vt <lb/>ad finem proximi lib. </s>
  <s xml:id="echoid-s42453" xml:space="preserve">monuimus, hac ratione. </s>
  <s xml:id="echoid-s42454" xml:space="preserve">Circumducto ſtylo ad lineam cuiuſque ſigni, vel ar-<lb/>cus diurni, circumuoluatur planum, donec vmbra ſtyli in horologio deſcripto cadat in horam <lb/>illius paralleli, ad cuius lineam ſtylus cylindri eſt accommodatus, &amp; </s>
  <s xml:id="echoid-s42455" xml:space="preserve">ipſe cylindrus in plano in eo <lb/>ſitu firmato circa eius axem vertatur, donec vmbra ſtyli æquidiſtet lineis ſignorum, aut arcuum <lb/>
<anchor type="note" xlink:label="note-0663-03a" xlink:href="note-0663-03"/>
diutnorum, extremumq́ue vmbræ punctum notetur. </s>
  <s xml:id="echoid-s42456" xml:space="preserve">Per hoc enim ducenda erit hora illa in cy-<lb/>lindro. </s>
  <s xml:id="echoid-s42457" xml:space="preserve">Non aliter eiuſdem horæ puncta, &amp; </s>
  <s xml:id="echoid-s42458" xml:space="preserve">aliarum omnium in omnibus lineis ſignorum, vel ar-<lb/>cuum diurnorum inueſtigari poterunt.</s>
  <s xml:id="echoid-s42459" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2099" type="float" level="2" n="6">
<note position="right" xlink:label="note-0663-02" xlink:href="note-0663-02a" xml:space="preserve">Deſcriptio hora <lb/>rum in cylin-<lb/>dro ex vmbra <lb/>caden te in ho-<lb/>ras horologii ho <lb/>rizon @a@is, vel <lb/>hemiſphæri@i <lb/>concaui.</note>
<note position="left" xlink:label="note-0663-03" xlink:href="note-0663-03a" xml:space="preserve">10</note>
</div>
</div>
<div xml:id="echoid-div2101" type="section" level="1" n="532">
<head xml:id="echoid-head561" style="it" xml:space="preserve">DE HORARVM DESCRIPTIONE <lb/>in quadrante. CAP. VI.</head>
<p>
  <s xml:id="echoid-s42460" xml:space="preserve">NON multum differt horarum in quadrante deſcriptio ab ea, quam præcedenti cap. </s>
  <s xml:id="echoid-s42461" xml:space="preserve">in cy-<lb/>lindro, vel in plano inſtar cylindri, tradidimus, cum vtrobique horæ ex altitudinibus Solis <lb/>
<anchor type="note" xlink:label="note-0663-04a" xlink:href="note-0663-04"/>
ſupra Horizontem deſcribantur. </s>
  <s xml:id="echoid-s42462" xml:space="preserve">Sit ergo quadrans A B C, in quo horæ ab occ. </s>
  <s xml:id="echoid-s42463" xml:space="preserve">deſcribendæ <lb/>
<anchor type="note" xlink:label="note-0663-05a" xlink:href="note-0663-05"/>
ſint, diuiſus in grad. </s>
  <s xml:id="echoid-s42464" xml:space="preserve">90. </s>
  <s xml:id="echoid-s42465" xml:space="preserve">quorum ordo à B, in C, progrediatur. </s>
  <s xml:id="echoid-s42466" xml:space="preserve">Deſcriptis ex A, duobus arcubus <lb/>per puncta D, &amp; </s>
  <s xml:id="echoid-s42467" xml:space="preserve">E, ad quamcunque diſtantiam, quorum ille, qui quadranti B C, propinquus eſt, <lb/>tropico ♑, hic vero à quadrante <lb/>
<anchor type="figure" xlink:label="fig-0663-01a" xlink:href="fig-0663-01"/>
B C, magis diſtans tropico ♋, tri-<lb/>buatur. </s>
  <s xml:id="echoid-s42468" xml:space="preserve">Quamuis enim plerique <lb/>priorem tropico ♋, &amp; </s>
  <s xml:id="echoid-s42469" xml:space="preserve">poſteriorẽ <lb/>tropico ♑, aſcribant, (quod æque <lb/>bene, atque illud, fieri poteſt, quan-<lb/>tum ad horarum deſcriptionem) <lb/>multò tamen commodius contra-<lb/>
<anchor type="note" xlink:label="note-0663-06a" xlink:href="note-0663-06"/>
rium fiet, vt nos diximus, propter <lb/>maiorem horarum diſtinctionem. <lb/></s>
  <s xml:id="echoid-s42470" xml:space="preserve">Diuiſa quoque portione rectę AB, <lb/>inter arcus per D, &amp; </s>
  <s xml:id="echoid-s42471" xml:space="preserve">E, deſcriptos <lb/>bifariam, deſcribatur per punctũ <lb/>diuiſionis ex A, arcus per F, tran-<lb/>ſiens pro Aequatore; </s>
  <s xml:id="echoid-s42472" xml:space="preserve">qui duci etiã <lb/>poſſet per punctum quodcunque <lb/>inter arcus per D, &amp; </s>
  <s xml:id="echoid-s42473" xml:space="preserve">E, deſcriptos, <lb/>licet rectam inter illos bifariam <lb/>
<anchor type="note" xlink:label="note-0663-07a" xlink:href="note-0663-07"/>
nõ diuideret. </s>
  <s xml:id="echoid-s42474" xml:space="preserve">Iam vero ex A, egre <lb/>diantur tres rectæ occultæ per alti-<lb/>tudines meridianas ♑, ♈, vel ♎, <lb/>&amp; </s>
  <s xml:id="echoid-s42475" xml:space="preserve">♋, hoc eſt, per grad. </s>
  <s xml:id="echoid-s42476" xml:space="preserve">24. </s>
  <s xml:id="echoid-s42477" xml:space="preserve">Min. <lb/></s>
  <s xml:id="echoid-s42478" xml:space="preserve">30. </s>
  <s xml:id="echoid-s42479" xml:space="preserve">per grad. </s>
  <s xml:id="echoid-s42480" xml:space="preserve">48. </s>
  <s xml:id="echoid-s42481" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42482" xml:space="preserve">per grad. </s>
  <s xml:id="echoid-s42483" xml:space="preserve">71. </s>
  <s xml:id="echoid-s42484" xml:space="preserve"><lb/>Min. </s>
  <s xml:id="echoid-s42485" xml:space="preserve">30. </s>
  <s xml:id="echoid-s42486" xml:space="preserve">ſecantes arcus per D, F, E, deſcriptos in punctis D, F, E, per quæ arcus circuli deſcriptus <lb/>D F E, erit linea meridiana. </s>
  <s xml:id="echoid-s42487" xml:space="preserve">Deinde ex A, educantur aliæ rectę occultæ per altitudines meridia-<lb/>nas arcuum diurnorum horarum 9. </s>
  <s xml:id="echoid-s42488" xml:space="preserve">10. </s>
  <s xml:id="echoid-s42489" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42490" xml:space="preserve">13. </s>
  <s xml:id="echoid-s42491" xml:space="preserve">14. </s>
  <s xml:id="echoid-s42492" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42493" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42494" xml:space="preserve">ex tabellis præcedentis cap. </s>
  <s xml:id="echoid-s42495" xml:space="preserve">excerptas, <lb/>(Facilius enim horę ab occ. </s>
  <s xml:id="echoid-s42496" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42497" xml:space="preserve">or. </s>
  <s xml:id="echoid-s42498" xml:space="preserve">per arcus diurnos deſcribuntur, quàm per initia ſignorum, quẽ-<lb/>admodum &amp; </s>
  <s xml:id="echoid-s42499" xml:space="preserve">in cylindro) quæ ſecent lineam meridianam D F E, in punctis M, L, K, I, H, G, <lb/>
<anchor type="note" xlink:label="note-0663-08a" xlink:href="note-0663-08"/>
per quæ ex A, arcus deſcribantur pro arcubus diurnis. </s>
  <s xml:id="echoid-s42500" xml:space="preserve">Quòd ſi ex A, per altitudines horarnm cu-<lb/>iuſuis arcus diurni ex tabellis antecedentis cap. </s>
  <s xml:id="echoid-s42501" xml:space="preserve">acceptas rectæ occultę emittantur, ſecabitur ar-<lb/>cus diurnus, cuius horarum altitudines ſumptæ ſunt, in horis ab occ. </s>
  <s xml:id="echoid-s42502" xml:space="preserve">Si igitur puncta horarum <lb/>reſpondentia lineis curuis coniungãtur, (omnes autẽ horæ antemeridianæ exprimuntur per cir-<lb/>culares lineas, pomeridianæ vero congruenter ducendæ ſunt per puncta, in quibus arcus diurni<unsure/> <lb/>ab arcubus horarum antemeridianarum ſecantur, vt hora 23. </s>
  <s xml:id="echoid-s42503" xml:space="preserve">per proxima puncta ipſi rectæ A B, <lb/>&amp; </s>
  <s xml:id="echoid-s42504" xml:space="preserve">22. </s>
  <s xml:id="echoid-s42505" xml:space="preserve">per ſequentia, &amp;</s>
  <s xml:id="echoid-s42506" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42507" xml:space="preserve">Itaque ſatis erit, ſi pro arcubus ſingulis horarum antemeridianarum <lb/>terna puncta reperiantur, nempe pro arcu horæ 15. </s>
  <s xml:id="echoid-s42508" xml:space="preserve">vnum in arcu diurno horarum 9. </s>
  <s xml:id="echoid-s42509" xml:space="preserve">quod in <lb/>recta A B, exiſtit, cum tunc Sol oriatur, alterum in Aequatore, ſeu arcu diurno horarum 12. </s>
  <s xml:id="echoid-s42510" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42511" xml:space="preserve"><lb/>in arcu diurno horarum 15. </s>
  <s xml:id="echoid-s42512" xml:space="preserve">tertium. </s>
  <s xml:id="echoid-s42513" xml:space="preserve">Item pro arcu horæ 17. </s>
  <s xml:id="echoid-s42514" xml:space="preserve">vnum in arcu diurno horarum <lb/>9. </s>
  <s xml:id="echoid-s42515" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42516" xml:space="preserve">alterum in arcu diurno horarum 12. </s>
  <s xml:id="echoid-s42517" xml:space="preserve">vel 11. </s>
  <s xml:id="echoid-s42518" xml:space="preserve">tertium denique in arcu diurno horarum 14.</s>
  <s xml:id="echoid-s42519" xml:space="preserve">
<pb o="648" file="0664" n="664" rhead="GNOMONICES"/>
quod idem eſt, quod H, cum tunc meridies ſit, &amp;</s>
  <s xml:id="echoid-s42520" xml:space="preserve">c.) </s>
  <s xml:id="echoid-s42521" xml:space="preserve">abſolutum erit horologium. </s>
  <s xml:id="echoid-s42522" xml:space="preserve">Quod vt horas <lb/>indicet, deſcribenda erunt ſigna Zodiaci, vel certe dies menſium ad latera A B, D E, dies quidem <lb/>menſium à 12. </s>
  <s xml:id="echoid-s42523" xml:space="preserve">die Iunii, vſque ad diem 12. </s>
  <s xml:id="echoid-s42524" xml:space="preserve">Decembris, aut ſigna à ♋, vſque ad ♑, iuxtam rectam <lb/>A B, dies vero menſium à die 12. </s>
  <s xml:id="echoid-s42525" xml:space="preserve">Decembris vſque ad diem 12. </s>
  <s xml:id="echoid-s42526" xml:space="preserve">Iunii, aut ſigna à ♑. </s>
  <s xml:id="echoid-s42527" xml:space="preserve">vſque ad ♋, <lb/>iuxta arcum D E. </s>
  <s xml:id="echoid-s42528" xml:space="preserve">Quod hac ratione fiet. </s>
  <s xml:id="echoid-s42529" xml:space="preserve">Ex loco Solis in principio cuiuslibet menſis, vel in prin-<lb/>cipio cuiusuis ſigni, quæratur eius declinatio, &amp; </s>
  <s xml:id="echoid-s42530" xml:space="preserve">ex hac altitudo meridiana, per quam ex A, occul-<lb/>ta recta educta ſecet arcum D E, in puncto, per quod arcus occultus deſcriptus ex A, ſecabit rectam <lb/>A B, vel circularem lineam iuxta arcum D E, deſcriptam in principio menſis propoſiti, vel ſigni <lb/>Zodiaci. </s>
  <s xml:id="echoid-s42531" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s42532" xml:space="preserve">ratione puncta reperientur pro die 10. </s>
  <s xml:id="echoid-s42533" xml:space="preserve">aut 20. </s>
  <s xml:id="echoid-s42534" xml:space="preserve">vel alio quocunque propoſiti <lb/>menſis, ſi locus Solis inueſtigetur, &amp; </s>
  <s xml:id="echoid-s42535" xml:space="preserve">declinatio, altitudoq́; </s>
  <s xml:id="echoid-s42536" xml:space="preserve">meridiana. </s>
  <s xml:id="echoid-s42537" xml:space="preserve">In exemplo deſcripti ſunt <lb/>
<anchor type="note" xlink:label="note-0664-01a" xlink:href="note-0664-01"/>
menſium dies: </s>
  <s xml:id="echoid-s42538" xml:space="preserve">In ſequenti vero figura ſigna Zodiaci. </s>
  <s xml:id="echoid-s42539" xml:space="preserve">Iam ſi ex A, filum cum perpendiculo libe-<lb/>re pendeat, vna cum nodulo mobili, extendaturq́; </s>
  <s xml:id="echoid-s42540" xml:space="preserve">filum, &amp; </s>
  <s xml:id="echoid-s42541" xml:space="preserve">nodulus in recta A B, vel linea circu-<lb/>lari prope D E, ad diem menſis ponatur, inſtrumentum denique ad Solem dirigatur, donec ra-<lb/>dius Solis per reſpondentia puncta pinnacidiorum tranſeat, indicabit nodulus inter horarias li-<lb/>neas horam præſentem, antemeridianam, vel pomeridianã, prout obſeruatio fit ante, vel poſt me-<lb/>ridiem, filum autem perpendiculi in quadrante B C, altitudinem Solis monſtrabit, qua altitudi-<lb/>ne creſcente, tempus erit antemeridianum, pomeridianum vero, eadem decreſcente.</s>
  <s xml:id="echoid-s42542" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2101" type="float" level="2" n="1">
<note position="right" xlink:label="note-0663-04" xlink:href="note-0663-04a" xml:space="preserve">Deſcriptio ho@a <lb/>rum ab occ. in <lb/>quadrante.</note>
<note position="left" xlink:label="note-0663-05" xlink:href="note-0663-05a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0663-01" xlink:href="fig-0663-01a">
    <image file="0663-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0663-01"/>
  </figure>
<note position="left" xlink:label="note-0663-06" xlink:href="note-0663-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0663-07" xlink:href="note-0663-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0663-08" xlink:href="note-0663-08a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0664-01" xlink:href="note-0664-01a" xml:space="preserve">10</note>
</div>
<note position="left" xml:space="preserve">Deſeciptio ho-<lb/>@ar<unsure/>um à mer. &amp; <lb/>med.noc. ĩ qua-<lb/>drante.</note>
<p>
  <s xml:id="echoid-s42543" xml:space="preserve">EADEM ratione horæ à mer. </s>
  <s xml:id="echoid-s42544" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42545" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42546" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42547" xml:space="preserve">deſcribentur ex earum altitudinibus in princi-<lb/>piis ſignorum: </s>
  <s xml:id="echoid-s42548" xml:space="preserve">ſatis autem erit, ſi puncta horarum reperiantur in duobus tropicis, &amp; </s>
  <s xml:id="echoid-s42549" xml:space="preserve">in Aequato <lb/>re. </s>
  <s xml:id="echoid-s42550" xml:space="preserve">arcus enim circulorum per terna puncta reſpondentia in dictis parallelis deſcripti dabunt ho <lb/>
<anchor type="note" xlink:label="note-0664-03a" xlink:href="note-0664-03"/>
ras à mer. </s>
  <s xml:id="echoid-s42551" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42552" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42553" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42554" xml:space="preserve">Omnia namque puncta horarũ in circunferentias circulorũ cadunt. </s>
  <s xml:id="echoid-s42555" xml:space="preserve">Hoc <lb/>
<anchor type="figure" xlink:label="fig-0664-01a" xlink:href="fig-0664-01"/>
<anchor type="note" xlink:label="note-0664-04a" xlink:href="note-0664-04"/>
<anchor type="note" xlink:label="note-0664-05a" xlink:href="note-0664-05"/>
ſolũ notandũ hic eſt, quando aliqua hora à mer. </s>
  <s xml:id="echoid-s42556" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42557" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42558" xml:space="preserve">punctũ nõ habet in aliquo parallelo, <lb/>accipiendã eſſe altitudinẽ horæ oppoſitæ, nẽpe à med. </s>
  <s xml:id="echoid-s42559" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42560" xml:space="preserve">vel mer. </s>
  <s xml:id="echoid-s42561" xml:space="preserve">in parallelo oppoſito, eamq́; </s>
  <s xml:id="echoid-s42562" xml:space="preserve">in <lb/>priorẽ parallelum extra quadrantẽ productum transferẽdam eſſe à recta A B, punctum in eo im-<lb/>primendo, per hoc enim hora illa ducenda erit. </s>
  <s xml:id="echoid-s42563" xml:space="preserve">Vt quoniam hora 5. </s>
  <s xml:id="echoid-s42564" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42565" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s42566" xml:space="preserve">a med. </s>
  <s xml:id="echoid-s42567" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42568" xml:space="preserve">pun-<lb/>ctum nõ habet in tropico ♑, cum hæc hora infra Horizontem ſit, Sole in principio ♑, exiſtente, <lb/>accipiemus altitudinem horæ 5. </s>
  <s xml:id="echoid-s42569" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42570" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42571" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s42572" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42573" xml:space="preserve">in tropico ♋, nempe gr. </s>
  <s xml:id="echoid-s42574" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42575" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42576" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42577" xml:space="preserve">duce-<lb/>musq́; </s>
  <s xml:id="echoid-s42578" xml:space="preserve">ex A, per hanc altitudinem rectam occultam, quæ tropicum ♑, ſecet in G. </s>
  <s xml:id="echoid-s42579" xml:space="preserve">Si enim pun-<lb/>
<anchor type="note" xlink:label="note-0664-06a" xlink:href="note-0664-06"/>
ctum G, à puncto N, transferatur in tropicum ♑, productum vſque ad H, ducenda erit hora 5. </s>
  <s xml:id="echoid-s42580" xml:space="preserve">à <lb/>mer. </s>
  <s xml:id="echoid-s42581" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s42582" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42583" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42584" xml:space="preserve">per punctum H. </s>
  <s xml:id="echoid-s42585" xml:space="preserve">Ratio huius rei eſt, quod illa hora infra Horizõtem apud <lb/>Antipodas eandem habet altitudinem in tropico ♑, quam hora oppoſita in tro pico ♋, oppoſito. <lb/></s>
  <s xml:id="echoid-s42586" xml:space="preserve">Id quod etiã in antecedenti cap. </s>
  <s xml:id="echoid-s42587" xml:space="preserve">monuimus faciendũ eſſe, cum horas in cylindro deſcriberemus. </s>
  <s xml:id="echoid-s42588" xml:space="preserve"><lb/>Pari ratione, quoniam hora 6. </s>
  <s xml:id="echoid-s42589" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42590" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42591" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42592" xml:space="preserve">punctum non habet in parallelo ♏, vel ♓, ac-<lb/>cipiemus altitudinem horæ 6. </s>
  <s xml:id="echoid-s42593" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42594" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42595" xml:space="preserve">vel mer. </s>
  <s xml:id="echoid-s42596" xml:space="preserve">in parallelo ♉, vel ♍, nempe grad. </s>
  <s xml:id="echoid-s42597" xml:space="preserve">7. </s>
  <s xml:id="echoid-s42598" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42599" xml:space="preserve">40. </s>
  <s xml:id="echoid-s42600" xml:space="preserve"><lb/>atque per hanc altitudinem ex A, ducemus rectam occul tam, quæ ſecet parallelum ♏, vel ♓, in I, <lb/>punctumq́; </s>
  <s xml:id="echoid-s42601" xml:space="preserve">I, à puncto O, transferemus in parallelum eundem vſque ad K. </s>
  <s xml:id="echoid-s42602" xml:space="preserve">Nam per K, ducenda <lb/>erit hora 6. </s>
  <s xml:id="echoid-s42603" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42604" xml:space="preserve">vel med. </s>
  <s xml:id="echoid-s42605" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42606" xml:space="preserve">Poſtremo, quia hora 7. </s>
  <s xml:id="echoid-s42607" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42608" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s42609" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42610" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42611" xml:space="preserve">nullum habet <lb/>punctum in parallelo ♈, vel ♎, accipiemus altitudinem horæ 7. </s>
  <s xml:id="echoid-s42612" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42613" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42614" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s42615" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42616" xml:space="preserve">in eo-<lb/>dem parallelo, cum nõ habeat oppoſitum, per quam inueniemus punctum L, horæ 7. </s>
  <s xml:id="echoid-s42617" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42618" xml:space="preserve">noc.</s>
  <s xml:id="echoid-s42619" xml:space="preserve">
<pb o="649" file="0665" n="665" rhead="LIBER OCTAVVS."/>
vel 5. </s>
  <s xml:id="echoid-s42620" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42621" xml:space="preserve">Hoc igitur punctum ſi transferatur à puncto P, in parallelum ♈, vel ♎, productum <lb/>vſque ad M, ducenda erit per M, hora 7. </s>
  <s xml:id="echoid-s42622" xml:space="preserve">mer. </s>
  <s xml:id="echoid-s42623" xml:space="preserve">vel 5. </s>
  <s xml:id="echoid-s42624" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42625" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42626" xml:space="preserve">at que ita de cæteris.</s>
  <s xml:id="echoid-s42627" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2102" type="float" level="2" n="2">
<note position="left" xlink:label="note-0664-03" xlink:href="note-0664-03a" xml:space="preserve">20</note>
  <figure xlink:label="fig-0664-01" xlink:href="fig-0664-01a">
    <image file="0664-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0664-01"/>
  </figure>
<note position="left" xlink:label="note-0664-04" xlink:href="note-0664-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0664-05" xlink:href="note-0664-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0664-06" xlink:href="note-0664-06a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s42628" xml:space="preserve">NON aliter horæ ab ortu Solis, &amp; </s>
  <s xml:id="echoid-s42629" xml:space="preserve">inæquales in quadrante delineari poterunt, ſi illarum alti-<lb/>
<anchor type="note" xlink:label="note-0665-01a" xlink:href="note-0665-01"/>
tudines in arcubus diurnis, &amp; </s>
  <s xml:id="echoid-s42630" xml:space="preserve">harum altitudines in parallelis ſignorum inueſtigentur. </s>
  <s xml:id="echoid-s42631" xml:space="preserve">Immo ho-<lb/>ræ ab occ. </s>
  <s xml:id="echoid-s42632" xml:space="preserve">erunt etiam horę ab or. </s>
  <s xml:id="echoid-s42633" xml:space="preserve">ſi eatum complementa vſque ad 24. </s>
  <s xml:id="echoid-s42634" xml:space="preserve">accipiantur, ita vt hora <lb/>23. </s>
  <s xml:id="echoid-s42635" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42636" xml:space="preserve">ſit 1. </s>
  <s xml:id="echoid-s42637" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s42638" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42639" xml:space="preserve">22. </s>
  <s xml:id="echoid-s42640" xml:space="preserve">ſit 2. </s>
  <s xml:id="echoid-s42641" xml:space="preserve">&amp;</s>
  <s xml:id="echoid-s42642" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42643" xml:space="preserve">Id quod etiam in cylindro præcedentis cap. </s>
  <s xml:id="echoid-s42644" xml:space="preserve">intelligi volo. <lb/></s>
  <s xml:id="echoid-s42645" xml:space="preserve">Ratio eſt, quòd quælibet hora ab occ. </s>
  <s xml:id="echoid-s42646" xml:space="preserve">eandem altitudinem habet ſupra Horizontem in quouis <lb/>parallelo, quam hora ab or. </s>
  <s xml:id="echoid-s42647" xml:space="preserve">quæ cum illa numerum 24. </s>
  <s xml:id="echoid-s42648" xml:space="preserve">componat.</s>
  <s xml:id="echoid-s42649" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2103" type="float" level="2" n="3">
<note position="right" xlink:label="note-0665-01" xlink:href="note-0665-01a" xml:space="preserve">Qua ratione ho <lb/>ræ ab occ. ĩ qua <lb/>drante, &amp; cylin <lb/>dio dent quo-<lb/>que horas ab <lb/>ortu Solis.</note>
</div>
<p>
  <s xml:id="echoid-s42650" xml:space="preserve">INVENIRI quoque poſſunt in ſingulis parallelis altitudines Solis tam pro horis à mer. </s>
  <s xml:id="echoid-s42651" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42652" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0665-02a" xlink:href="note-0665-02"/>
med. </s>
  <s xml:id="echoid-s42653" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42654" xml:space="preserve">quàm ab or. </s>
  <s xml:id="echoid-s42655" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42656" xml:space="preserve">vel etiam pro horis inæqualibus, Geometrice ſine tabulis altitu-<lb/>
<anchor type="note" xlink:label="note-0665-03a" xlink:href="note-0665-03"/>
dinum Solis, hac ratione. </s>
  <s xml:id="echoid-s42657" xml:space="preserve">Sint v. </s>
  <s xml:id="echoid-s42658" xml:space="preserve">g inquirendæ altitudines Solis in parallelo ♏, vel ♓, l O. </s>
  <s xml:id="echoid-s42659" xml:space="preserve">Pro-<lb/>ducto parallelo l O, in vtramque partem, ducatur ex A, per altitudinem meridianam ſignorum <lb/>oppoſitorum ♉, &amp; </s>
  <s xml:id="echoid-s42660" xml:space="preserve">♍, hoc eſt, per grad. </s>
  <s xml:id="echoid-s42661" xml:space="preserve">59. </s>
  <s xml:id="echoid-s42662" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42663" xml:space="preserve">30. </s>
  <s xml:id="echoid-s42664" xml:space="preserve">recta occulta ſecans arcum O l, produ-<lb/>ctum in Q, &amp; </s>
  <s xml:id="echoid-s42665" xml:space="preserve">arcui O Q, æqualis abſcindatur O a, atque per a, ipſi A B, parallela agatur <lb/>a R, quam in R, ſecet recta l R, ducta ex l, termino paralleli ♏, vel ♓, ad A B, vel ad a R, perpen-<lb/>dicularis. </s>
  <s xml:id="echoid-s42666" xml:space="preserve">Diuiſa autem recta l R, bifariam in S, deſcribatur ex S, ad interuallum S l, vel S R, cir <lb/>culus l n R α, qui in 24. </s>
  <s xml:id="echoid-s42667" xml:space="preserve">horas æquales diſtribuatur, initio facto à puncto l, meridiei, ſi horæ à <lb/>mer. </s>
  <s xml:id="echoid-s42668" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42669" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42670" xml:space="preserve">noc deſcribendæ ſint, vel à puncto α, vel ſ, ortus vel occaſus Solis , ſi horæ ab or. <lb/></s>
  <s xml:id="echoid-s42671" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42672" xml:space="preserve">deſiderentur. </s>
  <s xml:id="echoid-s42673" xml:space="preserve">Quòd ſi horæ inæquales ſint delineandæ, ſecandus erit tam arcus α l ſ, <lb/>quàm α R ſ, in 12. </s>
  <s xml:id="echoid-s42674" xml:space="preserve">partes æquales. </s>
  <s xml:id="echoid-s42675" xml:space="preserve">Erit autem punctum l, hora 12. </s>
  <s xml:id="echoid-s42676" xml:space="preserve">meridiei, &amp; </s>
  <s xml:id="echoid-s42677" xml:space="preserve">proxima puncta <lb/>
<anchor type="note" xlink:label="note-0665-04a" xlink:href="note-0665-04"/>
æqualiter ab l, diſtantia ad hor. </s>
  <s xml:id="echoid-s42678" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42679" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42680" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42681" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42682" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42683" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42684" xml:space="preserve">pertinebunt, ſi diuiſio circuli in 24. <lb/></s>
  <s xml:id="echoid-s42685" xml:space="preserve">partes æquales initium habuit ab l, &amp; </s>
  <s xml:id="echoid-s42686" xml:space="preserve">ſic de reliquis. </s>
  <s xml:id="echoid-s42687" xml:space="preserve">Si vero diuiſio eiuſdem circuli initium ha-<lb/>buit à recta α ſ, erit punctum α, vel ſ, hora 24. </s>
  <s xml:id="echoid-s42688" xml:space="preserve">proximum vero punctum diuiſionis verſus l, ho-<lb/>ra 23. </s>
  <s xml:id="echoid-s42689" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42690" xml:space="preserve">vel 1. </s>
  <s xml:id="echoid-s42691" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s42692" xml:space="preserve">ſequens deinde hora 22. </s>
  <s xml:id="echoid-s42693" xml:space="preserve">ab occ. </s>
  <s xml:id="echoid-s42694" xml:space="preserve">vel 2. </s>
  <s xml:id="echoid-s42695" xml:space="preserve">ab or. </s>
  <s xml:id="echoid-s42696" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42697" xml:space="preserve">ita deinceps; </s>
  <s xml:id="echoid-s42698" xml:space="preserve">adeo vt <lb/>recta α ſ, ſit veluti Horizon, cum in illam cadat filum perpendiculi, Sole oriente, vel occidente, <lb/>&amp; </s>
  <s xml:id="echoid-s42699" xml:space="preserve">α l ſ, ſit tanquam arcus diurnus, &amp; </s>
  <s xml:id="echoid-s42700" xml:space="preserve">α R l, nocturnus. </s>
  <s xml:id="echoid-s42701" xml:space="preserve">Denique ſi de horis inęqualibus agatur, <lb/>erit punctum α, vel ſ, hora 12. </s>
  <s xml:id="echoid-s42702" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42703" xml:space="preserve">proxima puncta diuiſionis verſus l, hor. </s>
  <s xml:id="echoid-s42704" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42705" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42706" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42707" xml:space="preserve">inæqualis, &amp;</s>
  <s xml:id="echoid-s42708" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42709" xml:space="preserve"><lb/>Exemplum dedimus in circulo l n R α, de horis à mer. </s>
  <s xml:id="echoid-s42710" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42711" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42712" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42713" xml:space="preserve">Iam vero ſi ex horis circuli <lb/>l n R α, ipſi α ſ, parallelæ occultæ agantur, vel ad l R, perpendiculares, (quod in horis à mer. </s>
  <s xml:id="echoid-s42714" xml:space="preserve"><lb/>vel med. </s>
  <s xml:id="echoid-s42715" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42716" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42717" xml:space="preserve">inæqualibus facile fiet, ſi bina quælibet puncta ab l, æqualiter remota rectis oc-<lb/>
<anchor type="note" xlink:label="note-0665-05a" xlink:href="note-0665-05"/>
cultis iungantur. </s>
  <s xml:id="echoid-s42718" xml:space="preserve">Idemq́uein horis ab or. </s>
  <s xml:id="echoid-s42719" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42720" xml:space="preserve">fieri poterit, ſi beneficio circini ſingulis arcu-<lb/>bus inter l, &amp; </s>
  <s xml:id="echoid-s42721" xml:space="preserve">horas arcus l α, ſumantur æquales arcus in arcu l ſ, &amp; </s>
  <s xml:id="echoid-s42722" xml:space="preserve">contra) ſecabunt hæ paralle-<lb/>lum l O, in altitudinibus horarum, ita vt arcus paralleli l O, inter O, &amp; </s>
  <s xml:id="echoid-s42723" xml:space="preserve">puncta ſectionum altitudi-<lb/>nes Solis ſupra Horizontem metiantur. </s>
  <s xml:id="echoid-s42724" xml:space="preserve">Puncta vero ſectionum arcus O a, dabunt altitudines <lb/>horatum nocturnarum ſupra faciem oppoſitam Horizontis, ita vt arcus paralleli O a, inter O, &amp; </s>
  <s xml:id="echoid-s42725" xml:space="preserve"><lb/>dicta puncta ſint altitudines Solis ſupra Horizontem apud Antipodas in horis paralleli l O a, qui <lb/>apud illos idem eſt, qui apud nos parallelus oppoſitus e f, ♉, &amp; </s>
  <s xml:id="echoid-s42726" xml:space="preserve">♍; </s>
  <s xml:id="echoid-s42727" xml:space="preserve">horæ tamen, quæ in noſtro <lb/>Horizontenumerantur à mer. </s>
  <s xml:id="echoid-s42728" xml:space="preserve">vel abor. </s>
  <s xml:id="echoid-s42729" xml:space="preserve">in eorum Horizonte numerandæ erunt à med. </s>
  <s xml:id="echoid-s42730" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42731" xml:space="preserve">vel <lb/>ab occ &amp; </s>
  <s xml:id="echoid-s42732" xml:space="preserve">econtrario. </s>
  <s xml:id="echoid-s42733" xml:space="preserve">Vnde cum huiuſmodi horæ infra Horizontem eaſdem habeant altitudi-<lb/>nes, quas horę oppoſitæ in oppoſito parallelo ſupra Horizontem habent, vt ex ijs conſtat, quæ in <lb/>
<anchor type="note" xlink:label="note-0665-06a" xlink:href="note-0665-06"/>
ſcholio propoſ. </s>
  <s xml:id="echoid-s42734" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42735" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42736" xml:space="preserve">5. </s>
  <s xml:id="echoid-s42737" xml:space="preserve">oſtenſa ſunt à nobis, (vbi nimirum demonſtrauimus, altitudines 24. </s>
  <s xml:id="echoid-s42738" xml:space="preserve">ho-<lb/>rarum cuiusuis paralleli ſupra vnam faciem plani æquales eſſe altitudinibus 24. </s>
  <s xml:id="echoid-s42739" xml:space="preserve">horarum paral-<lb/>leli oppoſiti ſupra alteram faciem plani, dummodo quæ prius à mer. </s>
  <s xml:id="echoid-s42740" xml:space="preserve">vel ab or. </s>
  <s xml:id="echoid-s42741" xml:space="preserve">numeraban-<lb/>tur, nunc à med. </s>
  <s xml:id="echoid-s42742" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42743" xml:space="preserve">vel ab occ. </s>
  <s xml:id="echoid-s42744" xml:space="preserve">numerentur, cuiuſmodi ſunt illæ, quæ in oppoſito parallelo <lb/>illis in priori parallelo opponuntur) eliciemus ex altitudinibus in arcu O a, contentis altitudines <lb/>oppoſitarum horarum in parallelo e f, ♉, &amp; </s>
  <s xml:id="echoid-s42745" xml:space="preserve">♍, qui parallelo O l, ♏, &amp; </s>
  <s xml:id="echoid-s42746" xml:space="preserve">♓, opponitur, hoc mo-<lb/>do. </s>
  <s xml:id="echoid-s42747" xml:space="preserve">Ex A, ad puncta altitudinum in arcu O a, rectæ occultæ ducantur, quæ ſecabunt arcum eb, <lb/>paralleli oppoſiti ad partes e, producti in arcus ſimiles arcubus arcus O a, vt ad finem cap. </s>
  <s xml:id="echoid-s42748" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42749" xml:space="preserve">in <lb/>ſphæram demonſtrauimus. </s>
  <s xml:id="echoid-s42750" xml:space="preserve">Quare ſi beneficio circini hi arcus paralleli e b, transferantur ex e, <lb/>in arcum e f, habebimus in parallelo e f, altitudines horarum, quæ horis arcus O a, opponuntur, <lb/>cum arcus paralleli e f, inrer e, &amp; </s>
  <s xml:id="echoid-s42751" xml:space="preserve">puncta altitudinum Solis ſimiles ſint arcubus paralleli O a, in-<lb/>ter O, &amp; </s>
  <s xml:id="echoid-s42752" xml:space="preserve">puncta altitudinum Solis, vtpote æquales arcubus paralleli e b, inter e, &amp; </s>
  <s xml:id="echoid-s42753" xml:space="preserve">puncta altitu-<lb/>
<anchor type="note" xlink:label="note-0665-07a" xlink:href="note-0665-07"/>
dinum Solis: </s>
  <s xml:id="echoid-s42754" xml:space="preserve">ita vt quemadmodum v. </s>
  <s xml:id="echoid-s42755" xml:space="preserve">g. </s>
  <s xml:id="echoid-s42756" xml:space="preserve">primum punctum ab O, verſus a, pertinet ad horam 6. <lb/></s>
  <s xml:id="echoid-s42757" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42758" xml:space="preserve">ita primum punctum ab e, verſus f, pertineat ad horam 6. </s>
  <s xml:id="echoid-s42759" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42760" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42761" xml:space="preserve">Item quemadmo-<lb/>dum ſecundum punctum ab O, verſus a, ſpectatad horam 7. </s>
  <s xml:id="echoid-s42762" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42763" xml:space="preserve">ita ſecundum punctum ab <lb/>e, verſus f, ad horam 7. </s>
  <s xml:id="echoid-s42764" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42765" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42766" xml:space="preserve">pertineat, &amp; </s>
  <s xml:id="echoid-s42767" xml:space="preserve">ita de cæteris. </s>
  <s xml:id="echoid-s42768" xml:space="preserve">Quemadmodum autem in paral-<lb/>lelo l O, ♏, &amp; </s>
  <s xml:id="echoid-s42769" xml:space="preserve">♓, altitudines Solis inueſtigauimus, ita quoque eaſdem explorabimus in alijs om-<lb/>nibus parallelis, ſi in vtram que partem producantur, ac per altitudines meridianas oppoſitorum <lb/>parallelorum ex A, ducantur rectæ occultæ, notenturq́ue puncta, in quibus paralleli ab ipſis ſe-<lb/>cantur, atque reliqua fiant, vt prius. </s>
  <s xml:id="echoid-s42770" xml:space="preserve">Ita vides in parallelo ♈, P F, in quo eadem eſt altitudo me <lb/>ridiana ſigni ♎, oppoſiti, quæ ♈, arcui P F, ęqualem eſſe ſumptum arcum P, &amp; </s>
  <s xml:id="echoid-s42771" xml:space="preserve">per T, ductam eſſe
<pb o="650" file="0666" n="666" rhead="GNOMONICES"/>
rectam T m, ipſi A B, parallelam. </s>
  <s xml:id="echoid-s42772" xml:space="preserve">Deinde ex F, ductam eſſe rectam F T, ad A B, vel ad T m, per-<lb/>pendicularem, quæ hic omnino cadit in T, cum recta ducta F T, ob æquales arcus P F, P T, ſece-<lb/>tur à recta A B, bifariam, &amp; </s>
  <s xml:id="echoid-s42773" xml:space="preserve">ad angulos rectos. </s>
  <s xml:id="echoid-s42774" xml:space="preserve">quod demonſtrabitur, vt in propoſ. </s>
  <s xml:id="echoid-s42775" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42776" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42777" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42778" xml:space="preserve">oſten-<lb/>ſum eſt, rectam M N, à recta E H, ſecari bifariam, &amp; </s>
  <s xml:id="echoid-s42779" xml:space="preserve">ad angulos rectos, propter æqualitatem ar-<lb/>cuum H M, H N. </s>
  <s xml:id="echoid-s42780" xml:space="preserve">Poſtremo ex V, vbi recta F T, bifariam diuiditur, ad interuallum V F, vel V T, <lb/>deſcriptum eſſe circulum F ß T N: </s>
  <s xml:id="echoid-s42781" xml:space="preserve">qui ſi diuidatur in horas, vt de circulo l n R α, diximus, inue <lb/>nientur in parallelo P F, altitudines Solis, vt in parallelo O l. </s>
  <s xml:id="echoid-s42782" xml:space="preserve">Rurſus cernis in parallelo ♑, N D, <lb/>in vtramque partem producto rectam ex A, per altitudinem meridianam tropici ♋, oppoſiti, <lb/>hoc eſt, per grad. </s>
  <s xml:id="echoid-s42783" xml:space="preserve">71. </s>
  <s xml:id="echoid-s42784" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42785" xml:space="preserve">30. </s>
  <s xml:id="echoid-s42786" xml:space="preserve">emiſſam ſecare parallelum N D, productum in X, arcuiq́ue N X, <lb/>æqualem eſſe ſumptum arcum N Y, &amp; </s>
  <s xml:id="echoid-s42787" xml:space="preserve">per Y, actam eſſe rectam Y Z, ipſi A B, parallelam. </s>
  <s xml:id="echoid-s42788" xml:space="preserve">Poſt <lb/>
<anchor type="note" xlink:label="note-0666-01a" xlink:href="note-0666-01"/>
hæc ex D, termino paralleli ♑, ductam eſſe rectam D Z, ad A B, vel ad Y Z, perpendicularem, <lb/>atque ex eius puncto medio {δι}<unsure/>, ad interuallum {δι}<unsure/> D, vel {δι}<unsure/> Z, deſcriptum eſſe circulum D θ Z: </s>
  <s xml:id="echoid-s42789" xml:space="preserve">qui <lb/>ſi diuidaturin horas, vt de alijs diximus, inueniemus in tropico ♑, N D, altitudines Solis, in ar-<lb/>cu vero N Y, depreſſiones Solis infra Horizontem, ad quas ſi ex A, lineæ occultæ ducantur, ſe-<lb/>cabitur tropicus ♋, E μ, ad partes μ, productus in punctis, quę ex μ, translata in arcum μ E, da-<lb/>bunt altitudines Solis in tropico ♋, vt de rectis ex A, ad puncta arcus Oa, ductis, ſecantibusq́ue <lb/>arcum e b, atque de punctis arcus eb, translatis in arcum e f, diximus. </s>
  <s xml:id="echoid-s42790" xml:space="preserve">Ad extremum, vt exem-<lb/>plum etiam ponamus de parallelis borealibus, vides in parallelo ♋, μ E, ex A, per altitudinem <lb/>meridianam Solis tropici ♑, oppoſiti, nempe per grad. </s>
  <s xml:id="echoid-s42791" xml:space="preserve">24. </s>
  <s xml:id="echoid-s42792" xml:space="preserve">Min. </s>
  <s xml:id="echoid-s42793" xml:space="preserve">30. </s>
  <s xml:id="echoid-s42794" xml:space="preserve">rectam emiſſam ſecare tro-<lb/>picum ♑ in q, arcuiq́ue μ q, in eodem tropico ad partes μ, producto acceptum eſſe arcum ęqua-<lb/>
<anchor type="note" xlink:label="note-0666-02a" xlink:href="note-0666-02"/>
lem μ g, &amp; </s>
  <s xml:id="echoid-s42795" xml:space="preserve">perg, ductam eſſe rectam g h, ipſi A B, parallelam. </s>
  <s xml:id="echoid-s42796" xml:space="preserve">Præterea ex E, termino paralleli <lb/>♋, ductam eſſe rectam Eh, perpendicularem ad A B, vel ad g h, atque ex eius medio puncto p, <lb/>ad interuallum p E, vel p h, deſcriptum eſſe circulum E π h. </s>
  <s xml:id="echoid-s42797" xml:space="preserve">qui ſi in horas, vt alij, diuidatur, <lb/>reperientur in parallelo ♋, μ E, altitudines Solis, in arcu vero μ g, depreſſiones Solis ſub Hori-<lb/>zonte, per quas ſi ex A, occultę lineę egrediantur, ſecabitur tropicus ♑, D N, ad partes N, pro-<lb/>ductus in punctis, quæ ex N, in arcum N D, translata dabunt altitudines Solis in tropico ♑; </s>
  <s xml:id="echoid-s42798" xml:space="preserve">non <lb/>ſecus ac de rectis ex A, prodeuntibus ad puncta arcus Oa, ſecantibusq́ue arcum e b, atque de pun-<lb/>ctis arcus e b, in arcum e f, translatis diximus. </s>
  <s xml:id="echoid-s42799" xml:space="preserve">Eademq́ue ratio eſt in omnibus alijs parallelis. <lb/></s>
  <s xml:id="echoid-s42800" xml:space="preserve">Sed ſatis eſt, ſi operatio inſtituatur vel in ſolis parallelis auſtralibus, vel in ſolis borealibus, cum <lb/>vna eademq́ue opera ex diuiſione vnius circuli in horas altitudines etiam inquirantur in op-<lb/>
<anchor type="note" xlink:label="note-0666-03a" xlink:href="note-0666-03"/>
poſito parallelo. </s>
  <s xml:id="echoid-s42801" xml:space="preserve">Libuit hanc rationem inueniendarum altitudinum Solis in parallelis in qua-<lb/>drante deſcriptis ex Gnomonica Andreæ Schoneri depromptam vberius explicare, vt planius ab <lb/>omnibus intelligeretur. </s>
  <s xml:id="echoid-s42802" xml:space="preserve">quam quoniam iucundiſſima, atque pulcherrima eſt, facile demonſtra-<lb/>bimus, ſi prius, qua ratione aliter, quàm in lib. </s>
  <s xml:id="echoid-s42803" xml:space="preserve">6. </s>
  <s xml:id="echoid-s42804" xml:space="preserve">traditum eſt, ex Analemmate altitudines <lb/>Solis ſupra Horizontem pro ſingulis horis cuiuſque paralleli inueſtigentur, doceamus.</s>
  <s xml:id="echoid-s42805" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2104" type="float" level="2" n="4">
<note position="right" xlink:label="note-0665-02" xlink:href="note-0665-02a" xml:space="preserve">Inuentio altitu <lb/>dinum Sol@@ in <lb/>ſingulis paralle <lb/>lis in quadran <lb/>te deſcripus pro <lb/>quibuslibet ho <lb/>ris, Geometric@ <lb/>ſine tabulis al <lb/>t@udinum So <lb/>lis.</note>
<note position="left" xlink:label="note-0665-03" xlink:href="note-0665-03a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0665-04" xlink:href="note-0665-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0665-05" xlink:href="note-0665-05a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0665-06" xlink:href="note-0665-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0665-07" xlink:href="note-0665-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0666-01" xlink:href="note-0666-01a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0666-02" xlink:href="note-0666-02a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0666-03" xlink:href="note-0666-03a" xml:space="preserve">30</note>
</div>
<p>
  <s xml:id="echoid-s42806" xml:space="preserve">SIT Meridianus Analemmatis A B C D, circa centrum E; </s>
  <s xml:id="echoid-s42807" xml:space="preserve">diameter Horizontis B D; </s>
  <s xml:id="echoid-s42808" xml:space="preserve">Verti-<lb/>
<anchor type="note" xlink:label="note-0666-04a" xlink:href="note-0666-04"/>
calis A C; </s>
  <s xml:id="echoid-s42809" xml:space="preserve">Aequatoris H I; </s>
  <s xml:id="echoid-s42810" xml:space="preserve">axis mundi F G; </s>
  <s xml:id="echoid-s42811" xml:space="preserve">diameter paralleli borealis K L. </s>
  <s xml:id="echoid-s42812" xml:space="preserve">Ducta recta L M, <lb/>ipſi B D, &amp; </s>
  <s xml:id="echoid-s42813" xml:space="preserve">K N, ipſi A C, parallela, ſecetur K N, bifariam in O, deſcribaturq́ue ex O, ad interual-<lb/>lum O K, vel O N, circulus K P N Q, quo diuiſo in 24. </s>
  <s xml:id="echoid-s42814" xml:space="preserve">horas ęquales, initio quidem facto à K, <lb/>pro horis à mer. </s>
  <s xml:id="echoid-s42815" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s42816" xml:space="preserve">med. </s>
  <s xml:id="echoid-s42817" xml:space="preserve">noc. </s>
  <s xml:id="echoid-s42818" xml:space="preserve">at pro horis ab or. </s>
  <s xml:id="echoid-s42819" xml:space="preserve">vel occ. </s>
  <s xml:id="echoid-s42820" xml:space="preserve">ab Horizonte B D: </s>
  <s xml:id="echoid-s42821" xml:space="preserve">Vel ſi de horis in-<lb/>
<anchor type="note" xlink:label="note-0666-05a" xlink:href="note-0666-05"/>
æqualibus agatur, diuiſo tam arcu π K ρ, quàm ρ N π, in 12. </s>
  <s xml:id="echoid-s42822" xml:space="preserve">partes ęquales, initio facto ab Ho-<lb/>rizonte B D, ducatur ex aſſumpta hora d, ipſi B D, parallela d f, ſecans rectas K N, K L, &amp; </s>
  <s xml:id="echoid-s42823" xml:space="preserve">cir-<lb/>cunferentiam Meridiani in punctis e, g, f. </s>
  <s xml:id="echoid-s42824" xml:space="preserve">Dico D f, altitudinem eſſe Solis pro hora d, (quæ in <lb/>exemplo ponitur hora 5. </s>
  <s xml:id="echoid-s42825" xml:space="preserve">à mer. </s>
  <s xml:id="echoid-s42826" xml:space="preserve">vel 7. </s>
  <s xml:id="echoid-s42827" xml:space="preserve">à med. </s>
  <s xml:id="echoid-s42828" xml:space="preserve">noc.) </s>
  <s xml:id="echoid-s42829" xml:space="preserve">in parallelo diametri k L. </s>
  <s xml:id="echoid-s42830" xml:space="preserve">Deſcripto enim <lb/>ex R, ad interuallum R K, vel R L, ſemicirculo paralleli K T L, erigatur in g, ad K L, perpendi-<lb/>cularis g h. </s>
  <s xml:id="echoid-s42831" xml:space="preserve">Quoniam igitur ex h, puncto paralleli ad diametrum K L, demiſſa eſt perpendicu-<lb/>laris g h, &amp; </s>
  <s xml:id="echoid-s42832" xml:space="preserve">per g, ad diametrum Verticalis A C, ducta perpendicularis d f, (cum enim d f, B D, <lb/>ſint æquidiſtantes, ſit autem B D, ad A C, perpendicularis, erit &amp; </s>
  <s xml:id="echoid-s42833" xml:space="preserve">d f, ad A C, perpendicularis) <lb/>
<anchor type="note" xlink:label="note-0666-06a" xlink:href="note-0666-06"/>
erit ex demonſtratis cap. </s>
  <s xml:id="echoid-s42834" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42835" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42836" xml:space="preserve">6. </s>
  <s xml:id="echoid-s42837" xml:space="preserve">D f, altitudo Solis, cuius diſtantia à meridie eſt arcus K h. </s>
  <s xml:id="echoid-s42838" xml:space="preserve">Sed <lb/>tam arcus ſemidiurnus K b, arcui K π, quàm arcus K h, (vt mox demonſtrabimus) ſimilis eſt ar-<lb/>
<anchor type="note" xlink:label="note-0666-07a" xlink:href="note-0666-07"/>
cui K d. </s>
  <s xml:id="echoid-s42839" xml:space="preserve">Igitur ſi à diſtantia Solis à meridie ſumpta in arcu K π, qui inſtar ſemidiurni eſt, nempe <lb/>in dato exemplo à diſtantia 5. </s>
  <s xml:id="echoid-s42840" xml:space="preserve">horarum, ducatur recta Horizontis diametro parallela, vel ad dia-<lb/>metrum Verticalis perpendicularis, indicabit hęc in Meridiano arcum D f, altitudinis Solis pro <lb/>diſtantia à meridie K h, quæ in arcu ſemidiurno paralleli Solis ſimilis eſt diſtantię K d, in arcu <lb/>K π. </s>
  <s xml:id="echoid-s42841" xml:space="preserve">Quòd autem tam arcus K b, K π, quàm k h, K d, ſimiles ſint, ita oſtendemus. </s>
  <s xml:id="echoid-s42842" xml:space="preserve">Ducta re-<lb/>cta O R, cum diametri K L, K N, bifariam ſecentur in R, O, centris, hoc eſt, proportionaliter, <lb/>
<anchor type="note" xlink:label="note-0666-08a" xlink:href="note-0666-08"/>
erit O R, ipſi L M, ac proinde &amp; </s>
  <s xml:id="echoid-s42843" xml:space="preserve">ipſis d f, B D, parallela. </s>
  <s xml:id="echoid-s42844" xml:space="preserve">Igitur erit, vt K R, ſinus totus ad K O, <lb/>
<anchor type="note" xlink:label="note-0666-09a" xlink:href="note-0666-09"/>
ſinum totum, ita K α, ad K a: </s>
  <s xml:id="echoid-s42845" xml:space="preserve">Vt autem K α, ad α L, ita eſt ka, ad a N, ac proinde &amp; </s>
  <s xml:id="echoid-s42846" xml:space="preserve">permutan-<lb/>
<anchor type="note" xlink:label="note-0666-10a" xlink:href="note-0666-10"/>
do, vt K α, ad K a, ita α L, ad a N. </s>
  <s xml:id="echoid-s42847" xml:space="preserve">Igitur erit quoque, vt k R, ſinus totus ad K O, ſinum totum, <lb/>ita α L, ſinus verſus arcus ſeminocturni b L, ad a N, ſinum verſum arcus π N. </s>
  <s xml:id="echoid-s42848" xml:space="preserve">Quare ex lem-<lb/>mate propoſ. </s>
  <s xml:id="echoid-s42849" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42850" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42851" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42852" xml:space="preserve">ſimiles erunt arcus b L, π N, ac proinde &amp; </s>
  <s xml:id="echoid-s42853" xml:space="preserve">reliquus b K, ex ſemicirculo
<pb o="651" file="0667" n="667" rhead="LIBER OCTAVVS."/>
K T L, reliquo π K, ex ſemicirculo K P N, ſimilis erit: </s>
  <s xml:id="echoid-s42854" xml:space="preserve">proptereaq́ue π K ρ, erit inſtar arcus diur <lb/>ni, &amp; </s>
  <s xml:id="echoid-s42855" xml:space="preserve">π N ρ, inſtar nocturni in parallelo, cuius declinatio H K; </s>
  <s xml:id="echoid-s42856" xml:space="preserve">atque tot horæ compre-<lb/>hendentur in arcubus K π, π N, quot in arcubus K b, b L. </s>
  <s xml:id="echoid-s42857" xml:space="preserve">Non aliter oſtendemus, arcus <lb/>K h, K d, ſimiles eſſe, propterea quòd ſinus toti K R, K O, eandem proportionem habent, <lb/>
<anchor type="note" xlink:label="note-0667-01a" xlink:href="note-0667-01"/>
<anchor type="figure" xlink:label="fig-0667-01a" xlink:href="fig-0667-01"/>
quam ſinus verſi K g, K e. </s>
  <s xml:id="echoid-s42858" xml:space="preserve">Eadem <lb/>ratio eſt de aliis horis. </s>
  <s xml:id="echoid-s42859" xml:space="preserve">Nam ſi k P, <lb/>diſtantia à meridie complectatur <lb/>6. </s>
  <s xml:id="echoid-s42860" xml:space="preserve">horas, tranſibit P L, æquidiſtans <lb/>ipſi B D, per centra O, R, cũ pro-<lb/>
<anchor type="note" xlink:label="note-0667-02a" xlink:href="note-0667-02"/>
portionaliter ſecet rectas K N, KL. <lb/></s>
  <s xml:id="echoid-s42861" xml:space="preserve">Vnde manifeſtum eſt, quadrantes <lb/>
<anchor type="note" xlink:label="note-0667-03a" xlink:href="note-0667-03"/>
k T, K P, ſimiles eſſe. </s>
  <s xml:id="echoid-s42862" xml:space="preserve">Si vero KZ, <lb/>diſtantia à meridie quadrantem <lb/>ſuperet, oſtendemus, arcum K L, <lb/>arcui k Z, ſimilem eſſe, quemad-<lb/>modum demonſtratum eſt, arcũ <lb/>K b, arcui K π, eſſe ſimilem. </s>
  <s xml:id="echoid-s42863" xml:space="preserve">Im-<lb/>mo eadem ratione, ſi k p, diſtan-<lb/>tia à meridie cadat infra Horizon <lb/>tem, arcus K ſ, arcui k p, ſimilis <lb/>
<anchor type="note" xlink:label="note-0667-04a" xlink:href="note-0667-04"/>
erit. </s>
  <s xml:id="echoid-s42864" xml:space="preserve">Idem prorſus demonſtrabi-<lb/>tur in Aequatore, &amp; </s>
  <s xml:id="echoid-s42865" xml:space="preserve">parallelo au-<lb/>ſtrali. </s>
  <s xml:id="echoid-s42866" xml:space="preserve">Pro Aequatore enim ducta <lb/>eſt I i, ipſi B D, parallela, ad quã <lb/>demiſſa eſt perpendicularis Hi, <lb/>quæ in μ, à recta B D, ſecatur bifa <lb/>riam, propterea quòd arcus D I, <lb/>atque adeo &amp; </s>
  <s xml:id="echoid-s42867" xml:space="preserve">B i, arcui B H, æqualis eſt. </s>
  <s xml:id="echoid-s42868" xml:space="preserve">Hinc enim fit, vt recta H i, bifariam, &amp; </s>
  <s xml:id="echoid-s42869" xml:space="preserve">ad rectos angulos <lb/>ſecetur à recta B D. </s>
  <s xml:id="echoid-s42870" xml:space="preserve">Poſtea deſcriptus eſt ex μ, circa H i, circulus H u i, à cuius puncto u, ducta eſt <lb/>θ ß, ipſi B D, parallela, &amp; </s>
  <s xml:id="echoid-s42871" xml:space="preserve">ex δ, ad HI, perpendicularis δ ε, vſque ad Meridianum, qui inſtar eſt <lb/>
<anchor type="note" xlink:label="note-0667-05a" xlink:href="note-0667-05"/>
Aequatoris circa HI, deſcripti. </s>
  <s xml:id="echoid-s42872" xml:space="preserve">Vbi perſpicuum eſt, arcum H ε, ſimilem eſſe arcui H u, quòd pro-<lb/>portionales ſint ſinus toti H E, H μ, ſinubus verſis H δ, H θ. </s>
  <s xml:id="echoid-s42873" xml:space="preserve">Pro parallelo autem auſtrali, cuius <lb/>diameter r t, ducta eſt t γ, ipſi B D, parallela, ad quam demiſſa eſt perpendicularis r γ, qua diuiſa <lb/>bifariam in λ, deſcriptus eſt circa r γ; </s>
  <s xml:id="echoid-s42874" xml:space="preserve">circulus r 8 γ, à cuius puncto 8, quod infra Horizontem <lb/>eſt, diſtatq́ue à meridie 8. </s>
  <s xml:id="echoid-s42875" xml:space="preserve">horis, ducta eſt φ χ, ipſi B D, parallela, atque ex ψad r t, excitata perpen <lb/>dicularis ψ ω, vſq; </s>
  <s xml:id="echoid-s42876" xml:space="preserve">ad parallelum diametri r t. </s>
  <s xml:id="echoid-s42877" xml:space="preserve">Vbi etiã manifeſtum eſt, arcum paralleli r 3 4 γ ω, <lb/>ſimilem eſſe arcui r 8, propterea quod eandem proportionem habent ſinus toti r ξ, r λ, quam ſi-<lb/>
<anchor type="note" xlink:label="note-0667-06a" xlink:href="note-0667-06"/>
nus verſi r ψ, r φ. </s>
  <s xml:id="echoid-s42878" xml:space="preserve">Ex quibus omnibus colligitur, D S, altitudinem eſſe Solis in boreali parallelo <lb/>diametri K L, quando Sol ſex horis à meridie abeſt; </s>
  <s xml:id="echoid-s42879" xml:space="preserve">Item D Y, eſſe Solis altitudinem, cum diſtan <lb/>tia Solis à meridie eſt arcus K Z; </s>
  <s xml:id="echoid-s42880" xml:space="preserve">ac denique D q, altitudinem Solis eſſe ſupra inferiorem faciem <lb/>
<anchor type="note" xlink:label="note-0667-07a" xlink:href="note-0667-07"/>
Horizontis, cum Solis diſtantia à meridie eſt arcus K p, quadrantem ſuperans: </s>
  <s xml:id="echoid-s42881" xml:space="preserve">Deinde D ß, eſſe <lb/>altitudinem Solis in Aequatore diſtantiam habentis arcum H u: </s>
  <s xml:id="echoid-s42882" xml:space="preserve">Poſtremo D χ, altitudinem So-<lb/>lis eſſe ſupra faciem inferiorem Horizontis in parallelo auſtrali diametri r t, quando diſtantia à@ <lb/>meridie eſt arcus r 8, infra Horizontem cadens.</s>
  <s xml:id="echoid-s42883" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2105" type="float" level="2" n="5">
<note position="left" xlink:label="note-0666-04" xlink:href="note-0666-04a" xml:space="preserve">Inu<unsure/>entio altitu <lb/>dinum Solis ſu <lb/>pra Horizon tẽ <lb/>pro ſingulis ho <lb/>ris ex Analem-<lb/>mate aliter, <lb/>quàm in lib. 6. <lb/>traditum eſt.</note>
<note position="left" xlink:label="note-0666-05" xlink:href="note-0666-05a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0666-06" xlink:href="note-0666-06a" xml:space="preserve">29. primi.</note>
<note position="left" xlink:label="note-0666-07" xlink:href="note-0666-07a" xml:space="preserve">50</note>
<note position="left" xlink:label="note-0666-08" xlink:href="note-0666-08a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0666-09" xlink:href="note-0666-09a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0666-10" xlink:href="note-0666-10a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0667-01" xlink:href="note-0667-01a" xml:space="preserve">4. ſexti.</note>
  <figure xlink:label="fig-0667-01" xlink:href="fig-0667-01a">
    <image file="0667-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0667-01"/>
  </figure>
<note position="left" xlink:label="note-0667-02" xlink:href="note-0667-02a" xml:space="preserve">10</note>
<note position="right" xlink:label="note-0667-03" xlink:href="note-0667-03a" xml:space="preserve">2. ſe@@@.</note>
<note position="left" xlink:label="note-0667-04" xlink:href="note-0667-04a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0667-05" xlink:href="note-0667-05a" xml:space="preserve">30</note>
<note position="right" xlink:label="note-0667-06" xlink:href="note-0667-06a" xml:space="preserve">4.ſexti.</note>
<note position="left" xlink:label="note-0667-07" xlink:href="note-0667-07a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s42884" xml:space="preserve">HIS oſtenſis, liquido conſtat, in parallelis præcedentis quadrantis recte inuentas eſſe altitudi-<lb/>nes Solis. </s>
  <s xml:id="echoid-s42885" xml:space="preserve">Nam v.</s>
  <s xml:id="echoid-s42886" xml:space="preserve">g. </s>
  <s xml:id="echoid-s42887" xml:space="preserve">in quadrante parallelus ♏, &amp; </s>
  <s xml:id="echoid-s42888" xml:space="preserve">♓, QlO a, reſpondet Meridiano proximi Ana <lb/>lemmatis A B C D, recta autem A B, Horizontis diametro A B, &amp; </s>
  <s xml:id="echoid-s42889" xml:space="preserve">arcus O l, arcui meridianæ al-<lb/>titudinis B r, &amp; </s>
  <s xml:id="echoid-s42890" xml:space="preserve">arcus O Q, hoc eſt, illi ęqualis O a, arcui B 6, cum hic æqualis ſit arcui depreſſio-<lb/>nis meridianæ D t, hoc e@t, arcui meridianæ altitudinis paralleli oppoſiti, quemadmodum &amp; </s>
  <s xml:id="echoid-s42891" xml:space="preserve">in <lb/>quadrante arcus O Q, vel O a, æqualis acceptus eſt altitudini meridianæ paralleli oppoſiti. </s>
  <s xml:id="echoid-s42892" xml:space="preserve">Dein-<lb/>
<anchor type="note" xlink:label="note-0667-08a" xlink:href="note-0667-08"/>
de recta R a, in quadrante reſpondet rectæ t γ, in Analemmate, cum tam R a, per finem depreſ-<lb/>ſionis meridianæ in quadrante parallela Horizonti A B, quàm t γ, per finem depreſſionis meri-<lb/>dianæ in Analemmate Horizonti B D, parallela ducatur: </s>
  <s xml:id="echoid-s42893" xml:space="preserve">Recta vero l R, in quadrante rectæ r γ, <lb/>in Analemmate reſpondet, cum vtraque ex fine altitudinis meridianæ perpendicularis ducatur <lb/>ad Horizontem. </s>
  <s xml:id="echoid-s42894" xml:space="preserve">Circulus denique α l n R, in quadrante reſpondet circulo r 8 γ, in Analemmate. <lb/></s>
  <s xml:id="echoid-s42895" xml:space="preserve">Vnde quemadmodum in Analemmate rectę per horas circuli r 8 γ, ductæ parallelæ Horizontis <lb/>di<unsure/>ametro B D, dant in Meridiano A B C D, altitudines Solis, ita quoque in quadrante rectæ per <lb/>horas circuli α l n R, ductæ æquidiſtantes Horizonti A C, eaſdem altitudines indicabunt in pa-<lb/>ral<unsure/>lelo Q l O a, qui inſtar eſt Meridiani in Analemmate. </s>
  <s xml:id="echoid-s42896" xml:space="preserve">Eademq́ue ratio eſt in cæteris parallelis <lb/>quadrantis. </s>
  <s xml:id="echoid-s42897" xml:space="preserve">Omnia enim, quæ in proximo Analemmate conſtruenda præcepimus pro Solis alti-<lb/>tudinibus inueſtigandis, eadem in ſingulis parallelis quadrantis facta ſunt, vt altitudines Solis in-
<pb o="652" file="0668" n="668" rhead="GNOMONICES"/>
uenirentur, vt perſpicuum eſt, ſi res paulo diligentius conſideretur.</s>
  <s xml:id="echoid-s42898" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2106" type="float" level="2" n="6">
<note position="left" xlink:label="note-0667-08" xlink:href="note-0667-08a" xml:space="preserve">50</note>
</div>
<note position="left" xml:space="preserve">Inuentio decli-<lb/>nationum om-<lb/>nium punctor<unsure/>ũ <lb/>Eclip@icæ in A-<lb/>nalẽmate, una <lb/>c<unsure/>um demonſtra <lb/>tione.</note>
<p>
  <s xml:id="echoid-s42899" xml:space="preserve">CVM hæc demonſtrarem, venit mihi in mentem, eadem fere ratione demonſtrari poſſe con <lb/>ſtructionem Analemmatis lib. </s>
  <s xml:id="echoid-s42900" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42901" xml:space="preserve">propoſ. </s>
  <s xml:id="echoid-s42902" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42903" xml:space="preserve">traditam, ac multò quidem facilius, quàm ibi. </s>
  <s xml:id="echoid-s42904" xml:space="preserve">Sit <lb/>enim Meridianus Analemmatis A B C D, circa centrum E, in quo diameter Horizontis B D; </s>
  <s xml:id="echoid-s42905" xml:space="preserve">Ver-<lb/>ticalis A C; </s>
  <s xml:id="echoid-s42906" xml:space="preserve">Aequatoris H I; </s>
  <s xml:id="echoid-s42907" xml:space="preserve">axis mundi F G; </s>
  <s xml:id="echoid-s42908" xml:space="preserve">diametri parallelorum ſemper apparentium, ſem-<lb/>perq́ue latentium maximorum D k, B L. </s>
  <s xml:id="echoid-s42909" xml:space="preserve">Supputata maxima declinatione à puncto H, ad vtraſq; <lb/></s>
  <s xml:id="echoid-s42910" xml:space="preserve">partes, vſque ad M, &amp; </s>
  <s xml:id="echoid-s42911" xml:space="preserve">N, iungatur recta M N, quæ in O, bifariam, &amp; </s>
  <s xml:id="echoid-s42912" xml:space="preserve">ad angulos rectos ſecabitur, <lb/>
<anchor type="figure" xlink:label="fig-0668-01a" xlink:href="fig-0668-01"/>
vt propoſ. </s>
  <s xml:id="echoid-s42913" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42914" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42915" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42916" xml:space="preserve">oſtenſum eſt. </s>
  <s xml:id="echoid-s42917" xml:space="preserve">Deſcripto quo-<lb/>que ex O, circa M N, circulo M P N Q, eoq́; <lb/></s>
  <s xml:id="echoid-s42918" xml:space="preserve">diuiſo in 12. </s>
  <s xml:id="echoid-s42919" xml:space="preserve">partes æquales, ducãtur per quæ-<lb/>
<anchor type="note" xlink:label="note-0668-02a" xlink:href="note-0668-02"/>
libet bina puncta à P Q, æqualiter diſtantia li-<lb/>neę rectæ Y S λ, X R μ, Z T ξ, α V π, quæ ex <lb/>ſcholio propoſ. </s>
  <s xml:id="echoid-s42920" xml:space="preserve">27. </s>
  <s xml:id="echoid-s42921" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42922" xml:space="preserve">3. </s>
  <s xml:id="echoid-s42923" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s42924" xml:space="preserve">æquidiſtabunt <lb/>rectæ Q P I. </s>
  <s xml:id="echoid-s42925" xml:space="preserve">Ducentur autem magis exquiſite <lb/>huiuſmodi parallelæ, ſi à puncto I, ſupputetur <lb/>quoque vtrinque maxima Solis declinatio vſ-<lb/>quead θ, &amp; </s>
  <s xml:id="echoid-s42926" xml:space="preserve">ρ, iunctaq́ue recta θ ρ, ſemicircu-<lb/>lus ex puncto 8, deſcribatur, qui in ſex æquales <lb/>partes ſecetur, &amp;</s>
  <s xml:id="echoid-s42927" xml:space="preserve">c. </s>
  <s xml:id="echoid-s42928" xml:space="preserve">vt propoſ. </s>
  <s xml:id="echoid-s42929" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42930" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42931" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42932" xml:space="preserve">monui-<lb/>mus. </s>
  <s xml:id="echoid-s42933" xml:space="preserve">Poſtremo iungantur rectę M θ, N ρ, quæ <lb/>
<anchor type="note" xlink:label="note-0668-03a" xlink:href="note-0668-03"/>
ex eodem ſcholio ipſi H I, æquidiſtabunt. </s>
  <s xml:id="echoid-s42934" xml:space="preserve">Dico <lb/>haſce rectas diametros eſſe parallelorum, nem-<lb/>pe communes eorum cum Meridiano ſectio-<lb/>nes, ita vt arcus H γ, H ß, H δ, H ε, metiantur <lb/>declinationes aliorum parallelorum, qui per ſi-<lb/>gnorum initia ducũtur, quemadmodum H M, <lb/>H N, maximas declinationes Solis metiuntur: <lb/></s>
  <s xml:id="echoid-s42935" xml:space="preserve">hoc ordine, vt arcus H γ, H ß, metiantur declinationes illorum punctorũ Eclipticę, quæ à prin-<lb/>cipio ♋, verſus ♈, vel ♎, tot gradibus abſunt, quot gradibus puncta X, Y, R, S, à puncto M, di-<lb/>ſtant; </s>
  <s xml:id="echoid-s42936" xml:space="preserve">arcus autem H δ, H ε<unsure/>, illorum punctorum Eclipticæ declinationes metiantur, quæ tantum <lb/>
<anchor type="note" xlink:label="note-0668-04a" xlink:href="note-0668-04"/>
à principio ♑, verſus ♈, vel ♎, diſtant, quanto ſpatio puncta Z, α, T, V, in ſuo circulo à puncto <lb/>N, abſunt. </s>
  <s xml:id="echoid-s42937" xml:space="preserve">Quod ita demonſtrabitur. </s>
  <s xml:id="echoid-s42938" xml:space="preserve">Ducta recta M ρ, quæ diameter erit Eclipticæ, poſito princi <lb/>pio ♋, in M, &amp; </s>
  <s xml:id="echoid-s42939" xml:space="preserve">principio ♑, in ρ; </s>
  <s xml:id="echoid-s42940" xml:space="preserve">ſecetq́ue M ρ, rectã X R μ, verbi gratia, in p, &amp; </s>
  <s xml:id="echoid-s42941" xml:space="preserve">ex p, ad M ρ, per-<lb/>pendicularis ducatur p b, intelligaturq́; </s>
  <s xml:id="echoid-s42942" xml:space="preserve">ſemicirculus M b ρ, inſtar Eclipticæ cõuerti circa M ρ, do <lb/>nec rectus ſit ad Meridianum A B C D. </s>
  <s xml:id="echoid-s42943" xml:space="preserve">Eſt enim in eo ſitu planum Eclipticæ rectum ad Meri-<lb/>dianum, ex propoſ. </s>
  <s xml:id="echoid-s42944" xml:space="preserve">15. </s>
  <s xml:id="echoid-s42945" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42946" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42947" xml:space="preserve">Theod. </s>
  <s xml:id="echoid-s42948" xml:space="preserve">cum Meridianus per eius polos ducatur. </s>
  <s xml:id="echoid-s42949" xml:space="preserve">Concipiatur quo-<lb/>que per b, punctum Eclipticæ duci circulus Aequatori æquidiſtans, &amp; </s>
  <s xml:id="echoid-s42950" xml:space="preserve">ad Meridianum rectus. </s>
  <s xml:id="echoid-s42951" xml:space="preserve">Et <lb/>quoniam tam Ecliptica, quàm hic parallelus rectus eſt ad Meridianum, erit quoque communis <lb/>eorum ſectio per punctum b, tranſiens ad Meridianum recta: </s>
  <s xml:id="echoid-s42952" xml:space="preserve">Eſt autem b p, ad Meridianum per-<lb/>
<anchor type="note" xlink:label="note-0668-05a" xlink:href="note-0668-05"/>
pendicularis, ex defin. </s>
  <s xml:id="echoid-s42953" xml:space="preserve">4. </s>
  <s xml:id="echoid-s42954" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42955" xml:space="preserve">11. </s>
  <s xml:id="echoid-s42956" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s42957" xml:space="preserve">Igitur b p, communis ſectio erit Eclipticę, &amp; </s>
  <s xml:id="echoid-s42958" xml:space="preserve">paralleli per <lb/>
<anchor type="note" xlink:label="note-0668-06a" xlink:href="note-0668-06"/>
b, ducti; </s>
  <s xml:id="echoid-s42959" xml:space="preserve">atque adeo dictus parallelus Meridianum ſecabit in p. </s>
  <s xml:id="echoid-s42960" xml:space="preserve">Cum ergo Meridianus in Aequa-<lb/>tore, &amp; </s>
  <s xml:id="echoid-s42961" xml:space="preserve">dicto parallelo faciat communes ſectiones parallelas, erit recta X R μ, per p, ducta paralle <lb/>
<anchor type="note" xlink:label="note-0668-07a" xlink:href="note-0668-07"/>
la diametro Aequatoris H I, communis ſectio dicti paralleli, &amp; </s>
  <s xml:id="echoid-s42962" xml:space="preserve">Meridiani, hoc eſt, diameter ip-<lb/>ſius paralleli. </s>
  <s xml:id="echoid-s42963" xml:space="preserve">Quocirca arcus H γ, declinatio erit eiuſdem paralleli, ſeu puncti Eclipticæ b: </s>
  <s xml:id="echoid-s42964" xml:space="preserve">Eſt <lb/>autem arcus Eclipticę M b, ſimilis arcui M X, in circulo M P N Q, ex lemmate propoſ. </s>
  <s xml:id="echoid-s42965" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42966" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42967" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s42968" xml:space="preserve">propterea quòd ita ſe habet M E, ſinus totus Eclipticæ ad M O, ſinum totum circuli M P N Q, <lb/>
<anchor type="note" xlink:label="note-0668-08a" xlink:href="note-0668-08"/>
vt M p, ſinus verſus arcus M b, ad M φ, ſinum verſum arcus M X. </s>
  <s xml:id="echoid-s42969" xml:space="preserve">Igitur recta X R μ, ducta dia-<lb/>metro Aequatoris parallela per punctum X, dat in Meridiano arcũ H γ, declinationis puncti Ecli <lb/>pticę b, quod totidẽ gradibus à puncto M, diſtat, quot gradibus punctũ X, ab eodẽ puncto M, di-<lb/>ſtat in circulo M P N Q. </s>
  <s xml:id="echoid-s42970" xml:space="preserve">Eademq́; </s>
  <s xml:id="echoid-s42971" xml:space="preserve">eſt ratio de alijs. </s>
  <s xml:id="echoid-s42972" xml:space="preserve">quod demonſtrandum erat. </s>
  <s xml:id="echoid-s42973" xml:space="preserve">Ex hac demõſtra-<lb/>
<anchor type="note" xlink:label="note-0668-09a" xlink:href="note-0668-09"/>
tione liquido cõſtat, ſi circulus A B C D, ſecetur in 12. </s>
  <s xml:id="echoid-s42974" xml:space="preserve">partes æquales, hoc eſt, in partes ſimiles <lb/>partibus circuli M P N Q, initio facto à puncto M, &amp; </s>
  <s xml:id="echoid-s42975" xml:space="preserve">quælibet bina puncta æqualiter remota ab <lb/>M, rectis lineis iungantur a 7, b 6, d 5, e 4, 23, quæ perpendiculares ſunt ad M ρ, in punctis l, <lb/>p, E, q, u, (quod demonſtrabitur, vt propoſ. </s>
  <s xml:id="echoid-s42976" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42977" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42978" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42979" xml:space="preserve">oſtenſum eſt, rectam<unsure/> M N, ſectam eſſe ad rectos <lb/>angulos) rectas per hæc puncta ductas rectæ H I, parallelas, quales ſunt ß λ, γ μ, δ ξ, ε π, auferre<unsure/> <lb/>quoque ex Meridiano arcus declinationum. </s>
  <s xml:id="echoid-s42980" xml:space="preserve">Id quod &amp; </s>
  <s xml:id="echoid-s42981" xml:space="preserve">in ſcholio propoſ. </s>
  <s xml:id="echoid-s42982" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42983" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42984" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42985" xml:space="preserve">tradidimus. <lb/></s>
  <s xml:id="echoid-s42986" xml:space="preserve">Hoc enim<unsure/> demonſtrauimus de puncto b, quod tot gradibus abeſt ab M, in circulo A B C D, quot <lb/>gradibus punctum X, diſtat in circulo M P N Q, ab M, eademq́ue ratio eſt de cęteris.</s>
  <s xml:id="echoid-s42987" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2107" type="float" level="2" n="7">
  <figure xlink:label="fig-0668-01" xlink:href="fig-0668-01a">
    <image file="0668-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0668-01"/>
  </figure>
<note position="left" xlink:label="note-0668-02" xlink:href="note-0668-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0668-03" xlink:href="note-0668-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0668-04" xlink:href="note-0668-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0668-05" xlink:href="note-0668-05a" xml:space="preserve">19. vndec.</note>
<note position="left" xlink:label="note-0668-06" xlink:href="note-0668-06a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0668-07" xlink:href="note-0668-07a" xml:space="preserve">16. vndec.</note>
<note position="left" xlink:label="note-0668-08" xlink:href="note-0668-08a" xml:space="preserve">4. ſex@@</note>
<note position="left" xlink:label="note-0668-09" xlink:href="note-0668-09a" xml:space="preserve">50</note>
</div>
<p>
  <s xml:id="echoid-s42988" xml:space="preserve">ANTEQVAM huic operi extremam manum apponerem, ſedulo in eam curam incumbe-<lb/>bam, vt praxim illam ſcholij propoſ. </s>
  <s xml:id="echoid-s42989" xml:space="preserve">33. </s>
  <s xml:id="echoid-s42990" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s42991" xml:space="preserve">1. </s>
  <s xml:id="echoid-s42992" xml:space="preserve">qua Andreas Schonerus breuiſſime ac facilime <lb/>radios arcuum diurnorum inquirit, ratione aliqua Geometrica corroborarem: </s>
  <s xml:id="echoid-s42993" xml:space="preserve">quam cum diu
<pb o="653" file="0669" n="669" rhead="LIBER OCTAVVS."/>
multumq́ue perueſtigaſſem, occurrit tandem mihi demonſtratio, quam libuit Appendicis loco <lb/>
<anchor type="note" xlink:label="note-0669-01a" xlink:href="note-0669-01"/>
hic ſubiungere. </s>
  <s xml:id="echoid-s42994" xml:space="preserve">Quæ vt planius intelligatur, repetenda erit tota conſtructio. </s>
  <s xml:id="echoid-s42995" xml:space="preserve">Ex A, centro ad <lb/>interuallum cuiuſlibet rectæ A B, circulus deſcribatur B C G D, in quo ſumantur duo arcus B C, <lb/>B D, complemento altitudinis poli æquales, ita vt ſi A B, ponatur communis ſectio Æquato-<lb/>ris, &amp; </s>
  <s xml:id="echoid-s42996" xml:space="preserve">Meridiani, quem refert circulus B C G D, arcus B C, B D, ſint declinationes du@rum <lb/>parallelorum, quorum al-<lb/>
<anchor type="figure" xlink:label="fig-0669-01a" xlink:href="fig-0669-01"/>
ter, nempequi per C, du-<lb/>citur, maximus eſt eorum, <lb/>qui ſemper apparent, @ha-<lb/>betq́ue arcum diurnum ho <lb/>
<anchor type="note" xlink:label="note-0669-02a" xlink:href="note-0669-02"/>
rarum 24. </s>
  <s xml:id="echoid-s42997" xml:space="preserve">cum totus ſupra <lb/>Horizontem extet, alter ve-<lb/>ro per D, ductus, maximus <lb/>eorum, qui ſemper occul-<lb/>tantur, habetq́; </s>
  <s xml:id="echoid-s42998" xml:space="preserve">arcum diur <lb/>num horarum o, cum to-<lb/>tus ſub Horizonte lateat. <lb/></s>
  <s xml:id="echoid-s42999" xml:space="preserve">Ducta a utem recta C D, ſe-<lb/>cante rectã A B, in E, erunt <lb/>
<anchor type="note" xlink:label="note-0669-03a" xlink:href="note-0669-03"/>
rectæ E C, E D, æquales, &amp; </s>
  <s xml:id="echoid-s43000" xml:space="preserve"><lb/>anguli ad E, recti. </s>
  <s xml:id="echoid-s43001" xml:space="preserve">quod de-<lb/>monſtrabitur, vt propoſ. </s>
  <s xml:id="echoid-s43002" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s43003" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43004" xml:space="preserve">1. </s>
  <s xml:id="echoid-s43005" xml:space="preserve">in Analemmate de-<lb/>monſtratum eſt, rectam <lb/>M N, in O, bifariam, &amp; </s>
  <s xml:id="echoid-s43006" xml:space="preserve">ad <lb/>angulos rectos ſecari. </s>
  <s xml:id="echoid-s43007" xml:space="preserve">De-<lb/>ſcripto deinde ex E, circa <lb/>C D, circulo, eoq́ue diui-<lb/>ſo in partes 48. </s>
  <s xml:id="echoid-s43008" xml:space="preserve">æquales, <lb/>
<anchor type="note" xlink:label="note-0669-04a" xlink:href="note-0669-04"/>
cõnectantur quælibet duo puncta à puncto C, vel D, æque remota lineis rectis occultis, quæ <lb/>omnes ipſi A B, parallelæ erunt, ex ſcholio propoſ. </s>
  <s xml:id="echoid-s43009" xml:space="preserve">27. </s>
  <s xml:id="echoid-s43010" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43011" xml:space="preserve">3. </s>
  <s xml:id="echoid-s43012" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s43013" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43014" xml:space="preserve">per puncta, quibus illæ <lb/>rectam C D, ſecant, ex A, rectæ educantur vſquead circumferentiam C B D. </s>
  <s xml:id="echoid-s43015" xml:space="preserve">Hæ enim abſcin-<lb/>dent arcus declinationum omnium arcuum diurnorum, ipſæq́ue lineæ radij arcuum diurnorũ <lb/>erunt, initio ſumpto à radi<unsure/>o A D, horæ 0. </s>
  <s xml:id="echoid-s43016" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43017" xml:space="preserve">progrediendo per radium A B, horarum 12, vſque <lb/>ad radium A C, horarum 24. </s>
  <s xml:id="echoid-s43018" xml:space="preserve">ita vt proxima linea ipſi A D, ſit radius arcus diurni horæ 1. </s>
  <s xml:id="echoid-s43019" xml:space="preserve">ſequẽs <lb/>horarum 2. </s>
  <s xml:id="echoid-s43020" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43021" xml:space="preserve">ſic deinceps; </s>
  <s xml:id="echoid-s43022" xml:space="preserve">adeo vt quælibet recta ex A, per aliquod punctorum ſemidiametri <lb/>D E, ducta radium illius arcus diurni referat, qui tot horis à 12. </s>
  <s xml:id="echoid-s43023" xml:space="preserve">horis deficit, quot partibus ex <lb/>12. </s>
  <s xml:id="echoid-s43024" xml:space="preserve">illis, in quas quadrans D F, diuiſus eſt, punctum illud quadrantis D F, per quod linea ipſi <lb/>A B, acta parallela punctum illius radij in ſemidiametro D E, offert, à puncto F, diſtat. </s>
  <s xml:id="echoid-s43025" xml:space="preserve">Hoc eſt, <lb/>vt quemadmodum S T, ipſi A B, æquidiſtans ducitur per punctum S, quatuor duodecimis par-<lb/>
<anchor type="note" xlink:label="note-0669-05a" xlink:href="note-0669-05"/>
tibus quadrantis D F, à puncto F, remotum, ita recta A T V, ſit radius arcus diurni horarum 8. <lb/></s>
  <s xml:id="echoid-s43026" xml:space="preserve">qui nimirum quatuor horis à 12. </s>
  <s xml:id="echoid-s43027" xml:space="preserve">horis deficit, &amp; </s>
  <s xml:id="echoid-s43028" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s43029" xml:space="preserve">Item vt quælibet recta ex A, per <lb/>aliquod punctorum ſemidiametri C E, ducta radium illius arcus diurni referat, qui tot horis ſu-<lb/>perat horas 12. </s>
  <s xml:id="echoid-s43030" xml:space="preserve">quot partibus ex illis 12. </s>
  <s xml:id="echoid-s43031" xml:space="preserve">in quas quadrans C F, diuiſus eſt, punctum illud quadran <lb/>tis C F, per quod linea ipſi A B, acta parallela punctum illius radij in ſemidiametro C E, offert, à <lb/>puncto F, diſtat. </s>
  <s xml:id="echoid-s43032" xml:space="preserve">Hoc eſt, vt quemadmodum H I, ipſi A B, æquidiſtans ducitur per punctum H, <lb/>quatuor duodecimis partibus quadrantis C F, à puncto F, remotum, ita recta A I K, radius ſit <lb/>arcus diurni horarum 16. </s>
  <s xml:id="echoid-s43033" xml:space="preserve">quatuor horis ſuperans horas 12. </s>
  <s xml:id="echoid-s43034" xml:space="preserve">atque ita de reliquis. </s>
  <s xml:id="echoid-s43035" xml:space="preserve">Quod in hunc <lb/>modum demonſtrabimus.</s>
  <s xml:id="echoid-s43036" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2108" type="float" level="2" n="8">
<note position="right" xlink:label="note-0669-01" xlink:href="note-0669-01a" xml:space="preserve">Inuen io decli-<lb/>nationum om-<lb/>nium arcuum <lb/>diurnorum f<unsure/>a-<lb/>cilima una cum <lb/>demonſtratio<unsure/>-<lb/>ne.</note>
  <figure xlink:label="fig-0669-01" xlink:href="fig-0669-01a">
    <image file="0669-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0669-01"/>
  </figure>
<note position="left" xlink:label="note-0669-02" xlink:href="note-0669-02a" xml:space="preserve">10</note>
<note position="left" xlink:label="note-0669-03" xlink:href="note-0669-03a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0669-04" xlink:href="note-0669-04a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0669-05" xlink:href="note-0669-05a" xml:space="preserve">40</note>
</div>
<p>
  <s xml:id="echoid-s43037" xml:space="preserve">DVCTA diametro Horizontis D e, ſecet axis a P, radium Aequatoris B A, productum ad <lb/>
<anchor type="note" xlink:label="note-0669-06a" xlink:href="note-0669-06"/>
angulos rectos in centro A, ſitq́ue polus arcticus n, &amp; </s>
  <s xml:id="echoid-s43038" xml:space="preserve">antarcticus p. </s>
  <s xml:id="echoid-s43039" xml:space="preserve">Ductis quoque K L, V X, dia <lb/>metris parallelorum, quorum prior oſtendendus eſt habere arcum diurnum horarum 16. </s>
  <s xml:id="echoid-s43040" xml:space="preserve">poſte-<lb/>rior vero horarum 8. </s>
  <s xml:id="echoid-s43041" xml:space="preserve">deſcribantur circa K L, V X, ex O, Z, ſemicirculi parallelorum K P L, V a X, <lb/>&amp; </s>
  <s xml:id="echoid-s43042" xml:space="preserve">ex M, Y, punctis, vbi parallelorum diametri ab Horizontis diametro ſecantur, erigantur ad <lb/>diametros perpendiculares M N, Y b, quæ communes ſectiones erunt parallelorum, &amp; </s>
  <s xml:id="echoid-s43043" xml:space="preserve">Horizon-<lb/>tis, vt in ſuperioribus demonſtratum eſt: </s>
  <s xml:id="echoid-s43044" xml:space="preserve">atque adeo K N, arcus erit ſemidiurnus paralleli K P L, <lb/>&amp; </s>
  <s xml:id="echoid-s43045" xml:space="preserve">V b, atcus ſemidiurnus paralleli V a X. </s>
  <s xml:id="echoid-s43046" xml:space="preserve">Quoniam igitur eſt, vt D A, ad A Q, ita D E, ad E I: <lb/></s>
  <s xml:id="echoid-s43047" xml:space="preserve">
<anchor type="note" xlink:label="note-0669-07a" xlink:href="note-0669-07"/>
<anchor type="note" xlink:label="note-0669-08a" xlink:href="note-0669-08"/>
Item vt D A, ad A Q, ita I R, ad R Q; </s>
  <s xml:id="echoid-s43048" xml:space="preserve">erit quoque vt D E, ad E I, ita I R, ad R Q: </s>
  <s xml:id="echoid-s43049" xml:space="preserve">Vt autem I R, <lb/>ad R Q, ita eſt, ex ijs, quæ in ſcholio propoſ. </s>
  <s xml:id="echoid-s43050" xml:space="preserve">4. </s>
  <s xml:id="echoid-s43051" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43052" xml:space="preserve">6. </s>
  <s xml:id="echoid-s43053" xml:space="preserve">Eucl. </s>
  <s xml:id="echoid-s43054" xml:space="preserve">demonſtrauimus, K O, ad O M; </s>
  <s xml:id="echoid-s43055" xml:space="preserve">quòd <lb/>in triangulo A K M, in quo recta A O, ducta eſt, recta I Q, baſi K M, ęquidiſtet, Igitur erit quo-<lb/>que, vt D E, ſinus totus circuli C F D, ad E I, ſinum rectum arcus F H, ita K O, ſinus totus paralle-
<pb o="654" file="0670" n="670" rhead="GNOMONICES"/>
li K P L, ad O M, ſinum rectum arcus P N: </s>
  <s xml:id="echoid-s43056" xml:space="preserve">ac propterea, ex lemmate propoſ. </s>
  <s xml:id="echoid-s43057" xml:space="preserve">1. </s>
  <s xml:id="echoid-s43058" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43059" xml:space="preserve">1. </s>
  <s xml:id="echoid-s43060" xml:space="preserve">arcus F H, <lb/>P N, ſimiles erunt. </s>
  <s xml:id="echoid-s43061" xml:space="preserve">Quare quemadmodum arcus F H, complectitur quatuor duodecimas partes <lb/>quadrantis C F, ita arcus P N, quatuor duodecimas partes, hoc eſt, quatuor ſemihoras, ſiue duas <lb/>horas, quadrantis L P, complectetur, quandoquidem quadrans in ſex horas, ſiue in 12. </s>
  <s xml:id="echoid-s43062" xml:space="preserve">ſemihoras <lb/>diſtribuitur; </s>
  <s xml:id="echoid-s43063" xml:space="preserve">ac proinde arcus ſemidiurnus us K P N, continebit octo horas, totusq́ue arcus diur-<lb/>nus horas 16. </s>
  <s xml:id="echoid-s43064" xml:space="preserve">quod demonſtrandum erat. </s>
  <s xml:id="echoid-s43065" xml:space="preserve">Eadem ratione oſtendemus, arcum, quo arcus ſemi-<lb/>diurnus paralleli, cuius declinatio per parallelam ductam v. </s>
  <s xml:id="echoid-s43066" xml:space="preserve">g. </s>
  <s xml:id="echoid-s43067" xml:space="preserve">per proximum punctum ipſi F, in <lb/>quadrante C F, inuenitur, à quadrante differt, continere vnam partem duodecimam, hoc eſt, <lb/>vnam ſemihoram, quemadmodum &amp; </s>
  <s xml:id="echoid-s43068" xml:space="preserve">arcus inter F, &amp; </s>
  <s xml:id="echoid-s43069" xml:space="preserve">proximum punctum duodecimam partem <lb/>quadrantis C F, comprehendit; </s>
  <s xml:id="echoid-s43070" xml:space="preserve">atque adeo arcum illum ſemidiurnum continere horas 6 {1/2}. </s>
  <s xml:id="echoid-s43071" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43072" xml:space="preserve">to <lb/>
<anchor type="note" xlink:label="note-0670-01a" xlink:href="note-0670-01"/>
<anchor type="figure" xlink:label="fig-0670-01a" xlink:href="fig-0670-01"/>
tum arcum diurnum horas <lb/>13. </s>
  <s xml:id="echoid-s43073" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43074" xml:space="preserve">ſic de cæteris. </s>
  <s xml:id="echoid-s43075" xml:space="preserve">Sed de-<lb/>monſtremus idem in paral-<lb/>lelis auſtralibus. </s>
  <s xml:id="echoid-s43076" xml:space="preserve">Quoniam <lb/>eſt in triangulis ſimilibus <lb/>
<anchor type="note" xlink:label="note-0670-02a" xlink:href="note-0670-02"/>
D d T, A D q, vt d D, ad <lb/>
<anchor type="note" xlink:label="note-0670-03a" xlink:href="note-0670-03"/>
d T, ita A d, ad d q; </s>
  <s xml:id="echoid-s43077" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43078" xml:space="preserve">per-<lb/>
<anchor type="note" xlink:label="note-0670-04a" xlink:href="note-0670-04"/>
mutando, vt D d, ad d A, <lb/>ita T d, ad d q: </s>
  <s xml:id="echoid-s43079" xml:space="preserve">Eſt autem vt <lb/>D d, ad d A, ita D T, ad T E; <lb/></s>
  <s xml:id="echoid-s43080" xml:space="preserve">
<anchor type="note" xlink:label="note-0670-05a" xlink:href="note-0670-05"/>
erit quoque, vt T d, ad d q, <lb/>ita D T, ad T E. </s>
  <s xml:id="echoid-s43081" xml:space="preserve">Vt autem <lb/>T d, ad d q, ita eſt, ex ſcho-<lb/>lio propoſ. </s>
  <s xml:id="echoid-s43082" xml:space="preserve">4. </s>
  <s xml:id="echoid-s43083" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43084" xml:space="preserve">6. </s>
  <s xml:id="echoid-s43085" xml:space="preserve">Eucl. <lb/></s>
  <s xml:id="echoid-s43086" xml:space="preserve">V Y, ad Y Z; </s>
  <s xml:id="echoid-s43087" xml:space="preserve">quòd in trian-<lb/>gulo A V Z, in quo recta <lb/>A Y, ducta eſt, recta T q, <lb/>baſi V Z, æquidiſtet. </s>
  <s xml:id="echoid-s43088" xml:space="preserve">Igitur <lb/>erit quoque, vt D T, ad T E, <lb/>ita V Y, ad Y Z: </s>
  <s xml:id="echoid-s43089" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43090" xml:space="preserve">com-<lb/>
<anchor type="note" xlink:label="note-0670-06a" xlink:href="note-0670-06"/>
ponendo, vt D E, ſinus to-<lb/>tuscirculi C F D, ad T E, ſi-<lb/>num rectum arcus F S, ita <lb/>V Z, ſinus totus paralleli <lb/>V a X, ad Y Z, ſinum rectũ <lb/>arcus a b. </s>
  <s xml:id="echoid-s43091" xml:space="preserve">Quare ex lemmate propoſ. </s>
  <s xml:id="echoid-s43092" xml:space="preserve">1. </s>
  <s xml:id="echoid-s43093" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s43094" xml:space="preserve">1. </s>
  <s xml:id="echoid-s43095" xml:space="preserve">arcus F S, a b, ſimiles ſunt: </s>
  <s xml:id="echoid-s43096" xml:space="preserve">atque idcirco quem-<lb/>admodum arcus F S, complectitur quatuor duodecimas partes quadrantis D F, ita arcus a b, qua-<lb/>tuor duodecimas partes, hoc eſt, quatuor ſemihoras, ſiue duas horas, quadrantis a V, complecte-<lb/>tur: </s>
  <s xml:id="echoid-s43097" xml:space="preserve">hoc eſt, arcus ſemidiurnus V b, quatuor cõtinebit horas, totusq́; </s>
  <s xml:id="echoid-s43098" xml:space="preserve">arcus diurnus horas 8. </s>
  <s xml:id="echoid-s43099" xml:space="preserve">quod <lb/>erat oſtendendum. </s>
  <s xml:id="echoid-s43100" xml:space="preserve">Non aliter demonſtrabimus, arcum, quo arcus ſemidiurnus paralleli, cuius <lb/>
<anchor type="note" xlink:label="note-0670-07a" xlink:href="note-0670-07"/>
declinatio per parallelam ductam v. </s>
  <s xml:id="echoid-s43101" xml:space="preserve">g. </s>
  <s xml:id="echoid-s43102" xml:space="preserve">per punctum tertio loco à puncto F, poſitum in quadran-<lb/>te D F, inuenitur, à quadrante differt, continere tres partes duodecimas, hoc eſt, hor 1 {1/2}. </s>
  <s xml:id="echoid-s43103" xml:space="preserve">quem-<lb/>admodum &amp; </s>
  <s xml:id="echoid-s43104" xml:space="preserve">arcus inter F, &amp; </s>
  <s xml:id="echoid-s43105" xml:space="preserve">tertium punctum verſus D, tres partes duodecimas quadrantis D F, <lb/>complectitur; </s>
  <s xml:id="echoid-s43106" xml:space="preserve">atque adeo arcnm illum ſemidiurnum comprehendere horas 7 {1/2}. </s>
  <s xml:id="echoid-s43107" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s43108" xml:space="preserve">totum arcum <lb/>diurnum horas 15. </s>
  <s xml:id="echoid-s43109" xml:space="preserve">Eademq́ue de c<unsure/>æteris ratio eſt. </s>
  <s xml:id="echoid-s43110" xml:space="preserve">Recte igitur praxi illa declinationes, &amp; </s>
  <s xml:id="echoid-s43111" xml:space="preserve">radij <lb/>arcuum diurnorum inueſtigantur. </s>
  <s xml:id="echoid-s43112" xml:space="preserve">Atque hic finem noſtræ Gnomonicæ imponamus. </s>
  <s xml:id="echoid-s43113" xml:space="preserve">Con-<lb/>ſtructiones enim aliorum horologiorum, quæ viatoria dici ſolent, &amp; </s>
  <s xml:id="echoid-s43114" xml:space="preserve">minus inſignia <lb/>ſunt, (ſi enim omnia perſequi vellemus, in immenſum propemodum excreſce-<lb/>ret volumen) ex alijs ſcriptoribus peti poſſunt. </s>
  <s xml:id="echoid-s43115" xml:space="preserve">De quibus fortaſſis alias <lb/>copioſius diſſeremus, præſertim cum deſcriptio horologij in for <lb/>
<anchor type="note" xlink:label="note-0670-08a" xlink:href="note-0670-08"/>
ma annuli ab Orontio tradita, &amp; </s>
  <s xml:id="echoid-s43116" xml:space="preserve">aliorum quorundam, <lb/>errore non careat. </s>
  <s xml:id="echoid-s43117" xml:space="preserve">Hæcinterim vt ſtudioſus <lb/>lector boni conſulat, vehe-<lb/>menter oro.</s>
  <s xml:id="echoid-s43118" xml:space="preserve"/>
</p>
<div xml:id="echoid-div2109" type="float" level="2" n="9">
<note position="left" xlink:label="note-0669-06" xlink:href="note-0669-06a" xml:space="preserve">50</note>
<note position="right" xlink:label="note-0669-07" xlink:href="note-0669-07a" xml:space="preserve">2. ſexti.</note>
<note position="right" xlink:label="note-0669-08" xlink:href="note-0669-08a" xml:space="preserve">11. quinti.</note>
<note position="left" xlink:label="note-0670-01" xlink:href="note-0670-01a" xml:space="preserve">10</note>
  <figure xlink:label="fig-0670-01" xlink:href="fig-0670-01a">
    <image file="0670-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0670-01"/>
  </figure>
<note position="left" xlink:label="note-0670-02" xlink:href="note-0670-02a" xml:space="preserve">4. ſexti.</note>
<note position="left" xlink:label="note-0670-03" xlink:href="note-0670-03a" xml:space="preserve">2. ſexti.</note>
<note position="left" xlink:label="note-0670-04" xlink:href="note-0670-04a" xml:space="preserve">11. qui@ti.</note>
<note position="left" xlink:label="note-0670-05" xlink:href="note-0670-05a" xml:space="preserve">20</note>
<note position="left" xlink:label="note-0670-06" xlink:href="note-0670-06a" xml:space="preserve">30</note>
<note position="left" xlink:label="note-0670-07" xlink:href="note-0670-07a" xml:space="preserve">40</note>
<note position="left" xlink:label="note-0670-08" xlink:href="note-0670-08a" xml:space="preserve">50</note>
</div>
</div>
<div xml:id="echoid-div2111" type="section" level="1" n="533">
<head xml:id="echoid-head562" xml:space="preserve">FINIS OCTAVI LIBRI.</head>
<pb file="0671" n="671"/>
</div>
<div xml:id="echoid-div2112" type="section" level="1" n="534">
<head xml:id="echoid-head563" xml:space="preserve"><emph style="bf">REGESTVM</emph></head>
<p>
  <s xml:id="echoid-s43119" xml:space="preserve">*** A B C D E F G H I K L M N O P Q R S T V X Y Z.</s>
  <s xml:id="echoid-s43120" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s43121" xml:space="preserve">AA BB CC DD EE FF GG HH II KK LL MM NN OO PP QQ RR <lb/>SS TT VV XX YY ZZ.</s>
  <s xml:id="echoid-s43122" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s43123" xml:space="preserve">AAa BBb CCc DDd EEe FFf GGg HHh.</s>
  <s xml:id="echoid-s43124" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div2113" type="section" level="1" n="535">
<head xml:id="echoid-head564" xml:space="preserve">Omnes ſunt terniones, præter ***, F, &amp; HHh, <lb/>qui quaterniones ſunt.</head>
  <figure>
    <image file="0671-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0671-01"/>
  </figure>
</div>
<div xml:id="echoid-div2114" type="section" level="1" n="536">
<head xml:id="echoid-head565" xml:space="preserve">ROMAE, <lb/>Apud Franciſcum Zanettum. M D LXXXI.</head>
<pb file="0672" n="672"/>
<pb file="0673" n="673"/>
<pb file="0674" n="674"/>
<pb file="0675" n="675"/>
<pb file="0676" n="676"/>
  </div></text>
</echo>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Wed, 29 Nov 2017 16:55:37 +0100
parents	22d6a63640c6
children